Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,4,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1856.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.a (trivial) |
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: | yes |
Analytic conductor: | \(109.507544971\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 58) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 1.44949 | 0.278954 | 0.139477 | − | 0.990225i | \(-0.455458\pi\) | ||||
0.139477 | + | 0.990225i | \(0.455458\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 19.6969 | 1.76175 | 0.880874 | − | 0.473351i | \(-0.156956\pi\) | ||||
0.880874 | + | 0.473351i | \(0.156956\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −11.5959 | −0.626121 | −0.313060 | − | 0.949733i | \(-0.601354\pi\) | ||||
−0.313060 | + | 0.949733i | \(0.601354\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −24.8990 | −0.922184 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −37.6515 | −1.03203 | −0.516017 | − | 0.856579i | \(-0.672586\pi\) | ||||
−0.516017 | + | 0.856579i | \(0.672586\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 44.5959 | 0.951437 | 0.475719 | − | 0.879598i | \(-0.342188\pi\) | ||||
0.475719 | + | 0.879598i | \(0.342188\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 28.5505 | 0.491447 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −61.1918 | −0.873012 | −0.436506 | − | 0.899701i | \(-0.643784\pi\) | ||||
−0.436506 | + | 0.899701i | \(0.643784\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 63.7980 | 0.770329 | 0.385165 | − | 0.922848i | \(-0.374145\pi\) | ||||
0.385165 | + | 0.922848i | \(0.374145\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −16.8082 | −0.174659 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −177.060 | −1.60520 | −0.802600 | − | 0.596517i | \(-0.796551\pi\) | ||||
−0.802600 | + | 0.596517i | \(0.796551\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 262.969 | 2.10376 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −75.2270 | −0.536202 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −29.0000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 233.994 | 1.35570 | 0.677849 | − | 0.735201i | \(-0.262912\pi\) | ||||
0.677849 | + | 0.735201i | \(0.262912\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −54.5755 | −0.287890 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −228.404 | −1.10307 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.2020 | −0.0453299 | −0.0226649 | − | 0.999743i | \(-0.507215\pi\) | ||||
−0.0226649 | + | 0.999743i | \(0.507215\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 64.6413 | 0.265408 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 347.959 | 1.32542 | 0.662708 | − | 0.748877i | \(-0.269407\pi\) | ||||
0.662708 | + | 0.748877i | \(0.269407\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −194.823 | −0.690935 | −0.345468 | − | 0.938431i | \(-0.612280\pi\) | ||||
−0.345468 | + | 0.938431i | \(0.612280\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −490.434 | −1.62466 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 14.5005 | 0.0450025 | 0.0225013 | − | 0.999747i | \(-0.492837\pi\) | ||||
0.0225013 | + | 0.999747i | \(0.492837\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −208.535 | −0.607973 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −88.6969 | −0.243531 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 606.373 | 1.57154 | 0.785772 | − | 0.618517i | \(-0.212266\pi\) | ||||
0.785772 | + | 0.618517i | \(0.212266\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −741.620 | −1.81818 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 92.4745 | 0.214887 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −702.372 | −1.54985 | −0.774925 | − | 0.632054i | \(-0.782212\pi\) | ||||
−0.774925 | + | 0.632054i | \(0.782212\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −543.394 | −1.14056 | −0.570282 | − | 0.821449i | \(-0.693166\pi\) | ||||
−0.570282 | + | 0.821449i | \(0.693166\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 288.727 | 0.577399 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 878.403 | 1.67619 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −407.010 | −0.742152 | −0.371076 | − | 0.928602i | \(-0.621011\pi\) | ||||
−0.371076 | + | 0.928602i | \(0.621011\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −256.647 | −0.447778 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −314.717 | −0.526057 | −0.263029 | − | 0.964788i | \(-0.584721\pi\) | ||||
−0.263029 | + | 0.964788i | \(0.584721\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −859.110 | −1.37741 | −0.688707 | − | 0.725040i | \(-0.741821\pi\) | ||||
−0.688707 | + | 0.725040i | \(0.741821\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 381.171 | 0.586852 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 436.604 | 0.646177 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −725.266 | −1.03290 | −0.516448 | − | 0.856319i | \(-0.672746\pi\) | ||||
−0.516448 | + | 0.856319i | \(0.672746\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 563.232 | 0.772609 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −820.919 | −1.08563 | −0.542817 | − | 0.839851i | \(-0.682642\pi\) | ||||
−0.542817 | + | 0.839851i | \(0.682642\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1205.29 | −1.53803 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −42.0352 | −0.0518005 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −648.363 | −0.772206 | −0.386103 | − | 0.922456i | \(-0.626179\pi\) | ||||
−0.386103 | + | 0.922456i | \(0.626179\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −517.131 | −0.595714 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 339.172 | 0.378178 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1256.62 | 1.35713 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −60.9490 | −0.0637983 | −0.0318991 | − | 0.999491i | \(-0.510156\pi\) | ||||
−0.0318991 | + | 0.999491i | \(0.510156\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 937.485 | 0.951725 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1100.16 | −1.08386 | −0.541930 | − | 0.840423i | \(-0.682306\pi\) | ||||
−0.541930 | + | 0.840423i | \(0.682306\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −747.930 | −0.715492 | −0.357746 | − | 0.933819i | \(-0.616455\pi\) | ||||
−0.357746 | + | 0.933819i | \(0.616455\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −331.069 | −0.307705 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 176.059 | 0.159068 | 0.0795340 | − | 0.996832i | \(-0.474657\pi\) | ||||
0.0795340 | + | 0.996832i | \(0.474657\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −173.856 | −0.152774 | −0.0763871 | − | 0.997078i | \(-0.524338\pi\) | ||||
−0.0763871 | + | 0.997078i | \(0.524338\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14.7878 | −0.0126450 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1707.65 | −1.42161 | −0.710807 | − | 0.703387i | \(-0.751670\pi\) | ||||
−0.710807 | + | 0.703387i | \(0.751670\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3487.54 | −2.82796 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1110.39 | −0.877400 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 709.576 | 0.546611 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 86.6378 | 0.0650922 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 504.363 | 0.369731 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2717.57 | 1.94454 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 881.473 | 0.615891 | 0.307945 | − | 0.951404i | \(-0.400359\pi\) | ||||
0.307945 | + | 0.951404i | \(0.400359\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −282.394 | −0.192739 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2025.49 | 1.35090 | 0.675451 | − | 0.737405i | \(-0.263949\pi\) | ||||
0.675451 | + | 0.737405i | \(0.263949\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −739.796 | −0.482319 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1481.74 | −0.944652 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1594.32 | 0.994248 | 0.497124 | − | 0.867679i | \(-0.334389\pi\) | ||||
0.497124 | + | 0.867679i | \(0.334389\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2855.40 | −1.74239 | −0.871195 | − | 0.490938i | \(-0.836654\pi\) | ||||
−0.871195 | + | 0.490938i | \(0.836654\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 21.0183 | 0.0125536 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1679.10 | −0.981915 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −571.211 | −0.327148 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −302.269 | −0.169597 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.3755 | 0.0101032 | 0.00505162 | − | 0.999987i | \(-0.498392\pi\) | ||||
0.00505162 | + | 0.999987i | \(0.498392\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 778.806 | 0.419724 | 0.209862 | − | 0.977731i | \(-0.432699\pi\) | ||||
0.209862 | + | 0.977731i | \(0.432699\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1523.61 | 0.805078 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4608.97 | 2.38840 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 511.896 | 0.260215 | 0.130107 | − | 0.991500i | \(-0.458468\pi\) | ||||
0.130107 | + | 0.991500i | \(0.458468\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 878.932 | 0.438389 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2053.18 | 1.00505 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1451.59 | −0.697529 | −0.348764 | − | 0.937210i | \(-0.613399\pi\) | ||||
−0.348764 | + | 0.937210i | \(0.613399\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1074.97 | −0.507190 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −600.374 | −0.278194 | −0.139097 | − | 0.990279i | \(-0.544420\pi\) | ||||
−0.139097 | + | 0.990279i | \(0.544420\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −208.204 | −0.0947675 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1588.50 | −0.710386 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2574.20 | 1.13129 | 0.565644 | − | 0.824650i | \(-0.308628\pi\) | ||||
0.565644 | + | 0.824650i | \(0.308628\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3049.37 | −1.31720 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1018.08 | −0.432337 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3828.72 | 1.59872 | 0.799362 | − | 0.600850i | \(-0.205171\pi\) | ||||
0.799362 | + | 0.600850i | \(0.205171\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2075.64 | −0.852381 | −0.426190 | − | 0.904633i | \(-0.640145\pi\) | ||||
−0.426190 | + | 0.904633i | \(0.640145\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −787.644 | −0.318166 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −200.949 | −0.0798598 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2303.97 | 0.900977 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 872.327 | 0.335727 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4070.08 | −1.54189 | −0.770944 | − | 0.636902i | \(-0.780215\pi\) | ||||
−0.770944 | + | 0.636902i | \(0.780215\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2373.24 | 0.885129 | 0.442565 | − | 0.896737i | \(-0.354069\pi\) | ||||
0.442565 | + | 0.896737i | \(0.354069\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1273.24 | 0.467581 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3108.58 | 1.12425 | 0.562125 | − | 0.827052i | \(-0.309984\pi\) | ||||
0.562125 | + | 0.827052i | \(0.309984\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4048.30 | 1.44209 | 0.721046 | − | 0.692887i | \(-0.243662\pi\) | ||||
0.721046 | + | 0.692887i | \(0.243662\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −589.957 | −0.207027 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 336.282 | 0.116268 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6853.73 | 2.33505 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4408.62 | 1.48029 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2402.09 | −0.795005 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3591.66 | 1.17185 | 0.585924 | − | 0.810366i | \(-0.300732\pi\) | ||||
0.585924 | + | 0.810366i | \(0.300732\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −456.180 | −0.146746 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3837.42 | −1.21725 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2713.38 | −0.848830 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1245.27 | −0.384236 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2728.91 | −0.830616 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 772.085 | 0.231850 | 0.115925 | − | 0.993258i | \(-0.463017\pi\) | ||||
0.115925 | + | 0.993258i | \(0.463017\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6547.67 | −1.94005 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4435.16 | −1.29679 | −0.648397 | − | 0.761303i | \(-0.724560\pi\) | ||||
−0.648397 | + | 0.761303i | \(0.724560\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2213.12 | −0.638634 | −0.319317 | − | 0.947648i | \(-0.603454\pi\) | ||||
−0.319317 | + | 0.947648i | \(0.603454\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 632.853 | 0.180254 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2980.41 | −0.837998 | −0.418999 | − | 0.907987i | \(-0.637619\pi\) | ||||
−0.418999 | + | 0.907987i | \(0.637619\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 285.616 | 0.0792831 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1051.27 | −0.288131 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 557.093 | 0.150775 | 0.0753877 | − | 0.997154i | \(-0.475981\pi\) | ||||
0.0753877 | + | 0.997154i | \(0.475981\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4168.65 | −1.11422 | −0.557109 | − | 0.830439i | \(-0.688089\pi\) | ||||
−0.557109 | + | 0.830439i | \(0.688089\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2847.53 | 0.751724 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4107.49 | −1.07109 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2845.13 | 0.732920 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1189.91 | −0.302842 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7132.56 | −1.79364 | −0.896819 | − | 0.442398i | \(-0.854128\pi\) | ||||
−0.896819 | + | 0.442398i | \(0.854128\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6666.59 | 1.65662 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1747.06 | −0.429039 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5564.76 | 1.35066 | 0.675331 | − | 0.737514i | \(-0.264001\pi\) | ||||
0.675331 | + | 0.737514i | \(0.264001\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 118.302 | 0.0283820 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 722.070 | 0.171245 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7188.72 | −1.68546 | −0.842729 | − | 0.538338i | \(-0.819053\pi\) | ||||
−0.842729 | + | 0.538338i | \(0.819053\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11943.7 | 2.76866 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −939.796 | −0.215410 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3184.38 | −0.721765 | −0.360883 | − | 0.932611i | \(-0.617524\pi\) | ||||
−0.360883 | + | 0.932611i | \(0.617524\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1732.34 | −0.388311 | −0.194155 | − | 0.980971i | \(-0.562197\pi\) | ||||
−0.194155 | + | 0.980971i | \(0.562197\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −749.576 | −0.166177 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9901.20 | −2.17114 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6061.31 | −1.31476 | −0.657381 | − | 0.753558i | \(-0.728336\pi\) | ||||
−0.657381 | + | 0.753558i | \(0.728336\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5826.22 | −1.25020 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6183.75 | 1.31278 | 0.656391 | − | 0.754421i | \(-0.272082\pi\) | ||||
0.656391 | + | 0.754421i | \(0.272082\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9076.75 | −1.90656 | −0.953281 | − | 0.302086i | \(-0.902317\pi\) | ||||
−0.953281 | + | 0.302086i | \(0.902317\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1821.46 | 0.378576 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4034.91 | −0.829871 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1168.56 | −0.237850 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −88.3449 | −0.0177968 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3636.66 | 0.725105 | 0.362553 | − | 0.931963i | \(-0.381905\pi\) | ||||
0.362553 | + | 0.931963i | \(0.381905\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13834.6 | −2.73044 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2832.41 | 0.553378 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7896.16 | −1.52725 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2259.15 | 0.432609 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1594.67 | −0.302348 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10703.2 | −2.00939 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4619.06 | −0.858708 | −0.429354 | − | 0.903136i | \(-0.641259\pi\) | ||||
−0.429354 | + | 0.903136i | \(0.641259\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1084.12 | −0.199590 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8094.07 | −1.47580 | −0.737898 | − | 0.674912i | \(-0.764182\pi\) | ||||
−0.737898 | + | 0.674912i | \(0.764182\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6901.79 | 1.24637 | 0.623183 | − | 0.782076i | \(-0.285839\pi\) | ||||
0.623183 | + | 0.782076i | \(0.285839\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5687.03 | 1.01723 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6119.75 | 1.08429 | 0.542144 | − | 0.840286i | \(-0.317613\pi\) | ||||
0.542144 | + | 0.840286i | \(0.317613\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1091.89 | 0.191644 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 255.196 | 0.0443727 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3903.91 | −0.672506 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11727.4 | 2.00159 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −252.003 | −0.0426171 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −168.147 | −0.0281770 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 198.924 | 0.0330328 | 0.0165164 | − | 0.999864i | \(-0.494742\pi\) | ||||
0.0165164 | + | 0.999864i | \(0.494742\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 254.020 | 0.0418025 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8016.85 | −1.30749 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2102.43 | 0.339841 | 0.169921 | − | 0.985458i | \(-0.445649\pi\) | ||||
0.169921 | + | 0.985458i | \(0.445649\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2475.23 | −0.396566 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8810.25 | −1.39912 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6395.55 | 1.00679 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5055.16 | −0.788871 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6543.83 | 1.01237 | 0.506183 | − | 0.862426i | \(-0.331056\pi\) | ||||
0.506183 | + | 0.862426i | \(0.331056\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −793.427 | −0.121694 | −0.0608469 | − | 0.998147i | \(-0.519380\pi\) | ||||
−0.0608469 | + | 0.998147i | \(0.519380\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3354.82 | −0.510162 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7378.84 | 1.11257 | 0.556284 | − | 0.830992i | \(-0.312227\pi\) | ||||
0.556284 | + | 0.830992i | \(0.312227\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6198.97 | −0.926780 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1028.52 | 0.152479 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7142.97 | 1.05012 | 0.525058 | − | 0.851066i | \(-0.324044\pi\) | ||||
0.525058 | + | 0.851066i | \(0.324044\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2788.82 | −0.406593 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 125.581 | 0.0181578 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16921.8 | −2.42666 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1806.47 | 0.256940 | 0.128470 | − | 0.991713i | \(-0.458993\pi\) | ||||
0.128470 | + | 0.991713i | \(0.458993\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8663.83 | −1.22228 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7031.46 | −0.983976 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9396.05 | −1.30431 | −0.652157 | − | 0.758084i | \(-0.726136\pi\) | ||||
−0.652157 | + | 0.758084i | \(0.726136\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3939.10 | 0.542437 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1293.28 | −0.176677 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −421.482 | −0.0571242 | −0.0285621 | − | 0.999592i | \(-0.509093\pi\) | ||||
−0.0285621 | + | 0.999592i | \(0.509093\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1277.69 | 0.171805 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3189.84 | −0.425570 | −0.212785 | − | 0.977099i | \(-0.568253\pi\) | ||||
−0.212785 | + | 0.977099i | \(0.568253\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8599.76 | 1.13840 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4850.89 | 0.637170 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4110.96 | 0.535820 | 0.267910 | − | 0.963444i | \(-0.413667\pi\) | ||||
0.267910 | + | 0.963444i | \(0.413667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10834.6 | 1.40136 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2935.93 | 0.376840 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14285.5 | −1.81970 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 827.505 | 0.104613 | 0.0523064 | − | 0.998631i | \(-0.483343\pi\) | ||||
0.0523064 | + | 0.998631i | \(0.483343\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1072.33 | −0.134545 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 675.145 | 0.0840776 | 0.0420388 | − | 0.999116i | \(-0.486615\pi\) | ||||
0.0420388 | + | 0.999116i | \(0.486615\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10435.2 | 1.28986 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11093.9 | 1.36114 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 384.122 | 0.0467819 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 764.847 | 0.0924676 | 0.0462338 | − | 0.998931i | \(-0.485278\pi\) | ||||
0.0462338 | + | 0.998931i | \(0.485278\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2310.95 | 0.277350 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8144.65 | 0.970393 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16169.6 | −1.91261 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4138.88 | −0.486047 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2573.33 | −0.300037 | −0.150019 | − | 0.988683i | \(-0.547933\pi\) | ||||
−0.150019 | + | 0.988683i | \(0.547933\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14287.4 | −1.65398 | −0.826992 | − | 0.562213i | \(-0.809950\pi\) | ||||
−0.826992 | + | 0.562213i | \(0.809950\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −361.048 | −0.0415006 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −16091.6 | −1.83660 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6301.15 | 0.714131 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2433.84 | −0.273909 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11283.2 | 1.26100 | 0.630500 | − | 0.776189i | \(-0.282850\pi\) | ||||
0.630500 | + | 0.776189i | \(0.282850\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8069.64 | 0.895617 | 0.447809 | − | 0.894129i | \(-0.352205\pi\) | ||||
0.447809 | + | 0.894129i | \(0.352205\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −827.965 | −0.0912595 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11296.1 | −1.23653 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7819.42 | 0.850116 | 0.425058 | − | 0.905166i | \(-0.360254\pi\) | ||||
0.425058 | + | 0.905166i | \(0.360254\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5192.30 | 0.560663 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10153.4 | −1.08894 | −0.544472 | − | 0.838779i | \(-0.683270\pi\) | ||||
−0.544472 | + | 0.838779i | \(0.683270\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12770.8 | −1.36043 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 26.6351 | 0.00281834 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13608.3 | 1.43033 | 0.715163 | − | 0.698958i | \(-0.246353\pi\) | ||||
0.715163 | + | 0.698958i | \(0.246353\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13101.2 | −1.36787 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1128.87 | 0.117084 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10185.9 | −1.04950 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1882.55 | −0.192696 | −0.0963479 | − | 0.995348i | \(-0.530716\pi\) | ||||
−0.0963479 | + | 0.995348i | \(0.530716\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4603.28 | 0.468111 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13947.2 | 1.40908 | 0.704542 | − | 0.709662i | \(-0.251153\pi\) | ||||
0.704542 | + | 0.709662i | \(0.251153\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12454.8 | 1.25016 | 0.625079 | − | 0.780562i | \(-0.285067\pi\) | ||||
0.625079 | + | 0.780562i | \(0.285067\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6680.66 | 0.666254 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6561.59 | −0.650180 | −0.325090 | − | 0.945683i | \(-0.605395\pi\) | ||||
−0.325090 | + | 0.945683i | \(0.605395\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4719.66 | 0.464677 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 741.988 | 0.0725881 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7335.38 | 0.713068 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16776.9 | 1.62058 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −15098.1 | −1.44925 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17407.5 | 1.66048 | 0.830240 | − | 0.557406i | \(-0.188203\pi\) | ||||
0.830240 | + | 0.557406i | \(0.188203\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −454.969 | −0.0431285 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2976.06 | 0.280363 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1200.51 | −0.112396 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2544.79 | 0.236787 | 0.118393 | − | 0.992967i | \(-0.462226\pi\) | ||||
0.118393 | + | 0.992967i | \(0.462226\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2104.06 | −0.194579 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2712.89 | 0.249351 | 0.124675 | − | 0.992198i | \(-0.460211\pi\) | ||||
0.124675 | + | 0.992198i | \(0.460211\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1774.56 | 0.162114 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 18465.6 | 1.67670 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3649.44 | 0.329375 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4583.79 | 0.411220 | 0.205610 | − | 0.978634i | \(-0.434082\pi\) | ||||
0.205610 | + | 0.978634i | \(0.434082\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −870.237 | −0.0776034 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1950.19 | 0.172872 | 0.0864359 | − | 0.996257i | \(-0.472452\pi\) | ||||
0.0864359 | + | 0.996257i | \(0.472452\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21669.8 | −1.90949 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −301.790 | −0.0264358 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8853.80 | 0.770997 | 0.385499 | − | 0.922708i | \(-0.374029\pi\) | ||||
0.385499 | + | 0.922708i | \(0.374029\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9962.17 | 0.862428 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4799.33 | −0.413052 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −14731.9 | −1.26052 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −545.967 | −0.0464441 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3731.28 | 0.315578 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19939.5 | −1.67671 | −0.838355 | − | 0.545125i | \(-0.816482\pi\) | ||||
−0.838355 | + | 0.545125i | \(0.816482\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12185.8 | −1.01883 | −0.509416 | − | 0.860520i | \(-0.670138\pi\) | ||||
−0.509416 | + | 0.860520i | \(0.670138\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4420.03 | −0.367440 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14318.5 | −1.18354 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19183.3 | 1.57667 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17488.4 | 1.42925 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15517.6 | 1.26105 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3467.83 | 0.280238 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5549.68 | 0.445971 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7851.65 | 0.627448 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −700.188 | −0.0556440 | −0.0278220 | − | 0.999613i | \(-0.508857\pi\) | ||||
−0.0278220 | + | 0.999613i | \(0.508857\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3008.62 | −0.237775 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3424.43 | −0.269150 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10664.2 | 0.833576 | 0.416788 | − | 0.909004i | \(-0.363156\pi\) | ||||
0.416788 | + | 0.909004i | \(0.363156\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13530.0 | 1.05181 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1850.14 | −0.143047 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8410.12 | 0.646718 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −291.273 | −0.0222772 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8410.60 | −0.639800 | −0.319900 | − | 0.947451i | \(-0.603649\pi\) | ||||
−0.319900 | + | 0.947451i | \(0.603649\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8688.31 | −0.657382 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3339.58 | 0.251332 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8770.15 | 0.656515 | 0.328257 | − | 0.944588i | \(-0.393539\pi\) | ||||
0.328257 | + | 0.944588i | \(0.393539\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −33635.5 | −2.50453 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6531.19 | −0.483746 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10493.4 | −0.773125 | −0.386562 | − | 0.922263i | \(-0.626338\pi\) | ||||
−0.386562 | + | 0.922263i | \(0.626338\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2517.50 | −0.184508 | −0.0922542 | − | 0.995735i | \(-0.529407\pi\) | ||||
−0.0922542 | + | 0.995735i | \(0.529407\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5899.54 | −0.430117 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −46561.4 | −3.37695 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1394.88 | 0.100641 | 0.0503203 | − | 0.998733i | \(-0.483976\pi\) | ||||
0.0503203 | + | 0.998733i | \(0.483976\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3439.99 | 0.246911 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9519.31 | 0.679738 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22830.9 | −1.62188 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −21871.3 | −1.54576 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24391.0 | 1.71504 | 0.857518 | − | 0.514455i | \(-0.172006\pi\) | ||||
0.857518 | + | 0.514455i | \(0.172006\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14928.4 | 1.04433 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4505.86 | 0.313615 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16089.4 | −1.11418 | −0.557092 | − | 0.830451i | \(-0.688083\pi\) | ||||
−0.557092 | + | 0.830451i | \(0.688083\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13976.5 | 0.962990 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5867.97 | 0.402278 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19228.2 | 1.31159 | 0.655796 | − | 0.754938i | \(-0.272333\pi\) | ||||
0.655796 | + | 0.754938i | \(0.272333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2345.94 | −0.159223 | −0.0796115 | − | 0.996826i | \(-0.525368\pi\) | ||||
−0.0796115 | + | 0.996826i | \(0.525368\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10134.1 | 0.684401 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1706.50 | 0.114676 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4621.11 | 0.309004 | 0.154502 | − | 0.987993i | \(-0.450623\pi\) | ||||
0.154502 | + | 0.987993i | \(0.450623\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 487.437 | 0.0324334 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 646.664 | 0.0428170 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10464.8 | 0.689511 | 0.344755 | − | 0.938693i | \(-0.387962\pi\) | ||||
0.344755 | + | 0.938693i | \(0.387962\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9934.41 | 0.651373 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11873.3 | −0.774718 | −0.387359 | − | 0.921929i | \(-0.626613\pi\) | ||||
−0.387359 | + | 0.921929i | \(0.626613\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13102.2 | 0.850762 | 0.425381 | − | 0.905014i | \(-0.360140\pi\) | ||||
0.425381 | + | 0.905014i | \(0.360140\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13319.7 | 0.860711 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7518.37 | 0.483494 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20656.7 | 1.32203 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3481.81 | −0.221770 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 624.282 | 0.0395735 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12279.7 | −0.774719 | −0.387359 | − | 0.921929i | \(-0.626613\pi\) | ||||
−0.387359 | + | 0.921929i | \(0.626613\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5206.07 | 0.326892 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17362.3 | 1.08504 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9299.80 | −0.578448 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7836.14 | 0.485122 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17054.4 | 1.05087 | 0.525435 | − | 0.850834i | \(-0.323903\pi\) | ||||
0.525435 | + | 0.850834i | \(0.323903\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20697.3 | −1.26940 | −0.634698 | − | 0.772761i | \(-0.718875\pi\) | ||||
−0.634698 | + | 0.772761i | \(0.718875\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5562.29 | −0.339558 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10613.6 | 0.644924 | 0.322462 | − | 0.946582i | \(-0.395490\pi\) | ||||
0.322462 | + | 0.946582i | \(0.395490\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 26445.4 | 1.59950 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3933.02 | −0.236785 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10019.4 | 0.600441 | 0.300220 | − | 0.953870i | \(-0.402940\pi\) | ||||
0.300220 | + | 0.953870i | \(0.402940\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 39896.0 | 2.37995 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 21391.0 | 1.27023 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2400.70 | 0.141909 | 0.0709545 | − | 0.997480i | \(-0.477395\pi\) | ||||
0.0709545 | + | 0.997480i | \(0.477395\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5037.05 | 0.296397 | 0.148199 | − | 0.988958i | \(-0.452653\pi\) | ||||
0.148199 | + | 0.988958i | \(0.452653\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3955.52 | −0.231704 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14571.7 | −0.849725 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5134.75 | 0.298078 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1119.13 | 0.0646757 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20459.6 | 1.17710 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20842.1 | −1.19377 | −0.596884 | − | 0.802328i | \(-0.703595\pi\) | ||||
−0.596884 | + | 0.802328i | \(0.703595\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −19782.4 | −1.12804 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23394.0 | 1.32807 | 0.664037 | − | 0.747700i | \(-0.268842\pi\) | ||||
0.664037 | + | 0.747700i | \(0.268842\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 706.759 | 0.0399454 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6428.72 | −0.361746 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8567.11 | −0.479958 | −0.239979 | − | 0.970778i | \(-0.577141\pi\) | ||||
−0.239979 | + | 0.970778i | \(0.577141\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 31403.2 | 1.75161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3207.90 | −0.178150 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 27041.8 | 1.49522 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11987.6 | −0.659959 | −0.329979 | − | 0.943988i | \(-0.607042\pi\) | ||||
−0.329979 | + | 0.943988i | \(0.607042\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10871.0 | −0.595895 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −56242.7 | −3.06965 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21292.3 | −1.15710 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4320.08 | −0.233763 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19429.6 | −1.04686 | −0.523428 | − | 0.852070i | \(-0.675347\pi\) | ||||
−0.523428 | + | 0.852070i | \(0.675347\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −650.869 | −0.0349189 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 413.997 | 0.0221164 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12757.4 | 0.678628 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 804.014 | 0.0425887 | 0.0212944 | − | 0.999773i | \(-0.493221\pi\) | ||||
0.0212944 | + | 0.999773i | \(0.493221\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 18058.4 | 0.952521 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −41431.1 | −2.17617 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −33073.2 | −1.72989 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 807.500 | 0.0420595 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4975.94 | −0.258096 | −0.129048 | − | 0.991638i | \(-0.541192\pi\) | ||||
−0.129048 | + | 0.991638i | \(0.541192\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8672.93 | 0.447984 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6042.42 | −0.310816 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7626.11 | −0.390658 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3761.32 | 0.191884 | 0.0959419 | − | 0.995387i | \(-0.469414\pi\) | ||||
0.0959419 | + | 0.995387i | \(0.469414\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11079.8 | −0.562912 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11921.6 | 0.603195 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21439.2 | −1.08032 | −0.540161 | − | 0.841562i | \(-0.681637\pi\) | ||||
−0.540161 | + | 0.841562i | \(0.681637\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5953.77 | −0.298787 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15324.6 | 0.765926 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22000.3 | 1.09512 | 0.547561 | − | 0.836766i | \(-0.315556\pi\) | ||||
0.547561 | + | 0.836766i | \(0.315556\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4123.98 | 0.204451 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13371.8 | 0.660246 | 0.330123 | − | 0.943938i | \(-0.392910\pi\) | ||||
0.330123 | + | 0.943938i | \(0.392910\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 361.942 | 0.0177994 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 20440.1 | 1.00115 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2041.57 | −0.0995958 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17764.8 | 0.863178 | 0.431589 | − | 0.902070i | \(-0.357953\pi\) | ||||
0.431589 | + | 0.902070i | \(0.357953\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10338.6 | −0.500343 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15340.1 | 0.739448 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33266.1 | −1.59719 | −0.798597 | − | 0.601867i | \(-0.794424\pi\) | ||||
−0.798597 | + | 0.601867i | \(0.794424\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9663.15 | 0.462121 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25327.3 | −1.20646 | −0.603228 | − | 0.797569i | \(-0.706119\pi\) | ||||
−0.603228 | + | 0.797569i | \(0.706119\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2016.02 | 0.0956551 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 30010.5 | 1.41834 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −31322.9 | −1.47458 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9587.28 | −0.449579 | −0.224789 | − | 0.974407i | \(-0.572169\pi\) | ||||
−0.224789 | + | 0.974407i | \(0.572169\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8066.07 | 0.376773 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2825.54 | −0.131472 | −0.0657359 | − | 0.997837i | \(-0.520939\pi\) | ||||
−0.0657359 | + | 0.997837i | \(0.520939\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 61533.4 | 2.85206 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 171.478 | 0.00791728 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22199.1 | 1.02101 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11849.6 | 0.542909 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2181.58 | 0.0995702 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10082.8 | 0.458433 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2132.09 | 0.0965702 | 0.0482851 | − | 0.998834i | \(-0.484624\pi\) | ||||
0.0482851 | + | 0.998834i | \(0.484624\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10420.0 | −0.470166 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19801.8 | 0.890103 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24233.1 | −1.08518 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 17312.3 | 0.772331 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5443.62 | −0.241936 | −0.120968 | − | 0.992656i | \(-0.538600\pi\) | ||||
−0.120968 | + | 0.992656i | \(0.538600\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −887.313 | −0.0392877 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16143.6 | 0.712117 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32346.8 | 1.42154 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 40441.3 | 1.77064 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4615.72 | −0.201340 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41193.5 | 1.79022 | 0.895109 | − | 0.445847i | \(-0.147098\pi\) | ||||
0.895109 | + | 0.445847i | \(0.147098\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18225.9 | −0.789145 | −0.394572 | − | 0.918865i | \(-0.629107\pi\) | ||||
−0.394572 | + | 0.918865i | \(0.629107\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2511.01 | −0.108321 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −28591.8 | −1.22887 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12429.3 | −0.532248 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12876.0 | 0.549359 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −46061.7 | −1.95806 | −0.979029 | − | 0.203720i | \(-0.934697\pi\) | ||||
−0.979029 | + | 0.203720i | \(0.934697\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40166.3 | −1.70122 | −0.850612 | − | 0.525793i | \(-0.823769\pi\) | ||||
−0.850612 | + | 0.525793i | \(0.823769\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −14351.7 | −0.605650 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23994.5 | −1.00891 | −0.504457 | − | 0.863437i | \(-0.668307\pi\) | ||||
−0.504457 | + | 0.863437i | \(0.668307\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13549.6 | 0.567668 | 0.283834 | − | 0.958873i | \(-0.408394\pi\) | ||||
0.283834 | + | 0.958873i | \(0.408394\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8785.81 | −0.366759 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12760.6 | 0.530767 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11825.5 | −0.490107 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −17602.7 | −0.726928 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −34768.5 | −1.43068 | −0.715341 | − | 0.698776i | \(-0.753729\pi\) | ||||
−0.715341 | + | 0.698776i | \(0.753729\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8963.29 | 0.366207 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4100.98 | −0.166956 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1004.64 | −0.0407556 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13156.7 | −0.531844 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1806.38 | 0.0727635 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4691.07 | −0.188299 | −0.0941496 | − | 0.995558i | \(-0.530013\pi\) | ||||
−0.0941496 | + | 0.995558i | \(0.530013\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −31288.7 | −1.25152 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14362.7 | −0.572485 | −0.286242 | − | 0.958157i | \(-0.592406\pi\) | ||||
−0.286242 | + | 0.958157i | \(0.592406\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1392.43 | 0.0553073 | 0.0276537 | − | 0.999618i | \(-0.491196\pi\) | ||||
0.0276537 | + | 0.999618i | \(0.491196\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5848.55 | −0.231496 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19162.2 | −0.755840 | −0.377920 | − | 0.925838i | \(-0.623361\pi\) | ||||
−0.377920 | + | 0.925838i | \(0.623361\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 50703.9 | 1.99304 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1693.81 | −0.0663494 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 27307.4 | 1.06598 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18151.0 | −0.706111 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1517.57 | 0.0588338 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −31512.8 | −1.21752 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6509.75 | 0.250649 | 0.125324 | − | 0.992116i | \(-0.460003\pi\) | ||||
0.125324 | + | 0.992116i | \(0.460003\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5271.30 | 0.202271 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −589.496 | −0.0225433 | −0.0112716 | − | 0.999936i | \(-0.503588\pi\) | ||||
−0.0112716 | + | 0.999936i | \(0.503588\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3903.57 | −0.148772 | −0.0743859 | − | 0.997230i | \(-0.523700\pi\) | ||||
−0.0743859 | + | 0.997230i | \(0.523700\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −20053.1 | −0.761669 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24136.6 | 0.913674 | 0.456837 | − | 0.889550i | \(-0.348982\pi\) | ||||
0.456837 | + | 0.889550i | \(0.348982\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10221.5 | −0.385622 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21206.5 | −0.797358 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 925.103 | 0.0346667 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 75414.0 | 2.81655 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −11445.4 | −0.426032 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6785.84 | −0.251747 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37105.1 | −1.37198 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3274.62 | 0.120678 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −40883.7 | −1.50168 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22174.3 | 0.811781 | 0.405890 | − | 0.913922i | \(-0.366962\pi\) | ||||
0.405890 | + | 0.913922i | \(0.366962\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 27392.8 | 0.999519 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46956.1 | 1.70771 | 0.853856 | − | 0.520509i | \(-0.174258\pi\) | ||||
0.853856 | + | 0.520509i | \(0.174258\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30908.9 | 1.12041 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −15514.2 | −0.560528 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −23487.4 | −0.845827 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 37166.4 | 1.33407 | 0.667033 | − | 0.745028i | \(-0.267564\pi\) | ||||
0.667033 | + | 0.745028i | \(0.267564\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6695.27 | −0.239540 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14035.1 | −0.500511 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2682.82 | −0.0953629 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 18622.7 | 0.659816 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29571.7 | 1.04437 | 0.522183 | − | 0.852833i | \(-0.325118\pi\) | ||||
0.522183 | + | 0.852833i | \(0.325118\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13304.1 | −0.468339 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −11732.3 | −0.411680 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 45381.1 | 1.58729 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8691.51 | 0.303030 | 0.151515 | − | 0.988455i | \(-0.451585\pi\) | ||||
0.151515 | + | 0.988455i | \(0.451585\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10004.1 | 0.347679 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2862.43 | 0.0991632 | 0.0495816 | − | 0.998770i | \(-0.484211\pi\) | ||||
0.0495816 | + | 0.998770i | \(0.484211\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −61609.7 | −2.12756 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 17182.2 | 0.591466 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36997.8 | 1.26955 | 0.634777 | − | 0.772695i | \(-0.281092\pi\) | ||||
0.634777 | + | 0.772695i | \(0.281092\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −38312.8 | −1.31052 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8870.51 | 0.302467 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20998.8 | 0.713764 | 0.356882 | − | 0.934150i | \(-0.383840\pi\) | ||||
0.356882 | + | 0.934150i | \(0.383840\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −80168.1 | −2.71642 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1582.69 | 0.0534599 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18487.6 | −0.622519 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24962.4 | 0.837917 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4383.69 | −0.146690 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 46745.7 | 1.55937 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30803.0 | 1.02436 | 0.512181 | − | 0.858878i | \(-0.328838\pi\) | ||||
0.512181 | + | 0.858878i | \(0.328838\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5658.68 | −0.187599 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −755.015 | −0.0249532 | −0.0124766 | − | 0.999922i | \(-0.503972\pi\) | ||||
−0.0124766 | + | 0.999922i | \(0.503972\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 33111.0 | 1.09095 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 16998.7 | 0.558353 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −44011.7 | −1.44121 | −0.720603 | − | 0.693348i | \(-0.756135\pi\) | ||||
−0.720603 | + | 0.693348i | \(0.756135\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24411.9 | 0.796943 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4328.84 | 0.140886 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 36334.8 | 1.17894 | 0.589471 | − | 0.807790i | \(-0.299336\pi\) | ||||
0.589471 | + | 0.807790i | \(0.299336\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 61229.6 | 1.98065 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −243.727 | −0.00786010 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 34495.4 | 1.10909 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9848.60 | −0.315692 | −0.157846 | − | 0.987464i | \(-0.550455\pi\) | ||||
−0.157846 | + | 0.987464i | \(0.550455\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 288.338 | 0.00921464 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 79739.1 | 2.54060 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3378.02 | −0.107305 | −0.0536525 | − | 0.998560i | \(-0.517086\pi\) | ||||
−0.0536525 | + | 0.998560i | \(0.517086\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 767.469 | 0.0243060 |
(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 | 1856.4.a.i.1.2 | 2 | ||
4.3 | odd | 2 | 1856.4.a.l.1.1 | 2 | |||
8.3 | odd | 2 | 58.4.a.c.1.2 | ✓ | 2 | ||
8.5 | even | 2 | 464.4.a.e.1.1 | 2 | |||
24.11 | even | 2 | 522.4.a.j.1.2 | 2 | |||
40.19 | odd | 2 | 1450.4.a.g.1.1 | 2 | |||
232.115 | odd | 2 | 1682.4.a.c.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
58.4.a.c.1.2 | ✓ | 2 | 8.3 | odd | 2 | ||
464.4.a.e.1.1 | 2 | 8.5 | even | 2 | |||
522.4.a.j.1.2 | 2 | 24.11 | even | 2 | |||
1450.4.a.g.1.1 | 2 | 40.19 | odd | 2 | |||
1682.4.a.c.1.1 | 2 | 232.115 | odd | 2 | |||
1856.4.a.i.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1856.4.a.l.1.1 | 2 | 4.3 | odd | 2 |