Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [32,6,Mod(1,32)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(32, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("32.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 32 = 2^{5} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 32.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: | \(5.13228223402\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 32.1 |
$q$-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 | ||||||||
\(3\) | 8.00000 | 0.513200 | 0.256600 | − | 0.966518i | \(-0.417398\pi\) | ||||
0.256600 | + | 0.966518i | \(0.417398\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 14.0000 | 0.250440 | 0.125220 | − | 0.992129i | \(-0.460036\pi\) | ||||
0.125220 | + | 0.992129i | \(0.460036\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 208.000 | 1.60442 | 0.802210 | − | 0.597042i | \(-0.203657\pi\) | ||||
0.802210 | + | 0.597042i | \(0.203657\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −179.000 | −0.736626 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 536.000 | 1.33562 | 0.667810 | − | 0.744332i | \(-0.267232\pi\) | ||||
0.667810 | + | 0.744332i | \(0.267232\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 694.000 | 1.13894 | 0.569470 | − | 0.822012i | \(-0.307148\pi\) | ||||
0.569470 | + | 0.822012i | \(0.307148\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 112.000 | 0.128526 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1278.00 | −1.07253 | −0.536264 | − | 0.844050i | \(-0.680165\pi\) | ||||
−0.536264 | + | 0.844050i | \(0.680165\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1112.00 | −0.706677 | −0.353338 | − | 0.935496i | \(-0.614954\pi\) | ||||
−0.353338 | + | 0.935496i | \(0.614954\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1664.00 | 0.823389 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3216.00 | −1.26764 | −0.633821 | − | 0.773480i | \(-0.718514\pi\) | ||||
−0.633821 | + | 0.773480i | \(0.718514\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2929.00 | −0.937280 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3376.00 | −0.891237 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2918.00 | 0.644303 | 0.322152 | − | 0.946688i | \(-0.395594\pi\) | ||||
0.322152 | + | 0.946688i | \(0.395594\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2624.00 | 0.490410 | 0.245205 | − | 0.969471i | \(-0.421145\pi\) | ||||
0.245205 | + | 0.969471i | \(0.421145\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4288.00 | 0.685441 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2912.00 | 0.401810 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9458.00 | −1.13578 | −0.567891 | − | 0.823104i | \(-0.692241\pi\) | ||||
−0.567891 | + | 0.823104i | \(0.692241\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5552.00 | 0.584505 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 170.000 | 0.0157939 | 0.00789695 | − | 0.999969i | \(-0.497486\pi\) | ||||
0.00789695 | + | 0.999969i | \(0.497486\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 19928.0 | 1.64359 | 0.821793 | − | 0.569786i | \(-0.192974\pi\) | ||||
0.821793 | + | 0.569786i | \(0.192974\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2506.00 | −0.184480 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −32.0000 | −0.00211303 | −0.00105651 | − | 0.999999i | \(-0.500336\pi\) | ||||
−0.00105651 | + | 0.999999i | \(0.500336\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 26457.0 | 1.57417 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10224.0 | −0.550422 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −22178.0 | −1.08451 | −0.542254 | − | 0.840215i | \(-0.682429\pi\) | ||||
−0.542254 | + | 0.840215i | \(0.682429\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7504.00 | 0.334492 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8896.00 | −0.362667 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −41480.0 | −1.55135 | −0.775673 | − | 0.631135i | \(-0.782589\pi\) | ||||
−0.775673 | + | 0.631135i | \(0.782589\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 15462.0 | 0.532036 | 0.266018 | − | 0.963968i | \(-0.414292\pi\) | ||||
0.266018 | + | 0.963968i | \(0.414292\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −37232.0 | −1.18186 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9716.00 | 0.285236 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 20744.0 | 0.564554 | 0.282277 | − | 0.959333i | \(-0.408910\pi\) | ||||
0.282277 | + | 0.959333i | \(0.408910\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −25728.0 | −0.650554 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −28592.0 | −0.673130 | −0.336565 | − | 0.941660i | \(-0.609265\pi\) | ||||
−0.336565 | + | 0.941660i | \(0.609265\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −53670.0 | −1.17876 | −0.589379 | − | 0.807857i | \(-0.700627\pi\) | ||||
−0.589379 | + | 0.807857i | \(0.700627\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −23432.0 | −0.481012 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 111488. | 2.14290 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 69152.0 | 1.24663 | 0.623314 | − | 0.781971i | \(-0.285786\pi\) | ||||
0.623314 | + | 0.781971i | \(0.285786\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 16489.0 | 0.279243 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 37800.0 | 0.602277 | 0.301139 | − | 0.953580i | \(-0.402633\pi\) | ||||
0.301139 | + | 0.953580i | \(0.402633\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −17892.0 | −0.268603 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 23344.0 | 0.330657 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −126806. | −1.69693 | −0.848467 | − | 0.529249i | \(-0.822474\pi\) | ||||
−0.848467 | + | 0.529249i | \(0.822474\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 144352. | 1.82734 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 20992.0 | 0.251679 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15568.0 | −0.176980 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 62290.0 | 0.672185 | 0.336093 | − | 0.941829i | \(-0.390894\pi\) | ||||
0.336093 | + | 0.941829i | \(0.390894\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −95944.0 | −0.983852 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6414.00 | 0.0625641 | 0.0312821 | − | 0.999511i | \(-0.490041\pi\) | ||||
0.0312821 | + | 0.999511i | \(0.490041\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 108432. | 1.00708 | 0.503541 | − | 0.863972i | \(-0.332030\pi\) | ||||
0.503541 | + | 0.863972i | \(0.332030\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 23296.0 | 0.206209 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −103976. | −0.877958 | −0.438979 | − | 0.898497i | \(-0.644660\pi\) | ||||
−0.438979 | + | 0.898497i | \(0.644660\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2486.00 | 0.0200417 | 0.0100209 | − | 0.999950i | \(-0.496810\pi\) | ||||
0.0100209 | + | 0.999950i | \(0.496810\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −75664.0 | −0.582884 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15794.0 | 0.116358 | 0.0581790 | − | 0.998306i | \(-0.481471\pi\) | ||||
0.0581790 | + | 0.998306i | \(0.481471\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −45024.0 | −0.317468 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −124226. | −0.838973 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −265824. | −1.72079 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 126245. | 0.783882 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1360.00 | 0.00810543 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −84756.0 | −0.485172 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1024.00 | −0.00563366 | −0.00281683 | − | 0.999996i | \(-0.500897\pi\) | ||||
−0.00281683 | + | 0.999996i | \(0.500897\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 159424. | 0.843489 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 22664.0 | 0.115387 | 0.0576937 | − | 0.998334i | \(-0.481625\pi\) | ||||
0.0576937 | + | 0.998334i | \(0.481625\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −231296. | −1.13381 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −47264.0 | −0.223201 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −53238.0 | −0.242337 | −0.121169 | − | 0.992632i | \(-0.538664\pi\) | ||||
−0.121169 | + | 0.992632i | \(0.538664\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19816.0 | −0.0869919 | −0.0434960 | − | 0.999054i | \(-0.513850\pi\) | ||||
−0.0434960 | + | 0.999054i | \(0.513850\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −256.000 | −0.00108441 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 371984. | 1.52119 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 40852.0 | 0.161359 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 211656. | 0.807862 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 452190. | 1.66861 | 0.834306 | − | 0.551302i | \(-0.185869\pi\) | ||||
0.834306 | + | 0.551302i | \(0.185869\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 263280. | 0.939670 | 0.469835 | − | 0.882754i | \(-0.344313\pi\) | ||||
0.469835 | + | 0.882754i | \(0.344313\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 228762. | 0.790051 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 36736.0 | 0.122818 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −353530. | −1.14466 | −0.572331 | − | 0.820023i | \(-0.693961\pi\) | ||||
−0.572331 | + | 0.820023i | \(0.693961\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −177424. | −0.556570 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −668928. | −2.03383 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 100936. | 0.297562 | 0.148781 | − | 0.988870i | \(-0.452465\pi\) | ||||
0.148781 | + | 0.988870i | \(0.452465\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 60032.0 | 0.171662 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 284944. | 0.790621 | 0.395310 | − | 0.918548i | \(-0.370637\pi\) | ||||
0.395310 | + | 0.918548i | \(0.370637\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 110343. | 0.297186 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 199048. | 0.520556 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 484374. | 1.23045 | 0.615227 | − | 0.788350i | \(-0.289064\pi\) | ||||
0.615227 | + | 0.788350i | \(0.289064\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −609232. | −1.50379 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −331840. | −0.796151 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −406680. | −0.948681 | −0.474341 | − | 0.880341i | \(-0.657313\pi\) | ||||
−0.474341 | + | 0.880341i | \(0.657313\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 570302. | 1.29392 | 0.646962 | − | 0.762523i | \(-0.276039\pi\) | ||||
0.646962 | + | 0.762523i | \(0.276039\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 123696. | 0.273041 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −132412. | −0.284445 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −685008. | −1.43249 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −702208. | −1.42992 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −138624. | −0.274951 | −0.137475 | − | 0.990505i | \(-0.543899\pi\) | ||||
−0.137475 | + | 0.990505i | \(0.543899\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 34482.0 | 0.0666345 | 0.0333173 | − | 0.999445i | \(-0.489393\pi\) | ||||
0.0333173 | + | 0.999445i | \(0.489393\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 77728.0 | 0.146383 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 643598. | 1.18154 | 0.590771 | − | 0.806839i | \(-0.298824\pi\) | ||||
0.590771 | + | 0.806839i | \(0.298824\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.10738e6 | −1.98227 | −0.991134 | − | 0.132865i | \(-0.957582\pi\) | ||||
−0.991134 | + | 0.132865i | \(0.957582\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 165952. | 0.289729 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 606944. | 1.03373 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2380.00 | 0.00395542 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 575664. | 0.933777 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −596032. | −0.943852 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −229976. | −0.355612 | −0.177806 | − | 0.984066i | \(-0.556900\pi\) | ||||
−0.177806 | + | 0.984066i | \(0.556900\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −228736. | −0.345450 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 278992. | 0.411619 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 545792. | 0.786824 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −429360. | −0.604939 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −886932. | −1.22155 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.08947e6 | 1.46708 | 0.733540 | − | 0.679646i | \(-0.237867\pi\) | ||||
0.733540 | + | 0.679646i | \(0.237867\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 524291. | 0.690424 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 687048. | 0.884958 | 0.442479 | − | 0.896779i | \(-0.354099\pi\) | ||||
0.442479 | + | 0.896779i | \(0.354099\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −699730. | −0.881743 | −0.440871 | − | 0.897570i | \(-0.645330\pi\) | ||||
−0.440871 | + | 0.897570i | \(0.645330\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 891904. | 1.09974 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 937722. | 1.13158 | 0.565789 | − | 0.824550i | \(-0.308572\pi\) | ||||
0.565789 | + | 0.824550i | \(0.308572\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −448.000 | −0.000529186 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 553216. | 0.639770 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −643488. | −0.728695 | −0.364347 | − | 0.931263i | \(-0.618708\pi\) | ||||
−0.364347 | + | 0.931263i | \(0.618708\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 157282. | 0.174436 | 0.0872181 | − | 0.996189i | \(-0.472202\pi\) | ||||
0.0872181 | + | 0.996189i | \(0.472202\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 952280. | 1.03454 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 370398. | 0.394233 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −771728. | −0.804863 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 302400. | 0.309089 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.58604e6 | 1.58902 | 0.794511 | − | 0.607250i | \(-0.207727\pi\) | ||||
0.794511 | + | 0.607250i | \(0.207727\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.72378e6 | −1.69309 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −143136. | −0.137847 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −654334. | −0.617969 | −0.308984 | − | 0.951067i | \(-0.599989\pi\) | ||||
−0.308984 | + | 0.951067i | \(0.599989\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.96726e6 | −1.82227 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −522322. | −0.474610 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 330192. | 0.294359 | 0.147179 | − | 0.989110i | \(-0.452981\pi\) | ||||
0.147179 | + | 0.989110i | \(0.452981\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −310492. | −0.271604 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.01445e6 | −0.870867 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.56956e6 | 1.32250 | 0.661252 | − | 0.750164i | \(-0.270026\pi\) | ||||
0.661252 | + | 0.750164i | \(0.270026\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −957792. | −0.792224 | −0.396112 | − | 0.918202i | \(-0.629641\pi\) | ||||
−0.396112 | + | 0.918202i | \(0.629641\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.15482e6 | 0.937791 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.56994e6 | −1.25185 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 565438. | 0.442778 | 0.221389 | − | 0.975186i | \(-0.428941\pi\) | ||||
0.221389 | + | 0.975186i | \(0.428941\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −469696. | −0.361249 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.34127e6 | −1.01333 | −0.506664 | − | 0.862143i | \(-0.669122\pi\) | ||||
−0.506664 | + | 0.862143i | \(0.669122\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 734264. | 0.544987 | 0.272494 | − | 0.962158i | \(-0.412152\pi\) | ||||
0.272494 | + | 0.962158i | \(0.412152\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −124544. | −0.0908261 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 35360.0 | 0.0253401 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 213427. | 0.150316 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 498320. | 0.344966 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.13320e6 | −0.771149 | −0.385574 | − | 0.922677i | \(-0.625997\pi\) | ||||
−0.385574 | + | 0.922677i | \(0.625997\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −580720. | −0.388519 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.80954e6 | −1.19035 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.23190e6 | −1.44377 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.14502e6 | 2.63700 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 51312.0 | 0.0321079 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 216468. | 0.133243 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.91377e6 | 1.76445 | 0.882224 | − | 0.470829i | \(-0.156045\pi\) | ||||
0.882224 | + | 0.470829i | \(0.156045\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 867456. | 0.516834 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.43813e6 | 0.843134 | 0.421567 | − | 0.906797i | \(-0.361480\pi\) | ||||
0.421567 | + | 0.906797i | \(0.361480\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.37601e6 | −0.793888 | −0.396944 | − | 0.917843i | \(-0.629929\pi\) | ||||
−0.396944 | + | 0.917843i | \(0.629929\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −521248. | −0.295984 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.23494e6 | −0.690235 | −0.345118 | − | 0.938559i | \(-0.612161\pi\) | ||||
−0.345118 | + | 0.938559i | \(0.612161\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.56405e6 | 0.860545 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −831808. | −0.450568 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.42114e6 | 0.757930 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.03273e6 | −1.06751 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19888.0 | 0.0102854 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6656.00 | −0.00339019 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.48930e6 | 0.747160 | 0.373580 | − | 0.927598i | \(-0.378130\pi\) | ||||
0.373580 | + | 0.927598i | \(0.378130\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.69298e6 | 0.836646 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 290416. | 0.141387 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 838226. | 0.402056 | 0.201028 | − | 0.979586i | \(-0.435572\pi\) | ||||
0.201028 | + | 0.979586i | \(0.435572\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 126352. | 0.0597149 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.40646e6 | 0.655002 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.00720e6 | 0.921203 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −360192. | −0.162924 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 350008. | 0.156047 | 0.0780233 | − | 0.996952i | \(-0.475139\pi\) | ||||
0.0780233 | + | 0.996952i | \(0.475139\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −383642. | −0.168602 | −0.0843010 | − | 0.996440i | \(-0.526866\pi\) | ||||
−0.0843010 | + | 0.996440i | \(0.526866\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.34294e6 | −1.01507 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.09309e6 | 1.74829 | 0.874147 | − | 0.485661i | \(-0.161421\pi\) | ||||
0.874147 | + | 0.485661i | \(0.161421\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −400288. | −0.168578 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.12659e6 | −0.883108 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.14430e6 | −1.28762 | −0.643811 | − | 0.765185i | \(-0.722648\pi\) | ||||
−0.643811 | + | 0.765185i | \(0.722648\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.23955e6 | −0.500608 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.00996e6 | 0.402288 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −751380. | −0.295208 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.47619e6 | 0.572108 | 0.286054 | − | 0.958214i | \(-0.407656\pi\) | ||||
0.286054 | + | 0.958214i | \(0.407656\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −30430.0 | −0.0116342 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.61302e6 | −1.74001 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.73981e6 | −1.39180 | −0.695901 | − | 0.718138i | \(-0.744995\pi\) | ||||
−0.695901 | + | 0.718138i | \(0.744995\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −678048. | −0.248990 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.02509e6 | 0.733823 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.89966e6 | −0.679324 | −0.339662 | − | 0.940548i | \(-0.610313\pi\) | ||||
−0.339662 | + | 0.940548i | \(0.610313\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8192.00 | −0.00289120 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.74310e6 | −0.607192 | −0.303596 | − | 0.952801i | \(-0.598187\pi\) | ||||
−0.303596 | + | 0.952801i | \(0.598187\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.56083e6 | 0.536666 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.56711e6 | −1.21071 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.69147e6 | −0.901812 | −0.450906 | − | 0.892571i | \(-0.648899\pi\) | ||||
−0.450906 | + | 0.892571i | \(0.648899\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.11005e6 | 1.35958 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 181312. | 0.0592168 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 968128. | 0.312205 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.37353e6 | 1.71113 | 0.855565 | − | 0.517695i | \(-0.173210\pi\) | ||||
0.855565 | + | 0.517695i | \(0.173210\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.85037e6 | −0.581870 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 156418. | 0.0485765 | 0.0242882 | − | 0.999705i | \(-0.492268\pi\) | ||||
0.0242882 | + | 0.999705i | \(0.492268\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.82106e6 | 0.558548 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 230846. | 0.0699334 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.06949e6 | −1.51697 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −306086. | −0.0904764 | −0.0452382 | − | 0.998976i | \(-0.514405\pi\) | ||||
−0.0452382 | + | 0.998976i | \(0.514405\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −425904. | −0.124368 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.62784e6 | −2.48901 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 529200. | 0.150834 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −158528. | −0.0446443 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.70868e6 | 1.86682 | 0.933409 | − | 0.358814i | \(-0.116819\pi\) | ||||
0.933409 | + | 0.358814i | \(0.116819\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.02347e6 | 1.10636 | 0.553179 | − | 0.833063i | \(-0.313415\pi\) | ||||
0.553179 | + | 0.833063i | \(0.313415\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5728.00 | 0.00155651 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.74326e6 | 1.00526 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.21610e6 | 0.853610 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.97587e6 | 0.780676 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.04304e6 | 1.82628 | 0.913139 | − | 0.407648i | \(-0.133651\pi\) | ||||
0.913139 | + | 0.407648i | \(0.133651\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.25142e6 | −0.320763 | −0.160381 | − | 0.987055i | \(-0.551272\pi\) | ||||
−0.160381 | + | 0.987055i | \(0.551272\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 326816. | 0.0828095 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.57619e6 | 0.895813 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.25406e6 | 0.310569 | 0.155285 | − | 0.987870i | \(-0.450371\pi\) | ||||
0.155285 | + | 0.987870i | \(0.450371\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.73580e6 | −1.15957 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.18081e6 | −1.25426 | −0.627131 | − | 0.778914i | \(-0.715771\pi\) | ||||
−0.627131 | + | 0.778914i | \(0.715771\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.77528e6 | −0.424979 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.61752e6 | 0.856332 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.73064e6 | −1.34149 | −0.670745 | − | 0.741688i | \(-0.734025\pi\) | ||||
−0.670745 | + | 0.741688i | \(0.734025\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 91120.0 | 0.0210947 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.10624e6 | 0.482239 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.02093e6 | 0.457638 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.24153e6 | −1.17400 | −0.586999 | − | 0.809588i | \(-0.699691\pi\) | ||||
−0.586999 | + | 0.809588i | \(0.699691\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.31453e6 | 0.955876 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −173994. | −0.0381313 | −0.0190657 | − | 0.999818i | \(-0.506069\pi\) | ||||
−0.0190657 | + | 0.999818i | \(0.506069\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.01277e6 | −0.869945 | −0.434972 | − | 0.900444i | \(-0.643242\pi\) | ||||
−0.434972 | + | 0.900444i | \(0.643242\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 293888. | 0.0630303 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −774616. | −0.164359 | −0.0821796 | − | 0.996618i | \(-0.526188\pi\) | ||||
−0.0821796 | + | 0.996618i | \(0.526188\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.31475e6 | 0.905782 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.82824e6 | −0.587441 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.06814e7 | 2.19521 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.25705e6 | 0.662354 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.96986e6 | 0.798876 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.33530e6 | −0.465054 | −0.232527 | − | 0.972590i | \(-0.574699\pi\) | ||||
−0.232527 | + | 0.972590i | \(0.574699\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.56385e6 | −1.29359 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.35142e6 | −1.04376 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 872060. | 0.168342 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.03947e6 | −0.198605 | −0.0993025 | − | 0.995057i | \(-0.531661\pi\) | ||||
−0.0993025 | + | 0.995057i | \(0.531661\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 807488. | 0.152709 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.85092e6 | −1.46966 | −0.734830 | − | 0.678251i | \(-0.762738\pi\) | ||||
−0.734830 | + | 0.678251i | \(0.762738\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.72920e6 | −0.691033 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.34322e6 | −0.246396 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.94714e6 | −1.07998 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.71644e6 | −0.488370 | −0.244185 | − | 0.969729i | \(-0.578520\pi\) | ||||
−0.244185 | + | 0.969729i | \(0.578520\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.27955e6 | 0.405747 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.62034e6 | 0.814242 | 0.407121 | − | 0.913374i | \(-0.366533\pi\) | ||||
0.407121 | + | 0.913374i | \(0.366533\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 89796.0 | 0.0156685 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 882744. | 0.152516 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.46198e6 | −0.763366 | −0.381683 | − | 0.924293i | \(-0.624655\pi\) | ||||
−0.381683 | + | 0.924293i | \(0.624655\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.11634e7 | −1.89122 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.75411e6 | 0.629816 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.51805e6 | 0.252213 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17152.0 | −0.00282220 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.87499e6 | 0.631470 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.74375e6 | 0.604245 | 0.302122 | − | 0.953269i | \(-0.402305\pi\) | ||||
0.302122 | + | 0.953269i | \(0.402305\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.28433e6 | −1.48421 | −0.742107 | − | 0.670282i | \(-0.766173\pi\) | ||||
−0.742107 | + | 0.670282i | \(0.766173\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.87386e6 | −0.771746 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.35347e6 | −0.525979 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.90631e6 | 0.606915 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.42492e6 | 1.14276 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 117980. | 0.0179883 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.45566e6 | −0.219875 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.25344e6 | −0.486863 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.41810e7 | 2.10249 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 862150. | 0.126645 | 0.0633227 | − | 0.997993i | \(-0.479830\pi\) | ||||
0.0633227 | + | 0.997993i | \(0.479830\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.56242e6 | 0.664042 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 34804.0 | 0.00501924 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.75442e6 | −0.250707 | −0.125353 | − | 0.992112i | \(-0.540006\pi\) | ||||
−0.125353 | + | 0.992112i | \(0.540006\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.76770e6 | −0.391911 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.24482e6 | −0.455314 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.43836e7 | 2.00012 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.05930e6 | −0.145977 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.00292e7 | −1.36971 | −0.684856 | − | 0.728678i | \(-0.740135\pi\) | ||||
−0.684856 | + | 0.728678i | \(0.740135\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.38300e7 | 1.87195 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.48006e6 | −0.735154 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.27460e6 | 0.701324 | 0.350662 | − | 0.936502i | \(-0.385957\pi\) | ||||
0.350662 | + | 0.936502i | \(0.385957\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 221116. | 0.0291406 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.42971e6 | 0.448023 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.36940e6 | 1.08371 | 0.541856 | − | 0.840471i | \(-0.317722\pi\) | ||||
0.541856 | + | 0.840471i | \(0.317722\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.02702e6 | −0.516884 | −0.258442 | − | 0.966027i | \(-0.583209\pi\) | ||||
−0.258442 | + | 0.966027i | \(0.583209\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.10899e6 | −0.141105 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.41966e6 | 1.18814 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.37568e6 | 0.297063 | 0.148532 | − | 0.988908i | \(-0.452545\pi\) | ||||
0.148532 | + | 0.988908i | \(0.452545\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 275856. | 0.0341968 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.86240e6 | 0.966306 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.18874e7 | −1.44849 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.73916e6 | −0.210112 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.44028e6 | 0.412096 | 0.206048 | − | 0.978542i | \(-0.433940\pi\) | ||||
0.206048 | + | 0.978542i | \(0.433940\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.91789e6 | −0.346562 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.14878e6 | 0.606368 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.22942e6 | −0.377127 | −0.188564 | − | 0.982061i | \(-0.560383\pi\) | ||||
−0.188564 | + | 0.982061i | \(0.560383\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.72154e6 | −0.430953 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.85901e6 | −1.01730 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.29714e6 | 1.05872 | 0.529361 | − | 0.848397i | \(-0.322432\pi\) | ||||
0.529361 | + | 0.848397i | \(0.322432\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.12782e7 | −1.27366 | −0.636828 | − | 0.771006i | \(-0.719754\pi\) | ||||
−0.636828 | + | 0.771006i | \(0.719754\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.71318e6 | −0.415865 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.76743e6 | 0.196315 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.00115e6 | −0.771255 | −0.385627 | − | 0.922655i | \(-0.626015\pi\) | ||||
−0.385627 | + | 0.922655i | \(0.626015\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.85555e6 | 0.530512 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22208.0 | −0.00240661 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.19432e6 | −0.665798 | −0.332899 | − | 0.942962i | \(-0.608027\pi\) | ||||
−0.332899 | + | 0.942962i | \(0.608027\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 19040.0 | 0.00202992 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.62407e6 | −0.277500 | −0.138750 | − | 0.990327i | \(-0.544308\pi\) | ||||
−0.138750 | + | 0.990327i | \(0.544308\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.83721e6 | 0.297622 | 0.148811 | − | 0.988866i | \(-0.452455\pi\) | ||||
0.148811 | + | 0.988866i | \(0.452455\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.08572e7 | 1.12977 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.63756e7 | −2.72259 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.96654e6 | 0.815774 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.76826e6 | −0.484385 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.20873e7 | 1.21816 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.29656e7 | −1.29634 | −0.648170 | − | 0.761496i | \(-0.724465\pi\) | ||||
−0.648170 | + | 0.761496i | \(0.724465\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.83981e6 | −0.182500 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14336.0 | −0.00141089 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.83612e7 | 1.79288 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.11797e6 | 0.495844 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.16798e7 | −1.12276 | −0.561382 | − | 0.827557i | \(-0.689730\pi\) | ||||
−0.561382 | + | 0.827557i | \(0.689730\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.02732e6 | −0.670289 | −0.335145 | − | 0.942167i | \(-0.608785\pi\) | ||||
−0.335145 | + | 0.942167i | \(0.608785\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.23194e6 | 0.211243 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.72821e6 | 0.913634 | 0.456817 | − | 0.889561i | \(-0.348989\pi\) | ||||
0.456817 | + | 0.889561i | \(0.348989\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.22333e7 | −2.07201 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.36634e6 | 0.403798 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.81425e6 | −0.900688 | −0.450344 | − | 0.892855i | \(-0.648699\pi\) | ||||
−0.450344 | + | 0.892855i | \(0.648699\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 317296. | 0.0288976 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.60693e6 | 0.868303 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.46652e7 | −1.31545 | −0.657724 | − | 0.753259i | \(-0.728481\pi\) | ||||
−0.657724 | + | 0.753259i | \(0.728481\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.41836e7 | −1.26265 | −0.631327 | − | 0.775517i | \(-0.717489\pi\) | ||||
−0.631327 | + | 0.775517i | \(0.717489\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.09546e6 | −0.626897 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.23814e6 | −0.283950 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.38429e6 | −0.816745 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.71578e6 | 0.752906 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.28763e6 | 0.710598 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.49941e6 | 0.468035 | 0.234018 | − | 0.972232i | \(-0.424813\pi\) | ||||
0.234018 | + | 0.972232i | \(0.424813\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.88830e6 | 0.835338 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.77375e7 | 1.48737 | 0.743687 | − | 0.668528i | \(-0.233075\pi\) | ||||
0.743687 | + | 0.668528i | \(0.233075\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.29563e7 | 1.07847 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.49638e6 | 0.454160 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.39670e6 | 0.770768 | 0.385384 | − | 0.922756i | \(-0.374069\pi\) | ||||
0.385384 | + | 0.922756i | \(0.374069\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −745332. | −0.0606909 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.59784e6 | −0.452510 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.53915e7 | −1.23519 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.34767e7 | 1.07371 | 0.536857 | − | 0.843673i | \(-0.319611\pi\) | ||||
0.536857 | + | 0.843673i | \(0.319611\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.99564e7 | −1.57851 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −277424. | −0.0217862 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −217260. | −0.0169394 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.50178e6 | 0.580726 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.15594e7 | 1.65707 | 0.828536 | − | 0.559935i | \(-0.189174\pi\) | ||||
0.828536 | + | 0.559935i | \(0.189174\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.05173e7 | 0.802631 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3584.00 | −0.000271578 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.33411e6 | 0.100379 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.38165e6 | −0.476779 | −0.238390 | − | 0.971170i | \(-0.576620\pi\) | ||||
−0.238390 | + | 0.971170i | \(0.576620\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.23782e7 | −0.918298 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.43878e6 | −0.621664 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.20778e6 | 0.380967 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.14790e6 | −0.373966 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.63566e7 | 1.17997 | 0.589986 | − | 0.807413i | \(-0.299133\pi\) | ||||
0.589986 | + | 0.807413i | \(0.299133\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.25539e7 | 1.61578 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.25826e6 | 0.0895207 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.54682e6 | −0.603893 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.13130e7 | 1.49558 | 0.747788 | − | 0.663937i | \(-0.231116\pi\) | ||||
0.747788 | + | 0.663937i | \(0.231116\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.61141e6 | 0.251686 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.54680e7 | −1.76279 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.21571e7 | 0.835737 | 0.417869 | − | 0.908507i | \(-0.362777\pi\) | ||||
0.417869 | + | 0.908507i | \(0.362777\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.96318e6 | 0.202321 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.11188e7 | 0.754030 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.92337e7 | 1.29555 | 0.647773 | − | 0.761834i | \(-0.275701\pi\) | ||||
0.647773 | + | 0.761834i | \(0.275701\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.17382e6 | −0.413056 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.66565e6 | −0.110691 | −0.0553454 | − | 0.998467i | \(-0.517626\pi\) | ||||
−0.0553454 | + | 0.998467i | \(0.517626\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.33066e6 | 0.417886 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.76620e6 | −0.443653 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.16270e7 | −1.40861 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.81290e6 | −0.634888 | −0.317444 | − | 0.948277i | \(-0.602825\pi\) | ||||
−0.317444 | + | 0.948277i | \(0.602825\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.26883e7 | 0.815486 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.68592e6 | 0.235331 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.92753e7 | −1.22254 | −0.611269 | − | 0.791423i | \(-0.709341\pi\) | ||||
−0.611269 | + | 0.791423i | \(0.709341\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.37902e7 | −0.868893 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.17863e7 | −0.737762 | −0.368881 | − | 0.929477i | \(-0.620259\pi\) | ||||
−0.368881 | + | 0.929477i | \(0.620259\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 517088. | 0.0321553 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.20267e6 | 0.197860 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.87871e7 | −1.76689 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.22941e7 | 0.749690 | 0.374845 | − | 0.927087i | \(-0.377696\pi\) | ||||
0.374845 | + | 0.927087i | \(0.377696\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.23467e6 | −0.317142 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.57086e6 | 0.154750 | 0.0773749 | − | 0.997002i | \(-0.475346\pi\) | ||||
0.0773749 | + | 0.997002i | \(0.475346\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.68570e6 | −0.459652 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.57381e7 | −0.935190 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −189040. | −0.0111612 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.53253e7 | −0.899046 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.85117e6 | −0.574227 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.94942e6 | −0.286669 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.54594e6 | −0.319182 | −0.159591 | − | 0.987183i | \(-0.551018\pi\) | ||||
−0.159591 | + | 0.987183i | \(0.551018\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.64154e6 | 0.151065 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.28515e6 | 0.186687 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.07306e7 | 0.605958 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.48394e6 | −0.139387 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.09610e7 | 1.16887 | 0.584436 | − | 0.811440i | \(-0.301316\pi\) | ||||
0.584436 | + | 0.811440i | \(0.301316\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 40896.0 | 0.00226628 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.26983e7 | 1.25000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.87671e7 | −1.57437 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.36499e6 | −0.509352 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.25565e7 | 0.678709 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.70297e7 | 1.45201 | 0.726005 | − | 0.687690i | \(-0.241375\pi\) | ||||
0.726005 | + | 0.687690i | \(0.241375\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.13052e6 | 0.113745 | 0.0568727 | − | 0.998381i | \(-0.481887\pi\) | ||||
0.0568727 | + | 0.998381i | \(0.481887\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.66234e6 | −0.406570 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.41310e6 | 0.0745212 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.21599e7 | −1.16148 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.58390e7 | −1.34607 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.58060e7 | 0.818396 | 0.409198 | − | 0.912446i | \(-0.365809\pi\) | ||||
0.409198 | + | 0.912446i | \(0.365809\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.28848e7 | 1.17773 | 0.588867 | − | 0.808230i | \(-0.299574\pi\) | ||||
0.588867 | + | 0.808230i | \(0.299574\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.25596e7 | −0.642450 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.55336e7 | 1.29822 | 0.649109 | − | 0.760695i | \(-0.275142\pi\) | ||||
0.649109 | + | 0.760695i | \(0.275142\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.31786e6 | 0.420364 | 0.210182 | − | 0.977662i | \(-0.432594\pi\) | ||||
0.210182 | + | 0.977662i | \(0.432594\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.52350e6 | 0.227234 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.38120e7 | −1.68834 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.98922e6 | 0.198003 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.85862e6 | −0.437072 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.66261e7 | −1.79633 | −0.898164 | − | 0.439660i | \(-0.855099\pi\) | ||||
−0.898164 | + | 0.439660i | \(0.855099\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.19964e7 | −0.584873 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.07302e7 | −0.520041 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.54480e6 | 0.0744271 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.62590e7 | 1.25768 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.87411e6 | 0.279687 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.04169e7 | 1.43976 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.74802e7 | 0.822571 | 0.411286 | − | 0.911507i | \(-0.365080\pi\) | ||||
0.411286 | + | 0.911507i | \(0.365080\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.78667e6 | 0.130368 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.31062e6 | 0.433038 | 0.216519 | − | 0.976278i | \(-0.430530\pi\) | ||||
0.216519 | + | 0.976278i | \(0.430530\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.49525e7 | 1.61620 | 0.808101 | − | 0.589045i | \(-0.200496\pi\) | ||||
0.808101 | + | 0.589045i | \(0.200496\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 282880. | 0.0130045 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.02349e7 | 0.924858 | 0.462429 | − | 0.886656i | \(-0.346978\pi\) | ||||
0.462429 | + | 0.886656i | \(0.346978\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.78124e6 | 0.308155 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.70742e6 | 0.0771421 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.70655e7 | 1.66502 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.43963e7 | 0.642994 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.11499e7 | −0.495149 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.76292e7 | −0.778419 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.98342e7 | −0.870797 | −0.435398 | − | 0.900238i | \(-0.643392\pi\) | ||||
−0.435398 | + | 0.900238i | \(0.643392\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.06562e6 | −0.395754 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.81023e7 | −1.65391 | −0.826954 | − | 0.562270i | \(-0.809928\pi\) | ||||
−0.826954 | + | 0.562270i | \(0.809928\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.41560e7 | 1.04261 | 0.521307 | − | 0.853369i | \(-0.325445\pi\) | ||||
0.521307 | + | 0.853369i | \(0.325445\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.64576e6 | −0.199388 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.02368e7 | −0.863638 | −0.431819 | − | 0.901960i | \(-0.642128\pi\) | ||||
−0.431819 | + | 0.901960i | \(0.642128\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −212992. | −0.00903876 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.83810e6 | 0.372962 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 35584.0 | 0.00149323 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.69352e6 | −0.237587 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.78552e7 | −0.740942 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.65683e6 | 0.315973 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.83435e7 | 1.16316 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.31602e7 | 1.35331 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.98423e6 | 0.324050 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.97976e7 | −0.799088 | −0.399544 | − | 0.916714i | \(-0.630831\pi\) | ||||
−0.399544 | + | 0.916714i | \(0.630831\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.14811e6 | −0.0460863 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.13242e7 | 0.851288 | 0.425644 | − | 0.904891i | \(-0.360048\pi\) | ||||
0.425644 | + | 0.904891i | \(0.360048\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.02608e7 | 0.804414 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.73174e6 | 0.0683803 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.71411e6 | 0.185130 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.49941e7 | −1.36680 | −0.683401 | − | 0.730043i | \(-0.739500\pi\) | ||||
−0.683401 | + | 0.730043i | \(0.739500\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.33101e7 | 0.905515 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.98428e7 | −0.766655 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.77025e7 | 1.06455 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.94093e7 | −0.741842 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.88107e7 | −1.09525 | −0.547627 | − | 0.836722i | \(-0.684469\pi\) | ||||
−0.547627 | + | 0.836722i | \(0.684469\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.94202e7 | −1.11243 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.15050e7 | 0.432697 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.59011e6 | −0.358752 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.28854e7 | 0.479457 | 0.239729 | − | 0.970840i | \(-0.422941\pi\) | ||||
0.239729 | + | 0.970840i | \(0.422941\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.10080e7 | −0.407424 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.27615e7 | −1.94242 | −0.971210 | − | 0.238227i | \(-0.923434\pi\) | ||||
−0.971210 | + | 0.238227i | \(0.923434\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −546720. | −0.0200210 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.83091e6 | −0.358108 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.53961e6 | −0.200726 | −0.100363 | − | 0.994951i | \(-0.532000\pi\) | ||||
−0.100363 | + | 0.994951i | \(0.532000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.72470e7 | −1.34253 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.87950e6 | −0.354229 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −228102. | −0.00813574 | −0.00406787 | − | 0.999992i | \(-0.501295\pi\) | ||||
−0.00406787 | + | 0.999992i | \(0.501295\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.94074e6 | −0.0688586 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.25124e7 | 0.441632 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.10735e7 | −0.388811 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.17438e7 | −0.759498 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.86117e7 | 0.646726 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 482748. | 0.0166879 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.36709e6 | −0.253355 | −0.126678 | − | 0.991944i | \(-0.540431\pi\) | ||||
−0.126678 | + | 0.991944i | \(0.540431\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.13691e7 | 0.388970 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.91161e7 | 0.650654 | 0.325327 | − | 0.945602i | \(-0.394526\pi\) | ||||
0.325327 | + | 0.945602i | \(0.394526\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.12173e6 | −0.139572 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.62618e7 | −0.547844 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.57040e7 | 1.86702 | 0.933512 | − | 0.358546i | \(-0.116727\pi\) | ||||
0.933512 | + | 0.358546i | \(0.116727\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.79680e7 | −2.26646 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −444994. | −0.0147632 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.55469e7 | 0.513167 | 0.256584 | − | 0.966522i | \(-0.417403\pi\) | ||||
0.256584 | + | 0.966522i | \(0.417403\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.01037e6 | 0.295905 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −53248.0 | −0.00173984 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.40884e7 | −2.08348 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.36890e7 | −0.766237 | −0.383118 | − | 0.923699i | \(-0.625150\pi\) | ||||
−0.383118 | + | 0.923699i | \(0.625150\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.19144e7 | 0.383442 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.55033e7 | −0.496438 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.71720e6 | 0.118434 | 0.0592172 | − | 0.998245i | \(-0.481140\pi\) | ||||
0.0592172 | + | 0.998245i | \(0.481140\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.19302e7 | 1.01225 |
(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 | 32.6.a.c.1.1 | yes | 1 | |
3.2 | odd | 2 | 288.6.a.e.1.1 | 1 | |||
4.3 | odd | 2 | 32.6.a.a.1.1 | ✓ | 1 | ||
5.2 | odd | 4 | 800.6.c.b.449.1 | 2 | |||
5.3 | odd | 4 | 800.6.c.b.449.2 | 2 | |||
5.4 | even | 2 | 800.6.a.a.1.1 | 1 | |||
8.3 | odd | 2 | 64.6.a.e.1.1 | 1 | |||
8.5 | even | 2 | 64.6.a.c.1.1 | 1 | |||
12.11 | even | 2 | 288.6.a.d.1.1 | 1 | |||
16.3 | odd | 4 | 256.6.b.h.129.1 | 2 | |||
16.5 | even | 4 | 256.6.b.b.129.1 | 2 | |||
16.11 | odd | 4 | 256.6.b.h.129.2 | 2 | |||
16.13 | even | 4 | 256.6.b.b.129.2 | 2 | |||
20.3 | even | 4 | 800.6.c.a.449.1 | 2 | |||
20.7 | even | 4 | 800.6.c.a.449.2 | 2 | |||
20.19 | odd | 2 | 800.6.a.e.1.1 | 1 | |||
24.5 | odd | 2 | 576.6.a.v.1.1 | 1 | |||
24.11 | even | 2 | 576.6.a.u.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.6.a.a.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
32.6.a.c.1.1 | yes | 1 | 1.1 | even | 1 | trivial | |
64.6.a.c.1.1 | 1 | 8.5 | even | 2 | |||
64.6.a.e.1.1 | 1 | 8.3 | odd | 2 | |||
256.6.b.b.129.1 | 2 | 16.5 | even | 4 | |||
256.6.b.b.129.2 | 2 | 16.13 | even | 4 | |||
256.6.b.h.129.1 | 2 | 16.3 | odd | 4 | |||
256.6.b.h.129.2 | 2 | 16.11 | odd | 4 | |||
288.6.a.d.1.1 | 1 | 12.11 | even | 2 | |||
288.6.a.e.1.1 | 1 | 3.2 | odd | 2 | |||
576.6.a.u.1.1 | 1 | 24.11 | even | 2 | |||
576.6.a.v.1.1 | 1 | 24.5 | odd | 2 | |||
800.6.a.a.1.1 | 1 | 5.4 | even | 2 | |||
800.6.a.e.1.1 | 1 | 20.19 | odd | 2 | |||
800.6.c.a.449.1 | 2 | 20.3 | even | 4 | |||
800.6.c.a.449.2 | 2 | 20.7 | even | 4 | |||
800.6.c.b.449.1 | 2 | 5.2 | odd | 4 | |||
800.6.c.b.449.2 | 2 | 5.3 | odd | 4 |