Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [354,5,Mod(235,354)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(354, 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("354.235");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 354.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: | \(36.5929669317\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 235.32 | ||
Character | \(\chi\) | \(=\) | 354.235 |
Dual form | 354.5.d.a.235.31 |
$q$-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 \(\left(\mathbb{Z}/354\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.82843i | 0.707107i | ||||||||
\(3\) | 5.19615 | 0.577350 | ||||||||
\(4\) | −8.00000 | −0.500000 | ||||||||
\(5\) | 13.0356 | 0.521424 | 0.260712 | − | 0.965417i | \(-0.416043\pi\) | ||||
0.260712 | + | 0.965417i | \(0.416043\pi\) | |||||||
\(6\) | 14.6969i | 0.408248i | ||||||||
\(7\) | 71.9157 | 1.46767 | 0.733833 | − | 0.679330i | \(-0.237729\pi\) | ||||
0.733833 | + | 0.679330i | \(0.237729\pi\) | |||||||
\(8\) | − | 22.6274i | − | 0.353553i | ||||||
\(9\) | 27.0000 | 0.333333 | ||||||||
\(10\) | 36.8702i | 0.368702i | ||||||||
\(11\) | − | 76.6106i | − | 0.633145i | −0.948568 | − | 0.316573i | \(-0.897468\pi\) | ||
0.948568 | − | 0.316573i | \(-0.102532\pi\) | |||||||
\(12\) | −41.5692 | −0.288675 | ||||||||
\(13\) | − | 118.606i | − | 0.701811i | −0.936411 | − | 0.350905i | \(-0.885874\pi\) | ||
0.936411 | − | 0.350905i | \(-0.114126\pi\) | |||||||
\(14\) | 203.408i | 1.03780i | ||||||||
\(15\) | 67.7349 | 0.301044 | ||||||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | 31.5143 | 0.109046 | 0.0545230 | − | 0.998513i | \(-0.482636\pi\) | ||||
0.0545230 | + | 0.998513i | \(0.482636\pi\) | |||||||
\(18\) | 76.3675i | 0.235702i | ||||||||
\(19\) | 461.021 | 1.27707 | 0.638534 | − | 0.769594i | \(-0.279541\pi\) | ||||
0.638534 | + | 0.769594i | \(0.279541\pi\) | |||||||
\(20\) | −104.285 | −0.260712 | ||||||||
\(21\) | 373.685 | 0.847358 | ||||||||
\(22\) | 216.687 | 0.447701 | ||||||||
\(23\) | − | 901.986i | − | 1.70508i | −0.522665 | − | 0.852538i | \(-0.675062\pi\) | ||
0.522665 | − | 0.852538i | \(-0.324938\pi\) | |||||||
\(24\) | − | 117.576i | − | 0.204124i | ||||||
\(25\) | −455.073 | −0.728117 | ||||||||
\(26\) | 335.469 | 0.496255 | ||||||||
\(27\) | 140.296 | 0.192450 | ||||||||
\(28\) | −575.325 | −0.733833 | ||||||||
\(29\) | −1161.22 | −1.38076 | −0.690378 | − | 0.723449i | \(-0.742556\pi\) | ||||
−0.690378 | + | 0.723449i | \(0.742556\pi\) | |||||||
\(30\) | 191.583i | 0.212870i | ||||||||
\(31\) | − | 457.352i | − | 0.475912i | −0.971276 | − | 0.237956i | \(-0.923523\pi\) | ||
0.971276 | − | 0.237956i | \(-0.0764774\pi\) | |||||||
\(32\) | 181.019i | 0.176777i | ||||||||
\(33\) | − | 398.080i | − | 0.365547i | ||||||
\(34\) | 89.1358i | 0.0771071i | ||||||||
\(35\) | 937.463 | 0.765276 | ||||||||
\(36\) | −216.000 | −0.166667 | ||||||||
\(37\) | 440.417i | 0.321707i | 0.986978 | + | 0.160853i | \(0.0514247\pi\) | ||||
−0.986978 | + | 0.160853i | \(0.948575\pi\) | |||||||
\(38\) | 1303.96i | 0.903023i | ||||||||
\(39\) | − | 616.295i | − | 0.405191i | ||||||
\(40\) | − | 294.962i | − | 0.184351i | ||||||
\(41\) | 2196.09 | 1.30642 | 0.653208 | − | 0.757179i | \(-0.273423\pi\) | ||||
0.653208 | + | 0.757179i | \(0.273423\pi\) | |||||||
\(42\) | 1056.94i | 0.599172i | ||||||||
\(43\) | − | 1247.28i | − | 0.674572i | −0.941402 | − | 0.337286i | \(-0.890491\pi\) | ||
0.941402 | − | 0.337286i | \(-0.109509\pi\) | |||||||
\(44\) | 612.885i | 0.316573i | ||||||||
\(45\) | 351.961 | 0.173808 | ||||||||
\(46\) | 2551.20 | 1.20567 | ||||||||
\(47\) | − | 1319.13i | − | 0.597162i | −0.954384 | − | 0.298581i | \(-0.903487\pi\) | ||
0.954384 | − | 0.298581i | \(-0.0965133\pi\) | |||||||
\(48\) | 332.554 | 0.144338 | ||||||||
\(49\) | 2770.86 | 1.15405 | ||||||||
\(50\) | − | 1287.14i | − | 0.514857i | ||||||
\(51\) | 163.753 | 0.0629577 | ||||||||
\(52\) | 948.848i | 0.350905i | ||||||||
\(53\) | 53.4409 | 0.0190249 | 0.00951244 | − | 0.999955i | \(-0.496972\pi\) | ||||
0.00951244 | + | 0.999955i | \(0.496972\pi\) | |||||||
\(54\) | 396.817i | 0.136083i | ||||||||
\(55\) | − | 998.664i | − | 0.330137i | ||||||
\(56\) | − | 1627.27i | − | 0.518899i | ||||||
\(57\) | 2395.54 | 0.737315 | ||||||||
\(58\) | − | 3284.41i | − | 0.976341i | ||||||
\(59\) | 729.257 | + | 3403.75i | 0.209496 | + | 0.977809i | ||||
\(60\) | −541.879 | −0.150522 | ||||||||
\(61\) | 235.014i | 0.0631589i | 0.999501 | + | 0.0315794i | \(0.0100537\pi\) | ||||
−0.999501 | + | 0.0315794i | \(0.989946\pi\) | |||||||
\(62\) | 1293.59 | 0.336521 | ||||||||
\(63\) | 1941.72 | 0.489222 | ||||||||
\(64\) | −512.000 | −0.125000 | ||||||||
\(65\) | − | 1546.10i | − | 0.365941i | ||||||
\(66\) | 1125.94 | 0.258480 | ||||||||
\(67\) | 5947.06i | 1.32481i | 0.749147 | + | 0.662404i | \(0.230464\pi\) | ||||
−0.749147 | + | 0.662404i | \(0.769536\pi\) | |||||||
\(68\) | −252.114 | −0.0545230 | ||||||||
\(69\) | − | 4686.85i | − | 0.984426i | ||||||
\(70\) | 2651.55i | 0.541132i | ||||||||
\(71\) | 7826.66 | 1.55260 | 0.776300 | − | 0.630363i | \(-0.217094\pi\) | ||||
0.776300 | + | 0.630363i | \(0.217094\pi\) | |||||||
\(72\) | − | 610.940i | − | 0.117851i | ||||||
\(73\) | 8267.19i | 1.55136i | 0.631127 | + | 0.775680i | \(0.282593\pi\) | ||||
−0.631127 | + | 0.775680i | \(0.717407\pi\) | |||||||
\(74\) | −1245.69 | −0.227481 | ||||||||
\(75\) | −2364.63 | −0.420379 | ||||||||
\(76\) | −3688.17 | −0.638534 | ||||||||
\(77\) | − | 5509.50i | − | 0.929246i | ||||||
\(78\) | 1743.15 | 0.286513 | ||||||||
\(79\) | 519.406 | 0.0832248 | 0.0416124 | − | 0.999134i | \(-0.486751\pi\) | ||||
0.0416124 | + | 0.999134i | \(0.486751\pi\) | |||||||
\(80\) | 834.278 | 0.130356 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | 6211.47i | 0.923776i | ||||||||
\(83\) | − | 6918.96i | − | 1.00435i | −0.864766 | − | 0.502174i | \(-0.832534\pi\) | ||
0.864766 | − | 0.502174i | \(-0.167466\pi\) | |||||||
\(84\) | −2989.48 | −0.423679 | ||||||||
\(85\) | 410.807 | 0.0568591 | ||||||||
\(86\) | 3527.85 | 0.476994 | ||||||||
\(87\) | −6033.85 | −0.797179 | ||||||||
\(88\) | −1733.50 | −0.223851 | ||||||||
\(89\) | 1209.41i | 0.152684i | 0.997082 | + | 0.0763422i | \(0.0243241\pi\) | ||||
−0.997082 | + | 0.0763422i | \(0.975676\pi\) | |||||||
\(90\) | 995.496i | 0.122901i | ||||||||
\(91\) | − | 8529.63i | − | 1.03002i | ||||||
\(92\) | 7215.88i | 0.852538i | ||||||||
\(93\) | − | 2376.47i | − | 0.274768i | ||||||
\(94\) | 3731.07 | 0.422257 | ||||||||
\(95\) | 6009.69 | 0.665893 | ||||||||
\(96\) | 940.604i | 0.102062i | ||||||||
\(97\) | 10730.3i | 1.14043i | 0.821497 | + | 0.570213i | \(0.193139\pi\) | ||||
−0.821497 | + | 0.570213i | \(0.806861\pi\) | |||||||
\(98\) | 7837.18i | 0.816033i | ||||||||
\(99\) | − | 2068.49i | − | 0.211048i | ||||||
\(100\) | 3640.59 | 0.364059 | ||||||||
\(101\) | 3057.38i | 0.299714i | 0.988708 | + | 0.149857i | \(0.0478813\pi\) | ||||
−0.988708 | + | 0.149857i | \(0.952119\pi\) | |||||||
\(102\) | 463.163i | 0.0445178i | ||||||||
\(103\) | 413.512i | 0.0389775i | 0.999810 | + | 0.0194887i | \(0.00620385\pi\) | ||||
−0.999810 | + | 0.0194887i | \(0.993796\pi\) | |||||||
\(104\) | −2683.75 | −0.248128 | ||||||||
\(105\) | 4871.20 | 0.441832 | ||||||||
\(106\) | 151.154i | 0.0134526i | ||||||||
\(107\) | −488.624 | −0.0426783 | −0.0213391 | − | 0.999772i | \(-0.506793\pi\) | ||||
−0.0213391 | + | 0.999772i | \(0.506793\pi\) | |||||||
\(108\) | −1122.37 | −0.0962250 | ||||||||
\(109\) | 12377.5i | 1.04179i | 0.853620 | + | 0.520896i | \(0.174402\pi\) | ||||
−0.853620 | + | 0.520896i | \(0.825598\pi\) | |||||||
\(110\) | 2824.65 | 0.233442 | ||||||||
\(111\) | 2288.47i | 0.185738i | ||||||||
\(112\) | 4602.60 | 0.366917 | ||||||||
\(113\) | 58.5659i | 0.00458657i | 0.999997 | + | 0.00229328i | \(0.000729976\pi\) | ||||
−0.999997 | + | 0.00229328i | \(0.999270\pi\) | |||||||
\(114\) | 6775.60i | 0.521360i | ||||||||
\(115\) | − | 11757.9i | − | 0.889067i | ||||||
\(116\) | 9289.72 | 0.690378 | ||||||||
\(117\) | − | 3202.36i | − | 0.233937i | ||||||
\(118\) | −9627.27 | + | 2062.65i | −0.691416 | + | 0.148136i | ||||
\(119\) | 2266.37 | 0.160043 | ||||||||
\(120\) | − | 1532.67i | − | 0.106435i | ||||||
\(121\) | 8771.82 | 0.599127 | ||||||||
\(122\) | −664.720 | −0.0446601 | ||||||||
\(123\) | 11411.2 | 0.754260 | ||||||||
\(124\) | 3658.81i | 0.237956i | ||||||||
\(125\) | −14079.4 | −0.901081 | ||||||||
\(126\) | 5492.02i | 0.345932i | ||||||||
\(127\) | 6961.62 | 0.431621 | 0.215811 | − | 0.976435i | \(-0.430761\pi\) | ||||
0.215811 | + | 0.976435i | \(0.430761\pi\) | |||||||
\(128\) | − | 1448.15i | − | 0.0883883i | ||||||
\(129\) | − | 6481.07i | − | 0.389464i | ||||||
\(130\) | 4373.03 | 0.258759 | ||||||||
\(131\) | 13594.7i | 0.792185i | 0.918211 | + | 0.396092i | \(0.129634\pi\) | ||||
−0.918211 | + | 0.396092i | \(0.870366\pi\) | |||||||
\(132\) | 3184.64i | 0.182773i | ||||||||
\(133\) | 33154.6 | 1.87431 | ||||||||
\(134\) | −16820.8 | −0.936780 | ||||||||
\(135\) | 1828.84 | 0.100348 | ||||||||
\(136\) | − | 713.087i | − | 0.0385536i | ||||||
\(137\) | −21151.7 | −1.12695 | −0.563475 | − | 0.826133i | \(-0.690536\pi\) | ||||
−0.563475 | + | 0.826133i | \(0.690536\pi\) | |||||||
\(138\) | 13256.4 | 0.696095 | ||||||||
\(139\) | 20763.3 | 1.07465 | 0.537324 | − | 0.843376i | \(-0.319435\pi\) | ||||
0.537324 | + | 0.843376i | \(0.319435\pi\) | |||||||
\(140\) | −7499.71 | −0.382638 | ||||||||
\(141\) | − | 6854.41i | − | 0.344772i | ||||||
\(142\) | 22137.1i | 1.09785i | ||||||||
\(143\) | −9086.48 | −0.444348 | ||||||||
\(144\) | 1728.00 | 0.0833333 | ||||||||
\(145\) | −15137.1 | −0.719959 | ||||||||
\(146\) | −23383.2 | −1.09698 | ||||||||
\(147\) | 14397.8 | 0.666288 | ||||||||
\(148\) | − | 3523.33i | − | 0.160853i | ||||||
\(149\) | − | 6501.17i | − | 0.292832i | −0.989223 | − | 0.146416i | \(-0.953226\pi\) | ||
0.989223 | − | 0.146416i | \(-0.0467738\pi\) | |||||||
\(150\) | − | 6688.18i | − | 0.297253i | ||||||
\(151\) | − | 4605.38i | − | 0.201982i | −0.994887 | − | 0.100991i | \(-0.967799\pi\) | ||
0.994887 | − | 0.100991i | \(-0.0322013\pi\) | |||||||
\(152\) | − | 10431.7i | − | 0.451511i | ||||||
\(153\) | 850.886 | 0.0363487 | ||||||||
\(154\) | 15583.2 | 0.657076 | ||||||||
\(155\) | − | 5961.85i | − | 0.248152i | ||||||
\(156\) | 4930.36i | 0.202595i | ||||||||
\(157\) | 8564.91i | 0.347475i | 0.984792 | + | 0.173737i | \(0.0555844\pi\) | ||||
−0.984792 | + | 0.173737i | \(0.944416\pi\) | |||||||
\(158\) | 1469.10i | 0.0588488i | ||||||||
\(159\) | 277.687 | 0.0109840 | ||||||||
\(160\) | 2359.69i | 0.0921756i | ||||||||
\(161\) | − | 64866.9i | − | 2.50248i | ||||||
\(162\) | 2061.92i | 0.0785674i | ||||||||
\(163\) | −1698.22 | −0.0639173 | −0.0319587 | − | 0.999489i | \(-0.510174\pi\) | ||||
−0.0319587 | + | 0.999489i | \(0.510174\pi\) | |||||||
\(164\) | −17568.7 | −0.653208 | ||||||||
\(165\) | − | 5189.21i | − | 0.190605i | ||||||
\(166\) | 19569.8 | 0.710182 | ||||||||
\(167\) | −40686.7 | −1.45888 | −0.729439 | − | 0.684046i | \(-0.760219\pi\) | ||||
−0.729439 | + | 0.684046i | \(0.760219\pi\) | |||||||
\(168\) | − | 8455.52i | − | 0.299586i | ||||||
\(169\) | 14493.6 | 0.507462 | ||||||||
\(170\) | 1161.94i | 0.0402055i | ||||||||
\(171\) | 12447.6 | 0.425689 | ||||||||
\(172\) | 9978.26i | 0.337286i | ||||||||
\(173\) | 373.836i | 0.0124908i | 0.999980 | + | 0.00624538i | \(0.00198798\pi\) | ||||
−0.999980 | + | 0.00624538i | \(0.998012\pi\) | |||||||
\(174\) | − | 17066.3i | − | 0.563691i | ||||||
\(175\) | −32726.9 | −1.06863 | ||||||||
\(176\) | − | 4903.08i | − | 0.158286i | ||||||
\(177\) | 3789.33 | + | 17686.4i | 0.120953 | + | 0.564539i | ||||
\(178\) | −3420.74 | −0.107964 | ||||||||
\(179\) | − | 48418.3i | − | 1.51114i | −0.655071 | − | 0.755568i | \(-0.727361\pi\) | ||
0.655071 | − | 0.755568i | \(-0.272639\pi\) | |||||||
\(180\) | −2815.69 | −0.0869040 | ||||||||
\(181\) | −46967.3 | −1.43363 | −0.716817 | − | 0.697262i | \(-0.754402\pi\) | ||||
−0.716817 | + | 0.697262i | \(0.754402\pi\) | |||||||
\(182\) | 24125.4 | 0.728337 | ||||||||
\(183\) | 1221.17i | 0.0364648i | ||||||||
\(184\) | −20409.6 | −0.602836 | ||||||||
\(185\) | 5741.09i | 0.167746i | ||||||||
\(186\) | 6721.67 | 0.194290 | ||||||||
\(187\) | − | 2414.33i | − | 0.0690419i | ||||||
\(188\) | 10553.0i | 0.298581i | ||||||||
\(189\) | 10089.5 | 0.282453 | ||||||||
\(190\) | 16998.0i | 0.470858i | ||||||||
\(191\) | 35697.0i | 0.978509i | 0.872141 | + | 0.489255i | \(0.162731\pi\) | ||||
−0.872141 | + | 0.489255i | \(0.837269\pi\) | |||||||
\(192\) | −2660.43 | −0.0721688 | ||||||||
\(193\) | 25170.3 | 0.675730 | 0.337865 | − | 0.941195i | \(-0.390295\pi\) | ||||
0.337865 | + | 0.941195i | \(0.390295\pi\) | |||||||
\(194\) | −30349.8 | −0.806403 | ||||||||
\(195\) | − | 8033.77i | − | 0.211276i | ||||||
\(196\) | −22166.9 | −0.577023 | ||||||||
\(197\) | −68867.3 | −1.77452 | −0.887260 | − | 0.461270i | \(-0.847394\pi\) | ||||
−0.887260 | + | 0.461270i | \(0.847394\pi\) | |||||||
\(198\) | 5850.56 | 0.149234 | ||||||||
\(199\) | −37635.2 | −0.950361 | −0.475180 | − | 0.879888i | \(-0.657617\pi\) | ||||
−0.475180 | + | 0.879888i | \(0.657617\pi\) | |||||||
\(200\) | 10297.1i | 0.257428i | ||||||||
\(201\) | 30901.8i | 0.764878i | ||||||||
\(202\) | −8647.57 | −0.211929 | ||||||||
\(203\) | −83509.6 | −2.02649 | ||||||||
\(204\) | −1310.02 | −0.0314789 | ||||||||
\(205\) | 28627.3 | 0.681196 | ||||||||
\(206\) | −1169.59 | −0.0275612 | ||||||||
\(207\) | − | 24353.6i | − | 0.568359i | ||||||
\(208\) | − | 7590.79i | − | 0.175453i | ||||||
\(209\) | − | 35319.1i | − | 0.808569i | ||||||
\(210\) | 13777.8i | 0.312423i | ||||||||
\(211\) | − | 46880.1i | − | 1.05299i | −0.850179 | − | 0.526494i | \(-0.823506\pi\) | ||
0.850179 | − | 0.526494i | \(-0.176494\pi\) | |||||||
\(212\) | −427.527 | −0.00951244 | ||||||||
\(213\) | 40668.5 | 0.896394 | ||||||||
\(214\) | − | 1382.04i | − | 0.0301781i | ||||||
\(215\) | − | 16259.1i | − | 0.351738i | ||||||
\(216\) | − | 3174.54i | − | 0.0680414i | ||||||
\(217\) | − | 32890.7i | − | 0.698480i | ||||||
\(218\) | −35008.9 | −0.736658 | ||||||||
\(219\) | 42957.6i | 0.895678i | ||||||||
\(220\) | 7989.31i | 0.165068i | ||||||||
\(221\) | − | 3737.78i | − | 0.0765296i | ||||||
\(222\) | −6472.78 | −0.131336 | ||||||||
\(223\) | 53767.4 | 1.08121 | 0.540604 | − | 0.841277i | \(-0.318196\pi\) | ||||
0.540604 | + | 0.841277i | \(0.318196\pi\) | |||||||
\(224\) | 13018.1i | 0.259449i | ||||||||
\(225\) | −12287.0 | −0.242706 | ||||||||
\(226\) | −165.649 | −0.00324319 | ||||||||
\(227\) | 13393.3i | 0.259918i | 0.991519 | + | 0.129959i | \(0.0414846\pi\) | ||||
−0.991519 | + | 0.129959i | \(0.958515\pi\) | |||||||
\(228\) | −19164.3 | −0.368658 | ||||||||
\(229\) | 5622.87i | 0.107223i | 0.998562 | + | 0.0536114i | \(0.0170732\pi\) | ||||
−0.998562 | + | 0.0536114i | \(0.982927\pi\) | |||||||
\(230\) | 33256.4 | 0.628666 | ||||||||
\(231\) | − | 28628.2i | − | 0.536501i | ||||||
\(232\) | 26275.3i | 0.488171i | ||||||||
\(233\) | − | 104467.i | − | 1.92428i | −0.272549 | − | 0.962142i | \(-0.587867\pi\) | ||
0.272549 | − | 0.962142i | \(-0.412133\pi\) | |||||||
\(234\) | 9057.65 | 0.165418 | ||||||||
\(235\) | − | 17195.7i | − | 0.311374i | ||||||
\(236\) | −5834.05 | − | 27230.0i | −0.104748 | − | 0.488905i | ||||
\(237\) | 2698.91 | 0.0480499 | ||||||||
\(238\) | 6410.26i | 0.113168i | ||||||||
\(239\) | −84162.7 | −1.47341 | −0.736706 | − | 0.676213i | \(-0.763620\pi\) | ||||
−0.736706 | + | 0.676213i | \(0.763620\pi\) | |||||||
\(240\) | 4335.04 | 0.0752610 | ||||||||
\(241\) | −53479.0 | −0.920766 | −0.460383 | − | 0.887720i | \(-0.652288\pi\) | ||||
−0.460383 | + | 0.887720i | \(0.652288\pi\) | |||||||
\(242\) | 24810.5i | 0.423647i | ||||||||
\(243\) | 3788.00 | 0.0641500 | ||||||||
\(244\) | − | 1880.11i | − | 0.0315794i | ||||||
\(245\) | 36119.8 | 0.601747 | ||||||||
\(246\) | 32275.7i | 0.533342i | ||||||||
\(247\) | − | 54679.9i | − | 0.896260i | ||||||
\(248\) | −10348.7 | −0.168260 | ||||||||
\(249\) | − | 35952.0i | − | 0.579861i | ||||||
\(250\) | − | 39822.5i | − | 0.637161i | ||||||
\(251\) | 8610.91 | 0.136679 | 0.0683395 | − | 0.997662i | \(-0.478230\pi\) | ||||
0.0683395 | + | 0.997662i | \(0.478230\pi\) | |||||||
\(252\) | −15533.8 | −0.244611 | ||||||||
\(253\) | −69101.6 | −1.07956 | ||||||||
\(254\) | 19690.4i | 0.305202i | ||||||||
\(255\) | 2134.62 | 0.0328276 | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | −24174.3 | −0.366005 | −0.183003 | − | 0.983112i | \(-0.558582\pi\) | ||||
−0.183003 | + | 0.983112i | \(0.558582\pi\) | |||||||
\(258\) | 18331.2 | 0.275393 | ||||||||
\(259\) | 31672.9i | 0.472159i | ||||||||
\(260\) | 12368.8i | 0.182970i | ||||||||
\(261\) | −31352.8 | −0.460252 | ||||||||
\(262\) | −38451.6 | −0.560159 | ||||||||
\(263\) | 15619.3 | 0.225814 | 0.112907 | − | 0.993606i | \(-0.463984\pi\) | ||||
0.112907 | + | 0.993606i | \(0.463984\pi\) | |||||||
\(264\) | −9007.53 | −0.129240 | ||||||||
\(265\) | 696.634 | 0.00992002 | ||||||||
\(266\) | 93775.5i | 1.32534i | ||||||||
\(267\) | 6284.29i | 0.0881524i | ||||||||
\(268\) | − | 47576.5i | − | 0.662404i | ||||||
\(269\) | 91681.8i | 1.26701i | 0.773741 | + | 0.633503i | \(0.218383\pi\) | ||||
−0.773741 | + | 0.633503i | \(0.781617\pi\) | |||||||
\(270\) | 5172.75i | 0.0709568i | ||||||||
\(271\) | −23909.2 | −0.325557 | −0.162779 | − | 0.986663i | \(-0.552046\pi\) | ||||
−0.162779 | + | 0.986663i | \(0.552046\pi\) | |||||||
\(272\) | 2016.91 | 0.0272615 | ||||||||
\(273\) | − | 44321.3i | − | 0.594685i | ||||||
\(274\) | − | 59826.1i | − | 0.796874i | ||||||
\(275\) | 34863.4i | 0.461004i | ||||||||
\(276\) | 37494.8i | 0.492213i | ||||||||
\(277\) | 145442. | 1.89553 | 0.947767 | − | 0.318964i | \(-0.103335\pi\) | ||||
0.947767 | + | 0.318964i | \(0.103335\pi\) | |||||||
\(278\) | 58727.4i | 0.759891i | ||||||||
\(279\) | − | 12348.5i | − | 0.158637i | ||||||
\(280\) | − | 21212.4i | − | 0.270566i | ||||||
\(281\) | −50468.8 | −0.639161 | −0.319581 | − | 0.947559i | \(-0.603542\pi\) | ||||
−0.319581 | + | 0.947559i | \(0.603542\pi\) | |||||||
\(282\) | 19387.2 | 0.243790 | ||||||||
\(283\) | 148907.i | 1.85927i | 0.368488 | + | 0.929633i | \(0.379876\pi\) | ||||
−0.368488 | + | 0.929633i | \(0.620124\pi\) | |||||||
\(284\) | −62613.3 | −0.776300 | ||||||||
\(285\) | 31227.2 | 0.384454 | ||||||||
\(286\) | − | 25700.4i | − | 0.314202i | ||||||
\(287\) | 157933. | 1.91738 | ||||||||
\(288\) | 4887.52i | 0.0589256i | ||||||||
\(289\) | −82527.9 | −0.988109 | ||||||||
\(290\) | − | 42814.3i | − | 0.509088i | ||||||
\(291\) | 55756.1i | 0.658425i | ||||||||
\(292\) | − | 66137.5i | − | 0.775680i | ||||||
\(293\) | 63017.4 | 0.734049 | 0.367024 | − | 0.930211i | \(-0.380377\pi\) | ||||
0.367024 | + | 0.930211i | \(0.380377\pi\) | |||||||
\(294\) | 40723.2i | 0.471137i | ||||||||
\(295\) | 9506.29 | + | 44370.0i | 0.109236 | + | 0.509853i | ||||
\(296\) | 9965.49 | 0.113741 | ||||||||
\(297\) | − | 10748.2i | − | 0.121849i | ||||||
\(298\) | 18388.1 | 0.207064 | ||||||||
\(299\) | −106981. | −1.19664 | ||||||||
\(300\) | 18917.0 | 0.210189 | ||||||||
\(301\) | − | 89699.2i | − | 0.990046i | ||||||
\(302\) | 13026.0 | 0.142823 | ||||||||
\(303\) | 15886.6i | 0.173040i | ||||||||
\(304\) | 29505.4 | 0.319267 | ||||||||
\(305\) | 3063.55i | 0.0329325i | ||||||||
\(306\) | 2406.67i | 0.0257024i | ||||||||
\(307\) | 9766.49 | 0.103624 | 0.0518122 | − | 0.998657i | \(-0.483500\pi\) | ||||
0.0518122 | + | 0.998657i | \(0.483500\pi\) | |||||||
\(308\) | 44076.0i | 0.464623i | ||||||||
\(309\) | 2148.67i | 0.0225037i | ||||||||
\(310\) | 16862.7 | 0.175470 | ||||||||
\(311\) | 57858.3 | 0.598198 | 0.299099 | − | 0.954222i | \(-0.403314\pi\) | ||||
0.299099 | + | 0.954222i | \(0.403314\pi\) | |||||||
\(312\) | −13945.2 | −0.143257 | ||||||||
\(313\) | 167799.i | 1.71278i | 0.516331 | + | 0.856389i | \(0.327297\pi\) | ||||
−0.516331 | + | 0.856389i | \(0.672703\pi\) | |||||||
\(314\) | −24225.2 | −0.245702 | ||||||||
\(315\) | 25311.5 | 0.255092 | ||||||||
\(316\) | −4155.25 | −0.0416124 | ||||||||
\(317\) | 45806.8 | 0.455839 | 0.227919 | − | 0.973680i | \(-0.426808\pi\) | ||||
0.227919 | + | 0.973680i | \(0.426808\pi\) | |||||||
\(318\) | 785.417i | 0.00776687i | ||||||||
\(319\) | 88961.4i | 0.874219i | ||||||||
\(320\) | −6674.22 | −0.0651780 | ||||||||
\(321\) | −2538.96 | −0.0246403 | ||||||||
\(322\) | 183471. | 1.76952 | ||||||||
\(323\) | 14528.8 | 0.139259 | ||||||||
\(324\) | −5832.00 | −0.0555556 | ||||||||
\(325\) | 53974.4i | 0.511001i | ||||||||
\(326\) | − | 4803.29i | − | 0.0451964i | ||||||
\(327\) | 64315.5i | 0.601479i | ||||||||
\(328\) | − | 49691.7i | − | 0.461888i | ||||||
\(329\) | − | 94866.2i | − | 0.876435i | ||||||
\(330\) | 14677.3 | 0.134778 | ||||||||
\(331\) | 161647. | 1.47540 | 0.737702 | − | 0.675127i | \(-0.235911\pi\) | ||||
0.737702 | + | 0.675127i | \(0.235911\pi\) | |||||||
\(332\) | 55351.7i | 0.502174i | ||||||||
\(333\) | 11891.3i | 0.107236i | ||||||||
\(334\) | − | 115079.i | − | 1.03158i | ||||||
\(335\) | 77523.5i | 0.690786i | ||||||||
\(336\) | 23915.8 | 0.211839 | ||||||||
\(337\) | − | 62124.9i | − | 0.547024i | −0.961869 | − | 0.273512i | \(-0.911815\pi\) | ||
0.961869 | − | 0.273512i | \(-0.0881853\pi\) | |||||||
\(338\) | 40994.1i | 0.358829i | ||||||||
\(339\) | 304.317i | 0.00264806i | ||||||||
\(340\) | −3286.46 | −0.0284296 | ||||||||
\(341\) | −35038.0 | −0.301321 | ||||||||
\(342\) | 35207.1i | 0.301008i | ||||||||
\(343\) | 26598.9 | 0.226087 | ||||||||
\(344\) | −28222.8 | −0.238497 | ||||||||
\(345\) | − | 61095.9i | − | 0.513303i | ||||||
\(346\) | −1057.37 | −0.00883230 | ||||||||
\(347\) | 14358.0i | 0.119243i | 0.998221 | + | 0.0596217i | \(0.0189894\pi\) | ||||
−0.998221 | + | 0.0596217i | \(0.981011\pi\) | |||||||
\(348\) | 48270.8 | 0.398590 | ||||||||
\(349\) | 169000.i | 1.38751i | 0.720212 | + | 0.693754i | \(0.244045\pi\) | ||||
−0.720212 | + | 0.693754i | \(0.755955\pi\) | |||||||
\(350\) | − | 92565.7i | − | 0.755638i | ||||||
\(351\) | − | 16640.0i | − | 0.135064i | ||||||
\(352\) | 13868.0 | 0.111925 | ||||||||
\(353\) | − | 187823.i | − | 1.50730i | −0.657278 | − | 0.753648i | \(-0.728292\pi\) | ||
0.657278 | − | 0.753648i | \(-0.271708\pi\) | |||||||
\(354\) | −50024.8 | + | 10717.8i | −0.399189 | + | 0.0855265i | ||||
\(355\) | 102025. | 0.809563 | ||||||||
\(356\) | − | 9675.30i | − | 0.0763422i | ||||||
\(357\) | 11776.4 | 0.0924009 | ||||||||
\(358\) | 136948. | 1.06853 | ||||||||
\(359\) | −203966. | −1.58259 | −0.791297 | − | 0.611432i | \(-0.790594\pi\) | ||||
−0.791297 | + | 0.611432i | \(0.790594\pi\) | |||||||
\(360\) | − | 7963.97i | − | 0.0614504i | ||||||
\(361\) | 82219.6 | 0.630900 | ||||||||
\(362\) | − | 132843.i | − | 1.01373i | ||||||
\(363\) | 45579.7 | 0.345906 | ||||||||
\(364\) | 68237.1i | 0.515012i | ||||||||
\(365\) | 107768.i | 0.808915i | ||||||||
\(366\) | −3453.99 | −0.0257845 | ||||||||
\(367\) | − | 21743.1i | − | 0.161432i | −0.996737 | − | 0.0807159i | \(-0.974279\pi\) | ||
0.996737 | − | 0.0807159i | \(-0.0257207\pi\) | |||||||
\(368\) | − | 57727.1i | − | 0.426269i | ||||||
\(369\) | 59294.3 | 0.435472 | ||||||||
\(370\) | −16238.3 | −0.118614 | ||||||||
\(371\) | 3843.24 | 0.0279222 | ||||||||
\(372\) | 19011.7i | 0.137384i | ||||||||
\(373\) | 47541.9 | 0.341711 | 0.170855 | − | 0.985296i | \(-0.445347\pi\) | ||||
0.170855 | + | 0.985296i | \(0.445347\pi\) | |||||||
\(374\) | 6828.75 | 0.0488200 | ||||||||
\(375\) | −73158.7 | −0.520240 | ||||||||
\(376\) | −29848.5 | −0.211129 | ||||||||
\(377\) | 137727.i | 0.969029i | ||||||||
\(378\) | 28537.4i | 0.199724i | ||||||||
\(379\) | −87143.6 | −0.606676 | −0.303338 | − | 0.952883i | \(-0.598101\pi\) | ||||
−0.303338 | + | 0.952883i | \(0.598101\pi\) | |||||||
\(380\) | −48077.5 | −0.332947 | ||||||||
\(381\) | 36173.6 | 0.249197 | ||||||||
\(382\) | −100966. | −0.691910 | ||||||||
\(383\) | −20889.8 | −0.142408 | −0.0712042 | − | 0.997462i | \(-0.522684\pi\) | ||||
−0.0712042 | + | 0.997462i | \(0.522684\pi\) | |||||||
\(384\) | − | 7524.83i | − | 0.0510310i | ||||||
\(385\) | − | 71819.6i | − | 0.484531i | ||||||
\(386\) | 71192.2i | 0.477813i | ||||||||
\(387\) | − | 33676.6i | − | 0.224857i | ||||||
\(388\) | − | 85842.2i | − | 0.570213i | ||||||
\(389\) | −226227. | −1.49501 | −0.747506 | − | 0.664255i | \(-0.768749\pi\) | ||||
−0.747506 | + | 0.664255i | \(0.768749\pi\) | |||||||
\(390\) | 22722.9 | 0.149395 | ||||||||
\(391\) | − | 28425.4i | − | 0.185932i | ||||||
\(392\) | − | 62697.5i | − | 0.408017i | ||||||
\(393\) | 70640.1i | 0.457368i | ||||||||
\(394\) | − | 194786.i | − | 1.25477i | ||||||
\(395\) | 6770.77 | 0.0433954 | ||||||||
\(396\) | 16547.9i | 0.105524i | ||||||||
\(397\) | 258128.i | 1.63777i | 0.573956 | + | 0.818886i | \(0.305408\pi\) | ||||
−0.573956 | + | 0.818886i | \(0.694592\pi\) | |||||||
\(398\) | − | 106449.i | − | 0.672006i | ||||||
\(399\) | 172277. | 1.08213 | ||||||||
\(400\) | −29124.7 | −0.182029 | ||||||||
\(401\) | − | 121353.i | − | 0.754678i | −0.926075 | − | 0.377339i | \(-0.876839\pi\) | ||
0.926075 | − | 0.377339i | \(-0.123161\pi\) | |||||||
\(402\) | −87403.6 | −0.540850 | ||||||||
\(403\) | −54244.6 | −0.334000 | ||||||||
\(404\) | − | 24459.0i | − | 0.149857i | ||||||
\(405\) | 9502.95 | 0.0579360 | ||||||||
\(406\) | − | 236201.i | − | 1.43294i | ||||||
\(407\) | 33740.6 | 0.203687 | ||||||||
\(408\) | − | 3705.31i | − | 0.0222589i | ||||||
\(409\) | 127039.i | 0.759434i | 0.925103 | + | 0.379717i | \(0.123979\pi\) | ||||
−0.925103 | + | 0.379717i | \(0.876021\pi\) | |||||||
\(410\) | 80970.2i | 0.481678i | ||||||||
\(411\) | −109908. | −0.650645 | ||||||||
\(412\) | − | 3308.10i | − | 0.0194887i | ||||||
\(413\) | 52445.0 | + | 244783.i | 0.307471 | + | 1.43510i | ||||
\(414\) | 68882.4 | 0.401890 | ||||||||
\(415\) | − | 90192.7i | − | 0.523691i | ||||||
\(416\) | 21470.0 | 0.124064 | ||||||||
\(417\) | 107889. | 0.620448 | ||||||||
\(418\) | 99897.5 | 0.571745 | ||||||||
\(419\) | 66337.2i | 0.377858i | 0.981991 | + | 0.188929i | \(0.0605017\pi\) | ||||
−0.981991 | + | 0.188929i | \(0.939498\pi\) | |||||||
\(420\) | −38969.6 | −0.220916 | ||||||||
\(421\) | − | 316689.i | − | 1.78677i | −0.449290 | − | 0.893386i | \(-0.648323\pi\) | ||
0.449290 | − | 0.893386i | \(-0.351677\pi\) | |||||||
\(422\) | 132597. | 0.744575 | ||||||||
\(423\) | − | 35616.5i | − | 0.199054i | ||||||
\(424\) | − | 1209.23i | − | 0.00672631i | ||||||
\(425\) | −14341.3 | −0.0793982 | ||||||||
\(426\) | 115028.i | 0.633847i | ||||||||
\(427\) | 16901.2i | 0.0926962i | ||||||||
\(428\) | 3908.99 | 0.0213391 | ||||||||
\(429\) | −47214.7 | −0.256545 | ||||||||
\(430\) | 45987.6 | 0.248716 | ||||||||
\(431\) | 19159.7i | 0.103142i | 0.998669 | + | 0.0515709i | \(0.0164228\pi\) | ||||
−0.998669 | + | 0.0515709i | \(0.983577\pi\) | |||||||
\(432\) | 8978.95 | 0.0481125 | ||||||||
\(433\) | 59077.3 | 0.315097 | 0.157549 | − | 0.987511i | \(-0.449641\pi\) | ||||
0.157549 | + | 0.987511i | \(0.449641\pi\) | |||||||
\(434\) | 93029.1 | 0.493900 | ||||||||
\(435\) | −78654.8 | −0.415668 | ||||||||
\(436\) | − | 99020.2i | − | 0.520896i | ||||||
\(437\) | − | 415834.i | − | 2.17750i | ||||||
\(438\) | −121502. | −0.633340 | ||||||||
\(439\) | 16622.3 | 0.0862507 | 0.0431253 | − | 0.999070i | \(-0.486269\pi\) | ||||
0.0431253 | + | 0.999070i | \(0.486269\pi\) | |||||||
\(440\) | −22597.2 | −0.116721 | ||||||||
\(441\) | 74813.3 | 0.384682 | ||||||||
\(442\) | 10572.0 | 0.0541146 | ||||||||
\(443\) | 166081.i | 0.846278i | 0.906065 | + | 0.423139i | \(0.139072\pi\) | ||||
−0.906065 | + | 0.423139i | \(0.860928\pi\) | |||||||
\(444\) | − | 18307.8i | − | 0.0928688i | ||||||
\(445\) | 15765.4i | 0.0796132i | ||||||||
\(446\) | 152077.i | 0.764530i | ||||||||
\(447\) | − | 33781.0i | − | 0.169067i | ||||||
\(448\) | −36820.8 | −0.183458 | ||||||||
\(449\) | 231721. | 1.14940 | 0.574702 | − | 0.818363i | \(-0.305118\pi\) | ||||
0.574702 | + | 0.818363i | \(0.305118\pi\) | |||||||
\(450\) | − | 34752.8i | − | 0.171619i | ||||||
\(451\) | − | 168243.i | − | 0.827151i | ||||||
\(452\) | − | 468.527i | − | 0.00229328i | ||||||
\(453\) | − | 23930.3i | − | 0.116614i | ||||||
\(454\) | −37882.1 | −0.183790 | ||||||||
\(455\) | − | 111189.i | − | 0.537079i | ||||||
\(456\) | − | 54204.8i | − | 0.260680i | ||||||
\(457\) | − | 58668.2i | − | 0.280912i | −0.990087 | − | 0.140456i | \(-0.955143\pi\) | ||
0.990087 | − | 0.140456i | \(-0.0448569\pi\) | |||||||
\(458\) | −15903.9 | −0.0758179 | ||||||||
\(459\) | 4421.33 | 0.0209859 | ||||||||
\(460\) | 94063.3i | 0.444534i | ||||||||
\(461\) | 92384.8 | 0.434709 | 0.217355 | − | 0.976093i | \(-0.430257\pi\) | ||||
0.217355 | + | 0.976093i | \(0.430257\pi\) | |||||||
\(462\) | 80972.8 | 0.379363 | ||||||||
\(463\) | 348577.i | 1.62606i | 0.582220 | + | 0.813031i | \(0.302184\pi\) | ||||
−0.582220 | + | 0.813031i | \(0.697816\pi\) | |||||||
\(464\) | −74317.8 | −0.345189 | ||||||||
\(465\) | − | 30978.7i | − | 0.143271i | ||||||
\(466\) | 295479. | 1.36067 | ||||||||
\(467\) | 270751.i | 1.24147i | 0.784021 | + | 0.620734i | \(0.213165\pi\) | ||||
−0.784021 | + | 0.620734i | \(0.786835\pi\) | |||||||
\(468\) | 25618.9i | 0.116968i | ||||||||
\(469\) | 427687.i | 1.94438i | ||||||||
\(470\) | 48636.7 | 0.220175 | ||||||||
\(471\) | 44504.6i | 0.200615i | ||||||||
\(472\) | 77018.2 | − | 16501.2i | 0.345708 | − | 0.0740681i | ||||
\(473\) | −95555.1 | −0.427102 | ||||||||
\(474\) | 7633.68i | 0.0339764i | ||||||||
\(475\) | −209798. | −0.929855 | ||||||||
\(476\) | −18131.0 | −0.0800216 | ||||||||
\(477\) | 1442.90 | 0.00634163 | ||||||||
\(478\) | − | 238048.i | − | 1.04186i | ||||||
\(479\) | 265996. | 1.15932 | 0.579660 | − | 0.814858i | \(-0.303185\pi\) | ||||
0.579660 | + | 0.814858i | \(0.303185\pi\) | |||||||
\(480\) | 12261.3i | 0.0532176i | ||||||||
\(481\) | 52236.1 | 0.225777 | ||||||||
\(482\) | − | 151262.i | − | 0.651080i | ||||||
\(483\) | − | 337058.i | − | 1.44481i | ||||||
\(484\) | −70174.6 | −0.299564 | ||||||||
\(485\) | 139875.i | 0.594645i | ||||||||
\(486\) | 10714.1i | 0.0453609i | ||||||||
\(487\) | 179950. | 0.758743 | 0.379371 | − | 0.925245i | \(-0.376140\pi\) | ||||
0.379371 | + | 0.925245i | \(0.376140\pi\) | |||||||
\(488\) | 5317.76 | 0.0223300 | ||||||||
\(489\) | −8824.21 | −0.0369027 | ||||||||
\(490\) | 102162.i | 0.425499i | ||||||||
\(491\) | 180154. | 0.747277 | 0.373639 | − | 0.927574i | \(-0.378110\pi\) | ||||
0.373639 | + | 0.927574i | \(0.378110\pi\) | |||||||
\(492\) | −91289.5 | −0.377130 | ||||||||
\(493\) | −36594.9 | −0.150566 | ||||||||
\(494\) | 154658. | 0.633751 | ||||||||
\(495\) | − | 26963.9i | − | 0.110046i | ||||||
\(496\) | − | 29270.5i | − | 0.118978i | ||||||
\(497\) | 562859. | 2.27870 | ||||||||
\(498\) | 101687. | 0.410024 | ||||||||
\(499\) | 348732. | 1.40052 | 0.700261 | − | 0.713887i | \(-0.253067\pi\) | ||||
0.700261 | + | 0.713887i | \(0.253067\pi\) | |||||||
\(500\) | 112635. | 0.450541 | ||||||||
\(501\) | −211414. | −0.842284 | ||||||||
\(502\) | 24355.3i | 0.0966466i | ||||||||
\(503\) | 337691.i | 1.33470i | 0.744744 | + | 0.667350i | \(0.232572\pi\) | ||||
−0.744744 | + | 0.667350i | \(0.767428\pi\) | |||||||
\(504\) | − | 43936.2i | − | 0.172966i | ||||||
\(505\) | 39854.7i | 0.156278i | ||||||||
\(506\) | − | 195449.i | − | 0.763365i | ||||||
\(507\) | 75311.0 | 0.292983 | ||||||||
\(508\) | −55692.9 | −0.215811 | ||||||||
\(509\) | − | 423913.i | − | 1.63622i | −0.575062 | − | 0.818110i | \(-0.695022\pi\) | ||
0.575062 | − | 0.818110i | \(-0.304978\pi\) | |||||||
\(510\) | 6037.61i | 0.0232126i | ||||||||
\(511\) | 594541.i | 2.27688i | ||||||||
\(512\) | 11585.2i | 0.0441942i | ||||||||
\(513\) | 64679.5 | 0.245772 | ||||||||
\(514\) | − | 68375.2i | − | 0.258805i | ||||||
\(515\) | 5390.38i | 0.0203238i | ||||||||
\(516\) | 51848.6i | 0.194732i | ||||||||
\(517\) | −101059. | −0.378090 | ||||||||
\(518\) | −89584.4 | −0.333867 | ||||||||
\(519\) | 1942.51i | 0.00721155i | ||||||||
\(520\) | −34984.2 | −0.129380 | ||||||||
\(521\) | 124425. | 0.458387 | 0.229194 | − | 0.973381i | \(-0.426391\pi\) | ||||
0.229194 | + | 0.973381i | \(0.426391\pi\) | |||||||
\(522\) | − | 88679.1i | − | 0.325447i | ||||||
\(523\) | −515652. | −1.88518 | −0.942591 | − | 0.333950i | \(-0.891618\pi\) | ||||
−0.942591 | + | 0.333950i | \(0.891618\pi\) | |||||||
\(524\) | − | 108757.i | − | 0.396092i | ||||||
\(525\) | −170054. | −0.616976 | ||||||||
\(526\) | 44178.1i | 0.159675i | ||||||||
\(527\) | − | 14413.1i | − | 0.0518963i | ||||||
\(528\) | − | 25477.1i | − | 0.0913867i | ||||||
\(529\) | −533737. | −1.90729 | ||||||||
\(530\) | 1970.38i | 0.00701452i | ||||||||
\(531\) | 19689.9 | + | 91901.4i | 0.0698321 | + | 0.325936i | ||||
\(532\) | −265237. | −0.937154 | ||||||||
\(533\) | − | 260469.i | − | 0.916857i | ||||||
\(534\) | −17774.7 | −0.0623331 | ||||||||
\(535\) | −6369.50 | −0.0222535 | ||||||||
\(536\) | 134567. | 0.468390 | ||||||||
\(537\) | − | 251589.i | − | 0.872454i | ||||||
\(538\) | −259315. | −0.895908 | ||||||||
\(539\) | − | 212277.i | − | 0.730678i | ||||||
\(540\) | −14630.7 | −0.0501740 | ||||||||
\(541\) | − | 273373.i | − | 0.934032i | −0.884249 | − | 0.467016i | \(-0.845329\pi\) | ||
0.884249 | − | 0.467016i | \(-0.154671\pi\) | |||||||
\(542\) | − | 67625.5i | − | 0.230204i | ||||||
\(543\) | −244049. | −0.827709 | ||||||||
\(544\) | 5704.69i | 0.0192768i | ||||||||
\(545\) | 161348.i | 0.543215i | ||||||||
\(546\) | 125359. | 0.420506 | ||||||||
\(547\) | −382095. | −1.27702 | −0.638508 | − | 0.769615i | \(-0.720448\pi\) | ||||
−0.638508 | + | 0.769615i | \(0.720448\pi\) | |||||||
\(548\) | 169214. | 0.563475 | ||||||||
\(549\) | 6345.38i | 0.0210530i | ||||||||
\(550\) | −98608.7 | −0.325979 | ||||||||
\(551\) | −535345. | −1.76332 | ||||||||
\(552\) | −106051. | −0.348047 | ||||||||
\(553\) | 37353.4 | 0.122146 | ||||||||
\(554\) | 411373.i | 1.34034i | ||||||||
\(555\) | 29831.6i | 0.0968480i | ||||||||
\(556\) | −166106. | −0.537324 | ||||||||
\(557\) | 67859.1 | 0.218724 | 0.109362 | − | 0.994002i | \(-0.465119\pi\) | ||||
0.109362 | + | 0.994002i | \(0.465119\pi\) | |||||||
\(558\) | 34926.8 | 0.112174 | ||||||||
\(559\) | −147935. | −0.473422 | ||||||||
\(560\) | 59997.7 | 0.191319 | ||||||||
\(561\) | − | 12545.2i | − | 0.0398614i | ||||||
\(562\) | − | 142747.i | − | 0.451955i | ||||||
\(563\) | 181249.i | 0.571818i | 0.958257 | + | 0.285909i | \(0.0922956\pi\) | ||||
−0.958257 | + | 0.285909i | \(0.907704\pi\) | |||||||
\(564\) | 54835.2i | 0.172386i | ||||||||
\(565\) | 763.441i | 0.00239155i | ||||||||
\(566\) | −421172. | −1.31470 | ||||||||
\(567\) | 52426.5 | 0.163074 | ||||||||
\(568\) | − | 177097.i | − | 0.548927i | ||||||
\(569\) | 162103.i | 0.500687i | 0.968157 | + | 0.250344i | \(0.0805436\pi\) | ||||
−0.968157 | + | 0.250344i | \(0.919456\pi\) | |||||||
\(570\) | 88324.0i | 0.271850i | ||||||||
\(571\) | 646936.i | 1.98422i | 0.125386 | + | 0.992108i | \(0.459983\pi\) | ||||
−0.125386 | + | 0.992108i | \(0.540017\pi\) | |||||||
\(572\) | 72691.8 | 0.222174 | ||||||||
\(573\) | 185487.i | 0.564942i | ||||||||
\(574\) | 446702.i | 1.35579i | ||||||||
\(575\) | 410470.i | 1.24150i | ||||||||
\(576\) | −13824.0 | −0.0416667 | ||||||||
\(577\) | −249691. | −0.749984 | −0.374992 | − | 0.927028i | \(-0.622355\pi\) | ||||
−0.374992 | + | 0.927028i | \(0.622355\pi\) | |||||||
\(578\) | − | 233424.i | − | 0.698699i | ||||||
\(579\) | 130788. | 0.390133 | ||||||||
\(580\) | 121097. | 0.359979 | ||||||||
\(581\) | − | 497581.i | − | 1.47405i | ||||||
\(582\) | −157702. | −0.465577 | ||||||||
\(583\) | − | 4094.14i | − | 0.0120455i | ||||||
\(584\) | 187065. | 0.548488 | ||||||||
\(585\) | − | 41744.7i | − | 0.121980i | ||||||
\(586\) | 178240.i | 0.519051i | ||||||||
\(587\) | − | 124990.i | − | 0.362744i | −0.983415 | − | 0.181372i | \(-0.941946\pi\) | ||
0.983415 | − | 0.181372i | \(-0.0580539\pi\) | |||||||
\(588\) | −115183. | −0.333144 | ||||||||
\(589\) | − | 210849.i | − | 0.607772i | ||||||
\(590\) | −125497. | + | 26887.9i | −0.360521 | + | 0.0772417i | ||||
\(591\) | −357845. | −1.02452 | ||||||||
\(592\) | 28186.7i | 0.0804267i | ||||||||
\(593\) | −562164. | −1.59865 | −0.799326 | − | 0.600898i | \(-0.794810\pi\) | ||||
−0.799326 | + | 0.600898i | \(0.794810\pi\) | |||||||
\(594\) | 30400.4 | 0.0861602 | ||||||||
\(595\) | 29543.5 | 0.0834503 | ||||||||
\(596\) | 52009.3i | 0.146416i | ||||||||
\(597\) | −195558. | −0.548691 | ||||||||
\(598\) | − | 302588.i | − | 0.846153i | ||||||
\(599\) | −128620. | −0.358471 | −0.179235 | − | 0.983806i | \(-0.557362\pi\) | ||||
−0.179235 | + | 0.983806i | \(0.557362\pi\) | |||||||
\(600\) | 53505.5i | 0.148626i | ||||||||
\(601\) | − | 443026.i | − | 1.22654i | −0.789874 | − | 0.613269i | \(-0.789854\pi\) | ||
0.789874 | − | 0.613269i | \(-0.210146\pi\) | |||||||
\(602\) | 253708. | 0.700068 | ||||||||
\(603\) | 160571.i | 0.441602i | ||||||||
\(604\) | 36843.1i | 0.100991i | ||||||||
\(605\) | 114346. | 0.312399 | ||||||||
\(606\) | −44934.1 | −0.122358 | ||||||||
\(607\) | 174622. | 0.473938 | 0.236969 | − | 0.971517i | \(-0.423846\pi\) | ||||
0.236969 | + | 0.971517i | \(0.423846\pi\) | |||||||
\(608\) | 83453.8i | 0.225756i | ||||||||
\(609\) | −433928. | −1.16999 | ||||||||
\(610\) | −8665.02 | −0.0232868 | ||||||||
\(611\) | −156457. | −0.419095 | ||||||||
\(612\) | −6807.08 | −0.0181743 | ||||||||
\(613\) | − | 528180.i | − | 1.40560i | −0.711389 | − | 0.702799i | \(-0.751933\pi\) | ||
0.711389 | − | 0.702799i | \(-0.248067\pi\) | |||||||
\(614\) | 27623.8i | 0.0732735i | ||||||||
\(615\) | 148752. | 0.393289 | ||||||||
\(616\) | −124666. | −0.328538 | ||||||||
\(617\) | 274885. | 0.722072 | 0.361036 | − | 0.932552i | \(-0.382423\pi\) | ||||
0.361036 | + | 0.932552i | \(0.382423\pi\) | |||||||
\(618\) | −6077.36 | −0.0159125 | ||||||||
\(619\) | −372699. | −0.972695 | −0.486347 | − | 0.873766i | \(-0.661671\pi\) | ||||
−0.486347 | + | 0.873766i | \(0.661671\pi\) | |||||||
\(620\) | 47694.8i | 0.124076i | ||||||||
\(621\) | − | 126545.i | − | 0.328142i | ||||||
\(622\) | 163648.i | 0.422990i | ||||||||
\(623\) | 86975.7i | 0.224090i | ||||||||
\(624\) | − | 39442.9i | − | 0.101298i | ||||||
\(625\) | 100888. | 0.258272 | ||||||||
\(626\) | −474608. | −1.21112 | ||||||||
\(627\) | − | 183523.i | − | 0.466828i | ||||||
\(628\) | − | 68519.3i | − | 0.173737i | ||||||
\(629\) | 13879.4i | 0.0350808i | ||||||||
\(630\) | 71591.8i | 0.180377i | ||||||||
\(631\) | −654254. | −1.64319 | −0.821594 | − | 0.570072i | \(-0.806915\pi\) | ||||
−0.821594 | + | 0.570072i | \(0.806915\pi\) | |||||||
\(632\) | − | 11752.8i | − | 0.0294244i | ||||||
\(633\) | − | 243596.i | − | 0.607943i | ||||||
\(634\) | 129561.i | 0.322327i | ||||||||
\(635\) | 90748.8 | 0.225057 | ||||||||
\(636\) | −2221.50 | −0.00549201 | ||||||||
\(637\) | − | 328641.i | − | 0.809922i | ||||||
\(638\) | −251621. | −0.618166 | ||||||||
\(639\) | 211320. | 0.517534 | ||||||||
\(640\) | − | 18877.6i | − | 0.0460878i | ||||||
\(641\) | 140139. | 0.341069 | 0.170535 | − | 0.985352i | \(-0.445451\pi\) | ||||
0.170535 | + | 0.985352i | \(0.445451\pi\) | |||||||
\(642\) | − | 7181.27i | − | 0.0174233i | ||||||
\(643\) | 290047. | 0.701531 | 0.350765 | − | 0.936463i | \(-0.385921\pi\) | ||||
0.350765 | + | 0.936463i | \(0.385921\pi\) | |||||||
\(644\) | 518935.i | 1.25124i | ||||||||
\(645\) | − | 84484.6i | − | 0.203076i | ||||||
\(646\) | 41093.5i | 0.0984710i | ||||||||
\(647\) | 379096. | 0.905608 | 0.452804 | − | 0.891610i | \(-0.350424\pi\) | ||||
0.452804 | + | 0.891610i | \(0.350424\pi\) | |||||||
\(648\) | − | 16495.4i | − | 0.0392837i | ||||||
\(649\) | 260764. | − | 55868.8i | 0.619095 | − | 0.132642i | ||||
\(650\) | −152663. | −0.361332 | ||||||||
\(651\) | − | 170905.i | − | 0.403268i | ||||||
\(652\) | 13585.8 | 0.0319587 | ||||||||
\(653\) | 3248.56 | 0.00761842 | 0.00380921 | − | 0.999993i | \(-0.498787\pi\) | ||||
0.00380921 | + | 0.999993i | \(0.498787\pi\) | |||||||
\(654\) | −181912. | −0.425310 | ||||||||
\(655\) | 177215.i | 0.413064i | ||||||||
\(656\) | 140549. | 0.326604 | ||||||||
\(657\) | 223214.i | 0.517120i | ||||||||
\(658\) | 268322. | 0.619733 | ||||||||
\(659\) | − | 530315.i | − | 1.22113i | −0.791965 | − | 0.610567i | \(-0.790942\pi\) | ||
0.791965 | − | 0.610567i | \(-0.209058\pi\) | |||||||
\(660\) | 41513.7i | 0.0953023i | ||||||||
\(661\) | −241571. | −0.552894 | −0.276447 | − | 0.961029i | \(-0.589157\pi\) | ||||
−0.276447 | + | 0.961029i | \(0.589157\pi\) | |||||||
\(662\) | 457206.i | 1.04327i | ||||||||
\(663\) | − | 19422.1i | − | 0.0441844i | ||||||
\(664\) | −156558. | −0.355091 | ||||||||
\(665\) | 432191. | 0.977309 | ||||||||
\(666\) | −33633.5 | −0.0758271 | ||||||||
\(667\) | 1.04740e6i | 2.35429i | ||||||||
\(668\) | 325493. | 0.729439 | ||||||||
\(669\) | 279384. | 0.624236 | ||||||||
\(670\) | −219269. | −0.488460 | ||||||||
\(671\) | 18004.6 | 0.0399887 | ||||||||
\(672\) | 67644.2i | 0.149793i | ||||||||
\(673\) | − | 720933.i | − | 1.59171i | −0.605485 | − | 0.795857i | \(-0.707021\pi\) | ||
0.605485 | − | 0.795857i | \(-0.292979\pi\) | |||||||
\(674\) | 175716. | 0.386804 | ||||||||
\(675\) | −63845.0 | −0.140126 | ||||||||
\(676\) | −115949. | −0.253731 | ||||||||
\(677\) | 53229.2 | 0.116138 | 0.0580688 | − | 0.998313i | \(-0.481506\pi\) | ||||
0.0580688 | + | 0.998313i | \(0.481506\pi\) | |||||||
\(678\) | −860.739 | −0.00187246 | ||||||||
\(679\) | 771675.i | 1.67377i | ||||||||
\(680\) | − | 9295.51i | − | 0.0201027i | ||||||
\(681\) | 69593.8i | 0.150064i | ||||||||
\(682\) | − | 99102.3i | − | 0.213066i | ||||||
\(683\) | − | 116305.i | − | 0.249320i | −0.992200 | − | 0.124660i | \(-0.960216\pi\) | ||
0.992200 | − | 0.124660i | \(-0.0397840\pi\) | |||||||
\(684\) | −99580.6 | −0.212845 | ||||||||
\(685\) | −275725. | −0.587619 | ||||||||
\(686\) | 75233.2i | 0.159868i | ||||||||
\(687\) | 29217.3i | 0.0619051i | ||||||||
\(688\) | − | 79826.1i | − | 0.168643i | ||||||
\(689\) | − | 6338.41i | − | 0.0133519i | ||||||
\(690\) | 172805. | 0.362960 | ||||||||
\(691\) | 363295.i | 0.760858i | 0.924810 | + | 0.380429i | \(0.124224\pi\) | ||||
−0.924810 | + | 0.380429i | \(0.875776\pi\) | |||||||
\(692\) | − | 2990.69i | − | 0.00624538i | ||||||
\(693\) | − | 148757.i | − | 0.309749i | ||||||
\(694\) | −40610.5 | −0.0843178 | ||||||||
\(695\) | 270661. | 0.560347 | ||||||||
\(696\) | 136530.i | 0.281846i | ||||||||
\(697\) | 69208.0 | 0.142459 | ||||||||
\(698\) | −478004. | −0.981117 | ||||||||
\(699\) | − | 542829.i | − | 1.11099i | ||||||
\(700\) | 261815. | 0.534317 | ||||||||
\(701\) | − | 795382.i | − | 1.61860i | −0.587395 | − | 0.809300i | \(-0.699847\pi\) | ||
0.587395 | − | 0.809300i | \(-0.300153\pi\) | |||||||
\(702\) | 47064.9 | 0.0955044 | ||||||||
\(703\) | 203042.i | 0.410841i | ||||||||
\(704\) | 39224.6i | 0.0791432i | ||||||||
\(705\) | − | 89351.2i | − | 0.179772i | ||||||
\(706\) | 531243. | 1.06582 | ||||||||
\(707\) | 219873.i | 0.439880i | ||||||||
\(708\) | −30314.6 | − | 141491.i | −0.0604764 | − | 0.282269i | ||||
\(709\) | 557121. | 1.10830 | 0.554150 | − | 0.832417i | \(-0.313044\pi\) | ||||
0.554150 | + | 0.832417i | \(0.313044\pi\) | |||||||
\(710\) | 288571.i | 0.572447i | ||||||||
\(711\) | 14024.0 | 0.0277416 | ||||||||
\(712\) | 27365.9 | 0.0539821 | ||||||||
\(713\) | −412524. | −0.811467 | ||||||||
\(714\) | 33308.7i | 0.0653373i | ||||||||
\(715\) | −118448. | −0.231694 | ||||||||
\(716\) | 387346.i | 0.755568i | ||||||||
\(717\) | −437322. | −0.850675 | ||||||||
\(718\) | − | 576904.i | − | 1.11906i | ||||||
\(719\) | − | 755892.i | − | 1.46218i | −0.682279 | − | 0.731092i | \(-0.739011\pi\) | ||
0.682279 | − | 0.731092i | \(-0.260989\pi\) | |||||||
\(720\) | 22525.5 | 0.0434520 | ||||||||
\(721\) | 29738.0i | 0.0572060i | ||||||||
\(722\) | 232552.i | 0.446114i | ||||||||
\(723\) | −277885. | −0.531605 | ||||||||
\(724\) | 375738. | 0.716817 | ||||||||
\(725\) | 528438. | 1.00535 | ||||||||
\(726\) | 128919.i | 0.244593i | ||||||||
\(727\) | −496616. | −0.939620 | −0.469810 | − | 0.882768i | \(-0.655678\pi\) | ||||
−0.469810 | + | 0.882768i | \(0.655678\pi\) | |||||||
\(728\) | −193004. | −0.364169 | ||||||||
\(729\) | 19683.0 | 0.0370370 | ||||||||
\(730\) | −304813. | −0.571990 | ||||||||
\(731\) | − | 39307.2i | − | 0.0735593i | ||||||
\(732\) | − | 9769.35i | − | 0.0182324i | ||||||
\(733\) | −456465. | −0.849570 | −0.424785 | − | 0.905294i | \(-0.639650\pi\) | ||||
−0.424785 | + | 0.905294i | \(0.639650\pi\) | |||||||
\(734\) | 61498.7 | 0.114150 | ||||||||
\(735\) | 187684. | 0.347419 | ||||||||
\(736\) | 163277. | 0.301418 | ||||||||
\(737\) | 455608. | 0.838796 | ||||||||
\(738\) | 167710.i | 0.307925i | ||||||||
\(739\) | − | 264440.i | − | 0.484214i | −0.970250 | − | 0.242107i | \(-0.922161\pi\) | ||
0.970250 | − | 0.242107i | \(-0.0778386\pi\) | |||||||
\(740\) | − | 45928.8i | − | 0.0838728i | ||||||
\(741\) | − | 284125.i | − | 0.517456i | ||||||
\(742\) | 10870.3i | 0.0197440i | ||||||||
\(743\) | −100102. | −0.181329 | −0.0906645 | − | 0.995881i | \(-0.528899\pi\) | ||||
−0.0906645 | + | 0.995881i | \(0.528899\pi\) | |||||||
\(744\) | −53773.3 | −0.0971451 | ||||||||
\(745\) | − | 84746.5i | − | 0.152690i | ||||||
\(746\) | 134469.i | 0.241626i | ||||||||
\(747\) | − | 186812.i | − | 0.334783i | ||||||
\(748\) | 19314.6i | 0.0345210i | ||||||||
\(749\) | −35139.7 | −0.0626375 | ||||||||
\(750\) | − | 206924.i | − | 0.367865i | ||||||
\(751\) | 112757.i | 0.199923i | 0.994991 | + | 0.0999616i | \(0.0318720\pi\) | ||||
−0.994991 | + | 0.0999616i | \(0.968128\pi\) | |||||||
\(752\) | − | 84424.4i | − | 0.149291i | ||||||
\(753\) | 44743.6 | 0.0789116 | ||||||||
\(754\) | −389551. | −0.685207 | ||||||||
\(755\) | − | 60033.9i | − | 0.105318i | ||||||
\(756\) | −80715.9 | −0.141226 | ||||||||
\(757\) | 594305. | 1.03709 | 0.518547 | − | 0.855049i | \(-0.326473\pi\) | ||||
0.518547 | + | 0.855049i | \(0.326473\pi\) | |||||||
\(758\) | − | 246479.i | − | 0.428985i | ||||||
\(759\) | −359063. | −0.623285 | ||||||||
\(760\) | − | 135984.i | − | 0.235429i | ||||||
\(761\) | −493882. | −0.852813 | −0.426407 | − | 0.904532i | \(-0.640221\pi\) | ||||
−0.426407 | + | 0.904532i | \(0.640221\pi\) | |||||||
\(762\) | 102314.i | 0.176209i | ||||||||
\(763\) | 890138.i | 1.52900i | ||||||||
\(764\) | − | 285576.i | − | 0.489255i | ||||||
\(765\) | 11091.8 | 0.0189530 | ||||||||
\(766\) | − | 59085.1i | − | 0.100698i | ||||||
\(767\) | 403706. | − | 86494.2i | 0.686237 | − | 0.147027i | ||||
\(768\) | 21283.4 | 0.0360844 | ||||||||
\(769\) | − | 526058.i | − | 0.889572i | −0.895637 | − | 0.444786i | \(-0.853280\pi\) | ||
0.895637 | − | 0.444786i | \(-0.146720\pi\) | |||||||
\(770\) | 203137. | 0.342615 | ||||||||
\(771\) | −125613. | −0.211313 | ||||||||
\(772\) | −201362. | −0.337865 | ||||||||
\(773\) | − | 820920.i | − | 1.37386i | −0.726725 | − | 0.686929i | \(-0.758958\pi\) | ||
0.726725 | − | 0.686929i | \(-0.241042\pi\) | |||||||
\(774\) | 95251.9 | 0.158998 | ||||||||
\(775\) | 208128.i | 0.346520i | ||||||||
\(776\) | 242798. | 0.403202 | ||||||||
\(777\) | 164577.i | 0.272601i | ||||||||
\(778\) | − | 639866.i | − | 1.05713i | ||||||
\(779\) | 1.01244e6 | 1.66838 | ||||||||
\(780\) | 64270.2i | 0.105638i | ||||||||
\(781\) | − | 599605.i | − | 0.983022i | ||||||
\(782\) | 80399.2 | 0.131474 | ||||||||
\(783\) | −162914. | −0.265726 | ||||||||
\(784\) | 177335. | 0.288511 | ||||||||
\(785\) | 111649.i | 0.181182i | ||||||||
\(786\) | −199800. | −0.323408 | ||||||||
\(787\) | 38812.3 | 0.0626643 | 0.0313321 | − | 0.999509i | \(-0.490025\pi\) | ||||
0.0313321 | + | 0.999509i | \(0.490025\pi\) | |||||||
\(788\) | 550939. | 0.887260 | ||||||||
\(789\) | 81160.4 | 0.130374 | ||||||||
\(790\) | 19150.6i | 0.0306852i | ||||||||
\(791\) | 4211.80i | 0.00673155i | ||||||||
\(792\) | −46804.5 | −0.0746169 | ||||||||
\(793\) | 27874.1 | 0.0443256 | ||||||||
\(794\) | −730095. | −1.15808 | ||||||||
\(795\) | 3619.81 | 0.00572733 | ||||||||
\(796\) | 301082. | 0.475180 | ||||||||
\(797\) | 209085.i | 0.329160i | 0.986364 | + | 0.164580i | \(0.0526269\pi\) | ||||
−0.986364 | + | 0.164580i | \(0.947373\pi\) | |||||||
\(798\) | 487272.i | 0.765183i | ||||||||
\(799\) | − | 41571.5i | − | 0.0651181i | ||||||
\(800\) | − | 82377.1i | − | 0.128714i | ||||||
\(801\) | 32654.1i | 0.0508948i | ||||||||
\(802\) | 343238. | 0.533638 | ||||||||
\(803\) | 633354. | 0.982236 | ||||||||
\(804\) | − | 247215.i | − | 0.382439i | ||||||
\(805\) | − | 845578.i | − | 1.30485i | ||||||
\(806\) | − | 153427.i | − | 0.236174i | ||||||
\(807\) | 476392.i | 0.731506i | ||||||||
\(808\) | 69180.6 | 0.105965 | ||||||||
\(809\) | 1.28940e6i | 1.97011i | 0.172233 | + | 0.985056i | \(0.444902\pi\) | ||||
−0.172233 | + | 0.985056i | \(0.555098\pi\) | |||||||
\(810\) | 26878.4i | 0.0409669i | ||||||||
\(811\) | 448438.i | 0.681806i | 0.940099 | + | 0.340903i | \(0.110733\pi\) | ||||
−0.940099 | + | 0.340903i | \(0.889267\pi\) | |||||||
\(812\) | 668077. | 1.01324 | ||||||||
\(813\) | −124236. | −0.187960 | ||||||||
\(814\) | 95432.8i | 0.144029i | ||||||||
\(815\) | −22137.3 | −0.0333280 | ||||||||
\(816\) | 10480.2 | 0.0157394 | ||||||||
\(817\) | − | 575024.i | − | 0.861473i | ||||||
\(818\) | −359320. | −0.537001 | ||||||||
\(819\) | − | 230300.i | − | 0.343341i | ||||||
\(820\) | −229018. | −0.340598 | ||||||||
\(821\) | − | 259012.i | − | 0.384268i | −0.981369 | − | 0.192134i | \(-0.938459\pi\) | ||
0.981369 | − | 0.192134i | \(-0.0615408\pi\) | |||||||
\(822\) | − | 310866.i | − | 0.460076i | ||||||
\(823\) | − | 837577.i | − | 1.23659i | −0.785947 | − | 0.618294i | \(-0.787824\pi\) | ||
0.785947 | − | 0.618294i | \(-0.212176\pi\) | |||||||
\(824\) | 9356.71 | 0.0137806 | ||||||||
\(825\) | 181156.i | 0.266161i | ||||||||
\(826\) | −692352. | + | 148337.i | −1.01477 | + | 0.217415i | ||||
\(827\) | 739452. | 1.08118 | 0.540592 | − | 0.841285i | \(-0.318200\pi\) | ||||
0.540592 | + | 0.841285i | \(0.318200\pi\) | |||||||
\(828\) | 194829.i | 0.284179i | ||||||||
\(829\) | 1.21521e6 | 1.76824 | 0.884122 | − | 0.467257i | \(-0.154758\pi\) | ||||
0.884122 | + | 0.467257i | \(0.154758\pi\) | |||||||
\(830\) | 255104. | 0.370306 | ||||||||
\(831\) | 755741. | 1.09439 | ||||||||
\(832\) | 60726.3i | 0.0877264i | ||||||||
\(833\) | 87321.8 | 0.125844 | ||||||||
\(834\) | 305156.i | 0.438723i | ||||||||
\(835\) | −530375. | −0.760694 | ||||||||
\(836\) | 282553.i | 0.404285i | ||||||||
\(837\) | − | 64164.6i | − | 0.0915893i | ||||||
\(838\) | −187630. | −0.267186 | ||||||||
\(839\) | 1.25452e6i | 1.78219i | 0.453818 | + | 0.891095i | \(0.350062\pi\) | ||||
−0.453818 | + | 0.891095i | \(0.649938\pi\) | |||||||
\(840\) | − | 110223.i | − | 0.156211i | ||||||
\(841\) | 641140. | 0.906485 | ||||||||
\(842\) | 895732. | 1.26344 | ||||||||
\(843\) | −262244. | −0.369020 | ||||||||
\(844\) | 375040.i | 0.526494i | ||||||||
\(845\) | 188933. | 0.264602 | ||||||||
\(846\) | 100739. | 0.140752 | ||||||||
\(847\) | 630831. | 0.879319 | ||||||||
\(848\) | 3420.22 | 0.00475622 | ||||||||
\(849\) | 773742.i | 1.07345i | ||||||||
\(850\) | − | 40563.3i | − | 0.0561430i | ||||||
\(851\) | 397250. | 0.548535 | ||||||||
\(852\) | −325348. | −0.448197 | ||||||||
\(853\) | −860547. | −1.18270 | −0.591352 | − | 0.806413i | \(-0.701406\pi\) | ||||
−0.591352 | + | 0.806413i | \(0.701406\pi\) | |||||||
\(854\) | −47803.8 | −0.0655461 | ||||||||
\(855\) | 162262. | 0.221964 | ||||||||
\(856\) | 11056.3i | 0.0150891i | ||||||||
\(857\) | − | 250066.i | − | 0.340481i | −0.985403 | − | 0.170240i | \(-0.945546\pi\) | ||
0.985403 | − | 0.170240i | \(-0.0544544\pi\) | |||||||
\(858\) | − | 133543.i | − | 0.181404i | ||||||
\(859\) | 1.05336e6i | 1.42755i | 0.700374 | + | 0.713776i | \(0.253017\pi\) | ||||
−0.700374 | + | 0.713776i | \(0.746983\pi\) | |||||||
\(860\) | 130073.i | 0.175869i | ||||||||
\(861\) | 820644. | 1.10700 | ||||||||
\(862\) | −54191.9 | −0.0729323 | ||||||||
\(863\) | − | 284135.i | − | 0.381507i | −0.981638 | − | 0.190754i | \(-0.938907\pi\) | ||
0.981638 | − | 0.190754i | \(-0.0610931\pi\) | |||||||
\(864\) | 25396.3i | 0.0340207i | ||||||||
\(865\) | 4873.18i | 0.00651298i | ||||||||
\(866\) | 167096.i | 0.222808i | ||||||||
\(867\) | −428827. | −0.570485 | ||||||||
\(868\) | 263126.i | 0.349240i | ||||||||
\(869\) | − | 39792.0i | − | 0.0526934i | ||||||
\(870\) | − | 222469.i | − | 0.293922i | ||||||
\(871\) | 705357. | 0.929764 | ||||||||
\(872\) | 280071. | 0.368329 | ||||||||
\(873\) | 289717.i | 0.380142i | ||||||||
\(874\) | 1.17616e6 | 1.53972 | ||||||||
\(875\) | −1.01253e6 | −1.32249 | ||||||||
\(876\) | − | 343661.i | − | 0.447839i | ||||||
\(877\) | 650765. | 0.846106 | 0.423053 | − | 0.906105i | \(-0.360958\pi\) | ||||
0.423053 | + | 0.906105i | \(0.360958\pi\) | |||||||
\(878\) | 47015.0i | 0.0609884i | ||||||||
\(879\) | 327448. | 0.423803 | ||||||||
\(880\) | − | 63914.5i | − | 0.0825342i | ||||||
\(881\) | 804733.i | 1.03681i | 0.855135 | + | 0.518406i | \(0.173474\pi\) | ||||
−0.855135 | + | 0.518406i | \(0.826526\pi\) | |||||||
\(882\) | 211604.i | 0.272011i | ||||||||
\(883\) | −1.12964e6 | −1.44883 | −0.724415 | − | 0.689364i | \(-0.757890\pi\) | ||||
−0.724415 | + | 0.689364i | \(0.757890\pi\) | |||||||
\(884\) | 29902.3i | 0.0382648i | ||||||||
\(885\) | 49396.1 | + | 230553.i | 0.0630676 | + | 0.294364i | ||||
\(886\) | −469748. | −0.598409 | ||||||||
\(887\) | 163030.i | 0.207214i | 0.994618 | + | 0.103607i | \(0.0330385\pi\) | ||||
−0.994618 | + | 0.103607i | \(0.966962\pi\) | |||||||
\(888\) | 51782.2 | 0.0656682 | ||||||||
\(889\) | 500649. | 0.633476 | ||||||||
\(890\) | −44591.3 | −0.0562951 | ||||||||
\(891\) | − | 55849.1i | − | 0.0703495i | ||||||
\(892\) | −430139. | −0.540604 | ||||||||
\(893\) | − | 608147.i | − | 0.762616i | ||||||
\(894\) | 95547.2 | 0.119548 | ||||||||
\(895\) | − | 631161.i | − | 0.787942i | ||||||
\(896\) | − | 104145.i | − | 0.129725i | ||||||
\(897\) | −555889. | −0.690881 | ||||||||
\(898\) | 655406.i | 0.812751i | ||||||||
\(899\) | 531084.i | 0.657118i | ||||||||
\(900\) | 98295.8 | 0.121353 | ||||||||
\(901\) | 1684.15 | 0.00207459 | ||||||||
\(902\) | 475864. | 0.584884 | ||||||||
\(903\) | − | 466091.i | − | 0.571603i | ||||||
\(904\) | 1325.19 | 0.00162160 | ||||||||
\(905\) | −612246. | −0.747530 | ||||||||
\(906\) | 67685.1 | 0.0824587 | ||||||||
\(907\) | 32431.9 | 0.0394237 | 0.0197119 | − | 0.999806i | \(-0.493725\pi\) | ||||
0.0197119 | + | 0.999806i | \(0.493725\pi\) | |||||||
\(908\) | − | 107147.i | − | 0.129959i | ||||||
\(909\) | 82549.2i | 0.0999045i | ||||||||
\(910\) | 314489. | 0.379772 | ||||||||
\(911\) | −542118. | −0.653216 | −0.326608 | − | 0.945160i | \(-0.605906\pi\) | ||||
−0.326608 | + | 0.945160i | \(0.605906\pi\) | |||||||
\(912\) | 153314. | 0.184329 | ||||||||
\(913\) | −530065. | −0.635899 | ||||||||
\(914\) | 165939. | 0.198635 | ||||||||
\(915\) | 15918.7i | 0.0190136i | ||||||||
\(916\) | − | 44983.0i | − | 0.0536114i | ||||||
\(917\) | 977671.i | 1.16266i | ||||||||
\(918\) | 12505.4i | 0.0148393i | ||||||||
\(919\) | − | 631129.i | − | 0.747286i | −0.927573 | − | 0.373643i | \(-0.878109\pi\) | ||
0.927573 | − | 0.373643i | \(-0.121891\pi\) | |||||||
\(920\) | −266051. | −0.314333 | ||||||||
\(921\) | 50748.2 | 0.0598276 | ||||||||
\(922\) | 261304.i | 0.307386i | ||||||||
\(923\) | − | 928289.i | − | 1.08963i | ||||||
\(924\) | 229026.i | 0.268250i | ||||||||
\(925\) | − | 200422.i | − | 0.234240i | ||||||
\(926\) | −985926. | −1.14980 | ||||||||
\(927\) | 11164.8i | 0.0129925i | ||||||||
\(928\) | − | 210202.i | − | 0.244085i | ||||||
\(929\) | 43280.6i | 0.0501490i | 0.999686 | + | 0.0250745i | \(0.00798230\pi\) | ||||
−0.999686 | + | 0.0250745i | \(0.992018\pi\) | |||||||
\(930\) | 87620.9 | 0.101308 | ||||||||
\(931\) | 1.27743e6 | 1.47379 | ||||||||
\(932\) | 835739.i | 0.962142i | ||||||||
\(933\) | 300641. | 0.345370 | ||||||||
\(934\) | −765799. | −0.877851 | ||||||||
\(935\) | − | 31472.2i | − | 0.0360001i | ||||||
\(936\) | −72461.2 | −0.0827092 | ||||||||
\(937\) | − | 399631.i | − | 0.455176i | −0.973757 | − | 0.227588i | \(-0.926916\pi\) | ||
0.973757 | − | 0.227588i | \(-0.0730840\pi\) | |||||||
\(938\) | −1.20968e6 | −1.37488 | ||||||||
\(939\) | 871910.i | 0.988873i | ||||||||
\(940\) | 137565.i | 0.155687i | ||||||||
\(941\) | − | 927158.i | − | 1.04707i | −0.852005 | − | 0.523533i | \(-0.824614\pi\) | ||
0.852005 | − | 0.523533i | \(-0.175386\pi\) | |||||||
\(942\) | −125878. | −0.141856 | ||||||||
\(943\) | − | 1.98084e6i | − | 2.22754i | ||||||
\(944\) | 46672.4 | + | 217840.i | 0.0523741 | + | 0.244452i | ||||
\(945\) | 131522. | 0.147277 | ||||||||
\(946\) | − | 270271.i | − | 0.302007i | ||||||
\(947\) | 528847. | 0.589698 | 0.294849 | − | 0.955544i | \(-0.404731\pi\) | ||||
0.294849 | + | 0.955544i | \(0.404731\pi\) | |||||||
\(948\) | −21591.3 | −0.0240249 | ||||||||
\(949\) | 980539. | 1.08876 | ||||||||
\(950\) | − | 593400.i | − | 0.657507i | ||||||
\(951\) | 238019. | 0.263179 | ||||||||
\(952\) | − | 51282.1i | − | 0.0565838i | ||||||
\(953\) | −594717. | −0.654824 | −0.327412 | − | 0.944882i | \(-0.606176\pi\) | ||||
−0.327412 | + | 0.944882i | \(0.606176\pi\) | |||||||
\(954\) | 4081.15i | 0.00448421i | ||||||||
\(955\) | 465331.i | 0.510218i | ||||||||
\(956\) | 673302. | 0.736706 | ||||||||
\(957\) | 462257.i | 0.504730i | ||||||||
\(958\) | 752349.i | 0.819763i | ||||||||
\(959\) | −1.52114e6 | −1.65399 | ||||||||
\(960\) | −34680.3 | −0.0376305 | ||||||||
\(961\) | 714351. | 0.773508 | ||||||||
\(962\) | 147746.i | 0.159649i | ||||||||
\(963\) | −13192.8 | −0.0142261 | ||||||||
\(964\) | 427832. | 0.460383 | ||||||||
\(965\) | 328109. | 0.352341 | ||||||||
\(966\) | 953345. | 1.02163 | ||||||||
\(967\) | − | 1.36543e6i | − | 1.46021i | −0.683336 | − | 0.730105i | \(-0.739471\pi\) | ||
0.683336 | − | 0.730105i | \(-0.260529\pi\) | |||||||
\(968\) | − | 198484.i | − | 0.211823i | ||||||
\(969\) | 75493.6 | 0.0804012 | ||||||||
\(970\) | −395628. | −0.420478 | ||||||||
\(971\) | 185537. | 0.196785 | 0.0983924 | − | 0.995148i | \(-0.468630\pi\) | ||||
0.0983924 | + | 0.995148i | \(0.468630\pi\) | |||||||
\(972\) | −30304.0 | −0.0320750 | ||||||||
\(973\) | 1.49320e6 | 1.57722 | ||||||||
\(974\) | 508976.i | 0.536512i | ||||||||
\(975\) | 280459.i | 0.295026i | ||||||||
\(976\) | 15040.9i | 0.0157897i | ||||||||
\(977\) | 1.42229e6i | 1.49004i | 0.667040 | + | 0.745022i | \(0.267561\pi\) | ||||
−0.667040 | + | 0.745022i | \(0.732439\pi\) | |||||||
\(978\) | − | 24958.6i | − | 0.0260941i | ||||||
\(979\) | 92653.8 | 0.0966714 | ||||||||
\(980\) | −288959. | −0.300873 | ||||||||
\(981\) | 334193.i | 0.347264i | ||||||||
\(982\) | 509554.i | 0.528405i | ||||||||
\(983\) | − | 688290.i | − | 0.712303i | −0.934428 | − | 0.356151i | \(-0.884089\pi\) | ||
0.934428 | − | 0.356151i | \(-0.115911\pi\) | |||||||
\(984\) | − | 258206.i | − | 0.266671i | ||||||
\(985\) | −897727. | −0.925277 | ||||||||
\(986\) | − | 103506.i | − | 0.106466i | ||||||
\(987\) | − | 492939.i | − | 0.506010i | ||||||
\(988\) | 437439.i | 0.448130i | ||||||||
\(989\) | −1.12503e6 | −1.15020 | ||||||||
\(990\) | 76265.5 | 0.0778140 | ||||||||
\(991\) | − | 817163.i | − | 0.832073i | −0.909348 | − | 0.416036i | \(-0.863419\pi\) | ||
0.909348 | − | 0.416036i | \(-0.136581\pi\) | |||||||
\(992\) | 82789.5 | 0.0841302 | ||||||||
\(993\) | 839941. | 0.851824 | ||||||||
\(994\) | 1.59201e6i | 1.61128i | ||||||||
\(995\) | −490598. | −0.495541 | ||||||||
\(996\) | 287616.i | 0.289930i | ||||||||
\(997\) | −1.58760e6 | −1.59716 | −0.798582 | − | 0.601886i | \(-0.794416\pi\) | ||||
−0.798582 | + | 0.601886i | \(0.794416\pi\) | |||||||
\(998\) | 986362.i | 0.990319i | ||||||||
\(999\) | 61788.8i | 0.0619125i |
(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 | 354.5.d.a.235.32 | yes | 40 | |
3.2 | odd | 2 | 1062.5.d.b.235.19 | 40 | |||
59.58 | odd | 2 | inner | 354.5.d.a.235.31 | ✓ | 40 | |
177.176 | even | 2 | 1062.5.d.b.235.20 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
354.5.d.a.235.31 | ✓ | 40 | 59.58 | odd | 2 | inner | |
354.5.d.a.235.32 | yes | 40 | 1.1 | even | 1 | trivial | |
1062.5.d.b.235.19 | 40 | 3.2 | odd | 2 | |||
1062.5.d.b.235.20 | 40 | 177.176 | even | 2 |