Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,5,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, 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("177.58");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (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: | \(18.2964834658\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.3 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.5.c.a.58.38 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 7.65331i | − | 1.91333i | −0.291195 | − | 0.956664i | \(-0.594053\pi\) | ||
0.291195 | − | 0.956664i | \(-0.405947\pi\) | |||||||
\(3\) | −5.19615 | −0.577350 | ||||||||
\(4\) | −42.5731 | −2.66082 | ||||||||
\(5\) | −38.1687 | −1.52675 | −0.763375 | − | 0.645956i | \(-0.776459\pi\) | ||||
−0.763375 | + | 0.645956i | \(0.776459\pi\) | |||||||
\(6\) | 39.7678i | 1.10466i | ||||||||
\(7\) | −35.1454 | −0.717253 | −0.358626 | − | 0.933481i | \(-0.616755\pi\) | ||||
−0.358626 | + | 0.933481i | \(0.616755\pi\) | |||||||
\(8\) | 203.372i | 3.17769i | ||||||||
\(9\) | 27.0000 | 0.333333 | ||||||||
\(10\) | 292.117i | 2.92117i | ||||||||
\(11\) | − | 147.824i | − | 1.22169i | −0.791752 | − | 0.610843i | \(-0.790831\pi\) | ||
0.791752 | − | 0.610843i | \(-0.209169\pi\) | |||||||
\(12\) | 221.217 | 1.53623 | ||||||||
\(13\) | − | 17.0918i | − | 0.101135i | −0.998721 | − | 0.0505674i | \(-0.983897\pi\) | ||
0.998721 | − | 0.0505674i | \(-0.0161030\pi\) | |||||||
\(14\) | 268.979i | 1.37234i | ||||||||
\(15\) | 198.331 | 0.881469 | ||||||||
\(16\) | 875.302 | 3.41915 | ||||||||
\(17\) | −354.287 | −1.22591 | −0.612953 | − | 0.790119i | \(-0.710019\pi\) | ||||
−0.612953 | + | 0.790119i | \(0.710019\pi\) | |||||||
\(18\) | − | 206.639i | − | 0.637776i | ||||||
\(19\) | −647.468 | −1.79354 | −0.896770 | − | 0.442498i | \(-0.854092\pi\) | ||||
−0.896770 | + | 0.442498i | \(0.854092\pi\) | |||||||
\(20\) | 1624.96 | 4.06241 | ||||||||
\(21\) | 182.621 | 0.414106 | ||||||||
\(22\) | −1131.34 | −2.33748 | ||||||||
\(23\) | − | 862.278i | − | 1.63001i | −0.579451 | − | 0.815007i | \(-0.696733\pi\) | ||
0.579451 | − | 0.815007i | \(-0.303267\pi\) | |||||||
\(24\) | − | 1056.75i | − | 1.83464i | ||||||
\(25\) | 831.852 | 1.33096 | ||||||||
\(26\) | −130.809 | −0.193504 | ||||||||
\(27\) | −140.296 | −0.192450 | ||||||||
\(28\) | 1496.25 | 1.90848 | ||||||||
\(29\) | 440.875 | 0.524227 | 0.262113 | − | 0.965037i | \(-0.415581\pi\) | ||||
0.262113 | + | 0.965037i | \(0.415581\pi\) | |||||||
\(30\) | − | 1517.88i | − | 1.68654i | ||||||
\(31\) | 347.019i | 0.361101i | 0.983566 | + | 0.180551i | \(0.0577880\pi\) | ||||
−0.983566 | + | 0.180551i | \(0.942212\pi\) | |||||||
\(32\) | − | 3445.00i | − | 3.36426i | ||||||
\(33\) | 768.116i | 0.705341i | ||||||||
\(34\) | 2711.47i | 2.34556i | ||||||||
\(35\) | 1341.45 | 1.09507 | ||||||||
\(36\) | −1149.47 | −0.886940 | ||||||||
\(37\) | 972.830i | 0.710613i | 0.934750 | + | 0.355307i | \(0.115624\pi\) | ||||
−0.934750 | + | 0.355307i | \(0.884376\pi\) | |||||||
\(38\) | 4955.27i | 3.43163i | ||||||||
\(39\) | 88.8114i | 0.0583902i | ||||||||
\(40\) | − | 7762.47i | − | 4.85154i | ||||||
\(41\) | 2783.36 | 1.65578 | 0.827889 | − | 0.560892i | \(-0.189542\pi\) | ||||
0.827889 | + | 0.560892i | \(0.189542\pi\) | |||||||
\(42\) | − | 1397.65i | − | 0.792321i | ||||||
\(43\) | − | 2837.80i | − | 1.53478i | −0.641183 | − | 0.767388i | \(-0.721556\pi\) | ||
0.641183 | − | 0.767388i | \(-0.278444\pi\) | |||||||
\(44\) | 6293.33i | 3.25069i | ||||||||
\(45\) | −1030.56 | −0.508916 | ||||||||
\(46\) | −6599.28 | −3.11875 | ||||||||
\(47\) | 1287.07i | 0.582649i | 0.956624 | + | 0.291324i | \(0.0940959\pi\) | ||||
−0.956624 | + | 0.291324i | \(0.905904\pi\) | |||||||
\(48\) | −4548.20 | −1.97405 | ||||||||
\(49\) | −1165.80 | −0.485548 | ||||||||
\(50\) | − | 6366.42i | − | 2.54657i | ||||||
\(51\) | 1840.93 | 0.707777 | ||||||||
\(52\) | 727.650i | 0.269101i | ||||||||
\(53\) | −1103.72 | −0.392923 | −0.196462 | − | 0.980511i | \(-0.562945\pi\) | ||||
−0.196462 | + | 0.980511i | \(0.562945\pi\) | |||||||
\(54\) | 1073.73i | 0.368220i | ||||||||
\(55\) | 5642.25i | 1.86521i | ||||||||
\(56\) | − | 7147.61i | − | 2.27921i | ||||||
\(57\) | 3364.34 | 1.03550 | ||||||||
\(58\) | − | 3374.15i | − | 1.00302i | ||||||
\(59\) | 1692.03 | + | 3042.10i | 0.486076 | + | 0.873917i | ||||
\(60\) | −8443.55 | −2.34543 | ||||||||
\(61\) | − | 5980.77i | − | 1.60730i | −0.595100 | − | 0.803651i | \(-0.702888\pi\) | ||
0.595100 | − | 0.803651i | \(-0.297112\pi\) | |||||||
\(62\) | 2655.84 | 0.690905 | ||||||||
\(63\) | −948.926 | −0.239084 | ||||||||
\(64\) | −12360.8 | −3.01777 | ||||||||
\(65\) | 652.371i | 0.154407i | ||||||||
\(66\) | 5878.63 | 1.34955 | ||||||||
\(67\) | 3352.44i | 0.746812i | 0.927668 | + | 0.373406i | \(0.121810\pi\) | ||||
−0.927668 | + | 0.373406i | \(0.878190\pi\) | |||||||
\(68\) | 15083.1 | 3.26192 | ||||||||
\(69\) | 4480.53i | 0.941089i | ||||||||
\(70\) | − | 10266.6i | − | 2.09522i | ||||||
\(71\) | −1396.21 | −0.276971 | −0.138486 | − | 0.990364i | \(-0.544223\pi\) | ||||
−0.138486 | + | 0.990364i | \(0.544223\pi\) | |||||||
\(72\) | 5491.06i | 1.05923i | ||||||||
\(73\) | − | 1649.77i | − | 0.309584i | −0.987947 | − | 0.154792i | \(-0.950529\pi\) | ||
0.987947 | − | 0.154792i | \(-0.0494707\pi\) | |||||||
\(74\) | 7445.37 | 1.35964 | ||||||||
\(75\) | −4322.43 | −0.768432 | ||||||||
\(76\) | 27564.7 | 4.77229 | ||||||||
\(77\) | 5195.33i | 0.876258i | ||||||||
\(78\) | 679.701 | 0.111719 | ||||||||
\(79\) | −8357.83 | −1.33918 | −0.669591 | − | 0.742730i | \(-0.733530\pi\) | ||||
−0.669591 | + | 0.742730i | \(0.733530\pi\) | |||||||
\(80\) | −33409.2 | −5.22018 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | − | 21301.9i | − | 3.16805i | ||||||
\(83\) | − | 5025.77i | − | 0.729536i | −0.931098 | − | 0.364768i | \(-0.881148\pi\) | ||
0.931098 | − | 0.364768i | \(-0.118852\pi\) | |||||||
\(84\) | −7774.74 | −1.10186 | ||||||||
\(85\) | 13522.7 | 1.87165 | ||||||||
\(86\) | −21718.6 | −2.93653 | ||||||||
\(87\) | −2290.85 | −0.302662 | ||||||||
\(88\) | 30063.3 | 3.88214 | ||||||||
\(89\) | 5292.92i | 0.668213i | 0.942535 | + | 0.334107i | \(0.108435\pi\) | ||||
−0.942535 | + | 0.334107i | \(0.891565\pi\) | |||||||
\(90\) | 7887.16i | 0.973724i | ||||||||
\(91\) | 600.697i | 0.0725392i | ||||||||
\(92\) | 36709.9i | 4.33718i | ||||||||
\(93\) | − | 1803.16i | − | 0.208482i | ||||||
\(94\) | 9850.36 | 1.11480 | ||||||||
\(95\) | 24713.0 | 2.73828 | ||||||||
\(96\) | 17900.7i | 1.94235i | ||||||||
\(97\) | 14051.7i | 1.49343i | 0.665142 | + | 0.746716i | \(0.268371\pi\) | ||||
−0.665142 | + | 0.746716i | \(0.731629\pi\) | |||||||
\(98\) | 8922.24i | 0.929013i | ||||||||
\(99\) | − | 3991.25i | − | 0.407229i | ||||||
\(100\) | −35414.5 | −3.54145 | ||||||||
\(101\) | 623.626i | 0.0611338i | 0.999533 | + | 0.0305669i | \(0.00973126\pi\) | ||||
−0.999533 | + | 0.0305669i | \(0.990269\pi\) | |||||||
\(102\) | − | 14089.2i | − | 1.35421i | ||||||
\(103\) | 8032.20i | 0.757112i | 0.925578 | + | 0.378556i | \(0.123579\pi\) | ||||
−0.925578 | + | 0.378556i | \(0.876421\pi\) | |||||||
\(104\) | 3475.99 | 0.321375 | ||||||||
\(105\) | −6970.40 | −0.632236 | ||||||||
\(106\) | 8447.13i | 0.751791i | ||||||||
\(107\) | 11098.7 | 0.969402 | 0.484701 | − | 0.874680i | \(-0.338928\pi\) | ||||
0.484701 | + | 0.874680i | \(0.338928\pi\) | |||||||
\(108\) | 5972.85 | 0.512075 | ||||||||
\(109\) | − | 7809.17i | − | 0.657283i | −0.944455 | − | 0.328641i | \(-0.893409\pi\) | ||
0.944455 | − | 0.328641i | \(-0.106591\pi\) | |||||||
\(110\) | 43181.9 | 3.56875 | ||||||||
\(111\) | − | 5054.97i | − | 0.410273i | ||||||
\(112\) | −30762.8 | −2.45239 | ||||||||
\(113\) | 3130.68i | 0.245178i | 0.992457 | + | 0.122589i | \(0.0391198\pi\) | ||||
−0.992457 | + | 0.122589i | \(0.960880\pi\) | |||||||
\(114\) | − | 25748.3i | − | 1.98125i | ||||||
\(115\) | 32912.0i | 2.48862i | ||||||||
\(116\) | −18769.4 | −1.39487 | ||||||||
\(117\) | − | 461.478i | − | 0.0337116i | ||||||
\(118\) | 23282.2 | − | 12949.6i | 1.67209 | − | 0.930022i | ||||
\(119\) | 12451.6 | 0.879285 | ||||||||
\(120\) | 40335.0i | 2.80104i | ||||||||
\(121\) | −7210.93 | −0.492516 | ||||||||
\(122\) | −45772.7 | −3.07530 | ||||||||
\(123\) | −14462.8 | −0.955964 | ||||||||
\(124\) | − | 14773.7i | − | 0.960827i | ||||||
\(125\) | −7895.26 | −0.505297 | ||||||||
\(126\) | 7262.42i | 0.457447i | ||||||||
\(127\) | −18711.5 | −1.16011 | −0.580056 | − | 0.814576i | \(-0.696969\pi\) | ||||
−0.580056 | + | 0.814576i | \(0.696969\pi\) | |||||||
\(128\) | 39481.1i | 2.40973i | ||||||||
\(129\) | 14745.6i | 0.886103i | ||||||||
\(130\) | 4992.80 | 0.295432 | ||||||||
\(131\) | − | 12408.9i | − | 0.723089i | −0.932355 | − | 0.361545i | \(-0.882249\pi\) | ||
0.932355 | − | 0.361545i | \(-0.117751\pi\) | |||||||
\(132\) | − | 32701.1i | − | 1.87679i | ||||||
\(133\) | 22755.5 | 1.28642 | ||||||||
\(134\) | 25657.2 | 1.42889 | ||||||||
\(135\) | 5354.92 | 0.293823 | ||||||||
\(136\) | − | 72052.2i | − | 3.89556i | ||||||
\(137\) | −24025.7 | −1.28007 | −0.640037 | − | 0.768344i | \(-0.721081\pi\) | ||||
−0.640037 | + | 0.768344i | \(0.721081\pi\) | |||||||
\(138\) | 34290.9 | 1.80061 | ||||||||
\(139\) | −3014.36 | −0.156014 | −0.0780072 | − | 0.996953i | \(-0.524856\pi\) | ||||
−0.0780072 | + | 0.996953i | \(0.524856\pi\) | |||||||
\(140\) | −57109.9 | −2.91377 | ||||||||
\(141\) | − | 6687.82i | − | 0.336393i | ||||||
\(142\) | 10685.6i | 0.529937i | ||||||||
\(143\) | −2526.57 | −0.123555 | ||||||||
\(144\) | 23633.2 | 1.13972 | ||||||||
\(145\) | −16827.6 | −0.800362 | ||||||||
\(146\) | −12626.2 | −0.592335 | ||||||||
\(147\) | 6057.68 | 0.280331 | ||||||||
\(148\) | − | 41416.4i | − | 1.89082i | ||||||
\(149\) | − | 10398.6i | − | 0.468383i | −0.972190 | − | 0.234192i | \(-0.924756\pi\) | ||
0.972190 | − | 0.234192i | \(-0.0752443\pi\) | |||||||
\(150\) | 33080.9i | 1.47026i | ||||||||
\(151\) | − | 35440.0i | − | 1.55432i | −0.629305 | − | 0.777159i | \(-0.716660\pi\) | ||
0.629305 | − | 0.777159i | \(-0.283340\pi\) | |||||||
\(152\) | − | 131677.i | − | 5.69932i | ||||||
\(153\) | −9565.75 | −0.408635 | ||||||||
\(154\) | 39761.5 | 1.67657 | ||||||||
\(155\) | − | 13245.3i | − | 0.551311i | ||||||
\(156\) | − | 3780.98i | − | 0.155366i | ||||||
\(157\) | 23302.5i | 0.945373i | 0.881231 | + | 0.472686i | \(0.156716\pi\) | ||||
−0.881231 | + | 0.472686i | \(0.843284\pi\) | |||||||
\(158\) | 63965.0i | 2.56229i | ||||||||
\(159\) | 5735.11 | 0.226854 | ||||||||
\(160\) | 131491.i | 5.13637i | ||||||||
\(161\) | 30305.1i | 1.16913i | ||||||||
\(162\) | − | 5579.26i | − | 0.212592i | ||||||
\(163\) | −8996.62 | −0.338613 | −0.169307 | − | 0.985563i | \(-0.554153\pi\) | ||||
−0.169307 | + | 0.985563i | \(0.554153\pi\) | |||||||
\(164\) | −118497. | −4.40573 | ||||||||
\(165\) | − | 29318.0i | − | 1.07688i | ||||||
\(166\) | −38463.8 | −1.39584 | ||||||||
\(167\) | −441.902 | −0.0158450 | −0.00792252 | − | 0.999969i | \(-0.502522\pi\) | ||||
−0.00792252 | + | 0.999969i | \(0.502522\pi\) | |||||||
\(168\) | 37140.0i | 1.31590i | ||||||||
\(169\) | 28268.9 | 0.989772 | ||||||||
\(170\) | − | 103493.i | − | 3.58108i | ||||||
\(171\) | −17481.6 | −0.597846 | ||||||||
\(172\) | 120814.i | 4.08376i | ||||||||
\(173\) | − | 2947.42i | − | 0.0984803i | −0.998787 | − | 0.0492402i | \(-0.984320\pi\) | ||
0.998787 | − | 0.0492402i | \(-0.0156800\pi\) | |||||||
\(174\) | 17532.6i | 0.579092i | ||||||||
\(175\) | −29235.8 | −0.954637 | ||||||||
\(176\) | − | 129391.i | − | 4.17713i | ||||||
\(177\) | −8792.04 | − | 15807.2i | −0.280636 | − | 0.504556i | ||||
\(178\) | 40508.3 | 1.27851 | ||||||||
\(179\) | 17326.2i | 0.540750i | 0.962755 | + | 0.270375i | \(0.0871477\pi\) | ||||
−0.962755 | + | 0.270375i | \(0.912852\pi\) | |||||||
\(180\) | 43874.0 | 1.35414 | ||||||||
\(181\) | −9276.44 | −0.283155 | −0.141578 | − | 0.989927i | \(-0.545217\pi\) | ||||
−0.141578 | + | 0.989927i | \(0.545217\pi\) | |||||||
\(182\) | 4597.32 | 0.138791 | ||||||||
\(183\) | 31077.0i | 0.927977i | ||||||||
\(184\) | 175364. | 5.17969 | ||||||||
\(185\) | − | 37131.7i | − | 1.08493i | ||||||
\(186\) | −13800.2 | −0.398894 | ||||||||
\(187\) | 52372.1i | 1.49767i | ||||||||
\(188\) | − | 54794.7i | − | 1.55032i | ||||||
\(189\) | 4930.76 | 0.138035 | ||||||||
\(190\) | − | 189136.i | − | 5.23923i | ||||||
\(191\) | 14709.0i | 0.403195i | 0.979468 | + | 0.201598i | \(0.0646134\pi\) | ||||
−0.979468 | + | 0.201598i | \(0.935387\pi\) | |||||||
\(192\) | 64228.6 | 1.74231 | ||||||||
\(193\) | −34249.4 | −0.919472 | −0.459736 | − | 0.888056i | \(-0.652056\pi\) | ||||
−0.459736 | + | 0.888056i | \(0.652056\pi\) | |||||||
\(194\) | 107542. | 2.85743 | ||||||||
\(195\) | − | 3389.82i | − | 0.0891471i | ||||||
\(196\) | 49631.8 | 1.29196 | ||||||||
\(197\) | 7911.51 | 0.203858 | 0.101929 | − | 0.994792i | \(-0.467499\pi\) | ||||
0.101929 | + | 0.994792i | \(0.467499\pi\) | |||||||
\(198\) | −30546.3 | −0.779162 | ||||||||
\(199\) | −57454.5 | −1.45084 | −0.725418 | − | 0.688309i | \(-0.758353\pi\) | ||||
−0.725418 | + | 0.688309i | \(0.758353\pi\) | |||||||
\(200\) | 169176.i | 4.22939i | ||||||||
\(201\) | − | 17419.8i | − | 0.431172i | ||||||
\(202\) | 4772.80 | 0.116969 | ||||||||
\(203\) | −15494.7 | −0.376003 | ||||||||
\(204\) | −78374.1 | −1.88327 | ||||||||
\(205\) | −106237. | −2.52796 | ||||||||
\(206\) | 61472.9 | 1.44860 | ||||||||
\(207\) | − | 23281.5i | − | 0.543338i | ||||||
\(208\) | − | 14960.5i | − | 0.345795i | ||||||
\(209\) | 95711.3i | 2.19114i | ||||||||
\(210\) | 53346.7i | 1.20967i | ||||||||
\(211\) | 49004.2i | 1.10070i | 0.834935 | + | 0.550349i | \(0.185505\pi\) | ||||
−0.834935 | + | 0.550349i | \(0.814495\pi\) | |||||||
\(212\) | 46988.9 | 1.04550 | ||||||||
\(213\) | 7254.93 | 0.159909 | ||||||||
\(214\) | − | 84941.6i | − | 1.85478i | ||||||
\(215\) | 108315.i | 2.34322i | ||||||||
\(216\) | − | 28532.4i | − | 0.611548i | ||||||
\(217\) | − | 12196.1i | − | 0.259001i | ||||||
\(218\) | −59766.0 | −1.25760 | ||||||||
\(219\) | 8572.47i | 0.178738i | ||||||||
\(220\) | − | 240208.i | − | 4.96298i | ||||||
\(221\) | 6055.39i | 0.123982i | ||||||||
\(222\) | −38687.3 | −0.784986 | ||||||||
\(223\) | 94322.8 | 1.89674 | 0.948368 | − | 0.317171i | \(-0.102733\pi\) | ||||
0.948368 | + | 0.317171i | \(0.102733\pi\) | |||||||
\(224\) | 121076.i | 2.41302i | ||||||||
\(225\) | 22460.0 | 0.443654 | ||||||||
\(226\) | 23960.1 | 0.469107 | ||||||||
\(227\) | − | 73496.8i | − | 1.42632i | −0.701002 | − | 0.713159i | \(-0.747264\pi\) | ||
0.701002 | − | 0.713159i | \(-0.252736\pi\) | |||||||
\(228\) | −143231. | −2.75528 | ||||||||
\(229\) | − | 71268.4i | − | 1.35902i | −0.733666 | − | 0.679510i | \(-0.762192\pi\) | ||
0.733666 | − | 0.679510i | \(-0.237808\pi\) | |||||||
\(230\) | 251886. | 4.76155 | ||||||||
\(231\) | − | 26995.7i | − | 0.505908i | ||||||
\(232\) | 89661.7i | 1.66583i | ||||||||
\(233\) | − | 21675.4i | − | 0.399259i | −0.979871 | − | 0.199630i | \(-0.936026\pi\) | ||
0.979871 | − | 0.199630i | \(-0.0639739\pi\) | |||||||
\(234\) | −3531.83 | −0.0645013 | ||||||||
\(235\) | − | 49125.9i | − | 0.889559i | ||||||
\(236\) | −72035.0 | − | 129512.i | −1.29336 | − | 2.32534i | ||||
\(237\) | 43428.6 | 0.773177 | ||||||||
\(238\) | − | 95295.6i | − | 1.68236i | ||||||
\(239\) | −556.432 | −0.00974129 | −0.00487065 | − | 0.999988i | \(-0.501550\pi\) | ||||
−0.00487065 | + | 0.999988i | \(0.501550\pi\) | |||||||
\(240\) | 173599. | 3.01387 | ||||||||
\(241\) | 34167.1 | 0.588266 | 0.294133 | − | 0.955764i | \(-0.404969\pi\) | ||||
0.294133 | + | 0.955764i | \(0.404969\pi\) | |||||||
\(242\) | 55187.5i | 0.942345i | ||||||||
\(243\) | −3788.00 | −0.0641500 | ||||||||
\(244\) | 254620.i | 4.27675i | ||||||||
\(245\) | 44497.2 | 0.741310 | ||||||||
\(246\) | 110688.i | 1.82907i | ||||||||
\(247\) | 11066.4i | 0.181389i | ||||||||
\(248\) | −70574.0 | −1.14747 | ||||||||
\(249\) | 26114.7i | 0.421198i | ||||||||
\(250\) | 60424.9i | 0.966798i | ||||||||
\(251\) | 57018.6 | 0.905043 | 0.452522 | − | 0.891753i | \(-0.350525\pi\) | ||||
0.452522 | + | 0.891753i | \(0.350525\pi\) | |||||||
\(252\) | 40398.7 | 0.636161 | ||||||||
\(253\) | −127465. | −1.99137 | ||||||||
\(254\) | 143205.i | 2.21967i | ||||||||
\(255\) | −70265.9 | −1.08060 | ||||||||
\(256\) | 104388. | 1.59283 | ||||||||
\(257\) | −3529.50 | −0.0534375 | −0.0267188 | − | 0.999643i | \(-0.508506\pi\) | ||||
−0.0267188 | + | 0.999643i | \(0.508506\pi\) | |||||||
\(258\) | 112853. | 1.69540 | ||||||||
\(259\) | − | 34190.5i | − | 0.509689i | ||||||
\(260\) | − | 27773.5i | − | 0.410850i | ||||||
\(261\) | 11903.6 | 0.174742 | ||||||||
\(262\) | −94969.4 | −1.38351 | ||||||||
\(263\) | 39797.7 | 0.575369 | 0.287684 | − | 0.957725i | \(-0.407115\pi\) | ||||
0.287684 | + | 0.957725i | \(0.407115\pi\) | |||||||
\(264\) | −156214. | −2.24136 | ||||||||
\(265\) | 42127.7 | 0.599896 | ||||||||
\(266\) | − | 174155.i | − | 2.46134i | ||||||
\(267\) | − | 27502.8i | − | 0.385793i | ||||||
\(268\) | − | 142724.i | − | 1.98713i | ||||||
\(269\) | 99994.5i | 1.38188i | 0.722910 | + | 0.690942i | \(0.242804\pi\) | ||||
−0.722910 | + | 0.690942i | \(0.757196\pi\) | |||||||
\(270\) | − | 40982.9i | − | 0.562180i | ||||||
\(271\) | −70921.8 | −0.965698 | −0.482849 | − | 0.875704i | \(-0.660398\pi\) | ||||
−0.482849 | + | 0.875704i | \(0.660398\pi\) | |||||||
\(272\) | −310108. | −4.19156 | ||||||||
\(273\) | − | 3121.31i | − | 0.0418805i | ||||||
\(274\) | 183876.i | 2.44920i | ||||||||
\(275\) | − | 122968.i | − | 1.62602i | ||||||
\(276\) | − | 190750.i | − | 2.50407i | ||||||
\(277\) | −27566.1 | −0.359265 | −0.179633 | − | 0.983734i | \(-0.557491\pi\) | ||||
−0.179633 | + | 0.983734i | \(0.557491\pi\) | |||||||
\(278\) | 23069.8i | 0.298507i | ||||||||
\(279\) | 9369.50i | 0.120367i | ||||||||
\(280\) | 272815.i | 3.47978i | ||||||||
\(281\) | 116989. | 1.48160 | 0.740802 | − | 0.671723i | \(-0.234446\pi\) | ||||
0.740802 | + | 0.671723i | \(0.234446\pi\) | |||||||
\(282\) | −51183.9 | −0.643629 | ||||||||
\(283\) | − | 124680.i | − | 1.55676i | −0.627791 | − | 0.778382i | \(-0.716041\pi\) | ||
0.627791 | − | 0.778382i | \(-0.283959\pi\) | |||||||
\(284\) | 59441.1 | 0.736971 | ||||||||
\(285\) | −128413. | −1.58095 | ||||||||
\(286\) | 19336.6i | 0.236401i | ||||||||
\(287\) | −97822.4 | −1.18761 | ||||||||
\(288\) | − | 93014.9i | − | 1.12142i | ||||||
\(289\) | 41998.2 | 0.502846 | ||||||||
\(290\) | 128787.i | 1.53136i | ||||||||
\(291\) | − | 73014.8i | − | 0.862234i | ||||||
\(292\) | 70236.0i | 0.823747i | ||||||||
\(293\) | −117066. | −1.36362 | −0.681812 | − | 0.731528i | \(-0.738808\pi\) | ||||
−0.681812 | + | 0.731528i | \(0.738808\pi\) | |||||||
\(294\) | − | 46361.3i | − | 0.536366i | ||||||
\(295\) | −64582.6 | − | 116113.i | −0.742116 | − | 1.33425i | ||||
\(296\) | −197847. | −2.25811 | ||||||||
\(297\) | 20739.1i | 0.235114i | ||||||||
\(298\) | −79583.5 | −0.896170 | ||||||||
\(299\) | −14737.8 | −0.164851 | ||||||||
\(300\) | 184019. | 2.04466 | ||||||||
\(301\) | 99735.6i | 1.10082i | ||||||||
\(302\) | −271233. | −2.97392 | ||||||||
\(303\) | − | 3240.45i | − | 0.0352956i | ||||||
\(304\) | −566730. | −6.13238 | ||||||||
\(305\) | 228278.i | 2.45395i | ||||||||
\(306\) | 73209.6i | 0.781853i | ||||||||
\(307\) | −74586.4 | −0.791376 | −0.395688 | − | 0.918385i | \(-0.629494\pi\) | ||||
−0.395688 | + | 0.918385i | \(0.629494\pi\) | |||||||
\(308\) | − | 221182.i | − | 2.33157i | ||||||
\(309\) | − | 41736.5i | − | 0.437119i | ||||||
\(310\) | −101370. | −1.05484 | ||||||||
\(311\) | 164539. | 1.70117 | 0.850587 | − | 0.525834i | \(-0.176247\pi\) | ||||
0.850587 | + | 0.525834i | \(0.176247\pi\) | |||||||
\(312\) | −18061.8 | −0.185546 | ||||||||
\(313\) | 135789.i | 1.38604i | 0.720919 | + | 0.693019i | \(0.243720\pi\) | ||||
−0.720919 | + | 0.693019i | \(0.756280\pi\) | |||||||
\(314\) | 178341. | 1.80881 | ||||||||
\(315\) | 36219.3 | 0.365022 | ||||||||
\(316\) | 355819. | 3.56332 | ||||||||
\(317\) | −92280.2 | −0.918311 | −0.459156 | − | 0.888356i | \(-0.651848\pi\) | ||||
−0.459156 | + | 0.888356i | \(0.651848\pi\) | |||||||
\(318\) | − | 43892.6i | − | 0.434047i | ||||||
\(319\) | − | 65171.8i | − | 0.640440i | ||||||
\(320\) | 471796. | 4.60738 | ||||||||
\(321\) | −57670.4 | −0.559684 | ||||||||
\(322\) | 231934. | 2.23693 | ||||||||
\(323\) | 229389. | 2.19871 | ||||||||
\(324\) | −31035.8 | −0.295647 | ||||||||
\(325\) | − | 14217.8i | − | 0.134607i | ||||||
\(326\) | 68853.9i | 0.647878i | ||||||||
\(327\) | 40577.7i | 0.379482i | ||||||||
\(328\) | 566059.i | 5.26156i | ||||||||
\(329\) | − | 45234.6i | − | 0.417907i | ||||||
\(330\) | −224380. | −2.06042 | ||||||||
\(331\) | 10830.5 | 0.0988536 | 0.0494268 | − | 0.998778i | \(-0.484261\pi\) | ||||
0.0494268 | + | 0.998778i | \(0.484261\pi\) | |||||||
\(332\) | 213963.i | 1.94116i | ||||||||
\(333\) | 26266.4i | 0.236871i | ||||||||
\(334\) | 3382.02i | 0.0303167i | ||||||||
\(335\) | − | 127958.i | − | 1.14019i | ||||||
\(336\) | 159848. | 1.41589 | ||||||||
\(337\) | − | 124414.i | − | 1.09549i | −0.836645 | − | 0.547746i | \(-0.815486\pi\) | ||
0.836645 | − | 0.547746i | \(-0.184514\pi\) | |||||||
\(338\) | − | 216350.i | − | 1.89376i | ||||||
\(339\) | − | 16267.5i | − | 0.141554i | ||||||
\(340\) | −575703. | −4.98013 | ||||||||
\(341\) | 51297.7 | 0.441153 | ||||||||
\(342\) | 133792.i | 1.14388i | ||||||||
\(343\) | 125357. | 1.06551 | ||||||||
\(344\) | 577130. | 4.87705 | ||||||||
\(345\) | − | 171016.i | − | 1.43681i | ||||||
\(346\) | −22557.5 | −0.188425 | ||||||||
\(347\) | − | 226048.i | − | 1.87733i | −0.344829 | − | 0.938665i | \(-0.612063\pi\) | ||
0.344829 | − | 0.938665i | \(-0.387937\pi\) | |||||||
\(348\) | 97528.7 | 0.805330 | ||||||||
\(349\) | 223773.i | 1.83720i | 0.395185 | + | 0.918602i | \(0.370681\pi\) | ||||
−0.395185 | + | 0.918602i | \(0.629319\pi\) | |||||||
\(350\) | 223750.i | 1.82653i | ||||||||
\(351\) | 2397.91i | 0.0194634i | ||||||||
\(352\) | −509253. | −4.11006 | ||||||||
\(353\) | 132923.i | 1.06672i | 0.845889 | + | 0.533358i | \(0.179070\pi\) | ||||
−0.845889 | + | 0.533358i | \(0.820930\pi\) | |||||||
\(354\) | −120978. | + | 67288.2i | −0.965381 | + | 0.536948i | ||||
\(355\) | 53291.6 | 0.422866 | ||||||||
\(356\) | − | 225336.i | − | 1.77800i | ||||||
\(357\) | −64700.2 | −0.507655 | ||||||||
\(358\) | 132603. | 1.03463 | ||||||||
\(359\) | 52427.0 | 0.406786 | 0.203393 | − | 0.979097i | \(-0.434803\pi\) | ||||
0.203393 | + | 0.979097i | \(0.434803\pi\) | |||||||
\(360\) | − | 209587.i | − | 1.61718i | ||||||
\(361\) | 288893. | 2.21678 | ||||||||
\(362\) | 70995.5i | 0.541768i | ||||||||
\(363\) | 37469.1 | 0.284354 | ||||||||
\(364\) | − | 25573.6i | − | 0.193014i | ||||||
\(365\) | 62969.7i | 0.472657i | ||||||||
\(366\) | 237842. | 1.77552 | ||||||||
\(367\) | 30282.9i | 0.224835i | 0.993661 | + | 0.112418i | \(0.0358595\pi\) | ||||
−0.993661 | + | 0.112418i | \(0.964141\pi\) | |||||||
\(368\) | − | 754753.i | − | 5.57326i | ||||||
\(369\) | 75150.8 | 0.551926 | ||||||||
\(370\) | −284180. | −2.07582 | ||||||||
\(371\) | 38790.7 | 0.281826 | ||||||||
\(372\) | 76766.2i | 0.554733i | ||||||||
\(373\) | 47523.7 | 0.341580 | 0.170790 | − | 0.985307i | \(-0.445368\pi\) | ||||
0.170790 | + | 0.985307i | \(0.445368\pi\) | |||||||
\(374\) | 400820. | 2.86554 | ||||||||
\(375\) | 41025.0 | 0.291733 | ||||||||
\(376\) | −261755. | −1.85148 | ||||||||
\(377\) | − | 7535.33i | − | 0.0530175i | ||||||
\(378\) | − | 37736.6i | − | 0.264107i | ||||||
\(379\) | 185993. | 1.29485 | 0.647425 | − | 0.762130i | \(-0.275846\pi\) | ||||
0.647425 | + | 0.762130i | \(0.275846\pi\) | |||||||
\(380\) | −1.05211e6 | −7.28609 | ||||||||
\(381\) | 97227.6 | 0.669791 | ||||||||
\(382\) | 112572. | 0.771445 | ||||||||
\(383\) | −141142. | −0.962188 | −0.481094 | − | 0.876669i | \(-0.659760\pi\) | ||||
−0.481094 | + | 0.876669i | \(0.659760\pi\) | |||||||
\(384\) | − | 205150.i | − | 1.39126i | ||||||
\(385\) | − | 198299.i | − | 1.33783i | ||||||
\(386\) | 262121.i | 1.75925i | ||||||||
\(387\) | − | 76620.6i | − | 0.511592i | ||||||
\(388\) | − | 598225.i | − | 3.97376i | ||||||
\(389\) | 58679.8 | 0.387784 | 0.193892 | − | 0.981023i | \(-0.437889\pi\) | ||||
0.193892 | + | 0.981023i | \(0.437889\pi\) | |||||||
\(390\) | −25943.3 | −0.170568 | ||||||||
\(391\) | 305494.i | 1.99825i | ||||||||
\(392\) | − | 237092.i | − | 1.54292i | ||||||
\(393\) | 64478.7i | 0.417476i | ||||||||
\(394\) | − | 60549.3i | − | 0.390046i | ||||||
\(395\) | 319008. | 2.04459 | ||||||||
\(396\) | 169920.i | 1.08356i | ||||||||
\(397\) | 277665.i | 1.76173i | 0.473365 | + | 0.880866i | \(0.343039\pi\) | ||||
−0.473365 | + | 0.880866i | \(0.656961\pi\) | |||||||
\(398\) | 439717.i | 2.77592i | ||||||||
\(399\) | −118241. | −0.742716 | ||||||||
\(400\) | 728121. | 4.55076 | ||||||||
\(401\) | − | 59794.3i | − | 0.371853i | −0.982564 | − | 0.185927i | \(-0.940471\pi\) | ||
0.982564 | − | 0.185927i | \(-0.0595286\pi\) | |||||||
\(402\) | −133319. | −0.824973 | ||||||||
\(403\) | 5931.16 | 0.0365199 | ||||||||
\(404\) | − | 26549.7i | − | 0.162666i | ||||||
\(405\) | −27825.0 | −0.169639 | ||||||||
\(406\) | 118586.i | 0.719417i | ||||||||
\(407\) | 143808. | 0.868146 | ||||||||
\(408\) | 374394.i | 2.24910i | ||||||||
\(409\) | − | 92288.3i | − | 0.551696i | −0.961201 | − | 0.275848i | \(-0.911041\pi\) | ||
0.961201 | − | 0.275848i | \(-0.0889587\pi\) | |||||||
\(410\) | 813068.i | 4.83681i | ||||||||
\(411\) | 124841. | 0.739051 | ||||||||
\(412\) | − | 341956.i | − | 2.01454i | ||||||
\(413\) | −59467.0 | − | 106916.i | −0.348639 | − | 0.626819i | ||||
\(414\) | −178180. | −1.03958 | ||||||||
\(415\) | 191827.i | 1.11382i | ||||||||
\(416\) | −58881.1 | −0.340243 | ||||||||
\(417\) | 15663.1 | 0.0900750 | ||||||||
\(418\) | 732508. | 4.19237 | ||||||||
\(419\) | − | 100145.i | − | 0.570429i | −0.958464 | − | 0.285214i | \(-0.907935\pi\) | ||
0.958464 | − | 0.285214i | \(-0.0920648\pi\) | |||||||
\(420\) | 296752. | 1.68227 | ||||||||
\(421\) | 102049.i | 0.575762i | 0.957666 | + | 0.287881i | \(0.0929507\pi\) | ||||
−0.957666 | + | 0.287881i | \(0.907049\pi\) | |||||||
\(422\) | 375044. | 2.10600 | ||||||||
\(423\) | 34750.9i | 0.194216i | ||||||||
\(424\) | − | 224467.i | − | 1.24859i | ||||||
\(425\) | −294714. | −1.63164 | ||||||||
\(426\) | − | 55524.2i | − | 0.305959i | ||||||
\(427\) | 210197.i | 1.15284i | ||||||||
\(428\) | −472506. | −2.57941 | ||||||||
\(429\) | 13128.5 | 0.0713344 | ||||||||
\(430\) | 828970. | 4.48334 | ||||||||
\(431\) | − | 259464.i | − | 1.39676i | −0.715725 | − | 0.698382i | \(-0.753904\pi\) | ||
0.715725 | − | 0.698382i | \(-0.246096\pi\) | |||||||
\(432\) | −122801. | −0.658015 | ||||||||
\(433\) | −332067. | −1.77113 | −0.885565 | − | 0.464516i | \(-0.846228\pi\) | ||||
−0.885565 | + | 0.464516i | \(0.846228\pi\) | |||||||
\(434\) | −93340.5 | −0.495554 | ||||||||
\(435\) | 87438.9 | 0.462089 | ||||||||
\(436\) | 332461.i | 1.74891i | ||||||||
\(437\) | 558297.i | 2.92350i | ||||||||
\(438\) | 65607.8 | 0.341985 | ||||||||
\(439\) | 70862.7 | 0.367696 | 0.183848 | − | 0.982955i | \(-0.441145\pi\) | ||||
0.183848 | + | 0.982955i | \(0.441145\pi\) | |||||||
\(440\) | −1.14748e6 | −5.92706 | ||||||||
\(441\) | −31476.6 | −0.161849 | ||||||||
\(442\) | 46343.8 | 0.237218 | ||||||||
\(443\) | − | 85593.5i | − | 0.436147i | −0.975932 | − | 0.218074i | \(-0.930023\pi\) | ||
0.975932 | − | 0.218074i | \(-0.0699773\pi\) | |||||||
\(444\) | 215206.i | 1.09166i | ||||||||
\(445\) | − | 202024.i | − | 1.02019i | ||||||
\(446\) | − | 721882.i | − | 3.62908i | ||||||
\(447\) | 54032.6i | 0.270421i | ||||||||
\(448\) | 434425. | 2.16451 | ||||||||
\(449\) | 70020.7 | 0.347323 | 0.173662 | − | 0.984805i | \(-0.444440\pi\) | ||||
0.173662 | + | 0.984805i | \(0.444440\pi\) | |||||||
\(450\) | − | 171893.i | − | 0.848856i | ||||||
\(451\) | − | 411448.i | − | 2.02284i | ||||||
\(452\) | − | 133283.i | − | 0.652376i | ||||||
\(453\) | 184152.i | 0.897386i | ||||||||
\(454\) | −562494. | −2.72901 | ||||||||
\(455\) | − | 22927.8i | − | 0.110749i | ||||||
\(456\) | 684214.i | 3.29050i | ||||||||
\(457\) | − | 97704.0i | − | 0.467821i | −0.972258 | − | 0.233911i | \(-0.924848\pi\) | ||
0.972258 | − | 0.233911i | \(-0.0751523\pi\) | |||||||
\(458\) | −545439. | −2.60025 | ||||||||
\(459\) | 49705.1 | 0.235926 | ||||||||
\(460\) | − | 1.40117e6i | − | 6.62178i | ||||||
\(461\) | 149231. | 0.702194 | 0.351097 | − | 0.936339i | \(-0.385809\pi\) | ||||
0.351097 | + | 0.936339i | \(0.385809\pi\) | |||||||
\(462\) | −206607. | −0.967967 | ||||||||
\(463\) | 350096.i | 1.63315i | 0.577242 | + | 0.816573i | \(0.304129\pi\) | ||||
−0.577242 | + | 0.816573i | \(0.695871\pi\) | |||||||
\(464\) | 385898. | 1.79241 | ||||||||
\(465\) | 68824.4i | 0.318300i | ||||||||
\(466\) | −165888. | −0.763914 | ||||||||
\(467\) | − | 370985.i | − | 1.70107i | −0.525917 | − | 0.850536i | \(-0.676278\pi\) | ||
0.525917 | − | 0.850536i | \(-0.323722\pi\) | |||||||
\(468\) | 19646.6i | 0.0897005i | ||||||||
\(469\) | − | 117823.i | − | 0.535653i | ||||||
\(470\) | −375976. | −1.70202 | ||||||||
\(471\) | − | 121083.i | − | 0.545811i | ||||||
\(472\) | −618680. | + | 344112.i | −2.77704 | + | 1.54460i | ||||
\(473\) | −419495. | −1.87501 | ||||||||
\(474\) | − | 332372.i | − | 1.47934i | ||||||
\(475\) | −538597. | −2.38713 | ||||||||
\(476\) | −530102. | −2.33962 | ||||||||
\(477\) | −29800.5 | −0.130974 | ||||||||
\(478\) | 4258.55i | 0.0186383i | ||||||||
\(479\) | −64617.2 | −0.281629 | −0.140814 | − | 0.990036i | \(-0.544972\pi\) | ||||
−0.140814 | + | 0.990036i | \(0.544972\pi\) | |||||||
\(480\) | − | 683248.i | − | 2.96549i | ||||||
\(481\) | 16627.4 | 0.0718677 | ||||||||
\(482\) | − | 261491.i | − | 1.12555i | ||||||
\(483\) | − | 157470.i | − | 0.674999i | ||||||
\(484\) | 306992. | 1.31050 | ||||||||
\(485\) | − | 536336.i | − | 2.28010i | ||||||
\(486\) | 28990.7i | 0.122740i | ||||||||
\(487\) | 177831. | 0.749808 | 0.374904 | − | 0.927064i | \(-0.377676\pi\) | ||||
0.374904 | + | 0.927064i | \(0.377676\pi\) | |||||||
\(488\) | 1.21632e6 | 5.10752 | ||||||||
\(489\) | 46747.8 | 0.195499 | ||||||||
\(490\) | − | 340550.i | − | 1.41837i | ||||||
\(491\) | −146359. | −0.607094 | −0.303547 | − | 0.952817i | \(-0.598171\pi\) | ||||
−0.303547 | + | 0.952817i | \(0.598171\pi\) | |||||||
\(492\) | 615726. | 2.54365 | ||||||||
\(493\) | −156196. | −0.642653 | ||||||||
\(494\) | 84694.3 | 0.347057 | ||||||||
\(495\) | 152341.i | 0.621736i | ||||||||
\(496\) | 303746.i | 1.23466i | ||||||||
\(497\) | 49070.4 | 0.198658 | ||||||||
\(498\) | 199864. | 0.805889 | ||||||||
\(499\) | 297990. | 1.19674 | 0.598372 | − | 0.801218i | \(-0.295815\pi\) | ||||
0.598372 | + | 0.801218i | \(0.295815\pi\) | |||||||
\(500\) | 336126. | 1.34450 | ||||||||
\(501\) | 2296.19 | 0.00914814 | ||||||||
\(502\) | − | 436381.i | − | 1.73164i | ||||||
\(503\) | 379938.i | 1.50168i | 0.660486 | + | 0.750839i | \(0.270350\pi\) | ||||
−0.660486 | + | 0.750839i | \(0.729650\pi\) | |||||||
\(504\) | − | 192985.i | − | 0.759737i | ||||||
\(505\) | − | 23803.0i | − | 0.0933359i | ||||||
\(506\) | 975532.i | 3.81013i | ||||||||
\(507\) | −146889. | −0.571445 | ||||||||
\(508\) | 796605. | 3.08685 | ||||||||
\(509\) | − | 68834.8i | − | 0.265688i | −0.991137 | − | 0.132844i | \(-0.957589\pi\) | ||
0.991137 | − | 0.132844i | \(-0.0424110\pi\) | |||||||
\(510\) | 537767.i | 2.06754i | ||||||||
\(511\) | 57981.9i | 0.222050i | ||||||||
\(512\) | − | 167216.i | − | 0.637880i | ||||||
\(513\) | 90837.2 | 0.345167 | ||||||||
\(514\) | 27012.3i | 0.102243i | ||||||||
\(515\) | − | 306579.i | − | 1.15592i | ||||||
\(516\) | − | 627768.i | − | 2.35776i | ||||||
\(517\) | 190260. | 0.711814 | ||||||||
\(518\) | −261670. | −0.975203 | ||||||||
\(519\) | 15315.2i | 0.0568576i | ||||||||
\(520\) | −132674. | −0.490659 | ||||||||
\(521\) | 450862. | 1.66099 | 0.830497 | − | 0.557023i | \(-0.188057\pi\) | ||||
0.830497 | + | 0.557023i | \(0.188057\pi\) | |||||||
\(522\) | − | 91102.0i | − | 0.334339i | ||||||
\(523\) | −157180. | −0.574639 | −0.287319 | − | 0.957835i | \(-0.592764\pi\) | ||||
−0.287319 | + | 0.957835i | \(0.592764\pi\) | |||||||
\(524\) | 528287.i | 1.92401i | ||||||||
\(525\) | 151913. | 0.551160 | ||||||||
\(526\) | − | 304584.i | − | 1.10087i | ||||||
\(527\) | − | 122944.i | − | 0.442677i | ||||||
\(528\) | 672334.i | 2.41166i | ||||||||
\(529\) | −463682. | −1.65695 | ||||||||
\(530\) | − | 322416.i | − | 1.14780i | ||||||
\(531\) | 45684.8 | + | 82136.8i | 0.162025 | + | 0.291306i | ||||
\(532\) | −968773. | −3.42294 | ||||||||
\(533\) | − | 47572.6i | − | 0.167457i | ||||||
\(534\) | −210487. | −0.738149 | ||||||||
\(535\) | −423623. | −1.48003 | ||||||||
\(536\) | −681793. | −2.37314 | ||||||||
\(537\) | − | 90029.5i | − | 0.312202i | ||||||
\(538\) | 765289. | 2.64400 | ||||||||
\(539\) | 172333.i | 0.593187i | ||||||||
\(540\) | −227976. | −0.781810 | ||||||||
\(541\) | 272034.i | 0.929455i | 0.885454 | + | 0.464727i | \(0.153848\pi\) | ||||
−0.885454 | + | 0.464727i | \(0.846152\pi\) | |||||||
\(542\) | 542787.i | 1.84770i | ||||||||
\(543\) | 48201.8 | 0.163480 | ||||||||
\(544\) | 1.22052e6i | 4.12426i | ||||||||
\(545\) | 298066.i | 1.00351i | ||||||||
\(546\) | −23888.4 | −0.0801311 | ||||||||
\(547\) | 351369. | 1.17433 | 0.587163 | − | 0.809469i | \(-0.300245\pi\) | ||||
0.587163 | + | 0.809469i | \(0.300245\pi\) | |||||||
\(548\) | 1.02285e6 | 3.40605 | ||||||||
\(549\) | − | 161481.i | − | 0.535768i | ||||||
\(550\) | −941109. | −3.11110 | ||||||||
\(551\) | −285452. | −0.940221 | ||||||||
\(552\) | −911216. | −2.99049 | ||||||||
\(553\) | 293739. | 0.960532 | ||||||||
\(554\) | 210972.i | 0.687392i | ||||||||
\(555\) | 192942.i | 0.626384i | ||||||||
\(556\) | 128331. | 0.415127 | ||||||||
\(557\) | 88233.8 | 0.284397 | 0.142198 | − | 0.989838i | \(-0.454583\pi\) | ||||
0.142198 | + | 0.989838i | \(0.454583\pi\) | |||||||
\(558\) | 71707.7 | 0.230302 | ||||||||
\(559\) | −48503.0 | −0.155219 | ||||||||
\(560\) | 1.17418e6 | 3.74419 | ||||||||
\(561\) | − | 272133.i | − | 0.864682i | ||||||
\(562\) | − | 895352.i | − | 2.83479i | ||||||
\(563\) | − | 203437.i | − | 0.641819i | −0.947110 | − | 0.320910i | \(-0.896011\pi\) | ||
0.947110 | − | 0.320910i | \(-0.103989\pi\) | |||||||
\(564\) | 284721.i | 0.895080i | ||||||||
\(565\) | − | 119494.i | − | 0.374326i | ||||||
\(566\) | −954212. | −2.97860 | ||||||||
\(567\) | −25621.0 | −0.0796948 | ||||||||
\(568\) | − | 283951.i | − | 0.880130i | ||||||
\(569\) | − | 20875.8i | − | 0.0644791i | −0.999480 | − | 0.0322395i | \(-0.989736\pi\) | ||
0.999480 | − | 0.0322395i | \(-0.0102639\pi\) | |||||||
\(570\) | 982781.i | 3.02487i | ||||||||
\(571\) | 308480.i | 0.946139i | 0.881025 | + | 0.473069i | \(0.156854\pi\) | ||||
−0.881025 | + | 0.473069i | \(0.843146\pi\) | |||||||
\(572\) | 107564. | 0.328757 | ||||||||
\(573\) | − | 76430.1i | − | 0.232785i | ||||||
\(574\) | 748665.i | 2.27229i | ||||||||
\(575\) | − | 717287.i | − | 2.16949i | ||||||
\(576\) | −333742. | −1.00592 | ||||||||
\(577\) | −332414. | −0.998454 | −0.499227 | − | 0.866471i | \(-0.666383\pi\) | ||||
−0.499227 | + | 0.866471i | \(0.666383\pi\) | |||||||
\(578\) | − | 321425.i | − | 0.962110i | ||||||
\(579\) | 177965. | 0.530857 | ||||||||
\(580\) | 716405. | 2.12962 | ||||||||
\(581\) | 176633.i | 0.523262i | ||||||||
\(582\) | −558805. | −1.64974 | ||||||||
\(583\) | 163157.i | 0.480029i | ||||||||
\(584\) | 335518. | 0.983763 | ||||||||
\(585\) | 17614.0i | 0.0514691i | ||||||||
\(586\) | 895940.i | 2.60906i | ||||||||
\(587\) | − | 398675.i | − | 1.15703i | −0.815673 | − | 0.578513i | \(-0.803633\pi\) | ||
0.815673 | − | 0.578513i | \(-0.196367\pi\) | |||||||
\(588\) | −257895. | −0.745912 | ||||||||
\(589\) | − | 224683.i | − | 0.647650i | ||||||
\(590\) | −888650. | + | 494271.i | −2.55286 | + | 1.41991i | ||||
\(591\) | −41109.4 | −0.117697 | ||||||||
\(592\) | 851520.i | 2.42969i | ||||||||
\(593\) | 150216. | 0.427177 | 0.213589 | − | 0.976924i | \(-0.431485\pi\) | ||||
0.213589 | + | 0.976924i | \(0.431485\pi\) | |||||||
\(594\) | 158723. | 0.449849 | ||||||||
\(595\) | −475260. | −1.34245 | ||||||||
\(596\) | 442700.i | 1.24628i | ||||||||
\(597\) | 298543. | 0.837640 | ||||||||
\(598\) | 112793.i | 0.315414i | ||||||||
\(599\) | −79272.8 | −0.220938 | −0.110469 | − | 0.993880i | \(-0.535235\pi\) | ||||
−0.110469 | + | 0.993880i | \(0.535235\pi\) | |||||||
\(600\) | − | 879063.i | − | 2.44184i | ||||||
\(601\) | 510334.i | 1.41288i | 0.707772 | + | 0.706441i | \(0.249700\pi\) | ||||
−0.707772 | + | 0.706441i | \(0.750300\pi\) | |||||||
\(602\) | 763307. | 2.10623 | ||||||||
\(603\) | 90515.8i | 0.248937i | ||||||||
\(604\) | 1.50879e6i | 4.13576i | ||||||||
\(605\) | 275232. | 0.751949 | ||||||||
\(606\) | −24800.2 | −0.0675320 | ||||||||
\(607\) | −108872. | −0.295487 | −0.147743 | − | 0.989026i | \(-0.547201\pi\) | ||||
−0.147743 | + | 0.989026i | \(0.547201\pi\) | |||||||
\(608\) | 2.23052e6i | 6.03392i | ||||||||
\(609\) | 80512.9 | 0.217085 | ||||||||
\(610\) | 1.74709e6 | 4.69521 | ||||||||
\(611\) | 21998.3 | 0.0589260 | ||||||||
\(612\) | 407244. | 1.08731 | ||||||||
\(613\) | 71190.4i | 0.189453i | 0.995503 | + | 0.0947263i | \(0.0301976\pi\) | ||||
−0.995503 | + | 0.0947263i | \(0.969802\pi\) | |||||||
\(614\) | 570833.i | 1.51416i | ||||||||
\(615\) | 552026. | 1.45952 | ||||||||
\(616\) | −1.05659e6 | −2.78448 | ||||||||
\(617\) | −463811. | −1.21835 | −0.609173 | − | 0.793037i | \(-0.708498\pi\) | ||||
−0.609173 | + | 0.793037i | \(0.708498\pi\) | |||||||
\(618\) | −319423. | −0.836351 | ||||||||
\(619\) | 192587. | 0.502627 | 0.251313 | − | 0.967906i | \(-0.419138\pi\) | ||||
0.251313 | + | 0.967906i | \(0.419138\pi\) | |||||||
\(620\) | 563892.i | 1.46694i | ||||||||
\(621\) | 120974.i | 0.313696i | ||||||||
\(622\) | − | 1.25927e6i | − | 3.25490i | ||||||
\(623\) | − | 186022.i | − | 0.479278i | ||||||
\(624\) | 77736.8i | 0.199645i | ||||||||
\(625\) | −218555. | −0.559501 | ||||||||
\(626\) | 1.03923e6 | 2.65194 | ||||||||
\(627\) | − | 497330.i | − | 1.26506i | ||||||
\(628\) | − | 992060.i | − | 2.51547i | ||||||
\(629\) | − | 344661.i | − | 0.871145i | ||||||
\(630\) | − | 277197.i | − | 0.698406i | ||||||
\(631\) | −13953.1 | −0.0350438 | −0.0175219 | − | 0.999846i | \(-0.505578\pi\) | ||||
−0.0175219 | + | 0.999846i | \(0.505578\pi\) | |||||||
\(632\) | − | 1.69975e6i | − | 4.25551i | ||||||
\(633\) | − | 254633.i | − | 0.635489i | ||||||
\(634\) | 706249.i | 1.75703i | ||||||||
\(635\) | 714192. | 1.77120 | ||||||||
\(636\) | −244162. | −0.603619 | ||||||||
\(637\) | 19925.6i | 0.0491058i | ||||||||
\(638\) | −498780. | −1.22537 | ||||||||
\(639\) | −37697.7 | −0.0923238 | ||||||||
\(640\) | − | 1.50694e6i | − | 3.67906i | ||||||
\(641\) | −416645. | −1.01403 | −0.507014 | − | 0.861938i | \(-0.669251\pi\) | ||||
−0.507014 | + | 0.861938i | \(0.669251\pi\) | |||||||
\(642\) | 441370.i | 1.07086i | ||||||||
\(643\) | 79601.2 | 0.192530 | 0.0962648 | − | 0.995356i | \(-0.469310\pi\) | ||||
0.0962648 | + | 0.995356i | \(0.469310\pi\) | |||||||
\(644\) | − | 1.29018e6i | − | 3.11085i | ||||||
\(645\) | − | 562822.i | − | 1.35286i | ||||||
\(646\) | − | 1.75559e6i | − | 4.20685i | ||||||
\(647\) | −681530. | −1.62808 | −0.814041 | − | 0.580807i | \(-0.802737\pi\) | ||||
−0.814041 | + | 0.580807i | \(0.802737\pi\) | |||||||
\(648\) | 148259.i | 0.353077i | ||||||||
\(649\) | 449696. | − | 250123.i | 1.06765 | − | 0.593832i | ||||
\(650\) | −108813. | −0.257546 | ||||||||
\(651\) | 63372.8i | 0.149534i | ||||||||
\(652\) | 383014. | 0.900990 | ||||||||
\(653\) | −383016. | −0.898237 | −0.449118 | − | 0.893472i | \(-0.648262\pi\) | ||||
−0.449118 | + | 0.893472i | \(0.648262\pi\) | |||||||
\(654\) | 310553. | 0.726074 | ||||||||
\(655\) | 473633.i | 1.10398i | ||||||||
\(656\) | 2.43628e6 | 5.66135 | ||||||||
\(657\) | − | 44543.9i | − | 0.103195i | ||||||
\(658\) | −346195. | −0.799592 | ||||||||
\(659\) | − | 527534.i | − | 1.21473i | −0.794423 | − | 0.607365i | \(-0.792227\pi\) | ||
0.794423 | − | 0.607365i | \(-0.207773\pi\) | |||||||
\(660\) | 1.24816e6i | 2.86538i | ||||||||
\(661\) | 282774. | 0.647197 | 0.323599 | − | 0.946194i | \(-0.395107\pi\) | ||||
0.323599 | + | 0.946194i | \(0.395107\pi\) | |||||||
\(662\) | − | 82889.2i | − | 0.189139i | ||||||
\(663\) | − | 31464.7i | − | 0.0715809i | ||||||
\(664\) | 1.02210e6 | 2.31824 | ||||||||
\(665\) | −868549. | −1.96404 | ||||||||
\(666\) | 201025. | 0.453212 | ||||||||
\(667\) | − | 380156.i | − | 0.854497i | ||||||
\(668\) | 18813.2 | 0.0421608 | ||||||||
\(669\) | −490116. | −1.09508 | ||||||||
\(670\) | −979304. | −2.18156 | ||||||||
\(671\) | −884102. | −1.96362 | ||||||||
\(672\) | − | 629128.i | − | 1.39316i | ||||||
\(673\) | 709243.i | 1.56590i | 0.622083 | + | 0.782952i | \(0.286287\pi\) | ||||
−0.622083 | + | 0.782952i | \(0.713713\pi\) | |||||||
\(674\) | −952178. | −2.09604 | ||||||||
\(675\) | −116706. | −0.256144 | ||||||||
\(676\) | −1.20349e6 | −2.63361 | ||||||||
\(677\) | −419269. | −0.914777 | −0.457389 | − | 0.889267i | \(-0.651215\pi\) | ||||
−0.457389 | + | 0.889267i | \(0.651215\pi\) | |||||||
\(678\) | −124500. | −0.270839 | ||||||||
\(679\) | − | 493853.i | − | 1.07117i | ||||||
\(680\) | 2.75014e6i | 5.94754i | ||||||||
\(681\) | 381900.i | 0.823486i | ||||||||
\(682\) | − | 392597.i | − | 0.844069i | ||||||
\(683\) | 341293.i | 0.731620i | 0.930690 | + | 0.365810i | \(0.119208\pi\) | ||||
−0.930690 | + | 0.365810i | \(0.880792\pi\) | |||||||
\(684\) | 744248. | 1.59076 | ||||||||
\(685\) | 917030. | 1.95435 | ||||||||
\(686\) | − | 959393.i | − | 2.03868i | ||||||
\(687\) | 370322.i | 0.784631i | ||||||||
\(688\) | − | 2.48393e6i | − | 5.24762i | ||||||
\(689\) | 18864.6i | 0.0397382i | ||||||||
\(690\) | −1.30884e6 | −2.74908 | ||||||||
\(691\) | − | 57041.7i | − | 0.119464i | −0.998214 | − | 0.0597319i | \(-0.980975\pi\) | ||
0.998214 | − | 0.0597319i | \(-0.0190246\pi\) | |||||||
\(692\) | 125481.i | 0.262039i | ||||||||
\(693\) | 140274.i | 0.292086i | ||||||||
\(694\) | −1.73001e6 | −3.59195 | ||||||||
\(695\) | 115054. | 0.238195 | ||||||||
\(696\) | − | 465896.i | − | 0.961769i | ||||||
\(697\) | −986109. | −2.02983 | ||||||||
\(698\) | 1.71261e6 | 3.51517 | ||||||||
\(699\) | 112629.i | 0.230512i | ||||||||
\(700\) | 1.24466e6 | 2.54012 | ||||||||
\(701\) | 292521.i | 0.595279i | 0.954678 | + | 0.297640i | \(0.0961994\pi\) | ||||
−0.954678 | + | 0.297640i | \(0.903801\pi\) | |||||||
\(702\) | 18351.9 | 0.0372398 | ||||||||
\(703\) | − | 629876.i | − | 1.27451i | ||||||
\(704\) | 1.82722e6i | 3.68677i | ||||||||
\(705\) | 255266.i | 0.513587i | ||||||||
\(706\) | 1.01730e6 | 2.04098 | ||||||||
\(707\) | − | 21917.6i | − | 0.0438484i | ||||||
\(708\) | 374305. | + | 672964.i | 0.746722 | + | 1.34253i | ||||
\(709\) | 265410. | 0.527988 | 0.263994 | − | 0.964524i | \(-0.414960\pi\) | ||||
0.263994 | + | 0.964524i | \(0.414960\pi\) | |||||||
\(710\) | − | 407857.i | − | 0.809080i | ||||||
\(711\) | −225661. | −0.446394 | ||||||||
\(712\) | −1.07643e6 | −2.12338 | ||||||||
\(713\) | 299226. | 0.588601 | ||||||||
\(714\) | 495170.i | 0.971311i | ||||||||
\(715\) | 96436.1 | 0.188637 | ||||||||
\(716\) | − | 737630.i | − | 1.43884i | ||||||
\(717\) | 2891.31 | 0.00562414 | ||||||||
\(718\) | − | 401240.i | − | 0.778315i | ||||||
\(719\) | 843328.i | 1.63132i | 0.578532 | + | 0.815659i | \(0.303626\pi\) | ||||
−0.578532 | + | 0.815659i | \(0.696374\pi\) | |||||||
\(720\) | −902047. | −1.74006 | ||||||||
\(721\) | − | 282295.i | − | 0.543041i | ||||||
\(722\) | − | 2.21099e6i | − | 4.24143i | ||||||
\(723\) | −177537. | −0.339636 | ||||||||
\(724\) | 394927. | 0.753425 | ||||||||
\(725\) | 366742. | 0.697726 | ||||||||
\(726\) | − | 286763.i | − | 0.544063i | ||||||
\(727\) | 361987. | 0.684895 | 0.342448 | − | 0.939537i | \(-0.388744\pi\) | ||||
0.342448 | + | 0.939537i | \(0.388744\pi\) | |||||||
\(728\) | −122165. | −0.230507 | ||||||||
\(729\) | 19683.0 | 0.0370370 | ||||||||
\(730\) | 481927. | 0.904347 | ||||||||
\(731\) | 1.00540e6i | 1.88149i | ||||||||
\(732\) | − | 1.32305e6i | − | 2.46918i | ||||||
\(733\) | 364992. | 0.679322 | 0.339661 | − | 0.940548i | \(-0.389688\pi\) | ||||
0.339661 | + | 0.940548i | \(0.389688\pi\) | |||||||
\(734\) | 231764. | 0.430184 | ||||||||
\(735\) | −231214. | −0.427996 | ||||||||
\(736\) | −2.97054e6 | −5.48379 | ||||||||
\(737\) | 495571. | 0.912369 | ||||||||
\(738\) | − | 575152.i | − | 1.05602i | ||||||
\(739\) | − | 397416.i | − | 0.727707i | −0.931456 | − | 0.363854i | \(-0.881461\pi\) | ||
0.931456 | − | 0.363854i | \(-0.118539\pi\) | |||||||
\(740\) | 1.58081e6i | 2.88680i | ||||||||
\(741\) | − | 57502.5i | − | 0.104725i | ||||||
\(742\) | − | 296878.i | − | 0.539224i | ||||||
\(743\) | 208889. | 0.378389 | 0.189195 | − | 0.981940i | \(-0.439412\pi\) | ||||
0.189195 | + | 0.981940i | \(0.439412\pi\) | |||||||
\(744\) | 366713. | 0.662492 | ||||||||
\(745\) | 396900.i | 0.715104i | ||||||||
\(746\) | − | 363714.i | − | 0.653555i | ||||||
\(747\) | − | 135696.i | − | 0.243179i | ||||||
\(748\) | − | 2.22965e6i | − | 3.98504i | ||||||
\(749\) | −390068. | −0.695306 | ||||||||
\(750\) | − | 313977.i | − | 0.558181i | ||||||
\(751\) | 1.12660e6i | 1.99751i | 0.0498694 | + | 0.998756i | \(0.484120\pi\) | ||||
−0.0498694 | + | 0.998756i | \(0.515880\pi\) | |||||||
\(752\) | 1.12658e6i | 1.99216i | ||||||||
\(753\) | −296277. | −0.522527 | ||||||||
\(754\) | −57670.2 | −0.101440 | ||||||||
\(755\) | 1.35270e6i | 2.37305i | ||||||||
\(756\) | −209918. | −0.367288 | ||||||||
\(757\) | −287250. | −0.501266 | −0.250633 | − | 0.968082i | \(-0.580639\pi\) | ||||
−0.250633 | + | 0.968082i | \(0.580639\pi\) | |||||||
\(758\) | − | 1.42347e6i | − | 2.47747i | ||||||
\(759\) | 662329. | 1.14972 | ||||||||
\(760\) | 5.02595e6i | 8.70143i | ||||||||
\(761\) | −39472.2 | −0.0681587 | −0.0340794 | − | 0.999419i | \(-0.510850\pi\) | ||||
−0.0340794 | + | 0.999419i | \(0.510850\pi\) | |||||||
\(762\) | − | 744113.i | − | 1.28153i | ||||||
\(763\) | 274456.i | 0.471438i | ||||||||
\(764\) | − | 626207.i | − | 1.07283i | ||||||
\(765\) | 365112. | 0.623884 | ||||||||
\(766\) | 1.08021e6i | 1.84098i | ||||||||
\(767\) | 51994.9 | − | 28919.8i | 0.0883833 | − | 0.0491591i | ||||
\(768\) | −542416. | −0.919623 | ||||||||
\(769\) | 696042.i | 1.17702i | 0.808491 | + | 0.588509i | \(0.200285\pi\) | ||||
−0.808491 | + | 0.588509i | \(0.799715\pi\) | |||||||
\(770\) | −1.51765e6 | −2.55970 | ||||||||
\(771\) | 18339.8 | 0.0308522 | ||||||||
\(772\) | 1.45810e6 | 2.44655 | ||||||||
\(773\) | 245846.i | 0.411438i | 0.978611 | + | 0.205719i | \(0.0659533\pi\) | ||||
−0.978611 | + | 0.205719i | \(0.934047\pi\) | |||||||
\(774\) | −586401. | −0.978843 | ||||||||
\(775\) | 288668.i | 0.480613i | ||||||||
\(776\) | −2.85773e6 | −4.74567 | ||||||||
\(777\) | 177659.i | 0.294269i | ||||||||
\(778\) | − | 449095.i | − | 0.741957i | ||||||
\(779\) | −1.80214e6 | −2.96970 | ||||||||
\(780\) | 144315.i | 0.237205i | ||||||||
\(781\) | 206394.i | 0.338372i | ||||||||
\(782\) | 2.33804e6 | 3.82330 | ||||||||
\(783\) | −61853.0 | −0.100887 | ||||||||
\(784\) | −1.02043e6 | −1.66016 | ||||||||
\(785\) | − | 889426.i | − | 1.44335i | ||||||
\(786\) | 493476. | 0.798768 | ||||||||
\(787\) | 437284. | 0.706016 | 0.353008 | − | 0.935620i | \(-0.385159\pi\) | ||||
0.353008 | + | 0.935620i | \(0.385159\pi\) | |||||||
\(788\) | −336818. | −0.542429 | ||||||||
\(789\) | −206795. | −0.332189 | ||||||||
\(790\) | − | 2.44146e6i | − | 3.91198i | ||||||
\(791\) | − | 110029.i | − | 0.175855i | ||||||
\(792\) | 811710. | 1.29405 | ||||||||
\(793\) | −102222. | −0.162554 | ||||||||
\(794\) | 2.12506e6 | 3.37077 | ||||||||
\(795\) | −218902. | −0.346350 | ||||||||
\(796\) | 2.44602e6 | 3.86041 | ||||||||
\(797\) | 377368.i | 0.594085i | 0.954864 | + | 0.297042i | \(0.0960003\pi\) | ||||
−0.954864 | + | 0.297042i | \(0.904000\pi\) | |||||||
\(798\) | 904936.i | 1.42106i | ||||||||
\(799\) | − | 455993.i | − | 0.714273i | ||||||
\(800\) | − | 2.86573e6i | − | 4.47770i | ||||||
\(801\) | 142909.i | 0.222738i | ||||||||
\(802\) | −457625. | −0.711477 | ||||||||
\(803\) | −243876. | −0.378214 | ||||||||
\(804\) | 741614.i | 1.14727i | ||||||||
\(805\) | − | 1.15671e6i | − | 1.78497i | ||||||
\(806\) | − | 45393.0i | − | 0.0698745i | ||||||
\(807\) | − | 519587.i | − | 0.797831i | ||||||
\(808\) | −126828. | −0.194264 | ||||||||
\(809\) | − | 84575.4i | − | 0.129225i | −0.997910 | − | 0.0646126i | \(-0.979419\pi\) | ||
0.997910 | − | 0.0646126i | \(-0.0205812\pi\) | |||||||
\(810\) | 212953.i | 0.324575i | ||||||||
\(811\) | − | 280073.i | − | 0.425823i | −0.977071 | − | 0.212911i | \(-0.931705\pi\) | ||
0.977071 | − | 0.212911i | \(-0.0682946\pi\) | |||||||
\(812\) | 659658. | 1.00048 | ||||||||
\(813\) | 368521. | 0.557546 | ||||||||
\(814\) | − | 1.10060e6i | − | 1.66105i | ||||||
\(815\) | 343390. | 0.516978 | ||||||||
\(816\) | 1.61137e6 | 2.42000 | ||||||||
\(817\) | 1.83738e6i | 2.75268i | ||||||||
\(818\) | −706311. | −1.05558 | ||||||||
\(819\) | 16218.8i | 0.0241797i | ||||||||
\(820\) | 4.52286e6 | 6.72644 | ||||||||
\(821\) | − | 475894.i | − | 0.706031i | −0.935617 | − | 0.353016i | \(-0.885156\pi\) | ||
0.935617 | − | 0.353016i | \(-0.114844\pi\) | |||||||
\(822\) | − | 955448.i | − | 1.41405i | ||||||
\(823\) | 448500.i | 0.662160i | 0.943603 | + | 0.331080i | \(0.107413\pi\) | ||||
−0.943603 | + | 0.331080i | \(0.892587\pi\) | |||||||
\(824\) | −1.63353e6 | −2.40587 | ||||||||
\(825\) | 638959.i | 0.938782i | ||||||||
\(826\) | −818261. | + | 455120.i | −1.19931 | + | 0.667061i | ||||
\(827\) | 794086. | 1.16107 | 0.580533 | − | 0.814237i | \(-0.302844\pi\) | ||||
0.580533 | + | 0.814237i | \(0.302844\pi\) | |||||||
\(828\) | 991166.i | 1.44573i | ||||||||
\(829\) | 351649. | 0.511682 | 0.255841 | − | 0.966719i | \(-0.417648\pi\) | ||||
0.255841 | + | 0.966719i | \(0.417648\pi\) | |||||||
\(830\) | 1.46811e6 | 2.13110 | ||||||||
\(831\) | 143238. | 0.207422 | ||||||||
\(832\) | 211268.i | 0.305202i | ||||||||
\(833\) | 413028. | 0.595237 | ||||||||
\(834\) | − | 119874.i | − | 0.172343i | ||||||
\(835\) | 16866.8 | 0.0241914 | ||||||||
\(836\) | − | 4.07473e6i | − | 5.83024i | ||||||
\(837\) | − | 48685.4i | − | 0.0694940i | ||||||
\(838\) | −766441. | −1.09142 | ||||||||
\(839\) | 249257.i | 0.354098i | 0.984202 | + | 0.177049i | \(0.0566551\pi\) | ||||
−0.984202 | + | 0.177049i | \(0.943345\pi\) | |||||||
\(840\) | − | 1.41759e6i | − | 2.00905i | ||||||
\(841\) | −512911. | −0.725186 | ||||||||
\(842\) | 781009. | 1.10162 | ||||||||
\(843\) | −607892. | −0.855404 | ||||||||
\(844\) | − | 2.08626e6i | − | 2.92876i | ||||||
\(845\) | −1.07899e6 | −1.51113 | ||||||||
\(846\) | 265960. | 0.371599 | ||||||||
\(847\) | 253431. | 0.353259 | ||||||||
\(848\) | −966090. | −1.34346 | ||||||||
\(849\) | 647854.i | 0.898798i | ||||||||
\(850\) | 2.25554e6i | 3.12185i | ||||||||
\(851\) | 838849. | 1.15831 | ||||||||
\(852\) | −308865. | −0.425490 | ||||||||
\(853\) | −526565. | −0.723692 | −0.361846 | − | 0.932238i | \(-0.617853\pi\) | ||||
−0.361846 | + | 0.932238i | \(0.617853\pi\) | |||||||
\(854\) | 1.60870e6 | 2.20577 | ||||||||
\(855\) | 667251. | 0.912761 | ||||||||
\(856\) | 2.25717e6i | 3.08046i | ||||||||
\(857\) | 972800.i | 1.32453i | 0.749269 | + | 0.662265i | \(0.230405\pi\) | ||||
−0.749269 | + | 0.662265i | \(0.769595\pi\) | |||||||
\(858\) | − | 100476.i | − | 0.136486i | ||||||
\(859\) | − | 1.07599e6i | − | 1.45822i | −0.684396 | − | 0.729110i | \(-0.739934\pi\) | ||
0.684396 | − | 0.729110i | \(-0.260066\pi\) | |||||||
\(860\) | − | 4.61132e6i | − | 6.23488i | ||||||
\(861\) | 508300. | 0.685668 | ||||||||
\(862\) | −1.98576e6 | −2.67247 | ||||||||
\(863\) | − | 119816.i | − | 0.160876i | −0.996760 | − | 0.0804381i | \(-0.974368\pi\) | ||
0.996760 | − | 0.0804381i | \(-0.0256320\pi\) | |||||||
\(864\) | 483320.i | 0.647451i | ||||||||
\(865\) | 112499.i | 0.150355i | ||||||||
\(866\) | 2.54141e6i | 3.38875i | ||||||||
\(867\) | −218229. | −0.290319 | ||||||||
\(868\) | 519226.i | 0.689156i | ||||||||
\(869\) | 1.23549e6i | 1.63606i | ||||||||
\(870\) | − | 669197.i | − | 0.884128i | ||||||
\(871\) | 57299.1 | 0.0755286 | ||||||||
\(872\) | 1.58817e6 | 2.08864 | ||||||||
\(873\) | 379396.i | 0.497811i | ||||||||
\(874\) | 4.27282e6 | 5.59360 | ||||||||
\(875\) | 277482. | 0.362426 | ||||||||
\(876\) | − | 364957.i | − | 0.475591i | ||||||
\(877\) | −1.46716e6 | −1.90756 | −0.953778 | − | 0.300512i | \(-0.902843\pi\) | ||||
−0.953778 | + | 0.300512i | \(0.902843\pi\) | |||||||
\(878\) | − | 542334.i | − | 0.703522i | ||||||
\(879\) | 608291. | 0.787289 | ||||||||
\(880\) | 4.93868e6i | 6.37742i | ||||||||
\(881\) | − | 220168.i | − | 0.283663i | −0.989891 | − | 0.141831i | \(-0.954701\pi\) | ||
0.989891 | − | 0.141831i | \(-0.0452991\pi\) | |||||||
\(882\) | 240900.i | 0.309671i | ||||||||
\(883\) | 1.11202e6 | 1.42624 | 0.713119 | − | 0.701044i | \(-0.247282\pi\) | ||||
0.713119 | + | 0.701044i | \(0.247282\pi\) | |||||||
\(884\) | − | 257797.i | − | 0.329893i | ||||||
\(885\) | 335581. | + | 603342.i | 0.428461 | + | 0.770330i | ||||
\(886\) | −655073. | −0.834493 | ||||||||
\(887\) | − | 23264.8i | − | 0.0295701i | −0.999891 | − | 0.0147851i | \(-0.995294\pi\) | ||
0.999891 | − | 0.0147851i | \(-0.00470640\pi\) | |||||||
\(888\) | 1.02804e6 | 1.30372 | ||||||||
\(889\) | 657621. | 0.832094 | ||||||||
\(890\) | −1.54615e6 | −1.95197 | ||||||||
\(891\) | − | 107764.i | − | 0.135743i | ||||||
\(892\) | −4.01562e6 | −5.04688 | ||||||||
\(893\) | − | 833337.i | − | 1.04500i | ||||||
\(894\) | 413528. | 0.517404 | ||||||||
\(895\) | − | 661318.i | − | 0.825590i | ||||||
\(896\) | − | 1.38758e6i | − | 1.72839i | ||||||
\(897\) | 76580.1 | 0.0951768 | ||||||||
\(898\) | − | 535890.i | − | 0.664543i | ||||||
\(899\) | 152992.i | 0.189299i | ||||||||
\(900\) | −956192. | −1.18048 | ||||||||
\(901\) | 391034. | 0.481687 | ||||||||
\(902\) | −3.14894e6 | −3.87036 | ||||||||
\(903\) | − | 518241.i | − | 0.635560i | ||||||
\(904\) | −636695. | −0.779102 | ||||||||
\(905\) | 354070. | 0.432307 | ||||||||
\(906\) | 1.40937e6 | 1.71699 | ||||||||
\(907\) | −1.05698e6 | −1.28485 | −0.642425 | − | 0.766348i | \(-0.722072\pi\) | ||||
−0.642425 | + | 0.766348i | \(0.722072\pi\) | |||||||
\(908\) | 3.12899e6i | 3.79518i | ||||||||
\(909\) | 16837.9i | 0.0203779i | ||||||||
\(910\) | −175474. | −0.211899 | ||||||||
\(911\) | 673892. | 0.811995 | 0.405997 | − | 0.913874i | \(-0.366924\pi\) | ||||
0.405997 | + | 0.913874i | \(0.366924\pi\) | |||||||
\(912\) | 2.94481e6 | 3.54053 | ||||||||
\(913\) | −742930. | −0.891264 | ||||||||
\(914\) | −747759. | −0.895095 | ||||||||
\(915\) | − | 1.18617e6i | − | 1.41679i | ||||||
\(916\) | 3.03412e6i | 3.61611i | ||||||||
\(917\) | 436117.i | 0.518638i | ||||||||
\(918\) | − | 380408.i | − | 0.451403i | ||||||
\(919\) | 1.40839e6i | 1.66760i | 0.552070 | + | 0.833798i | \(0.313838\pi\) | ||||
−0.552070 | + | 0.833798i | \(0.686162\pi\) | |||||||
\(920\) | −6.69340e6 | −7.90808 | ||||||||
\(921\) | 387562. | 0.456901 | ||||||||
\(922\) | − | 1.14211e6i | − | 1.34353i | ||||||
\(923\) | 23863.7i | 0.0280114i | ||||||||
\(924\) | 1.14929e6i | 1.34613i | ||||||||
\(925\) | 809250.i | 0.945800i | ||||||||
\(926\) | 2.67939e6 | 3.12474 | ||||||||
\(927\) | 216869.i | 0.252371i | ||||||||
\(928\) | − | 1.51881e6i | − | 1.76363i | ||||||
\(929\) | − | 1.48700e6i | − | 1.72298i | −0.507773 | − | 0.861491i | \(-0.669531\pi\) | ||
0.507773 | − | 0.861491i | \(-0.330469\pi\) | |||||||
\(930\) | 526734. | 0.609012 | ||||||||
\(931\) | 754819. | 0.870850 | ||||||||
\(932\) | 922789.i | 1.06236i | ||||||||
\(933\) | −854972. | −0.982174 | ||||||||
\(934\) | −2.83926e6 | −3.25471 | ||||||||
\(935\) | − | 1.99898e6i | − | 2.28657i | ||||||
\(936\) | 93851.9 | 0.107125 | ||||||||
\(937\) | 715876.i | 0.815378i | 0.913121 | + | 0.407689i | \(0.133665\pi\) | ||||
−0.913121 | + | 0.407689i | \(0.866335\pi\) | |||||||
\(938\) | −901734. | −1.02488 | ||||||||
\(939\) | − | 705579.i | − | 0.800230i | ||||||
\(940\) | 2.09144e6i | 2.36696i | ||||||||
\(941\) | − | 351558.i | − | 0.397025i | −0.980098 | − | 0.198512i | \(-0.936389\pi\) | ||
0.980098 | − | 0.198512i | \(-0.0636110\pi\) | |||||||
\(942\) | −926688. | −1.04432 | ||||||||
\(943\) | − | 2.40003e6i | − | 2.69894i | ||||||
\(944\) | 1.48104e6 | + | 2.66276e6i | 1.66197 | + | 2.98805i | ||||
\(945\) | −188201. | −0.210745 | ||||||||
\(946\) | 3.21052e6i | 3.58751i | ||||||||
\(947\) | 894274. | 0.997174 | 0.498587 | − | 0.866840i | \(-0.333852\pi\) | ||||
0.498587 | + | 0.866840i | \(0.333852\pi\) | |||||||
\(948\) | −1.84889e6 | −2.05728 | ||||||||
\(949\) | −28197.5 | −0.0313097 | ||||||||
\(950\) | 4.12205e6i | 4.56737i | ||||||||
\(951\) | 479502. | 0.530187 | ||||||||
\(952\) | 2.53230e6i | 2.79410i | ||||||||
\(953\) | −868548. | −0.956330 | −0.478165 | − | 0.878270i | \(-0.658698\pi\) | ||||
−0.478165 | + | 0.878270i | \(0.658698\pi\) | |||||||
\(954\) | 228072.i | 0.250597i | ||||||||
\(955\) | − | 561423.i | − | 0.615578i | ||||||
\(956\) | 23689.1 | 0.0259198 | ||||||||
\(957\) | 338643.i | 0.369758i | ||||||||
\(958\) | 494535.i | 0.538848i | ||||||||
\(959\) | 844393. | 0.918136 | ||||||||
\(960\) | −2.45152e6 | −2.66007 | ||||||||
\(961\) | 803099. | 0.869606 | ||||||||
\(962\) | − | 127254.i | − | 0.137506i | ||||||
\(963\) | 299664. | 0.323134 | ||||||||
\(964\) | −1.45460e6 | −1.56527 | ||||||||
\(965\) | 1.30726e6 | 1.40380 | ||||||||
\(966\) | −1.20517e6 | −1.29149 | ||||||||
\(967\) | − | 27414.2i | − | 0.0293172i | −0.999893 | − | 0.0146586i | \(-0.995334\pi\) | ||
0.999893 | − | 0.0146586i | \(-0.00466615\pi\) | |||||||
\(968\) | − | 1.46651e6i | − | 1.56507i | ||||||
\(969\) | −1.19194e6 | −1.26943 | ||||||||
\(970\) | −4.10474e6 | −4.36257 | ||||||||
\(971\) | −202062. | −0.214312 | −0.107156 | − | 0.994242i | \(-0.534174\pi\) | ||||
−0.107156 | + | 0.994242i | \(0.534174\pi\) | |||||||
\(972\) | 161267. | 0.170692 | ||||||||
\(973\) | 105941. | 0.111902 | ||||||||
\(974\) | − | 1.36100e6i | − | 1.43463i | ||||||
\(975\) | 73877.9i | 0.0777151i | ||||||||
\(976\) | − | 5.23498e6i | − | 5.49561i | ||||||
\(977\) | 231436.i | 0.242461i | 0.992624 | + | 0.121230i | \(0.0386840\pi\) | ||||
−0.992624 | + | 0.121230i | \(0.961316\pi\) | |||||||
\(978\) | − | 357775.i | − | 0.374053i | ||||||
\(979\) | 782420. | 0.816347 | ||||||||
\(980\) | −1.89438e6 | −1.97249 | ||||||||
\(981\) | − | 210848.i | − | 0.219094i | ||||||
\(982\) | 1.12013e6i | 1.16157i | ||||||||
\(983\) | 492235.i | 0.509407i | 0.967019 | + | 0.254704i | \(0.0819779\pi\) | ||||
−0.967019 | + | 0.254704i | \(0.918022\pi\) | |||||||
\(984\) | − | 2.94133e6i | − | 3.03776i | ||||||
\(985\) | −301972. | −0.311240 | ||||||||
\(986\) | 1.19542e6i | 1.22961i | ||||||||
\(987\) | 235046.i | 0.241279i | ||||||||
\(988\) | − | 471130.i | − | 0.482644i | ||||||
\(989\) | −2.44697e6 | −2.50171 | ||||||||
\(990\) | 1.16591e6 | 1.18958 | ||||||||
\(991\) | 861884.i | 0.877610i | 0.898582 | + | 0.438805i | \(0.144598\pi\) | ||||
−0.898582 | + | 0.438805i | \(0.855402\pi\) | |||||||
\(992\) | 1.19548e6 | 1.21484 | ||||||||
\(993\) | −56276.9 | −0.0570732 | ||||||||
\(994\) | − | 375551.i | − | 0.380099i | ||||||
\(995\) | 2.19297e6 | 2.21506 | ||||||||
\(996\) | − | 1.11178e6i | − | 1.12073i | ||||||
\(997\) | 740627. | 0.745091 | 0.372546 | − | 0.928014i | \(-0.378485\pi\) | ||||
0.372546 | + | 0.928014i | \(0.378485\pi\) | |||||||
\(998\) | − | 2.28061e6i | − | 2.28976i | ||||||
\(999\) | − | 136484.i | − | 0.136758i |
(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 | 177.5.c.a.58.3 | ✓ | 40 | |
3.2 | odd | 2 | 531.5.c.d.235.38 | 40 | |||
59.58 | odd | 2 | inner | 177.5.c.a.58.38 | yes | 40 | |
177.176 | even | 2 | 531.5.c.d.235.3 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.c.a.58.3 | ✓ | 40 | 1.1 | even | 1 | trivial | |
177.5.c.a.58.38 | yes | 40 | 59.58 | odd | 2 | inner | |
531.5.c.d.235.3 | 40 | 177.176 | even | 2 | |||
531.5.c.d.235.38 | 40 | 3.2 | odd | 2 |