Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [354,6,Mod(1,354)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(354, 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("354.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 354.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: | \(56.7758722138\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 6296x^{4} - 192180x^{3} - 1919598x^{2} - 7344954x - 8433643 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-17.9445\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 354.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | ||||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 17.9373 | 0.320871 | 0.160436 | − | 0.987046i | \(-0.448710\pi\) | ||||
0.160436 | + | 0.987046i | \(0.448710\pi\) | |||||||
\(6\) | 36.0000 | 0.408248 | ||||||||
\(7\) | 177.055 | 1.36573 | 0.682863 | − | 0.730546i | \(-0.260735\pi\) | ||||
0.682863 | + | 0.730546i | \(0.260735\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −71.7490 | −0.226890 | ||||||||
\(11\) | 129.074 | 0.321631 | 0.160816 | − | 0.986984i | \(-0.448588\pi\) | ||||
0.160816 | + | 0.986984i | \(0.448588\pi\) | |||||||
\(12\) | −144.000 | −0.288675 | ||||||||
\(13\) | −1171.27 | −1.92220 | −0.961100 | − | 0.276202i | \(-0.910924\pi\) | ||||
−0.961100 | + | 0.276202i | \(0.910924\pi\) | |||||||
\(14\) | −708.221 | −0.965714 | ||||||||
\(15\) | −161.435 | −0.185255 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 756.475 | 0.634852 | 0.317426 | − | 0.948283i | \(-0.397182\pi\) | ||||
0.317426 | + | 0.948283i | \(0.397182\pi\) | |||||||
\(18\) | −324.000 | −0.235702 | ||||||||
\(19\) | −227.613 | −0.144648 | −0.0723240 | − | 0.997381i | \(-0.523042\pi\) | ||||
−0.0723240 | + | 0.997381i | \(0.523042\pi\) | |||||||
\(20\) | 286.996 | 0.160436 | ||||||||
\(21\) | −1593.50 | −0.788502 | ||||||||
\(22\) | −516.297 | −0.227428 | ||||||||
\(23\) | −3364.96 | −1.32635 | −0.663177 | − | 0.748462i | \(-0.730793\pi\) | ||||
−0.663177 | + | 0.748462i | \(0.730793\pi\) | |||||||
\(24\) | 576.000 | 0.204124 | ||||||||
\(25\) | −2803.25 | −0.897042 | ||||||||
\(26\) | 4685.08 | 1.35920 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 2832.88 | 0.682863 | ||||||||
\(29\) | −450.000 | −0.0993613 | −0.0496806 | − | 0.998765i | \(-0.515820\pi\) | ||||
−0.0496806 | + | 0.998765i | \(0.515820\pi\) | |||||||
\(30\) | 645.741 | 0.130995 | ||||||||
\(31\) | 4615.07 | 0.862530 | 0.431265 | − | 0.902225i | \(-0.358067\pi\) | ||||
0.431265 | + | 0.902225i | \(0.358067\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | −1161.67 | −0.185694 | ||||||||
\(34\) | −3025.90 | −0.448908 | ||||||||
\(35\) | 3175.89 | 0.438222 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | 14879.9 | 1.78688 | 0.893440 | − | 0.449183i | \(-0.148285\pi\) | ||||
0.893440 | + | 0.449183i | \(0.148285\pi\) | |||||||
\(38\) | 910.451 | 0.102282 | ||||||||
\(39\) | 10541.4 | 1.10978 | ||||||||
\(40\) | −1147.98 | −0.113445 | ||||||||
\(41\) | −6233.02 | −0.579081 | −0.289540 | − | 0.957166i | \(-0.593502\pi\) | ||||
−0.289540 | + | 0.957166i | \(0.593502\pi\) | |||||||
\(42\) | 6373.99 | 0.557555 | ||||||||
\(43\) | 1391.12 | 0.114734 | 0.0573671 | − | 0.998353i | \(-0.481729\pi\) | ||||
0.0573671 | + | 0.998353i | \(0.481729\pi\) | |||||||
\(44\) | 2065.19 | 0.160816 | ||||||||
\(45\) | 1452.92 | 0.106957 | ||||||||
\(46\) | 13459.8 | 0.937875 | ||||||||
\(47\) | −2197.52 | −0.145107 | −0.0725536 | − | 0.997365i | \(-0.523115\pi\) | ||||
−0.0725536 | + | 0.997365i | \(0.523115\pi\) | |||||||
\(48\) | −2304.00 | −0.144338 | ||||||||
\(49\) | 14541.5 | 0.865208 | ||||||||
\(50\) | 11213.0 | 0.634304 | ||||||||
\(51\) | −6808.27 | −0.366532 | ||||||||
\(52\) | −18740.3 | −0.961100 | ||||||||
\(53\) | −25356.1 | −1.23992 | −0.619960 | − | 0.784634i | \(-0.712851\pi\) | ||||
−0.619960 | + | 0.784634i | \(0.712851\pi\) | |||||||
\(54\) | 2916.00 | 0.136083 | ||||||||
\(55\) | 2315.24 | 0.103202 | ||||||||
\(56\) | −11331.5 | −0.482857 | ||||||||
\(57\) | 2048.51 | 0.0835126 | ||||||||
\(58\) | 1800.00 | 0.0702590 | ||||||||
\(59\) | −3481.00 | −0.130189 | ||||||||
\(60\) | −2582.97 | −0.0926276 | ||||||||
\(61\) | −46047.3 | −1.58445 | −0.792226 | − | 0.610227i | \(-0.791078\pi\) | ||||
−0.792226 | + | 0.610227i | \(0.791078\pi\) | |||||||
\(62\) | −18460.3 | −0.609901 | ||||||||
\(63\) | 14341.5 | 0.455242 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −21009.4 | −0.616779 | ||||||||
\(66\) | 4646.67 | 0.131305 | ||||||||
\(67\) | 57443.2 | 1.56333 | 0.781667 | − | 0.623696i | \(-0.214370\pi\) | ||||
0.781667 | + | 0.623696i | \(0.214370\pi\) | |||||||
\(68\) | 12103.6 | 0.317426 | ||||||||
\(69\) | 30284.6 | 0.765771 | ||||||||
\(70\) | −12703.5 | −0.309870 | ||||||||
\(71\) | −40949.1 | −0.964048 | −0.482024 | − | 0.876158i | \(-0.660098\pi\) | ||||
−0.482024 | + | 0.876158i | \(0.660098\pi\) | |||||||
\(72\) | −5184.00 | −0.117851 | ||||||||
\(73\) | 30257.8 | 0.664553 | 0.332277 | − | 0.943182i | \(-0.392183\pi\) | ||||
0.332277 | + | 0.943182i | \(0.392183\pi\) | |||||||
\(74\) | −59519.5 | −1.26351 | ||||||||
\(75\) | 25229.3 | 0.517907 | ||||||||
\(76\) | −3641.80 | −0.0723240 | ||||||||
\(77\) | 22853.3 | 0.439260 | ||||||||
\(78\) | −42165.7 | −0.784734 | ||||||||
\(79\) | 10832.9 | 0.195288 | 0.0976441 | − | 0.995221i | \(-0.468869\pi\) | ||||
0.0976441 | + | 0.995221i | \(0.468869\pi\) | |||||||
\(80\) | 4591.94 | 0.0802179 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 24932.1 | 0.409472 | ||||||||
\(83\) | 69109.5 | 1.10114 | 0.550570 | − | 0.834789i | \(-0.314410\pi\) | ||||
0.550570 | + | 0.834789i | \(0.314410\pi\) | |||||||
\(84\) | −25495.9 | −0.394251 | ||||||||
\(85\) | 13569.1 | 0.203706 | ||||||||
\(86\) | −5564.47 | −0.0811293 | ||||||||
\(87\) | 4050.00 | 0.0573663 | ||||||||
\(88\) | −8260.75 | −0.113714 | ||||||||
\(89\) | −104198. | −1.39440 | −0.697198 | − | 0.716879i | \(-0.745570\pi\) | ||||
−0.697198 | + | 0.716879i | \(0.745570\pi\) | |||||||
\(90\) | −5811.67 | −0.0756301 | ||||||||
\(91\) | −207379. | −2.62520 | ||||||||
\(92\) | −53839.3 | −0.663177 | ||||||||
\(93\) | −41535.7 | −0.497982 | ||||||||
\(94\) | 8790.10 | 0.102606 | ||||||||
\(95\) | −4082.75 | −0.0464134 | ||||||||
\(96\) | 9216.00 | 0.102062 | ||||||||
\(97\) | −141345. | −1.52528 | −0.762641 | − | 0.646822i | \(-0.776098\pi\) | ||||
−0.762641 | + | 0.646822i | \(0.776098\pi\) | |||||||
\(98\) | −58166.2 | −0.611794 | ||||||||
\(99\) | 10455.0 | 0.107210 | ||||||||
\(100\) | −44852.1 | −0.448521 | ||||||||
\(101\) | −152774. | −1.49020 | −0.745101 | − | 0.666951i | \(-0.767599\pi\) | ||||
−0.745101 | + | 0.666951i | \(0.767599\pi\) | |||||||
\(102\) | 27233.1 | 0.259177 | ||||||||
\(103\) | 1917.32 | 0.0178074 | 0.00890372 | − | 0.999960i | \(-0.497166\pi\) | ||||
0.00890372 | + | 0.999960i | \(0.497166\pi\) | |||||||
\(104\) | 74961.2 | 0.679600 | ||||||||
\(105\) | −28583.0 | −0.253008 | ||||||||
\(106\) | 101425. | 0.876756 | ||||||||
\(107\) | −51979.6 | −0.438908 | −0.219454 | − | 0.975623i | \(-0.570428\pi\) | ||||
−0.219454 | + | 0.975623i | \(0.570428\pi\) | |||||||
\(108\) | −11664.0 | −0.0962250 | ||||||||
\(109\) | 38295.1 | 0.308729 | 0.154364 | − | 0.988014i | \(-0.450667\pi\) | ||||
0.154364 | + | 0.988014i | \(0.450667\pi\) | |||||||
\(110\) | −9260.96 | −0.0729750 | ||||||||
\(111\) | −133919. | −1.03166 | ||||||||
\(112\) | 45326.1 | 0.341432 | ||||||||
\(113\) | 81004.0 | 0.596775 | 0.298387 | − | 0.954445i | \(-0.403551\pi\) | ||||
0.298387 | + | 0.954445i | \(0.403551\pi\) | |||||||
\(114\) | −8194.06 | −0.0590523 | ||||||||
\(115\) | −60358.1 | −0.425589 | ||||||||
\(116\) | −7199.99 | −0.0496806 | ||||||||
\(117\) | −94872.8 | −0.640733 | ||||||||
\(118\) | 13924.0 | 0.0920575 | ||||||||
\(119\) | 133938. | 0.867033 | ||||||||
\(120\) | 10331.9 | 0.0654976 | ||||||||
\(121\) | −144391. | −0.896553 | ||||||||
\(122\) | 184189. | 1.12038 | ||||||||
\(123\) | 56097.2 | 0.334332 | ||||||||
\(124\) | 73841.2 | 0.431265 | ||||||||
\(125\) | −106337. | −0.608706 | ||||||||
\(126\) | −57365.9 | −0.321905 | ||||||||
\(127\) | −143563. | −0.789828 | −0.394914 | − | 0.918718i | \(-0.629226\pi\) | ||||
−0.394914 | + | 0.918718i | \(0.629226\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | −12520.1 | −0.0662418 | ||||||||
\(130\) | 84037.4 | 0.436128 | ||||||||
\(131\) | 24923.2 | 0.126889 | 0.0634447 | − | 0.997985i | \(-0.479791\pi\) | ||||
0.0634447 | + | 0.997985i | \(0.479791\pi\) | |||||||
\(132\) | −18586.7 | −0.0928469 | ||||||||
\(133\) | −40300.0 | −0.197550 | ||||||||
\(134\) | −229773. | −1.10544 | ||||||||
\(135\) | −13076.3 | −0.0617517 | ||||||||
\(136\) | −48414.4 | −0.224454 | ||||||||
\(137\) | −305691. | −1.39150 | −0.695748 | − | 0.718286i | \(-0.744927\pi\) | ||||
−0.695748 | + | 0.718286i | \(0.744927\pi\) | |||||||
\(138\) | −121138. | −0.541482 | ||||||||
\(139\) | −79638.6 | −0.349612 | −0.174806 | − | 0.984603i | \(-0.555930\pi\) | ||||
−0.174806 | + | 0.984603i | \(0.555930\pi\) | |||||||
\(140\) | 50814.2 | 0.219111 | ||||||||
\(141\) | 19777.7 | 0.0837777 | ||||||||
\(142\) | 163796. | 0.681685 | ||||||||
\(143\) | −151181. | −0.618239 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | −8071.76 | −0.0318822 | ||||||||
\(146\) | −121031. | −0.469910 | ||||||||
\(147\) | −130874. | −0.499528 | ||||||||
\(148\) | 238078. | 0.893440 | ||||||||
\(149\) | −36015.6 | −0.132900 | −0.0664500 | − | 0.997790i | \(-0.521167\pi\) | ||||
−0.0664500 | + | 0.997790i | \(0.521167\pi\) | |||||||
\(150\) | −100917. | −0.366216 | ||||||||
\(151\) | −115452. | −0.412060 | −0.206030 | − | 0.978546i | \(-0.566054\pi\) | ||||
−0.206030 | + | 0.978546i | \(0.566054\pi\) | |||||||
\(152\) | 14567.2 | 0.0511408 | ||||||||
\(153\) | 61274.5 | 0.211617 | ||||||||
\(154\) | −91413.1 | −0.310604 | ||||||||
\(155\) | 82781.8 | 0.276761 | ||||||||
\(156\) | 168663. | 0.554891 | ||||||||
\(157\) | 241308. | 0.781310 | 0.390655 | − | 0.920537i | \(-0.372249\pi\) | ||||
0.390655 | + | 0.920537i | \(0.372249\pi\) | |||||||
\(158\) | −43331.5 | −0.138090 | ||||||||
\(159\) | 228205. | 0.715868 | ||||||||
\(160\) | −18367.8 | −0.0567226 | ||||||||
\(161\) | −595783. | −1.81144 | ||||||||
\(162\) | −26244.0 | −0.0785674 | ||||||||
\(163\) | −466745. | −1.37598 | −0.687988 | − | 0.725722i | \(-0.741506\pi\) | ||||
−0.687988 | + | 0.725722i | \(0.741506\pi\) | |||||||
\(164\) | −99728.4 | −0.289540 | ||||||||
\(165\) | −20837.1 | −0.0595838 | ||||||||
\(166\) | −276438. | −0.778623 | ||||||||
\(167\) | −510227. | −1.41570 | −0.707852 | − | 0.706361i | \(-0.750335\pi\) | ||||
−0.707852 | + | 0.706361i | \(0.750335\pi\) | |||||||
\(168\) | 101984. | 0.278778 | ||||||||
\(169\) | 1.00058e6 | 2.69485 | ||||||||
\(170\) | −54276.3 | −0.144042 | ||||||||
\(171\) | −18436.6 | −0.0482160 | ||||||||
\(172\) | 22257.9 | 0.0573671 | ||||||||
\(173\) | −469483. | −1.19263 | −0.596313 | − | 0.802752i | \(-0.703368\pi\) | ||||
−0.596313 | + | 0.802752i | \(0.703368\pi\) | |||||||
\(174\) | −16200.0 | −0.0405641 | ||||||||
\(175\) | −496331. | −1.22511 | ||||||||
\(176\) | 33043.0 | 0.0804078 | ||||||||
\(177\) | 31329.0 | 0.0751646 | ||||||||
\(178\) | 416794. | 0.985987 | ||||||||
\(179\) | 51292.9 | 0.119653 | 0.0598266 | − | 0.998209i | \(-0.480945\pi\) | ||||
0.0598266 | + | 0.998209i | \(0.480945\pi\) | |||||||
\(180\) | 23246.7 | 0.0534786 | ||||||||
\(181\) | 612199. | 1.38898 | 0.694491 | − | 0.719502i | \(-0.255630\pi\) | ||||
0.694491 | + | 0.719502i | \(0.255630\pi\) | |||||||
\(182\) | 829517. | 1.85629 | ||||||||
\(183\) | 414425. | 0.914784 | ||||||||
\(184\) | 215357. | 0.468937 | ||||||||
\(185\) | 266904. | 0.573359 | ||||||||
\(186\) | 166143. | 0.352127 | ||||||||
\(187\) | 97641.5 | 0.204188 | ||||||||
\(188\) | −35160.4 | −0.0725536 | ||||||||
\(189\) | −129073. | −0.262834 | ||||||||
\(190\) | 16331.0 | 0.0328192 | ||||||||
\(191\) | −676635. | −1.34206 | −0.671029 | − | 0.741431i | \(-0.734147\pi\) | ||||
−0.671029 | + | 0.741431i | \(0.734147\pi\) | |||||||
\(192\) | −36864.0 | −0.0721688 | ||||||||
\(193\) | 659804. | 1.27503 | 0.637517 | − | 0.770436i | \(-0.279961\pi\) | ||||
0.637517 | + | 0.770436i | \(0.279961\pi\) | |||||||
\(194\) | 565379. | 1.07854 | ||||||||
\(195\) | 189084. | 0.356097 | ||||||||
\(196\) | 232665. | 0.432604 | ||||||||
\(197\) | −87290.0 | −0.160250 | −0.0801252 | − | 0.996785i | \(-0.525532\pi\) | ||||
−0.0801252 | + | 0.996785i | \(0.525532\pi\) | |||||||
\(198\) | −41820.1 | −0.0758092 | ||||||||
\(199\) | −73397.9 | −0.131387 | −0.0656933 | − | 0.997840i | \(-0.520926\pi\) | ||||
−0.0656933 | + | 0.997840i | \(0.520926\pi\) | |||||||
\(200\) | 179408. | 0.317152 | ||||||||
\(201\) | −516989. | −0.902592 | ||||||||
\(202\) | 611095. | 1.05373 | ||||||||
\(203\) | −79674.8 | −0.135700 | ||||||||
\(204\) | −108932. | −0.183266 | ||||||||
\(205\) | −111803. | −0.185811 | ||||||||
\(206\) | −7669.28 | −0.0125918 | ||||||||
\(207\) | −272561. | −0.442118 | ||||||||
\(208\) | −299845. | −0.480550 | ||||||||
\(209\) | −29378.9 | −0.0465233 | ||||||||
\(210\) | 114332. | 0.178904 | ||||||||
\(211\) | 792977. | 1.22618 | 0.613090 | − | 0.790013i | \(-0.289926\pi\) | ||||
0.613090 | + | 0.790013i | \(0.289926\pi\) | |||||||
\(212\) | −405698. | −0.619960 | ||||||||
\(213\) | 368542. | 0.556593 | ||||||||
\(214\) | 207919. | 0.310355 | ||||||||
\(215\) | 24952.8 | 0.0368149 | ||||||||
\(216\) | 46656.0 | 0.0680414 | ||||||||
\(217\) | 817123. | 1.17798 | ||||||||
\(218\) | −153180. | −0.218304 | ||||||||
\(219\) | −272320. | −0.383680 | ||||||||
\(220\) | 37043.8 | 0.0516011 | ||||||||
\(221\) | −886036. | −1.22031 | ||||||||
\(222\) | 535676. | 0.729490 | ||||||||
\(223\) | −283956. | −0.382375 | −0.191187 | − | 0.981554i | \(-0.561234\pi\) | ||||
−0.191187 | + | 0.981554i | \(0.561234\pi\) | |||||||
\(224\) | −181305. | −0.241429 | ||||||||
\(225\) | −227064. | −0.299014 | ||||||||
\(226\) | −324016. | −0.421984 | ||||||||
\(227\) | 892072. | 1.14904 | 0.574520 | − | 0.818490i | \(-0.305189\pi\) | ||||
0.574520 | + | 0.818490i | \(0.305189\pi\) | |||||||
\(228\) | 32776.2 | 0.0417563 | ||||||||
\(229\) | −48604.0 | −0.0612467 | −0.0306234 | − | 0.999531i | \(-0.509749\pi\) | ||||
−0.0306234 | + | 0.999531i | \(0.509749\pi\) | |||||||
\(230\) | 241432. | 0.300937 | ||||||||
\(231\) | −205679. | −0.253607 | ||||||||
\(232\) | 28800.0 | 0.0351295 | ||||||||
\(233\) | 114970. | 0.138738 | 0.0693689 | − | 0.997591i | \(-0.477901\pi\) | ||||
0.0693689 | + | 0.997591i | \(0.477901\pi\) | |||||||
\(234\) | 379491. | 0.453067 | ||||||||
\(235\) | −39417.6 | −0.0465608 | ||||||||
\(236\) | −55696.0 | −0.0650945 | ||||||||
\(237\) | −97495.9 | −0.112750 | ||||||||
\(238\) | −535751. | −0.613085 | ||||||||
\(239\) | −1.47234e6 | −1.66729 | −0.833647 | − | 0.552298i | \(-0.813751\pi\) | ||||
−0.833647 | + | 0.552298i | \(0.813751\pi\) | |||||||
\(240\) | −41327.4 | −0.0463138 | ||||||||
\(241\) | 416424. | 0.461842 | 0.230921 | − | 0.972973i | \(-0.425826\pi\) | ||||
0.230921 | + | 0.972973i | \(0.425826\pi\) | |||||||
\(242\) | 577563. | 0.633959 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | −736756. | −0.792226 | ||||||||
\(245\) | 260835. | 0.277620 | ||||||||
\(246\) | −224389. | −0.236409 | ||||||||
\(247\) | 266596. | 0.278042 | ||||||||
\(248\) | −295365. | −0.304951 | ||||||||
\(249\) | −621985. | −0.635743 | ||||||||
\(250\) | 425347. | 0.430420 | ||||||||
\(251\) | −269053. | −0.269559 | −0.134779 | − | 0.990876i | \(-0.543033\pi\) | ||||
−0.134779 | + | 0.990876i | \(0.543033\pi\) | |||||||
\(252\) | 229464. | 0.227621 | ||||||||
\(253\) | −434329. | −0.426597 | ||||||||
\(254\) | 574251. | 0.558493 | ||||||||
\(255\) | −122122. | −0.117610 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 1.10658e6 | 1.04508 | 0.522542 | − | 0.852613i | \(-0.324984\pi\) | ||||
0.522542 | + | 0.852613i | \(0.324984\pi\) | |||||||
\(258\) | 50080.2 | 0.0468400 | ||||||||
\(259\) | 2.63456e6 | 2.44039 | ||||||||
\(260\) | −336150. | −0.308389 | ||||||||
\(261\) | −36450.0 | −0.0331204 | ||||||||
\(262\) | −99692.8 | −0.0897244 | ||||||||
\(263\) | −1.13388e6 | −1.01083 | −0.505416 | − | 0.862876i | \(-0.668661\pi\) | ||||
−0.505416 | + | 0.862876i | \(0.668661\pi\) | |||||||
\(264\) | 74346.8 | 0.0656527 | ||||||||
\(265\) | −454820. | −0.397855 | ||||||||
\(266\) | 161200. | 0.139689 | ||||||||
\(267\) | 937786. | 0.805055 | ||||||||
\(268\) | 919092. | 0.781667 | ||||||||
\(269\) | 1.86128e6 | 1.56831 | 0.784155 | − | 0.620566i | \(-0.213097\pi\) | ||||
0.784155 | + | 0.620566i | \(0.213097\pi\) | |||||||
\(270\) | 52305.0 | 0.0436651 | ||||||||
\(271\) | −2.26306e6 | −1.87186 | −0.935928 | − | 0.352191i | \(-0.885437\pi\) | ||||
−0.935928 | + | 0.352191i | \(0.885437\pi\) | |||||||
\(272\) | 193658. | 0.158713 | ||||||||
\(273\) | 1.86641e6 | 1.51566 | ||||||||
\(274\) | 1.22277e6 | 0.983936 | ||||||||
\(275\) | −361828. | −0.288516 | ||||||||
\(276\) | 484554. | 0.382886 | ||||||||
\(277\) | 347075. | 0.271784 | 0.135892 | − | 0.990724i | \(-0.456610\pi\) | ||||
0.135892 | + | 0.990724i | \(0.456610\pi\) | |||||||
\(278\) | 318554. | 0.247213 | ||||||||
\(279\) | 373821. | 0.287510 | ||||||||
\(280\) | −203257. | −0.154935 | ||||||||
\(281\) | −216216. | −0.163351 | −0.0816754 | − | 0.996659i | \(-0.526027\pi\) | ||||
−0.0816754 | + | 0.996659i | \(0.526027\pi\) | |||||||
\(282\) | −79110.9 | −0.0592398 | ||||||||
\(283\) | −329179. | −0.244324 | −0.122162 | − | 0.992510i | \(-0.538983\pi\) | ||||
−0.122162 | + | 0.992510i | \(0.538983\pi\) | |||||||
\(284\) | −655186. | −0.482024 | ||||||||
\(285\) | 36744.7 | 0.0267968 | ||||||||
\(286\) | 604723. | 0.437161 | ||||||||
\(287\) | −1.10359e6 | −0.790866 | ||||||||
\(288\) | −82944.0 | −0.0589256 | ||||||||
\(289\) | −847603. | −0.596963 | ||||||||
\(290\) | 32287.0 | 0.0225441 | ||||||||
\(291\) | 1.27210e6 | 0.880622 | ||||||||
\(292\) | 484124. | 0.332277 | ||||||||
\(293\) | 1.93740e6 | 1.31841 | 0.659205 | − | 0.751963i | \(-0.270893\pi\) | ||||
0.659205 | + | 0.751963i | \(0.270893\pi\) | |||||||
\(294\) | 523496. | 0.353220 | ||||||||
\(295\) | −62439.6 | −0.0417739 | ||||||||
\(296\) | −952313. | −0.631757 | ||||||||
\(297\) | −94095.1 | −0.0618979 | ||||||||
\(298\) | 144062. | 0.0939745 | ||||||||
\(299\) | 3.94127e6 | 2.54952 | ||||||||
\(300\) | 403669. | 0.258954 | ||||||||
\(301\) | 246305. | 0.156695 | ||||||||
\(302\) | 461810. | 0.291371 | ||||||||
\(303\) | 1.37496e6 | 0.860369 | ||||||||
\(304\) | −58268.9 | −0.0361620 | ||||||||
\(305\) | −825962. | −0.508406 | ||||||||
\(306\) | −245098. | −0.149636 | ||||||||
\(307\) | −2.12186e6 | −1.28490 | −0.642452 | − | 0.766326i | \(-0.722083\pi\) | ||||
−0.642452 | + | 0.766326i | \(0.722083\pi\) | |||||||
\(308\) | 365652. | 0.219630 | ||||||||
\(309\) | −17255.9 | −0.0102811 | ||||||||
\(310\) | −331127. | −0.195700 | ||||||||
\(311\) | −1.86690e6 | −1.09451 | −0.547254 | − | 0.836967i | \(-0.684327\pi\) | ||||
−0.547254 | + | 0.836967i | \(0.684327\pi\) | |||||||
\(312\) | −674651. | −0.392367 | ||||||||
\(313\) | −1.91650e6 | −1.10573 | −0.552863 | − | 0.833272i | \(-0.686465\pi\) | ||||
−0.552863 | + | 0.833272i | \(0.686465\pi\) | |||||||
\(314\) | −965234. | −0.552470 | ||||||||
\(315\) | 257247. | 0.146074 | ||||||||
\(316\) | 173326. | 0.0976441 | ||||||||
\(317\) | −3.26042e6 | −1.82232 | −0.911162 | − | 0.412048i | \(-0.864814\pi\) | ||||
−0.911162 | + | 0.412048i | \(0.864814\pi\) | |||||||
\(318\) | −912821. | −0.506195 | ||||||||
\(319\) | −58083.4 | −0.0319577 | ||||||||
\(320\) | 73471.0 | 0.0401089 | ||||||||
\(321\) | 467817. | 0.253404 | ||||||||
\(322\) | 2.38313e6 | 1.28088 | ||||||||
\(323\) | −172183. | −0.0918300 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | 3.28337e6 | 1.72429 | ||||||||
\(326\) | 1.86698e6 | 0.972961 | ||||||||
\(327\) | −344656. | −0.178245 | ||||||||
\(328\) | 398914. | 0.204736 | ||||||||
\(329\) | −389083. | −0.198177 | ||||||||
\(330\) | 83348.6 | 0.0421321 | ||||||||
\(331\) | −482525. | −0.242075 | −0.121037 | − | 0.992648i | \(-0.538622\pi\) | ||||
−0.121037 | + | 0.992648i | \(0.538622\pi\) | |||||||
\(332\) | 1.10575e6 | 0.550570 | ||||||||
\(333\) | 1.20527e6 | 0.595626 | ||||||||
\(334\) | 2.04091e6 | 1.00105 | ||||||||
\(335\) | 1.03037e6 | 0.501629 | ||||||||
\(336\) | −407935. | −0.197126 | ||||||||
\(337\) | 301253. | 0.144496 | 0.0722482 | − | 0.997387i | \(-0.476983\pi\) | ||||
0.0722482 | + | 0.997387i | \(0.476983\pi\) | |||||||
\(338\) | −4.00231e6 | −1.90555 | ||||||||
\(339\) | −729036. | −0.344548 | ||||||||
\(340\) | 217105. | 0.101853 | ||||||||
\(341\) | 595687. | 0.277417 | ||||||||
\(342\) | 73746.5 | 0.0340939 | ||||||||
\(343\) | −401111. | −0.184089 | ||||||||
\(344\) | −89031.5 | −0.0405646 | ||||||||
\(345\) | 543223. | 0.245714 | ||||||||
\(346\) | 1.87793e6 | 0.843314 | ||||||||
\(347\) | 51889.7 | 0.0231343 | 0.0115672 | − | 0.999933i | \(-0.496318\pi\) | ||||
0.0115672 | + | 0.999933i | \(0.496318\pi\) | |||||||
\(348\) | 64799.9 | 0.0286831 | ||||||||
\(349\) | 3.68029e6 | 1.61740 | 0.808702 | − | 0.588218i | \(-0.200170\pi\) | ||||
0.808702 | + | 0.588218i | \(0.200170\pi\) | |||||||
\(350\) | 1.98532e6 | 0.866286 | ||||||||
\(351\) | 853855. | 0.369927 | ||||||||
\(352\) | −132172. | −0.0568569 | ||||||||
\(353\) | −2.00577e6 | −0.856732 | −0.428366 | − | 0.903605i | \(-0.640911\pi\) | ||||
−0.428366 | + | 0.903605i | \(0.640911\pi\) | |||||||
\(354\) | −125316. | −0.0531494 | ||||||||
\(355\) | −734515. | −0.309336 | ||||||||
\(356\) | −1.66717e6 | −0.697198 | ||||||||
\(357\) | −1.20544e6 | −0.500582 | ||||||||
\(358\) | −205171. | −0.0846076 | ||||||||
\(359\) | −97002.9 | −0.0397236 | −0.0198618 | − | 0.999803i | \(-0.506323\pi\) | ||||
−0.0198618 | + | 0.999803i | \(0.506323\pi\) | |||||||
\(360\) | −92986.7 | −0.0378151 | ||||||||
\(361\) | −2.42429e6 | −0.979077 | ||||||||
\(362\) | −2.44880e6 | −0.982158 | ||||||||
\(363\) | 1.29952e6 | 0.517625 | ||||||||
\(364\) | −3.31807e6 | −1.31260 | ||||||||
\(365\) | 542742. | 0.213236 | ||||||||
\(366\) | −1.65770e6 | −0.646850 | ||||||||
\(367\) | 709483. | 0.274965 | 0.137482 | − | 0.990504i | \(-0.456099\pi\) | ||||
0.137482 | + | 0.990504i | \(0.456099\pi\) | |||||||
\(368\) | −861429. | −0.331589 | ||||||||
\(369\) | −504875. | −0.193027 | ||||||||
\(370\) | −1.06762e6 | −0.405426 | ||||||||
\(371\) | −4.48944e6 | −1.69339 | ||||||||
\(372\) | −664571. | −0.248991 | ||||||||
\(373\) | 4.77061e6 | 1.77542 | 0.887712 | − | 0.460399i | \(-0.152294\pi\) | ||||
0.887712 | + | 0.460399i | \(0.152294\pi\) | |||||||
\(374\) | −390566. | −0.144383 | ||||||||
\(375\) | 957030. | 0.351437 | ||||||||
\(376\) | 140642. | 0.0513031 | ||||||||
\(377\) | 527071. | 0.190992 | ||||||||
\(378\) | 516293. | 0.185852 | ||||||||
\(379\) | −2.21714e6 | −0.792856 | −0.396428 | − | 0.918066i | \(-0.629750\pi\) | ||||
−0.396428 | + | 0.918066i | \(0.629750\pi\) | |||||||
\(380\) | −65324.0 | −0.0232067 | ||||||||
\(381\) | 1.29207e6 | 0.456008 | ||||||||
\(382\) | 2.70654e6 | 0.948978 | ||||||||
\(383\) | −1.42655e6 | −0.496924 | −0.248462 | − | 0.968642i | \(-0.579925\pi\) | ||||
−0.248462 | + | 0.968642i | \(0.579925\pi\) | |||||||
\(384\) | 147456. | 0.0510310 | ||||||||
\(385\) | 409925. | 0.140946 | ||||||||
\(386\) | −2.63922e6 | −0.901586 | ||||||||
\(387\) | 112680. | 0.0382447 | ||||||||
\(388\) | −2.26151e6 | −0.762641 | ||||||||
\(389\) | −964763. | −0.323256 | −0.161628 | − | 0.986852i | \(-0.551674\pi\) | ||||
−0.161628 | + | 0.986852i | \(0.551674\pi\) | |||||||
\(390\) | −756337. | −0.251799 | ||||||||
\(391\) | −2.54550e6 | −0.842039 | ||||||||
\(392\) | −930659. | −0.305897 | ||||||||
\(393\) | −224309. | −0.0732597 | ||||||||
\(394\) | 349160. | 0.113314 | ||||||||
\(395\) | 194312. | 0.0626624 | ||||||||
\(396\) | 167280. | 0.0536052 | ||||||||
\(397\) | −1.06320e6 | −0.338563 | −0.169282 | − | 0.985568i | \(-0.554145\pi\) | ||||
−0.169282 | + | 0.985568i | \(0.554145\pi\) | |||||||
\(398\) | 293592. | 0.0929043 | ||||||||
\(399\) | 362700. | 0.114055 | ||||||||
\(400\) | −717633. | −0.224260 | ||||||||
\(401\) | 1.80506e6 | 0.560571 | 0.280286 | − | 0.959917i | \(-0.409571\pi\) | ||||
0.280286 | + | 0.959917i | \(0.409571\pi\) | |||||||
\(402\) | 2.06796e6 | 0.638229 | ||||||||
\(403\) | −5.40549e6 | −1.65796 | ||||||||
\(404\) | −2.44438e6 | −0.745101 | ||||||||
\(405\) | 117686. | 0.0356524 | ||||||||
\(406\) | 318699. | 0.0959546 | ||||||||
\(407\) | 1.92061e6 | 0.574716 | ||||||||
\(408\) | 435730. | 0.129589 | ||||||||
\(409\) | 7056.72 | 0.00208590 | 0.00104295 | − | 0.999999i | \(-0.499668\pi\) | ||||
0.00104295 | + | 0.999999i | \(0.499668\pi\) | |||||||
\(410\) | 447214. | 0.131388 | ||||||||
\(411\) | 2.75122e6 | 0.803380 | ||||||||
\(412\) | 30677.1 | 0.00890372 | ||||||||
\(413\) | −616329. | −0.177802 | ||||||||
\(414\) | 1.09025e6 | 0.312625 | ||||||||
\(415\) | 1.23963e6 | 0.353324 | ||||||||
\(416\) | 1.19938e6 | 0.339800 | ||||||||
\(417\) | 716747. | 0.201849 | ||||||||
\(418\) | 117516. | 0.0328969 | ||||||||
\(419\) | −7.14594e6 | −1.98850 | −0.994248 | − | 0.107106i | \(-0.965842\pi\) | ||||
−0.994248 | + | 0.107106i | \(0.965842\pi\) | |||||||
\(420\) | −457327. | −0.126504 | ||||||||
\(421\) | −2.22390e6 | −0.611520 | −0.305760 | − | 0.952109i | \(-0.598911\pi\) | ||||
−0.305760 | + | 0.952109i | \(0.598911\pi\) | |||||||
\(422\) | −3.17191e6 | −0.867041 | ||||||||
\(423\) | −177999. | −0.0483691 | ||||||||
\(424\) | 1.62279e6 | 0.438378 | ||||||||
\(425\) | −2.12059e6 | −0.569488 | ||||||||
\(426\) | −1.47417e6 | −0.393571 | ||||||||
\(427\) | −8.15291e6 | −2.16393 | ||||||||
\(428\) | −831674. | −0.219454 | ||||||||
\(429\) | 1.36063e6 | 0.356940 | ||||||||
\(430\) | −99811.3 | −0.0260321 | ||||||||
\(431\) | 3.77074e6 | 0.977762 | 0.488881 | − | 0.872350i | \(-0.337405\pi\) | ||||
0.488881 | + | 0.872350i | \(0.337405\pi\) | |||||||
\(432\) | −186624. | −0.0481125 | ||||||||
\(433\) | −1.45537e6 | −0.373039 | −0.186519 | − | 0.982451i | \(-0.559721\pi\) | ||||
−0.186519 | + | 0.982451i | \(0.559721\pi\) | |||||||
\(434\) | −3.26849e6 | −0.832958 | ||||||||
\(435\) | 72645.8 | 0.0184072 | ||||||||
\(436\) | 612722. | 0.154364 | ||||||||
\(437\) | 765907. | 0.191855 | ||||||||
\(438\) | 1.08928e6 | 0.271303 | ||||||||
\(439\) | −4.42056e6 | −1.09475 | −0.547376 | − | 0.836887i | \(-0.684373\pi\) | ||||
−0.547376 | + | 0.836887i | \(0.684373\pi\) | |||||||
\(440\) | −148175. | −0.0364875 | ||||||||
\(441\) | 1.17787e6 | 0.288403 | ||||||||
\(442\) | 3.54414e6 | 0.862890 | ||||||||
\(443\) | 3.26090e6 | 0.789457 | 0.394729 | − | 0.918798i | \(-0.370839\pi\) | ||||
0.394729 | + | 0.918798i | \(0.370839\pi\) | |||||||
\(444\) | −2.14270e6 | −0.515828 | ||||||||
\(445\) | −1.86903e6 | −0.447422 | ||||||||
\(446\) | 1.13583e6 | 0.270380 | ||||||||
\(447\) | 324140. | 0.0767298 | ||||||||
\(448\) | 725218. | 0.170716 | ||||||||
\(449\) | 3.60837e6 | 0.844685 | 0.422343 | − | 0.906436i | \(-0.361208\pi\) | ||||
0.422343 | + | 0.906436i | \(0.361208\pi\) | |||||||
\(450\) | 908255. | 0.211435 | ||||||||
\(451\) | −804523. | −0.186250 | ||||||||
\(452\) | 1.29606e6 | 0.298387 | ||||||||
\(453\) | 1.03907e6 | 0.237903 | ||||||||
\(454\) | −3.56829e6 | −0.812494 | ||||||||
\(455\) | −3.71982e6 | −0.842351 | ||||||||
\(456\) | −131105. | −0.0295262 | ||||||||
\(457\) | 5.22448e6 | 1.17018 | 0.585090 | − | 0.810968i | \(-0.301059\pi\) | ||||
0.585090 | + | 0.810968i | \(0.301059\pi\) | |||||||
\(458\) | 194416. | 0.0433080 | ||||||||
\(459\) | −551470. | −0.122177 | ||||||||
\(460\) | −965729. | −0.212795 | ||||||||
\(461\) | −4.26501e6 | −0.934691 | −0.467346 | − | 0.884075i | \(-0.654790\pi\) | ||||
−0.467346 | + | 0.884075i | \(0.654790\pi\) | |||||||
\(462\) | 822718. | 0.179327 | ||||||||
\(463\) | 3.88520e6 | 0.842288 | 0.421144 | − | 0.906994i | \(-0.361629\pi\) | ||||
0.421144 | + | 0.906994i | \(0.361629\pi\) | |||||||
\(464\) | −115200. | −0.0248403 | ||||||||
\(465\) | −745036. | −0.159788 | ||||||||
\(466\) | −459880. | −0.0981024 | ||||||||
\(467\) | 2.26688e6 | 0.480991 | 0.240495 | − | 0.970650i | \(-0.422690\pi\) | ||||
0.240495 | + | 0.970650i | \(0.422690\pi\) | |||||||
\(468\) | −1.51796e6 | −0.320367 | ||||||||
\(469\) | 1.01706e7 | 2.13509 | ||||||||
\(470\) | 157670. | 0.0329234 | ||||||||
\(471\) | −2.17178e6 | −0.451089 | ||||||||
\(472\) | 222784. | 0.0460287 | ||||||||
\(473\) | 179557. | 0.0369021 | ||||||||
\(474\) | 389983. | 0.0797261 | ||||||||
\(475\) | 638056. | 0.129755 | ||||||||
\(476\) | 2.14301e6 | 0.433517 | ||||||||
\(477\) | −2.05385e6 | −0.413307 | ||||||||
\(478\) | 5.88934e6 | 1.17895 | ||||||||
\(479\) | −9.60722e6 | −1.91319 | −0.956597 | − | 0.291414i | \(-0.905874\pi\) | ||||
−0.956597 | + | 0.291414i | \(0.905874\pi\) | |||||||
\(480\) | 165310. | 0.0327488 | ||||||||
\(481\) | −1.74283e7 | −3.43474 | ||||||||
\(482\) | −1.66570e6 | −0.326571 | ||||||||
\(483\) | 5.36205e6 | 1.04583 | ||||||||
\(484\) | −2.31025e6 | −0.448277 | ||||||||
\(485\) | −2.53534e6 | −0.489419 | ||||||||
\(486\) | 236196. | 0.0453609 | ||||||||
\(487\) | 9.02101e6 | 1.72358 | 0.861792 | − | 0.507262i | \(-0.169342\pi\) | ||||
0.861792 | + | 0.507262i | \(0.169342\pi\) | |||||||
\(488\) | 2.94703e6 | 0.560189 | ||||||||
\(489\) | 4.20070e6 | 0.794420 | ||||||||
\(490\) | −1.04334e6 | −0.196307 | ||||||||
\(491\) | 4.09612e6 | 0.766777 | 0.383388 | − | 0.923587i | \(-0.374757\pi\) | ||||
0.383388 | + | 0.923587i | \(0.374757\pi\) | |||||||
\(492\) | 897556. | 0.167166 | ||||||||
\(493\) | −340413. | −0.0630797 | ||||||||
\(494\) | −1.06638e6 | −0.196606 | ||||||||
\(495\) | 187534. | 0.0344007 | ||||||||
\(496\) | 1.18146e6 | 0.215633 | ||||||||
\(497\) | −7.25026e6 | −1.31663 | ||||||||
\(498\) | 2.48794e6 | 0.449538 | ||||||||
\(499\) | 1.07181e6 | 0.192694 | 0.0963470 | − | 0.995348i | \(-0.469284\pi\) | ||||
0.0963470 | + | 0.995348i | \(0.469284\pi\) | |||||||
\(500\) | −1.70139e6 | −0.304353 | ||||||||
\(501\) | 4.59204e6 | 0.817357 | ||||||||
\(502\) | 1.07621e6 | 0.190607 | ||||||||
\(503\) | −3.28877e6 | −0.579580 | −0.289790 | − | 0.957090i | \(-0.593585\pi\) | ||||
−0.289790 | + | 0.957090i | \(0.593585\pi\) | |||||||
\(504\) | −917854. | −0.160952 | ||||||||
\(505\) | −2.74034e6 | −0.478164 | ||||||||
\(506\) | 1.73732e6 | 0.301650 | ||||||||
\(507\) | −9.00521e6 | −1.55587 | ||||||||
\(508\) | −2.29701e6 | −0.394914 | ||||||||
\(509\) | −651077. | −0.111388 | −0.0556939 | − | 0.998448i | \(-0.517737\pi\) | ||||
−0.0556939 | + | 0.998448i | \(0.517737\pi\) | |||||||
\(510\) | 488487. | 0.0831625 | ||||||||
\(511\) | 5.35730e6 | 0.907598 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 165930. | 0.0278375 | ||||||||
\(514\) | −4.42633e6 | −0.738986 | ||||||||
\(515\) | 34391.5 | 0.00571390 | ||||||||
\(516\) | −200321. | −0.0331209 | ||||||||
\(517\) | −283644. | −0.0466710 | ||||||||
\(518\) | −1.05382e7 | −1.72561 | ||||||||
\(519\) | 4.22535e6 | 0.688563 | ||||||||
\(520\) | 1.34460e6 | 0.218064 | ||||||||
\(521\) | 3.75752e6 | 0.606466 | 0.303233 | − | 0.952916i | \(-0.401934\pi\) | ||||
0.303233 | + | 0.952916i | \(0.401934\pi\) | |||||||
\(522\) | 145800. | 0.0234197 | ||||||||
\(523\) | −6.07184e6 | −0.970658 | −0.485329 | − | 0.874332i | \(-0.661300\pi\) | ||||
−0.485329 | + | 0.874332i | \(0.661300\pi\) | |||||||
\(524\) | 398771. | 0.0634447 | ||||||||
\(525\) | 4.46698e6 | 0.707319 | ||||||||
\(526\) | 4.53553e6 | 0.714766 | ||||||||
\(527\) | 3.49119e6 | 0.547579 | ||||||||
\(528\) | −297387. | −0.0464234 | ||||||||
\(529\) | 4.88658e6 | 0.759217 | ||||||||
\(530\) | 1.81928e6 | 0.281326 | ||||||||
\(531\) | −281961. | −0.0433963 | ||||||||
\(532\) | −644800. | −0.0987748 | ||||||||
\(533\) | 7.30055e6 | 1.11311 | ||||||||
\(534\) | −3.75114e6 | −0.569260 | ||||||||
\(535\) | −932372. | −0.140833 | ||||||||
\(536\) | −3.67637e6 | −0.552722 | ||||||||
\(537\) | −461636. | −0.0690818 | ||||||||
\(538\) | −7.44513e6 | −1.10896 | ||||||||
\(539\) | 1.87694e6 | 0.278278 | ||||||||
\(540\) | −209220. | −0.0308759 | ||||||||
\(541\) | −6.37512e6 | −0.936472 | −0.468236 | − | 0.883603i | \(-0.655110\pi\) | ||||
−0.468236 | + | 0.883603i | \(0.655110\pi\) | |||||||
\(542\) | 9.05223e6 | 1.32360 | ||||||||
\(543\) | −5.50979e6 | −0.801929 | ||||||||
\(544\) | −774630. | −0.112227 | ||||||||
\(545\) | 686909. | 0.0990622 | ||||||||
\(546\) | −7.46566e6 | −1.07173 | ||||||||
\(547\) | −3.35311e6 | −0.479158 | −0.239579 | − | 0.970877i | \(-0.577009\pi\) | ||||
−0.239579 | + | 0.970877i | \(0.577009\pi\) | |||||||
\(548\) | −4.89106e6 | −0.695748 | ||||||||
\(549\) | −3.72983e6 | −0.528151 | ||||||||
\(550\) | 1.44731e6 | 0.204012 | ||||||||
\(551\) | 102426. | 0.0143724 | ||||||||
\(552\) | −1.93821e6 | −0.270741 | ||||||||
\(553\) | 1.91802e6 | 0.266710 | ||||||||
\(554\) | −1.38830e6 | −0.192180 | ||||||||
\(555\) | −2.40214e6 | −0.331029 | ||||||||
\(556\) | −1.27422e6 | −0.174806 | ||||||||
\(557\) | 1.41555e7 | 1.93324 | 0.966621 | − | 0.256211i | \(-0.0824742\pi\) | ||||
0.966621 | + | 0.256211i | \(0.0824742\pi\) | |||||||
\(558\) | −1.49528e6 | −0.203300 | ||||||||
\(559\) | −1.62937e6 | −0.220542 | ||||||||
\(560\) | 813027. | 0.109556 | ||||||||
\(561\) | −878773. | −0.117888 | ||||||||
\(562\) | 864863. | 0.115506 | ||||||||
\(563\) | 1.32605e7 | 1.76315 | 0.881575 | − | 0.472045i | \(-0.156484\pi\) | ||||
0.881575 | + | 0.472045i | \(0.156484\pi\) | |||||||
\(564\) | 316443. | 0.0418888 | ||||||||
\(565\) | 1.45299e6 | 0.191488 | ||||||||
\(566\) | 1.31672e6 | 0.172763 | ||||||||
\(567\) | 1.16166e6 | 0.151747 | ||||||||
\(568\) | 2.62074e6 | 0.340843 | ||||||||
\(569\) | −487891. | −0.0631745 | −0.0315872 | − | 0.999501i | \(-0.510056\pi\) | ||||
−0.0315872 | + | 0.999501i | \(0.510056\pi\) | |||||||
\(570\) | −146979. | −0.0189482 | ||||||||
\(571\) | −6.58708e6 | −0.845479 | −0.422739 | − | 0.906251i | \(-0.638931\pi\) | ||||
−0.422739 | + | 0.906251i | \(0.638931\pi\) | |||||||
\(572\) | −2.41889e6 | −0.309119 | ||||||||
\(573\) | 6.08972e6 | 0.774837 | ||||||||
\(574\) | 4.41436e6 | 0.559227 | ||||||||
\(575\) | 9.43283e6 | 1.18980 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | −586957. | −0.0733951 | −0.0366975 | − | 0.999326i | \(-0.511684\pi\) | ||||
−0.0366975 | + | 0.999326i | \(0.511684\pi\) | |||||||
\(578\) | 3.39041e6 | 0.422117 | ||||||||
\(579\) | −5.93824e6 | −0.736142 | ||||||||
\(580\) | −129148. | −0.0159411 | ||||||||
\(581\) | 1.22362e7 | 1.50386 | ||||||||
\(582\) | −5.08841e6 | −0.622694 | ||||||||
\(583\) | −3.27283e6 | −0.398797 | ||||||||
\(584\) | −1.93650e6 | −0.234955 | ||||||||
\(585\) | −1.70176e6 | −0.205593 | ||||||||
\(586\) | −7.74960e6 | −0.932256 | ||||||||
\(587\) | 1.27863e7 | 1.53162 | 0.765808 | − | 0.643069i | \(-0.222339\pi\) | ||||
0.765808 | + | 0.643069i | \(0.222339\pi\) | |||||||
\(588\) | −2.09398e6 | −0.249764 | ||||||||
\(589\) | −1.05045e6 | −0.124763 | ||||||||
\(590\) | 249758. | 0.0295386 | ||||||||
\(591\) | 785610. | 0.0925206 | ||||||||
\(592\) | 3.80925e6 | 0.446720 | ||||||||
\(593\) | −1.59425e7 | −1.86175 | −0.930873 | − | 0.365342i | \(-0.880952\pi\) | ||||
−0.930873 | + | 0.365342i | \(0.880952\pi\) | |||||||
\(594\) | 376381. | 0.0437684 | ||||||||
\(595\) | 2.40248e6 | 0.278206 | ||||||||
\(596\) | −576249. | −0.0664500 | ||||||||
\(597\) | 660581. | 0.0758560 | ||||||||
\(598\) | −1.57651e7 | −1.80278 | ||||||||
\(599\) | 1.58353e7 | 1.80327 | 0.901633 | − | 0.432502i | \(-0.142369\pi\) | ||||
0.901633 | + | 0.432502i | \(0.142369\pi\) | |||||||
\(600\) | −1.61467e6 | −0.183108 | ||||||||
\(601\) | 1.39014e7 | 1.56991 | 0.784953 | − | 0.619555i | \(-0.212687\pi\) | ||||
0.784953 | + | 0.619555i | \(0.212687\pi\) | |||||||
\(602\) | −985218. | −0.110800 | ||||||||
\(603\) | 4.65290e6 | 0.521112 | ||||||||
\(604\) | −1.84724e6 | −0.206030 | ||||||||
\(605\) | −2.58998e6 | −0.287678 | ||||||||
\(606\) | −5.49986e6 | −0.608373 | ||||||||
\(607\) | 1.30722e7 | 1.44005 | 0.720027 | − | 0.693947i | \(-0.244130\pi\) | ||||
0.720027 | + | 0.693947i | \(0.244130\pi\) | |||||||
\(608\) | 233075. | 0.0255704 | ||||||||
\(609\) | 717073. | 0.0783466 | ||||||||
\(610\) | 3.30385e6 | 0.359497 | ||||||||
\(611\) | 2.57389e6 | 0.278925 | ||||||||
\(612\) | 980392. | 0.105809 | ||||||||
\(613\) | 673698. | 0.0724126 | 0.0362063 | − | 0.999344i | \(-0.488473\pi\) | ||||
0.0362063 | + | 0.999344i | \(0.488473\pi\) | |||||||
\(614\) | 8.48744e6 | 0.908564 | ||||||||
\(615\) | 1.00623e6 | 0.107278 | ||||||||
\(616\) | −1.46261e6 | −0.155302 | ||||||||
\(617\) | −1.47407e7 | −1.55885 | −0.779424 | − | 0.626497i | \(-0.784488\pi\) | ||||
−0.779424 | + | 0.626497i | \(0.784488\pi\) | |||||||
\(618\) | 69023.5 | 0.00726986 | ||||||||
\(619\) | −831351. | −0.0872082 | −0.0436041 | − | 0.999049i | \(-0.513884\pi\) | ||||
−0.0436041 | + | 0.999049i | \(0.513884\pi\) | |||||||
\(620\) | 1.32451e6 | 0.138381 | ||||||||
\(621\) | 2.45305e6 | 0.255257 | ||||||||
\(622\) | 7.46758e6 | 0.773934 | ||||||||
\(623\) | −1.84489e7 | −1.90436 | ||||||||
\(624\) | 2.69860e6 | 0.277446 | ||||||||
\(625\) | 6.85278e6 | 0.701725 | ||||||||
\(626\) | 7.66599e6 | 0.781866 | ||||||||
\(627\) | 264411. | 0.0268602 | ||||||||
\(628\) | 3.86093e6 | 0.390655 | ||||||||
\(629\) | 1.12563e7 | 1.13440 | ||||||||
\(630\) | −1.02899e6 | −0.103290 | ||||||||
\(631\) | 8.64886e6 | 0.864739 | 0.432370 | − | 0.901696i | \(-0.357678\pi\) | ||||
0.432370 | + | 0.901696i | \(0.357678\pi\) | |||||||
\(632\) | −693304. | −0.0690448 | ||||||||
\(633\) | −7.13679e6 | −0.707936 | ||||||||
\(634\) | 1.30417e7 | 1.28858 | ||||||||
\(635\) | −2.57512e6 | −0.253433 | ||||||||
\(636\) | 3.65129e6 | 0.357934 | ||||||||
\(637\) | −1.70321e7 | −1.66310 | ||||||||
\(638\) | 232334. | 0.0225975 | ||||||||
\(639\) | −3.31688e6 | −0.321349 | ||||||||
\(640\) | −293884. | −0.0283613 | ||||||||
\(641\) | 2.02662e6 | 0.194817 | 0.0974086 | − | 0.995244i | \(-0.468945\pi\) | ||||
0.0974086 | + | 0.995244i | \(0.468945\pi\) | |||||||
\(642\) | −1.87127e6 | −0.179184 | ||||||||
\(643\) | 1.79287e7 | 1.71010 | 0.855050 | − | 0.518546i | \(-0.173527\pi\) | ||||
0.855050 | + | 0.518546i | \(0.173527\pi\) | |||||||
\(644\) | −9.53253e6 | −0.905719 | ||||||||
\(645\) | −224575. | −0.0212551 | ||||||||
\(646\) | 688733. | 0.0649336 | ||||||||
\(647\) | 1.06475e7 | 0.999966 | 0.499983 | − | 0.866035i | \(-0.333340\pi\) | ||||
0.499983 | + | 0.866035i | \(0.333340\pi\) | |||||||
\(648\) | −419904. | −0.0392837 | ||||||||
\(649\) | −449308. | −0.0418728 | ||||||||
\(650\) | −1.31335e7 | −1.21926 | ||||||||
\(651\) | −7.35411e6 | −0.680107 | ||||||||
\(652\) | −7.46792e6 | −0.687988 | ||||||||
\(653\) | 1.96514e6 | 0.180348 | 0.0901740 | − | 0.995926i | \(-0.471258\pi\) | ||||
0.0901740 | + | 0.995926i | \(0.471258\pi\) | |||||||
\(654\) | 1.37862e6 | 0.126038 | ||||||||
\(655\) | 447054. | 0.0407152 | ||||||||
\(656\) | −1.59565e6 | −0.144770 | ||||||||
\(657\) | 2.45088e6 | 0.221518 | ||||||||
\(658\) | 1.55633e6 | 0.140132 | ||||||||
\(659\) | −9.99801e6 | −0.896809 | −0.448405 | − | 0.893831i | \(-0.648008\pi\) | ||||
−0.448405 | + | 0.893831i | \(0.648008\pi\) | |||||||
\(660\) | −333394. | −0.0297919 | ||||||||
\(661\) | −1.38512e7 | −1.23306 | −0.616529 | − | 0.787333i | \(-0.711462\pi\) | ||||
−0.616529 | + | 0.787333i | \(0.711462\pi\) | |||||||
\(662\) | 1.93010e6 | 0.171173 | ||||||||
\(663\) | 7.97432e6 | 0.704547 | ||||||||
\(664\) | −4.42301e6 | −0.389312 | ||||||||
\(665\) | −722872. | −0.0633880 | ||||||||
\(666\) | −4.82108e6 | −0.421171 | ||||||||
\(667\) | 1.51423e6 | 0.131788 | ||||||||
\(668\) | −8.16363e6 | −0.707852 | ||||||||
\(669\) | 2.55561e6 | 0.220764 | ||||||||
\(670\) | −4.12150e6 | −0.354706 | ||||||||
\(671\) | −5.94352e6 | −0.509609 | ||||||||
\(672\) | 1.63174e6 | 0.139389 | ||||||||
\(673\) | −2.79500e6 | −0.237873 | −0.118936 | − | 0.992902i | \(-0.537948\pi\) | ||||
−0.118936 | + | 0.992902i | \(0.537948\pi\) | |||||||
\(674\) | −1.20501e6 | −0.102174 | ||||||||
\(675\) | 2.04357e6 | 0.172636 | ||||||||
\(676\) | 1.60093e7 | 1.34742 | ||||||||
\(677\) | −1.51444e6 | −0.126993 | −0.0634966 | − | 0.997982i | \(-0.520225\pi\) | ||||
−0.0634966 | + | 0.997982i | \(0.520225\pi\) | |||||||
\(678\) | 2.91614e6 | 0.243632 | ||||||||
\(679\) | −2.50258e7 | −2.08312 | ||||||||
\(680\) | −868422. | −0.0720209 | ||||||||
\(681\) | −8.02865e6 | −0.663399 | ||||||||
\(682\) | −2.38275e6 | −0.196163 | ||||||||
\(683\) | 1.67217e6 | 0.137161 | 0.0685803 | − | 0.997646i | \(-0.478153\pi\) | ||||
0.0685803 | + | 0.997646i | \(0.478153\pi\) | |||||||
\(684\) | −294986. | −0.0241080 | ||||||||
\(685\) | −5.48327e6 | −0.446491 | ||||||||
\(686\) | 1.60444e6 | 0.130171 | ||||||||
\(687\) | 437436. | 0.0353608 | ||||||||
\(688\) | 356126. | 0.0286835 | ||||||||
\(689\) | 2.96989e7 | 2.38337 | ||||||||
\(690\) | −2.17289e6 | −0.173746 | ||||||||
\(691\) | −2.95289e6 | −0.235262 | −0.117631 | − | 0.993057i | \(-0.537530\pi\) | ||||
−0.117631 | + | 0.993057i | \(0.537530\pi\) | |||||||
\(692\) | −7.51172e6 | −0.596313 | ||||||||
\(693\) | 1.85112e6 | 0.146420 | ||||||||
\(694\) | −207559. | −0.0163585 | ||||||||
\(695\) | −1.42850e6 | −0.112181 | ||||||||
\(696\) | −259200. | −0.0202820 | ||||||||
\(697\) | −4.71513e6 | −0.367630 | ||||||||
\(698\) | −1.47212e7 | −1.14368 | ||||||||
\(699\) | −1.03473e6 | −0.0801003 | ||||||||
\(700\) | −7.94129e6 | −0.612556 | ||||||||
\(701\) | 1.17592e7 | 0.903823 | 0.451912 | − | 0.892063i | \(-0.350742\pi\) | ||||
0.451912 | + | 0.892063i | \(0.350742\pi\) | |||||||
\(702\) | −3.41542e6 | −0.261578 | ||||||||
\(703\) | −3.38685e6 | −0.258469 | ||||||||
\(704\) | 528688. | 0.0402039 | ||||||||
\(705\) | 354758. | 0.0268819 | ||||||||
\(706\) | 8.02309e6 | 0.605801 | ||||||||
\(707\) | −2.70494e7 | −2.03521 | ||||||||
\(708\) | 501264. | 0.0375823 | ||||||||
\(709\) | 3.00008e6 | 0.224139 | 0.112069 | − | 0.993700i | \(-0.464252\pi\) | ||||
0.112069 | + | 0.993700i | \(0.464252\pi\) | |||||||
\(710\) | 2.93806e6 | 0.218733 | ||||||||
\(711\) | 877463. | 0.0650961 | ||||||||
\(712\) | 6.66870e6 | 0.492993 | ||||||||
\(713\) | −1.55295e7 | −1.14402 | ||||||||
\(714\) | 4.82176e6 | 0.353965 | ||||||||
\(715\) | −2.71177e6 | −0.198375 | ||||||||
\(716\) | 820686. | 0.0598266 | ||||||||
\(717\) | 1.32510e7 | 0.962612 | ||||||||
\(718\) | 388012. | 0.0280888 | ||||||||
\(719\) | −5.75228e6 | −0.414971 | −0.207485 | − | 0.978238i | \(-0.566528\pi\) | ||||
−0.207485 | + | 0.978238i | \(0.566528\pi\) | |||||||
\(720\) | 371947. | 0.0267393 | ||||||||
\(721\) | 339471. | 0.0243201 | ||||||||
\(722\) | 9.69717e6 | 0.692312 | ||||||||
\(723\) | −3.74782e6 | −0.266644 | ||||||||
\(724\) | 9.79519e6 | 0.694491 | ||||||||
\(725\) | 1.26146e6 | 0.0891312 | ||||||||
\(726\) | −5.19807e6 | −0.366016 | ||||||||
\(727\) | 1.95045e7 | 1.36867 | 0.684333 | − | 0.729169i | \(-0.260093\pi\) | ||||
0.684333 | + | 0.729169i | \(0.260093\pi\) | |||||||
\(728\) | 1.32723e7 | 0.928147 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −2.17097e6 | −0.150781 | ||||||||
\(731\) | 1.05235e6 | 0.0728391 | ||||||||
\(732\) | 6.63081e6 | 0.457392 | ||||||||
\(733\) | 1.14697e6 | 0.0788480 | 0.0394240 | − | 0.999223i | \(-0.487448\pi\) | ||||
0.0394240 | + | 0.999223i | \(0.487448\pi\) | |||||||
\(734\) | −2.83793e6 | −0.194429 | ||||||||
\(735\) | −2.34752e6 | −0.160284 | ||||||||
\(736\) | 3.44571e6 | 0.234469 | ||||||||
\(737\) | 7.41445e6 | 0.502817 | ||||||||
\(738\) | 2.01950e6 | 0.136491 | ||||||||
\(739\) | −5.23498e6 | −0.352617 | −0.176309 | − | 0.984335i | \(-0.556416\pi\) | ||||
−0.176309 | + | 0.984335i | \(0.556416\pi\) | |||||||
\(740\) | 4.27047e6 | 0.286679 | ||||||||
\(741\) | −2.39936e6 | −0.160528 | ||||||||
\(742\) | 1.79578e7 | 1.19741 | ||||||||
\(743\) | 1.12611e7 | 0.748357 | 0.374179 | − | 0.927357i | \(-0.377925\pi\) | ||||
0.374179 | + | 0.927357i | \(0.377925\pi\) | |||||||
\(744\) | 2.65828e6 | 0.176063 | ||||||||
\(745\) | −646021. | −0.0426438 | ||||||||
\(746\) | −1.90824e7 | −1.25541 | ||||||||
\(747\) | 5.59787e6 | 0.367047 | ||||||||
\(748\) | 1.56226e6 | 0.102094 | ||||||||
\(749\) | −9.20326e6 | −0.599428 | ||||||||
\(750\) | −3.82812e6 | −0.248503 | ||||||||
\(751\) | 4.34861e6 | 0.281353 | 0.140676 | − | 0.990056i | \(-0.455072\pi\) | ||||
0.140676 | + | 0.990056i | \(0.455072\pi\) | |||||||
\(752\) | −562566. | −0.0362768 | ||||||||
\(753\) | 2.42148e6 | 0.155630 | ||||||||
\(754\) | −2.10828e6 | −0.135052 | ||||||||
\(755\) | −2.07090e6 | −0.132218 | ||||||||
\(756\) | −2.06517e6 | −0.131417 | ||||||||
\(757\) | 9.05995e6 | 0.574627 | 0.287314 | − | 0.957837i | \(-0.407238\pi\) | ||||
0.287314 | + | 0.957837i | \(0.407238\pi\) | |||||||
\(758\) | 8.86854e6 | 0.560634 | ||||||||
\(759\) | 3.90896e6 | 0.246296 | ||||||||
\(760\) | 261296. | 0.0164096 | ||||||||
\(761\) | 2.19264e7 | 1.37248 | 0.686238 | − | 0.727377i | \(-0.259261\pi\) | ||||
0.686238 | + | 0.727377i | \(0.259261\pi\) | |||||||
\(762\) | −5.16826e6 | −0.322446 | ||||||||
\(763\) | 6.78035e6 | 0.421639 | ||||||||
\(764\) | −1.08262e7 | −0.671029 | ||||||||
\(765\) | 1.09910e6 | 0.0679019 | ||||||||
\(766\) | 5.70620e6 | 0.351378 | ||||||||
\(767\) | 4.07719e6 | 0.250249 | ||||||||
\(768\) | −589824. | −0.0360844 | ||||||||
\(769\) | 3.18958e7 | 1.94499 | 0.972495 | − | 0.232923i | \(-0.0748291\pi\) | ||||
0.972495 | + | 0.232923i | \(0.0748291\pi\) | |||||||
\(770\) | −1.63970e6 | −0.0996638 | ||||||||
\(771\) | −9.95925e6 | −0.603380 | ||||||||
\(772\) | 1.05569e7 | 0.637517 | ||||||||
\(773\) | 1.23772e7 | 0.745028 | 0.372514 | − | 0.928027i | \(-0.378496\pi\) | ||||
0.372514 | + | 0.928027i | \(0.378496\pi\) | |||||||
\(774\) | −450722. | −0.0270431 | ||||||||
\(775\) | −1.29372e7 | −0.773726 | ||||||||
\(776\) | 9.04606e6 | 0.539268 | ||||||||
\(777\) | −2.37110e7 | −1.40896 | ||||||||
\(778\) | 3.85905e6 | 0.228576 | ||||||||
\(779\) | 1.41872e6 | 0.0837629 | ||||||||
\(780\) | 3.02535e6 | 0.178049 | ||||||||
\(781\) | −5.28548e6 | −0.310068 | ||||||||
\(782\) | 1.01820e7 | 0.595411 | ||||||||
\(783\) | 328050. | 0.0191221 | ||||||||
\(784\) | 3.72264e6 | 0.216302 | ||||||||
\(785\) | 4.32841e6 | 0.250700 | ||||||||
\(786\) | 897235. | 0.0518024 | ||||||||
\(787\) | −1.81664e7 | −1.04552 | −0.522758 | − | 0.852481i | \(-0.675097\pi\) | ||||
−0.522758 | + | 0.852481i | \(0.675097\pi\) | |||||||
\(788\) | −1.39664e6 | −0.0801252 | ||||||||
\(789\) | 1.02049e7 | 0.583604 | ||||||||
\(790\) | −777248. | −0.0443090 | ||||||||
\(791\) | 1.43422e7 | 0.815031 | ||||||||
\(792\) | −669121. | −0.0379046 | ||||||||
\(793\) | 5.39338e7 | 3.04563 | ||||||||
\(794\) | 4.25281e6 | 0.239400 | ||||||||
\(795\) | 4.09338e6 | 0.229702 | ||||||||
\(796\) | −1.17437e6 | −0.0656933 | ||||||||
\(797\) | 1.06279e7 | 0.592657 | 0.296329 | − | 0.955086i | \(-0.404238\pi\) | ||||
0.296329 | + | 0.955086i | \(0.404238\pi\) | |||||||
\(798\) | −1.45080e6 | −0.0806493 | ||||||||
\(799\) | −1.66237e6 | −0.0921215 | ||||||||
\(800\) | 2.87053e6 | 0.158576 | ||||||||
\(801\) | −8.44007e6 | −0.464799 | ||||||||
\(802\) | −7.22024e6 | −0.396384 | ||||||||
\(803\) | 3.90550e6 | 0.213741 | ||||||||
\(804\) | −8.27183e6 | −0.451296 | ||||||||
\(805\) | −1.06867e7 | −0.581239 | ||||||||
\(806\) | 2.16220e7 | 1.17235 | ||||||||
\(807\) | −1.67515e7 | −0.905464 | ||||||||
\(808\) | 9.77752e6 | 0.526866 | ||||||||
\(809\) | −8.62377e6 | −0.463261 | −0.231630 | − | 0.972804i | \(-0.574406\pi\) | ||||
−0.231630 | + | 0.972804i | \(0.574406\pi\) | |||||||
\(810\) | −470745. | −0.0252100 | ||||||||
\(811\) | −1.95998e7 | −1.04641 | −0.523203 | − | 0.852208i | \(-0.675263\pi\) | ||||
−0.523203 | + | 0.852208i | \(0.675263\pi\) | |||||||
\(812\) | −1.27480e6 | −0.0678501 | ||||||||
\(813\) | 2.03675e7 | 1.08072 | ||||||||
\(814\) | −7.68244e6 | −0.406385 | ||||||||
\(815\) | −8.37212e6 | −0.441511 | ||||||||
\(816\) | −1.74292e6 | −0.0916329 | ||||||||
\(817\) | −316636. | −0.0165961 | ||||||||
\(818\) | −28226.9 | −0.00147496 | ||||||||
\(819\) | −1.67977e7 | −0.875066 | ||||||||
\(820\) | −1.78885e6 | −0.0929053 | ||||||||
\(821\) | 2.85532e7 | 1.47842 | 0.739210 | − | 0.673476i | \(-0.235199\pi\) | ||||
0.739210 | + | 0.673476i | \(0.235199\pi\) | |||||||
\(822\) | −1.10049e7 | −0.568076 | ||||||||
\(823\) | 1.45951e7 | 0.751119 | 0.375559 | − | 0.926798i | \(-0.377451\pi\) | ||||
0.375559 | + | 0.926798i | \(0.377451\pi\) | |||||||
\(824\) | −122708. | −0.00629588 | ||||||||
\(825\) | 3.25645e6 | 0.166575 | ||||||||
\(826\) | 2.46532e6 | 0.125725 | ||||||||
\(827\) | 612107. | 0.0311217 | 0.0155609 | − | 0.999879i | \(-0.495047\pi\) | ||||
0.0155609 | + | 0.999879i | \(0.495047\pi\) | |||||||
\(828\) | −4.36098e6 | −0.221059 | ||||||||
\(829\) | −2.37608e6 | −0.120081 | −0.0600406 | − | 0.998196i | \(-0.519123\pi\) | ||||
−0.0600406 | + | 0.998196i | \(0.519123\pi\) | |||||||
\(830\) | −4.95854e6 | −0.249838 | ||||||||
\(831\) | −3.12367e6 | −0.156914 | ||||||||
\(832\) | −4.79752e6 | −0.240275 | ||||||||
\(833\) | 1.10003e7 | 0.549279 | ||||||||
\(834\) | −2.86699e6 | −0.142729 | ||||||||
\(835\) | −9.15207e6 | −0.454259 | ||||||||
\(836\) | −470063. | −0.0232617 | ||||||||
\(837\) | −3.36439e6 | −0.165994 | ||||||||
\(838\) | 2.85838e7 | 1.40608 | ||||||||
\(839\) | −3.87213e6 | −0.189909 | −0.0949545 | − | 0.995482i | \(-0.530271\pi\) | ||||
−0.0949545 | + | 0.995482i | \(0.530271\pi\) | |||||||
\(840\) | 1.82931e6 | 0.0894518 | ||||||||
\(841\) | −2.03086e7 | −0.990127 | ||||||||
\(842\) | 8.89561e6 | 0.432410 | ||||||||
\(843\) | 1.94594e6 | 0.0943106 | ||||||||
\(844\) | 1.26876e7 | 0.613090 | ||||||||
\(845\) | 1.79476e7 | 0.864700 | ||||||||
\(846\) | 711998. | 0.0342021 | ||||||||
\(847\) | −2.55651e7 | −1.22445 | ||||||||
\(848\) | −6.49117e6 | −0.309980 | ||||||||
\(849\) | 2.96261e6 | 0.141060 | ||||||||
\(850\) | 8.48237e6 | 0.402689 | ||||||||
\(851\) | −5.00701e7 | −2.37004 | ||||||||
\(852\) | 5.89667e6 | 0.278297 | ||||||||
\(853\) | 2.27953e7 | 1.07269 | 0.536343 | − | 0.844000i | \(-0.319806\pi\) | ||||
0.536343 | + | 0.844000i | \(0.319806\pi\) | |||||||
\(854\) | 3.26116e7 | 1.53013 | ||||||||
\(855\) | −330703. | −0.0154711 | ||||||||
\(856\) | 3.32670e6 | 0.155178 | ||||||||
\(857\) | 3.33059e7 | 1.54906 | 0.774531 | − | 0.632536i | \(-0.217986\pi\) | ||||
0.774531 | + | 0.632536i | \(0.217986\pi\) | |||||||
\(858\) | −5.44251e6 | −0.252395 | ||||||||
\(859\) | −2.20379e7 | −1.01903 | −0.509516 | − | 0.860461i | \(-0.670175\pi\) | ||||
−0.509516 | + | 0.860461i | \(0.670175\pi\) | |||||||
\(860\) | 399245. | 0.0184074 | ||||||||
\(861\) | 9.93231e6 | 0.456607 | ||||||||
\(862\) | −1.50830e7 | −0.691382 | ||||||||
\(863\) | 8.76342e6 | 0.400541 | 0.200270 | − | 0.979741i | \(-0.435818\pi\) | ||||
0.200270 | + | 0.979741i | \(0.435818\pi\) | |||||||
\(864\) | 746496. | 0.0340207 | ||||||||
\(865\) | −8.42123e6 | −0.382680 | ||||||||
\(866\) | 5.82148e6 | 0.263778 | ||||||||
\(867\) | 7.62842e6 | 0.344657 | ||||||||
\(868\) | 1.30740e7 | 0.588990 | ||||||||
\(869\) | 1.39825e6 | 0.0628107 | ||||||||
\(870\) | −290583. | −0.0130159 | ||||||||
\(871\) | −6.72815e7 | −3.00504 | ||||||||
\(872\) | −2.45089e6 | −0.109152 | ||||||||
\(873\) | −1.14489e7 | −0.508427 | ||||||||
\(874\) | −3.06363e6 | −0.135662 | ||||||||
\(875\) | −1.88275e7 | −0.831326 | ||||||||
\(876\) | −4.35712e6 | −0.191840 | ||||||||
\(877\) | 3.39809e7 | 1.49189 | 0.745943 | − | 0.666010i | \(-0.231999\pi\) | ||||
0.745943 | + | 0.666010i | \(0.231999\pi\) | |||||||
\(878\) | 1.76822e7 | 0.774106 | ||||||||
\(879\) | −1.74366e7 | −0.761184 | ||||||||
\(880\) | 592701. | 0.0258006 | ||||||||
\(881\) | 8.55016e6 | 0.371137 | 0.185569 | − | 0.982631i | \(-0.440587\pi\) | ||||
0.185569 | + | 0.982631i | \(0.440587\pi\) | |||||||
\(882\) | −4.71146e6 | −0.203931 | ||||||||
\(883\) | 8.43785e6 | 0.364192 | 0.182096 | − | 0.983281i | \(-0.441712\pi\) | ||||
0.182096 | + | 0.983281i | \(0.441712\pi\) | |||||||
\(884\) | −1.41766e7 | −0.610156 | ||||||||
\(885\) | 561956. | 0.0241182 | ||||||||
\(886\) | −1.30436e7 | −0.558231 | ||||||||
\(887\) | 3.45863e7 | 1.47603 | 0.738015 | − | 0.674784i | \(-0.235763\pi\) | ||||
0.738015 | + | 0.674784i | \(0.235763\pi\) | |||||||
\(888\) | 8.57081e6 | 0.364745 | ||||||||
\(889\) | −2.54185e7 | −1.07869 | ||||||||
\(890\) | 7.47613e6 | 0.316375 | ||||||||
\(891\) | 846856. | 0.0357368 | ||||||||
\(892\) | −4.54330e6 | −0.191187 | ||||||||
\(893\) | 500184. | 0.0209895 | ||||||||
\(894\) | −1.29656e6 | −0.0542562 | ||||||||
\(895\) | 920053. | 0.0383933 | ||||||||
\(896\) | −2.90087e6 | −0.120714 | ||||||||
\(897\) | −3.54714e7 | −1.47196 | ||||||||
\(898\) | −1.44335e7 | −0.597283 | ||||||||
\(899\) | −2.07678e6 | −0.0857021 | ||||||||
\(900\) | −3.63302e6 | −0.149507 | ||||||||
\(901\) | −1.91813e7 | −0.787165 | ||||||||
\(902\) | 3.21809e6 | 0.131699 | ||||||||
\(903\) | −2.21674e6 | −0.0904681 | ||||||||
\(904\) | −5.18426e6 | −0.210992 | ||||||||
\(905\) | 1.09812e7 | 0.445684 | ||||||||
\(906\) | −4.15629e6 | −0.168223 | ||||||||
\(907\) | −3.13405e7 | −1.26499 | −0.632497 | − | 0.774563i | \(-0.717970\pi\) | ||||
−0.632497 | + | 0.774563i | \(0.717970\pi\) | |||||||
\(908\) | 1.42732e7 | 0.574520 | ||||||||
\(909\) | −1.23747e7 | −0.496734 | ||||||||
\(910\) | 1.48793e7 | 0.595632 | ||||||||
\(911\) | 5.53480e6 | 0.220956 | 0.110478 | − | 0.993879i | \(-0.464762\pi\) | ||||
0.110478 | + | 0.993879i | \(0.464762\pi\) | |||||||
\(912\) | 524420. | 0.0208781 | ||||||||
\(913\) | 8.92026e6 | 0.354161 | ||||||||
\(914\) | −2.08979e7 | −0.827442 | ||||||||
\(915\) | 7.43366e6 | 0.293528 | ||||||||
\(916\) | −777663. | −0.0306234 | ||||||||
\(917\) | 4.41278e6 | 0.173296 | ||||||||
\(918\) | 2.20588e6 | 0.0863924 | ||||||||
\(919\) | −1.62062e7 | −0.632984 | −0.316492 | − | 0.948595i | \(-0.602505\pi\) | ||||
−0.316492 | + | 0.948595i | \(0.602505\pi\) | |||||||
\(920\) | 3.86292e6 | 0.150469 | ||||||||
\(921\) | 1.90967e7 | 0.741840 | ||||||||
\(922\) | 1.70601e7 | 0.660927 | ||||||||
\(923\) | 4.79624e7 | 1.85309 | ||||||||
\(924\) | −3.29087e6 | −0.126803 | ||||||||
\(925\) | −4.17121e7 | −1.60290 | ||||||||
\(926\) | −1.55408e7 | −0.595588 | ||||||||
\(927\) | 155303. | 0.00593581 | ||||||||
\(928\) | 460800. | 0.0175648 | ||||||||
\(929\) | −4.17835e7 | −1.58842 | −0.794210 | − | 0.607643i | \(-0.792115\pi\) | ||||
−0.794210 | + | 0.607643i | \(0.792115\pi\) | |||||||
\(930\) | 2.98014e6 | 0.112987 | ||||||||
\(931\) | −3.30984e6 | −0.125151 | ||||||||
\(932\) | 1.83952e6 | 0.0693689 | ||||||||
\(933\) | 1.68021e7 | 0.631915 | ||||||||
\(934\) | −9.06753e6 | −0.340112 | ||||||||
\(935\) | 1.75142e6 | 0.0655181 | ||||||||
\(936\) | 6.07186e6 | 0.226533 | ||||||||
\(937\) | −4.48196e7 | −1.66770 | −0.833852 | − | 0.551988i | \(-0.813869\pi\) | ||||
−0.833852 | + | 0.551988i | \(0.813869\pi\) | |||||||
\(938\) | −4.06825e7 | −1.50973 | ||||||||
\(939\) | 1.72485e7 | 0.638391 | ||||||||
\(940\) | −630681. | −0.0232804 | ||||||||
\(941\) | 6.67255e6 | 0.245651 | 0.122825 | − | 0.992428i | \(-0.460805\pi\) | ||||
0.122825 | + | 0.992428i | \(0.460805\pi\) | |||||||
\(942\) | 8.68710e6 | 0.318968 | ||||||||
\(943\) | 2.09739e7 | 0.768067 | ||||||||
\(944\) | −891136. | −0.0325472 | ||||||||
\(945\) | −2.31522e6 | −0.0843360 | ||||||||
\(946\) | −718230. | −0.0260937 | ||||||||
\(947\) | 4.65602e7 | 1.68710 | 0.843548 | − | 0.537054i | \(-0.180463\pi\) | ||||
0.843548 | + | 0.537054i | \(0.180463\pi\) | |||||||
\(948\) | −1.55993e6 | −0.0563748 | ||||||||
\(949\) | −3.54400e7 | −1.27740 | ||||||||
\(950\) | −2.55223e6 | −0.0917508 | ||||||||
\(951\) | 2.93438e7 | 1.05212 | ||||||||
\(952\) | −8.57202e6 | −0.306543 | ||||||||
\(953\) | −3.32352e7 | −1.18540 | −0.592702 | − | 0.805422i | \(-0.701939\pi\) | ||||
−0.592702 | + | 0.805422i | \(0.701939\pi\) | |||||||
\(954\) | 8.21539e6 | 0.292252 | ||||||||
\(955\) | −1.21370e7 | −0.430628 | ||||||||
\(956\) | −2.35574e7 | −0.833647 | ||||||||
\(957\) | 522750. | 0.0184508 | ||||||||
\(958\) | 3.84289e7 | 1.35283 | ||||||||
\(959\) | −5.41243e7 | −1.90040 | ||||||||
\(960\) | −661239. | −0.0231569 | ||||||||
\(961\) | −7.33024e6 | −0.256041 | ||||||||
\(962\) | 6.97134e7 | 2.42873 | ||||||||
\(963\) | −4.21035e6 | −0.146303 | ||||||||
\(964\) | 6.66278e6 | 0.230921 | ||||||||
\(965\) | 1.18351e7 | 0.409122 | ||||||||
\(966\) | −2.14482e7 | −0.739516 | ||||||||
\(967\) | −1.97095e7 | −0.677812 | −0.338906 | − | 0.940820i | \(-0.610057\pi\) | ||||
−0.338906 | + | 0.940820i | \(0.610057\pi\) | |||||||
\(968\) | 9.24101e6 | 0.316980 | ||||||||
\(969\) | 1.54965e6 | 0.0530181 | ||||||||
\(970\) | 1.01413e7 | 0.346072 | ||||||||
\(971\) | −1.68304e7 | −0.572857 | −0.286429 | − | 0.958102i | \(-0.592468\pi\) | ||||
−0.286429 | + | 0.958102i | \(0.592468\pi\) | |||||||
\(972\) | −944784. | −0.0320750 | ||||||||
\(973\) | −1.41004e7 | −0.477474 | ||||||||
\(974\) | −3.60840e7 | −1.21876 | ||||||||
\(975\) | −2.95503e7 | −0.995521 | ||||||||
\(976\) | −1.17881e7 | −0.396113 | ||||||||
\(977\) | 2.10662e7 | 0.706073 | 0.353037 | − | 0.935609i | \(-0.385149\pi\) | ||||
0.353037 | + | 0.935609i | \(0.385149\pi\) | |||||||
\(978\) | −1.68028e7 | −0.561740 | ||||||||
\(979\) | −1.34493e7 | −0.448481 | ||||||||
\(980\) | 4.17337e6 | 0.138810 | ||||||||
\(981\) | 3.10190e6 | 0.102910 | ||||||||
\(982\) | −1.63845e7 | −0.542193 | ||||||||
\(983\) | −5.73357e7 | −1.89252 | −0.946261 | − | 0.323404i | \(-0.895173\pi\) | ||||
−0.946261 | + | 0.323404i | \(0.895173\pi\) | |||||||
\(984\) | −3.59022e6 | −0.118204 | ||||||||
\(985\) | −1.56574e6 | −0.0514198 | ||||||||
\(986\) | 1.36165e6 | 0.0446041 | ||||||||
\(987\) | 3.50175e6 | 0.114417 | ||||||||
\(988\) | 4.26553e6 | 0.139021 | ||||||||
\(989\) | −4.68105e6 | −0.152178 | ||||||||
\(990\) | −750137. | −0.0243250 | ||||||||
\(991\) | 1.70841e7 | 0.552595 | 0.276298 | − | 0.961072i | \(-0.410892\pi\) | ||||
0.276298 | + | 0.961072i | \(0.410892\pi\) | |||||||
\(992\) | −4.72584e6 | −0.152475 | ||||||||
\(993\) | 4.34272e6 | 0.139762 | ||||||||
\(994\) | 2.90010e7 | 0.930995 | ||||||||
\(995\) | −1.31656e6 | −0.0421582 | ||||||||
\(996\) | −9.95177e6 | −0.317872 | ||||||||
\(997\) | 3.42297e7 | 1.09060 | 0.545299 | − | 0.838241i | \(-0.316416\pi\) | ||||
0.545299 | + | 0.838241i | \(0.316416\pi\) | |||||||
\(998\) | −4.28726e6 | −0.136255 | ||||||||
\(999\) | −1.08474e7 | −0.343885 |
(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 | 354.6.a.f.1.4 | ✓ | 6 | |
3.2 | odd | 2 | 1062.6.a.i.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
354.6.a.f.1.4 | ✓ | 6 | 1.1 | even | 1 | trivial | |
1062.6.a.i.1.3 | 6 | 3.2 | odd | 2 |