Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3100,3,Mod(1301,3100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3100.1301");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3100 = 2^{2} \cdot 5^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 3100.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: | \(84.4688819517\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 620) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1301.4 | ||
Character | \(\chi\) | \(=\) | 3100.1301 |
Dual form | 3100.3.d.h.1301.3 |
$q$-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 \(\left(\mathbb{Z}/3100\mathbb{Z}\right)^\times\).
\(n\) | \(1551\) | \(1801\) | \(2977\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.03111i | 1.01037i | 0.863011 | + | 0.505185i | \(0.168576\pi\) | ||||
−0.863011 | + | 0.505185i | \(0.831424\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 12.6370 | 1.80529 | 0.902645 | − | 0.430387i | \(-0.141623\pi\) | ||||
0.902645 | + | 0.430387i | \(0.141623\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.187623 | −0.0208470 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 17.2333i | − | 1.56666i | −0.621604 | − | 0.783331i | \(-0.713519\pi\) | ||
0.621604 | − | 0.783331i | \(-0.286481\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 14.9646i | − | 1.15112i | −0.817758 | − | 0.575562i | \(-0.804783\pi\) | ||
0.817758 | − | 0.575562i | \(-0.195217\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.62351i | 0.154324i | 0.997019 | + | 0.0771621i | \(0.0245859\pi\) | ||||
−0.997019 | + | 0.0771621i | \(0.975414\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 16.9683 | 0.893067 | 0.446533 | − | 0.894767i | \(-0.352658\pi\) | ||||
0.446533 | + | 0.894767i | \(0.352658\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 38.3042i | 1.82401i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 0.547465i | − | 0.0238028i | −0.999929 | − | 0.0119014i | \(-0.996212\pi\) | ||
0.999929 | − | 0.0119014i | \(-0.00378843\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 26.7113i | 0.989307i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 33.2290i | 1.14583i | 0.819615 | + | 0.572914i | \(0.194187\pi\) | ||||
−0.819615 | + | 0.572914i | \(0.805813\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −30.1720 | − | 7.11683i | −0.973291 | − | 0.229575i | ||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 52.2360 | 1.58291 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 62.3249i | − | 1.68446i | −0.539121 | − | 0.842228i | \(-0.681244\pi\) | ||
0.539121 | − | 0.842228i | \(-0.318756\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 45.3594 | 1.16306 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.8590 | −0.264854 | −0.132427 | − | 0.991193i | \(-0.542277\pi\) | ||||
−0.132427 | + | 0.991193i | \(0.542277\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 13.8424i | − | 0.321915i | −0.986961 | − | 0.160958i | \(-0.948542\pi\) | ||
0.986961 | − | 0.160958i | \(-0.0514583\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 38.8232 | 0.826025 | 0.413012 | − | 0.910725i | \(-0.364477\pi\) | ||||
0.413012 | + | 0.910725i | \(0.364477\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 110.694 | 2.25907 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.95215 | −0.155924 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 53.5576i | − | 1.01052i | −0.862967 | − | 0.505261i | \(-0.831396\pi\) | ||
0.862967 | − | 0.505261i | \(-0.168604\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 51.4327i | 0.902328i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −44.2110 | −0.749339 | −0.374669 | − | 0.927158i | \(-0.622244\pi\) | ||||
−0.374669 | + | 0.927158i | \(0.622244\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 71.3500i | 1.16967i | 0.811151 | + | 0.584836i | \(0.198841\pi\) | ||||
−0.811151 | + | 0.584836i | \(0.801159\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.37099 | −0.0376348 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 55.3337 | 0.825877 | 0.412938 | − | 0.910759i | \(-0.364502\pi\) | ||||
0.412938 | + | 0.910759i | \(0.364502\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.65943 | 0.0240497 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −61.5833 | −0.867371 | −0.433685 | − | 0.901064i | \(-0.642787\pi\) | ||||
−0.433685 | + | 0.901064i | \(0.642787\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 24.5806i | 0.336720i | 0.985726 | + | 0.168360i | \(0.0538471\pi\) | ||||
−0.985726 | + | 0.168360i | \(0.946153\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 217.778i | − | 2.82828i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 130.554i | − | 1.65258i | −0.563245 | − | 0.826290i | \(-0.690447\pi\) | ||
0.563245 | − | 0.826290i | \(-0.309553\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −82.6534 | −1.02041 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 122.621i | − | 1.47736i | −0.674058 | − | 0.738678i | \(-0.735450\pi\) | ||
0.674058 | − | 0.738678i | \(-0.264550\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −100.721 | −1.15771 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 149.213i | − | 1.67655i | −0.545244 | − | 0.838277i | \(-0.683563\pi\) | ||
0.545244 | − | 0.838277i | \(-0.316437\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 189.108i | − | 2.07811i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 21.5719 | − | 91.4547i | 0.231956 | − | 0.983384i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −25.3091 | −0.260919 | −0.130460 | − | 0.991454i | \(-0.541645\pi\) | ||||
−0.130460 | + | 0.991454i | \(0.541645\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.23336i | 0.0326602i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 165.922 | 1.64279 | 0.821396 | − | 0.570358i | \(-0.193196\pi\) | ||||
0.821396 | + | 0.570358i | \(0.193196\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −112.617 | −1.09337 | −0.546685 | − | 0.837338i | \(-0.684110\pi\) | ||||
−0.546685 | + | 0.837338i | \(0.684110\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −179.840 | −1.68075 | −0.840374 | − | 0.542008i | \(-0.817664\pi\) | ||||
−0.840374 | + | 0.542008i | \(0.817664\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 186.122 | 1.70754 | 0.853772 | − | 0.520647i | \(-0.174309\pi\) | ||||
0.853772 | + | 0.520647i | \(0.174309\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 188.914 | 1.70192 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −68.1282 | −0.602905 | −0.301452 | − | 0.953481i | \(-0.597471\pi\) | ||||
−0.301452 | + | 0.953481i | \(0.597471\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.80770i | 0.0239975i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 33.1534i | 0.278600i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −175.986 | −1.45443 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 32.9148i | − | 0.267600i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 137.718i | 1.08439i | 0.840252 | + | 0.542196i | \(0.182407\pi\) | ||||
−0.840252 | + | 0.542196i | \(0.817593\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 41.9577 | 0.325254 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 169.467 | 1.29365 | 0.646823 | − | 0.762641i | \(-0.276097\pi\) | ||||
0.646823 | + | 0.762641i | \(0.276097\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 214.428 | 1.61224 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 82.4262i | 0.601651i | 0.953679 | + | 0.300825i | \(0.0972621\pi\) | ||||
−0.953679 | + | 0.300825i | \(0.902738\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.1552i | 0.101836i | 0.998703 | + | 0.0509178i | \(0.0162147\pi\) | ||||
−0.998703 | + | 0.0509178i | \(0.983785\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 117.677i | 0.834590i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −257.890 | −1.80342 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 335.527i | 2.28250i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 62.8370 | 0.421725 | 0.210863 | − | 0.977516i | \(-0.432373\pi\) | ||||
0.210863 | + | 0.977516i | \(0.432373\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 29.1590i | 0.193106i | 0.995328 | + | 0.0965529i | \(0.0307817\pi\) | ||||
−0.995328 | + | 0.0965529i | \(0.969218\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 0.492230i | − | 0.00321719i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −30.4164 | −0.193735 | −0.0968675 | − | 0.995297i | \(-0.530882\pi\) | ||||
−0.0968675 | + | 0.995297i | \(0.530882\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 162.339 | 1.02100 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 6.91833i | − | 0.0429710i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −40.0086 | −0.245452 | −0.122726 | − | 0.992441i | \(-0.539164\pi\) | ||||
−0.122726 | + | 0.992441i | \(0.539164\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 297.432i | − | 1.78103i | −0.454953 | − | 0.890516i | \(-0.650344\pi\) | ||
0.454953 | − | 0.890516i | \(-0.349656\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −54.9400 | −0.325089 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.18363 | −0.0186177 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −79.8258 | −0.461421 | −0.230710 | − | 0.973022i | \(-0.574105\pi\) | ||||
−0.230710 | + | 0.973022i | \(0.574105\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 134.008i | − | 0.757109i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 183.941i | 1.02761i | 0.857908 | + | 0.513803i | \(0.171764\pi\) | ||||
−0.857908 | + | 0.513803i | \(0.828236\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 237.728i | − | 1.31341i | −0.754147 | − | 0.656706i | \(-0.771949\pi\) | ||
0.754147 | − | 0.656706i | \(-0.228051\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −216.270 | −1.18180 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 45.2117 | 0.241774 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 337.551i | 1.78598i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 70.2816 | 0.367967 | 0.183983 | − | 0.982929i | \(-0.441101\pi\) | ||||
0.183983 | + | 0.982929i | \(0.441101\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 374.846 | 1.94221 | 0.971104 | − | 0.238655i | \(-0.0767066\pi\) | ||||
0.971104 | + | 0.238655i | \(0.0767066\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 96.1079i | 0.487858i | 0.969793 | + | 0.243929i | \(0.0784363\pi\) | ||||
−0.969793 | + | 0.243929i | \(0.921564\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 369.081i | 1.85468i | 0.374225 | + | 0.927338i | \(0.377909\pi\) | ||||
−0.374225 | + | 0.927338i | \(0.622091\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 167.723i | 0.834441i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 419.916i | 2.06855i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.102717i | 0.000496217i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 292.419i | − | 1.39913i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 221.582 | 1.05015 | 0.525077 | − | 0.851055i | \(-0.324037\pi\) | ||||
0.525077 | + | 0.851055i | \(0.324037\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 186.666i | − | 0.876365i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −381.285 | − | 89.9356i | −1.75707 | − | 0.414450i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −74.5064 | −0.340212 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 39.2599 | 0.177646 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 64.3966i | 0.288774i | 0.989521 | + | 0.144387i | \(0.0461210\pi\) | ||||
−0.989521 | + | 0.144387i | \(0.953879\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 262.898 | 1.15814 | 0.579070 | − | 0.815278i | \(-0.303416\pi\) | ||||
0.579070 | + | 0.815278i | \(0.303416\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 230.765i | − | 1.00771i | −0.863789 | − | 0.503854i | \(-0.831915\pi\) | ||
0.863789 | − | 0.503854i | \(-0.168085\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 660.107 | 2.85761 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −312.427 | −1.34089 | −0.670443 | − | 0.741961i | \(-0.733896\pi\) | ||||
−0.670443 | + | 0.741961i | \(0.733896\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 395.723 | 1.66972 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 143.331i | − | 0.599710i | −0.953985 | − | 0.299855i | \(-0.903062\pi\) | ||
0.953985 | − | 0.299855i | \(-0.0969383\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 225.766i | − | 0.936788i | −0.883520 | − | 0.468394i | \(-0.844833\pi\) | ||
0.883520 | − | 0.468394i | \(-0.155167\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 10.1300i | − | 0.0416872i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 253.924i | − | 1.02803i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 371.676 | 1.49268 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 243.419i | 0.969796i | 0.874571 | + | 0.484898i | \(0.161143\pi\) | ||||
−0.874571 | + | 0.484898i | \(0.838857\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.43463 | −0.0372910 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −258.288 | −1.00501 | −0.502505 | − | 0.864574i | \(-0.667588\pi\) | ||||
−0.502505 | + | 0.864574i | \(0.667588\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 787.601i | − | 3.04093i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 6.23452i | − | 0.0238871i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 228.581i | 0.869131i | 0.900640 | + | 0.434565i | \(0.143098\pi\) | ||||
−0.900640 | + | 0.434565i | \(0.856902\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 452.282 | 1.69394 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 392.997i | 1.46095i | 0.682937 | + | 0.730477i | \(0.260702\pi\) | ||||
−0.682937 | + | 0.730477i | \(0.739298\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 41.7275i | 0.153976i | 0.997032 | + | 0.0769881i | \(0.0245303\pi\) | ||||
−0.997032 | + | 0.0769881i | \(0.975470\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 573.208 | 2.09966 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 110.025i | 0.397203i | 0.980080 | + | 0.198602i | \(0.0636400\pi\) | ||||
−0.980080 | + | 0.198602i | \(0.936360\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.66096 | + | 1.33528i | 0.0202902 | + | 0.00478595i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −116.027 | −0.412906 | −0.206453 | − | 0.978457i | \(-0.566192\pi\) | ||||
−0.206453 | + | 0.978457i | \(0.566192\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.224672 | −0.000793896 | −0.000396948 | − | 1.00000i | \(-0.500126\pi\) | ||||
−0.000396948 | 1.00000i | \(0.500126\pi\) | ||||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −137.225 | −0.478137 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 282.117 | 0.976184 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 76.7148i | − | 0.263625i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −218.773 | −0.746665 | −0.373333 | − | 0.927698i | \(-0.621785\pi\) | ||||
−0.373333 | + | 0.927698i | \(0.621785\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 460.323 | 1.54991 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.19261 | −0.0274000 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 174.926i | − | 0.581150i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 502.928i | 1.65983i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 262.356 | 0.854578 | 0.427289 | − | 0.904115i | \(-0.359469\pi\) | ||||
0.427289 | + | 0.904115i | \(0.359469\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 341.355i | − | 1.10471i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −203.126 | −0.653137 | −0.326569 | − | 0.945173i | \(-0.605892\pi\) | ||||
−0.326569 | + | 0.945173i | \(0.605892\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 435.858i | − | 1.39252i | −0.717791 | − | 0.696259i | \(-0.754847\pi\) | ||
0.717791 | − | 0.696259i | \(-0.245153\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.559661 | 0.00176549 | 0.000882745 | − | 1.00000i | \(-0.499719\pi\) | ||||
0.000882745 | 1.00000i | \(0.499719\pi\) | ||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 572.645 | 1.79513 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 545.115i | − | 1.69818i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 44.5164i | 0.137822i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 564.157i | 1.72525i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 490.609 | 1.49121 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 150.254i | 0.453940i | 0.973902 | + | 0.226970i | \(0.0728819\pi\) | ||||
−0.973902 | + | 0.226970i | \(0.927118\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.6936i | 0.0351158i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 30.0663i | − | 0.0892174i | −0.999005 | − | 0.0446087i | \(-0.985796\pi\) | ||
0.999005 | − | 0.0446087i | \(-0.0142041\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 206.504i | − | 0.609157i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −122.646 | + | 519.963i | −0.359667 | + | 1.52482i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 779.634 | 2.27299 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 76.6888i | − | 0.221005i | −0.993876 | − | 0.110503i | \(-0.964754\pi\) | ||
0.993876 | − | 0.110503i | \(-0.0352460\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −185.444 | −0.531358 | −0.265679 | − | 0.964062i | \(-0.585596\pi\) | ||||
−0.265679 | + | 0.964062i | \(0.585596\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 399.724 | 1.13882 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 356.386i | 1.00959i | 0.863239 | + | 0.504796i | \(0.168432\pi\) | ||||
−0.863239 | + | 0.504796i | \(0.831568\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −100.491 | −0.281489 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −115.055 | −0.320486 | −0.160243 | − | 0.987078i | \(-0.551228\pi\) | ||||
−0.160243 | + | 0.987078i | \(0.551228\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −73.0778 | −0.202431 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 533.434i | − | 1.46951i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 284.273i | − | 0.774587i | −0.921956 | − | 0.387293i | \(-0.873410\pi\) | ||
0.921956 | − | 0.387293i | \(-0.126590\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.03739 | 0.00552140 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 676.809i | − | 1.82428i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 200.493 | 0.537514 | 0.268757 | − | 0.963208i | \(-0.413387\pi\) | ||||
0.268757 | + | 0.963208i | \(0.413387\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 497.260 | 1.31899 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 475.405 | 1.25437 | 0.627183 | − | 0.778872i | \(-0.284208\pi\) | ||||
0.627183 | + | 0.778872i | \(0.284208\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −417.438 | −1.09564 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 490.353i | − | 1.28029i | −0.768252 | − | 0.640147i | \(-0.778873\pi\) | ||
0.768252 | − | 0.640147i | \(-0.221127\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.59714i | 0.00671096i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 313.964i | 0.807106i | 0.914956 | + | 0.403553i | \(0.132225\pi\) | ||||
−0.914956 | + | 0.403553i | \(0.867775\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.43628 | 0.00367335 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 513.674i | 1.30706i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −256.843 | −0.646960 | −0.323480 | − | 0.946235i | \(-0.604853\pi\) | ||||
−0.323480 | + | 0.946235i | \(0.604853\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 649.956i | 1.62896i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 567.989i | 1.41643i | 0.705996 | + | 0.708216i | \(0.250499\pi\) | ||||
−0.705996 | + | 0.708216i | \(0.749501\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −106.501 | + | 451.513i | −0.264270 | + | 1.12038i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1074.06 | −2.63898 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 511.380i | − | 1.25032i | −0.780497 | − | 0.625159i | \(-0.785034\pi\) | ||
0.780497 | − | 0.625159i | \(-0.214966\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −249.843 | −0.607890 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −558.696 | −1.35277 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −42.9058 | −0.102892 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 393.577 | 0.939325 | 0.469663 | − | 0.882846i | \(-0.344376\pi\) | ||||
0.469663 | + | 0.882846i | \(0.344376\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −244.177 | −0.579994 | −0.289997 | − | 0.957028i | \(-0.593654\pi\) | ||||
−0.289997 | + | 0.957028i | \(0.593654\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.28411 | −0.0172201 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 901.652i | 2.11160i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 781.692i | − | 1.82213i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 318.209 | 0.738304 | 0.369152 | − | 0.929369i | \(-0.379648\pi\) | ||||
0.369152 | + | 0.929369i | \(0.379648\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 494.720i | 1.14254i | 0.820762 | + | 0.571271i | \(0.193549\pi\) | ||||
−0.820762 | + | 0.571271i | \(0.806451\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 9.28954i | − | 0.0212575i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 525.555 | 1.19716 | 0.598582 | − | 0.801062i | \(-0.295731\pi\) | ||||
0.598582 | + | 0.801062i | \(0.295731\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.7688 | −0.0470948 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 381.481 | 0.861130 | 0.430565 | − | 0.902560i | \(-0.358314\pi\) | ||||
0.430565 | + | 0.902560i | \(0.358314\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 190.466i | 0.426098i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 522.611i | 1.16394i | 0.813209 | + | 0.581972i | \(0.197719\pi\) | ||||
−0.813209 | + | 0.581972i | \(0.802281\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 187.136i | 0.414936i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −88.3841 | −0.195108 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.68966i | 0.0168264i | 0.999965 | + | 0.00841320i | \(0.00267804\pi\) | ||||
−0.999965 | + | 0.00841320i | \(0.997322\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −70.0773 | −0.152674 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.9518i | 0.0389410i | 0.999810 | + | 0.0194705i | \(0.00619805\pi\) | ||||
−0.999810 | + | 0.0194705i | \(0.993802\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 485.364i | 1.04830i | 0.851625 | + | 0.524152i | \(0.175617\pi\) | ||||
−0.851625 | + | 0.524152i | \(0.824383\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 386.478 | 0.827576 | 0.413788 | − | 0.910373i | \(-0.364205\pi\) | ||||
0.413788 | + | 0.910373i | \(0.364205\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 699.254 | 1.49095 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 92.1954i | − | 0.195744i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −238.549 | −0.504333 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.0486i | 0.0210663i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −87.7891 | −0.183276 | −0.0916379 | − | 0.995792i | \(-0.529210\pi\) | ||||
−0.0916379 | + | 0.995792i | \(0.529210\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −932.669 | −1.93902 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 20.9702 | 0.0434166 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 182.759i | 0.375276i | 0.982238 | + | 0.187638i | \(0.0600832\pi\) | ||||
−0.982238 | + | 0.187638i | \(0.939917\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 121.270i | − | 0.247997i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 45.7608i | 0.0931992i | 0.998914 | + | 0.0465996i | \(0.0148385\pi\) | ||||
−0.998914 | + | 0.0465996i | \(0.985162\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −87.1767 | −0.176829 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −778.230 | −1.56586 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 775.048i | 1.55320i | 0.629993 | + | 0.776601i | \(0.283058\pi\) | ||||
−0.629993 | + | 0.776601i | \(0.716942\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 901.549 | 1.79950 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −35.4011 | −0.0703800 | −0.0351900 | − | 0.999381i | \(-0.511204\pi\) | ||||
−0.0351900 | + | 0.999381i | \(0.511204\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 166.529i | − | 0.328460i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 441.931i | 0.868234i | 0.900857 | + | 0.434117i | \(0.142940\pi\) | ||||
−0.900857 | + | 0.434117i | \(0.857060\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 310.625i | 0.607877i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 453.244i | 0.883517i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 669.051i | − | 1.29410i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 241.961i | − | 0.466205i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.82481 | −0.00734129 | −0.00367064 | − | 0.999993i | \(-0.501168\pi\) | ||||
−0.00367064 | + | 0.999993i | \(0.501168\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 222.757i | − | 0.425921i | −0.977061 | − | 0.212961i | \(-0.931689\pi\) | ||
0.977061 | − | 0.212961i | \(-0.0683106\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18.6711 | − | 79.1566i | 0.0354290 | − | 0.150202i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 528.700 | 0.999433 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.29499 | 0.0156215 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 162.501i | 0.304880i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −557.546 | −1.03826 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1907.63i | − | 3.53920i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −72.2331 | −0.133518 | −0.0667589 | − | 0.997769i | \(-0.521266\pi\) | ||||
−0.0667589 | + | 0.997769i | \(0.521266\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 720.578 | 1.32703 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.7149 | 0.0689487 | 0.0344744 | − | 0.999406i | \(-0.489024\pi\) | ||||
0.0344744 | + | 0.999406i | \(0.489024\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 13.3869i | − | 0.0243841i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 563.839i | 1.02330i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 1649.81i | − | 2.98339i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 136.072i | − | 0.244295i | −0.992512 | − | 0.122147i | \(-0.961022\pi\) | ||
0.992512 | − | 0.122147i | \(-0.0389781\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −207.146 | −0.370565 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 137.042i | 0.244281i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 264.828 | 0.470388 | 0.235194 | − | 0.971948i | \(-0.424428\pi\) | ||||
0.235194 | + | 0.971948i | \(0.424428\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1044.49 | −1.84214 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 53.5741i | − | 0.0941548i | −0.998891 | − | 0.0470774i | \(-0.985009\pi\) | ||
0.998891 | − | 0.0470774i | \(-0.0149907\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 621.926i | 1.08919i | 0.838700 | + | 0.544594i | \(0.183316\pi\) | ||||
−0.838700 | + | 0.544594i | \(0.816684\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 213.031i | 0.371782i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.3136 | −0.0282731 | −0.0141366 | − | 0.999900i | \(-0.504500\pi\) | ||||
−0.0141366 | + | 0.999900i | \(0.504500\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1136.20i | 1.96235i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 1549.56i | − | 2.66706i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −922.974 | −1.58315 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 239.436i | − | 0.407898i | −0.978981 | − | 0.203949i | \(-0.934622\pi\) | ||
0.978981 | − | 0.203949i | \(-0.0653777\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −511.967 | − | 120.760i | −0.869214 | − | 0.205026i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −291.314 | −0.492916 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −219.702 | −0.370493 | −0.185246 | − | 0.982692i | \(-0.559308\pi\) | ||||
−0.185246 | + | 0.982692i | \(0.559308\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1118.72 | −1.87391 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −403.870 | −0.674240 | −0.337120 | − | 0.941462i | \(-0.609453\pi\) | ||||
−0.337120 | + | 0.941462i | \(0.609453\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 406.825i | 0.676914i | 0.940982 | + | 0.338457i | \(0.109905\pi\) | ||||
−0.940982 | + | 0.338457i | \(0.890095\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.3819 | −0.0172170 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 271.236 | 0.446847 | 0.223423 | − | 0.974721i | \(-0.428277\pi\) | ||||
0.223423 | + | 0.974721i | \(0.428277\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1272.81 | −2.09000 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 580.974i | − | 0.950858i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 431.338i | − | 0.703651i | −0.936066 | − | 0.351825i | \(-0.885561\pi\) | ||
0.936066 | − | 0.351825i | \(-0.114439\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −44.3973 | −0.0719568 | −0.0359784 | − | 0.999353i | \(-0.511455\pi\) | ||||
−0.0359784 | + | 0.999353i | \(0.511455\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1027.51i | 1.65995i | 0.557799 | + | 0.829976i | \(0.311646\pi\) | ||||
−0.557799 | + | 0.829976i | \(0.688354\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14.6235 | 0.0235483 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 1885.61i | − | 3.02667i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 886.354 | 1.41364 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 163.510 | 0.259952 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 381.333i | − | 0.604331i | −0.953255 | − | 0.302165i | \(-0.902290\pi\) | ||
0.953255 | − | 0.302165i | \(-0.0977095\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 671.640i | 1.06104i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1656.50i | − | 2.60047i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.5544 | 0.0180821 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 712.516i | 1.11157i | 0.831326 | + | 0.555785i | \(0.187582\pi\) | ||||
−0.831326 | + | 0.555785i | \(0.812418\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 486.737i | 0.756978i | 0.925606 | + | 0.378489i | \(0.123556\pi\) | ||||
−0.925606 | + | 0.378489i | \(0.876444\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1113.31i | 1.72073i | 0.509676 | + | 0.860366i | \(0.329765\pi\) | ||||
−0.509676 | + | 0.860366i | \(0.670235\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 761.901i | 1.17396i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 272.604 | − | 1155.72i | 0.418747 | − | 1.77529i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −917.109 | −1.40445 | −0.702227 | − | 0.711953i | \(-0.747811\pi\) | ||||
−0.702227 | + | 0.711953i | \(0.747811\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 4.61187i | − | 0.00701960i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 602.233 | 0.913859 | 0.456929 | − | 0.889503i | \(-0.348949\pi\) | ||||
0.456929 | + | 0.889503i | \(0.348949\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 500.175 | 0.756694 | 0.378347 | − | 0.925664i | \(-0.376493\pi\) | ||||
0.378347 | + | 0.925664i | \(0.376493\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 119.001i | 0.179489i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.1917 | 0.0272740 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −195.193 | −0.291768 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1229.60 | 1.83248 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 830.738i | − | 1.23438i | −0.786814 | − | 0.617190i | \(-0.788271\pi\) | ||
0.786814 | − | 0.617190i | \(-0.211729\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 498.118i | 0.735772i | 0.929871 | + | 0.367886i | \(0.119918\pi\) | ||||
−0.929871 | + | 0.367886i | \(0.880082\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −319.832 | −0.471034 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 796.871i | 1.17015i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −928.620 | −1.35962 | −0.679810 | − | 0.733388i | \(-0.737938\pi\) | ||||
−0.679810 | + | 0.733388i | \(0.737938\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 699.475 | 1.01816 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −801.470 | −1.16324 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 772.022 | 1.11725 | 0.558627 | − | 0.829419i | \(-0.311329\pi\) | ||||
0.558627 | + | 0.829419i | \(0.311329\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 40.8600i | 0.0589611i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 28.4887i | − | 0.0408733i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 946.999i | − | 1.35479i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −373.767 | −0.533191 | −0.266595 | − | 0.963809i | \(-0.585899\pi\) | ||||
−0.266595 | + | 0.963809i | \(0.585899\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1057.55i | − | 1.50433i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2096.76 | 2.96572 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 506.220i | − | 0.713991i | −0.934106 | − | 0.356996i | \(-0.883801\pi\) | ||
0.934106 | − | 0.356996i | \(-0.116199\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 24.4949i | 0.0344513i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.89622 | + | 16.5181i | −0.00546454 | + | 0.0231671i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 434.451 | 0.605929 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 244.535i | 0.340105i | 0.985435 | + | 0.170052i | \(0.0543937\pi\) | ||||
−0.985435 | + | 0.170052i | \(0.945606\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1423.15 | −1.97385 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 684.321 | 0.946502 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 449.202 | 0.617884 | 0.308942 | − | 0.951081i | \(-0.400025\pi\) | ||||
0.308942 | + | 0.951081i | \(0.400025\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −713.176 | −0.978293 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 36.3156 | 0.0496793 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −979.538 | −1.33634 | −0.668171 | − | 0.744008i | \(-0.732922\pi\) | ||||
−0.668171 | + | 0.744008i | \(0.732922\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 953.582i | − | 1.29387i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 858.011i | − | 1.16104i | −0.814245 | − | 0.580522i | \(-0.802849\pi\) | ||
0.814245 | − | 0.580522i | \(-0.197151\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 769.671 | 1.03869 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 445.813i | 0.600017i | 0.953936 | + | 0.300009i | \(0.0969896\pi\) | ||||
−0.953936 | + | 0.300009i | \(0.903010\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 23.0064i | 0.0307984i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2272.64 | −3.03423 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −742.500 | −0.988682 | −0.494341 | − | 0.869268i | \(-0.664591\pi\) | ||||
−0.494341 | + | 0.869268i | \(0.664591\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −737.829 | −0.979852 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1414.38i | 1.86840i | 0.356747 | + | 0.934201i | \(0.383886\pi\) | ||||
−0.356747 | + | 0.934201i | \(0.616114\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 28.5974i | − | 0.0376777i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 528.815i | − | 0.694894i | −0.937700 | − | 0.347447i | \(-0.887049\pi\) | ||
0.937700 | − | 0.347447i | \(-0.112951\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2352.03 | 3.08261 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 661.601i | 0.862583i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −78.3658 | −0.101906 | −0.0509530 | − | 0.998701i | \(-0.516226\pi\) | ||||
−0.0509530 | + | 0.998701i | \(0.516226\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 782.899i | − | 1.01543i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 455.033i | − | 0.588659i | −0.955704 | − | 0.294330i | \(-0.904904\pi\) | ||
0.955704 | − | 0.294330i | \(-0.0950963\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2387.31 | 3.07246 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −184.258 | −0.236532 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1061.28i | 1.35888i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −887.589 | −1.13358 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1364.15i | − | 1.73336i | −0.498868 | − | 0.866678i | \(-0.666251\pi\) | ||
0.498868 | − | 0.866678i | \(-0.333749\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −692.855 | −0.878143 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −860.938 | −1.08842 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1067.73 | 1.34644 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 276.950i | 0.347490i | 0.984791 | + | 0.173745i | \(0.0555869\pi\) | ||||
−0.984791 | + | 0.173745i | \(0.944413\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 101.853i | 0.127476i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 27.9958i | 0.0349511i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 423.604 | 0.527527 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1191.22 | −1.47610 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 874.241i | 1.08064i | 0.841458 | + | 0.540322i | \(0.181698\pi\) | ||||
−0.841458 | + | 0.540322i | \(0.818302\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 555.744 | 0.685257 | 0.342629 | − | 0.939471i | \(-0.388683\pi\) | ||||
0.342629 | + | 0.939471i | \(0.388683\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −126.481 | −0.155573 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 234.881i | − | 0.287492i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 35.4810i | 0.0433224i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 366.443i | − | 0.446337i | −0.974780 | − | 0.223168i | \(-0.928360\pi\) | ||
0.974780 | − | 0.223168i | \(-0.0716400\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 663.118i | − | 0.805732i | −0.915259 | − | 0.402866i | \(-0.868014\pi\) | ||
0.915259 | − | 0.402866i | \(-0.131986\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1113.53i | − | 1.34646i | −0.739431 | − | 0.673232i | \(-0.764905\pi\) | ||
0.739431 | − | 0.673232i | \(-0.235095\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 292.757i | − | 0.353144i | −0.984288 | − | 0.176572i | \(-0.943499\pi\) | ||
0.984288 | − | 0.176572i | \(-0.0565009\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −333.499 | −0.401322 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 290.408i | 0.348629i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 190.100 | − | 805.933i | 0.227120 | − | 0.962883i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −424.914 | −0.506453 | −0.253227 | − | 0.967407i | \(-0.581492\pi\) | ||||
−0.253227 | + | 0.967407i | \(0.581492\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −263.168 | −0.312922 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 351.689i | − | 0.417187i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2223.94 | −2.62567 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 0.681007i | − | 0.000802128i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −34.1207 | −0.0400949 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 813.025 | 0.953136 | 0.476568 | − | 0.879138i | \(-0.341881\pi\) | ||||
0.476568 | + | 0.879138i | \(0.341881\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1205.01 | −1.40608 | −0.703040 | − | 0.711151i | \(-0.748174\pi\) | ||||
−0.703040 | + | 0.711151i | \(0.748174\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.0682i | 0.0361678i | 0.999836 | + | 0.0180839i | \(0.00575660\pi\) | ||||
−0.999836 | + | 0.0180839i | \(0.994243\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 415.945i | − | 0.483095i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1003.58i | 1.16290i | 0.813583 | + | 0.581449i | \(0.197514\pi\) | ||||
−0.813583 | + | 0.581449i | \(0.802486\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 855.128i | 0.986307i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2249.87 | −2.58904 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 828.049i | − | 0.950687i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.74857 | 0.00543937 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1215.09 | 1.38551 | 0.692755 | − | 0.721173i | \(-0.256397\pi\) | ||||
0.692755 | + | 0.721173i | \(0.256397\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 663.124i | − | 0.754408i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 770.265i | − | 0.874308i | −0.899387 | − | 0.437154i | \(-0.855986\pi\) | ||
0.899387 | − | 0.437154i | \(-0.144014\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1336.86i | 1.51400i | 0.653413 | + | 0.757002i | \(0.273336\pi\) | ||||
−0.653413 | + | 0.757002i | \(0.726664\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1032.96 | 1.16455 | 0.582275 | − | 0.812992i | \(-0.302163\pi\) | ||||
0.582275 | + | 0.812992i | \(0.302163\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1740.34i | 1.95764i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1424.39i | 1.59864i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 658.762 | 0.737695 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 24.8327i | − | 0.0276842i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 236.485 | − | 1002.59i | 0.263054 | − | 1.11522i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 140.509 | 0.155948 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 530.221 | 0.587177 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1575.76 | −1.73733 | −0.868665 | − | 0.495399i | \(-0.835022\pi\) | ||||
−0.868665 | + | 0.495399i | \(0.835022\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −31.1308 | −0.0342473 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 269.186i | − | 0.295484i | −0.989026 | − | 0.147742i | \(-0.952799\pi\) | ||
0.989026 | − | 0.147742i | \(-0.0472006\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2113.16 | −2.31452 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2141.57 | 2.33540 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 802.258 | 0.872968 | 0.436484 | − | 0.899712i | \(-0.356224\pi\) | ||||
0.436484 | + | 0.899712i | \(0.356224\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 795.228i | 0.863440i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 921.572i | 0.998452i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 21.1295 | 0.0227935 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 843.856i | 0.908349i | 0.890913 | + | 0.454174i | \(0.150066\pi\) | ||||
−0.890913 | + | 0.454174i | \(0.849934\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1878.29 | 2.01750 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 615.696i | − | 0.659910i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 297.497 | 0.317500 | 0.158750 | − | 0.987319i | \(-0.449254\pi\) | ||||
0.158750 | + | 0.987319i | \(0.449254\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1321.13 | 1.40696 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1112.43i | 1.18218i | 0.806605 | + | 0.591091i | \(0.201303\pi\) | ||||
−0.806605 | + | 0.591091i | \(0.798697\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.94492i | 0.00630427i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 1271.66i | − | 1.34283i | −0.741082 | − | 0.671414i | \(-0.765687\pi\) | ||
0.741082 | − | 0.671414i | \(-0.234313\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 367.839 | 0.387607 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.69639i | 0.00178380i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 321.088i | 0.336924i | 0.985708 | + | 0.168462i | \(0.0538800\pi\) | ||||
−0.985708 | + | 0.168462i | \(0.946120\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1735.75i | 1.81374i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1041.62i | 1.08615i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 859.701 | + | 429.458i | 0.894591 | + | 0.446887i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 33.7421 | 0.0350385 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1510.14i | − | 1.56167i | −0.624735 | − | 0.780836i | \(-0.714793\pi\) | ||
0.624735 | − | 0.780836i | \(-0.285207\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −134.934 | −0.139251 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −295.871 | −0.304708 | −0.152354 | − | 0.988326i | \(-0.548685\pi\) | ||||
−0.152354 | + | 0.988326i | \(0.548685\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 178.879i | 0.183843i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1086.22 | −1.11179 | −0.555895 | − | 0.831253i | \(-0.687624\pi\) | ||||
−0.555895 | + | 0.831253i | \(0.687624\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2571.44 | −2.62660 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −34.9208 | −0.0355971 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1136.59i | − | 1.15625i | −0.815949 | − | 0.578124i | \(-0.803785\pi\) | ||
0.815949 | − | 0.578124i | \(-0.196215\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1487.09i | 1.50668i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.57821 | −0.00766250 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1661.00i | 1.67608i | 0.545609 | + | 0.838040i | \(0.316299\pi\) | ||||
−0.545609 | + | 0.838040i | \(0.683701\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −455.436 | −0.458647 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 660.502 | 0.662489 | 0.331245 | − | 0.943545i | \(-0.392531\pi\) | ||||
0.331245 | + | 0.943545i | \(0.392531\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1664.78 | 1.66644 |
(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 | 3100.3.d.h.1301.4 | 24 | ||
5.2 | odd | 4 | 620.3.f.c.309.20 | yes | 24 | ||
5.3 | odd | 4 | 620.3.f.c.309.5 | ✓ | 24 | ||
5.4 | even | 2 | inner | 3100.3.d.h.1301.21 | 24 | ||
31.30 | odd | 2 | inner | 3100.3.d.h.1301.3 | 24 | ||
155.92 | even | 4 | 620.3.f.c.309.6 | yes | 24 | ||
155.123 | even | 4 | 620.3.f.c.309.19 | yes | 24 | ||
155.154 | odd | 2 | inner | 3100.3.d.h.1301.22 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
620.3.f.c.309.5 | ✓ | 24 | 5.3 | odd | 4 | ||
620.3.f.c.309.6 | yes | 24 | 155.92 | even | 4 | ||
620.3.f.c.309.19 | yes | 24 | 155.123 | even | 4 | ||
620.3.f.c.309.20 | yes | 24 | 5.2 | odd | 4 | ||
3100.3.d.h.1301.3 | 24 | 31.30 | odd | 2 | inner | ||
3100.3.d.h.1301.4 | 24 | 1.1 | even | 1 | trivial | ||
3100.3.d.h.1301.21 | 24 | 5.4 | even | 2 | inner | ||
3100.3.d.h.1301.22 | 24 | 155.154 | odd | 2 | inner |