Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [19,5,Mod(18,19)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(19, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("19.18");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 19.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.96402929859\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.12107488.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 35x^{2} + 142 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 18.3 | ||
Root | \(2.16425i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 19.18 |
Dual form | 19.5.b.b.18.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/19\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.16425i | 0.541063i | 0.962711 | + | 0.270532i | \(0.0871995\pi\) | ||||
−0.962711 | + | 0.270532i | \(0.912801\pi\) | |||||||
\(3\) | − | 16.8206i | − | 1.86895i | −0.356024 | − | 0.934477i | \(-0.615868\pi\) | ||
0.356024 | − | 0.934477i | \(-0.384132\pi\) | |||||||
\(4\) | 11.3160 | 0.707250 | ||||||||
\(5\) | −14.7720 | −0.590880 | −0.295440 | − | 0.955361i | \(-0.595466\pi\) | ||||
−0.295440 | + | 0.955361i | \(0.595466\pi\) | |||||||
\(6\) | 36.4040 | 1.01122 | ||||||||
\(7\) | 59.6320 | 1.21698 | 0.608490 | − | 0.793562i | \(-0.291776\pi\) | ||||
0.608490 | + | 0.793562i | \(0.291776\pi\) | |||||||
\(8\) | 59.1188i | 0.923731i | ||||||||
\(9\) | −201.932 | −2.49299 | ||||||||
\(10\) | − | 31.9704i | − | 0.319704i | ||||||
\(11\) | −17.1240 | −0.141521 | −0.0707605 | − | 0.997493i | \(-0.522543\pi\) | ||||
−0.0707605 | + | 0.997493i | \(0.522543\pi\) | |||||||
\(12\) | − | 190.342i | − | 1.32182i | ||||||
\(13\) | 163.384i | 0.966769i | 0.875408 | + | 0.483384i | \(0.160593\pi\) | ||||
−0.875408 | + | 0.483384i | \(0.839407\pi\) | |||||||
\(14\) | 129.059i | 0.658463i | ||||||||
\(15\) | 248.474i | 1.10433i | ||||||||
\(16\) | 53.1081 | 0.207453 | ||||||||
\(17\) | 177.528 | 0.614284 | 0.307142 | − | 0.951664i | \(-0.400627\pi\) | ||||
0.307142 | + | 0.951664i | \(0.400627\pi\) | |||||||
\(18\) | − | 437.032i | − | 1.34886i | ||||||
\(19\) | 272.004 | + | 237.349i | 0.753474 | + | 0.657478i | ||||
\(20\) | −167.160 | −0.417900 | ||||||||
\(21\) | − | 1003.05i | − | 2.27448i | ||||||
\(22\) | − | 37.0608i | − | 0.0765718i | ||||||
\(23\) | −502.236 | −0.949407 | −0.474703 | − | 0.880146i | \(-0.657445\pi\) | ||||
−0.474703 | + | 0.880146i | \(0.657445\pi\) | |||||||
\(24\) | 994.412 | 1.72641 | ||||||||
\(25\) | −406.788 | −0.650861 | ||||||||
\(26\) | −353.604 | −0.523083 | ||||||||
\(27\) | 2034.15i | 2.79033i | ||||||||
\(28\) | 674.796 | 0.860709 | ||||||||
\(29\) | − | 500.627i | − | 0.595275i | −0.954679 | − | 0.297638i | \(-0.903801\pi\) | ||
0.954679 | − | 0.297638i | \(-0.0961987\pi\) | |||||||
\(30\) | −537.760 | −0.597511 | ||||||||
\(31\) | − | 1465.70i | − | 1.52518i | −0.646880 | − | 0.762592i | \(-0.723926\pi\) | ||
0.646880 | − | 0.762592i | \(-0.276074\pi\) | |||||||
\(32\) | 1060.84i | 1.03598i | ||||||||
\(33\) | 288.036i | 0.264496i | ||||||||
\(34\) | 384.216i | 0.332367i | ||||||||
\(35\) | −880.884 | −0.719089 | ||||||||
\(36\) | −2285.06 | −1.76317 | ||||||||
\(37\) | − | 600.763i | − | 0.438833i | −0.975631 | − | 0.219417i | \(-0.929585\pi\) | ||
0.975631 | − | 0.219417i | \(-0.0704154\pi\) | |||||||
\(38\) | −513.684 | + | 588.686i | −0.355737 | + | 0.407677i | ||||
\(39\) | 2748.21 | 1.80685 | ||||||||
\(40\) | − | 873.303i | − | 0.545814i | ||||||
\(41\) | 325.088i | 0.193390i | 0.995314 | + | 0.0966948i | \(0.0308271\pi\) | ||||
−0.995314 | + | 0.0966948i | \(0.969173\pi\) | |||||||
\(42\) | 2170.84 | 1.23064 | ||||||||
\(43\) | −752.973 | −0.407232 | −0.203616 | − | 0.979051i | \(-0.565269\pi\) | ||||
−0.203616 | + | 0.979051i | \(0.565269\pi\) | |||||||
\(44\) | −193.776 | −0.100091 | ||||||||
\(45\) | 2982.94 | 1.47306 | ||||||||
\(46\) | − | 1086.97i | − | 0.513689i | ||||||
\(47\) | −2257.62 | −1.02201 | −0.511005 | − | 0.859578i | \(-0.670727\pi\) | ||||
−0.511005 | + | 0.859578i | \(0.670727\pi\) | |||||||
\(48\) | − | 893.309i | − | 0.387721i | ||||||
\(49\) | 1154.98 | 0.481040 | ||||||||
\(50\) | − | 880.392i | − | 0.352157i | ||||||
\(51\) | − | 2986.13i | − | 1.14807i | ||||||
\(52\) | 1848.85i | 0.683747i | ||||||||
\(53\) | 1501.20i | 0.534427i | 0.963637 | + | 0.267213i | \(0.0861028\pi\) | ||||
−0.963637 | + | 0.267213i | \(0.913897\pi\) | |||||||
\(54\) | −4402.41 | −1.50974 | ||||||||
\(55\) | 252.956 | 0.0836219 | ||||||||
\(56\) | 3525.37i | 1.12416i | ||||||||
\(57\) | 3992.36 | − | 4575.27i | 1.22880 | − | 1.40821i | ||||
\(58\) | 1083.48 | 0.322082 | ||||||||
\(59\) | 4555.57i | 1.30870i | 0.756193 | + | 0.654348i | \(0.227057\pi\) | ||||
−0.756193 | + | 0.654348i | \(0.772943\pi\) | |||||||
\(60\) | 2811.73i | 0.781036i | ||||||||
\(61\) | 770.012 | 0.206937 | 0.103468 | − | 0.994633i | \(-0.467006\pi\) | ||||
0.103468 | + | 0.994633i | \(0.467006\pi\) | |||||||
\(62\) | 3172.15 | 0.825221 | ||||||||
\(63\) | −12041.6 | −3.03392 | ||||||||
\(64\) | −1446.20 | −0.353075 | ||||||||
\(65\) | − | 2413.51i | − | 0.571244i | ||||||
\(66\) | −623.383 | −0.143109 | ||||||||
\(67\) | 1613.61i | 0.359458i | 0.983716 | + | 0.179729i | \(0.0575221\pi\) | ||||
−0.983716 | + | 0.179729i | \(0.942478\pi\) | |||||||
\(68\) | 2008.91 | 0.434452 | ||||||||
\(69\) | 8447.91i | 1.77440i | ||||||||
\(70\) | − | 1906.46i | − | 0.389073i | ||||||
\(71\) | − | 7676.78i | − | 1.52287i | −0.648242 | − | 0.761435i | \(-0.724495\pi\) | ||
0.648242 | − | 0.761435i | \(-0.275505\pi\) | |||||||
\(72\) | − | 11938.0i | − | 2.30285i | ||||||
\(73\) | −2330.98 | −0.437413 | −0.218707 | − | 0.975791i | \(-0.570184\pi\) | ||||
−0.218707 | + | 0.975791i | \(0.570184\pi\) | |||||||
\(74\) | 1300.20 | 0.237437 | ||||||||
\(75\) | 6842.41i | 1.21643i | ||||||||
\(76\) | 3078.00 | + | 2685.85i | 0.532895 | + | 0.465001i | ||||
\(77\) | −1021.14 | −0.172228 | ||||||||
\(78\) | 5947.83i | 0.977618i | ||||||||
\(79\) | 53.3968i | 0.00855580i | 0.999991 | + | 0.00427790i | \(0.00136170\pi\) | ||||
−0.999991 | + | 0.00427790i | \(0.998638\pi\) | |||||||
\(80\) | −784.513 | −0.122580 | ||||||||
\(81\) | 17859.1 | 2.72200 | ||||||||
\(82\) | −703.573 | −0.104636 | ||||||||
\(83\) | 9438.26 | 1.37005 | 0.685024 | − | 0.728520i | \(-0.259792\pi\) | ||||
0.685024 | + | 0.728520i | \(0.259792\pi\) | |||||||
\(84\) | − | 11350.5i | − | 1.60863i | ||||||
\(85\) | −2622.44 | −0.362968 | ||||||||
\(86\) | − | 1629.62i | − | 0.220339i | ||||||
\(87\) | −8420.83 | −1.11254 | ||||||||
\(88\) | − | 1012.35i | − | 0.130727i | ||||||
\(89\) | − | 9238.06i | − | 1.16627i | −0.812374 | − | 0.583137i | \(-0.801825\pi\) | ||
0.812374 | − | 0.583137i | \(-0.198175\pi\) | |||||||
\(90\) | 6455.84i | 0.797017i | ||||||||
\(91\) | 9742.91i | 1.17654i | ||||||||
\(92\) | −5683.31 | −0.671468 | ||||||||
\(93\) | −24654.0 | −2.85050 | ||||||||
\(94\) | − | 4886.06i | − | 0.552972i | ||||||
\(95\) | −4018.05 | − | 3506.13i | −0.445213 | − | 0.388490i | ||||
\(96\) | 17843.9 | 1.93619 | ||||||||
\(97\) | − | 2562.56i | − | 0.272352i | −0.990685 | − | 0.136176i | \(-0.956519\pi\) | ||
0.990685 | − | 0.136176i | \(-0.0434813\pi\) | |||||||
\(98\) | 2499.66i | 0.260273i | ||||||||
\(99\) | 3457.89 | 0.352810 | ||||||||
\(100\) | −4603.21 | −0.460321 | ||||||||
\(101\) | 7050.24 | 0.691133 | 0.345566 | − | 0.938394i | \(-0.387687\pi\) | ||||
0.345566 | + | 0.938394i | \(0.387687\pi\) | |||||||
\(102\) | 6462.73 | 0.621178 | ||||||||
\(103\) | 8275.94i | 0.780086i | 0.920797 | + | 0.390043i | \(0.127540\pi\) | ||||
−0.920797 | + | 0.390043i | \(0.872460\pi\) | |||||||
\(104\) | −9659.05 | −0.893034 | ||||||||
\(105\) | 14817.0i | 1.34394i | ||||||||
\(106\) | −3248.99 | −0.289159 | ||||||||
\(107\) | 6473.72i | 0.565440i | 0.959202 | + | 0.282720i | \(0.0912367\pi\) | ||||
−0.959202 | + | 0.282720i | \(0.908763\pi\) | |||||||
\(108\) | 23018.4i | 1.97346i | ||||||||
\(109\) | − | 5991.18i | − | 0.504266i | −0.967693 | − | 0.252133i | \(-0.918868\pi\) | ||
0.967693 | − | 0.252133i | \(-0.0811320\pi\) | |||||||
\(110\) | 547.461i | 0.0452448i | ||||||||
\(111\) | −10105.2 | −0.820159 | ||||||||
\(112\) | 3166.94 | 0.252467 | ||||||||
\(113\) | − | 20337.5i | − | 1.59273i | −0.604817 | − | 0.796364i | \(-0.706754\pi\) | ||
0.604817 | − | 0.796364i | \(-0.293246\pi\) | |||||||
\(114\) | 9902.04 | + | 8640.47i | 0.761930 | + | 0.664856i | ||||
\(115\) | 7419.03 | 0.560986 | ||||||||
\(116\) | − | 5665.09i | − | 0.421009i | ||||||
\(117\) | − | 32992.4i | − | 2.41014i | ||||||
\(118\) | −9859.42 | −0.708088 | ||||||||
\(119\) | 10586.4 | 0.747571 | ||||||||
\(120\) | −14689.5 | −1.02010 | ||||||||
\(121\) | −14347.8 | −0.979972 | ||||||||
\(122\) | 1666.50i | 0.111966i | ||||||||
\(123\) | 5468.17 | 0.361436 | ||||||||
\(124\) | − | 16585.9i | − | 1.07869i | ||||||
\(125\) | 15241.6 | 0.975461 | ||||||||
\(126\) | − | 26061.1i | − | 1.64154i | ||||||
\(127\) | 15199.0i | 0.942342i | 0.882042 | + | 0.471171i | \(0.156169\pi\) | ||||
−0.882042 | + | 0.471171i | \(0.843831\pi\) | |||||||
\(128\) | 13843.5i | 0.844940i | ||||||||
\(129\) | 12665.4i | 0.761098i | ||||||||
\(130\) | 5223.44 | 0.309079 | ||||||||
\(131\) | 29704.4 | 1.73092 | 0.865461 | − | 0.500976i | \(-0.167025\pi\) | ||||
0.865461 | + | 0.500976i | \(0.167025\pi\) | |||||||
\(132\) | 3259.42i | 0.187065i | ||||||||
\(133\) | 16220.2 | + | 14153.6i | 0.916963 | + | 0.800137i | ||||
\(134\) | −3492.26 | −0.194490 | ||||||||
\(135\) | − | 30048.4i | − | 1.64875i | ||||||
\(136\) | 10495.2i | 0.567433i | ||||||||
\(137\) | 7080.63 | 0.377251 | 0.188626 | − | 0.982049i | \(-0.439597\pi\) | ||||
0.188626 | + | 0.982049i | \(0.439597\pi\) | |||||||
\(138\) | −18283.4 | −0.960062 | ||||||||
\(139\) | −16337.3 | −0.845574 | −0.422787 | − | 0.906229i | \(-0.638948\pi\) | ||||
−0.422787 | + | 0.906229i | \(0.638948\pi\) | |||||||
\(140\) | −9968.09 | −0.508576 | ||||||||
\(141\) | 37974.5i | 1.91009i | ||||||||
\(142\) | 16614.5 | 0.823969 | ||||||||
\(143\) | − | 2797.79i | − | 0.136818i | ||||||
\(144\) | −10724.2 | −0.517179 | ||||||||
\(145\) | 7395.26i | 0.351736i | ||||||||
\(146\) | − | 5044.82i | − | 0.236668i | ||||||
\(147\) | − | 19427.4i | − | 0.899041i | ||||||
\(148\) | − | 6798.23i | − | 0.310365i | ||||||
\(149\) | −12128.3 | −0.546294 | −0.273147 | − | 0.961972i | \(-0.588065\pi\) | ||||
−0.273147 | + | 0.961972i | \(0.588065\pi\) | |||||||
\(150\) | −14808.7 | −0.658165 | ||||||||
\(151\) | − | 26542.8i | − | 1.16411i | −0.813151 | − | 0.582053i | \(-0.802250\pi\) | ||
0.813151 | − | 0.582053i | \(-0.197750\pi\) | |||||||
\(152\) | −14031.8 | + | 16080.5i | −0.607332 | + | 0.696007i | ||||
\(153\) | −35848.6 | −1.53140 | ||||||||
\(154\) | − | 2210.01i | − | 0.0931863i | ||||||
\(155\) | 21651.4i | 0.901201i | ||||||||
\(156\) | 31098.8 | 1.27789 | ||||||||
\(157\) | −8292.18 | −0.336411 | −0.168205 | − | 0.985752i | \(-0.553797\pi\) | ||||
−0.168205 | + | 0.985752i | \(0.553797\pi\) | |||||||
\(158\) | −115.564 | −0.00462923 | ||||||||
\(159\) | 25251.1 | 0.998819 | ||||||||
\(160\) | − | 15670.7i | − | 0.612138i | ||||||
\(161\) | −29949.4 | −1.15541 | ||||||||
\(162\) | 38651.5i | 1.47278i | ||||||||
\(163\) | 16703.6 | 0.628688 | 0.314344 | − | 0.949309i | \(-0.398215\pi\) | ||||
0.314344 | + | 0.949309i | \(0.398215\pi\) | |||||||
\(164\) | 3678.70i | 0.136775i | ||||||||
\(165\) | − | 4254.87i | − | 0.156285i | ||||||
\(166\) | 20426.8i | 0.741283i | ||||||||
\(167\) | 20319.3i | 0.728576i | 0.931286 | + | 0.364288i | \(0.118688\pi\) | ||||
−0.931286 | + | 0.364288i | \(0.881312\pi\) | |||||||
\(168\) | 59298.8 | 2.10101 | ||||||||
\(169\) | 1866.70 | 0.0653585 | ||||||||
\(170\) | − | 5675.64i | − | 0.196389i | ||||||
\(171\) | −54926.3 | − | 47928.5i | −1.87840 | − | 1.63908i | ||||
\(172\) | −8520.64 | −0.288015 | ||||||||
\(173\) | 19570.3i | 0.653893i | 0.945043 | + | 0.326946i | \(0.106020\pi\) | ||||
−0.945043 | + | 0.326946i | \(0.893980\pi\) | |||||||
\(174\) | − | 18224.8i | − | 0.601956i | ||||||
\(175\) | −24257.6 | −0.792084 | ||||||||
\(176\) | −909.424 | −0.0293590 | ||||||||
\(177\) | 76627.4 | 2.44589 | ||||||||
\(178\) | 19993.5 | 0.631028 | ||||||||
\(179\) | − | 23233.3i | − | 0.725110i | −0.931962 | − | 0.362555i | \(-0.881904\pi\) | ||
0.931962 | − | 0.362555i | \(-0.118096\pi\) | |||||||
\(180\) | 33755.0 | 1.04182 | ||||||||
\(181\) | − | 53293.1i | − | 1.62672i | −0.581759 | − | 0.813361i | \(-0.697635\pi\) | ||
0.581759 | − | 0.813361i | \(-0.302365\pi\) | |||||||
\(182\) | −21086.1 | −0.636582 | ||||||||
\(183\) | − | 12952.1i | − | 0.386756i | ||||||
\(184\) | − | 29691.6i | − | 0.876996i | ||||||
\(185\) | 8874.46i | 0.259298i | ||||||||
\(186\) | − | 53357.4i | − | 1.54230i | ||||||
\(187\) | −3040.00 | −0.0869340 | ||||||||
\(188\) | −25547.2 | −0.722817 | ||||||||
\(189\) | 121300.i | 3.39577i | ||||||||
\(190\) | 7588.15 | − | 8696.07i | 0.210198 | − | 0.240888i | ||||
\(191\) | 5420.24 | 0.148577 | 0.0742886 | − | 0.997237i | \(-0.476331\pi\) | ||||
0.0742886 | + | 0.997237i | \(0.476331\pi\) | |||||||
\(192\) | 24325.9i | 0.659882i | ||||||||
\(193\) | 38918.6i | 1.04482i | 0.852694 | + | 0.522411i | \(0.174967\pi\) | ||||
−0.852694 | + | 0.522411i | \(0.825033\pi\) | |||||||
\(194\) | 5546.04 | 0.147360 | ||||||||
\(195\) | −40596.6 | −1.06763 | ||||||||
\(196\) | 13069.7 | 0.340216 | ||||||||
\(197\) | −41122.0 | −1.05960 | −0.529800 | − | 0.848122i | \(-0.677733\pi\) | ||||
−0.529800 | + | 0.848122i | \(0.677733\pi\) | |||||||
\(198\) | 7483.75i | 0.190893i | ||||||||
\(199\) | 22778.9 | 0.575211 | 0.287606 | − | 0.957749i | \(-0.407141\pi\) | ||||
0.287606 | + | 0.957749i | \(0.407141\pi\) | |||||||
\(200\) | − | 24048.8i | − | 0.601220i | ||||||
\(201\) | 27141.8 | 0.671811 | ||||||||
\(202\) | 15258.5i | 0.373947i | ||||||||
\(203\) | − | 29853.4i | − | 0.724438i | ||||||
\(204\) | − | 33791.0i | − | 0.811972i | ||||||
\(205\) | − | 4802.20i | − | 0.114270i | ||||||
\(206\) | −17911.2 | −0.422076 | ||||||||
\(207\) | 101418. | 2.36686 | ||||||||
\(208\) | 8677.00i | 0.200559i | ||||||||
\(209\) | −4657.81 | − | 4064.38i | −0.106632 | − | 0.0930469i | ||||
\(210\) | −32067.7 | −0.727159 | ||||||||
\(211\) | 80470.1i | 1.80746i | 0.428099 | + | 0.903732i | \(0.359183\pi\) | ||||
−0.428099 | + | 0.903732i | \(0.640817\pi\) | |||||||
\(212\) | 16987.6i | 0.377973i | ||||||||
\(213\) | −129128. | −2.84617 | ||||||||
\(214\) | −14010.8 | −0.305939 | ||||||||
\(215\) | 11122.9 | 0.240625 | ||||||||
\(216\) | −120256. | −2.57751 | ||||||||
\(217\) | − | 87402.8i | − | 1.85612i | ||||||
\(218\) | 12966.4 | 0.272840 | ||||||||
\(219\) | 39208.4i | 0.817505i | ||||||||
\(220\) | 2862.45 | 0.0591416 | ||||||||
\(221\) | 29005.2i | 0.593870i | ||||||||
\(222\) | − | 21870.2i | − | 0.443758i | ||||||
\(223\) | 8564.16i | 0.172217i | 0.996286 | + | 0.0861083i | \(0.0274431\pi\) | ||||
−0.996286 | + | 0.0861083i | \(0.972557\pi\) | |||||||
\(224\) | 63260.0i | 1.26076i | ||||||||
\(225\) | 82143.5 | 1.62259 | ||||||||
\(226\) | 44015.6 | 0.861767 | ||||||||
\(227\) | − | 37739.2i | − | 0.732387i | −0.930539 | − | 0.366193i | \(-0.880661\pi\) | ||
0.930539 | − | 0.366193i | \(-0.119339\pi\) | |||||||
\(228\) | 45177.5 | − | 51773.8i | 0.869066 | − | 0.995956i | ||||
\(229\) | −44028.8 | −0.839587 | −0.419793 | − | 0.907620i | \(-0.637897\pi\) | ||||
−0.419793 | + | 0.907620i | \(0.637897\pi\) | |||||||
\(230\) | 16056.7i | 0.303529i | ||||||||
\(231\) | 17176.2i | 0.321886i | ||||||||
\(232\) | 29596.4 | 0.549874 | ||||||||
\(233\) | −5412.82 | −0.0997038 | −0.0498519 | − | 0.998757i | \(-0.515875\pi\) | ||||
−0.0498519 | + | 0.998757i | \(0.515875\pi\) | |||||||
\(234\) | 71404.0 | 1.30404 | ||||||||
\(235\) | 33349.6 | 0.603885 | ||||||||
\(236\) | 51550.9i | 0.925576i | ||||||||
\(237\) | 898.165 | 0.0159904 | ||||||||
\(238\) | 22911.6i | 0.404483i | ||||||||
\(239\) | −24069.2 | −0.421372 | −0.210686 | − | 0.977554i | \(-0.567570\pi\) | ||||
−0.210686 | + | 0.977554i | \(0.567570\pi\) | |||||||
\(240\) | 13196.0i | 0.229097i | ||||||||
\(241\) | − | 24651.4i | − | 0.424432i | −0.977223 | − | 0.212216i | \(-0.931932\pi\) | ||
0.977223 | − | 0.212216i | \(-0.0680680\pi\) | |||||||
\(242\) | − | 31052.2i | − | 0.530227i | ||||||
\(243\) | − | 135634.i | − | 2.29697i | ||||||
\(244\) | 8713.46 | 0.146356 | ||||||||
\(245\) | −17061.3 | −0.284237 | ||||||||
\(246\) | 11834.5i | 0.195560i | ||||||||
\(247\) | −38779.1 | + | 44441.1i | −0.635629 | + | 0.728435i | ||||
\(248\) | 86650.5 | 1.40886 | ||||||||
\(249\) | − | 158757.i | − | 2.56056i | ||||||
\(250\) | 32986.6i | 0.527786i | ||||||||
\(251\) | 91859.2 | 1.45806 | 0.729030 | − | 0.684482i | \(-0.239972\pi\) | ||||
0.729030 | + | 0.684482i | \(0.239972\pi\) | |||||||
\(252\) | −136263. | −2.14574 | ||||||||
\(253\) | 8600.31 | 0.134361 | ||||||||
\(254\) | −32894.6 | −0.509867 | ||||||||
\(255\) | 44111.1i | 0.678371i | ||||||||
\(256\) | −53100.0 | −0.810242 | ||||||||
\(257\) | − | 63651.3i | − | 0.963698i | −0.876254 | − | 0.481849i | \(-0.839965\pi\) | ||
0.876254 | − | 0.481849i | \(-0.160035\pi\) | |||||||
\(258\) | −27411.2 | −0.411803 | ||||||||
\(259\) | − | 35824.7i | − | 0.534051i | ||||||
\(260\) | − | 27311.3i | − | 0.404013i | ||||||
\(261\) | 101093.i | 1.48401i | ||||||||
\(262\) | 64287.8i | 0.936539i | ||||||||
\(263\) | 113072. | 1.63472 | 0.817360 | − | 0.576127i | \(-0.195437\pi\) | ||||
0.817360 | + | 0.576127i | \(0.195437\pi\) | |||||||
\(264\) | −17028.3 | −0.244323 | ||||||||
\(265\) | − | 22175.8i | − | 0.315782i | ||||||
\(266\) | −30632.0 | + | 35104.5i | −0.432925 | + | 0.496135i | ||||
\(267\) | −155390. | −2.17971 | ||||||||
\(268\) | 18259.6i | 0.254227i | ||||||||
\(269\) | − | 54854.5i | − | 0.758067i | −0.925383 | − | 0.379034i | \(-0.876257\pi\) | ||
0.925383 | − | 0.379034i | \(-0.123743\pi\) | |||||||
\(270\) | 65032.4 | 0.892077 | ||||||||
\(271\) | 61064.9 | 0.831482 | 0.415741 | − | 0.909483i | \(-0.363522\pi\) | ||||
0.415741 | + | 0.909483i | \(0.363522\pi\) | |||||||
\(272\) | 9428.17 | 0.127435 | ||||||||
\(273\) | 163881. | 2.19889 | ||||||||
\(274\) | 15324.3i | 0.204117i | ||||||||
\(275\) | 6965.85 | 0.0921104 | ||||||||
\(276\) | 95596.6i | 1.25494i | ||||||||
\(277\) | −31384.3 | −0.409027 | −0.204514 | − | 0.978864i | \(-0.565561\pi\) | ||||
−0.204514 | + | 0.978864i | \(0.565561\pi\) | |||||||
\(278\) | − | 35358.1i | − | 0.457509i | ||||||
\(279\) | 295972.i | 3.80227i | ||||||||
\(280\) | − | 52076.8i | − | 0.664245i | ||||||
\(281\) | 79910.3i | 1.01202i | 0.862527 | + | 0.506011i | \(0.168880\pi\) | ||||
−0.862527 | + | 0.506011i | \(0.831120\pi\) | |||||||
\(282\) | −82186.4 | −1.03348 | ||||||||
\(283\) | −99909.8 | −1.24749 | −0.623743 | − | 0.781630i | \(-0.714389\pi\) | ||||
−0.623743 | + | 0.781630i | \(0.714389\pi\) | |||||||
\(284\) | − | 86870.5i | − | 1.07705i | ||||||
\(285\) | −58975.1 | + | 67585.9i | −0.726071 | + | 0.832082i | ||||
\(286\) | 6055.13 | 0.0740272 | ||||||||
\(287\) | 19385.7i | 0.235351i | ||||||||
\(288\) | − | 214218.i | − | 2.58268i | ||||||
\(289\) | −52004.8 | −0.622655 | ||||||||
\(290\) | −16005.2 | −0.190312 | ||||||||
\(291\) | −43103.8 | −0.509014 | ||||||||
\(292\) | −26377.3 | −0.309361 | ||||||||
\(293\) | − | 1641.27i | − | 0.0191182i | −0.999954 | − | 0.00955908i | \(-0.996957\pi\) | ||
0.999954 | − | 0.00955908i | \(-0.00304279\pi\) | |||||||
\(294\) | 42045.8 | 0.486438 | ||||||||
\(295\) | − | 67294.9i | − | 0.773283i | ||||||
\(296\) | 35516.3 | 0.405364 | ||||||||
\(297\) | − | 34832.8i | − | 0.394890i | ||||||
\(298\) | − | 26248.7i | − | 0.295580i | ||||||
\(299\) | − | 82057.3i | − | 0.917857i | ||||||
\(300\) | 77428.8i | 0.860320i | ||||||||
\(301\) | −44901.3 | −0.495594 | ||||||||
\(302\) | 57445.3 | 0.629855 | ||||||||
\(303\) | − | 118589.i | − | 1.29170i | ||||||
\(304\) | 14445.6 | + | 12605.2i | 0.156311 | + | 0.136396i | ||||
\(305\) | −11374.6 | −0.122275 | ||||||||
\(306\) | − | 77585.5i | − | 0.828586i | ||||||
\(307\) | 72395.1i | 0.768126i | 0.923307 | + | 0.384063i | \(0.125476\pi\) | ||||
−0.923307 | + | 0.384063i | \(0.874524\pi\) | |||||||
\(308\) | −11555.2 | −0.121808 | ||||||||
\(309\) | 139206. | 1.45795 | ||||||||
\(310\) | −46859.0 | −0.487607 | ||||||||
\(311\) | −124301. | −1.28515 | −0.642573 | − | 0.766225i | \(-0.722133\pi\) | ||||
−0.642573 | + | 0.766225i | \(0.722133\pi\) | |||||||
\(312\) | 162471.i | 1.66904i | ||||||||
\(313\) | 87747.3 | 0.895664 | 0.447832 | − | 0.894118i | \(-0.352196\pi\) | ||||
0.447832 | + | 0.894118i | \(0.352196\pi\) | |||||||
\(314\) | − | 17946.4i | − | 0.182019i | ||||||
\(315\) | 177879. | 1.79268 | ||||||||
\(316\) | 604.238i | 0.00605110i | ||||||||
\(317\) | − | 40640.3i | − | 0.404426i | −0.979342 | − | 0.202213i | \(-0.935187\pi\) | ||
0.979342 | − | 0.202213i | \(-0.0648133\pi\) | |||||||
\(318\) | 54649.9i | 0.540424i | ||||||||
\(319\) | 8572.74i | 0.0842439i | ||||||||
\(320\) | 21363.2 | 0.208625 | ||||||||
\(321\) | 108892. | 1.05678 | ||||||||
\(322\) | − | 64818.0i | − | 0.625150i | ||||||
\(323\) | 48288.4 | + | 42136.2i | 0.462847 | + | 0.403878i | ||||
\(324\) | 202093. | 1.92514 | ||||||||
\(325\) | − | 66462.6i | − | 0.629232i | ||||||
\(326\) | 36150.9i | 0.340160i | ||||||||
\(327\) | −100775. | −0.942450 | ||||||||
\(328\) | −19218.8 | −0.178640 | ||||||||
\(329\) | −134626. | −1.24377 | ||||||||
\(330\) | 9208.62 | 0.0845603 | ||||||||
\(331\) | − | 146431.i | − | 1.33652i | −0.743927 | − | 0.668260i | \(-0.767039\pi\) | ||
0.743927 | − | 0.668260i | \(-0.232961\pi\) | |||||||
\(332\) | 106803. | 0.968967 | ||||||||
\(333\) | 121313.i | 1.09401i | ||||||||
\(334\) | −43976.0 | −0.394206 | ||||||||
\(335\) | − | 23836.2i | − | 0.212397i | ||||||
\(336\) | − | 53269.8i | − | 0.471848i | ||||||
\(337\) | 191079.i | 1.68249i | 0.540654 | + | 0.841245i | \(0.318177\pi\) | ||||
−0.540654 | + | 0.841245i | \(0.681823\pi\) | |||||||
\(338\) | 4040.02i | 0.0353631i | ||||||||
\(339\) | −342089. | −2.97674 | ||||||||
\(340\) | −29675.6 | −0.256709 | ||||||||
\(341\) | 25098.7i | 0.215845i | ||||||||
\(342\) | 103729. | − | 118875.i | 0.886849 | − | 1.01633i | ||||
\(343\) | −74302.9 | −0.631564 | ||||||||
\(344\) | − | 44514.8i | − | 0.376173i | ||||||
\(345\) | − | 124792.i | − | 1.04846i | ||||||
\(346\) | −42355.2 | −0.353797 | ||||||||
\(347\) | 75833.7 | 0.629801 | 0.314900 | − | 0.949125i | \(-0.398029\pi\) | ||||
0.314900 | + | 0.949125i | \(0.398029\pi\) | |||||||
\(348\) | −95290.2 | −0.786846 | ||||||||
\(349\) | 167272. | 1.37332 | 0.686659 | − | 0.726980i | \(-0.259077\pi\) | ||||
0.686659 | + | 0.726980i | \(0.259077\pi\) | |||||||
\(350\) | − | 52499.6i | − | 0.428568i | ||||||
\(351\) | −332347. | −2.69760 | ||||||||
\(352\) | − | 18165.9i | − | 0.146612i | ||||||
\(353\) | 71568.7 | 0.574346 | 0.287173 | − | 0.957879i | \(-0.407285\pi\) | ||||
0.287173 | + | 0.957879i | \(0.407285\pi\) | |||||||
\(354\) | 165841.i | 1.32338i | ||||||||
\(355\) | 113401.i | 0.899833i | ||||||||
\(356\) | − | 104538.i | − | 0.824848i | ||||||
\(357\) | − | 178069.i | − | 1.39718i | ||||||
\(358\) | 50282.7 | 0.392331 | ||||||||
\(359\) | −121681. | −0.944132 | −0.472066 | − | 0.881563i | \(-0.656492\pi\) | ||||
−0.472066 | + | 0.881563i | \(0.656492\pi\) | |||||||
\(360\) | 176348.i | 1.36071i | ||||||||
\(361\) | 17651.5 | + | 129120.i | 0.135446 | + | 0.990785i | ||||
\(362\) | 115340. | 0.880160 | ||||||||
\(363\) | 241338.i | 1.83152i | ||||||||
\(364\) | 110251.i | 0.832107i | ||||||||
\(365\) | 34433.2 | 0.258459 | ||||||||
\(366\) | 28031.5 | 0.209259 | ||||||||
\(367\) | 233608. | 1.73443 | 0.867214 | − | 0.497935i | \(-0.165908\pi\) | ||||
0.867214 | + | 0.497935i | \(0.165908\pi\) | |||||||
\(368\) | −26672.8 | −0.196958 | ||||||||
\(369\) | − | 65645.7i | − | 0.482118i | ||||||
\(370\) | −19206.6 | −0.140297 | ||||||||
\(371\) | 89519.8i | 0.650387i | ||||||||
\(372\) | −278984. | −2.01602 | ||||||||
\(373\) | 42576.8i | 0.306024i | 0.988224 | + | 0.153012i | \(0.0488973\pi\) | ||||
−0.988224 | + | 0.153012i | \(0.951103\pi\) | |||||||
\(374\) | − | 6579.32i | − | 0.0470368i | ||||||
\(375\) | − | 256372.i | − | 1.82309i | ||||||
\(376\) | − | 133468.i | − | 0.944062i | ||||||
\(377\) | 81794.3 | 0.575493 | ||||||||
\(378\) | −262525. | −1.83733 | ||||||||
\(379\) | 99133.0i | 0.690144i | 0.938576 | + | 0.345072i | \(0.112146\pi\) | ||||
−0.938576 | + | 0.345072i | \(0.887854\pi\) | |||||||
\(380\) | −45468.2 | − | 39675.3i | −0.314877 | − | 0.274760i | ||||
\(381\) | 255657. | 1.76119 | ||||||||
\(382\) | 11730.8i | 0.0803897i | ||||||||
\(383\) | 198667.i | 1.35434i | 0.735826 | + | 0.677171i | \(0.236794\pi\) | ||||
−0.735826 | + | 0.677171i | \(0.763206\pi\) | |||||||
\(384\) | 232856. | 1.57915 | ||||||||
\(385\) | 15084.3 | 0.101766 | ||||||||
\(386\) | −84229.6 | −0.565315 | ||||||||
\(387\) | 152049. | 1.01523 | ||||||||
\(388\) | − | 28998.0i | − | 0.192621i | ||||||
\(389\) | −252659. | −1.66969 | −0.834845 | − | 0.550485i | \(-0.814443\pi\) | ||||
−0.834845 | + | 0.550485i | \(0.814443\pi\) | |||||||
\(390\) | − | 87861.3i | − | 0.577655i | ||||||
\(391\) | −89161.0 | −0.583205 | ||||||||
\(392\) | 68280.8i | 0.444351i | ||||||||
\(393\) | − | 499645.i | − | 3.23501i | ||||||
\(394\) | − | 88998.6i | − | 0.573311i | ||||||
\(395\) | − | 788.777i | − | 0.00505545i | ||||||
\(396\) | 39129.5 | 0.249525 | ||||||||
\(397\) | 37586.2 | 0.238478 | 0.119239 | − | 0.992866i | \(-0.461955\pi\) | ||||
0.119239 | + | 0.992866i | \(0.461955\pi\) | |||||||
\(398\) | 49299.4i | 0.311226i | ||||||||
\(399\) | 238072. | − | 272832.i | 1.49542 | − | 1.71376i | ||||
\(400\) | −21603.7 | −0.135023 | ||||||||
\(401\) | 175688.i | 1.09258i | 0.837596 | + | 0.546290i | \(0.183960\pi\) | ||||
−0.837596 | + | 0.546290i | \(0.816040\pi\) | |||||||
\(402\) | 58741.8i | 0.363492i | ||||||||
\(403\) | 239472. | 1.47450 | ||||||||
\(404\) | 79780.6 | 0.488804 | ||||||||
\(405\) | −263814. | −1.60838 | ||||||||
\(406\) | 64610.3 | 0.391967 | ||||||||
\(407\) | 10287.5i | 0.0621041i | ||||||||
\(408\) | 176536. | 1.06051 | ||||||||
\(409\) | − | 276594.i | − | 1.65347i | −0.562591 | − | 0.826735i | \(-0.690195\pi\) | ||
0.562591 | − | 0.826735i | \(-0.309805\pi\) | |||||||
\(410\) | 10393.2 | 0.0618274 | ||||||||
\(411\) | − | 119100.i | − | 0.705066i | ||||||
\(412\) | 93650.5i | 0.551716i | ||||||||
\(413\) | 271658.i | 1.59266i | ||||||||
\(414\) | 219493.i | 1.28062i | ||||||||
\(415\) | −139422. | −0.809534 | ||||||||
\(416\) | −173324. | −1.00155 | ||||||||
\(417\) | 274804.i | 1.58034i | ||||||||
\(418\) | 8796.35 | − | 10080.7i | 0.0503443 | − | 0.0576949i | ||||
\(419\) | −91901.2 | −0.523471 | −0.261736 | − | 0.965140i | \(-0.584295\pi\) | ||||
−0.261736 | + | 0.965140i | \(0.584295\pi\) | |||||||
\(420\) | 167669.i | 0.950505i | ||||||||
\(421\) | − | 154865.i | − | 0.873753i | −0.899521 | − | 0.436877i | \(-0.856085\pi\) | ||
0.899521 | − | 0.436877i | \(-0.143915\pi\) | |||||||
\(422\) | −174158. | −0.977952 | ||||||||
\(423\) | 455886. | 2.54786 | ||||||||
\(424\) | −88749.4 | −0.493666 | ||||||||
\(425\) | −72216.3 | −0.399813 | ||||||||
\(426\) | − | 279466.i | − | 1.53996i | ||||||
\(427\) | 45917.4 | 0.251838 | ||||||||
\(428\) | 73256.7i | 0.399908i | ||||||||
\(429\) | −47060.5 | −0.255706 | ||||||||
\(430\) | 24072.8i | 0.130194i | ||||||||
\(431\) | − | 110424.i | − | 0.594443i | −0.954809 | − | 0.297221i | \(-0.903940\pi\) | ||
0.954809 | − | 0.297221i | \(-0.0960600\pi\) | |||||||
\(432\) | 108030.i | 0.578863i | ||||||||
\(433\) | − | 34749.0i | − | 0.185339i | −0.995697 | − | 0.0926694i | \(-0.970460\pi\) | ||
0.995697 | − | 0.0926694i | \(-0.0295400\pi\) | |||||||
\(434\) | 189162. | 1.00428 | ||||||||
\(435\) | 124393. | 0.657379 | ||||||||
\(436\) | − | 67796.3i | − | 0.356642i | ||||||
\(437\) | −136610. | − | 119205.i | −0.715353 | − | 0.624214i | ||||
\(438\) | −84856.9 | −0.442322 | ||||||||
\(439\) | − | 82718.3i | − | 0.429213i | −0.976701 | − | 0.214606i | \(-0.931153\pi\) | ||
0.976701 | − | 0.214606i | \(-0.0688468\pi\) | |||||||
\(440\) | 14954.5i | 0.0772441i | ||||||||
\(441\) | −233227. | −1.19923 | ||||||||
\(442\) | −62774.7 | −0.321322 | ||||||||
\(443\) | −214703. | −1.09404 | −0.547018 | − | 0.837121i | \(-0.684237\pi\) | ||||
−0.547018 | + | 0.837121i | \(0.684237\pi\) | |||||||
\(444\) | −114350. | −0.580058 | ||||||||
\(445\) | 136465.i | 0.689128i | ||||||||
\(446\) | −18535.0 | −0.0931801 | ||||||||
\(447\) | 204005.i | 1.02100i | ||||||||
\(448\) | −86239.6 | −0.429686 | ||||||||
\(449\) | 200750.i | 0.995781i | 0.867240 | + | 0.497891i | \(0.165892\pi\) | ||||
−0.867240 | + | 0.497891i | \(0.834108\pi\) | |||||||
\(450\) | 177779.i | 0.877923i | ||||||||
\(451\) | − | 5566.82i | − | 0.0273687i | ||||||
\(452\) | − | 230140.i | − | 1.12646i | ||||||
\(453\) | −446465. | −2.17566 | ||||||||
\(454\) | 81677.1 | 0.396268 | ||||||||
\(455\) | − | 143922.i | − | 0.695193i | ||||||
\(456\) | 270484. | + | 236023.i | 1.30081 | + | 1.13508i | ||||
\(457\) | 130986. | 0.627183 | 0.313591 | − | 0.949558i | \(-0.398468\pi\) | ||||
0.313591 | + | 0.949558i | \(0.398468\pi\) | |||||||
\(458\) | − | 95289.4i | − | 0.454270i | ||||||
\(459\) | 361118.i | 1.71405i | ||||||||
\(460\) | 83953.8 | 0.396757 | ||||||||
\(461\) | 35097.5 | 0.165149 | 0.0825743 | − | 0.996585i | \(-0.473686\pi\) | ||||
0.0825743 | + | 0.996585i | \(0.473686\pi\) | |||||||
\(462\) | −37173.6 | −0.174161 | ||||||||
\(463\) | −28532.2 | −0.133099 | −0.0665493 | − | 0.997783i | \(-0.521199\pi\) | ||||
−0.0665493 | + | 0.997783i | \(0.521199\pi\) | |||||||
\(464\) | − | 26587.3i | − | 0.123492i | ||||||
\(465\) | 364188. | 1.68430 | ||||||||
\(466\) | − | 11714.7i | − | 0.0539461i | ||||||
\(467\) | 402160. | 1.84402 | 0.922008 | − | 0.387170i | \(-0.126547\pi\) | ||||
0.922008 | + | 0.387170i | \(0.126547\pi\) | |||||||
\(468\) | − | 373343.i | − | 1.70457i | ||||||
\(469\) | 96222.7i | 0.437453i | ||||||||
\(470\) | 72176.9i | 0.326740i | ||||||||
\(471\) | 139479.i | 0.628736i | ||||||||
\(472\) | −269320. | −1.20888 | ||||||||
\(473\) | 12893.9 | 0.0576319 | ||||||||
\(474\) | 1943.86i | 0.00865182i | ||||||||
\(475\) | −110648. | − | 96550.9i | −0.490407 | − | 0.427926i | ||||
\(476\) | 119795. | 0.528720 | ||||||||
\(477\) | − | 303141.i | − | 1.33232i | ||||||
\(478\) | − | 52091.9i | − | 0.227989i | ||||||
\(479\) | −272020. | −1.18558 | −0.592788 | − | 0.805359i | \(-0.701973\pi\) | ||||
−0.592788 | + | 0.805359i | \(0.701973\pi\) | |||||||
\(480\) | −263591. | −1.14406 | ||||||||
\(481\) | 98154.9 | 0.424250 | ||||||||
\(482\) | 53351.9 | 0.229644 | ||||||||
\(483\) | 503766.i | 2.15941i | ||||||||
\(484\) | −162359. | −0.693085 | ||||||||
\(485\) | 37854.2i | 0.160928i | ||||||||
\(486\) | 293546. | 1.24281 | ||||||||
\(487\) | − | 412092.i | − | 1.73754i | −0.495212 | − | 0.868772i | \(-0.664910\pi\) | ||
0.495212 | − | 0.868772i | \(-0.335090\pi\) | |||||||
\(488\) | 45522.2i | 0.191154i | ||||||||
\(489\) | − | 280965.i | − | 1.17499i | ||||||
\(490\) | − | 36925.0i | − | 0.153790i | ||||||
\(491\) | 343889. | 1.42645 | 0.713223 | − | 0.700938i | \(-0.247235\pi\) | ||||
0.713223 | + | 0.700938i | \(0.247235\pi\) | |||||||
\(492\) | 61877.9 | 0.255626 | ||||||||
\(493\) | − | 88875.3i | − | 0.365668i | ||||||
\(494\) | −96181.8 | − | 83927.8i | −0.394130 | − | 0.343916i | ||||
\(495\) | −51080.0 | −0.208468 | ||||||||
\(496\) | − | 77840.6i | − | 0.316405i | ||||||
\(497\) | − | 457782.i | − | 1.85330i | ||||||
\(498\) | 343591. | 1.38542 | ||||||||
\(499\) | −166687. | −0.669425 | −0.334712 | − | 0.942320i | \(-0.608639\pi\) | ||||
−0.334712 | + | 0.942320i | \(0.608639\pi\) | |||||||
\(500\) | 172474. | 0.689895 | ||||||||
\(501\) | 341782. | 1.36168 | ||||||||
\(502\) | 198807.i | 0.788903i | ||||||||
\(503\) | −341395. | −1.34934 | −0.674669 | − | 0.738121i | \(-0.735714\pi\) | ||||
−0.674669 | + | 0.738121i | \(0.735714\pi\) | |||||||
\(504\) | − | 711885.i | − | 2.80252i | ||||||
\(505\) | −104146. | −0.408377 | ||||||||
\(506\) | 18613.3i | 0.0726978i | ||||||||
\(507\) | − | 31399.1i | − | 0.122152i | ||||||
\(508\) | 171992.i | 0.666472i | ||||||||
\(509\) | 390009.i | 1.50535i | 0.658390 | + | 0.752677i | \(0.271238\pi\) | ||||
−0.658390 | + | 0.752677i | \(0.728762\pi\) | |||||||
\(510\) | −95467.5 | −0.367042 | ||||||||
\(511\) | −139001. | −0.532323 | ||||||||
\(512\) | 106574.i | 0.406548i | ||||||||
\(513\) | −482804. | + | 553297.i | −1.83458 | + | 2.10244i | ||||
\(514\) | 137758. | 0.521422 | ||||||||
\(515\) | − | 122252.i | − | 0.460938i | ||||||
\(516\) | 143322.i | 0.538287i | ||||||||
\(517\) | 38659.6 | 0.144636 | ||||||||
\(518\) | 77533.7 | 0.288955 | ||||||||
\(519\) | 329185. | 1.22209 | ||||||||
\(520\) | 142684. | 0.527676 | ||||||||
\(521\) | 385501.i | 1.42020i | 0.704099 | + | 0.710102i | \(0.251351\pi\) | ||||
−0.704099 | + | 0.710102i | \(0.748649\pi\) | |||||||
\(522\) | −218790. | −0.802946 | ||||||||
\(523\) | 480249.i | 1.75575i | 0.478889 | + | 0.877875i | \(0.341039\pi\) | ||||
−0.478889 | + | 0.877875i | \(0.658961\pi\) | |||||||
\(524\) | 336135. | 1.22420 | ||||||||
\(525\) | 408027.i | 1.48037i | ||||||||
\(526\) | 244716.i | 0.884487i | ||||||||
\(527\) | − | 260203.i | − | 0.936896i | ||||||
\(528\) | 15297.0i | 0.0548706i | ||||||||
\(529\) | −27599.8 | −0.0986267 | ||||||||
\(530\) | 47994.1 | 0.170858 | ||||||||
\(531\) | − | 919916.i | − | 3.26257i | ||||||
\(532\) | 183547. | + | 160163.i | 0.648522 | + | 0.565897i | ||||
\(533\) | −53114.2 | −0.186963 | ||||||||
\(534\) | − | 336302.i | − | 1.17936i | ||||||
\(535\) | − | 95629.9i | − | 0.334107i | ||||||
\(536\) | −95394.5 | −0.332043 | ||||||||
\(537\) | −390797. | −1.35520 | ||||||||
\(538\) | 118719. | 0.410162 | ||||||||
\(539\) | −19777.9 | −0.0680772 | ||||||||
\(540\) | − | 340028.i | − | 1.16608i | ||||||
\(541\) | 398980. | 1.36319 | 0.681595 | − | 0.731730i | \(-0.261287\pi\) | ||||
0.681595 | + | 0.731730i | \(0.261287\pi\) | |||||||
\(542\) | 132160.i | 0.449885i | ||||||||
\(543\) | −896420. | −3.04027 | ||||||||
\(544\) | 188329.i | 0.636383i | ||||||||
\(545\) | 88501.8i | 0.297961i | ||||||||
\(546\) | 354681.i | 1.18974i | ||||||||
\(547\) | − | 4309.05i | − | 0.0144015i | −0.999974 | − | 0.00720073i | \(-0.997708\pi\) | ||
0.999974 | − | 0.00720073i | \(-0.00229208\pi\) | |||||||
\(548\) | 80124.5 | 0.266811 | ||||||||
\(549\) | −155490. | −0.515891 | ||||||||
\(550\) | 15075.9i | 0.0498376i | ||||||||
\(551\) | 118823. | − | 136172.i | 0.391380 | − | 0.448524i | ||||
\(552\) | −499430. | −1.63907 | ||||||||
\(553\) | 3184.16i | 0.0104122i | ||||||||
\(554\) | − | 67923.5i | − | 0.221310i | ||||||
\(555\) | 149274. | 0.484615 | ||||||||
\(556\) | −184873. | −0.598033 | ||||||||
\(557\) | −208935. | −0.673444 | −0.336722 | − | 0.941604i | \(-0.609318\pi\) | ||||
−0.336722 | + | 0.941604i | \(0.609318\pi\) | |||||||
\(558\) | −640559. | −2.05727 | ||||||||
\(559\) | − | 123024.i | − | 0.393699i | ||||||
\(560\) | −46782.1 | −0.149177 | ||||||||
\(561\) | 51134.5i | 0.162476i | ||||||||
\(562\) | −172946. | −0.547568 | ||||||||
\(563\) | − | 552442.i | − | 1.74289i | −0.490493 | − | 0.871445i | \(-0.663183\pi\) | ||
0.490493 | − | 0.871445i | \(-0.336817\pi\) | |||||||
\(564\) | 429720.i | 1.35091i | ||||||||
\(565\) | 300426.i | 0.941111i | ||||||||
\(566\) | − | 216230.i | − | 0.674969i | ||||||
\(567\) | 1.06497e6 | 3.31262 | ||||||||
\(568\) | 453842. | 1.40672 | ||||||||
\(569\) | 376174.i | 1.16189i | 0.813943 | + | 0.580944i | \(0.197317\pi\) | ||||
−0.813943 | + | 0.580944i | \(0.802683\pi\) | |||||||
\(570\) | −146273. | − | 127637.i | −0.450209 | − | 0.392850i | ||||
\(571\) | −390679. | −1.19825 | −0.599125 | − | 0.800656i | \(-0.704485\pi\) | ||||
−0.599125 | + | 0.800656i | \(0.704485\pi\) | |||||||
\(572\) | − | 31659.8i | − | 0.0967646i | ||||||
\(573\) | − | 91171.7i | − | 0.277684i | ||||||
\(574\) | −41955.5 | −0.127340 | ||||||||
\(575\) | 204304. | 0.617932 | ||||||||
\(576\) | 292034. | 0.880213 | ||||||||
\(577\) | −374980. | −1.12631 | −0.563153 | − | 0.826352i | \(-0.690412\pi\) | ||||
−0.563153 | + | 0.826352i | \(0.690412\pi\) | |||||||
\(578\) | − | 112552.i | − | 0.336896i | ||||||
\(579\) | 654633. | 1.95272 | ||||||||
\(580\) | 83684.8i | 0.248766i | ||||||||
\(581\) | 562823. | 1.66732 | ||||||||
\(582\) | − | 93287.6i | − | 0.275409i | ||||||
\(583\) | − | 25706.7i | − | 0.0756326i | ||||||
\(584\) | − | 137804.i | − | 0.404052i | ||||||
\(585\) | 487364.i | 1.42411i | ||||||||
\(586\) | 3552.13 | 0.0103441 | ||||||||
\(587\) | 269098. | 0.780970 | 0.390485 | − | 0.920609i | \(-0.372307\pi\) | ||||
0.390485 | + | 0.920609i | \(0.372307\pi\) | |||||||
\(588\) | − | 219840.i | − | 0.635847i | ||||||
\(589\) | 347884. | − | 398677.i | 1.00277 | − | 1.14919i | ||||
\(590\) | 145643. | 0.418395 | ||||||||
\(591\) | 691697.i | 1.98035i | ||||||||
\(592\) | − | 31905.3i | − | 0.0910374i | ||||||
\(593\) | 56198.5 | 0.159814 | 0.0799071 | − | 0.996802i | \(-0.474538\pi\) | ||||
0.0799071 | + | 0.996802i | \(0.474538\pi\) | |||||||
\(594\) | 75387.0 | 0.213660 | ||||||||
\(595\) | −156382. | −0.441725 | ||||||||
\(596\) | −137244. | −0.386367 | ||||||||
\(597\) | − | 383155.i | − | 1.07504i | ||||||
\(598\) | 177593. | 0.496619 | ||||||||
\(599\) | − | 149473.i | − | 0.416592i | −0.978066 | − | 0.208296i | \(-0.933208\pi\) | ||
0.978066 | − | 0.208296i | \(-0.0667917\pi\) | |||||||
\(600\) | −404515. | −1.12365 | ||||||||
\(601\) | 111386.i | 0.308377i | 0.988041 | + | 0.154188i | \(0.0492763\pi\) | ||||
−0.988041 | + | 0.154188i | \(0.950724\pi\) | |||||||
\(602\) | − | 97177.8i | − | 0.268148i | ||||||
\(603\) | − | 325839.i | − | 0.896125i | ||||||
\(604\) | − | 300358.i | − | 0.823314i | ||||||
\(605\) | 211945. | 0.579046 | ||||||||
\(606\) | 256657. | 0.698889 | ||||||||
\(607\) | 496593.i | 1.34779i | 0.738826 | + | 0.673896i | \(0.235381\pi\) | ||||
−0.738826 | + | 0.673896i | \(0.764619\pi\) | |||||||
\(608\) | −251790. | + | 288553.i | −0.681131 | + | 0.780581i | ||||
\(609\) | −502151. | −1.35394 | ||||||||
\(610\) | − | 24617.6i | − | 0.0661585i | ||||||
\(611\) | − | 368859.i | − | 0.988047i | ||||||
\(612\) | −405663. | −1.08309 | ||||||||
\(613\) | 21019.3 | 0.0559369 | 0.0279684 | − | 0.999609i | \(-0.491096\pi\) | ||||
0.0279684 | + | 0.999609i | \(0.491096\pi\) | |||||||
\(614\) | −156681. | −0.415605 | ||||||||
\(615\) | −80775.8 | −0.213566 | ||||||||
\(616\) | − | 60368.6i | − | 0.159092i | ||||||
\(617\) | −415170. | −1.09058 | −0.545288 | − | 0.838249i | \(-0.683580\pi\) | ||||
−0.545288 | + | 0.838249i | \(0.683580\pi\) | |||||||
\(618\) | 301277.i | 0.788841i | ||||||||
\(619\) | −40823.3 | −0.106543 | −0.0532717 | − | 0.998580i | \(-0.516965\pi\) | ||||
−0.0532717 | + | 0.998580i | \(0.516965\pi\) | |||||||
\(620\) | 245007.i | 0.637375i | ||||||||
\(621\) | − | 1.02162e6i | − | 2.64915i | ||||||
\(622\) | − | 269018.i | − | 0.695345i | ||||||
\(623\) | − | 550884.i | − | 1.41933i | ||||||
\(624\) | 145952. | 0.374836 | ||||||||
\(625\) | 29093.9 | 0.0744804 | ||||||||
\(626\) | 189907.i | 0.484611i | ||||||||
\(627\) | −68365.2 | + | 78347.0i | −0.173900 | + | 0.199291i | ||||
\(628\) | −93834.4 | −0.237926 | ||||||||
\(629\) | − | 106652.i | − | 0.269568i | ||||||
\(630\) | 384975.i | 0.969954i | ||||||||
\(631\) | −515651. | −1.29508 | −0.647541 | − | 0.762030i | \(-0.724203\pi\) | ||||
−0.647541 | + | 0.762030i | \(0.724203\pi\) | |||||||
\(632\) | −3156.75 | −0.00790326 | ||||||||
\(633\) | 1.35355e6 | 3.37807 | ||||||||
\(634\) | 87956.0 | 0.218820 | ||||||||
\(635\) | − | 224520.i | − | 0.556811i | ||||||
\(636\) | 285742. | 0.706415 | ||||||||
\(637\) | 188705.i | 0.465054i | ||||||||
\(638\) | −18553.6 | −0.0455813 | ||||||||
\(639\) | 1.55019e6i | 3.79649i | ||||||||
\(640\) | − | 204496.i | − | 0.499258i | ||||||
\(641\) | − | 100947.i | − | 0.245685i | −0.992426 | − | 0.122843i | \(-0.960799\pi\) | ||
0.992426 | − | 0.122843i | \(-0.0392010\pi\) | |||||||
\(642\) | 235670.i | 0.571786i | ||||||||
\(643\) | −256498. | −0.620386 | −0.310193 | − | 0.950674i | \(-0.600394\pi\) | ||||
−0.310193 | + | 0.950674i | \(0.600394\pi\) | |||||||
\(644\) | −338907. | −0.817163 | ||||||||
\(645\) | − | 187094.i | − | 0.449718i | ||||||
\(646\) | −91193.4 | + | 104508.i | −0.218524 | + | 0.250430i | ||||
\(647\) | 752626. | 1.79792 | 0.898961 | − | 0.438029i | \(-0.144323\pi\) | ||||
0.898961 | + | 0.438029i | \(0.144323\pi\) | |||||||
\(648\) | 1.05581e6i | 2.51440i | ||||||||
\(649\) | − | 78009.8i | − | 0.185208i | ||||||
\(650\) | 143842. | 0.340454 | ||||||||
\(651\) | −1.47017e6 | −3.46900 | ||||||||
\(652\) | 189018. | 0.444640 | ||||||||
\(653\) | −703535. | −1.64991 | −0.824953 | − | 0.565201i | \(-0.808798\pi\) | ||||
−0.824953 | + | 0.565201i | \(0.808798\pi\) | |||||||
\(654\) | − | 218103.i | − | 0.509925i | ||||||
\(655\) | −438793. | −1.02277 | ||||||||
\(656\) | 17264.8i | 0.0401194i | ||||||||
\(657\) | 470699. | 1.09047 | ||||||||
\(658\) | − | 291366.i | − | 0.672956i | ||||||
\(659\) | 813907.i | 1.87415i | 0.349130 | + | 0.937074i | \(0.386477\pi\) | ||||
−0.349130 | + | 0.937074i | \(0.613523\pi\) | |||||||
\(660\) | − | 48148.2i | − | 0.110533i | ||||||
\(661\) | − | 426236.i | − | 0.975545i | −0.872971 | − | 0.487772i | \(-0.837810\pi\) | ||
0.872971 | − | 0.487772i | \(-0.162190\pi\) | |||||||
\(662\) | 316913. | 0.723143 | ||||||||
\(663\) | 487885. | 1.10992 | ||||||||
\(664\) | 557979.i | 1.26556i | ||||||||
\(665\) | −239604. | − | 209077.i | −0.541815 | − | 0.472785i | ||||
\(666\) | −262553. | −0.591927 | ||||||||
\(667\) | 251433.i | 0.565158i | ||||||||
\(668\) | 229933.i | 0.515286i | ||||||||
\(669\) | 144054. | 0.321865 | ||||||||
\(670\) | 51587.6 | 0.114920 | ||||||||
\(671\) | −13185.7 | −0.0292859 | ||||||||
\(672\) | 1.06407e6 | 2.35631 | ||||||||
\(673\) | − | 513214.i | − | 1.13310i | −0.824027 | − | 0.566550i | \(-0.808278\pi\) | ||
0.824027 | − | 0.566550i | \(-0.191722\pi\) | |||||||
\(674\) | −413543. | −0.910334 | ||||||||
\(675\) | − | 827467.i | − | 1.81611i | ||||||
\(676\) | 21123.6 | 0.0462248 | ||||||||
\(677\) | − | 139181.i | − | 0.303671i | −0.988406 | − | 0.151836i | \(-0.951482\pi\) | ||
0.988406 | − | 0.151836i | \(-0.0485184\pi\) | |||||||
\(678\) | − | 740368.i | − | 1.61060i | ||||||
\(679\) | − | 152811.i | − | 0.331447i | ||||||
\(680\) | − | 155036.i | − | 0.335285i | ||||||
\(681\) | −634795. | −1.36880 | ||||||||
\(682\) | −54320.0 | −0.116786 | ||||||||
\(683\) | 340635.i | 0.730211i | 0.930966 | + | 0.365105i | \(0.118967\pi\) | ||||
−0.930966 | + | 0.365105i | \(0.881033\pi\) | |||||||
\(684\) | −621547. | − | 542359.i | −1.32850 | − | 1.15924i | ||||
\(685\) | −104595. | −0.222910 | ||||||||
\(686\) | − | 160810.i | − | 0.341716i | ||||||
\(687\) | 740590.i | 1.56915i | ||||||||
\(688\) | −39988.9 | −0.0844817 | ||||||||
\(689\) | −245273. | −0.516667 | ||||||||
\(690\) | 270083. | 0.567281 | ||||||||
\(691\) | 665671. | 1.39413 | 0.697065 | − | 0.717008i | \(-0.254489\pi\) | ||||
0.697065 | + | 0.717008i | \(0.254489\pi\) | |||||||
\(692\) | 221458.i | 0.462466i | ||||||||
\(693\) | 206201. | 0.429363 | ||||||||
\(694\) | 164123.i | 0.340762i | ||||||||
\(695\) | 241335. | 0.499633 | ||||||||
\(696\) | − | 497829.i | − | 1.02769i | ||||||
\(697\) | 57712.3i | 0.118796i | ||||||||
\(698\) | 362018.i | 0.743052i | ||||||||
\(699\) | 91046.8i | 0.186342i | ||||||||
\(700\) | −274499. | −0.560202 | ||||||||
\(701\) | −287944. | −0.585965 | −0.292982 | − | 0.956118i | \(-0.594648\pi\) | ||||
−0.292982 | + | 0.956118i | \(0.594648\pi\) | |||||||
\(702\) | − | 719283.i | − | 1.45957i | ||||||
\(703\) | 142591. | − | 163410.i | 0.288523 | − | 0.330649i | ||||
\(704\) | 24764.7 | 0.0499676 | ||||||||
\(705\) | − | 560959.i | − | 1.12863i | ||||||
\(706\) | 154893.i | 0.310758i | ||||||||
\(707\) | 420420. | 0.841095 | ||||||||
\(708\) | 867116. | 1.72986 | ||||||||
\(709\) | 461125. | 0.917331 | 0.458665 | − | 0.888609i | \(-0.348328\pi\) | ||||
0.458665 | + | 0.888609i | \(0.348328\pi\) | |||||||
\(710\) | −245430. | −0.486867 | ||||||||
\(711\) | − | 10782.5i | − | 0.0213295i | ||||||
\(712\) | 546143. | 1.07732 | ||||||||
\(713\) | 736129.i | 1.44802i | ||||||||
\(714\) | 385386. | 0.755961 | ||||||||
\(715\) | 41329.0i | 0.0808430i | ||||||||
\(716\) | − | 262908.i | − | 0.512834i | ||||||
\(717\) | 404858.i | 0.787525i | ||||||||
\(718\) | − | 263348.i | − | 0.510835i | ||||||
\(719\) | 680993. | 1.31730 | 0.658650 | − | 0.752449i | \(-0.271128\pi\) | ||||
0.658650 | + | 0.752449i | \(0.271128\pi\) | |||||||
\(720\) | 158418. | 0.305591 | ||||||||
\(721\) | 493511.i | 0.949349i | ||||||||
\(722\) | −279449. | + | 38202.3i | −0.536077 | + | 0.0732849i | ||||
\(723\) | −414651. | −0.793243 | ||||||||
\(724\) | − | 603065.i | − | 1.15050i | ||||||
\(725\) | 203649.i | 0.387441i | ||||||||
\(726\) | −522316. | −0.990970 | ||||||||
\(727\) | 11537.8 | 0.0218301 | 0.0109150 | − | 0.999940i | \(-0.496526\pi\) | ||||
0.0109150 | + | 0.999940i | \(0.496526\pi\) | |||||||
\(728\) | −575989. | −1.08680 | ||||||||
\(729\) | −834857. | −1.57093 | ||||||||
\(730\) | 74522.1i | 0.139843i | ||||||||
\(731\) | −133674. | −0.250156 | ||||||||
\(732\) | − | 146566.i | − | 0.273533i | ||||||
\(733\) | 27216.9 | 0.0506560 | 0.0253280 | − | 0.999679i | \(-0.491937\pi\) | ||||
0.0253280 | + | 0.999679i | \(0.491937\pi\) | |||||||
\(734\) | 505588.i | 0.938436i | ||||||||
\(735\) | 286981.i | 0.531226i | ||||||||
\(736\) | − | 532792.i | − | 0.983563i | ||||||
\(737\) | − | 27631.5i | − | 0.0508708i | ||||||
\(738\) | 142074. | 0.260857 | ||||||||
\(739\) | 488729. | 0.894909 | 0.447455 | − | 0.894307i | \(-0.352331\pi\) | ||||
0.447455 | + | 0.894307i | \(0.352331\pi\) | |||||||
\(740\) | 100423.i | 0.183388i | ||||||||
\(741\) | 747525. | + | 652287.i | 1.36141 | + | 1.18796i | ||||
\(742\) | −193744. | −0.351900 | ||||||||
\(743\) | − | 4601.59i | − | 0.00833548i | −0.999991 | − | 0.00416774i | \(-0.998673\pi\) | ||
0.999991 | − | 0.00416774i | \(-0.00132664\pi\) | |||||||
\(744\) | − | 1.45751e6i | − | 2.63309i | ||||||
\(745\) | 179159. | 0.322794 | ||||||||
\(746\) | −92146.9 | −0.165578 | ||||||||
\(747\) | −1.90589e6 | −3.41552 | ||||||||
\(748\) | −34400.6 | −0.0614841 | ||||||||
\(749\) | 386041.i | 0.688129i | ||||||||
\(750\) | 554854. | 0.986408 | ||||||||
\(751\) | − | 62141.6i | − | 0.110180i | −0.998481 | − | 0.0550900i | \(-0.982455\pi\) | ||
0.998481 | − | 0.0550900i | \(-0.0175446\pi\) | |||||||
\(752\) | −119898. | −0.212019 | ||||||||
\(753\) | − | 1.54513e6i | − | 2.72505i | ||||||
\(754\) | 177024.i | 0.311378i | ||||||||
\(755\) | 392090.i | 0.687847i | ||||||||
\(756\) | 1.37264e6i | 2.40166i | ||||||||
\(757\) | −295159. | −0.515067 | −0.257533 | − | 0.966269i | \(-0.582910\pi\) | ||||
−0.257533 | + | 0.966269i | \(0.582910\pi\) | |||||||
\(758\) | −214549. | −0.373412 | ||||||||
\(759\) | − | 144662.i | − | 0.251114i | ||||||
\(760\) | 207278. | − | 237542.i | 0.358861 | − | 0.411257i | ||||
\(761\) | 327534. | 0.565571 | 0.282785 | − | 0.959183i | \(-0.408742\pi\) | ||||
0.282785 | + | 0.959183i | \(0.408742\pi\) | |||||||
\(762\) | 553306.i | 0.952918i | ||||||||
\(763\) | − | 357266.i | − | 0.613681i | ||||||
\(764\) | 61335.5 | 0.105081 | ||||||||
\(765\) | 529556. | 0.904875 | ||||||||
\(766\) | −429966. | −0.732785 | ||||||||
\(767\) | −744307. | −1.26521 | ||||||||
\(768\) | 893173.i | 1.51430i | ||||||||
\(769\) | 805330. | 1.36182 | 0.680912 | − | 0.732365i | \(-0.261583\pi\) | ||||
0.680912 | + | 0.732365i | \(0.261583\pi\) | |||||||
\(770\) | 32646.2i | 0.0550619i | ||||||||
\(771\) | −1.07065e6 | −1.80111 | ||||||||
\(772\) | 440403.i | 0.738950i | ||||||||
\(773\) | 585854.i | 0.980462i | 0.871593 | + | 0.490231i | \(0.163088\pi\) | ||||
−0.871593 | + | 0.490231i | \(0.836912\pi\) | |||||||
\(774\) | 329073.i | 0.549301i | ||||||||
\(775\) | 596230.i | 0.992683i | ||||||||
\(776\) | 151496. | 0.251580 | ||||||||
\(777\) | −602592. | −0.998117 | ||||||||
\(778\) | − | 546819.i | − | 0.903409i | ||||||
\(779\) | −77159.5 | + | 88425.3i | −0.127149 | + | 0.145714i | ||||
\(780\) | −459391. | −0.755081 | ||||||||
\(781\) | 131457.i | 0.215518i | ||||||||
\(782\) | − | 192967.i | − | 0.315551i | ||||||
\(783\) | 1.01835e6 | 1.66101 | ||||||||
\(784\) | 61338.6 | 0.0997934 | ||||||||
\(785\) | 122492. | 0.198778 | ||||||||
\(786\) | 1.08136e6 | 1.75035 | ||||||||
\(787\) | 762631.i | 1.23130i | 0.788018 | + | 0.615652i | \(0.211107\pi\) | ||||
−0.788018 | + | 0.615652i | \(0.788893\pi\) | |||||||
\(788\) | −465337. | −0.749403 | ||||||||
\(789\) | − | 1.90194e6i | − | 3.05522i | ||||||
\(790\) | 1707.11 | 0.00273532 | ||||||||
\(791\) | − | 1.21277e6i | − | 1.93832i | ||||||
\(792\) | 204426.i | 0.325901i | ||||||||
\(793\) | 125808.i | 0.200060i | ||||||||
\(794\) | 81346.2i | 0.129032i | ||||||||
\(795\) | −373010. | −0.590182 | ||||||||
\(796\) | 257767. | 0.406818 | ||||||||
\(797\) | − | 739146.i | − | 1.16363i | −0.813322 | − | 0.581813i | \(-0.802343\pi\) | ||
0.813322 | − | 0.581813i | \(-0.197657\pi\) | |||||||
\(798\) | 590479. | + | 515249.i | 0.927253 | + | 0.809117i | ||||
\(799\) | −400791. | −0.627804 | ||||||||
\(800\) | − | 431537.i | − | 0.674276i | ||||||
\(801\) | 1.86546e6i | 2.90751i | ||||||||
\(802\) | −380233. | −0.591155 | ||||||||
\(803\) | 39915.7 | 0.0619031 | ||||||||
\(804\) | 307137. | 0.475138 | ||||||||
\(805\) | 442412. | 0.682708 | ||||||||
\(806\) | 518278.i | 0.797798i | ||||||||
\(807\) | −922685. | −1.41679 | ||||||||
\(808\) | 416802.i | 0.638421i | ||||||||
\(809\) | −283400. | −0.433015 | −0.216508 | − | 0.976281i | \(-0.569467\pi\) | ||||
−0.216508 | + | 0.976281i | \(0.569467\pi\) | |||||||
\(810\) | − | 570961.i | − | 0.870234i | ||||||
\(811\) | − | 14690.1i | − | 0.0223348i | −0.999938 | − | 0.0111674i | \(-0.996445\pi\) | ||
0.999938 | − | 0.0111674i | \(-0.00355477\pi\) | |||||||
\(812\) | − | 337821.i | − | 0.512359i | ||||||
\(813\) | − | 1.02715e6i | − | 1.55400i | ||||||
\(814\) | −22264.7 | −0.0336022 | ||||||||
\(815\) | −246746. | −0.371479 | ||||||||
\(816\) | − | 158587.i | − | 0.238171i | ||||||
\(817\) | −204812. | − | 178718.i | −0.306839 | − | 0.267746i | ||||
\(818\) | 598620. | 0.894632 | ||||||||
\(819\) | − | 1.96741e6i | − | 2.93310i | ||||||
\(820\) | − | 54341.7i | − | 0.0808176i | ||||||
\(821\) | 668244. | 0.991399 | 0.495699 | − | 0.868494i | \(-0.334912\pi\) | ||||
0.495699 | + | 0.868494i | \(0.334912\pi\) | |||||||
\(822\) | 257763. | 0.381485 | ||||||||
\(823\) | 6475.45 | 0.00956028 | 0.00478014 | − | 0.999989i | \(-0.498478\pi\) | ||||
0.00478014 | + | 0.999989i | \(0.498478\pi\) | |||||||
\(824\) | −489263. | −0.720590 | ||||||||
\(825\) | − | 117170.i | − | 0.172150i | ||||||
\(826\) | −587937. | −0.861729 | ||||||||
\(827\) | 55503.2i | 0.0811534i | 0.999176 | + | 0.0405767i | \(0.0129195\pi\) | ||||
−0.999176 | + | 0.0405767i | \(0.987080\pi\) | |||||||
\(828\) | 1.14764e6 | 1.67396 | ||||||||
\(829\) | 475443.i | 0.691813i | 0.938269 | + | 0.345907i | \(0.112429\pi\) | ||||
−0.938269 | + | 0.345907i | \(0.887571\pi\) | |||||||
\(830\) | − | 301745.i | − | 0.438009i | ||||||
\(831\) | 527902.i | 0.764453i | ||||||||
\(832\) | − | 236285.i | − | 0.341342i | ||||||
\(833\) | 205041. | 0.295495 | ||||||||
\(834\) | −594745. | −0.855064 | ||||||||
\(835\) | − | 300156.i | − | 0.430501i | ||||||
\(836\) | −52707.8 | − | 45992.5i | −0.0754158 | − | 0.0658074i | ||||
\(837\) | 2.98145e6 | 4.25576 | ||||||||
\(838\) | − | 198897.i | − | 0.283231i | ||||||
\(839\) | − | 389106.i | − | 0.552770i | −0.961047 | − | 0.276385i | \(-0.910864\pi\) | ||
0.961047 | − | 0.276385i | \(-0.0891364\pi\) | |||||||
\(840\) | −875962. | −1.24144 | ||||||||
\(841\) | 456654. | 0.645647 | ||||||||
\(842\) | 335167. | 0.472756 | ||||||||
\(843\) | 1.34414e6 | 1.89142 | ||||||||
\(844\) | 910600.i | 1.27833i | ||||||||
\(845\) | −27575.0 | −0.0386190 | ||||||||
\(846\) | 986653.i | 1.37855i | ||||||||
\(847\) | −855586. | −1.19261 | ||||||||
\(848\) | 79726.1i | 0.110869i | ||||||||
\(849\) | 1.68054e6i | 2.33149i | ||||||||
\(850\) | − | 156294.i | − | 0.216324i | ||||||
\(851\) | 301725.i | 0.416631i | ||||||||
\(852\) | −1.46121e6 | −2.01296 | ||||||||
\(853\) | −1.17337e6 | −1.61264 | −0.806322 | − | 0.591476i | \(-0.798545\pi\) | ||||
−0.806322 | + | 0.591476i | \(0.798545\pi\) | |||||||
\(854\) | 99376.9i | 0.136260i | ||||||||
\(855\) | 811372. | + | 707999.i | 1.10991 | + | 0.968502i | ||||
\(856\) | −382719. | −0.522314 | ||||||||
\(857\) | − | 170943.i | − | 0.232750i | −0.993205 | − | 0.116375i | \(-0.962873\pi\) | ||
0.993205 | − | 0.116375i | \(-0.0371274\pi\) | |||||||
\(858\) | − | 101851.i | − | 0.138353i | ||||||
\(859\) | 494381. | 0.670002 | 0.335001 | − | 0.942218i | \(-0.391263\pi\) | ||||
0.335001 | + | 0.942218i | \(0.391263\pi\) | |||||||
\(860\) | 125867. | 0.170182 | ||||||||
\(861\) | 326078. | 0.439861 | ||||||||
\(862\) | 238986. | 0.321631 | ||||||||
\(863\) | − | 1.38223e6i | − | 1.85591i | −0.372691 | − | 0.927956i | \(-0.621565\pi\) | ||
0.372691 | − | 0.927956i | \(-0.378435\pi\) | |||||||
\(864\) | −2.15790e6 | −2.89071 | ||||||||
\(865\) | − | 289093.i | − | 0.386372i | ||||||
\(866\) | 75205.6 | 0.100280 | ||||||||
\(867\) | 874751.i | 1.16371i | ||||||||
\(868\) | − | 989050.i | − | 1.31274i | ||||||
\(869\) | − | 914.368i | − | 0.00121083i | ||||||
\(870\) | 269217.i | 0.355684i | ||||||||
\(871\) | −263637. | −0.347513 | ||||||||
\(872\) | 354191. | 0.465806 | ||||||||
\(873\) | 517464.i | 0.678971i | ||||||||
\(874\) | 257991. | − | 295659.i | 0.337739 | − | 0.387052i | ||||
\(875\) | 908886. | 1.18712 | ||||||||
\(876\) | 443682.i | 0.578181i | ||||||||
\(877\) | − | 1.30994e6i | − | 1.70315i | −0.524235 | − | 0.851574i | \(-0.675649\pi\) | ||
0.524235 | − | 0.851574i | \(-0.324351\pi\) | |||||||
\(878\) | 179023. | 0.232231 | ||||||||
\(879\) | −27607.2 | −0.0357309 | ||||||||
\(880\) | 13434.0 | 0.0173476 | ||||||||
\(881\) | −1.16822e6 | −1.50513 | −0.752565 | − | 0.658517i | \(-0.771184\pi\) | ||||
−0.752565 | + | 0.658517i | \(0.771184\pi\) | |||||||
\(882\) | − | 504762.i | − | 0.648858i | ||||||
\(883\) | 761544. | 0.976728 | 0.488364 | − | 0.872640i | \(-0.337594\pi\) | ||||
0.488364 | + | 0.872640i | \(0.337594\pi\) | |||||||
\(884\) | 328223.i | 0.420015i | ||||||||
\(885\) | −1.13194e6 | −1.44523 | ||||||||
\(886\) | − | 464672.i | − | 0.591942i | ||||||
\(887\) | − | 347725.i | − | 0.441966i | −0.975278 | − | 0.220983i | \(-0.929074\pi\) | ||
0.975278 | − | 0.220983i | \(-0.0709265\pi\) | |||||||
\(888\) | − | 597406.i | − | 0.757606i | ||||||
\(889\) | 906349.i | 1.14681i | ||||||||
\(890\) | −295344. | −0.372862 | ||||||||
\(891\) | −305819. | −0.385220 | ||||||||
\(892\) | 96912.1i | 0.121800i | ||||||||
\(893\) | −614082. | − | 535845.i | −0.770058 | − | 0.671949i | ||||
\(894\) | −441518. | −0.552425 | ||||||||
\(895\) | 343202.i | 0.428453i | ||||||||
\(896\) | 825516.i | 1.02827i | ||||||||
\(897\) | −1.38025e6 | −1.71543 | ||||||||
\(898\) | −434475. | −0.538781 | ||||||||
\(899\) | −733769. | −0.907905 | ||||||||
\(900\) | 929537. | 1.14758 | ||||||||
\(901\) | 266506.i | 0.328290i | ||||||||
\(902\) | 12048.0 | 0.0148082 | ||||||||
\(903\) | 755266.i | 0.926242i | ||||||||
\(904\) | 1.20233e6 | 1.47125 | ||||||||
\(905\) | 787245.i | 0.961198i | ||||||||
\(906\) | − | 966264.i | − | 1.17717i | ||||||
\(907\) | 687599.i | 0.835835i | 0.908485 | + | 0.417917i | \(0.137240\pi\) | ||||
−0.908485 | + | 0.417917i | \(0.862760\pi\) | |||||||
\(908\) | − | 427057.i | − | 0.517981i | ||||||
\(909\) | −1.42367e6 | −1.72299 | ||||||||
\(910\) | 311484. | 0.376143 | ||||||||
\(911\) | 449372.i | 0.541464i | 0.962655 | + | 0.270732i | \(0.0872657\pi\) | ||||
−0.962655 | + | 0.270732i | \(0.912734\pi\) | |||||||
\(912\) | 212026. | − | 242984.i | 0.254918 | − | 0.292138i | ||||
\(913\) | −161621. | −0.193891 | ||||||||
\(914\) | 283488.i | 0.339346i | ||||||||
\(915\) | 191328.i | 0.228526i | ||||||||
\(916\) | −498230. | −0.593798 | ||||||||
\(917\) | 1.77133e6 | 2.10650 | ||||||||
\(918\) | −781552. | −0.927411 | ||||||||
\(919\) | 74612.4 | 0.0883446 | 0.0441723 | − | 0.999024i | \(-0.485935\pi\) | ||||
0.0441723 | + | 0.999024i | \(0.485935\pi\) | |||||||
\(920\) | 438604.i | 0.518200i | ||||||||
\(921\) | 1.21773e6 | 1.43559 | ||||||||
\(922\) | 75960.0i | 0.0893559i | ||||||||
\(923\) | 1.25426e6 | 1.47226 | ||||||||
\(924\) | 194366.i | 0.227654i | ||||||||
\(925\) | 244383.i | 0.285619i | ||||||||
\(926\) | − | 61751.0i | − | 0.0720148i | ||||||
\(927\) | − | 1.67118e6i | − | 1.94475i | ||||||
\(928\) | 531084. | 0.616691 | ||||||||
\(929\) | 178101. | 0.206365 | 0.103182 | − | 0.994662i | \(-0.467097\pi\) | ||||
0.103182 | + | 0.994662i | \(0.467097\pi\) | |||||||
\(930\) | 788196.i | 0.911315i | ||||||||
\(931\) | 314158. | + | 274133.i | 0.362451 | + | 0.316273i | ||||
\(932\) | −61251.5 | −0.0705156 | ||||||||
\(933\) | 2.09081e6i | 2.40188i | ||||||||
\(934\) | 870376.i | 0.997730i | ||||||||
\(935\) | 44906.8 | 0.0513676 | ||||||||
\(936\) | 1.95047e6 | 2.22632 | ||||||||
\(937\) | −1.24353e6 | −1.41637 | −0.708186 | − | 0.706026i | \(-0.750486\pi\) | ||||
−0.708186 | + | 0.706026i | \(0.750486\pi\) | |||||||
\(938\) | −208250. | −0.236690 | ||||||||
\(939\) | − | 1.47596e6i | − | 1.67395i | ||||||
\(940\) | 377384. | 0.427098 | ||||||||
\(941\) | − | 1.31010e6i | − | 1.47954i | −0.672861 | − | 0.739769i | \(-0.734935\pi\) | ||
0.672861 | − | 0.739769i | \(-0.265065\pi\) | |||||||
\(942\) | −301869. | −0.340186 | ||||||||
\(943\) | − | 163271.i | − | 0.183606i | ||||||
\(944\) | 241938.i | 0.271494i | ||||||||
\(945\) | − | 1.79185e6i | − | 2.00649i | ||||||
\(946\) | 27905.7i | 0.0311825i | ||||||||
\(947\) | 660926. | 0.736975 | 0.368488 | − | 0.929633i | \(-0.379876\pi\) | ||||
0.368488 | + | 0.929633i | \(0.379876\pi\) | |||||||
\(948\) | 10163.6 | 0.0113092 | ||||||||
\(949\) | − | 380844.i | − | 0.422877i | ||||||
\(950\) | 208961. | − | 239470.i | 0.231535 | − | 0.265341i | ||||
\(951\) | −683594. | −0.755853 | ||||||||
\(952\) | 625852.i | 0.690554i | ||||||||
\(953\) | 61065.5i | 0.0672373i | 0.999435 | + | 0.0336187i | \(0.0107032\pi\) | ||||
−0.999435 | + | 0.0336187i | \(0.989297\pi\) | |||||||
\(954\) | 656075. | 0.720869 | ||||||||
\(955\) | −80067.8 | −0.0877913 | ||||||||
\(956\) | −272367. | −0.298016 | ||||||||
\(957\) | 144199. | 0.157448 | ||||||||
\(958\) | − | 588719.i | − | 0.641471i | ||||||
\(959\) | 422232. | 0.459107 | ||||||||
\(960\) | − | 359342.i | − | 0.389911i | ||||||
\(961\) | −1.22476e6 | −1.32619 | ||||||||
\(962\) | 212432.i | 0.229546i | ||||||||
\(963\) | − | 1.30725e6i | − | 1.40964i | ||||||
\(964\) | − | 278956.i | − | 0.300179i | ||||||
\(965\) | − | 574905.i | − | 0.617364i | ||||||
\(966\) | −1.09028e6 | −1.16838 | ||||||||
\(967\) | −269267. | −0.287959 | −0.143979 | − | 0.989581i | \(-0.545990\pi\) | ||||
−0.143979 | + | 0.989581i | \(0.545990\pi\) | |||||||
\(968\) | − | 848222.i | − | 0.905230i | ||||||
\(969\) | 708755. | − | 812238.i | 0.754829 | − | 0.865040i | ||||
\(970\) | −81926.1 | −0.0870720 | ||||||||
\(971\) | 1.49753e6i | 1.58832i | 0.607709 | + | 0.794160i | \(0.292089\pi\) | ||||
−0.607709 | + | 0.794160i | \(0.707911\pi\) | |||||||
\(972\) | − | 1.53483e6i | − | 1.62453i | ||||||
\(973\) | −974228. | −1.02905 | ||||||||
\(974\) | 891871. | 0.940122 | ||||||||
\(975\) | −1.11794e6 | −1.17601 | ||||||||
\(976\) | 40893.9 | 0.0429298 | ||||||||
\(977\) | − | 1.59483e6i | − | 1.67080i | −0.549639 | − | 0.835402i | \(-0.685235\pi\) | ||
0.549639 | − | 0.835402i | \(-0.314765\pi\) | |||||||
\(978\) | 608079. | 0.635744 | ||||||||
\(979\) | 158193.i | 0.165052i | ||||||||
\(980\) | −193066. | −0.201027 | ||||||||
\(981\) | 1.20981e6i | 1.25713i | ||||||||
\(982\) | 744263.i | 0.771797i | ||||||||
\(983\) | 1.32566e6i | 1.37191i | 0.727642 | + | 0.685957i | \(0.240616\pi\) | ||||
−0.727642 | + | 0.685957i | \(0.759384\pi\) | |||||||
\(984\) | 323272.i | 0.333870i | ||||||||
\(985\) | 607455. | 0.626097 | ||||||||
\(986\) | 192349. | 0.197850 | ||||||||
\(987\) | 2.26450e6i | 2.32454i | ||||||||
\(988\) | −438824. | + | 502896.i | −0.449549 | + | 0.515186i | ||||
\(989\) | 378170. | 0.386629 | ||||||||
\(990\) | − | 110550.i | − | 0.112795i | ||||||
\(991\) | − | 666235.i | − | 0.678391i | −0.940716 | − | 0.339196i | \(-0.889845\pi\) | ||
0.940716 | − | 0.339196i | \(-0.110155\pi\) | |||||||
\(992\) | 1.55487e6 | 1.58005 | ||||||||
\(993\) | −2.46305e6 | −2.49790 | ||||||||
\(994\) | 990756. | 1.00275 | ||||||||
\(995\) | −336490. | −0.339881 | ||||||||
\(996\) | − | 1.79650e6i | − | 1.81096i | ||||||
\(997\) | −823511. | −0.828475 | −0.414237 | − | 0.910169i | \(-0.635952\pi\) | ||||
−0.414237 | + | 0.910169i | \(0.635952\pi\) | |||||||
\(998\) | − | 360754.i | − | 0.362201i | ||||||
\(999\) | 1.22204e6 | 1.22449 |
(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 | 19.5.b.b.18.3 | yes | 4 | |
3.2 | odd | 2 | 171.5.c.c.37.2 | 4 | |||
4.3 | odd | 2 | 304.5.e.c.113.4 | 4 | |||
19.18 | odd | 2 | inner | 19.5.b.b.18.2 | ✓ | 4 | |
57.56 | even | 2 | 171.5.c.c.37.3 | 4 | |||
76.75 | even | 2 | 304.5.e.c.113.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
19.5.b.b.18.2 | ✓ | 4 | 19.18 | odd | 2 | inner | |
19.5.b.b.18.3 | yes | 4 | 1.1 | even | 1 | trivial | |
171.5.c.c.37.2 | 4 | 3.2 | odd | 2 | |||
171.5.c.c.37.3 | 4 | 57.56 | even | 2 | |||
304.5.e.c.113.1 | 4 | 76.75 | even | 2 | |||
304.5.e.c.113.4 | 4 | 4.3 | odd | 2 |