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 | 1.13 | ||
Root | \(25.8045\) 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 | ||||||||
\(3\) | 27.3366 | 1.75364 | 0.876822 | − | 0.480815i | \(-0.159659\pi\) | ||||
0.876822 | + | 0.480815i | \(0.159659\pi\) | |||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | −91.1494 | −1.63053 | −0.815265 | − | 0.579088i | \(-0.803409\pi\) | ||||
−0.815265 | + | 0.579088i | \(0.803409\pi\) | |||||||
\(6\) | −109.346 | −1.24001 | ||||||||
\(7\) | 45.5647 | 0.351466 | 0.175733 | − | 0.984438i | \(-0.443770\pi\) | ||||
0.175733 | + | 0.984438i | \(0.443770\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 504.290 | 2.07527 | ||||||||
\(10\) | 364.597 | 1.15296 | ||||||||
\(11\) | −407.724 | −1.01598 | −0.507989 | − | 0.861364i | \(-0.669611\pi\) | ||||
−0.507989 | + | 0.861364i | \(0.669611\pi\) | |||||||
\(12\) | 437.386 | 0.876822 | ||||||||
\(13\) | −421.227 | −0.691287 | −0.345643 | − | 0.938366i | \(-0.612339\pi\) | ||||
−0.345643 | + | 0.938366i | \(0.612339\pi\) | |||||||
\(14\) | −182.259 | −0.248524 | ||||||||
\(15\) | −2491.71 | −2.85937 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −844.364 | −0.708610 | −0.354305 | − | 0.935130i | \(-0.615283\pi\) | ||||
−0.354305 | + | 0.935130i | \(0.615283\pi\) | |||||||
\(18\) | −2017.16 | −1.46744 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −1458.39 | −0.815265 | ||||||||
\(21\) | 1245.58 | 0.616346 | ||||||||
\(22\) | 1630.90 | 0.718405 | ||||||||
\(23\) | −4663.12 | −1.83805 | −0.919025 | − | 0.394200i | \(-0.871022\pi\) | ||||
−0.919025 | + | 0.394200i | \(0.871022\pi\) | |||||||
\(24\) | −1749.54 | −0.620007 | ||||||||
\(25\) | 5183.21 | 1.65863 | ||||||||
\(26\) | 1684.91 | 0.488814 | ||||||||
\(27\) | 7142.79 | 1.88564 | ||||||||
\(28\) | 729.035 | 0.175733 | ||||||||
\(29\) | 3994.60 | 0.882021 | 0.441010 | − | 0.897502i | \(-0.354620\pi\) | ||||
0.441010 | + | 0.897502i | \(0.354620\pi\) | |||||||
\(30\) | 9966.86 | 2.02188 | ||||||||
\(31\) | 7463.25 | 1.39484 | 0.697419 | − | 0.716664i | \(-0.254332\pi\) | ||||
0.697419 | + | 0.716664i | \(0.254332\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | −11145.8 | −1.78166 | ||||||||
\(34\) | 3377.45 | 0.501063 | ||||||||
\(35\) | −4153.19 | −0.573075 | ||||||||
\(36\) | 8068.65 | 1.03763 | ||||||||
\(37\) | 12556.5 | 1.50787 | 0.753934 | − | 0.656950i | \(-0.228154\pi\) | ||||
0.753934 | + | 0.656950i | \(0.228154\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −11514.9 | −1.21227 | ||||||||
\(40\) | 5833.56 | 0.576479 | ||||||||
\(41\) | 6250.11 | 0.580668 | 0.290334 | − | 0.956925i | \(-0.406234\pi\) | ||||
0.290334 | + | 0.956925i | \(0.406234\pi\) | |||||||
\(42\) | −4982.33 | −0.435823 | ||||||||
\(43\) | 1050.09 | 0.0866075 | 0.0433037 | − | 0.999062i | \(-0.486212\pi\) | ||||
0.0433037 | + | 0.999062i | \(0.486212\pi\) | |||||||
\(44\) | −6523.58 | −0.507989 | ||||||||
\(45\) | −45965.7 | −3.38379 | ||||||||
\(46\) | 18652.5 | 1.29970 | ||||||||
\(47\) | −5325.49 | −0.351653 | −0.175827 | − | 0.984421i | \(-0.556260\pi\) | ||||
−0.175827 | + | 0.984421i | \(0.556260\pi\) | |||||||
\(48\) | 6998.17 | 0.438411 | ||||||||
\(49\) | −14730.9 | −0.876472 | ||||||||
\(50\) | −20732.8 | −1.17283 | ||||||||
\(51\) | −23082.0 | −1.24265 | ||||||||
\(52\) | −6739.64 | −0.345643 | ||||||||
\(53\) | −5063.81 | −0.247621 | −0.123810 | − | 0.992306i | \(-0.539511\pi\) | ||||
−0.123810 | + | 0.992306i | \(0.539511\pi\) | |||||||
\(54\) | −28571.2 | −1.33335 | ||||||||
\(55\) | 37163.8 | 1.65658 | ||||||||
\(56\) | −2916.14 | −0.124262 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −15978.4 | −0.623683 | ||||||||
\(59\) | −7184.01 | −0.268681 | −0.134340 | − | 0.990935i | \(-0.542892\pi\) | ||||
−0.134340 | + | 0.990935i | \(0.542892\pi\) | |||||||
\(60\) | −39867.4 | −1.42968 | ||||||||
\(61\) | 46559.6 | 1.60208 | 0.801041 | − | 0.598609i | \(-0.204280\pi\) | ||||
0.801041 | + | 0.598609i | \(0.204280\pi\) | |||||||
\(62\) | −29853.0 | −0.986299 | ||||||||
\(63\) | 22977.8 | 0.729386 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 38394.6 | 1.12716 | ||||||||
\(66\) | 44583.1 | 1.25983 | ||||||||
\(67\) | 39163.7 | 1.06585 | 0.532926 | − | 0.846162i | \(-0.321093\pi\) | ||||
0.532926 | + | 0.846162i | \(0.321093\pi\) | |||||||
\(68\) | −13509.8 | −0.354305 | ||||||||
\(69\) | −127474. | −3.22329 | ||||||||
\(70\) | 16612.8 | 0.405226 | ||||||||
\(71\) | 21791.8 | 0.513036 | 0.256518 | − | 0.966539i | \(-0.417425\pi\) | ||||
0.256518 | + | 0.966539i | \(0.417425\pi\) | |||||||
\(72\) | −32274.6 | −0.733718 | ||||||||
\(73\) | −14064.7 | −0.308903 | −0.154452 | − | 0.988000i | \(-0.549361\pi\) | ||||
−0.154452 | + | 0.988000i | \(0.549361\pi\) | |||||||
\(74\) | −50225.9 | −1.06622 | ||||||||
\(75\) | 141691. | 2.90864 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −18577.8 | −0.357082 | ||||||||
\(78\) | 46059.7 | 0.857205 | ||||||||
\(79\) | 94861.5 | 1.71010 | 0.855052 | − | 0.518542i | \(-0.173525\pi\) | ||||
0.855052 | + | 0.518542i | \(0.173525\pi\) | |||||||
\(80\) | −23334.2 | −0.407632 | ||||||||
\(81\) | 72717.2 | 1.23147 | ||||||||
\(82\) | −25000.5 | −0.410595 | ||||||||
\(83\) | 24415.7 | 0.389022 | 0.194511 | − | 0.980900i | \(-0.437688\pi\) | ||||
0.194511 | + | 0.980900i | \(0.437688\pi\) | |||||||
\(84\) | 19929.3 | 0.308173 | ||||||||
\(85\) | 76963.2 | 1.15541 | ||||||||
\(86\) | −4200.36 | −0.0612407 | ||||||||
\(87\) | 109199. | 1.54675 | ||||||||
\(88\) | 26094.3 | 0.359202 | ||||||||
\(89\) | 51064.6 | 0.683352 | 0.341676 | − | 0.939818i | \(-0.389005\pi\) | ||||
0.341676 | + | 0.939818i | \(0.389005\pi\) | |||||||
\(90\) | 183863. | 2.39270 | ||||||||
\(91\) | −19193.1 | −0.242964 | ||||||||
\(92\) | −74609.9 | −0.919025 | ||||||||
\(93\) | 204020. | 2.44605 | ||||||||
\(94\) | 21301.9 | 0.248656 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −27992.7 | −0.310003 | ||||||||
\(97\) | −130349. | −1.40662 | −0.703311 | − | 0.710882i | \(-0.748296\pi\) | ||||
−0.703311 | + | 0.710882i | \(0.748296\pi\) | |||||||
\(98\) | 58923.4 | 0.619759 | ||||||||
\(99\) | −205611. | −2.10843 | ||||||||
\(100\) | 82931.3 | 0.829313 | ||||||||
\(101\) | 25512.9 | 0.248860 | 0.124430 | − | 0.992228i | \(-0.460290\pi\) | ||||
0.124430 | + | 0.992228i | \(0.460290\pi\) | |||||||
\(102\) | 92328.2 | 0.878686 | ||||||||
\(103\) | 39183.2 | 0.363921 | 0.181960 | − | 0.983306i | \(-0.441756\pi\) | ||||
0.181960 | + | 0.983306i | \(0.441756\pi\) | |||||||
\(104\) | 26958.6 | 0.244407 | ||||||||
\(105\) | −113534. | −1.00497 | ||||||||
\(106\) | 20255.2 | 0.175094 | ||||||||
\(107\) | −42926.8 | −0.362467 | −0.181234 | − | 0.983440i | \(-0.558009\pi\) | ||||
−0.181234 | + | 0.983440i | \(0.558009\pi\) | |||||||
\(108\) | 114285. | 0.942820 | ||||||||
\(109\) | −99136.9 | −0.799225 | −0.399613 | − | 0.916684i | \(-0.630855\pi\) | ||||
−0.399613 | + | 0.916684i | \(0.630855\pi\) | |||||||
\(110\) | −148655. | −1.17138 | ||||||||
\(111\) | 343252. | 2.64427 | ||||||||
\(112\) | 11664.6 | 0.0878665 | ||||||||
\(113\) | 168649. | 1.24248 | 0.621238 | − | 0.783622i | \(-0.286630\pi\) | ||||
0.621238 | + | 0.783622i | \(0.286630\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 425041. | 2.99699 | ||||||||
\(116\) | 63913.7 | 0.441010 | ||||||||
\(117\) | −212421. | −1.43461 | ||||||||
\(118\) | 28736.0 | 0.189986 | ||||||||
\(119\) | −38473.2 | −0.249052 | ||||||||
\(120\) | 159470. | 1.01094 | ||||||||
\(121\) | 5187.67 | 0.0322114 | ||||||||
\(122\) | −186238. | −1.13284 | ||||||||
\(123\) | 170857. | 1.01829 | ||||||||
\(124\) | 119412. | 0.697419 | ||||||||
\(125\) | −187604. | −1.07391 | ||||||||
\(126\) | −91911.3 | −0.515754 | ||||||||
\(127\) | 10346.6 | 0.0569232 | 0.0284616 | − | 0.999595i | \(-0.490939\pi\) | ||||
0.0284616 | + | 0.999595i | \(0.490939\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | 28705.9 | 0.151879 | ||||||||
\(130\) | −153578. | −0.797025 | ||||||||
\(131\) | −223804. | −1.13943 | −0.569717 | − | 0.821841i | \(-0.692947\pi\) | ||||
−0.569717 | + | 0.821841i | \(0.692947\pi\) | |||||||
\(132\) | −178333. | −0.890832 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −156655. | −0.753671 | ||||||||
\(135\) | −651061. | −3.07459 | ||||||||
\(136\) | 54039.3 | 0.250531 | ||||||||
\(137\) | 302878. | 1.37869 | 0.689344 | − | 0.724434i | \(-0.257899\pi\) | ||||
0.689344 | + | 0.724434i | \(0.257899\pi\) | |||||||
\(138\) | 509896. | 2.27921 | ||||||||
\(139\) | 290592. | 1.27570 | 0.637848 | − | 0.770162i | \(-0.279825\pi\) | ||||
0.637848 | + | 0.770162i | \(0.279825\pi\) | |||||||
\(140\) | −66451.1 | −0.286538 | ||||||||
\(141\) | −145581. | −0.616675 | ||||||||
\(142\) | −87167.3 | −0.362771 | ||||||||
\(143\) | 171744. | 0.702332 | ||||||||
\(144\) | 129098. | 0.518817 | ||||||||
\(145\) | −364106. | −1.43816 | ||||||||
\(146\) | 56258.7 | 0.218428 | ||||||||
\(147\) | −402692. | −1.53702 | ||||||||
\(148\) | 200904. | 0.753934 | ||||||||
\(149\) | −53376.0 | −0.196961 | −0.0984805 | − | 0.995139i | \(-0.531398\pi\) | ||||
−0.0984805 | + | 0.995139i | \(0.531398\pi\) | |||||||
\(150\) | −566765. | −2.05672 | ||||||||
\(151\) | −270164. | −0.964241 | −0.482120 | − | 0.876105i | \(-0.660133\pi\) | ||||
−0.482120 | + | 0.876105i | \(0.660133\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −425804. | −1.47056 | ||||||||
\(154\) | 74311.2 | 0.252495 | ||||||||
\(155\) | −680270. | −2.27432 | ||||||||
\(156\) | −184239. | −0.606136 | ||||||||
\(157\) | −351078. | −1.13672 | −0.568361 | − | 0.822779i | \(-0.692422\pi\) | ||||
−0.568361 | + | 0.822779i | \(0.692422\pi\) | |||||||
\(158\) | −379446. | −1.20923 | ||||||||
\(159\) | −138427. | −0.434239 | ||||||||
\(160\) | 93337.0 | 0.288240 | ||||||||
\(161\) | −212474. | −0.646012 | ||||||||
\(162\) | −290869. | −0.870782 | ||||||||
\(163\) | 448049. | 1.32086 | 0.660430 | − | 0.750887i | \(-0.270374\pi\) | ||||
0.660430 | + | 0.750887i | \(0.270374\pi\) | |||||||
\(164\) | 100002. | 0.290334 | ||||||||
\(165\) | 1.01593e6 | 2.90506 | ||||||||
\(166\) | −97662.9 | −0.275080 | ||||||||
\(167\) | 689648. | 1.91353 | 0.956767 | − | 0.290855i | \(-0.0939398\pi\) | ||||
0.956767 | + | 0.290855i | \(0.0939398\pi\) | |||||||
\(168\) | −79717.4 | −0.217911 | ||||||||
\(169\) | −193860. | −0.522122 | ||||||||
\(170\) | −307853. | −0.816998 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 16801.4 | 0.0433037 | ||||||||
\(173\) | 120304. | 0.305609 | 0.152804 | − | 0.988256i | \(-0.451170\pi\) | ||||
0.152804 | + | 0.988256i | \(0.451170\pi\) | |||||||
\(174\) | −436796. | −1.09372 | ||||||||
\(175\) | 236171. | 0.582951 | ||||||||
\(176\) | −104377. | −0.253995 | ||||||||
\(177\) | −196386. | −0.471171 | ||||||||
\(178\) | −204258. | −0.483203 | ||||||||
\(179\) | −5854.51 | −0.0136571 | −0.00682854 | − | 0.999977i | \(-0.502174\pi\) | ||||
−0.00682854 | + | 0.999977i | \(0.502174\pi\) | |||||||
\(180\) | −735452. | −1.69189 | ||||||||
\(181\) | −89093.8 | −0.202139 | −0.101070 | − | 0.994879i | \(-0.532227\pi\) | ||||
−0.101070 | + | 0.994879i | \(0.532227\pi\) | |||||||
\(182\) | 76772.4 | 0.171801 | ||||||||
\(183\) | 1.27278e6 | 2.80948 | ||||||||
\(184\) | 298440. | 0.649849 | ||||||||
\(185\) | −1.14451e6 | −2.45862 | ||||||||
\(186\) | −816080. | −1.72962 | ||||||||
\(187\) | 344267. | 0.719932 | ||||||||
\(188\) | −85207.8 | −0.175827 | ||||||||
\(189\) | 325459. | 0.662738 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 214632. | 0.425707 | 0.212854 | − | 0.977084i | \(-0.431724\pi\) | ||||
0.212854 | + | 0.977084i | \(0.431724\pi\) | |||||||
\(192\) | 111971. | 0.219206 | ||||||||
\(193\) | 274697. | 0.530836 | 0.265418 | − | 0.964133i | \(-0.414490\pi\) | ||||
0.265418 | + | 0.964133i | \(0.414490\pi\) | |||||||
\(194\) | 521395. | 0.994632 | ||||||||
\(195\) | 1.04958e6 | 1.97664 | ||||||||
\(196\) | −235694. | −0.438236 | ||||||||
\(197\) | 748460. | 1.37405 | 0.687026 | − | 0.726633i | \(-0.258916\pi\) | ||||
0.687026 | + | 0.726633i | \(0.258916\pi\) | |||||||
\(198\) | 822445. | 1.49088 | ||||||||
\(199\) | 163872. | 0.293340 | 0.146670 | − | 0.989185i | \(-0.453144\pi\) | ||||
0.146670 | + | 0.989185i | \(0.453144\pi\) | |||||||
\(200\) | −331725. | −0.586413 | ||||||||
\(201\) | 1.07060e6 | 1.86912 | ||||||||
\(202\) | −102051. | −0.175971 | ||||||||
\(203\) | 182013. | 0.310000 | ||||||||
\(204\) | −369313. | −0.621325 | ||||||||
\(205\) | −569694. | −0.946797 | ||||||||
\(206\) | −156733. | −0.257331 | ||||||||
\(207\) | −2.35157e6 | −3.81445 | ||||||||
\(208\) | −107834. | −0.172822 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 454137. | 0.710621 | ||||||||
\(211\) | −320828. | −0.496097 | −0.248048 | − | 0.968748i | \(-0.579789\pi\) | ||||
−0.248048 | + | 0.968748i | \(0.579789\pi\) | |||||||
\(212\) | −81020.9 | −0.123810 | ||||||||
\(213\) | 595715. | 0.899682 | ||||||||
\(214\) | 171707. | 0.256303 | ||||||||
\(215\) | −95715.0 | −0.141216 | ||||||||
\(216\) | −457139. | −0.666674 | ||||||||
\(217\) | 340060. | 0.490238 | ||||||||
\(218\) | 396548. | 0.565138 | ||||||||
\(219\) | −384481. | −0.541707 | ||||||||
\(220\) | 594620. | 0.828291 | ||||||||
\(221\) | 355669. | 0.489853 | ||||||||
\(222\) | −1.37301e6 | −1.86978 | ||||||||
\(223\) | 478407. | 0.644221 | 0.322111 | − | 0.946702i | \(-0.395608\pi\) | ||||
0.322111 | + | 0.946702i | \(0.395608\pi\) | |||||||
\(224\) | −46658.2 | −0.0621310 | ||||||||
\(225\) | 2.61384e6 | 3.44210 | ||||||||
\(226\) | −674597. | −0.878564 | ||||||||
\(227\) | 218041. | 0.280849 | 0.140425 | − | 0.990091i | \(-0.455153\pi\) | ||||
0.140425 | + | 0.990091i | \(0.455153\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −464565. | −0.585407 | −0.292703 | − | 0.956203i | \(-0.594555\pi\) | ||||
−0.292703 | + | 0.956203i | \(0.594555\pi\) | |||||||
\(230\) | −1.70016e6 | −2.11919 | ||||||||
\(231\) | −507854. | −0.626194 | ||||||||
\(232\) | −255655. | −0.311841 | ||||||||
\(233\) | 89624.8 | 0.108153 | 0.0540765 | − | 0.998537i | \(-0.482779\pi\) | ||||
0.0540765 | + | 0.998537i | \(0.482779\pi\) | |||||||
\(234\) | 849684. | 1.01442 | ||||||||
\(235\) | 485415. | 0.573381 | ||||||||
\(236\) | −114944. | −0.134340 | ||||||||
\(237\) | 2.59319e6 | 2.99891 | ||||||||
\(238\) | 153893. | 0.176106 | ||||||||
\(239\) | −753479. | −0.853250 | −0.426625 | − | 0.904429i | \(-0.640298\pi\) | ||||
−0.426625 | + | 0.904429i | \(0.640298\pi\) | |||||||
\(240\) | −637879. | −0.714842 | ||||||||
\(241\) | 278146. | 0.308482 | 0.154241 | − | 0.988033i | \(-0.450707\pi\) | ||||
0.154241 | + | 0.988033i | \(0.450707\pi\) | |||||||
\(242\) | −20750.7 | −0.0227769 | ||||||||
\(243\) | 252143. | 0.273925 | ||||||||
\(244\) | 744954. | 0.801041 | ||||||||
\(245\) | 1.34271e6 | 1.42911 | ||||||||
\(246\) | −683428. | −0.720037 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −477648. | −0.493150 | ||||||||
\(249\) | 667443. | 0.682206 | ||||||||
\(250\) | 750417. | 0.759369 | ||||||||
\(251\) | 1.21711e6 | 1.21940 | 0.609700 | − | 0.792632i | \(-0.291290\pi\) | ||||
0.609700 | + | 0.792632i | \(0.291290\pi\) | |||||||
\(252\) | 367645. | 0.364693 | ||||||||
\(253\) | 1.90127e6 | 1.86742 | ||||||||
\(254\) | −41386.5 | −0.0402508 | ||||||||
\(255\) | 2.10391e6 | 2.02618 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −390401. | −0.368704 | −0.184352 | − | 0.982860i | \(-0.559019\pi\) | ||||
−0.184352 | + | 0.982860i | \(0.559019\pi\) | |||||||
\(258\) | −114824. | −0.107394 | ||||||||
\(259\) | 572132. | 0.529964 | ||||||||
\(260\) | 614314. | 0.563582 | ||||||||
\(261\) | 2.01444e6 | 1.83043 | ||||||||
\(262\) | 895216. | 0.805702 | ||||||||
\(263\) | −821217. | −0.732097 | −0.366049 | − | 0.930596i | \(-0.619290\pi\) | ||||
−0.366049 | + | 0.930596i | \(0.619290\pi\) | |||||||
\(264\) | 713330. | 0.629913 | ||||||||
\(265\) | 461563. | 0.403753 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.39593e6 | 1.19836 | ||||||||
\(268\) | 626619. | 0.532926 | ||||||||
\(269\) | −589584. | −0.496781 | −0.248391 | − | 0.968660i | \(-0.579902\pi\) | ||||
−0.248391 | + | 0.968660i | \(0.579902\pi\) | |||||||
\(270\) | 2.60424e6 | 2.17406 | ||||||||
\(271\) | 405713. | 0.335580 | 0.167790 | − | 0.985823i | \(-0.446337\pi\) | ||||
0.167790 | + | 0.985823i | \(0.446337\pi\) | |||||||
\(272\) | −216157. | −0.177152 | ||||||||
\(273\) | −524674. | −0.426072 | ||||||||
\(274\) | −1.21151e6 | −0.974879 | ||||||||
\(275\) | −2.11332e6 | −1.68513 | ||||||||
\(276\) | −2.03958e6 | −1.61164 | ||||||||
\(277\) | 299189. | 0.234286 | 0.117143 | − | 0.993115i | \(-0.462626\pi\) | ||||
0.117143 | + | 0.993115i | \(0.462626\pi\) | |||||||
\(278\) | −1.16237e6 | −0.902054 | ||||||||
\(279\) | 3.76364e6 | 2.89466 | ||||||||
\(280\) | 265804. | 0.202613 | ||||||||
\(281\) | −446049. | −0.336990 | −0.168495 | − | 0.985703i | \(-0.553891\pi\) | ||||
−0.168495 | + | 0.985703i | \(0.553891\pi\) | |||||||
\(282\) | 582323. | 0.436055 | ||||||||
\(283\) | 1.75384e6 | 1.30174 | 0.650869 | − | 0.759190i | \(-0.274405\pi\) | ||||
0.650869 | + | 0.759190i | \(0.274405\pi\) | |||||||
\(284\) | 348669. | 0.256518 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −686978. | −0.496624 | ||||||||
\(287\) | 284784. | 0.204085 | ||||||||
\(288\) | −516393. | −0.366859 | ||||||||
\(289\) | −706907. | −0.497872 | ||||||||
\(290\) | 1.45642e6 | 1.01693 | ||||||||
\(291\) | −3.56329e6 | −2.46672 | ||||||||
\(292\) | −225035. | −0.154452 | ||||||||
\(293\) | 2.69988e6 | 1.83728 | 0.918641 | − | 0.395092i | \(-0.129287\pi\) | ||||
0.918641 | + | 0.395092i | \(0.129287\pi\) | |||||||
\(294\) | 1.61077e6 | 1.08684 | ||||||||
\(295\) | 654818. | 0.438092 | ||||||||
\(296\) | −803614. | −0.533112 | ||||||||
\(297\) | −2.91229e6 | −1.91577 | ||||||||
\(298\) | 213504. | 0.139272 | ||||||||
\(299\) | 1.96424e6 | 1.27062 | ||||||||
\(300\) | 2.26706e6 | 1.45432 | ||||||||
\(301\) | 47847.0 | 0.0304396 | ||||||||
\(302\) | 1.08066e6 | 0.681821 | ||||||||
\(303\) | 697435. | 0.436413 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.24388e6 | −2.61224 | ||||||||
\(306\) | 1.70322e6 | 1.03984 | ||||||||
\(307\) | −2.66934e6 | −1.61643 | −0.808217 | − | 0.588885i | \(-0.799567\pi\) | ||||
−0.808217 | + | 0.588885i | \(0.799567\pi\) | |||||||
\(308\) | −297245. | −0.178541 | ||||||||
\(309\) | 1.07114e6 | 0.638187 | ||||||||
\(310\) | 2.72108e6 | 1.60819 | ||||||||
\(311\) | 28946.6 | 0.0169706 | 0.00848529 | − | 0.999964i | \(-0.497299\pi\) | ||||
0.00848529 | + | 0.999964i | \(0.497299\pi\) | |||||||
\(312\) | 736956. | 0.428603 | ||||||||
\(313\) | 1.86500e6 | 1.07601 | 0.538007 | − | 0.842940i | \(-0.319177\pi\) | ||||
0.538007 | + | 0.842940i | \(0.319177\pi\) | |||||||
\(314\) | 1.40431e6 | 0.803784 | ||||||||
\(315\) | −2.09441e6 | −1.18929 | ||||||||
\(316\) | 1.51778e6 | 0.855052 | ||||||||
\(317\) | 1.23238e6 | 0.688806 | 0.344403 | − | 0.938822i | \(-0.388081\pi\) | ||||
0.344403 | + | 0.938822i | \(0.388081\pi\) | |||||||
\(318\) | 553709. | 0.307053 | ||||||||
\(319\) | −1.62869e6 | −0.896114 | ||||||||
\(320\) | −373348. | −0.203816 | ||||||||
\(321\) | −1.17347e6 | −0.635639 | ||||||||
\(322\) | 849894. | 0.456799 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.16348e6 | 0.615736 | ||||||||
\(325\) | −2.18331e6 | −1.14659 | ||||||||
\(326\) | −1.79220e6 | −0.933989 | ||||||||
\(327\) | −2.71007e6 | −1.40156 | ||||||||
\(328\) | −400007. | −0.205297 | ||||||||
\(329\) | −242654. | −0.123594 | ||||||||
\(330\) | −4.06373e6 | −2.05418 | ||||||||
\(331\) | 2.13752e6 | 1.07236 | 0.536179 | − | 0.844104i | \(-0.319867\pi\) | ||||
0.536179 | + | 0.844104i | \(0.319867\pi\) | |||||||
\(332\) | 390651. | 0.194511 | ||||||||
\(333\) | 6.33211e6 | 3.12923 | ||||||||
\(334\) | −2.75859e6 | −1.35307 | ||||||||
\(335\) | −3.56975e6 | −1.73790 | ||||||||
\(336\) | 318869. | 0.154087 | ||||||||
\(337\) | −563806. | −0.270430 | −0.135215 | − | 0.990816i | \(-0.543173\pi\) | ||||
−0.135215 | + | 0.990816i | \(0.543173\pi\) | |||||||
\(338\) | 775442. | 0.369196 | ||||||||
\(339\) | 4.61030e6 | 2.17886 | ||||||||
\(340\) | 1.23141e6 | 0.577705 | ||||||||
\(341\) | −3.04294e6 | −1.41712 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.43701e6 | −0.659516 | ||||||||
\(344\) | −67205.8 | −0.0306204 | ||||||||
\(345\) | 1.16192e7 | 5.25566 | ||||||||
\(346\) | −481217. | −0.216098 | ||||||||
\(347\) | −304874. | −0.135924 | −0.0679622 | − | 0.997688i | \(-0.521650\pi\) | ||||
−0.0679622 | + | 0.997688i | \(0.521650\pi\) | |||||||
\(348\) | 1.74718e6 | 0.773375 | ||||||||
\(349\) | 1.68045e6 | 0.738518 | 0.369259 | − | 0.929326i | \(-0.379611\pi\) | ||||
0.369259 | + | 0.929326i | \(0.379611\pi\) | |||||||
\(350\) | −944685. | −0.412208 | ||||||||
\(351\) | −3.00874e6 | −1.30352 | ||||||||
\(352\) | 417509. | 0.179601 | ||||||||
\(353\) | −568627. | −0.242879 | −0.121440 | − | 0.992599i | \(-0.538751\pi\) | ||||
−0.121440 | + | 0.992599i | \(0.538751\pi\) | |||||||
\(354\) | 785546. | 0.333168 | ||||||||
\(355\) | −1.98631e6 | −0.836520 | ||||||||
\(356\) | 817033. | 0.341676 | ||||||||
\(357\) | −1.05173e6 | −0.436749 | ||||||||
\(358\) | 23418.0 | 0.00965701 | ||||||||
\(359\) | −2.50156e6 | −1.02441 | −0.512205 | − | 0.858863i | \(-0.671171\pi\) | ||||
−0.512205 | + | 0.858863i | \(0.671171\pi\) | |||||||
\(360\) | 2.94181e6 | 1.19635 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 356375. | 0.142934 | ||||||||
\(363\) | 141813. | 0.0564873 | ||||||||
\(364\) | −307089. | −0.121482 | ||||||||
\(365\) | 1.28199e6 | 0.503676 | ||||||||
\(366\) | −5.09113e6 | −1.98660 | ||||||||
\(367\) | 1.59586e6 | 0.618487 | 0.309244 | − | 0.950983i | \(-0.399924\pi\) | ||||
0.309244 | + | 0.950983i | \(0.399924\pi\) | |||||||
\(368\) | −1.19376e6 | −0.459512 | ||||||||
\(369\) | 3.15187e6 | 1.20504 | ||||||||
\(370\) | 4.57806e6 | 1.73851 | ||||||||
\(371\) | −230731. | −0.0870303 | ||||||||
\(372\) | 3.26432e6 | 1.22302 | ||||||||
\(373\) | 2.04929e6 | 0.762661 | 0.381330 | − | 0.924439i | \(-0.375466\pi\) | ||||
0.381330 | + | 0.924439i | \(0.375466\pi\) | |||||||
\(374\) | −1.37707e6 | −0.509069 | ||||||||
\(375\) | −5.12847e6 | −1.88326 | ||||||||
\(376\) | 340831. | 0.124328 | ||||||||
\(377\) | −1.68264e6 | −0.609729 | ||||||||
\(378\) | −1.30184e6 | −0.468626 | ||||||||
\(379\) | −1.56118e6 | −0.558284 | −0.279142 | − | 0.960250i | \(-0.590050\pi\) | ||||
−0.279142 | + | 0.960250i | \(0.590050\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 282842. | 0.0998231 | ||||||||
\(382\) | −858528. | −0.301020 | ||||||||
\(383\) | −1.66122e6 | −0.578670 | −0.289335 | − | 0.957228i | \(-0.593434\pi\) | ||||
−0.289335 | + | 0.957228i | \(0.593434\pi\) | |||||||
\(384\) | −447883. | −0.155002 | ||||||||
\(385\) | 1.69335e6 | 0.582232 | ||||||||
\(386\) | −1.09879e6 | −0.375358 | ||||||||
\(387\) | 529550. | 0.179734 | ||||||||
\(388\) | −2.08558e6 | −0.703311 | ||||||||
\(389\) | −476806. | −0.159760 | −0.0798800 | − | 0.996804i | \(-0.525454\pi\) | ||||
−0.0798800 | + | 0.996804i | \(0.525454\pi\) | |||||||
\(390\) | −4.19832e6 | −1.39770 | ||||||||
\(391\) | 3.93737e6 | 1.30246 | ||||||||
\(392\) | 942775. | 0.309880 | ||||||||
\(393\) | −6.11804e6 | −1.99816 | ||||||||
\(394\) | −2.99384e6 | −0.971601 | ||||||||
\(395\) | −8.64657e6 | −2.78837 | ||||||||
\(396\) | −3.28978e6 | −1.05421 | ||||||||
\(397\) | 6.12746e6 | 1.95121 | 0.975606 | − | 0.219528i | \(-0.0704517\pi\) | ||||
0.975606 | + | 0.219528i | \(0.0704517\pi\) | |||||||
\(398\) | −655486. | −0.207423 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.32690e6 | 0.414657 | ||||||||
\(401\) | 2.00668e6 | 0.623187 | 0.311593 | − | 0.950216i | \(-0.399137\pi\) | ||||
0.311593 | + | 0.950216i | \(0.399137\pi\) | |||||||
\(402\) | −4.28241e6 | −1.32167 | ||||||||
\(403\) | −3.14373e6 | −0.964233 | ||||||||
\(404\) | 408206. | 0.124430 | ||||||||
\(405\) | −6.62813e6 | −2.00795 | ||||||||
\(406\) | −728051. | −0.219203 | ||||||||
\(407\) | −5.11957e6 | −1.53196 | ||||||||
\(408\) | 1.47725e6 | 0.439343 | ||||||||
\(409\) | −4.28407e6 | −1.26633 | −0.633167 | − | 0.774015i | \(-0.718245\pi\) | ||||
−0.633167 | + | 0.774015i | \(0.718245\pi\) | |||||||
\(410\) | 2.27878e6 | 0.669487 | ||||||||
\(411\) | 8.27965e6 | 2.41773 | ||||||||
\(412\) | 626931. | 0.181960 | ||||||||
\(413\) | −327337. | −0.0944322 | ||||||||
\(414\) | 9.40627e6 | 2.69722 | ||||||||
\(415\) | −2.22548e6 | −0.634312 | ||||||||
\(416\) | 431337. | 0.122203 | ||||||||
\(417\) | 7.94381e6 | 2.23712 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.21461e6 | −0.616257 | −0.308128 | − | 0.951345i | \(-0.599703\pi\) | ||||
−0.308128 | + | 0.951345i | \(0.599703\pi\) | |||||||
\(420\) | −1.81655e6 | −0.502485 | ||||||||
\(421\) | 1.84639e6 | 0.507713 | 0.253856 | − | 0.967242i | \(-0.418301\pi\) | ||||
0.253856 | + | 0.967242i | \(0.418301\pi\) | |||||||
\(422\) | 1.28331e6 | 0.350793 | ||||||||
\(423\) | −2.68559e6 | −0.729775 | ||||||||
\(424\) | 324084. | 0.0875472 | ||||||||
\(425\) | −4.37651e6 | −1.17532 | ||||||||
\(426\) | −2.38286e6 | −0.636171 | ||||||||
\(427\) | 2.12147e6 | 0.563077 | ||||||||
\(428\) | −686828. | −0.181234 | ||||||||
\(429\) | 4.69491e6 | 1.23164 | ||||||||
\(430\) | 382860. | 0.0998548 | ||||||||
\(431\) | 6.36295e6 | 1.64993 | 0.824965 | − | 0.565184i | \(-0.191195\pi\) | ||||
0.824965 | + | 0.565184i | \(0.191195\pi\) | |||||||
\(432\) | 1.82855e6 | 0.471410 | ||||||||
\(433\) | 2.31836e6 | 0.594239 | 0.297119 | − | 0.954840i | \(-0.403974\pi\) | ||||
0.297119 | + | 0.954840i | \(0.403974\pi\) | |||||||
\(434\) | −1.36024e6 | −0.346650 | ||||||||
\(435\) | −9.95341e6 | −2.52202 | ||||||||
\(436\) | −1.58619e6 | −0.399613 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 1.53792e6 | 0.383044 | ||||||||
\(439\) | 1.39024e6 | 0.344294 | 0.172147 | − | 0.985071i | \(-0.444930\pi\) | ||||
0.172147 | + | 0.985071i | \(0.444930\pi\) | |||||||
\(440\) | −2.37848e6 | −0.585690 | ||||||||
\(441\) | −7.42863e6 | −1.81891 | ||||||||
\(442\) | −1.42268e6 | −0.346378 | ||||||||
\(443\) | 615555. | 0.149025 | 0.0745123 | − | 0.997220i | \(-0.476260\pi\) | ||||
0.0745123 | + | 0.997220i | \(0.476260\pi\) | |||||||
\(444\) | 5.49202e6 | 1.32213 | ||||||||
\(445\) | −4.65450e6 | −1.11423 | ||||||||
\(446\) | −1.91363e6 | −0.455533 | ||||||||
\(447\) | −1.45912e6 | −0.345399 | ||||||||
\(448\) | 186633. | 0.0439332 | ||||||||
\(449\) | −6.26517e6 | −1.46662 | −0.733309 | − | 0.679896i | \(-0.762025\pi\) | ||||
−0.733309 | + | 0.679896i | \(0.762025\pi\) | |||||||
\(450\) | −1.04554e7 | −2.43393 | ||||||||
\(451\) | −2.54832e6 | −0.589946 | ||||||||
\(452\) | 2.69839e6 | 0.621238 | ||||||||
\(453\) | −7.38537e6 | −1.69094 | ||||||||
\(454\) | −872163. | −0.198590 | ||||||||
\(455\) | 1.74944e6 | 0.396160 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.16914e6 | 0.261863 | 0.130932 | − | 0.991391i | \(-0.458203\pi\) | ||||
0.130932 | + | 0.991391i | \(0.458203\pi\) | |||||||
\(458\) | 1.85826e6 | 0.413945 | ||||||||
\(459\) | −6.03111e6 | −1.33618 | ||||||||
\(460\) | 6.80065e6 | 1.49850 | ||||||||
\(461\) | 7.13723e6 | 1.56415 | 0.782073 | − | 0.623187i | \(-0.214162\pi\) | ||||
0.782073 | + | 0.623187i | \(0.214162\pi\) | |||||||
\(462\) | 2.03142e6 | 0.442786 | ||||||||
\(463\) | 5.20027e6 | 1.12739 | 0.563694 | − | 0.825984i | \(-0.309380\pi\) | ||||
0.563694 | + | 0.825984i | \(0.309380\pi\) | |||||||
\(464\) | 1.02262e6 | 0.220505 | ||||||||
\(465\) | −1.85963e7 | −3.98836 | ||||||||
\(466\) | −358499. | −0.0764757 | ||||||||
\(467\) | −7.61088e6 | −1.61489 | −0.807445 | − | 0.589943i | \(-0.799150\pi\) | ||||
−0.807445 | + | 0.589943i | \(0.799150\pi\) | |||||||
\(468\) | −3.39874e6 | −0.717303 | ||||||||
\(469\) | 1.78448e6 | 0.374610 | ||||||||
\(470\) | −1.94166e6 | −0.405442 | ||||||||
\(471\) | −9.59729e6 | −1.99341 | ||||||||
\(472\) | 459777. | 0.0949930 | ||||||||
\(473\) | −428147. | −0.0879913 | ||||||||
\(474\) | −1.03728e7 | −2.12055 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −615570. | −0.124526 | ||||||||
\(477\) | −2.55363e6 | −0.513880 | ||||||||
\(478\) | 3.01392e6 | 0.603339 | ||||||||
\(479\) | 7.65802e6 | 1.52503 | 0.762514 | − | 0.646972i | \(-0.223965\pi\) | ||||
0.762514 | + | 0.646972i | \(0.223965\pi\) | |||||||
\(480\) | 2.55152e6 | 0.505470 | ||||||||
\(481\) | −5.28913e6 | −1.04237 | ||||||||
\(482\) | −1.11258e6 | −0.218130 | ||||||||
\(483\) | −5.80831e6 | −1.13287 | ||||||||
\(484\) | 83002.8 | 0.0161057 | ||||||||
\(485\) | 1.18812e7 | 2.29354 | ||||||||
\(486\) | −1.00857e6 | −0.193694 | ||||||||
\(487\) | 4.14917e6 | 0.792755 | 0.396377 | − | 0.918088i | \(-0.370267\pi\) | ||||
0.396377 | + | 0.918088i | \(0.370267\pi\) | |||||||
\(488\) | −2.97981e6 | −0.566422 | ||||||||
\(489\) | 1.22482e7 | 2.31632 | ||||||||
\(490\) | −5.37083e6 | −1.01054 | ||||||||
\(491\) | −8.45106e6 | −1.58200 | −0.791001 | − | 0.611814i | \(-0.790440\pi\) | ||||
−0.791001 | + | 0.611814i | \(0.790440\pi\) | |||||||
\(492\) | 2.73371e6 | 0.509143 | ||||||||
\(493\) | −3.37290e6 | −0.625009 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.87413e7 | 3.43785 | ||||||||
\(496\) | 1.91059e6 | 0.348709 | ||||||||
\(497\) | 992937. | 0.180315 | ||||||||
\(498\) | −2.66977e6 | −0.482393 | ||||||||
\(499\) | −1.08443e7 | −1.94962 | −0.974809 | − | 0.223043i | \(-0.928401\pi\) | ||||
−0.974809 | + | 0.223043i | \(0.928401\pi\) | |||||||
\(500\) | −3.00167e6 | −0.536955 | ||||||||
\(501\) | 1.88526e7 | 3.35566 | ||||||||
\(502\) | −4.86845e6 | −0.862246 | ||||||||
\(503\) | −867118. | −0.152812 | −0.0764062 | − | 0.997077i | \(-0.524345\pi\) | ||||
−0.0764062 | + | 0.997077i | \(0.524345\pi\) | |||||||
\(504\) | −1.47058e6 | −0.257877 | ||||||||
\(505\) | −2.32548e6 | −0.405774 | ||||||||
\(506\) | −7.60506e6 | −1.32046 | ||||||||
\(507\) | −5.29949e6 | −0.915617 | ||||||||
\(508\) | 165546. | 0.0284616 | ||||||||
\(509\) | 7.09848e6 | 1.21443 | 0.607213 | − | 0.794539i | \(-0.292288\pi\) | ||||
0.607213 | + | 0.794539i | \(0.292288\pi\) | |||||||
\(510\) | −8.41565e6 | −1.43272 | ||||||||
\(511\) | −640852. | −0.108569 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.56160e6 | 0.260713 | ||||||||
\(515\) | −3.57152e6 | −0.593383 | ||||||||
\(516\) | 459294. | 0.0759394 | ||||||||
\(517\) | 2.17133e6 | 0.357272 | ||||||||
\(518\) | −2.28853e6 | −0.374741 | ||||||||
\(519\) | 3.28871e6 | 0.535929 | ||||||||
\(520\) | −2.45726e6 | −0.398513 | ||||||||
\(521\) | −6.12684e6 | −0.988877 | −0.494438 | − | 0.869213i | \(-0.664626\pi\) | ||||
−0.494438 | + | 0.869213i | \(0.664626\pi\) | |||||||
\(522\) | −8.05776e6 | −1.29431 | ||||||||
\(523\) | −1.12575e7 | −1.79965 | −0.899825 | − | 0.436251i | \(-0.856306\pi\) | ||||
−0.899825 | + | 0.436251i | \(0.856306\pi\) | |||||||
\(524\) | −3.58086e6 | −0.569717 | ||||||||
\(525\) | 6.45612e6 | 1.02229 | ||||||||
\(526\) | 3.28487e6 | 0.517671 | ||||||||
\(527\) | −6.30170e6 | −0.988396 | ||||||||
\(528\) | −2.85332e6 | −0.445416 | ||||||||
\(529\) | 1.53084e7 | 2.37843 | ||||||||
\(530\) | −1.84625e6 | −0.285497 | ||||||||
\(531\) | −3.62283e6 | −0.557585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.63272e6 | −0.401409 | ||||||||
\(534\) | −5.58373e6 | −0.847366 | ||||||||
\(535\) | 3.91275e6 | 0.591014 | ||||||||
\(536\) | −2.50648e6 | −0.376835 | ||||||||
\(537\) | −160042. | −0.0239497 | ||||||||
\(538\) | 2.35834e6 | 0.351277 | ||||||||
\(539\) | 6.00612e6 | 0.890476 | ||||||||
\(540\) | −1.04170e7 | −1.53730 | ||||||||
\(541\) | −3.79995e6 | −0.558194 | −0.279097 | − | 0.960263i | \(-0.590035\pi\) | ||||
−0.279097 | + | 0.960263i | \(0.590035\pi\) | |||||||
\(542\) | −1.62285e6 | −0.237291 | ||||||||
\(543\) | −2.43552e6 | −0.354481 | ||||||||
\(544\) | 864628. | 0.125266 | ||||||||
\(545\) | 9.03627e6 | 1.30316 | ||||||||
\(546\) | 2.09870e6 | 0.301278 | ||||||||
\(547\) | 235320. | 0.0336272 | 0.0168136 | − | 0.999859i | \(-0.494648\pi\) | ||||
0.0168136 | + | 0.999859i | \(0.494648\pi\) | |||||||
\(548\) | 4.84604e6 | 0.689344 | ||||||||
\(549\) | 2.34796e7 | 3.32475 | ||||||||
\(550\) | 8.45327e6 | 1.19157 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 8.15833e6 | 1.13960 | ||||||||
\(553\) | 4.32233e6 | 0.601043 | ||||||||
\(554\) | −1.19676e6 | −0.165665 | ||||||||
\(555\) | −3.12872e7 | −4.31155 | ||||||||
\(556\) | 4.64948e6 | 0.637848 | ||||||||
\(557\) | 5.73429e6 | 0.783144 | 0.391572 | − | 0.920147i | \(-0.371931\pi\) | ||||
0.391572 | + | 0.920147i | \(0.371931\pi\) | |||||||
\(558\) | −1.50546e7 | −2.04684 | ||||||||
\(559\) | −442327. | −0.0598706 | ||||||||
\(560\) | −1.06322e6 | −0.143269 | ||||||||
\(561\) | 9.41110e6 | 1.26251 | ||||||||
\(562\) | 1.78420e6 | 0.238288 | ||||||||
\(563\) | 1.69962e6 | 0.225986 | 0.112993 | − | 0.993596i | \(-0.463956\pi\) | ||||
0.112993 | + | 0.993596i | \(0.463956\pi\) | |||||||
\(564\) | −2.32929e6 | −0.308337 | ||||||||
\(565\) | −1.53723e7 | −2.02590 | ||||||||
\(566\) | −7.01536e6 | −0.920468 | ||||||||
\(567\) | 3.31333e6 | 0.432820 | ||||||||
\(568\) | −1.39468e6 | −0.181386 | ||||||||
\(569\) | −2.92415e6 | −0.378633 | −0.189317 | − | 0.981916i | \(-0.560627\pi\) | ||||
−0.189317 | + | 0.981916i | \(0.560627\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.29435e6 | −0.422844 | −0.211422 | − | 0.977395i | \(-0.567809\pi\) | ||||
−0.211422 | + | 0.977395i | \(0.567809\pi\) | |||||||
\(572\) | 2.74791e6 | 0.351166 | ||||||||
\(573\) | 5.86731e6 | 0.746539 | ||||||||
\(574\) | −1.13914e6 | −0.144310 | ||||||||
\(575\) | −2.41699e7 | −3.04864 | ||||||||
\(576\) | 2.06557e6 | 0.259409 | ||||||||
\(577\) | 1.15705e7 | 1.44681 | 0.723405 | − | 0.690424i | \(-0.242576\pi\) | ||||
0.723405 | + | 0.690424i | \(0.242576\pi\) | |||||||
\(578\) | 2.82763e6 | 0.352049 | ||||||||
\(579\) | 7.50928e6 | 0.930898 | ||||||||
\(580\) | −5.82569e6 | −0.719080 | ||||||||
\(581\) | 1.11249e6 | 0.136728 | ||||||||
\(582\) | 1.42532e7 | 1.74423 | ||||||||
\(583\) | 2.06463e6 | 0.251577 | ||||||||
\(584\) | 900139. | 0.109214 | ||||||||
\(585\) | 1.93620e7 | 2.33917 | ||||||||
\(586\) | −1.07995e7 | −1.29916 | ||||||||
\(587\) | 6.47153e6 | 0.775196 | 0.387598 | − | 0.921828i | \(-0.373305\pi\) | ||||
0.387598 | + | 0.921828i | \(0.373305\pi\) | |||||||
\(588\) | −6.44307e6 | −0.768510 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −2.61927e6 | −0.309778 | ||||||||
\(591\) | 2.04604e7 | 2.40960 | ||||||||
\(592\) | 3.21446e6 | 0.376967 | ||||||||
\(593\) | 3.80753e6 | 0.444638 | 0.222319 | − | 0.974974i | \(-0.428637\pi\) | ||||
0.222319 | + | 0.974974i | \(0.428637\pi\) | |||||||
\(594\) | 1.16491e7 | 1.35465 | ||||||||
\(595\) | 3.50680e6 | 0.406087 | ||||||||
\(596\) | −854016. | −0.0984805 | ||||||||
\(597\) | 4.47969e6 | 0.514414 | ||||||||
\(598\) | −7.85694e6 | −0.898464 | ||||||||
\(599\) | 2.46686e6 | 0.280917 | 0.140458 | − | 0.990087i | \(-0.455142\pi\) | ||||
0.140458 | + | 0.990087i | \(0.455142\pi\) | |||||||
\(600\) | −9.06825e6 | −1.02836 | ||||||||
\(601\) | −1.09126e7 | −1.23238 | −0.616188 | − | 0.787599i | \(-0.711324\pi\) | ||||
−0.616188 | + | 0.787599i | \(0.711324\pi\) | |||||||
\(602\) | −191388. | −0.0215240 | ||||||||
\(603\) | 1.97499e7 | 2.21193 | ||||||||
\(604\) | −4.32263e6 | −0.482120 | ||||||||
\(605\) | −472853. | −0.0525216 | ||||||||
\(606\) | −2.78974e6 | −0.308590 | ||||||||
\(607\) | 8.96624e6 | 0.987731 | 0.493865 | − | 0.869538i | \(-0.335584\pi\) | ||||
0.493865 | + | 0.869538i | \(0.335584\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.97561e6 | 0.543630 | ||||||||
\(610\) | 1.69755e7 | 1.84713 | ||||||||
\(611\) | 2.24324e6 | 0.243093 | ||||||||
\(612\) | −6.81287e6 | −0.735278 | ||||||||
\(613\) | −1.73012e7 | −1.85962 | −0.929811 | − | 0.368036i | \(-0.880030\pi\) | ||||
−0.929811 | + | 0.368036i | \(0.880030\pi\) | |||||||
\(614\) | 1.06774e7 | 1.14299 | ||||||||
\(615\) | −1.55735e7 | −1.66035 | ||||||||
\(616\) | 1.18898e6 | 0.126247 | ||||||||
\(617\) | 1.54949e7 | 1.63861 | 0.819306 | − | 0.573357i | \(-0.194359\pi\) | ||||
0.819306 | + | 0.573357i | \(0.194359\pi\) | |||||||
\(618\) | −4.28454e6 | −0.451267 | ||||||||
\(619\) | −936336. | −0.0982211 | −0.0491106 | − | 0.998793i | \(-0.515639\pi\) | ||||
−0.0491106 | + | 0.998793i | \(0.515639\pi\) | |||||||
\(620\) | −1.08843e7 | −1.13716 | ||||||||
\(621\) | −3.33077e7 | −3.46590 | ||||||||
\(622\) | −115786. | −0.0120000 | ||||||||
\(623\) | 2.32674e6 | 0.240175 | ||||||||
\(624\) | −2.94782e6 | −0.303068 | ||||||||
\(625\) | 902494. | 0.0924154 | ||||||||
\(626\) | −7.46000e6 | −0.760857 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.61725e6 | −0.568361 | ||||||||
\(629\) | −1.06022e7 | −1.06849 | ||||||||
\(630\) | 8.37766e6 | 0.840952 | ||||||||
\(631\) | −426665. | −0.0426593 | −0.0213296 | − | 0.999772i | \(-0.506790\pi\) | ||||
−0.0213296 | + | 0.999772i | \(0.506790\pi\) | |||||||
\(632\) | −6.07114e6 | −0.604613 | ||||||||
\(633\) | −8.77036e6 | −0.869977 | ||||||||
\(634\) | −4.92952e6 | −0.487059 | ||||||||
\(635\) | −943088. | −0.0928150 | ||||||||
\(636\) | −2.21484e6 | −0.217120 | ||||||||
\(637\) | 6.20504e6 | 0.605893 | ||||||||
\(638\) | 6.51478e6 | 0.633648 | ||||||||
\(639\) | 1.09894e7 | 1.06469 | ||||||||
\(640\) | 1.49339e6 | 0.144120 | ||||||||
\(641\) | 1.22135e7 | 1.17407 | 0.587034 | − | 0.809562i | \(-0.300295\pi\) | ||||
0.587034 | + | 0.809562i | \(0.300295\pi\) | |||||||
\(642\) | 4.69389e6 | 0.449465 | ||||||||
\(643\) | −1.11987e7 | −1.06817 | −0.534087 | − | 0.845430i | \(-0.679345\pi\) | ||||
−0.534087 | + | 0.845430i | \(0.679345\pi\) | |||||||
\(644\) | −3.39958e6 | −0.323006 | ||||||||
\(645\) | −2.61652e6 | −0.247643 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.69266e6 | −0.346799 | −0.173400 | − | 0.984852i | \(-0.555475\pi\) | ||||
−0.173400 | + | 0.984852i | \(0.555475\pi\) | |||||||
\(648\) | −4.65390e6 | −0.435391 | ||||||||
\(649\) | 2.92909e6 | 0.272974 | ||||||||
\(650\) | 8.73324e6 | 0.810759 | ||||||||
\(651\) | 9.29610e6 | 0.859703 | ||||||||
\(652\) | 7.16879e6 | 0.660430 | ||||||||
\(653\) | −7.23686e6 | −0.664151 | −0.332076 | − | 0.943253i | \(-0.607749\pi\) | ||||
−0.332076 | + | 0.943253i | \(0.607749\pi\) | |||||||
\(654\) | 1.08403e7 | 0.991050 | ||||||||
\(655\) | 2.03996e7 | 1.85788 | ||||||||
\(656\) | 1.60003e6 | 0.145167 | ||||||||
\(657\) | −7.09268e6 | −0.641058 | ||||||||
\(658\) | 970616. | 0.0873942 | ||||||||
\(659\) | −2.47898e6 | −0.222361 | −0.111181 | − | 0.993800i | \(-0.535463\pi\) | ||||
−0.111181 | + | 0.993800i | \(0.535463\pi\) | |||||||
\(660\) | 1.62549e7 | 1.45253 | ||||||||
\(661\) | −1.14917e7 | −1.02301 | −0.511505 | − | 0.859280i | \(-0.670912\pi\) | ||||
−0.511505 | + | 0.859280i | \(0.670912\pi\) | |||||||
\(662\) | −8.55008e6 | −0.758272 | ||||||||
\(663\) | 9.72279e6 | 0.859028 | ||||||||
\(664\) | −1.56261e6 | −0.137540 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.53284e7 | −2.21270 | ||||||||
\(667\) | −1.86273e7 | −1.62120 | ||||||||
\(668\) | 1.10344e7 | 0.956767 | ||||||||
\(669\) | 1.30780e7 | 1.12974 | ||||||||
\(670\) | 1.42790e7 | 1.22888 | ||||||||
\(671\) | −1.89835e7 | −1.62768 | ||||||||
\(672\) | −1.27548e6 | −0.108956 | ||||||||
\(673\) | −7.92995e6 | −0.674889 | −0.337445 | − | 0.941345i | \(-0.609563\pi\) | ||||
−0.337445 | + | 0.941345i | \(0.609563\pi\) | |||||||
\(674\) | 2.25522e6 | 0.191223 | ||||||||
\(675\) | 3.70226e7 | 3.12757 | ||||||||
\(676\) | −3.10177e6 | −0.261061 | ||||||||
\(677\) | −4.82621e6 | −0.404701 | −0.202351 | − | 0.979313i | \(-0.564858\pi\) | ||||
−0.202351 | + | 0.979313i | \(0.564858\pi\) | |||||||
\(678\) | −1.84412e7 | −1.54069 | ||||||||
\(679\) | −5.93930e6 | −0.494380 | ||||||||
\(680\) | −4.92565e6 | −0.408499 | ||||||||
\(681\) | 5.96050e6 | 0.492509 | ||||||||
\(682\) | 1.21718e7 | 1.00206 | ||||||||
\(683\) | 2.02601e7 | 1.66184 | 0.830920 | − | 0.556392i | \(-0.187815\pi\) | ||||
0.830920 | + | 0.556392i | \(0.187815\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.76071e7 | −2.24799 | ||||||||
\(686\) | 5.74805e6 | 0.466348 | ||||||||
\(687\) | −1.26996e7 | −1.02660 | ||||||||
\(688\) | 268823. | 0.0216519 | ||||||||
\(689\) | 2.13301e6 | 0.171177 | ||||||||
\(690\) | −4.64767e7 | −3.71631 | ||||||||
\(691\) | −2.37875e7 | −1.89519 | −0.947597 | − | 0.319468i | \(-0.896496\pi\) | ||||
−0.947597 | + | 0.319468i | \(0.896496\pi\) | |||||||
\(692\) | 1.92487e6 | 0.152804 | ||||||||
\(693\) | −9.36860e6 | −0.741040 | ||||||||
\(694\) | 1.21950e6 | 0.0961130 | ||||||||
\(695\) | −2.64873e7 | −2.08006 | ||||||||
\(696\) | −6.98873e6 | −0.546859 | ||||||||
\(697\) | −5.27737e6 | −0.411467 | ||||||||
\(698\) | −6.72179e6 | −0.522211 | ||||||||
\(699\) | 2.45004e6 | 0.189662 | ||||||||
\(700\) | 3.77874e6 | 0.291475 | ||||||||
\(701\) | −4.12864e6 | −0.317331 | −0.158665 | − | 0.987332i | \(-0.550719\pi\) | ||||
−0.158665 | + | 0.987332i | \(0.550719\pi\) | |||||||
\(702\) | 1.20350e7 | 0.921726 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −1.67004e6 | −0.126997 | ||||||||
\(705\) | 1.32696e7 | 1.00551 | ||||||||
\(706\) | 2.27451e6 | 0.171742 | ||||||||
\(707\) | 1.16249e6 | 0.0874659 | ||||||||
\(708\) | −3.14218e6 | −0.235585 | ||||||||
\(709\) | −6.76241e6 | −0.505226 | −0.252613 | − | 0.967567i | \(-0.581290\pi\) | ||||
−0.252613 | + | 0.967567i | \(0.581290\pi\) | |||||||
\(710\) | 7.94524e6 | 0.591509 | ||||||||
\(711\) | 4.78378e7 | 3.54893 | ||||||||
\(712\) | −3.26813e6 | −0.241601 | ||||||||
\(713\) | −3.48020e7 | −2.56378 | ||||||||
\(714\) | 4.20690e6 | 0.308828 | ||||||||
\(715\) | −1.56544e7 | −1.14517 | ||||||||
\(716\) | −93672.1 | −0.00682854 | ||||||||
\(717\) | −2.05976e7 | −1.49630 | ||||||||
\(718\) | 1.00062e7 | 0.724368 | ||||||||
\(719\) | 879312. | 0.0634338 | 0.0317169 | − | 0.999497i | \(-0.489903\pi\) | ||||
0.0317169 | + | 0.999497i | \(0.489903\pi\) | |||||||
\(720\) | −1.17672e7 | −0.845947 | ||||||||
\(721\) | 1.78537e6 | 0.127906 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.60356e6 | 0.540968 | ||||||||
\(724\) | −1.42550e6 | −0.101070 | ||||||||
\(725\) | 2.07049e7 | 1.46294 | ||||||||
\(726\) | −567254. | −0.0399425 | ||||||||
\(727\) | −1.59996e7 | −1.12273 | −0.561363 | − | 0.827570i | \(-0.689723\pi\) | ||||
−0.561363 | + | 0.827570i | \(0.689723\pi\) | |||||||
\(728\) | 1.22836e6 | 0.0859006 | ||||||||
\(729\) | −1.07775e7 | −0.751105 | ||||||||
\(730\) | −5.12795e6 | −0.356153 | ||||||||
\(731\) | −886658. | −0.0613709 | ||||||||
\(732\) | 2.03645e7 | 1.40474 | ||||||||
\(733\) | 2.83977e7 | 1.95219 | 0.976096 | − | 0.217340i | \(-0.0697381\pi\) | ||||
0.976096 | + | 0.217340i | \(0.0697381\pi\) | |||||||
\(734\) | −6.38346e6 | −0.437336 | ||||||||
\(735\) | 3.67051e7 | 2.50616 | ||||||||
\(736\) | 4.77504e6 | 0.324924 | ||||||||
\(737\) | −1.59680e7 | −1.08288 | ||||||||
\(738\) | −1.26075e7 | −0.852094 | ||||||||
\(739\) | 1.31039e7 | 0.882651 | 0.441325 | − | 0.897347i | \(-0.354508\pi\) | ||||
0.441325 | + | 0.897347i | \(0.354508\pi\) | |||||||
\(740\) | −1.83122e7 | −1.22931 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 922923. | 0.0615397 | ||||||||
\(743\) | 1.90268e7 | 1.26443 | 0.632214 | − | 0.774794i | \(-0.282147\pi\) | ||||
0.632214 | + | 0.774794i | \(0.282147\pi\) | |||||||
\(744\) | −1.30573e7 | −0.864809 | ||||||||
\(745\) | 4.86519e6 | 0.321151 | ||||||||
\(746\) | −8.19716e6 | −0.539283 | ||||||||
\(747\) | 1.23126e7 | 0.807325 | ||||||||
\(748\) | 5.50827e6 | 0.359966 | ||||||||
\(749\) | −1.95594e6 | −0.127395 | ||||||||
\(750\) | 2.05139e7 | 1.33166 | ||||||||
\(751\) | 1.38190e6 | 0.0894083 | 0.0447041 | − | 0.999000i | \(-0.485765\pi\) | ||||
0.0447041 | + | 0.999000i | \(0.485765\pi\) | |||||||
\(752\) | −1.36332e6 | −0.0879133 | ||||||||
\(753\) | 3.32717e7 | 2.13839 | ||||||||
\(754\) | 6.73055e6 | 0.431144 | ||||||||
\(755\) | 2.46253e7 | 1.57222 | ||||||||
\(756\) | 5.20734e6 | 0.331369 | ||||||||
\(757\) | 2.05255e7 | 1.30183 | 0.650915 | − | 0.759151i | \(-0.274386\pi\) | ||||
0.650915 | + | 0.759151i | \(0.274386\pi\) | |||||||
\(758\) | 6.24472e6 | 0.394767 | ||||||||
\(759\) | 5.19742e7 | 3.27479 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.00812e7 | −1.25698 | −0.628490 | − | 0.777818i | \(-0.716327\pi\) | ||||
−0.628490 | + | 0.777818i | \(0.716327\pi\) | |||||||
\(762\) | −1.13137e6 | −0.0705856 | ||||||||
\(763\) | −4.51714e6 | −0.280900 | ||||||||
\(764\) | 3.43411e6 | 0.212854 | ||||||||
\(765\) | 3.88118e7 | 2.39779 | ||||||||
\(766\) | 6.64489e6 | 0.409181 | ||||||||
\(767\) | 3.02610e6 | 0.185736 | ||||||||
\(768\) | 1.79153e6 | 0.109603 | ||||||||
\(769\) | 351782. | 0.0214515 | 0.0107257 | − | 0.999942i | \(-0.496586\pi\) | ||||
0.0107257 | + | 0.999942i | \(0.496586\pi\) | |||||||
\(770\) | −6.77342e6 | −0.411700 | ||||||||
\(771\) | −1.06722e7 | −0.646576 | ||||||||
\(772\) | 4.39515e6 | 0.265418 | ||||||||
\(773\) | −1.92449e7 | −1.15842 | −0.579210 | − | 0.815178i | \(-0.696639\pi\) | ||||
−0.579210 | + | 0.815178i | \(0.696639\pi\) | |||||||
\(774\) | −2.11820e6 | −0.127091 | ||||||||
\(775\) | 3.86836e7 | 2.31351 | ||||||||
\(776\) | 8.34232e6 | 0.497316 | ||||||||
\(777\) | 1.56401e7 | 0.929369 | ||||||||
\(778\) | 1.90723e6 | 0.112967 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 1.67933e7 | 0.988322 | ||||||||
\(781\) | −8.88504e6 | −0.521233 | ||||||||
\(782\) | −1.57495e7 | −0.920978 | ||||||||
\(783\) | 2.85326e7 | 1.66317 | ||||||||
\(784\) | −3.77110e6 | −0.219118 | ||||||||
\(785\) | 3.20005e7 | 1.85346 | ||||||||
\(786\) | 2.44722e7 | 1.41292 | ||||||||
\(787\) | 1.81602e7 | 1.04516 | 0.522580 | − | 0.852590i | \(-0.324970\pi\) | ||||
0.522580 | + | 0.852590i | \(0.324970\pi\) | |||||||
\(788\) | 1.19754e7 | 0.687026 | ||||||||
\(789\) | −2.24493e7 | −1.28384 | ||||||||
\(790\) | 3.45863e7 | 1.97168 | ||||||||
\(791\) | 7.68445e6 | 0.436688 | ||||||||
\(792\) | 1.31591e7 | 0.745442 | ||||||||
\(793\) | −1.96122e7 | −1.10750 | ||||||||
\(794\) | −2.45099e7 | −1.37972 | ||||||||
\(795\) | 1.26176e7 | 0.708040 | ||||||||
\(796\) | 2.62195e6 | 0.146670 | ||||||||
\(797\) | −2.32589e7 | −1.29701 | −0.648506 | − | 0.761210i | \(-0.724606\pi\) | ||||
−0.648506 | + | 0.761210i | \(0.724606\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.49665e6 | 0.249185 | ||||||||
\(800\) | −5.30760e6 | −0.293207 | ||||||||
\(801\) | 2.57514e7 | 1.41814 | ||||||||
\(802\) | −8.02674e6 | −0.440660 | ||||||||
\(803\) | 5.73450e6 | 0.313839 | ||||||||
\(804\) | 1.71296e7 | 0.934562 | ||||||||
\(805\) | 1.93668e7 | 1.05334 | ||||||||
\(806\) | 1.25749e7 | 0.681816 | ||||||||
\(807\) | −1.61172e7 | −0.871177 | ||||||||
\(808\) | −1.63282e6 | −0.0879854 | ||||||||
\(809\) | 9.11705e6 | 0.489760 | 0.244880 | − | 0.969553i | \(-0.421251\pi\) | ||||
0.244880 | + | 0.969553i | \(0.421251\pi\) | |||||||
\(810\) | 2.65125e7 | 1.41984 | ||||||||
\(811\) | −1.35484e7 | −0.723331 | −0.361665 | − | 0.932308i | \(-0.617792\pi\) | ||||
−0.361665 | + | 0.932308i | \(0.617792\pi\) | |||||||
\(812\) | 2.91220e6 | 0.155000 | ||||||||
\(813\) | 1.10908e7 | 0.588487 | ||||||||
\(814\) | 2.04783e7 | 1.08326 | ||||||||
\(815\) | −4.08394e7 | −2.15370 | ||||||||
\(816\) | −5.90900e6 | −0.310662 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 1.71363e7 | 0.895433 | ||||||||
\(819\) | −9.67889e6 | −0.504215 | ||||||||
\(820\) | −9.11510e6 | −0.473399 | ||||||||
\(821\) | −2.79975e7 | −1.44964 | −0.724822 | − | 0.688936i | \(-0.758078\pi\) | ||||
−0.724822 | + | 0.688936i | \(0.758078\pi\) | |||||||
\(822\) | −3.31186e7 | −1.70959 | ||||||||
\(823\) | 4.78334e6 | 0.246168 | 0.123084 | − | 0.992396i | \(-0.460722\pi\) | ||||
0.123084 | + | 0.992396i | \(0.460722\pi\) | |||||||
\(824\) | −2.50772e6 | −0.128665 | ||||||||
\(825\) | −5.77709e7 | −2.95512 | ||||||||
\(826\) | 1.30935e6 | 0.0667736 | ||||||||
\(827\) | −8.30069e6 | −0.422037 | −0.211018 | − | 0.977482i | \(-0.567678\pi\) | ||||
−0.211018 | + | 0.977482i | \(0.567678\pi\) | |||||||
\(828\) | −3.76251e7 | −1.90722 | ||||||||
\(829\) | −1.43347e7 | −0.724439 | −0.362220 | − | 0.932093i | \(-0.617981\pi\) | ||||
−0.362220 | + | 0.932093i | \(0.617981\pi\) | |||||||
\(830\) | 8.90191e6 | 0.448526 | ||||||||
\(831\) | 8.17883e6 | 0.410855 | ||||||||
\(832\) | −1.72535e6 | −0.0864109 | ||||||||
\(833\) | 1.24382e7 | 0.621077 | ||||||||
\(834\) | −3.17753e7 | −1.58188 | ||||||||
\(835\) | −6.28610e7 | −3.12007 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.33084e7 | 2.63016 | ||||||||
\(838\) | 8.85843e6 | 0.435759 | ||||||||
\(839\) | −3.22928e6 | −0.158380 | −0.0791901 | − | 0.996860i | \(-0.525233\pi\) | ||||
−0.0791901 | + | 0.996860i | \(0.525233\pi\) | |||||||
\(840\) | 7.26619e6 | 0.355311 | ||||||||
\(841\) | −4.55429e6 | −0.222040 | ||||||||
\(842\) | −7.38556e6 | −0.359007 | ||||||||
\(843\) | −1.21935e7 | −0.590960 | ||||||||
\(844\) | −5.13325e6 | −0.248048 | ||||||||
\(845\) | 1.76703e7 | 0.851336 | ||||||||
\(846\) | 1.07424e7 | 0.516029 | ||||||||
\(847\) | 236375. | 0.0113212 | ||||||||
\(848\) | −1.29633e6 | −0.0619052 | ||||||||
\(849\) | 4.79440e7 | 2.28279 | ||||||||
\(850\) | 1.75061e7 | 0.831076 | ||||||||
\(851\) | −5.85524e7 | −2.77154 | ||||||||
\(852\) | 9.53143e6 | 0.449841 | ||||||||
\(853\) | −1.77142e7 | −0.833585 | −0.416793 | − | 0.909002i | \(-0.636846\pi\) | ||||
−0.416793 | + | 0.909002i | \(0.636846\pi\) | |||||||
\(854\) | −8.48589e6 | −0.398156 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.74731e6 | 0.128152 | ||||||||
\(857\) | −3.00086e7 | −1.39571 | −0.697853 | − | 0.716241i | \(-0.745861\pi\) | ||||
−0.697853 | + | 0.716241i | \(0.745861\pi\) | |||||||
\(858\) | −1.87796e7 | −0.870902 | ||||||||
\(859\) | 8.81146e6 | 0.407441 | 0.203721 | − | 0.979029i | \(-0.434697\pi\) | ||||
0.203721 | + | 0.979029i | \(0.434697\pi\) | |||||||
\(860\) | −1.53144e6 | −0.0706080 | ||||||||
\(861\) | 7.78504e6 | 0.357893 | ||||||||
\(862\) | −2.54518e7 | −1.16668 | ||||||||
\(863\) | −2.72755e7 | −1.24666 | −0.623328 | − | 0.781961i | \(-0.714220\pi\) | ||||
−0.623328 | + | 0.781961i | \(0.714220\pi\) | |||||||
\(864\) | −7.31422e6 | −0.333337 | ||||||||
\(865\) | −1.09657e7 | −0.498304 | ||||||||
\(866\) | −9.27344e6 | −0.420190 | ||||||||
\(867\) | −1.93244e7 | −0.873090 | ||||||||
\(868\) | 5.44097e6 | 0.245119 | ||||||||
\(869\) | −3.86773e7 | −1.73743 | ||||||||
\(870\) | 3.98137e7 | 1.78334 | ||||||||
\(871\) | −1.64968e7 | −0.736809 | ||||||||
\(872\) | 6.34476e6 | 0.282569 | ||||||||
\(873\) | −6.57336e7 | −2.91912 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.54813e6 | −0.377443 | ||||||||
\(876\) | −6.15169e6 | −0.270853 | ||||||||
\(877\) | 900233. | 0.0395236 | 0.0197618 | − | 0.999805i | \(-0.493709\pi\) | ||||
0.0197618 | + | 0.999805i | \(0.493709\pi\) | |||||||
\(878\) | −5.56097e6 | −0.243453 | ||||||||
\(879\) | 7.38057e7 | 3.22194 | ||||||||
\(880\) | 9.51392e6 | 0.414146 | ||||||||
\(881\) | 2.95558e7 | 1.28293 | 0.641464 | − | 0.767153i | \(-0.278327\pi\) | ||||
0.641464 | + | 0.767153i | \(0.278327\pi\) | |||||||
\(882\) | 2.97145e7 | 1.28617 | ||||||||
\(883\) | −3.40301e7 | −1.46880 | −0.734399 | − | 0.678718i | \(-0.762536\pi\) | ||||
−0.734399 | + | 0.678718i | \(0.762536\pi\) | |||||||
\(884\) | 5.69071e6 | 0.244926 | ||||||||
\(885\) | 1.79005e7 | 0.768258 | ||||||||
\(886\) | −2.46222e6 | −0.105376 | ||||||||
\(887\) | −1.46269e7 | −0.624230 | −0.312115 | − | 0.950044i | \(-0.601037\pi\) | ||||
−0.312115 | + | 0.950044i | \(0.601037\pi\) | |||||||
\(888\) | −2.19681e7 | −0.934889 | ||||||||
\(889\) | 471440. | 0.0200066 | ||||||||
\(890\) | 1.86180e7 | 0.787877 | ||||||||
\(891\) | −2.96485e7 | −1.25115 | ||||||||
\(892\) | 7.65451e6 | 0.322111 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 5.83647e6 | 0.244234 | ||||||||
\(895\) | 533635. | 0.0222683 | ||||||||
\(896\) | −746532. | −0.0310655 | ||||||||
\(897\) | 5.36955e7 | 2.22821 | ||||||||
\(898\) | 2.50607e7 | 1.03706 | ||||||||
\(899\) | 2.98127e7 | 1.23028 | ||||||||
\(900\) | 4.18215e7 | 1.72105 | ||||||||
\(901\) | 4.27569e6 | 0.175467 | ||||||||
\(902\) | 1.01933e7 | 0.417155 | ||||||||
\(903\) | 1.30797e6 | 0.0533802 | ||||||||
\(904\) | −1.07936e7 | −0.439282 | ||||||||
\(905\) | 8.12084e6 | 0.329594 | ||||||||
\(906\) | 2.95415e7 | 1.19567 | ||||||||
\(907\) | 3.79280e7 | 1.53088 | 0.765441 | − | 0.643506i | \(-0.222521\pi\) | ||||
0.765441 | + | 0.643506i | \(0.222521\pi\) | |||||||
\(908\) | 3.48865e6 | 0.140425 | ||||||||
\(909\) | 1.28659e7 | 0.516452 | ||||||||
\(910\) | −6.99775e6 | −0.280127 | ||||||||
\(911\) | 4.47251e6 | 0.178548 | 0.0892740 | − | 0.996007i | \(-0.471545\pi\) | ||||
0.0892740 | + | 0.996007i | \(0.471545\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.95487e6 | −0.395238 | ||||||||
\(914\) | −4.67655e6 | −0.185165 | ||||||||
\(915\) | −1.16013e8 | −4.58094 | ||||||||
\(916\) | −7.43304e6 | −0.292703 | ||||||||
\(917\) | −1.01976e7 | −0.400472 | ||||||||
\(918\) | 2.41245e7 | 0.944824 | ||||||||
\(919\) | 1.37008e7 | 0.535129 | 0.267564 | − | 0.963540i | \(-0.413781\pi\) | ||||
0.267564 | + | 0.963540i | \(0.413781\pi\) | |||||||
\(920\) | −2.72026e7 | −1.05960 | ||||||||
\(921\) | −7.29707e7 | −2.83465 | ||||||||
\(922\) | −2.85489e7 | −1.10602 | ||||||||
\(923\) | −9.17931e6 | −0.354655 | ||||||||
\(924\) | −8.12566e6 | −0.313097 | ||||||||
\(925\) | 6.50828e7 | 2.50099 | ||||||||
\(926\) | −2.08011e7 | −0.797184 | ||||||||
\(927\) | 1.97597e7 | 0.755233 | ||||||||
\(928\) | −4.09047e6 | −0.155921 | ||||||||
\(929\) | −3.79074e7 | −1.44107 | −0.720534 | − | 0.693420i | \(-0.756103\pi\) | ||||
−0.720534 | + | 0.693420i | \(0.756103\pi\) | |||||||
\(930\) | 7.43851e7 | 2.82019 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.43400e6 | 0.0540765 | ||||||||
\(933\) | 791302. | 0.0297603 | ||||||||
\(934\) | 3.04435e7 | 1.14190 | ||||||||
\(935\) | −3.13797e7 | −1.17387 | ||||||||
\(936\) | 1.35949e7 | 0.507210 | ||||||||
\(937\) | −4.22209e7 | −1.57101 | −0.785504 | − | 0.618857i | \(-0.787596\pi\) | ||||
−0.785504 | + | 0.618857i | \(0.787596\pi\) | |||||||
\(938\) | −7.13792e6 | −0.264889 | ||||||||
\(939\) | 5.09828e7 | 1.88695 | ||||||||
\(940\) | 7.76663e6 | 0.286690 | ||||||||
\(941\) | −4.63842e7 | −1.70764 | −0.853820 | − | 0.520569i | \(-0.825720\pi\) | ||||
−0.853820 | + | 0.520569i | \(0.825720\pi\) | |||||||
\(942\) | 3.83891e7 | 1.40955 | ||||||||
\(943\) | −2.91450e7 | −1.06730 | ||||||||
\(944\) | −1.83911e6 | −0.0671702 | ||||||||
\(945\) | −2.96654e7 | −1.08061 | ||||||||
\(946\) | 1.71259e6 | 0.0622192 | ||||||||
\(947\) | 1.87834e7 | 0.680612 | 0.340306 | − | 0.940315i | \(-0.389469\pi\) | ||||
0.340306 | + | 0.940315i | \(0.389469\pi\) | |||||||
\(948\) | 4.14911e7 | 1.49946 | ||||||||
\(949\) | 5.92443e6 | 0.213541 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.36891e7 | 1.20792 | ||||||||
\(952\) | 2.46228e6 | 0.0880532 | ||||||||
\(953\) | −3.71098e7 | −1.32360 | −0.661799 | − | 0.749681i | \(-0.730207\pi\) | ||||
−0.661799 | + | 0.749681i | \(0.730207\pi\) | |||||||
\(954\) | 1.02145e7 | 0.363368 | ||||||||
\(955\) | −1.95636e7 | −0.694128 | ||||||||
\(956\) | −1.20557e7 | −0.426625 | ||||||||
\(957\) | −4.45230e7 | −1.57146 | ||||||||
\(958\) | −3.06321e7 | −1.07836 | ||||||||
\(959\) | 1.38005e7 | 0.484562 | ||||||||
\(960\) | −1.02061e7 | −0.357421 | ||||||||
\(961\) | 2.70709e7 | 0.945572 | ||||||||
\(962\) | 2.11565e7 | 0.737067 | ||||||||
\(963\) | −2.16476e7 | −0.752217 | ||||||||
\(964\) | 4.45033e6 | 0.154241 | ||||||||
\(965\) | −2.50385e7 | −0.865544 | ||||||||
\(966\) | 2.32332e7 | 0.801063 | ||||||||
\(967\) | 5.14144e6 | 0.176815 | 0.0884074 | − | 0.996084i | \(-0.471822\pi\) | ||||
0.0884074 | + | 0.996084i | \(0.471822\pi\) | |||||||
\(968\) | −332011. | −0.0113884 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.75248e7 | −1.62178 | ||||||||
\(971\) | −4.09741e6 | −0.139464 | −0.0697318 | − | 0.997566i | \(-0.522214\pi\) | ||||
−0.0697318 | + | 0.997566i | \(0.522214\pi\) | |||||||
\(972\) | 4.03429e6 | 0.136962 | ||||||||
\(973\) | 1.32407e7 | 0.448364 | ||||||||
\(974\) | −1.65967e7 | −0.560562 | ||||||||
\(975\) | −5.96843e7 | −2.01071 | ||||||||
\(976\) | 1.19193e7 | 0.400520 | ||||||||
\(977\) | 4.34176e7 | 1.45522 | 0.727612 | − | 0.685989i | \(-0.240630\pi\) | ||||
0.727612 | + | 0.685989i | \(0.240630\pi\) | |||||||
\(978\) | −4.89926e7 | −1.63789 | ||||||||
\(979\) | −2.08202e7 | −0.694271 | ||||||||
\(980\) | 2.14833e7 | 0.714557 | ||||||||
\(981\) | −4.99938e7 | −1.65861 | ||||||||
\(982\) | 3.38042e7 | 1.11864 | ||||||||
\(983\) | −949497. | −0.0313408 | −0.0156704 | − | 0.999877i | \(-0.504988\pi\) | ||||
−0.0156704 | + | 0.999877i | \(0.504988\pi\) | |||||||
\(984\) | −1.09348e7 | −0.360018 | ||||||||
\(985\) | −6.82217e7 | −2.24043 | ||||||||
\(986\) | 1.34916e7 | 0.441948 | ||||||||
\(987\) | −6.63334e6 | −0.216740 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.89670e6 | −0.159189 | ||||||||
\(990\) | −7.49653e7 | −2.43093 | ||||||||
\(991\) | 3.94885e7 | 1.27728 | 0.638641 | − | 0.769505i | \(-0.279497\pi\) | ||||
0.638641 | + | 0.769505i | \(0.279497\pi\) | |||||||
\(992\) | −7.64237e6 | −0.246575 | ||||||||
\(993\) | 5.84325e7 | 1.88054 | ||||||||
\(994\) | −3.97175e6 | −0.127502 | ||||||||
\(995\) | −1.49368e7 | −0.478299 | ||||||||
\(996\) | 1.06791e7 | 0.341103 | ||||||||
\(997\) | −1.95362e7 | −0.622447 | −0.311223 | − | 0.950337i | \(-0.600739\pi\) | ||||
−0.311223 | + | 0.950337i | \(0.600739\pi\) | |||||||
\(998\) | 4.33771e7 | 1.37859 | ||||||||
\(999\) | 8.96883e7 | 2.84330 |
(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.q.1.13 | 15 | ||
19.14 | odd | 18 | 38.6.e.b.25.5 | ✓ | 30 | ||
19.15 | odd | 18 | 38.6.e.b.35.5 | yes | 30 | ||
19.18 | odd | 2 | 722.6.a.r.1.3 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.6.e.b.25.5 | ✓ | 30 | 19.14 | odd | 18 | ||
38.6.e.b.35.5 | yes | 30 | 19.15 | odd | 18 | ||
722.6.a.q.1.13 | 15 | 1.1 | even | 1 | trivial | ||
722.6.a.r.1.3 | 15 | 19.18 | odd | 2 |