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 | 58.20 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.5.c.a.58.21 |
$q$-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 | \(-0.984511\pi\) | ||
0.998816 | − | 0.0486397i | \(-0.0154886\pi\) | |||||||
\(3\) | 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 | \(0.303516\pi\) | ||||
−0.578814 | + | 0.815460i | \(0.696484\pi\) | |||||||
\(12\) | 82.3517 | 0.571887 | ||||||||
\(13\) | 176.297i | 1.04318i | 0.853197 | + | 0.521589i | \(0.174661\pi\) | ||||
−0.853197 | + | 0.521589i | \(0.825339\pi\) | |||||||
\(14\) | 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 | \(0.296401\pi\) | ||||
−0.596895 | + | 0.802319i | \(0.703599\pi\) | |||||||
\(24\) | − | 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 | \(-0.855297\pi\) | ||
0.898437 | − | 0.439102i | \(-0.144703\pi\) | |||||||
\(32\) | − | 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 | \(-0.763044\pi\) | ||
0.735481 | − | 0.677546i | \(-0.236956\pi\) | |||||||
\(38\) | − | 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 | \(0.267986\pi\) | ||||
−0.666045 | + | 0.745912i | \(0.732014\pi\) | |||||||
\(44\) | 3127.58i | 1.61549i | ||||||||
\(45\) | −485.968 | −0.239984 | ||||||||
\(46\) | 330.304 | 0.156098 | ||||||||
\(47\) | 1437.11i | 0.650572i | 0.945616 | + | 0.325286i | \(0.105461\pi\) | ||||
−0.945616 | + | 0.325286i | \(0.894539\pi\) | |||||||
\(48\) | 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 | \(0.00492592\pi\) | ||||
−0.999880 | + | 0.0154746i | \(0.995074\pi\) | |||||||
\(62\) | −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 | \(0.00175589\pi\) | ||||
−0.999985 | + | 0.00551626i | \(0.998244\pi\) | |||||||
\(68\) | 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 | \(0.00627083\pi\) | ||||
−0.999806 | + | 0.0196991i | \(0.993729\pi\) | |||||||
\(74\) | −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 | \(-0.835642\pi\) | ||
0.869629 | − | 0.493705i | \(-0.164358\pi\) | |||||||
\(84\) | −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 | \(-0.804757\pi\) | ||
0.817710 | − | 0.575630i | \(-0.195243\pi\) | |||||||
\(90\) | 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 | \(0.0500400\pi\) | ||||
−0.987669 | + | 0.156559i | \(0.949960\pi\) | |||||||
\(98\) | 65.4030i | 0.00680997i | ||||||||
\(99\) | 5328.21i | 0.543640i | ||||||||
\(100\) | −4771.11 | −0.477111 | ||||||||
\(101\) | 4577.99i | 0.448779i | 0.974500 | + | 0.224389i | \(0.0720388\pi\) | ||||
−0.974500 | + | 0.224389i | \(0.927961\pi\) | |||||||
\(102\) | − | 983.862i | − | 0.0945658i | ||||||
\(103\) | − | 14158.2i | − | 1.33455i | −0.744812 | − | 0.667274i | \(-0.767461\pi\) | ||
0.744812 | − | 0.667274i | \(-0.232539\pi\) | |||||||
\(104\) | 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 | \(-0.717479\pi\) | ||
0.631302 | − | 0.775537i | \(-0.282521\pi\) | |||||||
\(110\) | −1382.11 | −0.114224 | ||||||||
\(111\) | − | 9639.49i | − | 0.782362i | ||||||
\(112\) | −11754.6 | −0.937071 | ||||||||
\(113\) | 15385.4i | 1.20490i | 0.798156 | + | 0.602451i | \(0.205809\pi\) | ||||
−0.798156 | + | 0.602451i | \(0.794191\pi\) | |||||||
\(114\) | − | 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 | \(0.196251\pi\) | ||||
−0.815883 | + | 0.578217i | \(0.803749\pi\) | |||||||
\(132\) | 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 | \(0.0614729\pi\) | ||||
−0.981410 | + | 0.191925i | \(0.938527\pi\) | |||||||
\(150\) | 608.683i | 0.0270526i | ||||||||
\(151\) | − | 43196.8i | − | 1.89452i | −0.320473 | − | 0.947258i | \(-0.603842\pi\) | ||
0.320473 | − | 0.947258i | \(-0.396158\pi\) | |||||||
\(152\) | − | 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 | \(0.0471394\pi\) | ||||
−0.989054 | + | 0.147552i | \(0.952861\pi\) | |||||||
\(158\) | 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 | \(-0.935186\pi\) | ||
0.979341 | − | 0.202215i | \(-0.0648139\pi\) | |||||||
\(174\) | − | 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 | \(0.00143309\pi\) | ||||
−0.999990 | + | 0.00450218i | \(0.998567\pi\) | |||||||
\(180\) | −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 | \(-0.765236\pi\) | ||
0.740130 | − | 0.672464i | \(-0.234764\pi\) | |||||||
\(192\) | 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 | \(0.00823730\pi\) | ||||
−0.999665 | + | 0.0258754i | \(0.991763\pi\) | |||||||
\(212\) | −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 | \(-0.788644\pi\) | ||
0.787538 | − | 0.616267i | \(-0.211356\pi\) | |||||||
\(228\) | 4629.53 | 0.0890569 | ||||||||
\(229\) | − | 36930.9i | − | 0.704236i | −0.935956 | − | 0.352118i | \(-0.885462\pi\) | ||
0.935956 | − | 0.352118i | \(-0.114538\pi\) | |||||||
\(230\) | −5945.07 | −0.112383 | ||||||||
\(231\) | − | 48454.7i | − | 0.908055i | ||||||
\(232\) | − | 3412.90i | − | 0.0634085i | ||||||
\(233\) | − | 53127.8i | − | 0.978610i | −0.872113 | − | 0.489305i | \(-0.837250\pi\) | ||
0.872113 | − | 0.489305i | \(-0.162750\pi\) | |||||||
\(234\) | 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 | \(0.0147061\pi\) | ||||
−0.998933 | + | 0.0461842i | \(0.985294\pi\) | |||||||
\(270\) | 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 | \(0.371594\pi\) | ||||
−0.392547 | + | 0.919732i | \(0.628406\pi\) | |||||||
\(284\) | −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 | \(0.0799329\pi\) | ||||
−0.968636 | + | 0.248486i | \(0.920067\pi\) | |||||||
\(314\) | 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 | \(-0.873144\pi\) | ||
0.921633 | − | 0.388064i | \(-0.126856\pi\) | |||||||
\(338\) | 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 | \(-0.892946\pi\) | ||
0.943975 | − | 0.330016i | \(-0.107054\pi\) | |||||||
\(348\) | 22679.1 | 0.187269 | ||||||||
\(349\) | 24382.5i | 0.200183i | 0.994978 | + | 0.100091i | \(0.0319135\pi\) | ||||
−0.994978 | + | 0.100091i | \(0.968086\pi\) | |||||||
\(350\) | − | 5535.36i | − | 0.0451866i | ||||||
\(351\) | 24733.8i | 0.200760i | ||||||||
\(352\) | 58231.5 | 0.469973 | ||||||||
\(353\) | 61148.2i | 0.490720i | 0.969432 | + | 0.245360i | \(0.0789062\pi\) | ||||
−0.969432 | + | 0.245360i | \(0.921094\pi\) | |||||||
\(354\) | 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 | \(0.343504\pi\) | ||||
−0.472078 | + | 0.881557i | \(0.656496\pi\) | |||||||
\(368\) | 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 | \(0.192083\pi\) | ||||
−0.823385 | + | 0.567483i | \(0.807917\pi\) | |||||||
\(398\) | − | 26437.2i | − | 0.166898i | ||||||
\(399\) | −13803.3 | −0.0867037 | ||||||||
\(400\) | −74886.0 | −0.468037 | ||||||||
\(401\) | − | 79311.1i | − | 0.493225i | −0.969114 | − | 0.246613i | \(-0.920682\pi\) | ||
0.969114 | − | 0.246613i | \(-0.0793175\pi\) | |||||||
\(402\) | 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 | \(0.0827204\pi\) | ||||
−0.966422 | + | 0.256959i | \(0.917280\pi\) | |||||||
\(410\) | 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 | \(0.297143\pi\) | ||||
−0.595023 | + | 0.803709i | \(0.702857\pi\) | |||||||
\(420\) | 70041.1 | 0.397058 | ||||||||
\(421\) | − | 254214.i | − | 1.43428i | −0.696928 | − | 0.717141i | \(-0.745450\pi\) | ||
0.696928 | − | 0.717141i | \(-0.254550\pi\) | |||||||
\(422\) | 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 | \(0.177620\pi\) | ||||
−0.848310 | + | 0.529500i | \(0.822380\pi\) | |||||||
\(432\) | 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 | \(-0.982934\pi\) | ||
0.998563 | − | 0.0535890i | \(-0.0170661\pi\) | |||||||
\(444\) | − | 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 | \(-0.763077\pi\) | ||
0.735551 | − | 0.677469i | \(-0.236923\pi\) | |||||||
\(458\) | −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 | \(0.242259\pi\) | ||||
−0.724093 | + | 0.689702i | \(0.757741\pi\) | |||||||
\(464\) | 68505.4 | 0.318192 | ||||||||
\(465\) | 78930.4i | 0.365038i | ||||||||
\(466\) | −20672.9 | −0.0951986 | ||||||||
\(467\) | 77026.5i | 0.353189i | 0.984284 | + | 0.176594i | \(0.0565081\pi\) | ||||
−0.984284 | + | 0.176594i | \(0.943492\pi\) | |||||||
\(468\) | 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 | \(-0.646454\pi\) | ||
0.444036 | − | 0.896009i | \(-0.353546\pi\) | |||||||
\(504\) | 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 | \(-0.690839\pi\) | ||
0.564260 | − | 0.825597i | \(-0.309161\pi\) | |||||||
\(510\) | 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 | \(-0.874024\pi\) | ||
0.922702 | − | 0.385515i | \(-0.125976\pi\) | |||||||
\(542\) | 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 | \(0.0285666\pi\) | ||||
−0.995976 | + | 0.0896243i | \(0.971433\pi\) | |||||||
\(564\) | 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 | \(-0.811187\pi\) | ||
0.829170 | − | 0.558996i | \(-0.188813\pi\) | |||||||
\(570\) | 2045.84i | 0.00629682i | ||||||||
\(571\) | − | 496112.i | − | 1.52163i | −0.648972 | − | 0.760813i | \(-0.724801\pi\) | ||
0.648972 | − | 0.760813i | \(-0.275199\pi\) | |||||||
\(572\) | −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 | \(0.294657\pi\) | ||||
−0.601282 | + | 0.799037i | \(0.705343\pi\) | |||||||
\(588\) | −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 | \(0.0697520\pi\) | ||||
−0.976086 | + | 0.217383i | \(0.930248\pi\) | |||||||
\(602\) | −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 | \(-0.717455\pi\) | ||
0.631244 | − | 0.775585i | \(-0.282545\pi\) | |||||||
\(614\) | 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 | \(-0.808792\pi\) | ||
0.824942 | − | 0.565218i | \(-0.191208\pi\) | |||||||
\(660\) | − | 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 | \(0.201516\pi\) | ||||
−0.806208 | + | 0.591633i | \(0.798484\pi\) | |||||||
\(674\) | −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 | \(0.209208\pi\) | ||||
−0.791678 | + | 0.610939i | \(0.790792\pi\) | |||||||
\(684\) | 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 | \(0.0507891\pi\) | ||||
−0.987297 | + | 0.158883i | \(0.949211\pi\) | |||||||
\(692\) | − | 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 | \(0.0947250\pi\) | ||||
−0.956047 | + | 0.293214i | \(0.905275\pi\) | |||||||
\(702\) | 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 | \(-0.830493\pi\) | ||
0.861529 | − | 0.507708i | \(-0.169507\pi\) | |||||||
\(720\) | −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 | \(0.100738\pi\) | ||||
−0.950337 | + | 0.311221i | \(0.899262\pi\) | |||||||
\(740\) | 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 | \(0.114991\pi\) | ||||
−0.935454 | + | 0.353449i | \(0.885009\pi\) | |||||||
\(752\) | 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 | \(-0.613908\pi\) | ||
0.350263 | − | 0.936651i | \(-0.386092\pi\) | |||||||
\(770\) | 65309.9 | 0.110153 | ||||||||
\(771\) | 549405. | 0.924237 | ||||||||
\(772\) | 813842. | 1.36554 | ||||||||
\(773\) | − | 392220.i | − | 0.656403i | −0.944608 | − | 0.328201i | \(-0.893558\pi\) | ||
0.944608 | − | 0.328201i | \(-0.106442\pi\) | |||||||
\(774\) | 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 | \(-0.996990\pi\) | ||
0.999955 | − | 0.00945534i | \(-0.00300977\pi\) | |||||||
\(798\) | 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 | \(-0.770317\pi\) | ||
0.750770 | − | 0.660563i | \(-0.229683\pi\) | |||||||
\(810\) | 5105.66i | 0.00778183i | ||||||||
\(811\) | − | 547154.i | − | 0.831893i | −0.909389 | − | 0.415947i | \(-0.863450\pi\) | ||
0.909389 | − | 0.415947i | \(-0.136550\pi\) | |||||||
\(812\) | −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 | \(0.329312\pi\) | ||||
−0.510901 | + | 0.859639i | \(0.670688\pi\) | |||||||
\(822\) | − | 38750.4i | − | 0.0573499i | ||||||
\(823\) | − | 563170.i | − | 0.831457i | −0.909489 | − | 0.415728i | \(-0.863527\pi\) | ||
0.909489 | − | 0.415728i | \(-0.136473\pi\) | |||||||
\(824\) | −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 | \(0.0533823\pi\) | ||||
−0.985970 | + | 0.166920i | \(0.946618\pi\) | |||||||
\(840\) | − | 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 | \(0.0658821\pi\) | ||||
−0.978657 | + | 0.205500i | \(0.934118\pi\) | |||||||
\(858\) | 70343.8i | 0.0955545i | ||||||||
\(859\) | − | 1.32940e6i | − | 1.80164i | −0.434191 | − | 0.900821i | \(-0.642966\pi\) | ||
0.434191 | − | 0.900821i | \(-0.357034\pi\) | |||||||
\(860\) | − | 786844.i | − | 1.06388i | ||||||
\(861\) | −363268. | −0.490028 | ||||||||
\(862\) | 76547.5 | 0.103019 | ||||||||
\(863\) | 707688.i | 0.950212i | 0.879929 | + | 0.475106i | \(0.157590\pi\) | ||||
−0.879929 | + | 0.475106i | \(0.842410\pi\) | |||||||
\(864\) | − | 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 | \(-0.745170\pi\) | ||
0.696296 | − | 0.717755i | \(-0.254830\pi\) | |||||||
\(882\) | 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 | \(0.0142863\pi\) | ||||
−0.998993 | + | 0.0448667i | \(0.985714\pi\) | |||||||
\(888\) | −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 | \(0.0332496\pi\) | ||||
−0.994549 | + | 0.104267i | \(0.966750\pi\) | |||||||
\(920\) | −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 | \(0.0741852\pi\) | ||||
−0.972964 | + | 0.230956i | \(0.925815\pi\) | |||||||
\(930\) | 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 | \(-0.979031\pi\) | ||
0.997831 | − | 0.0658282i | \(-0.0209689\pi\) | |||||||
\(938\) | −910.629 | −0.00103499 | ||||||||
\(939\) | 252989.i | 0.286927i | ||||||||
\(940\) | − | 409945.i | − | 0.463948i | ||||||
\(941\) | − | 31726.3i | − | 0.0358294i | −0.999840 | − | 0.0179147i | \(-0.994297\pi\) | ||
0.999840 | − | 0.0179147i | \(-0.00570273\pi\) | |||||||
\(942\) | 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 | \(-0.980796\pi\) | ||
0.998181 | − | 0.0602931i | \(-0.0192035\pi\) | |||||||
\(968\) | 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 | \(-0.940150\pi\) | ||
0.982375 | − | 0.186918i | \(-0.0598500\pi\) | |||||||
\(978\) | 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 | \(0.0965486\pi\) | ||||
−0.954351 | + | 0.298687i | \(0.903451\pi\) | |||||||
\(984\) | − | 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 | \(0.156861\pi\) | ||||
−0.881014 | + | 0.473090i | \(0.843139\pi\) | |||||||
\(992\) | −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.58.20 | ✓ | 40 | |
3.2 | odd | 2 | 531.5.c.d.235.21 | 40 | |||
59.58 | odd | 2 | inner | 177.5.c.a.58.21 | yes | 40 | |
177.176 | even | 2 | 531.5.c.d.235.20 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.c.a.58.20 | ✓ | 40 | 1.1 | even | 1 | trivial | |
177.5.c.a.58.21 | yes | 40 | 59.58 | odd | 2 | inner | |
531.5.c.d.235.20 | 40 | 177.176 | even | 2 | |||
531.5.c.d.235.21 | 40 | 3.2 | odd | 2 |