Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [38,6,Mod(1,38)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(38, 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("38.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 38.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: | \(6.09458515289\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 454x + 3760 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(14.3926\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 38.1 |
$q$-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 | ||||||||
\(3\) | 18.3926 | 1.17989 | 0.589944 | − | 0.807444i | \(-0.299150\pi\) | ||||
0.589944 | + | 0.807444i | \(0.299150\pi\) | |||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 42.3408 | 0.757415 | 0.378707 | − | 0.925517i | \(-0.376369\pi\) | ||||
0.378707 | + | 0.925517i | \(0.376369\pi\) | |||||||
\(6\) | 73.5705 | 0.834307 | ||||||||
\(7\) | −127.237 | −0.981454 | −0.490727 | − | 0.871313i | \(-0.663269\pi\) | ||||
−0.490727 | + | 0.871313i | \(0.663269\pi\) | |||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | 95.2889 | 0.392135 | ||||||||
\(10\) | 169.363 | 0.535573 | ||||||||
\(11\) | 381.793 | 0.951363 | 0.475681 | − | 0.879618i | \(-0.342202\pi\) | ||||
0.475681 | + | 0.879618i | \(0.342202\pi\) | |||||||
\(12\) | 294.282 | 0.589944 | ||||||||
\(13\) | −726.498 | −1.19227 | −0.596137 | − | 0.802883i | \(-0.703299\pi\) | ||||
−0.596137 | + | 0.802883i | \(0.703299\pi\) | |||||||
\(14\) | −508.950 | −0.693993 | ||||||||
\(15\) | 778.758 | 0.893664 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 1058.96 | 0.888704 | 0.444352 | − | 0.895852i | \(-0.353434\pi\) | ||||
0.444352 | + | 0.895852i | \(0.353434\pi\) | |||||||
\(18\) | 381.156 | 0.277282 | ||||||||
\(19\) | −361.000 | −0.229416 | ||||||||
\(20\) | 677.452 | 0.378707 | ||||||||
\(21\) | −2340.23 | −1.15801 | ||||||||
\(22\) | 1527.17 | 0.672715 | ||||||||
\(23\) | −1566.71 | −0.617545 | −0.308772 | − | 0.951136i | \(-0.599918\pi\) | ||||
−0.308772 | + | 0.951136i | \(0.599918\pi\) | |||||||
\(24\) | 1177.13 | 0.417153 | ||||||||
\(25\) | −1332.26 | −0.426323 | ||||||||
\(26\) | −2905.99 | −0.843065 | ||||||||
\(27\) | −2716.80 | −0.717212 | ||||||||
\(28\) | −2035.80 | −0.490727 | ||||||||
\(29\) | 740.979 | 0.163610 | 0.0818052 | − | 0.996648i | \(-0.473931\pi\) | ||||
0.0818052 | + | 0.996648i | \(0.473931\pi\) | |||||||
\(30\) | 3115.03 | 0.631916 | ||||||||
\(31\) | −7812.75 | −1.46016 | −0.730079 | − | 0.683363i | \(-0.760517\pi\) | ||||
−0.730079 | + | 0.683363i | \(0.760517\pi\) | |||||||
\(32\) | 1024.00 | 0.176777 | ||||||||
\(33\) | 7022.18 | 1.12250 | ||||||||
\(34\) | 4235.84 | 0.628408 | ||||||||
\(35\) | −5387.33 | −0.743368 | ||||||||
\(36\) | 1524.62 | 0.196068 | ||||||||
\(37\) | −457.587 | −0.0549503 | −0.0274751 | − | 0.999622i | \(-0.508747\pi\) | ||||
−0.0274751 | + | 0.999622i | \(0.508747\pi\) | |||||||
\(38\) | −1444.00 | −0.162221 | ||||||||
\(39\) | −13362.2 | −1.40675 | ||||||||
\(40\) | 2709.81 | 0.267786 | ||||||||
\(41\) | −4251.13 | −0.394952 | −0.197476 | − | 0.980308i | \(-0.563274\pi\) | ||||
−0.197476 | + | 0.980308i | \(0.563274\pi\) | |||||||
\(42\) | −9360.93 | −0.818834 | ||||||||
\(43\) | 23354.2 | 1.92617 | 0.963083 | − | 0.269206i | \(-0.0867612\pi\) | ||||
0.963083 | + | 0.269206i | \(0.0867612\pi\) | |||||||
\(44\) | 6108.69 | 0.475681 | ||||||||
\(45\) | 4034.60 | 0.297009 | ||||||||
\(46\) | −6266.83 | −0.436670 | ||||||||
\(47\) | 11928.2 | 0.787645 | 0.393823 | − | 0.919186i | \(-0.371152\pi\) | ||||
0.393823 | + | 0.919186i | \(0.371152\pi\) | |||||||
\(48\) | 4708.51 | 0.294972 | ||||||||
\(49\) | −617.621 | −0.0367478 | ||||||||
\(50\) | −5329.04 | −0.301456 | ||||||||
\(51\) | 19477.0 | 1.04857 | ||||||||
\(52\) | −11624.0 | −0.596137 | ||||||||
\(53\) | 17946.0 | 0.877562 | 0.438781 | − | 0.898594i | \(-0.355410\pi\) | ||||
0.438781 | + | 0.898594i | \(0.355410\pi\) | |||||||
\(54\) | −10867.2 | −0.507146 | ||||||||
\(55\) | 16165.4 | 0.720576 | ||||||||
\(56\) | −8143.20 | −0.346996 | ||||||||
\(57\) | −6639.74 | −0.270685 | ||||||||
\(58\) | 2963.92 | 0.115690 | ||||||||
\(59\) | 47789.2 | 1.78731 | 0.893655 | − | 0.448754i | \(-0.148132\pi\) | ||||
0.893655 | + | 0.448754i | \(0.148132\pi\) | |||||||
\(60\) | 12460.1 | 0.446832 | ||||||||
\(61\) | 8735.48 | 0.300582 | 0.150291 | − | 0.988642i | \(-0.451979\pi\) | ||||
0.150291 | + | 0.988642i | \(0.451979\pi\) | |||||||
\(62\) | −31251.0 | −1.03249 | ||||||||
\(63\) | −12124.3 | −0.384863 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −30760.5 | −0.903046 | ||||||||
\(66\) | 28088.7 | 0.793728 | ||||||||
\(67\) | −1796.43 | −0.0488905 | −0.0244452 | − | 0.999701i | \(-0.507782\pi\) | ||||
−0.0244452 | + | 0.999701i | \(0.507782\pi\) | |||||||
\(68\) | 16943.3 | 0.444352 | ||||||||
\(69\) | −28815.9 | −0.728634 | ||||||||
\(70\) | −21549.3 | −0.525640 | ||||||||
\(71\) | −45723.6 | −1.07645 | −0.538226 | − | 0.842801i | \(-0.680905\pi\) | ||||
−0.538226 | + | 0.842801i | \(0.680905\pi\) | |||||||
\(72\) | 6098.49 | 0.138641 | ||||||||
\(73\) | −73831.2 | −1.62156 | −0.810779 | − | 0.585352i | \(-0.800956\pi\) | ||||
−0.810779 | + | 0.585352i | \(0.800956\pi\) | |||||||
\(74\) | −1830.35 | −0.0388557 | ||||||||
\(75\) | −24503.8 | −0.503014 | ||||||||
\(76\) | −5776.00 | −0.114708 | ||||||||
\(77\) | −48578.4 | −0.933719 | ||||||||
\(78\) | −53448.9 | −0.994722 | ||||||||
\(79\) | 61784.6 | 1.11381 | 0.556907 | − | 0.830575i | \(-0.311988\pi\) | ||||
0.556907 | + | 0.830575i | \(0.311988\pi\) | |||||||
\(80\) | 10839.2 | 0.189354 | ||||||||
\(81\) | −73124.2 | −1.23837 | ||||||||
\(82\) | −17004.5 | −0.279273 | ||||||||
\(83\) | 82509.3 | 1.31464 | 0.657321 | − | 0.753610i | \(-0.271689\pi\) | ||||
0.657321 | + | 0.753610i | \(0.271689\pi\) | |||||||
\(84\) | −37443.7 | −0.579003 | ||||||||
\(85\) | 44837.1 | 0.673117 | ||||||||
\(86\) | 93416.7 | 1.36200 | ||||||||
\(87\) | 13628.5 | 0.193042 | ||||||||
\(88\) | 24434.7 | 0.336358 | ||||||||
\(89\) | −6673.72 | −0.0893085 | −0.0446543 | − | 0.999003i | \(-0.514219\pi\) | ||||
−0.0446543 | + | 0.999003i | \(0.514219\pi\) | |||||||
\(90\) | 16138.4 | 0.210017 | ||||||||
\(91\) | 92437.8 | 1.17016 | ||||||||
\(92\) | −25067.3 | −0.308772 | ||||||||
\(93\) | −143697. | −1.72282 | ||||||||
\(94\) | 47712.8 | 0.556949 | ||||||||
\(95\) | −15285.0 | −0.173763 | ||||||||
\(96\) | 18834.1 | 0.208577 | ||||||||
\(97\) | 163271. | 1.76189 | 0.880944 | − | 0.473220i | \(-0.156908\pi\) | ||||
0.880944 | + | 0.473220i | \(0.156908\pi\) | |||||||
\(98\) | −2470.48 | −0.0259846 | ||||||||
\(99\) | 36380.6 | 0.373063 | ||||||||
\(100\) | −21316.2 | −0.213162 | ||||||||
\(101\) | −30090.6 | −0.293513 | −0.146757 | − | 0.989173i | \(-0.546883\pi\) | ||||
−0.146757 | + | 0.989173i | \(0.546883\pi\) | |||||||
\(102\) | 77908.2 | 0.741451 | ||||||||
\(103\) | 98753.1 | 0.917186 | 0.458593 | − | 0.888646i | \(-0.348354\pi\) | ||||
0.458593 | + | 0.888646i | \(0.348354\pi\) | |||||||
\(104\) | −46495.9 | −0.421533 | ||||||||
\(105\) | −99087.2 | −0.877090 | ||||||||
\(106\) | 71784.0 | 0.620530 | ||||||||
\(107\) | −94862.2 | −0.801002 | −0.400501 | − | 0.916296i | \(-0.631164\pi\) | ||||
−0.400501 | + | 0.916296i | \(0.631164\pi\) | |||||||
\(108\) | −43468.7 | −0.358606 | ||||||||
\(109\) | 166646. | 1.34347 | 0.671734 | − | 0.740792i | \(-0.265550\pi\) | ||||
0.671734 | + | 0.740792i | \(0.265550\pi\) | |||||||
\(110\) | 64661.6 | 0.509524 | ||||||||
\(111\) | −8416.24 | −0.0648351 | ||||||||
\(112\) | −32572.8 | −0.245364 | ||||||||
\(113\) | −167569. | −1.23451 | −0.617257 | − | 0.786761i | \(-0.711756\pi\) | ||||
−0.617257 | + | 0.786761i | \(0.711756\pi\) | |||||||
\(114\) | −26559.0 | −0.191403 | ||||||||
\(115\) | −66335.6 | −0.467737 | ||||||||
\(116\) | 11855.7 | 0.0818052 | ||||||||
\(117\) | −69227.2 | −0.467533 | ||||||||
\(118\) | 191157. | 1.26382 | ||||||||
\(119\) | −134739. | −0.872222 | ||||||||
\(120\) | 49840.5 | 0.315958 | ||||||||
\(121\) | −15285.1 | −0.0949087 | ||||||||
\(122\) | 34941.9 | 0.212543 | ||||||||
\(123\) | −78189.4 | −0.465999 | ||||||||
\(124\) | −125004. | −0.730079 | ||||||||
\(125\) | −188724. | −1.08032 | ||||||||
\(126\) | −48497.3 | −0.272139 | ||||||||
\(127\) | 88964.9 | 0.489451 | 0.244726 | − | 0.969592i | \(-0.421302\pi\) | ||||
0.244726 | + | 0.969592i | \(0.421302\pi\) | |||||||
\(128\) | 16384.0 | 0.0883883 | ||||||||
\(129\) | 429545. | 2.27266 | ||||||||
\(130\) | −123042. | −0.638550 | ||||||||
\(131\) | 375118. | 1.90981 | 0.954904 | − | 0.296915i | \(-0.0959577\pi\) | ||||
0.954904 | + | 0.296915i | \(0.0959577\pi\) | |||||||
\(132\) | 112355. | 0.561251 | ||||||||
\(133\) | 45932.7 | 0.225161 | ||||||||
\(134\) | −7185.73 | −0.0345708 | ||||||||
\(135\) | −115031. | −0.543227 | ||||||||
\(136\) | 67773.4 | 0.314204 | ||||||||
\(137\) | −228683. | −1.04095 | −0.520477 | − | 0.853875i | \(-0.674246\pi\) | ||||
−0.520477 | + | 0.853875i | \(0.674246\pi\) | |||||||
\(138\) | −115264. | −0.515222 | ||||||||
\(139\) | 135000. | 0.592646 | 0.296323 | − | 0.955088i | \(-0.404240\pi\) | ||||
0.296323 | + | 0.955088i | \(0.404240\pi\) | |||||||
\(140\) | −86197.3 | −0.371684 | ||||||||
\(141\) | 219391. | 0.929333 | ||||||||
\(142\) | −182894. | −0.761166 | ||||||||
\(143\) | −277372. | −1.13429 | ||||||||
\(144\) | 24394.0 | 0.0980338 | ||||||||
\(145\) | 31373.6 | 0.123921 | ||||||||
\(146\) | −295325. | −1.14662 | ||||||||
\(147\) | −11359.7 | −0.0433583 | ||||||||
\(148\) | −7321.40 | −0.0274751 | ||||||||
\(149\) | −59731.8 | −0.220414 | −0.110207 | − | 0.993909i | \(-0.535151\pi\) | ||||
−0.110207 | + | 0.993909i | \(0.535151\pi\) | |||||||
\(150\) | −98015.1 | −0.355684 | ||||||||
\(151\) | −431016. | −1.53834 | −0.769168 | − | 0.639047i | \(-0.779329\pi\) | ||||
−0.769168 | + | 0.639047i | \(0.779329\pi\) | |||||||
\(152\) | −23104.0 | −0.0811107 | ||||||||
\(153\) | 100907. | 0.348492 | ||||||||
\(154\) | −194314. | −0.660239 | ||||||||
\(155\) | −330798. | −1.10594 | ||||||||
\(156\) | −213795. | −0.703375 | ||||||||
\(157\) | −230317. | −0.745722 | −0.372861 | − | 0.927887i | \(-0.621623\pi\) | ||||
−0.372861 | + | 0.927887i | \(0.621623\pi\) | |||||||
\(158\) | 247138. | 0.787585 | ||||||||
\(159\) | 330074. | 1.03543 | ||||||||
\(160\) | 43356.9 | 0.133893 | ||||||||
\(161\) | 199344. | 0.606092 | ||||||||
\(162\) | −292497. | −0.875656 | ||||||||
\(163\) | 573529. | 1.69078 | 0.845388 | − | 0.534152i | \(-0.179369\pi\) | ||||
0.845388 | + | 0.534152i | \(0.179369\pi\) | |||||||
\(164\) | −68018.0 | −0.197476 | ||||||||
\(165\) | 297324. | 0.850199 | ||||||||
\(166\) | 330037. | 0.929593 | ||||||||
\(167\) | 32331.8 | 0.0897095 | 0.0448548 | − | 0.998994i | \(-0.485717\pi\) | ||||
0.0448548 | + | 0.998994i | \(0.485717\pi\) | |||||||
\(168\) | −149775. | −0.409417 | ||||||||
\(169\) | 156507. | 0.421518 | ||||||||
\(170\) | 179349. | 0.475966 | ||||||||
\(171\) | −34399.3 | −0.0899620 | ||||||||
\(172\) | 373667. | 0.963083 | ||||||||
\(173\) | −640334. | −1.62664 | −0.813319 | − | 0.581818i | \(-0.802342\pi\) | ||||
−0.813319 | + | 0.581818i | \(0.802342\pi\) | |||||||
\(174\) | 54514.2 | 0.136501 | ||||||||
\(175\) | 169513. | 0.418417 | ||||||||
\(176\) | 97739.0 | 0.237841 | ||||||||
\(177\) | 878970. | 2.10883 | ||||||||
\(178\) | −26694.9 | −0.0631507 | ||||||||
\(179\) | 199033. | 0.464292 | 0.232146 | − | 0.972681i | \(-0.425425\pi\) | ||||
0.232146 | + | 0.972681i | \(0.425425\pi\) | |||||||
\(180\) | 64553.7 | 0.148505 | ||||||||
\(181\) | −816331. | −1.85212 | −0.926061 | − | 0.377374i | \(-0.876827\pi\) | ||||
−0.926061 | + | 0.377374i | \(0.876827\pi\) | |||||||
\(182\) | 369751. | 0.827430 | ||||||||
\(183\) | 160668. | 0.354652 | ||||||||
\(184\) | −100269. | −0.218335 | ||||||||
\(185\) | −19374.6 | −0.0416201 | ||||||||
\(186\) | −574788. | −1.21822 | ||||||||
\(187\) | 404303. | 0.845480 | ||||||||
\(188\) | 190851. | 0.393823 | ||||||||
\(189\) | 345678. | 0.703911 | ||||||||
\(190\) | −61140.1 | −0.122869 | ||||||||
\(191\) | −263614. | −0.522859 | −0.261430 | − | 0.965223i | \(-0.584194\pi\) | ||||
−0.261430 | + | 0.965223i | \(0.584194\pi\) | |||||||
\(192\) | 75336.2 | 0.147486 | ||||||||
\(193\) | −505817. | −0.977463 | −0.488731 | − | 0.872434i | \(-0.662540\pi\) | ||||
−0.488731 | + | 0.872434i | \(0.662540\pi\) | |||||||
\(194\) | 653082. | 1.24584 | ||||||||
\(195\) | −565766. | −1.06549 | ||||||||
\(196\) | −9881.93 | −0.0183739 | ||||||||
\(197\) | 864016. | 1.58619 | 0.793097 | − | 0.609095i | \(-0.208467\pi\) | ||||
0.793097 | + | 0.609095i | \(0.208467\pi\) | |||||||
\(198\) | 145523. | 0.263795 | ||||||||
\(199\) | −582580. | −1.04285 | −0.521427 | − | 0.853296i | \(-0.674600\pi\) | ||||
−0.521427 | + | 0.853296i | \(0.674600\pi\) | |||||||
\(200\) | −85264.6 | −0.150728 | ||||||||
\(201\) | −33041.1 | −0.0576853 | ||||||||
\(202\) | −120363. | −0.207545 | ||||||||
\(203\) | −94280.3 | −0.160576 | ||||||||
\(204\) | 311633. | 0.524285 | ||||||||
\(205\) | −179996. | −0.299143 | ||||||||
\(206\) | 395012. | 0.648549 | ||||||||
\(207\) | −149290. | −0.242161 | ||||||||
\(208\) | −185984. | −0.298069 | ||||||||
\(209\) | −137827. | −0.218258 | ||||||||
\(210\) | −396349. | −0.620197 | ||||||||
\(211\) | 374780. | 0.579523 | 0.289761 | − | 0.957099i | \(-0.406424\pi\) | ||||
0.289761 | + | 0.957099i | \(0.406424\pi\) | |||||||
\(212\) | 287136. | 0.438781 | ||||||||
\(213\) | −840977. | −1.27009 | ||||||||
\(214\) | −379449. | −0.566394 | ||||||||
\(215\) | 988834. | 1.45891 | ||||||||
\(216\) | −173875. | −0.253573 | ||||||||
\(217\) | 994075. | 1.43308 | ||||||||
\(218\) | 666582. | 0.949976 | ||||||||
\(219\) | −1.35795e6 | −1.91326 | ||||||||
\(220\) | 258646. | 0.360288 | ||||||||
\(221\) | −769332. | −1.05958 | ||||||||
\(222\) | −33664.9 | −0.0458454 | ||||||||
\(223\) | −773167. | −1.04114 | −0.520572 | − | 0.853818i | \(-0.674281\pi\) | ||||
−0.520572 | + | 0.853818i | \(0.674281\pi\) | |||||||
\(224\) | −130291. | −0.173498 | ||||||||
\(225\) | −126950. | −0.167176 | ||||||||
\(226\) | −670274. | −0.872934 | ||||||||
\(227\) | −490462. | −0.631743 | −0.315871 | − | 0.948802i | \(-0.602297\pi\) | ||||
−0.315871 | + | 0.948802i | \(0.602297\pi\) | |||||||
\(228\) | −106236. | −0.135342 | ||||||||
\(229\) | −57262.3 | −0.0721573 | −0.0360786 | − | 0.999349i | \(-0.511487\pi\) | ||||
−0.0360786 | + | 0.999349i | \(0.511487\pi\) | |||||||
\(230\) | −265342. | −0.330740 | ||||||||
\(231\) | −893484. | −1.10168 | ||||||||
\(232\) | 47422.6 | 0.0578450 | ||||||||
\(233\) | 292508. | 0.352979 | 0.176489 | − | 0.984303i | \(-0.443526\pi\) | ||||
0.176489 | + | 0.984303i | \(0.443526\pi\) | |||||||
\(234\) | −276909. | −0.330596 | ||||||||
\(235\) | 505049. | 0.596574 | ||||||||
\(236\) | 764628. | 0.893655 | ||||||||
\(237\) | 1.13638e6 | 1.31418 | ||||||||
\(238\) | −538957. | −0.616754 | ||||||||
\(239\) | 445282. | 0.504244 | 0.252122 | − | 0.967695i | \(-0.418872\pi\) | ||||
0.252122 | + | 0.967695i | \(0.418872\pi\) | |||||||
\(240\) | 199362. | 0.223416 | ||||||||
\(241\) | −1.34568e6 | −1.49244 | −0.746222 | − | 0.665697i | \(-0.768134\pi\) | ||||
−0.746222 | + | 0.665697i | \(0.768134\pi\) | |||||||
\(242\) | −61140.6 | −0.0671106 | ||||||||
\(243\) | −684766. | −0.743920 | ||||||||
\(244\) | 139768. | 0.150291 | ||||||||
\(245\) | −26150.5 | −0.0278333 | ||||||||
\(246\) | −312758. | −0.329511 | ||||||||
\(247\) | 262266. | 0.273526 | ||||||||
\(248\) | −500016. | −0.516244 | ||||||||
\(249\) | 1.51756e6 | 1.55113 | ||||||||
\(250\) | −754895. | −0.763900 | ||||||||
\(251\) | −1.09190e6 | −1.09396 | −0.546978 | − | 0.837147i | \(-0.684222\pi\) | ||||
−0.546978 | + | 0.837147i | \(0.684222\pi\) | |||||||
\(252\) | −193989. | −0.192431 | ||||||||
\(253\) | −598158. | −0.587509 | ||||||||
\(254\) | 355860. | 0.346094 | ||||||||
\(255\) | 824673. | 0.794203 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 1.51625e6 | 1.43198 | 0.715992 | − | 0.698108i | \(-0.245975\pi\) | ||||
0.715992 | + | 0.698108i | \(0.245975\pi\) | |||||||
\(258\) | 1.71818e6 | 1.60701 | ||||||||
\(259\) | 58222.3 | 0.0539312 | ||||||||
\(260\) | −492168. | −0.451523 | ||||||||
\(261\) | 70607.0 | 0.0641574 | ||||||||
\(262\) | 1.50047e6 | 1.35044 | ||||||||
\(263\) | −183186. | −0.163306 | −0.0816531 | − | 0.996661i | \(-0.526020\pi\) | ||||
−0.0816531 | + | 0.996661i | \(0.526020\pi\) | |||||||
\(264\) | 449419. | 0.396864 | ||||||||
\(265\) | 759847. | 0.664679 | ||||||||
\(266\) | 183731. | 0.159213 | ||||||||
\(267\) | −122747. | −0.105374 | ||||||||
\(268\) | −28742.9 | −0.0244452 | ||||||||
\(269\) | −1.10143e6 | −0.928059 | −0.464029 | − | 0.885820i | \(-0.653597\pi\) | ||||
−0.464029 | + | 0.885820i | \(0.653597\pi\) | |||||||
\(270\) | −460125. | −0.384119 | ||||||||
\(271\) | −1.02496e6 | −0.847779 | −0.423890 | − | 0.905714i | \(-0.639336\pi\) | ||||
−0.423890 | + | 0.905714i | \(0.639336\pi\) | |||||||
\(272\) | 271094. | 0.222176 | ||||||||
\(273\) | 1.70017e6 | 1.38066 | ||||||||
\(274\) | −914731. | −0.736066 | ||||||||
\(275\) | −508647. | −0.405588 | ||||||||
\(276\) | −461054. | −0.364317 | ||||||||
\(277\) | 2.38231e6 | 1.86551 | 0.932757 | − | 0.360505i | \(-0.117396\pi\) | ||||
0.932757 | + | 0.360505i | \(0.117396\pi\) | |||||||
\(278\) | 539998. | 0.419064 | ||||||||
\(279\) | −744468. | −0.572579 | ||||||||
\(280\) | −344789. | −0.262820 | ||||||||
\(281\) | 1.97944e6 | 1.49547 | 0.747733 | − | 0.664000i | \(-0.231143\pi\) | ||||
0.747733 | + | 0.664000i | \(0.231143\pi\) | |||||||
\(282\) | 877565. | 0.657138 | ||||||||
\(283\) | 70483.2 | 0.0523142 | 0.0261571 | − | 0.999658i | \(-0.491673\pi\) | ||||
0.0261571 | + | 0.999658i | \(0.491673\pi\) | |||||||
\(284\) | −731578. | −0.538226 | ||||||||
\(285\) | −281132. | −0.205021 | ||||||||
\(286\) | −1.10949e6 | −0.802061 | ||||||||
\(287\) | 540903. | 0.387627 | ||||||||
\(288\) | 97575.8 | 0.0693204 | ||||||||
\(289\) | −298463. | −0.210206 | ||||||||
\(290\) | 125494. | 0.0876253 | ||||||||
\(291\) | 3.00297e6 | 2.07883 | ||||||||
\(292\) | −1.18130e6 | −0.810779 | ||||||||
\(293\) | 842274. | 0.573171 | 0.286586 | − | 0.958055i | \(-0.407480\pi\) | ||||
0.286586 | + | 0.958055i | \(0.407480\pi\) | |||||||
\(294\) | −45438.7 | −0.0306590 | ||||||||
\(295\) | 2.02343e6 | 1.35373 | ||||||||
\(296\) | −29285.6 | −0.0194279 | ||||||||
\(297\) | −1.03725e6 | −0.682329 | ||||||||
\(298\) | −238927. | −0.155857 | ||||||||
\(299\) | 1.13821e6 | 0.736283 | ||||||||
\(300\) | −392060. | −0.251507 | ||||||||
\(301\) | −2.97153e6 | −1.89044 | ||||||||
\(302\) | −1.72406e6 | −1.08777 | ||||||||
\(303\) | −553446. | −0.346313 | ||||||||
\(304\) | −92416.0 | −0.0573539 | ||||||||
\(305\) | 369867. | 0.227665 | ||||||||
\(306\) | 403628. | 0.246421 | ||||||||
\(307\) | −2.79322e6 | −1.69145 | −0.845725 | − | 0.533619i | \(-0.820832\pi\) | ||||
−0.845725 | + | 0.533619i | \(0.820832\pi\) | |||||||
\(308\) | −777254. | −0.466859 | ||||||||
\(309\) | 1.81633e6 | 1.08218 | ||||||||
\(310\) | −1.32319e6 | −0.782021 | ||||||||
\(311\) | −1.49358e6 | −0.875642 | −0.437821 | − | 0.899062i | \(-0.644250\pi\) | ||||
−0.437821 | + | 0.899062i | \(0.644250\pi\) | |||||||
\(312\) | −855182. | −0.497361 | ||||||||
\(313\) | −395047. | −0.227923 | −0.113961 | − | 0.993485i | \(-0.536354\pi\) | ||||
−0.113961 | + | 0.993485i | \(0.536354\pi\) | |||||||
\(314\) | −921268. | −0.527305 | ||||||||
\(315\) | −513353. | −0.291501 | ||||||||
\(316\) | 988554. | 0.556907 | ||||||||
\(317\) | −2.17633e6 | −1.21640 | −0.608201 | − | 0.793783i | \(-0.708108\pi\) | ||||
−0.608201 | + | 0.793783i | \(0.708108\pi\) | |||||||
\(318\) | 1.32030e6 | 0.732156 | ||||||||
\(319\) | 282900. | 0.155653 | ||||||||
\(320\) | 173428. | 0.0946768 | ||||||||
\(321\) | −1.74476e6 | −0.945093 | ||||||||
\(322\) | 797376. | 0.428572 | ||||||||
\(323\) | −382284. | −0.203883 | ||||||||
\(324\) | −1.16999e6 | −0.619183 | ||||||||
\(325\) | 967884. | 0.508294 | ||||||||
\(326\) | 2.29412e6 | 1.19556 | ||||||||
\(327\) | 3.06505e6 | 1.58514 | ||||||||
\(328\) | −272072. | −0.139637 | ||||||||
\(329\) | −1.51772e6 | −0.773038 | ||||||||
\(330\) | 1.18930e6 | 0.601181 | ||||||||
\(331\) | −2.05875e6 | −1.03284 | −0.516420 | − | 0.856335i | \(-0.672736\pi\) | ||||
−0.516420 | + | 0.856335i | \(0.672736\pi\) | |||||||
\(332\) | 1.32015e6 | 0.657321 | ||||||||
\(333\) | −43603.0 | −0.0215479 | ||||||||
\(334\) | 129327. | 0.0634342 | ||||||||
\(335\) | −76062.4 | −0.0370303 | ||||||||
\(336\) | −599099. | −0.289501 | ||||||||
\(337\) | 587423. | 0.281758 | 0.140879 | − | 0.990027i | \(-0.455007\pi\) | ||||
0.140879 | + | 0.990027i | \(0.455007\pi\) | |||||||
\(338\) | 626026. | 0.298058 | ||||||||
\(339\) | −3.08203e6 | −1.45659 | ||||||||
\(340\) | 717394. | 0.336558 | ||||||||
\(341\) | −2.98285e6 | −1.38914 | ||||||||
\(342\) | −137597. | −0.0636128 | ||||||||
\(343\) | 2.21707e6 | 1.01752 | ||||||||
\(344\) | 1.49467e6 | 0.681002 | ||||||||
\(345\) | −1.22009e6 | −0.551878 | ||||||||
\(346\) | −2.56133e6 | −1.15021 | ||||||||
\(347\) | 3.01162e6 | 1.34269 | 0.671346 | − | 0.741144i | \(-0.265716\pi\) | ||||
0.671346 | + | 0.741144i | \(0.265716\pi\) | |||||||
\(348\) | 218057. | 0.0965209 | ||||||||
\(349\) | 561200. | 0.246635 | 0.123317 | − | 0.992367i | \(-0.460647\pi\) | ||||
0.123317 | + | 0.992367i | \(0.460647\pi\) | |||||||
\(350\) | 678054. | 0.295865 | ||||||||
\(351\) | 1.97375e6 | 0.855113 | ||||||||
\(352\) | 390956. | 0.168179 | ||||||||
\(353\) | 1.93598e6 | 0.826922 | 0.413461 | − | 0.910522i | \(-0.364320\pi\) | ||||
0.413461 | + | 0.910522i | \(0.364320\pi\) | |||||||
\(354\) | 3.51588e6 | 1.49117 | ||||||||
\(355\) | −1.93597e6 | −0.815320 | ||||||||
\(356\) | −106779. | −0.0446543 | ||||||||
\(357\) | −2.47821e6 | −1.02912 | ||||||||
\(358\) | 796130. | 0.328304 | ||||||||
\(359\) | −388348. | −0.159032 | −0.0795161 | − | 0.996834i | \(-0.525338\pi\) | ||||
−0.0795161 | + | 0.996834i | \(0.525338\pi\) | |||||||
\(360\) | 258215. | 0.105009 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | −3.26532e6 | −1.30965 | ||||||||
\(363\) | −281134. | −0.111982 | ||||||||
\(364\) | 1.47900e6 | 0.585081 | ||||||||
\(365\) | −3.12607e6 | −1.22819 | ||||||||
\(366\) | 642674. | 0.250777 | ||||||||
\(367\) | 3.42147e6 | 1.32601 | 0.663006 | − | 0.748614i | \(-0.269280\pi\) | ||||
0.663006 | + | 0.748614i | \(0.269280\pi\) | |||||||
\(368\) | −401077. | −0.154386 | ||||||||
\(369\) | −405085. | −0.154875 | ||||||||
\(370\) | −77498.4 | −0.0294299 | ||||||||
\(371\) | −2.28340e6 | −0.861287 | ||||||||
\(372\) | −2.29915e6 | −0.861411 | ||||||||
\(373\) | −1.26109e6 | −0.469325 | −0.234663 | − | 0.972077i | \(-0.575399\pi\) | ||||
−0.234663 | + | 0.972077i | \(0.575399\pi\) | |||||||
\(374\) | 1.61721e6 | 0.597844 | ||||||||
\(375\) | −3.47113e6 | −1.27465 | ||||||||
\(376\) | 763405. | 0.278475 | ||||||||
\(377\) | −538320. | −0.195068 | ||||||||
\(378\) | 1.38271e6 | 0.497740 | ||||||||
\(379\) | −3713.47 | −0.00132795 | −0.000663975 | − | 1.00000i | \(-0.500211\pi\) | ||||
−0.000663975 | 1.00000i | \(0.500211\pi\) | ||||||||
\(380\) | −244560. | −0.0868814 | ||||||||
\(381\) | 1.63630e6 | 0.577498 | ||||||||
\(382\) | −1.05446e6 | −0.369717 | ||||||||
\(383\) | 3.31467e6 | 1.15463 | 0.577316 | − | 0.816521i | \(-0.304100\pi\) | ||||
0.577316 | + | 0.816521i | \(0.304100\pi\) | |||||||
\(384\) | 301345. | 0.104288 | ||||||||
\(385\) | −2.05685e6 | −0.707212 | ||||||||
\(386\) | −2.02327e6 | −0.691171 | ||||||||
\(387\) | 2.22539e6 | 0.755318 | ||||||||
\(388\) | 2.61233e6 | 0.880944 | ||||||||
\(389\) | 722620. | 0.242123 | 0.121061 | − | 0.992645i | \(-0.461370\pi\) | ||||
0.121061 | + | 0.992645i | \(0.461370\pi\) | |||||||
\(390\) | −2.26307e6 | −0.753417 | ||||||||
\(391\) | −1.65908e6 | −0.548814 | ||||||||
\(392\) | −39527.7 | −0.0129923 | ||||||||
\(393\) | 6.89941e6 | 2.25336 | ||||||||
\(394\) | 3.45607e6 | 1.12161 | ||||||||
\(395\) | 2.61601e6 | 0.843619 | ||||||||
\(396\) | 582090. | 0.186532 | ||||||||
\(397\) | −15238.6 | −0.00485253 | −0.00242626 | − | 0.999997i | \(-0.500772\pi\) | ||||
−0.00242626 | + | 0.999997i | \(0.500772\pi\) | |||||||
\(398\) | −2.33032e6 | −0.737408 | ||||||||
\(399\) | 844824. | 0.265665 | ||||||||
\(400\) | −341059. | −0.106581 | ||||||||
\(401\) | −3.59956e6 | −1.11786 | −0.558932 | − | 0.829213i | \(-0.688789\pi\) | ||||
−0.558932 | + | 0.829213i | \(0.688789\pi\) | |||||||
\(402\) | −132165. | −0.0407896 | ||||||||
\(403\) | 5.67595e6 | 1.74091 | ||||||||
\(404\) | −481450. | −0.146757 | ||||||||
\(405\) | −3.09614e6 | −0.937956 | ||||||||
\(406\) | −377121. | −0.113544 | ||||||||
\(407\) | −174704. | −0.0522776 | ||||||||
\(408\) | 1.24653e6 | 0.370726 | ||||||||
\(409\) | 5.83495e6 | 1.72476 | 0.862381 | − | 0.506260i | \(-0.168972\pi\) | ||||
0.862381 | + | 0.506260i | \(0.168972\pi\) | |||||||
\(410\) | −719984. | −0.211526 | ||||||||
\(411\) | −4.20608e6 | −1.22821 | ||||||||
\(412\) | 1.58005e6 | 0.458593 | ||||||||
\(413\) | −6.08058e6 | −1.75416 | ||||||||
\(414\) | −597159. | −0.171234 | ||||||||
\(415\) | 3.49351e6 | 0.995730 | ||||||||
\(416\) | −743934. | −0.210766 | ||||||||
\(417\) | 2.48300e6 | 0.699256 | ||||||||
\(418\) | −551309. | −0.154331 | ||||||||
\(419\) | 5.97054e6 | 1.66142 | 0.830708 | − | 0.556708i | \(-0.187936\pi\) | ||||
0.830708 | + | 0.556708i | \(0.187936\pi\) | |||||||
\(420\) | −1.58540e6 | −0.438545 | ||||||||
\(421\) | 1.65047e6 | 0.453838 | 0.226919 | − | 0.973914i | \(-0.427135\pi\) | ||||
0.226919 | + | 0.973914i | \(0.427135\pi\) | |||||||
\(422\) | 1.49912e6 | 0.409784 | ||||||||
\(423\) | 1.13663e6 | 0.308864 | ||||||||
\(424\) | 1.14854e6 | 0.310265 | ||||||||
\(425\) | −1.41081e6 | −0.378875 | ||||||||
\(426\) | −3.36391e6 | −0.898091 | ||||||||
\(427\) | −1.11148e6 | −0.295007 | ||||||||
\(428\) | −1.51779e6 | −0.400501 | ||||||||
\(429\) | −5.10160e6 | −1.33833 | ||||||||
\(430\) | 3.95534e6 | 1.03160 | ||||||||
\(431\) | 2.35721e6 | 0.611231 | 0.305616 | − | 0.952155i | \(-0.401138\pi\) | ||||
0.305616 | + | 0.952155i | \(0.401138\pi\) | |||||||
\(432\) | −695500. | −0.179303 | ||||||||
\(433\) | −483266. | −0.123870 | −0.0619351 | − | 0.998080i | \(-0.519727\pi\) | ||||
−0.0619351 | + | 0.998080i | \(0.519727\pi\) | |||||||
\(434\) | 3.97630e6 | 1.01334 | ||||||||
\(435\) | 577043. | 0.146213 | ||||||||
\(436\) | 2.66633e6 | 0.671734 | ||||||||
\(437\) | 565582. | 0.141674 | ||||||||
\(438\) | −5.43180e6 | −1.35288 | ||||||||
\(439\) | −3.28743e6 | −0.814132 | −0.407066 | − | 0.913399i | \(-0.633448\pi\) | ||||
−0.407066 | + | 0.913399i | \(0.633448\pi\) | |||||||
\(440\) | 1.03459e6 | 0.254762 | ||||||||
\(441\) | −58852.4 | −0.0144101 | ||||||||
\(442\) | −3.07733e6 | −0.749235 | ||||||||
\(443\) | 3.05552e6 | 0.739733 | 0.369867 | − | 0.929085i | \(-0.379403\pi\) | ||||
0.369867 | + | 0.929085i | \(0.379403\pi\) | |||||||
\(444\) | −134660. | −0.0324176 | ||||||||
\(445\) | −282570. | −0.0676436 | ||||||||
\(446\) | −3.09267e6 | −0.736201 | ||||||||
\(447\) | −1.09863e6 | −0.260064 | ||||||||
\(448\) | −521165. | −0.122682 | ||||||||
\(449\) | −3.85698e6 | −0.902884 | −0.451442 | − | 0.892300i | \(-0.649090\pi\) | ||||
−0.451442 | + | 0.892300i | \(0.649090\pi\) | |||||||
\(450\) | −507798. | −0.118212 | ||||||||
\(451\) | −1.62305e6 | −0.375743 | ||||||||
\(452\) | −2.68110e6 | −0.617257 | ||||||||
\(453\) | −7.92752e6 | −1.81506 | ||||||||
\(454\) | −1.96185e6 | −0.446710 | ||||||||
\(455\) | 3.91389e6 | 0.886298 | ||||||||
\(456\) | −424943. | −0.0957015 | ||||||||
\(457\) | 3.81819e6 | 0.855198 | 0.427599 | − | 0.903968i | \(-0.359359\pi\) | ||||
0.427599 | + | 0.903968i | \(0.359359\pi\) | |||||||
\(458\) | −229049. | −0.0510229 | ||||||||
\(459\) | −2.87698e6 | −0.637389 | ||||||||
\(460\) | −1.06137e6 | −0.233869 | ||||||||
\(461\) | −4.56025e6 | −0.999392 | −0.499696 | − | 0.866201i | \(-0.666555\pi\) | ||||
−0.499696 | + | 0.866201i | \(0.666555\pi\) | |||||||
\(462\) | −3.57394e6 | −0.779008 | ||||||||
\(463\) | −5.10875e6 | −1.10755 | −0.553774 | − | 0.832667i | \(-0.686813\pi\) | ||||
−0.553774 | + | 0.832667i | \(0.686813\pi\) | |||||||
\(464\) | 189691. | 0.0409026 | ||||||||
\(465\) | −6.08424e6 | −1.30489 | ||||||||
\(466\) | 1.17003e6 | 0.249594 | ||||||||
\(467\) | −4.72680e6 | −1.00294 | −0.501470 | − | 0.865175i | \(-0.667207\pi\) | ||||
−0.501470 | + | 0.865175i | \(0.667207\pi\) | |||||||
\(468\) | −1.10764e6 | −0.233766 | ||||||||
\(469\) | 228574. | 0.0479837 | ||||||||
\(470\) | 2.02020e6 | 0.421841 | ||||||||
\(471\) | −4.23613e6 | −0.879868 | ||||||||
\(472\) | 3.05851e6 | 0.631910 | ||||||||
\(473\) | 8.91646e6 | 1.83248 | ||||||||
\(474\) | 4.54553e6 | 0.929262 | ||||||||
\(475\) | 480946. | 0.0978052 | ||||||||
\(476\) | −2.15583e6 | −0.436111 | ||||||||
\(477\) | 1.71005e6 | 0.344123 | ||||||||
\(478\) | 1.78113e6 | 0.356554 | ||||||||
\(479\) | 1.06702e6 | 0.212487 | 0.106243 | − | 0.994340i | \(-0.466118\pi\) | ||||
0.106243 | + | 0.994340i | \(0.466118\pi\) | |||||||
\(480\) | 797448. | 0.157979 | ||||||||
\(481\) | 332436. | 0.0655158 | ||||||||
\(482\) | −5.38271e6 | −1.05532 | ||||||||
\(483\) | 3.66646e6 | 0.715120 | ||||||||
\(484\) | −244562. | −0.0474544 | ||||||||
\(485\) | 6.91300e6 | 1.33448 | ||||||||
\(486\) | −2.73906e6 | −0.526031 | ||||||||
\(487\) | −2.94327e6 | −0.562351 | −0.281175 | − | 0.959656i | \(-0.590724\pi\) | ||||
−0.281175 | + | 0.959656i | \(0.590724\pi\) | |||||||
\(488\) | 559071. | 0.106272 | ||||||||
\(489\) | 1.05487e7 | 1.99493 | ||||||||
\(490\) | −104602. | −0.0196811 | ||||||||
\(491\) | 9.75253e6 | 1.82563 | 0.912817 | − | 0.408370i | \(-0.133903\pi\) | ||||
0.912817 | + | 0.408370i | \(0.133903\pi\) | |||||||
\(492\) | −1.25103e6 | −0.233000 | ||||||||
\(493\) | 784666. | 0.145401 | ||||||||
\(494\) | 1.04906e6 | 0.193412 | ||||||||
\(495\) | 1.54038e6 | 0.282563 | ||||||||
\(496\) | −2.00006e6 | −0.365039 | ||||||||
\(497\) | 5.81776e6 | 1.05649 | ||||||||
\(498\) | 6.07025e6 | 1.09682 | ||||||||
\(499\) | −1.58150e6 | −0.284327 | −0.142164 | − | 0.989843i | \(-0.545406\pi\) | ||||
−0.142164 | + | 0.989843i | \(0.545406\pi\) | |||||||
\(500\) | −3.01958e6 | −0.540159 | ||||||||
\(501\) | 594667. | 0.105847 | ||||||||
\(502\) | −4.36762e6 | −0.773544 | ||||||||
\(503\) | −1.02913e7 | −1.81364 | −0.906822 | − | 0.421514i | \(-0.861499\pi\) | ||||
−0.906822 | + | 0.421514i | \(0.861499\pi\) | |||||||
\(504\) | −775956. | −0.136070 | ||||||||
\(505\) | −1.27406e6 | −0.222311 | ||||||||
\(506\) | −2.39263e6 | −0.415432 | ||||||||
\(507\) | 2.87857e6 | 0.497344 | ||||||||
\(508\) | 1.42344e6 | 0.244726 | ||||||||
\(509\) | −5.02362e6 | −0.859454 | −0.429727 | − | 0.902959i | \(-0.641390\pi\) | ||||
−0.429727 | + | 0.902959i | \(0.641390\pi\) | |||||||
\(510\) | 3.29869e6 | 0.561586 | ||||||||
\(511\) | 9.39410e6 | 1.59149 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | 980763. | 0.164540 | ||||||||
\(514\) | 6.06501e6 | 1.01257 | ||||||||
\(515\) | 4.18128e6 | 0.694690 | ||||||||
\(516\) | 6.87272e6 | 1.13633 | ||||||||
\(517\) | 4.55411e6 | 0.749336 | ||||||||
\(518\) | 232889. | 0.0381351 | ||||||||
\(519\) | −1.17774e7 | −1.91925 | ||||||||
\(520\) | −1.96867e6 | −0.319275 | ||||||||
\(521\) | 2.09428e6 | 0.338018 | 0.169009 | − | 0.985615i | \(-0.445943\pi\) | ||||
0.169009 | + | 0.985615i | \(0.445943\pi\) | |||||||
\(522\) | 282428. | 0.0453661 | ||||||||
\(523\) | −3.78110e6 | −0.604454 | −0.302227 | − | 0.953236i | \(-0.597730\pi\) | ||||
−0.302227 | + | 0.953236i | \(0.597730\pi\) | |||||||
\(524\) | 6.00189e6 | 0.954904 | ||||||||
\(525\) | 3.11780e6 | 0.493685 | ||||||||
\(526\) | −732744. | −0.115475 | ||||||||
\(527\) | −8.27338e6 | −1.29765 | ||||||||
\(528\) | 1.79768e6 | 0.280625 | ||||||||
\(529\) | −3.98177e6 | −0.618639 | ||||||||
\(530\) | 3.03939e6 | 0.469999 | ||||||||
\(531\) | 4.55378e6 | 0.700868 | ||||||||
\(532\) | 734924. | 0.112581 | ||||||||
\(533\) | 3.08844e6 | 0.470891 | ||||||||
\(534\) | −490989. | −0.0745107 | ||||||||
\(535\) | −4.01654e6 | −0.606691 | ||||||||
\(536\) | −114972. | −0.0172854 | ||||||||
\(537\) | 3.66073e6 | 0.547813 | ||||||||
\(538\) | −4.40571e6 | −0.656237 | ||||||||
\(539\) | −235803. | −0.0349605 | ||||||||
\(540\) | −1.84050e6 | −0.271613 | ||||||||
\(541\) | 4.24352e6 | 0.623352 | 0.311676 | − | 0.950189i | \(-0.399110\pi\) | ||||
0.311676 | + | 0.950189i | \(0.399110\pi\) | |||||||
\(542\) | −4.09983e6 | −0.599470 | ||||||||
\(543\) | −1.50145e7 | −2.18530 | ||||||||
\(544\) | 1.08437e6 | 0.157102 | ||||||||
\(545\) | 7.05590e6 | 1.01756 | ||||||||
\(546\) | 6.80070e6 | 0.976274 | ||||||||
\(547\) | 6.71988e6 | 0.960270 | 0.480135 | − | 0.877195i | \(-0.340588\pi\) | ||||
0.480135 | + | 0.877195i | \(0.340588\pi\) | |||||||
\(548\) | −3.65892e6 | −0.520477 | ||||||||
\(549\) | 832394. | 0.117869 | ||||||||
\(550\) | −2.03459e6 | −0.286794 | ||||||||
\(551\) | −267493. | −0.0375348 | ||||||||
\(552\) | −1.84422e6 | −0.257611 | ||||||||
\(553\) | −7.86132e6 | −1.09316 | ||||||||
\(554\) | 9.52923e6 | 1.31912 | ||||||||
\(555\) | −356350. | −0.0491071 | ||||||||
\(556\) | 2.15999e6 | 0.296323 | ||||||||
\(557\) | −634310. | −0.0866290 | −0.0433145 | − | 0.999061i | \(-0.513792\pi\) | ||||
−0.0433145 | + | 0.999061i | \(0.513792\pi\) | |||||||
\(558\) | −2.97787e6 | −0.404875 | ||||||||
\(559\) | −1.69668e7 | −2.29652 | ||||||||
\(560\) | −1.37916e6 | −0.185842 | ||||||||
\(561\) | 7.43620e6 | 0.997571 | ||||||||
\(562\) | 7.91776e6 | 1.05745 | ||||||||
\(563\) | 4.74103e6 | 0.630379 | 0.315190 | − | 0.949029i | \(-0.397932\pi\) | ||||
0.315190 | + | 0.949029i | \(0.397932\pi\) | |||||||
\(564\) | 3.51026e6 | 0.464666 | ||||||||
\(565\) | −7.09498e6 | −0.935040 | ||||||||
\(566\) | 281933. | 0.0369917 | ||||||||
\(567\) | 9.30414e6 | 1.21540 | ||||||||
\(568\) | −2.92631e6 | −0.380583 | ||||||||
\(569\) | −1.17115e7 | −1.51647 | −0.758234 | − | 0.651983i | \(-0.773937\pi\) | ||||
−0.758234 | + | 0.651983i | \(0.773937\pi\) | |||||||
\(570\) | −1.12453e6 | −0.144971 | ||||||||
\(571\) | −64636.9 | −0.00829642 | −0.00414821 | − | 0.999991i | \(-0.501320\pi\) | ||||
−0.00414821 | + | 0.999991i | \(0.501320\pi\) | |||||||
\(572\) | −4.43795e6 | −0.567143 | ||||||||
\(573\) | −4.84855e6 | −0.616916 | ||||||||
\(574\) | 2.16361e6 | 0.274094 | ||||||||
\(575\) | 2.08726e6 | 0.263274 | ||||||||
\(576\) | 390303. | 0.0490169 | ||||||||
\(577\) | 2.26070e6 | 0.282685 | 0.141343 | − | 0.989961i | \(-0.454858\pi\) | ||||
0.141343 | + | 0.989961i | \(0.454858\pi\) | |||||||
\(578\) | −1.19385e6 | −0.148638 | ||||||||
\(579\) | −9.30331e6 | −1.15330 | ||||||||
\(580\) | 501978. | 0.0619604 | ||||||||
\(581\) | −1.04983e7 | −1.29026 | ||||||||
\(582\) | 1.20119e7 | 1.46996 | ||||||||
\(583\) | 6.85166e6 | 0.834880 | ||||||||
\(584\) | −4.72520e6 | −0.573308 | ||||||||
\(585\) | −2.93113e6 | −0.354116 | ||||||||
\(586\) | 3.36910e6 | 0.405293 | ||||||||
\(587\) | −6.43586e6 | −0.770923 | −0.385462 | − | 0.922724i | \(-0.625958\pi\) | ||||
−0.385462 | + | 0.922724i | \(0.625958\pi\) | |||||||
\(588\) | −181755. | −0.0216792 | ||||||||
\(589\) | 2.82040e6 | 0.334983 | ||||||||
\(590\) | 8.09373e6 | 0.957235 | ||||||||
\(591\) | 1.58915e7 | 1.87153 | ||||||||
\(592\) | −117142. | −0.0137376 | ||||||||
\(593\) | −1.59757e7 | −1.86562 | −0.932808 | − | 0.360372i | \(-0.882650\pi\) | ||||
−0.932808 | + | 0.360372i | \(0.882650\pi\) | |||||||
\(594\) | −4.14901e6 | −0.482479 | ||||||||
\(595\) | −5.70496e6 | −0.660633 | ||||||||
\(596\) | −955709. | −0.110207 | ||||||||
\(597\) | −1.07152e7 | −1.23045 | ||||||||
\(598\) | 4.55284e6 | 0.520630 | ||||||||
\(599\) | 1.57534e7 | 1.79393 | 0.896967 | − | 0.442097i | \(-0.145765\pi\) | ||||
0.896967 | + | 0.442097i | \(0.145765\pi\) | |||||||
\(600\) | −1.56824e6 | −0.177842 | ||||||||
\(601\) | 1.86110e6 | 0.210176 | 0.105088 | − | 0.994463i | \(-0.466488\pi\) | ||||
0.105088 | + | 0.994463i | \(0.466488\pi\) | |||||||
\(602\) | −1.18861e7 | −1.33674 | ||||||||
\(603\) | −171180. | −0.0191717 | ||||||||
\(604\) | −6.89625e6 | −0.769168 | ||||||||
\(605\) | −647185. | −0.0718852 | ||||||||
\(606\) | −2.21378e6 | −0.244880 | ||||||||
\(607\) | −4.80555e6 | −0.529385 | −0.264693 | − | 0.964333i | \(-0.585270\pi\) | ||||
−0.264693 | + | 0.964333i | \(0.585270\pi\) | |||||||
\(608\) | −369664. | −0.0405554 | ||||||||
\(609\) | −1.73406e6 | −0.189462 | ||||||||
\(610\) | 1.47947e6 | 0.160983 | ||||||||
\(611\) | −8.66582e6 | −0.939089 | ||||||||
\(612\) | 1.61451e6 | 0.174246 | ||||||||
\(613\) | 1.45069e7 | 1.55928 | 0.779641 | − | 0.626227i | \(-0.215402\pi\) | ||||
0.779641 | + | 0.626227i | \(0.215402\pi\) | |||||||
\(614\) | −1.11729e7 | −1.19604 | ||||||||
\(615\) | −3.31060e6 | −0.352955 | ||||||||
\(616\) | −3.10902e6 | −0.330120 | ||||||||
\(617\) | 5.83804e6 | 0.617382 | 0.308691 | − | 0.951162i | \(-0.400109\pi\) | ||||
0.308691 | + | 0.951162i | \(0.400109\pi\) | |||||||
\(618\) | 7.26532e6 | 0.765215 | ||||||||
\(619\) | −3.44553e6 | −0.361435 | −0.180717 | − | 0.983535i | \(-0.557842\pi\) | ||||
−0.180717 | + | 0.983535i | \(0.557842\pi\) | |||||||
\(620\) | −5.29277e6 | −0.552972 | ||||||||
\(621\) | 4.25643e6 | 0.442911 | ||||||||
\(622\) | −5.97430e6 | −0.619172 | ||||||||
\(623\) | 849147. | 0.0876522 | ||||||||
\(624\) | −3.42073e6 | −0.351687 | ||||||||
\(625\) | −3.82740e6 | −0.391925 | ||||||||
\(626\) | −1.58019e6 | −0.161166 | ||||||||
\(627\) | −2.53501e6 | −0.257520 | ||||||||
\(628\) | −3.68507e6 | −0.372861 | ||||||||
\(629\) | −484566. | −0.0488345 | ||||||||
\(630\) | −2.05341e6 | −0.206122 | ||||||||
\(631\) | 5.33650e6 | 0.533560 | 0.266780 | − | 0.963757i | \(-0.414040\pi\) | ||||
0.266780 | + | 0.963757i | \(0.414040\pi\) | |||||||
\(632\) | 3.95421e6 | 0.393793 | ||||||||
\(633\) | 6.89319e6 | 0.683772 | ||||||||
\(634\) | −8.70533e6 | −0.860126 | ||||||||
\(635\) | 3.76684e6 | 0.370718 | ||||||||
\(636\) | 5.28119e6 | 0.517713 | ||||||||
\(637\) | 448700. | 0.0438135 | ||||||||
\(638\) | 1.13160e6 | 0.110063 | ||||||||
\(639\) | −4.35695e6 | −0.422115 | ||||||||
\(640\) | 693711. | 0.0669466 | ||||||||
\(641\) | 7.67654e6 | 0.737939 | 0.368970 | − | 0.929441i | \(-0.379711\pi\) | ||||
0.368970 | + | 0.929441i | \(0.379711\pi\) | |||||||
\(642\) | −6.97906e6 | −0.668281 | ||||||||
\(643\) | −1.13614e7 | −1.08369 | −0.541844 | − | 0.840479i | \(-0.682274\pi\) | ||||
−0.541844 | + | 0.840479i | \(0.682274\pi\) | |||||||
\(644\) | 3.18950e6 | 0.303046 | ||||||||
\(645\) | 1.81873e7 | 1.72135 | ||||||||
\(646\) | −1.52914e6 | −0.144167 | ||||||||
\(647\) | 6.38485e6 | 0.599639 | 0.299819 | − | 0.953996i | \(-0.403074\pi\) | ||||
0.299819 | + | 0.953996i | \(0.403074\pi\) | |||||||
\(648\) | −4.67995e6 | −0.437828 | ||||||||
\(649\) | 1.82456e7 | 1.70038 | ||||||||
\(650\) | 3.87154e6 | 0.359418 | ||||||||
\(651\) | 1.82837e7 | 1.69087 | ||||||||
\(652\) | 9.17646e6 | 0.845388 | ||||||||
\(653\) | 1.71696e7 | 1.57572 | 0.787858 | − | 0.615857i | \(-0.211190\pi\) | ||||
0.787858 | + | 0.615857i | \(0.211190\pi\) | |||||||
\(654\) | 1.22602e7 | 1.12086 | ||||||||
\(655\) | 1.58828e7 | 1.44652 | ||||||||
\(656\) | −1.08829e6 | −0.0987380 | ||||||||
\(657\) | −7.03529e6 | −0.635871 | ||||||||
\(658\) | −6.07086e6 | −0.546620 | ||||||||
\(659\) | 2.50142e6 | 0.224375 | 0.112187 | − | 0.993687i | \(-0.464214\pi\) | ||||
0.112187 | + | 0.993687i | \(0.464214\pi\) | |||||||
\(660\) | 4.75719e6 | 0.425099 | ||||||||
\(661\) | −2.60082e6 | −0.231530 | −0.115765 | − | 0.993277i | \(-0.536932\pi\) | ||||
−0.115765 | + | 0.993277i | \(0.536932\pi\) | |||||||
\(662\) | −8.23500e6 | −0.730329 | ||||||||
\(663\) | −1.41500e7 | −1.25018 | ||||||||
\(664\) | 5.28060e6 | 0.464796 | ||||||||
\(665\) | 1.94483e6 | 0.170540 | ||||||||
\(666\) | −174412. | −0.0152367 | ||||||||
\(667\) | −1.16090e6 | −0.101037 | ||||||||
\(668\) | 517309. | 0.0448548 | ||||||||
\(669\) | −1.42206e7 | −1.22843 | ||||||||
\(670\) | −304249. | −0.0261844 | ||||||||
\(671\) | 3.33515e6 | 0.285962 | ||||||||
\(672\) | −2.39640e6 | −0.204708 | ||||||||
\(673\) | 5.73660e6 | 0.488222 | 0.244111 | − | 0.969747i | \(-0.421504\pi\) | ||||
0.244111 | + | 0.969747i | \(0.421504\pi\) | |||||||
\(674\) | 2.34969e6 | 0.199233 | ||||||||
\(675\) | 3.61948e6 | 0.305764 | ||||||||
\(676\) | 2.50411e6 | 0.210759 | ||||||||
\(677\) | 1.91455e7 | 1.60544 | 0.802721 | − | 0.596354i | \(-0.203385\pi\) | ||||
0.802721 | + | 0.596354i | \(0.203385\pi\) | |||||||
\(678\) | −1.23281e7 | −1.02996 | ||||||||
\(679\) | −2.07741e7 | −1.72921 | ||||||||
\(680\) | 2.86958e6 | 0.237983 | ||||||||
\(681\) | −9.02088e6 | −0.745386 | ||||||||
\(682\) | −1.19314e7 | −0.982270 | ||||||||
\(683\) | −246438. | −0.0202142 | −0.0101071 | − | 0.999949i | \(-0.503217\pi\) | ||||
−0.0101071 | + | 0.999949i | \(0.503217\pi\) | |||||||
\(684\) | −550389. | −0.0449810 | ||||||||
\(685\) | −9.68260e6 | −0.788434 | ||||||||
\(686\) | 8.86826e6 | 0.719496 | ||||||||
\(687\) | −1.05320e6 | −0.0851375 | ||||||||
\(688\) | 5.97867e6 | 0.481541 | ||||||||
\(689\) | −1.30377e7 | −1.04630 | ||||||||
\(690\) | −4.88035e6 | −0.390236 | ||||||||
\(691\) | −1.77933e7 | −1.41763 | −0.708813 | − | 0.705396i | \(-0.750769\pi\) | ||||
−0.708813 | + | 0.705396i | \(0.750769\pi\) | |||||||
\(692\) | −1.02453e7 | −0.813319 | ||||||||
\(693\) | −4.62898e6 | −0.366144 | ||||||||
\(694\) | 1.20465e7 | 0.949427 | ||||||||
\(695\) | 5.71598e6 | 0.448879 | ||||||||
\(696\) | 872227. | 0.0682506 | ||||||||
\(697\) | −4.50177e6 | −0.350995 | ||||||||
\(698\) | 2.24480e6 | 0.174397 | ||||||||
\(699\) | 5.38000e6 | 0.416475 | ||||||||
\(700\) | 2.71221e6 | 0.209208 | ||||||||
\(701\) | 6.50720e6 | 0.500148 | 0.250074 | − | 0.968227i | \(-0.419545\pi\) | ||||
0.250074 | + | 0.968227i | \(0.419545\pi\) | |||||||
\(702\) | 7.89499e6 | 0.604657 | ||||||||
\(703\) | 165189. | 0.0126065 | ||||||||
\(704\) | 1.56382e6 | 0.118920 | ||||||||
\(705\) | 9.28919e6 | 0.703890 | ||||||||
\(706\) | 7.74393e6 | 0.584722 | ||||||||
\(707\) | 3.82866e6 | 0.288070 | ||||||||
\(708\) | 1.40635e7 | 1.05441 | ||||||||
\(709\) | −8.66886e6 | −0.647659 | −0.323829 | − | 0.946115i | \(-0.604970\pi\) | ||||
−0.323829 | + | 0.946115i | \(0.604970\pi\) | |||||||
\(710\) | −7.74389e6 | −0.576519 | ||||||||
\(711\) | 5.88739e6 | 0.436766 | ||||||||
\(712\) | −427118. | −0.0315753 | ||||||||
\(713\) | 1.22403e7 | 0.901713 | ||||||||
\(714\) | −9.91284e6 | −0.727700 | ||||||||
\(715\) | −1.17441e7 | −0.859124 | ||||||||
\(716\) | 3.18452e6 | 0.232146 | ||||||||
\(717\) | 8.18991e6 | 0.594951 | ||||||||
\(718\) | −1.55339e6 | −0.112453 | ||||||||
\(719\) | −5.47557e6 | −0.395009 | −0.197504 | − | 0.980302i | \(-0.563284\pi\) | ||||
−0.197504 | + | 0.980302i | \(0.563284\pi\) | |||||||
\(720\) | 1.03286e6 | 0.0742523 | ||||||||
\(721\) | −1.25651e7 | −0.900176 | ||||||||
\(722\) | 521284. | 0.0372161 | ||||||||
\(723\) | −2.47505e7 | −1.76092 | ||||||||
\(724\) | −1.30613e7 | −0.926061 | ||||||||
\(725\) | −987176. | −0.0697509 | ||||||||
\(726\) | −1.12454e6 | −0.0791830 | ||||||||
\(727\) | 1.67131e7 | 1.17279 | 0.586395 | − | 0.810025i | \(-0.300547\pi\) | ||||
0.586395 | + | 0.810025i | \(0.300547\pi\) | |||||||
\(728\) | 5.91602e6 | 0.413715 | ||||||||
\(729\) | 5.17455e6 | 0.360623 | ||||||||
\(730\) | −1.25043e7 | −0.868463 | ||||||||
\(731\) | 2.47311e7 | 1.71179 | ||||||||
\(732\) | 2.57070e6 | 0.177326 | ||||||||
\(733\) | 1.89538e7 | 1.30298 | 0.651489 | − | 0.758658i | \(-0.274145\pi\) | ||||
0.651489 | + | 0.758658i | \(0.274145\pi\) | |||||||
\(734\) | 1.36859e7 | 0.937632 | ||||||||
\(735\) | −480977. | −0.0328402 | ||||||||
\(736\) | −1.60431e6 | −0.109168 | ||||||||
\(737\) | −685866. | −0.0465126 | ||||||||
\(738\) | −1.62034e6 | −0.109513 | ||||||||
\(739\) | −1.13520e7 | −0.764646 | −0.382323 | − | 0.924029i | \(-0.624876\pi\) | ||||
−0.382323 | + | 0.924029i | \(0.624876\pi\) | |||||||
\(740\) | −309994. | −0.0208101 | ||||||||
\(741\) | 4.82376e6 | 0.322731 | ||||||||
\(742\) | −9.13362e6 | −0.609022 | ||||||||
\(743\) | 4.47868e6 | 0.297631 | 0.148815 | − | 0.988865i | \(-0.452454\pi\) | ||||
0.148815 | + | 0.988865i | \(0.452454\pi\) | |||||||
\(744\) | −9.19661e6 | −0.609110 | ||||||||
\(745\) | −2.52909e6 | −0.166945 | ||||||||
\(746\) | −5.04436e6 | −0.331863 | ||||||||
\(747\) | 7.86222e6 | 0.515518 | ||||||||
\(748\) | 6.46885e6 | 0.422740 | ||||||||
\(749\) | 1.20700e7 | 0.786147 | ||||||||
\(750\) | −1.38845e7 | −0.901317 | ||||||||
\(751\) | −1.06842e7 | −0.691260 | −0.345630 | − | 0.938371i | \(-0.612335\pi\) | ||||
−0.345630 | + | 0.938371i | \(0.612335\pi\) | |||||||
\(752\) | 3.05362e6 | 0.196911 | ||||||||
\(753\) | −2.00830e7 | −1.29075 | ||||||||
\(754\) | −2.15328e6 | −0.137934 | ||||||||
\(755\) | −1.82495e7 | −1.16516 | ||||||||
\(756\) | 5.53085e6 | 0.351955 | ||||||||
\(757\) | 2.13637e7 | 1.35499 | 0.677496 | − | 0.735526i | \(-0.263065\pi\) | ||||
0.677496 | + | 0.735526i | \(0.263065\pi\) | |||||||
\(758\) | −14853.9 | −0.000939002 0 | ||||||||
\(759\) | −1.10017e7 | −0.693195 | ||||||||
\(760\) | −978241. | −0.0614344 | ||||||||
\(761\) | −1.30365e7 | −0.816020 | −0.408010 | − | 0.912977i | \(-0.633777\pi\) | ||||
−0.408010 | + | 0.912977i | \(0.633777\pi\) | |||||||
\(762\) | 6.54520e6 | 0.408353 | ||||||||
\(763\) | −2.12036e7 | −1.31855 | ||||||||
\(764\) | −4.21782e6 | −0.261430 | ||||||||
\(765\) | 4.27248e6 | 0.263953 | ||||||||
\(766\) | 1.32587e7 | 0.816448 | ||||||||
\(767\) | −3.47188e7 | −2.13096 | ||||||||
\(768\) | 1.20538e6 | 0.0737430 | ||||||||
\(769\) | −2.54632e6 | −0.155273 | −0.0776366 | − | 0.996982i | \(-0.524737\pi\) | ||||
−0.0776366 | + | 0.996982i | \(0.524737\pi\) | |||||||
\(770\) | −8.22738e6 | −0.500075 | ||||||||
\(771\) | 2.78879e7 | 1.68958 | ||||||||
\(772\) | −8.09307e6 | −0.488731 | ||||||||
\(773\) | −2.94957e7 | −1.77546 | −0.887729 | − | 0.460366i | \(-0.847718\pi\) | ||||
−0.887729 | + | 0.460366i | \(0.847718\pi\) | |||||||
\(774\) | 8.90158e6 | 0.534090 | ||||||||
\(775\) | 1.04086e7 | 0.622499 | ||||||||
\(776\) | 1.04493e7 | 0.622922 | ||||||||
\(777\) | 1.07086e6 | 0.0636327 | ||||||||
\(778\) | 2.89048e6 | 0.171207 | ||||||||
\(779\) | 1.53466e6 | 0.0906082 | ||||||||
\(780\) | −9.05226e6 | −0.532746 | ||||||||
\(781\) | −1.74570e7 | −1.02410 | ||||||||
\(782\) | −6.63632e6 | −0.388070 | ||||||||
\(783\) | −2.01309e6 | −0.117343 | ||||||||
\(784\) | −158111. | −0.00918696 | ||||||||
\(785\) | −9.75179e6 | −0.564820 | ||||||||
\(786\) | 2.75976e7 | 1.59337 | ||||||||
\(787\) | 2.33229e6 | 0.134229 | 0.0671144 | − | 0.997745i | \(-0.478621\pi\) | ||||
0.0671144 | + | 0.997745i | \(0.478621\pi\) | |||||||
\(788\) | 1.38243e7 | 0.793097 | ||||||||
\(789\) | −3.36927e6 | −0.192683 | ||||||||
\(790\) | 1.04640e7 | 0.596529 | ||||||||
\(791\) | 2.13210e7 | 1.21162 | ||||||||
\(792\) | 2.32836e6 | 0.131898 | ||||||||
\(793\) | −6.34631e6 | −0.358376 | ||||||||
\(794\) | −60954.3 | −0.00343126 | ||||||||
\(795\) | 1.39756e7 | 0.784246 | ||||||||
\(796\) | −9.32129e6 | −0.521427 | ||||||||
\(797\) | −1.36130e7 | −0.759117 | −0.379559 | − | 0.925168i | \(-0.623924\pi\) | ||||
−0.379559 | + | 0.925168i | \(0.623924\pi\) | |||||||
\(798\) | 3.37930e6 | 0.187853 | ||||||||
\(799\) | 1.26315e7 | 0.699983 | ||||||||
\(800\) | −1.36423e6 | −0.0753640 | ||||||||
\(801\) | −635931. | −0.0350210 | ||||||||
\(802\) | −1.43983e7 | −0.790449 | ||||||||
\(803\) | −2.81882e7 | −1.54269 | ||||||||
\(804\) | −528658. | −0.0288426 | ||||||||
\(805\) | 8.44038e6 | 0.459063 | ||||||||
\(806\) | 2.27038e7 | 1.23101 | ||||||||
\(807\) | −2.02582e7 | −1.09501 | ||||||||
\(808\) | −1.92580e6 | −0.103773 | ||||||||
\(809\) | −1.98815e7 | −1.06801 | −0.534007 | − | 0.845480i | \(-0.679314\pi\) | ||||
−0.534007 | + | 0.845480i | \(0.679314\pi\) | |||||||
\(810\) | −1.23845e7 | −0.663235 | ||||||||
\(811\) | 3.08578e6 | 0.164745 | 0.0823725 | − | 0.996602i | \(-0.473750\pi\) | ||||
0.0823725 | + | 0.996602i | \(0.473750\pi\) | |||||||
\(812\) | −1.50848e6 | −0.0802880 | ||||||||
\(813\) | −1.88517e7 | −1.00028 | ||||||||
\(814\) | −698815. | −0.0369659 | ||||||||
\(815\) | 2.42836e7 | 1.28062 | ||||||||
\(816\) | 4.98612e6 | 0.262143 | ||||||||
\(817\) | −8.43086e6 | −0.441893 | ||||||||
\(818\) | 2.33398e7 | 1.21959 | ||||||||
\(819\) | 8.80830e6 | 0.458862 | ||||||||
\(820\) | −2.87994e6 | −0.149571 | ||||||||
\(821\) | −1.50937e7 | −0.781515 | −0.390757 | − | 0.920494i | \(-0.627787\pi\) | ||||
−0.390757 | + | 0.920494i | \(0.627787\pi\) | |||||||
\(822\) | −1.68243e7 | −0.868476 | ||||||||
\(823\) | 1.59595e7 | 0.821333 | 0.410667 | − | 0.911786i | \(-0.365296\pi\) | ||||
0.410667 | + | 0.911786i | \(0.365296\pi\) | |||||||
\(824\) | 6.32020e6 | 0.324274 | ||||||||
\(825\) | −9.35536e6 | −0.478548 | ||||||||
\(826\) | −2.43223e7 | −1.24038 | ||||||||
\(827\) | −1.75451e7 | −0.892058 | −0.446029 | − | 0.895019i | \(-0.647162\pi\) | ||||
−0.446029 | + | 0.895019i | \(0.647162\pi\) | |||||||
\(828\) | −2.38864e6 | −0.121081 | ||||||||
\(829\) | 1.52529e7 | 0.770845 | 0.385422 | − | 0.922740i | \(-0.374056\pi\) | ||||
0.385422 | + | 0.922740i | \(0.374056\pi\) | |||||||
\(830\) | 1.39740e7 | 0.704087 | ||||||||
\(831\) | 4.38169e7 | 2.20110 | ||||||||
\(832\) | −2.97574e6 | −0.149034 | ||||||||
\(833\) | −654035. | −0.0326579 | ||||||||
\(834\) | 9.93199e6 | 0.494449 | ||||||||
\(835\) | 1.36895e6 | 0.0679473 | ||||||||
\(836\) | −2.20524e6 | −0.109129 | ||||||||
\(837\) | 2.12257e7 | 1.04724 | ||||||||
\(838\) | 2.38822e7 | 1.17480 | ||||||||
\(839\) | 1.53885e7 | 0.754728 | 0.377364 | − | 0.926065i | \(-0.376831\pi\) | ||||
0.377364 | + | 0.926065i | \(0.376831\pi\) | |||||||
\(840\) | −6.34158e6 | −0.310098 | ||||||||
\(841\) | −1.99621e7 | −0.973232 | ||||||||
\(842\) | 6.60186e6 | 0.320912 | ||||||||
\(843\) | 3.64071e7 | 1.76448 | ||||||||
\(844\) | 5.99648e6 | 0.289761 | ||||||||
\(845\) | 6.62661e6 | 0.319264 | ||||||||
\(846\) | 4.54650e6 | 0.218399 | ||||||||
\(847\) | 1.94484e6 | 0.0931486 | ||||||||
\(848\) | 4.59418e6 | 0.219391 | ||||||||
\(849\) | 1.29637e6 | 0.0617249 | ||||||||
\(850\) | −5.64324e6 | −0.267905 | ||||||||
\(851\) | 716906. | 0.0339342 | ||||||||
\(852\) | −1.34556e7 | −0.635046 | ||||||||
\(853\) | 1.91103e7 | 0.899278 | 0.449639 | − | 0.893210i | \(-0.351553\pi\) | ||||
0.449639 | + | 0.893210i | \(0.351553\pi\) | |||||||
\(854\) | −4.44592e6 | −0.208601 | ||||||||
\(855\) | −1.45649e6 | −0.0681385 | ||||||||
\(856\) | −6.07118e6 | −0.283197 | ||||||||
\(857\) | −2.43080e6 | −0.113057 | −0.0565284 | − | 0.998401i | \(-0.518003\pi\) | ||||
−0.0565284 | + | 0.998401i | \(0.518003\pi\) | |||||||
\(858\) | −2.04064e7 | −0.946342 | ||||||||
\(859\) | 3.05663e7 | 1.41338 | 0.706692 | − | 0.707521i | \(-0.250187\pi\) | ||||
0.706692 | + | 0.707521i | \(0.250187\pi\) | |||||||
\(860\) | 1.58213e7 | 0.729453 | ||||||||
\(861\) | 9.94863e6 | 0.457357 | ||||||||
\(862\) | 9.42885e6 | 0.432206 | ||||||||
\(863\) | 9.33024e6 | 0.426448 | 0.213224 | − | 0.977003i | \(-0.431604\pi\) | ||||
0.213224 | + | 0.977003i | \(0.431604\pi\) | |||||||
\(864\) | −2.78200e6 | −0.126786 | ||||||||
\(865\) | −2.71122e7 | −1.23204 | ||||||||
\(866\) | −1.93307e6 | −0.0875895 | ||||||||
\(867\) | −5.48951e6 | −0.248020 | ||||||||
\(868\) | 1.59052e7 | 0.716539 | ||||||||
\(869\) | 2.35889e7 | 1.05964 | ||||||||
\(870\) | 2.30817e6 | 0.103388 | ||||||||
\(871\) | 1.30511e6 | 0.0582908 | ||||||||
\(872\) | 1.06653e7 | 0.474988 | ||||||||
\(873\) | 1.55579e7 | 0.690899 | ||||||||
\(874\) | 2.26233e6 | 0.100179 | ||||||||
\(875\) | 2.40127e7 | 1.06028 | ||||||||
\(876\) | −2.17272e7 | −0.956629 | ||||||||
\(877\) | −2.97688e7 | −1.30696 | −0.653481 | − | 0.756943i | \(-0.726692\pi\) | ||||
−0.653481 | + | 0.756943i | \(0.726692\pi\) | |||||||
\(878\) | −1.31497e7 | −0.575678 | ||||||||
\(879\) | 1.54916e7 | 0.676278 | ||||||||
\(880\) | 4.13834e6 | 0.180144 | ||||||||
\(881\) | −4.20040e6 | −0.182327 | −0.0911634 | − | 0.995836i | \(-0.529059\pi\) | ||||
−0.0911634 | + | 0.995836i | \(0.529059\pi\) | |||||||
\(882\) | −235410. | −0.0101895 | ||||||||
\(883\) | 1.23924e7 | 0.534876 | 0.267438 | − | 0.963575i | \(-0.413823\pi\) | ||||
0.267438 | + | 0.963575i | \(0.413823\pi\) | |||||||
\(884\) | −1.23093e7 | −0.529789 | ||||||||
\(885\) | 3.72162e7 | 1.59726 | ||||||||
\(886\) | 1.22221e7 | 0.523070 | ||||||||
\(887\) | −2.74194e7 | −1.17017 | −0.585084 | − | 0.810972i | \(-0.698939\pi\) | ||||
−0.585084 | + | 0.810972i | \(0.698939\pi\) | |||||||
\(888\) | −538639. | −0.0229227 | ||||||||
\(889\) | −1.13197e7 | −0.480374 | ||||||||
\(890\) | −1.13028e6 | −0.0478312 | ||||||||
\(891\) | −2.79183e7 | −1.17813 | ||||||||
\(892\) | −1.23707e7 | −0.520572 | ||||||||
\(893\) | −4.30608e6 | −0.180698 | ||||||||
\(894\) | −4.39450e6 | −0.183893 | ||||||||
\(895\) | 8.42719e6 | 0.351662 | ||||||||
\(896\) | −2.08466e6 | −0.0867491 | ||||||||
\(897\) | 2.09347e7 | 0.868731 | ||||||||
\(898\) | −1.54279e7 | −0.638436 | ||||||||
\(899\) | −5.78908e6 | −0.238897 | ||||||||
\(900\) | −2.03119e6 | −0.0835882 | ||||||||
\(901\) | 1.90041e7 | 0.779893 | ||||||||
\(902\) | −6.49220e6 | −0.265690 | ||||||||
\(903\) | −5.46542e7 | −2.23051 | ||||||||
\(904\) | −1.07244e7 | −0.436467 | ||||||||
\(905\) | −3.45641e7 | −1.40282 | ||||||||
\(906\) | −3.17101e7 | −1.28344 | ||||||||
\(907\) | −1.27225e7 | −0.513516 | −0.256758 | − | 0.966476i | \(-0.582654\pi\) | ||||
−0.256758 | + | 0.966476i | \(0.582654\pi\) | |||||||
\(908\) | −7.84738e6 | −0.315871 | ||||||||
\(909\) | −2.86730e6 | −0.115097 | ||||||||
\(910\) | 1.56555e7 | 0.626707 | ||||||||
\(911\) | −276582. | −0.0110415 | −0.00552076 | − | 0.999985i | \(-0.501757\pi\) | ||||
−0.00552076 | + | 0.999985i | \(0.501757\pi\) | |||||||
\(912\) | −1.69977e6 | −0.0676712 | ||||||||
\(913\) | 3.15015e7 | 1.25070 | ||||||||
\(914\) | 1.52728e7 | 0.604717 | ||||||||
\(915\) | 6.80283e6 | 0.268619 | ||||||||
\(916\) | −916197. | −0.0360786 | ||||||||
\(917\) | −4.77291e7 | −1.87439 | ||||||||
\(918\) | −1.15079e7 | −0.450702 | ||||||||
\(919\) | 2.48623e7 | 0.971075 | 0.485538 | − | 0.874216i | \(-0.338624\pi\) | ||||
0.485538 | + | 0.874216i | \(0.338624\pi\) | |||||||
\(920\) | −4.24548e6 | −0.165370 | ||||||||
\(921\) | −5.13747e7 | −1.99572 | ||||||||
\(922\) | −1.82410e7 | −0.706677 | ||||||||
\(923\) | 3.32181e7 | 1.28343 | ||||||||
\(924\) | −1.42957e7 | −0.550842 | ||||||||
\(925\) | 609625. | 0.0234266 | ||||||||
\(926\) | −2.04350e7 | −0.783155 | ||||||||
\(927\) | 9.41007e6 | 0.359661 | ||||||||
\(928\) | 758762. | 0.0289225 | ||||||||
\(929\) | −1.03940e7 | −0.395133 | −0.197566 | − | 0.980290i | \(-0.563304\pi\) | ||||
−0.197566 | + | 0.980290i | \(0.563304\pi\) | |||||||
\(930\) | −2.43370e7 | −0.922697 | ||||||||
\(931\) | 222961. | 0.00843053 | ||||||||
\(932\) | 4.68014e6 | 0.176489 | ||||||||
\(933\) | −2.74708e7 | −1.03316 | ||||||||
\(934\) | −1.89072e7 | −0.709186 | ||||||||
\(935\) | 1.71185e7 | 0.640379 | ||||||||
\(936\) | −4.43054e6 | −0.165298 | ||||||||
\(937\) | 6.95767e6 | 0.258890 | 0.129445 | − | 0.991587i | \(-0.458680\pi\) | ||||
0.129445 | + | 0.991587i | \(0.458680\pi\) | |||||||
\(938\) | 914295. | 0.0339296 | ||||||||
\(939\) | −7.26595e6 | −0.268923 | ||||||||
\(940\) | 8.08079e6 | 0.298287 | ||||||||
\(941\) | −3.11961e7 | −1.14849 | −0.574243 | − | 0.818685i | \(-0.694704\pi\) | ||||
−0.574243 | + | 0.818685i | \(0.694704\pi\) | |||||||
\(942\) | −1.69445e7 | −0.622160 | ||||||||
\(943\) | 6.66027e6 | 0.243901 | ||||||||
\(944\) | 1.22340e7 | 0.446828 | ||||||||
\(945\) | 1.46363e7 | 0.533152 | ||||||||
\(946\) | 3.56659e7 | 1.29576 | ||||||||
\(947\) | −6.85370e6 | −0.248342 | −0.124171 | − | 0.992261i | \(-0.539627\pi\) | ||||
−0.124171 | + | 0.992261i | \(0.539627\pi\) | |||||||
\(948\) | 1.81821e7 | 0.657088 | ||||||||
\(949\) | 5.36382e7 | 1.93334 | ||||||||
\(950\) | 1.92378e6 | 0.0691588 | ||||||||
\(951\) | −4.00285e7 | −1.43522 | ||||||||
\(952\) | −8.62332e6 | −0.308377 | ||||||||
\(953\) | −6.47990e6 | −0.231119 | −0.115560 | − | 0.993301i | \(-0.536866\pi\) | ||||
−0.115560 | + | 0.993301i | \(0.536866\pi\) | |||||||
\(954\) | 6.84022e6 | 0.243332 | ||||||||
\(955\) | −1.11616e7 | −0.396021 | ||||||||
\(956\) | 7.12452e6 | 0.252122 | ||||||||
\(957\) | 5.20328e6 | 0.183653 | ||||||||
\(958\) | 4.26806e6 | 0.150251 | ||||||||
\(959\) | 2.90970e7 | 1.02165 | ||||||||
\(960\) | 3.18979e6 | 0.111708 | ||||||||
\(961\) | 3.24099e7 | 1.13206 | ||||||||
\(962\) | 1.32975e6 | 0.0463267 | ||||||||
\(963\) | −9.03931e6 | −0.314101 | ||||||||
\(964\) | −2.15308e7 | −0.746222 | ||||||||
\(965\) | −2.14167e7 | −0.740345 | ||||||||
\(966\) | 1.46658e7 | 0.505666 | ||||||||
\(967\) | −1.13014e7 | −0.388658 | −0.194329 | − | 0.980936i | \(-0.562253\pi\) | ||||
−0.194329 | + | 0.980936i | \(0.562253\pi\) | |||||||
\(968\) | −978249. | −0.0335553 | ||||||||
\(969\) | −7.03121e6 | −0.240559 | ||||||||
\(970\) | 2.76520e7 | 0.943620 | ||||||||
\(971\) | −2.10630e7 | −0.716923 | −0.358461 | − | 0.933545i | \(-0.616699\pi\) | ||||
−0.358461 | + | 0.933545i | \(0.616699\pi\) | |||||||
\(972\) | −1.09562e7 | −0.371960 | ||||||||
\(973\) | −1.71770e7 | −0.581655 | ||||||||
\(974\) | −1.17731e7 | −0.397642 | ||||||||
\(975\) | 1.78019e7 | 0.599730 | ||||||||
\(976\) | 2.23628e6 | 0.0751454 | ||||||||
\(977\) | 1.26107e7 | 0.422670 | 0.211335 | − | 0.977414i | \(-0.432219\pi\) | ||||
0.211335 | + | 0.977414i | \(0.432219\pi\) | |||||||
\(978\) | 4.21948e7 | 1.41063 | ||||||||
\(979\) | −2.54798e6 | −0.0849648 | ||||||||
\(980\) | −418409. | −0.0139167 | ||||||||
\(981\) | 1.58795e7 | 0.526821 | ||||||||
\(982\) | 3.90101e7 | 1.29092 | ||||||||
\(983\) | 3.62410e7 | 1.19623 | 0.598117 | − | 0.801409i | \(-0.295916\pi\) | ||||
0.598117 | + | 0.801409i | \(0.295916\pi\) | |||||||
\(984\) | −5.00412e6 | −0.164756 | ||||||||
\(985\) | 3.65831e7 | 1.20141 | ||||||||
\(986\) | 3.13867e6 | 0.102814 | ||||||||
\(987\) | −2.79148e7 | −0.912098 | ||||||||
\(988\) | 4.19625e6 | 0.136763 | ||||||||
\(989\) | −3.65892e7 | −1.18949 | ||||||||
\(990\) | 6.16153e6 | 0.199802 | ||||||||
\(991\) | 2.12245e7 | 0.686522 | 0.343261 | − | 0.939240i | \(-0.388469\pi\) | ||||
0.343261 | + | 0.939240i | \(0.388469\pi\) | |||||||
\(992\) | −8.00026e6 | −0.258122 | ||||||||
\(993\) | −3.78658e7 | −1.21864 | ||||||||
\(994\) | 2.32710e7 | 0.747050 | ||||||||
\(995\) | −2.46669e7 | −0.789872 | ||||||||
\(996\) | 2.42810e7 | 0.775566 | ||||||||
\(997\) | 536321. | 0.0170878 | 0.00854392 | − | 0.999964i | \(-0.497280\pi\) | ||||
0.00854392 | + | 0.999964i | \(0.497280\pi\) | |||||||
\(998\) | −6.32601e6 | −0.201050 | ||||||||
\(999\) | 1.24317e6 | 0.0394110 |
(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 | 38.6.a.d.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 342.6.a.l.1.2 | 3 | |||
4.3 | odd | 2 | 304.6.a.h.1.1 | 3 | |||
5.4 | even | 2 | 950.6.a.f.1.1 | 3 | |||
19.18 | odd | 2 | 722.6.a.d.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.6.a.d.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
304.6.a.h.1.1 | 3 | 4.3 | odd | 2 | |||
342.6.a.l.1.2 | 3 | 3.2 | odd | 2 | |||
722.6.a.d.1.1 | 3 | 19.18 | odd | 2 | |||
950.6.a.f.1.1 | 3 | 5.4 | even | 2 |