Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(451,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, 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("900.451");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.c (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: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.8405.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} + 8x^{2} - 7x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 100) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 451.1 | ||
Root | \(0.500000 - 0.220086i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.451 |
Dual form | 900.3.c.m.451.2 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.35078 | − | 1.47492i | −0.675391 | − | 0.737460i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.350781 | + | 3.98459i | −0.0876953 | + | 0.996147i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.9190i | 1.55986i | 0.625867 | + | 0.779930i | \(0.284745\pi\) | ||||
−0.625867 | + | 0.779930i | \(0.715255\pi\) | |||||||
\(8\) | 6.35078 | − | 4.86493i | 0.793848 | − | 0.608117i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.3592i | 1.03265i | 0.856392 | + | 0.516327i | \(0.172701\pi\) | ||||
−0.856392 | + | 0.516327i | \(0.827299\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.8062 | 0.831250 | 0.415625 | − | 0.909536i | \(-0.363563\pi\) | ||||
0.415625 | + | 0.909536i | \(0.363563\pi\) | |||||||
\(14\) | 16.1047 | − | 14.7492i | 1.15033 | − | 1.05351i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −15.7539 | − | 2.79544i | −0.984619 | − | 0.174715i | ||||
\(17\) | 15.8062 | 0.929779 | 0.464890 | − | 0.885369i | \(-0.346094\pi\) | ||||
0.464890 | + | 0.885369i | \(0.346094\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 24.9192i | − | 1.31154i | −0.754961 | − | 0.655770i | \(-0.772344\pi\) | ||
0.754961 | − | 0.655770i | \(-0.227656\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 16.7539 | − | 15.3438i | 0.761541 | − | 0.697445i | ||||
\(23\) | 20.9577i | 0.911204i | 0.890184 | + | 0.455602i | \(0.150576\pi\) | ||||
−0.890184 | + | 0.455602i | \(0.849424\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −14.5969 | − | 15.9384i | −0.561418 | − | 0.613014i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −43.5078 | − | 3.83019i | −1.55385 | − | 0.136792i | ||||
\(29\) | −22.8062 | −0.786422 | −0.393211 | − | 0.919448i | \(-0.628636\pi\) | ||||
−0.393211 | + | 0.919448i | \(0.628636\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 22.7184i | 0.732851i | 0.930447 | + | 0.366426i | \(0.119419\pi\) | ||||
−0.930447 | + | 0.366426i | \(0.880581\pi\) | |||||||
\(32\) | 17.1570 | + | 27.0118i | 0.536157 | + | 0.844118i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −21.3508 | − | 23.3130i | −0.627964 | − | 0.685675i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 19.1938 | 0.518750 | 0.259375 | − | 0.965777i | \(-0.416483\pi\) | ||||
0.259375 | + | 0.965777i | \(0.416483\pi\) | |||||||
\(38\) | −36.7539 | + | 33.6604i | −0.967208 | + | 0.885801i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −17.0000 | −0.414634 | −0.207317 | − | 0.978274i | \(-0.566473\pi\) | ||||
−0.207317 | + | 0.978274i | \(0.566473\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.51730i | 0.151565i | 0.997124 | + | 0.0757825i | \(0.0241455\pi\) | ||||
−0.997124 | + | 0.0757825i | \(0.975855\pi\) | |||||||
\(44\) | −45.2617 | − | 3.98459i | −1.02868 | − | 0.0905588i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 30.9109 | − | 28.3093i | 0.671977 | − | 0.615419i | ||||
\(47\) | 38.9195i | 0.828074i | 0.910260 | + | 0.414037i | \(0.135882\pi\) | ||||
−0.910260 | + | 0.414037i | \(0.864118\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −70.2250 | −1.43316 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.79063 | + | 43.0585i | −0.0728967 | + | 0.828047i | ||||
\(53\) | 13.2250 | 0.249528 | 0.124764 | − | 0.992186i | \(-0.460183\pi\) | ||||
0.124764 | + | 0.992186i | \(0.460183\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 53.1203 | + | 69.3443i | 0.948577 | + | 1.23829i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 30.8062 | + | 33.6374i | 0.531142 | + | 0.579955i | ||||
\(59\) | − | 95.6301i | − | 1.62085i | −0.585842 | − | 0.810425i | \(-0.699236\pi\) | ||
0.585842 | − | 0.810425i | \(-0.300764\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −92.0312 | −1.50871 | −0.754354 | − | 0.656467i | \(-0.772050\pi\) | ||||
−0.754354 | + | 0.656467i | \(0.772050\pi\) | |||||||
\(62\) | 33.5078 | − | 30.6876i | 0.540449 | − | 0.494961i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 16.6648 | − | 61.7923i | 0.260388 | − | 0.965504i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 54.1549i | 0.808282i | 0.914697 | + | 0.404141i | \(0.132430\pi\) | ||||
−0.914697 | + | 0.404141i | \(0.867570\pi\) | |||||||
\(68\) | −5.54453 | + | 62.9814i | −0.0815372 | + | 0.926197i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 68.5100i | 0.964930i | 0.875915 | + | 0.482465i | \(0.160258\pi\) | ||||
−0.875915 | + | 0.482465i | \(0.839742\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −44.1938 | −0.605394 | −0.302697 | − | 0.953087i | \(-0.597887\pi\) | ||||
−0.302697 | + | 0.953087i | \(0.597887\pi\) | |||||||
\(74\) | −25.9266 | − | 28.3093i | −0.350359 | − | 0.382558i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 99.2930 | + | 8.74120i | 1.30649 | + | 0.115016i | ||||
\(77\) | −124.031 | −1.61080 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 81.7152i | 1.03437i | 0.855874 | + | 0.517185i | \(0.173020\pi\) | ||||
−0.855874 | + | 0.517185i | \(0.826980\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 22.9633 | + | 25.0736i | 0.280040 | + | 0.305776i | ||||
\(83\) | 27.9152i | 0.336327i | 0.985759 | + | 0.168164i | \(0.0537837\pi\) | ||||
−0.985759 | + | 0.168164i | \(0.946216\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 9.61250 | − | 8.80344i | 0.111773 | − | 0.102366i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 55.2617 | + | 72.1397i | 0.627974 | + | 0.819770i | ||||
\(89\) | 42.1938 | 0.474087 | 0.237044 | − | 0.971499i | \(-0.423822\pi\) | ||||
0.237044 | + | 0.971499i | \(0.423822\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 117.994i | 1.29663i | ||||||||
\(92\) | −83.5078 | − | 7.35156i | −0.907694 | − | 0.0799083i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 57.4031 | − | 52.5717i | 0.610672 | − | 0.559273i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −154.837 | −1.59626 | −0.798131 | − | 0.602483i | \(-0.794178\pi\) | ||||
−0.798131 | + | 0.602483i | \(0.794178\pi\) | |||||||
\(98\) | 94.8586 | + | 103.576i | 0.967945 | + | 1.05690i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.96876 | 0.0392946 | 0.0196473 | − | 0.999807i | \(-0.493746\pi\) | ||||
0.0196473 | + | 0.999807i | \(0.493746\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 66.0396i | − | 0.641161i | −0.947221 | − | 0.320580i | \(-0.896122\pi\) | ||
0.947221 | − | 0.320580i | \(-0.103878\pi\) | |||||||
\(104\) | 68.6281 | − | 52.5717i | 0.659886 | − | 0.505497i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −17.8641 | − | 19.5058i | −0.168529 | − | 0.184017i | ||||
\(107\) | 96.0703i | 0.897853i | 0.893569 | + | 0.448927i | \(0.148194\pi\) | ||||
−0.893569 | + | 0.448927i | \(0.851806\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 112.806 | 1.03492 | 0.517460 | − | 0.855707i | \(-0.326878\pi\) | ||||
0.517460 | + | 0.855707i | \(0.326878\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 30.5234 | − | 172.017i | 0.272531 | − | 1.53587i | ||||
\(113\) | 18.2250 | 0.161283 | 0.0806416 | − | 0.996743i | \(-0.474303\pi\) | ||||
0.0806416 | + | 0.996743i | \(0.474303\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.00000 | − | 90.8735i | 0.0689655 | − | 0.783393i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −141.047 | + | 129.175i | −1.19531 | + | 1.09471i | ||||
\(119\) | 172.589i | 1.45033i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.03124 | −0.0663739 | ||||||||
\(122\) | 124.314 | + | 135.739i | 1.01897 | + | 1.11261i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −90.5234 | − | 7.96918i | −0.730028 | − | 0.0642676i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 51.5992i | 0.406293i | 0.979148 | + | 0.203146i | \(0.0651167\pi\) | ||||
−0.979148 | + | 0.203146i | \(0.934883\pi\) | |||||||
\(128\) | −113.649 | + | 58.8885i | −0.887885 | + | 0.460066i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 158.674i | 1.21125i | 0.795750 | + | 0.605625i | \(0.207077\pi\) | ||||
−0.795750 | + | 0.605625i | \(0.792923\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 272.094 | 2.04582 | ||||||||
\(134\) | 79.8742 | − | 73.1514i | 0.596076 | − | 0.545906i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 100.382 | − | 76.8964i | 0.738103 | − | 0.565414i | ||||
\(137\) | 209.837 | 1.53166 | 0.765830 | − | 0.643043i | \(-0.222328\pi\) | ||||
0.765830 | + | 0.643043i | \(0.222328\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 84.6258i | − | 0.608819i | −0.952541 | − | 0.304410i | \(-0.901541\pi\) | ||
0.952541 | − | 0.304410i | \(-0.0984591\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 101.047 | − | 92.5421i | 0.711598 | − | 0.651705i | ||||
\(143\) | 122.750i | 0.858393i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 59.6961 | + | 65.1823i | 0.408877 | + | 0.446454i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.73280 | + | 76.4792i | −0.0454919 | + | 0.516751i | ||||
\(149\) | −170.869 | −1.14677 | −0.573385 | − | 0.819286i | \(-0.694370\pi\) | ||||
−0.573385 | + | 0.819286i | \(0.694370\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 181.392i | 1.20127i | 0.799522 | + | 0.600636i | \(0.205086\pi\) | ||||
−0.799522 | + | 0.600636i | \(0.794914\pi\) | |||||||
\(152\) | −121.230 | − | 158.257i | −0.797569 | − | 1.04116i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 167.539 | + | 182.936i | 1.08792 | + | 1.18790i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 25.1625 | 0.160271 | 0.0801354 | − | 0.996784i | \(-0.474465\pi\) | ||||
0.0801354 | + | 0.996784i | \(0.474465\pi\) | |||||||
\(158\) | 120.523 | − | 110.379i | 0.762807 | − | 0.698603i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −228.837 | −1.42135 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.00838i | 0.0491312i | 0.999698 | + | 0.0245656i | \(0.00782026\pi\) | ||||
−0.999698 | + | 0.0245656i | \(0.992180\pi\) | |||||||
\(164\) | 5.96328 | − | 67.7380i | 0.0363615 | − | 0.413037i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 41.1727 | − | 37.7073i | 0.248028 | − | 0.227152i | ||||
\(167\) | − | 187.555i | − | 1.12308i | −0.827449 | − | 0.561541i | \(-0.810209\pi\) | ||
0.827449 | − | 0.561541i | \(-0.189791\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −52.2250 | −0.309024 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −25.9688 | − | 2.28614i | −0.150981 | − | 0.0132915i | ||||
\(173\) | 123.225 | 0.712283 | 0.356142 | − | 0.934432i | \(-0.384092\pi\) | ||||
0.356142 | + | 0.934432i | \(0.384092\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 31.7539 | − | 178.952i | 0.180420 | − | 1.01677i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −56.9945 | − | 62.2324i | −0.320194 | − | 0.349620i | ||||
\(179\) | − | 138.511i | − | 0.773805i | −0.922121 | − | 0.386903i | \(-0.873545\pi\) | ||
0.922121 | − | 0.386903i | \(-0.126455\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −194.125 | −1.07251 | −0.536257 | − | 0.844055i | \(-0.680162\pi\) | ||||
−0.536257 | + | 0.844055i | \(0.680162\pi\) | |||||||
\(182\) | 174.031 | − | 159.384i | 0.956216 | − | 0.875734i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 101.958 | + | 133.098i | 0.554118 | + | 0.723357i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 179.546i | 0.960140i | ||||||||
\(188\) | −155.078 | − | 13.6522i | −0.824884 | − | 0.0726182i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 67.4454i | 0.353117i | 0.984290 | + | 0.176559i | \(0.0564965\pi\) | ||||
−0.984290 | + | 0.176559i | \(0.943503\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 153.869 | 0.797247 | 0.398624 | − | 0.917115i | \(-0.369488\pi\) | ||||
0.398624 | + | 0.917115i | \(0.369488\pi\) | |||||||
\(194\) | 209.152 | + | 228.373i | 1.07810 | + | 1.17718i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 24.6336 | − | 279.818i | 0.125682 | − | 1.42764i | ||||
\(197\) | −261.287 | −1.32633 | −0.663166 | − | 0.748472i | \(-0.730788\pi\) | ||||
−0.663166 | + | 0.748472i | \(0.730788\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 227.184i | 1.14163i | 0.821080 | + | 0.570814i | \(0.193372\pi\) | ||||
−0.821080 | + | 0.570814i | \(0.806628\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.36092 | − | 5.85360i | −0.0265392 | − | 0.0289782i | ||||
\(203\) | − | 249.022i | − | 1.22671i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −97.4031 | + | 89.2050i | −0.472831 | + | 0.433034i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −170.241 | − | 30.2082i | −0.818464 | − | 0.145232i | ||||
\(209\) | 283.062 | 1.35437 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 193.816i | 0.918559i | 0.888292 | + | 0.459280i | \(0.151892\pi\) | ||||
−0.888292 | + | 0.459280i | \(0.848108\pi\) | |||||||
\(212\) | −4.63908 | + | 52.6962i | −0.0218824 | + | 0.248567i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 141.696 | − | 129.770i | 0.662131 | − | 0.606402i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −248.062 | −1.14315 | ||||||||
\(218\) | −152.377 | − | 166.380i | −0.698975 | − | 0.763212i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 170.806 | 0.772879 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 25.3594i | − | 0.113719i | −0.998382 | − | 0.0568597i | \(-0.981891\pi\) | ||
0.998382 | − | 0.0568597i | \(-0.0181088\pi\) | |||||||
\(224\) | −294.942 | + | 187.338i | −1.31671 | + | 0.836330i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −24.6180 | − | 26.8804i | −0.108929 | − | 0.118940i | ||||
\(227\) | 374.584i | 1.65015i | 0.565024 | + | 0.825074i | \(0.308867\pi\) | ||||
−0.565024 | + | 0.825074i | \(0.691133\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −259.287 | −1.13226 | −0.566130 | − | 0.824316i | \(-0.691560\pi\) | ||||
−0.566130 | + | 0.824316i | \(0.691560\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −144.837 | + | 110.951i | −0.624300 | + | 0.478237i | ||||
\(233\) | 153.225 | 0.657618 | 0.328809 | − | 0.944396i | \(-0.393353\pi\) | ||||
0.328809 | + | 0.944396i | \(0.393353\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 381.047 | + | 33.5452i | 1.61461 | + | 0.142141i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 254.555 | − | 233.130i | 1.06956 | − | 0.979536i | ||||
\(239\) | 187.213i | 0.783320i | 0.920110 | + | 0.391660i | \(0.128099\pi\) | ||||
−0.920110 | + | 0.391660i | \(0.871901\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −65.0937 | −0.270098 | −0.135049 | − | 0.990839i | \(-0.543119\pi\) | ||||
−0.135049 | + | 0.990839i | \(0.543119\pi\) | |||||||
\(242\) | 10.8485 | + | 11.8454i | 0.0448283 | + | 0.0489481i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 32.2828 | − | 366.707i | 0.132307 | − | 1.50290i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 269.284i | − | 1.09022i | ||||||
\(248\) | 110.523 | + | 144.279i | 0.445659 | + | 0.581772i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 443.363i | − | 1.76639i | −0.469008 | − | 0.883194i | \(-0.655388\pi\) | ||
0.469008 | − | 0.883194i | \(-0.344612\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −238.062 | −0.940958 | ||||||||
\(254\) | 76.1047 | − | 69.6992i | 0.299625 | − | 0.274406i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 240.371 | + | 88.0781i | 0.938949 | + | 0.344055i | ||||
\(257\) | −241.287 | −0.938862 | −0.469431 | − | 0.882969i | \(-0.655541\pi\) | ||||
−0.469431 | + | 0.882969i | \(0.655541\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 209.577i | 0.809177i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 234.031 | − | 214.334i | 0.893249 | − | 0.818067i | ||||
\(263\) | − | 379.170i | − | 1.44171i | −0.693086 | − | 0.720855i | \(-0.743749\pi\) | ||
0.693086 | − | 0.720855i | \(-0.256251\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −367.539 | − | 401.317i | −1.38173 | − | 1.50871i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −215.785 | − | 18.9965i | −0.805168 | − | 0.0708825i | ||||
\(269\) | −120.713 | −0.448745 | −0.224373 | − | 0.974503i | \(-0.572033\pi\) | ||||
−0.224373 | + | 0.974503i | \(0.572033\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 114.302i | − | 0.421777i | −0.977510 | − | 0.210889i | \(-0.932364\pi\) | ||
0.977510 | − | 0.210889i | \(-0.0676358\pi\) | |||||||
\(272\) | −249.010 | − | 44.1854i | −0.915478 | − | 0.162446i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −283.445 | − | 309.494i | −1.03447 | − | 1.12954i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 197.256 | 0.712116 | 0.356058 | − | 0.934464i | \(-0.384120\pi\) | ||||
0.356058 | + | 0.934464i | \(0.384120\pi\) | |||||||
\(278\) | −124.816 | + | 114.311i | −0.448980 | + | 0.411191i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.0625 | −0.0358096 | −0.0179048 | − | 0.999840i | \(-0.505700\pi\) | ||||
−0.0179048 | + | 0.999840i | \(0.505700\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 541.280i | − | 1.91265i | −0.292307 | − | 0.956324i | \(-0.594423\pi\) | ||
0.292307 | − | 0.956324i | \(-0.405577\pi\) | |||||||
\(284\) | −272.984 | − | 24.0320i | −0.961213 | − | 0.0846198i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 181.047 | − | 165.809i | 0.633031 | − | 0.579751i | ||||
\(287\) | − | 185.623i | − | 0.646771i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −39.1625 | −0.135510 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 15.5023 | − | 176.094i | 0.0530902 | − | 0.603061i | ||||
\(293\) | −344.994 | −1.17745 | −0.588726 | − | 0.808332i | \(-0.700370\pi\) | ||||
−0.588726 | + | 0.808332i | \(0.700370\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 121.895 | − | 93.3763i | 0.411808 | − | 0.315461i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 230.806 | + | 252.018i | 0.774518 | + | 0.845697i | ||||
\(299\) | 226.474i | 0.757438i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −71.1625 | −0.236420 | ||||||||
\(302\) | 267.539 | − | 245.021i | 0.885891 | − | 0.811328i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −69.6602 | + | 392.575i | −0.229145 | + | 1.29137i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 181.307i | 0.590576i | 0.955408 | + | 0.295288i | \(0.0954156\pi\) | ||||
−0.955408 | + | 0.295288i | \(0.904584\pi\) | |||||||
\(308\) | 43.5078 | − | 494.214i | 0.141259 | − | 1.60459i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 91.9382i | 0.295621i | 0.989016 | + | 0.147811i | \(0.0472226\pi\) | ||||
−0.989016 | + | 0.147811i | \(0.952777\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −401.287 | −1.28207 | −0.641034 | − | 0.767512i | \(-0.721494\pi\) | ||||
−0.641034 | + | 0.767512i | \(0.721494\pi\) | |||||||
\(314\) | −33.9890 | − | 37.1127i | −0.108245 | − | 0.118193i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −325.602 | − | 28.6641i | −1.03038 | − | 0.0907093i | ||||
\(317\) | 552.900 | 1.74416 | 0.872082 | − | 0.489360i | \(-0.162770\pi\) | ||||
0.872082 | + | 0.489360i | \(0.162770\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 259.061i | − | 0.812102i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 309.109 | + | 337.517i | 0.959967 | + | 1.04819i | ||||
\(323\) | − | 393.880i | − | 1.21944i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.8117 | − | 10.8176i | 0.0362323 | − | 0.0331827i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −107.963 | + | 82.7039i | −0.329156 | + | 0.252146i | ||||
\(329\) | −424.962 | −1.29168 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 602.037i | − | 1.81884i | −0.415875 | − | 0.909422i | \(-0.636525\pi\) | ||
0.415875 | − | 0.909422i | \(-0.363475\pi\) | |||||||
\(332\) | −111.230 | − | 9.79211i | −0.335032 | − | 0.0294943i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −276.628 | + | 253.345i | −0.828228 | + | 0.758519i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.1000 | 0.0952523 | 0.0476261 | − | 0.998865i | \(-0.484834\pi\) | ||||
0.0476261 | + | 0.998865i | \(0.484834\pi\) | |||||||
\(338\) | 70.5445 | + | 77.0277i | 0.208712 | + | 0.227893i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −258.062 | −0.756781 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 231.756i | − | 0.675674i | ||||||
\(344\) | 31.7062 | + | 41.3899i | 0.0921693 | + | 0.120320i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −166.450 | − | 181.747i | −0.481069 | − | 0.525281i | ||||
\(347\) | − | 522.438i | − | 1.50558i | −0.658259 | − | 0.752792i | \(-0.728707\pi\) | ||
0.658259 | − | 0.752792i | \(-0.271293\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 128.931 | 0.369430 | 0.184715 | − | 0.982792i | \(-0.440864\pi\) | ||||
0.184715 | + | 0.982792i | \(0.440864\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −306.832 | + | 194.890i | −0.871682 | + | 0.553665i | ||||
\(353\) | −594.837 | −1.68509 | −0.842546 | − | 0.538624i | \(-0.818944\pi\) | ||||
−0.842546 | + | 0.538624i | \(0.818944\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −14.8008 | + | 168.125i | −0.0415752 | + | 0.472261i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −204.293 | + | 187.098i | −0.570651 | + | 0.522621i | ||||
\(359\) | − | 26.0554i | − | 0.0725778i | −0.999341 | − | 0.0362889i | \(-0.988446\pi\) | ||
0.999341 | − | 0.0362889i | \(-0.0115537\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −259.969 | −0.720135 | ||||||||
\(362\) | 262.220 | + | 286.319i | 0.724366 | + | 0.790936i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −470.156 | − | 41.3899i | −1.29164 | − | 0.113709i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 420.915i | 1.14691i | 0.819238 | + | 0.573453i | \(0.194397\pi\) | ||||
−0.819238 | + | 0.573453i | \(0.805603\pi\) | |||||||
\(368\) | 58.5859 | − | 330.166i | 0.159201 | − | 0.897189i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 144.404i | 0.389229i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 218.713 | 0.586361 | 0.293180 | − | 0.956057i | \(-0.405286\pi\) | ||||
0.293180 | + | 0.956057i | \(0.405286\pi\) | |||||||
\(374\) | 264.816 | − | 242.528i | 0.708065 | − | 0.648470i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 189.341 | + | 247.169i | 0.503566 | + | 0.657364i | ||||
\(377\) | −246.450 | −0.653713 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 246.282i | − | 0.649820i | −0.945745 | − | 0.324910i | \(-0.894666\pi\) | ||
0.945745 | − | 0.324910i | \(-0.105334\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 99.4766 | − | 91.1039i | 0.260410 | − | 0.238492i | ||||
\(383\) | 406.106i | 1.06033i | 0.847895 | + | 0.530164i | \(0.177870\pi\) | ||||
−0.847895 | + | 0.530164i | \(0.822130\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −207.843 | − | 226.944i | −0.538453 | − | 0.587938i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 54.3141 | − | 616.964i | 0.139985 | − | 1.59011i | ||||
\(389\) | 201.225 | 0.517288 | 0.258644 | − | 0.965973i | \(-0.416724\pi\) | ||||
0.258644 | + | 0.965973i | \(0.416724\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 331.263i | 0.847219i | ||||||||
\(392\) | −445.984 | + | 341.640i | −1.13771 | + | 0.871530i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 352.942 | + | 385.378i | 0.895792 | + | 0.978117i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −96.7750 | −0.243766 | −0.121883 | − | 0.992544i | \(-0.538893\pi\) | ||||
−0.121883 | + | 0.992544i | \(0.538893\pi\) | |||||||
\(398\) | 335.078 | − | 306.876i | 0.841905 | − | 0.771044i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −279.094 | −0.695994 | −0.347997 | − | 0.937496i | \(-0.613138\pi\) | ||||
−0.347997 | + | 0.937496i | \(0.613138\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 245.501i | 0.609182i | ||||||||
\(404\) | −1.39217 | + | 15.8139i | −0.00344595 | + | 0.0391432i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −367.287 | + | 336.374i | −0.904649 | + | 0.828507i | ||||
\(407\) | 218.026i | 0.535689i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 521.837 | 1.27589 | 0.637943 | − | 0.770083i | \(-0.279785\pi\) | ||||
0.637943 | + | 0.770083i | \(0.279785\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 263.141 | + | 23.1654i | 0.638691 | + | 0.0562268i | ||||
\(413\) | 1044.19 | 2.52830 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 185.403 | + | 291.896i | 0.445681 | + | 0.701673i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −382.355 | − | 417.495i | −0.914726 | − | 0.998791i | ||||
\(419\) | 252.103i | 0.601678i | 0.953675 | + | 0.300839i | \(0.0972667\pi\) | ||||
−0.953675 | + | 0.300839i | \(0.902733\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 776.187 | 1.84368 | 0.921838 | − | 0.387576i | \(-0.126687\pi\) | ||||
0.921838 | + | 0.387576i | \(0.126687\pi\) | |||||||
\(422\) | 285.863 | − | 261.803i | 0.677401 | − | 0.620386i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 83.9890 | − | 64.3387i | 0.198087 | − | 0.151742i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 1004.89i | − | 2.35337i | ||||||
\(428\) | −382.801 | − | 33.6996i | −0.894394 | − | 0.0787375i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 588.904i | − | 1.36637i | −0.730247 | − | 0.683183i | \(-0.760595\pi\) | ||
0.730247 | − | 0.683183i | \(-0.239405\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 541.931 | 1.25157 | 0.625787 | − | 0.779994i | \(-0.284778\pi\) | ||||
0.625787 | + | 0.779994i | \(0.284778\pi\) | |||||||
\(434\) | 335.078 | + | 365.872i | 0.772069 | + | 0.843024i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −39.5703 | + | 449.487i | −0.0907576 | + | 1.03093i | ||||
\(437\) | 522.250 | 1.19508 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 4.04683i | − | 0.00921830i | −0.999989 | − | 0.00460915i | \(-0.998533\pi\) | ||
0.999989 | − | 0.00460915i | \(-0.00146714\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −230.722 | − | 251.926i | −0.521995 | − | 0.569968i | ||||
\(443\) | 342.635i | 0.773444i | 0.922196 | + | 0.386722i | \(0.126393\pi\) | ||||
−0.922196 | + | 0.386722i | \(0.873607\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −37.4031 | + | 34.2550i | −0.0838635 | + | 0.0768050i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 674.711 | + | 181.964i | 1.50605 | + | 0.406169i | ||||
\(449\) | 484.444 | 1.07894 | 0.539470 | − | 0.842005i | \(-0.318625\pi\) | ||||
0.539470 | + | 0.842005i | \(0.318625\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 193.106i | − | 0.428174i | ||||||
\(452\) | −6.39298 | + | 72.6191i | −0.0141438 | + | 0.160662i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 552.481 | − | 505.981i | 1.21692 | − | 1.11449i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 698.537 | 1.52853 | 0.764264 | − | 0.644903i | \(-0.223102\pi\) | ||||
0.764264 | + | 0.644903i | \(0.223102\pi\) | |||||||
\(458\) | 350.241 | + | 382.428i | 0.764718 | + | 0.834997i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 820.250 | 1.77928 | 0.889642 | − | 0.456659i | \(-0.150954\pi\) | ||||
0.889642 | + | 0.456659i | \(0.150954\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 881.956i | 1.90487i | 0.304736 | + | 0.952437i | \(0.401432\pi\) | ||||
−0.304736 | + | 0.952437i | \(0.598568\pi\) | |||||||
\(464\) | 359.287 | + | 63.7534i | 0.774326 | + | 0.137400i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −206.973 | − | 225.995i | −0.444149 | − | 0.484967i | ||||
\(467\) | 57.2361i | 0.122561i | 0.998121 | + | 0.0612807i | \(0.0195185\pi\) | ||||
−0.998121 | + | 0.0612807i | \(0.980482\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −591.319 | −1.26081 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −465.234 | − | 607.326i | −0.985666 | − | 1.28671i | ||||
\(473\) | −74.0312 | −0.156514 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −687.695 | − | 60.5409i | −1.44474 | − | 0.127187i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 276.125 | − | 252.884i | 0.577667 | − | 0.529047i | ||||
\(479\) | − | 651.449i | − | 1.36002i | −0.733203 | − | 0.680010i | \(-0.761976\pi\) | ||
0.733203 | − | 0.680010i | \(-0.238024\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 207.412 | 0.431211 | ||||||||
\(482\) | 87.9274 | + | 96.0081i | 0.182422 | + | 0.199187i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.81721 | − | 32.0012i | 0.00582068 | − | 0.0661182i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 53.0187i | 0.108868i | 0.998517 | + | 0.0544340i | \(0.0173355\pi\) | ||||
−0.998517 | + | 0.0544340i | \(0.982665\pi\) | |||||||
\(488\) | −584.470 | + | 447.726i | −1.19768 | + | 0.917471i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.6537i | 0.0441013i | 0.999757 | + | 0.0220506i | \(0.00701950\pi\) | ||||
−0.999757 | + | 0.0220506i | \(0.992980\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −360.481 | −0.731199 | ||||||||
\(494\) | −397.172 | + | 363.743i | −0.803992 | + | 0.736322i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 63.5078 | − | 357.903i | 0.128040 | − | 0.721579i | ||||
\(497\) | −748.062 | −1.50516 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 203.401i | 0.407617i | 0.979011 | + | 0.203808i | \(0.0653320\pi\) | ||||
−0.979011 | + | 0.203808i | \(0.934668\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −653.926 | + | 598.887i | −1.30264 | + | 1.19300i | ||||
\(503\) | − | 84.5406i | − | 0.168073i | −0.996463 | − | 0.0840363i | \(-0.973219\pi\) | ||
0.996463 | − | 0.0840363i | \(-0.0267812\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 321.570 | + | 351.123i | 0.635514 | + | 0.693919i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −205.602 | − | 18.1000i | −0.404727 | − | 0.0356299i | ||||
\(509\) | 101.225 | 0.198870 | 0.0994352 | − | 0.995044i | \(-0.468296\pi\) | ||||
0.0994352 | + | 0.995044i | \(0.468296\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 482.552i | − | 0.944330i | ||||||
\(512\) | −194.780 | − | 473.502i | −0.380431 | − | 0.924809i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 325.927 | + | 355.880i | 0.634098 | + | 0.692373i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −442.094 | −0.855114 | ||||||||
\(518\) | 309.109 | − | 283.093i | 0.596736 | − | 0.546511i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 671.375 | 1.28863 | 0.644314 | − | 0.764761i | \(-0.277143\pi\) | ||||
0.644314 | + | 0.764761i | \(0.277143\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 848.589i | 1.62254i | 0.584671 | + | 0.811270i | \(0.301223\pi\) | ||||
−0.584671 | + | 0.811270i | \(0.698777\pi\) | |||||||
\(524\) | −632.250 | − | 55.6598i | −1.20658 | − | 0.106221i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −559.245 | + | 512.175i | −1.06320 | + | 0.973717i | ||||
\(527\) | 359.092i | 0.681390i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 89.7750 | 0.169707 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −95.4453 | + | 1084.18i | −0.179409 | + | 2.03794i | ||||
\(533\) | −183.706 | −0.344665 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 263.460 | + | 343.926i | 0.491530 | + | 0.641653i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 163.056 | + | 178.041i | 0.303078 | + | 0.330932i | ||||
\(539\) | − | 797.699i | − | 1.47996i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 824.250 | 1.52357 | 0.761784 | − | 0.647831i | \(-0.224324\pi\) | ||||
0.761784 | + | 0.647831i | \(0.224324\pi\) | |||||||
\(542\) | −168.586 | + | 154.397i | −0.311044 | + | 0.284865i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 271.188 | + | 426.955i | 0.498508 | + | 0.784844i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 275.020i | 0.502778i | 0.967886 | + | 0.251389i | \(0.0808873\pi\) | ||||
−0.967886 | + | 0.251389i | \(0.919113\pi\) | |||||||
\(548\) | −73.6070 | + | 836.116i | −0.134319 | + | 1.52576i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 568.314i | 1.03142i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −892.250 | −1.61347 | ||||||||
\(554\) | −266.450 | − | 290.937i | −0.480957 | − | 0.525158i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 337.199 | + | 29.6851i | 0.606473 | + | 0.0533905i | ||||
\(557\) | 154.681 | 0.277704 | 0.138852 | − | 0.990313i | \(-0.455659\pi\) | ||||
0.138852 | + | 0.990313i | \(0.455659\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 70.4275i | 0.125988i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13.5922 | + | 14.8414i | 0.0241854 | + | 0.0264081i | ||||
\(563\) | 767.327i | 1.36293i | 0.731853 | + | 0.681463i | \(0.238656\pi\) | ||||
−0.731853 | + | 0.681463i | \(0.761344\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −798.344 | + | 731.150i | −1.41050 | + | 1.29179i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 333.297 | + | 435.092i | 0.586790 | + | 0.766008i | ||||
\(569\) | −346.025 | −0.608128 | −0.304064 | − | 0.952652i | \(-0.598344\pi\) | ||||
−0.304064 | + | 0.952652i | \(0.598344\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 389.407i | 0.681973i | 0.940068 | + | 0.340986i | \(0.110761\pi\) | ||||
−0.940068 | + | 0.340986i | \(0.889239\pi\) | |||||||
\(572\) | −489.109 | − | 43.0585i | −0.855086 | − | 0.0752770i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −273.780 | + | 250.736i | −0.476968 | + | 0.436823i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 800.475 | 1.38730 | 0.693652 | − | 0.720310i | \(-0.256000\pi\) | ||||
0.693652 | + | 0.720310i | \(0.256000\pi\) | |||||||
\(578\) | 52.9000 | + | 57.7616i | 0.0915224 | + | 0.0999335i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −304.806 | −0.524623 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 150.225i | 0.257676i | ||||||||
\(584\) | −280.665 | + | 215.000i | −0.480590 | + | 0.368150i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 466.011 | + | 508.838i | 0.795241 | + | 0.868325i | ||||
\(587\) | − | 758.780i | − | 1.29264i | −0.763066 | − | 0.646320i | \(-0.776307\pi\) | ||
0.763066 | − | 0.646320i | \(-0.223693\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 566.125 | 0.961163 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −302.377 | − | 53.6549i | −0.510771 | − | 0.0906333i | ||||
\(593\) | −1049.84 | −1.77038 | −0.885192 | − | 0.465226i | \(-0.845973\pi\) | ||||
−0.885192 | + | 0.465226i | \(0.845973\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 59.9375 | − | 680.842i | 0.100566 | − | 1.14235i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 334.031 | − | 305.917i | 0.558581 | − | 0.511567i | ||||
\(599\) | 269.427i | 0.449794i | 0.974383 | + | 0.224897i | \(0.0722046\pi\) | ||||
−0.974383 | + | 0.224897i | \(0.927795\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −567.031 | −0.943480 | −0.471740 | − | 0.881738i | \(-0.656374\pi\) | ||||
−0.471740 | + | 0.881738i | \(0.656374\pi\) | |||||||
\(602\) | 96.1250 | + | 104.959i | 0.159676 | + | 0.174351i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −722.773 | − | 63.6289i | −1.19664 | − | 0.105346i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 846.770i | − | 1.39501i | −0.716581 | − | 0.697504i | \(-0.754294\pi\) | ||
0.716581 | − | 0.697504i | \(-0.245706\pi\) | |||||||
\(608\) | 673.113 | − | 427.540i | 1.10709 | − | 0.703191i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 420.573i | 0.688336i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 306.775 | 0.500449 | 0.250224 | − | 0.968188i | \(-0.419496\pi\) | ||||
0.250224 | + | 0.968188i | \(0.419496\pi\) | |||||||
\(614\) | 267.413 | − | 244.906i | 0.435526 | − | 0.398870i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −787.695 | + | 603.404i | −1.27873 | + | 0.979552i | ||||
\(617\) | 435.150 | 0.705267 | 0.352634 | − | 0.935761i | \(-0.385286\pi\) | ||||
0.352634 | + | 0.935761i | \(0.385286\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 123.460i | 0.199451i | 0.995015 | + | 0.0997254i | \(0.0317964\pi\) | ||||
−0.995015 | + | 0.0997254i | \(0.968204\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 135.602 | − | 124.188i | 0.218009 | − | 0.199660i | ||||
\(623\) | 460.714i | 0.739509i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 542.052 | + | 591.867i | 0.865897 | + | 0.945475i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.82653 | + | 100.262i | −0.0140550 | + | 0.159653i | ||||
\(629\) | 303.381 | 0.482323 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 519.684i | − | 0.823588i | −0.911277 | − | 0.411794i | \(-0.864902\pi\) | ||
0.911277 | − | 0.411794i | \(-0.135098\pi\) | |||||||
\(632\) | 397.539 | + | 518.955i | 0.629017 | + | 0.821132i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −746.847 | − | 815.484i | −1.17799 | − | 1.28625i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −758.869 | −1.19132 | ||||||||
\(638\) | −382.094 | + | 349.934i | −0.598893 | + | 0.548486i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 82.1875 | 0.128218 | 0.0641088 | − | 0.997943i | \(-0.479580\pi\) | ||||
0.0641088 | + | 0.997943i | \(0.479580\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 513.023i | − | 0.797859i | −0.916982 | − | 0.398930i | \(-0.869382\pi\) | ||
0.916982 | − | 0.398930i | \(-0.130618\pi\) | |||||||
\(644\) | 80.2719 | − | 911.823i | 0.124646 | − | 1.41587i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −580.941 | + | 532.045i | −0.899290 | + | 0.823600i | ||||
\(647\) | 573.440i | 0.886306i | 0.896446 | + | 0.443153i | \(0.146140\pi\) | ||||
−0.896446 | + | 0.443153i | \(0.853860\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1086.28 | 1.67378 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −31.9101 | − | 2.80919i | −0.0489419 | − | 0.00430857i | ||||
\(653\) | 767.256 | 1.17497 | 0.587486 | − | 0.809235i | \(-0.300118\pi\) | ||||
0.587486 | + | 0.809235i | \(0.300118\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 267.816 | + | 47.5224i | 0.408257 | + | 0.0724427i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 574.031 | + | 626.786i | 0.872388 | + | 0.952562i | ||||
\(659\) | 1054.84i | 1.60067i | 0.599552 | + | 0.800336i | \(0.295345\pi\) | ||||
−0.599552 | + | 0.800336i | \(0.704655\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 618.281 | 0.935372 | 0.467686 | − | 0.883895i | \(-0.345088\pi\) | ||||
0.467686 | + | 0.883895i | \(0.345088\pi\) | |||||||
\(662\) | −887.957 | + | 813.220i | −1.34132 | + | 1.22843i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 135.805 | + | 177.283i | 0.204526 | + | 0.266993i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 477.966i | − | 0.716591i | ||||||
\(668\) | 747.328 | + | 65.7906i | 1.11875 | + | 0.0984889i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1045.40i | − | 1.55797i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.7750 | 0.0397846 | 0.0198923 | − | 0.999802i | \(-0.493668\pi\) | ||||
0.0198923 | + | 0.999802i | \(0.493668\pi\) | |||||||
\(674\) | −43.3601 | − | 47.3450i | −0.0643325 | − | 0.0702448i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18.3195 | − | 208.095i | 0.0270999 | − | 0.307833i | ||||
\(677\) | 264.837 | 0.391193 | 0.195596 | − | 0.980684i | \(-0.437336\pi\) | ||||
0.195596 | + | 0.980684i | \(0.437336\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1690.67i | − | 2.48995i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 348.586 | + | 380.622i | 0.511123 | + | 0.558096i | ||||
\(683\) | 761.435i | 1.11484i | 0.830231 | + | 0.557419i | \(0.188208\pi\) | ||||
−0.830231 | + | 0.557419i | \(0.811792\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −341.822 | + | 313.052i | −0.498283 | + | 0.456344i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 18.2187 | − | 102.673i | 0.0264807 | − | 0.149234i | ||||
\(689\) | 142.913 | 0.207420 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 715.984i | − | 1.03616i | −0.855333 | − | 0.518078i | \(-0.826648\pi\) | ||
0.855333 | − | 0.518078i | \(-0.173352\pi\) | |||||||
\(692\) | −43.2250 | + | 491.001i | −0.0624639 | + | 0.709539i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −770.554 | + | 705.699i | −1.11031 | + | 1.01686i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −268.706 | −0.385518 | ||||||||
\(698\) | −174.158 | − | 190.163i | −0.249510 | − | 0.272440i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.03124 | −0.00860377 | −0.00430188 | − | 0.999991i | \(-0.501369\pi\) | ||||
−0.00430188 | + | 0.999991i | \(0.501369\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 478.294i | − | 0.680361i | ||||||
\(704\) | 701.910 | + | 189.299i | 0.997031 | + | 0.268891i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 803.495 | + | 877.338i | 1.13810 | + | 1.24269i | ||||
\(707\) | 43.3349i | 0.0612941i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −170.913 | −0.241061 | −0.120531 | − | 0.992710i | \(-0.538460\pi\) | ||||
−0.120531 | + | 0.992710i | \(0.538460\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 267.963 | − | 205.270i | 0.376353 | − | 0.288300i | ||||
\(713\) | −476.125 | −0.667777 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 551.910 | + | 48.5871i | 0.770824 | + | 0.0678591i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −38.4297 | + | 35.1952i | −0.0535233 | + | 0.0490184i | ||||
\(719\) | − | 1369.42i | − | 1.90462i | −0.305131 | − | 0.952310i | \(-0.598700\pi\) | ||
0.305131 | − | 0.952310i | \(-0.401300\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 721.087 | 1.00012 | ||||||||
\(722\) | 351.161 | + | 383.433i | 0.486372 | + | 0.531071i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 68.0954 | − | 773.508i | 0.0940544 | − | 1.06838i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1006.13i | 1.38394i | 0.721925 | + | 0.691971i | \(0.243258\pi\) | ||||
−0.721925 | + | 0.691971i | \(0.756742\pi\) | |||||||
\(728\) | 574.031 | + | 749.352i | 0.788504 | + | 1.02933i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 103.014i | 0.140922i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −365.319 | −0.498388 | −0.249194 | − | 0.968454i | \(-0.580166\pi\) | ||||
−0.249194 | + | 0.968454i | \(0.580166\pi\) | |||||||
\(734\) | 620.816 | − | 568.563i | 0.845798 | − | 0.774610i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −566.105 | + | 359.572i | −0.769164 | + | 0.488549i | ||||
\(737\) | −615.156 | −0.834676 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 187.213i | − | 0.253334i | −0.991945 | − | 0.126667i | \(-0.959572\pi\) | ||
0.991945 | − | 0.126667i | \(-0.0404279\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 212.984 | − | 195.058i | 0.287041 | − | 0.262882i | ||||
\(743\) | 183.678i | 0.247212i | 0.992331 | + | 0.123606i | \(0.0394459\pi\) | ||||
−0.992331 | + | 0.123606i | \(0.960554\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −295.433 | − | 322.584i | −0.396022 | − | 0.432418i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −715.418 | − | 62.9814i | −0.956441 | − | 0.0841997i | ||||
\(749\) | −1048.99 | −1.40053 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 569.734i | − | 0.758634i | −0.925267 | − | 0.379317i | \(-0.876159\pi\) | ||
0.925267 | − | 0.379317i | \(-0.123841\pi\) | |||||||
\(752\) | 108.797 | − | 613.134i | 0.144677 | − | 0.815337i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 332.900 | + | 363.494i | 0.441512 | + | 0.482088i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1131.60 | 1.49485 | 0.747424 | − | 0.664347i | \(-0.231290\pi\) | ||||
0.747424 | + | 0.664347i | \(0.231290\pi\) | |||||||
\(758\) | −363.246 | + | 332.673i | −0.479216 | + | 0.438882i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −753.125 | −0.989652 | −0.494826 | − | 0.868992i | \(-0.664768\pi\) | ||||
−0.494826 | + | 0.868992i | \(0.664768\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1231.73i | 1.61433i | ||||||||
\(764\) | −268.742 | − | 23.6586i | −0.351757 | − | 0.0309667i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 598.973 | − | 548.560i | 0.781950 | − | 0.716135i | ||||
\(767\) | − | 1033.40i | − | 1.34733i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −648.319 | −0.843067 | −0.421534 | − | 0.906813i | \(-0.638508\pi\) | ||||
−0.421534 | + | 0.906813i | \(0.638508\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −53.9742 | + | 613.104i | −0.0699148 | + | 0.794176i | ||||
\(773\) | 709.506 | 0.917861 | 0.458930 | − | 0.888472i | \(-0.348233\pi\) | ||||
0.458930 | + | 0.888472i | \(0.348233\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −983.339 | + | 753.274i | −1.26719 | + | 0.970714i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −271.811 | − | 296.791i | −0.349371 | − | 0.381479i | ||||
\(779\) | 423.627i | 0.543809i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −778.219 | −0.996439 | ||||||||
\(782\) | 488.586 | − | 447.463i | 0.624790 | − | 0.572204i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1106.32 | + | 196.310i | 1.41112 | + | 0.250395i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.67819i | 0.00467369i | 0.999997 | + | 0.00233684i | \(0.000743841\pi\) | ||||
−0.999997 | + | 0.00233684i | \(0.999256\pi\) | |||||||
\(788\) | 91.6547 | − | 1041.12i | 0.116313 | − | 1.32122i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 198.999i | 0.251579i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −994.512 | −1.25411 | ||||||||
\(794\) | 130.722 | + | 142.735i | 0.164637 | + | 0.179768i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −905.234 | − | 79.6918i | −1.13723 | − | 0.100115i | ||||
\(797\) | 1379.02 | 1.73027 | 0.865135 | − | 0.501539i | \(-0.167233\pi\) | ||||
0.865135 | + | 0.501539i | \(0.167233\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 615.171i | 0.769926i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 376.995 | + | 411.641i | 0.470068 | + | 0.513268i | ||||
\(803\) | − | 502.005i | − | 0.625162i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 362.094 | − | 331.617i | 0.449248 | − | 0.411436i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 25.2047 | − | 19.3077i | 0.0311939 | − | 0.0238957i | ||||
\(809\) | 1333.79 | 1.64869 | 0.824343 | − | 0.566090i | \(-0.191545\pi\) | ||||
0.824343 | + | 0.566090i | \(0.191545\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 204.820i | 0.252553i | 0.991995 | + | 0.126276i | \(0.0403026\pi\) | ||||
−0.991995 | + | 0.126276i | \(0.959697\pi\) | |||||||
\(812\) | 992.250 | + | 87.3522i | 1.22198 | + | 0.107577i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 321.570 | − | 294.505i | 0.395050 | − | 0.361799i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 162.406 | 0.198784 | ||||||||
\(818\) | −704.888 | − | 769.669i | −0.861722 | − | 0.940915i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 493.813 | 0.601477 | 0.300738 | − | 0.953707i | \(-0.402767\pi\) | ||||
0.300738 | + | 0.953707i | \(0.402767\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 173.312i | − | 0.210586i | −0.994441 | − | 0.105293i | \(-0.966422\pi\) | ||
0.994441 | − | 0.105293i | \(-0.0335780\pi\) | |||||||
\(824\) | −321.278 | − | 419.403i | −0.389901 | − | 0.508984i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1410.47 | − | 1540.09i | −1.70759 | − | 1.86452i | ||||
\(827\) | 693.777i | 0.838908i | 0.907776 | + | 0.419454i | \(0.137779\pi\) | ||||
−0.907776 | + | 0.419454i | \(0.862221\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1125.57 | −1.35774 | −0.678871 | − | 0.734257i | \(-0.737531\pi\) | ||||
−0.678871 | + | 0.734257i | \(0.737531\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 180.084 | − | 667.742i | 0.216448 | − | 0.802575i | ||||
\(833\) | −1109.99 | −1.33253 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −99.2930 | + | 1127.89i | −0.118771 | + | 1.34915i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 371.832 | − | 340.536i | 0.443714 | − | 0.406368i | ||||
\(839\) | − | 1243.69i | − | 1.48235i | −0.671313 | − | 0.741174i | \(-0.734269\pi\) | ||
0.671313 | − | 0.741174i | \(-0.265731\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −320.875 | −0.381540 | ||||||||
\(842\) | −1048.46 | − | 1144.81i | −1.24520 | − | 1.35964i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −772.277 | − | 67.9870i | −0.915021 | − | 0.0805533i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 87.6933i | − | 0.103534i | ||||||
\(848\) | −208.345 | − | 36.9696i | −0.245690 | − | 0.0435963i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 402.257i | 0.472687i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1027.09 | 1.20409 | 0.602044 | − | 0.798463i | \(-0.294353\pi\) | ||||
0.602044 | + | 0.798463i | \(0.294353\pi\) | |||||||
\(854\) | −1482.13 | + | 1357.39i | −1.73552 | + | 1.58945i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 467.376 | + | 610.122i | 0.546000 | + | 0.712759i | ||||
\(857\) | 341.775 | 0.398804 | 0.199402 | − | 0.979918i | \(-0.436100\pi\) | ||||
0.199402 | + | 0.979918i | \(0.436100\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 300.167i | − | 0.349438i | −0.984618 | − | 0.174719i | \(-0.944098\pi\) | ||
0.984618 | − | 0.174719i | \(-0.0559017\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −868.586 | + | 795.480i | −1.00764 | + | 0.922830i | ||||
\(863\) | − | 1312.54i | − | 1.52091i | −0.649394 | − | 0.760453i | \(-0.724977\pi\) | ||
0.649394 | − | 0.760453i | \(-0.275023\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −732.030 | − | 799.305i | −0.845301 | − | 0.922986i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 87.0156 | − | 988.427i | 0.100248 | − | 1.13874i | ||||
\(869\) | −928.219 | −1.06815 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 585.212i | 0.671885i | ||||||||
\(872\) | 716.408 | − | 548.795i | 0.821569 | − | 0.629352i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −705.445 | − | 770.277i | −0.807146 | − | 0.881324i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1543.22 | 1.75966 | 0.879832 | − | 0.475285i | \(-0.157655\pi\) | ||||
0.879832 | + | 0.475285i | \(0.157655\pi\) | |||||||
\(878\) | −5.96876 | + | 5.46639i | −0.00679813 | + | 0.00622595i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 254.437 | 0.288805 | 0.144403 | − | 0.989519i | \(-0.453874\pi\) | ||||
0.144403 | + | 0.989519i | \(0.453874\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 380.661i | 0.431099i | 0.976493 | + | 0.215550i | \(0.0691543\pi\) | ||||
−0.976493 | + | 0.215550i | \(0.930846\pi\) | |||||||
\(884\) | −59.9156 | + | 680.593i | −0.0677778 | + | 0.769901i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 505.360 | − | 462.826i | 0.570384 | − | 0.522376i | ||||
\(887\) | 851.315i | 0.959769i | 0.877332 | + | 0.479884i | \(0.159321\pi\) | ||||
−0.877332 | + | 0.479884i | \(0.840679\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −563.412 | −0.633760 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 101.047 | + | 8.89560i | 0.113281 | + | 0.00997265i | ||||
\(893\) | 969.844 | 1.08605 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −643.005 | − | 1240.94i | −0.717639 | − | 1.38498i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −654.377 | − | 714.516i | −0.728705 | − | 0.795675i | ||||
\(899\) | − | 518.121i | − | 0.576330i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 209.038 | 0.232006 | ||||||||
\(902\) | −284.816 | + | 260.844i | −0.315761 | + | 0.289184i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 115.743 | − | 88.6634i | 0.128034 | − | 0.0980790i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 531.313i | 0.585791i | 0.956144 | + | 0.292896i | \(0.0946188\pi\) | ||||
−0.956144 | + | 0.292896i | \(0.905381\pi\) | |||||||
\(908\) | −1492.56 | − | 131.397i | −1.64379 | − | 0.144710i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 316.638i | − | 0.347572i | −0.984783 | − | 0.173786i | \(-0.944400\pi\) | ||
0.984783 | − | 0.173786i | \(-0.0556001\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −317.094 | −0.347310 | ||||||||
\(914\) | −943.571 | − | 1030.29i | −1.03235 | − | 1.12723i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 90.9531 | − | 1033.15i | 0.0992938 | − | 1.12790i | ||||
\(917\) | −1732.56 | −1.88938 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 715.203i | 0.778240i | 0.921187 | + | 0.389120i | \(0.127221\pi\) | ||||
−0.921187 | + | 0.389120i | \(0.872779\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1107.98 | − | 1209.80i | −1.20171 | − | 1.31215i | ||||
\(923\) | 740.337i | 0.802098i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1300.82 | − | 1191.33i | 1.40477 | − | 1.28653i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −391.287 | − | 616.037i | −0.421646 | − | 0.663833i | ||||
\(929\) | 301.225 | 0.324246 | 0.162123 | − | 0.986771i | \(-0.448166\pi\) | ||||
0.162123 | + | 0.986771i | \(0.448166\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1749.95i | 1.87965i | ||||||||
\(932\) | −53.7484 | + | 610.539i | −0.0576700 | + | 0.655084i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 84.4187 | − | 77.3135i | 0.0903841 | − | 0.0827767i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1386.43 | −1.47965 | −0.739824 | − | 0.672800i | \(-0.765091\pi\) | ||||
−0.739824 | + | 0.672800i | \(0.765091\pi\) | |||||||
\(938\) | 798.742 | + | 872.148i | 0.851537 | + | 0.929795i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 697.844 | 0.741598 | 0.370799 | − | 0.928713i | \(-0.379084\pi\) | ||||
0.370799 | + | 0.928713i | \(0.379084\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 356.281i | − | 0.377816i | ||||||
\(944\) | −267.328 | + | 1506.55i | −0.283186 | + | 1.59592i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 100.000 | + | 109.190i | 0.105708 | + | 0.115423i | ||||
\(947\) | 310.121i | 0.327477i | 0.986504 | + | 0.163738i | \(0.0523553\pi\) | ||||
−0.986504 | + | 0.163738i | \(0.947645\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −477.569 | −0.503234 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 839.633 | + | 1096.07i | 0.881967 | + | 1.15134i | ||||
\(953\) | 552.725 | 0.579984 | 0.289992 | − | 0.957029i | \(-0.406347\pi\) | ||||
0.289992 | + | 0.957029i | \(0.406347\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −745.969 | − | 65.6709i | −0.780302 | − | 0.0686934i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −960.836 | + | 879.965i | −1.00296 | + | 0.918544i | ||||
\(959\) | 2291.22i | 2.38918i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 444.875 | 0.462929 | ||||||||
\(962\) | −280.169 | − | 305.917i | −0.291236 | − | 0.318001i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 22.8336 | − | 259.372i | 0.0236864 | − | 0.269058i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1606.13i | − | 1.66094i | −0.557060 | − | 0.830472i | \(-0.688071\pi\) | ||
0.557060 | − | 0.830472i | \(-0.311929\pi\) | |||||||
\(968\) | −51.0047 | + | 39.0715i | −0.0526908 | + | 0.0403631i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1265.13i | − | 1.30291i | −0.758686 | − | 0.651457i | \(-0.774158\pi\) | ||
0.758686 | − | 0.651457i | \(-0.225842\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 924.031 | 0.949672 | ||||||||
\(974\) | 78.1984 | − | 71.6167i | 0.0802858 | − | 0.0735284i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1449.85 | + | 257.268i | 1.48550 | + | 0.263594i | ||||
\(977\) | 592.244 | 0.606186 | 0.303093 | − | 0.952961i | \(-0.401981\pi\) | ||||
0.303093 | + | 0.952961i | \(0.401981\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 479.287i | 0.489568i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 31.9375 | − | 29.2494i | 0.0325229 | − | 0.0297856i | ||||
\(983\) | − | 1087.34i | − | 1.10615i | −0.833132 | − | 0.553074i | \(-0.813455\pi\) | ||
0.833132 | − | 0.553074i | \(-0.186545\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 486.931 | + | 531.681i | 0.493845 | + | 0.539230i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1072.98 | + | 94.4596i | 1.08602 | + | 0.0956069i | ||||
\(989\) | −136.588 | −0.138107 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 182.812i | − | 0.184472i | −0.995737 | − | 0.0922360i | \(-0.970599\pi\) | ||
0.995737 | − | 0.0922360i | \(-0.0294014\pi\) | |||||||
\(992\) | −613.664 | + | 389.780i | −0.618613 | + | 0.392923i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1010.47 | + | 1103.33i | 1.01657 | + | 1.10999i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −237.087 | −0.237801 | −0.118900 | − | 0.992906i | \(-0.537937\pi\) | ||||
−0.118900 | + | 0.992906i | \(0.537937\pi\) | |||||||
\(998\) | 300.000 | − | 274.750i | 0.300601 | − | 0.275301i | ||||
\(999\) | 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 | 900.3.c.m.451.1 | 4 | ||
3.2 | odd | 2 | 100.3.b.d.51.4 | yes | 4 | ||
4.3 | odd | 2 | inner | 900.3.c.m.451.2 | 4 | ||
5.2 | odd | 4 | 900.3.f.d.199.7 | 8 | |||
5.3 | odd | 4 | 900.3.f.d.199.2 | 8 | |||
5.4 | even | 2 | 900.3.c.l.451.4 | 4 | |||
12.11 | even | 2 | 100.3.b.d.51.3 | ✓ | 4 | ||
15.2 | even | 4 | 100.3.d.a.99.2 | 8 | |||
15.8 | even | 4 | 100.3.d.a.99.7 | 8 | |||
15.14 | odd | 2 | 100.3.b.e.51.1 | yes | 4 | ||
20.3 | even | 4 | 900.3.f.d.199.8 | 8 | |||
20.7 | even | 4 | 900.3.f.d.199.1 | 8 | |||
20.19 | odd | 2 | 900.3.c.l.451.3 | 4 | |||
24.5 | odd | 2 | 1600.3.b.p.1151.3 | 4 | |||
24.11 | even | 2 | 1600.3.b.p.1151.2 | 4 | |||
60.23 | odd | 4 | 100.3.d.a.99.1 | 8 | |||
60.47 | odd | 4 | 100.3.d.a.99.8 | 8 | |||
60.59 | even | 2 | 100.3.b.e.51.2 | yes | 4 | ||
120.29 | odd | 2 | 1600.3.b.o.1151.2 | 4 | |||
120.53 | even | 4 | 1600.3.h.o.1599.4 | 8 | |||
120.59 | even | 2 | 1600.3.b.o.1151.3 | 4 | |||
120.77 | even | 4 | 1600.3.h.o.1599.6 | 8 | |||
120.83 | odd | 4 | 1600.3.h.o.1599.5 | 8 | |||
120.107 | odd | 4 | 1600.3.h.o.1599.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
100.3.b.d.51.3 | ✓ | 4 | 12.11 | even | 2 | ||
100.3.b.d.51.4 | yes | 4 | 3.2 | odd | 2 | ||
100.3.b.e.51.1 | yes | 4 | 15.14 | odd | 2 | ||
100.3.b.e.51.2 | yes | 4 | 60.59 | even | 2 | ||
100.3.d.a.99.1 | 8 | 60.23 | odd | 4 | |||
100.3.d.a.99.2 | 8 | 15.2 | even | 4 | |||
100.3.d.a.99.7 | 8 | 15.8 | even | 4 | |||
100.3.d.a.99.8 | 8 | 60.47 | odd | 4 | |||
900.3.c.l.451.3 | 4 | 20.19 | odd | 2 | |||
900.3.c.l.451.4 | 4 | 5.4 | even | 2 | |||
900.3.c.m.451.1 | 4 | 1.1 | even | 1 | trivial | ||
900.3.c.m.451.2 | 4 | 4.3 | odd | 2 | inner | ||
900.3.f.d.199.1 | 8 | 20.7 | even | 4 | |||
900.3.f.d.199.2 | 8 | 5.3 | odd | 4 | |||
900.3.f.d.199.7 | 8 | 5.2 | odd | 4 | |||
900.3.f.d.199.8 | 8 | 20.3 | even | 4 | |||
1600.3.b.o.1151.2 | 4 | 120.29 | odd | 2 | |||
1600.3.b.o.1151.3 | 4 | 120.59 | even | 2 | |||
1600.3.b.p.1151.2 | 4 | 24.11 | even | 2 | |||
1600.3.b.p.1151.3 | 4 | 24.5 | odd | 2 | |||
1600.3.h.o.1599.3 | 8 | 120.107 | odd | 4 | |||
1600.3.h.o.1599.4 | 8 | 120.53 | even | 4 | |||
1600.3.h.o.1599.5 | 8 | 120.83 | odd | 4 | |||
1600.3.h.o.1599.6 | 8 | 120.77 | even | 4 |