Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [722,6,Mod(1,722)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(722, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("722.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 722 = 2 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 722.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: | \(115.797117905\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 2871 x^{13} - 4674 x^{12} + 3170019 x^{11} + 9081402 x^{10} - 1680307373 x^{9} + \cdots - 34\!\cdots\!72 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3\cdot 19^{6} \) |
Twist minimal: | no (minimal twist has level 38) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-3.66933\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 722.1 |
$q$-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 | ||||||||
\(3\) | 2.13724 | 0.137104 | 0.0685520 | − | 0.997648i | \(-0.478162\pi\) | ||||
0.0685520 | + | 0.997648i | \(0.478162\pi\) | |||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | −10.7945 | −0.193097 | −0.0965487 | − | 0.995328i | \(-0.530780\pi\) | ||||
−0.0965487 | + | 0.995328i | \(0.530780\pi\) | |||||||
\(6\) | 8.54896 | 0.0969472 | ||||||||
\(7\) | −195.108 | −1.50498 | −0.752488 | − | 0.658606i | \(-0.771147\pi\) | ||||
−0.752488 | + | 0.658606i | \(0.771147\pi\) | |||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | −238.432 | −0.981202 | ||||||||
\(10\) | −43.1779 | −0.136541 | ||||||||
\(11\) | −17.0907 | −0.0425870 | −0.0212935 | − | 0.999773i | \(-0.506778\pi\) | ||||
−0.0212935 | + | 0.999773i | \(0.506778\pi\) | |||||||
\(12\) | 34.1959 | 0.0685520 | ||||||||
\(13\) | −263.186 | −0.431921 | −0.215960 | − | 0.976402i | \(-0.569288\pi\) | ||||
−0.215960 | + | 0.976402i | \(0.569288\pi\) | |||||||
\(14\) | −780.432 | −1.06418 | ||||||||
\(15\) | −23.0704 | −0.0264744 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −577.725 | −0.484840 | −0.242420 | − | 0.970171i | \(-0.577941\pi\) | ||||
−0.242420 | + | 0.970171i | \(0.577941\pi\) | |||||||
\(18\) | −953.729 | −0.693815 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −172.712 | −0.0965487 | ||||||||
\(21\) | −416.993 | −0.206338 | ||||||||
\(22\) | −68.3627 | −0.0301136 | ||||||||
\(23\) | −565.508 | −0.222905 | −0.111452 | − | 0.993770i | \(-0.535550\pi\) | ||||
−0.111452 | + | 0.993770i | \(0.535550\pi\) | |||||||
\(24\) | 136.783 | 0.0484736 | ||||||||
\(25\) | −3008.48 | −0.962713 | ||||||||
\(26\) | −1052.74 | −0.305414 | ||||||||
\(27\) | −1028.94 | −0.271631 | ||||||||
\(28\) | −3121.73 | −0.752488 | ||||||||
\(29\) | 6712.34 | 1.48210 | 0.741052 | − | 0.671447i | \(-0.234327\pi\) | ||||
0.741052 | + | 0.671447i | \(0.234327\pi\) | |||||||
\(30\) | −92.2816 | −0.0187203 | ||||||||
\(31\) | 9280.96 | 1.73456 | 0.867279 | − | 0.497823i | \(-0.165867\pi\) | ||||
0.867279 | + | 0.497823i | \(0.165867\pi\) | |||||||
\(32\) | 1024.00 | 0.176777 | ||||||||
\(33\) | −36.5269 | −0.00583886 | ||||||||
\(34\) | −2310.90 | −0.342834 | ||||||||
\(35\) | 2106.09 | 0.290607 | ||||||||
\(36\) | −3814.92 | −0.490601 | ||||||||
\(37\) | 1713.65 | 0.205787 | 0.102894 | − | 0.994692i | \(-0.467190\pi\) | ||||
0.102894 | + | 0.994692i | \(0.467190\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −562.492 | −0.0592181 | ||||||||
\(40\) | −690.846 | −0.0682703 | ||||||||
\(41\) | 1219.00 | 0.113252 | 0.0566258 | − | 0.998395i | \(-0.481966\pi\) | ||||
0.0566258 | + | 0.998395i | \(0.481966\pi\) | |||||||
\(42\) | −1667.97 | −0.145903 | ||||||||
\(43\) | −15472.5 | −1.27612 | −0.638058 | − | 0.769988i | \(-0.720262\pi\) | ||||
−0.638058 | + | 0.769988i | \(0.720262\pi\) | |||||||
\(44\) | −273.451 | −0.0212935 | ||||||||
\(45\) | 2573.75 | 0.189468 | ||||||||
\(46\) | −2262.03 | −0.157617 | ||||||||
\(47\) | 1492.69 | 0.0985657 | 0.0492829 | − | 0.998785i | \(-0.484306\pi\) | ||||
0.0492829 | + | 0.998785i | \(0.484306\pi\) | |||||||
\(48\) | 547.134 | 0.0342760 | ||||||||
\(49\) | 21260.1 | 1.26495 | ||||||||
\(50\) | −12033.9 | −0.680741 | ||||||||
\(51\) | −1234.74 | −0.0664736 | ||||||||
\(52\) | −4210.97 | −0.215960 | ||||||||
\(53\) | 25666.2 | 1.25508 | 0.627541 | − | 0.778583i | \(-0.284061\pi\) | ||||
0.627541 | + | 0.778583i | \(0.284061\pi\) | |||||||
\(54\) | −4115.75 | −0.192072 | ||||||||
\(55\) | 184.485 | 0.00822345 | ||||||||
\(56\) | −12486.9 | −0.532090 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 26849.4 | 1.04801 | ||||||||
\(59\) | 2971.17 | 0.111121 | 0.0555607 | − | 0.998455i | \(-0.482305\pi\) | ||||
0.0555607 | + | 0.998455i | \(0.482305\pi\) | |||||||
\(60\) | −369.126 | −0.0132372 | ||||||||
\(61\) | 11469.3 | 0.394651 | 0.197326 | − | 0.980338i | \(-0.436774\pi\) | ||||
0.197326 | + | 0.980338i | \(0.436774\pi\) | |||||||
\(62\) | 37123.8 | 1.22652 | ||||||||
\(63\) | 46520.0 | 1.47669 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 2840.95 | 0.0834028 | ||||||||
\(66\) | −146.108 | −0.00412870 | ||||||||
\(67\) | −4196.56 | −0.114211 | −0.0571053 | − | 0.998368i | \(-0.518187\pi\) | ||||
−0.0571053 | + | 0.998368i | \(0.518187\pi\) | |||||||
\(68\) | −9243.60 | −0.242420 | ||||||||
\(69\) | −1208.63 | −0.0305611 | ||||||||
\(70\) | 8424.35 | 0.205490 | ||||||||
\(71\) | 67410.0 | 1.58701 | 0.793503 | − | 0.608567i | \(-0.208255\pi\) | ||||
0.793503 | + | 0.608567i | \(0.208255\pi\) | |||||||
\(72\) | −15259.7 | −0.346907 | ||||||||
\(73\) | −45625.5 | −1.00208 | −0.501038 | − | 0.865425i | \(-0.667048\pi\) | ||||
−0.501038 | + | 0.865425i | \(0.667048\pi\) | |||||||
\(74\) | 6854.61 | 0.145514 | ||||||||
\(75\) | −6429.85 | −0.131992 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3334.53 | 0.0640925 | ||||||||
\(78\) | −2249.97 | −0.0418735 | ||||||||
\(79\) | 33434.2 | 0.602730 | 0.301365 | − | 0.953509i | \(-0.402558\pi\) | ||||
0.301365 | + | 0.953509i | \(0.402558\pi\) | |||||||
\(80\) | −2763.39 | −0.0482744 | ||||||||
\(81\) | 55739.9 | 0.943961 | ||||||||
\(82\) | 4876.00 | 0.0800809 | ||||||||
\(83\) | 66875.6 | 1.06555 | 0.532773 | − | 0.846258i | \(-0.321150\pi\) | ||||
0.532773 | + | 0.846258i | \(0.321150\pi\) | |||||||
\(84\) | −6671.88 | −0.103169 | ||||||||
\(85\) | 6236.23 | 0.0936214 | ||||||||
\(86\) | −61890.1 | −0.902351 | ||||||||
\(87\) | 14345.9 | 0.203203 | ||||||||
\(88\) | −1093.80 | −0.0150568 | ||||||||
\(89\) | −86080.7 | −1.15194 | −0.575972 | − | 0.817470i | \(-0.695376\pi\) | ||||
−0.575972 | + | 0.817470i | \(0.695376\pi\) | |||||||
\(90\) | 10295.0 | 0.133974 | ||||||||
\(91\) | 51349.6 | 0.650031 | ||||||||
\(92\) | −9048.13 | −0.111452 | ||||||||
\(93\) | 19835.6 | 0.237815 | ||||||||
\(94\) | 5970.77 | 0.0696965 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2188.53 | 0.0242368 | ||||||||
\(97\) | 130701. | 1.41042 | 0.705211 | − | 0.708998i | \(-0.250852\pi\) | ||||
0.705211 | + | 0.708998i | \(0.250852\pi\) | |||||||
\(98\) | 85040.4 | 0.894458 | ||||||||
\(99\) | 4074.97 | 0.0417865 | ||||||||
\(100\) | −48135.7 | −0.481357 | ||||||||
\(101\) | −18239.4 | −0.177913 | −0.0889564 | − | 0.996036i | \(-0.528353\pi\) | ||||
−0.0889564 | + | 0.996036i | \(0.528353\pi\) | |||||||
\(102\) | −4938.95 | −0.0470039 | ||||||||
\(103\) | 26800.0 | 0.248910 | 0.124455 | − | 0.992225i | \(-0.460282\pi\) | ||||
0.124455 | + | 0.992225i | \(0.460282\pi\) | |||||||
\(104\) | −16843.9 | −0.152707 | ||||||||
\(105\) | 4501.22 | 0.0398434 | ||||||||
\(106\) | 102665. | 0.887478 | ||||||||
\(107\) | 168247. | 1.42065 | 0.710327 | − | 0.703872i | \(-0.248547\pi\) | ||||
0.710327 | + | 0.703872i | \(0.248547\pi\) | |||||||
\(108\) | −16463.0 | −0.135815 | ||||||||
\(109\) | −16094.3 | −0.129750 | −0.0648748 | − | 0.997893i | \(-0.520665\pi\) | ||||
−0.0648748 | + | 0.997893i | \(0.520665\pi\) | |||||||
\(110\) | 737.939 | 0.00581486 | ||||||||
\(111\) | 3662.49 | 0.0282143 | ||||||||
\(112\) | −49947.6 | −0.376244 | ||||||||
\(113\) | −103218. | −0.760427 | −0.380213 | − | 0.924899i | \(-0.624149\pi\) | ||||
−0.380213 | + | 0.924899i | \(0.624149\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6104.36 | 0.0430423 | ||||||||
\(116\) | 107397. | 0.741052 | ||||||||
\(117\) | 62752.0 | 0.423802 | ||||||||
\(118\) | 11884.7 | 0.0785747 | ||||||||
\(119\) | 112719. | 0.729673 | ||||||||
\(120\) | −1476.51 | −0.00936013 | ||||||||
\(121\) | −160759. | −0.998186 | ||||||||
\(122\) | 45877.3 | 0.279061 | ||||||||
\(123\) | 2605.30 | 0.0155272 | ||||||||
\(124\) | 148495. | 0.867279 | ||||||||
\(125\) | 66207.7 | 0.378995 | ||||||||
\(126\) | 186080. | 1.04418 | ||||||||
\(127\) | −213253. | −1.17324 | −0.586620 | − | 0.809863i | \(-0.699542\pi\) | ||||
−0.586620 | + | 0.809863i | \(0.699542\pi\) | |||||||
\(128\) | 16384.0 | 0.0883883 | ||||||||
\(129\) | −33068.5 | −0.174961 | ||||||||
\(130\) | 11363.8 | 0.0589747 | ||||||||
\(131\) | −322898. | −1.64394 | −0.821971 | − | 0.569529i | \(-0.807126\pi\) | ||||
−0.821971 | + | 0.569529i | \(0.807126\pi\) | |||||||
\(132\) | −584.430 | −0.00291943 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −16786.2 | −0.0807591 | ||||||||
\(135\) | 11106.8 | 0.0524512 | ||||||||
\(136\) | −36974.4 | −0.171417 | ||||||||
\(137\) | −297608. | −1.35470 | −0.677349 | − | 0.735662i | \(-0.736871\pi\) | ||||
−0.677349 | + | 0.735662i | \(0.736871\pi\) | |||||||
\(138\) | −4834.51 | −0.0216100 | ||||||||
\(139\) | −42527.0 | −0.186693 | −0.0933464 | − | 0.995634i | \(-0.529756\pi\) | ||||
−0.0933464 | + | 0.995634i | \(0.529756\pi\) | |||||||
\(140\) | 33697.4 | 0.145304 | ||||||||
\(141\) | 3190.25 | 0.0135138 | ||||||||
\(142\) | 269640. | 1.12218 | ||||||||
\(143\) | 4498.02 | 0.0183942 | ||||||||
\(144\) | −61038.6 | −0.245301 | ||||||||
\(145\) | −72456.2 | −0.286191 | ||||||||
\(146\) | −182502. | −0.708574 | ||||||||
\(147\) | 45437.9 | 0.173430 | ||||||||
\(148\) | 27418.4 | 0.102894 | ||||||||
\(149\) | 397969. | 1.46853 | 0.734266 | − | 0.678862i | \(-0.237526\pi\) | ||||
0.734266 | + | 0.678862i | \(0.237526\pi\) | |||||||
\(150\) | −25719.4 | −0.0933324 | ||||||||
\(151\) | −312906. | −1.11679 | −0.558394 | − | 0.829576i | \(-0.688582\pi\) | ||||
−0.558394 | + | 0.829576i | \(0.688582\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 137748. | 0.475726 | ||||||||
\(154\) | 13338.1 | 0.0453202 | ||||||||
\(155\) | −100183. | −0.334939 | ||||||||
\(156\) | −8999.87 | −0.0296091 | ||||||||
\(157\) | 451929. | 1.46326 | 0.731629 | − | 0.681703i | \(-0.238760\pi\) | ||||
0.731629 | + | 0.681703i | \(0.238760\pi\) | |||||||
\(158\) | 133737. | 0.426195 | ||||||||
\(159\) | 54854.9 | 0.172077 | ||||||||
\(160\) | −11053.5 | −0.0341351 | ||||||||
\(161\) | 110335. | 0.335466 | ||||||||
\(162\) | 222960. | 0.667481 | ||||||||
\(163\) | 440059. | 1.29730 | 0.648652 | − | 0.761085i | \(-0.275333\pi\) | ||||
0.648652 | + | 0.761085i | \(0.275333\pi\) | |||||||
\(164\) | 19504.0 | 0.0566258 | ||||||||
\(165\) | 394.289 | 0.00112747 | ||||||||
\(166\) | 267502. | 0.753455 | ||||||||
\(167\) | 121109. | 0.336034 | 0.168017 | − | 0.985784i | \(-0.446264\pi\) | ||||
0.168017 | + | 0.985784i | \(0.446264\pi\) | |||||||
\(168\) | −26687.5 | −0.0729517 | ||||||||
\(169\) | −302026. | −0.813444 | ||||||||
\(170\) | 24944.9 | 0.0662003 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −247561. | −0.638058 | ||||||||
\(173\) | 562940. | 1.43003 | 0.715017 | − | 0.699107i | \(-0.246419\pi\) | ||||
0.715017 | + | 0.699107i | \(0.246419\pi\) | |||||||
\(174\) | 57383.5 | 0.143686 | ||||||||
\(175\) | 586978. | 1.44886 | ||||||||
\(176\) | −4375.21 | −0.0106468 | ||||||||
\(177\) | 6350.11 | 0.0152352 | ||||||||
\(178\) | −344323. | −0.814547 | ||||||||
\(179\) | −560560. | −1.30764 | −0.653822 | − | 0.756648i | \(-0.726836\pi\) | ||||
−0.653822 | + | 0.756648i | \(0.726836\pi\) | |||||||
\(180\) | 41180.0 | 0.0947338 | ||||||||
\(181\) | −467614. | −1.06094 | −0.530471 | − | 0.847703i | \(-0.677985\pi\) | ||||
−0.530471 | + | 0.847703i | \(0.677985\pi\) | |||||||
\(182\) | 205399. | 0.459641 | ||||||||
\(183\) | 24512.7 | 0.0541083 | ||||||||
\(184\) | −36192.5 | −0.0788087 | ||||||||
\(185\) | −18498.0 | −0.0397370 | ||||||||
\(186\) | 79342.6 | 0.168160 | ||||||||
\(187\) | 9873.70 | 0.0206479 | ||||||||
\(188\) | 23883.1 | 0.0492829 | ||||||||
\(189\) | 200754. | 0.408798 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 50390.1 | 0.0999452 | 0.0499726 | − | 0.998751i | \(-0.484087\pi\) | ||||
0.0499726 | + | 0.998751i | \(0.484087\pi\) | |||||||
\(192\) | 8754.14 | 0.0171380 | ||||||||
\(193\) | 817525. | 1.57982 | 0.789910 | − | 0.613223i | \(-0.210127\pi\) | ||||
0.789910 | + | 0.613223i | \(0.210127\pi\) | |||||||
\(194\) | 522803. | 0.997319 | ||||||||
\(195\) | 6071.80 | 0.0114349 | ||||||||
\(196\) | 340162. | 0.632477 | ||||||||
\(197\) | 455871. | 0.836905 | 0.418453 | − | 0.908239i | \(-0.362573\pi\) | ||||
0.418453 | + | 0.908239i | \(0.362573\pi\) | |||||||
\(198\) | 16299.9 | 0.0295475 | ||||||||
\(199\) | 547135. | 0.979403 | 0.489702 | − | 0.871890i | \(-0.337106\pi\) | ||||
0.489702 | + | 0.871890i | \(0.337106\pi\) | |||||||
\(200\) | −192543. | −0.340371 | ||||||||
\(201\) | −8969.06 | −0.0156587 | ||||||||
\(202\) | −72957.6 | −0.125803 | ||||||||
\(203\) | −1.30963e6 | −2.23053 | ||||||||
\(204\) | −19755.8 | −0.0332368 | ||||||||
\(205\) | −13158.5 | −0.0218686 | ||||||||
\(206\) | 107200. | 0.176006 | ||||||||
\(207\) | 134835. | 0.218715 | ||||||||
\(208\) | −67375.6 | −0.107980 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 18004.9 | 0.0281736 | ||||||||
\(211\) | 31898.8 | 0.0493251 | 0.0246625 | − | 0.999696i | \(-0.492149\pi\) | ||||
0.0246625 | + | 0.999696i | \(0.492149\pi\) | |||||||
\(212\) | 410660. | 0.627541 | ||||||||
\(213\) | 144071. | 0.217585 | ||||||||
\(214\) | 672989. | 1.00455 | ||||||||
\(215\) | 167018. | 0.246415 | ||||||||
\(216\) | −65851.9 | −0.0960360 | ||||||||
\(217\) | −1.81079e6 | −2.61047 | ||||||||
\(218\) | −64377.2 | −0.0917468 | ||||||||
\(219\) | −97512.7 | −0.137389 | ||||||||
\(220\) | 2951.76 | 0.00411172 | ||||||||
\(221\) | 152049. | 0.209413 | ||||||||
\(222\) | 14649.9 | 0.0199505 | ||||||||
\(223\) | 1.22713e6 | 1.65245 | 0.826224 | − | 0.563341i | \(-0.190484\pi\) | ||||
0.826224 | + | 0.563341i | \(0.190484\pi\) | |||||||
\(224\) | −199790. | −0.266045 | ||||||||
\(225\) | 717318. | 0.944617 | ||||||||
\(226\) | −412870. | −0.537703 | ||||||||
\(227\) | 243999. | 0.314285 | 0.157143 | − | 0.987576i | \(-0.449772\pi\) | ||||
0.157143 | + | 0.987576i | \(0.449772\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.29079e6 | −1.62654 | −0.813272 | − | 0.581884i | \(-0.802316\pi\) | ||||
−0.813272 | + | 0.581884i | \(0.802316\pi\) | |||||||
\(230\) | 24417.4 | 0.0304355 | ||||||||
\(231\) | 7126.69 | 0.00878734 | ||||||||
\(232\) | 429590. | 0.524003 | ||||||||
\(233\) | 1.23246e6 | 1.48725 | 0.743624 | − | 0.668598i | \(-0.233105\pi\) | ||||
0.743624 | + | 0.668598i | \(0.233105\pi\) | |||||||
\(234\) | 251008. | 0.299673 | ||||||||
\(235\) | −16112.8 | −0.0190328 | ||||||||
\(236\) | 47538.7 | 0.0555607 | ||||||||
\(237\) | 71456.9 | 0.0826368 | ||||||||
\(238\) | 450875. | 0.515957 | ||||||||
\(239\) | −299709. | −0.339395 | −0.169698 | − | 0.985496i | \(-0.554279\pi\) | ||||
−0.169698 | + | 0.985496i | \(0.554279\pi\) | |||||||
\(240\) | −5906.02 | −0.00661861 | ||||||||
\(241\) | −334121. | −0.370563 | −0.185281 | − | 0.982686i | \(-0.559320\pi\) | ||||
−0.185281 | + | 0.982686i | \(0.559320\pi\) | |||||||
\(242\) | −643036. | −0.705824 | ||||||||
\(243\) | 369161. | 0.401052 | ||||||||
\(244\) | 183509. | 0.197326 | ||||||||
\(245\) | −229492. | −0.244260 | ||||||||
\(246\) | 10421.2 | 0.0109794 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 593981. | 0.613259 | ||||||||
\(249\) | 142929. | 0.146091 | ||||||||
\(250\) | 264831. | 0.267990 | ||||||||
\(251\) | 1.78722e6 | 1.79058 | 0.895290 | − | 0.445484i | \(-0.146968\pi\) | ||||
0.895290 | + | 0.445484i | \(0.146968\pi\) | |||||||
\(252\) | 744320. | 0.738343 | ||||||||
\(253\) | 9664.91 | 0.00949285 | ||||||||
\(254\) | −853013. | −0.829605 | ||||||||
\(255\) | 13328.3 | 0.0128359 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 1.30644e6 | 1.23384 | 0.616919 | − | 0.787026i | \(-0.288381\pi\) | ||||
0.616919 | + | 0.787026i | \(0.288381\pi\) | |||||||
\(258\) | −132274. | −0.123716 | ||||||||
\(259\) | −334347. | −0.309705 | ||||||||
\(260\) | 45455.2 | 0.0417014 | ||||||||
\(261\) | −1.60044e6 | −1.45424 | ||||||||
\(262\) | −1.29159e6 | −1.16244 | ||||||||
\(263\) | 2.21793e6 | 1.97724 | 0.988619 | − | 0.150441i | \(-0.0480694\pi\) | ||||
0.988619 | + | 0.150441i | \(0.0480694\pi\) | |||||||
\(264\) | −2337.72 | −0.00206435 | ||||||||
\(265\) | −277053. | −0.242353 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −183975. | −0.157936 | ||||||||
\(268\) | −67145.0 | −0.0571053 | ||||||||
\(269\) | 433462. | 0.365233 | 0.182616 | − | 0.983184i | \(-0.441543\pi\) | ||||
0.182616 | + | 0.983184i | \(0.441543\pi\) | |||||||
\(270\) | 44427.3 | 0.0370886 | ||||||||
\(271\) | −1.44684e6 | −1.19673 | −0.598366 | − | 0.801223i | \(-0.704183\pi\) | ||||
−0.598366 | + | 0.801223i | \(0.704183\pi\) | |||||||
\(272\) | −147898. | −0.121210 | ||||||||
\(273\) | 109747. | 0.0891219 | ||||||||
\(274\) | −1.19043e6 | −0.957916 | ||||||||
\(275\) | 51416.9 | 0.0409991 | ||||||||
\(276\) | −19338.0 | −0.0152806 | ||||||||
\(277\) | 1.64595e6 | 1.28889 | 0.644446 | − | 0.764650i | \(-0.277088\pi\) | ||||
0.644446 | + | 0.764650i | \(0.277088\pi\) | |||||||
\(278\) | −170108. | −0.132012 | ||||||||
\(279\) | −2.21288e6 | −1.70195 | ||||||||
\(280\) | 134790. | 0.102745 | ||||||||
\(281\) | 925545. | 0.699249 | 0.349625 | − | 0.936890i | \(-0.386309\pi\) | ||||
0.349625 | + | 0.936890i | \(0.386309\pi\) | |||||||
\(282\) | 12761.0 | 0.00955567 | ||||||||
\(283\) | −2.12008e6 | −1.57357 | −0.786786 | − | 0.617226i | \(-0.788257\pi\) | ||||
−0.786786 | + | 0.617226i | \(0.788257\pi\) | |||||||
\(284\) | 1.07856e6 | 0.793503 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 17992.1 | 0.0130067 | ||||||||
\(287\) | −237836. | −0.170441 | ||||||||
\(288\) | −244155. | −0.173454 | ||||||||
\(289\) | −1.08609e6 | −0.764930 | ||||||||
\(290\) | −289825. | −0.202367 | ||||||||
\(291\) | 279339. | 0.193375 | ||||||||
\(292\) | −730008. | −0.501038 | ||||||||
\(293\) | −943155. | −0.641821 | −0.320910 | − | 0.947110i | \(-0.603989\pi\) | ||||
−0.320910 | + | 0.947110i | \(0.603989\pi\) | |||||||
\(294\) | 181752. | 0.122634 | ||||||||
\(295\) | −32072.2 | −0.0214572 | ||||||||
\(296\) | 109674. | 0.0727568 | ||||||||
\(297\) | 17585.2 | 0.0115680 | ||||||||
\(298\) | 1.59188e6 | 1.03841 | ||||||||
\(299\) | 148834. | 0.0962771 | ||||||||
\(300\) | −102878. | −0.0659960 | ||||||||
\(301\) | 3.01881e6 | 1.92053 | ||||||||
\(302\) | −1.25162e6 | −0.789689 | ||||||||
\(303\) | −38982.0 | −0.0243926 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −123805. | −0.0762062 | ||||||||
\(306\) | 550993. | 0.336389 | ||||||||
\(307\) | −2.09504e6 | −1.26867 | −0.634333 | − | 0.773060i | \(-0.718725\pi\) | ||||
−0.634333 | + | 0.773060i | \(0.718725\pi\) | |||||||
\(308\) | 53352.4 | 0.0320463 | ||||||||
\(309\) | 57278.0 | 0.0341265 | ||||||||
\(310\) | −400732. | −0.236837 | ||||||||
\(311\) | 638862. | 0.374547 | 0.187273 | − | 0.982308i | \(-0.440035\pi\) | ||||
0.187273 | + | 0.982308i | \(0.440035\pi\) | |||||||
\(312\) | −35999.5 | −0.0209368 | ||||||||
\(313\) | 1.13152e6 | 0.652833 | 0.326417 | − | 0.945226i | \(-0.394159\pi\) | ||||
0.326417 | + | 0.945226i | \(0.394159\pi\) | |||||||
\(314\) | 1.80772e6 | 1.03468 | ||||||||
\(315\) | −502159. | −0.285144 | ||||||||
\(316\) | 534947. | 0.301365 | ||||||||
\(317\) | −1.17244e6 | −0.655301 | −0.327651 | − | 0.944799i | \(-0.606257\pi\) | ||||
−0.327651 | + | 0.944799i | \(0.606257\pi\) | |||||||
\(318\) | 219420. | 0.121677 | ||||||||
\(319\) | −114718. | −0.0631185 | ||||||||
\(320\) | −44214.2 | −0.0241372 | ||||||||
\(321\) | 359585. | 0.194777 | ||||||||
\(322\) | 441340. | 0.237210 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 891839. | 0.471980 | ||||||||
\(325\) | 791789. | 0.415816 | ||||||||
\(326\) | 1.76023e6 | 0.917332 | ||||||||
\(327\) | −34397.4 | −0.0177892 | ||||||||
\(328\) | 78016.0 | 0.0400405 | ||||||||
\(329\) | −291236. | −0.148339 | ||||||||
\(330\) | 1577.15 | 0.000797241 0 | ||||||||
\(331\) | −738377. | −0.370432 | −0.185216 | − | 0.982698i | \(-0.559298\pi\) | ||||
−0.185216 | + | 0.982698i | \(0.559298\pi\) | |||||||
\(332\) | 1.07001e6 | 0.532773 | ||||||||
\(333\) | −408590. | −0.201919 | ||||||||
\(334\) | 484434. | 0.237612 | ||||||||
\(335\) | 45299.7 | 0.0220538 | ||||||||
\(336\) | −106750. | −0.0515846 | ||||||||
\(337\) | 1.96851e6 | 0.944197 | 0.472099 | − | 0.881546i | \(-0.343497\pi\) | ||||
0.472099 | + | 0.881546i | \(0.343497\pi\) | |||||||
\(338\) | −1.20810e6 | −0.575192 | ||||||||
\(339\) | −220601. | −0.104258 | ||||||||
\(340\) | 99779.8 | 0.0468107 | ||||||||
\(341\) | −158618. | −0.0738697 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −868834. | −0.398751 | ||||||||
\(344\) | −990242. | −0.451175 | ||||||||
\(345\) | 13046.5 | 0.00590128 | ||||||||
\(346\) | 2.25176e6 | 1.01119 | ||||||||
\(347\) | 2.63680e6 | 1.17559 | 0.587793 | − | 0.809012i | \(-0.299997\pi\) | ||||
0.587793 | + | 0.809012i | \(0.299997\pi\) | |||||||
\(348\) | 229534. | 0.101601 | ||||||||
\(349\) | −496602. | −0.218245 | −0.109123 | − | 0.994028i | \(-0.534804\pi\) | ||||
−0.109123 | + | 0.994028i | \(0.534804\pi\) | |||||||
\(350\) | 2.34791e6 | 1.02450 | ||||||||
\(351\) | 270802. | 0.117323 | ||||||||
\(352\) | −17500.9 | −0.00752840 | ||||||||
\(353\) | −2.17439e6 | −0.928753 | −0.464377 | − | 0.885638i | \(-0.653722\pi\) | ||||
−0.464377 | + | 0.885638i | \(0.653722\pi\) | |||||||
\(354\) | 25400.4 | 0.0107729 | ||||||||
\(355\) | −727655. | −0.306447 | ||||||||
\(356\) | −1.37729e6 | −0.575972 | ||||||||
\(357\) | 240907. | 0.100041 | ||||||||
\(358\) | −2.24224e6 | −0.924644 | ||||||||
\(359\) | −257893. | −0.105610 | −0.0528048 | − | 0.998605i | \(-0.516816\pi\) | ||||
−0.0528048 | + | 0.998605i | \(0.516816\pi\) | |||||||
\(360\) | 164720. | 0.0669869 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −1.87046e6 | −0.750199 | ||||||||
\(363\) | −343581. | −0.136855 | ||||||||
\(364\) | 821594. | 0.325015 | ||||||||
\(365\) | 492503. | 0.193498 | ||||||||
\(366\) | 98050.9 | 0.0382603 | ||||||||
\(367\) | −2.62085e6 | −1.01573 | −0.507863 | − | 0.861438i | \(-0.669564\pi\) | ||||
−0.507863 | + | 0.861438i | \(0.669564\pi\) | |||||||
\(368\) | −144770. | −0.0557262 | ||||||||
\(369\) | −290649. | −0.111123 | ||||||||
\(370\) | −73991.9 | −0.0280983 | ||||||||
\(371\) | −5.00768e6 | −1.88887 | ||||||||
\(372\) | 317370. | 0.118907 | ||||||||
\(373\) | −3.45002e6 | −1.28396 | −0.641978 | − | 0.766723i | \(-0.721886\pi\) | ||||
−0.641978 | + | 0.766723i | \(0.721886\pi\) | |||||||
\(374\) | 39494.8 | 0.0146003 | ||||||||
\(375\) | 141502. | 0.0519617 | ||||||||
\(376\) | 95532.4 | 0.0348482 | ||||||||
\(377\) | −1.76659e6 | −0.640152 | ||||||||
\(378\) | 803015. | 0.289064 | ||||||||
\(379\) | −3.09133e6 | −1.10547 | −0.552736 | − | 0.833356i | \(-0.686416\pi\) | ||||
−0.552736 | + | 0.833356i | \(0.686416\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −455774. | −0.160856 | ||||||||
\(382\) | 201560. | 0.0706719 | ||||||||
\(383\) | 625110. | 0.217751 | 0.108875 | − | 0.994055i | \(-0.465275\pi\) | ||||
0.108875 | + | 0.994055i | \(0.465275\pi\) | |||||||
\(384\) | 35016.6 | 0.0121184 | ||||||||
\(385\) | −35994.5 | −0.0123761 | ||||||||
\(386\) | 3.27010e6 | 1.11710 | ||||||||
\(387\) | 3.68915e6 | 1.25213 | ||||||||
\(388\) | 2.09121e6 | 0.705211 | ||||||||
\(389\) | −3.13033e6 | −1.04886 | −0.524428 | − | 0.851455i | \(-0.675721\pi\) | ||||
−0.524428 | + | 0.851455i | \(0.675721\pi\) | |||||||
\(390\) | 24287.2 | 0.00808567 | ||||||||
\(391\) | 326708. | 0.108073 | ||||||||
\(392\) | 1.36065e6 | 0.447229 | ||||||||
\(393\) | −690110. | −0.225391 | ||||||||
\(394\) | 1.82348e6 | 0.591781 | ||||||||
\(395\) | −360905. | −0.116386 | ||||||||
\(396\) | 65199.5 | 0.0208933 | ||||||||
\(397\) | 4.04982e6 | 1.28961 | 0.644807 | − | 0.764346i | \(-0.276938\pi\) | ||||
0.644807 | + | 0.764346i | \(0.276938\pi\) | |||||||
\(398\) | 2.18854e6 | 0.692543 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −770171. | −0.240678 | ||||||||
\(401\) | 4.13849e6 | 1.28523 | 0.642615 | − | 0.766189i | \(-0.277849\pi\) | ||||
0.642615 | + | 0.766189i | \(0.277849\pi\) | |||||||
\(402\) | −35876.3 | −0.0110724 | ||||||||
\(403\) | −2.44262e6 | −0.749191 | ||||||||
\(404\) | −291830. | −0.0889564 | ||||||||
\(405\) | −601683. | −0.182276 | ||||||||
\(406\) | −5.23852e6 | −1.57722 | ||||||||
\(407\) | −29287.5 | −0.00876387 | ||||||||
\(408\) | −79023.2 | −0.0235020 | ||||||||
\(409\) | −3.28825e6 | −0.971979 | −0.485990 | − | 0.873965i | \(-0.661541\pi\) | ||||
−0.485990 | + | 0.873965i | \(0.661541\pi\) | |||||||
\(410\) | −52633.8 | −0.0154634 | ||||||||
\(411\) | −636059. | −0.185735 | ||||||||
\(412\) | 428800. | 0.124455 | ||||||||
\(413\) | −579699. | −0.167235 | ||||||||
\(414\) | 539341. | 0.154655 | ||||||||
\(415\) | −721887. | −0.205754 | ||||||||
\(416\) | −269502. | −0.0763535 | ||||||||
\(417\) | −90890.4 | −0.0255964 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.77322e6 | 1.04997 | 0.524985 | − | 0.851111i | \(-0.324071\pi\) | ||||
0.524985 | + | 0.851111i | \(0.324071\pi\) | |||||||
\(420\) | 72019.5 | 0.0199217 | ||||||||
\(421\) | −392214. | −0.107849 | −0.0539247 | − | 0.998545i | \(-0.517173\pi\) | ||||
−0.0539247 | + | 0.998545i | \(0.517173\pi\) | |||||||
\(422\) | 127595. | 0.0348781 | ||||||||
\(423\) | −355906. | −0.0967129 | ||||||||
\(424\) | 1.64264e6 | 0.443739 | ||||||||
\(425\) | 1.73807e6 | 0.466762 | ||||||||
\(426\) | 576286. | 0.153856 | ||||||||
\(427\) | −2.23776e6 | −0.593941 | ||||||||
\(428\) | 2.69195e6 | 0.710327 | ||||||||
\(429\) | 9613.36 | 0.00252192 | ||||||||
\(430\) | 668072. | 0.174242 | ||||||||
\(431\) | 5.99845e6 | 1.55541 | 0.777707 | − | 0.628627i | \(-0.216383\pi\) | ||||
0.777707 | + | 0.628627i | \(0.216383\pi\) | |||||||
\(432\) | −263408. | −0.0679077 | ||||||||
\(433\) | 2.29152e6 | 0.587359 | 0.293680 | − | 0.955904i | \(-0.405120\pi\) | ||||
0.293680 | + | 0.955904i | \(0.405120\pi\) | |||||||
\(434\) | −7.24315e6 | −1.84588 | ||||||||
\(435\) | −154856. | −0.0392379 | ||||||||
\(436\) | −257509. | −0.0648748 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −390051. | −0.0971484 | ||||||||
\(439\) | 168827. | 0.0418101 | 0.0209050 | − | 0.999781i | \(-0.493345\pi\) | ||||
0.0209050 | + | 0.999781i | \(0.493345\pi\) | |||||||
\(440\) | 11807.0 | 0.00290743 | ||||||||
\(441\) | −5.06909e6 | −1.24118 | ||||||||
\(442\) | 608196. | 0.148077 | ||||||||
\(443\) | −3.11020e6 | −0.752972 | −0.376486 | − | 0.926422i | \(-0.622868\pi\) | ||||
−0.376486 | + | 0.926422i | \(0.622868\pi\) | |||||||
\(444\) | 58599.8 | 0.0141071 | ||||||||
\(445\) | 929196. | 0.222437 | ||||||||
\(446\) | 4.90851e6 | 1.16846 | ||||||||
\(447\) | 850555. | 0.201342 | ||||||||
\(448\) | −799162. | −0.188122 | ||||||||
\(449\) | 5.05277e6 | 1.18281 | 0.591403 | − | 0.806376i | \(-0.298574\pi\) | ||||
0.591403 | + | 0.806376i | \(0.298574\pi\) | |||||||
\(450\) | 2.86927e6 | 0.667945 | ||||||||
\(451\) | −20833.5 | −0.00482305 | ||||||||
\(452\) | −1.65148e6 | −0.380213 | ||||||||
\(453\) | −668755. | −0.153116 | ||||||||
\(454\) | 975997. | 0.222233 | ||||||||
\(455\) | −554292. | −0.125519 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.57909e6 | 0.577665 | 0.288832 | − | 0.957380i | \(-0.406733\pi\) | ||||
0.288832 | + | 0.957380i | \(0.406733\pi\) | |||||||
\(458\) | −5.16315e6 | −1.15014 | ||||||||
\(459\) | 594442. | 0.131698 | ||||||||
\(460\) | 97669.8 | 0.0215212 | ||||||||
\(461\) | −7.85829e6 | −1.72217 | −0.861085 | − | 0.508461i | \(-0.830214\pi\) | ||||
−0.861085 | + | 0.508461i | \(0.830214\pi\) | |||||||
\(462\) | 28506.7 | 0.00621359 | ||||||||
\(463\) | 4.86915e6 | 1.05560 | 0.527802 | − | 0.849367i | \(-0.323016\pi\) | ||||
0.527802 | + | 0.849367i | \(0.323016\pi\) | |||||||
\(464\) | 1.71836e6 | 0.370526 | ||||||||
\(465\) | −214115. | −0.0459214 | ||||||||
\(466\) | 4.92984e6 | 1.05164 | ||||||||
\(467\) | 1.77798e6 | 0.377254 | 0.188627 | − | 0.982049i | \(-0.439596\pi\) | ||||
0.188627 | + | 0.982049i | \(0.439596\pi\) | |||||||
\(468\) | 1.00403e6 | 0.211901 | ||||||||
\(469\) | 818782. | 0.171884 | ||||||||
\(470\) | −64451.4 | −0.0134582 | ||||||||
\(471\) | 965881. | 0.200619 | ||||||||
\(472\) | 190155. | 0.0392873 | ||||||||
\(473\) | 264436. | 0.0543460 | ||||||||
\(474\) | 285828. | 0.0584330 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.80350e6 | 0.364837 | ||||||||
\(477\) | −6.11966e6 | −1.23149 | ||||||||
\(478\) | −1.19884e6 | −0.239989 | ||||||||
\(479\) | −9.95603e6 | −1.98266 | −0.991328 | − | 0.131408i | \(-0.958050\pi\) | ||||
−0.991328 | + | 0.131408i | \(0.958050\pi\) | |||||||
\(480\) | −23624.1 | −0.00468007 | ||||||||
\(481\) | −451009. | −0.0888838 | ||||||||
\(482\) | −1.33649e6 | −0.262027 | ||||||||
\(483\) | 235813. | 0.0459938 | ||||||||
\(484\) | −2.57214e6 | −0.499093 | ||||||||
\(485\) | −1.41085e6 | −0.272349 | ||||||||
\(486\) | 1.47665e6 | 0.283586 | ||||||||
\(487\) | −758898. | −0.144998 | −0.0724988 | − | 0.997368i | \(-0.523097\pi\) | ||||
−0.0724988 | + | 0.997368i | \(0.523097\pi\) | |||||||
\(488\) | 734037. | 0.139530 | ||||||||
\(489\) | 940512. | 0.177866 | ||||||||
\(490\) | −917966. | −0.172718 | ||||||||
\(491\) | 1.85836e6 | 0.347877 | 0.173938 | − | 0.984757i | \(-0.444351\pi\) | ||||
0.173938 | + | 0.984757i | \(0.444351\pi\) | |||||||
\(492\) | 41684.7 | 0.00776362 | ||||||||
\(493\) | −3.87788e6 | −0.718584 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −43987.1 | −0.00806887 | ||||||||
\(496\) | 2.37593e6 | 0.433639 | ||||||||
\(497\) | −1.31522e7 | −2.38841 | ||||||||
\(498\) | 571717. | 0.103302 | ||||||||
\(499\) | −7.70818e6 | −1.38580 | −0.692900 | − | 0.721034i | \(-0.743667\pi\) | ||||
−0.692900 | + | 0.721034i | \(0.743667\pi\) | |||||||
\(500\) | 1.05932e6 | 0.189497 | ||||||||
\(501\) | 258838. | 0.0460717 | ||||||||
\(502\) | 7.14888e6 | 1.26613 | ||||||||
\(503\) | −6.63172e6 | −1.16871 | −0.584354 | − | 0.811499i | \(-0.698652\pi\) | ||||
−0.584354 | + | 0.811499i | \(0.698652\pi\) | |||||||
\(504\) | 2.97728e6 | 0.522088 | ||||||||
\(505\) | 196885. | 0.0343545 | ||||||||
\(506\) | 38659.6 | 0.00671246 | ||||||||
\(507\) | −645503. | −0.111527 | ||||||||
\(508\) | −3.41205e6 | −0.586620 | ||||||||
\(509\) | 1.10429e7 | 1.88924 | 0.944620 | − | 0.328166i | \(-0.106431\pi\) | ||||
0.944620 | + | 0.328166i | \(0.106431\pi\) | |||||||
\(510\) | 53313.3 | 0.00907634 | ||||||||
\(511\) | 8.90190e6 | 1.50810 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.22578e6 | 0.872456 | ||||||||
\(515\) | −289292. | −0.0480638 | ||||||||
\(516\) | −529097. | −0.0874804 | ||||||||
\(517\) | −25511.1 | −0.00419762 | ||||||||
\(518\) | −1.33739e6 | −0.218994 | ||||||||
\(519\) | 1.20314e6 | 0.196064 | ||||||||
\(520\) | 181821. | 0.0294873 | ||||||||
\(521\) | 5.31342e6 | 0.857590 | 0.428795 | − | 0.903402i | \(-0.358938\pi\) | ||||
0.428795 | + | 0.903402i | \(0.358938\pi\) | |||||||
\(522\) | −6.40175e6 | −1.02831 | ||||||||
\(523\) | 186790. | 0.0298607 | 0.0149303 | − | 0.999889i | \(-0.495247\pi\) | ||||
0.0149303 | + | 0.999889i | \(0.495247\pi\) | |||||||
\(524\) | −5.16636e6 | −0.821971 | ||||||||
\(525\) | 1.25451e6 | 0.198645 | ||||||||
\(526\) | 8.87173e6 | 1.39812 | ||||||||
\(527\) | −5.36184e6 | −0.840983 | ||||||||
\(528\) | −9350.88 | −0.00145971 | ||||||||
\(529\) | −6.11654e6 | −0.950314 | ||||||||
\(530\) | −1.10821e6 | −0.171370 | ||||||||
\(531\) | −708423. | −0.109033 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −320823. | −0.0489157 | ||||||||
\(534\) | −735901. | −0.111678 | ||||||||
\(535\) | −1.81614e6 | −0.274325 | ||||||||
\(536\) | −268580. | −0.0403796 | ||||||||
\(537\) | −1.19805e6 | −0.179283 | ||||||||
\(538\) | 1.73385e6 | 0.258259 | ||||||||
\(539\) | −363349. | −0.0538707 | ||||||||
\(540\) | 177709. | 0.0262256 | ||||||||
\(541\) | −486912. | −0.0715249 | −0.0357624 | − | 0.999360i | \(-0.511386\pi\) | ||||
−0.0357624 | + | 0.999360i | \(0.511386\pi\) | |||||||
\(542\) | −5.78735e6 | −0.846217 | ||||||||
\(543\) | −999405. | −0.145459 | ||||||||
\(544\) | −591590. | −0.0857085 | ||||||||
\(545\) | 173730. | 0.0250543 | ||||||||
\(546\) | 438986. | 0.0630187 | ||||||||
\(547\) | −5.31296e6 | −0.759221 | −0.379610 | − | 0.925146i | \(-0.623942\pi\) | ||||
−0.379610 | + | 0.925146i | \(0.623942\pi\) | |||||||
\(548\) | −4.76172e6 | −0.677349 | ||||||||
\(549\) | −2.73466e6 | −0.387233 | ||||||||
\(550\) | 205668. | 0.0289908 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −77352.1 | −0.0108050 | ||||||||
\(553\) | −6.52328e6 | −0.907095 | ||||||||
\(554\) | 6.58379e6 | 0.911384 | ||||||||
\(555\) | −39534.6 | −0.00544810 | ||||||||
\(556\) | −680432. | −0.0933464 | ||||||||
\(557\) | −3.60173e6 | −0.491897 | −0.245948 | − | 0.969283i | \(-0.579099\pi\) | ||||
−0.245948 | + | 0.969283i | \(0.579099\pi\) | |||||||
\(558\) | −8.85152e6 | −1.20346 | ||||||||
\(559\) | 4.07215e6 | 0.551181 | ||||||||
\(560\) | 539158. | 0.0726518 | ||||||||
\(561\) | 21102.5 | 0.00283091 | ||||||||
\(562\) | 3.70218e6 | 0.494444 | ||||||||
\(563\) | −1.99766e6 | −0.265614 | −0.132807 | − | 0.991142i | \(-0.542399\pi\) | ||||
−0.132807 | + | 0.991142i | \(0.542399\pi\) | |||||||
\(564\) | 51043.9 | 0.00675688 | ||||||||
\(565\) | 1.11418e6 | 0.146836 | ||||||||
\(566\) | −8.48033e6 | −1.11268 | ||||||||
\(567\) | −1.08753e7 | −1.42064 | ||||||||
\(568\) | 4.31424e6 | 0.561091 | ||||||||
\(569\) | −5.80414e6 | −0.751549 | −0.375775 | − | 0.926711i | \(-0.622623\pi\) | ||||
−0.375775 | + | 0.926711i | \(0.622623\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.27354e6 | 0.291818 | 0.145909 | − | 0.989298i | \(-0.453389\pi\) | ||||
0.145909 | + | 0.989298i | \(0.453389\pi\) | |||||||
\(572\) | 71968.4 | 0.00919712 | ||||||||
\(573\) | 107696. | 0.0137029 | ||||||||
\(574\) | −951346. | −0.120520 | ||||||||
\(575\) | 1.70132e6 | 0.214593 | ||||||||
\(576\) | −976618. | −0.122650 | ||||||||
\(577\) | 1.48551e7 | 1.85753 | 0.928766 | − | 0.370667i | \(-0.120871\pi\) | ||||
0.928766 | + | 0.370667i | \(0.120871\pi\) | |||||||
\(578\) | −4.34436e6 | −0.540887 | ||||||||
\(579\) | 1.74725e6 | 0.216600 | ||||||||
\(580\) | −1.15930e6 | −0.143095 | ||||||||
\(581\) | −1.30480e7 | −1.60362 | ||||||||
\(582\) | 1.11736e6 | 0.136736 | ||||||||
\(583\) | −438653. | −0.0534503 | ||||||||
\(584\) | −2.92003e6 | −0.354287 | ||||||||
\(585\) | −677375. | −0.0818350 | ||||||||
\(586\) | −3.77262e6 | −0.453836 | ||||||||
\(587\) | 9.06829e6 | 1.08625 | 0.543125 | − | 0.839652i | \(-0.317241\pi\) | ||||
0.543125 | + | 0.839652i | \(0.317241\pi\) | |||||||
\(588\) | 727007. | 0.0867152 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −128289. | −0.0151726 | ||||||||
\(591\) | 974306. | 0.114743 | ||||||||
\(592\) | 438695. | 0.0514468 | ||||||||
\(593\) | 1.15630e6 | 0.135031 | 0.0675157 | − | 0.997718i | \(-0.478493\pi\) | ||||
0.0675157 | + | 0.997718i | \(0.478493\pi\) | |||||||
\(594\) | 70340.9 | 0.00817978 | ||||||||
\(595\) | −1.21674e6 | −0.140898 | ||||||||
\(596\) | 6.36750e6 | 0.734266 | ||||||||
\(597\) | 1.16936e6 | 0.134280 | ||||||||
\(598\) | 595335. | 0.0680782 | ||||||||
\(599\) | −7.49253e6 | −0.853221 | −0.426610 | − | 0.904436i | \(-0.640292\pi\) | ||||
−0.426610 | + | 0.904436i | \(0.640292\pi\) | |||||||
\(600\) | −411510. | −0.0466662 | ||||||||
\(601\) | 2.46573e6 | 0.278458 | 0.139229 | − | 0.990260i | \(-0.455538\pi\) | ||||
0.139229 | + | 0.990260i | \(0.455538\pi\) | |||||||
\(602\) | 1.20753e7 | 1.35802 | ||||||||
\(603\) | 1.00060e6 | 0.112064 | ||||||||
\(604\) | −5.00649e6 | −0.558394 | ||||||||
\(605\) | 1.73531e6 | 0.192747 | ||||||||
\(606\) | −155928. | −0.0172481 | ||||||||
\(607\) | 1.30412e7 | 1.43663 | 0.718316 | − | 0.695717i | \(-0.244913\pi\) | ||||
0.718316 | + | 0.695717i | \(0.244913\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.79900e6 | −0.305815 | ||||||||
\(610\) | −495222. | −0.0538859 | ||||||||
\(611\) | −392856. | −0.0425726 | ||||||||
\(612\) | 2.20397e6 | 0.237863 | ||||||||
\(613\) | −3.93935e6 | −0.423422 | −0.211711 | − | 0.977332i | \(-0.567904\pi\) | ||||
−0.211711 | + | 0.977332i | \(0.567904\pi\) | |||||||
\(614\) | −8.38017e6 | −0.897082 | ||||||||
\(615\) | −28122.8 | −0.00299827 | ||||||||
\(616\) | 213410. | 0.0226601 | ||||||||
\(617\) | −7.55827e6 | −0.799299 | −0.399649 | − | 0.916668i | \(-0.630868\pi\) | ||||
−0.399649 | + | 0.916668i | \(0.630868\pi\) | |||||||
\(618\) | 229112. | 0.0241311 | ||||||||
\(619\) | −7.12628e6 | −0.747543 | −0.373772 | − | 0.927521i | \(-0.621936\pi\) | ||||
−0.373772 | + | 0.927521i | \(0.621936\pi\) | |||||||
\(620\) | −1.60293e6 | −0.167469 | ||||||||
\(621\) | 581872. | 0.0605478 | ||||||||
\(622\) | 2.55545e6 | 0.264845 | ||||||||
\(623\) | 1.67950e7 | 1.73365 | ||||||||
\(624\) | −143998. | −0.0148045 | ||||||||
\(625\) | 8.68682e6 | 0.889530 | ||||||||
\(626\) | 4.52609e6 | 0.461623 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.23086e6 | 0.731629 | ||||||||
\(629\) | −990019. | −0.0997739 | ||||||||
\(630\) | −2.00864e6 | −0.201628 | ||||||||
\(631\) | −8.65646e6 | −0.865499 | −0.432750 | − | 0.901514i | \(-0.642457\pi\) | ||||
−0.432750 | + | 0.901514i | \(0.642457\pi\) | |||||||
\(632\) | 2.13979e6 | 0.213097 | ||||||||
\(633\) | 68175.4 | 0.00676267 | ||||||||
\(634\) | −4.68975e6 | −0.463368 | ||||||||
\(635\) | 2.30196e6 | 0.226549 | ||||||||
\(636\) | 877679. | 0.0860385 | ||||||||
\(637\) | −5.59536e6 | −0.546360 | ||||||||
\(638\) | −458874. | −0.0446315 | ||||||||
\(639\) | −1.60727e7 | −1.55717 | ||||||||
\(640\) | −176857. | −0.0170676 | ||||||||
\(641\) | 1.37461e7 | 1.32141 | 0.660703 | − | 0.750648i | \(-0.270258\pi\) | ||||
0.660703 | + | 0.750648i | \(0.270258\pi\) | |||||||
\(642\) | 1.43834e6 | 0.137728 | ||||||||
\(643\) | 5.32095e6 | 0.507530 | 0.253765 | − | 0.967266i | \(-0.418331\pi\) | ||||
0.253765 | + | 0.967266i | \(0.418331\pi\) | |||||||
\(644\) | 1.76536e6 | 0.167733 | ||||||||
\(645\) | 356958. | 0.0337845 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.91181e7 | −1.79549 | −0.897747 | − | 0.440512i | \(-0.854797\pi\) | ||||
−0.897747 | + | 0.440512i | \(0.854797\pi\) | |||||||
\(648\) | 3.56736e6 | 0.333741 | ||||||||
\(649\) | −50779.3 | −0.00473233 | ||||||||
\(650\) | 3.16716e6 | 0.294026 | ||||||||
\(651\) | −3.87009e6 | −0.357906 | ||||||||
\(652\) | 7.04094e6 | 0.648652 | ||||||||
\(653\) | −1.02824e7 | −0.943648 | −0.471824 | − | 0.881693i | \(-0.656404\pi\) | ||||
−0.471824 | + | 0.881693i | \(0.656404\pi\) | |||||||
\(654\) | −137590. | −0.0125789 | ||||||||
\(655\) | 3.48551e6 | 0.317441 | ||||||||
\(656\) | 312064. | 0.0283129 | ||||||||
\(657\) | 1.08786e7 | 0.983239 | ||||||||
\(658\) | −1.16495e6 | −0.104892 | ||||||||
\(659\) | 1.01629e7 | 0.911598 | 0.455799 | − | 0.890083i | \(-0.349354\pi\) | ||||
0.455799 | + | 0.890083i | \(0.349354\pi\) | |||||||
\(660\) | 6308.62 | 0.000563734 0 | ||||||||
\(661\) | −1.78429e7 | −1.58841 | −0.794203 | − | 0.607653i | \(-0.792111\pi\) | ||||
−0.794203 | + | 0.607653i | \(0.792111\pi\) | |||||||
\(662\) | −2.95351e6 | −0.261935 | ||||||||
\(663\) | 324965. | 0.0287113 | ||||||||
\(664\) | 4.28004e6 | 0.376728 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.63436e6 | −0.142778 | ||||||||
\(667\) | −3.79588e6 | −0.330368 | ||||||||
\(668\) | 1.93774e6 | 0.168017 | ||||||||
\(669\) | 2.62267e6 | 0.226557 | ||||||||
\(670\) | 181199. | 0.0155944 | ||||||||
\(671\) | −196019. | −0.0168070 | ||||||||
\(672\) | −427000. | −0.0364758 | ||||||||
\(673\) | 9.67106e6 | 0.823069 | 0.411535 | − | 0.911394i | \(-0.364993\pi\) | ||||
0.411535 | + | 0.911394i | \(0.364993\pi\) | |||||||
\(674\) | 7.87404e6 | 0.667648 | ||||||||
\(675\) | 3.09553e6 | 0.261503 | ||||||||
\(676\) | −4.83242e6 | −0.406722 | ||||||||
\(677\) | −1.11065e7 | −0.931331 | −0.465665 | − | 0.884961i | \(-0.654185\pi\) | ||||
−0.465665 | + | 0.884961i | \(0.654185\pi\) | |||||||
\(678\) | −882403. | −0.0737213 | ||||||||
\(679\) | −2.55008e7 | −2.12265 | ||||||||
\(680\) | 399119. | 0.0331002 | ||||||||
\(681\) | 521485. | 0.0430898 | ||||||||
\(682\) | −634471. | −0.0522337 | ||||||||
\(683\) | 323437. | 0.0265301 | 0.0132650 | − | 0.999912i | \(-0.495777\pi\) | ||||
0.0132650 | + | 0.999912i | \(0.495777\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.21252e6 | 0.261589 | ||||||||
\(686\) | −3.47534e6 | −0.281959 | ||||||||
\(687\) | −2.75872e6 | −0.223006 | ||||||||
\(688\) | −3.96097e6 | −0.319029 | ||||||||
\(689\) | −6.75499e6 | −0.542096 | ||||||||
\(690\) | 52186.0 | 0.00417283 | ||||||||
\(691\) | 7.15505e6 | 0.570056 | 0.285028 | − | 0.958519i | \(-0.407997\pi\) | ||||
0.285028 | + | 0.958519i | \(0.407997\pi\) | |||||||
\(692\) | 9.00704e6 | 0.715017 | ||||||||
\(693\) | −795058. | −0.0628877 | ||||||||
\(694\) | 1.05472e7 | 0.831264 | ||||||||
\(695\) | 459057. | 0.0360499 | ||||||||
\(696\) | 918137. | 0.0718430 | ||||||||
\(697\) | −704246. | −0.0549089 | ||||||||
\(698\) | −1.98641e6 | −0.154323 | ||||||||
\(699\) | 2.63407e6 | 0.203908 | ||||||||
\(700\) | 9.39165e6 | 0.724431 | ||||||||
\(701\) | −1.67109e7 | −1.28441 | −0.642206 | − | 0.766532i | \(-0.721981\pi\) | ||||
−0.642206 | + | 0.766532i | \(0.721981\pi\) | |||||||
\(702\) | 1.08321e6 | 0.0829599 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −70003.4 | −0.00532338 | ||||||||
\(705\) | −34437.0 | −0.00260947 | ||||||||
\(706\) | −8.69755e6 | −0.656728 | ||||||||
\(707\) | 3.55865e6 | 0.267755 | ||||||||
\(708\) | 101602. | 0.00761760 | ||||||||
\(709\) | −4.46568e6 | −0.333635 | −0.166818 | − | 0.985988i | \(-0.553349\pi\) | ||||
−0.166818 | + | 0.985988i | \(0.553349\pi\) | |||||||
\(710\) | −2.91062e6 | −0.216691 | ||||||||
\(711\) | −7.97179e6 | −0.591401 | ||||||||
\(712\) | −5.50917e6 | −0.407273 | ||||||||
\(713\) | −5.24846e6 | −0.386641 | ||||||||
\(714\) | 963628. | 0.0707398 | ||||||||
\(715\) | −48553.8 | −0.00355188 | ||||||||
\(716\) | −8.96896e6 | −0.653822 | ||||||||
\(717\) | −640551. | −0.0465325 | ||||||||
\(718\) | −1.03157e6 | −0.0746772 | ||||||||
\(719\) | 8.11538e6 | 0.585446 | 0.292723 | − | 0.956197i | \(-0.405439\pi\) | ||||
0.292723 | + | 0.956197i | \(0.405439\pi\) | |||||||
\(720\) | 658880. | 0.0473669 | ||||||||
\(721\) | −5.22889e6 | −0.374603 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −714098. | −0.0508056 | ||||||||
\(724\) | −7.48183e6 | −0.530471 | ||||||||
\(725\) | −2.01939e7 | −1.42684 | ||||||||
\(726\) | −1.37432e6 | −0.0967714 | ||||||||
\(727\) | 8.96301e6 | 0.628952 | 0.314476 | − | 0.949265i | \(-0.398171\pi\) | ||||
0.314476 | + | 0.949265i | \(0.398171\pi\) | |||||||
\(728\) | 3.28638e6 | 0.229821 | ||||||||
\(729\) | −1.27558e7 | −0.888975 | ||||||||
\(730\) | 1.97001e6 | 0.136824 | ||||||||
\(731\) | 8.93887e6 | 0.618713 | ||||||||
\(732\) | 392204. | 0.0270542 | ||||||||
\(733\) | −9.84603e6 | −0.676864 | −0.338432 | − | 0.940991i | \(-0.609896\pi\) | ||||
−0.338432 | + | 0.940991i | \(0.609896\pi\) | |||||||
\(734\) | −1.04834e7 | −0.718227 | ||||||||
\(735\) | −490479. | −0.0334890 | ||||||||
\(736\) | −579080. | −0.0394043 | ||||||||
\(737\) | 71722.1 | 0.00486389 | ||||||||
\(738\) | −1.16260e6 | −0.0785756 | ||||||||
\(739\) | −1.22360e7 | −0.824189 | −0.412094 | − | 0.911141i | \(-0.635203\pi\) | ||||
−0.412094 | + | 0.911141i | \(0.635203\pi\) | |||||||
\(740\) | −295968. | −0.0198685 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.00307e7 | −1.33563 | ||||||||
\(743\) | 2.14702e6 | 0.142680 | 0.0713402 | − | 0.997452i | \(-0.477272\pi\) | ||||
0.0713402 | + | 0.997452i | \(0.477272\pi\) | |||||||
\(744\) | 1.26948e6 | 0.0840802 | ||||||||
\(745\) | −4.29586e6 | −0.283570 | ||||||||
\(746\) | −1.38001e7 | −0.907894 | ||||||||
\(747\) | −1.59453e7 | −1.04552 | ||||||||
\(748\) | 157979. | 0.0103240 | ||||||||
\(749\) | −3.28263e7 | −2.13805 | ||||||||
\(750\) | 566007. | 0.0367425 | ||||||||
\(751\) | 1.97210e7 | 1.27594 | 0.637968 | − | 0.770063i | \(-0.279775\pi\) | ||||
0.637968 | + | 0.770063i | \(0.279775\pi\) | |||||||
\(752\) | 382130. | 0.0246414 | ||||||||
\(753\) | 3.81972e6 | 0.245496 | ||||||||
\(754\) | −7.06637e6 | −0.452656 | ||||||||
\(755\) | 3.37765e6 | 0.215649 | ||||||||
\(756\) | 3.21206e6 | 0.204399 | ||||||||
\(757\) | 2.62195e7 | 1.66297 | 0.831484 | − | 0.555549i | \(-0.187492\pi\) | ||||
0.831484 | + | 0.555549i | \(0.187492\pi\) | |||||||
\(758\) | −1.23653e7 | −0.781687 | ||||||||
\(759\) | 20656.2 | 0.00130151 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.89872e7 | 1.81445 | 0.907225 | − | 0.420645i | \(-0.138196\pi\) | ||||
0.907225 | + | 0.420645i | \(0.138196\pi\) | |||||||
\(762\) | −1.82310e6 | −0.113742 | ||||||||
\(763\) | 3.14013e6 | 0.195270 | ||||||||
\(764\) | 806242. | 0.0499726 | ||||||||
\(765\) | −1.48692e6 | −0.0918616 | ||||||||
\(766\) | 2.50044e6 | 0.153973 | ||||||||
\(767\) | −781970. | −0.0479956 | ||||||||
\(768\) | 140066. | 0.00856900 | ||||||||
\(769\) | −1.35288e7 | −0.824982 | −0.412491 | − | 0.910962i | \(-0.635341\pi\) | ||||
−0.412491 | + | 0.910962i | \(0.635341\pi\) | |||||||
\(770\) | −143978. | −0.00875122 | ||||||||
\(771\) | 2.79219e6 | 0.169164 | ||||||||
\(772\) | 1.30804e7 | 0.789910 | ||||||||
\(773\) | 1.28806e7 | 0.775331 | 0.387665 | − | 0.921800i | \(-0.373282\pi\) | ||||
0.387665 | + | 0.921800i | \(0.373282\pi\) | |||||||
\(774\) | 1.47566e7 | 0.885389 | ||||||||
\(775\) | −2.79216e7 | −1.66988 | ||||||||
\(776\) | 8.36485e6 | 0.498659 | ||||||||
\(777\) | −714580. | −0.0424618 | ||||||||
\(778\) | −1.25213e7 | −0.741653 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 97148.8 | 0.00571743 | ||||||||
\(781\) | −1.15208e6 | −0.0675859 | ||||||||
\(782\) | 1.30683e6 | 0.0764192 | ||||||||
\(783\) | −6.90657e6 | −0.402585 | ||||||||
\(784\) | 5.44258e6 | 0.316239 | ||||||||
\(785\) | −4.87834e6 | −0.282551 | ||||||||
\(786\) | −2.76044e6 | −0.159376 | ||||||||
\(787\) | 332357. | 0.0191279 | 0.00956395 | − | 0.999954i | \(-0.496956\pi\) | ||||
0.00956395 | + | 0.999954i | \(0.496956\pi\) | |||||||
\(788\) | 7.29393e6 | 0.418453 | ||||||||
\(789\) | 4.74026e6 | 0.271087 | ||||||||
\(790\) | −1.44362e6 | −0.0822971 | ||||||||
\(791\) | 2.01386e7 | 1.14442 | ||||||||
\(792\) | 260798. | 0.0147738 | ||||||||
\(793\) | −3.01857e6 | −0.170458 | ||||||||
\(794\) | 1.61993e7 | 0.911894 | ||||||||
\(795\) | −592130. | −0.0332276 | ||||||||
\(796\) | 8.75415e6 | 0.489702 | ||||||||
\(797\) | 3.13377e7 | 1.74752 | 0.873760 | − | 0.486358i | \(-0.161675\pi\) | ||||
0.873760 | + | 0.486358i | \(0.161675\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −862366. | −0.0477886 | ||||||||
\(800\) | −3.08068e6 | −0.170185 | ||||||||
\(801\) | 2.05244e7 | 1.13029 | ||||||||
\(802\) | 1.65540e7 | 0.908795 | ||||||||
\(803\) | 779771. | 0.0426754 | ||||||||
\(804\) | −143505. | −0.00782937 | ||||||||
\(805\) | −1.19101e6 | −0.0647777 | ||||||||
\(806\) | −9.77047e6 | −0.529758 | ||||||||
\(807\) | 926412. | 0.0500749 | ||||||||
\(808\) | −1.16732e6 | −0.0629016 | ||||||||
\(809\) | −6.58593e6 | −0.353790 | −0.176895 | − | 0.984230i | \(-0.556605\pi\) | ||||
−0.176895 | + | 0.984230i | \(0.556605\pi\) | |||||||
\(810\) | −2.40673e6 | −0.128889 | ||||||||
\(811\) | −2.66167e7 | −1.42103 | −0.710514 | − | 0.703683i | \(-0.751537\pi\) | ||||
−0.710514 | + | 0.703683i | \(0.751537\pi\) | |||||||
\(812\) | −2.09541e7 | −1.11527 | ||||||||
\(813\) | −3.09224e6 | −0.164077 | ||||||||
\(814\) | −117150. | −0.00619699 | ||||||||
\(815\) | −4.75020e6 | −0.250506 | ||||||||
\(816\) | −316093. | −0.0166184 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −1.31530e7 | −0.687293 | ||||||||
\(819\) | −1.22434e7 | −0.637812 | ||||||||
\(820\) | −210535. | −0.0109343 | ||||||||
\(821\) | 3.28657e7 | 1.70171 | 0.850854 | − | 0.525403i | \(-0.176085\pi\) | ||||
0.850854 | + | 0.525403i | \(0.176085\pi\) | |||||||
\(822\) | −2.54424e6 | −0.131334 | ||||||||
\(823\) | 8.94904e6 | 0.460550 | 0.230275 | − | 0.973126i | \(-0.426037\pi\) | ||||
0.230275 | + | 0.973126i | \(0.426037\pi\) | |||||||
\(824\) | 1.71520e6 | 0.0880028 | ||||||||
\(825\) | 109890. | 0.00562115 | ||||||||
\(826\) | −2.31880e6 | −0.118253 | ||||||||
\(827\) | −1.31486e7 | −0.668523 | −0.334262 | − | 0.942480i | \(-0.608487\pi\) | ||||
−0.334262 | + | 0.942480i | \(0.608487\pi\) | |||||||
\(828\) | 2.15736e6 | 0.109357 | ||||||||
\(829\) | −1.07264e6 | −0.0542088 | −0.0271044 | − | 0.999633i | \(-0.508629\pi\) | ||||
−0.0271044 | + | 0.999633i | \(0.508629\pi\) | |||||||
\(830\) | −2.88755e6 | −0.145490 | ||||||||
\(831\) | 3.51779e6 | 0.176712 | ||||||||
\(832\) | −1.07801e6 | −0.0539901 | ||||||||
\(833\) | −1.22825e7 | −0.613301 | ||||||||
\(834\) | −363562. | −0.0180994 | ||||||||
\(835\) | −1.30730e6 | −0.0648873 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.54952e6 | −0.471159 | ||||||||
\(838\) | 1.50929e7 | 0.742441 | ||||||||
\(839\) | 3.48927e7 | 1.71131 | 0.855656 | − | 0.517544i | \(-0.173154\pi\) | ||||
0.855656 | + | 0.517544i | \(0.173154\pi\) | |||||||
\(840\) | 288078. | 0.0140868 | ||||||||
\(841\) | 2.45443e7 | 1.19663 | ||||||||
\(842\) | −1.56886e6 | −0.0762610 | ||||||||
\(843\) | 1.97811e6 | 0.0958699 | ||||||||
\(844\) | 510380. | 0.0246625 | ||||||||
\(845\) | 3.26021e6 | 0.157074 | ||||||||
\(846\) | −1.42362e6 | −0.0683864 | ||||||||
\(847\) | 3.13653e7 | 1.50225 | ||||||||
\(848\) | 6.57055e6 | 0.313771 | ||||||||
\(849\) | −4.53113e6 | −0.215743 | ||||||||
\(850\) | 6.95229e6 | 0.330051 | ||||||||
\(851\) | −969084. | −0.0458709 | ||||||||
\(852\) | 2.30514e6 | 0.108792 | ||||||||
\(853\) | 1.81891e7 | 0.855931 | 0.427966 | − | 0.903795i | \(-0.359230\pi\) | ||||
0.427966 | + | 0.903795i | \(0.359230\pi\) | |||||||
\(854\) | −8.95103e6 | −0.419980 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.07678e7 | 0.502277 | ||||||||
\(857\) | 3.36435e7 | 1.56477 | 0.782383 | − | 0.622797i | \(-0.214004\pi\) | ||||
0.782383 | + | 0.622797i | \(0.214004\pi\) | |||||||
\(858\) | 38453.4 | 0.00178327 | ||||||||
\(859\) | 3.14828e7 | 1.45576 | 0.727882 | − | 0.685702i | \(-0.240505\pi\) | ||||
0.727882 | + | 0.685702i | \(0.240505\pi\) | |||||||
\(860\) | 2.67229e6 | 0.123207 | ||||||||
\(861\) | −508314. | −0.0233681 | ||||||||
\(862\) | 2.39938e7 | 1.09984 | ||||||||
\(863\) | −4.88137e6 | −0.223108 | −0.111554 | − | 0.993758i | \(-0.535583\pi\) | ||||
−0.111554 | + | 0.993758i | \(0.535583\pi\) | |||||||
\(864\) | −1.05363e6 | −0.0480180 | ||||||||
\(865\) | −6.07664e6 | −0.276136 | ||||||||
\(866\) | 9.16607e6 | 0.415326 | ||||||||
\(867\) | −2.32124e6 | −0.104875 | ||||||||
\(868\) | −2.89726e7 | −1.30523 | ||||||||
\(869\) | −571413. | −0.0256685 | ||||||||
\(870\) | −619425. | −0.0277454 | ||||||||
\(871\) | 1.10448e6 | 0.0493300 | ||||||||
\(872\) | −1.03004e6 | −0.0458734 | ||||||||
\(873\) | −3.11633e7 | −1.38391 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.29176e7 | −0.570379 | ||||||||
\(876\) | −1.56020e6 | −0.0686943 | ||||||||
\(877\) | −5.94390e6 | −0.260959 | −0.130480 | − | 0.991451i | \(-0.541652\pi\) | ||||
−0.130480 | + | 0.991451i | \(0.541652\pi\) | |||||||
\(878\) | 675308. | 0.0295642 | ||||||||
\(879\) | −2.01575e6 | −0.0879963 | ||||||||
\(880\) | 47228.1 | 0.00205586 | ||||||||
\(881\) | −1.95504e7 | −0.848627 | −0.424313 | − | 0.905515i | \(-0.639484\pi\) | ||||
−0.424313 | + | 0.905515i | \(0.639484\pi\) | |||||||
\(882\) | −2.02764e7 | −0.877644 | ||||||||
\(883\) | 2.19741e7 | 0.948439 | 0.474219 | − | 0.880407i | \(-0.342730\pi\) | ||||
0.474219 | + | 0.880407i | \(0.342730\pi\) | |||||||
\(884\) | 2.43278e6 | 0.104706 | ||||||||
\(885\) | −68546.1 | −0.00294188 | ||||||||
\(886\) | −1.24408e7 | −0.532432 | ||||||||
\(887\) | 2.36382e6 | 0.100880 | 0.0504401 | − | 0.998727i | \(-0.483938\pi\) | ||||
0.0504401 | + | 0.998727i | \(0.483938\pi\) | |||||||
\(888\) | 234399. | 0.00997525 | ||||||||
\(889\) | 4.16074e7 | 1.76570 | ||||||||
\(890\) | 3.71679e6 | 0.157287 | ||||||||
\(891\) | −952633. | −0.0402005 | ||||||||
\(892\) | 1.96341e7 | 0.826224 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 3.40222e6 | 0.142370 | ||||||||
\(895\) | 6.05095e6 | 0.252503 | ||||||||
\(896\) | −3.19665e6 | −0.133022 | ||||||||
\(897\) | 318093. | 0.0132000 | ||||||||
\(898\) | 2.02111e7 | 0.836370 | ||||||||
\(899\) | 6.22969e7 | 2.57080 | ||||||||
\(900\) | 1.14771e7 | 0.472308 | ||||||||
\(901\) | −1.48280e7 | −0.608515 | ||||||||
\(902\) | −83334.1 | −0.00341041 | ||||||||
\(903\) | 6.45193e6 | 0.263312 | ||||||||
\(904\) | −6.60592e6 | −0.268851 | ||||||||
\(905\) | 5.04765e6 | 0.204865 | ||||||||
\(906\) | −2.67502e6 | −0.108270 | ||||||||
\(907\) | 2.62203e7 | 1.05833 | 0.529163 | − | 0.848520i | \(-0.322506\pi\) | ||||
0.529163 | + | 0.848520i | \(0.322506\pi\) | |||||||
\(908\) | 3.90399e6 | 0.157143 | ||||||||
\(909\) | 4.34886e6 | 0.174568 | ||||||||
\(910\) | −2.21717e6 | −0.0887555 | ||||||||
\(911\) | −1.31649e7 | −0.525558 | −0.262779 | − | 0.964856i | \(-0.584639\pi\) | ||||
−0.262779 | + | 0.964856i | \(0.584639\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.14295e6 | −0.0453785 | ||||||||
\(914\) | 1.03164e7 | 0.408471 | ||||||||
\(915\) | −264602. | −0.0104482 | ||||||||
\(916\) | −2.06526e7 | −0.813272 | ||||||||
\(917\) | 6.29999e7 | 2.47409 | ||||||||
\(918\) | 2.37777e6 | 0.0931243 | ||||||||
\(919\) | 778178. | 0.0303942 | 0.0151971 | − | 0.999885i | \(-0.495162\pi\) | ||||
0.0151971 | + | 0.999885i | \(0.495162\pi\) | |||||||
\(920\) | 390679. | 0.0152178 | ||||||||
\(921\) | −4.47761e6 | −0.173939 | ||||||||
\(922\) | −3.14332e7 | −1.21776 | ||||||||
\(923\) | −1.77414e7 | −0.685461 | ||||||||
\(924\) | 114027. | 0.00439367 | ||||||||
\(925\) | −5.15549e6 | −0.198114 | ||||||||
\(926\) | 1.94766e7 | 0.746425 | ||||||||
\(927\) | −6.38998e6 | −0.244231 | ||||||||
\(928\) | 6.87343e6 | 0.262002 | ||||||||
\(929\) | −3.15227e7 | −1.19835 | −0.599176 | − | 0.800618i | \(-0.704505\pi\) | ||||
−0.599176 | + | 0.800618i | \(0.704505\pi\) | |||||||
\(930\) | −856462. | −0.0324714 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.97194e7 | 0.743624 | ||||||||
\(933\) | 1.36540e6 | 0.0513519 | ||||||||
\(934\) | 7.11190e6 | 0.266759 | ||||||||
\(935\) | −106581. | −0.00398706 | ||||||||
\(936\) | 4.01613e6 | 0.149837 | ||||||||
\(937\) | 2.86621e7 | 1.06650 | 0.533248 | − | 0.845959i | \(-0.320971\pi\) | ||||
0.533248 | + | 0.845959i | \(0.320971\pi\) | |||||||
\(938\) | 3.27513e6 | 0.121541 | ||||||||
\(939\) | 2.41834e6 | 0.0895061 | ||||||||
\(940\) | −257805. | −0.00951640 | ||||||||
\(941\) | 4.04755e7 | 1.49011 | 0.745054 | − | 0.667004i | \(-0.232423\pi\) | ||||
0.745054 | + | 0.667004i | \(0.232423\pi\) | |||||||
\(942\) | 3.86352e6 | 0.141859 | ||||||||
\(943\) | −689354. | −0.0252443 | ||||||||
\(944\) | 760620. | 0.0277803 | ||||||||
\(945\) | −2.16703e6 | −0.0789379 | ||||||||
\(946\) | 1.05774e6 | 0.0384285 | ||||||||
\(947\) | −1.22165e7 | −0.442663 | −0.221331 | − | 0.975199i | \(-0.571040\pi\) | ||||
−0.221331 | + | 0.975199i | \(0.571040\pi\) | |||||||
\(948\) | 1.14331e6 | 0.0413184 | ||||||||
\(949\) | 1.20080e7 | 0.432817 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.50578e6 | −0.0898445 | ||||||||
\(952\) | 7.21399e6 | 0.257978 | ||||||||
\(953\) | 3.60105e7 | 1.28439 | 0.642195 | − | 0.766541i | \(-0.278024\pi\) | ||||
0.642195 | + | 0.766541i | \(0.278024\pi\) | |||||||
\(954\) | −2.44786e7 | −0.870795 | ||||||||
\(955\) | −543935. | −0.0192992 | ||||||||
\(956\) | −4.79535e6 | −0.169698 | ||||||||
\(957\) | −245181. | −0.00865380 | ||||||||
\(958\) | −3.98241e7 | −1.40195 | ||||||||
\(959\) | 5.80656e7 | 2.03879 | ||||||||
\(960\) | −94496.3 | −0.00330931 | ||||||||
\(961\) | 5.75070e7 | 2.00869 | ||||||||
\(962\) | −1.80404e6 | −0.0628503 | ||||||||
\(963\) | −4.01155e7 | −1.39395 | ||||||||
\(964\) | −5.34594e6 | −0.185281 | ||||||||
\(965\) | −8.82475e6 | −0.305059 | ||||||||
\(966\) | 943250. | 0.0325225 | ||||||||
\(967\) | 5.59094e6 | 0.192273 | 0.0961366 | − | 0.995368i | \(-0.469351\pi\) | ||||
0.0961366 | + | 0.995368i | \(0.469351\pi\) | |||||||
\(968\) | −1.02886e7 | −0.352912 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.64339e6 | −0.192580 | ||||||||
\(971\) | −1.20028e7 | −0.408539 | −0.204270 | − | 0.978915i | \(-0.565482\pi\) | ||||
−0.204270 | + | 0.978915i | \(0.565482\pi\) | |||||||
\(972\) | 5.90658e6 | 0.200526 | ||||||||
\(973\) | 8.29735e6 | 0.280968 | ||||||||
\(974\) | −3.03559e6 | −0.102529 | ||||||||
\(975\) | 1.69224e6 | 0.0570101 | ||||||||
\(976\) | 2.93615e6 | 0.0986628 | ||||||||
\(977\) | 3.21099e7 | 1.07622 | 0.538111 | − | 0.842874i | \(-0.319138\pi\) | ||||
0.538111 | + | 0.842874i | \(0.319138\pi\) | |||||||
\(978\) | 3.76205e6 | 0.125770 | ||||||||
\(979\) | 1.47118e6 | 0.0490578 | ||||||||
\(980\) | −3.67186e6 | −0.122130 | ||||||||
\(981\) | 3.83740e6 | 0.127311 | ||||||||
\(982\) | 7.43342e6 | 0.245986 | ||||||||
\(983\) | 5.11520e6 | 0.168842 | 0.0844208 | − | 0.996430i | \(-0.473096\pi\) | ||||
0.0844208 | + | 0.996430i | \(0.473096\pi\) | |||||||
\(984\) | 166739. | 0.00548971 | ||||||||
\(985\) | −4.92089e6 | −0.161604 | ||||||||
\(986\) | −1.55115e7 | −0.508116 | ||||||||
\(987\) | −622442. | −0.0203379 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.74984e6 | 0.284452 | ||||||||
\(990\) | −175949. | −0.00570555 | ||||||||
\(991\) | 4.69664e6 | 0.151916 | 0.0759580 | − | 0.997111i | \(-0.475799\pi\) | ||||
0.0759580 | + | 0.997111i | \(0.475799\pi\) | |||||||
\(992\) | 9.50370e6 | 0.306629 | ||||||||
\(993\) | −1.57809e6 | −0.0507877 | ||||||||
\(994\) | −5.26089e7 | −1.68886 | ||||||||
\(995\) | −5.90603e6 | −0.189120 | ||||||||
\(996\) | 2.28687e6 | 0.0730454 | ||||||||
\(997\) | −6.09683e6 | −0.194252 | −0.0971262 | − | 0.995272i | \(-0.530965\pi\) | ||||
−0.0971262 | + | 0.995272i | \(0.530965\pi\) | |||||||
\(998\) | −3.08327e7 | −0.979908 | ||||||||
\(999\) | −1.76324e6 | −0.0558982 |
(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 | 722.6.a.r.1.9 | 15 | ||
19.4 | even | 9 | 38.6.e.b.35.3 | yes | 30 | ||
19.5 | even | 9 | 38.6.e.b.25.3 | ✓ | 30 | ||
19.18 | odd | 2 | 722.6.a.q.1.7 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.6.e.b.25.3 | ✓ | 30 | 19.5 | even | 9 | ||
38.6.e.b.35.3 | yes | 30 | 19.4 | even | 9 | ||
722.6.a.q.1.7 | 15 | 19.18 | odd | 2 | |||
722.6.a.r.1.9 | 15 | 1.1 | even | 1 | trivial |