Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [201,5,Mod(133,201)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(201, 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("201.133");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 201 = 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 201.b (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: | \(20.7773625799\) |
Analytic rank: | \(0\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 133.17 | ||
Character | \(\chi\) | \(=\) | 201.133 |
Dual form | 201.5.b.a.133.30 |
$q$-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 \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).
\(n\) | \(68\) | \(136\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.53609i | − | 0.634022i | −0.948422 | − | 0.317011i | \(-0.897321\pi\) | ||
0.948422 | − | 0.317011i | \(-0.102679\pi\) | |||||||
\(3\) | 5.19615i | 0.577350i | ||||||||
\(4\) | 9.56827 | 0.598017 | ||||||||
\(5\) | − | 8.16007i | − | 0.326403i | −0.986593 | − | 0.163201i | \(-0.947818\pi\) | ||
0.986593 | − | 0.163201i | \(-0.0521820\pi\) | |||||||
\(6\) | 13.1779 | 0.366053 | ||||||||
\(7\) | − | 69.7059i | − | 1.42257i | −0.702904 | − | 0.711285i | \(-0.748114\pi\) | ||
0.702904 | − | 0.711285i | \(-0.251886\pi\) | |||||||
\(8\) | − | 64.8433i | − | 1.01318i | ||||||
\(9\) | −27.0000 | −0.333333 | ||||||||
\(10\) | −20.6946 | −0.206946 | ||||||||
\(11\) | 42.4935i | 0.351186i | 0.984463 | + | 0.175593i | \(0.0561843\pi\) | ||||
−0.984463 | + | 0.175593i | \(0.943816\pi\) | |||||||
\(12\) | 49.7182i | 0.345265i | ||||||||
\(13\) | − | 8.13871i | − | 0.0481581i | −0.999710 | − | 0.0240790i | \(-0.992335\pi\) | ||
0.999710 | − | 0.0240790i | \(-0.00766533\pi\) | |||||||
\(14\) | −176.780 | −0.901940 | ||||||||
\(15\) | 42.4009 | 0.188449 | ||||||||
\(16\) | −11.3560 | −0.0443595 | ||||||||
\(17\) | −51.4498 | −0.178027 | −0.0890134 | − | 0.996030i | \(-0.528371\pi\) | ||||
−0.0890134 | + | 0.996030i | \(0.528371\pi\) | |||||||
\(18\) | 68.4743i | 0.211341i | ||||||||
\(19\) | −552.939 | −1.53169 | −0.765844 | − | 0.643027i | \(-0.777678\pi\) | ||||
−0.765844 | + | 0.643027i | \(0.777678\pi\) | |||||||
\(20\) | − | 78.0777i | − | 0.195194i | ||||||
\(21\) | 362.203 | 0.821321 | ||||||||
\(22\) | 107.767 | 0.222659 | ||||||||
\(23\) | −661.237 | −1.24998 | −0.624988 | − | 0.780635i | \(-0.714896\pi\) | ||||
−0.624988 | + | 0.780635i | \(0.714896\pi\) | |||||||
\(24\) | 336.936 | 0.584958 | ||||||||
\(25\) | 558.413 | 0.893461 | ||||||||
\(26\) | −20.6405 | −0.0305332 | ||||||||
\(27\) | − | 140.296i | − | 0.192450i | ||||||
\(28\) | − | 666.965i | − | 0.850721i | ||||||
\(29\) | 952.351 | 1.13240 | 0.566202 | − | 0.824267i | \(-0.308412\pi\) | ||||
0.566202 | + | 0.824267i | \(0.308412\pi\) | |||||||
\(30\) | − | 107.532i | − | 0.119481i | ||||||
\(31\) | − | 1572.07i | − | 1.63587i | −0.575314 | − | 0.817933i | \(-0.695120\pi\) | ||
0.575314 | − | 0.817933i | \(-0.304880\pi\) | |||||||
\(32\) | − | 1008.69i | − | 0.985052i | ||||||
\(33\) | −220.803 | −0.202757 | ||||||||
\(34\) | 130.481i | 0.112873i | ||||||||
\(35\) | −568.805 | −0.464331 | ||||||||
\(36\) | −258.343 | −0.199339 | ||||||||
\(37\) | −824.332 | −0.602142 | −0.301071 | − | 0.953602i | \(-0.597344\pi\) | ||||
−0.301071 | + | 0.953602i | \(0.597344\pi\) | |||||||
\(38\) | 1402.30i | 0.971123i | ||||||||
\(39\) | 42.2900 | 0.0278041 | ||||||||
\(40\) | −529.126 | −0.330704 | ||||||||
\(41\) | − | 1049.72i | − | 0.624463i | −0.950006 | − | 0.312231i | \(-0.898924\pi\) | ||
0.950006 | − | 0.312231i | \(-0.101076\pi\) | |||||||
\(42\) | − | 918.577i | − | 0.520735i | ||||||
\(43\) | − | 2489.51i | − | 1.34641i | −0.739456 | − | 0.673205i | \(-0.764917\pi\) | ||
0.739456 | − | 0.673205i | \(-0.235083\pi\) | |||||||
\(44\) | 406.589i | 0.210015i | ||||||||
\(45\) | 220.322i | 0.108801i | ||||||||
\(46\) | 1676.95i | 0.792511i | ||||||||
\(47\) | −3338.19 | −1.51118 | −0.755589 | − | 0.655046i | \(-0.772649\pi\) | ||||
−0.755589 | + | 0.655046i | \(0.772649\pi\) | |||||||
\(48\) | − | 59.0076i | − | 0.0256109i | ||||||
\(49\) | −2457.92 | −1.02371 | ||||||||
\(50\) | − | 1416.18i | − | 0.566474i | ||||||
\(51\) | − | 267.341i | − | 0.102784i | ||||||
\(52\) | − | 77.8734i | − | 0.0287993i | ||||||
\(53\) | 5321.62i | 1.89449i | 0.320512 | + | 0.947245i | \(0.396145\pi\) | ||||
−0.320512 | + | 0.947245i | \(0.603855\pi\) | |||||||
\(54\) | −355.803 | −0.122018 | ||||||||
\(55\) | 346.750 | 0.114628 | ||||||||
\(56\) | −4519.96 | −1.44132 | ||||||||
\(57\) | − | 2873.16i | − | 0.884320i | ||||||
\(58\) | − | 2415.24i | − | 0.717968i | ||||||
\(59\) | 6339.83 | 1.82127 | 0.910634 | − | 0.413214i | \(-0.135594\pi\) | ||||
0.910634 | + | 0.413214i | \(0.135594\pi\) | |||||||
\(60\) | 405.704 | 0.112695 | ||||||||
\(61\) | − | 5490.98i | − | 1.47567i | −0.674979 | − | 0.737837i | \(-0.735847\pi\) | ||
0.674979 | − | 0.737837i | \(-0.264153\pi\) | |||||||
\(62\) | −3986.90 | −1.03717 | ||||||||
\(63\) | 1882.06i | 0.474190i | ||||||||
\(64\) | −2739.83 | −0.668904 | ||||||||
\(65\) | −66.4124 | −0.0157189 | ||||||||
\(66\) | 559.975i | 0.128552i | ||||||||
\(67\) | 3106.61 | + | 3240.39i | 0.692049 | + | 0.721851i | ||||
\(68\) | −492.285 | −0.106463 | ||||||||
\(69\) | − | 3435.89i | − | 0.721674i | ||||||
\(70\) | 1442.54i | 0.294396i | ||||||||
\(71\) | −238.544 | −0.0473208 | −0.0236604 | − | 0.999720i | \(-0.507532\pi\) | ||||
−0.0236604 | + | 0.999720i | \(0.507532\pi\) | |||||||
\(72\) | 1750.77i | 0.337726i | ||||||||
\(73\) | −3348.79 | −0.628408 | −0.314204 | − | 0.949355i | \(-0.601738\pi\) | ||||
−0.314204 | + | 0.949355i | \(0.601738\pi\) | |||||||
\(74\) | 2090.58i | 0.381771i | ||||||||
\(75\) | 2901.60i | 0.515840i | ||||||||
\(76\) | −5290.67 | −0.915974 | ||||||||
\(77\) | 2962.05 | 0.499587 | ||||||||
\(78\) | − | 107.251i | − | 0.0176284i | ||||||
\(79\) | − | 1448.51i | − | 0.232096i | −0.993244 | − | 0.116048i | \(-0.962977\pi\) | ||
0.993244 | − | 0.116048i | \(-0.0370226\pi\) | |||||||
\(80\) | 92.6659i | 0.0144790i | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | −2662.19 | −0.395923 | ||||||||
\(83\) | 1344.13 | 0.195113 | 0.0975563 | − | 0.995230i | \(-0.468897\pi\) | ||||
0.0975563 | + | 0.995230i | \(0.468897\pi\) | |||||||
\(84\) | 3465.65 | 0.491164 | ||||||||
\(85\) | 419.833i | 0.0581084i | ||||||||
\(86\) | −6313.62 | −0.853653 | ||||||||
\(87\) | 4948.56i | 0.653793i | ||||||||
\(88\) | 2755.42 | 0.355813 | ||||||||
\(89\) | 4416.22 | 0.557533 | 0.278766 | − | 0.960359i | \(-0.410075\pi\) | ||||
0.278766 | + | 0.960359i | \(0.410075\pi\) | |||||||
\(90\) | 558.755 | 0.0689821 | ||||||||
\(91\) | −567.316 | −0.0685082 | ||||||||
\(92\) | −6326.89 | −0.747506 | ||||||||
\(93\) | 8168.70 | 0.944467 | ||||||||
\(94\) | 8465.95i | 0.958120i | ||||||||
\(95\) | 4512.02i | 0.499947i | ||||||||
\(96\) | 5241.32 | 0.568720 | ||||||||
\(97\) | − | 4826.09i | − | 0.512922i | −0.966555 | − | 0.256461i | \(-0.917443\pi\) | ||
0.966555 | − | 0.256461i | \(-0.0825566\pi\) | |||||||
\(98\) | 6233.49i | 0.649051i | ||||||||
\(99\) | − | 1147.32i | − | 0.117062i | ||||||
\(100\) | 5343.05 | 0.534305 | ||||||||
\(101\) | − | 3271.88i | − | 0.320741i | −0.987057 | − | 0.160371i | \(-0.948731\pi\) | ||
0.987057 | − | 0.160371i | \(-0.0512690\pi\) | |||||||
\(102\) | −677.999 | −0.0651672 | ||||||||
\(103\) | 18834.7 | 1.77536 | 0.887678 | − | 0.460465i | \(-0.152317\pi\) | ||||
0.887678 | + | 0.460465i | \(0.152317\pi\) | |||||||
\(104\) | −527.741 | −0.0487926 | ||||||||
\(105\) | − | 2955.60i | − | 0.268081i | ||||||
\(106\) | 13496.1 | 1.20115 | ||||||||
\(107\) | 1334.21 | 0.116535 | 0.0582674 | − | 0.998301i | \(-0.481442\pi\) | ||||
0.0582674 | + | 0.998301i | \(0.481442\pi\) | |||||||
\(108\) | − | 1342.39i | − | 0.115088i | ||||||
\(109\) | − | 16139.4i | − | 1.35842i | −0.733943 | − | 0.679211i | \(-0.762322\pi\) | ||
0.733943 | − | 0.679211i | \(-0.237678\pi\) | |||||||
\(110\) | − | 879.387i | − | 0.0726766i | ||||||
\(111\) | − | 4283.35i | − | 0.347647i | ||||||
\(112\) | 791.582i | 0.0631044i | ||||||||
\(113\) | 21501.8i | 1.68390i | 0.539553 | + | 0.841951i | \(0.318593\pi\) | ||||
−0.539553 | + | 0.841951i | \(0.681407\pi\) | |||||||
\(114\) | −7286.57 | −0.560678 | ||||||||
\(115\) | 5395.74i | 0.407995i | ||||||||
\(116\) | 9112.35 | 0.677196 | ||||||||
\(117\) | 219.745i | 0.0160527i | ||||||||
\(118\) | − | 16078.4i | − | 1.15472i | ||||||
\(119\) | 3586.35i | 0.253256i | ||||||||
\(120\) | − | 2749.42i | − | 0.190932i | ||||||
\(121\) | 12835.3 | 0.876668 | ||||||||
\(122\) | −13925.6 | −0.935609 | ||||||||
\(123\) | 5454.52 | 0.360534 | ||||||||
\(124\) | − | 15042.0i | − | 0.978275i | ||||||
\(125\) | − | 9656.73i | − | 0.618031i | ||||||
\(126\) | 4773.07 | 0.300647 | ||||||||
\(127\) | −1460.37 | −0.0905431 | −0.0452715 | − | 0.998975i | \(-0.514415\pi\) | ||||
−0.0452715 | + | 0.998975i | \(0.514415\pi\) | |||||||
\(128\) | − | 9190.65i | − | 0.560953i | ||||||
\(129\) | 12935.9 | 0.777350 | ||||||||
\(130\) | 168.428i | 0.00996613i | ||||||||
\(131\) | 6483.08 | 0.377780 | 0.188890 | − | 0.981998i | \(-0.439511\pi\) | ||||
0.188890 | + | 0.981998i | \(0.439511\pi\) | |||||||
\(132\) | −2112.70 | −0.121252 | ||||||||
\(133\) | 38543.1i | 2.17893i | ||||||||
\(134\) | 8217.90 | − | 7878.62i | 0.457669 | − | 0.438774i | ||||
\(135\) | −1144.83 | −0.0628162 | ||||||||
\(136\) | 3336.17i | 0.180373i | ||||||||
\(137\) | 32095.2i | 1.71001i | 0.518619 | + | 0.855006i | \(0.326446\pi\) | ||||
−0.518619 | + | 0.855006i | \(0.673554\pi\) | |||||||
\(138\) | −8713.71 | −0.457557 | ||||||||
\(139\) | 28368.8i | 1.46829i | 0.678994 | + | 0.734144i | \(0.262416\pi\) | ||||
−0.678994 | + | 0.734144i | \(0.737584\pi\) | |||||||
\(140\) | −5442.48 | −0.277677 | ||||||||
\(141\) | − | 17345.8i | − | 0.872479i | ||||||
\(142\) | 604.969i | 0.0300024i | ||||||||
\(143\) | 345.842 | 0.0169124 | ||||||||
\(144\) | 306.613 | 0.0147865 | ||||||||
\(145\) | − | 7771.25i | − | 0.369619i | ||||||
\(146\) | 8492.81i | 0.398424i | ||||||||
\(147\) | − | 12771.7i | − | 0.591037i | ||||||
\(148\) | −7887.43 | −0.360091 | ||||||||
\(149\) | −9734.03 | −0.438450 | −0.219225 | − | 0.975674i | \(-0.570353\pi\) | ||||
−0.219225 | + | 0.975674i | \(0.570353\pi\) | |||||||
\(150\) | 7358.71 | 0.327054 | ||||||||
\(151\) | 791.752 | 0.0347245 | 0.0173622 | − | 0.999849i | \(-0.494473\pi\) | ||||
0.0173622 | + | 0.999849i | \(0.494473\pi\) | |||||||
\(152\) | 35854.4i | 1.55187i | ||||||||
\(153\) | 1389.14 | 0.0593423 | ||||||||
\(154\) | − | 7512.01i | − | 0.316749i | ||||||
\(155\) | −12828.2 | −0.533951 | ||||||||
\(156\) | 404.642 | 0.0166273 | ||||||||
\(157\) | 28652.3 | 1.16241 | 0.581206 | − | 0.813757i | \(-0.302581\pi\) | ||||
0.581206 | + | 0.813757i | \(0.302581\pi\) | |||||||
\(158\) | −3673.55 | −0.147154 | ||||||||
\(159\) | −27651.9 | −1.09378 | ||||||||
\(160\) | −8231.01 | −0.321524 | ||||||||
\(161\) | 46092.1i | 1.77818i | ||||||||
\(162\) | − | 1848.81i | − | 0.0704468i | ||||||
\(163\) | −33278.1 | −1.25252 | −0.626258 | − | 0.779615i | \(-0.715415\pi\) | ||||
−0.626258 | + | 0.779615i | \(0.715415\pi\) | |||||||
\(164\) | − | 10044.0i | − | 0.373439i | ||||||
\(165\) | 1801.76i | 0.0661805i | ||||||||
\(166\) | − | 3408.83i | − | 0.123706i | ||||||
\(167\) | −19217.5 | −0.689072 | −0.344536 | − | 0.938773i | \(-0.611964\pi\) | ||||
−0.344536 | + | 0.938773i | \(0.611964\pi\) | |||||||
\(168\) | − | 23486.4i | − | 0.832144i | ||||||
\(169\) | 28494.8 | 0.997681 | ||||||||
\(170\) | 1064.73 | 0.0368420 | ||||||||
\(171\) | 14929.4 | 0.510562 | ||||||||
\(172\) | − | 23820.3i | − | 0.805176i | ||||||
\(173\) | −36614.7 | −1.22338 | −0.611692 | − | 0.791096i | \(-0.709511\pi\) | ||||
−0.611692 | + | 0.791096i | \(0.709511\pi\) | |||||||
\(174\) | 12550.0 | 0.414519 | ||||||||
\(175\) | − | 38924.7i | − | 1.27101i | ||||||
\(176\) | − | 482.557i | − | 0.0155784i | ||||||
\(177\) | 32942.7i | 1.05151i | ||||||||
\(178\) | − | 11199.9i | − | 0.353488i | ||||||
\(179\) | 49518.1i | 1.54546i | 0.634734 | + | 0.772730i | \(0.281110\pi\) | ||||
−0.634734 | + | 0.772730i | \(0.718890\pi\) | |||||||
\(180\) | 2108.10i | 0.0650647i | ||||||||
\(181\) | 51803.6 | 1.58126 | 0.790629 | − | 0.612296i | \(-0.209754\pi\) | ||||
0.790629 | + | 0.612296i | \(0.209754\pi\) | |||||||
\(182\) | 1438.76i | 0.0434357i | ||||||||
\(183\) | 28532.0 | 0.851980 | ||||||||
\(184\) | 42876.8i | 1.26645i | ||||||||
\(185\) | 6726.60i | 0.196541i | ||||||||
\(186\) | − | 20716.5i | − | 0.598813i | ||||||
\(187\) | − | 2186.28i | − | 0.0625205i | ||||||
\(188\) | −31940.7 | −0.903710 | ||||||||
\(189\) | −9779.47 | −0.273774 | ||||||||
\(190\) | 11442.9 | 0.316977 | ||||||||
\(191\) | − | 29898.4i | − | 0.819562i | −0.912184 | − | 0.409781i | \(-0.865605\pi\) | ||
0.912184 | − | 0.409781i | \(-0.134395\pi\) | |||||||
\(192\) | − | 14236.6i | − | 0.386192i | ||||||
\(193\) | −39039.5 | −1.04807 | −0.524035 | − | 0.851697i | \(-0.675574\pi\) | ||||
−0.524035 | + | 0.851697i | \(0.675574\pi\) | |||||||
\(194\) | −12239.4 | −0.325204 | ||||||||
\(195\) | − | 345.089i | − | 0.00907532i | ||||||
\(196\) | −23518.0 | −0.612193 | ||||||||
\(197\) | − | 17800.8i | − | 0.458676i | −0.973347 | − | 0.229338i | \(-0.926344\pi\) | ||
0.973347 | − | 0.229338i | \(-0.0736561\pi\) | |||||||
\(198\) | −2909.71 | −0.0742198 | ||||||||
\(199\) | 11121.0 | 0.280827 | 0.140413 | − | 0.990093i | \(-0.455157\pi\) | ||||
0.140413 | + | 0.990093i | \(0.455157\pi\) | |||||||
\(200\) | − | 36209.4i | − | 0.905234i | ||||||
\(201\) | −16837.6 | + | 16142.4i | −0.416761 | + | 0.399554i | ||||
\(202\) | −8297.78 | −0.203357 | ||||||||
\(203\) | − | 66384.5i | − | 1.61092i | ||||||
\(204\) | − | 2557.99i | − | 0.0614664i | ||||||
\(205\) | −8565.80 | −0.203826 | ||||||||
\(206\) | − | 47766.5i | − | 1.12561i | ||||||
\(207\) | 17853.4 | 0.416658 | ||||||||
\(208\) | 92.4234i | 0.00213627i | ||||||||
\(209\) | − | 23496.3i | − | 0.537907i | ||||||
\(210\) | −7495.65 | −0.169969 | ||||||||
\(211\) | 24317.1 | 0.546194 | 0.273097 | − | 0.961987i | \(-0.411952\pi\) | ||||
0.273097 | + | 0.961987i | \(0.411952\pi\) | |||||||
\(212\) | 50918.7i | 1.13294i | ||||||||
\(213\) | − | 1239.51i | − | 0.0273207i | ||||||
\(214\) | − | 3383.66i | − | 0.0738855i | ||||||
\(215\) | −20314.6 | −0.439472 | ||||||||
\(216\) | −9097.27 | −0.194986 | ||||||||
\(217\) | −109582. | −2.32713 | ||||||||
\(218\) | −40930.9 | −0.861269 | ||||||||
\(219\) | − | 17400.8i | − | 0.362812i | ||||||
\(220\) | 3317.79 | 0.0685495 | ||||||||
\(221\) | 418.735i | 0.00857343i | ||||||||
\(222\) | −10863.0 | −0.220415 | ||||||||
\(223\) | 44620.8 | 0.897278 | 0.448639 | − | 0.893713i | \(-0.351909\pi\) | ||||
0.448639 | + | 0.893713i | \(0.351909\pi\) | |||||||
\(224\) | −70311.9 | −1.40131 | ||||||||
\(225\) | −15077.2 | −0.297820 | ||||||||
\(226\) | 54530.3 | 1.06763 | ||||||||
\(227\) | 33993.9 | 0.659705 | 0.329853 | − | 0.944032i | \(-0.393001\pi\) | ||||
0.329853 | + | 0.944032i | \(0.393001\pi\) | |||||||
\(228\) | − | 27491.1i | − | 0.528838i | ||||||
\(229\) | 36241.4i | 0.691089i | 0.938402 | + | 0.345544i | \(0.112306\pi\) | ||||
−0.938402 | + | 0.345544i | \(0.887694\pi\) | |||||||
\(230\) | 13684.1 | 0.258678 | ||||||||
\(231\) | 15391.3i | 0.288436i | ||||||||
\(232\) | − | 61753.6i | − | 1.14732i | ||||||
\(233\) | − | 33280.3i | − | 0.613021i | −0.951867 | − | 0.306510i | \(-0.900839\pi\) | ||
0.951867 | − | 0.306510i | \(-0.0991614\pi\) | |||||||
\(234\) | 557.293 | 0.0101777 | ||||||||
\(235\) | 27239.9i | 0.493253i | ||||||||
\(236\) | 60661.2 | 1.08915 | ||||||||
\(237\) | 7526.68 | 0.134001 | ||||||||
\(238\) | 9095.30 | 0.160570 | ||||||||
\(239\) | − | 10500.7i | − | 0.183832i | −0.995767 | − | 0.0919161i | \(-0.970701\pi\) | ||
0.995767 | − | 0.0919161i | \(-0.0292992\pi\) | |||||||
\(240\) | −481.506 | −0.00835948 | ||||||||
\(241\) | 25198.2 | 0.433846 | 0.216923 | − | 0.976189i | \(-0.430398\pi\) | ||||
0.216923 | + | 0.976189i | \(0.430398\pi\) | |||||||
\(242\) | − | 32551.4i | − | 0.555827i | ||||||
\(243\) | 3788.00i | 0.0641500i | ||||||||
\(244\) | − | 52539.2i | − | 0.882477i | ||||||
\(245\) | 20056.8i | 0.334140i | ||||||||
\(246\) | − | 13833.1i | − | 0.228586i | ||||||
\(247\) | 4500.21i | 0.0737631i | ||||||||
\(248\) | −101938. | −1.65742 | ||||||||
\(249\) | 6984.31i | 0.112648i | ||||||||
\(250\) | −24490.3 | −0.391845 | ||||||||
\(251\) | − | 104168.i | − | 1.65344i | −0.562616 | − | 0.826719i | \(-0.690205\pi\) | ||
0.562616 | − | 0.826719i | \(-0.309795\pi\) | |||||||
\(252\) | 18008.1i | 0.283574i | ||||||||
\(253\) | − | 28098.3i | − | 0.438974i | ||||||
\(254\) | 3703.62i | 0.0574063i | ||||||||
\(255\) | −2181.52 | −0.0335489 | ||||||||
\(256\) | −67145.6 | −1.02456 | ||||||||
\(257\) | 47433.0 | 0.718149 | 0.359074 | − | 0.933309i | \(-0.383092\pi\) | ||||
0.359074 | + | 0.933309i | \(0.383092\pi\) | |||||||
\(258\) | − | 32806.5i | − | 0.492857i | ||||||
\(259\) | 57460.8i | 0.856589i | ||||||||
\(260\) | −635.452 | −0.00940017 | ||||||||
\(261\) | −25713.5 | −0.377468 | ||||||||
\(262\) | − | 16441.7i | − | 0.239521i | ||||||
\(263\) | 2241.07 | 0.0323999 | 0.0161999 | − | 0.999869i | \(-0.494843\pi\) | ||||
0.0161999 | + | 0.999869i | \(0.494843\pi\) | |||||||
\(264\) | 14317.6i | 0.205429i | ||||||||
\(265\) | 43424.8 | 0.618366 | ||||||||
\(266\) | 97748.7 | 1.38149 | ||||||||
\(267\) | 22947.3i | 0.321892i | ||||||||
\(268\) | 29724.8 | + | 31004.9i | 0.413857 | + | 0.431679i | ||||
\(269\) | 130716. | 1.80644 | 0.903218 | − | 0.429182i | \(-0.141198\pi\) | ||||
0.903218 | + | 0.429182i | \(0.141198\pi\) | |||||||
\(270\) | 2903.38i | 0.0398268i | ||||||||
\(271\) | − | 23195.9i | − | 0.315843i | −0.987452 | − | 0.157922i | \(-0.949521\pi\) | ||
0.987452 | − | 0.157922i | \(-0.0504794\pi\) | |||||||
\(272\) | 584.264 | 0.00789717 | ||||||||
\(273\) | − | 2947.86i | − | 0.0395532i | ||||||
\(274\) | 81396.2 | 1.08418 | ||||||||
\(275\) | 23728.9i | 0.313771i | ||||||||
\(276\) | − | 32875.5i | − | 0.431573i | ||||||
\(277\) | −122354. | −1.59462 | −0.797312 | − | 0.603568i | \(-0.793745\pi\) | ||||
−0.797312 | + | 0.603568i | \(0.793745\pi\) | |||||||
\(278\) | 71945.7 | 0.930926 | ||||||||
\(279\) | 42445.8i | 0.545288i | ||||||||
\(280\) | 36883.2i | 0.470449i | ||||||||
\(281\) | 103622.i | 1.31232i | 0.754621 | + | 0.656161i | \(0.227821\pi\) | ||||
−0.754621 | + | 0.656161i | \(0.772179\pi\) | |||||||
\(282\) | −43990.4 | −0.553171 | ||||||||
\(283\) | 69630.9 | 0.869419 | 0.434710 | − | 0.900571i | \(-0.356851\pi\) | ||||
0.434710 | + | 0.900571i | \(0.356851\pi\) | |||||||
\(284\) | −2282.45 | −0.0282986 | ||||||||
\(285\) | −23445.1 | −0.288644 | ||||||||
\(286\) | − | 877.086i | − | 0.0107228i | ||||||
\(287\) | −73171.9 | −0.888342 | ||||||||
\(288\) | 27234.7i | 0.328351i | ||||||||
\(289\) | −80873.9 | −0.968306 | ||||||||
\(290\) | −19708.6 | −0.234347 | ||||||||
\(291\) | 25077.1 | 0.296136 | ||||||||
\(292\) | −32042.1 | −0.375799 | ||||||||
\(293\) | 131459. | 1.53129 | 0.765643 | − | 0.643266i | \(-0.222421\pi\) | ||||
0.765643 | + | 0.643266i | \(0.222421\pi\) | |||||||
\(294\) | −32390.2 | −0.374730 | ||||||||
\(295\) | − | 51733.5i | − | 0.594467i | ||||||
\(296\) | 53452.4i | 0.610076i | ||||||||
\(297\) | 5961.67 | 0.0675858 | ||||||||
\(298\) | 24686.3i | 0.277987i | ||||||||
\(299\) | 5381.62i | 0.0601964i | ||||||||
\(300\) | 27763.3i | 0.308481i | ||||||||
\(301\) | −173534. | −1.91536 | ||||||||
\(302\) | − | 2007.95i | − | 0.0220161i | ||||||
\(303\) | 17001.2 | 0.185180 | ||||||||
\(304\) | 6279.19 | 0.0679448 | ||||||||
\(305\) | −44806.8 | −0.481664 | ||||||||
\(306\) | − | 3522.99i | − | 0.0376243i | ||||||
\(307\) | −115161. | −1.22188 | −0.610942 | − | 0.791675i | \(-0.709209\pi\) | ||||
−0.610942 | + | 0.791675i | \(0.709209\pi\) | |||||||
\(308\) | 28341.7 | 0.298761 | ||||||||
\(309\) | 97868.2i | 1.02500i | ||||||||
\(310\) | 32533.3i | 0.338536i | ||||||||
\(311\) | − | 36460.2i | − | 0.376962i | −0.982077 | − | 0.188481i | \(-0.939644\pi\) | ||
0.982077 | − | 0.188481i | \(-0.0603564\pi\) | |||||||
\(312\) | − | 2742.22i | − | 0.0281704i | ||||||
\(313\) | 3411.80i | 0.0348253i | 0.999848 | + | 0.0174127i | \(0.00554290\pi\) | ||||
−0.999848 | + | 0.0174127i | \(0.994457\pi\) | |||||||
\(314\) | − | 72664.6i | − | 0.736994i | ||||||
\(315\) | 15357.7 | 0.154777 | ||||||||
\(316\) | − | 13859.7i | − | 0.138797i | ||||||
\(317\) | 143439. | 1.42741 | 0.713706 | − | 0.700445i | \(-0.247015\pi\) | ||||
0.713706 | + | 0.700445i | \(0.247015\pi\) | |||||||
\(318\) | 70127.7i | 0.693483i | ||||||||
\(319\) | 40468.7i | 0.397684i | ||||||||
\(320\) | 22357.2i | 0.218332i | ||||||||
\(321\) | 6932.74i | 0.0672813i | ||||||||
\(322\) | 116894. | 1.12740 | ||||||||
\(323\) | 28448.6 | 0.272681 | ||||||||
\(324\) | 6975.27 | 0.0664463 | ||||||||
\(325\) | − | 4544.76i | − | 0.0430274i | ||||||
\(326\) | 84396.2i | 0.794123i | ||||||||
\(327\) | 83862.9 | 0.784285 | ||||||||
\(328\) | −68067.5 | −0.632691 | ||||||||
\(329\) | 232692.i | 2.14976i | ||||||||
\(330\) | 4569.43 | 0.0419599 | ||||||||
\(331\) | − | 174114.i | − | 1.58920i | −0.607135 | − | 0.794599i | \(-0.707681\pi\) | ||
0.607135 | − | 0.794599i | \(-0.292319\pi\) | |||||||
\(332\) | 12861.0 | 0.116681 | ||||||||
\(333\) | 22257.0 | 0.200714 | ||||||||
\(334\) | 48737.3i | 0.436887i | ||||||||
\(335\) | 26441.8 | − | 25350.1i | 0.235614 | − | 0.225887i | ||||
\(336\) | −4113.18 | −0.0364334 | ||||||||
\(337\) | 100618.i | 0.885964i | 0.896531 | + | 0.442982i | \(0.146079\pi\) | ||||
−0.896531 | + | 0.442982i | \(0.853921\pi\) | |||||||
\(338\) | − | 72265.2i | − | 0.632551i | ||||||
\(339\) | −111726. | −0.972202 | ||||||||
\(340\) | 4017.08i | 0.0347498i | ||||||||
\(341\) | 66802.6 | 0.574493 | ||||||||
\(342\) | − | 37862.1i | − | 0.323708i | ||||||
\(343\) | 3967.46i | 0.0337228i | ||||||||
\(344\) | −161428. | −1.36415 | ||||||||
\(345\) | −28037.1 | −0.235556 | ||||||||
\(346\) | 92857.9i | 0.775652i | ||||||||
\(347\) | − | 149814.i | − | 1.24421i | −0.782935 | − | 0.622104i | \(-0.786278\pi\) | ||
0.782935 | − | 0.622104i | \(-0.213722\pi\) | |||||||
\(348\) | 47349.1i | 0.390979i | ||||||||
\(349\) | −128819. | −1.05762 | −0.528808 | − | 0.848742i | \(-0.677361\pi\) | ||||
−0.528808 | + | 0.848742i | \(0.677361\pi\) | |||||||
\(350\) | −98716.5 | −0.805849 | ||||||||
\(351\) | −1141.83 | −0.00926802 | ||||||||
\(352\) | 42862.9 | 0.345936 | ||||||||
\(353\) | − | 46449.1i | − | 0.372759i | −0.982478 | − | 0.186379i | \(-0.940325\pi\) | ||
0.982478 | − | 0.186379i | \(-0.0596754\pi\) | |||||||
\(354\) | 83545.6 | 0.666680 | ||||||||
\(355\) | 1946.54i | 0.0154456i | ||||||||
\(356\) | 42255.5 | 0.333414 | ||||||||
\(357\) | −18635.2 | −0.146217 | ||||||||
\(358\) | 125582. | 0.979856 | ||||||||
\(359\) | −55914.3 | −0.433844 | −0.216922 | − | 0.976189i | \(-0.569602\pi\) | ||||
−0.216922 | + | 0.976189i | \(0.569602\pi\) | |||||||
\(360\) | 14286.4 | 0.110235 | ||||||||
\(361\) | 175421. | 1.34607 | ||||||||
\(362\) | − | 131378.i | − | 1.00255i | ||||||
\(363\) | 66694.2i | 0.506145i | ||||||||
\(364\) | −5428.24 | −0.0409690 | ||||||||
\(365\) | 27326.3i | 0.205114i | ||||||||
\(366\) | − | 72359.5i | − | 0.540174i | ||||||
\(367\) | 45255.2i | 0.335997i | 0.985787 | + | 0.167999i | \(0.0537304\pi\) | ||||
−0.985787 | + | 0.167999i | \(0.946270\pi\) | |||||||
\(368\) | 7509.02 | 0.0554482 | ||||||||
\(369\) | 28342.5i | 0.208154i | ||||||||
\(370\) | 17059.2 | 0.124611 | ||||||||
\(371\) | 370948. | 2.69504 | ||||||||
\(372\) | 78160.3 | 0.564807 | ||||||||
\(373\) | − | 31935.1i | − | 0.229536i | −0.993392 | − | 0.114768i | \(-0.963388\pi\) | ||
0.993392 | − | 0.114768i | \(-0.0366124\pi\) | |||||||
\(374\) | −5544.59 | −0.0396394 | ||||||||
\(375\) | 50177.8 | 0.356820 | ||||||||
\(376\) | 216460.i | 1.53109i | ||||||||
\(377\) | − | 7750.91i | − | 0.0545343i | ||||||
\(378\) | 24801.6i | 0.173578i | ||||||||
\(379\) | 52284.2i | 0.363992i | 0.983299 | + | 0.181996i | \(0.0582558\pi\) | ||||
−0.983299 | + | 0.181996i | \(0.941744\pi\) | |||||||
\(380\) | 43172.2i | 0.298976i | ||||||||
\(381\) | − | 7588.30i | − | 0.0522751i | ||||||
\(382\) | −75825.0 | −0.519620 | ||||||||
\(383\) | − | 140143.i | − | 0.955377i | −0.878529 | − | 0.477689i | \(-0.841475\pi\) | ||
0.878529 | − | 0.477689i | \(-0.158525\pi\) | |||||||
\(384\) | 47756.0 | 0.323866 | ||||||||
\(385\) | − | 24170.5i | − | 0.163066i | ||||||
\(386\) | 99007.7i | 0.664499i | ||||||||
\(387\) | 67216.8i | 0.448803i | ||||||||
\(388\) | − | 46177.3i | − | 0.306736i | ||||||
\(389\) | 100857. | 0.666513 | 0.333257 | − | 0.942836i | \(-0.391852\pi\) | ||||
0.333257 | + | 0.942836i | \(0.391852\pi\) | |||||||
\(390\) | −875.176 | −0.00575395 | ||||||||
\(391\) | 34020.5 | 0.222529 | ||||||||
\(392\) | 159380.i | 1.03719i | ||||||||
\(393\) | 33687.1i | 0.218111i | ||||||||
\(394\) | −45144.3 | −0.290811 | ||||||||
\(395\) | −11819.9 | −0.0757567 | ||||||||
\(396\) | − | 10977.9i | − | 0.0700050i | ||||||
\(397\) | 259406. | 1.64588 | 0.822942 | − | 0.568126i | \(-0.192331\pi\) | ||||
0.822942 | + | 0.568126i | \(0.192331\pi\) | |||||||
\(398\) | − | 28203.9i | − | 0.178050i | ||||||
\(399\) | −200276. | −1.25801 | ||||||||
\(400\) | −6341.35 | −0.0396335 | ||||||||
\(401\) | − | 62793.9i | − | 0.390507i | −0.980753 | − | 0.195253i | \(-0.937447\pi\) | ||
0.980753 | − | 0.195253i | \(-0.0625529\pi\) | |||||||
\(402\) | 40938.5 | + | 42701.5i | 0.253326 | + | 0.264235i | ||||
\(403\) | −12794.6 | −0.0787801 | ||||||||
\(404\) | − | 31306.3i | − | 0.191809i | ||||||
\(405\) | − | 5948.69i | − | 0.0362670i | ||||||
\(406\) | −168357. | −1.02136 | ||||||||
\(407\) | − | 35028.7i | − | 0.211464i | ||||||
\(408\) | −17335.3 | −0.104138 | ||||||||
\(409\) | − | 73604.2i | − | 0.440003i | −0.975500 | − | 0.220002i | \(-0.929394\pi\) | ||
0.975500 | − | 0.220002i | \(-0.0706063\pi\) | |||||||
\(410\) | 21723.6i | 0.129230i | ||||||||
\(411\) | −166772. | −0.987275 | ||||||||
\(412\) | 180216. | 1.06169 | ||||||||
\(413\) | − | 441924.i | − | 2.59088i | ||||||
\(414\) | − | 45277.8i | − | 0.264170i | ||||||
\(415\) | − | 10968.2i | − | 0.0636853i | ||||||
\(416\) | −8209.47 | −0.0474382 | ||||||||
\(417\) | −147409. | −0.847717 | ||||||||
\(418\) | −59588.7 | −0.341045 | ||||||||
\(419\) | −182512. | −1.03959 | −0.519797 | − | 0.854290i | \(-0.673992\pi\) | ||||
−0.519797 | + | 0.854290i | \(0.673992\pi\) | |||||||
\(420\) | − | 28279.9i | − | 0.160317i | ||||||
\(421\) | 25338.0 | 0.142958 | 0.0714790 | − | 0.997442i | \(-0.477228\pi\) | ||||
0.0714790 | + | 0.997442i | \(0.477228\pi\) | |||||||
\(422\) | − | 61670.2i | − | 0.346299i | ||||||
\(423\) | 90131.2 | 0.503726 | ||||||||
\(424\) | 345072. | 1.91945 | ||||||||
\(425\) | −28730.2 | −0.159060 | ||||||||
\(426\) | −3143.51 | −0.0173219 | ||||||||
\(427\) | −382754. | −2.09925 | ||||||||
\(428\) | 12766.0 | 0.0696897 | ||||||||
\(429\) | 1797.05i | 0.00976440i | ||||||||
\(430\) | 51519.5i | 0.278635i | ||||||||
\(431\) | −146413. | −0.788179 | −0.394090 | − | 0.919072i | \(-0.628940\pi\) | ||||
−0.394090 | + | 0.919072i | \(0.628940\pi\) | |||||||
\(432\) | 1593.21i | 0.00853698i | ||||||||
\(433\) | 307516.i | 1.64018i | 0.572232 | + | 0.820092i | \(0.306078\pi\) | ||||
−0.572232 | + | 0.820092i | \(0.693922\pi\) | |||||||
\(434\) | 277910.i | 1.47545i | ||||||||
\(435\) | 40380.6 | 0.213400 | ||||||||
\(436\) | − | 154426.i | − | 0.812359i | ||||||
\(437\) | 365624. | 1.91457 | ||||||||
\(438\) | −44130.0 | −0.230030 | ||||||||
\(439\) | −88851.9 | −0.461039 | −0.230520 | − | 0.973068i | \(-0.574043\pi\) | ||||
−0.230520 | + | 0.973068i | \(0.574043\pi\) | |||||||
\(440\) | − | 22484.4i | − | 0.116138i | ||||||
\(441\) | 66363.8 | 0.341235 | ||||||||
\(442\) | 1061.95 | 0.00543574 | ||||||||
\(443\) | − | 145343.i | − | 0.740606i | −0.928911 | − | 0.370303i | \(-0.879254\pi\) | ||
0.928911 | − | 0.370303i | \(-0.120746\pi\) | |||||||
\(444\) | − | 40984.3i | − | 0.207899i | ||||||
\(445\) | − | 36036.6i | − | 0.181980i | ||||||
\(446\) | − | 113162.i | − | 0.568894i | ||||||
\(447\) | − | 50579.5i | − | 0.253139i | ||||||
\(448\) | 190982.i | 0.951562i | ||||||||
\(449\) | −216267. | −1.07275 | −0.536373 | − | 0.843981i | \(-0.680206\pi\) | ||||
−0.536373 | + | 0.843981i | \(0.680206\pi\) | |||||||
\(450\) | 38237.0i | 0.188825i | ||||||||
\(451\) | 44606.4 | 0.219303 | ||||||||
\(452\) | 205735.i | 1.00700i | ||||||||
\(453\) | 4114.07i | 0.0200482i | ||||||||
\(454\) | − | 86211.6i | − | 0.418267i | ||||||
\(455\) | 4629.34i | 0.0223613i | ||||||||
\(456\) | −186305. | −0.895973 | ||||||||
\(457\) | −413963. | −1.98212 | −0.991058 | − | 0.133428i | \(-0.957401\pi\) | ||||
−0.991058 | + | 0.133428i | \(0.957401\pi\) | |||||||
\(458\) | 91911.3 | 0.438165 | ||||||||
\(459\) | 7218.20i | 0.0342613i | ||||||||
\(460\) | 51627.9i | 0.243988i | ||||||||
\(461\) | 115022. | 0.541226 | 0.270613 | − | 0.962688i | \(-0.412774\pi\) | ||||
0.270613 | + | 0.962688i | \(0.412774\pi\) | |||||||
\(462\) | 39033.6 | 0.182875 | ||||||||
\(463\) | − | 172721.i | − | 0.805719i | −0.915262 | − | 0.402859i | \(-0.868016\pi\) | ||
0.915262 | − | 0.402859i | \(-0.131984\pi\) | |||||||
\(464\) | −10814.9 | −0.0502328 | ||||||||
\(465\) | − | 66657.1i | − | 0.308277i | ||||||
\(466\) | −84401.6 | −0.388668 | ||||||||
\(467\) | −126068. | −0.578058 | −0.289029 | − | 0.957320i | \(-0.593332\pi\) | ||||
−0.289029 | + | 0.957320i | \(0.593332\pi\) | |||||||
\(468\) | 2102.58i | 0.00959977i | ||||||||
\(469\) | 225874. | − | 216549.i | 1.02688 | − | 0.984488i | ||||
\(470\) | 69082.7 | 0.312733 | ||||||||
\(471\) | 148882.i | 0.671118i | ||||||||
\(472\) | − | 411096.i | − | 1.84527i | ||||||
\(473\) | 105788. | 0.472840 | ||||||||
\(474\) | − | 19088.3i | − | 0.0849593i | ||||||
\(475\) | −308769. | −1.36850 | ||||||||
\(476\) | 34315.2i | 0.151451i | ||||||||
\(477\) | − | 143684.i | − | 0.631496i | ||||||
\(478\) | −26630.6 | −0.116554 | ||||||||
\(479\) | 137760. | 0.600417 | 0.300208 | − | 0.953874i | \(-0.402944\pi\) | ||||
0.300208 | + | 0.953874i | \(0.402944\pi\) | |||||||
\(480\) | − | 42769.6i | − | 0.185632i | ||||||
\(481\) | 6709.00i | 0.0289980i | ||||||||
\(482\) | − | 63904.9i | − | 0.275068i | ||||||
\(483\) | −239502. | −1.02663 | ||||||||
\(484\) | 122812. | 0.524262 | ||||||||
\(485\) | −39381.2 | −0.167419 | ||||||||
\(486\) | 9606.68 | 0.0406725 | ||||||||
\(487\) | − | 134028.i | − | 0.565115i | −0.959250 | − | 0.282558i | \(-0.908817\pi\) | ||
0.959250 | − | 0.282558i | \(-0.0911829\pi\) | |||||||
\(488\) | −356053. | −1.49512 | ||||||||
\(489\) | − | 172918.i | − | 0.723141i | ||||||
\(490\) | 50865.7 | 0.211852 | ||||||||
\(491\) | −59774.2 | −0.247942 | −0.123971 | − | 0.992286i | \(-0.539563\pi\) | ||||
−0.123971 | + | 0.992286i | \(0.539563\pi\) | |||||||
\(492\) | 52190.3 | 0.215605 | ||||||||
\(493\) | −48998.2 | −0.201598 | ||||||||
\(494\) | 11412.9 | 0.0467674 | ||||||||
\(495\) | −9362.24 | −0.0382093 | ||||||||
\(496\) | 17852.4i | 0.0725661i | ||||||||
\(497\) | 16627.9i | 0.0673172i | ||||||||
\(498\) | 17712.8 | 0.0714215 | ||||||||
\(499\) | 382461.i | 1.53598i | 0.640460 | + | 0.767992i | \(0.278744\pi\) | ||||
−0.640460 | + | 0.767992i | \(0.721256\pi\) | |||||||
\(500\) | − | 92398.2i | − | 0.369593i | ||||||
\(501\) | − | 99857.3i | − | 0.397836i | ||||||
\(502\) | −264180. | −1.04831 | ||||||||
\(503\) | − | 394723.i | − | 1.56011i | −0.625708 | − | 0.780057i | \(-0.715190\pi\) | ||
0.625708 | − | 0.780057i | \(-0.284810\pi\) | |||||||
\(504\) | 122039. | 0.480438 | ||||||||
\(505\) | −26698.8 | −0.104691 | ||||||||
\(506\) | −71259.6 | −0.278319 | ||||||||
\(507\) | 148063.i | 0.576011i | ||||||||
\(508\) | −13973.2 | −0.0541463 | ||||||||
\(509\) | −49356.1 | −0.190504 | −0.0952522 | − | 0.995453i | \(-0.530366\pi\) | ||||
−0.0952522 | + | 0.995453i | \(0.530366\pi\) | |||||||
\(510\) | 5532.52i | 0.0212707i | ||||||||
\(511\) | 233430.i | 0.893955i | ||||||||
\(512\) | 23236.5i | 0.0886404i | ||||||||
\(513\) | 77575.2i | 0.294773i | ||||||||
\(514\) | − | 120294.i | − | 0.455322i | ||||||
\(515\) | − | 153693.i | − | 0.579481i | ||||||
\(516\) | 123774. | 0.464868 | ||||||||
\(517\) | − | 141852.i | − | 0.530705i | ||||||
\(518\) | 145726. | 0.543096 | ||||||||
\(519\) | − | 190255.i | − | 0.706321i | ||||||
\(520\) | 4306.40i | 0.0159260i | ||||||||
\(521\) | 164403.i | 0.605668i | 0.953043 | + | 0.302834i | \(0.0979328\pi\) | ||||
−0.953043 | + | 0.302834i | \(0.902067\pi\) | |||||||
\(522\) | 65211.6i | 0.239323i | ||||||||
\(523\) | 12914.4 | 0.0472142 | 0.0236071 | − | 0.999721i | \(-0.492485\pi\) | ||||
0.0236071 | + | 0.999721i | \(0.492485\pi\) | |||||||
\(524\) | 62031.9 | 0.225919 | ||||||||
\(525\) | 202259. | 0.733819 | ||||||||
\(526\) | − | 5683.54i | − | 0.0205422i | ||||||
\(527\) | 80882.4i | 0.291228i | ||||||||
\(528\) | 2507.44 | 0.00899420 | ||||||||
\(529\) | 157393. | 0.562438 | ||||||||
\(530\) | − | 110129.i | − | 0.392058i | ||||||
\(531\) | −171175. | −0.607089 | ||||||||
\(532\) | 368791.i | 1.30304i | ||||||||
\(533\) | −8543.39 | −0.0300729 | ||||||||
\(534\) | 58196.4 | 0.204086 | ||||||||
\(535\) | − | 10887.2i | − | 0.0380372i | ||||||
\(536\) | 210118. | − | 201443.i | 0.731363 | − | 0.701168i | ||||
\(537\) | −257304. | −0.892272 | ||||||||
\(538\) | − | 331506.i | − | 1.14532i | ||||||
\(539\) | − | 104445.i | − | 0.359511i | ||||||
\(540\) | −10954.0 | −0.0375651 | ||||||||
\(541\) | − | 173516.i | − | 0.592849i | −0.955056 | − | 0.296424i | \(-0.904206\pi\) | ||
0.955056 | − | 0.296424i | \(-0.0957943\pi\) | |||||||
\(542\) | −58826.7 | −0.200252 | ||||||||
\(543\) | 269179.i | 0.912939i | ||||||||
\(544\) | 51897.0i | 0.175366i | ||||||||
\(545\) | −131699. | −0.443393 | ||||||||
\(546\) | −7476.03 | −0.0250776 | ||||||||
\(547\) | − | 184590.i | − | 0.616925i | −0.951236 | − | 0.308463i | \(-0.900186\pi\) | ||
0.951236 | − | 0.308463i | \(-0.0998145\pi\) | |||||||
\(548\) | 307095.i | 1.02262i | ||||||||
\(549\) | 148256.i | 0.491891i | ||||||||
\(550\) | 60178.6 | 0.198938 | ||||||||
\(551\) | −526592. | −1.73449 | ||||||||
\(552\) | −222794. | −0.731183 | ||||||||
\(553\) | −100970. | −0.330173 | ||||||||
\(554\) | 310300.i | 1.01103i | ||||||||
\(555\) | −34952.5 | −0.113473 | ||||||||
\(556\) | 271440.i | 0.878061i | ||||||||
\(557\) | −132778. | −0.427971 | −0.213986 | − | 0.976837i | \(-0.568645\pi\) | ||||
−0.213986 | + | 0.976837i | \(0.568645\pi\) | |||||||
\(558\) | 107646. | 0.345725 | ||||||||
\(559\) | −20261.4 | −0.0648405 | ||||||||
\(560\) | 6459.36 | 0.0205975 | ||||||||
\(561\) | 11360.2 | 0.0360962 | ||||||||
\(562\) | 262795. | 0.832041 | ||||||||
\(563\) | 221405.i | 0.698506i | 0.937028 | + | 0.349253i | \(0.113565\pi\) | ||||
−0.937028 | + | 0.349253i | \(0.886435\pi\) | |||||||
\(564\) | − | 165969.i | − | 0.521757i | ||||||
\(565\) | 175456. | 0.549630 | ||||||||
\(566\) | − | 176590.i | − | 0.551231i | ||||||
\(567\) | − | 50815.6i | − | 0.158063i | ||||||
\(568\) | 15468.0i | 0.0479444i | ||||||||
\(569\) | −244081. | −0.753891 | −0.376946 | − | 0.926235i | \(-0.623026\pi\) | ||||
−0.376946 | + | 0.926235i | \(0.623026\pi\) | |||||||
\(570\) | 59458.9i | 0.183007i | ||||||||
\(571\) | 453087. | 1.38966 | 0.694831 | − | 0.719173i | \(-0.255479\pi\) | ||||
0.694831 | + | 0.719173i | \(0.255479\pi\) | |||||||
\(572\) | 3309.11 | 0.0101139 | ||||||||
\(573\) | 155357. | 0.473174 | ||||||||
\(574\) | 185570.i | 0.563228i | ||||||||
\(575\) | −369244. | −1.11680 | ||||||||
\(576\) | 73975.4 | 0.222968 | ||||||||
\(577\) | − | 123405.i | − | 0.370665i | −0.982676 | − | 0.185333i | \(-0.940664\pi\) | ||
0.982676 | − | 0.185333i | \(-0.0593362\pi\) | |||||||
\(578\) | 205103.i | 0.613927i | ||||||||
\(579\) | − | 202855.i | − | 0.605103i | ||||||
\(580\) | − | 74357.4i | − | 0.221039i | ||||||
\(581\) | − | 93693.9i | − | 0.277561i | ||||||
\(582\) | − | 63597.6i | − | 0.187756i | ||||||
\(583\) | −226134. | −0.665318 | ||||||||
\(584\) | 217147.i | 0.636689i | ||||||||
\(585\) | 1793.14 | 0.00523964 | ||||||||
\(586\) | − | 333392.i | − | 0.970868i | ||||||
\(587\) | − | 192782.i | − | 0.559488i | −0.960075 | − | 0.279744i | \(-0.909750\pi\) | ||
0.960075 | − | 0.279744i | \(-0.0902496\pi\) | |||||||
\(588\) | − | 122203.i | − | 0.353450i | ||||||
\(589\) | 869257.i | 2.50563i | ||||||||
\(590\) | −131201. | −0.376905 | ||||||||
\(591\) | 92495.5 | 0.264817 | ||||||||
\(592\) | 9361.13 | 0.0267107 | ||||||||
\(593\) | − | 381805.i | − | 1.08576i | −0.839812 | − | 0.542878i | \(-0.817335\pi\) | ||
0.839812 | − | 0.542878i | \(-0.182665\pi\) | |||||||
\(594\) | − | 15119.3i | − | 0.0428508i | ||||||
\(595\) | 29264.9 | 0.0826633 | ||||||||
\(596\) | −93137.8 | −0.262200 | ||||||||
\(597\) | 57786.5i | 0.162135i | ||||||||
\(598\) | 13648.2 | 0.0381658 | ||||||||
\(599\) | − | 63839.1i | − | 0.177923i | −0.996035 | − | 0.0889617i | \(-0.971645\pi\) | ||
0.996035 | − | 0.0889617i | \(-0.0283549\pi\) | |||||||
\(600\) | 188149. | 0.522637 | ||||||||
\(601\) | 454809. | 1.25916 | 0.629579 | − | 0.776936i | \(-0.283227\pi\) | ||||
0.629579 | + | 0.776936i | \(0.283227\pi\) | |||||||
\(602\) | 440097.i | 1.21438i | ||||||||
\(603\) | −83878.4 | − | 87490.5i | −0.230683 | − | 0.240617i | ||||
\(604\) | 7575.70 | 0.0207658 | ||||||||
\(605\) | − | 104737.i | − | 0.286147i | ||||||
\(606\) | − | 43116.5i | − | 0.117408i | ||||||
\(607\) | 56775.6 | 0.154093 | 0.0770467 | − | 0.997027i | \(-0.475451\pi\) | ||||
0.0770467 | + | 0.997027i | \(0.475451\pi\) | |||||||
\(608\) | 557746.i | 1.50879i | ||||||||
\(609\) | 344944. | 0.930067 | ||||||||
\(610\) | 113634.i | 0.305385i | ||||||||
\(611\) | 27168.6i | 0.0727754i | ||||||||
\(612\) | 13291.7 | 0.0354877 | ||||||||
\(613\) | 433945. | 1.15482 | 0.577409 | − | 0.816455i | \(-0.304064\pi\) | ||||
0.577409 | + | 0.816455i | \(0.304064\pi\) | |||||||
\(614\) | 292059.i | 0.774701i | ||||||||
\(615\) | − | 44509.2i | − | 0.117679i | ||||||
\(616\) | − | 192069.i | − | 0.506170i | ||||||
\(617\) | 4914.68 | 0.0129100 | 0.00645499 | − | 0.999979i | \(-0.497945\pi\) | ||||
0.00645499 | + | 0.999979i | \(0.497945\pi\) | |||||||
\(618\) | 248202. | 0.649873 | ||||||||
\(619\) | −539171. | −1.40717 | −0.703583 | − | 0.710613i | \(-0.748418\pi\) | ||||
−0.703583 | + | 0.710613i | \(0.748418\pi\) | |||||||
\(620\) | −122743. | −0.319311 | ||||||||
\(621\) | 92769.0i | 0.240558i | ||||||||
\(622\) | −92466.1 | −0.239002 | ||||||||
\(623\) | − | 307836.i | − | 0.793129i | ||||||
\(624\) | −480.246 | −0.00123337 | ||||||||
\(625\) | 270209. | 0.691734 | ||||||||
\(626\) | 8652.63 | 0.0220800 | ||||||||
\(627\) | 122090. | 0.310561 | ||||||||
\(628\) | 274153. | 0.695141 | ||||||||
\(629\) | 42411.7 | 0.107197 | ||||||||
\(630\) | − | 38948.5i | − | 0.0981319i | ||||||
\(631\) | 211466.i | 0.531106i | 0.964096 | + | 0.265553i | \(0.0855545\pi\) | ||||
−0.964096 | + | 0.265553i | \(0.914445\pi\) | |||||||
\(632\) | −93926.2 | −0.235154 | ||||||||
\(633\) | 126355.i | 0.315345i | ||||||||
\(634\) | − | 363774.i | − | 0.905011i | ||||||
\(635\) | 11916.7i | 0.0295535i | ||||||||
\(636\) | −264581. | −0.654101 | ||||||||
\(637\) | 20004.3i | 0.0492997i | ||||||||
\(638\) | 102632. | 0.252140 | ||||||||
\(639\) | 6440.69 | 0.0157736 | ||||||||
\(640\) | −74996.3 | −0.183096 | ||||||||
\(641\) | − | 62879.9i | − | 0.153037i | −0.997068 | − | 0.0765184i | \(-0.975620\pi\) | ||
0.997068 | − | 0.0765184i | \(-0.0243804\pi\) | |||||||
\(642\) | 17582.0 | 0.0426578 | ||||||||
\(643\) | 337262. | 0.815729 | 0.407864 | − | 0.913043i | \(-0.366274\pi\) | ||||
0.407864 | + | 0.913043i | \(0.366274\pi\) | |||||||
\(644\) | 441022.i | 1.06338i | ||||||||
\(645\) | − | 105558.i | − | 0.253729i | ||||||
\(646\) | − | 72148.0i | − | 0.172886i | ||||||
\(647\) | 307016.i | 0.733420i | 0.930335 | + | 0.366710i | \(0.119516\pi\) | ||||
−0.930335 | + | 0.366710i | \(0.880484\pi\) | |||||||
\(648\) | − | 47270.8i | − | 0.112575i | ||||||
\(649\) | 269402.i | 0.639604i | ||||||||
\(650\) | −11525.9 | −0.0272803 | ||||||||
\(651\) | − | 569407.i | − | 1.34357i | ||||||
\(652\) | −318414. | −0.749026 | ||||||||
\(653\) | 574452.i | 1.34718i | 0.739103 | + | 0.673592i | \(0.235250\pi\) | ||||
−0.739103 | + | 0.673592i | \(0.764750\pi\) | |||||||
\(654\) | − | 212683.i | − | 0.497254i | ||||||
\(655\) | − | 52902.4i | − | 0.123308i | ||||||
\(656\) | 11920.7i | 0.0277008i | ||||||||
\(657\) | 90417.3 | 0.209469 | ||||||||
\(658\) | 590127. | 1.36299 | ||||||||
\(659\) | 636830. | 1.46640 | 0.733201 | − | 0.680012i | \(-0.238025\pi\) | ||||
0.733201 | + | 0.680012i | \(0.238025\pi\) | |||||||
\(660\) | 17239.8i | 0.0395770i | ||||||||
\(661\) | − | 761413.i | − | 1.74268i | −0.490680 | − | 0.871340i | \(-0.663252\pi\) | ||
0.490680 | − | 0.871340i | \(-0.336748\pi\) | |||||||
\(662\) | −441568. | −1.00759 | ||||||||
\(663\) | −2175.81 | −0.00494987 | ||||||||
\(664\) | − | 87157.9i | − | 0.197684i | ||||||
\(665\) | 314515. | 0.711209 | ||||||||
\(666\) | − | 56445.6i | − | 0.127257i | ||||||
\(667\) | −629730. | −1.41548 | ||||||||
\(668\) | −183879. | −0.412077 | ||||||||
\(669\) | 231856.i | 0.518044i | ||||||||
\(670\) | −64290.1 | − | 67058.6i | −0.143217 | − | 0.149384i | ||||
\(671\) | 233331. | 0.518236 | ||||||||
\(672\) | − | 365351.i | − | 0.809044i | ||||||
\(673\) | 694522.i | 1.53340i | 0.642004 | + | 0.766701i | \(0.278103\pi\) | ||||
−0.642004 | + | 0.766701i | \(0.721897\pi\) | |||||||
\(674\) | 255176. | 0.561720 | ||||||||
\(675\) | − | 78343.2i | − | 0.171947i | ||||||
\(676\) | 272645. | 0.596630 | ||||||||
\(677\) | 335951.i | 0.732990i | 0.930420 | + | 0.366495i | \(0.119442\pi\) | ||||
−0.930420 | + | 0.366495i | \(0.880558\pi\) | |||||||
\(678\) | 283348.i | 0.616397i | ||||||||
\(679\) | −336407. | −0.729668 | ||||||||
\(680\) | 27223.4 | 0.0588741 | ||||||||
\(681\) | 176638.i | 0.380881i | ||||||||
\(682\) | − | 169417.i | − | 0.364241i | ||||||
\(683\) | − | 268779.i | − | 0.576175i | −0.957604 | − | 0.288087i | \(-0.906981\pi\) | ||
0.957604 | − | 0.288087i | \(-0.0930193\pi\) | |||||||
\(684\) | 142848. | 0.305325 | ||||||||
\(685\) | 261899. | 0.558152 | ||||||||
\(686\) | 10061.8 | 0.0213810 | ||||||||
\(687\) | −188316. | −0.399000 | ||||||||
\(688\) | 28271.0i | 0.0597260i | ||||||||
\(689\) | 43311.1 | 0.0912349 | ||||||||
\(690\) | 71104.4i | 0.149348i | ||||||||
\(691\) | −20490.6 | −0.0429139 | −0.0214569 | − | 0.999770i | \(-0.506830\pi\) | ||||
−0.0214569 | + | 0.999770i | \(0.506830\pi\) | |||||||
\(692\) | −350339. | −0.731604 | ||||||||
\(693\) | −79975.3 | −0.166529 | ||||||||
\(694\) | −379941. | −0.788854 | ||||||||
\(695\) | 231491. | 0.479253 | ||||||||
\(696\) | 320881. | 0.662408 | ||||||||
\(697\) | 54007.9i | 0.111171i | ||||||||
\(698\) | 326695.i | 0.670551i | ||||||||
\(699\) | 172929. | 0.353928 | ||||||||
\(700\) | − | 372442.i | − | 0.760086i | ||||||
\(701\) | 343916.i | 0.699869i | 0.936774 | + | 0.349935i | \(0.113796\pi\) | ||||
−0.936774 | + | 0.349935i | \(0.886204\pi\) | |||||||
\(702\) | 2895.78i | 0.00587613i | ||||||||
\(703\) | 455805. | 0.922293 | ||||||||
\(704\) | − | 116425.i | − | 0.234910i | ||||||
\(705\) | −141543. | −0.284780 | ||||||||
\(706\) | −117799. | −0.236337 | ||||||||
\(707\) | −228070. | −0.456277 | ||||||||
\(708\) | 315205.i | 0.628820i | ||||||||
\(709\) | 392130. | 0.780076 | 0.390038 | − | 0.920799i | \(-0.372462\pi\) | ||||
0.390038 | + | 0.920799i | \(0.372462\pi\) | |||||||
\(710\) | 4936.58 | 0.00979287 | ||||||||
\(711\) | 39109.8i | 0.0773653i | ||||||||
\(712\) | − | 286362.i | − | 0.564879i | ||||||
\(713\) | 1.03951e6i | 2.04479i | ||||||||
\(714\) | 47260.6i | 0.0927049i | ||||||||
\(715\) | − | 2822.10i | − | 0.00552026i | ||||||
\(716\) | 473802.i | 0.924211i | ||||||||
\(717\) | 54563.1 | 0.106136 | ||||||||
\(718\) | 141803.i | 0.275066i | ||||||||
\(719\) | −122930. | −0.237794 | −0.118897 | − | 0.992907i | \(-0.537936\pi\) | ||||
−0.118897 | + | 0.992907i | \(0.537936\pi\) | |||||||
\(720\) | − | 2501.98i | − | 0.00482635i | ||||||
\(721\) | − | 1.31289e6i | − | 2.52557i | ||||||
\(722\) | − | 444882.i | − | 0.853434i | ||||||
\(723\) | 130934.i | 0.250481i | ||||||||
\(724\) | 495670. | 0.945618 | ||||||||
\(725\) | 531805. | 1.01176 | ||||||||
\(726\) | 169142. | 0.320907 | ||||||||
\(727\) | − | 81782.9i | − | 0.154737i | −0.997003 | − | 0.0773684i | \(-0.975348\pi\) | ||
0.997003 | − | 0.0773684i | \(-0.0246518\pi\) | |||||||
\(728\) | 36786.7i | 0.0694109i | ||||||||
\(729\) | −19683.0 | −0.0370370 | ||||||||
\(730\) | 69301.9 | 0.130047 | ||||||||
\(731\) | 128085.i | 0.239697i | ||||||||
\(732\) | 273001. | 0.509498 | ||||||||
\(733\) | 358817.i | 0.667828i | 0.942603 | + | 0.333914i | \(0.108370\pi\) | ||||
−0.942603 | + | 0.333914i | \(0.891630\pi\) | |||||||
\(734\) | 114771. | 0.213030 | ||||||||
\(735\) | −104218. | −0.192916 | ||||||||
\(736\) | 666985.i | 1.23129i | ||||||||
\(737\) | −137695. | + | 132011.i | −0.253504 | + | 0.243038i | ||||
\(738\) | 71879.0 | 0.131974 | ||||||||
\(739\) | − | 286254.i | − | 0.524158i | −0.965046 | − | 0.262079i | \(-0.915592\pi\) | ||
0.965046 | − | 0.262079i | \(-0.0844081\pi\) | |||||||
\(740\) | 64361.9i | 0.117535i | ||||||||
\(741\) | −23383.8 | −0.0425871 | ||||||||
\(742\) | − | 940757.i | − | 1.70872i | ||||||
\(743\) | −187651. | −0.339917 | −0.169958 | − | 0.985451i | \(-0.554363\pi\) | ||||
−0.169958 | + | 0.985451i | \(0.554363\pi\) | |||||||
\(744\) | − | 529686.i | − | 0.956913i | ||||||
\(745\) | 79430.3i | 0.143111i | ||||||||
\(746\) | −80990.1 | −0.145531 | ||||||||
\(747\) | −36291.5 | −0.0650375 | ||||||||
\(748\) | − | 20918.9i | − | 0.0373883i | ||||||
\(749\) | − | 93002.1i | − | 0.165779i | ||||||
\(750\) | − | 127255.i | − | 0.226232i | ||||||
\(751\) | −11651.4 | −0.0206585 | −0.0103292 | − | 0.999947i | \(-0.503288\pi\) | ||||
−0.0103292 | + | 0.999947i | \(0.503288\pi\) | |||||||
\(752\) | 37908.6 | 0.0670351 | ||||||||
\(753\) | 541274. | 0.954612 | ||||||||
\(754\) | −19657.0 | −0.0345759 | ||||||||
\(755\) | − | 6460.75i | − | 0.0113342i | ||||||
\(756\) | −93572.6 | −0.163721 | ||||||||
\(757\) | 507606.i | 0.885799i | 0.896571 | + | 0.442899i | \(0.146050\pi\) | ||||
−0.896571 | + | 0.442899i | \(0.853950\pi\) | |||||||
\(758\) | 132597. | 0.230779 | ||||||||
\(759\) | 146003. | 0.253442 | ||||||||
\(760\) | 292574. | 0.506535 | ||||||||
\(761\) | 946519. | 1.63441 | 0.817203 | − | 0.576350i | \(-0.195523\pi\) | ||||
0.817203 | + | 0.576350i | \(0.195523\pi\) | |||||||
\(762\) | −19244.6 | −0.0331435 | ||||||||
\(763\) | −1.12501e6 | −1.93245 | ||||||||
\(764\) | − | 286076.i | − | 0.490112i | ||||||
\(765\) | − | 11335.5i | − | 0.0193695i | ||||||
\(766\) | −355416. | −0.605730 | ||||||||
\(767\) | − | 51598.1i | − | 0.0877087i | ||||||
\(768\) | − | 348899.i | − | 0.591530i | ||||||
\(769\) | 651018.i | 1.10088i | 0.834874 | + | 0.550441i | \(0.185540\pi\) | ||||
−0.834874 | + | 0.550441i | \(0.814460\pi\) | |||||||
\(770\) | −61298.5 | −0.103388 | ||||||||
\(771\) | 246469.i | 0.414623i | ||||||||
\(772\) | −373541. | −0.626763 | ||||||||
\(773\) | −1.09679e6 | −1.83554 | −0.917771 | − | 0.397109i | \(-0.870013\pi\) | ||||
−0.917771 | + | 0.397109i | \(0.870013\pi\) | |||||||
\(774\) | 170468. | 0.284551 | ||||||||
\(775\) | − | 877863.i | − | 1.46158i | ||||||
\(776\) | −312939. | −0.519681 | ||||||||
\(777\) | −298575. | −0.494552 | ||||||||
\(778\) | − | 255783.i | − | 0.422584i | ||||||
\(779\) | 580432.i | 0.956482i | ||||||||
\(780\) | − | 3301.90i | − | 0.00542719i | ||||||
\(781\) | − | 10136.6i | − | 0.0166184i | ||||||
\(782\) | − | 86278.9i | − | 0.141088i | ||||||
\(783\) | − | 133611.i | − | 0.217931i | ||||||
\(784\) | 27912.2 | 0.0454110 | ||||||||
\(785\) | − | 233804.i | − | 0.379414i | ||||||
\(786\) | 85433.4 | 0.138287 | ||||||||
\(787\) | 283075.i | 0.457037i | 0.973540 | + | 0.228519i | \(0.0733881\pi\) | ||||
−0.973540 | + | 0.228519i | \(0.926612\pi\) | |||||||
\(788\) | − | 170322.i | − | 0.274296i | ||||||
\(789\) | 11644.9i | 0.0187061i | ||||||||
\(790\) | 29976.4i | 0.0480314i | ||||||||
\(791\) | 1.49880e6 | 2.39547 | ||||||||
\(792\) | −74396.3 | −0.118604 | ||||||||
\(793\) | −44689.5 | −0.0710656 | ||||||||
\(794\) | − | 657876.i | − | 1.04353i | ||||||
\(795\) | 225642.i | 0.357014i | ||||||||
\(796\) | 106409. | 0.167939 | ||||||||
\(797\) | −731479. | −1.15156 | −0.575778 | − | 0.817606i | \(-0.695301\pi\) | ||||
−0.575778 | + | 0.817606i | \(0.695301\pi\) | |||||||
\(798\) | 507917.i | 0.797604i | ||||||||
\(799\) | 171749. | 0.269030 | ||||||||
\(800\) | − | 563268.i | − | 0.880106i | ||||||
\(801\) | −119238. | −0.185844 | ||||||||
\(802\) | −159251. | −0.247590 | ||||||||
\(803\) | − | 142302.i | − | 0.220688i | ||||||
\(804\) | −161106. | + | 154455.i | −0.249230 | + | 0.238940i | ||||
\(805\) | 376115. | 0.580402 | ||||||||
\(806\) | 32448.2i | 0.0499483i | ||||||||
\(807\) | 679218.i | 1.04295i | ||||||||
\(808\) | −212160. | −0.324968 | ||||||||
\(809\) | 460289.i | 0.703289i | 0.936134 | + | 0.351645i | \(0.114377\pi\) | ||||
−0.936134 | + | 0.351645i | \(0.885623\pi\) | |||||||
\(810\) | −15086.4 | −0.0229940 | ||||||||
\(811\) | − | 85621.2i | − | 0.130179i | −0.997879 | − | 0.0650893i | \(-0.979267\pi\) | ||
0.997879 | − | 0.0650893i | \(-0.0207332\pi\) | |||||||
\(812\) | − | 635185.i | − | 0.963359i | ||||||
\(813\) | 120529. | 0.182352 | ||||||||
\(814\) | −88835.9 | −0.134073 | ||||||||
\(815\) | 271552.i | 0.408825i | ||||||||
\(816\) | 3035.93i | 0.00455943i | ||||||||
\(817\) | 1.37655e6i | 2.06228i | ||||||||
\(818\) | −186667. | −0.278972 | ||||||||
\(819\) | 15317.5 | 0.0228361 | ||||||||
\(820\) | −81959.9 | −0.121892 | ||||||||
\(821\) | −1.12464e6 | −1.66850 | −0.834249 | − | 0.551388i | \(-0.814098\pi\) | ||||
−0.834249 | + | 0.551388i | \(0.814098\pi\) | |||||||
\(822\) | 422947.i | 0.625954i | ||||||||
\(823\) | −88269.9 | −0.130321 | −0.0651603 | − | 0.997875i | \(-0.520756\pi\) | ||||
−0.0651603 | + | 0.997875i | \(0.520756\pi\) | |||||||
\(824\) | − | 1.22131e6i | − | 1.79875i | ||||||
\(825\) | −123299. | −0.181156 | ||||||||
\(826\) | −1.12076e6 | −1.64267 | ||||||||
\(827\) | −762169. | −1.11440 | −0.557199 | − | 0.830379i | \(-0.688124\pi\) | ||||
−0.557199 | + | 0.830379i | \(0.688124\pi\) | |||||||
\(828\) | 170826. | 0.249169 | ||||||||
\(829\) | −832615. | −1.21153 | −0.605767 | − | 0.795642i | \(-0.707133\pi\) | ||||
−0.605767 | + | 0.795642i | \(0.707133\pi\) | |||||||
\(830\) | −27816.3 | −0.0403778 | ||||||||
\(831\) | − | 635769.i | − | 0.920656i | ||||||
\(832\) | 22298.7i | 0.0322131i | ||||||||
\(833\) | 126459. | 0.182247 | ||||||||
\(834\) | 373841.i | 0.537471i | ||||||||
\(835\) | 156816.i | 0.224915i | ||||||||
\(836\) | − | 224819.i | − | 0.321677i | ||||||
\(837\) | −220555. | −0.314822 | ||||||||
\(838\) | 462867.i | 0.659125i | ||||||||
\(839\) | −847059. | −1.20334 | −0.601672 | − | 0.798743i | \(-0.705499\pi\) | ||||
−0.601672 | + | 0.798743i | \(0.705499\pi\) | |||||||
\(840\) | −191651. | −0.271614 | ||||||||
\(841\) | 199691. | 0.282337 | ||||||||
\(842\) | − | 64259.4i | − | 0.0906384i | ||||||
\(843\) | −538437. | −0.757670 | ||||||||
\(844\) | 232672. | 0.326633 | ||||||||
\(845\) | − | 232519.i | − | 0.325646i | ||||||
\(846\) | − | 228581.i | − | 0.319373i | ||||||
\(847\) | − | 894697.i | − | 1.24712i | ||||||
\(848\) | − | 60432.4i | − | 0.0840385i | ||||||
\(849\) | 361813.i | 0.501960i | ||||||||
\(850\) | 72862.3i | 0.100848i | ||||||||
\(851\) | 545079. | 0.752662 | ||||||||
\(852\) | − | 11860.0i | − | 0.0163382i | ||||||
\(853\) | −556392. | −0.764686 | −0.382343 | − | 0.924020i | \(-0.624883\pi\) | ||||
−0.382343 | + | 0.924020i | \(0.624883\pi\) | |||||||
\(854\) | 970697.i | 1.33097i | ||||||||
\(855\) | − | 121825.i | − | 0.166649i | ||||||
\(856\) | − | 86514.4i | − | 0.118070i | ||||||
\(857\) | − | 892287.i | − | 1.21491i | −0.794355 | − | 0.607454i | \(-0.792191\pi\) | ||
0.794355 | − | 0.607454i | \(-0.207809\pi\) | |||||||
\(858\) | 4557.47 | 0.00619084 | ||||||||
\(859\) | 970247. | 1.31491 | 0.657455 | − | 0.753494i | \(-0.271633\pi\) | ||||
0.657455 | + | 0.753494i | \(0.271633\pi\) | |||||||
\(860\) | −194375. | −0.262811 | ||||||||
\(861\) | − | 380212.i | − | 0.512885i | ||||||
\(862\) | 371316.i | 0.499723i | ||||||||
\(863\) | 115316. | 0.154834 | 0.0774170 | − | 0.996999i | \(-0.475333\pi\) | ||||
0.0774170 | + | 0.996999i | \(0.475333\pi\) | |||||||
\(864\) | −141516. | −0.189573 | ||||||||
\(865\) | 298778.i | 0.399316i | ||||||||
\(866\) | 779888. | 1.03991 | ||||||||
\(867\) | − | 420233.i | − | 0.559052i | ||||||
\(868\) | −1.04851e6 | −1.39166 | ||||||||
\(869\) | 61552.2 | 0.0815088 | ||||||||
\(870\) | − | 102409.i | − | 0.135300i | ||||||
\(871\) | 26372.6 | − | 25283.8i | 0.0347629 | − | 0.0333277i | ||||
\(872\) | −1.04653e6 | −1.37632 | ||||||||
\(873\) | 130304.i | 0.170974i | ||||||||
\(874\) | − | 927253.i | − | 1.21388i | ||||||
\(875\) | −673131. | −0.879192 | ||||||||
\(876\) | − | 166496.i | − | 0.216967i | ||||||
\(877\) | 87113.3 | 0.113262 | 0.0566311 | − | 0.998395i | \(-0.481964\pi\) | ||||
0.0566311 | + | 0.998395i | \(0.481964\pi\) | |||||||
\(878\) | 225336.i | 0.292309i | ||||||||
\(879\) | 683083.i | 0.884088i | ||||||||
\(880\) | −3937.70 | −0.00508484 | ||||||||
\(881\) | 10742.7 | 0.0138408 | 0.00692038 | − | 0.999976i | \(-0.497797\pi\) | ||||
0.00692038 | + | 0.999976i | \(0.497797\pi\) | |||||||
\(882\) | − | 168304.i | − | 0.216350i | ||||||
\(883\) | − | 945802.i | − | 1.21305i | −0.795064 | − | 0.606525i | \(-0.792563\pi\) | ||
0.795064 | − | 0.606525i | \(-0.207437\pi\) | |||||||
\(884\) | 4006.57i | 0.00512705i | ||||||||
\(885\) | 268815. | 0.343215 | ||||||||
\(886\) | −368603. | −0.469560 | ||||||||
\(887\) | −48296.9 | −0.0613864 | −0.0306932 | − | 0.999529i | \(-0.509771\pi\) | ||||
−0.0306932 | + | 0.999529i | \(0.509771\pi\) | |||||||
\(888\) | −277747. | −0.352228 | ||||||||
\(889\) | 101796.i | 0.128804i | ||||||||
\(890\) | −91392.0 | −0.115379 | ||||||||
\(891\) | 30977.8i | 0.0390207i | ||||||||
\(892\) | 426943. | 0.536587 | ||||||||
\(893\) | 1.84582e6 | 2.31465 | ||||||||
\(894\) | −128274. | −0.160496 | ||||||||
\(895\) | 404071. | 0.504443 | ||||||||
\(896\) | −640643. | −0.797995 | ||||||||
\(897\) | −27963.7 | −0.0347544 | ||||||||
\(898\) | 548471.i | 0.680144i | ||||||||
\(899\) | − | 1.49716e6i | − | 1.85246i | ||||||
\(900\) | −144262. | −0.178102 | ||||||||
\(901\) | − | 273796.i | − | 0.337270i | ||||||
\(902\) | − | 113126.i | − | 0.139043i | ||||||
\(903\) | − | 901708.i | − | 1.10584i | ||||||
\(904\) | 1.39425e6 | 1.70609 | ||||||||
\(905\) | − | 422721.i | − | 0.516127i | ||||||
\(906\) | 10433.6 | 0.0127110 | ||||||||
\(907\) | −1.18879e6 | −1.44508 | −0.722540 | − | 0.691329i | \(-0.757025\pi\) | ||||
−0.722540 | + | 0.691329i | \(0.757025\pi\) | |||||||
\(908\) | 325263. | 0.394515 | ||||||||
\(909\) | 88340.9i | 0.106914i | ||||||||
\(910\) | 11740.4 | 0.0141775 | ||||||||
\(911\) | −135791. | −0.163619 | −0.0818095 | − | 0.996648i | \(-0.526070\pi\) | ||||
−0.0818095 | + | 0.996648i | \(0.526070\pi\) | |||||||
\(912\) | 32627.6i | 0.0392279i | ||||||||
\(913\) | 57116.8i | 0.0685208i | ||||||||
\(914\) | 1.04985e6i | 1.25670i | ||||||||
\(915\) | − | 232823.i | − | 0.278089i | ||||||
\(916\) | 346767.i | 0.413283i | ||||||||
\(917\) | − | 451909.i | − | 0.537419i | ||||||
\(918\) | 18306.0 | 0.0217224 | ||||||||
\(919\) | 440505.i | 0.521578i | 0.965396 | + | 0.260789i | \(0.0839827\pi\) | ||||
−0.965396 | + | 0.260789i | \(0.916017\pi\) | |||||||
\(920\) | 349878. | 0.413371 | ||||||||
\(921\) | − | 598396.i | − | 0.705455i | ||||||
\(922\) | − | 291705.i | − | 0.343149i | ||||||
\(923\) | 1941.44i | 0.00227888i | ||||||||
\(924\) | 147268.i | 0.172490i | ||||||||
\(925\) | −460318. | −0.537990 | ||||||||
\(926\) | −438036. | −0.510843 | ||||||||
\(927\) | −508538. | −0.591785 | ||||||||
\(928\) | − | 960630.i | − | 1.11548i | ||||||
\(929\) | 1.16404e6i | 1.34876i | 0.738384 | + | 0.674381i | \(0.235589\pi\) | ||||
−0.738384 | + | 0.674381i | \(0.764411\pi\) | |||||||
\(930\) | −169048. | −0.195454 | ||||||||
\(931\) | 1.35908e6 | 1.56800 | ||||||||
\(932\) | − | 318435.i | − | 0.366597i | ||||||
\(933\) | 189453. | 0.217639 | ||||||||
\(934\) | 319719.i | 0.366501i | ||||||||
\(935\) | −17840.2 | −0.0204069 | ||||||||
\(936\) | 14249.0 | 0.0162642 | ||||||||
\(937\) | − | 391873.i | − | 0.446341i | −0.974779 | − | 0.223170i | \(-0.928359\pi\) | ||
0.974779 | − | 0.223170i | \(-0.0716407\pi\) | |||||||
\(938\) | −549187. | − | 572837.i | −0.624186 | − | 0.651066i | ||||
\(939\) | −17728.2 | −0.0201064 | ||||||||
\(940\) | 260638.i | 0.294973i | ||||||||
\(941\) | − | 1.56608e6i | − | 1.76863i | −0.466895 | − | 0.884313i | \(-0.654627\pi\) | ||
0.466895 | − | 0.884313i | \(-0.345373\pi\) | |||||||
\(942\) | 377577. | 0.425504 | ||||||||
\(943\) | 694115.i | 0.780563i | ||||||||
\(944\) | −71995.3 | −0.0807904 | ||||||||
\(945\) | 79801.1i | 0.0893605i | ||||||||
\(946\) | − | 268288.i | − | 0.299791i | ||||||
\(947\) | 573431. | 0.639412 | 0.319706 | − | 0.947517i | \(-0.396416\pi\) | ||||
0.319706 | + | 0.947517i | \(0.396416\pi\) | |||||||
\(948\) | 72017.3 | 0.0801346 | ||||||||
\(949\) | 27254.8i | 0.0302629i | ||||||||
\(950\) | 783064.i | 0.867661i | ||||||||
\(951\) | 745332.i | 0.824117i | ||||||||
\(952\) | 232551. | 0.256593 | ||||||||
\(953\) | 1.50854e6 | 1.66100 | 0.830502 | − | 0.557016i | \(-0.188054\pi\) | ||||
0.830502 | + | 0.557016i | \(0.188054\pi\) | |||||||
\(954\) | −364394. | −0.400382 | ||||||||
\(955\) | −243973. | −0.267507 | ||||||||
\(956\) | − | 100473.i | − | 0.109935i | ||||||
\(957\) | −210282. | −0.229603 | ||||||||
\(958\) | − | 349372.i | − | 0.380677i | ||||||
\(959\) | 2.23723e6 | 2.43261 | ||||||||
\(960\) | −116171. | −0.126054 | ||||||||
\(961\) | −1.54787e6 | −1.67606 | ||||||||
\(962\) | 17014.6 | 0.0183853 | ||||||||
\(963\) | −36023.6 | −0.0388449 | ||||||||
\(964\) | 241103. | 0.259447 | ||||||||
\(965\) | 318565.i | 0.342093i | ||||||||
\(966\) | 607397.i | 0.650906i | ||||||||
\(967\) | −318251. | −0.340343 | −0.170171 | − | 0.985414i | \(-0.554432\pi\) | ||||
−0.170171 | + | 0.985414i | \(0.554432\pi\) | |||||||
\(968\) | − | 832284.i | − | 0.888220i | ||||||
\(969\) | 147823.i | 0.157433i | ||||||||
\(970\) | 99874.1i | 0.106147i | ||||||||
\(971\) | 562745. | 0.596861 | 0.298431 | − | 0.954431i | \(-0.403537\pi\) | ||||
0.298431 | + | 0.954431i | \(0.403537\pi\) | |||||||
\(972\) | 36244.5i | 0.0383628i | ||||||||
\(973\) | 1.97747e6 | 2.08874 | ||||||||
\(974\) | −339906. | −0.358295 | ||||||||
\(975\) | 23615.3 | 0.0248419 | ||||||||
\(976\) | 62355.7i | 0.0654601i | ||||||||
\(977\) | 585418. | 0.613306 | 0.306653 | − | 0.951821i | \(-0.400791\pi\) | ||||
0.306653 | + | 0.951821i | \(0.400791\pi\) | |||||||
\(978\) | −438535. | −0.458487 | ||||||||
\(979\) | 187660.i | 0.195798i | ||||||||
\(980\) | 191908.i | 0.199821i | ||||||||
\(981\) | 435764.i | 0.452807i | ||||||||
\(982\) | 151592.i | 0.157201i | ||||||||
\(983\) | 1.91764e6i | 1.98454i | 0.124093 | + | 0.992271i | \(0.460398\pi\) | ||||
−0.124093 | + | 0.992271i | \(0.539602\pi\) | |||||||
\(984\) | − | 353689.i | − | 0.365285i | ||||||
\(985\) | −145255. | −0.149713 | ||||||||
\(986\) | 124264.i | 0.127818i | ||||||||
\(987\) | −1.20910e6 | −1.24116 | ||||||||
\(988\) | 43059.2i | 0.0441115i | ||||||||
\(989\) | 1.64616e6i | 1.68298i | ||||||||
\(990\) | 23743.5i | 0.0242255i | ||||||||
\(991\) | 512865.i | 0.522223i | 0.965309 | + | 0.261111i | \(0.0840890\pi\) | ||||
−0.965309 | + | 0.261111i | \(0.915911\pi\) | |||||||
\(992\) | −1.58573e6 | −1.61141 | ||||||||
\(993\) | 904723. | 0.917524 | ||||||||
\(994\) | 42169.9 | 0.0426805 | ||||||||
\(995\) | − | 90748.2i | − | 0.0916625i | ||||||
\(996\) | 66827.7i | 0.0673656i | ||||||||
\(997\) | 169477. | 0.170499 | 0.0852493 | − | 0.996360i | \(-0.472831\pi\) | ||||
0.0852493 | + | 0.996360i | \(0.472831\pi\) | |||||||
\(998\) | 969955. | 0.973847 | ||||||||
\(999\) | 115651.i | 0.115882i |
(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 | 201.5.b.a.133.17 | ✓ | 46 | |
67.66 | odd | 2 | inner | 201.5.b.a.133.30 | yes | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
201.5.b.a.133.17 | ✓ | 46 | 1.1 | even | 1 | trivial | |
201.5.b.a.133.30 | yes | 46 | 67.66 | odd | 2 | inner |