Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [69,5,Mod(22,69)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(69, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("69.22");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(7.13252745279\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 5598 x^{14} + 11369517 x^{12} + 11272666128 x^{10} + 5958872960073 x^{8} + \cdots + 13\!\cdots\!52 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 22.1 | ||
Root | \(-32.2151i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 69.22 |
Dual form | 69.5.d.a.22.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(47\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −6.46704 | −1.61676 | −0.808380 | − | 0.588661i | \(-0.799655\pi\) | ||||
−0.808380 | + | 0.588661i | \(0.799655\pi\) | |||||||
\(3\) | 5.19615 | 0.577350 | ||||||||
\(4\) | 25.8226 | 1.61391 | ||||||||
\(5\) | − | 30.6703i | − | 1.22681i | −0.789767 | − | 0.613406i | \(-0.789799\pi\) | ||
0.789767 | − | 0.613406i | \(-0.210201\pi\) | |||||||
\(6\) | −33.6037 | −0.933436 | ||||||||
\(7\) | 37.9803i | 0.775108i | 0.921847 | + | 0.387554i | \(0.126680\pi\) | ||||
−0.921847 | + | 0.387554i | \(0.873320\pi\) | |||||||
\(8\) | −63.5230 | −0.992546 | ||||||||
\(9\) | 27.0000 | 0.333333 | ||||||||
\(10\) | 198.346i | 1.98346i | ||||||||
\(11\) | − | 2.87351i | − | 0.0237480i | −0.999930 | − | 0.0118740i | \(-0.996220\pi\) | ||
0.999930 | − | 0.0118740i | \(-0.00377970\pi\) | |||||||
\(12\) | 134.178 | 0.931792 | ||||||||
\(13\) | −18.8732 | −0.111676 | −0.0558379 | − | 0.998440i | \(-0.517783\pi\) | ||||
−0.0558379 | + | 0.998440i | \(0.517783\pi\) | |||||||
\(14\) | − | 245.620i | − | 1.25316i | ||||||
\(15\) | − | 159.368i | − | 0.708301i | ||||||
\(16\) | −2.35578 | −0.00920227 | ||||||||
\(17\) | − | 445.446i | − | 1.54134i | −0.637237 | − | 0.770668i | \(-0.719923\pi\) | ||
0.637237 | − | 0.770668i | \(-0.280077\pi\) | |||||||
\(18\) | −174.610 | −0.538920 | ||||||||
\(19\) | − | 401.904i | − | 1.11331i | −0.830745 | − | 0.556654i | \(-0.812085\pi\) | ||
0.830745 | − | 0.556654i | \(-0.187915\pi\) | |||||||
\(20\) | − | 791.987i | − | 1.97997i | ||||||
\(21\) | 197.351i | 0.447509i | ||||||||
\(22\) | 18.5831i | 0.0383948i | ||||||||
\(23\) | 60.7534 | − | 525.500i | 0.114846 | − | 0.993383i | ||||
\(24\) | −330.075 | −0.573047 | ||||||||
\(25\) | −315.668 | −0.505069 | ||||||||
\(26\) | 122.054 | 0.180553 | ||||||||
\(27\) | 140.296 | 0.192450 | ||||||||
\(28\) | 980.749i | 1.25096i | ||||||||
\(29\) | −922.372 | −1.09676 | −0.548378 | − | 0.836230i | \(-0.684755\pi\) | ||||
−0.548378 | + | 0.836230i | \(0.684755\pi\) | |||||||
\(30\) | 1030.64i | 1.14515i | ||||||||
\(31\) | 767.928 | 0.799093 | 0.399546 | − | 0.916713i | \(-0.369168\pi\) | ||||
0.399546 | + | 0.916713i | \(0.369168\pi\) | |||||||
\(32\) | 1031.60 | 1.00742 | ||||||||
\(33\) | − | 14.9312i | − | 0.0137109i | ||||||
\(34\) | 2880.72i | 2.49197i | ||||||||
\(35\) | 1164.87 | 0.950913 | ||||||||
\(36\) | 697.210 | 0.537970 | ||||||||
\(37\) | − | 1758.86i | − | 1.28477i | −0.766380 | − | 0.642387i | \(-0.777944\pi\) | ||
0.766380 | − | 0.642387i | \(-0.222056\pi\) | |||||||
\(38\) | 2599.13i | 1.79995i | ||||||||
\(39\) | −98.0681 | −0.0644761 | ||||||||
\(40\) | 1948.27i | 1.21767i | ||||||||
\(41\) | −2565.91 | −1.52642 | −0.763208 | − | 0.646153i | \(-0.776377\pi\) | ||||
−0.763208 | + | 0.646153i | \(0.776377\pi\) | |||||||
\(42\) | − | 1276.28i | − | 0.723514i | ||||||
\(43\) | 17.6066i | 0.00952221i | 0.999989 | + | 0.00476110i | \(0.00151551\pi\) | ||||
−0.999989 | + | 0.00476110i | \(0.998484\pi\) | |||||||
\(44\) | − | 74.2014i | − | 0.0383272i | ||||||
\(45\) | − | 828.099i | − | 0.408938i | ||||||
\(46\) | −392.894 | + | 3398.43i | −0.185678 | + | 1.60606i | ||||
\(47\) | −2034.86 | −0.921166 | −0.460583 | − | 0.887617i | \(-0.652360\pi\) | ||||
−0.460583 | + | 0.887617i | \(0.652360\pi\) | |||||||
\(48\) | −12.2410 | −0.00531294 | ||||||||
\(49\) | 958.496 | 0.399207 | ||||||||
\(50\) | 2041.44 | 0.816576 | ||||||||
\(51\) | − | 2314.61i | − | 0.889891i | ||||||
\(52\) | −487.355 | −0.180235 | ||||||||
\(53\) | 1304.09i | 0.464252i | 0.972686 | + | 0.232126i | \(0.0745682\pi\) | ||||
−0.972686 | + | 0.232126i | \(0.925432\pi\) | |||||||
\(54\) | −907.300 | −0.311145 | ||||||||
\(55\) | −88.1315 | −0.0291344 | ||||||||
\(56\) | − | 2412.62i | − | 0.769331i | ||||||
\(57\) | − | 2088.35i | − | 0.642768i | ||||||
\(58\) | 5965.01 | 1.77319 | ||||||||
\(59\) | 4380.32 | 1.25835 | 0.629175 | − | 0.777264i | \(-0.283393\pi\) | ||||
0.629175 | + | 0.777264i | \(0.283393\pi\) | |||||||
\(60\) | − | 4115.28i | − | 1.14313i | ||||||
\(61\) | 735.665i | 0.197706i | 0.995102 | + | 0.0988532i | \(0.0315174\pi\) | ||||
−0.995102 | + | 0.0988532i | \(0.968483\pi\) | |||||||
\(62\) | −4966.22 | −1.29194 | ||||||||
\(63\) | 1025.47i | 0.258369i | ||||||||
\(64\) | −6633.72 | −1.61956 | ||||||||
\(65\) | 578.847i | 0.137005i | ||||||||
\(66\) | 96.5606i | 0.0221673i | ||||||||
\(67\) | − | 3483.41i | − | 0.775988i | −0.921662 | − | 0.387994i | \(-0.873168\pi\) | ||
0.921662 | − | 0.387994i | \(-0.126832\pi\) | |||||||
\(68\) | − | 11502.6i | − | 2.48758i | ||||||
\(69\) | 315.684 | − | 2730.58i | 0.0663062 | − | 0.573530i | ||||
\(70\) | −7533.25 | −1.53740 | ||||||||
\(71\) | 5667.75 | 1.12433 | 0.562165 | − | 0.827025i | \(-0.309968\pi\) | ||||
0.562165 | + | 0.827025i | \(0.309968\pi\) | |||||||
\(72\) | −1715.12 | −0.330849 | ||||||||
\(73\) | 2214.08 | 0.415477 | 0.207739 | − | 0.978184i | \(-0.433390\pi\) | ||||
0.207739 | + | 0.978184i | \(0.433390\pi\) | |||||||
\(74\) | 11374.6i | 2.07717i | ||||||||
\(75\) | −1640.26 | −0.291602 | ||||||||
\(76\) | − | 10378.2i | − | 1.79678i | ||||||
\(77\) | 109.137 | 0.0184073 | ||||||||
\(78\) | 634.210 | 0.104242 | ||||||||
\(79\) | 3995.75i | 0.640243i | 0.947377 | + | 0.320121i | \(0.103724\pi\) | ||||
−0.947377 | + | 0.320121i | \(0.896276\pi\) | |||||||
\(80\) | 72.2526i | 0.0112895i | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | 16593.8 | 2.46785 | ||||||||
\(83\) | 9286.49i | 1.34802i | 0.738723 | + | 0.674009i | \(0.235429\pi\) | ||||
−0.738723 | + | 0.674009i | \(0.764571\pi\) | |||||||
\(84\) | 5096.12i | 0.722240i | ||||||||
\(85\) | −13662.0 | −1.89093 | ||||||||
\(86\) | − | 113.862i | − | 0.0153951i | ||||||
\(87\) | −4792.79 | −0.633213 | ||||||||
\(88\) | 182.534i | 0.0235710i | ||||||||
\(89\) | 10926.4i | 1.37942i | 0.724084 | + | 0.689712i | \(0.242263\pi\) | ||||
−0.724084 | + | 0.689712i | \(0.757737\pi\) | |||||||
\(90\) | 5355.34i | 0.661154i | ||||||||
\(91\) | − | 716.811i | − | 0.0865609i | ||||||
\(92\) | 1568.81 | − | 13569.8i | 0.185351 | − | 1.60323i | ||||
\(93\) | 3990.27 | 0.461356 | ||||||||
\(94\) | 13159.5 | 1.48930 | ||||||||
\(95\) | −12326.5 | −1.36582 | ||||||||
\(96\) | 5360.36 | 0.581637 | ||||||||
\(97\) | − | 10200.5i | − | 1.08412i | −0.840338 | − | 0.542062i | \(-0.817644\pi\) | ||
0.840338 | − | 0.542062i | \(-0.182356\pi\) | |||||||
\(98\) | −6198.63 | −0.645422 | ||||||||
\(99\) | − | 77.5848i | − | 0.00791601i | ||||||
\(100\) | −8151.37 | −0.815137 | ||||||||
\(101\) | 9869.64 | 0.967517 | 0.483758 | − | 0.875202i | \(-0.339271\pi\) | ||||
0.483758 | + | 0.875202i | \(0.339271\pi\) | |||||||
\(102\) | 14968.6i | 1.43874i | ||||||||
\(103\) | − | 998.879i | − | 0.0941539i | −0.998891 | − | 0.0470769i | \(-0.985009\pi\) | ||
0.998891 | − | 0.0470769i | \(-0.0149906\pi\) | |||||||
\(104\) | 1198.88 | 0.110843 | ||||||||
\(105\) | 6052.83 | 0.549010 | ||||||||
\(106\) | − | 8433.57i | − | 0.750585i | ||||||
\(107\) | − | 5796.64i | − | 0.506301i | −0.967427 | − | 0.253150i | \(-0.918533\pi\) | ||
0.967427 | − | 0.253150i | \(-0.0814667\pi\) | |||||||
\(108\) | 3622.81 | 0.310597 | ||||||||
\(109\) | 20927.9i | 1.76146i | 0.473615 | + | 0.880732i | \(0.342949\pi\) | ||||
−0.473615 | + | 0.880732i | \(0.657051\pi\) | |||||||
\(110\) | 569.949 | 0.0471033 | ||||||||
\(111\) | − | 9139.28i | − | 0.741765i | ||||||
\(112\) | − | 89.4733i | − | 0.00713276i | ||||||
\(113\) | − | 24530.2i | − | 1.92107i | −0.278156 | − | 0.960536i | \(-0.589723\pi\) | ||
0.278156 | − | 0.960536i | \(-0.410277\pi\) | |||||||
\(114\) | 13505.5i | 1.03920i | ||||||||
\(115\) | −16117.2 | − | 1863.32i | −1.21870 | − | 0.140894i | ||||
\(116\) | −23818.0 | −1.77007 | ||||||||
\(117\) | −509.577 | −0.0372253 | ||||||||
\(118\) | −28327.7 | −2.03445 | ||||||||
\(119\) | 16918.2 | 1.19470 | ||||||||
\(120\) | 10123.5i | 0.703021i | ||||||||
\(121\) | 14632.7 | 0.999436 | ||||||||
\(122\) | − | 4757.58i | − | 0.319644i | ||||||
\(123\) | −13332.8 | −0.881277 | ||||||||
\(124\) | 19829.9 | 1.28966 | ||||||||
\(125\) | − | 9487.30i | − | 0.607187i | ||||||
\(126\) | − | 6631.74i | − | 0.417721i | ||||||
\(127\) | 27149.7 | 1.68329 | 0.841643 | − | 0.540034i | \(-0.181589\pi\) | ||||
0.841643 | + | 0.540034i | \(0.181589\pi\) | |||||||
\(128\) | 26394.9 | 1.61102 | ||||||||
\(129\) | 91.4864i | 0.00549765i | ||||||||
\(130\) | − | 3743.43i | − | 0.221505i | ||||||
\(131\) | −23768.2 | −1.38501 | −0.692505 | − | 0.721413i | \(-0.743493\pi\) | ||||
−0.692505 | + | 0.721413i | \(0.743493\pi\) | |||||||
\(132\) | − | 385.562i | − | 0.0221282i | ||||||
\(133\) | 15264.4 | 0.862934 | ||||||||
\(134\) | 22527.3i | 1.25459i | ||||||||
\(135\) | − | 4302.93i | − | 0.236100i | ||||||
\(136\) | 28296.1i | 1.52985i | ||||||||
\(137\) | 33951.5i | 1.80891i | 0.426566 | + | 0.904456i | \(0.359723\pi\) | ||||
−0.426566 | + | 0.904456i | \(0.640277\pi\) | |||||||
\(138\) | −2041.54 | + | 17658.7i | −0.107201 | + | 0.927260i | ||||
\(139\) | −12417.8 | −0.642708 | −0.321354 | − | 0.946959i | \(-0.604138\pi\) | ||||
−0.321354 | + | 0.946959i | \(0.604138\pi\) | |||||||
\(140\) | 30079.9 | 1.53469 | ||||||||
\(141\) | −10573.4 | −0.531836 | ||||||||
\(142\) | −36653.6 | −1.81777 | ||||||||
\(143\) | 54.2324i | 0.00265208i | ||||||||
\(144\) | −63.6061 | −0.00306742 | ||||||||
\(145\) | 28289.4i | 1.34551i | ||||||||
\(146\) | −14318.5 | −0.671726 | ||||||||
\(147\) | 4980.49 | 0.230482 | ||||||||
\(148\) | − | 45418.2i | − | 2.07351i | ||||||
\(149\) | 27210.8i | 1.22566i | 0.790216 | + | 0.612828i | \(0.209968\pi\) | ||||
−0.790216 | + | 0.612828i | \(0.790032\pi\) | |||||||
\(150\) | 10607.6 | 0.471450 | ||||||||
\(151\) | 19847.0 | 0.870445 | 0.435223 | − | 0.900323i | \(-0.356670\pi\) | ||||
0.435223 | + | 0.900323i | \(0.356670\pi\) | |||||||
\(152\) | 25530.1i | 1.10501i | ||||||||
\(153\) | − | 12027.0i | − | 0.513779i | ||||||
\(154\) | −705.792 | −0.0297602 | ||||||||
\(155\) | − | 23552.6i | − | 0.980337i | ||||||
\(156\) | −2532.37 | −0.104059 | ||||||||
\(157\) | − | 19686.5i | − | 0.798673i | −0.916805 | − | 0.399336i | \(-0.869241\pi\) | ||
0.916805 | − | 0.399336i | \(-0.130759\pi\) | |||||||
\(158\) | − | 25840.7i | − | 1.03512i | ||||||
\(159\) | 6776.23i | 0.268036i | ||||||||
\(160\) | − | 31639.6i | − | 1.23592i | ||||||
\(161\) | 19958.6 | + | 2307.43i | 0.769980 | + | 0.0890178i | ||||
\(162\) | −4714.47 | −0.179640 | ||||||||
\(163\) | −27266.0 | −1.02623 | −0.513117 | − | 0.858318i | \(-0.671509\pi\) | ||||
−0.513117 | + | 0.858318i | \(0.671509\pi\) | |||||||
\(164\) | −66258.3 | −2.46350 | ||||||||
\(165\) | −457.945 | −0.0168207 | ||||||||
\(166\) | − | 60056.1i | − | 2.17942i | ||||||
\(167\) | 2373.33 | 0.0850992 | 0.0425496 | − | 0.999094i | \(-0.486452\pi\) | ||||
0.0425496 | + | 0.999094i | \(0.486452\pi\) | |||||||
\(168\) | − | 12536.4i | − | 0.444173i | ||||||
\(169\) | −28204.8 | −0.987529 | ||||||||
\(170\) | 88352.5 | 3.05718 | ||||||||
\(171\) | − | 10851.4i | − | 0.371102i | ||||||
\(172\) | 454.647i | 0.0153680i | ||||||||
\(173\) | −41114.3 | −1.37373 | −0.686865 | − | 0.726785i | \(-0.741013\pi\) | ||||
−0.686865 | + | 0.726785i | \(0.741013\pi\) | |||||||
\(174\) | 30995.1 | 1.02375 | ||||||||
\(175\) | − | 11989.2i | − | 0.391484i | ||||||
\(176\) | 6.76936i | 0.000218536i | ||||||||
\(177\) | 22760.8 | 0.726509 | ||||||||
\(178\) | − | 70661.5i | − | 2.23020i | ||||||
\(179\) | 42221.7 | 1.31774 | 0.658870 | − | 0.752256i | \(-0.271035\pi\) | ||||
0.658870 | + | 0.752256i | \(0.271035\pi\) | |||||||
\(180\) | − | 21383.6i | − | 0.659989i | ||||||
\(181\) | 38216.7i | 1.16653i | 0.812282 | + | 0.583264i | \(0.198225\pi\) | ||||
−0.812282 | + | 0.583264i | \(0.801775\pi\) | |||||||
\(182\) | 4635.64i | 0.139948i | ||||||||
\(183\) | 3822.63i | 0.114146i | ||||||||
\(184\) | −3859.23 | + | 33381.3i | −0.113990 | + | 0.985979i | ||||
\(185\) | −53944.7 | −1.57618 | ||||||||
\(186\) | −25805.2 | −0.745902 | ||||||||
\(187\) | −1279.99 | −0.0366037 | ||||||||
\(188\) | −52545.2 | −1.48668 | ||||||||
\(189\) | 5328.49i | 0.149170i | ||||||||
\(190\) | 79716.1 | 2.20820 | ||||||||
\(191\) | − | 7251.62i | − | 0.198778i | −0.995049 | − | 0.0993889i | \(-0.968311\pi\) | ||
0.995049 | − | 0.0993889i | \(-0.0316888\pi\) | |||||||
\(192\) | −34469.8 | −0.935054 | ||||||||
\(193\) | 56100.9 | 1.50611 | 0.753053 | − | 0.657960i | \(-0.228580\pi\) | ||||
0.753053 | + | 0.657960i | \(0.228580\pi\) | |||||||
\(194\) | 65967.2i | 1.75277i | ||||||||
\(195\) | 3007.78i | 0.0791001i | ||||||||
\(196\) | 24750.8 | 0.644285 | ||||||||
\(197\) | 611.120 | 0.0157469 | 0.00787343 | − | 0.999969i | \(-0.497494\pi\) | ||||
0.00787343 | + | 0.999969i | \(0.497494\pi\) | |||||||
\(198\) | 501.744i | 0.0127983i | ||||||||
\(199\) | − | 16019.0i | − | 0.404511i | −0.979333 | − | 0.202255i | \(-0.935173\pi\) | ||
0.979333 | − | 0.202255i | \(-0.0648271\pi\) | |||||||
\(200\) | 20052.2 | 0.501305 | ||||||||
\(201\) | − | 18100.3i | − | 0.448017i | ||||||
\(202\) | −63827.3 | −1.56424 | ||||||||
\(203\) | − | 35032.0i | − | 0.850105i | ||||||
\(204\) | − | 59769.1i | − | 1.43620i | ||||||
\(205\) | 78697.1i | 1.87263i | ||||||||
\(206\) | 6459.79i | 0.152224i | ||||||||
\(207\) | 1640.34 | − | 14188.5i | 0.0382819 | − | 0.331128i | ||||
\(208\) | 44.4612 | 0.00102767 | ||||||||
\(209\) | −1154.88 | −0.0264388 | ||||||||
\(210\) | −39143.9 | −0.887617 | ||||||||
\(211\) | −71443.1 | −1.60470 | −0.802352 | − | 0.596851i | \(-0.796419\pi\) | ||||
−0.802352 | + | 0.596851i | \(0.796419\pi\) | |||||||
\(212\) | 33674.8i | 0.749262i | ||||||||
\(213\) | 29450.5 | 0.649133 | ||||||||
\(214\) | 37487.1i | 0.818566i | ||||||||
\(215\) | 539.999 | 0.0116820 | ||||||||
\(216\) | −8912.03 | −0.191016 | ||||||||
\(217\) | 29166.1i | 0.619383i | ||||||||
\(218\) | − | 135342.i | − | 2.84786i | ||||||
\(219\) | 11504.7 | 0.239876 | ||||||||
\(220\) | −2275.78 | −0.0470203 | ||||||||
\(221\) | 8407.00i | 0.172130i | ||||||||
\(222\) | 59104.1i | 1.19925i | ||||||||
\(223\) | 33361.2 | 0.670861 | 0.335430 | − | 0.942065i | \(-0.391118\pi\) | ||||
0.335430 | + | 0.942065i | \(0.391118\pi\) | |||||||
\(224\) | 39180.6i | 0.780863i | ||||||||
\(225\) | −8523.05 | −0.168356 | ||||||||
\(226\) | 158637.i | 3.10591i | ||||||||
\(227\) | − | 38396.9i | − | 0.745151i | −0.928002 | − | 0.372576i | \(-0.878475\pi\) | ||
0.928002 | − | 0.372576i | \(-0.121525\pi\) | |||||||
\(228\) | − | 53926.7i | − | 1.03737i | ||||||
\(229\) | 36981.1i | 0.705195i | 0.935775 | + | 0.352598i | \(0.114702\pi\) | ||||
−0.935775 | + | 0.352598i | \(0.885298\pi\) | |||||||
\(230\) | 104231. | + | 12050.2i | 1.97034 | + | 0.227792i | ||||
\(231\) | 567.091 | 0.0106275 | ||||||||
\(232\) | 58591.8 | 1.08858 | ||||||||
\(233\) | 1258.03 | 0.0231729 | 0.0115864 | − | 0.999933i | \(-0.496312\pi\) | ||||
0.0115864 | + | 0.999933i | \(0.496312\pi\) | |||||||
\(234\) | 3295.45 | 0.0601843 | ||||||||
\(235\) | 62409.7i | 1.13010i | ||||||||
\(236\) | 113111. | 2.03087 | ||||||||
\(237\) | 20762.5i | 0.369644i | ||||||||
\(238\) | −109411. | −1.93155 | ||||||||
\(239\) | 64284.0 | 1.12540 | 0.562700 | − | 0.826661i | \(-0.309762\pi\) | ||||
0.562700 | + | 0.826661i | \(0.309762\pi\) | |||||||
\(240\) | 375.435i | 0.00651798i | ||||||||
\(241\) | 75781.7i | 1.30476i | 0.757893 | + | 0.652379i | \(0.226229\pi\) | ||||
−0.757893 | + | 0.652379i | \(0.773771\pi\) | |||||||
\(242\) | −94630.5 | −1.61585 | ||||||||
\(243\) | 3788.00 | 0.0641500 | ||||||||
\(244\) | 18996.8i | 0.319081i | ||||||||
\(245\) | − | 29397.4i | − | 0.489752i | ||||||
\(246\) | 86223.9 | 1.42481 | ||||||||
\(247\) | 7585.22i | 0.124330i | ||||||||
\(248\) | −48781.1 | −0.793137 | ||||||||
\(249\) | 48254.0i | 0.778278i | ||||||||
\(250\) | 61354.7i | 0.981676i | ||||||||
\(251\) | − | 41556.8i | − | 0.659622i | −0.944047 | − | 0.329811i | \(-0.893015\pi\) | ||
0.944047 | − | 0.329811i | \(-0.106985\pi\) | |||||||
\(252\) | 26480.2i | 0.416985i | ||||||||
\(253\) | −1510.03 | − | 174.575i | −0.0235909 | − | 0.00272736i | ||||
\(254\) | −175578. | −2.72147 | ||||||||
\(255\) | −70989.7 | −1.09173 | ||||||||
\(256\) | −64557.1 | −0.985064 | ||||||||
\(257\) | −1221.34 | −0.0184914 | −0.00924571 | − | 0.999957i | \(-0.502943\pi\) | ||||
−0.00924571 | + | 0.999957i | \(0.502943\pi\) | |||||||
\(258\) | − | 591.646i | − | 0.00888838i | ||||||
\(259\) | 66801.9 | 0.995839 | ||||||||
\(260\) | 14947.3i | 0.221114i | ||||||||
\(261\) | −24904.0 | −0.365585 | ||||||||
\(262\) | 153710. | 2.23923 | ||||||||
\(263\) | − | 76995.0i | − | 1.11314i | −0.830800 | − | 0.556571i | \(-0.812117\pi\) | ||
0.830800 | − | 0.556571i | \(-0.187883\pi\) | |||||||
\(264\) | 948.474i | 0.0136087i | ||||||||
\(265\) | 39996.7 | 0.569551 | ||||||||
\(266\) | −98715.7 | −1.39516 | ||||||||
\(267\) | 56775.3i | 0.796410i | ||||||||
\(268\) | − | 89950.6i | − | 1.25238i | ||||||
\(269\) | −42071.1 | −0.581405 | −0.290703 | − | 0.956813i | \(-0.593889\pi\) | ||||
−0.290703 | + | 0.956813i | \(0.593889\pi\) | |||||||
\(270\) | 27827.2i | 0.381717i | ||||||||
\(271\) | −20682.6 | −0.281623 | −0.140811 | − | 0.990036i | \(-0.544971\pi\) | ||||
−0.140811 | + | 0.990036i | \(0.544971\pi\) | |||||||
\(272\) | 1049.37i | 0.0141838i | ||||||||
\(273\) | − | 3724.66i | − | 0.0499759i | ||||||
\(274\) | − | 219566.i | − | 2.92458i | ||||||
\(275\) | 907.076i | 0.0119944i | ||||||||
\(276\) | 8151.77 | − | 70510.5i | 0.107012 | − | 0.925627i | ||||
\(277\) | 49755.5 | 0.648457 | 0.324229 | − | 0.945979i | \(-0.394895\pi\) | ||||
0.324229 | + | 0.945979i | \(0.394895\pi\) | |||||||
\(278\) | 80306.1 | 1.03910 | ||||||||
\(279\) | 20734.1 | 0.266364 | ||||||||
\(280\) | −73995.9 | −0.943825 | ||||||||
\(281\) | − | 124430.i | − | 1.57584i | −0.615777 | − | 0.787920i | \(-0.711158\pi\) | ||
0.615777 | − | 0.787920i | \(-0.288842\pi\) | |||||||
\(282\) | 68378.7 | 0.859850 | ||||||||
\(283\) | − | 127805.i | − | 1.59579i | −0.602799 | − | 0.797893i | \(-0.705948\pi\) | ||
0.602799 | − | 0.797893i | \(-0.294052\pi\) | |||||||
\(284\) | 146356. | 1.81457 | ||||||||
\(285\) | −64050.5 | −0.788556 | ||||||||
\(286\) | − | 350.723i | − | 0.00428777i | ||||||
\(287\) | − | 97453.9i | − | 1.18314i | ||||||
\(288\) | 27853.3 | 0.335808 | ||||||||
\(289\) | −114901. | −1.37572 | ||||||||
\(290\) | − | 182949.i | − | 2.17537i | ||||||
\(291\) | − | 53003.5i | − | 0.625920i | ||||||
\(292\) | 57173.2 | 0.670543 | ||||||||
\(293\) | 154004.i | 1.79389i | 0.442138 | + | 0.896947i | \(0.354220\pi\) | ||||
−0.442138 | + | 0.896947i | \(0.645780\pi\) | |||||||
\(294\) | −32209.0 | −0.372634 | ||||||||
\(295\) | − | 134346.i | − | 1.54376i | ||||||
\(296\) | 111728.i | 1.27520i | ||||||||
\(297\) | − | 403.142i | − | 0.00457031i | ||||||
\(298\) | − | 175973.i | − | 1.98159i | ||||||
\(299\) | −1146.61 | + | 9917.87i | −0.0128255 | + | 0.110937i | ||||
\(300\) | −42355.8 | −0.470620 | ||||||||
\(301\) | −668.703 | −0.00738074 | ||||||||
\(302\) | −128351. | −1.40730 | ||||||||
\(303\) | 51284.1 | 0.558596 | ||||||||
\(304\) | 946.798i | 0.0102450i | ||||||||
\(305\) | 22563.1 | 0.242549 | ||||||||
\(306\) | 77779.3i | 0.830656i | ||||||||
\(307\) | −97973.3 | −1.03952 | −0.519758 | − | 0.854314i | \(-0.673978\pi\) | ||||
−0.519758 | + | 0.854314i | \(0.673978\pi\) | |||||||
\(308\) | 2818.19 | 0.0297077 | ||||||||
\(309\) | − | 5190.33i | − | 0.0543598i | ||||||
\(310\) | 152316.i | 1.58497i | ||||||||
\(311\) | −24925.3 | −0.257704 | −0.128852 | − | 0.991664i | \(-0.541129\pi\) | ||||
−0.128852 | + | 0.991664i | \(0.541129\pi\) | |||||||
\(312\) | 6229.58 | 0.0639955 | ||||||||
\(313\) | − | 1190.84i | − | 0.0121553i | −0.999982 | − | 0.00607764i | \(-0.998065\pi\) | ||
0.999982 | − | 0.00607764i | \(-0.00193459\pi\) | |||||||
\(314\) | 127313.i | 1.29126i | ||||||||
\(315\) | 31451.4 | 0.316971 | ||||||||
\(316\) | 103181.i | 1.03329i | ||||||||
\(317\) | 129908. | 1.29275 | 0.646377 | − | 0.763018i | \(-0.276283\pi\) | ||||
0.646377 | + | 0.763018i | \(0.276283\pi\) | |||||||
\(318\) | − | 43822.1i | − | 0.433350i | ||||||
\(319\) | 2650.45i | 0.0260458i | ||||||||
\(320\) | 203458.i | 1.98690i | ||||||||
\(321\) | − | 30120.2i | − | 0.292313i | ||||||
\(322\) | −129073. | − | 14922.2i | −1.24487 | − | 0.143920i | ||||
\(323\) | −179027. | −1.71598 | ||||||||
\(324\) | 18824.7 | 0.179323 | ||||||||
\(325\) | 5957.68 | 0.0564040 | ||||||||
\(326\) | 176330. | 1.65917 | ||||||||
\(327\) | 108745.i | 1.01698i | ||||||||
\(328\) | 162994. | 1.51504 | ||||||||
\(329\) | − | 77284.5i | − | 0.714004i | ||||||
\(330\) | 2961.54 | 0.0271951 | ||||||||
\(331\) | 89871.7 | 0.820290 | 0.410145 | − | 0.912020i | \(-0.365478\pi\) | ||||
0.410145 | + | 0.912020i | \(0.365478\pi\) | |||||||
\(332\) | 239801.i | 2.17558i | ||||||||
\(333\) | − | 47489.1i | − | 0.428258i | ||||||
\(334\) | −15348.4 | −0.137585 | ||||||||
\(335\) | −106837. | −0.951992 | ||||||||
\(336\) | − | 464.917i | − | 0.00411810i | ||||||
\(337\) | 28151.1i | 0.247877i | 0.992290 | + | 0.123938i | \(0.0395525\pi\) | ||||
−0.992290 | + | 0.123938i | \(0.960448\pi\) | |||||||
\(338\) | 182402. | 1.59660 | ||||||||
\(339\) | − | 127462.i | − | 1.10913i | ||||||
\(340\) | −352787. | −3.05179 | ||||||||
\(341\) | − | 2206.65i | − | 0.0189769i | ||||||
\(342\) | 70176.5i | 0.599983i | ||||||||
\(343\) | 127595.i | 1.08454i | ||||||||
\(344\) | − | 1118.42i | − | 0.00945123i | ||||||
\(345\) | −83747.7 | − | 9682.12i | −0.703614 | − | 0.0813453i | ||||
\(346\) | 265888. | 2.22099 | ||||||||
\(347\) | 17305.7 | 0.143725 | 0.0718623 | − | 0.997415i | \(-0.477106\pi\) | ||||
0.0718623 | + | 0.997415i | \(0.477106\pi\) | |||||||
\(348\) | −123762. | −1.02195 | ||||||||
\(349\) | 92761.0 | 0.761578 | 0.380789 | − | 0.924662i | \(-0.375652\pi\) | ||||
0.380789 | + | 0.924662i | \(0.375652\pi\) | |||||||
\(350\) | 77534.5i | 0.632935i | ||||||||
\(351\) | −2647.84 | −0.0214920 | ||||||||
\(352\) | − | 2964.32i | − | 0.0239243i | ||||||
\(353\) | 203342. | 1.63184 | 0.815920 | − | 0.578165i | \(-0.196231\pi\) | ||||
0.815920 | + | 0.578165i | \(0.196231\pi\) | |||||||
\(354\) | −147195. | −1.17459 | ||||||||
\(355\) | − | 173832.i | − | 1.37934i | ||||||
\(356\) | 282148.i | 2.22627i | ||||||||
\(357\) | 87909.4 | 0.689762 | ||||||||
\(358\) | −273050. | −2.13047 | ||||||||
\(359\) | 91489.8i | 0.709878i | 0.934889 | + | 0.354939i | \(0.115498\pi\) | ||||
−0.934889 | + | 0.354939i | \(0.884502\pi\) | |||||||
\(360\) | 52603.3i | 0.405890i | ||||||||
\(361\) | −31205.8 | −0.239453 | ||||||||
\(362\) | − | 247149.i | − | 1.88600i | ||||||
\(363\) | 76034.0 | 0.577025 | ||||||||
\(364\) | − | 18509.9i | − | 0.139702i | ||||||
\(365\) | − | 67906.5i | − | 0.509713i | ||||||
\(366\) | − | 24721.1i | − | 0.184546i | ||||||
\(367\) | − | 80073.3i | − | 0.594505i | −0.954799 | − | 0.297253i | \(-0.903930\pi\) | ||
0.954799 | − | 0.297253i | \(-0.0960704\pi\) | |||||||
\(368\) | −143.122 | + | 1237.96i | −0.00105684 | + | 0.00914139i | ||||
\(369\) | −69279.4 | −0.508805 | ||||||||
\(370\) | 348862. | 2.54830 | ||||||||
\(371\) | −49529.6 | −0.359846 | ||||||||
\(372\) | 103039. | 0.744588 | ||||||||
\(373\) | − | 76100.2i | − | 0.546976i | −0.961875 | − | 0.273488i | \(-0.911823\pi\) | ||
0.961875 | − | 0.273488i | \(-0.0881773\pi\) | |||||||
\(374\) | 8277.77 | 0.0591793 | ||||||||
\(375\) | − | 49297.5i | − | 0.350560i | ||||||
\(376\) | 129260. | 0.914300 | ||||||||
\(377\) | 17408.1 | 0.122481 | ||||||||
\(378\) | − | 34459.5i | − | 0.241171i | ||||||
\(379\) | − | 162209.i | − | 1.12927i | −0.825342 | − | 0.564634i | \(-0.809017\pi\) | ||
0.825342 | − | 0.564634i | \(-0.190983\pi\) | |||||||
\(380\) | −318303. | −2.20431 | ||||||||
\(381\) | 141074. | 0.971846 | ||||||||
\(382\) | 46896.5i | 0.321376i | ||||||||
\(383\) | 209744.i | 1.42986i | 0.699197 | + | 0.714929i | \(0.253541\pi\) | ||||
−0.699197 | + | 0.714929i | \(0.746459\pi\) | |||||||
\(384\) | 137152. | 0.930120 | ||||||||
\(385\) | − | 3347.26i | − | 0.0225823i | ||||||
\(386\) | −362807. | −2.43501 | ||||||||
\(387\) | 475.377i | 0.00317407i | ||||||||
\(388\) | − | 263404.i | − | 1.74968i | ||||||
\(389\) | 43194.3i | 0.285448i | 0.989763 | + | 0.142724i | \(0.0455861\pi\) | ||||
−0.989763 | + | 0.142724i | \(0.954414\pi\) | |||||||
\(390\) | − | 19451.4i | − | 0.127886i | ||||||
\(391\) | −234082. | − | 27062.3i | −1.53114 | − | 0.177016i | ||||
\(392\) | −60886.5 | −0.396231 | ||||||||
\(393\) | −123503. | −0.799636 | ||||||||
\(394\) | −3952.14 | −0.0254589 | ||||||||
\(395\) | 122551. | 0.785458 | ||||||||
\(396\) | − | 2003.44i | − | 0.0127757i | ||||||
\(397\) | −167885. | −1.06520 | −0.532599 | − | 0.846367i | \(-0.678785\pi\) | ||||
−0.532599 | + | 0.846367i | \(0.678785\pi\) | |||||||
\(398\) | 103596.i | 0.653996i | ||||||||
\(399\) | 79316.3 | 0.498215 | ||||||||
\(400\) | 743.646 | 0.00464779 | ||||||||
\(401\) | − | 81170.0i | − | 0.504785i | −0.967625 | − | 0.252393i | \(-0.918783\pi\) | ||
0.967625 | − | 0.252393i | \(-0.0812175\pi\) | |||||||
\(402\) | 117055.i | 0.724335i | ||||||||
\(403\) | −14493.3 | −0.0892393 | ||||||||
\(404\) | 254860. | 1.56149 | ||||||||
\(405\) | − | 22358.7i | − | 0.136313i | ||||||
\(406\) | 226553.i | 1.37442i | ||||||||
\(407\) | −5054.09 | −0.0305108 | ||||||||
\(408\) | 147031.i | 0.883258i | ||||||||
\(409\) | −149090. | −0.891254 | −0.445627 | − | 0.895219i | \(-0.647019\pi\) | ||||
−0.445627 | + | 0.895219i | \(0.647019\pi\) | |||||||
\(410\) | − | 508937.i | − | 3.02759i | ||||||
\(411\) | 176417.i | 1.04438i | ||||||||
\(412\) | − | 25793.6i | − | 0.151956i | ||||||
\(413\) | 166366.i | 0.975358i | ||||||||
\(414\) | −10608.1 | + | 91757.5i | −0.0618926 | + | 0.535354i | ||||
\(415\) | 284820. | 1.65376 | ||||||||
\(416\) | −19469.7 | −0.112505 | ||||||||
\(417\) | −64524.6 | −0.371068 | ||||||||
\(418\) | 7468.62 | 0.0427452 | ||||||||
\(419\) | 142909.i | 0.814013i | 0.913425 | + | 0.407006i | \(0.133427\pi\) | ||||
−0.913425 | + | 0.407006i | \(0.866573\pi\) | |||||||
\(420\) | 156300. | 0.886053 | ||||||||
\(421\) | 20088.3i | 0.113339i | 0.998393 | + | 0.0566693i | \(0.0180481\pi\) | ||||
−0.998393 | + | 0.0566693i | \(0.981952\pi\) | |||||||
\(422\) | 462025. | 2.59442 | ||||||||
\(423\) | −54941.1 | −0.307055 | ||||||||
\(424\) | − | 82839.4i | − | 0.460792i | ||||||
\(425\) | 140613.i | 0.778482i | ||||||||
\(426\) | −190458. | −1.04949 | ||||||||
\(427\) | −27940.8 | −0.153244 | ||||||||
\(428\) | − | 149684.i | − | 0.817124i | ||||||
\(429\) | 281.800i | 0.00153118i | ||||||||
\(430\) | −3492.19 | −0.0188869 | ||||||||
\(431\) | 52245.2i | 0.281249i | 0.990063 | + | 0.140625i | \(0.0449111\pi\) | ||||
−0.990063 | + | 0.140625i | \(0.955089\pi\) | |||||||
\(432\) | −330.507 | −0.00177098 | ||||||||
\(433\) | 10421.5i | 0.0555848i | 0.999614 | + | 0.0277924i | \(0.00884773\pi\) | ||||
−0.999614 | + | 0.0277924i | \(0.991152\pi\) | |||||||
\(434\) | − | 188619.i | − | 1.00139i | ||||||
\(435\) | 146996.i | 0.776833i | ||||||||
\(436\) | 540414.i | 2.84285i | ||||||||
\(437\) | −211200. | − | 24417.0i | −1.10594 | − | 0.127859i | ||||
\(438\) | −74401.2 | −0.387821 | ||||||||
\(439\) | 66984.2 | 0.347571 | 0.173785 | − | 0.984784i | \(-0.444400\pi\) | ||||
0.173785 | + | 0.984784i | \(0.444400\pi\) | |||||||
\(440\) | 5598.37 | 0.0289172 | ||||||||
\(441\) | 25879.4 | 0.133069 | ||||||||
\(442\) | − | 54368.4i | − | 0.278293i | ||||||
\(443\) | −222081. | −1.13163 | −0.565814 | − | 0.824533i | \(-0.691438\pi\) | ||||
−0.565814 | + | 0.824533i | \(0.691438\pi\) | |||||||
\(444\) | − | 236000.i | − | 1.19714i | ||||||
\(445\) | 335117. | 1.69229 | ||||||||
\(446\) | −215748. | −1.08462 | ||||||||
\(447\) | 141391.i | 0.707633i | ||||||||
\(448\) | − | 251951.i | − | 1.25533i | ||||||
\(449\) | 97092.3 | 0.481606 | 0.240803 | − | 0.970574i | \(-0.422589\pi\) | ||||
0.240803 | + | 0.970574i | \(0.422589\pi\) | |||||||
\(450\) | 55118.9 | 0.272192 | ||||||||
\(451\) | 7373.15i | 0.0362493i | ||||||||
\(452\) | − | 633432.i | − | 3.10044i | ||||||
\(453\) | 103128. | 0.502552 | ||||||||
\(454\) | 248314.i | 1.20473i | ||||||||
\(455\) | −21984.8 | −0.106194 | ||||||||
\(456\) | 132658.i | 0.637977i | ||||||||
\(457\) | 80986.2i | 0.387774i | 0.981024 | + | 0.193887i | \(0.0621095\pi\) | ||||
−0.981024 | + | 0.193887i | \(0.937890\pi\) | |||||||
\(458\) | − | 239158.i | − | 1.14013i | ||||||
\(459\) | − | 62494.4i | − | 0.296630i | ||||||
\(460\) | −416189. | − | 48115.8i | −1.96687 | − | 0.227391i | ||||
\(461\) | −7531.74 | −0.0354400 | −0.0177200 | − | 0.999843i | \(-0.505641\pi\) | ||||
−0.0177200 | + | 0.999843i | \(0.505641\pi\) | |||||||
\(462\) | −3667.40 | −0.0171820 | ||||||||
\(463\) | 147202. | 0.686674 | 0.343337 | − | 0.939212i | \(-0.388443\pi\) | ||||
0.343337 | + | 0.939212i | \(0.388443\pi\) | |||||||
\(464\) | 2172.91 | 0.0100927 | ||||||||
\(465\) | − | 122383.i | − | 0.565998i | ||||||
\(466\) | −8135.75 | −0.0374650 | ||||||||
\(467\) | 91391.0i | 0.419054i | 0.977803 | + | 0.209527i | \(0.0671924\pi\) | ||||
−0.977803 | + | 0.209527i | \(0.932808\pi\) | |||||||
\(468\) | −13158.6 | −0.0600783 | ||||||||
\(469\) | 132301. | 0.601475 | ||||||||
\(470\) | − | 403606.i | − | 1.82710i | ||||||
\(471\) | − | 102294.i | − | 0.461114i | ||||||
\(472\) | −278251. | −1.24897 | ||||||||
\(473\) | 50.5926 | 0.000226134 | ||||||||
\(474\) | − | 134272.i | − | 0.597626i | ||||||
\(475\) | 126868.i | 0.562298i | ||||||||
\(476\) | 436871. | 1.92814 | ||||||||
\(477\) | 35210.3i | 0.154751i | ||||||||
\(478\) | −415727. | −1.81950 | ||||||||
\(479\) | 416999.i | 1.81745i | 0.417390 | + | 0.908727i | \(0.362945\pi\) | ||||
−0.417390 | + | 0.908727i | \(0.637055\pi\) | |||||||
\(480\) | − | 164404.i | − | 0.713559i | ||||||
\(481\) | 33195.3i | 0.143478i | ||||||||
\(482\) | − | 490083.i | − | 2.10948i | ||||||
\(483\) | 103708. | + | 11989.8i | 0.444548 | + | 0.0513945i | ||||
\(484\) | 377855. | 1.61300 | ||||||||
\(485\) | −312854. | −1.33002 | ||||||||
\(486\) | −24497.1 | −0.103715 | ||||||||
\(487\) | −252578. | −1.06497 | −0.532485 | − | 0.846440i | \(-0.678742\pi\) | ||||
−0.532485 | + | 0.846440i | \(0.678742\pi\) | |||||||
\(488\) | − | 46731.7i | − | 0.196233i | ||||||
\(489\) | −141678. | −0.592497 | ||||||||
\(490\) | 190114.i | 0.791812i | ||||||||
\(491\) | 458417. | 1.90151 | 0.950753 | − | 0.309951i | \(-0.100313\pi\) | ||||
0.950753 | + | 0.309951i | \(0.100313\pi\) | |||||||
\(492\) | −344288. | −1.42230 | ||||||||
\(493\) | 410867.i | 1.69047i | ||||||||
\(494\) | − | 49053.9i | − | 0.201011i | ||||||
\(495\) | −2379.55 | −0.00971146 | ||||||||
\(496\) | −1809.07 | −0.00735347 | ||||||||
\(497\) | 215263.i | 0.871478i | ||||||||
\(498\) | − | 312061.i | − | 1.25829i | ||||||
\(499\) | −57901.6 | −0.232536 | −0.116268 | − | 0.993218i | \(-0.537093\pi\) | ||||
−0.116268 | + | 0.993218i | \(0.537093\pi\) | |||||||
\(500\) | − | 244987.i | − | 0.979946i | ||||||
\(501\) | 12332.2 | 0.0491320 | ||||||||
\(502\) | 268750.i | 1.06645i | ||||||||
\(503\) | 244716.i | 0.967223i | 0.875283 | + | 0.483611i | \(0.160675\pi\) | ||||
−0.875283 | + | 0.483611i | \(0.839325\pi\) | |||||||
\(504\) | − | 65140.8i | − | 0.256444i | ||||||
\(505\) | − | 302705.i | − | 1.18696i | ||||||
\(506\) | 9765.41 | + | 1128.99i | 0.0381408 | + | 0.00440948i | ||||
\(507\) | −146556. | −0.570150 | ||||||||
\(508\) | 701076. | 2.71667 | ||||||||
\(509\) | 65168.6 | 0.251537 | 0.125769 | − | 0.992060i | \(-0.459860\pi\) | ||||
0.125769 | + | 0.992060i | \(0.459860\pi\) | |||||||
\(510\) | 459093. | 1.76506 | ||||||||
\(511\) | 84091.3i | 0.322040i | ||||||||
\(512\) | −4824.57 | −0.0184043 | ||||||||
\(513\) | − | 56385.6i | − | 0.214256i | ||||||
\(514\) | 7898.45 | 0.0298962 | ||||||||
\(515\) | −30635.9 | −0.115509 | ||||||||
\(516\) | 2362.41i | 0.00887272i | ||||||||
\(517\) | 5847.18i | 0.0218759i | ||||||||
\(518\) | −432010. | −1.61003 | ||||||||
\(519\) | −213636. | −0.793123 | ||||||||
\(520\) | − | 36770.1i | − | 0.135984i | ||||||
\(521\) | − | 73665.5i | − | 0.271387i | −0.990751 | − | 0.135693i | \(-0.956674\pi\) | ||
0.990751 | − | 0.135693i | \(-0.0433262\pi\) | |||||||
\(522\) | 161055. | 0.591064 | ||||||||
\(523\) | − | 443396.i | − | 1.62102i | −0.585726 | − | 0.810509i | \(-0.699190\pi\) | ||
0.585726 | − | 0.810509i | \(-0.300810\pi\) | |||||||
\(524\) | −613755. | −2.23528 | ||||||||
\(525\) | − | 62297.6i | − | 0.226023i | ||||||
\(526\) | 497929.i | 1.79968i | ||||||||
\(527\) | − | 342071.i | − | 1.23167i | ||||||
\(528\) | 35.1746i | 0.000126172i | ||||||||
\(529\) | −272459. | − | 63851.8i | −0.973621 | − | 0.228172i | ||||
\(530\) | −258660. | −0.920827 | ||||||||
\(531\) | 118269. | 0.419450 | ||||||||
\(532\) | 394167. | 1.39270 | ||||||||
\(533\) | 48426.9 | 0.170464 | ||||||||
\(534\) | − | 367168.i | − | 1.28760i | ||||||
\(535\) | −177785. | −0.621136 | ||||||||
\(536\) | 221276.i | 0.770204i | ||||||||
\(537\) | 219391. | 0.760798 | ||||||||
\(538\) | 272075. | 0.939992 | ||||||||
\(539\) | − | 2754.25i | − | 0.00948037i | ||||||
\(540\) | − | 111113.i | − | 0.381045i | ||||||
\(541\) | 217747. | 0.743974 | 0.371987 | − | 0.928238i | \(-0.378677\pi\) | ||||
0.371987 | + | 0.928238i | \(0.378677\pi\) | |||||||
\(542\) | 133755. | 0.455316 | ||||||||
\(543\) | 198580.i | 0.673496i | ||||||||
\(544\) | − | 459523.i | − | 1.55278i | ||||||
\(545\) | 641867. | 2.16099 | ||||||||
\(546\) | 24087.5i | 0.0807991i | ||||||||
\(547\) | 400661. | 1.33907 | 0.669533 | − | 0.742782i | \(-0.266494\pi\) | ||||
0.669533 | + | 0.742782i | \(0.266494\pi\) | |||||||
\(548\) | 876715.i | 2.91942i | ||||||||
\(549\) | 19863.0i | 0.0659021i | ||||||||
\(550\) | − | 5866.10i | − | 0.0193921i | ||||||
\(551\) | 370705.i | 1.22103i | ||||||||
\(552\) | −20053.2 | + | 173454.i | −0.0658120 | + | 0.569255i | ||||
\(553\) | −151760. | −0.496257 | ||||||||
\(554\) | −321770. | −1.04840 | ||||||||
\(555\) | −280305. | −0.910006 | ||||||||
\(556\) | −320659. | −1.03727 | ||||||||
\(557\) | − | 344709.i | − | 1.11107i | −0.831492 | − | 0.555536i | \(-0.812513\pi\) | ||
0.831492 | − | 0.555536i | \(-0.187487\pi\) | |||||||
\(558\) | −134088. | −0.430647 | ||||||||
\(559\) | − | 332.292i | − | 0.00106340i | ||||||
\(560\) | −2744.18 | −0.00875056 | ||||||||
\(561\) | −6651.04 | −0.0211331 | ||||||||
\(562\) | 804693.i | 2.54776i | ||||||||
\(563\) | 301392.i | 0.950857i | 0.879754 | + | 0.475429i | \(0.157707\pi\) | ||||
−0.879754 | + | 0.475429i | \(0.842293\pi\) | |||||||
\(564\) | −273033. | −0.858335 | ||||||||
\(565\) | −752348. | −2.35680 | ||||||||
\(566\) | 826519.i | 2.58000i | ||||||||
\(567\) | 27687.6i | 0.0861232i | ||||||||
\(568\) | −360032. | −1.11595 | ||||||||
\(569\) | − | 21821.5i | − | 0.0674000i | −0.999432 | − | 0.0337000i | \(-0.989271\pi\) | ||
0.999432 | − | 0.0337000i | \(-0.0107291\pi\) | |||||||
\(570\) | 414217. | 1.27491 | ||||||||
\(571\) | − | 324837.i | − | 0.996307i | −0.867089 | − | 0.498153i | \(-0.834012\pi\) | ||
0.867089 | − | 0.498153i | \(-0.165988\pi\) | |||||||
\(572\) | 1400.42i | 0.00428022i | ||||||||
\(573\) | − | 37680.5i | − | 0.114764i | ||||||
\(574\) | 630238.i | 1.91285i | ||||||||
\(575\) | −19177.9 | + | 165884.i | −0.0580050 | + | 0.501728i | ||||
\(576\) | −179110. | −0.539853 | ||||||||
\(577\) | 30900.0 | 0.0928127 | 0.0464063 | − | 0.998923i | \(-0.485223\pi\) | ||||
0.0464063 | + | 0.998923i | \(0.485223\pi\) | |||||||
\(578\) | 743070. | 2.22420 | ||||||||
\(579\) | 291509. | 0.869550 | ||||||||
\(580\) | 730506.i | 2.17154i | ||||||||
\(581\) | −352704. | −1.04486 | ||||||||
\(582\) | 342776.i | 1.01196i | ||||||||
\(583\) | 3747.30 | 0.0110251 | ||||||||
\(584\) | −140645. | −0.412380 | ||||||||
\(585\) | 15628.9i | 0.0456684i | ||||||||
\(586\) | − | 995950.i | − | 2.90029i | ||||||
\(587\) | 360981. | 1.04763 | 0.523816 | − | 0.851831i | \(-0.324508\pi\) | ||||
0.523816 | + | 0.851831i | \(0.324508\pi\) | |||||||
\(588\) | 128609. | 0.371978 | ||||||||
\(589\) | − | 308633.i | − | 0.889636i | ||||||
\(590\) | 868819.i | 2.49589i | ||||||||
\(591\) | 3175.47 | 0.00909146 | ||||||||
\(592\) | 4143.48i | 0.0118228i | ||||||||
\(593\) | 376995. | 1.07208 | 0.536038 | − | 0.844194i | \(-0.319920\pi\) | ||||
0.536038 | + | 0.844194i | \(0.319920\pi\) | |||||||
\(594\) | 2607.14i | 0.00738909i | ||||||||
\(595\) | − | 518886.i | − | 1.46568i | ||||||
\(596\) | 702653.i | 1.97810i | ||||||||
\(597\) | − | 83237.3i | − | 0.233544i | ||||||
\(598\) | 7415.18 | − | 64139.2i | 0.0207357 | − | 0.179358i | ||||
\(599\) | 44444.7 | 0.123870 | 0.0619350 | − | 0.998080i | \(-0.480273\pi\) | ||||
0.0619350 | + | 0.998080i | \(0.480273\pi\) | |||||||
\(600\) | 104194. | 0.289428 | ||||||||
\(601\) | 132070. | 0.365643 | 0.182821 | − | 0.983146i | \(-0.441477\pi\) | ||||
0.182821 | + | 0.983146i | \(0.441477\pi\) | |||||||
\(602\) | 4324.53 | 0.0119329 | ||||||||
\(603\) | − | 94052.0i | − | 0.258663i | ||||||
\(604\) | 512501. | 1.40482 | ||||||||
\(605\) | − | 448791.i | − | 1.22612i | ||||||
\(606\) | −331657. | −0.903115 | ||||||||
\(607\) | 300182. | 0.814719 | 0.407360 | − | 0.913268i | \(-0.366450\pi\) | ||||
0.407360 | + | 0.913268i | \(0.366450\pi\) | |||||||
\(608\) | − | 414605.i | − | 1.12157i | ||||||
\(609\) | − | 182031.i | − | 0.490808i | ||||||
\(610\) | −145916. | −0.392143 | ||||||||
\(611\) | 38404.3 | 0.102872 | ||||||||
\(612\) | − | 310569.i | − | 0.829193i | ||||||
\(613\) | 236992.i | 0.630686i | 0.948978 | + | 0.315343i | \(0.102119\pi\) | ||||
−0.948978 | + | 0.315343i | \(0.897881\pi\) | |||||||
\(614\) | 633597. | 1.68065 | ||||||||
\(615\) | 408922.i | 1.08116i | ||||||||
\(616\) | −6932.69 | −0.0182701 | ||||||||
\(617\) | 109059.i | 0.286479i | 0.989688 | + | 0.143239i | \(0.0457519\pi\) | ||||
−0.989688 | + | 0.143239i | \(0.954248\pi\) | |||||||
\(618\) | 33566.0i | 0.0878867i | ||||||||
\(619\) | − | 316224.i | − | 0.825304i | −0.910889 | − | 0.412652i | \(-0.864603\pi\) | ||
0.910889 | − | 0.412652i | \(-0.135397\pi\) | |||||||
\(620\) | − | 608189.i | − | 1.58218i | ||||||
\(621\) | 8523.46 | − | 73725.6i | 0.0221021 | − | 0.191177i | ||||
\(622\) | 161193. | 0.416645 | ||||||||
\(623\) | −414989. | −1.06920 | ||||||||
\(624\) | 231.027 | 0.000593326 | ||||||||
\(625\) | −488271. | −1.24997 | ||||||||
\(626\) | 7701.22i | 0.0196522i | ||||||||
\(627\) | −6000.91 | −0.0152645 | ||||||||
\(628\) | − | 508356.i | − | 1.28899i | ||||||
\(629\) | −783475. | −1.98027 | ||||||||
\(630\) | −203398. | −0.512466 | ||||||||
\(631\) | − | 383989.i | − | 0.964407i | −0.876059 | − | 0.482203i | \(-0.839837\pi\) | ||
0.876059 | − | 0.482203i | \(-0.160163\pi\) | |||||||
\(632\) | − | 253822.i | − | 0.635470i | ||||||
\(633\) | −371229. | −0.926477 | ||||||||
\(634\) | −840117. | −2.09007 | ||||||||
\(635\) | − | 832691.i | − | 2.06508i | ||||||
\(636\) | 174980.i | 0.432587i | ||||||||
\(637\) | −18089.9 | −0.0445818 | ||||||||
\(638\) | − | 17140.5i | − | 0.0421098i | ||||||
\(639\) | 153029. | 0.374777 | ||||||||
\(640\) | − | 809539.i | − | 1.97641i | ||||||
\(641\) | − | 676424.i | − | 1.64628i | −0.567841 | − | 0.823138i | \(-0.692221\pi\) | ||
0.567841 | − | 0.823138i | \(-0.307779\pi\) | |||||||
\(642\) | 194789.i | 0.472600i | ||||||||
\(643\) | 143739.i | 0.347659i | 0.984776 | + | 0.173830i | \(0.0556142\pi\) | ||||
−0.984776 | + | 0.173830i | \(0.944386\pi\) | |||||||
\(644\) | 515384. | + | 59583.8i | 1.24268 | + | 0.143667i | ||||
\(645\) | 2805.92 | 0.00674459 | ||||||||
\(646\) | 1.15777e6 | 2.77433 | ||||||||
\(647\) | −590807. | −1.41136 | −0.705679 | − | 0.708532i | \(-0.749358\pi\) | ||||
−0.705679 | + | 0.708532i | \(0.749358\pi\) | |||||||
\(648\) | −46308.2 | −0.110283 | ||||||||
\(649\) | − | 12586.9i | − | 0.0298833i | ||||||
\(650\) | −38528.5 | −0.0911918 | ||||||||
\(651\) | 151552.i | 0.357601i | ||||||||
\(652\) | −704079. | −1.65625 | ||||||||
\(653\) | −231344. | −0.542541 | −0.271270 | − | 0.962503i | \(-0.587444\pi\) | ||||
−0.271270 | + | 0.962503i | \(0.587444\pi\) | |||||||
\(654\) | − | 703257.i | − | 1.64421i | ||||||
\(655\) | 728977.i | 1.69915i | ||||||||
\(656\) | 6044.71 | 0.0140465 | ||||||||
\(657\) | 59780.1 | 0.138492 | ||||||||
\(658\) | 499802.i | 1.15437i | ||||||||
\(659\) | − | 564690.i | − | 1.30029i | −0.759812 | − | 0.650143i | \(-0.774709\pi\) | ||
0.759812 | − | 0.650143i | \(-0.225291\pi\) | |||||||
\(660\) | −11825.3 | −0.0271472 | ||||||||
\(661\) | − | 640670.i | − | 1.46633i | −0.680051 | − | 0.733165i | \(-0.738042\pi\) | ||
0.680051 | − | 0.733165i | \(-0.261958\pi\) | |||||||
\(662\) | −581204. | −1.32621 | ||||||||
\(663\) | 43684.0i | 0.0993793i | ||||||||
\(664\) | − | 589905.i | − | 1.33797i | ||||||
\(665\) | − | 468165.i | − | 1.05866i | ||||||
\(666\) | 307114.i | 0.692390i | ||||||||
\(667\) | −56037.2 | + | 484706.i | −0.125958 | + | 1.08950i | ||||
\(668\) | 61285.5 | 0.137342 | ||||||||
\(669\) | 173350. | 0.387322 | ||||||||
\(670\) | 690921. | 1.53914 | ||||||||
\(671\) | 2113.94 | 0.00469513 | ||||||||
\(672\) | 203588.i | 0.450831i | ||||||||
\(673\) | 460196. | 1.01604 | 0.508022 | − | 0.861344i | \(-0.330377\pi\) | ||||
0.508022 | + | 0.861344i | \(0.330377\pi\) | |||||||
\(674\) | − | 182054.i | − | 0.400757i | ||||||
\(675\) | −44287.0 | −0.0972007 | ||||||||
\(676\) | −728321. | −1.59378 | ||||||||
\(677\) | 156681.i | 0.341852i | 0.985284 | + | 0.170926i | \(0.0546759\pi\) | ||||
−0.985284 | + | 0.170926i | \(0.945324\pi\) | |||||||
\(678\) | 824305.i | 1.79320i | ||||||||
\(679\) | 387419. | 0.840314 | ||||||||
\(680\) | 867849. | 1.87684 | ||||||||
\(681\) | − | 199516.i | − | 0.430213i | ||||||
\(682\) | 14270.5i | 0.0306810i | ||||||||
\(683\) | 448126. | 0.960635 | 0.480318 | − | 0.877095i | \(-0.340521\pi\) | ||||
0.480318 | + | 0.877095i | \(0.340521\pi\) | |||||||
\(684\) | − | 280211.i | − | 0.598926i | ||||||
\(685\) | 1.04130e6 | 2.21920 | ||||||||
\(686\) | − | 825160.i | − | 1.75344i | ||||||
\(687\) | 192160.i | 0.407145i | ||||||||
\(688\) | − | 41.4772i | − | 8.76260e-5i | ||||||
\(689\) | − | 24612.3i | − | 0.0518458i | ||||||
\(690\) | 541599. | + | 62614.6i | 1.13757 | + | 0.131516i | ||||
\(691\) | −274108. | −0.574070 | −0.287035 | − | 0.957920i | \(-0.592670\pi\) | ||||
−0.287035 | + | 0.957920i | \(0.592670\pi\) | |||||||
\(692\) | −1.06168e6 | −2.21708 | ||||||||
\(693\) | 2946.69 | 0.00613576 | ||||||||
\(694\) | −111917. | −0.232368 | ||||||||
\(695\) | 380857.i | 0.788482i | ||||||||
\(696\) | 304452. | 0.628493 | ||||||||
\(697\) | 1.14297e6i | 2.35272i | ||||||||
\(698\) | −599889. | −1.23129 | ||||||||
\(699\) | 6536.93 | 0.0133789 | ||||||||
\(700\) | − | 309592.i | − | 0.631820i | ||||||
\(701\) | − | 247781.i | − | 0.504234i | −0.967697 | − | 0.252117i | \(-0.918873\pi\) | ||
0.967697 | − | 0.252117i | \(-0.0811267\pi\) | |||||||
\(702\) | 17123.7 | 0.0347474 | ||||||||
\(703\) | −706891. | −1.43035 | ||||||||
\(704\) | 19062.1i | 0.0384613i | ||||||||
\(705\) | 324290.i | 0.652463i | ||||||||
\(706\) | −1.31502e6 | −2.63829 | ||||||||
\(707\) | 374852.i | 0.749930i | ||||||||
\(708\) | 587742. | 1.17252 | ||||||||
\(709\) | 360175.i | 0.716508i | 0.933624 | + | 0.358254i | \(0.116628\pi\) | ||||
−0.933624 | + | 0.358254i | \(0.883372\pi\) | |||||||
\(710\) | 1.12418e6i | 2.23007i | ||||||||
\(711\) | 107885.i | 0.213414i | ||||||||
\(712\) | − | 694078.i | − | 1.36914i | ||||||
\(713\) | 46654.2 | − | 403546.i | 0.0917723 | − | 0.793805i | ||||
\(714\) | −568514. | −1.11518 | ||||||||
\(715\) | 1663.32 | 0.00325360 | ||||||||
\(716\) | 1.09027e6 | 2.12672 | ||||||||
\(717\) | 334030. | 0.649750 | ||||||||
\(718\) | − | 591668.i | − | 1.14770i | ||||||
\(719\) | 380773. | 0.736559 | 0.368280 | − | 0.929715i | \(-0.379947\pi\) | ||||
0.368280 | + | 0.929715i | \(0.379947\pi\) | |||||||
\(720\) | 1950.82i | 0.00376316i | ||||||||
\(721\) | 37937.7 | 0.0729795 | ||||||||
\(722\) | 201809. | 0.387139 | ||||||||
\(723\) | 393773.i | 0.753303i | ||||||||
\(724\) | 986853.i | 1.88267i | ||||||||
\(725\) | 291164. | 0.553938 | ||||||||
\(726\) | −491714. | −0.932910 | ||||||||
\(727\) | 115974.i | 0.219428i | 0.993963 | + | 0.109714i | \(0.0349934\pi\) | ||||
−0.993963 | + | 0.109714i | \(0.965007\pi\) | |||||||
\(728\) | 45533.9i | 0.0859157i | ||||||||
\(729\) | 19683.0 | 0.0370370 | ||||||||
\(730\) | 439154.i | 0.824083i | ||||||||
\(731\) | 7842.77 | 0.0146769 | ||||||||
\(732\) | 98710.2i | 0.184221i | ||||||||
\(733\) | − | 564579.i | − | 1.05079i | −0.850858 | − | 0.525396i | \(-0.823917\pi\) | ||
0.850858 | − | 0.525396i | \(-0.176083\pi\) | |||||||
\(734\) | 517837.i | 0.961172i | ||||||||
\(735\) | − | 152753.i | − | 0.282759i | ||||||
\(736\) | 62673.3 | − | 542107.i | 0.115698 | − | 1.00076i | ||||
\(737\) | −10009.6 | −0.0184282 | ||||||||
\(738\) | 448033. | 0.822616 | ||||||||
\(739\) | −181881. | −0.333042 | −0.166521 | − | 0.986038i | \(-0.553253\pi\) | ||||
−0.166521 | + | 0.986038i | \(0.553253\pi\) | |||||||
\(740\) | −1.39299e6 | −2.54381 | ||||||||
\(741\) | 39414.0i | 0.0717817i | ||||||||
\(742\) | 320310. | 0.581784 | ||||||||
\(743\) | 750026.i | 1.35862i | 0.733850 | + | 0.679311i | \(0.237721\pi\) | ||||
−0.733850 | + | 0.679311i | \(0.762279\pi\) | |||||||
\(744\) | −253474. | −0.457918 | ||||||||
\(745\) | 834564. | 1.50365 | ||||||||
\(746\) | 492143.i | 0.884328i | ||||||||
\(747\) | 250735.i | 0.449339i | ||||||||
\(748\) | −33052.7 | −0.0590751 | ||||||||
\(749\) | 220158. | 0.392438 | ||||||||
\(750\) | 318808.i | 0.566771i | ||||||||
\(751\) | − | 764417.i | − | 1.35535i | −0.735363 | − | 0.677674i | \(-0.762988\pi\) | ||
0.735363 | − | 0.677674i | \(-0.237012\pi\) | |||||||
\(752\) | 4793.68 | 0.00847683 | ||||||||
\(753\) | − | 215936.i | − | 0.380833i | ||||||
\(754\) | −112579. | −0.198023 | ||||||||
\(755\) | − | 608715.i | − | 1.06787i | ||||||
\(756\) | 137595.i | 0.240747i | ||||||||
\(757\) | 1.05333e6i | 1.83811i | 0.394130 | + | 0.919055i | \(0.371046\pi\) | ||||
−0.394130 | + | 0.919055i | \(0.628954\pi\) | |||||||
\(758\) | 1.04901e6i | 1.82575i | ||||||||
\(759\) | −7846.34 | − | 907.120i | −0.0136202 | − | 0.00157464i | ||||
\(760\) | 783017. | 1.35564 | ||||||||
\(761\) | −869147. | −1.50080 | −0.750402 | − | 0.660982i | \(-0.770140\pi\) | ||||
−0.750402 | + | 0.660982i | \(0.770140\pi\) | |||||||
\(762\) | −912332. | −1.57124 | ||||||||
\(763\) | −794850. | −1.36533 | ||||||||
\(764\) | − | 187255.i | − | 0.320810i | ||||||
\(765\) | −368873. | −0.630310 | ||||||||
\(766\) | − | 1.35643e6i | − | 2.31174i | ||||||
\(767\) | −82670.7 | −0.140527 | ||||||||
\(768\) | −335449. | −0.568727 | ||||||||
\(769\) | 213097.i | 0.360350i | 0.983635 | + | 0.180175i | \(0.0576665\pi\) | ||||
−0.983635 | + | 0.180175i | \(0.942334\pi\) | |||||||
\(770\) | 21646.9i | 0.0365101i | ||||||||
\(771\) | −6346.27 | −0.0106760 | ||||||||
\(772\) | 1.44867e6 | 2.43072 | ||||||||
\(773\) | − | 679272.i | − | 1.13680i | −0.822752 | − | 0.568401i | \(-0.807562\pi\) | ||
0.822752 | − | 0.568401i | \(-0.192438\pi\) | |||||||
\(774\) | − | 3074.28i | − | 0.00513171i | ||||||
\(775\) | −242411. | −0.403597 | ||||||||
\(776\) | 647968.i | 1.07604i | ||||||||
\(777\) | 347113. | 0.574948 | ||||||||
\(778\) | − | 279339.i | − | 0.461501i | ||||||
\(779\) | 1.03125e6i | 1.69937i | ||||||||
\(780\) | 77668.6i | 0.127660i | ||||||||
\(781\) | − | 16286.3i | − | 0.0267006i | ||||||
\(782\) | 1.51382e6 | + | 175013.i | 2.47548 | + | 0.286192i | ||||
\(783\) | −129405. | −0.211071 | ||||||||
\(784\) | −2258.01 | −0.00367361 | ||||||||
\(785\) | −603791. | −0.979822 | ||||||||
\(786\) | 798698. | 1.29282 | ||||||||
\(787\) | − | 57080.5i | − | 0.0921591i | −0.998938 | − | 0.0460795i | \(-0.985327\pi\) | ||
0.998938 | − | 0.0460795i | \(-0.0146728\pi\) | |||||||
\(788\) | 15780.7 | 0.0254140 | ||||||||
\(789\) | − | 400078.i | − | 0.642673i | ||||||
\(790\) | −792542. | −1.26990 | ||||||||
\(791\) | 931663. | 1.48904 | ||||||||
\(792\) | 4928.41i | 0.00785700i | ||||||||
\(793\) | − | 13884.4i | − | 0.0220790i | ||||||
\(794\) | 1.08572e6 | 1.72217 | ||||||||
\(795\) | 207829. | 0.328830 | ||||||||
\(796\) | − | 413652.i | − | 0.652844i | ||||||
\(797\) | − | 166613.i | − | 0.262297i | −0.991363 | − | 0.131148i | \(-0.958134\pi\) | ||
0.991363 | − | 0.131148i | \(-0.0418664\pi\) | |||||||
\(798\) | −512942. | −0.805494 | ||||||||
\(799\) | 906419.i | 1.41983i | ||||||||
\(800\) | −325644. | −0.508819 | ||||||||
\(801\) | 295013.i | 0.459808i | ||||||||
\(802\) | 524929.i | 0.816116i | ||||||||
\(803\) | − | 6362.17i | − | 0.00986676i | ||||||
\(804\) | − | 467397.i | − | 0.723059i | ||||||
\(805\) | 70769.7 | − | 612138.i | 0.109208 | − | 0.944621i | ||||
\(806\) | 93728.5 | 0.144279 | ||||||||
\(807\) | −218608. | −0.335674 | ||||||||
\(808\) | −626949. | −0.960305 | ||||||||
\(809\) | −92633.7 | −0.141538 | −0.0707688 | − | 0.997493i | \(-0.522545\pi\) | ||||
−0.0707688 | + | 0.997493i | \(0.522545\pi\) | |||||||
\(810\) | 144594.i | 0.220385i | ||||||||
\(811\) | −1.07406e6 | −1.63300 | −0.816501 | − | 0.577345i | \(-0.804089\pi\) | ||||
−0.816501 | + | 0.577345i | \(0.804089\pi\) | |||||||
\(812\) | − | 904616.i | − | 1.37199i | ||||||
\(813\) | −107470. | −0.162595 | ||||||||
\(814\) | 32685.0 | 0.0493287 | ||||||||
\(815\) | 836258.i | 1.25900i | ||||||||
\(816\) | 5452.71i | 0.00818902i | ||||||||
\(817\) | 7076.15 | 0.0106011 | ||||||||
\(818\) | 964170. | 1.44094 | ||||||||
\(819\) | − | 19353.9i | − | 0.0288536i | ||||||
\(820\) | 2.03216e6i | 3.02225i | ||||||||
\(821\) | −90301.1 | −0.133970 | −0.0669849 | − | 0.997754i | \(-0.521338\pi\) | ||||
−0.0669849 | + | 0.997754i | \(0.521338\pi\) | |||||||
\(822\) | − | 1.14090e6i | − | 1.68851i | ||||||
\(823\) | 1.01440e6 | 1.49765 | 0.748827 | − | 0.662765i | \(-0.230617\pi\) | ||||
0.748827 | + | 0.662765i | \(0.230617\pi\) | |||||||
\(824\) | 63451.7i | 0.0934521i | ||||||||
\(825\) | 4713.31i | 0.00692497i | ||||||||
\(826\) | − | 1.07589e6i | − | 1.57692i | ||||||
\(827\) | − | 633034.i | − | 0.925584i | −0.886467 | − | 0.462792i | \(-0.846848\pi\) | ||
0.886467 | − | 0.462792i | \(-0.153152\pi\) | |||||||
\(828\) | 42357.8 | − | 366383.i | 0.0617836 | − | 0.534411i | ||||
\(829\) | 431150. | 0.627364 | 0.313682 | − | 0.949528i | \(-0.398437\pi\) | ||||
0.313682 | + | 0.949528i | \(0.398437\pi\) | |||||||
\(830\) | −1.84194e6 | −2.67374 | ||||||||
\(831\) | 258537. | 0.374387 | ||||||||
\(832\) | 125200. | 0.180866 | ||||||||
\(833\) | − | 426958.i | − | 0.615312i | ||||||
\(834\) | 417283. | 0.599927 | ||||||||
\(835\) | − | 72790.8i | − | 0.104401i | ||||||
\(836\) | −29821.9 | −0.0426699 | ||||||||
\(837\) | 107737. | 0.153785 | ||||||||
\(838\) | − | 924197.i | − | 1.31606i | ||||||
\(839\) | − | 363057.i | − | 0.515764i | −0.966176 | − | 0.257882i | \(-0.916975\pi\) | ||
0.966176 | − | 0.257882i | \(-0.0830246\pi\) | |||||||
\(840\) | −384494. | −0.544918 | ||||||||
\(841\) | 143489. | 0.202874 | ||||||||
\(842\) | − | 129911.i | − | 0.183241i | ||||||
\(843\) | − | 646557.i | − | 0.909812i | ||||||
\(844\) | −1.84484e6 | −2.58985 | ||||||||
\(845\) | 865050.i | 1.21151i | ||||||||
\(846\) | 355306. | 0.496435 | ||||||||
\(847\) | 555756.i | 0.774671i | ||||||||
\(848\) | − | 3072.14i | − | 0.00427218i | ||||||
\(849\) | − | 664094.i | − | 0.921327i | ||||||
\(850\) | − | 909351.i | − | 1.25862i | ||||||
\(851\) | −924278. | − | 106856.i | −1.27627 | − | 0.147551i | ||||
\(852\) | 760488. | 1.04764 | ||||||||
\(853\) | −249641. | −0.343097 | −0.171549 | − | 0.985176i | \(-0.554877\pi\) | ||||
−0.171549 | + | 0.985176i | \(0.554877\pi\) | |||||||
\(854\) | 180694. | 0.247758 | ||||||||
\(855\) | −332816. | −0.455273 | ||||||||
\(856\) | 368220.i | 0.502527i | ||||||||
\(857\) | −995475. | −1.35540 | −0.677702 | − | 0.735337i | \(-0.737024\pi\) | ||||
−0.677702 | + | 0.735337i | \(0.737024\pi\) | |||||||
\(858\) | − | 1822.41i | − | 0.00247555i | ||||||
\(859\) | −265730. | −0.360125 | −0.180063 | − | 0.983655i | \(-0.557630\pi\) | ||||
−0.180063 | + | 0.983655i | \(0.557630\pi\) | |||||||
\(860\) | 13944.2 | 0.0188537 | ||||||||
\(861\) | − | 506385.i | − | 0.683085i | ||||||
\(862\) | − | 337871.i | − | 0.454713i | ||||||
\(863\) | 1.24867e6 | 1.67658 | 0.838292 | − | 0.545222i | \(-0.183555\pi\) | ||||
0.838292 | + | 0.545222i | \(0.183555\pi\) | |||||||
\(864\) | 144730. | 0.193879 | ||||||||
\(865\) | 1.26099e6i | 1.68531i | ||||||||
\(866\) | − | 67396.5i | − | 0.0898672i | ||||||
\(867\) | −597044. | −0.794270 | ||||||||
\(868\) | 753145.i | 0.999630i | ||||||||
\(869\) | 11481.8 | 0.0152045 | ||||||||
\(870\) | − | 950630.i | − | 1.25595i | ||||||
\(871\) | 65743.1i | 0.0866591i | ||||||||
\(872\) | − | 1.32941e6i | − | 1.74833i | ||||||
\(873\) | − | 275414.i | − | 0.361375i | ||||||
\(874\) | 1.36584e6 | + | 157906.i | 1.78804 | + | 0.206716i | ||||
\(875\) | 360331. | 0.470636 | ||||||||
\(876\) | 297081. | 0.387138 | ||||||||
\(877\) | −1.11188e6 | −1.44563 | −0.722816 | − | 0.691040i | \(-0.757153\pi\) | ||||
−0.722816 | + | 0.691040i | \(0.757153\pi\) | |||||||
\(878\) | −433189. | −0.561938 | ||||||||
\(879\) | 800228.i | 1.03571i | ||||||||
\(880\) | 207.619 | 0.000268102 | ||||||||
\(881\) | − | 494568.i | − | 0.637198i | −0.947890 | − | 0.318599i | \(-0.896788\pi\) | ||
0.947890 | − | 0.318599i | \(-0.103212\pi\) | |||||||
\(882\) | −167363. | −0.215141 | ||||||||
\(883\) | 1.25154e6 | 1.60518 | 0.802588 | − | 0.596533i | \(-0.203456\pi\) | ||||
0.802588 | + | 0.596533i | \(0.203456\pi\) | |||||||
\(884\) | 217090.i | 0.277802i | ||||||||
\(885\) | − | 698081.i | − | 0.891290i | ||||||
\(886\) | 1.43621e6 | 1.82957 | ||||||||
\(887\) | 954894. | 1.21369 | 0.606845 | − | 0.794820i | \(-0.292435\pi\) | ||||
0.606845 | + | 0.794820i | \(0.292435\pi\) | |||||||
\(888\) | 580554.i | 0.736236i | ||||||||
\(889\) | 1.03116e6i | 1.30473i | ||||||||
\(890\) | −2.16721e6 | −2.73603 | ||||||||
\(891\) | − | 2094.79i | − | 0.00263867i | ||||||
\(892\) | 861473. | 1.08271 | ||||||||
\(893\) | 817817.i | 1.02554i | ||||||||
\(894\) | − | 914384.i | − | 1.14407i | ||||||
\(895\) | − | 1.29495e6i | − | 1.61662i | ||||||
\(896\) | 1.00249e6i | 1.24871i | ||||||||
\(897\) | −5957.97 | + | 51534.8i | −0.00740480 | + | 0.0640495i | ||||
\(898\) | −627899. | −0.778641 | ||||||||
\(899\) | −708315. | −0.876410 | ||||||||
\(900\) | −220087. | −0.271712 | ||||||||
\(901\) | 580900. | 0.715569 | ||||||||
\(902\) | − | 47682.5i | − | 0.0586065i | ||||||
\(903\) | −3474.68 | −0.00426127 | ||||||||
\(904\) | 1.55823e6i | 1.90675i | ||||||||
\(905\) | 1.17212e6 | 1.43111 | ||||||||
\(906\) | −666934. | −0.812505 | ||||||||
\(907\) | − | 901053.i | − | 1.09531i | −0.836705 | − | 0.547653i | \(-0.815521\pi\) | ||
0.836705 | − | 0.547653i | \(-0.184479\pi\) | |||||||
\(908\) | − | 991507.i | − | 1.20261i | ||||||
\(909\) | 266480. | 0.322506 | ||||||||
\(910\) | 142177. | 0.171690 | ||||||||
\(911\) | 433818.i | 0.522722i | 0.965241 | + | 0.261361i | \(0.0841713\pi\) | ||||
−0.965241 | + | 0.261361i | \(0.915829\pi\) | |||||||
\(912\) | 4919.71i | 0.00591493i | ||||||||
\(913\) | 26684.8 | 0.0320127 | ||||||||
\(914\) | − | 523741.i | − | 0.626937i | ||||||
\(915\) | 117241. | 0.140036 | ||||||||
\(916\) | 954949.i | 1.13812i | ||||||||
\(917\) | − | 902722.i | − | 1.07353i | ||||||
\(918\) | 404153.i | 0.479580i | ||||||||
\(919\) | 885622.i | 1.04862i | 0.851528 | + | 0.524309i | \(0.175676\pi\) | ||||
−0.851528 | + | 0.524309i | \(0.824324\pi\) | |||||||
\(920\) | 1.02382e6 | + | 118364.i | 1.20961 | + | 0.139844i | ||||
\(921\) | −509084. | −0.600165 | ||||||||
\(922\) | 48708.1 | 0.0572980 | ||||||||
\(923\) | −106969. | −0.125561 | ||||||||
\(924\) | 14643.8 | 0.0171518 | ||||||||
\(925\) | 555215.i | 0.648900i | ||||||||
\(926\) | −951959. | −1.11019 | ||||||||
\(927\) | − | 26969.7i | − | 0.0313846i | ||||||
\(928\) | −951521. | −1.10490 | ||||||||
\(929\) | 873695. | 1.01234 | 0.506172 | − | 0.862432i | \(-0.331060\pi\) | ||||
0.506172 | + | 0.862432i | \(0.331060\pi\) | |||||||
\(930\) | 791455.i | 0.915082i | ||||||||
\(931\) | − | 385223.i | − | 0.444440i | ||||||
\(932\) | 32485.7 | 0.0373990 | ||||||||
\(933\) | −129516. | −0.148785 | ||||||||
\(934\) | − | 591029.i | − | 0.677509i | ||||||
\(935\) | 39257.8i | 0.0449058i | ||||||||
\(936\) | 32369.8 | 0.0369478 | ||||||||
\(937\) | − | 1.14527e6i | − | 1.30445i | −0.758026 | − | 0.652224i | \(-0.773836\pi\) | ||
0.758026 | − | 0.652224i | \(-0.226164\pi\) | |||||||
\(938\) | −855595. | −0.972440 | ||||||||
\(939\) | − | 6187.79i | − | 0.00701786i | ||||||
\(940\) | 1.61158e6i | 1.82388i | ||||||||
\(941\) | 436365.i | 0.492800i | 0.969168 | + | 0.246400i | \(0.0792477\pi\) | ||||
−0.969168 | + | 0.246400i | \(0.920752\pi\) | |||||||
\(942\) | 661539.i | 0.745510i | ||||||||
\(943\) | −155887. | + | 1.34838e6i | −0.175302 | + | 1.51632i | ||||
\(944\) | −10319.1 | −0.0115797 | ||||||||
\(945\) | 163426. | 0.183003 | ||||||||
\(946\) | −327.184 | −0.000365604 | ||||||||
\(947\) | 185120. | 0.206421 | 0.103211 | − | 0.994660i | \(-0.467088\pi\) | ||||
0.103211 | + | 0.994660i | \(0.467088\pi\) | |||||||
\(948\) | 536142.i | 0.596573i | ||||||||
\(949\) | −41786.8 | −0.0463987 | ||||||||
\(950\) | − | 820463.i | − | 0.909100i | ||||||
\(951\) | 675020. | 0.746372 | ||||||||
\(952\) | −1.07469e6 | −1.18580 | ||||||||
\(953\) | 874426.i | 0.962803i | 0.876500 | + | 0.481401i | \(0.159872\pi\) | ||||
−0.876500 | + | 0.481401i | \(0.840128\pi\) | |||||||
\(954\) | − | 227706.i | − | 0.250195i | ||||||
\(955\) | −222409. | −0.243863 | ||||||||
\(956\) | 1.65998e6 | 1.81630 | ||||||||
\(957\) | 13772.1i | 0.0150375i | ||||||||
\(958\) | − | 2.69675e6i | − | 2.93839i | ||||||
\(959\) | −1.28949e6 | −1.40210 | ||||||||
\(960\) | 1.05720e6i | 1.14714i | ||||||||
\(961\) | −333807. | −0.361451 | ||||||||
\(962\) | − | 214675.i | − | 0.231970i | ||||||
\(963\) | − | 156509.i | − | 0.168767i | ||||||
\(964\) | 1.95688e6i | 2.10576i | ||||||||
\(965\) | − | 1.72063e6i | − | 1.84771i | ||||||
\(966\) | −670685. | − | 77538.3i | −0.718727 | − | 0.0830925i | ||||
\(967\) | 642170. | 0.686748 | 0.343374 | − | 0.939199i | \(-0.388430\pi\) | ||||
0.343374 | + | 0.939199i | \(0.388430\pi\) | |||||||
\(968\) | −929515. | −0.991987 | ||||||||
\(969\) | −930249. | −0.990722 | ||||||||
\(970\) | 2.02324e6 | 2.15032 | ||||||||
\(971\) | − | 129817.i | − | 0.137687i | −0.997627 | − | 0.0688433i | \(-0.978069\pi\) | ||
0.997627 | − | 0.0688433i | \(-0.0219309\pi\) | |||||||
\(972\) | 97815.8 | 0.103532 | ||||||||
\(973\) | − | 471630.i | − | 0.498168i | ||||||
\(974\) | 1.63343e6 | 1.72180 | ||||||||
\(975\) | 30957.0 | 0.0325649 | ||||||||
\(976\) | − | 1733.07i | − | 0.00181935i | ||||||
\(977\) | − | 386284.i | − | 0.404685i | −0.979315 | − | 0.202343i | \(-0.935145\pi\) | ||
0.979315 | − | 0.202343i | \(-0.0648554\pi\) | |||||||
\(978\) | 916240. | 0.957925 | ||||||||
\(979\) | 31397.2 | 0.0327586 | ||||||||
\(980\) | − | 759116.i | − | 0.790417i | ||||||
\(981\) | 565055.i | 0.587155i | ||||||||
\(982\) | −2.96460e6 | −3.07428 | ||||||||
\(983\) | − | 270499.i | − | 0.279936i | −0.990156 | − | 0.139968i | \(-0.955300\pi\) | ||
0.990156 | − | 0.139968i | \(-0.0446999\pi\) | |||||||
\(984\) | 846941. | 0.874708 | ||||||||
\(985\) | − | 18743.2i | − | 0.0193185i | ||||||
\(986\) | − | 2.65709e6i | − | 2.73308i | ||||||
\(987\) | − | 401582.i | − | 0.412230i | ||||||
\(988\) | 195870.i | 0.200657i | ||||||||
\(989\) | 9252.25 | + | 1069.66i | 0.00945920 | + | 0.00109358i | ||||
\(990\) | 15388.6 | 0.0157011 | ||||||||
\(991\) | −217838. | −0.221813 | −0.110906 | − | 0.993831i | \(-0.535375\pi\) | ||||
−0.110906 | + | 0.993831i | \(0.535375\pi\) | |||||||
\(992\) | 792197. | 0.805025 | ||||||||
\(993\) | 466987. | 0.473594 | ||||||||
\(994\) | − | 1.39211e6i | − | 1.40897i | ||||||
\(995\) | −491308. | −0.496259 | ||||||||
\(996\) | 1.24604e6i | 1.25607i | ||||||||
\(997\) | −446564. | −0.449256 | −0.224628 | − | 0.974445i | \(-0.572117\pi\) | ||||
−0.224628 | + | 0.974445i | \(0.572117\pi\) | |||||||
\(998\) | 374452. | 0.375954 | ||||||||
\(999\) | − | 246761.i | − | 0.247255i |
(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 | 69.5.d.a.22.1 | ✓ | 16 | |
3.2 | odd | 2 | 207.5.d.c.91.16 | 16 | |||
4.3 | odd | 2 | 1104.5.c.c.1057.2 | 16 | |||
23.22 | odd | 2 | inner | 69.5.d.a.22.2 | yes | 16 | |
69.68 | even | 2 | 207.5.d.c.91.15 | 16 | |||
92.91 | even | 2 | 1104.5.c.c.1057.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.5.d.a.22.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
69.5.d.a.22.2 | yes | 16 | 23.22 | odd | 2 | inner | |
207.5.d.c.91.15 | 16 | 69.68 | even | 2 | |||
207.5.d.c.91.16 | 16 | 3.2 | odd | 2 | |||
1104.5.c.c.1057.2 | 16 | 4.3 | odd | 2 | |||
1104.5.c.c.1057.7 | 16 | 92.91 | even | 2 |