Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,6,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, 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("289.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.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: | \(46.3509239260\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | no (minimal twist has level 17) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.27 | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 10.5085 | 1.85765 | 0.928826 | − | 0.370516i | \(-0.120819\pi\) | ||||
0.928826 | + | 0.370516i | \(0.120819\pi\) | |||||||
\(3\) | −25.0990 | −1.61010 | −0.805052 | − | 0.593204i | \(-0.797863\pi\) | ||||
−0.805052 | + | 0.593204i | \(0.797863\pi\) | |||||||
\(4\) | 78.4279 | 2.45087 | ||||||||
\(5\) | 55.7139 | 0.996641 | 0.498320 | − | 0.866993i | \(-0.333950\pi\) | ||||
0.498320 | + | 0.866993i | \(0.333950\pi\) | |||||||
\(6\) | −263.753 | −2.99101 | ||||||||
\(7\) | −91.7804 | −0.707953 | −0.353977 | − | 0.935254i | \(-0.615171\pi\) | ||||
−0.353977 | + | 0.935254i | \(0.615171\pi\) | |||||||
\(8\) | 487.886 | 2.69522 | ||||||||
\(9\) | 386.962 | 1.59244 | ||||||||
\(10\) | 585.468 | 1.85141 | ||||||||
\(11\) | 39.2153 | 0.0977179 | 0.0488589 | − | 0.998806i | \(-0.484442\pi\) | ||||
0.0488589 | + | 0.998806i | \(0.484442\pi\) | |||||||
\(12\) | −1968.47 | −3.94616 | ||||||||
\(13\) | 243.603 | 0.399783 | 0.199891 | − | 0.979818i | \(-0.435941\pi\) | ||||
0.199891 | + | 0.979818i | \(0.435941\pi\) | |||||||
\(14\) | −964.471 | −1.31513 | ||||||||
\(15\) | −1398.37 | −1.60470 | ||||||||
\(16\) | 2617.24 | 2.55590 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 4066.38 | 2.95819 | ||||||||
\(19\) | 620.383 | 0.394254 | 0.197127 | − | 0.980378i | \(-0.436839\pi\) | ||||
0.197127 | + | 0.980378i | \(0.436839\pi\) | |||||||
\(20\) | 4369.53 | 2.44264 | ||||||||
\(21\) | 2303.60 | 1.13988 | ||||||||
\(22\) | 412.093 | 0.181526 | ||||||||
\(23\) | 3748.31 | 1.47746 | 0.738731 | − | 0.674001i | \(-0.235425\pi\) | ||||
0.738731 | + | 0.674001i | \(0.235425\pi\) | |||||||
\(24\) | −12245.5 | −4.33958 | ||||||||
\(25\) | −20.9596 | −0.00670707 | ||||||||
\(26\) | 2559.89 | 0.742658 | ||||||||
\(27\) | −3613.31 | −0.953884 | ||||||||
\(28\) | −7198.14 | −1.73510 | ||||||||
\(29\) | −4569.03 | −1.00886 | −0.504428 | − | 0.863454i | \(-0.668297\pi\) | ||||
−0.504428 | + | 0.863454i | \(0.668297\pi\) | |||||||
\(30\) | −14694.7 | −2.98097 | ||||||||
\(31\) | 6666.42 | 1.24592 | 0.622958 | − | 0.782255i | \(-0.285931\pi\) | ||||
0.622958 | + | 0.782255i | \(0.285931\pi\) | |||||||
\(32\) | 11890.9 | 2.05276 | ||||||||
\(33\) | −984.267 | −0.157336 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5113.44 | −0.705575 | ||||||||
\(36\) | 30348.6 | 3.90286 | ||||||||
\(37\) | 3052.25 | 0.366536 | 0.183268 | − | 0.983063i | \(-0.441332\pi\) | ||||
0.183268 | + | 0.983063i | \(0.441332\pi\) | |||||||
\(38\) | 6519.27 | 0.732386 | ||||||||
\(39\) | −6114.20 | −0.643692 | ||||||||
\(40\) | 27182.1 | 2.68616 | ||||||||
\(41\) | 6773.72 | 0.629314 | 0.314657 | − | 0.949205i | \(-0.398111\pi\) | ||||
0.314657 | + | 0.949205i | \(0.398111\pi\) | |||||||
\(42\) | 24207.3 | 2.11750 | ||||||||
\(43\) | 16032.4 | 1.32229 | 0.661145 | − | 0.750258i | \(-0.270071\pi\) | ||||
0.661145 | + | 0.750258i | \(0.270071\pi\) | |||||||
\(44\) | 3075.58 | 0.239494 | ||||||||
\(45\) | 21559.2 | 1.58709 | ||||||||
\(46\) | 39389.0 | 2.74461 | ||||||||
\(47\) | 21852.3 | 1.44295 | 0.721476 | − | 0.692440i | \(-0.243464\pi\) | ||||
0.721476 | + | 0.692440i | \(0.243464\pi\) | |||||||
\(48\) | −65690.3 | −4.11527 | ||||||||
\(49\) | −8383.37 | −0.498802 | ||||||||
\(50\) | −220.253 | −0.0124594 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 19105.3 | 0.979817 | ||||||||
\(53\) | 4754.78 | 0.232510 | 0.116255 | − | 0.993219i | \(-0.462911\pi\) | ||||
0.116255 | + | 0.993219i | \(0.462911\pi\) | |||||||
\(54\) | −37970.4 | −1.77199 | ||||||||
\(55\) | 2184.84 | 0.0973896 | ||||||||
\(56\) | −44778.4 | −1.90809 | ||||||||
\(57\) | −15571.0 | −0.634790 | ||||||||
\(58\) | −48013.5 | −1.87410 | ||||||||
\(59\) | 38999.6 | 1.45858 | 0.729291 | − | 0.684204i | \(-0.239850\pi\) | ||||
0.729291 | + | 0.684204i | \(0.239850\pi\) | |||||||
\(60\) | −109671. | −3.93290 | ||||||||
\(61\) | −12199.9 | −0.419791 | −0.209896 | − | 0.977724i | \(-0.567312\pi\) | ||||
−0.209896 | + | 0.977724i | \(0.567312\pi\) | |||||||
\(62\) | 70053.9 | 2.31448 | ||||||||
\(63\) | −35515.5 | −1.12737 | ||||||||
\(64\) | 41203.0 | 1.25742 | ||||||||
\(65\) | 13572.1 | 0.398440 | ||||||||
\(66\) | −10343.1 | −0.292276 | ||||||||
\(67\) | −43024.2 | −1.17092 | −0.585458 | − | 0.810703i | \(-0.699085\pi\) | ||||
−0.585458 | + | 0.810703i | \(0.699085\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −94079.1 | −2.37887 | ||||||||
\(70\) | −53734.5 | −1.31071 | ||||||||
\(71\) | 58762.3 | 1.38342 | 0.691709 | − | 0.722177i | \(-0.256858\pi\) | ||||
0.691709 | + | 0.722177i | \(0.256858\pi\) | |||||||
\(72\) | 188793. | 4.29196 | ||||||||
\(73\) | 47753.8 | 1.04882 | 0.524409 | − | 0.851466i | \(-0.324286\pi\) | ||||
0.524409 | + | 0.851466i | \(0.324286\pi\) | |||||||
\(74\) | 32074.5 | 0.680896 | ||||||||
\(75\) | 526.065 | 0.0107991 | ||||||||
\(76\) | 48655.3 | 0.966265 | ||||||||
\(77\) | −3599.20 | −0.0691797 | ||||||||
\(78\) | −64250.9 | −1.19576 | ||||||||
\(79\) | −12919.1 | −0.232898 | −0.116449 | − | 0.993197i | \(-0.537151\pi\) | ||||
−0.116449 | + | 0.993197i | \(0.537151\pi\) | |||||||
\(80\) | 145817. | 2.54732 | ||||||||
\(81\) | −3341.15 | −0.0565827 | ||||||||
\(82\) | 71181.4 | 1.16905 | ||||||||
\(83\) | −66422.1 | −1.05832 | −0.529160 | − | 0.848522i | \(-0.677493\pi\) | ||||
−0.529160 | + | 0.848522i | \(0.677493\pi\) | |||||||
\(84\) | 180666. | 2.79370 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 168476. | 2.45636 | ||||||||
\(87\) | 114678. | 1.62436 | ||||||||
\(88\) | 19132.6 | 0.263371 | ||||||||
\(89\) | −72990.1 | −0.976763 | −0.488381 | − | 0.872630i | \(-0.662413\pi\) | ||||
−0.488381 | + | 0.872630i | \(0.662413\pi\) | |||||||
\(90\) | 226554. | 2.94826 | ||||||||
\(91\) | −22358.0 | −0.283028 | ||||||||
\(92\) | 293972. | 3.62107 | ||||||||
\(93\) | −167321. | −2.00605 | ||||||||
\(94\) | 229634. | 2.68050 | ||||||||
\(95\) | 34564.0 | 0.392929 | ||||||||
\(96\) | −298450. | −3.30516 | ||||||||
\(97\) | 83758.6 | 0.903858 | 0.451929 | − | 0.892054i | \(-0.350736\pi\) | ||||
0.451929 | + | 0.892054i | \(0.350736\pi\) | |||||||
\(98\) | −88096.4 | −0.926601 | ||||||||
\(99\) | 15174.8 | 0.155609 | ||||||||
\(100\) | −1643.82 | −0.0164382 | ||||||||
\(101\) | −91093.1 | −0.888551 | −0.444275 | − | 0.895890i | \(-0.646539\pi\) | ||||
−0.444275 | + | 0.895890i | \(0.646539\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 92993.8 | 0.863697 | 0.431848 | − | 0.901946i | \(-0.357862\pi\) | ||||
0.431848 | + | 0.901946i | \(0.357862\pi\) | |||||||
\(104\) | 118851. | 1.07750 | ||||||||
\(105\) | 128343. | 1.13605 | ||||||||
\(106\) | 49965.5 | 0.431922 | ||||||||
\(107\) | −38460.1 | −0.324752 | −0.162376 | − | 0.986729i | \(-0.551916\pi\) | ||||
−0.162376 | + | 0.986729i | \(0.551916\pi\) | |||||||
\(108\) | −283384. | −2.33785 | ||||||||
\(109\) | −102431. | −0.825785 | −0.412893 | − | 0.910780i | \(-0.635482\pi\) | ||||
−0.412893 | + | 0.910780i | \(0.635482\pi\) | |||||||
\(110\) | 22959.3 | 0.180916 | ||||||||
\(111\) | −76608.7 | −0.590161 | ||||||||
\(112\) | −240212. | −1.80946 | ||||||||
\(113\) | −190807. | −1.40572 | −0.702858 | − | 0.711330i | \(-0.748093\pi\) | ||||
−0.702858 | + | 0.711330i | \(0.748093\pi\) | |||||||
\(114\) | −163628. | −1.17922 | ||||||||
\(115\) | 208833. | 1.47250 | ||||||||
\(116\) | −358340. | −2.47258 | ||||||||
\(117\) | 94265.1 | 0.636629 | ||||||||
\(118\) | 409827. | 2.70954 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −682244. | −4.32500 | ||||||||
\(121\) | −159513. | −0.990451 | ||||||||
\(122\) | −128203. | −0.779826 | ||||||||
\(123\) | −170014. | −1.01326 | ||||||||
\(124\) | 522834. | 3.05358 | ||||||||
\(125\) | −175274. | −1.00333 | ||||||||
\(126\) | −373214. | −2.09426 | ||||||||
\(127\) | −211847. | −1.16550 | −0.582751 | − | 0.812651i | \(-0.698024\pi\) | ||||
−0.582751 | + | 0.812651i | \(0.698024\pi\) | |||||||
\(128\) | 52472.8 | 0.283080 | ||||||||
\(129\) | −402397. | −2.12903 | ||||||||
\(130\) | 142622. | 0.740163 | ||||||||
\(131\) | 73275.1 | 0.373060 | 0.186530 | − | 0.982449i | \(-0.440276\pi\) | ||||
0.186530 | + | 0.982449i | \(0.440276\pi\) | |||||||
\(132\) | −77194.0 | −0.385610 | ||||||||
\(133\) | −56938.9 | −0.279113 | ||||||||
\(134\) | −452118. | −2.17515 | ||||||||
\(135\) | −201312. | −0.950680 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 44705.6 | 0.203498 | 0.101749 | − | 0.994810i | \(-0.467556\pi\) | ||||
0.101749 | + | 0.994810i | \(0.467556\pi\) | |||||||
\(138\) | −988627. | −4.41911 | ||||||||
\(139\) | 110984. | 0.487218 | 0.243609 | − | 0.969874i | \(-0.421669\pi\) | ||||
0.243609 | + | 0.969874i | \(0.421669\pi\) | |||||||
\(140\) | −401037. | −1.72927 | ||||||||
\(141\) | −548471. | −2.32330 | ||||||||
\(142\) | 617502. | 2.56991 | ||||||||
\(143\) | 9552.97 | 0.0390659 | ||||||||
\(144\) | 1.01277e6 | 4.07011 | ||||||||
\(145\) | −254559. | −1.00547 | ||||||||
\(146\) | 501819. | 1.94834 | ||||||||
\(147\) | 210415. | 0.803124 | ||||||||
\(148\) | 239382. | 0.898333 | ||||||||
\(149\) | 199107. | 0.734720 | 0.367360 | − | 0.930079i | \(-0.380262\pi\) | ||||
0.367360 | + | 0.930079i | \(0.380262\pi\) | |||||||
\(150\) | 5528.14 | 0.0200609 | ||||||||
\(151\) | 8828.12 | 0.0315084 | 0.0157542 | − | 0.999876i | \(-0.494985\pi\) | ||||
0.0157542 | + | 0.999876i | \(0.494985\pi\) | |||||||
\(152\) | 302676. | 1.06260 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −37822.0 | −0.128512 | ||||||||
\(155\) | 371412. | 1.24173 | ||||||||
\(156\) | −479524. | −1.57761 | ||||||||
\(157\) | −68893.6 | −0.223064 | −0.111532 | − | 0.993761i | \(-0.535576\pi\) | ||||
−0.111532 | + | 0.993761i | \(0.535576\pi\) | |||||||
\(158\) | −135760. | −0.432643 | ||||||||
\(159\) | −119341. | −0.374365 | ||||||||
\(160\) | 662487. | 2.04587 | ||||||||
\(161\) | −344021. | −1.04597 | ||||||||
\(162\) | −35110.4 | −0.105111 | ||||||||
\(163\) | −166914. | −0.492066 | −0.246033 | − | 0.969261i | \(-0.579127\pi\) | ||||
−0.246033 | + | 0.969261i | \(0.579127\pi\) | |||||||
\(164\) | 531248. | 1.54237 | ||||||||
\(165\) | −54837.4 | −0.156807 | ||||||||
\(166\) | −697994. | −1.96599 | ||||||||
\(167\) | −574203. | −1.59321 | −0.796607 | − | 0.604497i | \(-0.793374\pi\) | ||||
−0.796607 | + | 0.604497i | \(0.793374\pi\) | |||||||
\(168\) | 1.12389e6 | 3.07222 | ||||||||
\(169\) | −311951. | −0.840174 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 240065. | 0.627824 | ||||||||
\(172\) | 1.25739e6 | 3.24076 | ||||||||
\(173\) | −217487. | −0.552482 | −0.276241 | − | 0.961088i | \(-0.589089\pi\) | ||||
−0.276241 | + | 0.961088i | \(0.589089\pi\) | |||||||
\(174\) | 1.20509e6 | 3.01750 | ||||||||
\(175\) | 1923.68 | 0.00474829 | ||||||||
\(176\) | 102636. | 0.249757 | ||||||||
\(177\) | −978854. | −2.34847 | ||||||||
\(178\) | −767015. | −1.81449 | ||||||||
\(179\) | 628318. | 1.46571 | 0.732854 | − | 0.680386i | \(-0.238188\pi\) | ||||
0.732854 | + | 0.680386i | \(0.238188\pi\) | |||||||
\(180\) | 1.69084e6 | 3.88975 | ||||||||
\(181\) | −69023.1 | −0.156602 | −0.0783011 | − | 0.996930i | \(-0.524950\pi\) | ||||
−0.0783011 | + | 0.996930i | \(0.524950\pi\) | |||||||
\(182\) | −234948. | −0.525767 | ||||||||
\(183\) | 306207. | 0.675908 | ||||||||
\(184\) | 1.82875e6 | 3.98208 | ||||||||
\(185\) | 170053. | 0.365305 | ||||||||
\(186\) | −1.75829e6 | −3.72655 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1.71383e6 | 3.53649 | ||||||||
\(189\) | 331631. | 0.675306 | ||||||||
\(190\) | 363214. | 0.729926 | ||||||||
\(191\) | −357545. | −0.709164 | −0.354582 | − | 0.935025i | \(-0.615377\pi\) | ||||
−0.354582 | + | 0.935025i | \(0.615377\pi\) | |||||||
\(192\) | −1.03416e6 | −2.02457 | ||||||||
\(193\) | 141090. | 0.272649 | 0.136325 | − | 0.990664i | \(-0.456471\pi\) | ||||
0.136325 | + | 0.990664i | \(0.456471\pi\) | |||||||
\(194\) | 880175. | 1.67905 | ||||||||
\(195\) | −340646. | −0.641530 | ||||||||
\(196\) | −657490. | −1.22250 | ||||||||
\(197\) | −696431. | −1.27853 | −0.639267 | − | 0.768985i | \(-0.720762\pi\) | ||||
−0.639267 | + | 0.768985i | \(0.720762\pi\) | |||||||
\(198\) | 159464. | 0.289068 | ||||||||
\(199\) | −198110. | −0.354628 | −0.177314 | − | 0.984154i | \(-0.556741\pi\) | ||||
−0.177314 | + | 0.984154i | \(0.556741\pi\) | |||||||
\(200\) | −10225.9 | −0.0180770 | ||||||||
\(201\) | 1.07987e6 | 1.88530 | ||||||||
\(202\) | −957249. | −1.65062 | ||||||||
\(203\) | 419347. | 0.714223 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 377390. | 0.627200 | ||||||||
\(206\) | 977223. | 1.60445 | ||||||||
\(207\) | 1.45045e6 | 2.35276 | ||||||||
\(208\) | 637568. | 1.02181 | ||||||||
\(209\) | 24328.5 | 0.0385256 | ||||||||
\(210\) | 1.34868e6 | 2.11039 | ||||||||
\(211\) | −121671. | −0.188140 | −0.0940700 | − | 0.995566i | \(-0.529988\pi\) | ||||
−0.0940700 | + | 0.995566i | \(0.529988\pi\) | |||||||
\(212\) | 372908. | 0.569852 | ||||||||
\(213\) | −1.47488e6 | −2.22745 | ||||||||
\(214\) | −404157. | −0.603276 | ||||||||
\(215\) | 893226. | 1.31785 | ||||||||
\(216\) | −1.76288e6 | −2.57093 | ||||||||
\(217\) | −611847. | −0.882050 | ||||||||
\(218\) | −1.07640e6 | −1.53402 | ||||||||
\(219\) | −1.19857e6 | −1.68871 | ||||||||
\(220\) | 171352. | 0.238690 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −805040. | −1.09631 | ||||||||
\(223\) | −566505. | −0.762854 | −0.381427 | − | 0.924399i | \(-0.624567\pi\) | ||||
−0.381427 | + | 0.924399i | \(0.624567\pi\) | |||||||
\(224\) | −1.09135e6 | −1.45326 | ||||||||
\(225\) | −8110.56 | −0.0106806 | ||||||||
\(226\) | −2.00509e6 | −2.61133 | ||||||||
\(227\) | −918955. | −1.18367 | −0.591833 | − | 0.806060i | \(-0.701596\pi\) | ||||
−0.591833 | + | 0.806060i | \(0.701596\pi\) | |||||||
\(228\) | −1.22120e6 | −1.55579 | ||||||||
\(229\) | 1.45495e6 | 1.83341 | 0.916706 | − | 0.399562i | \(-0.130838\pi\) | ||||
0.916706 | + | 0.399562i | \(0.130838\pi\) | |||||||
\(230\) | 2.19452e6 | 2.73539 | ||||||||
\(231\) | 90336.4 | 0.111387 | ||||||||
\(232\) | −2.22917e6 | −2.71908 | ||||||||
\(233\) | 9096.89 | 0.0109775 | 0.00548875 | − | 0.999985i | \(-0.498253\pi\) | ||||
0.00548875 | + | 0.999985i | \(0.498253\pi\) | |||||||
\(234\) | 990582. | 1.18263 | ||||||||
\(235\) | 1.21747e6 | 1.43810 | ||||||||
\(236\) | 3.05866e6 | 3.57480 | ||||||||
\(237\) | 324258. | 0.374990 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −725823. | −0.821932 | −0.410966 | − | 0.911651i | \(-0.634808\pi\) | ||||
−0.410966 | + | 0.911651i | \(0.634808\pi\) | |||||||
\(240\) | −3.65987e6 | −4.10145 | ||||||||
\(241\) | 1.07312e6 | 1.19016 | 0.595081 | − | 0.803666i | \(-0.297120\pi\) | ||||
0.595081 | + | 0.803666i | \(0.297120\pi\) | |||||||
\(242\) | −1.67624e6 | −1.83991 | ||||||||
\(243\) | 961894. | 1.04499 | ||||||||
\(244\) | −956816. | −1.02885 | ||||||||
\(245\) | −467070. | −0.497127 | ||||||||
\(246\) | −1.78658e6 | −1.88229 | ||||||||
\(247\) | 151127. | 0.157616 | ||||||||
\(248\) | 3.25246e6 | 3.35801 | ||||||||
\(249\) | 1.66713e6 | 1.70401 | ||||||||
\(250\) | −1.84186e6 | −1.86383 | ||||||||
\(251\) | 1.39837e6 | 1.40099 | 0.700497 | − | 0.713655i | \(-0.252962\pi\) | ||||
0.700497 | + | 0.713655i | \(0.252962\pi\) | |||||||
\(252\) | −2.78541e6 | −2.76304 | ||||||||
\(253\) | 146991. | 0.144374 | ||||||||
\(254\) | −2.22619e6 | −2.16510 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −767088. | −0.731552 | ||||||||
\(257\) | 210631. | 0.198925 | 0.0994627 | − | 0.995041i | \(-0.468288\pi\) | ||||
0.0994627 | + | 0.995041i | \(0.468288\pi\) | |||||||
\(258\) | −4.22858e6 | −3.95499 | ||||||||
\(259\) | −280137. | −0.259490 | ||||||||
\(260\) | 1.06443e6 | 0.976525 | ||||||||
\(261\) | −1.76804e6 | −1.60654 | ||||||||
\(262\) | 770009. | 0.693015 | ||||||||
\(263\) | 307281. | 0.273934 | 0.136967 | − | 0.990576i | \(-0.456265\pi\) | ||||
0.136967 | + | 0.990576i | \(0.456265\pi\) | |||||||
\(264\) | −480210. | −0.424055 | ||||||||
\(265\) | 264908. | 0.231729 | ||||||||
\(266\) | −598341. | −0.518495 | ||||||||
\(267\) | 1.83198e6 | 1.57269 | ||||||||
\(268\) | −3.37430e6 | −2.86977 | ||||||||
\(269\) | 25857.9 | 0.0217878 | 0.0108939 | − | 0.999941i | \(-0.496532\pi\) | ||||
0.0108939 | + | 0.999941i | \(0.496532\pi\) | |||||||
\(270\) | −2.11548e6 | −1.76603 | ||||||||
\(271\) | 1.25525e6 | 1.03827 | 0.519133 | − | 0.854694i | \(-0.326255\pi\) | ||||
0.519133 | + | 0.854694i | \(0.326255\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 561164. | 0.455704 | ||||||||
\(274\) | 469787. | 0.378029 | ||||||||
\(275\) | −821.937 | −0.000655400 0 | ||||||||
\(276\) | −7.37843e6 | −5.83030 | ||||||||
\(277\) | 1.23777e6 | 0.969259 | 0.484629 | − | 0.874720i | \(-0.338954\pi\) | ||||
0.484629 | + | 0.874720i | \(0.338954\pi\) | |||||||
\(278\) | 1.16627e6 | 0.905082 | ||||||||
\(279\) | 2.57965e6 | 1.98404 | ||||||||
\(280\) | −2.49478e6 | −1.90168 | ||||||||
\(281\) | 1.25678e6 | 0.949493 | 0.474747 | − | 0.880123i | \(-0.342540\pi\) | ||||
0.474747 | + | 0.880123i | \(0.342540\pi\) | |||||||
\(282\) | −5.76359e6 | −4.31589 | ||||||||
\(283\) | 20473.4 | 0.0151958 | 0.00759791 | − | 0.999971i | \(-0.497581\pi\) | ||||
0.00759791 | + | 0.999971i | \(0.497581\pi\) | |||||||
\(284\) | 4.60861e6 | 3.39058 | ||||||||
\(285\) | −867522. | −0.632657 | ||||||||
\(286\) | 100387. | 0.0725709 | ||||||||
\(287\) | −621694. | −0.445525 | ||||||||
\(288\) | 4.60132e6 | 3.26889 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −2.67502e6 | −1.86781 | ||||||||
\(291\) | −2.10226e6 | −1.45531 | ||||||||
\(292\) | 3.74523e6 | 2.57052 | ||||||||
\(293\) | 385468. | 0.262313 | 0.131156 | − | 0.991362i | \(-0.458131\pi\) | ||||
0.131156 | + | 0.991362i | \(0.458131\pi\) | |||||||
\(294\) | 2.21113e6 | 1.49192 | ||||||||
\(295\) | 2.17282e6 | 1.45368 | ||||||||
\(296\) | 1.48915e6 | 0.987894 | ||||||||
\(297\) | −141697. | −0.0932116 | ||||||||
\(298\) | 2.09231e6 | 1.36485 | ||||||||
\(299\) | 913100. | 0.590664 | ||||||||
\(300\) | 41258.2 | 0.0264672 | ||||||||
\(301\) | −1.47146e6 | −0.936120 | ||||||||
\(302\) | 92770.0 | 0.0585316 | ||||||||
\(303\) | 2.28635e6 | 1.43066 | ||||||||
\(304\) | 1.62369e6 | 1.00767 | ||||||||
\(305\) | −679707. | −0.418381 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −378716. | −0.229333 | −0.114667 | − | 0.993404i | \(-0.536580\pi\) | ||||
−0.114667 | + | 0.993404i | \(0.536580\pi\) | |||||||
\(308\) | −282277. | −0.169551 | ||||||||
\(309\) | −2.33406e6 | −1.39064 | ||||||||
\(310\) | 3.90298e6 | 2.30670 | ||||||||
\(311\) | −281786. | −0.165203 | −0.0826016 | − | 0.996583i | \(-0.526323\pi\) | ||||
−0.0826016 | + | 0.996583i | \(0.526323\pi\) | |||||||
\(312\) | −2.98303e6 | −1.73489 | ||||||||
\(313\) | −1.42330e6 | −0.821175 | −0.410588 | − | 0.911821i | \(-0.634676\pi\) | ||||
−0.410588 | + | 0.911821i | \(0.634676\pi\) | |||||||
\(314\) | −723967. | −0.414376 | ||||||||
\(315\) | −1.97871e6 | −1.12358 | ||||||||
\(316\) | −1.01322e6 | −0.570803 | ||||||||
\(317\) | −1.61666e6 | −0.903589 | −0.451795 | − | 0.892122i | \(-0.649216\pi\) | ||||
−0.451795 | + | 0.892122i | \(0.649216\pi\) | |||||||
\(318\) | −1.25409e6 | −0.695440 | ||||||||
\(319\) | −179176. | −0.0985832 | ||||||||
\(320\) | 2.29558e6 | 1.25319 | ||||||||
\(321\) | 965312. | 0.522884 | ||||||||
\(322\) | −3.61514e6 | −1.94306 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −262040. | −0.138677 | ||||||||
\(325\) | −5105.82 | −0.00268137 | ||||||||
\(326\) | −1.75401e6 | −0.914088 | ||||||||
\(327\) | 2.57093e6 | 1.32960 | ||||||||
\(328\) | 3.30480e6 | 1.69614 | ||||||||
\(329\) | −2.00561e6 | −1.02154 | ||||||||
\(330\) | −576257. | −0.291294 | ||||||||
\(331\) | −2.34866e6 | −1.17829 | −0.589143 | − | 0.808029i | \(-0.700534\pi\) | ||||
−0.589143 | + | 0.808029i | \(0.700534\pi\) | |||||||
\(332\) | −5.20934e6 | −2.59381 | ||||||||
\(333\) | 1.18111e6 | 0.583685 | ||||||||
\(334\) | −6.03400e6 | −2.95964 | ||||||||
\(335\) | −2.39705e6 | −1.16698 | ||||||||
\(336\) | 6.02908e6 | 2.91342 | ||||||||
\(337\) | 724801. | 0.347651 | 0.173826 | − | 0.984776i | \(-0.444387\pi\) | ||||
0.173826 | + | 0.984776i | \(0.444387\pi\) | |||||||
\(338\) | −3.27812e6 | −1.56075 | ||||||||
\(339\) | 4.78907e6 | 2.26335 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 261426. | 0.121748 | ||||||||
\(342\) | 2.52271e6 | 1.16628 | ||||||||
\(343\) | 2.31198e6 | 1.06108 | ||||||||
\(344\) | 7.82198e6 | 3.56386 | ||||||||
\(345\) | −5.24151e6 | −2.37088 | ||||||||
\(346\) | −2.28545e6 | −1.02632 | ||||||||
\(347\) | −988484. | −0.440703 | −0.220352 | − | 0.975421i | \(-0.570720\pi\) | ||||
−0.220352 | + | 0.975421i | \(0.570720\pi\) | |||||||
\(348\) | 8.99398e6 | 3.98111 | ||||||||
\(349\) | 3.00138e6 | 1.31904 | 0.659519 | − | 0.751688i | \(-0.270760\pi\) | ||||
0.659519 | + | 0.751688i | \(0.270760\pi\) | |||||||
\(350\) | 20214.9 | 0.00882067 | ||||||||
\(351\) | −880213. | −0.381347 | ||||||||
\(352\) | 466304. | 0.200592 | ||||||||
\(353\) | −755428. | −0.322668 | −0.161334 | − | 0.986900i | \(-0.551580\pi\) | ||||
−0.161334 | + | 0.986900i | \(0.551580\pi\) | |||||||
\(354\) | −1.02863e7 | −4.36264 | ||||||||
\(355\) | 3.27388e6 | 1.37877 | ||||||||
\(356\) | −5.72446e6 | −2.39392 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.60266e6 | 2.72277 | ||||||||
\(359\) | −577718. | −0.236581 | −0.118291 | − | 0.992979i | \(-0.537741\pi\) | ||||
−0.118291 | + | 0.992979i | \(0.537741\pi\) | |||||||
\(360\) | 1.05184e7 | 4.27754 | ||||||||
\(361\) | −2.09122e6 | −0.844564 | ||||||||
\(362\) | −725327. | −0.290913 | ||||||||
\(363\) | 4.00363e6 | 1.59473 | ||||||||
\(364\) | −1.75349e6 | −0.693664 | ||||||||
\(365\) | 2.66055e6 | 1.04530 | ||||||||
\(366\) | 3.21777e6 | 1.25560 | ||||||||
\(367\) | 1.61209e6 | 0.624777 | 0.312389 | − | 0.949954i | \(-0.398871\pi\) | ||||
0.312389 | + | 0.949954i | \(0.398871\pi\) | |||||||
\(368\) | 9.81025e6 | 3.77625 | ||||||||
\(369\) | 2.62117e6 | 1.00214 | ||||||||
\(370\) | 1.78700e6 | 0.678609 | ||||||||
\(371\) | −436396. | −0.164606 | ||||||||
\(372\) | −1.31226e7 | −4.91658 | ||||||||
\(373\) | 4.75990e6 | 1.77144 | 0.885719 | − | 0.464222i | \(-0.153666\pi\) | ||||
0.885719 | + | 0.464222i | \(0.153666\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.39920e6 | 1.61546 | ||||||||
\(376\) | 1.06614e7 | 3.88907 | ||||||||
\(377\) | −1.11303e6 | −0.403323 | ||||||||
\(378\) | 3.48493e6 | 1.25448 | ||||||||
\(379\) | 258919. | 0.0925906 | 0.0462953 | − | 0.998928i | \(-0.485258\pi\) | ||||
0.0462953 | + | 0.998928i | \(0.485258\pi\) | |||||||
\(380\) | 2.71078e6 | 0.963019 | ||||||||
\(381\) | 5.31715e6 | 1.87658 | ||||||||
\(382\) | −3.75725e6 | −1.31738 | ||||||||
\(383\) | −3.77627e6 | −1.31542 | −0.657712 | − | 0.753269i | \(-0.728476\pi\) | ||||
−0.657712 | + | 0.753269i | \(0.728476\pi\) | |||||||
\(384\) | −1.31702e6 | −0.455789 | ||||||||
\(385\) | −200525. | −0.0689473 | ||||||||
\(386\) | 1.48264e6 | 0.506487 | ||||||||
\(387\) | 6.20392e6 | 2.10566 | ||||||||
\(388\) | 6.56902e6 | 2.21524 | ||||||||
\(389\) | 5.83173e6 | 1.95400 | 0.976998 | − | 0.213247i | \(-0.0684040\pi\) | ||||
0.976998 | + | 0.213247i | \(0.0684040\pi\) | |||||||
\(390\) | −3.57967e6 | −1.19174 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −4.09013e6 | −1.34438 | ||||||||
\(393\) | −1.83914e6 | −0.600665 | ||||||||
\(394\) | −7.31842e6 | −2.37507 | ||||||||
\(395\) | −719775. | −0.232116 | ||||||||
\(396\) | 1.19013e6 | 0.381379 | ||||||||
\(397\) | −4.95232e6 | −1.57700 | −0.788501 | − | 0.615034i | \(-0.789142\pi\) | ||||
−0.788501 | + | 0.615034i | \(0.789142\pi\) | |||||||
\(398\) | −2.08183e6 | −0.658776 | ||||||||
\(399\) | 1.42911e6 | 0.449401 | ||||||||
\(400\) | −54856.4 | −0.0171426 | ||||||||
\(401\) | −4.41230e6 | −1.37026 | −0.685132 | − | 0.728419i | \(-0.740256\pi\) | ||||
−0.685132 | + | 0.728419i | \(0.740256\pi\) | |||||||
\(402\) | 1.13477e7 | 3.50223 | ||||||||
\(403\) | 1.62396e6 | 0.498096 | ||||||||
\(404\) | −7.14425e6 | −2.17772 | ||||||||
\(405\) | −186149. | −0.0563926 | ||||||||
\(406\) | 4.40670e6 | 1.32678 | ||||||||
\(407\) | 119695. | 0.0358171 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.93079e6 | 1.16191 | 0.580954 | − | 0.813936i | \(-0.302679\pi\) | ||||
0.580954 | + | 0.813936i | \(0.302679\pi\) | |||||||
\(410\) | 3.96579e6 | 1.16512 | ||||||||
\(411\) | −1.12207e6 | −0.327653 | ||||||||
\(412\) | 7.29331e6 | 2.11681 | ||||||||
\(413\) | −3.57940e6 | −1.03261 | ||||||||
\(414\) | 1.52421e7 | 4.37062 | ||||||||
\(415\) | −3.70063e6 | −1.05477 | ||||||||
\(416\) | 2.89665e6 | 0.820659 | ||||||||
\(417\) | −2.78559e6 | −0.784472 | ||||||||
\(418\) | 255655. | 0.0715672 | ||||||||
\(419\) | −5.92822e6 | −1.64964 | −0.824819 | − | 0.565396i | \(-0.808723\pi\) | ||||
−0.824819 | + | 0.565396i | \(0.808723\pi\) | |||||||
\(420\) | 1.00656e7 | 2.78431 | ||||||||
\(421\) | −4.51963e6 | −1.24279 | −0.621395 | − | 0.783497i | \(-0.713434\pi\) | ||||
−0.621395 | + | 0.783497i | \(0.713434\pi\) | |||||||
\(422\) | −1.27858e6 | −0.349499 | ||||||||
\(423\) | 8.45599e6 | 2.29781 | ||||||||
\(424\) | 2.31979e6 | 0.626664 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.54987e7 | −4.13782 | ||||||||
\(427\) | 1.11972e6 | 0.297192 | ||||||||
\(428\) | −3.01635e6 | −0.795925 | ||||||||
\(429\) | −239770. | −0.0629002 | ||||||||
\(430\) | 9.38644e6 | 2.44810 | ||||||||
\(431\) | 5.14428e6 | 1.33393 | 0.666963 | − | 0.745091i | \(-0.267594\pi\) | ||||
0.666963 | + | 0.745091i | \(0.267594\pi\) | |||||||
\(432\) | −9.45692e6 | −2.43804 | ||||||||
\(433\) | 5.56099e6 | 1.42539 | 0.712693 | − | 0.701476i | \(-0.247475\pi\) | ||||
0.712693 | + | 0.701476i | \(0.247475\pi\) | |||||||
\(434\) | −6.42957e6 | −1.63854 | ||||||||
\(435\) | 6.38918e6 | 1.61891 | ||||||||
\(436\) | −8.03349e6 | −2.02389 | ||||||||
\(437\) | 2.32539e6 | 0.582495 | ||||||||
\(438\) | −1.25952e7 | −3.13703 | ||||||||
\(439\) | −5.87215e6 | −1.45424 | −0.727119 | − | 0.686511i | \(-0.759141\pi\) | ||||
−0.727119 | + | 0.686511i | \(0.759141\pi\) | |||||||
\(440\) | 1.06595e6 | 0.262486 | ||||||||
\(441\) | −3.24404e6 | −0.794311 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.24535e6 | −1.99618 | −0.998090 | − | 0.0617826i | \(-0.980321\pi\) | ||||
−0.998090 | + | 0.0617826i | \(0.980321\pi\) | |||||||
\(444\) | −6.00826e6 | −1.44641 | ||||||||
\(445\) | −4.06657e6 | −0.973482 | ||||||||
\(446\) | −5.95310e6 | −1.41712 | ||||||||
\(447\) | −4.99741e6 | −1.18298 | ||||||||
\(448\) | −3.78163e6 | −0.890192 | ||||||||
\(449\) | 1.93885e6 | 0.453866 | 0.226933 | − | 0.973910i | \(-0.427130\pi\) | ||||
0.226933 | + | 0.973910i | \(0.427130\pi\) | |||||||
\(450\) | −85229.6 | −0.0198408 | ||||||||
\(451\) | 265633. | 0.0614952 | ||||||||
\(452\) | −1.49646e7 | −3.44523 | ||||||||
\(453\) | −221577. | −0.0507318 | ||||||||
\(454\) | −9.65681e6 | −2.19884 | ||||||||
\(455\) | −1.24565e6 | −0.282077 | ||||||||
\(456\) | −7.59688e6 | −1.71090 | ||||||||
\(457\) | −6.52362e6 | −1.46116 | −0.730581 | − | 0.682826i | \(-0.760751\pi\) | ||||
−0.730581 | + | 0.682826i | \(0.760751\pi\) | |||||||
\(458\) | 1.52893e7 | 3.40584 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.63784e7 | 3.60891 | ||||||||
\(461\) | 1.85704e6 | 0.406976 | 0.203488 | − | 0.979077i | \(-0.434772\pi\) | ||||
0.203488 | + | 0.979077i | \(0.434772\pi\) | |||||||
\(462\) | 949297. | 0.206917 | ||||||||
\(463\) | 1.55830e6 | 0.337830 | 0.168915 | − | 0.985631i | \(-0.445974\pi\) | ||||
0.168915 | + | 0.985631i | \(0.445974\pi\) | |||||||
\(464\) | −1.19583e7 | −2.57854 | ||||||||
\(465\) | −9.32210e6 | −1.99932 | ||||||||
\(466\) | 95594.4 | 0.0203924 | ||||||||
\(467\) | −289142. | −0.0613507 | −0.0306753 | − | 0.999529i | \(-0.509766\pi\) | ||||
−0.0306753 | + | 0.999529i | \(0.509766\pi\) | |||||||
\(468\) | 7.39301e6 | 1.56030 | ||||||||
\(469\) | 3.94878e6 | 0.828954 | ||||||||
\(470\) | 1.27938e7 | 2.67150 | ||||||||
\(471\) | 1.72916e6 | 0.359157 | ||||||||
\(472\) | 1.90274e7 | 3.93119 | ||||||||
\(473\) | 628715. | 0.129211 | ||||||||
\(474\) | 3.40745e6 | 0.696601 | ||||||||
\(475\) | −13003.0 | −0.00264429 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.83992e6 | 0.370257 | ||||||||
\(478\) | −7.62728e6 | −1.52686 | ||||||||
\(479\) | 1.78964e6 | 0.356390 | 0.178195 | − | 0.983995i | \(-0.442974\pi\) | ||||
0.178195 | + | 0.983995i | \(0.442974\pi\) | |||||||
\(480\) | −1.66278e7 | −3.29406 | ||||||||
\(481\) | 743538. | 0.146535 | ||||||||
\(482\) | 1.12769e7 | 2.21091 | ||||||||
\(483\) | 8.63461e6 | 1.68413 | ||||||||
\(484\) | −1.25103e7 | −2.42747 | ||||||||
\(485\) | 4.66652e6 | 0.900822 | ||||||||
\(486\) | 1.01080e7 | 1.94123 | ||||||||
\(487\) | −2.29704e6 | −0.438880 | −0.219440 | − | 0.975626i | \(-0.570423\pi\) | ||||
−0.219440 | + | 0.975626i | \(0.570423\pi\) | |||||||
\(488\) | −5.95219e6 | −1.13143 | ||||||||
\(489\) | 4.18938e6 | 0.792278 | ||||||||
\(490\) | −4.90819e6 | −0.923488 | ||||||||
\(491\) | −5.01563e6 | −0.938905 | −0.469452 | − | 0.882958i | \(-0.655549\pi\) | ||||
−0.469452 | + | 0.882958i | \(0.655549\pi\) | |||||||
\(492\) | −1.33338e7 | −2.48337 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 1.58811e6 | 0.292795 | ||||||||
\(495\) | 845450. | 0.155087 | ||||||||
\(496\) | 1.74477e7 | 3.18444 | ||||||||
\(497\) | −5.39323e6 | −0.979395 | ||||||||
\(498\) | 1.75190e7 | 3.16545 | ||||||||
\(499\) | −6.02420e6 | −1.08305 | −0.541524 | − | 0.840685i | \(-0.682153\pi\) | ||||
−0.541524 | + | 0.840685i | \(0.682153\pi\) | |||||||
\(500\) | −1.37464e7 | −2.45902 | ||||||||
\(501\) | 1.44119e7 | 2.56524 | ||||||||
\(502\) | 1.46947e7 | 2.60256 | ||||||||
\(503\) | −1.65203e6 | −0.291137 | −0.145569 | − | 0.989348i | \(-0.546501\pi\) | ||||
−0.145569 | + | 0.989348i | \(0.546501\pi\) | |||||||
\(504\) | −1.73275e7 | −3.03851 | ||||||||
\(505\) | −5.07516e6 | −0.885566 | ||||||||
\(506\) | 1.54465e6 | 0.268197 | ||||||||
\(507\) | 7.82966e6 | 1.35277 | ||||||||
\(508\) | −1.66147e7 | −2.85649 | ||||||||
\(509\) | −88594.7 | −0.0151570 | −0.00757850 | − | 0.999971i | \(-0.502412\pi\) | ||||
−0.00757850 | + | 0.999971i | \(0.502412\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.38286e6 | −0.742515 | ||||||||
\(512\) | −9.74005e6 | −1.64205 | ||||||||
\(513\) | −2.24164e6 | −0.376072 | ||||||||
\(514\) | 2.21341e6 | 0.369534 | ||||||||
\(515\) | 5.18105e6 | 0.860795 | ||||||||
\(516\) | −3.15592e7 | −5.21797 | ||||||||
\(517\) | 856943. | 0.141002 | ||||||||
\(518\) | −2.94381e6 | −0.482043 | ||||||||
\(519\) | 5.45871e6 | 0.889553 | ||||||||
\(520\) | 6.62163e6 | 1.07388 | ||||||||
\(521\) | −6.98311e6 | −1.12708 | −0.563540 | − | 0.826089i | \(-0.690561\pi\) | ||||
−0.563540 | + | 0.826089i | \(0.690561\pi\) | |||||||
\(522\) | −1.85794e7 | −2.98439 | ||||||||
\(523\) | 4.70205e6 | 0.751680 | 0.375840 | − | 0.926685i | \(-0.377354\pi\) | ||||
0.375840 | + | 0.926685i | \(0.377354\pi\) | |||||||
\(524\) | 5.74681e6 | 0.914321 | ||||||||
\(525\) | −48282.5 | −0.00764524 | ||||||||
\(526\) | 3.22905e6 | 0.508874 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −2.57607e6 | −0.402135 | ||||||||
\(529\) | 7.61351e6 | 1.18289 | ||||||||
\(530\) | 2.78377e6 | 0.430471 | ||||||||
\(531\) | 1.50914e7 | 2.32270 | ||||||||
\(532\) | −4.46560e6 | −0.684071 | ||||||||
\(533\) | 1.65010e6 | 0.251589 | ||||||||
\(534\) | 1.92513e7 | 2.92151 | ||||||||
\(535\) | −2.14276e6 | −0.323661 | ||||||||
\(536\) | −2.09909e7 | −3.15587 | ||||||||
\(537\) | −1.57702e7 | −2.35994 | ||||||||
\(538\) | 271727. | 0.0404741 | ||||||||
\(539\) | −328756. | −0.0487419 | ||||||||
\(540\) | −1.57885e7 | −2.33000 | ||||||||
\(541\) | 1.03093e7 | 1.51439 | 0.757193 | − | 0.653191i | \(-0.226570\pi\) | ||||
0.757193 | + | 0.653191i | \(0.226570\pi\) | |||||||
\(542\) | 1.31908e7 | 1.92874 | ||||||||
\(543\) | 1.73241e6 | 0.252146 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.70686e6 | −0.823011 | ||||||||
\(546\) | 5.89697e6 | 0.846540 | ||||||||
\(547\) | 8.53248e6 | 1.21929 | 0.609645 | − | 0.792675i | \(-0.291312\pi\) | ||||
0.609645 | + | 0.792675i | \(0.291312\pi\) | |||||||
\(548\) | 3.50616e6 | 0.498748 | ||||||||
\(549\) | −4.72091e6 | −0.668491 | ||||||||
\(550\) | −8637.30 | −0.00121751 | ||||||||
\(551\) | −2.83455e6 | −0.397745 | ||||||||
\(552\) | −4.58999e7 | −6.41156 | ||||||||
\(553\) | 1.18572e6 | 0.164881 | ||||||||
\(554\) | 1.30070e7 | 1.80055 | ||||||||
\(555\) | −4.26817e6 | −0.588179 | ||||||||
\(556\) | 8.70424e6 | 1.19411 | ||||||||
\(557\) | −1.10890e7 | −1.51445 | −0.757224 | − | 0.653156i | \(-0.773445\pi\) | ||||
−0.757224 | + | 0.653156i | \(0.773445\pi\) | |||||||
\(558\) | 2.71082e7 | 3.68566 | ||||||||
\(559\) | 3.90553e6 | 0.528629 | ||||||||
\(560\) | −1.33831e7 | −1.80338 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.32068e7 | 1.76383 | ||||||||
\(563\) | −1.18645e7 | −1.57753 | −0.788765 | − | 0.614695i | \(-0.789279\pi\) | ||||
−0.788765 | + | 0.614695i | \(0.789279\pi\) | |||||||
\(564\) | −4.30154e7 | −5.69412 | ||||||||
\(565\) | −1.06306e7 | −1.40099 | ||||||||
\(566\) | 215144. | 0.0282286 | ||||||||
\(567\) | 306652. | 0.0400579 | ||||||||
\(568\) | 2.86693e7 | 3.72861 | ||||||||
\(569\) | 4.61227e6 | 0.597220 | 0.298610 | − | 0.954375i | \(-0.403477\pi\) | ||||
0.298610 | + | 0.954375i | \(0.403477\pi\) | |||||||
\(570\) | −9.11633e6 | −1.17526 | ||||||||
\(571\) | −4.14651e6 | −0.532222 | −0.266111 | − | 0.963942i | \(-0.585739\pi\) | ||||
−0.266111 | + | 0.963942i | \(0.585739\pi\) | |||||||
\(572\) | 749219. | 0.0957456 | ||||||||
\(573\) | 8.97403e6 | 1.14183 | ||||||||
\(574\) | −6.53305e6 | −0.827630 | ||||||||
\(575\) | −78563.1 | −0.00990943 | ||||||||
\(576\) | 1.59440e7 | 2.00236 | ||||||||
\(577\) | 3.84164e6 | 0.480372 | 0.240186 | − | 0.970727i | \(-0.422792\pi\) | ||||
0.240186 | + | 0.970727i | \(0.422792\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.54123e6 | −0.438993 | ||||||||
\(580\) | −1.99645e7 | −2.46427 | ||||||||
\(581\) | 6.09624e6 | 0.749241 | ||||||||
\(582\) | −2.20916e7 | −2.70345 | ||||||||
\(583\) | 186460. | 0.0227204 | ||||||||
\(584\) | 2.32984e7 | 2.82679 | ||||||||
\(585\) | 5.25188e6 | 0.634490 | ||||||||
\(586\) | 4.05068e6 | 0.487286 | ||||||||
\(587\) | 7.59787e6 | 0.910115 | 0.455058 | − | 0.890462i | \(-0.349619\pi\) | ||||
0.455058 | + | 0.890462i | \(0.349619\pi\) | |||||||
\(588\) | 1.65024e7 | 1.96835 | ||||||||
\(589\) | 4.13573e6 | 0.491207 | ||||||||
\(590\) | 2.28330e7 | 2.70044 | ||||||||
\(591\) | 1.74797e7 | 2.05857 | ||||||||
\(592\) | 7.98850e6 | 0.936830 | ||||||||
\(593\) | −5.19082e6 | −0.606176 | −0.303088 | − | 0.952963i | \(-0.598018\pi\) | ||||
−0.303088 | + | 0.952963i | \(0.598018\pi\) | |||||||
\(594\) | −1.48902e6 | −0.173155 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.56156e7 | 1.80070 | ||||||||
\(597\) | 4.97237e6 | 0.570989 | ||||||||
\(598\) | 9.59528e6 | 1.09725 | ||||||||
\(599\) | 2.90719e6 | 0.331059 | 0.165530 | − | 0.986205i | \(-0.447067\pi\) | ||||
0.165530 | + | 0.986205i | \(0.447067\pi\) | |||||||
\(600\) | 256660. | 0.0291059 | ||||||||
\(601\) | 1.62974e7 | 1.84049 | 0.920244 | − | 0.391346i | \(-0.127990\pi\) | ||||
0.920244 | + | 0.391346i | \(0.127990\pi\) | |||||||
\(602\) | −1.54628e7 | −1.73898 | ||||||||
\(603\) | −1.66487e7 | −1.86461 | ||||||||
\(604\) | 692371. | 0.0772230 | ||||||||
\(605\) | −8.88710e6 | −0.987124 | ||||||||
\(606\) | 2.40260e7 | 2.65767 | ||||||||
\(607\) | −5.21457e6 | −0.574443 | −0.287221 | − | 0.957864i | \(-0.592732\pi\) | ||||
−0.287221 | + | 0.957864i | \(0.592732\pi\) | |||||||
\(608\) | 7.37689e6 | 0.809309 | ||||||||
\(609\) | −1.05252e7 | −1.14997 | ||||||||
\(610\) | −7.14268e6 | −0.777206 | ||||||||
\(611\) | 5.32327e6 | 0.576867 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.70208e6 | −0.505404 | −0.252702 | − | 0.967544i | \(-0.581319\pi\) | ||||
−0.252702 | + | 0.967544i | \(0.581319\pi\) | |||||||
\(614\) | −3.97972e6 | −0.426022 | ||||||||
\(615\) | −9.47213e6 | −1.00986 | ||||||||
\(616\) | −1.75600e6 | −0.186454 | ||||||||
\(617\) | −2.49670e6 | −0.264031 | −0.132015 | − | 0.991248i | \(-0.542145\pi\) | ||||
−0.132015 | + | 0.991248i | \(0.542145\pi\) | |||||||
\(618\) | −2.45274e7 | −2.58333 | ||||||||
\(619\) | 1.43885e7 | 1.50935 | 0.754674 | − | 0.656100i | \(-0.227795\pi\) | ||||
0.754674 | + | 0.656100i | \(0.227795\pi\) | |||||||
\(620\) | 2.91291e7 | 3.04332 | ||||||||
\(621\) | −1.35438e7 | −1.40933 | ||||||||
\(622\) | −2.96114e6 | −0.306890 | ||||||||
\(623\) | 6.69906e6 | 0.691502 | ||||||||
\(624\) | −1.60024e7 | −1.64521 | ||||||||
\(625\) | −9.69969e6 | −0.993248 | ||||||||
\(626\) | −1.49567e7 | −1.52546 | ||||||||
\(627\) | −610622. | −0.0620303 | ||||||||
\(628\) | −5.40318e6 | −0.546702 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −2.07932e7 | −2.08723 | ||||||||
\(631\) | 9.85263e6 | 0.985096 | 0.492548 | − | 0.870285i | \(-0.336066\pi\) | ||||
0.492548 | + | 0.870285i | \(0.336066\pi\) | |||||||
\(632\) | −6.30307e6 | −0.627710 | ||||||||
\(633\) | 3.05383e6 | 0.302925 | ||||||||
\(634\) | −1.69886e7 | −1.67855 | ||||||||
\(635\) | −1.18028e7 | −1.16159 | ||||||||
\(636\) | −9.35963e6 | −0.917521 | ||||||||
\(637\) | −2.04221e6 | −0.199413 | ||||||||
\(638\) | −1.88287e6 | −0.183133 | ||||||||
\(639\) | 2.27388e7 | 2.20300 | ||||||||
\(640\) | 2.92347e6 | 0.282129 | ||||||||
\(641\) | −1.65245e6 | −0.158849 | −0.0794243 | − | 0.996841i | \(-0.525308\pi\) | ||||
−0.0794243 | + | 0.996841i | \(0.525308\pi\) | |||||||
\(642\) | 1.01440e7 | 0.971337 | ||||||||
\(643\) | −1.26355e7 | −1.20522 | −0.602609 | − | 0.798037i | \(-0.705872\pi\) | ||||
−0.602609 | + | 0.798037i | \(0.705872\pi\) | |||||||
\(644\) | −2.69809e7 | −2.56355 | ||||||||
\(645\) | −2.24191e7 | −2.12187 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.03508e6 | 0.191126 | 0.0955630 | − | 0.995423i | \(-0.469535\pi\) | ||||
0.0955630 | + | 0.995423i | \(0.469535\pi\) | |||||||
\(648\) | −1.63010e6 | −0.152503 | ||||||||
\(649\) | 1.52938e6 | 0.142529 | ||||||||
\(650\) | −53654.3 | −0.00498105 | ||||||||
\(651\) | 1.53568e7 | 1.42019 | ||||||||
\(652\) | −1.30907e7 | −1.20599 | ||||||||
\(653\) | −1.28934e7 | −1.18328 | −0.591638 | − | 0.806204i | \(-0.701518\pi\) | ||||
−0.591638 | + | 0.806204i | \(0.701518\pi\) | |||||||
\(654\) | 2.70166e7 | 2.46994 | ||||||||
\(655\) | 4.08244e6 | 0.371806 | ||||||||
\(656\) | 1.77285e7 | 1.60847 | ||||||||
\(657\) | 1.84789e7 | 1.67018 | ||||||||
\(658\) | −2.10759e7 | −1.89767 | ||||||||
\(659\) | 9.82029e6 | 0.880868 | 0.440434 | − | 0.897785i | \(-0.354825\pi\) | ||||
0.440434 | + | 0.897785i | \(0.354825\pi\) | |||||||
\(660\) | −4.30078e6 | −0.384315 | ||||||||
\(661\) | 5.98007e6 | 0.532356 | 0.266178 | − | 0.963924i | \(-0.414239\pi\) | ||||
0.266178 | + | 0.963924i | \(0.414239\pi\) | |||||||
\(662\) | −2.46808e7 | −2.18884 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.24064e7 | −2.85240 | ||||||||
\(665\) | −3.17229e6 | −0.278176 | ||||||||
\(666\) | 1.24116e7 | 1.08428 | ||||||||
\(667\) | −1.71262e7 | −1.49055 | ||||||||
\(668\) | −4.50336e7 | −3.90477 | ||||||||
\(669\) | 1.42187e7 | 1.22827 | ||||||||
\(670\) | −2.51893e7 | −2.16785 | ||||||||
\(671\) | −478425. | −0.0410211 | ||||||||
\(672\) | 2.73918e7 | 2.33990 | ||||||||
\(673\) | 4.37408e6 | 0.372262 | 0.186131 | − | 0.982525i | \(-0.440405\pi\) | ||||
0.186131 | + | 0.982525i | \(0.440405\pi\) | |||||||
\(674\) | 7.61655e6 | 0.645815 | ||||||||
\(675\) | 75733.5 | 0.00639777 | ||||||||
\(676\) | −2.44656e7 | −2.05916 | ||||||||
\(677\) | −1.16472e6 | −0.0976674 | −0.0488337 | − | 0.998807i | \(-0.515550\pi\) | ||||
−0.0488337 | + | 0.998807i | \(0.515550\pi\) | |||||||
\(678\) | 5.03258e7 | 4.20452 | ||||||||
\(679\) | −7.68740e6 | −0.639889 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.30649e7 | 1.90583 | ||||||||
\(682\) | 2.74719e6 | 0.226166 | ||||||||
\(683\) | −7.13327e6 | −0.585109 | −0.292555 | − | 0.956249i | \(-0.594505\pi\) | ||||
−0.292555 | + | 0.956249i | \(0.594505\pi\) | |||||||
\(684\) | 1.88278e7 | 1.53872 | ||||||||
\(685\) | 2.49072e6 | 0.202814 | ||||||||
\(686\) | 2.42954e7 | 1.97112 | ||||||||
\(687\) | −3.65179e7 | −2.95199 | ||||||||
\(688\) | 4.19606e7 | 3.37965 | ||||||||
\(689\) | 1.15828e6 | 0.0929534 | ||||||||
\(690\) | −5.50803e7 | −4.40426 | ||||||||
\(691\) | 2.58026e6 | 0.205574 | 0.102787 | − | 0.994703i | \(-0.467224\pi\) | ||||
0.102787 | + | 0.994703i | \(0.467224\pi\) | |||||||
\(692\) | −1.70570e7 | −1.35406 | ||||||||
\(693\) | −1.39275e6 | −0.110164 | ||||||||
\(694\) | −1.03875e7 | −0.818673 | ||||||||
\(695\) | 6.18335e6 | 0.485581 | ||||||||
\(696\) | 5.59500e7 | 4.37801 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 3.15399e7 | 2.45031 | ||||||||
\(699\) | −228323. | −0.0176749 | ||||||||
\(700\) | 150870. | 0.0116375 | ||||||||
\(701\) | 8.38631e6 | 0.644578 | 0.322289 | − | 0.946641i | \(-0.395548\pi\) | ||||
0.322289 | + | 0.946641i | \(0.395548\pi\) | |||||||
\(702\) | −9.24969e6 | −0.708410 | ||||||||
\(703\) | 1.89357e6 | 0.144508 | ||||||||
\(704\) | 1.61579e6 | 0.122872 | ||||||||
\(705\) | −3.05575e7 | −2.31550 | ||||||||
\(706\) | −7.93839e6 | −0.599405 | ||||||||
\(707\) | 8.36056e6 | 0.629052 | ||||||||
\(708\) | −7.67695e7 | −5.75580 | ||||||||
\(709\) | −6.64715e6 | −0.496615 | −0.248307 | − | 0.968681i | \(-0.579874\pi\) | ||||
−0.248307 | + | 0.968681i | \(0.579874\pi\) | |||||||
\(710\) | 3.44035e7 | 2.56128 | ||||||||
\(711\) | −4.99921e6 | −0.370875 | ||||||||
\(712\) | −3.56109e7 | −2.63259 | ||||||||
\(713\) | 2.49878e7 | 1.84079 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 532233. | 0.0389347 | ||||||||
\(716\) | 4.92777e7 | 3.59226 | ||||||||
\(717\) | 1.82175e7 | 1.32340 | ||||||||
\(718\) | −6.07094e6 | −0.439486 | ||||||||
\(719\) | 1.98127e7 | 1.42929 | 0.714647 | − | 0.699485i | \(-0.246587\pi\) | ||||
0.714647 | + | 0.699485i | \(0.246587\pi\) | |||||||
\(720\) | 5.64256e7 | 4.05644 | ||||||||
\(721\) | −8.53501e6 | −0.611457 | ||||||||
\(722\) | −2.19756e7 | −1.56891 | ||||||||
\(723\) | −2.69343e7 | −1.91629 | ||||||||
\(724\) | −5.41334e6 | −0.383812 | ||||||||
\(725\) | 95765.0 | 0.00676646 | ||||||||
\(726\) | 4.20720e7 | 2.96245 | ||||||||
\(727\) | −9.55304e6 | −0.670356 | −0.335178 | − | 0.942155i | \(-0.608797\pi\) | ||||
−0.335178 | + | 0.942155i | \(0.608797\pi\) | |||||||
\(728\) | −1.09081e7 | −0.762821 | ||||||||
\(729\) | −2.33307e7 | −1.62596 | ||||||||
\(730\) | 2.79583e7 | 1.94180 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 2.40152e7 | 1.65656 | ||||||||
\(733\) | −5.29912e6 | −0.364287 | −0.182144 | − | 0.983272i | \(-0.558304\pi\) | ||||
−0.182144 | + | 0.983272i | \(0.558304\pi\) | |||||||
\(734\) | 1.69406e7 | 1.16062 | ||||||||
\(735\) | 1.17230e7 | 0.800426 | ||||||||
\(736\) | 4.45707e7 | 3.03288 | ||||||||
\(737\) | −1.68721e6 | −0.114419 | ||||||||
\(738\) | 2.75445e7 | 1.86163 | ||||||||
\(739\) | −8.93627e6 | −0.601929 | −0.300964 | − | 0.953635i | \(-0.597309\pi\) | ||||
−0.300964 | + | 0.953635i | \(0.597309\pi\) | |||||||
\(740\) | 1.33369e7 | 0.895315 | ||||||||
\(741\) | −3.79314e6 | −0.253778 | ||||||||
\(742\) | −4.58585e6 | −0.305781 | ||||||||
\(743\) | −570526. | −0.0379143 | −0.0189572 | − | 0.999820i | \(-0.506035\pi\) | ||||
−0.0189572 | + | 0.999820i | \(0.506035\pi\) | |||||||
\(744\) | −8.16335e7 | −5.40675 | ||||||||
\(745\) | 1.10931e7 | 0.732252 | ||||||||
\(746\) | 5.00193e7 | 3.29072 | ||||||||
\(747\) | −2.57028e7 | −1.68531 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.52988e6 | 0.229909 | ||||||||
\(750\) | 4.62289e7 | 3.00096 | ||||||||
\(751\) | 6.99921e6 | 0.452845 | 0.226422 | − | 0.974029i | \(-0.427297\pi\) | ||||
0.226422 | + | 0.974029i | \(0.427297\pi\) | |||||||
\(752\) | 5.71927e7 | 3.68804 | ||||||||
\(753\) | −3.50976e7 | −2.25575 | ||||||||
\(754\) | −1.16962e7 | −0.749234 | ||||||||
\(755\) | 491849. | 0.0314025 | ||||||||
\(756\) | 2.60091e7 | 1.65509 | ||||||||
\(757\) | −2.02906e7 | −1.28693 | −0.643465 | − | 0.765476i | \(-0.722504\pi\) | ||||
−0.643465 | + | 0.765476i | \(0.722504\pi\) | |||||||
\(758\) | 2.72085e6 | 0.172001 | ||||||||
\(759\) | −3.68934e6 | −0.232458 | ||||||||
\(760\) | 1.68633e7 | 1.05903 | ||||||||
\(761\) | −1.78173e7 | −1.11527 | −0.557636 | − | 0.830085i | \(-0.688292\pi\) | ||||
−0.557636 | + | 0.830085i | \(0.688292\pi\) | |||||||
\(762\) | 5.58751e7 | 3.48603 | ||||||||
\(763\) | 9.40119e6 | 0.584617 | ||||||||
\(764\) | −2.80415e7 | −1.73807 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.96828e7 | −2.44360 | ||||||||
\(767\) | 9.50043e6 | 0.583116 | ||||||||
\(768\) | 1.92532e7 | 1.17788 | ||||||||
\(769\) | −7.00151e6 | −0.426949 | −0.213475 | − | 0.976949i | \(-0.568478\pi\) | ||||
−0.213475 | + | 0.976949i | \(0.568478\pi\) | |||||||
\(770\) | −2.10721e6 | −0.128080 | ||||||||
\(771\) | −5.28665e6 | −0.320291 | ||||||||
\(772\) | 1.10654e7 | 0.668228 | ||||||||
\(773\) | −1.14209e7 | −0.687469 | −0.343734 | − | 0.939067i | \(-0.611692\pi\) | ||||
−0.343734 | + | 0.939067i | \(0.611692\pi\) | |||||||
\(774\) | 6.51937e7 | 3.91159 | ||||||||
\(775\) | −139725. | −0.00835644 | ||||||||
\(776\) | 4.08647e7 | 2.43609 | ||||||||
\(777\) | 7.03117e6 | 0.417806 | ||||||||
\(778\) | 6.12826e7 | 3.62985 | ||||||||
\(779\) | 4.20230e6 | 0.248109 | ||||||||
\(780\) | −2.67162e7 | −1.57231 | ||||||||
\(781\) | 2.30438e6 | 0.135185 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.65093e7 | 0.962332 | ||||||||
\(784\) | −2.19413e7 | −1.27489 | ||||||||
\(785\) | −3.83833e6 | −0.222315 | ||||||||
\(786\) | −1.93265e7 | −1.11583 | ||||||||
\(787\) | 7.23244e6 | 0.416244 | 0.208122 | − | 0.978103i | \(-0.433265\pi\) | ||||
0.208122 | + | 0.978103i | \(0.433265\pi\) | |||||||
\(788\) | −5.46196e7 | −3.13352 | ||||||||
\(789\) | −7.71245e6 | −0.441062 | ||||||||
\(790\) | −7.56374e6 | −0.431190 | ||||||||
\(791\) | 1.75123e7 | 0.995182 | ||||||||
\(792\) | 7.40360e6 | 0.419401 | ||||||||
\(793\) | −2.97194e6 | −0.167825 | ||||||||
\(794\) | −5.20413e7 | −2.92952 | ||||||||
\(795\) | −6.64893e6 | −0.373107 | ||||||||
\(796\) | −1.55373e7 | −0.869149 | ||||||||
\(797\) | −2.10646e7 | −1.17465 | −0.587324 | − | 0.809352i | \(-0.699819\pi\) | ||||
−0.587324 | + | 0.809352i | \(0.699819\pi\) | |||||||
\(798\) | 1.50178e7 | 0.834831 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −249228. | −0.0137680 | ||||||||
\(801\) | −2.82444e7 | −1.55543 | ||||||||
\(802\) | −4.63665e7 | −2.54547 | ||||||||
\(803\) | 1.87268e6 | 0.102488 | ||||||||
\(804\) | 8.46917e7 | 4.62062 | ||||||||
\(805\) | −1.91668e7 | −1.04246 | ||||||||
\(806\) | 1.70653e7 | 0.925289 | ||||||||
\(807\) | −649009. | −0.0350806 | ||||||||
\(808\) | −4.44431e7 | −2.39484 | ||||||||
\(809\) | 4.12289e6 | 0.221478 | 0.110739 | − | 0.993850i | \(-0.464678\pi\) | ||||
0.110739 | + | 0.993850i | \(0.464678\pi\) | |||||||
\(810\) | −1.95614e6 | −0.104758 | ||||||||
\(811\) | −7.45417e6 | −0.397967 | −0.198984 | − | 0.980003i | \(-0.563764\pi\) | ||||
−0.198984 | + | 0.980003i | \(0.563764\pi\) | |||||||
\(812\) | 3.28885e7 | 1.75047 | ||||||||
\(813\) | −3.15057e7 | −1.67172 | ||||||||
\(814\) | 1.25781e6 | 0.0665357 | ||||||||
\(815\) | −9.29943e6 | −0.490413 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.94621e6 | 0.521318 | ||||||||
\(818\) | 4.13066e7 | 2.15842 | ||||||||
\(819\) | −8.65168e6 | −0.450703 | ||||||||
\(820\) | 2.95979e7 | 1.53719 | ||||||||
\(821\) | 2.38165e7 | 1.23316 | 0.616581 | − | 0.787292i | \(-0.288517\pi\) | ||||
0.616581 | + | 0.787292i | \(0.288517\pi\) | |||||||
\(822\) | −1.17912e7 | −0.608666 | ||||||||
\(823\) | −2.95580e7 | −1.52116 | −0.760582 | − | 0.649242i | \(-0.775086\pi\) | ||||
−0.760582 | + | 0.649242i | \(0.775086\pi\) | |||||||
\(824\) | 4.53704e7 | 2.32785 | ||||||||
\(825\) | 20629.8 | 0.00105526 | ||||||||
\(826\) | −3.76140e7 | −1.91823 | ||||||||
\(827\) | 3.28549e7 | 1.67046 | 0.835231 | − | 0.549899i | \(-0.185334\pi\) | ||||
0.835231 | + | 0.549899i | \(0.185334\pi\) | |||||||
\(828\) | 1.13756e8 | 5.76632 | ||||||||
\(829\) | 351675. | 0.0177728 | 0.00888640 | − | 0.999961i | \(-0.497171\pi\) | ||||
0.00888640 | + | 0.999961i | \(0.497171\pi\) | |||||||
\(830\) | −3.88880e7 | −1.95939 | ||||||||
\(831\) | −3.10668e7 | −1.56061 | ||||||||
\(832\) | 1.00372e7 | 0.502694 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2.92723e7 | −1.45728 | ||||||||
\(835\) | −3.19911e7 | −1.58786 | ||||||||
\(836\) | 1.90803e6 | 0.0944214 | ||||||||
\(837\) | −2.40878e7 | −1.18846 | ||||||||
\(838\) | −6.22965e7 | −3.06446 | ||||||||
\(839\) | 3.05399e7 | 1.49783 | 0.748915 | − | 0.662666i | \(-0.230575\pi\) | ||||
0.748915 | + | 0.662666i | \(0.230575\pi\) | |||||||
\(840\) | 6.26166e7 | 3.06190 | ||||||||
\(841\) | 364895. | 0.0177901 | ||||||||
\(842\) | −4.74944e7 | −2.30867 | ||||||||
\(843\) | −3.15439e7 | −1.52878 | ||||||||
\(844\) | −9.54241e6 | −0.461107 | ||||||||
\(845\) | −1.73800e7 | −0.837351 | ||||||||
\(846\) | 8.88596e7 | 4.26853 | ||||||||
\(847\) | 1.46402e7 | 0.701193 | ||||||||
\(848\) | 1.24444e7 | 0.594272 | ||||||||
\(849\) | −513863. | −0.0244669 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.14408e7 | 0.541543 | ||||||||
\(852\) | −1.15672e8 | −5.45919 | ||||||||
\(853\) | −6.72309e6 | −0.316371 | −0.158185 | − | 0.987409i | \(-0.550564\pi\) | ||||
−0.158185 | + | 0.987409i | \(0.550564\pi\) | |||||||
\(854\) | 1.17665e7 | 0.552080 | ||||||||
\(855\) | 1.33749e7 | 0.625715 | ||||||||
\(856\) | −1.87642e7 | −0.875276 | ||||||||
\(857\) | 3.83745e7 | 1.78480 | 0.892402 | − | 0.451241i | \(-0.149019\pi\) | ||||
0.892402 | + | 0.451241i | \(0.149019\pi\) | |||||||
\(858\) | −2.51962e6 | −0.116847 | ||||||||
\(859\) | 2.40545e7 | 1.11228 | 0.556140 | − | 0.831089i | \(-0.312282\pi\) | ||||
0.556140 | + | 0.831089i | \(0.312282\pi\) | |||||||
\(860\) | 7.00539e7 | 3.22988 | ||||||||
\(861\) | 1.56039e7 | 0.717342 | ||||||||
\(862\) | 5.40586e7 | 2.47797 | ||||||||
\(863\) | −367366. | −0.0167908 | −0.00839540 | − | 0.999965i | \(-0.502672\pi\) | ||||
−0.00839540 | + | 0.999965i | \(0.502672\pi\) | |||||||
\(864\) | −4.29654e7 | −1.95810 | ||||||||
\(865\) | −1.21171e7 | −0.550626 | ||||||||
\(866\) | 5.84375e7 | 2.64787 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.79859e7 | −2.16179 | ||||||||
\(869\) | −506628. | −0.0227583 | ||||||||
\(870\) | 6.71405e7 | 3.00737 | ||||||||
\(871\) | −1.04808e7 | −0.468112 | ||||||||
\(872\) | −4.99749e7 | −2.22567 | ||||||||
\(873\) | 3.24114e7 | 1.43934 | ||||||||
\(874\) | 2.44363e7 | 1.08207 | ||||||||
\(875\) | 1.60867e7 | 0.710308 | ||||||||
\(876\) | −9.40016e7 | −4.13881 | ||||||||
\(877\) | −6.61357e6 | −0.290360 | −0.145180 | − | 0.989405i | \(-0.546376\pi\) | ||||
−0.145180 | + | 0.989405i | \(0.546376\pi\) | |||||||
\(878\) | −6.17073e7 | −2.70147 | ||||||||
\(879\) | −9.67487e6 | −0.422351 | ||||||||
\(880\) | 5.71826e6 | 0.248918 | ||||||||
\(881\) | 3432.14 | 0.000148979 0 | 7.44895e−5 | − | 1.00000i | \(-0.499976\pi\) | ||||
7.44895e−5 | 1.00000i | \(0.499976\pi\) | ||||||||
\(882\) | −3.40899e7 | −1.47555 | ||||||||
\(883\) | −4.47460e7 | −1.93131 | −0.965655 | − | 0.259826i | \(-0.916335\pi\) | ||||
−0.965655 | + | 0.259826i | \(0.916335\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.45358e7 | −2.34058 | ||||||||
\(886\) | −8.66460e7 | −3.70821 | ||||||||
\(887\) | −3.38852e7 | −1.44611 | −0.723055 | − | 0.690790i | \(-0.757263\pi\) | ||||
−0.723055 | + | 0.690790i | \(0.757263\pi\) | |||||||
\(888\) | −3.73763e7 | −1.59061 | ||||||||
\(889\) | 1.94434e7 | 0.825120 | ||||||||
\(890\) | −4.27334e7 | −1.80839 | ||||||||
\(891\) | −131024. | −0.00552914 | ||||||||
\(892\) | −4.44298e7 | −1.86966 | ||||||||
\(893\) | 1.35568e7 | 0.568889 | ||||||||
\(894\) | −5.25151e7 | −2.19756 | ||||||||
\(895\) | 3.50061e7 | 1.46078 | ||||||||
\(896\) | −4.81597e6 | −0.200408 | ||||||||
\(897\) | −2.29179e7 | −0.951030 | ||||||||
\(898\) | 2.03743e7 | 0.843125 | ||||||||
\(899\) | −3.04591e7 | −1.25695 | ||||||||
\(900\) | −636095. | −0.0261767 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 2.79140e6 | 0.114237 | ||||||||
\(903\) | 3.69322e7 | 1.50725 | ||||||||
\(904\) | −9.30920e7 | −3.78871 | ||||||||
\(905\) | −3.84555e6 | −0.156076 | ||||||||
\(906\) | −2.32844e6 | −0.0942420 | ||||||||
\(907\) | −1.52397e7 | −0.615117 | −0.307558 | − | 0.951529i | \(-0.599512\pi\) | ||||
−0.307558 | + | 0.951529i | \(0.599512\pi\) | |||||||
\(908\) | −7.20717e7 | −2.90102 | ||||||||
\(909\) | −3.52496e7 | −1.41496 | ||||||||
\(910\) | −1.30899e7 | −0.524001 | ||||||||
\(911\) | −1.28387e7 | −0.512539 | −0.256269 | − | 0.966605i | \(-0.582493\pi\) | ||||
−0.256269 | + | 0.966605i | \(0.582493\pi\) | |||||||
\(912\) | −4.07532e7 | −1.62246 | ||||||||
\(913\) | −2.60476e6 | −0.103417 | ||||||||
\(914\) | −6.85533e7 | −2.71433 | ||||||||
\(915\) | 1.70600e7 | 0.673637 | ||||||||
\(916\) | 1.14109e8 | 4.49346 | ||||||||
\(917\) | −6.72521e6 | −0.264109 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.68255e7 | −1.43833 | −0.719167 | − | 0.694837i | \(-0.755477\pi\) | ||||
−0.719167 | + | 0.694837i | \(0.755477\pi\) | |||||||
\(920\) | 1.01887e8 | 3.96870 | ||||||||
\(921\) | 9.50540e6 | 0.369251 | ||||||||
\(922\) | 1.95147e7 | 0.756021 | ||||||||
\(923\) | 1.43147e7 | 0.553066 | ||||||||
\(924\) | 7.08489e6 | 0.272994 | ||||||||
\(925\) | −63974.0 | −0.00245838 | ||||||||
\(926\) | 1.63753e7 | 0.627571 | ||||||||
\(927\) | 3.59851e7 | 1.37538 | ||||||||
\(928\) | −5.43298e7 | −2.07094 | ||||||||
\(929\) | −7.85506e6 | −0.298614 | −0.149307 | − | 0.988791i | \(-0.547704\pi\) | ||||
−0.149307 | + | 0.988791i | \(0.547704\pi\) | |||||||
\(930\) | −9.79610e7 | −3.71403 | ||||||||
\(931\) | −5.20090e6 | −0.196655 | ||||||||
\(932\) | 713450. | 0.0269044 | ||||||||
\(933\) | 7.07256e6 | 0.265994 | ||||||||
\(934\) | −3.03844e6 | −0.113968 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.59906e7 | 1.71585 | ||||||||
\(937\) | 3.43040e7 | 1.27643 | 0.638213 | − | 0.769860i | \(-0.279674\pi\) | ||||
0.638213 | + | 0.769860i | \(0.279674\pi\) | |||||||
\(938\) | 4.14956e7 | 1.53991 | ||||||||
\(939\) | 3.57235e7 | 1.32218 | ||||||||
\(940\) | 9.54840e7 | 3.52461 | ||||||||
\(941\) | −3.64166e7 | −1.34068 | −0.670341 | − | 0.742053i | \(-0.733852\pi\) | ||||
−0.670341 | + | 0.742053i | \(0.733852\pi\) | |||||||
\(942\) | 1.81709e7 | 0.667188 | ||||||||
\(943\) | 2.53900e7 | 0.929787 | ||||||||
\(944\) | 1.02072e8 | 3.72799 | ||||||||
\(945\) | 1.84765e7 | 0.673037 | ||||||||
\(946\) | 6.60683e6 | 0.240030 | ||||||||
\(947\) | 2.86479e7 | 1.03805 | 0.519024 | − | 0.854760i | \(-0.326295\pi\) | ||||
0.519024 | + | 0.854760i | \(0.326295\pi\) | |||||||
\(948\) | 2.54309e7 | 0.919052 | ||||||||
\(949\) | 1.16330e7 | 0.419300 | ||||||||
\(950\) | −136641. | −0.00491216 | ||||||||
\(951\) | 4.05767e7 | 1.45487 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.06993e6 | −0.287831 | −0.143915 | − | 0.989590i | \(-0.545969\pi\) | ||||
−0.143915 | + | 0.989590i | \(0.545969\pi\) | |||||||
\(954\) | 1.93348e7 | 0.687809 | ||||||||
\(955\) | −1.99202e7 | −0.706782 | ||||||||
\(956\) | −5.69247e7 | −2.01445 | ||||||||
\(957\) | 4.49715e6 | 0.158729 | ||||||||
\(958\) | 1.88063e7 | 0.662050 | ||||||||
\(959\) | −4.10309e6 | −0.144067 | ||||||||
\(960\) | −5.76169e7 | −2.01777 | ||||||||
\(961\) | 1.58120e7 | 0.552305 | ||||||||
\(962\) | 7.81345e6 | 0.272211 | ||||||||
\(963\) | −1.48826e7 | −0.517146 | ||||||||
\(964\) | 8.41627e7 | 2.91694 | ||||||||
\(965\) | 7.86070e6 | 0.271733 | ||||||||
\(966\) | 9.07365e7 | 3.12852 | ||||||||
\(967\) | 1.89152e7 | 0.650495 | 0.325248 | − | 0.945629i | \(-0.394552\pi\) | ||||
0.325248 | + | 0.945629i | \(0.394552\pi\) | |||||||
\(968\) | −7.78243e7 | −2.66948 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.90380e7 | 1.67341 | ||||||||
\(971\) | 2.00268e7 | 0.681652 | 0.340826 | − | 0.940126i | \(-0.389293\pi\) | ||||
0.340826 | + | 0.940126i | \(0.389293\pi\) | |||||||
\(972\) | 7.54393e7 | 2.56113 | ||||||||
\(973\) | −1.01862e7 | −0.344928 | ||||||||
\(974\) | −2.41383e7 | −0.815286 | ||||||||
\(975\) | 128151. | 0.00431729 | ||||||||
\(976\) | −3.19302e7 | −1.07295 | ||||||||
\(977\) | 4.96053e7 | 1.66261 | 0.831307 | − | 0.555813i | \(-0.187593\pi\) | ||||
0.831307 | + | 0.555813i | \(0.187593\pi\) | |||||||
\(978\) | 4.40240e7 | 1.47178 | ||||||||
\(979\) | −2.86233e6 | −0.0954472 | ||||||||
\(980\) | −3.66313e7 | −1.21839 | ||||||||
\(981\) | −3.96371e7 | −1.31501 | ||||||||
\(982\) | −5.27066e7 | −1.74416 | ||||||||
\(983\) | 1.22095e7 | 0.403008 | 0.201504 | − | 0.979488i | \(-0.435417\pi\) | ||||
0.201504 | + | 0.979488i | \(0.435417\pi\) | |||||||
\(984\) | −8.29474e7 | −2.73096 | ||||||||
\(985\) | −3.88009e7 | −1.27424 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.03388e7 | 1.64479 | ||||||||
\(988\) | 1.18526e7 | 0.386296 | ||||||||
\(989\) | 6.00944e7 | 1.95363 | ||||||||
\(990\) | 8.88438e6 | 0.288097 | ||||||||
\(991\) | −1.64521e7 | −0.532153 | −0.266077 | − | 0.963952i | \(-0.585727\pi\) | ||||
−0.266077 | + | 0.963952i | \(0.585727\pi\) | |||||||
\(992\) | 7.92696e7 | 2.55757 | ||||||||
\(993\) | 5.89492e7 | 1.89716 | ||||||||
\(994\) | −5.66746e7 | −1.81938 | ||||||||
\(995\) | −1.10375e7 | −0.353437 | ||||||||
\(996\) | 1.30750e8 | 4.17630 | ||||||||
\(997\) | −5.49706e6 | −0.175143 | −0.0875714 | − | 0.996158i | \(-0.527911\pi\) | ||||
−0.0875714 | + | 0.996158i | \(0.527911\pi\) | |||||||
\(998\) | −6.33051e7 | −2.01193 | ||||||||
\(999\) | −1.10287e7 | −0.349633 |
(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 | 289.6.a.j.1.27 | 28 | ||
17.10 | odd | 16 | 17.6.d.a.15.1 | yes | 28 | ||
17.12 | odd | 16 | 17.6.d.a.8.1 | ✓ | 28 | ||
17.16 | even | 2 | inner | 289.6.a.j.1.28 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.6.d.a.8.1 | ✓ | 28 | 17.12 | odd | 16 | ||
17.6.d.a.15.1 | yes | 28 | 17.10 | odd | 16 | ||
289.6.a.j.1.27 | 28 | 1.1 | even | 1 | trivial | ||
289.6.a.j.1.28 | 28 | 17.16 | even | 2 | inner |