Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,5,Mod(13,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.13");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.j (of order \(18\), degree \(6\), 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: | \(7.85611719437\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 29.5 | ||
Character | \(\chi\) | \(=\) | 76.29 |
Dual form | 76.5.j.a.21.5 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{17}{18}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 2.92113 | + | 3.48127i | 0.324570 | + | 0.386808i | 0.903513 | − | 0.428560i | \(-0.140979\pi\) |
−0.578943 | + | 0.815368i | \(0.696535\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 20.0929 | + | 7.31321i | 0.803715 | + | 0.292528i | 0.711025 | − | 0.703167i | \(-0.248231\pi\) |
0.0926900 | + | 0.995695i | \(0.470453\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −36.0108 | + | 62.3725i | −0.734914 | + | 1.27291i | 0.219847 | + | 0.975534i | \(0.429444\pi\) |
−0.954761 | + | 0.297374i | \(0.903889\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 10.4793 | − | 59.4309i | 0.129374 | − | 0.733715i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 55.1380 | + | 95.5017i | 0.455686 | + | 0.789271i | 0.998727 | − | 0.0504351i | \(-0.0160608\pi\) |
−0.543042 | + | 0.839706i | \(0.682727\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −18.3793 | + | 21.9036i | −0.108753 | + | 0.129607i | −0.817675 | − | 0.575680i | \(-0.804737\pi\) |
0.708922 | + | 0.705287i | \(0.249182\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 33.2347 | + | 91.3116i | 0.147710 | + | 0.405829i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 66.2932 | + | 375.967i | 0.229388 | + | 1.30092i | 0.854116 | + | 0.520082i | \(0.174099\pi\) |
−0.624728 | + | 0.780842i | \(0.714790\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −20.3946 | + | 360.423i | −0.0564948 | + | 0.998403i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −322.328 | + | 56.8351i | −0.730902 | + | 0.128878i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 225.549 | − | 82.0931i | 0.426369 | − | 0.155185i | −0.119918 | − | 0.992784i | \(-0.538263\pi\) |
0.546287 | + | 0.837598i | \(0.316041\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −128.537 | − | 107.855i | −0.205659 | − | 0.172569i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 556.293 | − | 321.176i | 0.763090 | − | 0.440570i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1172.95 | + | 206.823i | 1.39471 | + | 0.245926i | 0.819969 | − | 0.572407i | \(-0.193990\pi\) |
0.574744 | + | 0.818333i | \(0.305102\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −806.771 | − | 465.789i | −0.839512 | − | 0.484692i | 0.0175864 | − | 0.999845i | \(-0.494402\pi\) |
−0.857098 | + | 0.515153i | \(0.827735\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −171.402 | + | 470.923i | −0.157394 | + | 0.432436i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1179.70 | + | 989.888i | −0.963023 | + | 0.808072i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1391.16i | − | 1.01619i | −0.861302 | − | 0.508094i | \(-0.830350\pi\) | ||
0.861302 | − | 0.508094i | \(-0.169650\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −129.941 | −0.0854311 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1665.47 | − | 1984.83i | −0.990760 | − | 1.18074i | −0.983526 | − | 0.180768i | \(-0.942142\pi\) |
−0.00723414 | − | 0.999974i | \(-0.502303\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2036.86 | + | 741.355i | 1.10160 | + | 0.400949i | 0.827905 | − | 0.560868i | \(-0.189532\pi\) |
0.273693 | + | 0.961817i | \(0.411755\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 645.190 | − | 1117.50i | 0.318612 | − | 0.551852i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 593.018 | − | 3363.17i | 0.268456 | − | 1.52249i | −0.490556 | − | 0.871410i | \(-0.663206\pi\) |
0.759012 | − | 0.651077i | \(-0.225683\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1393.05 | − | 2412.84i | −0.580196 | − | 1.00493i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1115.19 | + | 1329.03i | −0.428755 | + | 0.510971i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −799.720 | − | 2197.21i | −0.284699 | − | 0.782205i | −0.996786 | − | 0.0801131i | \(-0.974472\pi\) |
0.712086 | − | 0.702092i | \(-0.247750\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 409.456 | + | 2322.14i | 0.135357 | + | 0.767650i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1314.31 | + | 981.846i | −0.404527 | + | 0.302199i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −186.660 | + | 32.9132i | −0.0536225 | + | 0.00945509i | −0.200395 | − | 0.979715i | \(-0.564223\pi\) |
0.146773 | + | 0.989170i | \(0.453111\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1412.65 | + | 514.161i | −0.379641 | + | 0.138178i | −0.524790 | − | 0.851232i | \(-0.675856\pi\) |
0.145149 | + | 0.989410i | \(0.453634\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3329.49 | + | 2793.77i | 0.838873 | + | 0.703898i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −529.478 | + | 305.695i | −0.125320 | + | 0.0723537i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7401.57 | + | 1305.10i | 1.64882 | + | 0.290732i | 0.919398 | − | 0.393329i | \(-0.128677\pi\) |
0.729425 | + | 0.684061i | \(0.239788\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 944.647 | + | 545.392i | 0.198414 | + | 0.114554i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1338.30 | + | 3676.95i | −0.265483 | + | 0.729409i | 0.733291 | + | 0.679915i | \(0.237983\pi\) |
−0.998774 | + | 0.0494941i | \(0.984239\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2645.33 | − | 2219.70i | 0.496403 | − | 0.416532i | −0.359911 | − | 0.932987i | \(-0.617193\pi\) |
0.856314 | + | 0.516455i | \(0.172749\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 762.533i | − | 0.135561i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7942.24 | −1.33956 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 685.145 | + | 816.524i | 0.109781 | + | 0.130832i | 0.818137 | − | 0.575024i | \(-0.195007\pi\) |
−0.708356 | + | 0.705856i | \(0.750563\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1850.27 | − | 673.444i | −0.282011 | − | 0.102643i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2624.90 | + | 4546.46i | −0.381028 | + | 0.659960i | −0.991209 | − | 0.132302i | \(-0.957763\pi\) |
0.610182 | + | 0.792262i | \(0.291096\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1417.51 | + | 8039.08i | −0.196195 | + | 1.11268i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2706.35 | + | 4687.53i | 0.357557 | + | 0.619306i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −333.507 | + | 397.458i | −0.0421042 | + | 0.0501778i | −0.786686 | − | 0.617354i | \(-0.788205\pi\) |
0.744581 | + | 0.667532i | \(0.232649\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −704.329 | − | 1935.13i | −0.0850536 | − | 0.233683i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −735.146 | − | 4169.22i | −0.0849978 | − | 0.482047i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3045.64 | + | 7092.79i | −0.337467 | + | 0.785905i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13798.9 | − | 2433.11i | 1.46656 | − | 0.258594i | 0.617366 | − | 0.786676i | \(-0.288200\pi\) |
0.849193 | + | 0.528082i | \(0.177089\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6253.56 | − | 2276.11i | 0.638053 | − | 0.232232i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5816.06 | + | 4880.25i | 0.570146 | + | 0.478409i | 0.881694 | − | 0.471821i | \(-0.156403\pi\) |
−0.311548 | + | 0.950230i | \(0.600848\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8868.49 | + | 5120.23i | −0.835941 | + | 0.482631i | −0.855882 | − | 0.517171i | \(-0.826985\pi\) |
0.0199417 | + | 0.999801i | \(0.493652\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6892.14 | − | 1215.27i | −0.625137 | − | 0.110229i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −849.798 | − | 490.631i | −0.0742247 | − | 0.0428536i | 0.462428 | − | 0.886657i | \(-0.346978\pi\) |
−0.536653 | + | 0.843803i | \(0.680312\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6094.78 | − | 16745.3i | 0.512985 | − | 1.40942i | −0.365126 | − | 0.930958i | \(-0.618974\pi\) |
0.878111 | − | 0.478457i | \(-0.158804\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4843.01 | − | 4063.77i | 0.393069 | − | 0.329824i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10436.4i | 0.817324i | 0.912686 | + | 0.408662i | \(0.134004\pi\) | ||||
−0.912686 | + | 0.408662i | \(0.865996\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5132.29 | 0.388075 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1109.15 | + | 1321.83i | 0.0810248 | + | 0.0965616i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −25837.3 | − | 9404.00i | −1.82454 | − | 0.664077i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1240.11 | − | 2147.94i | 0.0847013 | − | 0.146707i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2044.67 | − | 11595.9i | 0.135149 | − | 0.766467i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8475.91 | − | 14680.7i | −0.542458 | − | 0.939565i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2218.85 | − | 2644.32i | 0.137569 | − | 0.163948i | −0.692861 | − | 0.721071i | \(-0.743650\pi\) |
0.830430 | + | 0.557123i | \(0.188095\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3369.07 | + | 9256.44i | 0.202456 | + | 0.556243i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2311.17 | − | 13107.3i | −0.134676 | − | 0.763784i | −0.975085 | − | 0.221832i | \(-0.928796\pi\) |
0.840409 | − | 0.541952i | \(-0.182315\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −21746.1 | − | 14251.2i | −1.22936 | − | 0.805653i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 13526.3 | − | 2385.06i | 0.742186 | − | 0.130867i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 504.996 | − | 183.804i | 0.0269059 | − | 0.00979293i | −0.328532 | − | 0.944493i | \(-0.606554\pi\) |
0.355438 | + | 0.934700i | \(0.384332\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7577.41 | − | 6358.20i | −0.392185 | − | 0.329083i | 0.425278 | − | 0.905063i | \(-0.360176\pi\) |
−0.817464 | + | 0.575980i | \(0.804621\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13440.4 | − | 7759.82i | 0.676042 | − | 0.390313i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3105.23 | − | 547.535i | −0.151852 | − | 0.0267757i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 22055.5 | + | 12733.7i | 1.04901 | + | 0.605647i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4330.45 | − | 11897.8i | 0.200400 | − | 0.550595i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −21693.6 | + | 18203.1i | −0.977146 | + | 0.819923i | −0.983656 | − | 0.180056i | \(-0.942372\pi\) |
0.00651023 | + | 0.999979i | \(0.497928\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17781.4i | 0.779850i | 0.920847 | + | 0.389925i | \(0.127499\pi\) | ||||
−0.920847 | + | 0.389925i | \(0.872501\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 23038.8 | 0.984185 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12803.9 | − | 15259.1i | −0.532942 | − | 0.635136i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −30266.2 | − | 11016.0i | −1.22789 | − | 0.446915i | −0.355015 | − | 0.934861i | \(-0.615524\pi\) |
−0.872874 | + | 0.487946i | \(0.837746\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5313.01 | − | 9202.39i | 0.210158 | − | 0.364004i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3001.84 | + | 17024.3i | −0.115807 | + | 0.656776i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20771.9 | + | 35978.0i | 0.781810 | + | 1.35414i | 0.930886 | + | 0.365309i | \(0.119037\pi\) |
−0.149076 | + | 0.988826i | \(0.547630\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6887.92 | + | 8208.71i | −0.253000 | + | 0.301513i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8320.45 | − | 22860.3i | −0.298342 | − | 0.819687i | −0.994777 | − | 0.102068i | \(-0.967454\pi\) |
0.696436 | − | 0.717619i | \(-0.254768\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4817.60 | + | 27321.9i | 0.168677 | + | 0.956617i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 21206.6 | + | 4989.05i | 0.725234 | + | 0.170618i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7993.40 | + | 1409.45i | −0.267079 | + | 0.0470932i | −0.305584 | − | 0.952165i | \(-0.598852\pi\) |
0.0385050 | + | 0.999258i | \(0.487740\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11355.9 | − | 4133.22i | 0.370806 | − | 0.134962i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −659.838 | − | 553.670i | −0.0210616 | − | 0.0176728i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −17021.7 | + | 9827.49i | −0.531248 | + | 0.306716i | −0.741525 | − | 0.670926i | \(-0.765897\pi\) |
0.210277 | + | 0.977642i | \(0.432564\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 52617.3 | + | 9277.85i | 1.60610 | + | 0.283198i | 0.903564 | − | 0.428453i | \(-0.140941\pi\) |
0.702533 | + | 0.711651i | \(0.252052\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5916.46 | − | 3415.87i | −0.176669 | − | 0.102000i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10173.9 | − | 27952.4i | 0.297264 | − | 0.816726i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −32250.2 | + | 27061.2i | −0.922253 | + | 0.773862i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 46263.1i | 1.29512i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3031.85 | −0.0831075 | −0.0415538 | − | 0.999136i | \(-0.513231\pi\) | ||||
−0.0415538 | + | 0.999136i | \(0.513231\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 43770.8 | + | 52164.1i | 1.17509 | + | 1.40041i | 0.898242 | + | 0.439500i | \(0.144844\pi\) |
0.276845 | + | 0.960915i | \(0.410711\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2610.88 | − | 950.283i | −0.0686623 | − | 0.0249910i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3966.59 | + | 6870.34i | −0.102208 | + | 0.177030i | −0.912594 | − | 0.408867i | \(-0.865924\pi\) |
0.810386 | + | 0.585896i | \(0.199257\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10936.9 | − | 62026.3i | 0.276178 | − | 1.56628i | −0.459018 | − | 0.888427i | \(-0.651799\pi\) |
0.735195 | − | 0.677855i | \(-0.237090\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 17077.6 | + | 29579.2i | 0.422702 | + | 0.732141i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −55139.1 | + | 65712.2i | −1.33803 | + | 1.59461i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18948.6 | − | 52060.8i | −0.450888 | − | 1.23881i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2515.28 | − | 14264.9i | −0.0587010 | − | 0.332910i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −35545.6 | + | 17925.3i | −0.813754 | + | 0.410368i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −40436.8 | + | 7130.10i | −0.908264 | + | 0.160151i | −0.608215 | − | 0.793773i | \(-0.708114\pi\) |
−0.300049 | + | 0.953924i | \(0.597003\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −16709.8 | + | 6081.87i | −0.368309 | + | 0.134053i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 35504.6 | + | 29791.9i | 0.768082 | + | 0.644498i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 58104.9 | − | 33546.9i | 1.23394 | − | 0.712414i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 15454.7 | + | 2725.09i | 0.322236 | + | 0.0568188i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9453.45 | − | 5457.95i | −0.193556 | − | 0.111749i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20272.3 | − | 55697.7i | 0.407656 | − | 1.12003i | −0.550763 | − | 0.834661i | \(-0.685663\pi\) |
0.958419 | − | 0.285364i | \(-0.0921144\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7756.93 | + | 6508.83i | −0.153223 | + | 0.128570i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 87779.7i | − | 1.70350i | −0.523947 | − | 0.851751i | \(-0.675541\pi\) | ||
0.523947 | − | 0.851751i | \(-0.324459\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −30764.0 | −0.586640 | −0.293320 | − | 0.956014i | \(-0.594760\pi\) | ||||
−0.293320 | + | 0.956014i | \(0.594760\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −23200.3 | − | 27649.1i | −0.434781 | − | 0.518152i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 26105.0 | + | 9501.45i | 0.480853 | + | 0.175016i | 0.571062 | − | 0.820907i | \(-0.306531\pi\) |
−0.0902096 | + | 0.995923i | \(0.528754\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 36511.0 | − | 63239.0i | 0.661132 | − | 1.14511i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −841.141 | + | 4770.35i | −0.0149752 | + | 0.0849285i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 42411.9 | + | 73459.6i | 0.742492 | + | 1.28603i | 0.951357 | + | 0.308090i | \(0.0996898\pi\) |
−0.208865 | + | 0.977945i | \(0.566977\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28331.8 | + | 33764.5i | −0.487797 | + | 0.581334i | −0.952656 | − | 0.304051i | \(-0.901661\pi\) |
0.464859 | + | 0.885385i | \(0.346105\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −20855.9 | − | 57301.1i | −0.353197 | − | 0.970400i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10344.8 | − | 58668.5i | −0.172342 | − | 0.977401i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7519.73 | − | 7071.04i | −0.123256 | − | 0.115902i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −23495.1 | + | 4142.83i | −0.378948 | + | 0.0668187i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −34909.5 | + | 12706.0i | −0.554111 | + | 0.201680i | −0.603872 | − | 0.797081i | \(-0.706376\pi\) |
0.0497613 | + | 0.998761i | \(0.484154\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20276.3 | + | 17013.9i | 0.316773 | + | 0.265804i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −32126.9 | + | 18548.5i | −0.494070 | + | 0.285252i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 64595.5 | + | 11389.9i | 0.977993 | + | 0.172447i | 0.639725 | − | 0.768603i | \(-0.279048\pi\) |
0.338267 | + | 0.941050i | \(0.390159\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 86770.2 | + | 50096.8i | 1.29351 | + | 0.746811i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 24583.4 | − | 67542.4i | 0.360879 | − | 0.991506i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −59033.7 | + | 49535.1i | −0.853470 | + | 0.716146i | −0.960551 | − | 0.278104i | \(-0.910294\pi\) |
0.107081 | + | 0.994250i | \(0.465850\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 49996.9i | − | 0.711952i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2357.88 | −0.0330749 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −69947.8 | − | 83360.5i | −0.966650 | − | 1.15201i | −0.988343 | − | 0.152245i | \(-0.951350\pi\) |
0.0216924 | − | 0.999765i | \(-0.493095\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −82365.7 | − | 29978.7i | −1.12152 | − | 0.408201i | −0.286315 | − | 0.958136i | \(-0.592430\pi\) |
−0.835208 | + | 0.549935i | \(0.814653\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4679.26 | − | 8104.72i | 0.0627845 | − | 0.108746i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3213.11 | − | 18222.4i | 0.0424874 | − | 0.240958i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3982.46 | + | 6897.82i | 0.0519029 | + | 0.0898985i | 0.890810 | − | 0.454377i | \(-0.150138\pi\) |
−0.838907 | + | 0.544275i | \(0.816805\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −36136.7 | + | 43066.0i | −0.464237 | + | 0.553256i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −34569.7 | − | 94979.4i | −0.437807 | − | 1.20286i | −0.940916 | − | 0.338641i | \(-0.890033\pi\) |
0.503109 | − | 0.864223i | \(-0.332190\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6296.57 | − | 35709.6i | −0.0786196 | − | 0.445874i | −0.998552 | − | 0.0537968i | \(-0.982868\pi\) |
0.919932 | − | 0.392077i | \(-0.128243\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −33588.6 | + | 10116.3i | −0.413526 | + | 0.124547i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 183773. | − | 32404.2i | 2.23110 | − | 0.393403i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −58472.5 | + | 21282.2i | −0.700093 | + | 0.254813i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 48778.6 | + | 40930.1i | 0.576028 | + | 0.483345i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 86673.3 | − | 50040.9i | 1.00960 | − | 0.582894i | 0.0985267 | − | 0.995134i | \(-0.468587\pi\) |
0.911075 | + | 0.412241i | \(0.135254\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3991.24 | − | 703.763i | −0.0458631 | − | 0.00808690i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 61345.7 | + | 35417.9i | 0.695458 | + | 0.401523i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2347.30 | + | 6449.15i | −0.0262558 | + | 0.0721373i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −119589. | + | 100347.i | −1.31995 | + | 1.10757i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 34503.1i | 0.375814i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −32144.3 | −0.345544 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19427.7 | + | 23153.0i | 0.206132 | + | 0.245658i | 0.859199 | − | 0.511642i | \(-0.170963\pi\) |
−0.653067 | + | 0.757300i | \(0.726518\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −43730.9 | − | 15916.8i | −0.458007 | − | 0.166701i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −89682.7 | + | 155335.i | −0.927231 | + | 1.60601i | −0.139297 | + | 0.990251i | \(0.544484\pi\) |
−0.787934 | + | 0.615760i | \(0.788849\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13398.2 | + | 75984.8i | −0.136759 | + | 0.775600i | 0.836859 | + | 0.547418i | \(0.184389\pi\) |
−0.973618 | + | 0.228182i | \(0.926722\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 46467.5 | + | 80484.2i | 0.468305 | + | 0.811128i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 33428.4 | − | 39838.4i | 0.332657 | − | 0.396445i | −0.573625 | − | 0.819118i | \(-0.694463\pi\) |
0.906283 | + | 0.422672i | \(0.138908\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 44922.3 | + | 123423.i | 0.441449 | + | 1.21287i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −774.353 | − | 4391.58i | −0.00751500 | − | 0.0426197i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −136859. | + | 16225.9i | −1.31181 | + | 0.155526i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4724.84 | − | 833.118i | 0.0447323 | − | 0.00788750i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 76098.4 | − | 27697.6i | 0.711672 | − | 0.259028i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 188414. | + | 158098.i | 1.74069 | + | 1.46062i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 134064. | − | 77401.8i | 1.22365 | − | 0.706473i | 0.257953 | − | 0.966157i | \(-0.416952\pi\) |
0.965693 | + | 0.259685i | \(0.0836187\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −82678.0 | − | 14578.4i | −0.745593 | − | 0.131468i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 139174. | + | 80352.3i | 1.24014 | + | 0.715993i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 56873.9 | − | 156260.i | 0.500788 | − | 1.37590i | −0.389720 | − | 0.920934i | \(-0.627428\pi\) |
0.890507 | − | 0.454969i | \(-0.150350\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −36331.9 | + | 30486.1i | −0.316147 | + | 0.265279i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 102731.i | − | 0.883469i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 27735.7 | 0.235750 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 14992.1 | + | 17866.9i | 0.125958 | + | 0.150110i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −97436.4 | − | 35463.9i | −0.809212 | − | 0.294529i | −0.0959134 | − | 0.995390i | \(-0.530577\pi\) |
−0.713298 | + | 0.700861i | \(0.752799\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −91112.1 | + | 157811.i | −0.748041 | + | 1.29564i | 0.200720 | + | 0.979649i | \(0.435672\pi\) |
−0.948761 | + | 0.315996i | \(0.897661\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3189.37 | + | 18087.8i | −0.0258875 | + | 0.146815i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 79186.0 | + | 137154.i | 0.635476 | + | 1.10068i | 0.986414 | + | 0.164278i | \(0.0525295\pi\) |
−0.350938 | + | 0.936399i | \(0.614137\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −53780.6 | + | 64093.2i | −0.426745 | + | 0.508575i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −42736.2 | − | 117417.i | −0.335320 | − | 0.921285i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −31561.2 | − | 178993.i | −0.244886 | − | 1.38882i | −0.820756 | − | 0.571279i | \(-0.806448\pi\) |
0.575870 | − | 0.817542i | \(-0.304664\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −129489. | − | 14701.4i | −0.993617 | − | 0.112809i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11100.1 | − | 1957.24i | 0.0842390 | − | 0.0148536i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 69385.5 | − | 25254.2i | 0.520814 | − | 0.189561i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −88559.0 | − | 74309.9i | −0.657508 | − | 0.551714i | 0.251831 | − | 0.967771i | \(-0.418967\pi\) |
−0.909339 | + | 0.416057i | \(0.863412\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −135413. | + | 78180.7i | −0.994506 | + | 0.574179i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 165844. | + | 29242.8i | 1.20490 | + | 0.212457i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −158975. | − | 91784.3i | −1.14265 | − | 0.659706i | −0.195561 | − | 0.980692i | \(-0.562653\pi\) |
−0.947084 | + | 0.320985i | \(0.895986\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 26348.2 | − | 72391.2i | 0.187365 | − | 0.514782i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −26088.2 | + | 21890.6i | −0.183553 | + | 0.154020i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 227813.i | 1.58599i | 0.609228 | + | 0.792995i | \(0.291479\pi\) | ||||
−0.609228 | + | 0.792995i | \(0.708521\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15687.1 | 0.108067 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11702.7 | + | 13946.7i | 0.0797789 | + | 0.0950768i | 0.804457 | − | 0.594010i | \(-0.202456\pi\) |
−0.724679 | + | 0.689087i | \(0.758012\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −159582. | − | 58083.3i | −1.07662 | − | 0.391859i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 65404.2 | − | 113283.i | 0.436700 | − | 0.756387i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19572.2 | − | 111000.i | 0.129342 | − | 0.733537i | −0.849291 | − | 0.527925i | \(-0.822970\pi\) |
0.978634 | − | 0.205612i | \(-0.0659186\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 45816.7 | + | 79356.8i | 0.299688 | + | 0.519076i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 38878.8 | − | 46334.0i | 0.251726 | − | 0.299995i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7795.12 | + | 21416.9i | 0.0499607 | + | 0.137266i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32755.9 | − | 185768.i | −0.207830 | − | 1.17866i | −0.892924 | − | 0.450207i | \(-0.851350\pi\) |
0.685094 | − | 0.728455i | \(-0.259761\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13910.9 | − | 117334.i | −0.0873798 | − | 0.737015i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 252009. | − | 44436.0i | 1.56721 | − | 0.276341i | 0.678427 | − | 0.734668i | \(-0.262662\pi\) |
0.888784 | + | 0.458327i | \(0.151551\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 25030.3 | − | 9110.30i | 0.154119 | − | 0.0560948i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −32252.2 | − | 27062.8i | −0.196630 | − | 0.164992i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 132858. | − | 76705.8i | 0.802047 | − | 0.463062i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 198698. | + | 35035.8i | 1.18781 | + | 0.209443i | 0.732422 | − | 0.680851i | \(-0.238390\pi\) |
0.455386 | + | 0.890294i | \(0.349501\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2115.03 | + | 1221.11i | 0.0125208 | + | 0.00722890i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4668.89 | − | 12827.7i | 0.0273724 | − | 0.0752052i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −85991.0 | + | 72155.0i | −0.499295 | + | 0.418958i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 44952.2i | − | 0.258511i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −248905. | −1.41777 | −0.708884 | − | 0.705325i | \(-0.750801\pi\) | ||||
−0.708884 | + | 0.705325i | \(0.750801\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33536.2 | − | 39966.9i | −0.189212 | − | 0.225494i | 0.663096 | − | 0.748535i | \(-0.269242\pi\) |
−0.852308 | + | 0.523040i | \(0.824798\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −193662. | − | 70487.2i | −1.08234 | − | 0.393940i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 32029.0 | − | 55475.8i | 0.177323 | − | 0.307133i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18801.0 | − | 106626.i | 0.103116 | − | 0.584797i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7164.66 | − | 12409.6i | −0.0389297 | − | 0.0674282i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −75081.8 | + | 89479.0i | −0.404185 | + | 0.481689i | −0.929291 | − | 0.369348i | \(-0.879581\pi\) |
0.525106 | + | 0.851037i | \(0.324026\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −95539.5 | − | 262493.i | −0.509574 | − | 1.40004i | −0.881678 | − | 0.471851i | \(-0.843586\pi\) |
0.372104 | − | 0.928191i | \(-0.378636\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 20097.4 | + | 113978.i | 0.106209 | + | 0.602341i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 24988.3 | + | 82967.4i | 0.130850 | + | 0.434455i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −104136. | + | 18362.1i | −0.540348 | + | 0.0952780i | −0.437160 | − | 0.899384i | \(-0.644016\pi\) |
−0.103188 | + | 0.994662i | \(0.532904\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −157995. | + | 57505.6i | −0.812394 | + | 0.295687i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 45631.2 | + | 38289.2i | 0.232517 | + | 0.195105i | 0.751600 | − | 0.659619i | \(-0.229282\pi\) |
−0.519083 | + | 0.854724i | \(0.673727\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9607.82 | + | 5547.08i | −0.0485182 | + | 0.0280120i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −126740. | − | 22347.7i | −0.634305 | − | 0.111845i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 278912. | + | 161030.i | 1.38349 | + | 0.798756i | 0.992571 | − | 0.121670i | \(-0.0388250\pi\) |
0.390916 | + | 0.920426i | \(0.372158\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 97723.9 | − | 268494.i | 0.480450 | − | 1.32002i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −61901.7 | + | 51941.7i | −0.301652 | + | 0.253116i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 44033.2i | − | 0.212695i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 259740. | 1.24367 | 0.621837 | − | 0.783146i | \(-0.286386\pi\) | ||||
0.621837 | + | 0.783146i | \(0.286386\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 157630. | + | 187856.i | 0.748192 | + | 0.891661i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 197505. | + | 71885.8i | 0.929342 | + | 0.338253i | 0.761949 | − | 0.647638i | \(-0.224243\pi\) |
0.167393 | + | 0.985890i | \(0.446465\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 121468. | − | 210389.i | 0.566631 | − | 0.981433i | −0.430265 | − | 0.902703i | \(-0.641580\pi\) |
0.996896 | − | 0.0787306i | \(-0.0250867\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 15719.2 | − | 89147.9i | 0.0726983 | − | 0.412292i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −79005.0 | − | 136841.i | −0.362261 | − | 0.627454i | 0.626072 | − | 0.779765i | \(-0.284662\pi\) |
−0.988333 | + | 0.152312i | \(0.951328\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −347938. | + | 414657.i | −1.58182 | + | 1.88514i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −50062.0 | − | 137544.i | −0.225666 | − | 0.620012i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 41507.4 | + | 235400.i | 0.185525 | + | 1.05217i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 41495.1 | − | 44128.1i | 0.183912 | − | 0.195582i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −138963. | + | 24502.9i | −0.610748 | + | 0.107691i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −190477. | + | 69328.0i | −0.830179 | + | 0.302161i | −0.721932 | − | 0.691964i | \(-0.756746\pi\) |
−0.108247 | + | 0.994124i | \(0.534524\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 30471.4 | + | 25568.6i | 0.131705 | + | 0.110514i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −68034.9 | + | 39280.0i | −0.291634 | + | 0.168375i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 295053. | + | 52025.7i | 1.25434 | + | 0.221174i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −99429.3 | − | 57405.5i | −0.419234 | − | 0.242045i | 0.275516 | − | 0.961297i | \(-0.411151\pi\) |
−0.694750 | + | 0.719252i | \(0.744485\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −64571.7 | + | 177409.i | −0.270038 | + | 0.741922i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 125947. | − | 105682.i | 0.522428 | − | 0.438369i | −0.343050 | − | 0.939317i | \(-0.611460\pi\) |
0.865477 | + | 0.500949i | \(0.167015\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 454703.i | 1.87083i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 142298. | 0.580748 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −181147. | − | 215883.i | −0.733363 | − | 0.873988i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −63335.8 | − | 23052.3i | −0.254359 | − | 0.0925793i | 0.211693 | − | 0.977336i | \(-0.432102\pi\) |
−0.466053 | + | 0.884757i | \(0.654324\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 55277.6 | − | 95743.6i | 0.220229 | − | 0.381447i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25707.1 | + | 145792.i | −0.101606 | + | 0.576233i | 0.890916 | + | 0.454167i | \(0.150063\pi\) |
−0.992522 | + | 0.122066i | \(0.961048\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 81171.1 | + | 140592.i | 0.318287 | + | 0.551289i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −81042.2 | + | 96582.4i | −0.315279 | + | 0.375735i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18261.1 | + | 50171.8i | 0.0704839 | + | 0.193653i | 0.969933 | − | 0.243373i | \(-0.0782539\pi\) |
−0.899449 | + | 0.437026i | \(0.856032\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 43187.6 | + | 244929.i | 0.165393 | + | 0.937991i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 104414. | + | 207051.i | 0.396756 | + | 0.786761i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −215639. | + | 38022.9i | −0.813041 | + | 0.143361i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 353887. | − | 128804.i | 1.32399 | − | 0.481891i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −28256.5 | − | 23710.0i | −0.104902 | − | 0.0880231i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −309057. | + | 178434.i | −1.13858 | + | 0.657360i | −0.946079 | − | 0.323937i | \(-0.894994\pi\) |
−0.192502 | + | 0.981297i | \(0.561660\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 112140. | + | 19773.3i | 0.409974 | + | 0.0722896i | 0.374832 | − | 0.927093i | \(-0.377700\pi\) |
0.0351424 | + | 0.999382i | \(0.488812\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 47561.1 | + | 27459.4i | 0.172557 | + | 0.0996259i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 121638. | − | 334198.i | 0.437974 | − | 1.20332i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −170238. | + | 142846.i | −0.608337 | + | 0.510455i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11438.3i | 0.0405669i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 74085.0 | 0.260781 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13486.8 | − | 16072.9i | −0.0471196 | − | 0.0561549i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −83934.8 | − | 30549.8i | −0.291068 | − | 0.105940i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 153620. | − | 266078.i | 0.528774 | − | 0.915864i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36704.4 | − | 208161.i | 0.125407 | − | 0.711221i | −0.855658 | − | 0.517542i | \(-0.826847\pi\) |
0.981065 | − | 0.193678i | \(-0.0620419\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 121403. | + | 210277.i | 0.411748 | + | 0.713168i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 244923. | − | 291888.i | 0.824588 | − | 0.982705i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2504.61 | − | 6881.36i | −0.00837077 | − | 0.0229985i | 0.935437 | − | 0.353494i | \(-0.115006\pi\) |
−0.943808 | + | 0.330495i | \(0.892784\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15753.6 | + | 89342.8i | 0.0522678 | + | 0.296425i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −98466.0 | + | 418542.i | −0.324327 | + | 1.37859i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −75601.2 | + | 13330.5i | −0.247217 | + | 0.0435910i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 127029. | − | 46234.8i | 0.412399 | − | 0.150101i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 330651. | + | 277449.i | 1.06576 | + | 0.894280i | 0.994662 | − | 0.103189i | \(-0.0329048\pi\) |
0.0710994 | + | 0.997469i | \(0.477349\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −53674.3 | + | 30988.9i | −0.171768 | + | 0.0991704i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −188415. | − | 33222.6i | −0.598672 | − | 0.105562i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −227258. | − | 131207.i | −0.716971 | − | 0.413943i | 0.0966658 | − | 0.995317i | \(-0.469182\pi\) |
−0.813637 | + | 0.581373i | \(0.802516\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −76323.6 | + | 209697.i | −0.239090 | + | 0.656895i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 108634. | − | 91154.8i | 0.337909 | − | 0.283539i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 592913.i | − | 1.83133i | −0.401943 | − | 0.915665i | \(-0.631665\pi\) | ||
0.401943 | − | 0.915665i | \(-0.368335\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37331.0 | −0.114498 | −0.0572489 | − | 0.998360i | \(-0.518233\pi\) | ||||
−0.0572489 | + | 0.998360i | \(0.518233\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8856.42 | − | 10554.7i | −0.0269742 | − | 0.0321466i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −37845.6 | − | 13774.7i | −0.114467 | − | 0.0416625i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −121380. | + | 210236.i | −0.364581 | + | 0.631473i | −0.988709 | − | 0.149849i | \(-0.952121\pi\) |
0.624128 | + | 0.781322i | \(0.285454\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −53736.7 | + | 304756.i | −0.160293 | + | 0.909066i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −189049. | − | 327443.i | −0.560045 | − | 0.970027i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 165743. | − | 197525.i | 0.487638 | − | 0.581144i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12619.2 | + | 34670.9i | 0.0368739 | + | 0.101310i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18243.6 | + | 103464.i | 0.0529460 | + | 0.300272i | 0.999769 | − | 0.0214825i | \(-0.00683861\pi\) |
−0.946823 | + | 0.321754i | \(0.895727\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 184335. | − | 281280.i | 0.531346 | − | 0.810789i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −35504.5 | + | 6260.40i | −0.101650 | + | 0.0179237i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −177281. | + | 64525.0i | −0.504142 | + | 0.183493i | −0.581556 | − | 0.813506i | \(-0.697556\pi\) |
0.0774143 | + | 0.996999i | \(0.475334\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −450372. | − | 377907.i | −1.27215 | − | 1.06746i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 247879. | − | 143113.i | 0.695489 | − | 0.401541i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −345357. | − | 60895.7i | −0.962530 | − | 0.169720i | −0.329764 | − | 0.944063i | \(-0.606969\pi\) |
−0.632766 | + | 0.774343i | \(0.718080\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −184895. | − | 106749.i | −0.511889 | − | 0.295539i | 0.221721 | − | 0.975110i | \(-0.428833\pi\) |
−0.733610 | + | 0.679571i | \(0.762166\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 155126. | − | 426205.i | 0.426629 | − | 1.17215i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 40625.7 | − | 34089.0i | 0.110992 | − | 0.0931331i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 94696.2i | 0.257013i | 0.991709 | + | 0.128507i | \(0.0410183\pi\) | ||||
−0.991709 | + | 0.128507i | \(0.958982\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −389830. | −1.05109 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 62766.3 | + | 74802.0i | 0.168130 | + | 0.200369i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −81985.0 | − | 29840.1i | −0.218179 | − | 0.0794108i | 0.230618 | − | 0.973044i | \(-0.425925\pi\) |
−0.448797 | + | 0.893634i | \(0.648147\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 125886. | − | 218042.i | 0.332835 | − | 0.576486i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28590.9 | − | 162147.i | 0.0751031 | − | 0.425931i | −0.923953 | − | 0.382505i | \(-0.875062\pi\) |
0.999057 | − | 0.0434262i | \(-0.0138274\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −161150. | − | 279120.i | −0.420580 | − | 0.728466i | 0.575416 | − | 0.817861i | \(-0.304840\pi\) |
−0.995996 | + | 0.0893948i | \(0.971507\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 99104.9 | − | 118109.i | 0.256988 | − | 0.306266i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12780.6 | − | 35114.5i | −0.0329288 | − | 0.0904711i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −44731.7 | − | 253686.i | −0.114513 | − | 0.649436i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −166236. | − | 71381.6i | −0.422854 | − | 0.181573i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 523031. | − | 92224.5i | 1.32198 | − | 0.233101i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 146067. | − | 53164.2i | 0.366855 | − | 0.133524i | −0.152013 | − | 0.988378i | \(-0.548576\pi\) |
0.518868 | + | 0.854854i | \(0.326353\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −142943. | − | 119943.i | −0.356743 | − | 0.299343i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 63921.5 | − | 36905.1i | 0.158526 | − | 0.0915248i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 78453.1 | + | 13833.4i | 0.193344 | + | 0.0340918i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 204500. | + | 118068.i | 0.500832 | + | 0.289155i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −221071. | + | 607387.i | −0.538041 | + | 1.47826i | 0.311248 | + | 0.950329i | \(0.399253\pi\) |
−0.849290 | + | 0.527927i | \(0.822969\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 375051. | − | 314705.i | 0.907127 | − | 0.761170i | −0.0644434 | − | 0.997921i | \(-0.520527\pi\) |
0.971570 | + | 0.236752i | \(0.0760828\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 210627.i | 0.506285i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 230175. | 0.549858 | 0.274929 | − | 0.961465i | \(-0.411346\pi\) | ||||
0.274929 | + | 0.961465i | \(0.411346\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13435.3 | − | 16011.6i | −0.0318976 | − | 0.0380141i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 286518. | + | 104284.i | 0.676067 | + | 0.246068i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −361571. | + | 626259.i | −0.847944 | + | 1.46868i | 0.0350959 | + | 0.999384i | \(0.488826\pi\) |
−0.883040 | + | 0.469298i | \(0.844507\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 49418.4 | − | 280265.i | 0.115188 | − | 0.653261i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −104198. | − | 180475.i | −0.241394 | − | 0.418107i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −200214. | + | 238606.i | −0.461025 | + | 0.549428i | −0.945604 | − | 0.325320i | \(-0.894528\pi\) |
0.484580 | + | 0.874747i | \(0.338973\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 255188. | + | 701123.i | 0.584060 | + | 1.60469i | 0.781176 | + | 0.624311i | \(0.214620\pi\) |
−0.197117 | + | 0.980380i | \(0.563158\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8614.18 | − | 48853.4i | −0.0195969 | − | 0.111139i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −332719. | − | 445381.i | −0.752376 | − | 1.00714i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 281537. | − | 49642.6i | 0.632826 | − | 0.111584i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 253117. | − | 92127.0i | 0.565547 | − | 0.205842i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −126994. | − | 106560.i | −0.282057 | − | 0.236674i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −166906. | + | 96363.3i | −0.368504 | + | 0.212756i | −0.672805 | − | 0.739820i | \(-0.734911\pi\) |
0.304301 | + | 0.952576i | \(0.401577\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −106145. | − | 18716.2i | −0.232965 | − | 0.0410781i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −48977.6 | − | 28277.2i | −0.106861 | − | 0.0616963i | 0.445617 | − | 0.895224i | \(-0.352984\pi\) |
−0.552478 | + | 0.833527i | \(0.686318\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −345148. | + | 948287.i | −0.748628 | + | 2.05684i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 305585. | − | 256416.i | 0.658928 | − | 0.552906i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 603564.i | 1.29384i | 0.762556 | + | 0.646922i | \(0.223944\pi\) | ||||
−0.762556 | + | 0.646922i | \(0.776056\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11491.0 | 0.0244894 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −89865.7 | − | 107098.i | −0.190406 | − | 0.226917i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 62825.2 | + | 22866.5i | 0.132341 | + | 0.0481683i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −345267. | + | 598020.i | −0.723100 | + | 1.25245i | 0.236651 | + | 0.971595i | \(0.423950\pi\) |
−0.959751 | + | 0.280852i | \(0.909383\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −83228.9 | + | 472015.i | −0.173304 | + | 0.982854i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −105753. | − | 183170.i | −0.218939 | − | 0.379214i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 635821. | − | 757742.i | 1.30879 | − | 1.55975i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 43179.1 | + | 118634.i | 0.0883729 | + | 0.242803i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −105203. | − | 596633.i | −0.214087 | − | 1.21415i | −0.882484 | − | 0.470343i | \(-0.844130\pi\) |
0.668397 | − | 0.743805i | \(-0.266981\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 501407. | + | 28372.2i | 1.01457 | + | 0.0574093i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 326805. | − | 57624.6i | 0.657523 | − | 0.115939i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −513834. | + | 187020.i | −1.02798 | + | 0.374154i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 304300. | + | 255338.i | 0.605353 | + | 0.507952i | 0.893161 | − | 0.449736i | \(-0.148482\pi\) |
−0.287808 | + | 0.957688i | \(0.592927\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 55706.6 | − | 32162.2i | 0.110196 | − | 0.0636219i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −220205. | − | 38828.0i | −0.433159 | − | 0.0763776i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −58388.7 | − | 33710.7i | −0.114213 | − | 0.0659411i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −131842. | + | 362232.i | −0.256457 | + | 0.704610i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −186996. | + | 156909.i | −0.361722 | + | 0.303521i | −0.805477 | − | 0.592627i | \(-0.798091\pi\) |
0.443754 | + | 0.896148i | \(0.353646\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 737533.i | − | 1.41877i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −200304. | −0.383189 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −128461. | − | 153094.i | −0.244397 | − | 0.291261i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 633293. | + | 230500.i | 1.19822 | + | 0.436116i | 0.862602 | − | 0.505883i | \(-0.168833\pi\) |
0.335616 | + | 0.941999i | \(0.391056\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 58812.7 | − | 101867.i | 0.110666 | − | 0.191680i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −143695. | + | 814938.i | −0.268911 | + | 1.52507i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −63729.5 | − | 110383.i | −0.118613 | − | 0.205444i | 0.800605 | − | 0.599192i | \(-0.204511\pi\) |
−0.919218 | + | 0.393748i | \(0.871178\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 174022. | − | 207392.i | 0.322129 | − | 0.383899i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 283468. | + | 778823.i | 0.521879 | + | 1.43385i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −43423.8 | − | 246269.i | −0.0795132 | − | 0.450942i | −0.998406 | − | 0.0564352i | \(-0.982027\pi\) |
0.918893 | − | 0.394507i | \(-0.129085\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2650.09 | − | 46833.7i | 0.00482641 | − | 0.0852946i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −592950. | + | 104553.i | −1.07409 | + | 0.189391i | −0.682600 | − | 0.730792i | \(-0.739151\pi\) |
−0.391489 | + | 0.920183i | \(0.628040\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −569010. | + | 207103.i | −1.02520 | + | 0.373141i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 242693. | + | 203644.i | 0.434927 | + | 0.364947i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 61203.8 | − | 35336.0i | 0.109097 | − | 0.0629874i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 184265. | + | 32491.0i | 0.326711 | + | 0.0576080i | 0.334598 | − | 0.942361i | \(-0.391399\pi\) |
−0.00788703 | + | 0.999969i | \(0.502511\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −146208. | − | 84413.5i | −0.257859 | − | 0.148875i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −130039. | + | 357278.i | −0.228128 | + | 0.626777i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 156846. | − | 131610.i | 0.273705 | − | 0.229666i | −0.495595 | − | 0.868554i | \(-0.665050\pi\) |
0.769300 | + | 0.638888i | \(0.220605\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 120287.i | 0.208803i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −976866. | −1.68681 | −0.843404 | − | 0.537280i | \(-0.819452\pi\) | ||||
−0.843404 | + | 0.537280i | \(0.819452\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 824966. | + | 983156.i | 1.41706 | + | 1.68878i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 462915. | + | 168487.i | 0.791004 | + | 0.287902i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2709.76 | − | 4693.44i | 0.00460617 | − | 0.00797813i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40758.6 | − | 231154.i | 0.0689235 | − | 0.390884i | −0.930758 | − | 0.365636i | \(-0.880851\pi\) |
0.999681 | − | 0.0252479i | \(-0.00803752\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 149040. | + | 258146.i | 0.250724 | + | 0.434266i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −91616.0 | + | 109184.i | −0.153325 | + | 0.182725i | −0.837239 | − | 0.546837i | \(-0.815832\pi\) |
0.683914 | + | 0.729562i | \(0.260276\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 53462.1 | + | 146886.i | 0.0890108 | + | 0.244555i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 79066.8 | + | 448410.i | 0.130964 | + | 0.742734i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 749345. | − | 559794.i | 1.23483 | − | 0.922472i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −424946. | + | 74929.5i | −0.696677 | + | 0.122843i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 718932. | − | 261670.i | 1.17264 | − | 0.426806i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −527573. | − | 442686.i | −0.856137 | − | 0.718384i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −230126. | + | 132863.i | −0.371549 | + | 0.214514i | −0.674135 | − | 0.738608i | \(-0.735483\pi\) |
0.302586 | + | 0.953122i | \(0.402150\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −344890. | − | 60813.5i | −0.554022 | − | 0.0976890i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −650945. | − | 375823.i | −1.04038 | − | 0.600662i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14701.5 | − | 40391.9i | 0.0233784 | − | 0.0642315i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 174053. | − | 146047.i | 0.275389 | − | 0.231079i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 926703.i | − | 1.45889i | −0.684037 | − | 0.729447i | \(-0.739777\pi\) | ||
0.684037 | − | 0.729447i | \(-0.260223\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.30376e6 | 2.04222 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 20126.4 | + | 23985.7i | 0.0313690 | + | 0.0373842i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 357843. | + | 130244.i | 0.554960 | + | 0.201989i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −184818. | + | 320114.i | −0.285202 | + | 0.493984i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 85873.8 | − | 487014.i | 0.131860 | − | 0.747816i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −547564. | − | 948408.i | −0.836638 | − | 1.44910i | −0.892690 | − | 0.450671i | \(-0.851185\pi\) |
0.0560523 | − | 0.998428i | \(-0.482149\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 577529. | − | 688272.i | 0.878076 | − | 1.04645i | −0.120479 | − | 0.992716i | \(-0.538443\pi\) |
0.998555 | − | 0.0537344i | \(-0.0171124\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −136237. | − | 374309.i | −0.206118 | − | 0.566303i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 154253. | + | 874811.i | 0.232230 | + | 1.31704i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −308743. | + | 719011.i | −0.462543 | + | 1.07719i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −122387. | + | 21580.2i | −0.182460 | + | 0.0321727i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 681125. | − | 247909.i | 1.01051 | − | 0.367795i | 0.216881 | − | 0.976198i | \(-0.430412\pi\) |
0.793628 | + | 0.608403i | \(0.208189\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −906038. | − | 760256.i | −1.33766 | − | 1.12243i | −0.982220 | − | 0.187734i | \(-0.939886\pi\) |
−0.355443 | − | 0.934698i | \(-0.615670\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 72823.2 | − | 42044.5i | 0.106995 | − | 0.0617733i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.24093e6 | − | 218809.i | −1.81441 | − | 0.319930i | −0.839643 | − | 0.543138i | \(-0.817236\pi\) |
−0.974771 | + | 0.223208i | \(0.928347\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −232054. | − | 133976.i | −0.337660 | − | 0.194948i | 0.321577 | − | 0.946883i | \(-0.395787\pi\) |
−0.659237 | + | 0.751935i | \(0.729120\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12379.9 | + | 34013.5i | −0.0179273 | + | 0.0492548i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 814797. | − | 683696.i | 1.17425 | − | 0.985311i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 520178.i | − | 0.746068i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −598401. | −0.854164 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −551640. | − | 657418.i | −0.783667 | − | 0.933938i | 0.215426 | − | 0.976520i | \(-0.430886\pi\) |
−0.999093 | + | 0.0425824i | \(0.986441\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 668419. | + | 243284.i | 0.945054 | + | 0.343971i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 229666. | − | 397794.i | 0.323178 | − | 0.559761i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −103012. | + | 584209.i | −0.144269 | + | 0.818191i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 89314.8 | + | 154698.i | 0.124496 | + | 0.215634i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 105922. | − | 126233.i | 0.146950 | − | 0.175128i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −114205. | − | 313775.i | −0.157698 | − | 0.433271i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43477.0 | + | 246571.i | 0.0597533 | + | 0.338878i | 0.999999 | − | 0.00161981i | \(-0.000515602\pi\) |
−0.940245 | + | 0.340498i | \(0.889404\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 389615. | + | 255332.i | 0.532971 | + | 0.349280i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.34106e6 | + | 236466.i | −1.82595 | + | 0.321963i | −0.978077 | − | 0.208243i | \(-0.933225\pi\) |
−0.847868 | + | 0.530207i | \(0.822114\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.01299e6 | + | 368699.i | −1.37284 | + | 0.499673i | −0.920000 | − | 0.391919i | \(-0.871811\pi\) |
−0.452840 | + | 0.891592i | \(0.649589\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 649634. | + | 545108.i | 0.876320 | + | 0.735319i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −391822. | + | 226219.i | −0.526099 | + | 0.303743i | −0.739426 | − | 0.673237i | \(-0.764903\pi\) |
0.213327 | + | 0.976981i | \(0.431570\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −170918. | − | 30137.5i | −0.228431 | − | 0.0402786i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −244895. | − | 141390.i | −0.325793 | − | 0.188097i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −40201.9 | + | 110454.i | −0.0532363 | + | 0.146265i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −164622. | + | 138134.i | −0.216996 | + | 0.182081i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 845576.i | − | 1.10949i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.22090e6 | 1.59464 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −679353. | − | 809621.i | −0.883276 | − | 1.05265i | −0.998242 | − | 0.0592775i | \(-0.981120\pi\) |
0.114966 | − | 0.993369i | \(-0.463324\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 427390. | + | 155557.i | 0.553155 | + | 0.201332i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 394829. | − | 683865.i | 0.508695 | − | 0.881086i | −0.491254 | − | 0.871016i | \(-0.663461\pi\) |
0.999949 | − | 0.0100696i | \(-0.00320531\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 85348.0 | − | 484033.i | 0.109464 | − | 0.620802i | −0.879879 | − | 0.475198i | \(-0.842376\pi\) |
0.989343 | − | 0.145604i | \(-0.0465125\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9208.94 | − | 15950.4i | −0.0117577 | − | 0.0203650i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −113784. | + | 135603.i | −0.144622 | + | 0.172354i | −0.833493 | − | 0.552530i | \(-0.813662\pi\) |
0.688871 | + | 0.724884i | \(0.258107\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 85030.4 | + | 233619.i | 0.107590 | + | 0.295600i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −37705.1 | − | 213836.i | −0.0474947 | − | 0.269356i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.20007e6 | + | 282328.i | 1.50489 | + | 0.354039i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −413886. | + | 72979.2i | −0.516695 | + | 0.0911073i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −29308.0 | + | 10667.2i | −0.0364251 | + | 0.0132577i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −849969. | − | 713209.i | −1.05168 | − | 0.882465i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 773064. | − | 446329.i | 0.952283 | − | 0.549801i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −698670. | − | 123194.i | −0.856834 | − | 0.151083i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 989383. | + | 571220.i | 1.20800 | + | 0.697439i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −278572. | + | 765369.i | −0.338628 | + | 0.930371i | 0.647157 | + | 0.762357i | \(0.275958\pi\) |
−0.985784 | + | 0.168015i | \(0.946264\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 350986. | − | 294512.i | 0.424778 | − | 0.356431i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.12646e6i | 1.35731i | 0.734457 | + | 0.678656i | \(0.237437\pi\) | ||||
−0.734457 | + | 0.678656i | \(0.762563\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −578927. | −0.694516 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −93897.7 | − | 111903.i | −0.112153 | − | 0.133659i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 900762. | + | 327851.i | 1.07120 | + | 0.389886i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 737353. | − | 1.27713e6i | 0.873060 | − | 1.51218i | 0.0142453 | − | 0.999899i | \(-0.495465\pi\) |
0.858815 | − | 0.512286i | \(-0.171201\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −23851.1 | + | 135266.i | −0.0281183 | + | 0.159467i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −55941.4 | − | 96893.3i | −0.0656644 | − | 0.113734i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −150044. | + | 178816.i | −0.175362 | + | 0.208989i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 211364. | + | 580719.i | 0.245965 | + | 0.675782i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 124449. | + | 705786.i | 0.144198 | + | 0.817790i | 0.968007 | + | 0.250922i | \(0.0807339\pi\) |
−0.823809 | + | 0.566868i | \(0.808155\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 898053. | − | 452880.i | 1.03610 | − | 0.522496i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −802738. | + | 141544.i | −0.922169 | + | 0.162603i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −845904. | + | 307884.i | −0.967605 | + | 0.352179i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −351489. | − | 294934.i | −0.400343 | − | 0.335927i | 0.420283 | − | 0.907393i | \(-0.361931\pi\) |
−0.820626 | + | 0.571465i | \(0.806375\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −303661. | + | 175319.i | −0.344396 | + | 0.198837i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −53702.3 | − | 9469.16i | −0.0606475 | − | 0.0106938i | 0.143242 | − | 0.989688i | \(-0.454247\pi\) |
−0.203890 | + | 0.978994i | \(0.565358\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −538585. | − | 310952.i | −0.605663 | − | 0.349680i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −338332. | + | 929559.i | −0.378861 | + | 1.04091i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −149800. | + | 125697.i | −0.167036 | + | 0.140160i | −0.722474 | − | 0.691398i | \(-0.756995\pi\) |
0.555438 | + | 0.831558i | \(0.312551\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 98738.8i | 0.109637i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 236337. | 0.261319 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.08819e6 | + | 1.29686e6i | 1.19817 | + | 1.42793i | 0.876718 | + | 0.481004i | \(0.159728\pi\) |
0.321456 | + | 0.946925i | \(0.395828\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −60918.5 | − | 22172.5i | −0.0667948 | − | 0.0243113i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −298445. | + | 516921.i | −0.325867 | + | 0.564418i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6721.01 | + | 38116.8i | −0.00730798 | + | 0.0414456i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27840.9 | − | 48221.8i | −0.0301465 | − | 0.0522152i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −38063.9 | + | 45362.8i | −0.0410451 | + | 0.0489156i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 497995. | + | 1.36823e6i | 0.534775 | + | 1.46928i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 193856. | + | 1.09941e6i | 0.207313 | + | 1.17573i | 0.893758 | + | 0.448549i | \(0.148059\pi\) |
−0.686445 | + | 0.727182i | \(0.740830\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −456271. | − | 429047.i | −0.485932 | − | 0.456938i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −88596.1 | + | 15621.9i | −0.0939671 | + | 0.0165689i | −0.220434 | − | 0.975402i | \(-0.570747\pi\) |
0.126467 | + | 0.991971i | \(0.459636\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 669445. | − | 243658.i | 0.707114 | − | 0.257368i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 16702.2 | + | 14014.8i | 0.0175697 | + | 0.0147427i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −51203.2 | + | 29562.2i | −0.0536424 | + | 0.0309704i | −0.526581 | − | 0.850125i | \(-0.676526\pi\) |
0.472939 | + | 0.881095i | \(0.343193\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −56346.9 | − | 9935.47i | −0.0587901 | − | 0.0103663i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −931317. | − | 537696.i | −0.967742 | − | 0.558726i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 244561. | − | 671927.i | 0.253093 | − | 0.695368i | −0.746458 | − | 0.665432i | \(-0.768247\pi\) |
0.999552 | − | 0.0299364i | \(-0.00953046\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −129945. | + | 109036.i | −0.133932 | + | 0.112383i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.11775e6i | 1.14739i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 520271. | 0.531909 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 214603. | + | 255754.i | 0.218518 | + | 0.260420i | 0.864156 | − | 0.503224i | \(-0.167853\pi\) |
−0.645638 | + | 0.763644i | \(0.723408\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 661075. | + | 240612.i | 0.670428 | + | 0.244016i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 673366. | − | 1.16630e6i | 0.680150 | − | 1.17805i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −231991. | + | 1.31569e6i | −0.233389 | + | 1.32362i | 0.612590 | + | 0.790401i | \(0.290128\pi\) |
−0.845979 | + | 0.533216i | \(0.820983\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −446807. | − | 773893.i | −0.447702 | − | 0.775443i |
(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 | 76.5.j.a.29.5 | yes | 42 | |
19.2 | odd | 18 | inner | 76.5.j.a.21.5 | ✓ | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.5.j.a.21.5 | ✓ | 42 | 19.2 | odd | 18 | inner | |
76.5.j.a.29.5 | yes | 42 | 1.1 | even | 1 | trivial |