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 | 1.12 | ||
Root | \(-20.7673\) 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 | ||||||||
\(3\) | 22.6466 | 1.45278 | 0.726391 | − | 0.687281i | \(-0.241196\pi\) | ||||
0.726391 | + | 0.687281i | \(0.241196\pi\) | |||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 79.6824 | 1.42540 | 0.712701 | − | 0.701468i | \(-0.247472\pi\) | ||||
0.712701 | + | 0.701468i | \(0.247472\pi\) | |||||||
\(6\) | 90.5866 | 1.02727 | ||||||||
\(7\) | 191.779 | 1.47930 | 0.739648 | − | 0.672994i | \(-0.234992\pi\) | ||||
0.739648 | + | 0.672994i | \(0.234992\pi\) | |||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | 269.871 | 1.11058 | ||||||||
\(10\) | 318.730 | 1.00791 | ||||||||
\(11\) | −358.282 | −0.892777 | −0.446388 | − | 0.894839i | \(-0.647290\pi\) | ||||
−0.446388 | + | 0.894839i | \(0.647290\pi\) | |||||||
\(12\) | 362.346 | 0.726391 | ||||||||
\(13\) | −443.782 | −0.728301 | −0.364150 | − | 0.931340i | \(-0.618641\pi\) | ||||
−0.364150 | + | 0.931340i | \(0.618641\pi\) | |||||||
\(14\) | 767.114 | 1.04602 | ||||||||
\(15\) | 1804.54 | 2.07080 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 991.683 | 0.832244 | 0.416122 | − | 0.909309i | \(-0.363389\pi\) | ||||
0.416122 | + | 0.909309i | \(0.363389\pi\) | |||||||
\(18\) | 1079.48 | 0.785298 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 1274.92 | 0.712701 | ||||||||
\(21\) | 4343.14 | 2.14910 | ||||||||
\(22\) | −1433.13 | −0.631289 | ||||||||
\(23\) | 1339.07 | 0.527819 | 0.263910 | − | 0.964547i | \(-0.414988\pi\) | ||||
0.263910 | + | 0.964547i | \(0.414988\pi\) | |||||||
\(24\) | 1449.39 | 0.513636 | ||||||||
\(25\) | 3224.28 | 1.03177 | ||||||||
\(26\) | −1775.13 | −0.514986 | ||||||||
\(27\) | 608.528 | 0.160646 | ||||||||
\(28\) | 3068.46 | 0.739648 | ||||||||
\(29\) | −5075.65 | −1.12072 | −0.560359 | − | 0.828250i | \(-0.689337\pi\) | ||||
−0.560359 | + | 0.828250i | \(0.689337\pi\) | |||||||
\(30\) | 7218.16 | 1.46428 | ||||||||
\(31\) | −6551.33 | −1.22440 | −0.612202 | − | 0.790701i | \(-0.709716\pi\) | ||||
−0.612202 | + | 0.790701i | \(0.709716\pi\) | |||||||
\(32\) | 1024.00 | 0.176777 | ||||||||
\(33\) | −8113.88 | −1.29701 | ||||||||
\(34\) | 3966.73 | 0.588485 | ||||||||
\(35\) | 15281.4 | 2.10859 | ||||||||
\(36\) | 4317.93 | 0.555289 | ||||||||
\(37\) | 13217.2 | 1.58721 | 0.793607 | − | 0.608430i | \(-0.208201\pi\) | ||||
0.793607 | + | 0.608430i | \(0.208201\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10050.2 | −1.05806 | ||||||||
\(40\) | 5099.67 | 0.503956 | ||||||||
\(41\) | −9883.49 | −0.918228 | −0.459114 | − | 0.888377i | \(-0.651833\pi\) | ||||
−0.459114 | + | 0.888377i | \(0.651833\pi\) | |||||||
\(42\) | 17372.6 | 1.51964 | ||||||||
\(43\) | 11277.0 | 0.930084 | 0.465042 | − | 0.885289i | \(-0.346039\pi\) | ||||
0.465042 | + | 0.885289i | \(0.346039\pi\) | |||||||
\(44\) | −5732.51 | −0.446388 | ||||||||
\(45\) | 21503.9 | 1.58302 | ||||||||
\(46\) | 5356.30 | 0.373224 | ||||||||
\(47\) | 28164.4 | 1.85976 | 0.929879 | − | 0.367865i | \(-0.119911\pi\) | ||||
0.929879 | + | 0.367865i | \(0.119911\pi\) | |||||||
\(48\) | 5797.54 | 0.363196 | ||||||||
\(49\) | 19972.0 | 1.18831 | ||||||||
\(50\) | 12897.1 | 0.729572 | ||||||||
\(51\) | 22458.3 | 1.20907 | ||||||||
\(52\) | −7100.50 | −0.364150 | ||||||||
\(53\) | 30630.6 | 1.49784 | 0.748922 | − | 0.662658i | \(-0.230572\pi\) | ||||
0.748922 | + | 0.662658i | \(0.230572\pi\) | |||||||
\(54\) | 2434.11 | 0.113594 | ||||||||
\(55\) | −28548.7 | −1.27257 | ||||||||
\(56\) | 12273.8 | 0.523010 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −20302.6 | −0.792468 | ||||||||
\(59\) | −41141.7 | −1.53869 | −0.769347 | − | 0.638831i | \(-0.779418\pi\) | ||||
−0.769347 | + | 0.638831i | \(0.779418\pi\) | |||||||
\(60\) | 28872.6 | 1.03540 | ||||||||
\(61\) | −16045.6 | −0.552119 | −0.276059 | − | 0.961141i | \(-0.589029\pi\) | ||||
−0.276059 | + | 0.961141i | \(0.589029\pi\) | |||||||
\(62\) | −26205.3 | −0.865785 | ||||||||
\(63\) | 51755.4 | 1.64287 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −35361.6 | −1.03812 | ||||||||
\(66\) | −32455.5 | −0.917125 | ||||||||
\(67\) | 22175.1 | 0.603501 | 0.301750 | − | 0.953387i | \(-0.402429\pi\) | ||||
0.301750 | + | 0.953387i | \(0.402429\pi\) | |||||||
\(68\) | 15866.9 | 0.416122 | ||||||||
\(69\) | 30325.5 | 0.766807 | ||||||||
\(70\) | 61125.5 | 1.49100 | ||||||||
\(71\) | 16579.0 | 0.390312 | 0.195156 | − | 0.980772i | \(-0.437479\pi\) | ||||
0.195156 | + | 0.980772i | \(0.437479\pi\) | |||||||
\(72\) | 17271.7 | 0.392649 | ||||||||
\(73\) | 6083.45 | 0.133611 | 0.0668055 | − | 0.997766i | \(-0.478719\pi\) | ||||
0.0668055 | + | 0.997766i | \(0.478719\pi\) | |||||||
\(74\) | 52868.9 | 1.12233 | ||||||||
\(75\) | 73019.2 | 1.49894 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −68710.7 | −1.32068 | ||||||||
\(78\) | −40200.7 | −0.748164 | ||||||||
\(79\) | −90542.9 | −1.63225 | −0.816125 | − | 0.577876i | \(-0.803882\pi\) | ||||
−0.816125 | + | 0.577876i | \(0.803882\pi\) | |||||||
\(80\) | 20398.7 | 0.356350 | ||||||||
\(81\) | −51797.4 | −0.877194 | ||||||||
\(82\) | −39534.0 | −0.649286 | ||||||||
\(83\) | −100994. | −1.60916 | −0.804582 | − | 0.593842i | \(-0.797610\pi\) | ||||
−0.804582 | + | 0.593842i | \(0.797610\pi\) | |||||||
\(84\) | 69490.3 | 1.07455 | ||||||||
\(85\) | 79019.7 | 1.18628 | ||||||||
\(86\) | 45108.0 | 0.657668 | ||||||||
\(87\) | −114946. | −1.62816 | ||||||||
\(88\) | −22930.0 | −0.315644 | ||||||||
\(89\) | 109943. | 1.47127 | 0.735636 | − | 0.677377i | \(-0.236884\pi\) | ||||
0.735636 | + | 0.677377i | \(0.236884\pi\) | |||||||
\(90\) | 86015.7 | 1.11936 | ||||||||
\(91\) | −85107.8 | −1.07737 | ||||||||
\(92\) | 21425.2 | 0.263910 | ||||||||
\(93\) | −148366. | −1.77879 | ||||||||
\(94\) | 112658. | 1.31505 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 23190.2 | 0.256818 | ||||||||
\(97\) | −81781.7 | −0.882525 | −0.441262 | − | 0.897378i | \(-0.645469\pi\) | ||||
−0.441262 | + | 0.897378i | \(0.645469\pi\) | |||||||
\(98\) | 79888.0 | 0.840266 | ||||||||
\(99\) | −96689.7 | −0.991499 | ||||||||
\(100\) | 51588.5 | 0.515885 | ||||||||
\(101\) | −120671. | −1.17706 | −0.588531 | − | 0.808475i | \(-0.700294\pi\) | ||||
−0.588531 | + | 0.808475i | \(0.700294\pi\) | |||||||
\(102\) | 89833.2 | 0.854941 | ||||||||
\(103\) | 62072.2 | 0.576506 | 0.288253 | − | 0.957554i | \(-0.406926\pi\) | ||||
0.288253 | + | 0.957554i | \(0.406926\pi\) | |||||||
\(104\) | −28402.0 | −0.257493 | ||||||||
\(105\) | 346072. | 3.06332 | ||||||||
\(106\) | 122523. | 1.05914 | ||||||||
\(107\) | 17422.5 | 0.147113 | 0.0735565 | − | 0.997291i | \(-0.476565\pi\) | ||||
0.0735565 | + | 0.997291i | \(0.476565\pi\) | |||||||
\(108\) | 9736.45 | 0.0803232 | ||||||||
\(109\) | −87033.0 | −0.701645 | −0.350823 | − | 0.936442i | \(-0.614098\pi\) | ||||
−0.350823 | + | 0.936442i | \(0.614098\pi\) | |||||||
\(110\) | −114195. | −0.899840 | ||||||||
\(111\) | 299326. | 2.30588 | ||||||||
\(112\) | 49095.3 | 0.369824 | ||||||||
\(113\) | 3534.27 | 0.0260378 | 0.0130189 | − | 0.999915i | \(-0.495856\pi\) | ||||
0.0130189 | + | 0.999915i | \(0.495856\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 106701. | 0.752354 | ||||||||
\(116\) | −81210.4 | −0.560359 | ||||||||
\(117\) | −119764. | −0.808835 | ||||||||
\(118\) | −164567. | −1.08802 | ||||||||
\(119\) | 190184. | 1.23113 | ||||||||
\(120\) | 115490. | 0.732138 | ||||||||
\(121\) | −32685.2 | −0.202949 | ||||||||
\(122\) | −64182.6 | −0.390407 | ||||||||
\(123\) | −223828. | −1.33399 | ||||||||
\(124\) | −104821. | −0.612202 | ||||||||
\(125\) | 7911.08 | 0.0452857 | ||||||||
\(126\) | 207022. | 1.16169 | ||||||||
\(127\) | −228868. | −1.25914 | −0.629572 | − | 0.776942i | \(-0.716770\pi\) | ||||
−0.629572 | + | 0.776942i | \(0.716770\pi\) | |||||||
\(128\) | 16384.0 | 0.0883883 | ||||||||
\(129\) | 255386. | 1.35121 | ||||||||
\(130\) | −141446. | −0.734063 | ||||||||
\(131\) | 21885.7 | 0.111425 | 0.0557125 | − | 0.998447i | \(-0.482257\pi\) | ||||
0.0557125 | + | 0.998447i | \(0.482257\pi\) | |||||||
\(132\) | −129822. | −0.648506 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 88700.2 | 0.426739 | ||||||||
\(135\) | 48489.0 | 0.228986 | ||||||||
\(136\) | 63467.7 | 0.294243 | ||||||||
\(137\) | −34032.4 | −0.154914 | −0.0774571 | − | 0.996996i | \(-0.524680\pi\) | ||||
−0.0774571 | + | 0.996996i | \(0.524680\pi\) | |||||||
\(138\) | 121302. | 0.542214 | ||||||||
\(139\) | 56195.7 | 0.246698 | 0.123349 | − | 0.992363i | \(-0.460636\pi\) | ||||
0.123349 | + | 0.992363i | \(0.460636\pi\) | |||||||
\(140\) | 244502. | 1.05430 | ||||||||
\(141\) | 637830. | 2.70183 | ||||||||
\(142\) | 66315.9 | 0.275992 | ||||||||
\(143\) | 158999. | 0.650210 | ||||||||
\(144\) | 69086.9 | 0.277645 | ||||||||
\(145\) | −404440. | −1.59747 | ||||||||
\(146\) | 24333.8 | 0.0944773 | ||||||||
\(147\) | 452299. | 1.72636 | ||||||||
\(148\) | 211475. | 0.793607 | ||||||||
\(149\) | 38644.7 | 0.142602 | 0.0713009 | − | 0.997455i | \(-0.477285\pi\) | ||||
0.0713009 | + | 0.997455i | \(0.477285\pi\) | |||||||
\(150\) | 292077. | 1.05991 | ||||||||
\(151\) | −177062. | −0.631949 | −0.315974 | − | 0.948768i | \(-0.602331\pi\) | ||||
−0.315974 | + | 0.948768i | \(0.602331\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 267626. | 0.924272 | ||||||||
\(154\) | −274843. | −0.933862 | ||||||||
\(155\) | −522025. | −1.74527 | ||||||||
\(156\) | −160803. | −0.529032 | ||||||||
\(157\) | 34176.2 | 0.110656 | 0.0553280 | − | 0.998468i | \(-0.482380\pi\) | ||||
0.0553280 | + | 0.998468i | \(0.482380\pi\) | |||||||
\(158\) | −362171. | −1.15417 | ||||||||
\(159\) | 693681. | 2.17604 | ||||||||
\(160\) | 81594.8 | 0.251978 | ||||||||
\(161\) | 256806. | 0.780800 | ||||||||
\(162\) | −207190. | −0.620270 | ||||||||
\(163\) | −151256. | −0.445907 | −0.222953 | − | 0.974829i | \(-0.571570\pi\) | ||||
−0.222953 | + | 0.974829i | \(0.571570\pi\) | |||||||
\(164\) | −158136. | −0.459114 | ||||||||
\(165\) | −646533. | −1.84876 | ||||||||
\(166\) | −403976. | −1.13785 | ||||||||
\(167\) | −247523. | −0.686791 | −0.343396 | − | 0.939191i | \(-0.611577\pi\) | ||||
−0.343396 | + | 0.939191i | \(0.611577\pi\) | |||||||
\(168\) | 277961. | 0.759820 | ||||||||
\(169\) | −174351. | −0.469578 | ||||||||
\(170\) | 316079. | 0.838828 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 180432. | 0.465042 | ||||||||
\(173\) | −110496. | −0.280692 | −0.140346 | − | 0.990103i | \(-0.544822\pi\) | ||||
−0.140346 | + | 0.990103i | \(0.544822\pi\) | |||||||
\(174\) | −459786. | −1.15128 | ||||||||
\(175\) | 618348. | 1.52629 | ||||||||
\(176\) | −91720.1 | −0.223194 | ||||||||
\(177\) | −931722. | −2.23539 | ||||||||
\(178\) | 439772. | 1.04035 | ||||||||
\(179\) | −218130. | −0.508842 | −0.254421 | − | 0.967094i | \(-0.581885\pi\) | ||||
−0.254421 | + | 0.967094i | \(0.581885\pi\) | |||||||
\(180\) | 344063. | 0.791510 | ||||||||
\(181\) | 296875. | 0.673561 | 0.336780 | − | 0.941583i | \(-0.390662\pi\) | ||||
0.336780 | + | 0.941583i | \(0.390662\pi\) | |||||||
\(182\) | −340431. | −0.761817 | ||||||||
\(183\) | −363380. | −0.802109 | ||||||||
\(184\) | 85700.8 | 0.186612 | ||||||||
\(185\) | 1.05318e6 | 2.26242 | ||||||||
\(186\) | −593462. | −1.25780 | ||||||||
\(187\) | −355302. | −0.743008 | ||||||||
\(188\) | 450631. | 0.929879 | ||||||||
\(189\) | 116703. | 0.237644 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 108735. | 0.215668 | 0.107834 | − | 0.994169i | \(-0.465609\pi\) | ||||
0.107834 | + | 0.994169i | \(0.465609\pi\) | |||||||
\(192\) | 92760.7 | 0.181598 | ||||||||
\(193\) | 433570. | 0.837849 | 0.418925 | − | 0.908021i | \(-0.362407\pi\) | ||||
0.418925 | + | 0.908021i | \(0.362407\pi\) | |||||||
\(194\) | −327127. | −0.624039 | ||||||||
\(195\) | −800821. | −1.50817 | ||||||||
\(196\) | 319552. | 0.594157 | ||||||||
\(197\) | −228260. | −0.419049 | −0.209524 | − | 0.977803i | \(-0.567192\pi\) | ||||
−0.209524 | + | 0.977803i | \(0.567192\pi\) | |||||||
\(198\) | −386759. | −0.701096 | ||||||||
\(199\) | 914820. | 1.63758 | 0.818791 | − | 0.574092i | \(-0.194645\pi\) | ||||
0.818791 | + | 0.574092i | \(0.194645\pi\) | |||||||
\(200\) | 206354. | 0.364786 | ||||||||
\(201\) | 502191. | 0.876756 | ||||||||
\(202\) | −482684. | −0.832309 | ||||||||
\(203\) | −973401. | −1.65787 | ||||||||
\(204\) | 359333. | 0.604535 | ||||||||
\(205\) | −787540. | −1.30884 | ||||||||
\(206\) | 248289. | 0.407651 | ||||||||
\(207\) | 361377. | 0.586185 | ||||||||
\(208\) | −113608. | −0.182075 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.38429e6 | 2.16610 | ||||||||
\(211\) | 399878. | 0.618332 | 0.309166 | − | 0.951008i | \(-0.399950\pi\) | ||||
0.309166 | + | 0.951008i | \(0.399950\pi\) | |||||||
\(212\) | 490090. | 0.748922 | ||||||||
\(213\) | 375458. | 0.567038 | ||||||||
\(214\) | 69690.0 | 0.104025 | ||||||||
\(215\) | 898577. | 1.32574 | ||||||||
\(216\) | 38945.8 | 0.0567971 | ||||||||
\(217\) | −1.25640e6 | −1.81126 | ||||||||
\(218\) | −348132. | −0.496138 | ||||||||
\(219\) | 137770. | 0.194108 | ||||||||
\(220\) | −456780. | −0.636283 | ||||||||
\(221\) | −440091. | −0.606124 | ||||||||
\(222\) | 1.19730e6 | 1.63050 | ||||||||
\(223\) | 1.20223e6 | 1.61892 | 0.809459 | − | 0.587177i | \(-0.199761\pi\) | ||||
0.809459 | + | 0.587177i | \(0.199761\pi\) | |||||||
\(224\) | 196381. | 0.261505 | ||||||||
\(225\) | 870139. | 1.14586 | ||||||||
\(226\) | 14137.1 | 0.0184115 | ||||||||
\(227\) | 172708. | 0.222458 | 0.111229 | − | 0.993795i | \(-0.464521\pi\) | ||||
0.111229 | + | 0.993795i | \(0.464521\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 106292. | 0.133941 | 0.0669704 | − | 0.997755i | \(-0.478667\pi\) | ||||
0.0669704 | + | 0.997755i | \(0.478667\pi\) | |||||||
\(230\) | 426803. | 0.531995 | ||||||||
\(231\) | −1.55607e6 | −1.91866 | ||||||||
\(232\) | −324842. | −0.396234 | ||||||||
\(233\) | 506211. | 0.610860 | 0.305430 | − | 0.952215i | \(-0.401200\pi\) | ||||
0.305430 | + | 0.952215i | \(0.401200\pi\) | |||||||
\(234\) | −479054. | −0.571933 | ||||||||
\(235\) | 2.24421e6 | 2.65090 | ||||||||
\(236\) | −658267. | −0.769347 | ||||||||
\(237\) | −2.05049e6 | −2.37130 | ||||||||
\(238\) | 760734. | 0.870544 | ||||||||
\(239\) | −762857. | −0.863871 | −0.431935 | − | 0.901905i | \(-0.642169\pi\) | ||||
−0.431935 | + | 0.901905i | \(0.642169\pi\) | |||||||
\(240\) | 461962. | 0.517700 | ||||||||
\(241\) | 226268. | 0.250947 | 0.125473 | − | 0.992097i | \(-0.459955\pi\) | ||||
0.125473 | + | 0.992097i | \(0.459955\pi\) | |||||||
\(242\) | −130741. | −0.143507 | ||||||||
\(243\) | −1.32091e6 | −1.43502 | ||||||||
\(244\) | −256730. | −0.276059 | ||||||||
\(245\) | 1.59142e6 | 1.69383 | ||||||||
\(246\) | −895312. | −0.943271 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −419285. | −0.432892 | ||||||||
\(249\) | −2.28717e6 | −2.33777 | ||||||||
\(250\) | 31644.3 | 0.0320218 | ||||||||
\(251\) | −1.07704e6 | −1.07906 | −0.539532 | − | 0.841965i | \(-0.681399\pi\) | ||||
−0.539532 | + | 0.841965i | \(0.681399\pi\) | |||||||
\(252\) | 828086. | 0.821437 | ||||||||
\(253\) | −479766. | −0.471225 | ||||||||
\(254\) | −915471. | −0.890349 | ||||||||
\(255\) | 1.78953e6 | 1.72341 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 464815. | 0.438983 | 0.219491 | − | 0.975614i | \(-0.429560\pi\) | ||||
0.219491 | + | 0.975614i | \(0.429560\pi\) | |||||||
\(258\) | 1.02154e6 | 0.955449 | ||||||||
\(259\) | 2.53478e6 | 2.34796 | ||||||||
\(260\) | −565785. | −0.519061 | ||||||||
\(261\) | −1.36977e6 | −1.24465 | ||||||||
\(262\) | 87543.0 | 0.0787894 | ||||||||
\(263\) | 1.47729e6 | 1.31697 | 0.658484 | − | 0.752594i | \(-0.271198\pi\) | ||||
0.658484 | + | 0.752594i | \(0.271198\pi\) | |||||||
\(264\) | −519288. | −0.458563 | ||||||||
\(265\) | 2.44072e6 | 2.13503 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.48984e6 | 2.13744 | ||||||||
\(268\) | 354801. | 0.301750 | ||||||||
\(269\) | −620419. | −0.522762 | −0.261381 | − | 0.965236i | \(-0.584178\pi\) | ||||
−0.261381 | + | 0.965236i | \(0.584178\pi\) | |||||||
\(270\) | 193956. | 0.161917 | ||||||||
\(271\) | −1.51293e6 | −1.25139 | −0.625697 | − | 0.780066i | \(-0.715186\pi\) | ||||
−0.625697 | + | 0.780066i | \(0.715186\pi\) | |||||||
\(272\) | 253871. | 0.208061 | ||||||||
\(273\) | −1.92741e6 | −1.56519 | ||||||||
\(274\) | −136130. | −0.109541 | ||||||||
\(275\) | −1.15520e6 | −0.921141 | ||||||||
\(276\) | 485209. | 0.383403 | ||||||||
\(277\) | 2.23980e6 | 1.75392 | 0.876961 | − | 0.480562i | \(-0.159567\pi\) | ||||
0.876961 | + | 0.480562i | \(0.159567\pi\) | |||||||
\(278\) | 224783. | 0.174442 | ||||||||
\(279\) | −1.76801e6 | −1.35980 | ||||||||
\(280\) | 978008. | 0.745499 | ||||||||
\(281\) | −419780. | −0.317144 | −0.158572 | − | 0.987347i | \(-0.550689\pi\) | ||||
−0.158572 | + | 0.987347i | \(0.550689\pi\) | |||||||
\(282\) | 2.55132e6 | 1.91048 | ||||||||
\(283\) | −1.21876e6 | −0.904587 | −0.452294 | − | 0.891869i | \(-0.649394\pi\) | ||||
−0.452294 | + | 0.891869i | \(0.649394\pi\) | |||||||
\(284\) | 265264. | 0.195156 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 635995. | 0.459768 | ||||||||
\(287\) | −1.89544e6 | −1.35833 | ||||||||
\(288\) | 276347. | 0.196324 | ||||||||
\(289\) | −436422. | −0.307370 | ||||||||
\(290\) | −1.61776e6 | −1.12959 | ||||||||
\(291\) | −1.85208e6 | −1.28212 | ||||||||
\(292\) | 97335.1 | 0.0668055 | ||||||||
\(293\) | 714114. | 0.485957 | 0.242979 | − | 0.970032i | \(-0.421875\pi\) | ||||
0.242979 | + | 0.970032i | \(0.421875\pi\) | |||||||
\(294\) | 1.80920e6 | 1.22072 | ||||||||
\(295\) | −3.27827e6 | −2.19326 | ||||||||
\(296\) | 845902. | 0.561165 | ||||||||
\(297\) | −218024. | −0.143421 | ||||||||
\(298\) | 154579. | 0.100835 | ||||||||
\(299\) | −594256. | −0.384411 | ||||||||
\(300\) | 1.16831e6 | 0.749469 | ||||||||
\(301\) | 2.16268e6 | 1.37587 | ||||||||
\(302\) | −708246. | −0.446855 | ||||||||
\(303\) | −2.73279e6 | −1.71002 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.27856e6 | −0.786991 | ||||||||
\(306\) | 1.07050e6 | 0.653559 | ||||||||
\(307\) | 254547. | 0.154143 | 0.0770713 | − | 0.997026i | \(-0.475443\pi\) | ||||
0.0770713 | + | 0.997026i | \(0.475443\pi\) | |||||||
\(308\) | −1.09937e6 | −0.660340 | ||||||||
\(309\) | 1.40573e6 | 0.837538 | ||||||||
\(310\) | −2.08810e6 | −1.23409 | ||||||||
\(311\) | −2.39467e6 | −1.40392 | −0.701962 | − | 0.712214i | \(-0.747693\pi\) | ||||
−0.701962 | + | 0.712214i | \(0.747693\pi\) | |||||||
\(312\) | −643210. | −0.374082 | ||||||||
\(313\) | 567326. | 0.327320 | 0.163660 | − | 0.986517i | \(-0.447670\pi\) | ||||
0.163660 | + | 0.986517i | \(0.447670\pi\) | |||||||
\(314\) | 136705. | 0.0782456 | ||||||||
\(315\) | 4.12399e6 | 2.34176 | ||||||||
\(316\) | −1.44869e6 | −0.816125 | ||||||||
\(317\) | 1.17888e6 | 0.658900 | 0.329450 | − | 0.944173i | \(-0.393137\pi\) | ||||
0.329450 | + | 0.944173i | \(0.393137\pi\) | |||||||
\(318\) | 2.77473e6 | 1.53869 | ||||||||
\(319\) | 1.81851e6 | 1.00055 | ||||||||
\(320\) | 326379. | 0.178175 | ||||||||
\(321\) | 394561. | 0.213723 | ||||||||
\(322\) | 1.02722e6 | 0.552109 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −828759. | −0.438597 | ||||||||
\(325\) | −1.43088e6 | −0.751439 | ||||||||
\(326\) | −605025. | −0.315304 | ||||||||
\(327\) | −1.97101e6 | −1.01934 | ||||||||
\(328\) | −632543. | −0.324643 | ||||||||
\(329\) | 5.40134e6 | 2.75113 | ||||||||
\(330\) | −2.58613e6 | −1.30727 | ||||||||
\(331\) | −668070. | −0.335160 | −0.167580 | − | 0.985859i | \(-0.553595\pi\) | ||||
−0.167580 | + | 0.985859i | \(0.553595\pi\) | |||||||
\(332\) | −1.61590e6 | −0.804582 | ||||||||
\(333\) | 3.56694e6 | 1.76273 | ||||||||
\(334\) | −990093. | −0.485635 | ||||||||
\(335\) | 1.76696e6 | 0.860231 | ||||||||
\(336\) | 1.11184e6 | 0.537274 | ||||||||
\(337\) | −2.79679e6 | −1.34148 | −0.670742 | − | 0.741691i | \(-0.734024\pi\) | ||||
−0.670742 | + | 0.741691i | \(0.734024\pi\) | |||||||
\(338\) | −697404. | −0.332042 | ||||||||
\(339\) | 80039.4 | 0.0378272 | ||||||||
\(340\) | 1.26431e6 | 0.593141 | ||||||||
\(341\) | 2.34722e6 | 1.09312 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 606981. | 0.278574 | ||||||||
\(344\) | 721727. | 0.328834 | ||||||||
\(345\) | 2.41641e6 | 1.09301 | ||||||||
\(346\) | −441983. | −0.198479 | ||||||||
\(347\) | 1.46987e6 | 0.655321 | 0.327661 | − | 0.944795i | \(-0.393740\pi\) | ||||
0.327661 | + | 0.944795i | \(0.393740\pi\) | |||||||
\(348\) | −1.83914e6 | −0.814081 | ||||||||
\(349\) | 2.93939e6 | 1.29179 | 0.645897 | − | 0.763424i | \(-0.276483\pi\) | ||||
0.645897 | + | 0.763424i | \(0.276483\pi\) | |||||||
\(350\) | 2.47339e6 | 1.07925 | ||||||||
\(351\) | −270054. | −0.116999 | ||||||||
\(352\) | −366880. | −0.157822 | ||||||||
\(353\) | −2.44075e6 | −1.04253 | −0.521263 | − | 0.853396i | \(-0.674539\pi\) | ||||
−0.521263 | + | 0.853396i | \(0.674539\pi\) | |||||||
\(354\) | −3.72689e6 | −1.58066 | ||||||||
\(355\) | 1.32105e6 | 0.556351 | ||||||||
\(356\) | 1.75909e6 | 0.735636 | ||||||||
\(357\) | 4.30702e6 | 1.78857 | ||||||||
\(358\) | −872521. | −0.359806 | ||||||||
\(359\) | 548005. | 0.224413 | 0.112207 | − | 0.993685i | \(-0.464208\pi\) | ||||
0.112207 | + | 0.993685i | \(0.464208\pi\) | |||||||
\(360\) | 1.37625e6 | 0.559682 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 1.18750e6 | 0.476279 | ||||||||
\(363\) | −740210. | −0.294841 | ||||||||
\(364\) | −1.36172e6 | −0.538686 | ||||||||
\(365\) | 484743. | 0.190449 | ||||||||
\(366\) | −1.45352e6 | −0.567177 | ||||||||
\(367\) | 3.61119e6 | 1.39954 | 0.699771 | − | 0.714368i | \(-0.253286\pi\) | ||||
0.699771 | + | 0.714368i | \(0.253286\pi\) | |||||||
\(368\) | 342803. | 0.131955 | ||||||||
\(369\) | −2.66726e6 | −1.01976 | ||||||||
\(370\) | 4.21272e6 | 1.59977 | ||||||||
\(371\) | 5.87430e6 | 2.21575 | ||||||||
\(372\) | −2.37385e6 | −0.889397 | ||||||||
\(373\) | −502139. | −0.186875 | −0.0934377 | − | 0.995625i | \(-0.529786\pi\) | ||||
−0.0934377 | + | 0.995625i | \(0.529786\pi\) | |||||||
\(374\) | −1.42121e6 | −0.525386 | ||||||||
\(375\) | 179159. | 0.0657902 | ||||||||
\(376\) | 1.80252e6 | 0.657524 | ||||||||
\(377\) | 2.25248e6 | 0.816220 | ||||||||
\(378\) | 466811. | 0.168039 | ||||||||
\(379\) | 240568. | 0.0860278 | 0.0430139 | − | 0.999074i | \(-0.486304\pi\) | ||||
0.0430139 | + | 0.999074i | \(0.486304\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.18309e6 | −1.82926 | ||||||||
\(382\) | 434939. | 0.152500 | ||||||||
\(383\) | 2.57949e6 | 0.898540 | 0.449270 | − | 0.893396i | \(-0.351684\pi\) | ||||
0.449270 | + | 0.893396i | \(0.351684\pi\) | |||||||
\(384\) | 371043. | 0.128409 | ||||||||
\(385\) | −5.47504e6 | −1.88250 | ||||||||
\(386\) | 1.73428e6 | 0.592449 | ||||||||
\(387\) | 3.04333e6 | 1.03293 | ||||||||
\(388\) | −1.30851e6 | −0.441262 | ||||||||
\(389\) | 263297. | 0.0882209 | 0.0441104 | − | 0.999027i | \(-0.485955\pi\) | ||||
0.0441104 | + | 0.999027i | \(0.485955\pi\) | |||||||
\(390\) | −3.20328e6 | −1.06643 | ||||||||
\(391\) | 1.32794e6 | 0.439274 | ||||||||
\(392\) | 1.27821e6 | 0.420133 | ||||||||
\(393\) | 495639. | 0.161876 | ||||||||
\(394\) | −913041. | −0.296312 | ||||||||
\(395\) | −7.21467e6 | −2.32661 | ||||||||
\(396\) | −1.54704e6 | −0.495749 | ||||||||
\(397\) | 3.08689e6 | 0.982981 | 0.491491 | − | 0.870883i | \(-0.336452\pi\) | ||||
0.491491 | + | 0.870883i | \(0.336452\pi\) | |||||||
\(398\) | 3.65928e6 | 1.15794 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 825416. | 0.257943 | ||||||||
\(401\) | −1.67059e6 | −0.518809 | −0.259405 | − | 0.965769i | \(-0.583526\pi\) | ||||
−0.259405 | + | 0.965769i | \(0.583526\pi\) | |||||||
\(402\) | 2.00876e6 | 0.619960 | ||||||||
\(403\) | 2.90736e6 | 0.891735 | ||||||||
\(404\) | −1.93074e6 | −0.588531 | ||||||||
\(405\) | −4.12734e6 | −1.25035 | ||||||||
\(406\) | −3.89360e6 | −1.17229 | ||||||||
\(407\) | −4.73549e6 | −1.41703 | ||||||||
\(408\) | 1.43733e6 | 0.427471 | ||||||||
\(409\) | −6.11240e6 | −1.80677 | −0.903386 | − | 0.428829i | \(-0.858926\pi\) | ||||
−0.903386 | + | 0.428829i | \(0.858926\pi\) | |||||||
\(410\) | −3.15016e6 | −0.925493 | ||||||||
\(411\) | −770720. | −0.225057 | ||||||||
\(412\) | 993155. | 0.288253 | ||||||||
\(413\) | −7.89010e6 | −2.27618 | ||||||||
\(414\) | 1.44551e6 | 0.414495 | ||||||||
\(415\) | −8.04744e6 | −2.29370 | ||||||||
\(416\) | −454432. | −0.128747 | ||||||||
\(417\) | 1.27264e6 | 0.358399 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.09637e6 | 0.305087 | 0.152543 | − | 0.988297i | \(-0.451254\pi\) | ||||
0.152543 | + | 0.988297i | \(0.451254\pi\) | |||||||
\(420\) | 5.53715e6 | 1.53166 | ||||||||
\(421\) | −5.42330e6 | −1.49128 | −0.745638 | − | 0.666351i | \(-0.767855\pi\) | ||||
−0.745638 | + | 0.666351i | \(0.767855\pi\) | |||||||
\(422\) | 1.59951e6 | 0.437227 | ||||||||
\(423\) | 7.60075e6 | 2.06541 | ||||||||
\(424\) | 1.96036e6 | 0.529568 | ||||||||
\(425\) | 3.19747e6 | 0.858685 | ||||||||
\(426\) | 1.50183e6 | 0.400957 | ||||||||
\(427\) | −3.07721e6 | −0.816747 | ||||||||
\(428\) | 278760. | 0.0735565 | ||||||||
\(429\) | 3.60079e6 | 0.944614 | ||||||||
\(430\) | 3.59431e6 | 0.937442 | ||||||||
\(431\) | −5.46122e6 | −1.41611 | −0.708054 | − | 0.706158i | \(-0.750427\pi\) | ||||
−0.708054 | + | 0.706158i | \(0.750427\pi\) | |||||||
\(432\) | 155783. | 0.0401616 | ||||||||
\(433\) | −5.18650e6 | −1.32940 | −0.664699 | − | 0.747112i | \(-0.731440\pi\) | ||||
−0.664699 | + | 0.747112i | \(0.731440\pi\) | |||||||
\(434\) | −5.02562e6 | −1.28075 | ||||||||
\(435\) | −9.15921e6 | −2.32078 | ||||||||
\(436\) | −1.39253e6 | −0.350823 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 551079. | 0.137255 | ||||||||
\(439\) | −429040. | −0.106252 | −0.0531259 | − | 0.998588i | \(-0.516918\pi\) | ||||
−0.0531259 | + | 0.998588i | \(0.516918\pi\) | |||||||
\(440\) | −1.82712e6 | −0.449920 | ||||||||
\(441\) | 5.38986e6 | 1.31972 | ||||||||
\(442\) | −1.76036e6 | −0.428594 | ||||||||
\(443\) | 3.49738e6 | 0.846708 | 0.423354 | − | 0.905964i | \(-0.360853\pi\) | ||||
0.423354 | + | 0.905964i | \(0.360853\pi\) | |||||||
\(444\) | 4.78921e6 | 1.15294 | ||||||||
\(445\) | 8.76052e6 | 2.09715 | ||||||||
\(446\) | 4.80891e6 | 1.14475 | ||||||||
\(447\) | 875174. | 0.207169 | ||||||||
\(448\) | 785525. | 0.184912 | ||||||||
\(449\) | −2.86674e6 | −0.671076 | −0.335538 | − | 0.942027i | \(-0.608918\pi\) | ||||
−0.335538 | + | 0.942027i | \(0.608918\pi\) | |||||||
\(450\) | 3.48056e6 | 0.810247 | ||||||||
\(451\) | 3.54107e6 | 0.819773 | ||||||||
\(452\) | 56548.3 | 0.0130189 | ||||||||
\(453\) | −4.00985e6 | −0.918085 | ||||||||
\(454\) | 690831. | 0.157301 | ||||||||
\(455\) | −6.78159e6 | −1.53569 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.29130e6 | −1.40913 | −0.704563 | − | 0.709642i | \(-0.748857\pi\) | ||||
−0.704563 | + | 0.709642i | \(0.748857\pi\) | |||||||
\(458\) | 425169. | 0.0947105 | ||||||||
\(459\) | 603467. | 0.133697 | ||||||||
\(460\) | 1.70721e6 | 0.376177 | ||||||||
\(461\) | 4.49087e6 | 0.984188 | 0.492094 | − | 0.870542i | \(-0.336232\pi\) | ||||
0.492094 | + | 0.870542i | \(0.336232\pi\) | |||||||
\(462\) | −6.22427e6 | −1.35670 | ||||||||
\(463\) | 6.06753e6 | 1.31541 | 0.657703 | − | 0.753277i | \(-0.271528\pi\) | ||||
0.657703 | + | 0.753277i | \(0.271528\pi\) | |||||||
\(464\) | −1.29937e6 | −0.280180 | ||||||||
\(465\) | −1.18221e7 | −2.53550 | ||||||||
\(466\) | 2.02484e6 | 0.431943 | ||||||||
\(467\) | −6.88549e6 | −1.46097 | −0.730487 | − | 0.682927i | \(-0.760707\pi\) | ||||
−0.730487 | + | 0.682927i | \(0.760707\pi\) | |||||||
\(468\) | −1.91622e6 | −0.404418 | ||||||||
\(469\) | 4.25270e6 | 0.892756 | ||||||||
\(470\) | 8.97684e6 | 1.87447 | ||||||||
\(471\) | 773977. | 0.160759 | ||||||||
\(472\) | −2.63307e6 | −0.544011 | ||||||||
\(473\) | −4.04034e6 | −0.830357 | ||||||||
\(474\) | −8.20197e6 | −1.67677 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.04294e6 | 0.615567 | ||||||||
\(477\) | 8.26631e6 | 1.66347 | ||||||||
\(478\) | −3.05143e6 | −0.610849 | ||||||||
\(479\) | 6.11464e6 | 1.21768 | 0.608839 | − | 0.793294i | \(-0.291636\pi\) | ||||
0.608839 | + | 0.793294i | \(0.291636\pi\) | |||||||
\(480\) | 1.84785e6 | 0.366069 | ||||||||
\(481\) | −5.86556e6 | −1.15597 | ||||||||
\(482\) | 905074. | 0.177446 | ||||||||
\(483\) | 5.81579e6 | 1.13433 | ||||||||
\(484\) | −522963. | −0.101475 | ||||||||
\(485\) | −6.51656e6 | −1.25795 | ||||||||
\(486\) | −5.28364e6 | −1.01471 | ||||||||
\(487\) | −1.92140e6 | −0.367109 | −0.183554 | − | 0.983010i | \(-0.558760\pi\) | ||||
−0.183554 | + | 0.983010i | \(0.558760\pi\) | |||||||
\(488\) | −1.02692e6 | −0.195204 | ||||||||
\(489\) | −3.42545e6 | −0.647806 | ||||||||
\(490\) | 6.36567e6 | 1.19772 | ||||||||
\(491\) | −4.28233e6 | −0.801634 | −0.400817 | − | 0.916158i | \(-0.631274\pi\) | ||||
−0.400817 | + | 0.916158i | \(0.631274\pi\) | |||||||
\(492\) | −3.58125e6 | −0.666993 | ||||||||
\(493\) | −5.03344e6 | −0.932711 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.70447e6 | −1.41328 | ||||||||
\(496\) | −1.67714e6 | −0.306101 | ||||||||
\(497\) | 3.17949e6 | 0.577387 | ||||||||
\(498\) | −9.14870e6 | −1.65305 | ||||||||
\(499\) | 7.37167e6 | 1.32530 | 0.662650 | − | 0.748929i | \(-0.269432\pi\) | ||||
0.662650 | + | 0.748929i | \(0.269432\pi\) | |||||||
\(500\) | 126577. | 0.0226428 | ||||||||
\(501\) | −5.60557e6 | −0.997759 | ||||||||
\(502\) | −4.30816e6 | −0.763014 | ||||||||
\(503\) | 7.06701e6 | 1.24542 | 0.622710 | − | 0.782453i | \(-0.286032\pi\) | ||||
0.622710 | + | 0.782453i | \(0.286032\pi\) | |||||||
\(504\) | 3.31234e6 | 0.580844 | ||||||||
\(505\) | −9.61535e6 | −1.67779 | ||||||||
\(506\) | −1.91906e6 | −0.333206 | ||||||||
\(507\) | −3.94846e6 | −0.682195 | ||||||||
\(508\) | −3.66188e6 | −0.629572 | ||||||||
\(509\) | 8.87828e6 | 1.51892 | 0.759459 | − | 0.650555i | \(-0.225464\pi\) | ||||
0.759459 | + | 0.650555i | \(0.225464\pi\) | |||||||
\(510\) | 7.15812e6 | 1.21864 | ||||||||
\(511\) | 1.16667e6 | 0.197650 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.85926e6 | 0.310408 | ||||||||
\(515\) | 4.94606e6 | 0.821753 | ||||||||
\(516\) | 4.08618e6 | 0.675605 | ||||||||
\(517\) | −1.00908e7 | −1.66035 | ||||||||
\(518\) | 1.01391e7 | 1.66026 | ||||||||
\(519\) | −2.50236e6 | −0.407785 | ||||||||
\(520\) | −2.26314e6 | −0.367031 | ||||||||
\(521\) | 4.73223e6 | 0.763786 | 0.381893 | − | 0.924207i | \(-0.375272\pi\) | ||||
0.381893 | + | 0.924207i | \(0.375272\pi\) | |||||||
\(522\) | −5.47907e6 | −0.880098 | ||||||||
\(523\) | −1.80814e6 | −0.289053 | −0.144526 | − | 0.989501i | \(-0.546166\pi\) | ||||
−0.144526 | + | 0.989501i | \(0.546166\pi\) | |||||||
\(524\) | 350172. | 0.0557125 | ||||||||
\(525\) | 1.40035e7 | 2.21737 | ||||||||
\(526\) | 5.90915e6 | 0.931238 | ||||||||
\(527\) | −6.49684e6 | −1.01900 | ||||||||
\(528\) | −2.07715e6 | −0.324253 | ||||||||
\(529\) | −4.64322e6 | −0.721407 | ||||||||
\(530\) | 9.76289e6 | 1.50969 | ||||||||
\(531\) | −1.11029e7 | −1.70884 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.38611e6 | 0.668747 | ||||||||
\(534\) | 9.95937e6 | 1.51140 | ||||||||
\(535\) | 1.38827e6 | 0.209695 | ||||||||
\(536\) | 1.41920e6 | 0.213370 | ||||||||
\(537\) | −4.93992e6 | −0.739237 | ||||||||
\(538\) | −2.48168e6 | −0.369649 | ||||||||
\(539\) | −7.15561e6 | −1.06090 | ||||||||
\(540\) | 775824. | 0.114493 | ||||||||
\(541\) | 1.16521e6 | 0.171163 | 0.0855817 | − | 0.996331i | \(-0.472725\pi\) | ||||
0.0855817 | + | 0.996331i | \(0.472725\pi\) | |||||||
\(542\) | −6.05170e6 | −0.884870 | ||||||||
\(543\) | 6.72321e6 | 0.978537 | ||||||||
\(544\) | 1.01548e6 | 0.147121 | ||||||||
\(545\) | −6.93500e6 | −1.00013 | ||||||||
\(546\) | −7.70962e6 | −1.10675 | ||||||||
\(547\) | −4.11534e6 | −0.588081 | −0.294040 | − | 0.955793i | \(-0.595000\pi\) | ||||
−0.294040 | + | 0.955793i | \(0.595000\pi\) | |||||||
\(548\) | −544519. | −0.0774571 | ||||||||
\(549\) | −4.33025e6 | −0.613171 | ||||||||
\(550\) | −4.62081e6 | −0.651345 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 1.94083e6 | 0.271107 | ||||||||
\(553\) | −1.73642e7 | −2.41458 | ||||||||
\(554\) | 8.95921e6 | 1.24021 | ||||||||
\(555\) | 2.38510e7 | 3.28680 | ||||||||
\(556\) | 899131. | 0.123349 | ||||||||
\(557\) | 8.90734e6 | 1.21649 | 0.608247 | − | 0.793748i | \(-0.291873\pi\) | ||||
0.608247 | + | 0.793748i | \(0.291873\pi\) | |||||||
\(558\) | −7.07204e6 | −0.961522 | ||||||||
\(559\) | −5.00452e6 | −0.677381 | ||||||||
\(560\) | 3.91203e6 | 0.527148 | ||||||||
\(561\) | −8.04640e6 | −1.07943 | ||||||||
\(562\) | −1.67912e6 | −0.224255 | ||||||||
\(563\) | 4.55469e6 | 0.605603 | 0.302801 | − | 0.953054i | \(-0.402078\pi\) | ||||
0.302801 | + | 0.953054i | \(0.402078\pi\) | |||||||
\(564\) | 1.02053e7 | 1.35091 | ||||||||
\(565\) | 281619. | 0.0371143 | ||||||||
\(566\) | −4.87502e6 | −0.639640 | ||||||||
\(567\) | −9.93364e6 | −1.29763 | ||||||||
\(568\) | 1.06105e6 | 0.137996 | ||||||||
\(569\) | 6.90310e6 | 0.893848 | 0.446924 | − | 0.894572i | \(-0.352519\pi\) | ||||
0.446924 | + | 0.894572i | \(0.352519\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.20907e6 | −0.411897 | −0.205949 | − | 0.978563i | \(-0.566028\pi\) | ||||
−0.205949 | + | 0.978563i | \(0.566028\pi\) | |||||||
\(572\) | 2.54398e6 | 0.325105 | ||||||||
\(573\) | 2.46248e6 | 0.313318 | ||||||||
\(574\) | −7.58177e6 | −0.960485 | ||||||||
\(575\) | 4.31755e6 | 0.544588 | ||||||||
\(576\) | 1.10539e6 | 0.138822 | ||||||||
\(577\) | −6.19764e6 | −0.774973 | −0.387487 | − | 0.921875i | \(-0.626657\pi\) | ||||
−0.387487 | + | 0.921875i | \(0.626657\pi\) | |||||||
\(578\) | −1.74569e6 | −0.217344 | ||||||||
\(579\) | 9.81890e6 | 1.21721 | ||||||||
\(580\) | −6.47104e6 | −0.798737 | ||||||||
\(581\) | −1.93685e7 | −2.38043 | ||||||||
\(582\) | −7.40832e6 | −0.906593 | ||||||||
\(583\) | −1.09744e7 | −1.33724 | ||||||||
\(584\) | 389341. | 0.0472387 | ||||||||
\(585\) | −9.54305e6 | −1.15292 | ||||||||
\(586\) | 2.85645e6 | 0.343624 | ||||||||
\(587\) | 1.05771e7 | 1.26698 | 0.633492 | − | 0.773749i | \(-0.281621\pi\) | ||||
0.633492 | + | 0.773749i | \(0.281621\pi\) | |||||||
\(588\) | 7.23678e6 | 0.863182 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −1.31131e7 | −1.55087 | ||||||||
\(591\) | −5.16933e6 | −0.608787 | ||||||||
\(592\) | 3.38361e6 | 0.396804 | ||||||||
\(593\) | −9.74395e6 | −1.13788 | −0.568942 | − | 0.822377i | \(-0.692647\pi\) | ||||
−0.568942 | + | 0.822377i | \(0.692647\pi\) | |||||||
\(594\) | −872098. | −0.101414 | ||||||||
\(595\) | 1.51543e7 | 1.75486 | ||||||||
\(596\) | 618316. | 0.0713009 | ||||||||
\(597\) | 2.07176e7 | 2.37905 | ||||||||
\(598\) | −2.37703e6 | −0.271820 | ||||||||
\(599\) | 9.74002e6 | 1.10916 | 0.554578 | − | 0.832131i | \(-0.312880\pi\) | ||||
0.554578 | + | 0.832131i | \(0.312880\pi\) | |||||||
\(600\) | 4.67323e6 | 0.529955 | ||||||||
\(601\) | −3.60512e6 | −0.407131 | −0.203565 | − | 0.979061i | \(-0.565253\pi\) | ||||
−0.203565 | + | 0.979061i | \(0.565253\pi\) | |||||||
\(602\) | 8.65074e6 | 0.972886 | ||||||||
\(603\) | 5.98440e6 | 0.670235 | ||||||||
\(604\) | −2.83299e6 | −0.315974 | ||||||||
\(605\) | −2.60444e6 | −0.289284 | ||||||||
\(606\) | −1.09312e7 | −1.20916 | ||||||||
\(607\) | −1.80180e6 | −0.198488 | −0.0992441 | − | 0.995063i | \(-0.531642\pi\) | ||||
−0.0992441 | + | 0.995063i | \(0.531642\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.20443e7 | −2.40853 | ||||||||
\(610\) | −5.11422e6 | −0.556487 | ||||||||
\(611\) | −1.24989e7 | −1.35446 | ||||||||
\(612\) | 4.28202e6 | 0.462136 | ||||||||
\(613\) | −7.30558e6 | −0.785241 | −0.392621 | − | 0.919700i | \(-0.628431\pi\) | ||||
−0.392621 | + | 0.919700i | \(0.628431\pi\) | |||||||
\(614\) | 1.01819e6 | 0.108995 | ||||||||
\(615\) | −1.78351e7 | −1.90147 | ||||||||
\(616\) | −4.39749e6 | −0.466931 | ||||||||
\(617\) | −1.34101e7 | −1.41814 | −0.709072 | − | 0.705136i | \(-0.750886\pi\) | ||||
−0.709072 | + | 0.705136i | \(0.750886\pi\) | |||||||
\(618\) | 5.62290e6 | 0.592229 | ||||||||
\(619\) | 1.77599e7 | 1.86300 | 0.931500 | − | 0.363741i | \(-0.118501\pi\) | ||||
0.931500 | + | 0.363741i | \(0.118501\pi\) | |||||||
\(620\) | −8.35240e6 | −0.872634 | ||||||||
\(621\) | 814864. | 0.0847923 | ||||||||
\(622\) | −9.57866e6 | −0.992725 | ||||||||
\(623\) | 2.10847e7 | 2.17644 | ||||||||
\(624\) | −2.57284e6 | −0.264516 | ||||||||
\(625\) | −9.44551e6 | −0.967220 | ||||||||
\(626\) | 2.26931e6 | 0.231450 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 546820. | 0.0553280 | ||||||||
\(629\) | 1.31073e7 | 1.32095 | ||||||||
\(630\) | 1.64960e7 | 1.65587 | ||||||||
\(631\) | −3.04664e6 | −0.304612 | −0.152306 | − | 0.988333i | \(-0.548670\pi\) | ||||
−0.152306 | + | 0.988333i | \(0.548670\pi\) | |||||||
\(632\) | −5.79474e6 | −0.577087 | ||||||||
\(633\) | 9.05590e6 | 0.898302 | ||||||||
\(634\) | 4.71550e6 | 0.465913 | ||||||||
\(635\) | −1.82367e7 | −1.79479 | ||||||||
\(636\) | 1.10989e7 | 1.08802 | ||||||||
\(637\) | −8.86321e6 | −0.865451 | ||||||||
\(638\) | 7.27405e6 | 0.707497 | ||||||||
\(639\) | 4.47418e6 | 0.433472 | ||||||||
\(640\) | 1.30552e6 | 0.125989 | ||||||||
\(641\) | 6.41199e6 | 0.616379 | 0.308189 | − | 0.951325i | \(-0.400277\pi\) | ||||
0.308189 | + | 0.951325i | \(0.400277\pi\) | |||||||
\(642\) | 1.57824e6 | 0.151125 | ||||||||
\(643\) | 7.29876e6 | 0.696180 | 0.348090 | − | 0.937461i | \(-0.386830\pi\) | ||||
0.348090 | + | 0.937461i | \(0.386830\pi\) | |||||||
\(644\) | 4.10889e6 | 0.390400 | ||||||||
\(645\) | 2.03498e7 | 1.92602 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.74699e6 | −0.915397 | −0.457699 | − | 0.889107i | \(-0.651326\pi\) | ||||
−0.457699 | + | 0.889107i | \(0.651326\pi\) | |||||||
\(648\) | −3.31504e6 | −0.310135 | ||||||||
\(649\) | 1.47403e7 | 1.37371 | ||||||||
\(650\) | −5.72351e6 | −0.531348 | ||||||||
\(651\) | −2.84533e7 | −2.63136 | ||||||||
\(652\) | −2.42010e6 | −0.222953 | ||||||||
\(653\) | 1.24278e7 | 1.14054 | 0.570269 | − | 0.821458i | \(-0.306839\pi\) | ||||
0.570269 | + | 0.821458i | \(0.306839\pi\) | |||||||
\(654\) | −7.88402e6 | −0.720781 | ||||||||
\(655\) | 1.74391e6 | 0.158826 | ||||||||
\(656\) | −2.53017e6 | −0.229557 | ||||||||
\(657\) | 1.64174e6 | 0.148386 | ||||||||
\(658\) | 2.16053e7 | 1.94534 | ||||||||
\(659\) | 7.62574e6 | 0.684019 | 0.342010 | − | 0.939696i | \(-0.388892\pi\) | ||||
0.342010 | + | 0.939696i | \(0.388892\pi\) | |||||||
\(660\) | −1.03445e7 | −0.924381 | ||||||||
\(661\) | 1.11061e7 | 0.988681 | 0.494340 | − | 0.869268i | \(-0.335410\pi\) | ||||
0.494340 | + | 0.869268i | \(0.335410\pi\) | |||||||
\(662\) | −2.67228e6 | −0.236994 | ||||||||
\(663\) | −9.96658e6 | −0.880566 | ||||||||
\(664\) | −6.46361e6 | −0.568925 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.42677e7 | 1.24644 | ||||||||
\(667\) | −6.79667e6 | −0.591537 | ||||||||
\(668\) | −3.96037e6 | −0.343396 | ||||||||
\(669\) | 2.72264e7 | 2.35194 | ||||||||
\(670\) | 7.06785e6 | 0.608275 | ||||||||
\(671\) | 5.74886e6 | 0.492919 | ||||||||
\(672\) | 4.44738e6 | 0.379910 | ||||||||
\(673\) | −4.52106e6 | −0.384771 | −0.192386 | − | 0.981319i | \(-0.561622\pi\) | ||||
−0.192386 | + | 0.981319i | \(0.561622\pi\) | |||||||
\(674\) | −1.11872e7 | −0.948573 | ||||||||
\(675\) | 1.96207e6 | 0.165750 | ||||||||
\(676\) | −2.78962e6 | −0.234789 | ||||||||
\(677\) | −1.32041e7 | −1.10723 | −0.553616 | − | 0.832772i | \(-0.686752\pi\) | ||||
−0.553616 | + | 0.832772i | \(0.686752\pi\) | |||||||
\(678\) | 320157. | 0.0267479 | ||||||||
\(679\) | −1.56840e7 | −1.30551 | ||||||||
\(680\) | 5.05726e6 | 0.419414 | ||||||||
\(681\) | 3.91125e6 | 0.323183 | ||||||||
\(682\) | 9.38888e6 | 0.772953 | ||||||||
\(683\) | 889471. | 0.0729592 | 0.0364796 | − | 0.999334i | \(-0.488386\pi\) | ||||
0.0364796 | + | 0.999334i | \(0.488386\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.71178e6 | −0.220815 | ||||||||
\(686\) | 2.42792e6 | 0.196981 | ||||||||
\(687\) | 2.40716e6 | 0.194587 | ||||||||
\(688\) | 2.88691e6 | 0.232521 | ||||||||
\(689\) | −1.35933e7 | −1.09088 | ||||||||
\(690\) | 9.66565e6 | 0.772873 | ||||||||
\(691\) | −1.59304e7 | −1.26921 | −0.634604 | − | 0.772838i | \(-0.718837\pi\) | ||||
−0.634604 | + | 0.772838i | \(0.718837\pi\) | |||||||
\(692\) | −1.76793e6 | −0.140346 | ||||||||
\(693\) | −1.85430e7 | −1.46672 | ||||||||
\(694\) | 5.87947e6 | 0.463382 | ||||||||
\(695\) | 4.47781e6 | 0.351644 | ||||||||
\(696\) | −7.35657e6 | −0.575642 | ||||||||
\(697\) | −9.80129e6 | −0.764190 | ||||||||
\(698\) | 1.17576e7 | 0.913437 | ||||||||
\(699\) | 1.14640e7 | 0.887447 | ||||||||
\(700\) | 9.89357e6 | 0.763147 | ||||||||
\(701\) | −1.65606e7 | −1.27286 | −0.636432 | − | 0.771333i | \(-0.719590\pi\) | ||||
−0.636432 | + | 0.771333i | \(0.719590\pi\) | |||||||
\(702\) | −1.08021e6 | −0.0827308 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −1.46752e6 | −0.111597 | ||||||||
\(705\) | 5.08238e7 | 3.85119 | ||||||||
\(706\) | −9.76301e6 | −0.737177 | ||||||||
\(707\) | −2.31421e7 | −1.74122 | ||||||||
\(708\) | −1.49075e7 | −1.11769 | ||||||||
\(709\) | −1.24095e7 | −0.927124 | −0.463562 | − | 0.886064i | \(-0.653429\pi\) | ||||
−0.463562 | + | 0.886064i | \(0.653429\pi\) | |||||||
\(710\) | 5.28421e6 | 0.393400 | ||||||||
\(711\) | −2.44349e7 | −1.81274 | ||||||||
\(712\) | 7.03636e6 | 0.520173 | ||||||||
\(713\) | −8.77271e6 | −0.646264 | ||||||||
\(714\) | 1.72281e7 | 1.26471 | ||||||||
\(715\) | 1.26694e7 | 0.926811 | ||||||||
\(716\) | −3.49008e6 | −0.254421 | ||||||||
\(717\) | −1.72762e7 | −1.25502 | ||||||||
\(718\) | 2.19202e6 | 0.158684 | ||||||||
\(719\) | −2.10450e7 | −1.51819 | −0.759096 | − | 0.650979i | \(-0.774359\pi\) | ||||
−0.759096 | + | 0.650979i | \(0.774359\pi\) | |||||||
\(720\) | 5.50501e6 | 0.395755 | ||||||||
\(721\) | 1.19041e7 | 0.852823 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.12422e6 | 0.364571 | ||||||||
\(724\) | 4.74999e6 | 0.336780 | ||||||||
\(725\) | −1.63653e7 | −1.15632 | ||||||||
\(726\) | −2.96084e6 | −0.208484 | ||||||||
\(727\) | 1.41438e7 | 0.992496 | 0.496248 | − | 0.868181i | \(-0.334711\pi\) | ||||
0.496248 | + | 0.868181i | \(0.334711\pi\) | |||||||
\(728\) | −5.44690e6 | −0.380909 | ||||||||
\(729\) | −1.73274e7 | −1.20758 | ||||||||
\(730\) | 1.93897e6 | 0.134668 | ||||||||
\(731\) | 1.11832e7 | 0.774056 | ||||||||
\(732\) | −5.81408e6 | −0.401055 | ||||||||
\(733\) | 1.46251e7 | 1.00540 | 0.502699 | − | 0.864462i | \(-0.332340\pi\) | ||||
0.502699 | + | 0.864462i | \(0.332340\pi\) | |||||||
\(734\) | 1.44448e7 | 0.989625 | ||||||||
\(735\) | 3.60403e7 | 2.46076 | ||||||||
\(736\) | 1.37121e6 | 0.0933061 | ||||||||
\(737\) | −7.94492e6 | −0.538792 | ||||||||
\(738\) | −1.06691e7 | −0.721083 | ||||||||
\(739\) | −2.91473e7 | −1.96330 | −0.981650 | − | 0.190693i | \(-0.938926\pi\) | ||||
−0.981650 | + | 0.190693i | \(0.938926\pi\) | |||||||
\(740\) | 1.68509e7 | 1.13121 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.34972e7 | 1.56677 | ||||||||
\(743\) | −1.72429e7 | −1.14588 | −0.572939 | − | 0.819598i | \(-0.694197\pi\) | ||||
−0.572939 | + | 0.819598i | \(0.694197\pi\) | |||||||
\(744\) | −9.49540e6 | −0.628899 | ||||||||
\(745\) | 3.07931e6 | 0.203265 | ||||||||
\(746\) | −2.00856e6 | −0.132141 | ||||||||
\(747\) | −2.72553e7 | −1.78710 | ||||||||
\(748\) | −5.68483e6 | −0.371504 | ||||||||
\(749\) | 3.34126e6 | 0.217623 | ||||||||
\(750\) | 716638. | 0.0465207 | ||||||||
\(751\) | 3.59549e6 | 0.232626 | 0.116313 | − | 0.993213i | \(-0.462892\pi\) | ||||
0.116313 | + | 0.993213i | \(0.462892\pi\) | |||||||
\(752\) | 7.21010e6 | 0.464940 | ||||||||
\(753\) | −2.43913e7 | −1.56765 | ||||||||
\(754\) | 9.00992e6 | 0.577155 | ||||||||
\(755\) | −1.41087e7 | −0.900781 | ||||||||
\(756\) | 1.86724e6 | 0.118822 | ||||||||
\(757\) | 1.43218e7 | 0.908358 | 0.454179 | − | 0.890910i | \(-0.349933\pi\) | ||||
0.454179 | + | 0.890910i | \(0.349933\pi\) | |||||||
\(758\) | 962270. | 0.0608309 | ||||||||
\(759\) | −1.08651e7 | −0.684587 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.54776e7 | 1.59477 | 0.797384 | − | 0.603473i | \(-0.206217\pi\) | ||||
0.797384 | + | 0.603473i | \(0.206217\pi\) | |||||||
\(762\) | −2.07323e7 | −1.29348 | ||||||||
\(763\) | −1.66911e7 | −1.03794 | ||||||||
\(764\) | 1.73976e6 | 0.107834 | ||||||||
\(765\) | 2.13251e7 | 1.31746 | ||||||||
\(766\) | 1.03180e7 | 0.635364 | ||||||||
\(767\) | 1.82579e7 | 1.12063 | ||||||||
\(768\) | 1.48417e6 | 0.0907989 | ||||||||
\(769\) | 1.84621e7 | 1.12581 | 0.562905 | − | 0.826522i | \(-0.309684\pi\) | ||||
0.562905 | + | 0.826522i | \(0.309684\pi\) | |||||||
\(770\) | −2.19001e7 | −1.33113 | ||||||||
\(771\) | 1.05265e7 | 0.637747 | ||||||||
\(772\) | 6.93712e6 | 0.418925 | ||||||||
\(773\) | −1.35477e7 | −0.815484 | −0.407742 | − | 0.913097i | \(-0.633684\pi\) | ||||
−0.407742 | + | 0.913097i | \(0.633684\pi\) | |||||||
\(774\) | 1.21733e7 | 0.730392 | ||||||||
\(775\) | −2.11233e7 | −1.26330 | ||||||||
\(776\) | −5.23403e6 | −0.312020 | ||||||||
\(777\) | 5.74042e7 | 3.41108 | ||||||||
\(778\) | 1.05319e6 | 0.0623816 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −1.28131e7 | −0.754083 | ||||||||
\(781\) | −5.93994e6 | −0.348461 | ||||||||
\(782\) | 5.31175e6 | 0.310614 | ||||||||
\(783\) | −3.08868e6 | −0.180040 | ||||||||
\(784\) | 5.11283e6 | 0.297079 | ||||||||
\(785\) | 2.72324e6 | 0.157729 | ||||||||
\(786\) | 1.98255e6 | 0.114464 | ||||||||
\(787\) | 1.58174e7 | 0.910330 | 0.455165 | − | 0.890407i | \(-0.349580\pi\) | ||||
0.455165 | + | 0.890407i | \(0.349580\pi\) | |||||||
\(788\) | −3.65216e6 | −0.209524 | ||||||||
\(789\) | 3.34556e7 | 1.91327 | ||||||||
\(790\) | −2.88587e7 | −1.64516 | ||||||||
\(791\) | 677797. | 0.0385175 | ||||||||
\(792\) | −6.18814e6 | −0.350548 | ||||||||
\(793\) | 7.12076e6 | 0.402109 | ||||||||
\(794\) | 1.23476e7 | 0.695073 | ||||||||
\(795\) | 5.52742e7 | 3.10173 | ||||||||
\(796\) | 1.46371e7 | 0.818791 | ||||||||
\(797\) | −1.51049e7 | −0.842312 | −0.421156 | − | 0.906988i | \(-0.638375\pi\) | ||||
−0.421156 | + | 0.906988i | \(0.638375\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.79302e7 | 1.54777 | ||||||||
\(800\) | 3.30167e6 | 0.182393 | ||||||||
\(801\) | 2.96704e7 | 1.63396 | ||||||||
\(802\) | −6.68234e6 | −0.366854 | ||||||||
\(803\) | −2.17959e6 | −0.119285 | ||||||||
\(804\) | 8.03505e6 | 0.438378 | ||||||||
\(805\) | 2.04629e7 | 1.11295 | ||||||||
\(806\) | 1.16294e7 | 0.630552 | ||||||||
\(807\) | −1.40504e7 | −0.759460 | ||||||||
\(808\) | −7.72294e6 | −0.416154 | ||||||||
\(809\) | 1.01681e7 | 0.546220 | 0.273110 | − | 0.961983i | \(-0.411948\pi\) | ||||
0.273110 | + | 0.961983i | \(0.411948\pi\) | |||||||
\(810\) | −1.65094e7 | −0.884134 | ||||||||
\(811\) | −2.16511e7 | −1.15592 | −0.577961 | − | 0.816065i | \(-0.696151\pi\) | ||||
−0.577961 | + | 0.816065i | \(0.696151\pi\) | |||||||
\(812\) | −1.55744e7 | −0.828937 | ||||||||
\(813\) | −3.42627e7 | −1.81801 | ||||||||
\(814\) | −1.89419e7 | −1.00199 | ||||||||
\(815\) | −1.20525e7 | −0.635597 | ||||||||
\(816\) | 5.74932e6 | 0.302267 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −2.44496e7 | −1.27758 | ||||||||
\(819\) | −2.29681e7 | −1.19651 | ||||||||
\(820\) | −1.26006e7 | −0.654422 | ||||||||
\(821\) | −1.37109e6 | −0.0709920 | −0.0354960 | − | 0.999370i | \(-0.511301\pi\) | ||||
−0.0354960 | + | 0.999370i | \(0.511301\pi\) | |||||||
\(822\) | −3.08288e6 | −0.159139 | ||||||||
\(823\) | 2.72302e7 | 1.40136 | 0.700682 | − | 0.713473i | \(-0.252879\pi\) | ||||
0.700682 | + | 0.713473i | \(0.252879\pi\) | |||||||
\(824\) | 3.97262e6 | 0.203826 | ||||||||
\(825\) | −2.61614e7 | −1.33822 | ||||||||
\(826\) | −3.15604e7 | −1.60950 | ||||||||
\(827\) | −1.63661e7 | −0.832113 | −0.416057 | − | 0.909339i | \(-0.636588\pi\) | ||||
−0.416057 | + | 0.909339i | \(0.636588\pi\) | |||||||
\(828\) | 5.78203e6 | 0.293092 | ||||||||
\(829\) | 4.82305e6 | 0.243745 | 0.121872 | − | 0.992546i | \(-0.461110\pi\) | ||||
0.121872 | + | 0.992546i | \(0.461110\pi\) | |||||||
\(830\) | −3.21898e7 | −1.62189 | ||||||||
\(831\) | 5.07240e7 | 2.54807 | ||||||||
\(832\) | −1.81773e6 | −0.0910376 | ||||||||
\(833\) | 1.98059e7 | 0.988968 | ||||||||
\(834\) | 5.09058e6 | 0.253426 | ||||||||
\(835\) | −1.97232e7 | −0.978953 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.98667e6 | −0.196696 | ||||||||
\(838\) | 4.38549e6 | 0.215729 | ||||||||
\(839\) | 9.95403e6 | 0.488196 | 0.244098 | − | 0.969751i | \(-0.421508\pi\) | ||||
0.244098 | + | 0.969751i | \(0.421508\pi\) | |||||||
\(840\) | 2.21486e7 | 1.08305 | ||||||||
\(841\) | 5.25107e6 | 0.256010 | ||||||||
\(842\) | −2.16932e7 | −1.05449 | ||||||||
\(843\) | −9.50662e6 | −0.460741 | ||||||||
\(844\) | 6.39805e6 | 0.309166 | ||||||||
\(845\) | −1.38927e7 | −0.669337 | ||||||||
\(846\) | 3.04030e7 | 1.46046 | ||||||||
\(847\) | −6.26832e6 | −0.300222 | ||||||||
\(848\) | 7.84144e6 | 0.374461 | ||||||||
\(849\) | −2.76007e7 | −1.31417 | ||||||||
\(850\) | 1.27899e7 | 0.607182 | ||||||||
\(851\) | 1.76988e7 | 0.837762 | ||||||||
\(852\) | 6.00733e6 | 0.283519 | ||||||||
\(853\) | 1.72788e7 | 0.813094 | 0.406547 | − | 0.913630i | \(-0.366733\pi\) | ||||
0.406547 | + | 0.913630i | \(0.366733\pi\) | |||||||
\(854\) | −1.23088e7 | −0.577527 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.11504e6 | 0.0520123 | ||||||||
\(857\) | 7.03868e6 | 0.327370 | 0.163685 | − | 0.986513i | \(-0.447662\pi\) | ||||
0.163685 | + | 0.986513i | \(0.447662\pi\) | |||||||
\(858\) | 1.44032e7 | 0.667943 | ||||||||
\(859\) | −2.23544e7 | −1.03366 | −0.516832 | − | 0.856087i | \(-0.672889\pi\) | ||||
−0.516832 | + | 0.856087i | \(0.672889\pi\) | |||||||
\(860\) | 1.43772e7 | 0.662871 | ||||||||
\(861\) | −4.29254e7 | −1.97336 | ||||||||
\(862\) | −2.18449e7 | −1.00134 | ||||||||
\(863\) | −5.27273e6 | −0.240995 | −0.120498 | − | 0.992714i | \(-0.538449\pi\) | ||||
−0.120498 | + | 0.992714i | \(0.538449\pi\) | |||||||
\(864\) | 623133. | 0.0283986 | ||||||||
\(865\) | −8.80457e6 | −0.400099 | ||||||||
\(866\) | −2.07460e7 | −0.940026 | ||||||||
\(867\) | −9.88349e6 | −0.446542 | ||||||||
\(868\) | −2.01025e7 | −0.905628 | ||||||||
\(869\) | 3.24399e7 | 1.45723 | ||||||||
\(870\) | −3.66368e7 | −1.64104 | ||||||||
\(871\) | −9.84088e6 | −0.439530 | ||||||||
\(872\) | −5.57011e6 | −0.248069 | ||||||||
\(873\) | −2.20705e7 | −0.980113 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.51718e6 | 0.0669909 | ||||||||
\(876\) | 2.20431e6 | 0.0970540 | ||||||||
\(877\) | 5.66757e6 | 0.248827 | 0.124414 | − | 0.992230i | \(-0.460295\pi\) | ||||
0.124414 | + | 0.992230i | \(0.460295\pi\) | |||||||
\(878\) | −1.71616e6 | −0.0751313 | ||||||||
\(879\) | 1.61723e7 | 0.705991 | ||||||||
\(880\) | −7.30848e6 | −0.318141 | ||||||||
\(881\) | 1.22064e7 | 0.529842 | 0.264921 | − | 0.964270i | \(-0.414654\pi\) | ||||
0.264921 | + | 0.964270i | \(0.414654\pi\) | |||||||
\(882\) | 2.15594e7 | 0.933181 | ||||||||
\(883\) | 3.45683e7 | 1.49203 | 0.746013 | − | 0.665931i | \(-0.231965\pi\) | ||||
0.746013 | + | 0.665931i | \(0.231965\pi\) | |||||||
\(884\) | −7.04145e6 | −0.303062 | ||||||||
\(885\) | −7.42418e7 | −3.18633 | ||||||||
\(886\) | 1.39895e7 | 0.598713 | ||||||||
\(887\) | 2.33388e7 | 0.996021 | 0.498011 | − | 0.867171i | \(-0.334064\pi\) | ||||
0.498011 | + | 0.867171i | \(0.334064\pi\) | |||||||
\(888\) | 1.91568e7 | 0.815251 | ||||||||
\(889\) | −4.38919e7 | −1.86265 | ||||||||
\(890\) | 3.50421e7 | 1.48291 | ||||||||
\(891\) | 1.85581e7 | 0.783139 | ||||||||
\(892\) | 1.92356e7 | 0.809459 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 3.50070e6 | 0.146491 | ||||||||
\(895\) | −1.73811e7 | −0.725305 | ||||||||
\(896\) | 3.14210e6 | 0.130752 | ||||||||
\(897\) | −1.34579e7 | −0.558466 | ||||||||
\(898\) | −1.14669e7 | −0.474522 | ||||||||
\(899\) | 3.32522e7 | 1.37221 | ||||||||
\(900\) | 1.39222e7 | 0.572931 | ||||||||
\(901\) | 3.03759e7 | 1.24657 | ||||||||
\(902\) | 1.41643e7 | 0.579667 | ||||||||
\(903\) | 4.89775e7 | 1.99884 | ||||||||
\(904\) | 226193. | 0.00920574 | ||||||||
\(905\) | 2.36557e7 | 0.960095 | ||||||||
\(906\) | −1.60394e7 | −0.649184 | ||||||||
\(907\) | −2.99211e6 | −0.120770 | −0.0603851 | − | 0.998175i | \(-0.519233\pi\) | ||||
−0.0603851 | + | 0.998175i | \(0.519233\pi\) | |||||||
\(908\) | 2.76332e6 | 0.111229 | ||||||||
\(909\) | −3.25655e7 | −1.30722 | ||||||||
\(910\) | −2.71264e7 | −1.08590 | ||||||||
\(911\) | −9.95825e6 | −0.397546 | −0.198773 | − | 0.980046i | \(-0.563696\pi\) | ||||
−0.198773 | + | 0.980046i | \(0.563696\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.61843e7 | 1.43662 | ||||||||
\(914\) | −2.51652e7 | −0.996402 | ||||||||
\(915\) | −2.89550e7 | −1.14333 | ||||||||
\(916\) | 1.70068e6 | 0.0669704 | ||||||||
\(917\) | 4.19722e6 | 0.164831 | ||||||||
\(918\) | 2.41387e6 | 0.0945381 | ||||||||
\(919\) | −5.59078e6 | −0.218365 | −0.109183 | − | 0.994022i | \(-0.534823\pi\) | ||||
−0.109183 | + | 0.994022i | \(0.534823\pi\) | |||||||
\(920\) | 6.82884e6 | 0.265997 | ||||||||
\(921\) | 5.76464e6 | 0.223936 | ||||||||
\(922\) | 1.79635e7 | 0.695926 | ||||||||
\(923\) | −7.35744e6 | −0.284264 | ||||||||
\(924\) | −2.48971e7 | −0.959331 | ||||||||
\(925\) | 4.26160e7 | 1.63764 | ||||||||
\(926\) | 2.42701e7 | 0.930132 | ||||||||
\(927\) | 1.67514e7 | 0.640255 | ||||||||
\(928\) | −5.19747e6 | −0.198117 | ||||||||
\(929\) | 2.46507e7 | 0.937107 | 0.468553 | − | 0.883435i | \(-0.344775\pi\) | ||||
0.468553 | + | 0.883435i | \(0.344775\pi\) | |||||||
\(930\) | −4.72885e7 | −1.79287 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 8.09937e6 | 0.305430 | ||||||||
\(933\) | −5.42311e7 | −2.03960 | ||||||||
\(934\) | −2.75419e7 | −1.03306 | ||||||||
\(935\) | −2.83113e7 | −1.05909 | ||||||||
\(936\) | −7.66487e6 | −0.285966 | ||||||||
\(937\) | −3.14819e7 | −1.17142 | −0.585709 | − | 0.810522i | \(-0.699184\pi\) | ||||
−0.585709 | + | 0.810522i | \(0.699184\pi\) | |||||||
\(938\) | 1.70108e7 | 0.631274 | ||||||||
\(939\) | 1.28480e7 | 0.475524 | ||||||||
\(940\) | 3.59074e7 | 1.32545 | ||||||||
\(941\) | −1.02201e7 | −0.376254 | −0.188127 | − | 0.982145i | \(-0.560242\pi\) | ||||
−0.188127 | + | 0.982145i | \(0.560242\pi\) | |||||||
\(942\) | 3.09591e6 | 0.113674 | ||||||||
\(943\) | −1.32347e7 | −0.484659 | ||||||||
\(944\) | −1.05323e7 | −0.384674 | ||||||||
\(945\) | 9.29914e6 | 0.338738 | ||||||||
\(946\) | −1.61614e7 | −0.587151 | ||||||||
\(947\) | 1.55025e7 | 0.561728 | 0.280864 | − | 0.959748i | \(-0.409379\pi\) | ||||
0.280864 | + | 0.959748i | \(0.409379\pi\) | |||||||
\(948\) | −3.28079e7 | −1.18565 | ||||||||
\(949\) | −2.69972e6 | −0.0973091 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.66976e7 | 0.957239 | ||||||||
\(952\) | 1.21717e7 | 0.435272 | ||||||||
\(953\) | −3.57658e7 | −1.27566 | −0.637832 | − | 0.770176i | \(-0.720168\pi\) | ||||
−0.637832 | + | 0.770176i | \(0.720168\pi\) | |||||||
\(954\) | 3.30652e7 | 1.17625 | ||||||||
\(955\) | 8.66424e6 | 0.307413 | ||||||||
\(956\) | −1.22057e7 | −0.431935 | ||||||||
\(957\) | 4.11832e7 | 1.45358 | ||||||||
\(958\) | 2.44586e7 | 0.861028 | ||||||||
\(959\) | −6.52669e6 | −0.229164 | ||||||||
\(960\) | 7.39139e6 | 0.258850 | ||||||||
\(961\) | 1.42907e7 | 0.499167 | ||||||||
\(962\) | −2.34622e7 | −0.817394 | ||||||||
\(963\) | 4.70182e6 | 0.163380 | ||||||||
\(964\) | 3.62030e6 | 0.125473 | ||||||||
\(965\) | 3.45479e7 | 1.19427 | ||||||||
\(966\) | 2.32632e7 | 0.802095 | ||||||||
\(967\) | 1.25453e7 | 0.431434 | 0.215717 | − | 0.976456i | \(-0.430791\pi\) | ||||
0.215717 | + | 0.976456i | \(0.430791\pi\) | |||||||
\(968\) | −2.09185e6 | −0.0717534 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.60662e7 | −0.889507 | ||||||||
\(971\) | 2.46429e7 | 0.838772 | 0.419386 | − | 0.907808i | \(-0.362245\pi\) | ||||
0.419386 | + | 0.907808i | \(0.362245\pi\) | |||||||
\(972\) | −2.11346e7 | −0.717509 | ||||||||
\(973\) | 1.07771e7 | 0.364940 | ||||||||
\(974\) | −7.68559e6 | −0.259585 | ||||||||
\(975\) | −3.24046e7 | −1.09168 | ||||||||
\(976\) | −4.10769e6 | −0.138030 | ||||||||
\(977\) | 3.71024e7 | 1.24356 | 0.621778 | − | 0.783194i | \(-0.286411\pi\) | ||||
0.621778 | + | 0.783194i | \(0.286411\pi\) | |||||||
\(978\) | −1.37018e7 | −0.458068 | ||||||||
\(979\) | −3.93906e7 | −1.31352 | ||||||||
\(980\) | 2.54627e7 | 0.846913 | ||||||||
\(981\) | −2.34876e7 | −0.779232 | ||||||||
\(982\) | −1.71293e7 | −0.566841 | ||||||||
\(983\) | −1.69378e7 | −0.559079 | −0.279539 | − | 0.960134i | \(-0.590182\pi\) | ||||
−0.279539 | + | 0.960134i | \(0.590182\pi\) | |||||||
\(984\) | −1.43250e7 | −0.471636 | ||||||||
\(985\) | −1.81883e7 | −0.597313 | ||||||||
\(986\) | −2.01337e7 | −0.659526 | ||||||||
\(987\) | 1.22322e8 | 3.99680 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.51007e7 | 0.490916 | ||||||||
\(990\) | −3.08179e7 | −0.999343 | ||||||||
\(991\) | 3.65959e6 | 0.118372 | 0.0591859 | − | 0.998247i | \(-0.481150\pi\) | ||||
0.0591859 | + | 0.998247i | \(0.481150\pi\) | |||||||
\(992\) | −6.70856e6 | −0.216446 | ||||||||
\(993\) | −1.51295e7 | −0.486914 | ||||||||
\(994\) | 1.27180e7 | 0.408274 | ||||||||
\(995\) | 7.28950e7 | 2.33421 | ||||||||
\(996\) | −3.65948e7 | −1.16888 | ||||||||
\(997\) | 2.59425e7 | 0.826559 | 0.413280 | − | 0.910604i | \(-0.364383\pi\) | ||||
0.413280 | + | 0.910604i | \(0.364383\pi\) | |||||||
\(998\) | 2.94867e7 | 0.937129 | ||||||||
\(999\) | 8.04305e6 | 0.254980 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 722.6.a.r.1.12 | 15 | ||
19.9 | even | 9 | 38.6.e.b.5.4 | ✓ | 30 | ||
19.17 | even | 9 | 38.6.e.b.23.4 | yes | 30 | ||
19.18 | odd | 2 | 722.6.a.q.1.4 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.6.e.b.5.4 | ✓ | 30 | 19.9 | even | 9 | ||
38.6.e.b.23.4 | yes | 30 | 19.17 | even | 9 | ||
722.6.a.q.1.4 | 15 | 19.18 | odd | 2 | |||
722.6.a.r.1.12 | 15 | 1.1 | even | 1 | trivial |