Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2496,4,Mod(1,2496)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2496, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2496.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2496 = 2^{6} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2496.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: | \(147.268767374\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{113}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 28 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 312) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(5.81507\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2496.1 |
$q$-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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −13.6301 | −1.21912 | −0.609559 | − | 0.792741i | \(-0.708653\pi\) | ||||
−0.609559 | + | 0.792741i | \(0.708653\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 15.6301 | 0.843949 | 0.421974 | − | 0.906608i | \(-0.361337\pi\) | ||||
0.421974 | + | 0.906608i | \(0.361337\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −50.5206 | −1.38478 | −0.692388 | − | 0.721526i | \(-0.743441\pi\) | ||||
−0.692388 | + | 0.721526i | \(0.743441\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.0000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 40.8904 | 0.703858 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | 0.0285336 | 0.0142668 | − | 0.999898i | \(-0.495459\pi\) | ||||
0.0142668 | + | 0.999898i | \(0.495459\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 18.1507 | 0.219161 | 0.109581 | − | 0.993978i | \(-0.465049\pi\) | ||||
0.109581 | + | 0.993978i | \(0.465049\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −46.8904 | −0.487254 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 64.0000 | 0.580214 | 0.290107 | − | 0.956994i | \(-0.406309\pi\) | ||||
0.290107 | + | 0.956994i | \(0.406309\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 60.7809 | 0.486247 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 103.781 | 0.664539 | 0.332269 | − | 0.943185i | \(-0.392186\pi\) | ||||
0.332269 | + | 0.943185i | \(0.392186\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −34.4522 | −0.199606 | −0.0998032 | − | 0.995007i | \(-0.531821\pi\) | ||||
−0.0998032 | + | 0.995007i | \(0.531821\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 151.562 | 0.799500 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −213.041 | −1.02887 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 267.343 | 1.18786 | 0.593930 | − | 0.804516i | \(-0.297575\pi\) | ||||
0.593930 | + | 0.804516i | \(0.297575\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 39.0000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −147.411 | −0.561506 | −0.280753 | − | 0.959780i | \(-0.590584\pi\) | ||||
−0.280753 | + | 0.959780i | \(0.590584\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −166.959 | −0.592116 | −0.296058 | − | 0.955170i | \(-0.595672\pi\) | ||||
−0.296058 | + | 0.955170i | \(0.595672\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −122.671 | −0.406372 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 325.781 | 1.01106 | 0.505532 | − | 0.862808i | \(-0.331296\pi\) | ||||
0.505532 | + | 0.862808i | \(0.331296\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −98.6985 | −0.287751 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.00000 | −0.0164739 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 111.041 | 0.287786 | 0.143893 | − | 0.989593i | \(-0.454038\pi\) | ||||
0.143893 | + | 0.989593i | \(0.454038\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 688.603 | 1.68820 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −54.4522 | −0.126533 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 24.3015 | 0.0536234 | 0.0268117 | − | 0.999641i | \(-0.491465\pi\) | ||||
0.0268117 | + | 0.999641i | \(0.491465\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 640.987 | 1.34541 | 0.672704 | − | 0.739911i | \(-0.265133\pi\) | ||||
0.672704 | + | 0.739911i | \(0.265133\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 140.671 | 0.281316 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 177.192 | 0.338122 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −382.589 | −0.697622 | −0.348811 | − | 0.937193i | \(-0.613415\pi\) | ||||
−0.348811 | + | 0.937193i | \(0.613415\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −192.000 | −0.334987 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −510.247 | −0.852890 | −0.426445 | − | 0.904514i | \(-0.640234\pi\) | ||||
−0.426445 | + | 0.904514i | \(0.640234\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −291.781 | −0.467813 | −0.233907 | − | 0.972259i | \(-0.575151\pi\) | ||||
−0.233907 | + | 0.972259i | \(0.575151\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −182.343 | −0.280735 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −789.644 | −1.16868 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 794.685 | 1.13176 | 0.565880 | − | 0.824487i | \(-0.308536\pi\) | ||||
0.565880 | + | 0.824487i | \(0.308536\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 945.507 | 1.25040 | 0.625198 | − | 0.780466i | \(-0.285018\pi\) | ||||
0.625198 | + | 0.780466i | \(0.285018\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −27.2603 | −0.0347858 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −311.343 | −0.383672 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 317.329 | 0.377941 | 0.188971 | − | 0.981983i | \(-0.439485\pi\) | ||||
0.188971 | + | 0.981983i | \(0.439485\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −203.192 | −0.234069 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 103.357 | 0.115243 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −247.397 | −0.267183 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1572.88 | 1.64641 | 0.823204 | − | 0.567746i | \(-0.192184\pi\) | ||||
0.823204 | + | 0.567746i | \(0.192184\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −454.685 | −0.461592 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1820.44 | −1.79347 | −0.896735 | − | 0.442568i | \(-0.854068\pi\) | ||||
−0.896735 | + | 0.442568i | \(0.854068\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −859.015 | −0.821759 | −0.410880 | − | 0.911690i | \(-0.634778\pi\) | ||||
−0.410880 | + | 0.911690i | \(0.634778\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 639.123 | 0.594020 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1126.74 | −1.01800 | −0.509001 | − | 0.860766i | \(-0.669985\pi\) | ||||
−0.509001 | + | 0.860766i | \(0.669985\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 682.659 | 0.599879 | 0.299940 | − | 0.953958i | \(-0.403033\pi\) | ||||
0.299940 | + | 0.953958i | \(0.403033\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −802.028 | −0.685812 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 771.946 | 0.642642 | 0.321321 | − | 0.946970i | \(-0.395873\pi\) | ||||
0.321321 | + | 0.946970i | \(0.395873\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −872.329 | −0.707349 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −117.000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 31.2603 | 0.0240809 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1221.33 | 0.917603 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 442.233 | 0.324185 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 875.316 | 0.626325 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2182.99 | 1.52527 | 0.762633 | − | 0.646832i | \(-0.223906\pi\) | ||||
0.762633 | + | 0.646832i | \(0.223906\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 500.877 | 0.341858 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 881.918 | 0.588195 | 0.294097 | − | 0.955775i | \(-0.404981\pi\) | ||||
0.294097 | + | 0.955775i | \(0.404981\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 283.699 | 0.184961 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 368.014 | 0.234619 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2764.40 | −1.72393 | −0.861965 | − | 0.506967i | \(-0.830767\pi\) | ||||
−0.861965 | + | 0.506967i | \(0.830767\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1453.40 | 0.886875 | 0.443438 | − | 0.896305i | \(-0.353759\pi\) | ||||
0.443438 | + | 0.896305i | \(0.353759\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −977.343 | −0.583738 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 656.768 | 0.384068 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1414.55 | −0.810151 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 296.096 | 0.166133 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −560.123 | −0.307967 | −0.153983 | − | 0.988073i | \(-0.549210\pi\) | ||||
−0.153983 | + | 0.988073i | \(0.549210\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2962.23 | 1.59645 | 0.798223 | − | 0.602363i | \(-0.205774\pi\) | ||||
0.798223 | + | 0.602363i | \(0.205774\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 18.0000 | 0.00951120 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 469.588 | 0.243344 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1837.92 | −0.934280 | −0.467140 | − | 0.884183i | \(-0.654716\pi\) | ||||
−0.467140 | + | 0.884183i | \(0.654716\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −333.123 | −0.166154 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1000.33 | 0.489671 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1793.52 | 0.861838 | 0.430919 | − | 0.902391i | \(-0.358190\pi\) | ||||
0.430919 | + | 0.902391i | \(0.358190\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2065.81 | −0.974685 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3919.37 | −1.81611 | −0.908054 | − | 0.418853i | \(-0.862432\pi\) | ||||
−0.908054 | + | 0.418853i | \(0.862432\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 163.357 | 0.0730537 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3864.60 | −1.69838 | −0.849192 | − | 0.528084i | \(-0.822911\pi\) | ||||
−0.849192 | + | 0.528084i | \(0.822911\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 950.014 | 0.410367 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −72.9044 | −0.0309595 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2829.04 | 1.18130 | 0.590650 | − | 0.806928i | \(-0.298871\pi\) | ||||
0.590650 | + | 0.806928i | \(0.298871\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1126.74 | −0.462707 | −0.231353 | − | 0.972870i | \(-0.574315\pi\) | ||||
−0.231353 | + | 0.972870i | \(0.574315\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1922.96 | −0.776772 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3643.92 | −1.44814 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −101.041 | −0.0395126 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −422.014 | −0.162418 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −662.136 | −0.250840 | −0.125420 | − | 0.992104i | \(-0.540028\pi\) | ||||
−0.125420 | + | 0.992104i | \(0.540028\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1290.49 | −0.481305 | −0.240652 | − | 0.970611i | \(-0.577361\pi\) | ||||
−0.240652 | + | 0.970611i | \(0.577361\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −531.576 | −0.195215 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1320.01 | 0.477396 | 0.238698 | − | 0.971094i | \(-0.423279\pi\) | ||||
0.238698 | + | 0.971094i | \(0.423279\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2711.97 | 0.966064 | 0.483032 | − | 0.875603i | \(-0.339535\pi\) | ||||
0.483032 | + | 0.875603i | \(0.339535\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1147.77 | 0.402772 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1622.11 | 0.560837 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2009.23 | 0.684541 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 576.000 | 0.193405 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −916.985 | −0.303489 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1612.06 | 0.525964 | 0.262982 | − | 0.964801i | \(-0.415294\pi\) | ||||
0.262982 | + | 0.964801i | \(0.415294\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1530.74 | 0.492416 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2275.67 | 0.721859 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −538.493 | −0.168457 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 875.343 | 0.270092 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −26.0000 | −0.00791380 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5602.10 | 1.68226 | 0.841130 | − | 0.540832i | \(-0.181891\pi\) | ||||
0.841130 | + | 0.540832i | \(0.181891\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 547.028 | 0.162082 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1427.23 | −0.417308 | −0.208654 | − | 0.977990i | \(-0.566908\pi\) | ||||
−0.208654 | + | 0.977990i | \(0.566908\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4826.33 | −1.39272 | −0.696360 | − | 0.717692i | \(-0.745198\pi\) | ||||
−0.696360 | + | 0.717692i | \(0.745198\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2368.93 | 0.674737 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6244.17 | −1.75566 | −0.877830 | − | 0.478972i | \(-0.841010\pi\) | ||||
−0.877830 | + | 0.478972i | \(0.841010\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4440.44 | −1.23261 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2384.06 | −0.653422 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6638.69 | −1.79674 | −0.898370 | − | 0.439239i | \(-0.855248\pi\) | ||||
−0.898370 | + | 0.439239i | \(0.855248\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4526.19 | −1.20978 | −0.604891 | − | 0.796308i | \(-0.706784\pi\) | ||||
−0.604891 | + | 0.796308i | \(0.706784\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1345.28 | 0.350802 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −235.959 | −0.0607844 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2836.52 | −0.721917 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2070.36 | 0.520636 | 0.260318 | − | 0.965523i | \(-0.416173\pi\) | ||||
0.260318 | + | 0.965523i | \(0.416173\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3233.32 | −0.803466 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 81.7809 | 0.0200836 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6154.58 | −1.49382 | −0.746910 | − | 0.664925i | \(-0.768464\pi\) | ||||
−0.746910 | + | 0.664925i | \(0.768464\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4178.60 | 1.00249 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 934.028 | 0.221513 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4111.51 | −0.963979 | −0.481990 | − | 0.876177i | \(-0.660086\pi\) | ||||
−0.481990 | + | 0.876177i | \(0.660086\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1513.51 | −0.350845 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −951.986 | −0.218204 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −822.851 | −0.186506 | −0.0932530 | − | 0.995642i | \(-0.529727\pi\) | ||||
−0.0932530 | + | 0.995642i | \(0.529727\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1685.41 | −0.377791 | −0.188896 | − | 0.981997i | \(-0.560491\pi\) | ||||
−0.188896 | + | 0.981997i | \(0.560491\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 609.576 | 0.135140 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3070.69 | −0.673343 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 185.235 | 0.0401794 | 0.0200897 | − | 0.999798i | \(-0.493605\pi\) | ||||
0.0200897 | + | 0.999798i | \(0.493605\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −310.070 | −0.0665354 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1008.34 | −0.214066 | −0.107033 | − | 0.994255i | \(-0.534135\pi\) | ||||
−0.107033 | + | 0.994255i | \(0.534135\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6664.63 | −1.39990 | −0.699949 | − | 0.714193i | \(-0.746794\pi\) | ||||
−0.699949 | + | 0.714193i | \(0.746794\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 742.191 | 0.154258 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2304.06 | −0.473882 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4909.00 | −0.999186 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4718.63 | −0.950554 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7954.02 | 1.58593 | 0.792967 | − | 0.609265i | \(-0.208535\pi\) | ||||
0.792967 | + | 0.609265i | \(0.208535\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −331.232 | −0.0653732 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1364.06 | 0.266500 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −832.000 | −0.160922 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2609.59 | −0.499715 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5461.32 | 1.03546 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8736.74 | −1.64021 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8831.69 | 1.64186 | 0.820930 | − | 0.571029i | \(-0.193456\pi\) | ||||
0.820930 | + | 0.571029i | \(0.193456\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2577.04 | 0.474443 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8043.24 | −1.46653 | −0.733264 | − | 0.679944i | \(-0.762004\pi\) | ||||
−0.733264 | + | 0.679944i | \(0.762004\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9939.81 | −1.79499 | −0.897494 | − | 0.441026i | \(-0.854615\pi\) | ||||
−0.897494 | + | 0.441026i | \(0.854615\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1917.37 | −0.342957 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6640.48 | −1.17655 | −0.588275 | − | 0.808661i | \(-0.700193\pi\) | ||||
−0.588275 | + | 0.808661i | \(0.700193\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5243.07 | −0.920237 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3380.22 | 0.587743 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 36.3015 | 0.00625346 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −790.151 | −0.134861 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2047.98 | −0.346340 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5092.00 | 0.853286 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2007.63 | −0.333382 | −0.166691 | − | 0.986009i | \(-0.553308\pi\) | ||||
−0.166691 | + | 0.986009i | \(0.553308\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2406.08 | 0.395954 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5214.74 | 0.850483 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4991.43 | −0.806826 | −0.403413 | − | 0.915018i | \(-0.632176\pi\) | ||||
−0.403413 | + | 0.915018i | \(0.632176\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2315.84 | −0.371029 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1740.54 | 0.276410 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6903.81 | −1.08680 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2616.99 | 0.408388 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10913.8 | −1.68842 | −0.844209 | − | 0.536013i | \(-0.819930\pi\) | ||||
−0.844209 | + | 0.536013i | \(0.819930\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9148.00 | −1.40310 | −0.701549 | − | 0.712621i | \(-0.747508\pi\) | ||||
−0.701549 | + | 0.712621i | \(0.747508\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 351.000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1337.64 | 0.201686 | 0.100843 | − | 0.994902i | \(-0.467846\pi\) | ||||
0.100843 | + | 0.994902i | \(0.467846\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6954.74 | 1.03977 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −93.7809 | −0.0139031 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7865.89 | −1.15639 | −0.578197 | − | 0.815897i | \(-0.696244\pi\) | ||||
−0.578197 | + | 0.815897i | \(0.696244\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6529.55 | −0.951968 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3663.99 | −0.529778 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3977.02 | 0.570319 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1935.86 | −0.275344 | −0.137672 | − | 0.990478i | \(-0.543962\pi\) | ||||
−0.137672 | + | 0.990478i | \(0.543962\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1326.70 | −0.187169 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1735.59 | 0.242877 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5604.36 | 0.777970 | 0.388985 | − | 0.921244i | \(-0.372826\pi\) | ||||
0.388985 | + | 0.921244i | \(0.372826\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2625.95 | −0.361609 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1349.15 | −0.184310 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 271.521 | 0.0367998 | 0.0183999 | − | 0.999831i | \(-0.494143\pi\) | ||||
0.0183999 | + | 0.999831i | \(0.494143\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6548.96 | −0.880613 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5763.16 | 0.768887 | 0.384443 | − | 0.923149i | \(-0.374393\pi\) | ||||
0.384443 | + | 0.923149i | \(0.374393\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10763.0 | 1.42476 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1502.63 | −0.197372 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6596.09 | 0.859730 | 0.429865 | − | 0.902893i | \(-0.358561\pi\) | ||||
0.429865 | + | 0.902893i | \(0.358561\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 128.000 | 0.0165556 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2645.75 | −0.339594 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10831.7 | −1.37975 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7173.42 | −0.906861 | −0.453430 | − | 0.891292i | \(-0.649800\pi\) | ||||
−0.453430 | + | 0.891292i | \(0.649800\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −851.096 | −0.106787 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3759.83 | −0.468222 | −0.234111 | − | 0.972210i | \(-0.575218\pi\) | ||||
−0.234111 | + | 0.972210i | \(0.575218\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 447.878 | 0.0553608 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1104.04 | −0.135457 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13506.3 | −1.64492 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10857.1 | 1.31259 | 0.656295 | − | 0.754505i | \(-0.272123\pi\) | ||||
0.656295 | + | 0.754505i | \(0.272123\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8293.20 | 0.995312 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 379.835 | 0.0452554 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12887.4 | −1.52438 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4360.20 | −0.512038 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9802.86 | 1.14296 | 0.571481 | − | 0.820616i | \(-0.306369\pi\) | ||||
0.571481 | + | 0.820616i | \(0.306369\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5004.96 | −0.579398 | −0.289699 | − | 0.957118i | \(-0.593555\pi\) | ||||
−0.289699 | + | 0.957118i | \(0.593555\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2932.03 | 0.337021 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 121.562 | 0.0138744 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10018.7 | 1.13546 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1970.30 | −0.221742 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9275.81 | 1.03666 | 0.518330 | − | 0.855181i | \(-0.326554\pi\) | ||||
0.518330 | + | 0.855181i | \(0.326554\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3160.88 | 0.350813 | 0.175406 | − | 0.984496i | \(-0.443876\pi\) | ||||
0.175406 | + | 0.984496i | \(0.443876\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4243.65 | 0.467741 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1161.65 | 0.127160 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14035.4 | 1.52591 | 0.762954 | − | 0.646453i | \(-0.223748\pi\) | ||||
0.762954 | + | 0.646453i | \(0.223748\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −888.287 | −0.0959170 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 761.046 | 0.0816217 | 0.0408108 | − | 0.999167i | \(-0.487006\pi\) | ||||
0.0408108 | + | 0.999167i | \(0.487006\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4325.24 | −0.460755 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1680.37 | 0.177805 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8385.22 | 0.881343 | 0.440672 | − | 0.897668i | \(-0.354740\pi\) | ||||
0.440672 | + | 0.897668i | \(0.354740\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7447.29 | 0.777559 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8886.70 | −0.921708 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2769.54 | 0.285358 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16484.7 | 1.68736 | 0.843679 | − | 0.536848i | \(-0.180385\pi\) | ||||
0.843679 | + | 0.536848i | \(0.180385\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −54.0000 | −0.00549129 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2478.45 | −0.250396 | −0.125198 | − | 0.992132i | \(-0.539957\pi\) | ||||
−0.125198 | + | 0.992132i | \(0.539957\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2588.90 | 0.259863 | 0.129931 | − | 0.991523i | \(-0.458524\pi\) | ||||
0.129931 | + | 0.991523i | \(0.458524\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1408.77 | −0.140494 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13670.7 | −1.35461 | −0.677306 | − | 0.735701i | \(-0.736853\pi\) | ||||
−0.677306 | + | 0.735701i | \(0.736853\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5979.92 | −0.588757 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5513.76 | 0.539407 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8434.86 | 0.819948 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1103.22 | 0.106566 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 999.370 | 0.0959288 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8034.36 | −0.766386 | −0.383193 | − | 0.923668i | \(-0.625176\pi\) | ||||
−0.383193 | + | 0.923668i | \(0.625176\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3475.45 | −0.329453 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3000.99 | −0.282712 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −21438.6 | −2.00716 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7890.43 | 0.734188 | 0.367094 | − | 0.930184i | \(-0.380353\pi\) | ||||
0.367094 | + | 0.930184i | \(0.380353\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5380.57 | −0.497582 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2217.87 | 0.203852 | 0.101926 | − | 0.994792i | \(-0.467500\pi\) | ||||
0.101926 | + | 0.994792i | \(0.467500\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 207.562 | 0.0189617 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6197.43 | 0.562735 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7975.23 | −0.719795 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6636.90 | −0.595407 | −0.297704 | − | 0.954658i | \(-0.596221\pi\) | ||||
−0.297704 | + | 0.954658i | \(0.596221\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11758.1 | 1.04853 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9418.80 | 0.834917 | 0.417459 | − | 0.908696i | \(-0.362921\pi\) | ||||
0.417459 | + | 0.908696i | \(0.362921\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24812.9 | 2.18645 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −507.000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11177.6 | 0.973353 | 0.486676 | − | 0.873582i | \(-0.338209\pi\) | ||||
0.486676 | + | 0.873582i | \(0.338209\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4560.58 | −0.394810 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −490.070 | −0.0421776 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11708.5 | 1.00182 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16458.6 | −1.40010 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11593.8 | 0.980562 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2993.21 | 0.251699 | 0.125849 | − | 0.992049i | \(-0.459834\pi\) | ||||
0.125849 | + | 0.992049i | \(0.459834\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15198.3 | −1.27070 | −0.635351 | − | 0.772224i | \(-0.719144\pi\) | ||||
−0.635351 | + | 0.772224i | \(0.719144\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2850.04 | −0.236926 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −68.9044 | −0.00569549 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8071.00 | −0.663352 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 218.713 | 0.0178745 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1916.34 | 0.155734 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15357.6 | 1.24106 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8487.13 | −0.682024 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4986.31 | 0.398470 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2043.27 | 0.162379 | 0.0811894 | − | 0.996699i | \(-0.474128\pi\) | ||||
0.0811894 | + | 0.996699i | \(0.474128\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3380.22 | 0.267144 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9304.74 | −0.731323 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4616.69 | −0.360869 | −0.180434 | − | 0.983587i | \(-0.557750\pi\) | ||||
−0.180434 | + | 0.983587i | \(0.557750\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5768.88 | 0.448470 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1883.70 | 0.145641 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12421.0 | 0.955148 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10931.8 | 0.836085 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18077.9 | −1.37520 | −0.687600 | − | 0.726089i | \(-0.741336\pi\) | ||||
−0.687600 | + | 0.726089i | \(0.741336\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2170.46 | 0.164223 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 303.123 | 0.0228126 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13561.8 | 1.01520 | 0.507602 | − | 0.861592i | \(-0.330532\pi\) | ||||
0.507602 | + | 0.861592i | \(0.330532\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10521.7 | −0.783456 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1266.04 | 0.0937721 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7280.83 | −0.536429 | −0.268215 | − | 0.963359i | \(-0.586434\pi\) | ||||
−0.268215 | + | 0.963359i | \(0.586434\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17884.5 | −1.31076 | −0.655380 | − | 0.755299i | \(-0.727492\pi\) | ||||
−0.655380 | + | 0.755299i | \(0.727492\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1986.41 | 0.144823 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3889.98 | 0.282127 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12067.2 | −0.870645 | −0.435323 | − | 0.900275i | \(-0.643366\pi\) | ||||
−0.435323 | + | 0.900275i | \(0.643366\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3871.48 | 0.277881 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14778.4 | 1.05527 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5609.86 | −0.398519 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1594.73 | 0.112707 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9202.11 | −0.647038 | −0.323519 | − | 0.946222i | \(-0.604866\pi\) | ||||
−0.323519 | + | 0.946222i | \(0.604866\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −625.332 | −0.0437460 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3960.04 | −0.275625 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16985.1 | −1.17621 | −0.588106 | − | 0.808784i | \(-0.700126\pi\) | ||||
−0.588106 | + | 0.808784i | \(0.700126\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −426.082 | −0.0293574 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8135.92 | −0.557757 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −541.705 | −0.0369507 | −0.0184753 | − | 0.999829i | \(-0.505881\pi\) | ||||
−0.0184753 | + | 0.999829i | \(0.505881\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24039.4 | −1.63160 | −0.815798 | − | 0.578337i | \(-0.803702\pi\) | ||||
−0.815798 | + | 0.578337i | \(0.803702\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3443.30 | −0.232541 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −16646.9 | −1.11867 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22951.8 | −1.53474 | −0.767369 | − | 0.641206i | \(-0.778435\pi\) | ||||
−0.767369 | + | 0.641206i | \(0.778435\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4866.33 | −0.323799 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4235.15 | −0.280419 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19479.1 | 1.28345 | 0.641725 | − | 0.766935i | \(-0.278219\pi\) | ||||
0.641725 | + | 0.766935i | \(0.278219\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6027.70 | −0.395220 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12586.6 | 0.821258 | 0.410629 | − | 0.911803i | \(-0.365309\pi\) | ||||
0.410629 | + | 0.911803i | \(0.365309\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10589.4 | 0.687598 | 0.343799 | − | 0.939043i | \(-0.388286\pi\) | ||||
0.343799 | + | 0.939043i | \(0.388286\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1728.00 | −0.111662 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4959.89 | 0.318963 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19528.3 | −1.24981 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2750.96 | 0.175219 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 534.685 | 0.0338940 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11104.0 | 0.700547 | 0.350273 | − | 0.936647i | \(-0.386089\pi\) | ||||
0.350273 | + | 0.936647i | \(0.386089\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4836.17 | −0.303666 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −29754.4 | −1.85948 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1283.08 | 0.0798077 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4592.22 | −0.284297 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15811.9 | 0.974311 | 0.487155 | − | 0.873315i | \(-0.338035\pi\) | ||||
0.487155 | + | 0.873315i | \(0.338035\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1406.62 | 0.0862704 | 0.0431352 | − | 0.999069i | \(-0.486265\pi\) | ||||
0.0431352 | + | 0.999069i | \(0.486265\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6827.02 | −0.416765 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11661.8 | 0.708613 | 0.354307 | − | 0.935129i | \(-0.384717\pi\) | ||||
0.354307 | + | 0.935129i | \(0.384717\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1227.72 | −0.0742564 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1615.48 | 0.0972590 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5545.04 | 0.332303 | 0.166152 | − | 0.986100i | \(-0.446866\pi\) | ||||
0.166152 | + | 0.986100i | \(0.446866\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12020.7 | −0.717078 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2626.03 | −0.155938 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10950.0 | 0.647272 | 0.323636 | − | 0.946182i | \(-0.395095\pi\) | ||||
0.323636 | + | 0.946182i | \(0.395095\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18488.8 | −1.08795 | −0.543973 | − | 0.839103i | \(-0.683081\pi\) | ||||
−0.543973 | + | 0.839103i | \(0.683081\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 78.0000 | 0.00456903 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3866.85 | −0.225489 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6641.98 | 0.385575 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16806.3 | −0.971254 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −32383.0 | −1.86309 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5865.80 | −0.335973 | −0.167987 | − | 0.985789i | \(-0.553727\pi\) | ||||
−0.167987 | + | 0.985789i | \(0.553727\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1641.08 | −0.0935783 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10258.6 | 0.582376 | 0.291188 | − | 0.956666i | \(-0.405950\pi\) | ||||
0.291188 | + | 0.956666i | \(0.405950\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24584.3 | 1.38948 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4281.70 | 0.240933 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26215.4 | −1.46867 | −0.734337 | − | 0.678785i | \(-0.762507\pi\) | ||||
−0.734337 | + | 0.678785i | \(0.762507\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 37679.2 | 2.10167 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14479.0 | 0.804088 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1443.54 | −0.0798176 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7290.15 | −0.401346 | −0.200673 | − | 0.979658i | \(-0.564313\pi\) | ||||
−0.200673 | + | 0.979658i | \(0.564313\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7106.80 | −0.389560 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −19810.0 | −1.08120 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −294.822 | −0.0160218 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18732.5 | 1.01363 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15472.1 | −0.833628 | −0.416814 | − | 0.908992i | \(-0.636853\pi\) | ||||
−0.416814 | + | 0.908992i | \(0.636853\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4852.46 | 0.260333 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13321.3 | 0.711645 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −28453.7 | −1.51360 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17594.7 | −0.931994 | −0.465997 | − | 0.884786i | \(-0.654304\pi\) | ||||
−0.465997 | + | 0.884786i | \(0.654304\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7152.17 | 0.377253 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2204.94 | −0.115814 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8951.84 | −0.468223 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19916.1 | 1.03735 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12944.2 | 0.671400 | 0.335700 | − | 0.941969i | \(-0.391027\pi\) | ||||
0.335700 | + | 0.941969i | \(0.391027\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13426.5 | −0.693523 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13578.6 | 0.698469 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6307.89 | 0.323130 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20231.8 | −1.03213 | −0.516063 | − | 0.856551i | \(-0.672603\pi\) | ||||
−0.516063 | + | 0.856551i | \(0.672603\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −333.918 | −0.0168952 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26581.0 | 1.33942 | 0.669708 | − | 0.742624i | \(-0.266419\pi\) | ||||
0.669708 | + | 0.742624i | \(0.266419\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4035.83 | −0.202536 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19328.6 | 0.966050 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1018.30 | −0.0506886 | −0.0253443 | − | 0.999679i | \(-0.508068\pi\) | ||||
−0.0253443 | + | 0.999679i | \(0.508068\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 707.878 | 0.0350939 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31784.2 | 1.56938 | 0.784691 | − | 0.619888i | \(-0.212822\pi\) | ||||
0.784691 | + | 0.619888i | \(0.212822\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7634.56 | 0.375448 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8509.57 | 0.416799 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17611.1 | −0.859141 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3549.69 | 0.172477 | 0.0862385 | − | 0.996275i | \(-0.472515\pi\) | ||||
0.0862385 | + | 0.996275i | \(0.472515\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6211.07 | −0.300589 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −40375.7 | −1.94625 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18852.3 | 0.905151 | 0.452576 | − | 0.891726i | \(-0.350505\pi\) | ||||
0.452576 | + | 0.891726i | \(0.350505\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9699.95 | 0.463881 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8131.76 | −0.387353 | −0.193677 | − | 0.981065i | \(-0.562041\pi\) | ||||
−0.193677 | + | 0.981065i | \(0.562041\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10670.1 | 0.506267 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −245.343 | −0.0115953 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −315.919 | −0.0148725 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15773.3 | −0.739662 | −0.369831 | − | 0.929099i | \(-0.620584\pi\) | ||||
−0.369831 | + | 0.929099i | \(0.620584\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18463.7 | 0.862458 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23061.4 | −1.07304 | −0.536521 | − | 0.843887i | \(-0.680262\pi\) | ||||
−0.536521 | + | 0.843887i | \(0.680262\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2094.03 | −0.0970580 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12535.8 | −0.578790 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2675.62 | −0.123060 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25778.0 | 1.18106 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2802.08 | −0.127891 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 25051.1 | 1.13900 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38874.7 | −1.76078 | −0.880390 | − | 0.474251i | \(-0.842719\pi\) | ||||
−0.880390 | + | 0.474251i | \(0.842719\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12334.5 | 0.556554 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12065.6 | 0.542357 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8332.83 | −0.373149 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4540.52 | 0.202561 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8956.95 | −0.398082 | −0.199041 | − | 0.979991i | \(-0.563783\pi\) | ||||
−0.199041 | + | 0.979991i | \(0.563783\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 651.562 | 0.0288493 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2855.96 | 0.125980 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14740.9 | 0.647816 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13634.6 | −0.596966 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2468.55 | 0.107679 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21956.3 | −0.954195 | −0.477098 | − | 0.878850i | \(-0.658311\pi\) | ||||
−0.477098 | + | 0.878850i | \(0.658311\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14652.2 | 0.634414 | 0.317207 | − | 0.948356i | \(-0.397255\pi\) | ||||
0.317207 | + | 0.948356i | \(0.397255\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5056.23 | 0.218118 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −24446.0 | −1.05068 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3030.42 | −0.129769 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1828.73 | −0.0780231 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12172.5 | −0.517444 | −0.258722 | − | 0.965952i | \(-0.583301\pi\) | ||||
−0.258722 | + | 0.965952i | \(0.583301\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22022.1 | 0.932738 | 0.466369 | − | 0.884590i | \(-0.345562\pi\) | ||||
0.466369 | + | 0.884590i | \(0.345562\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9212.06 | 0.388755 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7620.60 | 0.320428 | 0.160214 | − | 0.987082i | \(-0.448781\pi\) | ||||
0.160214 | + | 0.987082i | \(0.448781\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18727.6 | −0.784603 | −0.392302 | − | 0.919837i | \(-0.628321\pi\) | ||||
−0.392302 | + | 0.919837i | \(0.628321\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −555.705 | −0.0231976 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −197.397 | −0.00821057 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 53421.6 | 2.21405 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 930.209 | 0.0384143 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6853.37 | −0.282008 | −0.141004 | − | 0.990009i | \(-0.545033\pi\) | ||||
−0.141004 | + | 0.990009i | \(0.545033\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13618.5 | −0.558388 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3025.02 | 0.123591 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2303.49 | −0.0937783 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19089.6 | 0.774410 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19993.9 | 0.808232 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17109.9 | 0.689214 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16744.0 | 0.672102 | 0.336051 | − | 0.941844i | \(-0.390909\pi\) | ||||
0.336051 | + | 0.941844i | \(0.390909\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2226.57 | −0.0890611 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28271.8 | 1.12689 | 0.563446 | − | 0.826153i | \(-0.309475\pi\) | ||||
0.563446 | + | 0.826153i | \(0.309475\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40681.8 | 1.61589 | 0.807943 | − | 0.589260i | \(-0.200581\pi\) | ||||
0.807943 | + | 0.589260i | \(0.200581\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6912.17 | 0.273596 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16589.8 | −0.654371 | −0.327186 | − | 0.944960i | \(-0.606100\pi\) | ||||
−0.327186 | + | 0.944960i | \(0.606100\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 52675.1 | 2.07053 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14727.0 | 0.576880 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −40148.0 | −1.56723 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4973.66 | 0.193486 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14155.9 | 0.548803 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13681.3 | 0.528586 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41833.7 | 1.61074 | 0.805372 | − | 0.592769i | \(-0.201965\pi\) | ||||
0.805372 | + | 0.592769i | \(0.201965\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −23862.0 | −0.915639 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24676.3 | −0.943663 | −0.471831 | − | 0.881689i | \(-0.656407\pi\) | ||||
−0.471831 | + | 0.881689i | \(0.656407\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30567.6 | 1.16499 | 0.582493 | − | 0.812836i | \(-0.302077\pi\) | ||||
0.582493 | + | 0.812836i | \(0.302077\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 993.697 | 0.0377432 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19020.9 | −0.720023 | −0.360012 | − | 0.932948i | \(-0.617227\pi\) | ||||
−0.360012 | + | 0.932948i | \(0.617227\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 34120.4 | 1.28725 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4092.17 | −0.153864 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5913.16 | 0.221586 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −38560.3 | −1.44014 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2496.00 | 0.0929086 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3575.48 | −0.132646 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 222.082 | 0.00821158 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7828.77 | 0.288511 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 15357.6 | 0.564094 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −39186.2 | −1.43457 | −0.717287 | − | 0.696778i | \(-0.754616\pi\) | ||||
−0.717287 | + | 0.696778i | \(0.754616\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16384.0 | −0.597823 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1303.25 | 0.0473969 | 0.0236985 | − | 0.999719i | \(-0.492456\pi\) | ||||
0.0236985 | + | 0.999719i | \(0.492456\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −47767.6 | −1.73152 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 26210.2 | 0.946976 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13784.5 | 0.496406 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11710.2 | −0.420330 | −0.210165 | − | 0.977666i | \(-0.567400\pi\) | ||||
−0.210165 | + | 0.977666i | \(0.567400\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26495.1 | −0.947928 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6633.21 | 0.236549 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16249.3 | 0.577594 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7731.13 | −0.273920 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34967.9 | 1.23494 | 0.617470 | − | 0.786595i | \(-0.288158\pi\) | ||||
0.617470 | + | 0.786595i | \(0.288158\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1791.45 | −0.0630638 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24129.7 | 0.846700 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1377.21 | 0.0481705 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6538.36 | −0.227960 | −0.113980 | − | 0.993483i | \(-0.536360\pi\) | ||||
−0.113980 | + | 0.993483i | \(0.536360\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 29819.4 | 1.03634 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26190.2 | 0.907309 | 0.453654 | − | 0.891178i | \(-0.350120\pi\) | ||||
0.453654 | + | 0.891178i | \(0.350120\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9434.31 | −0.325793 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5752.11 | 0.198007 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44316.2 | 1.52068 | 0.760340 | − | 0.649526i | \(-0.225032\pi\) | ||||
0.760340 | + | 0.649526i | \(0.225032\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3793.15 | 0.129748 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19921.4 | 0.679282 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10052.0 | −0.341676 | −0.170838 | − | 0.985299i | \(-0.554647\pi\) | ||||
−0.170838 | + | 0.985299i | \(0.554647\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9025.00 | 0.305803 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 15729.2 | 0.531299 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −43208.0 | −1.45491 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28604.0 | −0.960157 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10140.7 | −0.339334 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17589.6 | 0.586767 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10809.8 | 0.359482 | 0.179741 | − | 0.983714i | \(-0.442474\pi\) | ||||
0.179741 | + | 0.983714i | \(0.442474\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −108.904 | −0.00361044 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16280.1 | 0.538056 | 0.269028 | − | 0.963132i | \(-0.413298\pi\) | ||||
0.269028 | + | 0.963132i | \(0.413298\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22716.8 | 0.748477 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2370.45 | 0.0778618 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 56327.0 | 1.84448 | 0.922242 | − | 0.386613i | \(-0.126355\pi\) | ||||
0.922242 | + | 0.386613i | \(0.126355\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16031.6 | −0.523364 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6143.93 | 0.199960 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −32733.6 | −1.06210 | −0.531048 | − | 0.847342i | \(-0.678202\pi\) | ||||
−0.531048 | + | 0.847342i | \(0.678202\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17992.0 | −0.582002 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −15276.0 | −0.492645 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10685.4 | −0.343554 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2430.76 | 0.0779168 | 0.0389584 | − | 0.999241i | \(-0.487596\pi\) | ||||
0.0389584 | + | 0.999241i | \(0.487596\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6022.90 | 0.192478 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −36964.6 | −1.17775 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38619.5 | 1.22677 | 0.613387 | − | 0.789783i | \(-0.289807\pi\) | ||||
0.613387 | + | 0.789783i | \(0.289807\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7218.25 | −0.228604 |
(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 | 2496.4.a.v.1.1 | 2 | ||
4.3 | odd | 2 | 2496.4.a.be.1.1 | 2 | |||
8.3 | odd | 2 | 312.4.a.c.1.2 | ✓ | 2 | ||
8.5 | even | 2 | 624.4.a.q.1.2 | 2 | |||
24.5 | odd | 2 | 1872.4.a.x.1.1 | 2 | |||
24.11 | even | 2 | 936.4.a.d.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
312.4.a.c.1.2 | ✓ | 2 | 8.3 | odd | 2 | ||
624.4.a.q.1.2 | 2 | 8.5 | even | 2 | |||
936.4.a.d.1.1 | 2 | 24.11 | even | 2 | |||
1872.4.a.x.1.1 | 2 | 24.5 | odd | 2 | |||
2496.4.a.v.1.1 | 2 | 1.1 | even | 1 | trivial | ||
2496.4.a.be.1.1 | 2 | 4.3 | odd | 2 |