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 | 58.21 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.5.c.a.58.20 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.389117i | 0.0972793i | 0.998816 | + | 0.0486397i | \(0.0154886\pi\) | ||||
−0.998816 | + | 0.0486397i | \(0.984511\pi\) | |||||||
\(3\) | 5.19615 | 0.577350 | ||||||||
\(4\) | 15.8486 | 0.990537 | ||||||||
\(5\) | −17.9988 | −0.719952 | −0.359976 | − | 0.932962i | \(-0.617215\pi\) | ||||
−0.359976 | + | 0.932962i | \(0.617215\pi\) | |||||||
\(6\) | 2.02191i | 0.0561643i | ||||||||
\(7\) | −47.2538 | −0.964363 | −0.482181 | − | 0.876071i | \(-0.660155\pi\) | ||||
−0.482181 | + | 0.876071i | \(0.660155\pi\) | |||||||
\(8\) | 12.3928i | 0.193638i | ||||||||
\(9\) | 27.0000 | 0.333333 | ||||||||
\(10\) | − | 7.00365i | − | 0.0700365i | ||||||
\(11\) | − | 197.341i | − | 1.63092i | −0.578814 | − | 0.815460i | \(-0.696484\pi\) | ||
0.578814 | − | 0.815460i | \(-0.303516\pi\) | |||||||
\(12\) | 82.3517 | 0.571887 | ||||||||
\(13\) | − | 176.297i | − | 1.04318i | −0.853197 | − | 0.521589i | \(-0.825339\pi\) | ||
0.853197 | − | 0.521589i | \(-0.174661\pi\) | |||||||
\(14\) | − | 18.3873i | − | 0.0938126i | ||||||
\(15\) | −93.5245 | −0.415665 | ||||||||
\(16\) | 248.755 | 0.971700 | ||||||||
\(17\) | 486.600 | 1.68374 | 0.841868 | − | 0.539683i | \(-0.181456\pi\) | ||||
0.841868 | + | 0.539683i | \(0.181456\pi\) | |||||||
\(18\) | 10.5062i | 0.0324264i | ||||||||
\(19\) | 56.2166 | 0.155725 | 0.0778624 | − | 0.996964i | \(-0.475191\pi\) | ||||
0.0778624 | + | 0.996964i | \(0.475191\pi\) | |||||||
\(20\) | −285.256 | −0.713139 | ||||||||
\(21\) | −245.538 | −0.556775 | ||||||||
\(22\) | 76.7889 | 0.158655 | ||||||||
\(23\) | − | 848.854i | − | 1.60464i | −0.596895 | − | 0.802319i | \(-0.703599\pi\) | ||
0.596895 | − | 0.802319i | \(-0.296401\pi\) | |||||||
\(24\) | 64.3951i | 0.111797i | ||||||||
\(25\) | −301.043 | −0.481669 | ||||||||
\(26\) | 68.6003 | 0.101480 | ||||||||
\(27\) | 140.296 | 0.192450 | ||||||||
\(28\) | −748.906 | −0.955237 | ||||||||
\(29\) | 275.393 | 0.327459 | 0.163729 | − | 0.986505i | \(-0.447648\pi\) | ||||
0.163729 | + | 0.986505i | \(0.447648\pi\) | |||||||
\(30\) | − | 36.3920i | − | 0.0404356i | ||||||
\(31\) | 843.954i | 0.878204i | 0.898437 | + | 0.439102i | \(0.144703\pi\) | ||||
−0.898437 | + | 0.439102i | \(0.855297\pi\) | |||||||
\(32\) | 295.080i | 0.288164i | ||||||||
\(33\) | − | 1025.42i | − | 0.941612i | ||||||
\(34\) | 189.344i | 0.163793i | ||||||||
\(35\) | 850.512 | 0.694295 | ||||||||
\(36\) | 427.912 | 0.330179 | ||||||||
\(37\) | 1855.12i | 1.35509i | 0.735481 | + | 0.677546i | \(0.236956\pi\) | ||||
−0.735481 | + | 0.677546i | \(0.763044\pi\) | |||||||
\(38\) | 21.8749i | 0.0151488i | ||||||||
\(39\) | − | 916.067i | − | 0.602279i | ||||||
\(40\) | − | 223.056i | − | 0.139410i | ||||||
\(41\) | 1479.48 | 0.880118 | 0.440059 | − | 0.897969i | \(-0.354958\pi\) | ||||
0.440059 | + | 0.897969i | \(0.354958\pi\) | |||||||
\(42\) | − | 95.5430i | − | 0.0541627i | ||||||
\(43\) | − | 2758.38i | − | 1.49182i | −0.666045 | − | 0.745912i | \(-0.732014\pi\) | ||
0.666045 | − | 0.745912i | \(-0.267986\pi\) | |||||||
\(44\) | − | 3127.58i | − | 1.61549i | ||||||
\(45\) | −485.968 | −0.239984 | ||||||||
\(46\) | 330.304 | 0.156098 | ||||||||
\(47\) | − | 1437.11i | − | 0.650572i | −0.945616 | − | 0.325286i | \(-0.894539\pi\) | ||
0.945616 | − | 0.325286i | \(-0.105461\pi\) | |||||||
\(48\) | 1292.57 | 0.561011 | ||||||||
\(49\) | −168.080 | −0.0700043 | ||||||||
\(50\) | − | 117.141i | − | 0.0468564i | ||||||
\(51\) | 2528.45 | 0.972106 | ||||||||
\(52\) | − | 2794.06i | − | 1.03331i | ||||||
\(53\) | −1119.21 | −0.398439 | −0.199219 | − | 0.979955i | \(-0.563841\pi\) | ||||
−0.199219 | + | 0.979955i | \(0.563841\pi\) | |||||||
\(54\) | 54.5917i | 0.0187214i | ||||||||
\(55\) | 3551.91i | 1.17418i | ||||||||
\(56\) | − | 585.608i | − | 0.186737i | ||||||
\(57\) | 292.110 | 0.0899077 | ||||||||
\(58\) | 107.160i | 0.0318550i | ||||||||
\(59\) | −1640.41 | − | 3070.25i | −0.471247 | − | 0.882001i | ||||
\(60\) | −1482.23 | −0.411731 | ||||||||
\(61\) | − | 115.162i | − | 0.0309492i | −0.999880 | − | 0.0154746i | \(-0.995074\pi\) | ||
0.999880 | − | 0.0154746i | \(-0.00492592\pi\) | |||||||
\(62\) | −328.397 | −0.0854311 | ||||||||
\(63\) | −1275.85 | −0.321454 | ||||||||
\(64\) | 3865.26 | 0.943667 | ||||||||
\(65\) | 3173.14i | 0.751038i | ||||||||
\(66\) | 399.007 | 0.0915994 | ||||||||
\(67\) | − | 49.5250i | − | 0.0110325i | −0.999985 | − | 0.00551626i | \(-0.998244\pi\) | ||
0.999985 | − | 0.00551626i | \(-0.00175589\pi\) | |||||||
\(68\) | 7711.92 | 1.66780 | ||||||||
\(69\) | − | 4410.77i | − | 0.926439i | ||||||
\(70\) | 330.949i | 0.0675406i | ||||||||
\(71\) | −2085.72 | −0.413751 | −0.206876 | − | 0.978367i | \(-0.566330\pi\) | ||||
−0.206876 | + | 0.978367i | \(0.566330\pi\) | |||||||
\(72\) | 334.607i | 0.0645460i | ||||||||
\(73\) | − | 209.953i | − | 0.0393982i | −0.999806 | − | 0.0196991i | \(-0.993729\pi\) | ||
0.999806 | − | 0.0196991i | \(-0.00627083\pi\) | |||||||
\(74\) | −721.859 | −0.131822 | ||||||||
\(75\) | −1564.26 | −0.278092 | ||||||||
\(76\) | 890.954 | 0.154251 | ||||||||
\(77\) | 9325.12i | 1.57280i | ||||||||
\(78\) | 356.457 | 0.0585893 | ||||||||
\(79\) | −6542.76 | −1.04835 | −0.524176 | − | 0.851610i | \(-0.675626\pi\) | ||||
−0.524176 | + | 0.851610i | \(0.675626\pi\) | |||||||
\(80\) | −4477.30 | −0.699577 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | 575.691i | 0.0856173i | ||||||||
\(83\) | 6802.27i | 0.987410i | 0.869629 | + | 0.493705i | \(0.164358\pi\) | ||||
−0.869629 | + | 0.493705i | \(0.835642\pi\) | |||||||
\(84\) | −3891.43 | −0.551506 | ||||||||
\(85\) | −8758.22 | −1.21221 | ||||||||
\(86\) | 1073.33 | 0.145124 | ||||||||
\(87\) | 1430.98 | 0.189058 | ||||||||
\(88\) | 2445.62 | 0.315808 | ||||||||
\(89\) | 9119.14i | 1.15126i | 0.817710 | + | 0.575630i | \(0.195243\pi\) | ||||
−0.817710 | + | 0.575630i | \(0.804757\pi\) | |||||||
\(90\) | − | 189.099i | − | 0.0233455i | ||||||
\(91\) | 8330.70i | 1.00600i | ||||||||
\(92\) | − | 13453.1i | − | 1.58945i | ||||||
\(93\) | 4385.31i | 0.507031i | ||||||||
\(94\) | 559.206 | 0.0632872 | ||||||||
\(95\) | −1011.83 | −0.112114 | ||||||||
\(96\) | 1533.28i | 0.166372i | ||||||||
\(97\) | − | 2946.12i | − | 0.313117i | −0.987669 | − | 0.156559i | \(-0.949960\pi\) | ||
0.987669 | − | 0.156559i | \(-0.0500400\pi\) | |||||||
\(98\) | − | 65.4030i | − | 0.00680997i | ||||||
\(99\) | − | 5328.21i | − | 0.543640i | ||||||
\(100\) | −4771.11 | −0.477111 | ||||||||
\(101\) | − | 4577.99i | − | 0.448779i | −0.974500 | − | 0.224389i | \(-0.927961\pi\) | ||
0.974500 | − | 0.224389i | \(-0.0720388\pi\) | |||||||
\(102\) | 983.862i | 0.0945658i | ||||||||
\(103\) | 14158.2i | 1.33455i | 0.744812 | + | 0.667274i | \(0.232539\pi\) | ||||
−0.744812 | + | 0.667274i | \(0.767461\pi\) | |||||||
\(104\) | 2184.82 | 0.201999 | ||||||||
\(105\) | 4419.39 | 0.400852 | ||||||||
\(106\) | − | 435.506i | − | 0.0387598i | ||||||
\(107\) | 2298.00 | 0.200717 | 0.100358 | − | 0.994951i | \(-0.468001\pi\) | ||||
0.100358 | + | 0.994951i | \(0.468001\pi\) | |||||||
\(108\) | 2223.50 | 0.190629 | ||||||||
\(109\) | 18428.3i | 1.55107i | 0.631302 | + | 0.775537i | \(0.282521\pi\) | ||||
−0.631302 | + | 0.775537i | \(0.717479\pi\) | |||||||
\(110\) | −1382.11 | −0.114224 | ||||||||
\(111\) | 9639.49i | 0.782362i | ||||||||
\(112\) | −11754.6 | −0.937071 | ||||||||
\(113\) | − | 15385.4i | − | 1.20490i | −0.798156 | − | 0.602451i | \(-0.794191\pi\) | ||
0.798156 | − | 0.602451i | \(-0.205809\pi\) | |||||||
\(114\) | 113.665i | 0.00874616i | ||||||||
\(115\) | 15278.4i | 1.15526i | ||||||||
\(116\) | 4364.59 | 0.324360 | ||||||||
\(117\) | − | 4760.02i | − | 0.347726i | ||||||
\(118\) | 1194.69 | − | 638.312i | 0.0858005 | − | 0.0458426i | ||||
\(119\) | −22993.7 | −1.62373 | ||||||||
\(120\) | − | 1159.03i | − | 0.0804885i | ||||||
\(121\) | −24302.6 | −1.65990 | ||||||||
\(122\) | 44.8115 | 0.00301072 | ||||||||
\(123\) | 7687.59 | 0.508136 | ||||||||
\(124\) | 13375.5i | 0.869893i | ||||||||
\(125\) | 16667.7 | 1.06673 | ||||||||
\(126\) | − | 496.456i | − | 0.0312709i | ||||||
\(127\) | 28666.4 | 1.77732 | 0.888661 | − | 0.458564i | \(-0.151636\pi\) | ||||
0.888661 | + | 0.458564i | \(0.151636\pi\) | |||||||
\(128\) | 6225.33i | 0.379964i | ||||||||
\(129\) | − | 14333.0i | − | 0.861305i | ||||||
\(130\) | −1234.72 | −0.0730605 | ||||||||
\(131\) | − | 19845.6i | − | 1.15643i | −0.815883 | − | 0.578217i | \(-0.803749\pi\) | ||
0.815883 | − | 0.578217i | \(-0.196251\pi\) | |||||||
\(132\) | − | 16251.4i | − | 0.932701i | ||||||
\(133\) | −2656.45 | −0.150175 | ||||||||
\(134\) | 19.2710 | 0.00107324 | ||||||||
\(135\) | −2525.16 | −0.138555 | ||||||||
\(136\) | 6030.35i | 0.326035i | ||||||||
\(137\) | 19165.2 | 1.02111 | 0.510555 | − | 0.859845i | \(-0.329440\pi\) | ||||
0.510555 | + | 0.859845i | \(0.329440\pi\) | |||||||
\(138\) | 1716.31 | 0.0901233 | ||||||||
\(139\) | −20252.2 | −1.04820 | −0.524099 | − | 0.851658i | \(-0.675598\pi\) | ||||
−0.524099 | + | 0.851658i | \(0.675598\pi\) | |||||||
\(140\) | 13479.4 | 0.687725 | ||||||||
\(141\) | − | 7467.46i | − | 0.375608i | ||||||
\(142\) | − | 811.590i | − | 0.0402495i | ||||||
\(143\) | −34790.7 | −1.70134 | ||||||||
\(144\) | 6716.39 | 0.323900 | ||||||||
\(145\) | −4956.74 | −0.235755 | ||||||||
\(146\) | 81.6964 | 0.00383263 | ||||||||
\(147\) | −873.371 | −0.0404170 | ||||||||
\(148\) | 29401.0i | 1.34227i | ||||||||
\(149\) | − | 8521.84i | − | 0.383849i | −0.981410 | − | 0.191925i | \(-0.938527\pi\) | ||
0.981410 | − | 0.191925i | \(-0.0614729\pi\) | |||||||
\(150\) | − | 608.683i | − | 0.0270526i | ||||||
\(151\) | 43196.8i | 1.89452i | 0.320473 | + | 0.947258i | \(0.396158\pi\) | ||||
−0.320473 | + | 0.947258i | \(0.603842\pi\) | |||||||
\(152\) | 696.684i | 0.0301542i | ||||||||
\(153\) | 13138.2 | 0.561245 | ||||||||
\(154\) | −3628.57 | −0.153001 | ||||||||
\(155\) | − | 15190.2i | − | 0.632265i | ||||||
\(156\) | − | 14518.4i | − | 0.596580i | ||||||
\(157\) | − | 7274.02i | − | 0.295104i | −0.989054 | − | 0.147552i | \(-0.952861\pi\) | ||
0.989054 | − | 0.147552i | \(-0.0471394\pi\) | |||||||
\(158\) | − | 2545.90i | − | 0.101983i | ||||||
\(159\) | −5815.61 | −0.230039 | ||||||||
\(160\) | − | 5311.09i | − | 0.207465i | ||||||
\(161\) | 40111.6i | 1.54745i | ||||||||
\(162\) | 283.667i | 0.0108088i | ||||||||
\(163\) | −15415.8 | −0.580219 | −0.290109 | − | 0.956994i | \(-0.593692\pi\) | ||||
−0.290109 | + | 0.956994i | \(0.593692\pi\) | |||||||
\(164\) | 23447.6 | 0.871789 | ||||||||
\(165\) | 18456.3i | 0.677916i | ||||||||
\(166\) | −2646.88 | −0.0960546 | ||||||||
\(167\) | 37730.3 | 1.35288 | 0.676438 | − | 0.736500i | \(-0.263523\pi\) | ||||
0.676438 | + | 0.736500i | \(0.263523\pi\) | |||||||
\(168\) | − | 3042.91i | − | 0.107813i | ||||||
\(169\) | −2519.67 | −0.0882205 | ||||||||
\(170\) | − | 3407.97i | − | 0.117923i | ||||||
\(171\) | 1517.85 | 0.0519083 | ||||||||
\(172\) | − | 43716.4i | − | 1.47771i | ||||||
\(173\) | 12104.2i | 0.404430i | 0.979341 | + | 0.202215i | \(0.0648139\pi\) | ||||
−0.979341 | + | 0.202215i | \(0.935186\pi\) | |||||||
\(174\) | 556.821i | 0.0183915i | ||||||||
\(175\) | 14225.4 | 0.464503 | ||||||||
\(176\) | − | 49089.7i | − | 1.58476i | ||||||
\(177\) | −8523.82 | − | 15953.5i | −0.272074 | − | 0.509224i | ||||
\(178\) | −3548.41 | −0.111994 | ||||||||
\(179\) | − | 288.509i | − | 0.00900436i | −0.999990 | − | 0.00450218i | \(-0.998567\pi\) | ||
0.999990 | − | 0.00450218i | \(-0.00143309\pi\) | |||||||
\(180\) | −7701.90 | −0.237713 | ||||||||
\(181\) | −12771.6 | −0.389841 | −0.194921 | − | 0.980819i | \(-0.562445\pi\) | ||||
−0.194921 | + | 0.980819i | \(0.562445\pi\) | |||||||
\(182\) | −3241.62 | −0.0978632 | ||||||||
\(183\) | − | 598.400i | − | 0.0178685i | ||||||
\(184\) | 10519.7 | 0.310719 | ||||||||
\(185\) | − | 33389.9i | − | 0.975601i | ||||||
\(186\) | −1706.40 | −0.0493237 | ||||||||
\(187\) | − | 96026.2i | − | 2.74604i | ||||||
\(188\) | − | 22776.2i | − | 0.644415i | ||||||
\(189\) | −6629.52 | −0.185592 | ||||||||
\(190\) | − | 393.722i | − | 0.0109064i | ||||||
\(191\) | 49064.3i | 1.34493i | 0.740130 | + | 0.672464i | \(0.234764\pi\) | ||||
−0.740130 | + | 0.672464i | \(0.765236\pi\) | |||||||
\(192\) | 20084.5 | 0.544827 | ||||||||
\(193\) | 51351.0 | 1.37859 | 0.689294 | − | 0.724481i | \(-0.257921\pi\) | ||||
0.689294 | + | 0.724481i | \(0.257921\pi\) | |||||||
\(194\) | 1146.39 | 0.0304598 | ||||||||
\(195\) | 16488.1i | 0.433612i | ||||||||
\(196\) | −2663.84 | −0.0693418 | ||||||||
\(197\) | −30154.4 | −0.776996 | −0.388498 | − | 0.921450i | \(-0.627006\pi\) | ||||
−0.388498 | + | 0.921450i | \(0.627006\pi\) | |||||||
\(198\) | 2073.30 | 0.0528849 | ||||||||
\(199\) | 67941.6 | 1.71565 | 0.857827 | − | 0.513939i | \(-0.171814\pi\) | ||||
0.857827 | + | 0.513939i | \(0.171814\pi\) | |||||||
\(200\) | − | 3730.78i | − | 0.0932694i | ||||||
\(201\) | − | 257.339i | − | 0.00636963i | ||||||
\(202\) | 1781.38 | 0.0436569 | ||||||||
\(203\) | −13013.4 | −0.315789 | ||||||||
\(204\) | 40072.3 | 0.962906 | ||||||||
\(205\) | −26628.8 | −0.633643 | ||||||||
\(206\) | −5509.21 | −0.129824 | ||||||||
\(207\) | − | 22919.1i | − | 0.534880i | ||||||
\(208\) | − | 43854.8i | − | 1.01366i | ||||||
\(209\) | − | 11093.9i | − | 0.253975i | ||||||
\(210\) | 1719.66i | 0.0389946i | ||||||||
\(211\) | − | 2303.99i | − | 0.0517507i | −0.999665 | − | 0.0258754i | \(-0.991763\pi\) | ||
0.999665 | − | 0.0258754i | \(-0.00823730\pi\) | |||||||
\(212\) | −17738.0 | −0.394668 | ||||||||
\(213\) | −10837.7 | −0.238879 | ||||||||
\(214\) | 894.193i | 0.0195256i | ||||||||
\(215\) | 49647.6i | 1.07404i | ||||||||
\(216\) | 1738.67i | 0.0372657i | ||||||||
\(217\) | − | 39880.0i | − | 0.846907i | ||||||
\(218\) | −7170.78 | −0.150888 | ||||||||
\(219\) | − | 1090.95i | − | 0.0227466i | ||||||
\(220\) | 56292.7i | 1.16307i | ||||||||
\(221\) | − | 85786.1i | − | 1.75644i | ||||||
\(222\) | −3750.89 | −0.0761077 | ||||||||
\(223\) | 28222.6 | 0.567527 | 0.283764 | − | 0.958894i | \(-0.408417\pi\) | ||||
0.283764 | + | 0.958894i | \(0.408417\pi\) | |||||||
\(224\) | − | 13943.7i | − | 0.277895i | ||||||
\(225\) | −8128.16 | −0.160556 | ||||||||
\(226\) | 5986.73 | 0.117212 | ||||||||
\(227\) | 63511.2i | 1.23253i | 0.787538 | + | 0.616267i | \(0.211356\pi\) | ||||
−0.787538 | + | 0.616267i | \(0.788644\pi\) | |||||||
\(228\) | 4629.53 | 0.0890569 | ||||||||
\(229\) | 36930.9i | 0.704236i | 0.935956 | + | 0.352118i | \(0.114538\pi\) | ||||
−0.935956 | + | 0.352118i | \(0.885462\pi\) | |||||||
\(230\) | −5945.07 | −0.112383 | ||||||||
\(231\) | 48454.7i | 0.908055i | ||||||||
\(232\) | 3412.90i | 0.0634085i | ||||||||
\(233\) | 53127.8i | 0.978610i | 0.872113 | + | 0.489305i | \(0.162750\pi\) | ||||
−0.872113 | + | 0.489305i | \(0.837250\pi\) | |||||||
\(234\) | 1852.21 | 0.0338266 | ||||||||
\(235\) | 25866.3i | 0.468381i | ||||||||
\(236\) | −25998.2 | − | 48659.1i | −0.466787 | − | 0.873655i | ||||
\(237\) | −33997.2 | −0.605266 | ||||||||
\(238\) | − | 8947.24i | − | 0.157956i | ||||||
\(239\) | −24487.8 | −0.428700 | −0.214350 | − | 0.976757i | \(-0.568763\pi\) | ||||
−0.214350 | + | 0.976757i | \(0.568763\pi\) | |||||||
\(240\) | −23264.7 | −0.403901 | ||||||||
\(241\) | 12746.1 | 0.219454 | 0.109727 | − | 0.993962i | \(-0.465002\pi\) | ||||
0.109727 | + | 0.993962i | \(0.465002\pi\) | |||||||
\(242\) | − | 9456.55i | − | 0.161474i | ||||||
\(243\) | 3788.00 | 0.0641500 | ||||||||
\(244\) | − | 1825.16i | − | 0.0306563i | ||||||
\(245\) | 3025.25 | 0.0503998 | ||||||||
\(246\) | 2991.38i | 0.0494312i | ||||||||
\(247\) | − | 9910.83i | − | 0.162449i | ||||||
\(248\) | −10459.0 | −0.170054 | ||||||||
\(249\) | 35345.6i | 0.570082i | ||||||||
\(250\) | 6485.68i | 0.103771i | ||||||||
\(251\) | 44798.5 | 0.711076 | 0.355538 | − | 0.934662i | \(-0.384298\pi\) | ||||
0.355538 | + | 0.934662i | \(0.384298\pi\) | |||||||
\(252\) | −20220.5 | −0.318412 | ||||||||
\(253\) | −167514. | −2.61704 | ||||||||
\(254\) | 11154.6i | 0.172897i | ||||||||
\(255\) | −45509.0 | −0.699870 | ||||||||
\(256\) | 59421.8 | 0.906705 | ||||||||
\(257\) | 105733. | 1.60083 | 0.800413 | − | 0.599449i | \(-0.204614\pi\) | ||||
0.800413 | + | 0.599449i | \(0.204614\pi\) | |||||||
\(258\) | 5577.21 | 0.0837871 | ||||||||
\(259\) | − | 87661.4i | − | 1.30680i | ||||||
\(260\) | 50289.7i | 0.743931i | ||||||||
\(261\) | 7435.61 | 0.109153 | ||||||||
\(262\) | 7722.25 | 0.112497 | ||||||||
\(263\) | 9304.75 | 0.134522 | 0.0672610 | − | 0.997735i | \(-0.478574\pi\) | ||||
0.0672610 | + | 0.997735i | \(0.478574\pi\) | |||||||
\(264\) | 12707.8 | 0.182332 | ||||||||
\(265\) | 20144.5 | 0.286857 | ||||||||
\(266\) | − | 1033.67i | − | 0.0146089i | ||||||
\(267\) | 47384.4i | 0.664681i | ||||||||
\(268\) | − | 784.901i | − | 0.0109281i | ||||||
\(269\) | − | 6683.88i | − | 0.0923685i | −0.998933 | − | 0.0461842i | \(-0.985294\pi\) | ||
0.998933 | − | 0.0461842i | \(-0.0147061\pi\) | |||||||
\(270\) | − | 982.585i | − | 0.0134785i | ||||||
\(271\) | −137964. | −1.87856 | −0.939282 | − | 0.343145i | \(-0.888508\pi\) | ||||
−0.939282 | + | 0.343145i | \(0.888508\pi\) | |||||||
\(272\) | 121044. | 1.63609 | ||||||||
\(273\) | 43287.6i | 0.580816i | ||||||||
\(274\) | 7457.51i | 0.0993329i | ||||||||
\(275\) | 59408.2i | 0.785563i | ||||||||
\(276\) | − | 69904.5i | − | 0.917671i | ||||||
\(277\) | 96139.5 | 1.25298 | 0.626488 | − | 0.779431i | \(-0.284492\pi\) | ||||
0.626488 | + | 0.779431i | \(0.284492\pi\) | |||||||
\(278\) | − | 7880.49i | − | 0.101968i | ||||||
\(279\) | 22786.8i | 0.292735i | ||||||||
\(280\) | 10540.3i | 0.134442i | ||||||||
\(281\) | −13544.9 | −0.171539 | −0.0857696 | − | 0.996315i | \(-0.527335\pi\) | ||||
−0.0857696 | + | 0.996315i | \(0.527335\pi\) | |||||||
\(282\) | 2905.72 | 0.0365389 | ||||||||
\(283\) | − | 147321.i | − | 1.83946i | −0.392547 | − | 0.919732i | \(-0.628406\pi\) | ||
0.392547 | − | 0.919732i | \(-0.371594\pi\) | |||||||
\(284\) | −33055.7 | −0.409836 | ||||||||
\(285\) | −5257.64 | −0.0647293 | ||||||||
\(286\) | − | 13537.7i | − | 0.165505i | ||||||
\(287\) | −69910.9 | −0.848753 | ||||||||
\(288\) | 7967.17i | 0.0960548i | ||||||||
\(289\) | 153258. | 1.83497 | ||||||||
\(290\) | − | 1928.76i | − | 0.0229341i | ||||||
\(291\) | − | 15308.5i | − | 0.180778i | ||||||
\(292\) | − | 3327.46i | − | 0.0390254i | ||||||
\(293\) | 21384.4 | 0.249094 | 0.124547 | − | 0.992214i | \(-0.460252\pi\) | ||||
0.124547 | + | 0.992214i | \(0.460252\pi\) | |||||||
\(294\) | − | 339.844i | − | 0.00393174i | ||||||
\(295\) | 29525.4 | + | 55260.8i | 0.339275 | + | 0.634999i | ||||
\(296\) | −22990.2 | −0.262397 | ||||||||
\(297\) | − | 27686.2i | − | 0.313871i | ||||||
\(298\) | 3316.00 | 0.0373406 | ||||||||
\(299\) | −149650. | −1.67392 | ||||||||
\(300\) | −24791.4 | −0.275460 | ||||||||
\(301\) | 130344.i | 1.43866i | ||||||||
\(302\) | −16808.6 | −0.184297 | ||||||||
\(303\) | − | 23788.0i | − | 0.259103i | ||||||
\(304\) | 13984.2 | 0.151318 | ||||||||
\(305\) | 2072.78i | 0.0222820i | ||||||||
\(306\) | 5112.30i | 0.0545976i | ||||||||
\(307\) | −89703.8 | −0.951775 | −0.475887 | − | 0.879506i | \(-0.657873\pi\) | ||||
−0.475887 | + | 0.879506i | \(0.657873\pi\) | |||||||
\(308\) | 147790.i | 1.55791i | ||||||||
\(309\) | 73568.3i | 0.770502i | ||||||||
\(310\) | 5910.76 | 0.0615063 | ||||||||
\(311\) | −23438.7 | −0.242333 | −0.121166 | − | 0.992632i | \(-0.538663\pi\) | ||||
−0.121166 | + | 0.992632i | \(0.538663\pi\) | |||||||
\(312\) | 11352.7 | 0.116624 | ||||||||
\(313\) | − | 48687.8i | − | 0.496971i | −0.968636 | − | 0.248486i | \(-0.920067\pi\) | ||
0.968636 | − | 0.248486i | \(-0.0799329\pi\) | |||||||
\(314\) | 2830.45 | 0.0287075 | ||||||||
\(315\) | 22963.8 | 0.231432 | ||||||||
\(316\) | −103694. | −1.03843 | ||||||||
\(317\) | −126653. | −1.26036 | −0.630182 | − | 0.776448i | \(-0.717020\pi\) | ||||
−0.630182 | + | 0.776448i | \(0.717020\pi\) | |||||||
\(318\) | − | 2262.95i | − | 0.0223780i | ||||||
\(319\) | − | 54346.4i | − | 0.534059i | ||||||
\(320\) | −69570.1 | −0.679395 | ||||||||
\(321\) | 11940.8 | 0.115884 | ||||||||
\(322\) | −15608.1 | −0.150535 | ||||||||
\(323\) | 27355.0 | 0.262199 | ||||||||
\(324\) | 11553.6 | 0.110060 | ||||||||
\(325\) | 53073.0i | 0.502466i | ||||||||
\(326\) | − | 5998.57i | − | 0.0564433i | ||||||
\(327\) | 95756.4i | 0.895514i | ||||||||
\(328\) | 18334.9i | 0.170424i | ||||||||
\(329\) | 67909.0i | 0.627387i | ||||||||
\(330\) | −7181.65 | −0.0659472 | ||||||||
\(331\) | 177452. | 1.61966 | 0.809831 | − | 0.586663i | \(-0.199559\pi\) | ||||
0.809831 | + | 0.586663i | \(0.199559\pi\) | |||||||
\(332\) | 107806.i | 0.978066i | ||||||||
\(333\) | 50088.2i | 0.451697i | ||||||||
\(334\) | 14681.5i | 0.131607i | ||||||||
\(335\) | 891.390i | 0.00794289i | ||||||||
\(336\) | −61078.8 | −0.541018 | ||||||||
\(337\) | 88144.0i | 0.776127i | 0.921633 | + | 0.388064i | \(0.126856\pi\) | ||||
−0.921633 | + | 0.388064i | \(0.873144\pi\) | |||||||
\(338\) | − | 980.446i | − | 0.00858203i | ||||||
\(339\) | − | 79944.9i | − | 0.695651i | ||||||
\(340\) | −138805. | −1.20074 | ||||||||
\(341\) | 166547. | 1.43228 | ||||||||
\(342\) | 590.621i | 0.00504960i | ||||||||
\(343\) | 121399. | 1.03187 | ||||||||
\(344\) | 34184.2 | 0.288874 | ||||||||
\(345\) | 79388.7i | 0.666992i | ||||||||
\(346\) | −4709.95 | −0.0393427 | ||||||||
\(347\) | 79473.9i | 0.660033i | 0.943975 | + | 0.330016i | \(0.107054\pi\) | ||||
−0.943975 | + | 0.330016i | \(0.892946\pi\) | |||||||
\(348\) | 22679.1 | 0.187269 | ||||||||
\(349\) | − | 24382.5i | − | 0.200183i | −0.994978 | − | 0.100091i | \(-0.968086\pi\) | ||
0.994978 | − | 0.100091i | \(-0.0319135\pi\) | |||||||
\(350\) | 5535.36i | 0.0451866i | ||||||||
\(351\) | − | 24733.8i | − | 0.200760i | ||||||
\(352\) | 58231.5 | 0.469973 | ||||||||
\(353\) | − | 61148.2i | − | 0.490720i | −0.969432 | − | 0.245360i | \(-0.921094\pi\) | ||
0.969432 | − | 0.245360i | \(-0.0789062\pi\) | |||||||
\(354\) | 6207.77 | − | 3316.77i | 0.0495370 | − | 0.0264672i | ||||
\(355\) | 37540.5 | 0.297881 | ||||||||
\(356\) | 144525.i | 1.14037i | ||||||||
\(357\) | −119479. | −0.937462 | ||||||||
\(358\) | 112.264 | 0.000875939 | ||||||||
\(359\) | −241084. | −1.87059 | −0.935297 | − | 0.353864i | \(-0.884868\pi\) | ||||
−0.935297 | + | 0.353864i | \(0.884868\pi\) | |||||||
\(360\) | − | 6022.52i | − | 0.0464701i | ||||||
\(361\) | −127161. | −0.975750 | ||||||||
\(362\) | − | 4969.64i | − | 0.0379235i | ||||||
\(363\) | −126280. | −0.958343 | ||||||||
\(364\) | 132030.i | 0.996482i | ||||||||
\(365\) | 3778.91i | 0.0283648i | ||||||||
\(366\) | 232.848 | 0.00173824 | ||||||||
\(367\) | − | 237472.i | − | 1.76311i | −0.472078 | − | 0.881557i | \(-0.656496\pi\) | ||
0.472078 | − | 0.881557i | \(-0.343504\pi\) | |||||||
\(368\) | − | 211157.i | − | 1.55923i | ||||||
\(369\) | 39945.9 | 0.293373 | ||||||||
\(370\) | 12992.6 | 0.0949058 | ||||||||
\(371\) | 52887.1 | 0.384239 | ||||||||
\(372\) | 69501.0i | 0.502233i | ||||||||
\(373\) | −168379. | −1.21023 | −0.605117 | − | 0.796137i | \(-0.706874\pi\) | ||||
−0.605117 | + | 0.796137i | \(0.706874\pi\) | |||||||
\(374\) | 37365.5 | 0.267133 | ||||||||
\(375\) | 86607.7 | 0.615877 | ||||||||
\(376\) | 17809.9 | 0.125976 | ||||||||
\(377\) | − | 48551.0i | − | 0.341598i | ||||||
\(378\) | − | 2579.66i | − | 0.0180542i | ||||||
\(379\) | 234352. | 1.63152 | 0.815758 | − | 0.578394i | \(-0.196320\pi\) | ||||
0.815758 | + | 0.578394i | \(0.196320\pi\) | |||||||
\(380\) | −16036.1 | −0.111053 | ||||||||
\(381\) | 148955. | 1.02614 | ||||||||
\(382\) | −19091.8 | −0.130834 | ||||||||
\(383\) | 114382. | 0.779762 | 0.389881 | − | 0.920865i | \(-0.372516\pi\) | ||||
0.389881 | + | 0.920865i | \(0.372516\pi\) | |||||||
\(384\) | 32347.7i | 0.219372i | ||||||||
\(385\) | − | 167841.i | − | 1.13234i | ||||||
\(386\) | 19981.6i | 0.134108i | ||||||||
\(387\) | − | 74476.3i | − | 0.497274i | ||||||
\(388\) | − | 46691.9i | − | 0.310154i | ||||||
\(389\) | −248829. | −1.64438 | −0.822189 | − | 0.569215i | \(-0.807247\pi\) | ||||
−0.822189 | + | 0.569215i | \(0.807247\pi\) | |||||||
\(390\) | −6415.81 | −0.0421815 | ||||||||
\(391\) | − | 413052.i | − | 2.70179i | ||||||
\(392\) | − | 2082.99i | − | 0.0135555i | ||||||
\(393\) | − | 103121.i | − | 0.667668i | ||||||
\(394\) | − | 11733.6i | − | 0.0755857i | ||||||
\(395\) | 117762. | 0.754763 | ||||||||
\(396\) | − | 84444.7i | − | 0.538495i | ||||||
\(397\) | − | 178881.i | − | 1.13497i | −0.823385 | − | 0.567483i | \(-0.807917\pi\) | ||
0.823385 | − | 0.567483i | \(-0.192083\pi\) | |||||||
\(398\) | 26437.2i | 0.166898i | ||||||||
\(399\) | −13803.3 | −0.0867037 | ||||||||
\(400\) | −74886.0 | −0.468037 | ||||||||
\(401\) | 79311.1i | 0.493225i | 0.969114 | + | 0.246613i | \(0.0793175\pi\) | ||||
−0.969114 | + | 0.246613i | \(0.920682\pi\) | |||||||
\(402\) | 100.135 | 0.000619633 | ||||||||
\(403\) | 148787. | 0.916123 | ||||||||
\(404\) | − | 72554.7i | − | 0.444532i | ||||||
\(405\) | −13121.1 | −0.0799947 | ||||||||
\(406\) | − | 5063.72i | − | 0.0307198i | ||||||
\(407\) | 366092. | 2.21004 | ||||||||
\(408\) | 31334.6i | 0.188237i | ||||||||
\(409\) | − | 85968.6i | − | 0.513917i | −0.966422 | − | 0.256959i | \(-0.917280\pi\) | ||
0.966422 | − | 0.256959i | \(-0.0827204\pi\) | |||||||
\(410\) | − | 10361.7i | − | 0.0616404i | ||||||
\(411\) | 99585.3 | 0.589538 | ||||||||
\(412\) | 224388.i | 1.32192i | ||||||||
\(413\) | 77515.6 | + | 145081.i | 0.454453 | + | 0.850569i | ||||
\(414\) | 8918.20 | 0.0520327 | ||||||||
\(415\) | − | 122433.i | − | 0.710888i | ||||||
\(416\) | 52021.8 | 0.300607 | ||||||||
\(417\) | −105234. | −0.605177 | ||||||||
\(418\) | 4316.81 | 0.0247065 | ||||||||
\(419\) | − | 282200.i | − | 1.60742i | −0.595023 | − | 0.803709i | \(-0.702857\pi\) | ||
0.595023 | − | 0.803709i | \(-0.297143\pi\) | |||||||
\(420\) | 70041.1 | 0.397058 | ||||||||
\(421\) | 254214.i | 1.43428i | 0.696928 | + | 0.717141i | \(0.254550\pi\) | ||||
−0.696928 | + | 0.717141i | \(0.745450\pi\) | |||||||
\(422\) | 896.524 | 0.00503427 | ||||||||
\(423\) | − | 38802.1i | − | 0.216857i | ||||||
\(424\) | − | 13870.2i | − | 0.0771529i | ||||||
\(425\) | −146487. | −0.811003 | ||||||||
\(426\) | − | 4217.15i | − | 0.0232380i | ||||||
\(427\) | 5441.84i | 0.0298463i | ||||||||
\(428\) | 36420.1 | 0.198817 | ||||||||
\(429\) | −180778. | −0.982269 | ||||||||
\(430\) | −19318.7 | −0.104482 | ||||||||
\(431\) | − | 196721.i | − | 1.05900i | −0.848310 | − | 0.529500i | \(-0.822380\pi\) | ||
0.848310 | − | 0.529500i | \(-0.177620\pi\) | |||||||
\(432\) | 34899.4 | 0.187004 | ||||||||
\(433\) | 246611. | 1.31533 | 0.657667 | − | 0.753309i | \(-0.271543\pi\) | ||||
0.657667 | + | 0.753309i | \(0.271543\pi\) | |||||||
\(434\) | 15518.0 | 0.0823866 | ||||||||
\(435\) | −25756.0 | −0.136113 | ||||||||
\(436\) | 292063.i | 1.53640i | ||||||||
\(437\) | − | 47719.7i | − | 0.249882i | ||||||
\(438\) | 424.507 | 0.00221277 | ||||||||
\(439\) | 73628.2 | 0.382046 | 0.191023 | − | 0.981586i | \(-0.438820\pi\) | ||||
0.191023 | + | 0.981586i | \(0.438820\pi\) | |||||||
\(440\) | −44018.2 | −0.227367 | ||||||||
\(441\) | −4538.17 | −0.0233348 | ||||||||
\(442\) | 33380.9 | 0.170865 | ||||||||
\(443\) | 21033.6i | 0.107178i | 0.998563 | + | 0.0535890i | \(0.0170661\pi\) | ||||
−0.998563 | + | 0.0535890i | \(0.982934\pi\) | |||||||
\(444\) | 152772.i | 0.774959i | ||||||||
\(445\) | − | 164134.i | − | 0.828853i | ||||||
\(446\) | 10981.9i | 0.0552087i | ||||||||
\(447\) | − | 44280.8i | − | 0.221616i | ||||||
\(448\) | −182648. | −0.910038 | ||||||||
\(449\) | 99536.9 | 0.493732 | 0.246866 | − | 0.969050i | \(-0.420599\pi\) | ||||
0.246866 | + | 0.969050i | \(0.420599\pi\) | |||||||
\(450\) | − | 3162.81i | − | 0.0156188i | ||||||
\(451\) | − | 291962.i | − | 1.43540i | ||||||
\(452\) | − | 243837.i | − | 1.19350i | ||||||
\(453\) | 224457.i | 1.09380i | ||||||||
\(454\) | −24713.3 | −0.119900 | ||||||||
\(455\) | − | 149943.i | − | 0.724274i | ||||||
\(456\) | 3620.07i | 0.0174096i | ||||||||
\(457\) | 282977.i | 1.35494i | 0.735551 | + | 0.677469i | \(0.236923\pi\) | ||||
−0.735551 | + | 0.677469i | \(0.763077\pi\) | |||||||
\(458\) | −14370.4 | −0.0685077 | ||||||||
\(459\) | 68268.1 | 0.324035 | ||||||||
\(460\) | 242140.i | 1.14433i | ||||||||
\(461\) | 3519.59 | 0.0165611 | 0.00828057 | − | 0.999966i | \(-0.497364\pi\) | ||||
0.00828057 | + | 0.999966i | \(0.497364\pi\) | |||||||
\(462\) | −18854.6 | −0.0883350 | ||||||||
\(463\) | − | 295702.i | − | 1.37940i | −0.724093 | − | 0.689702i | \(-0.757741\pi\) | ||
0.724093 | − | 0.689702i | \(-0.242259\pi\) | |||||||
\(464\) | 68505.4 | 0.318192 | ||||||||
\(465\) | − | 78930.4i | − | 0.365038i | ||||||
\(466\) | −20672.9 | −0.0951986 | ||||||||
\(467\) | − | 77026.5i | − | 0.353189i | −0.984284 | − | 0.176594i | \(-0.943492\pi\) | ||
0.984284 | − | 0.176594i | \(-0.0565081\pi\) | |||||||
\(468\) | − | 75439.6i | − | 0.344435i | ||||||
\(469\) | 2340.24i | 0.0106394i | ||||||||
\(470\) | −10065.0 | −0.0455638 | ||||||||
\(471\) | − | 37796.9i | − | 0.170378i | ||||||
\(472\) | 38049.1 | − | 20329.3i | 0.170789 | − | 0.0912513i | ||||
\(473\) | −544342. | −2.43304 | ||||||||
\(474\) | − | 13228.9i | − | 0.0588799i | ||||||
\(475\) | −16923.6 | −0.0750077 | ||||||||
\(476\) | −364417. | −1.60837 | ||||||||
\(477\) | −30218.8 | −0.132813 | ||||||||
\(478\) | − | 9528.62i | − | 0.0417037i | ||||||
\(479\) | 76085.5 | 0.331612 | 0.165806 | − | 0.986158i | \(-0.446977\pi\) | ||||
0.165806 | + | 0.986158i | \(0.446977\pi\) | |||||||
\(480\) | − | 27597.3i | − | 0.119780i | ||||||
\(481\) | 327052. | 1.41360 | ||||||||
\(482\) | 4959.73i | 0.0213483i | ||||||||
\(483\) | 208426.i | 0.893423i | ||||||||
\(484\) | −385161. | −1.64419 | ||||||||
\(485\) | 53026.7i | 0.225430i | ||||||||
\(486\) | 1473.97i | 0.00624047i | ||||||||
\(487\) | 174246. | 0.734690 | 0.367345 | − | 0.930085i | \(-0.380267\pi\) | ||||
0.367345 | + | 0.930085i | \(0.380267\pi\) | |||||||
\(488\) | 1427.18 | 0.00599295 | ||||||||
\(489\) | −80103.0 | −0.334989 | ||||||||
\(490\) | 1177.18i | 0.00490285i | ||||||||
\(491\) | 328811. | 1.36390 | 0.681951 | − | 0.731398i | \(-0.261132\pi\) | ||||
0.681951 | + | 0.731398i | \(0.261132\pi\) | |||||||
\(492\) | 121838. | 0.503328 | ||||||||
\(493\) | 134006. | 0.551354 | ||||||||
\(494\) | 3856.48 | 0.0158029 | ||||||||
\(495\) | 95901.5i | 0.391395i | ||||||||
\(496\) | 209938.i | 0.853351i | ||||||||
\(497\) | 98558.2 | 0.399006 | ||||||||
\(498\) | −13753.6 | −0.0554572 | ||||||||
\(499\) | −289611. | −1.16309 | −0.581546 | − | 0.813513i | \(-0.697552\pi\) | ||||
−0.581546 | + | 0.813513i | \(0.697552\pi\) | |||||||
\(500\) | 264159. | 1.05664 | ||||||||
\(501\) | 196053. | 0.781083 | ||||||||
\(502\) | 17431.9i | 0.0691730i | ||||||||
\(503\) | 453397.i | 1.79202i | 0.444036 | + | 0.896009i | \(0.353546\pi\) | ||||
−0.444036 | + | 0.896009i | \(0.646454\pi\) | |||||||
\(504\) | − | 15811.4i | − | 0.0622458i | ||||||
\(505\) | 82398.4i | 0.323099i | ||||||||
\(506\) | − | 65182.6i | − | 0.254584i | ||||||
\(507\) | −13092.6 | −0.0509341 | ||||||||
\(508\) | 454323. | 1.76050 | ||||||||
\(509\) | 427793.i | 1.65119i | 0.564260 | + | 0.825597i | \(0.309161\pi\) | ||||
−0.564260 | + | 0.825597i | \(0.690839\pi\) | |||||||
\(510\) | − | 17708.4i | − | 0.0680829i | ||||||
\(511\) | 9921.08i | 0.0379942i | ||||||||
\(512\) | 122727.i | 0.468167i | ||||||||
\(513\) | 7886.98 | 0.0299692 | ||||||||
\(514\) | 41142.5i | 0.155727i | ||||||||
\(515\) | − | 254831.i | − | 0.960811i | ||||||
\(516\) | − | 227157.i | − | 0.853154i | ||||||
\(517\) | −283602. | −1.06103 | ||||||||
\(518\) | 34110.6 | 0.127125 | ||||||||
\(519\) | 62895.1i | 0.233498i | ||||||||
\(520\) | −39324.2 | −0.145430 | ||||||||
\(521\) | −142162. | −0.523730 | −0.261865 | − | 0.965105i | \(-0.584337\pi\) | ||||
−0.261865 | + | 0.965105i | \(0.584337\pi\) | |||||||
\(522\) | 2893.32i | 0.0106183i | ||||||||
\(523\) | −197294. | −0.721289 | −0.360645 | − | 0.932703i | \(-0.617443\pi\) | ||||
−0.360645 | + | 0.932703i | \(0.617443\pi\) | |||||||
\(524\) | − | 314524.i | − | 1.14549i | ||||||
\(525\) | 73917.4 | 0.268181 | ||||||||
\(526\) | 3620.64i | 0.0130862i | ||||||||
\(527\) | 410668.i | 1.47866i | ||||||||
\(528\) | − | 255077.i | − | 0.914964i | ||||||
\(529\) | −440712. | −1.57487 | ||||||||
\(530\) | 7838.58i | 0.0279052i | ||||||||
\(531\) | −44291.1 | − | 82896.7i | −0.157082 | − | 0.294000i | ||||
\(532\) | −42101.0 | −0.148754 | ||||||||
\(533\) | − | 260828.i | − | 0.918120i | ||||||
\(534\) | −18438.1 | −0.0646597 | ||||||||
\(535\) | −41361.3 | −0.144506 | ||||||||
\(536\) | 613.755 | 0.00213632 | ||||||||
\(537\) | − | 1499.14i | − | 0.00519867i | ||||||
\(538\) | 2600.81 | 0.00898554 | ||||||||
\(539\) | 33169.2i | 0.114171i | ||||||||
\(540\) | −40020.3 | −0.137244 | ||||||||
\(541\) | 225666.i | 0.771029i | 0.922702 | + | 0.385515i | \(0.125976\pi\) | ||||
−0.922702 | + | 0.385515i | \(0.874024\pi\) | |||||||
\(542\) | − | 53684.1i | − | 0.182746i | ||||||
\(543\) | −66363.1 | −0.225075 | ||||||||
\(544\) | 143586.i | 0.485193i | ||||||||
\(545\) | − | 331688.i | − | 1.11670i | ||||||
\(546\) | −16844.0 | −0.0565014 | ||||||||
\(547\) | 648.964 | 0.00216893 | 0.00108447 | − | 0.999999i | \(-0.499655\pi\) | ||||
0.00108447 | + | 0.999999i | \(0.499655\pi\) | |||||||
\(548\) | 303741. | 1.01145 | ||||||||
\(549\) | − | 3109.38i | − | 0.0103164i | ||||||
\(550\) | −23116.8 | −0.0764190 | ||||||||
\(551\) | 15481.7 | 0.0509935 | ||||||||
\(552\) | 54662.0 | 0.179394 | ||||||||
\(553\) | 309170. | 1.01099 | ||||||||
\(554\) | 37409.6i | 0.121889i | ||||||||
\(555\) | − | 173499.i | − | 0.563264i | ||||||
\(556\) | −320969. | −1.03828 | ||||||||
\(557\) | 179490. | 0.578536 | 0.289268 | − | 0.957248i | \(-0.406588\pi\) | ||||
0.289268 | + | 0.957248i | \(0.406588\pi\) | |||||||
\(558\) | −8866.72 | −0.0284770 | ||||||||
\(559\) | −486295. | −1.55624 | ||||||||
\(560\) | 211569. | 0.674647 | ||||||||
\(561\) | − | 498967.i | − | 1.58543i | ||||||
\(562\) | − | 5270.56i | − | 0.0166872i | ||||||
\(563\) | − | 56816.3i | − | 0.179249i | −0.995976 | − | 0.0896243i | \(-0.971433\pi\) | ||
0.995976 | − | 0.0896243i | \(-0.0285666\pi\) | |||||||
\(564\) | − | 118349.i | − | 0.372053i | ||||||
\(565\) | 276919.i | 0.867472i | ||||||||
\(566\) | 57325.1 | 0.178942 | ||||||||
\(567\) | −34448.0 | −0.107151 | ||||||||
\(568\) | − | 25848.0i | − | 0.0801180i | ||||||
\(569\) | 361962.i | 1.11799i | 0.829170 | + | 0.558996i | \(0.188813\pi\) | ||||
−0.829170 | + | 0.558996i | \(0.811187\pi\) | |||||||
\(570\) | − | 2045.84i | − | 0.00629682i | ||||||
\(571\) | 496112.i | 1.52163i | 0.648972 | + | 0.760813i | \(0.275199\pi\) | ||||
−0.648972 | + | 0.760813i | \(0.724801\pi\) | |||||||
\(572\) | −551383. | −1.68524 | ||||||||
\(573\) | 254946.i | 0.776494i | ||||||||
\(574\) | − | 27203.6i | − | 0.0825661i | ||||||
\(575\) | 255541.i | 0.772904i | ||||||||
\(576\) | 104362. | 0.314556 | ||||||||
\(577\) | −9847.40 | −0.0295781 | −0.0147890 | − | 0.999891i | \(-0.504708\pi\) | ||||
−0.0147890 | + | 0.999891i | \(0.504708\pi\) | |||||||
\(578\) | 59635.5i | 0.178504i | ||||||||
\(579\) | 266828. | 0.795929 | ||||||||
\(580\) | −78557.4 | −0.233524 | ||||||||
\(581\) | − | 321433.i | − | 0.952222i | ||||||
\(582\) | 5956.80 | 0.0175860 | ||||||||
\(583\) | 220867.i | 0.649821i | ||||||||
\(584\) | 2601.92 | 0.00762900 | ||||||||
\(585\) | 85674.7i | 0.250346i | ||||||||
\(586\) | 8321.06i | 0.0242317i | ||||||||
\(587\) | − | 550647.i | − | 1.59807i | −0.601282 | − | 0.799037i | \(-0.705343\pi\) | ||
0.601282 | − | 0.799037i | \(-0.294657\pi\) | |||||||
\(588\) | −13841.7 | −0.0400345 | ||||||||
\(589\) | 47444.3i | 0.136758i | ||||||||
\(590\) | −21502.9 | + | 11488.9i | −0.0617723 | + | 0.0330045i | ||||
\(591\) | −156687. | −0.448599 | ||||||||
\(592\) | 461471.i | 1.31674i | ||||||||
\(593\) | −455801. | −1.29618 | −0.648090 | − | 0.761563i | \(-0.724432\pi\) | ||||
−0.648090 | + | 0.761563i | \(0.724432\pi\) | |||||||
\(594\) | 10773.2 | 0.0305331 | ||||||||
\(595\) | 413859. | 1.16901 | ||||||||
\(596\) | − | 135059.i | − | 0.380217i | ||||||
\(597\) | 353035. | 0.990533 | ||||||||
\(598\) | − | 58231.6i | − | 0.162838i | ||||||
\(599\) | 556678. | 1.55149 | 0.775747 | − | 0.631044i | \(-0.217373\pi\) | ||||
0.775747 | + | 0.631044i | \(0.217373\pi\) | |||||||
\(600\) | − | 19385.7i | − | 0.0538491i | ||||||
\(601\) | − | 157038.i | − | 0.434766i | −0.976086 | − | 0.217383i | \(-0.930248\pi\) | ||
0.976086 | − | 0.217383i | \(-0.0697520\pi\) | |||||||
\(602\) | −50719.1 | −0.139952 | ||||||||
\(603\) | − | 1337.17i | − | 0.00367751i | ||||||
\(604\) | 684609.i | 1.87659i | ||||||||
\(605\) | 437417. | 1.19505 | ||||||||
\(606\) | 9256.31 | 0.0252053 | ||||||||
\(607\) | −550937. | −1.49529 | −0.747644 | − | 0.664100i | \(-0.768815\pi\) | ||||
−0.747644 | + | 0.664100i | \(0.768815\pi\) | |||||||
\(608\) | 16588.4i | 0.0448743i | ||||||||
\(609\) | −67619.4 | −0.182321 | ||||||||
\(610\) | −806.554 | −0.00216757 | ||||||||
\(611\) | −253359. | −0.678662 | ||||||||
\(612\) | 208222. | 0.555934 | ||||||||
\(613\) | 582881.i | 1.55117i | 0.631244 | + | 0.775585i | \(0.282545\pi\) | ||||
−0.631244 | + | 0.775585i | \(0.717455\pi\) | |||||||
\(614\) | − | 34905.3i | − | 0.0925880i | ||||||
\(615\) | −138368. | −0.365834 | ||||||||
\(616\) | −115565. | −0.304554 | ||||||||
\(617\) | −498475. | −1.30940 | −0.654701 | − | 0.755888i | \(-0.727205\pi\) | ||||
−0.654701 | + | 0.755888i | \(0.727205\pi\) | |||||||
\(618\) | −28626.7 | −0.0749539 | ||||||||
\(619\) | 469002. | 1.22403 | 0.612017 | − | 0.790844i | \(-0.290358\pi\) | ||||
0.612017 | + | 0.790844i | \(0.290358\pi\) | |||||||
\(620\) | − | 240743.i | − | 0.626282i | ||||||
\(621\) | − | 119091.i | − | 0.308813i | ||||||
\(622\) | − | 9120.40i | − | 0.0235740i | ||||||
\(623\) | − | 430914.i | − | 1.11023i | ||||||
\(624\) | − | 227876.i | − | 0.585234i | ||||||
\(625\) | −111846. | −0.286327 | ||||||||
\(626\) | 18945.3 | 0.0483450 | ||||||||
\(627\) | − | 57645.4i | − | 0.146632i | ||||||
\(628\) | − | 115283.i | − | 0.292311i | ||||||
\(629\) | 902701.i | 2.28162i | ||||||||
\(630\) | 8935.62i | 0.0225135i | ||||||||
\(631\) | −55781.7 | −0.140098 | −0.0700492 | − | 0.997544i | \(-0.522316\pi\) | ||||
−0.0700492 | + | 0.997544i | \(0.522316\pi\) | |||||||
\(632\) | − | 81083.4i | − | 0.203001i | ||||||
\(633\) | − | 11971.9i | − | 0.0298783i | ||||||
\(634\) | − | 49282.7i | − | 0.122607i | ||||||
\(635\) | −515962. | −1.27959 | ||||||||
\(636\) | −92169.2 | −0.227862 | ||||||||
\(637\) | 29632.1i | 0.0730269i | ||||||||
\(638\) | 21147.1 | 0.0519529 | ||||||||
\(639\) | −56314.5 | −0.137917 | ||||||||
\(640\) | − | 112048.i | − | 0.273556i | ||||||
\(641\) | −77645.7 | −0.188974 | −0.0944869 | − | 0.995526i | \(-0.530121\pi\) | ||||
−0.0944869 | + | 0.995526i | \(0.530121\pi\) | |||||||
\(642\) | 4646.36i | 0.0112731i | ||||||||
\(643\) | 295599. | 0.714960 | 0.357480 | − | 0.933921i | \(-0.383636\pi\) | ||||
0.357480 | + | 0.933921i | \(0.383636\pi\) | |||||||
\(644\) | 635711.i | 1.53281i | ||||||||
\(645\) | 257976.i | 0.620098i | ||||||||
\(646\) | 10644.3i | 0.0255066i | ||||||||
\(647\) | −392444. | −0.937496 | −0.468748 | − | 0.883332i | \(-0.655295\pi\) | ||||
−0.468748 | + | 0.883332i | \(0.655295\pi\) | |||||||
\(648\) | 9034.38i | 0.0215153i | ||||||||
\(649\) | −605886. | + | 323721.i | −1.43847 | + | 0.768565i | ||||
\(650\) | −20651.6 | −0.0488796 | ||||||||
\(651\) | − | 207223.i | − | 0.488962i | ||||||
\(652\) | −244319. | −0.574728 | ||||||||
\(653\) | −225024. | −0.527720 | −0.263860 | − | 0.964561i | \(-0.584996\pi\) | ||||
−0.263860 | + | 0.964561i | \(0.584996\pi\) | |||||||
\(654\) | −37260.5 | −0.0871150 | ||||||||
\(655\) | 357197.i | 0.832577i | ||||||||
\(656\) | 368028. | 0.855210 | ||||||||
\(657\) | − | 5668.74i | − | 0.0131327i | ||||||
\(658\) | −26424.6 | −0.0610318 | ||||||||
\(659\) | 490926.i | 1.13044i | 0.824942 | + | 0.565218i | \(0.191208\pi\) | ||||
−0.824942 | + | 0.565218i | \(0.808792\pi\) | |||||||
\(660\) | 292506.i | 0.671500i | ||||||||
\(661\) | −209902. | −0.480412 | −0.240206 | − | 0.970722i | \(-0.577215\pi\) | ||||
−0.240206 | + | 0.970722i | \(0.577215\pi\) | |||||||
\(662\) | 69049.6i | 0.157560i | ||||||||
\(663\) | − | 445758.i | − | 1.01408i | ||||||
\(664\) | −84299.4 | −0.191200 | ||||||||
\(665\) | 47812.9 | 0.108119 | ||||||||
\(666\) | −19490.2 | −0.0439408 | ||||||||
\(667\) | − | 233768.i | − | 0.525453i | ||||||
\(668\) | 597973. | 1.34007 | ||||||||
\(669\) | 146649. | 0.327662 | ||||||||
\(670\) | −346.855 | −0.000772679 | ||||||||
\(671\) | −22726.2 | −0.0504757 | ||||||||
\(672\) | − | 72453.4i | − | 0.160443i | ||||||
\(673\) | − | 535935.i | − | 1.18327i | −0.806208 | − | 0.591633i | \(-0.798484\pi\) | ||
0.806208 | − | 0.591633i | \(-0.201516\pi\) | |||||||
\(674\) | −34298.4 | −0.0755012 | ||||||||
\(675\) | −42235.2 | −0.0926972 | ||||||||
\(676\) | −39933.1 | −0.0873857 | ||||||||
\(677\) | 589822. | 1.28690 | 0.643448 | − | 0.765489i | \(-0.277503\pi\) | ||||
0.643448 | + | 0.765489i | \(0.277503\pi\) | |||||||
\(678\) | 31107.9 | 0.0676725 | ||||||||
\(679\) | 139215.i | 0.301959i | ||||||||
\(680\) | − | 108539.i | − | 0.234730i | ||||||
\(681\) | 330014.i | 0.711603i | ||||||||
\(682\) | 64806.3i | 0.139331i | ||||||||
\(683\) | − | 569992.i | − | 1.22188i | −0.791678 | − | 0.610939i | \(-0.790792\pi\) | ||
0.791678 | − | 0.610939i | \(-0.209208\pi\) | |||||||
\(684\) | 24055.8 | 0.0514170 | ||||||||
\(685\) | −344951. | −0.735150 | ||||||||
\(686\) | 47238.4i | 0.100380i | ||||||||
\(687\) | 191898.i | 0.406591i | ||||||||
\(688\) | − | 686161.i | − | 1.44960i | ||||||
\(689\) | 197314.i | 0.415642i | ||||||||
\(690\) | −30891.5 | −0.0648845 | ||||||||
\(691\) | − | 151727.i | − | 0.317765i | −0.987297 | − | 0.158883i | \(-0.949211\pi\) | ||
0.987297 | − | 0.158883i | \(-0.0507891\pi\) | |||||||
\(692\) | 191834.i | 0.400602i | ||||||||
\(693\) | 251778.i | 0.524266i | ||||||||
\(694\) | −30924.7 | −0.0642076 | ||||||||
\(695\) | 364516. | 0.754652 | ||||||||
\(696\) | 17734.0i | 0.0366089i | ||||||||
\(697\) | 719914. | 1.48189 | ||||||||
\(698\) | 9487.65 | 0.0194737 | ||||||||
\(699\) | 276060.i | 0.565001i | ||||||||
\(700\) | 225453. | 0.460108 | ||||||||
\(701\) | − | 288172.i | − | 0.586429i | −0.956047 | − | 0.293214i | \(-0.905275\pi\) | ||
0.956047 | − | 0.293214i | \(-0.0947250\pi\) | |||||||
\(702\) | 9624.35 | 0.0195298 | ||||||||
\(703\) | 104289.i | 0.211021i | ||||||||
\(704\) | − | 762776.i | − | 1.53905i | ||||||
\(705\) | 134405.i | 0.270420i | ||||||||
\(706\) | 23793.8 | 0.0477369 | ||||||||
\(707\) | 216328.i | 0.432786i | ||||||||
\(708\) | −135090. | − | 252840.i | −0.269500 | − | 0.504405i | ||||
\(709\) | −17367.9 | −0.0345506 | −0.0172753 | − | 0.999851i | \(-0.505499\pi\) | ||||
−0.0172753 | + | 0.999851i | \(0.505499\pi\) | |||||||
\(710\) | 14607.7i | 0.0289777i | ||||||||
\(711\) | −176655. | −0.349450 | ||||||||
\(712\) | −113012. | −0.222928 | ||||||||
\(713\) | 716394. | 1.40920 | ||||||||
\(714\) | − | 46491.2i | − | 0.0911957i | ||||||
\(715\) | 626191. | 1.22488 | ||||||||
\(716\) | − | 4572.46i | − | 0.00891915i | ||||||
\(717\) | −127242. | −0.247510 | ||||||||
\(718\) | − | 93810.0i | − | 0.181970i | ||||||
\(719\) | 524931.i | 1.01542i | 0.861529 | + | 0.507708i | \(0.169507\pi\) | ||||
−0.861529 | + | 0.507708i | \(0.830493\pi\) | |||||||
\(720\) | −120887. | −0.233192 | ||||||||
\(721\) | − | 669029.i | − | 1.28699i | ||||||
\(722\) | − | 49480.4i | − | 0.0949203i | ||||||
\(723\) | 66230.7 | 0.126702 | ||||||||
\(724\) | −202412. | −0.386152 | ||||||||
\(725\) | −82905.1 | −0.157727 | ||||||||
\(726\) | − | 49137.7i | − | 0.0932269i | ||||||
\(727\) | 416443. | 0.787928 | 0.393964 | − | 0.919126i | \(-0.371103\pi\) | ||||
0.393964 | + | 0.919126i | \(0.371103\pi\) | |||||||
\(728\) | −103241. | −0.194800 | ||||||||
\(729\) | 19683.0 | 0.0370370 | ||||||||
\(730\) | −1470.44 | −0.00275931 | ||||||||
\(731\) | − | 1.34223e6i | − | 2.51184i | ||||||
\(732\) | − | 9483.79i | − | 0.0176994i | ||||||
\(733\) | −22984.6 | −0.0427788 | −0.0213894 | − | 0.999771i | \(-0.506809\pi\) | ||||
−0.0213894 | + | 0.999771i | \(0.506809\pi\) | |||||||
\(734\) | 92404.5 | 0.171515 | ||||||||
\(735\) | 15719.6 | 0.0290983 | ||||||||
\(736\) | 250480. | 0.462400 | ||||||||
\(737\) | −9773.32 | −0.0179931 | ||||||||
\(738\) | 15543.6i | 0.0285391i | ||||||||
\(739\) | − | 339929.i | − | 0.622442i | −0.950337 | − | 0.311221i | \(-0.899262\pi\) | ||
0.950337 | − | 0.311221i | \(-0.100738\pi\) | |||||||
\(740\) | − | 529184.i | − | 0.966369i | ||||||
\(741\) | − | 51498.2i | − | 0.0937898i | ||||||
\(742\) | 20579.3i | 0.0373786i | ||||||||
\(743\) | −28658.0 | −0.0519121 | −0.0259560 | − | 0.999663i | \(-0.508263\pi\) | ||||
−0.0259560 | + | 0.999663i | \(0.508263\pi\) | |||||||
\(744\) | −54346.5 | −0.0981806 | ||||||||
\(745\) | 153383.i | 0.276353i | ||||||||
\(746\) | − | 65519.0i | − | 0.117731i | ||||||
\(747\) | 183661.i | 0.329137i | ||||||||
\(748\) | − | 1.52188e6i | − | 2.72005i | ||||||
\(749\) | −108589. | −0.193564 | ||||||||
\(750\) | 33700.6i | 0.0599121i | ||||||||
\(751\) | − | 398692.i | − | 0.706899i | −0.935454 | − | 0.353449i | \(-0.885009\pi\) | ||
0.935454 | − | 0.353449i | \(-0.114991\pi\) | |||||||
\(752\) | − | 357489.i | − | 0.632161i | ||||||
\(753\) | 232780. | 0.410540 | ||||||||
\(754\) | 18892.0 | 0.0332304 | ||||||||
\(755\) | − | 777492.i | − | 1.36396i | ||||||
\(756\) | −105069. | −0.183835 | ||||||||
\(757\) | 55848.3 | 0.0974581 | 0.0487290 | − | 0.998812i | \(-0.484483\pi\) | ||||
0.0487290 | + | 0.998812i | \(0.484483\pi\) | |||||||
\(758\) | 91190.6i | 0.158713i | ||||||||
\(759\) | −870428. | −1.51095 | ||||||||
\(760\) | − | 12539.5i | − | 0.0217096i | ||||||
\(761\) | −31452.4 | −0.0543106 | −0.0271553 | − | 0.999631i | \(-0.508645\pi\) | ||||
−0.0271553 | + | 0.999631i | \(0.508645\pi\) | |||||||
\(762\) | 57961.1i | 0.0998220i | ||||||||
\(763\) | − | 870808.i | − | 1.49580i | ||||||
\(764\) | 777600.i | 1.33220i | ||||||||
\(765\) | −236472. | −0.404070 | ||||||||
\(766\) | 44508.2i | 0.0758547i | ||||||||
\(767\) | −541276. | + | 289199.i | −0.920085 | + | 0.491594i | ||||
\(768\) | 308765. | 0.523486 | ||||||||
\(769\) | 1.10780e6i | 1.87330i | 0.350263 | + | 0.936651i | \(0.386092\pi\) | ||||
−0.350263 | + | 0.936651i | \(0.613908\pi\) | |||||||
\(770\) | 65309.9 | 0.110153 | ||||||||
\(771\) | 549405. | 0.924237 | ||||||||
\(772\) | 813842. | 1.36554 | ||||||||
\(773\) | 392220.i | 0.656403i | 0.944608 | + | 0.328201i | \(0.106442\pi\) | ||||
−0.944608 | + | 0.328201i | \(0.893558\pi\) | |||||||
\(774\) | 28980.0 | 0.0483745 | ||||||||
\(775\) | − | 254066.i | − | 0.423003i | ||||||
\(776\) | 36510.8 | 0.0606314 | ||||||||
\(777\) | − | 455502.i | − | 0.754481i | ||||||
\(778\) | − | 96823.6i | − | 0.159964i | ||||||
\(779\) | 83171.3 | 0.137056 | ||||||||
\(780\) | 261313.i | 0.429509i | ||||||||
\(781\) | 411599.i | 0.674795i | ||||||||
\(782\) | 160726. | 0.262828 | ||||||||
\(783\) | 38636.6 | 0.0630195 | ||||||||
\(784\) | −41810.8 | −0.0680232 | ||||||||
\(785\) | 130924.i | 0.212461i | ||||||||
\(786\) | 40126.0 | 0.0649503 | ||||||||
\(787\) | 208960. | 0.337376 | 0.168688 | − | 0.985670i | \(-0.446047\pi\) | ||||
0.168688 | + | 0.985670i | \(0.446047\pi\) | |||||||
\(788\) | −477905. | −0.769643 | ||||||||
\(789\) | 48348.9 | 0.0776663 | ||||||||
\(790\) | 45823.2i | 0.0734228i | ||||||||
\(791\) | 727018.i | 1.16196i | ||||||||
\(792\) | 66031.7 | 0.105269 | ||||||||
\(793\) | −20302.7 | −0.0322855 | ||||||||
\(794\) | 69605.7 | 0.110409 | ||||||||
\(795\) | 104674. | 0.165617 | ||||||||
\(796\) | 1.07678e6 | 1.69942 | ||||||||
\(797\) | 12012.2i | 0.0189107i | 0.999955 | + | 0.00945534i | \(0.00300977\pi\) | ||||
−0.999955 | + | 0.00945534i | \(0.996990\pi\) | |||||||
\(798\) | − | 5371.11i | − | 0.00843448i | ||||||
\(799\) | − | 699299.i | − | 1.09539i | ||||||
\(800\) | − | 88831.9i | − | 0.138800i | ||||||
\(801\) | 246217.i | 0.383754i | ||||||||
\(802\) | −30861.3 | −0.0479806 | ||||||||
\(803\) | −41432.4 | −0.0642553 | ||||||||
\(804\) | − | 4078.46i | − | 0.00630935i | ||||||
\(805\) | − | 721960.i | − | 1.11409i | ||||||
\(806\) | 57895.5i | 0.0891199i | ||||||||
\(807\) | − | 34730.4i | − | 0.0533290i | ||||||
\(808\) | 56734.3 | 0.0869007 | ||||||||
\(809\) | 864652.i | 1.32113i | 0.750770 | + | 0.660563i | \(0.229683\pi\) | ||||
−0.750770 | + | 0.660563i | \(0.770317\pi\) | |||||||
\(810\) | − | 5105.66i | − | 0.00778183i | ||||||
\(811\) | 547154.i | 0.831893i | 0.909389 | + | 0.415947i | \(0.136550\pi\) | ||||
−0.909389 | + | 0.415947i | \(0.863450\pi\) | |||||||
\(812\) | −206243. | −0.312801 | ||||||||
\(813\) | −716880. | −1.08459 | ||||||||
\(814\) | 142453.i | 0.214992i | ||||||||
\(815\) | 277467. | 0.417730 | ||||||||
\(816\) | 628964. | 0.944595 | ||||||||
\(817\) | − | 155067.i | − | 0.232314i | ||||||
\(818\) | 33451.9 | 0.0499935 | ||||||||
\(819\) | 224929.i | 0.335334i | ||||||||
\(820\) | −422030. | −0.627647 | ||||||||
\(821\) | − | 1.15886e6i | − | 1.71928i | −0.510901 | − | 0.859639i | \(-0.670688\pi\) | ||
0.510901 | − | 0.859639i | \(-0.329312\pi\) | |||||||
\(822\) | 38750.4i | 0.0573499i | ||||||||
\(823\) | 563170.i | 0.831457i | 0.909489 | + | 0.415728i | \(0.136473\pi\) | ||||
−0.909489 | + | 0.415728i | \(0.863527\pi\) | |||||||
\(824\) | −175461. | −0.258419 | ||||||||
\(825\) | 308694.i | 0.453545i | ||||||||
\(826\) | −56453.4 | + | 30162.7i | −0.0827428 | + | 0.0442089i | ||||
\(827\) | −1.33840e6 | −1.95692 | −0.978461 | − | 0.206431i | \(-0.933815\pi\) | ||||
−0.978461 | + | 0.206431i | \(0.933815\pi\) | |||||||
\(828\) | − | 363235.i | − | 0.529818i | ||||||
\(829\) | −153786. | −0.223773 | −0.111887 | − | 0.993721i | \(-0.535689\pi\) | ||||
−0.111887 | + | 0.993721i | \(0.535689\pi\) | |||||||
\(830\) | 47640.7 | 0.0691547 | ||||||||
\(831\) | 499556. | 0.723405 | ||||||||
\(832\) | − | 681434.i | − | 0.984413i | ||||||
\(833\) | −81787.8 | −0.117869 | ||||||||
\(834\) | − | 40948.2i | − | 0.0588712i | ||||||
\(835\) | −679101. | −0.974006 | ||||||||
\(836\) | − | 175822.i | − | 0.251571i | ||||||
\(837\) | 118403.i | 0.169010i | ||||||||
\(838\) | 109809. | 0.156369 | ||||||||
\(839\) | − | 234998.i | − | 0.333841i | −0.985970 | − | 0.166920i | \(-0.946618\pi\) | ||
0.985970 | − | 0.166920i | \(-0.0533823\pi\) | |||||||
\(840\) | 54768.8i | 0.0776201i | ||||||||
\(841\) | −631440. | −0.892771 | ||||||||
\(842\) | −98919.0 | −0.139526 | ||||||||
\(843\) | −70381.4 | −0.0990382 | ||||||||
\(844\) | − | 36515.0i | − | 0.0512610i | ||||||
\(845\) | 45351.0 | 0.0635146 | ||||||||
\(846\) | 15098.6 | 0.0210957 | ||||||||
\(847\) | 1.14839e6 | 1.60074 | ||||||||
\(848\) | −278410. | −0.387163 | ||||||||
\(849\) | − | 765502.i | − | 1.06202i | ||||||
\(850\) | − | 57000.8i | − | 0.0788938i | ||||||
\(851\) | 1.57473e6 | 2.17443 | ||||||||
\(852\) | −171763. | −0.236619 | ||||||||
\(853\) | −544134. | −0.747839 | −0.373919 | − | 0.927461i | \(-0.621986\pi\) | ||||
−0.373919 | + | 0.927461i | \(0.621986\pi\) | |||||||
\(854\) | −2117.52 | −0.00290343 | ||||||||
\(855\) | −27319.5 | −0.0373715 | ||||||||
\(856\) | 28478.8i | 0.0388664i | ||||||||
\(857\) | − | 301859.i | − | 0.411000i | −0.978657 | − | 0.205500i | \(-0.934118\pi\) | ||
0.978657 | − | 0.205500i | \(-0.0658821\pi\) | |||||||
\(858\) | − | 70343.8i | − | 0.0955545i | ||||||
\(859\) | 1.32940e6i | 1.80164i | 0.434191 | + | 0.900821i | \(0.357034\pi\) | ||||
−0.434191 | + | 0.900821i | \(0.642966\pi\) | |||||||
\(860\) | 786844.i | 1.06388i | ||||||||
\(861\) | −363268. | −0.490028 | ||||||||
\(862\) | 76547.5 | 0.103019 | ||||||||
\(863\) | − | 707688.i | − | 0.950212i | −0.879929 | − | 0.475106i | \(-0.842410\pi\) | ||
0.879929 | − | 0.475106i | \(-0.157590\pi\) | |||||||
\(864\) | 41398.6i | 0.0554573i | ||||||||
\(865\) | − | 217861.i | − | 0.291170i | ||||||
\(866\) | 95960.5i | 0.127955i | ||||||||
\(867\) | 796354. | 1.05942 | ||||||||
\(868\) | − | 632042.i | − | 0.838893i | ||||||
\(869\) | 1.29116e6i | 1.70978i | ||||||||
\(870\) | − | 10022.1i | − | 0.0132410i | ||||||
\(871\) | −8731.11 | −0.0115089 | ||||||||
\(872\) | −228379. | −0.300347 | ||||||||
\(873\) | − | 79545.3i | − | 0.104372i | ||||||
\(874\) | 18568.6 | 0.0243084 | ||||||||
\(875\) | −787610. | −1.02872 | ||||||||
\(876\) | − | 17290.0i | − | 0.0225313i | ||||||
\(877\) | −423150. | −0.550168 | −0.275084 | − | 0.961420i | \(-0.588706\pi\) | ||||
−0.275084 | + | 0.961420i | \(0.588706\pi\) | |||||||
\(878\) | 28650.0i | 0.0371652i | ||||||||
\(879\) | 111117. | 0.143814 | ||||||||
\(880\) | 883555.i | 1.14095i | ||||||||
\(881\) | 1.11419e6i | 1.43551i | 0.696296 | + | 0.717755i | \(0.254830\pi\) | ||||
−0.696296 | + | 0.717755i | \(0.745170\pi\) | |||||||
\(882\) | − | 1765.88i | − | 0.00226999i | ||||||
\(883\) | −25385.3 | −0.0325583 | −0.0162792 | − | 0.999867i | \(-0.505182\pi\) | ||||
−0.0162792 | + | 0.999867i | \(0.505182\pi\) | |||||||
\(884\) | − | 1.35959e6i | − | 1.73982i | ||||||
\(885\) | 153419. | + | 287143.i | 0.195881 | + | 0.366617i | ||||
\(886\) | −8184.52 | −0.0104262 | ||||||||
\(887\) | − | 70599.4i | − | 0.0897334i | −0.998993 | − | 0.0448667i | \(-0.985714\pi\) | ||
0.998993 | − | 0.0448667i | \(-0.0142863\pi\) | |||||||
\(888\) | −119461. | −0.151495 | ||||||||
\(889\) | −1.35460e6 | −1.71398 | ||||||||
\(890\) | 63867.2 | 0.0806303 | ||||||||
\(891\) | − | 143862.i | − | 0.181213i | ||||||
\(892\) | 447288. | 0.562156 | ||||||||
\(893\) | − | 80789.7i | − | 0.101310i | ||||||
\(894\) | 17230.4 | 0.0215586 | ||||||||
\(895\) | 5192.82i | 0.00648271i | ||||||||
\(896\) | − | 294170.i | − | 0.366423i | ||||||
\(897\) | −777607. | −0.966440 | ||||||||
\(898\) | 38731.5i | 0.0480299i | ||||||||
\(899\) | 232419.i | 0.287576i | ||||||||
\(900\) | −128820. | −0.159037 | ||||||||
\(901\) | −544609. | −0.670866 | ||||||||
\(902\) | 113608. | 0.139635 | ||||||||
\(903\) | 677287.i | 0.830610i | ||||||||
\(904\) | 190669. | 0.233315 | ||||||||
\(905\) | 229873. | 0.280667 | ||||||||
\(906\) | −87340.3 | −0.106404 | ||||||||
\(907\) | −575833. | −0.699975 | −0.349987 | − | 0.936754i | \(-0.613814\pi\) | ||||
−0.349987 | + | 0.936754i | \(0.613814\pi\) | |||||||
\(908\) | 1.00656e6i | 1.22087i | ||||||||
\(909\) | − | 123606.i | − | 0.149593i | ||||||
\(910\) | 58345.3 | 0.0704569 | ||||||||
\(911\) | 805946. | 0.971112 | 0.485556 | − | 0.874206i | \(-0.338617\pi\) | ||||
0.485556 | + | 0.874206i | \(0.338617\pi\) | |||||||
\(912\) | 72663.9 | 0.0873633 | ||||||||
\(913\) | 1.34237e6 | 1.61039 | ||||||||
\(914\) | −110111. | −0.131807 | ||||||||
\(915\) | 10770.5i | 0.0128645i | ||||||||
\(916\) | 585302.i | 0.697572i | ||||||||
\(917\) | 937778.i | 1.11522i | ||||||||
\(918\) | 26564.3i | 0.0315219i | ||||||||
\(919\) | − | 176120.i | − | 0.208534i | −0.994549 | − | 0.104267i | \(-0.966750\pi\) | ||
0.994549 | − | 0.104267i | \(-0.0332496\pi\) | |||||||
\(920\) | −189342. | −0.223703 | ||||||||
\(921\) | −466115. | −0.549507 | ||||||||
\(922\) | 1369.53i | 0.00161106i | ||||||||
\(923\) | 367706.i | 0.431616i | ||||||||
\(924\) | 767939.i | 0.899462i | ||||||||
\(925\) | − | 558471.i | − | 0.652705i | ||||||
\(926\) | 115063. | 0.134188 | ||||||||
\(927\) | 382272.i | 0.444849i | ||||||||
\(928\) | 81263.0i | 0.0943620i | ||||||||
\(929\) | − | 398648.i | − | 0.461911i | −0.972964 | − | 0.230956i | \(-0.925815\pi\) | ||
0.972964 | − | 0.230956i | \(-0.0741852\pi\) | |||||||
\(930\) | 30713.2 | 0.0355107 | ||||||||
\(931\) | −9448.91 | −0.0109014 | ||||||||
\(932\) | 842000.i | 0.969350i | ||||||||
\(933\) | −121791. | −0.139911 | ||||||||
\(934\) | 29972.4 | 0.0343580 | ||||||||
\(935\) | 1.72836e6i | 1.97702i | ||||||||
\(936\) | 58990.2 | 0.0673330 | ||||||||
\(937\) | 115590.i | 0.131656i | 0.997831 | + | 0.0658282i | \(0.0209689\pi\) | ||||
−0.997831 | + | 0.0658282i | \(0.979031\pi\) | |||||||
\(938\) | −910.629 | −0.00103499 | ||||||||
\(939\) | − | 252989.i | − | 0.286927i | ||||||
\(940\) | 409945.i | 0.463948i | ||||||||
\(941\) | 31726.3i | 0.0358294i | 0.999840 | + | 0.0179147i | \(0.00570273\pi\) | ||||
−0.999840 | + | 0.0179147i | \(0.994297\pi\) | |||||||
\(942\) | 14707.4 | 0.0165743 | ||||||||
\(943\) | − | 1.25586e6i | − | 1.41227i | ||||||
\(944\) | −408060. | − | 763740.i | −0.457910 | − | 0.857041i | ||||
\(945\) | 119323. | 0.133617 | ||||||||
\(946\) | − | 211813.i | − | 0.236685i | ||||||
\(947\) | 1.57588e6 | 1.75721 | 0.878605 | − | 0.477549i | \(-0.158475\pi\) | ||||
0.878605 | + | 0.477549i | \(0.158475\pi\) | |||||||
\(948\) | −538807. | −0.599538 | ||||||||
\(949\) | −37014.1 | −0.0410994 | ||||||||
\(950\) | − | 6585.27i | − | 0.00729670i | ||||||
\(951\) | −658107. | −0.727671 | ||||||||
\(952\) | − | 284957.i | − | 0.314417i | ||||||
\(953\) | 490152. | 0.539691 | 0.269845 | − | 0.962904i | \(-0.413027\pi\) | ||||
0.269845 | + | 0.962904i | \(0.413027\pi\) | |||||||
\(954\) | − | 11758.7i | − | 0.0129199i | ||||||
\(955\) | − | 883099.i | − | 0.968284i | ||||||
\(956\) | −388097. | −0.424643 | ||||||||
\(957\) | − | 282392.i | − | 0.308339i | ||||||
\(958\) | 29606.2i | 0.0322590i | ||||||||
\(959\) | −905628. | −0.984720 | ||||||||
\(960\) | −361497. | −0.392249 | ||||||||
\(961\) | 211263. | 0.228758 | ||||||||
\(962\) | 127262.i | 0.137514i | ||||||||
\(963\) | 62046.1 | 0.0669055 | ||||||||
\(964\) | 202008. | 0.217377 | ||||||||
\(965\) | −924258. | −0.992518 | ||||||||
\(966\) | −81102.1 | −0.0869116 | ||||||||
\(967\) | 112759.i | 0.120586i | 0.998181 | + | 0.0602931i | \(0.0192035\pi\) | ||||
−0.998181 | + | 0.0602931i | \(0.980796\pi\) | |||||||
\(968\) | − | 301178.i | − | 0.321420i | ||||||
\(969\) | 142141. | 0.151381 | ||||||||
\(970\) | −20633.6 | −0.0219296 | ||||||||
\(971\) | −1.66125e6 | −1.76196 | −0.880978 | − | 0.473156i | \(-0.843115\pi\) | ||||
−0.880978 | + | 0.473156i | \(0.843115\pi\) | |||||||
\(972\) | 60034.4 | 0.0635430 | ||||||||
\(973\) | 956994. | 1.01084 | ||||||||
\(974\) | 67802.0i | 0.0714701i | ||||||||
\(975\) | 275775.i | 0.290099i | ||||||||
\(976\) | − | 28647.1i | − | 0.0300733i | ||||||
\(977\) | 356838.i | 0.373837i | 0.982375 | + | 0.186918i | \(0.0598500\pi\) | ||||
−0.982375 | + | 0.186918i | \(0.940150\pi\) | |||||||
\(978\) | − | 31169.5i | − | 0.0325875i | ||||||
\(979\) | 1.79958e6 | 1.87761 | ||||||||
\(980\) | 47945.9 | 0.0499228 | ||||||||
\(981\) | 497565.i | 0.517025i | ||||||||
\(982\) | 127946.i | 0.132679i | ||||||||
\(983\) | − | 577236.i | − | 0.597374i | −0.954351 | − | 0.298687i | \(-0.903451\pi\) | ||
0.954351 | − | 0.298687i | \(-0.0965486\pi\) | |||||||
\(984\) | 95271.1i | 0.0983945i | ||||||||
\(985\) | 542744. | 0.559400 | ||||||||
\(986\) | 52144.1i | 0.0536354i | ||||||||
\(987\) | 352866.i | 0.362222i | ||||||||
\(988\) | − | 157073.i | − | 0.160911i | ||||||
\(989\) | −2.34146e6 | −2.39384 | ||||||||
\(990\) | −37316.9 | −0.0380746 | ||||||||
\(991\) | − | 929225.i | − | 0.946180i | −0.881014 | − | 0.473090i | \(-0.843139\pi\) | ||
0.881014 | − | 0.473090i | \(-0.156861\pi\) | |||||||
\(992\) | −249034. | −0.253067 | ||||||||
\(993\) | 922067. | 0.935112 | ||||||||
\(994\) | 38350.7i | 0.0388151i | ||||||||
\(995\) | −1.22287e6 | −1.23519 | ||||||||
\(996\) | 560178.i | 0.564687i | ||||||||
\(997\) | 977120. | 0.983009 | 0.491504 | − | 0.870875i | \(-0.336447\pi\) | ||||
0.491504 | + | 0.870875i | \(0.336447\pi\) | |||||||
\(998\) | − | 112693.i | − | 0.113145i | ||||||
\(999\) | 260266.i | 0.260787i |
(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.58.21 | yes | 40 | |
3.2 | odd | 2 | 531.5.c.d.235.20 | 40 | |||
59.58 | odd | 2 | inner | 177.5.c.a.58.20 | ✓ | 40 | |
177.176 | even | 2 | 531.5.c.d.235.21 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.c.a.58.20 | ✓ | 40 | 59.58 | odd | 2 | inner | |
177.5.c.a.58.21 | yes | 40 | 1.1 | even | 1 | trivial | |
531.5.c.d.235.20 | 40 | 3.2 | odd | 2 | |||
531.5.c.d.235.21 | 40 | 177.176 | even | 2 |