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 | 58.26 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.5.c.a.58.15 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.33963i | 0.584908i | 0.956280 | + | 0.292454i | \(0.0944718\pi\) | ||||
−0.956280 | + | 0.292454i | \(0.905528\pi\) | |||||||
\(3\) | −5.19615 | −0.577350 | ||||||||
\(4\) | 10.5261 | 0.657883 | ||||||||
\(5\) | 30.0439 | 1.20176 | 0.600878 | − | 0.799341i | \(-0.294818\pi\) | ||||
0.600878 | + | 0.799341i | \(0.294818\pi\) | |||||||
\(6\) | − | 12.1571i | − | 0.337697i | ||||||
\(7\) | −41.7287 | −0.851607 | −0.425803 | − | 0.904816i | \(-0.640008\pi\) | ||||
−0.425803 | + | 0.904816i | \(0.640008\pi\) | |||||||
\(8\) | 62.0613i | 0.969708i | ||||||||
\(9\) | 27.0000 | 0.333333 | ||||||||
\(10\) | 70.2916i | 0.702916i | ||||||||
\(11\) | 117.370i | 0.970001i | 0.874514 | + | 0.485000i | \(0.161181\pi\) | ||||
−0.874514 | + | 0.485000i | \(0.838819\pi\) | |||||||
\(12\) | −54.6954 | −0.379829 | ||||||||
\(13\) | − | 118.348i | − | 0.700284i | −0.936697 | − | 0.350142i | \(-0.886133\pi\) | ||
0.936697 | − | 0.350142i | \(-0.113867\pi\) | |||||||
\(14\) | − | 97.6298i | − | 0.498111i | ||||||
\(15\) | −156.113 | −0.693834 | ||||||||
\(16\) | 23.2175 | 0.0906934 | ||||||||
\(17\) | 263.868 | 0.913040 | 0.456520 | − | 0.889713i | \(-0.349096\pi\) | ||||
0.456520 | + | 0.889713i | \(0.349096\pi\) | |||||||
\(18\) | 63.1700i | 0.194969i | ||||||||
\(19\) | 373.890 | 1.03571 | 0.517854 | − | 0.855469i | \(-0.326731\pi\) | ||||
0.517854 | + | 0.855469i | \(0.326731\pi\) | |||||||
\(20\) | 316.246 | 0.790615 | ||||||||
\(21\) | 216.829 | 0.491675 | ||||||||
\(22\) | −274.603 | −0.567361 | ||||||||
\(23\) | 503.177i | 0.951185i | 0.879666 | + | 0.475592i | \(0.157766\pi\) | ||||
−0.879666 | + | 0.475592i | \(0.842234\pi\) | |||||||
\(24\) | − | 322.480i | − | 0.559861i | ||||||
\(25\) | 277.635 | 0.444217 | ||||||||
\(26\) | 276.891 | 0.409601 | ||||||||
\(27\) | −140.296 | −0.192450 | ||||||||
\(28\) | −439.242 | −0.560258 | ||||||||
\(29\) | −549.815 | −0.653763 | −0.326882 | − | 0.945065i | \(-0.605998\pi\) | ||||
−0.326882 | + | 0.945065i | \(0.605998\pi\) | |||||||
\(30\) | − | 365.246i | − | 0.405829i | ||||||
\(31\) | 450.839i | 0.469135i | 0.972100 | + | 0.234568i | \(0.0753674\pi\) | ||||
−0.972100 | + | 0.234568i | \(0.924633\pi\) | |||||||
\(32\) | 1047.30i | 1.02276i | ||||||||
\(33\) | − | 609.873i | − | 0.560030i | ||||||
\(34\) | 617.355i | 0.534044i | ||||||||
\(35\) | −1253.69 | −1.02342 | ||||||||
\(36\) | 284.206 | 0.219294 | ||||||||
\(37\) | 1430.88i | 1.04520i | 0.852577 | + | 0.522601i | \(0.175038\pi\) | ||||
−0.852577 | + | 0.522601i | \(0.824962\pi\) | |||||||
\(38\) | 874.765i | 0.605793i | ||||||||
\(39\) | 614.954i | 0.404309i | ||||||||
\(40\) | 1864.56i | 1.16535i | ||||||||
\(41\) | 1441.61 | 0.857591 | 0.428796 | − | 0.903401i | \(-0.358938\pi\) | ||||
0.428796 | + | 0.903401i | \(0.358938\pi\) | |||||||
\(42\) | 507.299i | 0.287585i | ||||||||
\(43\) | 3202.06i | 1.73178i | 0.500236 | + | 0.865889i | \(0.333247\pi\) | ||||
−0.500236 | + | 0.865889i | \(0.666753\pi\) | |||||||
\(44\) | 1235.45i | 0.638147i | ||||||||
\(45\) | 811.185 | 0.400585 | ||||||||
\(46\) | −1177.25 | −0.556355 | ||||||||
\(47\) | − | 967.133i | − | 0.437815i | −0.975746 | − | 0.218907i | \(-0.929751\pi\) | ||
0.975746 | − | 0.218907i | \(-0.0702493\pi\) | |||||||
\(48\) | −120.642 | −0.0523618 | ||||||||
\(49\) | −659.713 | −0.274766 | ||||||||
\(50\) | 649.564i | 0.259826i | ||||||||
\(51\) | −1371.10 | −0.527144 | ||||||||
\(52\) | − | 1245.75i | − | 0.460705i | ||||||
\(53\) | 1662.12 | 0.591713 | 0.295856 | − | 0.955232i | \(-0.404395\pi\) | ||||
0.295856 | + | 0.955232i | \(0.404395\pi\) | |||||||
\(54\) | − | 328.241i | − | 0.112566i | ||||||
\(55\) | 3526.26i | 1.16570i | ||||||||
\(56\) | − | 2589.74i | − | 0.825810i | ||||||
\(57\) | −1942.79 | −0.597966 | ||||||||
\(58\) | − | 1286.36i | − | 0.382391i | ||||||
\(59\) | −34.3306 | − | 3480.83i | −0.00986228 | − | 0.999951i | ||||
\(60\) | −1643.26 | −0.456462 | ||||||||
\(61\) | − | 1712.94i | − | 0.460343i | −0.973150 | − | 0.230172i | \(-0.926071\pi\) | ||
0.973150 | − | 0.230172i | \(-0.0739288\pi\) | |||||||
\(62\) | −1054.80 | −0.274401 | ||||||||
\(63\) | −1126.68 | −0.283869 | ||||||||
\(64\) | −2078.82 | −0.507524 | ||||||||
\(65\) | − | 3555.63i | − | 0.841570i | ||||||
\(66\) | 1426.88 | 0.327566 | ||||||||
\(67\) | 5062.54i | 1.12777i | 0.825854 | + | 0.563883i | \(0.190693\pi\) | ||||
−0.825854 | + | 0.563883i | \(0.809307\pi\) | |||||||
\(68\) | 2777.51 | 0.600673 | ||||||||
\(69\) | − | 2614.58i | − | 0.549167i | ||||||
\(70\) | − | 2933.18i | − | 0.598608i | ||||||
\(71\) | 6150.31 | 1.22006 | 0.610028 | − | 0.792380i | \(-0.291158\pi\) | ||||
0.610028 | + | 0.792380i | \(0.291158\pi\) | |||||||
\(72\) | 1675.66i | 0.323236i | ||||||||
\(73\) | − | 4170.58i | − | 0.782619i | −0.920259 | − | 0.391309i | \(-0.872022\pi\) | ||
0.920259 | − | 0.391309i | \(-0.127978\pi\) | |||||||
\(74\) | −3347.74 | −0.611347 | ||||||||
\(75\) | −1442.64 | −0.256469 | ||||||||
\(76\) | 3935.62 | 0.681374 | ||||||||
\(77\) | − | 4897.71i | − | 0.826059i | ||||||
\(78\) | −1438.77 | −0.236483 | ||||||||
\(79\) | −5990.22 | −0.959818 | −0.479909 | − | 0.877318i | \(-0.659330\pi\) | ||||
−0.479909 | + | 0.877318i | \(0.659330\pi\) | |||||||
\(80\) | 697.544 | 0.108991 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | 3372.84i | 0.501612i | ||||||||
\(83\) | 2937.78i | 0.426445i | 0.977004 | + | 0.213222i | \(0.0683959\pi\) | ||||
−0.977004 | + | 0.213222i | \(0.931604\pi\) | |||||||
\(84\) | 2282.37 | 0.323465 | ||||||||
\(85\) | 7927.64 | 1.09725 | ||||||||
\(86\) | −7491.63 | −1.01293 | ||||||||
\(87\) | 2856.92 | 0.377450 | ||||||||
\(88\) | −7284.15 | −0.940618 | ||||||||
\(89\) | 3877.47i | 0.489518i | 0.969584 | + | 0.244759i | \(0.0787088\pi\) | ||||
−0.969584 | + | 0.244759i | \(0.921291\pi\) | |||||||
\(90\) | 1897.87i | 0.234305i | ||||||||
\(91\) | 4938.51i | 0.596367i | ||||||||
\(92\) | 5296.50i | 0.625769i | ||||||||
\(93\) | − | 2342.63i | − | 0.270855i | ||||||
\(94\) | 2262.73 | 0.256081 | ||||||||
\(95\) | 11233.1 | 1.24467 | ||||||||
\(96\) | − | 5441.94i | − | 0.590488i | ||||||
\(97\) | 2340.59i | 0.248760i | 0.992235 | + | 0.124380i | \(0.0396942\pi\) | ||||
−0.992235 | + | 0.124380i | \(0.960306\pi\) | |||||||
\(98\) | − | 1543.48i | − | 0.160713i | ||||||
\(99\) | 3168.99i | 0.323334i | ||||||||
\(100\) | 2922.43 | 0.292243 | ||||||||
\(101\) | − | 18031.3i | − | 1.76761i | −0.467860 | − | 0.883803i | \(-0.654975\pi\) | ||
0.467860 | − | 0.883803i | \(-0.345025\pi\) | |||||||
\(102\) | − | 3207.87i | − | 0.308330i | ||||||
\(103\) | − | 12277.9i | − | 1.15731i | −0.815572 | − | 0.578656i | \(-0.803577\pi\) | ||
0.815572 | − | 0.578656i | \(-0.196423\pi\) | |||||||
\(104\) | 7344.83 | 0.679071 | ||||||||
\(105\) | 6514.38 | 0.590874 | ||||||||
\(106\) | 3888.75i | 0.346097i | ||||||||
\(107\) | 7815.43 | 0.682630 | 0.341315 | − | 0.939949i | \(-0.389128\pi\) | ||||
0.341315 | + | 0.939949i | \(0.389128\pi\) | |||||||
\(108\) | −1476.78 | −0.126610 | ||||||||
\(109\) | − | 4707.99i | − | 0.396262i | −0.980176 | − | 0.198131i | \(-0.936513\pi\) | ||
0.980176 | − | 0.198131i | \(-0.0634872\pi\) | |||||||
\(110\) | −8250.13 | −0.681829 | ||||||||
\(111\) | − | 7435.08i | − | 0.603448i | ||||||
\(112\) | −968.837 | −0.0772351 | ||||||||
\(113\) | − | 8859.89i | − | 0.693860i | −0.937891 | − | 0.346930i | \(-0.887224\pi\) | ||
0.937891 | − | 0.346930i | \(-0.112776\pi\) | |||||||
\(114\) | − | 4545.41i | − | 0.349755i | ||||||
\(115\) | 15117.4i | 1.14309i | ||||||||
\(116\) | −5787.42 | −0.430100 | ||||||||
\(117\) | − | 3195.40i | − | 0.233428i | ||||||
\(118\) | 8143.86 | − | 80.3209i | 0.584879 | − | 0.00576852i | ||||
\(119\) | −11010.9 | −0.777551 | ||||||||
\(120\) | − | 9688.56i | − | 0.672817i | ||||||
\(121\) | 865.256 | 0.0590981 | ||||||||
\(122\) | 4007.64 | 0.269258 | ||||||||
\(123\) | −7490.83 | −0.495131 | ||||||||
\(124\) | 4745.59i | 0.308636i | ||||||||
\(125\) | −10436.2 | −0.667916 | ||||||||
\(126\) | − | 2636.00i | − | 0.166037i | ||||||
\(127\) | −7759.81 | −0.481109 | −0.240554 | − | 0.970636i | \(-0.577329\pi\) | ||||
−0.240554 | + | 0.970636i | \(0.577329\pi\) | |||||||
\(128\) | 11893.2i | 0.725901i | ||||||||
\(129\) | − | 16638.4i | − | 0.999843i | ||||||
\(130\) | 8318.87 | 0.492241 | ||||||||
\(131\) | − | 26570.9i | − | 1.54833i | −0.632984 | − | 0.774165i | \(-0.718170\pi\) | ||
0.632984 | − | 0.774165i | \(-0.281830\pi\) | |||||||
\(132\) | − | 6419.60i | − | 0.368435i | ||||||
\(133\) | −15602.0 | −0.882015 | ||||||||
\(134\) | −11844.5 | −0.659639 | ||||||||
\(135\) | −4215.04 | −0.231278 | ||||||||
\(136\) | 16376.0i | 0.885382i | ||||||||
\(137\) | −6370.46 | −0.339414 | −0.169707 | − | 0.985495i | \(-0.554282\pi\) | ||||
−0.169707 | + | 0.985495i | \(0.554282\pi\) | |||||||
\(138\) | 6117.16 | 0.321212 | ||||||||
\(139\) | 26487.6 | 1.37092 | 0.685461 | − | 0.728109i | \(-0.259601\pi\) | ||||
0.685461 | + | 0.728109i | \(0.259601\pi\) | |||||||
\(140\) | −13196.5 | −0.673293 | ||||||||
\(141\) | 5025.37i | 0.252773i | ||||||||
\(142\) | 14389.4i | 0.713620i | ||||||||
\(143\) | 13890.5 | 0.679276 | ||||||||
\(144\) | 626.873 | 0.0302311 | ||||||||
\(145\) | −16518.6 | −0.785664 | ||||||||
\(146\) | 9757.60 | 0.457760 | ||||||||
\(147\) | 3427.97 | 0.158636 | ||||||||
\(148\) | 15061.7i | 0.687621i | ||||||||
\(149\) | − | 37732.0i | − | 1.69956i | −0.527136 | − | 0.849781i | \(-0.676734\pi\) | ||
0.527136 | − | 0.849781i | \(-0.323266\pi\) | |||||||
\(150\) | − | 3375.24i | − | 0.150010i | ||||||
\(151\) | 19425.6i | 0.851961i | 0.904732 | + | 0.425981i | \(0.140071\pi\) | ||||
−0.904732 | + | 0.425981i | \(0.859929\pi\) | |||||||
\(152\) | 23204.1i | 1.00433i | ||||||||
\(153\) | 7124.45 | 0.304347 | ||||||||
\(154\) | 11458.8 | 0.483168 | ||||||||
\(155\) | 13545.0i | 0.563786i | ||||||||
\(156\) | 6473.09i | 0.265988i | ||||||||
\(157\) | − | 40542.8i | − | 1.64480i | −0.568907 | − | 0.822402i | \(-0.692634\pi\) | ||
0.568907 | − | 0.822402i | \(-0.307366\pi\) | |||||||
\(158\) | − | 14014.9i | − | 0.561405i | ||||||
\(159\) | −8636.63 | −0.341626 | ||||||||
\(160\) | 31465.0i | 1.22910i | ||||||||
\(161\) | − | 20996.9i | − | 0.810036i | ||||||
\(162\) | 1705.59i | 0.0649897i | ||||||||
\(163\) | −6024.65 | −0.226755 | −0.113377 | − | 0.993552i | \(-0.536167\pi\) | ||||
−0.113377 | + | 0.993552i | \(0.536167\pi\) | |||||||
\(164\) | 15174.6 | 0.564195 | ||||||||
\(165\) | − | 18323.0i | − | 0.673020i | ||||||
\(166\) | −6873.32 | −0.249431 | ||||||||
\(167\) | −38348.4 | −1.37504 | −0.687519 | − | 0.726167i | \(-0.741300\pi\) | ||||
−0.687519 | + | 0.726167i | \(0.741300\pi\) | |||||||
\(168\) | 13456.7i | 0.476782i | ||||||||
\(169\) | 14554.8 | 0.509602 | ||||||||
\(170\) | 18547.7i | 0.641790i | ||||||||
\(171\) | 10095.0 | 0.345236 | ||||||||
\(172\) | 33705.3i | 1.13931i | ||||||||
\(173\) | 6642.40i | 0.221938i | 0.993824 | + | 0.110969i | \(0.0353955\pi\) | ||||
−0.993824 | + | 0.110969i | \(0.964604\pi\) | |||||||
\(174\) | 6684.14i | 0.220774i | ||||||||
\(175\) | −11585.4 | −0.378298 | ||||||||
\(176\) | 2725.04i | 0.0879727i | ||||||||
\(177\) | 178.387 | + | 18086.9i | 0.00569399 | + | 0.577322i | ||||
\(178\) | −9071.85 | −0.286323 | ||||||||
\(179\) | − | 15505.0i | − | 0.483910i | −0.970287 | − | 0.241955i | \(-0.922211\pi\) | ||
0.970287 | − | 0.241955i | \(-0.0777887\pi\) | |||||||
\(180\) | 8538.64 | 0.263538 | ||||||||
\(181\) | −7207.84 | −0.220013 | −0.110006 | − | 0.993931i | \(-0.535087\pi\) | ||||
−0.110006 | + | 0.993931i | \(0.535087\pi\) | |||||||
\(182\) | −11554.3 | −0.348819 | ||||||||
\(183\) | 8900.68i | 0.265779i | ||||||||
\(184\) | −31227.8 | −0.922372 | ||||||||
\(185\) | 42989.3i | 1.25608i | ||||||||
\(186\) | 5480.88 | 0.158425 | ||||||||
\(187\) | 30970.3i | 0.885649i | ||||||||
\(188\) | − | 10180.2i | − | 0.288031i | ||||||
\(189\) | 5854.38 | 0.163892 | ||||||||
\(190\) | 26281.3i | 0.728015i | ||||||||
\(191\) | − | 24422.5i | − | 0.669459i | −0.942314 | − | 0.334729i | \(-0.891355\pi\) | ||
0.942314 | − | 0.334729i | \(-0.108645\pi\) | |||||||
\(192\) | 10801.9 | 0.293019 | ||||||||
\(193\) | −42315.7 | −1.13602 | −0.568011 | − | 0.823021i | \(-0.692287\pi\) | ||||
−0.568011 | + | 0.823021i | \(0.692287\pi\) | |||||||
\(194\) | −5476.11 | −0.145502 | ||||||||
\(195\) | 18475.6i | 0.485881i | ||||||||
\(196\) | −6944.23 | −0.180764 | ||||||||
\(197\) | −3081.53 | −0.0794024 | −0.0397012 | − | 0.999212i | \(-0.512641\pi\) | ||||
−0.0397012 | + | 0.999212i | \(0.512641\pi\) | |||||||
\(198\) | −7414.27 | −0.189120 | ||||||||
\(199\) | 71081.9 | 1.79495 | 0.897476 | − | 0.441064i | \(-0.145399\pi\) | ||||
0.897476 | + | 0.441064i | \(0.145399\pi\) | |||||||
\(200\) | 17230.4i | 0.430761i | ||||||||
\(201\) | − | 26305.8i | − | 0.651116i | ||||||
\(202\) | 42186.7 | 1.03389 | ||||||||
\(203\) | 22943.1 | 0.556749 | ||||||||
\(204\) | −14432.4 | −0.346799 | ||||||||
\(205\) | 43311.6 | 1.03062 | ||||||||
\(206\) | 28725.8 | 0.676920 | ||||||||
\(207\) | 13585.8i | 0.317062i | ||||||||
\(208\) | − | 2747.74i | − | 0.0635111i | ||||||
\(209\) | 43883.5i | 1.00464i | ||||||||
\(210\) | 15241.2i | 0.345606i | ||||||||
\(211\) | − | 31417.1i | − | 0.705670i | −0.935686 | − | 0.352835i | \(-0.885218\pi\) | ||
0.935686 | − | 0.352835i | \(-0.114782\pi\) | |||||||
\(212\) | 17495.7 | 0.389278 | ||||||||
\(213\) | −31957.9 | −0.704400 | ||||||||
\(214\) | 18285.2i | 0.399275i | ||||||||
\(215\) | 96202.3i | 2.08117i | ||||||||
\(216\) | − | 8706.96i | − | 0.186620i | ||||||
\(217\) | − | 18812.9i | − | 0.399519i | ||||||
\(218\) | 11015.0 | 0.231777 | ||||||||
\(219\) | 21670.9i | 0.451845i | ||||||||
\(220\) | 37117.8i | 0.766897i | ||||||||
\(221\) | − | 31228.3i | − | 0.639387i | ||||||
\(222\) | 17395.3 | 0.352961 | ||||||||
\(223\) | −55061.3 | −1.10723 | −0.553613 | − | 0.832774i | \(-0.686751\pi\) | ||||
−0.553613 | + | 0.832774i | \(0.686751\pi\) | |||||||
\(224\) | − | 43702.6i | − | 0.870986i | ||||||
\(225\) | 7496.16 | 0.148072 | ||||||||
\(226\) | 20728.9 | 0.405844 | ||||||||
\(227\) | 23259.5i | 0.451386i | 0.974198 | + | 0.225693i | \(0.0724646\pi\) | ||||
−0.974198 | + | 0.225693i | \(0.927535\pi\) | |||||||
\(228\) | −20450.1 | −0.393392 | ||||||||
\(229\) | − | 16859.6i | − | 0.321496i | −0.986995 | − | 0.160748i | \(-0.948609\pi\) | ||
0.986995 | − | 0.160748i | \(-0.0513907\pi\) | |||||||
\(230\) | −35369.1 | −0.668603 | ||||||||
\(231\) | 25449.2i | 0.476926i | ||||||||
\(232\) | − | 34122.3i | − | 0.633960i | ||||||
\(233\) | 56400.3i | 1.03889i | 0.854504 | + | 0.519445i | \(0.173861\pi\) | ||||
−0.854504 | + | 0.519445i | \(0.826139\pi\) | |||||||
\(234\) | 7476.04 | 0.136534 | ||||||||
\(235\) | − | 29056.4i | − | 0.526147i | ||||||
\(236\) | −361.368 | − | 36639.7i | −0.00648823 | − | 0.657851i | ||||
\(237\) | 31126.1 | 0.554151 | ||||||||
\(238\) | − | 25761.4i | − | 0.454795i | ||||||
\(239\) | 17569.0 | 0.307575 | 0.153788 | − | 0.988104i | \(-0.450853\pi\) | ||||
0.153788 | + | 0.988104i | \(0.450853\pi\) | |||||||
\(240\) | −3624.55 | −0.0629261 | ||||||||
\(241\) | 97271.4 | 1.67475 | 0.837377 | − | 0.546625i | \(-0.184088\pi\) | ||||
0.837377 | + | 0.546625i | \(0.184088\pi\) | |||||||
\(242\) | 2024.38i | 0.0345670i | ||||||||
\(243\) | −3788.00 | −0.0641500 | ||||||||
\(244\) | − | 18030.6i | − | 0.302852i | ||||||
\(245\) | −19820.3 | −0.330202 | ||||||||
\(246\) | − | 17525.8i | − | 0.289606i | ||||||
\(247\) | − | 44249.2i | − | 0.725289i | ||||||
\(248\) | −27979.7 | −0.454924 | ||||||||
\(249\) | − | 15265.1i | − | 0.246208i | ||||||
\(250\) | − | 24416.8i | − | 0.390669i | ||||||
\(251\) | −41339.8 | −0.656177 | −0.328089 | − | 0.944647i | \(-0.606404\pi\) | ||||
−0.328089 | + | 0.944647i | \(0.606404\pi\) | |||||||
\(252\) | −11859.5 | −0.186753 | ||||||||
\(253\) | −59057.9 | −0.922650 | ||||||||
\(254\) | − | 18155.1i | − | 0.281404i | ||||||
\(255\) | −41193.2 | −0.633498 | ||||||||
\(256\) | −61086.7 | −0.932109 | ||||||||
\(257\) | −14776.8 | −0.223725 | −0.111863 | − | 0.993724i | \(-0.535682\pi\) | ||||
−0.111863 | + | 0.993724i | \(0.535682\pi\) | |||||||
\(258\) | 38927.7 | 0.584816 | ||||||||
\(259\) | − | 59708.9i | − | 0.890102i | ||||||
\(260\) | − | 37427.1i | − | 0.553655i | ||||||
\(261\) | −14845.0 | −0.217921 | ||||||||
\(262\) | 62166.1 | 0.905630 | ||||||||
\(263\) | 46511.4 | 0.672431 | 0.336216 | − | 0.941785i | \(-0.390853\pi\) | ||||
0.336216 | + | 0.941785i | \(0.390853\pi\) | |||||||
\(264\) | 37849.5 | 0.543066 | ||||||||
\(265\) | 49936.6 | 0.711094 | ||||||||
\(266\) | − | 36502.8i | − | 0.515897i | ||||||
\(267\) | − | 20147.9i | − | 0.282623i | ||||||
\(268\) | 53289.0i | 0.741939i | ||||||||
\(269\) | 52167.3i | 0.720931i | 0.932773 | + | 0.360465i | \(0.117382\pi\) | ||||
−0.932773 | + | 0.360465i | \(0.882618\pi\) | |||||||
\(270\) | − | 9861.64i | − | 0.135276i | ||||||
\(271\) | −118272. | −1.61044 | −0.805220 | − | 0.592977i | \(-0.797953\pi\) | ||||
−0.805220 | + | 0.592977i | \(0.797953\pi\) | |||||||
\(272\) | 6126.37 | 0.0828066 | ||||||||
\(273\) | − | 25661.3i | − | 0.344312i | ||||||
\(274\) | − | 14904.5i | − | 0.198526i | ||||||
\(275\) | 32586.1i | 0.430891i | ||||||||
\(276\) | − | 27521.4i | − | 0.361288i | ||||||
\(277\) | −116769. | −1.52184 | −0.760919 | − | 0.648847i | \(-0.775252\pi\) | ||||
−0.760919 | + | 0.648847i | \(0.775252\pi\) | |||||||
\(278\) | 61971.2i | 0.801863i | ||||||||
\(279\) | 12172.6i | 0.156378i | ||||||||
\(280\) | − | 77805.9i | − | 0.992422i | ||||||
\(281\) | 148473. | 1.88034 | 0.940169 | − | 0.340710i | \(-0.110667\pi\) | ||||
0.940169 | + | 0.340710i | \(0.110667\pi\) | |||||||
\(282\) | −11757.5 | −0.147849 | ||||||||
\(283\) | − | 30655.6i | − | 0.382769i | −0.981515 | − | 0.191385i | \(-0.938702\pi\) | ||
0.981515 | − | 0.191385i | \(-0.0612978\pi\) | |||||||
\(284\) | 64738.9 | 0.802655 | ||||||||
\(285\) | −58369.0 | −0.718609 | ||||||||
\(286\) | 32498.7i | 0.397314i | ||||||||
\(287\) | −60156.6 | −0.730331 | ||||||||
\(288\) | 28277.1i | 0.340919i | ||||||||
\(289\) | −13894.4 | −0.166359 | ||||||||
\(290\) | − | 38647.4i | − | 0.459541i | ||||||
\(291\) | − | 12162.0i | − | 0.143622i | ||||||
\(292\) | − | 43900.0i | − | 0.514872i | ||||||
\(293\) | 77404.6 | 0.901636 | 0.450818 | − | 0.892616i | \(-0.351132\pi\) | ||||
0.450818 | + | 0.892616i | \(0.351132\pi\) | |||||||
\(294\) | 8020.18i | 0.0927875i | ||||||||
\(295\) | −1031.42 | − | 104578.i | −0.0118520 | − | 1.20170i | ||||
\(296\) | −88802.5 | −1.01354 | ||||||||
\(297\) | − | 16466.6i | − | 0.186677i | ||||||
\(298\) | 88278.8 | 0.994086 | ||||||||
\(299\) | 59550.0 | 0.666100 | ||||||||
\(300\) | −15185.4 | −0.168726 | ||||||||
\(301\) | − | 133618.i | − | 1.47479i | ||||||
\(302\) | −45448.7 | −0.498319 | ||||||||
\(303\) | 93693.6i | 1.02053i | ||||||||
\(304\) | 8680.80 | 0.0939318 | ||||||||
\(305\) | − | 51463.3i | − | 0.553220i | ||||||
\(306\) | 16668.6i | 0.178015i | ||||||||
\(307\) | −124048. | −1.31617 | −0.658085 | − | 0.752943i | \(-0.728633\pi\) | ||||
−0.658085 | + | 0.752943i | \(0.728633\pi\) | |||||||
\(308\) | − | 51553.9i | − | 0.543451i | ||||||
\(309\) | 63798.0i | 0.668174i | ||||||||
\(310\) | −31690.2 | −0.329762 | ||||||||
\(311\) | −3890.57 | −0.0402247 | −0.0201123 | − | 0.999798i | \(-0.506402\pi\) | ||||
−0.0201123 | + | 0.999798i | \(0.506402\pi\) | |||||||
\(312\) | −38164.9 | −0.392062 | ||||||||
\(313\) | 18870.8i | 0.192620i | 0.995351 | + | 0.0963099i | \(0.0307040\pi\) | ||||
−0.995351 | + | 0.0963099i | \(0.969296\pi\) | |||||||
\(314\) | 94855.1 | 0.962058 | ||||||||
\(315\) | −33849.7 | −0.341141 | ||||||||
\(316\) | −63053.9 | −0.631448 | ||||||||
\(317\) | −31502.4 | −0.313491 | −0.156745 | − | 0.987639i | \(-0.550100\pi\) | ||||
−0.156745 | + | 0.987639i | \(0.550100\pi\) | |||||||
\(318\) | − | 20206.5i | − | 0.199819i | ||||||
\(319\) | − | 64531.9i | − | 0.634151i | ||||||
\(320\) | −62455.8 | −0.609920 | ||||||||
\(321\) | −40610.2 | −0.394117 | ||||||||
\(322\) | 49125.1 | 0.473796 | ||||||||
\(323\) | 98657.8 | 0.945642 | ||||||||
\(324\) | 7673.55 | 0.0730981 | ||||||||
\(325\) | − | 32857.6i | − | 0.311078i | ||||||
\(326\) | − | 14095.4i | − | 0.132631i | ||||||
\(327\) | 24463.4i | 0.228782i | ||||||||
\(328\) | 89468.3i | 0.831614i | ||||||||
\(329\) | 40357.2i | 0.372846i | ||||||||
\(330\) | 42868.9 | 0.393654 | ||||||||
\(331\) | 4457.32 | 0.0406834 | 0.0203417 | − | 0.999793i | \(-0.493525\pi\) | ||||
0.0203417 | + | 0.999793i | \(0.493525\pi\) | |||||||
\(332\) | 30923.4i | 0.280551i | ||||||||
\(333\) | 38633.8i | 0.348401i | ||||||||
\(334\) | − | 89721.1i | − | 0.804270i | ||||||
\(335\) | 152099.i | 1.35530i | ||||||||
\(336\) | 5034.22 | 0.0445917 | ||||||||
\(337\) | − | 46555.0i | − | 0.409927i | −0.978770 | − | 0.204964i | \(-0.934292\pi\) | ||
0.978770 | − | 0.204964i | \(-0.0657076\pi\) | |||||||
\(338\) | 34052.7i | 0.298070i | ||||||||
\(339\) | 46037.4i | 0.400600i | ||||||||
\(340\) | 83447.3 | 0.721863 | ||||||||
\(341\) | −52915.0 | −0.455061 | ||||||||
\(342\) | 23618.7i | 0.201931i | ||||||||
\(343\) | 127720. | 1.08560 | ||||||||
\(344\) | −198724. | −1.67932 | ||||||||
\(345\) | − | 78552.3i | − | 0.659964i | ||||||
\(346\) | −15540.8 | −0.129814 | ||||||||
\(347\) | − | 173485.i | − | 1.44080i | −0.693560 | − | 0.720399i | \(-0.743959\pi\) | ||
0.693560 | − | 0.720399i | \(-0.256041\pi\) | |||||||
\(348\) | 30072.3 | 0.248318 | ||||||||
\(349\) | 160924.i | 1.32120i | 0.750737 | + | 0.660601i | \(0.229699\pi\) | ||||
−0.750737 | + | 0.660601i | \(0.770301\pi\) | |||||||
\(350\) | − | 27105.5i | − | 0.221269i | ||||||
\(351\) | 16603.8i | 0.134770i | ||||||||
\(352\) | −122922. | −0.992074 | ||||||||
\(353\) | − | 109289.i | − | 0.877055i | −0.898718 | − | 0.438527i | \(-0.855500\pi\) | ||
0.898718 | − | 0.438527i | \(-0.144500\pi\) | |||||||
\(354\) | −42316.7 | + | 417.359i | −0.337680 | + | 0.00333046i | ||||
\(355\) | 184779. | 1.46621 | ||||||||
\(356\) | 40814.8i | 0.322045i | ||||||||
\(357\) | 57214.3 | 0.448919 | ||||||||
\(358\) | 36275.9 | 0.283043 | ||||||||
\(359\) | 127764. | 0.991336 | 0.495668 | − | 0.868512i | \(-0.334923\pi\) | ||||
0.495668 | + | 0.868512i | \(0.334923\pi\) | |||||||
\(360\) | 50343.2i | 0.388451i | ||||||||
\(361\) | 9472.92 | 0.0726891 | ||||||||
\(362\) | − | 16863.7i | − | 0.128687i | ||||||
\(363\) | −4496.00 | −0.0341203 | ||||||||
\(364\) | 51983.4i | 0.392339i | ||||||||
\(365\) | − | 125300.i | − | 0.940516i | ||||||
\(366\) | −20824.3 | −0.155456 | ||||||||
\(367\) | − | 131014.i | − | 0.972718i | −0.873759 | − | 0.486359i | \(-0.838325\pi\) | ||
0.873759 | − | 0.486359i | \(-0.161675\pi\) | |||||||
\(368\) | 11682.5i | 0.0862662i | ||||||||
\(369\) | 38923.5 | 0.285864 | ||||||||
\(370\) | −100579. | −0.734690 | ||||||||
\(371\) | −69358.2 | −0.503907 | ||||||||
\(372\) | − | 24658.8i | − | 0.178191i | ||||||
\(373\) | 162049. | 1.16474 | 0.582369 | − | 0.812924i | \(-0.302126\pi\) | ||||
0.582369 | + | 0.812924i | \(0.302126\pi\) | |||||||
\(374\) | −72459.0 | −0.518023 | ||||||||
\(375\) | 54228.0 | 0.385621 | ||||||||
\(376\) | 60021.6 | 0.424553 | ||||||||
\(377\) | 65069.5i | 0.457820i | ||||||||
\(378\) | 13697.1i | 0.0958615i | ||||||||
\(379\) | −170314. | −1.18569 | −0.592847 | − | 0.805315i | \(-0.701996\pi\) | ||||
−0.592847 | + | 0.805315i | \(0.701996\pi\) | |||||||
\(380\) | 118241. | 0.818845 | ||||||||
\(381\) | 40321.1 | 0.277768 | ||||||||
\(382\) | 57139.7 | 0.391572 | ||||||||
\(383\) | 197908. | 1.34916 | 0.674582 | − | 0.738200i | \(-0.264324\pi\) | ||||
0.674582 | + | 0.738200i | \(0.264324\pi\) | |||||||
\(384\) | − | 61798.7i | − | 0.419099i | ||||||
\(385\) | − | 147146.i | − | 0.992722i | ||||||
\(386\) | − | 99003.0i | − | 0.664468i | ||||||
\(387\) | 86455.6i | 0.577259i | ||||||||
\(388\) | 24637.3i | 0.163655i | ||||||||
\(389\) | −130696. | −0.863699 | −0.431849 | − | 0.901946i | \(-0.642139\pi\) | ||||
−0.431849 | + | 0.901946i | \(0.642139\pi\) | |||||||
\(390\) | −43226.1 | −0.284195 | ||||||||
\(391\) | 132772.i | 0.868470i | ||||||||
\(392\) | − | 40942.7i | − | 0.266443i | ||||||
\(393\) | 138066.i | 0.893929i | ||||||||
\(394\) | − | 7209.64i | − | 0.0464431i | ||||||
\(395\) | −179970. | −1.15347 | ||||||||
\(396\) | 33357.2i | 0.212716i | ||||||||
\(397\) | 35127.3i | 0.222876i | 0.993771 | + | 0.111438i | \(0.0355457\pi\) | ||||
−0.993771 | + | 0.111438i | \(0.964454\pi\) | |||||||
\(398\) | 166305.i | 1.04988i | ||||||||
\(399\) | 81070.2 | 0.509232 | ||||||||
\(400\) | 6446.00 | 0.0402875 | ||||||||
\(401\) | 177132.i | 1.10156i | 0.834650 | + | 0.550780i | \(0.185670\pi\) | ||||
−0.834650 | + | 0.550780i | \(0.814330\pi\) | |||||||
\(402\) | 61545.7 | 0.380843 | ||||||||
\(403\) | 53355.9 | 0.328528 | ||||||||
\(404\) | − | 189800.i | − | 1.16288i | ||||||
\(405\) | 21902.0 | 0.133528 | ||||||||
\(406\) | 53678.3i | 0.325647i | ||||||||
\(407\) | −167943. | −1.01385 | ||||||||
\(408\) | − | 85092.3i | − | 0.511176i | ||||||
\(409\) | − | 194928.i | − | 1.16527i | −0.812733 | − | 0.582636i | \(-0.802021\pi\) | ||
0.812733 | − | 0.582636i | \(-0.197979\pi\) | |||||||
\(410\) | 101333.i | 0.602815i | ||||||||
\(411\) | 33101.9 | 0.195961 | ||||||||
\(412\) | − | 129239.i | − | 0.761376i | ||||||
\(413\) | 1432.57 | + | 145251.i | 0.00839878 | + | 0.851565i | ||||
\(414\) | −31785.7 | −0.185452 | ||||||||
\(415\) | 88262.3i | 0.512483i | ||||||||
\(416\) | 123946. | 0.716219 | ||||||||
\(417\) | −137634. | −0.791502 | ||||||||
\(418\) | −102671. | −0.587620 | ||||||||
\(419\) | 86241.5i | 0.491234i | 0.969367 | + | 0.245617i | \(0.0789906\pi\) | ||||
−0.969367 | + | 0.245617i | \(0.921009\pi\) | |||||||
\(420\) | 68571.2 | 0.388726 | ||||||||
\(421\) | − | 51752.7i | − | 0.291990i | −0.989285 | − | 0.145995i | \(-0.953362\pi\) | ||
0.989285 | − | 0.145995i | \(-0.0466384\pi\) | |||||||
\(422\) | 73504.5 | 0.412752 | ||||||||
\(423\) | − | 26112.6i | − | 0.145938i | ||||||
\(424\) | 103153.i | 0.573789i | ||||||||
\(425\) | 73259.2 | 0.405587 | ||||||||
\(426\) | − | 74769.7i | − | 0.412009i | ||||||
\(427\) | 71478.7i | 0.392031i | ||||||||
\(428\) | 82266.2 | 0.449091 | ||||||||
\(429\) | −72177.2 | −0.392180 | ||||||||
\(430\) | −225078. | −1.21729 | ||||||||
\(431\) | 184933.i | 0.995545i | 0.867308 | + | 0.497773i | \(0.165849\pi\) | ||||
−0.867308 | + | 0.497773i | \(0.834151\pi\) | |||||||
\(432\) | −3257.33 | −0.0174539 | ||||||||
\(433\) | −201660. | −1.07558 | −0.537790 | − | 0.843079i | \(-0.680741\pi\) | ||||
−0.537790 | + | 0.843079i | \(0.680741\pi\) | |||||||
\(434\) | 44015.3 | 0.233681 | ||||||||
\(435\) | 85833.1 | 0.453603 | ||||||||
\(436\) | − | 49556.9i | − | 0.260694i | ||||||
\(437\) | 188133.i | 0.985149i | ||||||||
\(438\) | −50702.0 | −0.264288 | ||||||||
\(439\) | 264954. | 1.37480 | 0.687402 | − | 0.726277i | \(-0.258751\pi\) | ||||
0.687402 | + | 0.726277i | \(0.258751\pi\) | |||||||
\(440\) | −218844. | −1.13039 | ||||||||
\(441\) | −17812.3 | −0.0915887 | ||||||||
\(442\) | 73062.7 | 0.373982 | ||||||||
\(443\) | 377029.i | 1.92117i | 0.277978 | + | 0.960587i | \(0.410336\pi\) | ||||
−0.277978 | + | 0.960587i | \(0.589664\pi\) | |||||||
\(444\) | − | 78262.7i | − | 0.396998i | ||||||
\(445\) | 116494.i | 0.588281i | ||||||||
\(446\) | − | 128823.i | − | 0.647625i | ||||||
\(447\) | 196061.i | 0.981242i | ||||||||
\(448\) | 86746.5 | 0.432211 | ||||||||
\(449\) | 108089. | 0.536155 | 0.268078 | − | 0.963397i | \(-0.413612\pi\) | ||||
0.268078 | + | 0.963397i | \(0.413612\pi\) | |||||||
\(450\) | 17538.2i | 0.0866086i | ||||||||
\(451\) | 169202.i | 0.831864i | ||||||||
\(452\) | − | 93260.4i | − | 0.456479i | ||||||
\(453\) | − | 100938.i | − | 0.491880i | ||||||
\(454\) | −54418.5 | −0.264019 | ||||||||
\(455\) | 148372.i | 0.716687i | ||||||||
\(456\) | − | 120572.i | − | 0.579852i | ||||||
\(457\) | 265515.i | 1.27132i | 0.771968 | + | 0.635662i | \(0.219273\pi\) | ||||
−0.771968 | + | 0.635662i | \(0.780727\pi\) | |||||||
\(458\) | 39445.2 | 0.188046 | ||||||||
\(459\) | −37019.7 | −0.175715 | ||||||||
\(460\) | 159128.i | 0.752021i | ||||||||
\(461\) | 216820. | 1.02023 | 0.510114 | − | 0.860107i | \(-0.329603\pi\) | ||||
0.510114 | + | 0.860107i | \(0.329603\pi\) | |||||||
\(462\) | −59541.8 | −0.278957 | ||||||||
\(463\) | 245917.i | 1.14716i | 0.819148 | + | 0.573582i | \(0.194447\pi\) | ||||
−0.819148 | + | 0.573582i | \(0.805553\pi\) | |||||||
\(464\) | −12765.3 | −0.0592920 | ||||||||
\(465\) | − | 70381.6i | − | 0.325502i | ||||||
\(466\) | −131956. | −0.607654 | ||||||||
\(467\) | − | 198167.i | − | 0.908651i | −0.890836 | − | 0.454326i | \(-0.849880\pi\) | ||
0.890836 | − | 0.454326i | \(-0.150120\pi\) | |||||||
\(468\) | − | 33635.2i | − | 0.153568i | ||||||
\(469\) | − | 211254.i | − | 0.960414i | ||||||
\(470\) | 67981.3 | 0.307747 | ||||||||
\(471\) | 210666.i | 0.949628i | ||||||||
\(472\) | 216025. | − | 2130.60i | 0.969661 | − | 0.00956353i | ||||
\(473\) | −375826. | −1.67983 | ||||||||
\(474\) | 72823.6i | 0.324127i | ||||||||
\(475\) | 103805. | 0.460078 | ||||||||
\(476\) | −115902. | −0.511538 | ||||||||
\(477\) | 44877.3 | 0.197238 | ||||||||
\(478\) | 41105.0i | 0.179903i | ||||||||
\(479\) | −419986. | −1.83048 | −0.915238 | − | 0.402915i | \(-0.867997\pi\) | ||||
−0.915238 | + | 0.402915i | \(0.867997\pi\) | |||||||
\(480\) | − | 163497.i | − | 0.709623i | ||||||
\(481\) | 169342. | 0.731939 | ||||||||
\(482\) | 227579.i | 0.979577i | ||||||||
\(483\) | 109103.i | 0.467674i | ||||||||
\(484\) | 9107.80 | 0.0388797 | ||||||||
\(485\) | 70320.3i | 0.298949i | ||||||||
\(486\) | − | 8862.51i | − | 0.0375218i | ||||||
\(487\) | −336768. | −1.41995 | −0.709975 | − | 0.704227i | \(-0.751294\pi\) | ||||
−0.709975 | + | 0.704227i | \(0.751294\pi\) | |||||||
\(488\) | 106307. | 0.446399 | ||||||||
\(489\) | 31305.0 | 0.130917 | ||||||||
\(490\) | − | 46372.3i | − | 0.193137i | ||||||
\(491\) | 279399. | 1.15894 | 0.579471 | − | 0.814993i | \(-0.303259\pi\) | ||||
0.579471 | + | 0.814993i | \(0.303259\pi\) | |||||||
\(492\) | −78849.5 | −0.325738 | ||||||||
\(493\) | −145079. | −0.596912 | ||||||||
\(494\) | 103527. | 0.424227 | ||||||||
\(495\) | 95208.9i | 0.388568i | ||||||||
\(496\) | 10467.4i | 0.0425474i | ||||||||
\(497\) | −256644. | −1.03901 | ||||||||
\(498\) | 35714.8 | 0.144009 | ||||||||
\(499\) | 23800.2 | 0.0955826 | 0.0477913 | − | 0.998857i | \(-0.484782\pi\) | ||||
0.0477913 | + | 0.998857i | \(0.484782\pi\) | |||||||
\(500\) | −109853. | −0.439410 | ||||||||
\(501\) | 199264. | 0.793878 | ||||||||
\(502\) | − | 96719.9i | − | 0.383803i | ||||||
\(503\) | − | 25529.1i | − | 0.100902i | −0.998727 | − | 0.0504509i | \(-0.983934\pi\) | ||
0.998727 | − | 0.0504509i | \(-0.0160659\pi\) | |||||||
\(504\) | − | 69923.0i | − | 0.275270i | ||||||
\(505\) | − | 541732.i | − | 2.12423i | ||||||
\(506\) | − | 138174.i | − | 0.539665i | ||||||
\(507\) | −75628.7 | −0.294219 | ||||||||
\(508\) | −81680.7 | −0.316513 | ||||||||
\(509\) | − | 6537.03i | − | 0.0252316i | −0.999920 | − | 0.0126158i | \(-0.995984\pi\) | ||
0.999920 | − | 0.0126158i | \(-0.00401584\pi\) | |||||||
\(510\) | − | 96376.9i | − | 0.370538i | ||||||
\(511\) | 174033.i | 0.666483i | ||||||||
\(512\) | 47370.3i | 0.180703i | ||||||||
\(513\) | −52455.3 | −0.199322 | ||||||||
\(514\) | − | 34572.3i | − | 0.130859i | ||||||
\(515\) | − | 368877.i | − | 1.39081i | ||||||
\(516\) | − | 175138.i | − | 0.657780i | ||||||
\(517\) | 113513. | 0.424681 | ||||||||
\(518\) | 139697. | 0.520627 | ||||||||
\(519\) | − | 34514.9i | − | 0.128136i | ||||||
\(520\) | 220667. | 0.816078 | ||||||||
\(521\) | −307294. | −1.13208 | −0.566042 | − | 0.824376i | \(-0.691526\pi\) | ||||
−0.566042 | + | 0.824376i | \(0.691526\pi\) | |||||||
\(522\) | − | 34731.8i | − | 0.127464i | ||||||
\(523\) | −92199.8 | −0.337075 | −0.168537 | − | 0.985695i | \(-0.553904\pi\) | ||||
−0.168537 | + | 0.985695i | \(0.553904\pi\) | |||||||
\(524\) | − | 279689.i | − | 1.01862i | ||||||
\(525\) | 60199.4 | 0.218410 | ||||||||
\(526\) | 108819.i | 0.393310i | ||||||||
\(527\) | 118962.i | 0.428339i | ||||||||
\(528\) | − | 14159.7i | − | 0.0507910i | ||||||
\(529\) | 26654.1 | 0.0952472 | ||||||||
\(530\) | 116833.i | 0.415924i | ||||||||
\(531\) | −926.926 | − | 93982.4i | −0.00328743 | − | 0.333317i | ||||
\(532\) | −164228. | −0.580263 | ||||||||
\(533\) | − | 170612.i | − | 0.600557i | ||||||
\(534\) | 47138.7 | 0.165308 | ||||||||
\(535\) | 234806. | 0.820354 | ||||||||
\(536\) | −314188. | −1.09360 | ||||||||
\(537\) | 80566.2i | 0.279386i | ||||||||
\(538\) | −122052. | −0.421678 | ||||||||
\(539\) | − | 77430.6i | − | 0.266523i | ||||||
\(540\) | −44368.1 | −0.152154 | ||||||||
\(541\) | − | 234603.i | − | 0.801564i | −0.916173 | − | 0.400782i | \(-0.868738\pi\) | ||
0.916173 | − | 0.400782i | \(-0.131262\pi\) | |||||||
\(542\) | − | 276713.i | − | 0.941958i | ||||||
\(543\) | 37453.0 | 0.127024 | ||||||||
\(544\) | 276350.i | 0.933816i | ||||||||
\(545\) | − | 141446.i | − | 0.476210i | ||||||
\(546\) | 60037.9 | 0.201391 | ||||||||
\(547\) | −246372. | −0.823411 | −0.411706 | − | 0.911317i | \(-0.635067\pi\) | ||||
−0.411706 | + | 0.911317i | \(0.635067\pi\) | |||||||
\(548\) | −67056.3 | −0.223295 | ||||||||
\(549\) | − | 46249.3i | − | 0.153448i | ||||||
\(550\) | −76239.4 | −0.252031 | ||||||||
\(551\) | −205570. | −0.677107 | ||||||||
\(552\) | 162265. | 0.532532 | ||||||||
\(553\) | 249964. | 0.817387 | ||||||||
\(554\) | − | 273197.i | − | 0.890134i | ||||||
\(555\) | − | 223379.i | − | 0.725197i | ||||||
\(556\) | 278812. | 0.901907 | ||||||||
\(557\) | 567300. | 1.82853 | 0.914266 | − | 0.405115i | \(-0.132769\pi\) | ||||
0.914266 | + | 0.405115i | \(0.132769\pi\) | |||||||
\(558\) | −28479.5 | −0.0914669 | ||||||||
\(559\) | 378957. | 1.21274 | ||||||||
\(560\) | −29107.6 | −0.0928177 | ||||||||
\(561\) | − | 160926.i | − | 0.511330i | ||||||
\(562\) | 347373.i | 1.09982i | ||||||||
\(563\) | − | 327570.i | − | 1.03344i | −0.856153 | − | 0.516722i | \(-0.827152\pi\) | ||
0.856153 | − | 0.516722i | \(-0.172848\pi\) | |||||||
\(564\) | 52897.7i | 0.166295i | ||||||||
\(565\) | − | 266186.i | − | 0.833850i | ||||||
\(566\) | 71722.8 | 0.223885 | ||||||||
\(567\) | −30420.2 | −0.0946230 | ||||||||
\(568\) | 381696.i | 1.18310i | ||||||||
\(569\) | − | 379301.i | − | 1.17154i | −0.810476 | − | 0.585772i | \(-0.800791\pi\) | ||
0.810476 | − | 0.585772i | \(-0.199209\pi\) | |||||||
\(570\) | − | 136562.i | − | 0.420320i | ||||||
\(571\) | 580504.i | 1.78046i | 0.455509 | + | 0.890231i | \(0.349457\pi\) | ||||
−0.455509 | + | 0.890231i | \(0.650543\pi\) | |||||||
\(572\) | 146213. | 0.446884 | ||||||||
\(573\) | 126903.i | 0.386512i | ||||||||
\(574\) | − | 140744.i | − | 0.427176i | ||||||
\(575\) | 139700.i | 0.422532i | ||||||||
\(576\) | −56128.1 | −0.169175 | ||||||||
\(577\) | −34030.7 | −0.102216 | −0.0511080 | − | 0.998693i | \(-0.516275\pi\) | ||||
−0.0511080 | + | 0.998693i | \(0.516275\pi\) | |||||||
\(578\) | − | 32507.8i | − | 0.0973044i | ||||||
\(579\) | 219879. | 0.655882 | ||||||||
\(580\) | −173877. | −0.516875 | ||||||||
\(581\) | − | 122590.i | − | 0.363163i | ||||||
\(582\) | 28454.7 | 0.0840055 | ||||||||
\(583\) | 195083.i | 0.573962i | ||||||||
\(584\) | 258831. | 0.758912 | ||||||||
\(585\) | − | 96002.1i | − | 0.280523i | ||||||
\(586\) | 181098.i | 0.527374i | ||||||||
\(587\) | − | 360445.i | − | 1.04607i | −0.852310 | − | 0.523037i | \(-0.824799\pi\) | ||
0.852310 | − | 0.523037i | \(-0.175201\pi\) | |||||||
\(588\) | 36083.3 | 0.104364 | ||||||||
\(589\) | 168564.i | 0.485886i | ||||||||
\(590\) | 244673. | − | 2413.15i | 0.702882 | − | 0.00693235i | ||||
\(591\) | 16012.1 | 0.0458430 | ||||||||
\(592\) | 33221.5i | 0.0947930i | ||||||||
\(593\) | 203460. | 0.578589 | 0.289294 | − | 0.957240i | \(-0.406579\pi\) | ||||
0.289294 | + | 0.957240i | \(0.406579\pi\) | |||||||
\(594\) | 38525.7 | 0.109189 | ||||||||
\(595\) | −330810. | −0.934426 | ||||||||
\(596\) | − | 397172.i | − | 1.11811i | ||||||
\(597\) | −369352. | −1.03632 | ||||||||
\(598\) | 139325.i | 0.389607i | ||||||||
\(599\) | 68798.6 | 0.191746 | 0.0958729 | − | 0.995394i | \(-0.469436\pi\) | ||||
0.0958729 | + | 0.995394i | \(0.469436\pi\) | |||||||
\(600\) | − | 89531.9i | − | 0.248700i | ||||||
\(601\) | 549707.i | 1.52189i | 0.648818 | + | 0.760943i | \(0.275263\pi\) | ||||
−0.648818 | + | 0.760943i | \(0.724737\pi\) | |||||||
\(602\) | 312616. | 0.862618 | ||||||||
\(603\) | 136689.i | 0.375922i | ||||||||
\(604\) | 204476.i | 0.560491i | ||||||||
\(605\) | 25995.7 | 0.0710215 | ||||||||
\(606\) | −219208. | −0.596914 | ||||||||
\(607\) | −350392. | −0.950991 | −0.475495 | − | 0.879718i | \(-0.657731\pi\) | ||||
−0.475495 | + | 0.879718i | \(0.657731\pi\) | |||||||
\(608\) | 391576.i | 1.05928i | ||||||||
\(609\) | −119216. | −0.321439 | ||||||||
\(610\) | 120405. | 0.323583 | ||||||||
\(611\) | −114458. | −0.306595 | ||||||||
\(612\) | 74992.9 | 0.200224 | ||||||||
\(613\) | − | 450003.i | − | 1.19755i | −0.800917 | − | 0.598776i | \(-0.795654\pi\) | ||
0.800917 | − | 0.598776i | \(-0.204346\pi\) | |||||||
\(614\) | − | 290226.i | − | 0.769838i | ||||||
\(615\) | −225054. | −0.595026 | ||||||||
\(616\) | 303958. | 0.801037 | ||||||||
\(617\) | 165810. | 0.435552 | 0.217776 | − | 0.975999i | \(-0.430120\pi\) | ||||
0.217776 | + | 0.975999i | \(0.430120\pi\) | |||||||
\(618\) | −149264. | −0.390820 | ||||||||
\(619\) | −286451. | −0.747599 | −0.373799 | − | 0.927510i | \(-0.621945\pi\) | ||||
−0.373799 | + | 0.927510i | \(0.621945\pi\) | |||||||
\(620\) | 142576.i | 0.370905i | ||||||||
\(621\) | − | 70593.8i | − | 0.183056i | ||||||
\(622\) | − | 9102.49i | − | 0.0235277i | ||||||
\(623\) | − | 161802.i | − | 0.416877i | ||||||
\(624\) | 14277.7i | 0.0366682i | ||||||||
\(625\) | −487066. | −1.24689 | ||||||||
\(626\) | −44150.6 | −0.112665 | ||||||||
\(627\) | − | 228026.i | − | 0.580027i | ||||||
\(628\) | − | 426758.i | − | 1.08209i | ||||||
\(629\) | 377565.i | 0.954312i | ||||||||
\(630\) | − | 79195.8i | − | 0.199536i | ||||||
\(631\) | 94171.7 | 0.236517 | 0.118258 | − | 0.992983i | \(-0.462269\pi\) | ||||
0.118258 | + | 0.992983i | \(0.462269\pi\) | |||||||
\(632\) | − | 371761.i | − | 0.930743i | ||||||
\(633\) | 163248.i | 0.407419i | ||||||||
\(634\) | − | 73703.9i | − | 0.183363i | ||||||
\(635\) | −233135. | −0.578175 | ||||||||
\(636\) | −90910.3 | −0.224750 | ||||||||
\(637\) | 78075.7i | 0.192414i | ||||||||
\(638\) | 150981. | 0.370920 | ||||||||
\(639\) | 166058. | 0.406686 | ||||||||
\(640\) | 357317.i | 0.872356i | ||||||||
\(641\) | 739487. | 1.79976 | 0.899880 | − | 0.436137i | \(-0.143654\pi\) | ||||
0.899880 | + | 0.436137i | \(0.143654\pi\) | |||||||
\(642\) | − | 95012.8i | − | 0.230522i | ||||||
\(643\) | 446727. | 1.08049 | 0.540244 | − | 0.841508i | \(-0.318332\pi\) | ||||
0.540244 | + | 0.841508i | \(0.318332\pi\) | |||||||
\(644\) | − | 221016.i | − | 0.532909i | ||||||
\(645\) | − | 499882.i | − | 1.20157i | ||||||
\(646\) | 230823.i | 0.553113i | ||||||||
\(647\) | −370357. | −0.884732 | −0.442366 | − | 0.896835i | \(-0.645861\pi\) | ||||
−0.442366 | + | 0.896835i | \(0.645861\pi\) | |||||||
\(648\) | 45242.7i | 0.107745i | ||||||||
\(649\) | 408546. | − | 4029.38i | 0.969954 | − | 0.00956642i | ||||
\(650\) | 76874.6 | 0.181952 | ||||||||
\(651\) | 97754.8i | 0.230662i | ||||||||
\(652\) | −63416.2 | −0.149178 | ||||||||
\(653\) | −339613. | −0.796449 | −0.398224 | − | 0.917288i | \(-0.630373\pi\) | ||||
−0.398224 | + | 0.917288i | \(0.630373\pi\) | |||||||
\(654\) | −57235.4 | −0.133816 | ||||||||
\(655\) | − | 798293.i | − | 1.86071i | ||||||
\(656\) | 33470.6 | 0.0777779 | ||||||||
\(657\) | − | 112606.i | − | 0.260873i | ||||||
\(658\) | −94421.0 | −0.218081 | ||||||||
\(659\) | − | 387109.i | − | 0.891378i | −0.895188 | − | 0.445689i | \(-0.852959\pi\) | ||
0.895188 | − | 0.445689i | \(-0.147041\pi\) | |||||||
\(660\) | − | 192870.i | − | 0.442768i | ||||||
\(661\) | −367793. | −0.841784 | −0.420892 | − | 0.907111i | \(-0.638283\pi\) | ||||
−0.420892 | + | 0.907111i | \(0.638283\pi\) | |||||||
\(662\) | 10428.5i | 0.0237961i | ||||||||
\(663\) | 162267.i | 0.369150i | ||||||||
\(664\) | −182322. | −0.413527 | ||||||||
\(665\) | −468744. | −1.05997 | ||||||||
\(666\) | −90388.9 | −0.203782 | ||||||||
\(667\) | − | 276654.i | − | 0.621850i | ||||||
\(668\) | −403660. | −0.904614 | ||||||||
\(669\) | 286107. | 0.639257 | ||||||||
\(670\) | −355854. | −0.792725 | ||||||||
\(671\) | 201048. | 0.446533 | ||||||||
\(672\) | 227085.i | 0.502864i | ||||||||
\(673\) | − | 356274.i | − | 0.786600i | −0.919410 | − | 0.393300i | \(-0.871333\pi\) | ||
0.919410 | − | 0.393300i | \(-0.128667\pi\) | |||||||
\(674\) | 108922. | 0.239770 | ||||||||
\(675\) | −38951.2 | −0.0854896 | ||||||||
\(676\) | 153205. | 0.335259 | ||||||||
\(677\) | 427232. | 0.932152 | 0.466076 | − | 0.884745i | \(-0.345667\pi\) | ||||
0.466076 | + | 0.884745i | \(0.345667\pi\) | |||||||
\(678\) | −107710. | −0.234314 | ||||||||
\(679\) | − | 97669.7i | − | 0.211846i | ||||||
\(680\) | 492000.i | 1.06401i | ||||||||
\(681\) | − | 120860.i | − | 0.260608i | ||||||
\(682\) | − | 123802.i | − | 0.266169i | ||||||
\(683\) | 816072.i | 1.74939i | 0.484673 | + | 0.874695i | \(0.338939\pi\) | ||||
−0.484673 | + | 0.874695i | \(0.661061\pi\) | |||||||
\(684\) | 106262. | 0.227125 | ||||||||
\(685\) | −191393. | −0.407893 | ||||||||
\(686\) | 298817.i | 0.634975i | ||||||||
\(687\) | 87605.0i | 0.185616i | ||||||||
\(688\) | 74343.8i | 0.157061i | ||||||||
\(689\) | − | 196709.i | − | 0.414367i | ||||||
\(690\) | 183783. | 0.386018 | ||||||||
\(691\) | 101566.i | 0.212712i | 0.994328 | + | 0.106356i | \(0.0339183\pi\) | ||||
−0.994328 | + | 0.106356i | \(0.966082\pi\) | |||||||
\(692\) | 69918.7i | 0.146010i | ||||||||
\(693\) | − | 132238.i | − | 0.275353i | ||||||
\(694\) | 405891. | 0.842733 | ||||||||
\(695\) | 795790. | 1.64751 | ||||||||
\(696\) | 177304.i | 0.366017i | ||||||||
\(697\) | 380396. | 0.783015 | ||||||||
\(698\) | −376502. | −0.772782 | ||||||||
\(699\) | − | 293064.i | − | 0.599803i | ||||||
\(700\) | −121949. | −0.248876 | ||||||||
\(701\) | − | 265473.i | − | 0.540236i | −0.962827 | − | 0.270118i | \(-0.912937\pi\) | ||
0.962827 | − | 0.270118i | \(-0.0870628\pi\) | |||||||
\(702\) | −38846.7 | −0.0788278 | ||||||||
\(703\) | 534993.i | 1.08252i | ||||||||
\(704\) | − | 243991.i | − | 0.492299i | ||||||
\(705\) | 150982.i | 0.303771i | ||||||||
\(706\) | 255696. | 0.512996 | ||||||||
\(707\) | 752425.i | 1.50530i | ||||||||
\(708\) | 1877.72 | + | 190385.i | 0.00374598 | + | 0.379811i | ||||
\(709\) | −380605. | −0.757150 | −0.378575 | − | 0.925571i | \(-0.623586\pi\) | ||||
−0.378575 | + | 0.925571i | \(0.623586\pi\) | |||||||
\(710\) | 432315.i | 0.857597i | ||||||||
\(711\) | −161736. | −0.319939 | ||||||||
\(712\) | −240641. | −0.474689 | ||||||||
\(713\) | −226852. | −0.446234 | ||||||||
\(714\) | 133860.i | 0.262576i | ||||||||
\(715\) | 417325. | 0.816324 | ||||||||
\(716\) | − | 163207.i | − | 0.318356i | ||||||
\(717\) | −91291.2 | −0.177579 | ||||||||
\(718\) | 298921.i | 0.579840i | ||||||||
\(719\) | 356832.i | 0.690249i | 0.938557 | + | 0.345124i | \(0.112163\pi\) | ||||
−0.938557 | + | 0.345124i | \(0.887837\pi\) | |||||||
\(720\) | 18833.7 | 0.0363304 | ||||||||
\(721\) | 512342.i | 0.985575i | ||||||||
\(722\) | 22163.1i | 0.0425164i | ||||||||
\(723\) | −505437. | −0.966920 | ||||||||
\(724\) | −75870.6 | −0.144743 | ||||||||
\(725\) | −152648. | −0.290413 | ||||||||
\(726\) | − | 10519.0i | − | 0.0199572i | ||||||
\(727\) | 84925.0 | 0.160682 | 0.0803409 | − | 0.996767i | \(-0.474399\pi\) | ||||
0.0803409 | + | 0.996767i | \(0.474399\pi\) | |||||||
\(728\) | −306491. | −0.578302 | ||||||||
\(729\) | 19683.0 | 0.0370370 | ||||||||
\(730\) | 293156. | 0.550115 | ||||||||
\(731\) | 844922.i | 1.58118i | ||||||||
\(732\) | 93689.8i | 0.174852i | ||||||||
\(733\) | −359849. | −0.669750 | −0.334875 | − | 0.942263i | \(-0.608694\pi\) | ||||
−0.334875 | + | 0.942263i | \(0.608694\pi\) | |||||||
\(734\) | 306525. | 0.568950 | ||||||||
\(735\) | 102990. | 0.190642 | ||||||||
\(736\) | −526978. | −0.972830 | ||||||||
\(737\) | −594191. | −1.09393 | ||||||||
\(738\) | 91066.6i | 0.167204i | ||||||||
\(739\) | − | 813633.i | − | 1.48984i | −0.667154 | − | 0.744920i | \(-0.732488\pi\) | ||
0.667154 | − | 0.744920i | \(-0.267512\pi\) | |||||||
\(740\) | 452511.i | 0.826353i | ||||||||
\(741\) | 229925.i | 0.418746i | ||||||||
\(742\) | − | 162273.i | − | 0.294739i | ||||||
\(743\) | −407788. | −0.738680 | −0.369340 | − | 0.929294i | \(-0.620416\pi\) | ||||
−0.369340 | + | 0.929294i | \(0.620416\pi\) | |||||||
\(744\) | 145387. | 0.262651 | ||||||||
\(745\) | − | 1.13361e6i | − | 2.04246i | ||||||
\(746\) | 379135.i | 0.681265i | ||||||||
\(747\) | 79320.0i | 0.142148i | ||||||||
\(748\) | 325997.i | 0.582654i | ||||||||
\(749\) | −326128. | −0.581332 | ||||||||
\(750\) | 126873.i | 0.225553i | ||||||||
\(751\) | 726139.i | 1.28748i | 0.765245 | + | 0.643739i | \(0.222618\pi\) | ||||
−0.765245 | + | 0.643739i | \(0.777382\pi\) | |||||||
\(752\) | − | 22454.4i | − | 0.0397069i | ||||||
\(753\) | 214808. | 0.378844 | ||||||||
\(754\) | −152239. | −0.267782 | ||||||||
\(755\) | 583620.i | 1.02385i | ||||||||
\(756\) | 61624.0 | 0.107822 | ||||||||
\(757\) | 226073. | 0.394508 | 0.197254 | − | 0.980352i | \(-0.436798\pi\) | ||||
0.197254 | + | 0.980352i | \(0.436798\pi\) | |||||||
\(758\) | − | 398472.i | − | 0.693521i | ||||||
\(759\) | 306874. | 0.532692 | ||||||||
\(760\) | 697142.i | 1.20696i | ||||||||
\(761\) | −32895.1 | −0.0568018 | −0.0284009 | − | 0.999597i | \(-0.509042\pi\) | ||||
−0.0284009 | + | 0.999597i | \(0.509042\pi\) | |||||||
\(762\) | 94336.5i | 0.162469i | ||||||||
\(763\) | 196458.i | 0.337459i | ||||||||
\(764\) | − | 257075.i | − | 0.440426i | ||||||
\(765\) | 214046. | 0.365750 | ||||||||
\(766\) | 463031.i | 0.789137i | ||||||||
\(767\) | −411949. | + | 4062.96i | −0.700250 | + | 0.00690639i | ||||
\(768\) | 317416. | 0.538153 | ||||||||
\(769\) | − | 954320.i | − | 1.61377i | −0.590710 | − | 0.806884i | \(-0.701152\pi\) | ||
0.590710 | − | 0.806884i | \(-0.298848\pi\) | |||||||
\(770\) | 344268. | 0.580650 | ||||||||
\(771\) | 76782.7 | 0.129168 | ||||||||
\(772\) | −445420. | −0.747370 | ||||||||
\(773\) | 430986.i | 0.721280i | 0.932705 | + | 0.360640i | \(0.117442\pi\) | ||||
−0.932705 | + | 0.360640i | \(0.882558\pi\) | |||||||
\(774\) | −202274. | −0.337643 | ||||||||
\(775\) | 125169.i | 0.208398i | ||||||||
\(776\) | −145260. | −0.241225 | ||||||||
\(777\) | 310257.i | 0.513900i | ||||||||
\(778\) | − | 305780.i | − | 0.505184i | ||||||
\(779\) | 539004. | 0.888213 | ||||||||
\(780\) | 194477.i | 0.319653i | ||||||||
\(781\) | 721862.i | 1.18346i | ||||||||
\(782\) | −310639. | −0.507974 | ||||||||
\(783\) | 77136.9 | 0.125817 | ||||||||
\(784\) | −15316.9 | −0.0249195 | ||||||||
\(785\) | − | 1.21806e6i | − | 1.97665i | ||||||
\(786\) | −323024. | −0.522866 | ||||||||
\(787\) | 449468. | 0.725687 | 0.362844 | − | 0.931850i | \(-0.381806\pi\) | ||||
0.362844 | + | 0.931850i | \(0.381806\pi\) | |||||||
\(788\) | −32436.6 | −0.0522375 | ||||||||
\(789\) | −241680. | −0.388228 | ||||||||
\(790\) | − | 421062.i | − | 0.674671i | ||||||
\(791\) | 369712.i | 0.590895i | ||||||||
\(792\) | −196672. | −0.313539 | ||||||||
\(793\) | −202723. | −0.322371 | ||||||||
\(794\) | −82184.9 | −0.130362 | ||||||||
\(795\) | −259478. | −0.410550 | ||||||||
\(796\) | 748217. | 1.18087 | ||||||||
\(797\) | 300325.i | 0.472797i | 0.971656 | + | 0.236398i | \(0.0759671\pi\) | ||||
−0.971656 | + | 0.236398i | \(0.924033\pi\) | |||||||
\(798\) | 189674.i | 0.297853i | ||||||||
\(799\) | − | 255196.i | − | 0.399742i | ||||||
\(800\) | 290768.i | 0.454325i | ||||||||
\(801\) | 104692.i | 0.163173i | ||||||||
\(802\) | −414424. | −0.644311 | ||||||||
\(803\) | 489501. | 0.759141 | ||||||||
\(804\) | − | 276898.i | − | 0.428358i | ||||||
\(805\) | − | 630830.i | − | 0.973465i | ||||||
\(806\) | 124833.i | 0.192158i | ||||||||
\(807\) | − | 271069.i | − | 0.416230i | ||||||
\(808\) | 1.11905e6 | 1.71406 | ||||||||
\(809\) | − | 676692.i | − | 1.03394i | −0.856005 | − | 0.516968i | \(-0.827060\pi\) | ||
0.856005 | − | 0.516968i | \(-0.172940\pi\) | |||||||
\(810\) | 51242.6i | 0.0781018i | ||||||||
\(811\) | − | 435345.i | − | 0.661899i | −0.943648 | − | 0.330950i | \(-0.892631\pi\) | ||
0.943648 | − | 0.330950i | \(-0.107369\pi\) | |||||||
\(812\) | 241502. | 0.366276 | ||||||||
\(813\) | 614561. | 0.929788 | ||||||||
\(814\) | − | 392924.i | − | 0.593007i | ||||||
\(815\) | −181004. | −0.272504 | ||||||||
\(816\) | −31833.5 | −0.0478084 | ||||||||
\(817\) | 1.19722e6i | 1.79362i | ||||||||
\(818\) | 456059. | 0.681576 | ||||||||
\(819\) | 133340.i | 0.198789i | ||||||||
\(820\) | 455904. | 0.678024 | ||||||||
\(821\) | − | 1.03403e6i | − | 1.53408i | −0.641599 | − | 0.767040i | \(-0.721729\pi\) | ||
0.641599 | − | 0.767040i | \(-0.278271\pi\) | |||||||
\(822\) | 77446.2i | 0.114619i | ||||||||
\(823\) | − | 1.06922e6i | − | 1.57858i | −0.614020 | − | 0.789291i | \(-0.710449\pi\) | ||
0.614020 | − | 0.789291i | \(-0.289551\pi\) | |||||||
\(824\) | 761984. | 1.12226 | ||||||||
\(825\) | − | 169322.i | − | 0.248775i | ||||||
\(826\) | −339833. | + | 3351.69i | −0.498087 | + | 0.00491251i | ||||
\(827\) | 344792. | 0.504135 | 0.252067 | − | 0.967710i | \(-0.418890\pi\) | ||||
0.252067 | + | 0.967710i | \(0.418890\pi\) | |||||||
\(828\) | 143006.i | 0.208590i | ||||||||
\(829\) | 71136.1 | 0.103510 | 0.0517549 | − | 0.998660i | \(-0.483519\pi\) | ||||
0.0517549 | + | 0.998660i | \(0.483519\pi\) | |||||||
\(830\) | −206501. | −0.299755 | ||||||||
\(831\) | 606750. | 0.878634 | ||||||||
\(832\) | 246024.i | 0.355411i | ||||||||
\(833\) | −174077. | −0.250872 | ||||||||
\(834\) | − | 322012.i | − | 0.462956i | ||||||
\(835\) | −1.15214e6 | −1.65246 | ||||||||
\(836\) | 461924.i | 0.660934i | ||||||||
\(837\) | − | 63250.9i | − | 0.0902851i | ||||||
\(838\) | −201773. | −0.287326 | ||||||||
\(839\) | 708706.i | 1.00680i | 0.864054 | + | 0.503399i | \(0.167917\pi\) | ||||
−0.864054 | + | 0.503399i | \(0.832083\pi\) | |||||||
\(840\) | 404291.i | 0.572975i | ||||||||
\(841\) | −404984. | −0.572593 | ||||||||
\(842\) | 121082. | 0.170787 | ||||||||
\(843\) | −771490. | −1.08561 | ||||||||
\(844\) | − | 330701.i | − | 0.464248i | ||||||
\(845\) | 437281. | 0.612418 | ||||||||
\(846\) | 61093.8 | 0.0853604 | ||||||||
\(847\) | −36106.0 | −0.0503284 | ||||||||
\(848\) | 38590.3 | 0.0536644 | ||||||||
\(849\) | 159291.i | 0.220992i | ||||||||
\(850\) | 171400.i | 0.237231i | ||||||||
\(851\) | −719987. | −0.994181 | ||||||||
\(852\) | −336393. | −0.463413 | ||||||||
\(853\) | 1.25574e6 | 1.72584 | 0.862922 | − | 0.505337i | \(-0.168632\pi\) | ||||
0.862922 | + | 0.505337i | \(0.168632\pi\) | |||||||
\(854\) | −167234. | −0.229302 | ||||||||
\(855\) | 303294. | 0.414889 | ||||||||
\(856\) | 485036.i | 0.661952i | ||||||||
\(857\) | − | 799600.i | − | 1.08871i | −0.838856 | − | 0.544353i | \(-0.816775\pi\) | ||
0.838856 | − | 0.544353i | \(-0.183225\pi\) | |||||||
\(858\) | − | 168868.i | − | 0.229389i | ||||||
\(859\) | 853825.i | 1.15713i | 0.815636 | + | 0.578565i | \(0.196387\pi\) | ||||
−0.815636 | + | 0.578565i | \(0.803613\pi\) | |||||||
\(860\) | 1.01264e6i | 1.36917i | ||||||||
\(861\) | 312583. | 0.421657 | ||||||||
\(862\) | −432676. | −0.582302 | ||||||||
\(863\) | − | 365706.i | − | 0.491033i | −0.969392 | − | 0.245516i | \(-0.921043\pi\) | ||
0.969392 | − | 0.245516i | \(-0.0789575\pi\) | |||||||
\(864\) | − | 146932.i | − | 0.196829i | ||||||
\(865\) | 199563.i | 0.266716i | ||||||||
\(866\) | − | 471809.i | − | 0.629115i | ||||||
\(867\) | 72197.6 | 0.0960472 | ||||||||
\(868\) | − | 198027.i | − | 0.262837i | ||||||
\(869\) | − | 703073.i | − | 0.931024i | ||||||
\(870\) | 200818.i | 0.265316i | ||||||||
\(871\) | 599142. | 0.789757 | ||||||||
\(872\) | 292184. | 0.384259 | ||||||||
\(873\) | 63195.8i | 0.0829201i | ||||||||
\(874\) | −440161. | −0.576221 | ||||||||
\(875\) | 435489. | 0.568802 | ||||||||
\(876\) | 228111.i | 0.297261i | ||||||||
\(877\) | 538704. | 0.700408 | 0.350204 | − | 0.936674i | \(-0.386112\pi\) | ||||
0.350204 | + | 0.936674i | \(0.386112\pi\) | |||||||
\(878\) | 619894.i | 0.804134i | ||||||||
\(879\) | −402206. | −0.520560 | ||||||||
\(880\) | 81870.8i | 0.105722i | ||||||||
\(881\) | 131412.i | 0.169311i | 0.996410 | + | 0.0846554i | \(0.0269789\pi\) | ||||
−0.996410 | + | 0.0846554i | \(0.973021\pi\) | |||||||
\(882\) | − | 41674.1i | − | 0.0535709i | ||||||
\(883\) | 152864. | 0.196058 | 0.0980289 | − | 0.995184i | \(-0.468746\pi\) | ||||
0.0980289 | + | 0.995184i | \(0.468746\pi\) | |||||||
\(884\) | − | 328713.i | − | 0.420642i | ||||||
\(885\) | 5359.44 | + | 543402.i | 0.00684278 | + | 0.693800i | ||||
\(886\) | −882108. | −1.12371 | ||||||||
\(887\) | − | 437411.i | − | 0.555959i | −0.960587 | − | 0.277980i | \(-0.910335\pi\) | ||
0.960587 | − | 0.277980i | \(-0.0896648\pi\) | |||||||
\(888\) | 461431. | 0.585169 | ||||||||
\(889\) | 323807. | 0.409716 | ||||||||
\(890\) | −272554. | −0.344090 | ||||||||
\(891\) | 85562.8i | 0.107778i | ||||||||
\(892\) | −579582. | −0.728426 | ||||||||
\(893\) | − | 361602.i | − | 0.453448i | ||||||
\(894\) | −458710. | −0.573936 | ||||||||
\(895\) | − | 465830.i | − | 0.581542i | ||||||
\(896\) | − | 496286.i | − | 0.618182i | ||||||
\(897\) | −309431. | −0.384573 | ||||||||
\(898\) | 252889.i | 0.313601i | ||||||||
\(899\) | − | 247878.i | − | 0.306703i | ||||||
\(900\) | 78905.5 | 0.0974142 | ||||||||
\(901\) | 438581. | 0.540257 | ||||||||
\(902\) | −395870. | −0.486564 | ||||||||
\(903\) | 694299.i | 0.851473i | ||||||||
\(904\) | 549857. | 0.672841 | ||||||||
\(905\) | −216551. | −0.264402 | ||||||||
\(906\) | 236158. | 0.287704 | ||||||||
\(907\) | 1.20250e6 | 1.46174 | 0.730870 | − | 0.682517i | \(-0.239115\pi\) | ||||
0.730870 | + | 0.682517i | \(0.239115\pi\) | |||||||
\(908\) | 244832.i | 0.296959i | ||||||||
\(909\) | − | 486846.i | − | 0.589202i | ||||||
\(910\) | −347136. | −0.419196 | ||||||||
\(911\) | −1.26490e6 | −1.52412 | −0.762059 | − | 0.647508i | \(-0.775811\pi\) | ||||
−0.762059 | + | 0.647508i | \(0.775811\pi\) | |||||||
\(912\) | −45106.8 | −0.0542315 | ||||||||
\(913\) | −344807. | −0.413652 | ||||||||
\(914\) | −621206. | −0.743607 | ||||||||
\(915\) | 267411.i | 0.319402i | ||||||||
\(916\) | − | 177466.i | − | 0.211507i | ||||||
\(917\) | 1.10877e6i | 1.31857i | ||||||||
\(918\) | − | 86612.5i | − | 0.102777i | ||||||
\(919\) | − | 831045.i | − | 0.983996i | −0.870596 | − | 0.491998i | \(-0.836267\pi\) | ||
0.870596 | − | 0.491998i | \(-0.163733\pi\) | |||||||
\(920\) | −938205. | −1.10847 | ||||||||
\(921\) | 644571. | 0.759891 | ||||||||
\(922\) | 507279.i | 0.596740i | ||||||||
\(923\) | − | 727876.i | − | 0.854386i | ||||||
\(924\) | 267882.i | 0.313761i | ||||||||
\(925\) | 397264.i | 0.464297i | ||||||||
\(926\) | −575354. | −0.670985 | ||||||||
\(927\) | − | 331504.i | − | 0.385771i | ||||||
\(928\) | − | 575822.i | − | 0.668640i | ||||||
\(929\) | − | 1.33453e6i | − | 1.54631i | −0.634217 | − | 0.773155i | \(-0.718677\pi\) | ||
0.634217 | − | 0.773155i | \(-0.281323\pi\) | |||||||
\(930\) | 164667. | 0.190388 | ||||||||
\(931\) | −246660. | −0.284577 | ||||||||
\(932\) | 593677.i | 0.683468i | ||||||||
\(933\) | 20216.0 | 0.0232237 | ||||||||
\(934\) | 463637. | 0.531477 | ||||||||
\(935\) | 930468.i | 1.06433i | ||||||||
\(936\) | 198311. | 0.226357 | ||||||||
\(937\) | − | 1.31851e6i | − | 1.50177i | −0.660431 | − | 0.750887i | \(-0.729626\pi\) | ||
0.660431 | − | 0.750887i | \(-0.270374\pi\) | |||||||
\(938\) | 494255. | 0.561753 | ||||||||
\(939\) | − | 98055.4i | − | 0.111209i | ||||||
\(940\) | − | 305852.i | − | 0.346143i | ||||||
\(941\) | 1.26151e6i | 1.42466i | 0.701842 | + | 0.712332i | \(0.252361\pi\) | ||||
−0.701842 | + | 0.712332i | \(0.747639\pi\) | |||||||
\(942\) | −492882. | −0.555445 | ||||||||
\(943\) | 725385.i | 0.815728i | ||||||||
\(944\) | −797.070 | − | 80816.2i | −0.000894443 | − | 0.0906890i | ||||
\(945\) | 175888. | 0.196958 | ||||||||
\(946\) | − | 879294.i | − | 0.982543i | ||||||
\(947\) | 1.34445e6 | 1.49914 | 0.749572 | − | 0.661923i | \(-0.230259\pi\) | ||||
0.749572 | + | 0.661923i | \(0.230259\pi\) | |||||||
\(948\) | 327637. | 0.364567 | ||||||||
\(949\) | −493579. | −0.548055 | ||||||||
\(950\) | 242866.i | 0.269103i | ||||||||
\(951\) | 163691. | 0.180994 | ||||||||
\(952\) | − | 683351.i | − | 0.753997i | ||||||
\(953\) | 654376. | 0.720513 | 0.360256 | − | 0.932853i | \(-0.382689\pi\) | ||||
0.360256 | + | 0.932853i | \(0.382689\pi\) | |||||||
\(954\) | 104996.i | 0.115366i | ||||||||
\(955\) | − | 733748.i | − | 0.804526i | ||||||
\(956\) | 184934. | 0.202349 | ||||||||
\(957\) | 335317.i | 0.366127i | ||||||||
\(958\) | − | 982612.i | − | 1.07066i | ||||||
\(959\) | 265831. | 0.289047 | ||||||||
\(960\) | 324530. | 0.352137 | ||||||||
\(961\) | 720265. | 0.779912 | ||||||||
\(962\) | 396198.i | 0.428117i | ||||||||
\(963\) | 211017. | 0.227543 | ||||||||
\(964\) | 1.02389e6 | 1.10179 | ||||||||
\(965\) | −1.27133e6 | −1.36522 | ||||||||
\(966\) | −255261. | −0.273546 | ||||||||
\(967\) | − | 1.67352e6i | − | 1.78969i | −0.446373 | − | 0.894847i | \(-0.647284\pi\) | ||
0.446373 | − | 0.894847i | \(-0.352716\pi\) | |||||||
\(968\) | 53698.9i | 0.0573080i | ||||||||
\(969\) | −512641. | −0.545966 | ||||||||
\(970\) | −164524. | −0.174858 | ||||||||
\(971\) | −1.34581e6 | −1.42740 | −0.713700 | − | 0.700451i | \(-0.752982\pi\) | ||||
−0.713700 | + | 0.700451i | \(0.752982\pi\) | |||||||
\(972\) | −39872.9 | −0.0422032 | ||||||||
\(973\) | −1.10529e6 | −1.16749 | ||||||||
\(974\) | − | 787913.i | − | 0.830539i | ||||||
\(975\) | 170733.i | 0.179601i | ||||||||
\(976\) | − | 39770.1i | − | 0.0417501i | ||||||
\(977\) | − | 108100.i | − | 0.113250i | −0.998396 | − | 0.0566248i | \(-0.981966\pi\) | ||
0.998396 | − | 0.0566248i | \(-0.0180339\pi\) | |||||||
\(978\) | 73242.1i | 0.0765743i | ||||||||
\(979\) | −455099. | −0.474833 | ||||||||
\(980\) | −208632. | −0.217234 | ||||||||
\(981\) | − | 127116.i | − | 0.132087i | ||||||
\(982\) | 653690.i | 0.677874i | ||||||||
\(983\) | 412747.i | 0.427147i | 0.976927 | + | 0.213573i | \(0.0685103\pi\) | ||||
−0.976927 | + | 0.213573i | \(0.931490\pi\) | |||||||
\(984\) | − | 464891.i | − | 0.480132i | ||||||
\(985\) | −92581.1 | −0.0954223 | ||||||||
\(986\) | − | 339431.i | − | 0.349138i | ||||||
\(987\) | − | 209702.i | − | 0.215263i | ||||||
\(988\) | − | 465772.i | − | 0.477155i | ||||||
\(989\) | −1.61120e6 | −1.64724 | ||||||||
\(990\) | −222754. | −0.227276 | ||||||||
\(991\) | − | 1.11405e6i | − | 1.13438i | −0.823588 | − | 0.567188i | \(-0.808031\pi\) | ||
0.823588 | − | 0.567188i | \(-0.191969\pi\) | |||||||
\(992\) | −472164. | −0.479810 | ||||||||
\(993\) | −23160.9 | −0.0234886 | ||||||||
\(994\) | − | 600453.i | − | 0.607724i | ||||||
\(995\) | 2.13558e6 | 2.15709 | ||||||||
\(996\) | − | 160683.i | − | 0.161976i | ||||||
\(997\) | −289466. | −0.291210 | −0.145605 | − | 0.989343i | \(-0.546513\pi\) | ||||
−0.145605 | + | 0.989343i | \(0.546513\pi\) | |||||||
\(998\) | 55683.6i | 0.0559070i | ||||||||
\(999\) | − | 200747.i | − | 0.201149i |
(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.58.26 | yes | 40 | |
3.2 | odd | 2 | 531.5.c.d.235.15 | 40 | |||
59.58 | odd | 2 | inner | 177.5.c.a.58.15 | ✓ | 40 | |
177.176 | even | 2 | 531.5.c.d.235.26 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.c.a.58.15 | ✓ | 40 | 59.58 | odd | 2 | inner | |
177.5.c.a.58.26 | yes | 40 | 1.1 | even | 1 | trivial | |
531.5.c.d.235.15 | 40 | 3.2 | odd | 2 | |||
531.5.c.d.235.26 | 40 | 177.176 | even | 2 |