Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,6,Mod(1,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, 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("147.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.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: | \(23.5764215125\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 97x^{2} + 7x + 294 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 7 \) |
Twist minimal: | no (minimal twist has level 21) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.74818\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.74818 | 0.485814 | 0.242907 | − | 0.970050i | \(-0.421899\pi\) | ||||
0.242907 | + | 0.970050i | \(0.421899\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | −24.4475 | −0.763984 | ||||||||
\(5\) | −58.3673 | −1.04411 | −0.522053 | − | 0.852913i | \(-0.674834\pi\) | ||||
−0.522053 | + | 0.852913i | \(0.674834\pi\) | |||||||
\(6\) | −24.7336 | −0.280485 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −155.128 | −0.856969 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −160.404 | −0.507242 | ||||||||
\(11\) | 17.4241 | 0.0434179 | 0.0217089 | − | 0.999764i | \(-0.493089\pi\) | ||||
0.0217089 | + | 0.999764i | \(0.493089\pi\) | |||||||
\(12\) | 220.027 | 0.441087 | ||||||||
\(13\) | −889.933 | −1.46049 | −0.730246 | − | 0.683185i | \(-0.760594\pi\) | ||||
−0.730246 | + | 0.683185i | \(0.760594\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 525.305 | 0.602815 | ||||||||
\(16\) | 356.000 | 0.347656 | ||||||||
\(17\) | −1026.64 | −0.861577 | −0.430788 | − | 0.902453i | \(-0.641764\pi\) | ||||
−0.430788 | + | 0.902453i | \(0.641764\pi\) | |||||||
\(18\) | 222.603 | 0.161938 | ||||||||
\(19\) | 1739.40 | 1.10539 | 0.552696 | − | 0.833383i | \(-0.313599\pi\) | ||||
0.552696 | + | 0.833383i | \(0.313599\pi\) | |||||||
\(20\) | 1426.93 | 0.797680 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 47.8846 | 0.0210930 | ||||||||
\(23\) | 3936.22 | 1.55153 | 0.775764 | − | 0.631023i | \(-0.217364\pi\) | ||||
0.775764 | + | 0.631023i | \(0.217364\pi\) | |||||||
\(24\) | 1396.15 | 0.494771 | ||||||||
\(25\) | 281.739 | 0.0901563 | ||||||||
\(26\) | −2445.70 | −0.709528 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5633.53 | 1.24390 | 0.621950 | − | 0.783057i | \(-0.286341\pi\) | ||||
0.621950 | + | 0.783057i | \(0.286341\pi\) | |||||||
\(30\) | 1443.63 | 0.292856 | ||||||||
\(31\) | 3096.53 | 0.578724 | 0.289362 | − | 0.957220i | \(-0.406557\pi\) | ||||
0.289362 | + | 0.957220i | \(0.406557\pi\) | |||||||
\(32\) | 5942.45 | 1.02587 | ||||||||
\(33\) | −156.817 | −0.0250673 | ||||||||
\(34\) | −2821.38 | −0.418566 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1980.25 | −0.254661 | ||||||||
\(37\) | 5026.86 | 0.603660 | 0.301830 | − | 0.953362i | \(-0.402402\pi\) | ||||
0.301830 | + | 0.953362i | \(0.402402\pi\) | |||||||
\(38\) | 4780.20 | 0.537015 | ||||||||
\(39\) | 8009.40 | 0.843215 | ||||||||
\(40\) | 9054.40 | 0.894766 | ||||||||
\(41\) | −18367.0 | −1.70639 | −0.853195 | − | 0.521592i | \(-0.825338\pi\) | ||||
−0.853195 | + | 0.521592i | \(0.825338\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1630.91 | −0.134511 | −0.0672557 | − | 0.997736i | \(-0.521424\pi\) | ||||
−0.0672557 | + | 0.997736i | \(0.521424\pi\) | |||||||
\(44\) | −425.976 | −0.0331706 | ||||||||
\(45\) | −4727.75 | −0.348035 | ||||||||
\(46\) | 10817.4 | 0.753755 | ||||||||
\(47\) | 9605.23 | 0.634254 | 0.317127 | − | 0.948383i | \(-0.397282\pi\) | ||||
0.317127 | + | 0.948383i | \(0.397282\pi\) | |||||||
\(48\) | −3204.00 | −0.200720 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 774.269 | 0.0437992 | ||||||||
\(51\) | 9239.72 | 0.497432 | ||||||||
\(52\) | 21756.6 | 1.11579 | ||||||||
\(53\) | −23256.5 | −1.13725 | −0.568624 | − | 0.822598i | \(-0.692524\pi\) | ||||
−0.568624 | + | 0.822598i | \(0.692524\pi\) | |||||||
\(54\) | −2003.42 | −0.0934950 | ||||||||
\(55\) | −1017.00 | −0.0453328 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −15654.6 | −0.638198 | ||||||||
\(58\) | 15482.0 | 0.604304 | ||||||||
\(59\) | 3603.24 | 0.134761 | 0.0673803 | − | 0.997727i | \(-0.478536\pi\) | ||||
0.0673803 | + | 0.997727i | \(0.478536\pi\) | |||||||
\(60\) | −12842.4 | −0.460541 | ||||||||
\(61\) | −22876.6 | −0.787167 | −0.393584 | − | 0.919289i | \(-0.628765\pi\) | ||||
−0.393584 | + | 0.919289i | \(0.628765\pi\) | |||||||
\(62\) | 8509.83 | 0.281152 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4938.92 | 0.150724 | ||||||||
\(65\) | 51943.0 | 1.52491 | ||||||||
\(66\) | −430.961 | −0.0121781 | ||||||||
\(67\) | 47012.8 | 1.27947 | 0.639733 | − | 0.768597i | \(-0.279045\pi\) | ||||
0.639733 | + | 0.768597i | \(0.279045\pi\) | |||||||
\(68\) | 25098.7 | 0.658231 | ||||||||
\(69\) | −35426.0 | −0.895776 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1599.63 | −0.0376595 | −0.0188298 | − | 0.999823i | \(-0.505994\pi\) | ||||
−0.0188298 | + | 0.999823i | \(0.505994\pi\) | |||||||
\(72\) | −12565.4 | −0.285656 | ||||||||
\(73\) | −5931.35 | −0.130271 | −0.0651353 | − | 0.997876i | \(-0.520748\pi\) | ||||
−0.0651353 | + | 0.997876i | \(0.520748\pi\) | |||||||
\(74\) | 13814.7 | 0.293267 | ||||||||
\(75\) | −2535.65 | −0.0520518 | ||||||||
\(76\) | −42524.1 | −0.844502 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 22011.3 | 0.409646 | ||||||||
\(79\) | −88468.9 | −1.59486 | −0.797431 | − | 0.603411i | \(-0.793808\pi\) | ||||
−0.797431 | + | 0.603411i | \(0.793808\pi\) | |||||||
\(80\) | −20778.8 | −0.362990 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −50475.8 | −0.828989 | ||||||||
\(83\) | 95823.9 | 1.52679 | 0.763394 | − | 0.645933i | \(-0.223531\pi\) | ||||
0.763394 | + | 0.645933i | \(0.223531\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 59921.9 | 0.899577 | ||||||||
\(86\) | −4482.04 | −0.0653476 | ||||||||
\(87\) | −50701.7 | −0.718166 | ||||||||
\(88\) | −2702.96 | −0.0372078 | ||||||||
\(89\) | 46507.9 | 0.622374 | 0.311187 | − | 0.950349i | \(-0.399273\pi\) | ||||
0.311187 | + | 0.950349i | \(0.399273\pi\) | |||||||
\(90\) | −12992.7 | −0.169081 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −96230.8 | −1.18534 | ||||||||
\(93\) | −27868.8 | −0.334126 | ||||||||
\(94\) | 26396.9 | 0.308130 | ||||||||
\(95\) | −101524. | −1.15415 | ||||||||
\(96\) | −53482.0 | −0.592284 | ||||||||
\(97\) | 75981.8 | 0.819937 | 0.409968 | − | 0.912100i | \(-0.365540\pi\) | ||||
0.409968 | + | 0.912100i | \(0.365540\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1411.35 | 0.0144726 | ||||||||
\(100\) | −6887.80 | −0.0688780 | ||||||||
\(101\) | 46157.4 | 0.450234 | 0.225117 | − | 0.974332i | \(-0.427724\pi\) | ||||
0.225117 | + | 0.974332i | \(0.427724\pi\) | |||||||
\(102\) | 25392.4 | 0.241659 | ||||||||
\(103\) | 81973.6 | 0.761344 | 0.380672 | − | 0.924710i | \(-0.375693\pi\) | ||||
0.380672 | + | 0.924710i | \(0.375693\pi\) | |||||||
\(104\) | 138054. | 1.25160 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −63913.2 | −0.552491 | ||||||||
\(107\) | −2853.67 | −0.0240960 | −0.0120480 | − | 0.999927i | \(-0.503835\pi\) | ||||
−0.0120480 | + | 0.999927i | \(0.503835\pi\) | |||||||
\(108\) | 17822.2 | 0.147029 | ||||||||
\(109\) | −166278. | −1.34051 | −0.670254 | − | 0.742132i | \(-0.733815\pi\) | ||||
−0.670254 | + | 0.742132i | \(0.733815\pi\) | |||||||
\(110\) | −2794.89 | −0.0220234 | ||||||||
\(111\) | −45241.7 | −0.348523 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 260304. | 1.91772 | 0.958858 | − | 0.283886i | \(-0.0916237\pi\) | ||||
0.958858 | + | 0.283886i | \(0.0916237\pi\) | |||||||
\(114\) | −43021.8 | −0.310046 | ||||||||
\(115\) | −229746. | −1.61996 | ||||||||
\(116\) | −137726. | −0.950320 | ||||||||
\(117\) | −72084.6 | −0.486831 | ||||||||
\(118\) | 9902.35 | 0.0654687 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −81489.6 | −0.516593 | ||||||||
\(121\) | −160747. | −0.998115 | ||||||||
\(122\) | −62869.1 | −0.382417 | ||||||||
\(123\) | 165303. | 0.985185 | ||||||||
\(124\) | −75702.5 | −0.442136 | ||||||||
\(125\) | 165953. | 0.949973 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −233743. | −1.28596 | −0.642982 | − | 0.765882i | \(-0.722303\pi\) | ||||
−0.642982 | + | 0.765882i | \(0.722303\pi\) | |||||||
\(128\) | −176585. | −0.952642 | ||||||||
\(129\) | 14678.2 | 0.0776602 | ||||||||
\(130\) | 142749. | 0.740822 | ||||||||
\(131\) | 157290. | 0.800797 | 0.400398 | − | 0.916341i | \(-0.368872\pi\) | ||||
0.400398 | + | 0.916341i | \(0.368872\pi\) | |||||||
\(132\) | 3833.78 | 0.0191510 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 129200. | 0.621583 | ||||||||
\(135\) | 42549.7 | 0.200938 | ||||||||
\(136\) | 159260. | 0.738345 | ||||||||
\(137\) | −171548. | −0.780878 | −0.390439 | − | 0.920629i | \(-0.627677\pi\) | ||||
−0.390439 | + | 0.920629i | \(0.627677\pi\) | |||||||
\(138\) | −97357.0 | −0.435181 | ||||||||
\(139\) | −210625. | −0.924642 | −0.462321 | − | 0.886713i | \(-0.652983\pi\) | ||||
−0.462321 | + | 0.886713i | \(0.652983\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −86447.1 | −0.366187 | ||||||||
\(142\) | −4396.08 | −0.0182955 | ||||||||
\(143\) | −15506.3 | −0.0634114 | ||||||||
\(144\) | 28836.0 | 0.115885 | ||||||||
\(145\) | −328814. | −1.29876 | ||||||||
\(146\) | −16300.4 | −0.0632873 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −122894. | −0.461187 | ||||||||
\(149\) | 239413. | 0.883450 | 0.441725 | − | 0.897151i | \(-0.354367\pi\) | ||||
0.441725 | + | 0.897151i | \(0.354367\pi\) | |||||||
\(150\) | −6968.42 | −0.0252875 | ||||||||
\(151\) | 217039. | 0.774634 | 0.387317 | − | 0.921947i | \(-0.373402\pi\) | ||||
0.387317 | + | 0.921947i | \(0.373402\pi\) | |||||||
\(152\) | −269830. | −0.947287 | ||||||||
\(153\) | −83157.5 | −0.287192 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −180736. | −0.604249 | ||||||||
\(156\) | −195810. | −0.644203 | ||||||||
\(157\) | −166904. | −0.540404 | −0.270202 | − | 0.962804i | \(-0.587091\pi\) | ||||
−0.270202 | + | 0.962804i | \(0.587091\pi\) | |||||||
\(158\) | −243129. | −0.774807 | ||||||||
\(159\) | 209309. | 0.656590 | ||||||||
\(160\) | −346844. | −1.07111 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 18030.8 | 0.0539794 | ||||||||
\(163\) | 506172. | 1.49221 | 0.746104 | − | 0.665830i | \(-0.231922\pi\) | ||||
0.746104 | + | 0.665830i | \(0.231922\pi\) | |||||||
\(164\) | 449027. | 1.30366 | ||||||||
\(165\) | 9152.97 | 0.0261729 | ||||||||
\(166\) | 263342. | 0.741736 | ||||||||
\(167\) | 565560. | 1.56923 | 0.784616 | − | 0.619982i | \(-0.212860\pi\) | ||||
0.784616 | + | 0.619982i | \(0.212860\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 420688. | 1.13304 | ||||||||
\(170\) | 164676. | 0.437027 | ||||||||
\(171\) | 140892. | 0.368464 | ||||||||
\(172\) | 39871.7 | 0.102765 | ||||||||
\(173\) | 659435. | 1.67516 | 0.837581 | − | 0.546313i | \(-0.183969\pi\) | ||||
0.837581 | + | 0.546313i | \(0.183969\pi\) | |||||||
\(174\) | −139338. | −0.348895 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6202.98 | 0.0150945 | ||||||||
\(177\) | −32429.1 | −0.0778041 | ||||||||
\(178\) | 127812. | 0.302358 | ||||||||
\(179\) | 165290. | 0.385580 | 0.192790 | − | 0.981240i | \(-0.438246\pi\) | ||||
0.192790 | + | 0.981240i | \(0.438246\pi\) | |||||||
\(180\) | 115582. | 0.265893 | ||||||||
\(181\) | −148492. | −0.336904 | −0.168452 | − | 0.985710i | \(-0.553877\pi\) | ||||
−0.168452 | + | 0.985710i | \(0.553877\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 205889. | 0.454471 | ||||||||
\(184\) | −610618. | −1.32961 | ||||||||
\(185\) | −293404. | −0.630285 | ||||||||
\(186\) | −76588.5 | −0.162323 | ||||||||
\(187\) | −17888.2 | −0.0374078 | ||||||||
\(188\) | −234824. | −0.484560 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −279007. | −0.560701 | ||||||||
\(191\) | 385911. | 0.765426 | 0.382713 | − | 0.923867i | \(-0.374990\pi\) | ||||
0.382713 | + | 0.923867i | \(0.374990\pi\) | |||||||
\(192\) | −44450.3 | −0.0870204 | ||||||||
\(193\) | 496296. | 0.959063 | 0.479531 | − | 0.877525i | \(-0.340807\pi\) | ||||
0.479531 | + | 0.877525i | \(0.340807\pi\) | |||||||
\(194\) | 208812. | 0.398337 | ||||||||
\(195\) | −467487. | −0.880406 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 441439. | 0.810411 | 0.405206 | − | 0.914226i | \(-0.367200\pi\) | ||||
0.405206 | + | 0.914226i | \(0.367200\pi\) | |||||||
\(198\) | 3878.65 | 0.00703101 | ||||||||
\(199\) | 75838.8 | 0.135756 | 0.0678779 | − | 0.997694i | \(-0.478377\pi\) | ||||
0.0678779 | + | 0.997694i | \(0.478377\pi\) | |||||||
\(200\) | −43705.5 | −0.0772612 | ||||||||
\(201\) | −423115. | −0.738700 | ||||||||
\(202\) | 126849. | 0.218730 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −225888. | −0.380030 | ||||||||
\(205\) | 1.07203e6 | 1.78165 | ||||||||
\(206\) | 225278. | 0.369872 | ||||||||
\(207\) | 318834. | 0.517176 | ||||||||
\(208\) | −316816. | −0.507749 | ||||||||
\(209\) | 30307.5 | 0.0479938 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 778704. | 1.20411 | 0.602055 | − | 0.798454i | \(-0.294349\pi\) | ||||
0.602055 | + | 0.798454i | \(0.294349\pi\) | |||||||
\(212\) | 568564. | 0.868840 | ||||||||
\(213\) | 14396.7 | 0.0217427 | ||||||||
\(214\) | −7842.41 | −0.0117062 | ||||||||
\(215\) | 95191.9 | 0.140444 | ||||||||
\(216\) | 113088. | 0.164924 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −456963. | −0.651238 | ||||||||
\(219\) | 53382.1 | 0.0752117 | ||||||||
\(220\) | 24863.0 | 0.0346336 | ||||||||
\(221\) | 913637. | 1.25833 | ||||||||
\(222\) | −124333. | −0.169318 | ||||||||
\(223\) | −738085. | −0.993903 | −0.496951 | − | 0.867778i | \(-0.665547\pi\) | ||||
−0.496951 | + | 0.867778i | \(0.665547\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 22820.8 | 0.0300521 | ||||||||
\(226\) | 715362. | 0.931654 | ||||||||
\(227\) | 544115. | 0.700852 | 0.350426 | − | 0.936590i | \(-0.386037\pi\) | ||||
0.350426 | + | 0.936590i | \(0.386037\pi\) | |||||||
\(228\) | 382716. | 0.487573 | ||||||||
\(229\) | 233562. | 0.294316 | 0.147158 | − | 0.989113i | \(-0.452987\pi\) | ||||
0.147158 | + | 0.989113i | \(0.452987\pi\) | |||||||
\(230\) | −631385. | −0.787000 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −873917. | −1.06598 | ||||||||
\(233\) | −618100. | −0.745880 | −0.372940 | − | 0.927856i | \(-0.621650\pi\) | ||||
−0.372940 | + | 0.927856i | \(0.621650\pi\) | |||||||
\(234\) | −198102. | −0.236509 | ||||||||
\(235\) | −560631. | −0.662228 | ||||||||
\(236\) | −88090.2 | −0.102955 | ||||||||
\(237\) | 796220. | 0.920794 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 937500. | 1.06164 | 0.530819 | − | 0.847485i | \(-0.321884\pi\) | ||||
0.530819 | + | 0.847485i | \(0.321884\pi\) | |||||||
\(240\) | 187009. | 0.209572 | ||||||||
\(241\) | −932036. | −1.03369 | −0.516845 | − | 0.856079i | \(-0.672894\pi\) | ||||
−0.516845 | + | 0.856079i | \(0.672894\pi\) | |||||||
\(242\) | −441763. | −0.484899 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 559276. | 0.601383 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 454282. | 0.478617 | ||||||||
\(247\) | −1.54795e6 | −1.61442 | ||||||||
\(248\) | −480359. | −0.495948 | ||||||||
\(249\) | −862416. | −0.881492 | ||||||||
\(250\) | 456070. | 0.461510 | ||||||||
\(251\) | −214975. | −0.215379 | −0.107690 | − | 0.994185i | \(-0.534345\pi\) | ||||
−0.107690 | + | 0.994185i | \(0.534345\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 68585.1 | 0.0673641 | ||||||||
\(254\) | −642367. | −0.624740 | ||||||||
\(255\) | −539297. | −0.519371 | ||||||||
\(256\) | −643334. | −0.613531 | ||||||||
\(257\) | −79187.0 | −0.0747862 | −0.0373931 | − | 0.999301i | \(-0.511905\pi\) | ||||
−0.0373931 | + | 0.999301i | \(0.511905\pi\) | |||||||
\(258\) | 40338.4 | 0.0377285 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.26988e6 | −1.16501 | ||||||||
\(261\) | 456316. | 0.414633 | ||||||||
\(262\) | 432261. | 0.389039 | ||||||||
\(263\) | −432828. | −0.385856 | −0.192928 | − | 0.981213i | \(-0.561798\pi\) | ||||
−0.192928 | + | 0.981213i | \(0.561798\pi\) | |||||||
\(264\) | 24326.7 | 0.0214819 | ||||||||
\(265\) | 1.35742e6 | 1.18741 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −418571. | −0.359328 | ||||||||
\(268\) | −1.14934e6 | −0.977492 | ||||||||
\(269\) | 4691.86 | 0.00395334 | 0.00197667 | − | 0.999998i | \(-0.499371\pi\) | ||||
0.00197667 | + | 0.999998i | \(0.499371\pi\) | |||||||
\(270\) | 116934. | 0.0976187 | ||||||||
\(271\) | −105264. | −0.0870678 | −0.0435339 | − | 0.999052i | \(-0.513862\pi\) | ||||
−0.0435339 | + | 0.999052i | \(0.513862\pi\) | |||||||
\(272\) | −365482. | −0.299533 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −471444. | −0.379362 | ||||||||
\(275\) | 4909.04 | 0.00391440 | ||||||||
\(276\) | 866077. | 0.684359 | ||||||||
\(277\) | −763117. | −0.597574 | −0.298787 | − | 0.954320i | \(-0.596582\pi\) | ||||
−0.298787 | + | 0.954320i | \(0.596582\pi\) | |||||||
\(278\) | −578837. | −0.449205 | ||||||||
\(279\) | 250819. | 0.192908 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −729540. | −0.551167 | −0.275584 | − | 0.961277i | \(-0.588871\pi\) | ||||
−0.275584 | + | 0.961277i | \(0.588871\pi\) | |||||||
\(282\) | −237572. | −0.177899 | ||||||||
\(283\) | 1.19043e6 | 0.883563 | 0.441781 | − | 0.897123i | \(-0.354347\pi\) | ||||
0.441781 | + | 0.897123i | \(0.354347\pi\) | |||||||
\(284\) | 39107.0 | 0.0287713 | ||||||||
\(285\) | 913718. | 0.666346 | ||||||||
\(286\) | −42614.1 | −0.0308062 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 481338. | 0.341955 | ||||||||
\(289\) | −365877. | −0.257686 | ||||||||
\(290\) | −903639. | −0.630958 | ||||||||
\(291\) | −683836. | −0.473391 | ||||||||
\(292\) | 145007. | 0.0995246 | ||||||||
\(293\) | 1.02503e6 | 0.697537 | 0.348769 | − | 0.937209i | \(-0.386600\pi\) | ||||
0.348769 | + | 0.937209i | \(0.386600\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −210311. | −0.140704 | ||||||||
\(296\) | −779807. | −0.517318 | ||||||||
\(297\) | −12702.2 | −0.00835577 | ||||||||
\(298\) | 657950. | 0.429193 | ||||||||
\(299\) | −3.50297e6 | −2.26599 | ||||||||
\(300\) | 61990.2 | 0.0397667 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 596464. | 0.376328 | ||||||||
\(303\) | −415417. | −0.259943 | ||||||||
\(304\) | 619228. | 0.384297 | ||||||||
\(305\) | 1.33525e6 | 0.821886 | ||||||||
\(306\) | −228532. | −0.139522 | ||||||||
\(307\) | 709845. | 0.429850 | 0.214925 | − | 0.976631i | \(-0.431049\pi\) | ||||
0.214925 | + | 0.976631i | \(0.431049\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −737762. | −0.439562 | ||||||||
\(310\) | −496696. | −0.293553 | ||||||||
\(311\) | −1.56763e6 | −0.919058 | −0.459529 | − | 0.888163i | \(-0.651982\pi\) | ||||
−0.459529 | + | 0.888163i | \(0.651982\pi\) | |||||||
\(312\) | −1.24248e6 | −0.722609 | ||||||||
\(313\) | −372952. | −0.215175 | −0.107588 | − | 0.994196i | \(-0.534313\pi\) | ||||
−0.107588 | + | 0.994196i | \(0.534313\pi\) | |||||||
\(314\) | −458684. | −0.262536 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.16284e6 | 1.21845 | ||||||||
\(317\) | −3.02816e6 | −1.69251 | −0.846253 | − | 0.532781i | \(-0.821147\pi\) | ||||
−0.846253 | + | 0.532781i | \(0.821147\pi\) | |||||||
\(318\) | 575218. | 0.318981 | ||||||||
\(319\) | 98159.1 | 0.0540075 | ||||||||
\(320\) | −288271. | −0.157372 | ||||||||
\(321\) | 25683.1 | 0.0139118 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.78573e6 | −0.952380 | ||||||||
\(324\) | −160400. | −0.0848871 | ||||||||
\(325\) | −250728. | −0.131673 | ||||||||
\(326\) | 1.39105e6 | 0.724936 | ||||||||
\(327\) | 1.49651e6 | 0.773943 | ||||||||
\(328\) | 2.84923e6 | 1.46232 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 25154.0 | 0.0127152 | ||||||||
\(331\) | 1.06690e6 | 0.535244 | 0.267622 | − | 0.963524i | \(-0.413762\pi\) | ||||
0.267622 | + | 0.963524i | \(0.413762\pi\) | |||||||
\(332\) | −2.34266e6 | −1.16644 | ||||||||
\(333\) | 407176. | 0.201220 | ||||||||
\(334\) | 1.55426e6 | 0.762356 | ||||||||
\(335\) | −2.74401e6 | −1.33590 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.55734e6 | 0.746981 | 0.373490 | − | 0.927634i | \(-0.378161\pi\) | ||||
0.373490 | + | 0.927634i | \(0.378161\pi\) | |||||||
\(338\) | 1.15613e6 | 0.550445 | ||||||||
\(339\) | −2.34273e6 | −1.10719 | ||||||||
\(340\) | −1.46494e6 | −0.687263 | ||||||||
\(341\) | 53954.3 | 0.0251270 | ||||||||
\(342\) | 387196. | 0.179005 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 253000. | 0.115272 | ||||||||
\(345\) | 2.06772e6 | 0.935284 | ||||||||
\(346\) | 1.81225e6 | 0.813818 | ||||||||
\(347\) | −2.23496e6 | −0.996428 | −0.498214 | − | 0.867054i | \(-0.666011\pi\) | ||||
−0.498214 | + | 0.867054i | \(0.666011\pi\) | |||||||
\(348\) | 1.23953e6 | 0.548667 | ||||||||
\(349\) | 1.72982e6 | 0.760218 | 0.380109 | − | 0.924942i | \(-0.375886\pi\) | ||||
0.380109 | + | 0.924942i | \(0.375886\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 648761. | 0.281072 | ||||||||
\(352\) | 103542. | 0.0445409 | ||||||||
\(353\) | 2.36574e6 | 1.01048 | 0.505242 | − | 0.862978i | \(-0.331403\pi\) | ||||
0.505242 | + | 0.862978i | \(0.331403\pi\) | |||||||
\(354\) | −89121.2 | −0.0377983 | ||||||||
\(355\) | 93366.3 | 0.0393205 | ||||||||
\(356\) | −1.13700e6 | −0.475484 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 454247. | 0.187320 | ||||||||
\(359\) | 51028.7 | 0.0208967 | 0.0104484 | − | 0.999945i | \(-0.496674\pi\) | ||||
0.0104484 | + | 0.999945i | \(0.496674\pi\) | |||||||
\(360\) | 733406. | 0.298255 | ||||||||
\(361\) | 549424. | 0.221891 | ||||||||
\(362\) | −408083. | −0.163673 | ||||||||
\(363\) | 1.44673e6 | 0.576262 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 346197. | 0.136016 | ||||||||
\(366\) | 565822. | 0.220789 | ||||||||
\(367\) | −3.76823e6 | −1.46040 | −0.730200 | − | 0.683233i | \(-0.760573\pi\) | ||||
−0.730200 | + | 0.683233i | \(0.760573\pi\) | |||||||
\(368\) | 1.40130e6 | 0.539399 | ||||||||
\(369\) | −1.48773e6 | −0.568797 | ||||||||
\(370\) | −806328. | −0.306201 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 681322. | 0.255267 | ||||||||
\(373\) | 4.63440e6 | 1.72473 | 0.862366 | − | 0.506285i | \(-0.168982\pi\) | ||||
0.862366 | + | 0.506285i | \(0.168982\pi\) | |||||||
\(374\) | −49160.0 | −0.0181733 | ||||||||
\(375\) | −1.49358e6 | −0.548467 | ||||||||
\(376\) | −1.49004e6 | −0.543536 | ||||||||
\(377\) | −5.01346e6 | −1.81670 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.17169e6 | −1.49181 | −0.745905 | − | 0.666052i | \(-0.767983\pi\) | ||||
−0.745905 | + | 0.666052i | \(0.767983\pi\) | |||||||
\(380\) | 2.48201e6 | 0.881749 | ||||||||
\(381\) | 2.10368e6 | 0.742451 | ||||||||
\(382\) | 1.06055e6 | 0.371855 | ||||||||
\(383\) | 4.17172e6 | 1.45318 | 0.726588 | − | 0.687074i | \(-0.241105\pi\) | ||||
0.726588 | + | 0.687074i | \(0.241105\pi\) | |||||||
\(384\) | 1.58927e6 | 0.550008 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.36391e6 | 0.465927 | ||||||||
\(387\) | −132104. | −0.0448372 | ||||||||
\(388\) | −1.85757e6 | −0.626419 | ||||||||
\(389\) | 2.75394e6 | 0.922743 | 0.461371 | − | 0.887207i | \(-0.347358\pi\) | ||||
0.461371 | + | 0.887207i | \(0.347358\pi\) | |||||||
\(390\) | −1.28474e6 | −0.427714 | ||||||||
\(391\) | −4.04106e6 | −1.33676 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.41561e6 | −0.462340 | ||||||||
\(394\) | 1.21316e6 | 0.393709 | ||||||||
\(395\) | 5.16369e6 | 1.66520 | ||||||||
\(396\) | −34504.0 | −0.0110569 | ||||||||
\(397\) | 2.53204e6 | 0.806297 | 0.403148 | − | 0.915135i | \(-0.367916\pi\) | ||||
0.403148 | + | 0.915135i | \(0.367916\pi\) | |||||||
\(398\) | 208419. | 0.0659522 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 100299. | 0.0313434 | ||||||||
\(401\) | −2.15747e6 | −0.670014 | −0.335007 | − | 0.942216i | \(-0.608739\pi\) | ||||
−0.335007 | + | 0.942216i | \(0.608739\pi\) | |||||||
\(402\) | −1.16280e6 | −0.358871 | ||||||||
\(403\) | −2.75571e6 | −0.845221 | ||||||||
\(404\) | −1.12843e6 | −0.343972 | ||||||||
\(405\) | −382948. | −0.116012 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 87588.5 | 0.0262096 | ||||||||
\(408\) | −1.43334e6 | −0.426283 | ||||||||
\(409\) | 4.32804e6 | 1.27933 | 0.639665 | − | 0.768653i | \(-0.279073\pi\) | ||||
0.639665 | + | 0.768653i | \(0.279073\pi\) | |||||||
\(410\) | 2.94614e6 | 0.865552 | ||||||||
\(411\) | 1.54393e6 | 0.450840 | ||||||||
\(412\) | −2.00405e6 | −0.581655 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 876213. | 0.251252 | ||||||||
\(415\) | −5.59298e6 | −1.59413 | ||||||||
\(416\) | −5.28838e6 | −1.49827 | ||||||||
\(417\) | 1.89563e6 | 0.533843 | ||||||||
\(418\) | 83290.6 | 0.0233161 | ||||||||
\(419\) | 1.51129e6 | 0.420544 | 0.210272 | − | 0.977643i | \(-0.432565\pi\) | ||||
0.210272 | + | 0.977643i | \(0.432565\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.11586e6 | 0.306835 | 0.153418 | − | 0.988161i | \(-0.450972\pi\) | ||||
0.153418 | + | 0.988161i | \(0.450972\pi\) | |||||||
\(422\) | 2.14002e6 | 0.584974 | ||||||||
\(423\) | 778024. | 0.211418 | ||||||||
\(424\) | 3.60774e6 | 0.974586 | ||||||||
\(425\) | −289243. | −0.0776766 | ||||||||
\(426\) | 39564.8 | 0.0105629 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 69765.2 | 0.0184090 | ||||||||
\(429\) | 139557. | 0.0366106 | ||||||||
\(430\) | 261605. | 0.0682298 | ||||||||
\(431\) | 6.21345e6 | 1.61116 | 0.805581 | − | 0.592485i | \(-0.201853\pi\) | ||||
0.805581 | + | 0.592485i | \(0.201853\pi\) | |||||||
\(432\) | −259524. | −0.0669065 | ||||||||
\(433\) | −3.24118e6 | −0.830775 | −0.415388 | − | 0.909644i | \(-0.636354\pi\) | ||||
−0.415388 | + | 0.909644i | \(0.636354\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.95932e6 | 0.749841 | ||||||||
\(436\) | 4.06509e6 | 1.02413 | ||||||||
\(437\) | 6.84667e6 | 1.71505 | ||||||||
\(438\) | 146704. | 0.0365389 | ||||||||
\(439\) | −2.30497e6 | −0.570825 | −0.285413 | − | 0.958405i | \(-0.592131\pi\) | ||||
−0.285413 | + | 0.958405i | \(0.592131\pi\) | |||||||
\(440\) | 157765. | 0.0388488 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.51084e6 | 0.611313 | ||||||||
\(443\) | 1.53266e6 | 0.371052 | 0.185526 | − | 0.982639i | \(-0.440601\pi\) | ||||
0.185526 | + | 0.982639i | \(0.440601\pi\) | |||||||
\(444\) | 1.10605e6 | 0.266266 | ||||||||
\(445\) | −2.71454e6 | −0.649824 | ||||||||
\(446\) | −2.02839e6 | −0.482852 | ||||||||
\(447\) | −2.15472e6 | −0.510060 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.55718e6 | −0.832702 | −0.416351 | − | 0.909204i | \(-0.636691\pi\) | ||||
−0.416351 | + | 0.909204i | \(0.636691\pi\) | |||||||
\(450\) | 62715.8 | 0.0145997 | ||||||||
\(451\) | −320028. | −0.0740878 | ||||||||
\(452\) | −6.36378e6 | −1.46511 | ||||||||
\(453\) | −1.95336e6 | −0.447235 | ||||||||
\(454\) | 1.49533e6 | 0.340484 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.42847e6 | 0.546916 | ||||||||
\(457\) | 2.51883e6 | 0.564167 | 0.282083 | − | 0.959390i | \(-0.408974\pi\) | ||||
0.282083 | + | 0.959390i | \(0.408974\pi\) | |||||||
\(458\) | 641872. | 0.142983 | ||||||||
\(459\) | 748417. | 0.165811 | ||||||||
\(460\) | 5.61673e6 | 1.23762 | ||||||||
\(461\) | 6.63271e6 | 1.45358 | 0.726789 | − | 0.686861i | \(-0.241012\pi\) | ||||
0.726789 | + | 0.686861i | \(0.241012\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.40432e6 | −0.954830 | −0.477415 | − | 0.878678i | \(-0.658426\pi\) | ||||
−0.477415 | + | 0.878678i | \(0.658426\pi\) | |||||||
\(464\) | 2.00554e6 | 0.432450 | ||||||||
\(465\) | 1.62663e6 | 0.348863 | ||||||||
\(466\) | −1.69865e6 | −0.362359 | ||||||||
\(467\) | −245845. | −0.0521637 | −0.0260819 | − | 0.999660i | \(-0.508303\pi\) | ||||
−0.0260819 | + | 0.999660i | \(0.508303\pi\) | |||||||
\(468\) | 1.76229e6 | 0.371931 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.54072e6 | −0.321720 | ||||||||
\(471\) | 1.50214e6 | 0.312002 | ||||||||
\(472\) | −558963. | −0.115486 | ||||||||
\(473\) | −28417.2 | −0.00584020 | ||||||||
\(474\) | 2.18816e6 | 0.447335 | ||||||||
\(475\) | 490057. | 0.0996581 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.88378e6 | −0.379083 | ||||||||
\(478\) | 2.57642e6 | 0.515759 | ||||||||
\(479\) | 40351.1 | 0.00803557 | 0.00401779 | − | 0.999992i | \(-0.498721\pi\) | ||||
0.00401779 | + | 0.999992i | \(0.498721\pi\) | |||||||
\(480\) | 3.12160e6 | 0.618407 | ||||||||
\(481\) | −4.47357e6 | −0.881640 | ||||||||
\(482\) | −2.56140e6 | −0.502181 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.92987e6 | 0.762544 | ||||||||
\(485\) | −4.43485e6 | −0.856101 | ||||||||
\(486\) | −162277. | −0.0311650 | ||||||||
\(487\) | −3.30968e6 | −0.632359 | −0.316180 | − | 0.948699i | \(-0.602400\pi\) | ||||
−0.316180 | + | 0.948699i | \(0.602400\pi\) | |||||||
\(488\) | 3.54880e6 | 0.674578 | ||||||||
\(489\) | −4.55555e6 | −0.861526 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.97959e6 | −0.370570 | −0.185285 | − | 0.982685i | \(-0.559321\pi\) | ||||
−0.185285 | + | 0.982685i | \(0.559321\pi\) | |||||||
\(492\) | −4.04124e6 | −0.752666 | ||||||||
\(493\) | −5.78358e6 | −1.07171 | ||||||||
\(494\) | −4.25405e6 | −0.784306 | ||||||||
\(495\) | −82376.8 | −0.0151109 | ||||||||
\(496\) | 1.10237e6 | 0.201197 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −2.37007e6 | −0.428241 | ||||||||
\(499\) | −3.16995e6 | −0.569904 | −0.284952 | − | 0.958542i | \(-0.591978\pi\) | ||||
−0.284952 | + | 0.958542i | \(0.591978\pi\) | |||||||
\(500\) | −4.05715e6 | −0.725764 | ||||||||
\(501\) | −5.09004e6 | −0.905997 | ||||||||
\(502\) | −590791. | −0.104634 | ||||||||
\(503\) | 4.01273e6 | 0.707164 | 0.353582 | − | 0.935403i | \(-0.384963\pi\) | ||||
0.353582 | + | 0.935403i | \(0.384963\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.69408e6 | −0.470092 | ||||||||
\(506\) | 188484. | 0.0327264 | ||||||||
\(507\) | −3.78619e6 | −0.654158 | ||||||||
\(508\) | 5.71442e6 | 0.982456 | ||||||||
\(509\) | −4.11257e6 | −0.703590 | −0.351795 | − | 0.936077i | \(-0.614429\pi\) | ||||
−0.351795 | + | 0.936077i | \(0.614429\pi\) | |||||||
\(510\) | −1.48209e6 | −0.252318 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 3.88273e6 | 0.654580 | ||||||||
\(513\) | −1.26802e6 | −0.212733 | ||||||||
\(514\) | −217620. | −0.0363322 | ||||||||
\(515\) | −4.78457e6 | −0.794923 | ||||||||
\(516\) | −358845. | −0.0593312 | ||||||||
\(517\) | 167363. | 0.0275380 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.93492e6 | −0.967155 | ||||||||
\(520\) | −8.05781e6 | −1.30680 | ||||||||
\(521\) | −8.55515e6 | −1.38081 | −0.690404 | − | 0.723424i | \(-0.742567\pi\) | ||||
−0.690404 | + | 0.723424i | \(0.742567\pi\) | |||||||
\(522\) | 1.25404e6 | 0.201435 | ||||||||
\(523\) | 1.79364e6 | 0.286735 | 0.143368 | − | 0.989670i | \(-0.454207\pi\) | ||||
0.143368 | + | 0.989670i | \(0.454207\pi\) | |||||||
\(524\) | −3.84534e6 | −0.611796 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.18949e6 | −0.187455 | ||||||||
\(527\) | −3.17901e6 | −0.498615 | ||||||||
\(528\) | −55826.8 | −0.00871482 | ||||||||
\(529\) | 9.05749e6 | 1.40724 | ||||||||
\(530\) | 3.73044e6 | 0.576859 | ||||||||
\(531\) | 291862. | 0.0449202 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.63454e7 | 2.49217 | ||||||||
\(534\) | −1.15031e6 | −0.174567 | ||||||||
\(535\) | 166561. | 0.0251588 | ||||||||
\(536\) | −7.29299e6 | −1.09646 | ||||||||
\(537\) | −1.48761e6 | −0.222614 | ||||||||
\(538\) | 12894.1 | 0.00192059 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.04023e6 | −0.153514 | ||||||||
\(541\) | −357561. | −0.0525239 | −0.0262619 | − | 0.999655i | \(-0.508360\pi\) | ||||
−0.0262619 | + | 0.999655i | \(0.508360\pi\) | |||||||
\(542\) | −289285. | −0.0422988 | ||||||||
\(543\) | 1.33643e6 | 0.194512 | ||||||||
\(544\) | −6.10073e6 | −0.883862 | ||||||||
\(545\) | 9.70522e6 | 1.39963 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.79404e6 | −0.542167 | −0.271084 | − | 0.962556i | \(-0.587382\pi\) | ||||
−0.271084 | + | 0.962556i | \(0.587382\pi\) | |||||||
\(548\) | 4.19391e6 | 0.596578 | ||||||||
\(549\) | −1.85300e6 | −0.262389 | ||||||||
\(550\) | 13490.9 | 0.00190167 | ||||||||
\(551\) | 9.79897e6 | 1.37500 | ||||||||
\(552\) | 5.49556e6 | 0.767652 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.09718e6 | −0.290310 | ||||||||
\(555\) | 2.64064e6 | 0.363895 | ||||||||
\(556\) | 5.14926e6 | 0.706412 | ||||||||
\(557\) | −4.89599e6 | −0.668655 | −0.334328 | − | 0.942457i | \(-0.608509\pi\) | ||||
−0.334328 | + | 0.942457i | \(0.608509\pi\) | |||||||
\(558\) | 689296. | 0.0937175 | ||||||||
\(559\) | 1.45140e6 | 0.196453 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 160994. | 0.0215974 | ||||||||
\(562\) | −2.00491e6 | −0.267765 | ||||||||
\(563\) | 4.33167e6 | 0.575949 | 0.287974 | − | 0.957638i | \(-0.407018\pi\) | ||||
0.287974 | + | 0.957638i | \(0.407018\pi\) | |||||||
\(564\) | 2.11342e6 | 0.279761 | ||||||||
\(565\) | −1.51932e7 | −2.00230 | ||||||||
\(566\) | 3.27151e6 | 0.429248 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 248148. | 0.0322730 | ||||||||
\(569\) | −2.19696e6 | −0.284473 | −0.142236 | − | 0.989833i | \(-0.545429\pi\) | ||||
−0.142236 | + | 0.989833i | \(0.545429\pi\) | |||||||
\(570\) | 2.51106e6 | 0.323721 | ||||||||
\(571\) | −7.47692e6 | −0.959693 | −0.479846 | − | 0.877353i | \(-0.659308\pi\) | ||||
−0.479846 | + | 0.877353i | \(0.659308\pi\) | |||||||
\(572\) | 379090. | 0.0484454 | ||||||||
\(573\) | −3.47320e6 | −0.441919 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.10899e6 | 0.139880 | ||||||||
\(576\) | 400052. | 0.0502413 | ||||||||
\(577\) | 1.36622e6 | 0.170837 | 0.0854183 | − | 0.996345i | \(-0.472777\pi\) | ||||
0.0854183 | + | 0.996345i | \(0.472777\pi\) | |||||||
\(578\) | −1.00550e6 | −0.125187 | ||||||||
\(579\) | −4.46666e6 | −0.553715 | ||||||||
\(580\) | 8.03867e6 | 0.992234 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1.87931e6 | −0.229980 | ||||||||
\(583\) | −405224. | −0.0493769 | ||||||||
\(584\) | 920118. | 0.111638 | ||||||||
\(585\) | 4.20738e6 | 0.508302 | ||||||||
\(586\) | 2.81697e6 | 0.338874 | ||||||||
\(587\) | 9.27217e6 | 1.11067 | 0.555336 | − | 0.831626i | \(-0.312590\pi\) | ||||
0.555336 | + | 0.831626i | \(0.312590\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.38612e6 | 0.639717 | ||||||||
\(590\) | −577973. | −0.0683562 | ||||||||
\(591\) | −3.97295e6 | −0.467891 | ||||||||
\(592\) | 1.78956e6 | 0.209866 | ||||||||
\(593\) | −9.21045e6 | −1.07558 | −0.537792 | − | 0.843078i | \(-0.680741\pi\) | ||||
−0.537792 | + | 0.843078i | \(0.680741\pi\) | |||||||
\(594\) | −34907.9 | −0.00405936 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.85305e6 | −0.674942 | ||||||||
\(597\) | −682549. | −0.0783787 | ||||||||
\(598\) | −9.62681e6 | −1.10085 | ||||||||
\(599\) | −1.36916e7 | −1.55915 | −0.779575 | − | 0.626309i | \(-0.784565\pi\) | ||||
−0.779575 | + | 0.626309i | \(0.784565\pi\) | |||||||
\(600\) | 393350. | 0.0446068 | ||||||||
\(601\) | −1.61113e6 | −0.181946 | −0.0909732 | − | 0.995853i | \(-0.528998\pi\) | ||||
−0.0909732 | + | 0.995853i | \(0.528998\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.80803e6 | 0.426489 | ||||||||
\(604\) | −5.30607e6 | −0.591808 | ||||||||
\(605\) | 9.38239e6 | 1.04214 | ||||||||
\(606\) | −1.14164e6 | −0.126284 | ||||||||
\(607\) | 1.40656e7 | 1.54948 | 0.774742 | − | 0.632278i | \(-0.217880\pi\) | ||||
0.774742 | + | 0.632278i | \(0.217880\pi\) | |||||||
\(608\) | 1.03363e7 | 1.13398 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.66950e6 | 0.399284 | ||||||||
\(611\) | −8.54802e6 | −0.926323 | ||||||||
\(612\) | 2.03299e6 | 0.219410 | ||||||||
\(613\) | 1.35968e7 | 1.46146 | 0.730729 | − | 0.682667i | \(-0.239180\pi\) | ||||
0.730729 | + | 0.682667i | \(0.239180\pi\) | |||||||
\(614\) | 1.95078e6 | 0.208828 | ||||||||
\(615\) | −9.64828e6 | −1.02864 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.74287e6 | −0.607318 | −0.303659 | − | 0.952781i | \(-0.598208\pi\) | ||||
−0.303659 | + | 0.952781i | \(0.598208\pi\) | |||||||
\(618\) | −2.02750e6 | −0.213546 | ||||||||
\(619\) | 6.02598e6 | 0.632122 | 0.316061 | − | 0.948739i | \(-0.397640\pi\) | ||||
0.316061 | + | 0.948739i | \(0.397640\pi\) | |||||||
\(620\) | 4.41855e6 | 0.461637 | ||||||||
\(621\) | −2.86950e6 | −0.298592 | ||||||||
\(622\) | −4.30814e6 | −0.446492 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2.85135e6 | 0.293149 | ||||||||
\(625\) | −1.05667e7 | −1.08203 | ||||||||
\(626\) | −1.02494e6 | −0.104535 | ||||||||
\(627\) | −272768. | −0.0277092 | ||||||||
\(628\) | 4.08039e6 | 0.412860 | ||||||||
\(629\) | −5.16075e6 | −0.520099 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.90670e6 | −0.690554 | −0.345277 | − | 0.938501i | \(-0.612215\pi\) | ||||
−0.345277 | + | 0.938501i | \(0.612215\pi\) | |||||||
\(632\) | 1.37240e7 | 1.36675 | ||||||||
\(633\) | −7.00834e6 | −0.695194 | ||||||||
\(634\) | −8.32193e6 | −0.822244 | ||||||||
\(635\) | 1.36429e7 | 1.34268 | ||||||||
\(636\) | −5.11708e6 | −0.501625 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 269759. | 0.0262376 | ||||||||
\(639\) | −129570. | −0.0125532 | ||||||||
\(640\) | 1.03068e7 | 0.994658 | ||||||||
\(641\) | 1.64966e7 | 1.58580 | 0.792900 | − | 0.609352i | \(-0.208570\pi\) | ||||
0.792900 | + | 0.609352i | \(0.208570\pi\) | |||||||
\(642\) | 70581.7 | 0.00675857 | ||||||||
\(643\) | −1.70171e7 | −1.62315 | −0.811576 | − | 0.584247i | \(-0.801390\pi\) | ||||
−0.811576 | + | 0.584247i | \(0.801390\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −856727. | −0.0810855 | ||||||||
\(646\) | −4.90752e6 | −0.462680 | ||||||||
\(647\) | −3.48573e6 | −0.327366 | −0.163683 | − | 0.986513i | \(-0.552337\pi\) | ||||
−0.163683 | + | 0.986513i | \(0.552337\pi\) | |||||||
\(648\) | −1.01779e6 | −0.0952188 | ||||||||
\(649\) | 62783.2 | 0.00585102 | ||||||||
\(650\) | −689047. | −0.0639684 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.23746e7 | −1.14002 | ||||||||
\(653\) | 1.54449e7 | 1.41743 | 0.708716 | − | 0.705494i | \(-0.249275\pi\) | ||||
0.708716 | + | 0.705494i | \(0.249275\pi\) | |||||||
\(654\) | 4.11267e6 | 0.375993 | ||||||||
\(655\) | −9.18058e6 | −0.836116 | ||||||||
\(656\) | −6.53865e6 | −0.593238 | ||||||||
\(657\) | −480439. | −0.0434235 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.11193e6 | −0.279136 | −0.139568 | − | 0.990212i | \(-0.544571\pi\) | ||||
−0.139568 | + | 0.990212i | \(0.544571\pi\) | |||||||
\(660\) | −223767. | −0.0199957 | ||||||||
\(661\) | −8.17220e6 | −0.727504 | −0.363752 | − | 0.931496i | \(-0.618504\pi\) | ||||
−0.363752 | + | 0.931496i | \(0.618504\pi\) | |||||||
\(662\) | 2.93202e6 | 0.260029 | ||||||||
\(663\) | −8.22273e6 | −0.726495 | ||||||||
\(664\) | −1.48650e7 | −1.30841 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.11899e6 | 0.0977556 | ||||||||
\(667\) | 2.21748e7 | 1.92995 | ||||||||
\(668\) | −1.38265e7 | −1.19887 | ||||||||
\(669\) | 6.64276e6 | 0.573830 | ||||||||
\(670\) | −7.54103e6 | −0.648998 | ||||||||
\(671\) | −398604. | −0.0341771 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.60182e7 | 1.36325 | 0.681627 | − | 0.731700i | \(-0.261273\pi\) | ||||
0.681627 | + | 0.731700i | \(0.261273\pi\) | |||||||
\(674\) | 4.27986e6 | 0.362894 | ||||||||
\(675\) | −205387. | −0.0173506 | ||||||||
\(676\) | −1.02848e7 | −0.865621 | ||||||||
\(677\) | −1.02437e6 | −0.0858984 | −0.0429492 | − | 0.999077i | \(-0.513675\pi\) | ||||
−0.0429492 | + | 0.999077i | \(0.513675\pi\) | |||||||
\(678\) | −6.43826e6 | −0.537891 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −9.29556e6 | −0.770910 | ||||||||
\(681\) | −4.89704e6 | −0.404637 | ||||||||
\(682\) | 148276. | 0.0122070 | ||||||||
\(683\) | −5.39377e6 | −0.442426 | −0.221213 | − | 0.975226i | \(-0.571002\pi\) | ||||
−0.221213 | + | 0.975226i | \(0.571002\pi\) | |||||||
\(684\) | −3.44445e6 | −0.281501 | ||||||||
\(685\) | 1.00128e7 | 0.815319 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.10206e6 | −0.169924 | ||||||||
\(688\) | −580605. | −0.0467638 | ||||||||
\(689\) | 2.06968e7 | 1.66094 | ||||||||
\(690\) | 5.68246e6 | 0.454375 | ||||||||
\(691\) | 905653. | 0.0721550 | 0.0360775 | − | 0.999349i | \(-0.488514\pi\) | ||||
0.0360775 | + | 0.999349i | \(0.488514\pi\) | |||||||
\(692\) | −1.61215e7 | −1.27980 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.14207e6 | −0.484079 | ||||||||
\(695\) | 1.22936e7 | 0.965424 | ||||||||
\(696\) | 7.86526e6 | 0.615446 | ||||||||
\(697\) | 1.88562e7 | 1.47019 | ||||||||
\(698\) | 4.75387e6 | 0.369325 | ||||||||
\(699\) | 5.56290e6 | 0.430634 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.12573e7 | 0.865246 | 0.432623 | − | 0.901575i | \(-0.357588\pi\) | ||||
0.432623 | + | 0.901575i | \(0.357588\pi\) | |||||||
\(702\) | 1.78291e6 | 0.136549 | ||||||||
\(703\) | 8.74374e6 | 0.667281 | ||||||||
\(704\) | 86056.2 | 0.00654411 | ||||||||
\(705\) | 5.04568e6 | 0.382338 | ||||||||
\(706\) | 6.50147e6 | 0.490908 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 792812. | 0.0594411 | ||||||||
\(709\) | 4.35509e6 | 0.325373 | 0.162687 | − | 0.986678i | \(-0.447984\pi\) | ||||
0.162687 | + | 0.986678i | \(0.447984\pi\) | |||||||
\(710\) | 256587. | 0.0191025 | ||||||||
\(711\) | −7.16598e6 | −0.531620 | ||||||||
\(712\) | −7.21467e6 | −0.533355 | ||||||||
\(713\) | 1.21886e7 | 0.897907 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 905060. | 0.0662082 | ||||||||
\(716\) | −4.04093e6 | −0.294577 | ||||||||
\(717\) | −8.43750e6 | −0.612937 | ||||||||
\(718\) | 140236. | 0.0101519 | ||||||||
\(719\) | 1.41444e7 | 1.02038 | 0.510191 | − | 0.860061i | \(-0.329575\pi\) | ||||
0.510191 | + | 0.860061i | \(0.329575\pi\) | |||||||
\(720\) | −1.68308e6 | −0.120997 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.50992e6 | 0.107798 | ||||||||
\(723\) | 8.38833e6 | 0.596801 | ||||||||
\(724\) | 3.63025e6 | 0.257389 | ||||||||
\(725\) | 1.58718e6 | 0.112145 | ||||||||
\(726\) | 3.97587e6 | 0.279956 | ||||||||
\(727\) | 6.26406e6 | 0.439561 | 0.219781 | − | 0.975549i | \(-0.429466\pi\) | ||||
0.219781 | + | 0.975549i | \(0.429466\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 951411. | 0.0660786 | ||||||||
\(731\) | 1.67435e6 | 0.115892 | ||||||||
\(732\) | −5.03348e6 | −0.347209 | ||||||||
\(733\) | 2.04177e7 | 1.40361 | 0.701806 | − | 0.712368i | \(-0.252377\pi\) | ||||
0.701806 | + | 0.712368i | \(0.252377\pi\) | |||||||
\(734\) | −1.03558e7 | −0.709484 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.33908e7 | 1.59166 | ||||||||
\(737\) | 819155. | 0.0555517 | ||||||||
\(738\) | −4.08854e6 | −0.276330 | ||||||||
\(739\) | 1.48451e7 | 0.999937 | 0.499969 | − | 0.866043i | \(-0.333345\pi\) | ||||
0.499969 | + | 0.866043i | \(0.333345\pi\) | |||||||
\(740\) | 7.17300e6 | 0.481528 | ||||||||
\(741\) | 1.39316e7 | 0.932083 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.36601e7 | 1.57234 | 0.786168 | − | 0.618013i | \(-0.212062\pi\) | ||||
0.786168 | + | 0.618013i | \(0.212062\pi\) | |||||||
\(744\) | 4.32323e6 | 0.286336 | ||||||||
\(745\) | −1.39739e7 | −0.922415 | ||||||||
\(746\) | 1.27362e7 | 0.837900 | ||||||||
\(747\) | 7.76174e6 | 0.508929 | ||||||||
\(748\) | 437322. | 0.0285790 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −4.10463e6 | −0.266453 | ||||||||
\(751\) | 2.06573e7 | 1.33652 | 0.668258 | − | 0.743929i | \(-0.267040\pi\) | ||||
0.668258 | + | 0.743929i | \(0.267040\pi\) | |||||||
\(752\) | 3.41946e6 | 0.220503 | ||||||||
\(753\) | 1.93478e6 | 0.124349 | ||||||||
\(754\) | −1.37779e7 | −0.882581 | ||||||||
\(755\) | −1.26680e7 | −0.808799 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.26697e7 | −0.803573 | −0.401787 | − | 0.915733i | \(-0.631611\pi\) | ||||
−0.401787 | + | 0.915733i | \(0.631611\pi\) | |||||||
\(758\) | −1.14646e7 | −0.724743 | ||||||||
\(759\) | −617266. | −0.0388927 | ||||||||
\(760\) | 1.57492e7 | 0.989067 | ||||||||
\(761\) | −1.62752e7 | −1.01874 | −0.509372 | − | 0.860546i | \(-0.670122\pi\) | ||||
−0.509372 | + | 0.860546i | \(0.670122\pi\) | |||||||
\(762\) | 5.78130e6 | 0.360694 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −9.43455e6 | −0.584774 | ||||||||
\(765\) | 4.85367e6 | 0.299859 | ||||||||
\(766\) | 1.14646e7 | 0.705974 | ||||||||
\(767\) | −3.20664e6 | −0.196817 | ||||||||
\(768\) | 5.79000e6 | 0.354222 | ||||||||
\(769\) | −1.60471e7 | −0.978547 | −0.489273 | − | 0.872130i | \(-0.662738\pi\) | ||||
−0.489273 | + | 0.872130i | \(0.662738\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 712683. | 0.0431778 | ||||||||
\(772\) | −1.21332e7 | −0.732709 | ||||||||
\(773\) | −2.15677e6 | −0.129824 | −0.0649121 | − | 0.997891i | \(-0.520677\pi\) | ||||
−0.0649121 | + | 0.997891i | \(0.520677\pi\) | |||||||
\(774\) | −363045. | −0.0217825 | ||||||||
\(775\) | 872413. | 0.0521756 | ||||||||
\(776\) | −1.17869e7 | −0.702661 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.56833e6 | 0.448282 | ||||||||
\(779\) | −3.19476e7 | −1.88623 | ||||||||
\(780\) | 1.14289e7 | 0.672616 | ||||||||
\(781\) | −27872.2 | −0.00163510 | ||||||||
\(782\) | −1.11056e7 | −0.649418 | ||||||||
\(783\) | −4.10684e6 | −0.239389 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.74175e6 | 0.564239 | ||||||||
\(786\) | −3.89035e6 | −0.224612 | ||||||||
\(787\) | −1.40101e7 | −0.806312 | −0.403156 | − | 0.915131i | \(-0.632087\pi\) | ||||
−0.403156 | + | 0.915131i | \(0.632087\pi\) | |||||||
\(788\) | −1.07921e7 | −0.619142 | ||||||||
\(789\) | 3.89545e6 | 0.222774 | ||||||||
\(790\) | 1.41908e7 | 0.808980 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −218940. | −0.0124026 | ||||||||
\(793\) | 2.03587e7 | 1.14965 | ||||||||
\(794\) | 6.95852e6 | 0.391711 | ||||||||
\(795\) | −1.22168e7 | −0.685550 | ||||||||
\(796\) | −1.85407e6 | −0.103715 | ||||||||
\(797\) | −4.73289e6 | −0.263925 | −0.131963 | − | 0.991255i | \(-0.542128\pi\) | ||||
−0.131963 | + | 0.991255i | \(0.542128\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.86107e6 | −0.546459 | ||||||||
\(800\) | 1.67422e6 | 0.0924883 | ||||||||
\(801\) | 3.76714e6 | 0.207458 | ||||||||
\(802\) | −5.92912e6 | −0.325502 | ||||||||
\(803\) | −103348. | −0.00565607 | ||||||||
\(804\) | 1.03441e7 | 0.564355 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.57318e6 | −0.410621 | ||||||||
\(807\) | −42226.7 | −0.00228246 | ||||||||
\(808\) | −7.16031e6 | −0.385836 | ||||||||
\(809\) | 8.10892e6 | 0.435604 | 0.217802 | − | 0.975993i | \(-0.430111\pi\) | ||||
0.217802 | + | 0.975993i | \(0.430111\pi\) | |||||||
\(810\) | −1.05241e6 | −0.0563602 | ||||||||
\(811\) | 9.13444e6 | 0.487674 | 0.243837 | − | 0.969816i | \(-0.421594\pi\) | ||||
0.243837 | + | 0.969816i | \(0.421594\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 947378. | 0.0502686 | ||||||||
\(814\) | 240709. | 0.0127330 | ||||||||
\(815\) | −2.95439e7 | −1.55802 | ||||||||
\(816\) | 3.28934e6 | 0.172935 | ||||||||
\(817\) | −2.83681e6 | −0.148688 | ||||||||
\(818\) | 1.18942e7 | 0.621517 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.62085e7 | −1.36115 | ||||||||
\(821\) | 1.70155e6 | 0.0881023 | 0.0440511 | − | 0.999029i | \(-0.485974\pi\) | ||||
0.0440511 | + | 0.999029i | \(0.485974\pi\) | |||||||
\(822\) | 4.24299e6 | 0.219025 | ||||||||
\(823\) | −2.49207e7 | −1.28251 | −0.641256 | − | 0.767327i | \(-0.721586\pi\) | ||||
−0.641256 | + | 0.767327i | \(0.721586\pi\) | |||||||
\(824\) | −1.27164e7 | −0.652448 | ||||||||
\(825\) | −44181.4 | −0.00225998 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.91232e7 | −0.972292 | −0.486146 | − | 0.873878i | \(-0.661598\pi\) | ||||
−0.486146 | + | 0.873878i | \(0.661598\pi\) | |||||||
\(828\) | −7.79469e6 | −0.395115 | ||||||||
\(829\) | 2.20267e7 | 1.11318 | 0.556588 | − | 0.830789i | \(-0.312110\pi\) | ||||
0.556588 | + | 0.830789i | \(0.312110\pi\) | |||||||
\(830\) | −1.53705e7 | −0.774450 | ||||||||
\(831\) | 6.86805e6 | 0.345009 | ||||||||
\(832\) | −4.39531e6 | −0.220131 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 5.20953e6 | 0.259348 | ||||||||
\(835\) | −3.30102e7 | −1.63844 | ||||||||
\(836\) | −740943. | −0.0366665 | ||||||||
\(837\) | −2.25737e6 | −0.111375 | ||||||||
\(838\) | 4.15329e6 | 0.204306 | ||||||||
\(839\) | −4.28039e6 | −0.209932 | −0.104966 | − | 0.994476i | \(-0.533473\pi\) | ||||
−0.104966 | + | 0.994476i | \(0.533473\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.12255e7 | 0.547286 | ||||||||
\(842\) | 3.06659e6 | 0.149065 | ||||||||
\(843\) | 6.56586e6 | 0.318216 | ||||||||
\(844\) | −1.90374e7 | −0.919922 | ||||||||
\(845\) | −2.45544e7 | −1.18301 | ||||||||
\(846\) | 2.13815e6 | 0.102710 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −8.27933e6 | −0.395372 | ||||||||
\(849\) | −1.07139e7 | −0.510125 | ||||||||
\(850\) | −794892. | −0.0377364 | ||||||||
\(851\) | 1.97868e7 | 0.936596 | ||||||||
\(852\) | −351963. | −0.0166111 | ||||||||
\(853\) | 1.72415e7 | 0.811341 | 0.405670 | − | 0.914019i | \(-0.367038\pi\) | ||||
0.405670 | + | 0.914019i | \(0.367038\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.22346e6 | −0.384715 | ||||||||
\(856\) | 442685. | 0.0206495 | ||||||||
\(857\) | −2.08340e7 | −0.968991 | −0.484495 | − | 0.874794i | \(-0.660997\pi\) | ||||
−0.484495 | + | 0.874794i | \(0.660997\pi\) | |||||||
\(858\) | 383527. | 0.0177860 | ||||||||
\(859\) | 1.58356e7 | 0.732238 | 0.366119 | − | 0.930568i | \(-0.380686\pi\) | ||||
0.366119 | + | 0.930568i | \(0.380686\pi\) | |||||||
\(860\) | −2.32720e6 | −0.107297 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.70757e7 | 0.782726 | ||||||||
\(863\) | −1.59282e7 | −0.728012 | −0.364006 | − | 0.931397i | \(-0.618591\pi\) | ||||
−0.364006 | + | 0.931397i | \(0.618591\pi\) | |||||||
\(864\) | −4.33204e6 | −0.197428 | ||||||||
\(865\) | −3.84894e7 | −1.74905 | ||||||||
\(866\) | −8.90735e6 | −0.403603 | ||||||||
\(867\) | 3.29289e6 | 0.148775 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.54149e6 | −0.0692455 | ||||||||
\(870\) | 8.13275e6 | 0.364283 | ||||||||
\(871\) | −4.18382e7 | −1.86865 | ||||||||
\(872\) | 2.57944e7 | 1.14877 | ||||||||
\(873\) | 6.15453e6 | 0.273312 | ||||||||
\(874\) | 1.88159e7 | 0.833195 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.30506e6 | −0.0574606 | ||||||||
\(877\) | 5.20734e6 | 0.228621 | 0.114311 | − | 0.993445i | \(-0.463534\pi\) | ||||
0.114311 | + | 0.993445i | \(0.463534\pi\) | |||||||
\(878\) | −6.33446e6 | −0.277315 | ||||||||
\(879\) | −9.22527e6 | −0.402723 | ||||||||
\(880\) | −362051. | −0.0157603 | ||||||||
\(881\) | 932829. | 0.0404913 | 0.0202457 | − | 0.999795i | \(-0.493555\pi\) | ||||
0.0202457 | + | 0.999795i | \(0.493555\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.33789e7 | 0.577457 | 0.288728 | − | 0.957411i | \(-0.406768\pi\) | ||||
0.288728 | + | 0.957411i | \(0.406768\pi\) | |||||||
\(884\) | −2.23361e7 | −0.961341 | ||||||||
\(885\) | 1.89280e6 | 0.0812357 | ||||||||
\(886\) | 4.21202e6 | 0.180263 | ||||||||
\(887\) | 6.96900e6 | 0.297414 | 0.148707 | − | 0.988881i | \(-0.452489\pi\) | ||||
0.148707 | + | 0.988881i | \(0.452489\pi\) | |||||||
\(888\) | 7.01826e6 | 0.298674 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −7.46004e6 | −0.315694 | ||||||||
\(891\) | 114320. | 0.00482421 | ||||||||
\(892\) | 1.80443e7 | 0.759326 | ||||||||
\(893\) | 1.67074e7 | 0.701099 | ||||||||
\(894\) | −5.92155e6 | −0.247794 | ||||||||
\(895\) | −9.64753e6 | −0.402586 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.15268e7 | 1.30827 | ||||||||
\(898\) | −9.77577e6 | −0.404539 | ||||||||
\(899\) | 1.74444e7 | 0.719874 | ||||||||
\(900\) | −557912. | −0.0229593 | ||||||||
\(901\) | 2.38760e7 | 0.979826 | ||||||||
\(902\) | −879496. | −0.0359929 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.03804e7 | −1.64342 | ||||||||
\(905\) | 8.66706e6 | 0.351763 | ||||||||
\(906\) | −5.36817e6 | −0.217273 | ||||||||
\(907\) | −3.76563e7 | −1.51992 | −0.759959 | − | 0.649972i | \(-0.774781\pi\) | ||||
−0.759959 | + | 0.649972i | \(0.774781\pi\) | |||||||
\(908\) | −1.33023e7 | −0.535440 | ||||||||
\(909\) | 3.73875e6 | 0.150078 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.09942e7 | −1.23733 | −0.618663 | − | 0.785657i | \(-0.712325\pi\) | ||||
−0.618663 | + | 0.785657i | \(0.712325\pi\) | |||||||
\(912\) | −5.57305e6 | −0.221874 | ||||||||
\(913\) | 1.66965e6 | 0.0662899 | ||||||||
\(914\) | 6.92219e6 | 0.274080 | ||||||||
\(915\) | −1.20172e7 | −0.474516 | ||||||||
\(916\) | −5.71002e6 | −0.224853 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.05679e6 | 0.0805531 | ||||||||
\(919\) | 716014. | 0.0279662 | 0.0139831 | − | 0.999902i | \(-0.495549\pi\) | ||||
0.0139831 | + | 0.999902i | \(0.495549\pi\) | |||||||
\(920\) | 3.56401e7 | 1.38826 | ||||||||
\(921\) | −6.38860e6 | −0.248174 | ||||||||
\(922\) | 1.82279e7 | 0.706169 | ||||||||
\(923\) | 1.42357e6 | 0.0550014 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.41626e6 | 0.0544238 | ||||||||
\(926\) | −1.21039e7 | −0.463870 | ||||||||
\(927\) | 6.63986e6 | 0.253781 | ||||||||
\(928\) | 3.34769e7 | 1.27607 | ||||||||
\(929\) | −4.17630e7 | −1.58764 | −0.793820 | − | 0.608153i | \(-0.791911\pi\) | ||||
−0.793820 | + | 0.608153i | \(0.791911\pi\) | |||||||
\(930\) | 4.47026e6 | 0.169483 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.51110e7 | 0.569840 | ||||||||
\(933\) | 1.41087e7 | 0.530618 | ||||||||
\(934\) | −675626. | −0.0253419 | ||||||||
\(935\) | 1.04409e6 | 0.0390577 | ||||||||
\(936\) | 1.11823e7 | 0.417199 | ||||||||
\(937\) | 2.17917e7 | 0.810854 | 0.405427 | − | 0.914127i | \(-0.367123\pi\) | ||||
0.405427 | + | 0.914127i | \(0.367123\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.35657e6 | 0.124232 | ||||||||
\(940\) | 1.37060e7 | 0.505932 | ||||||||
\(941\) | 2.15218e6 | 0.0792329 | 0.0396164 | − | 0.999215i | \(-0.487386\pi\) | ||||
0.0396164 | + | 0.999215i | \(0.487386\pi\) | |||||||
\(942\) | 4.12815e6 | 0.151575 | ||||||||
\(943\) | −7.22965e7 | −2.64751 | ||||||||
\(944\) | 1.28275e6 | 0.0468504 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −78095.5 | −0.00283725 | ||||||||
\(947\) | −2.64249e7 | −0.957501 | −0.478750 | − | 0.877951i | \(-0.658910\pi\) | ||||
−0.478750 | + | 0.877951i | \(0.658910\pi\) | |||||||
\(948\) | −1.94656e7 | −0.703472 | ||||||||
\(949\) | 5.27850e6 | 0.190259 | ||||||||
\(950\) | 1.34677e6 | 0.0484153 | ||||||||
\(951\) | 2.72534e7 | 0.977169 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.07051e6 | 0.323519 | 0.161759 | − | 0.986830i | \(-0.448283\pi\) | ||||
0.161759 | + | 0.986830i | \(0.448283\pi\) | |||||||
\(954\) | −5.17697e6 | −0.184164 | ||||||||
\(955\) | −2.25246e7 | −0.799186 | ||||||||
\(956\) | −2.29195e7 | −0.811075 | ||||||||
\(957\) | −883432. | −0.0311812 | ||||||||
\(958\) | 110892. | 0.00390380 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.59444e6 | 0.0908585 | ||||||||
\(961\) | −1.90406e7 | −0.665079 | ||||||||
\(962\) | −1.22942e7 | −0.428314 | ||||||||
\(963\) | −231148. | −0.00803200 | ||||||||
\(964\) | 2.27860e7 | 0.789723 | ||||||||
\(965\) | −2.89674e7 | −1.00136 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.80108e7 | 0.619395 | 0.309698 | − | 0.950835i | \(-0.399772\pi\) | ||||
0.309698 | + | 0.950835i | \(0.399772\pi\) | |||||||
\(968\) | 2.49364e7 | 0.855354 | ||||||||
\(969\) | 1.60716e7 | 0.549857 | ||||||||
\(970\) | −1.21878e7 | −0.415906 | ||||||||
\(971\) | 4.67631e7 | 1.59168 | 0.795838 | − | 0.605509i | \(-0.207030\pi\) | ||||
0.795838 | + | 0.605509i | \(0.207030\pi\) | |||||||
\(972\) | 1.44360e6 | 0.0490096 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −9.09561e6 | −0.307209 | ||||||||
\(975\) | 2.25656e6 | 0.0760212 | ||||||||
\(976\) | −8.14408e6 | −0.273664 | ||||||||
\(977\) | 4.32433e6 | 0.144938 | 0.0724690 | − | 0.997371i | \(-0.476912\pi\) | ||||
0.0724690 | + | 0.997371i | \(0.476912\pi\) | |||||||
\(978\) | −1.25195e7 | −0.418542 | ||||||||
\(979\) | 810357. | 0.0270221 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.34685e7 | −0.446836 | ||||||||
\(982\) | −5.44026e6 | −0.180028 | ||||||||
\(983\) | −2.08733e7 | −0.688982 | −0.344491 | − | 0.938790i | \(-0.611949\pi\) | ||||
−0.344491 | + | 0.938790i | \(0.611949\pi\) | |||||||
\(984\) | −2.56431e7 | −0.844273 | ||||||||
\(985\) | −2.57656e7 | −0.846155 | ||||||||
\(986\) | −1.58943e7 | −0.520655 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.78436e7 | 1.23339 | ||||||||
\(989\) | −6.41963e6 | −0.208698 | ||||||||
\(990\) | −226386. | −0.00734112 | ||||||||
\(991\) | 4.12209e7 | 1.33332 | 0.666658 | − | 0.745364i | \(-0.267724\pi\) | ||||
0.666658 | + | 0.745364i | \(0.267724\pi\) | |||||||
\(992\) | 1.84010e7 | 0.593693 | ||||||||
\(993\) | −9.60206e6 | −0.309023 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.42650e6 | −0.141743 | ||||||||
\(996\) | 2.10839e7 | 0.673446 | ||||||||
\(997\) | 5.34615e7 | 1.70335 | 0.851674 | − | 0.524073i | \(-0.175588\pi\) | ||||
0.851674 | + | 0.524073i | \(0.175588\pi\) | |||||||
\(998\) | −8.71160e6 | −0.276867 | ||||||||
\(999\) | −3.66458e6 | −0.116174 |
(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 | 147.6.a.l.1.3 | 4 | ||
3.2 | odd | 2 | 441.6.a.v.1.2 | 4 | |||
7.2 | even | 3 | 147.6.e.o.67.2 | 8 | |||
7.3 | odd | 6 | 21.6.e.c.16.2 | yes | 8 | ||
7.4 | even | 3 | 147.6.e.o.79.2 | 8 | |||
7.5 | odd | 6 | 21.6.e.c.4.2 | ✓ | 8 | ||
7.6 | odd | 2 | 147.6.a.m.1.3 | 4 | |||
21.5 | even | 6 | 63.6.e.e.46.3 | 8 | |||
21.17 | even | 6 | 63.6.e.e.37.3 | 8 | |||
21.20 | even | 2 | 441.6.a.w.1.2 | 4 | |||
28.3 | even | 6 | 336.6.q.j.289.1 | 8 | |||
28.19 | even | 6 | 336.6.q.j.193.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.6.e.c.4.2 | ✓ | 8 | 7.5 | odd | 6 | ||
21.6.e.c.16.2 | yes | 8 | 7.3 | odd | 6 | ||
63.6.e.e.37.3 | 8 | 21.17 | even | 6 | |||
63.6.e.e.46.3 | 8 | 21.5 | even | 6 | |||
147.6.a.l.1.3 | 4 | 1.1 | even | 1 | trivial | ||
147.6.a.m.1.3 | 4 | 7.6 | odd | 2 | |||
147.6.e.o.67.2 | 8 | 7.2 | even | 3 | |||
147.6.e.o.79.2 | 8 | 7.4 | even | 3 | |||
336.6.q.j.193.1 | 8 | 28.19 | even | 6 | |||
336.6.q.j.289.1 | 8 | 28.3 | even | 6 | |||
441.6.a.v.1.2 | 4 | 3.2 | odd | 2 | |||
441.6.a.w.1.2 | 4 | 21.20 | even | 2 |