Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,3,Mod(22,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.22");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.f (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: | \(13.1607967686\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 22.16 | ||
Character | \(\chi\) | \(=\) | 483.22 |
Dual form | 483.3.f.a.22.15 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.65091 | −0.825457 | −0.412729 | − | 0.910854i | \(-0.635424\pi\) | ||||
−0.412729 | + | 0.910854i | \(0.635424\pi\) | |||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | −1.27448 | −0.318620 | ||||||||
\(5\) | − | 4.21491i | − | 0.842982i | −0.906833 | − | 0.421491i | \(-0.861507\pi\) | ||
0.906833 | − | 0.421491i | \(-0.138493\pi\) | |||||||
\(6\) | 2.85947 | 0.476578 | ||||||||
\(7\) | − | 2.64575i | − | 0.377964i | ||||||
\(8\) | 8.70772 | 1.08846 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 6.95846i | 0.695846i | ||||||||
\(11\) | 4.54772i | 0.413429i | 0.978401 | + | 0.206714i | \(0.0662771\pi\) | ||||
−0.978401 | + | 0.206714i | \(0.933723\pi\) | |||||||
\(12\) | 2.20747 | 0.183956 | ||||||||
\(13\) | 7.59356 | 0.584120 | 0.292060 | − | 0.956400i | \(-0.405659\pi\) | ||||
0.292060 | + | 0.956400i | \(0.405659\pi\) | |||||||
\(14\) | 4.36791i | 0.311994i | ||||||||
\(15\) | 7.30044i | 0.486696i | ||||||||
\(16\) | −9.27777 | −0.579861 | ||||||||
\(17\) | − | 3.10823i | − | 0.182837i | −0.995813 | − | 0.0914186i | \(-0.970860\pi\) | ||
0.995813 | − | 0.0914186i | \(-0.0291401\pi\) | |||||||
\(18\) | −4.95274 | −0.275152 | ||||||||
\(19\) | 12.4447i | 0.654986i | 0.944854 | + | 0.327493i | \(0.106204\pi\) | ||||
−0.944854 | + | 0.327493i | \(0.893796\pi\) | |||||||
\(20\) | 5.37182i | 0.268591i | ||||||||
\(21\) | 4.58258i | 0.218218i | ||||||||
\(22\) | − | 7.50789i | − | 0.341268i | ||||||
\(23\) | 22.5013 | + | 4.76355i | 0.978317 | + | 0.207111i | ||||
\(24\) | −15.0822 | −0.628425 | ||||||||
\(25\) | 7.23453 | 0.289381 | ||||||||
\(26\) | −12.5363 | −0.482166 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 3.37196i | 0.120427i | ||||||||
\(29\) | −6.35643 | −0.219187 | −0.109594 | − | 0.993976i | \(-0.534955\pi\) | ||||
−0.109594 | + | 0.993976i | \(0.534955\pi\) | |||||||
\(30\) | − | 12.0524i | − | 0.401747i | ||||||
\(31\) | −30.1298 | −0.971929 | −0.485965 | − | 0.873978i | \(-0.661532\pi\) | ||||
−0.485965 | + | 0.873978i | \(0.661532\pi\) | |||||||
\(32\) | −19.5141 | −0.609815 | ||||||||
\(33\) | − | 7.87688i | − | 0.238693i | ||||||
\(34\) | 5.13142i | 0.150924i | ||||||||
\(35\) | −11.1516 | −0.318617 | ||||||||
\(36\) | −3.82344 | −0.106207 | ||||||||
\(37\) | − | 62.2116i | − | 1.68140i | −0.541505 | − | 0.840698i | \(-0.682145\pi\) | ||
0.541505 | − | 0.840698i | \(-0.317855\pi\) | |||||||
\(38\) | − | 20.5452i | − | 0.540663i | ||||||
\(39\) | −13.1524 | −0.337242 | ||||||||
\(40\) | − | 36.7022i | − | 0.917556i | ||||||
\(41\) | 58.9776 | 1.43848 | 0.719239 | − | 0.694762i | \(-0.244491\pi\) | ||||
0.719239 | + | 0.694762i | \(0.244491\pi\) | |||||||
\(42\) | − | 7.56544i | − | 0.180130i | ||||||
\(43\) | − | 46.9531i | − | 1.09193i | −0.837807 | − | 0.545966i | \(-0.816163\pi\) | ||
0.837807 | − | 0.545966i | \(-0.183837\pi\) | |||||||
\(44\) | − | 5.79598i | − | 0.131727i | ||||||
\(45\) | − | 12.6447i | − | 0.280994i | ||||||
\(46\) | −37.1477 | − | 7.86422i | −0.807559 | − | 0.170961i | ||||
\(47\) | 7.95046 | 0.169159 | 0.0845794 | − | 0.996417i | \(-0.473045\pi\) | ||||
0.0845794 | + | 0.996417i | \(0.473045\pi\) | |||||||
\(48\) | 16.0696 | 0.334783 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | −11.9436 | −0.238872 | ||||||||
\(51\) | 5.38361i | 0.105561i | ||||||||
\(52\) | −9.67785 | −0.186112 | ||||||||
\(53\) | 24.5223i | 0.462684i | 0.972872 | + | 0.231342i | \(0.0743116\pi\) | ||||
−0.972872 | + | 0.231342i | \(0.925688\pi\) | |||||||
\(54\) | 8.57840 | 0.158859 | ||||||||
\(55\) | 19.1682 | 0.348513 | ||||||||
\(56\) | − | 23.0385i | − | 0.411401i | ||||||
\(57\) | − | 21.5549i | − | 0.378156i | ||||||
\(58\) | 10.4939 | 0.180930 | ||||||||
\(59\) | −32.6762 | −0.553833 | −0.276917 | − | 0.960894i | \(-0.589313\pi\) | ||||
−0.276917 | + | 0.960894i | \(0.589313\pi\) | |||||||
\(60\) | − | 9.30427i | − | 0.155071i | ||||||
\(61\) | − | 81.8893i | − | 1.34245i | −0.741255 | − | 0.671224i | \(-0.765769\pi\) | ||
0.741255 | − | 0.671224i | \(-0.234231\pi\) | |||||||
\(62\) | 49.7417 | 0.802286 | ||||||||
\(63\) | − | 7.93725i | − | 0.125988i | ||||||
\(64\) | 69.3271 | 1.08324 | ||||||||
\(65\) | − | 32.0062i | − | 0.492402i | ||||||
\(66\) | 13.0041i | 0.197031i | ||||||||
\(67\) | − | 100.648i | − | 1.50220i | −0.660186 | − | 0.751102i | \(-0.729522\pi\) | ||
0.660186 | − | 0.751102i | \(-0.270478\pi\) | |||||||
\(68\) | 3.96138i | 0.0582556i | ||||||||
\(69\) | −38.9734 | − | 8.25072i | −0.564832 | − | 0.119576i | ||||
\(70\) | 18.4103 | 0.263005 | ||||||||
\(71\) | −40.6975 | −0.573205 | −0.286602 | − | 0.958050i | \(-0.592526\pi\) | ||||
−0.286602 | + | 0.958050i | \(0.592526\pi\) | |||||||
\(72\) | 26.1232 | 0.362822 | ||||||||
\(73\) | −57.2966 | −0.784885 | −0.392443 | − | 0.919777i | \(-0.628370\pi\) | ||||
−0.392443 | + | 0.919777i | \(0.628370\pi\) | |||||||
\(74\) | 102.706i | 1.38792i | ||||||||
\(75\) | −12.5306 | −0.167074 | ||||||||
\(76\) | − | 15.8606i | − | 0.208692i | ||||||
\(77\) | 12.0321 | 0.156261 | ||||||||
\(78\) | 21.7135 | 0.278379 | ||||||||
\(79\) | − | 116.054i | − | 1.46904i | −0.678587 | − | 0.734520i | \(-0.737408\pi\) | ||
0.678587 | − | 0.734520i | \(-0.262592\pi\) | |||||||
\(80\) | 39.1050i | 0.488812i | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | −97.3670 | −1.18740 | ||||||||
\(83\) | 38.4315i | 0.463031i | 0.972831 | + | 0.231515i | \(0.0743684\pi\) | ||||
−0.972831 | + | 0.231515i | \(0.925632\pi\) | |||||||
\(84\) | − | 5.84041i | − | 0.0695287i | ||||||
\(85\) | −13.1009 | −0.154128 | ||||||||
\(86\) | 77.5155i | 0.901343i | ||||||||
\(87\) | 11.0097 | 0.126548 | ||||||||
\(88\) | 39.6002i | 0.450003i | ||||||||
\(89\) | 21.3831i | 0.240260i | 0.992758 | + | 0.120130i | \(0.0383311\pi\) | ||||
−0.992758 | + | 0.120130i | \(0.961669\pi\) | |||||||
\(90\) | 20.8754i | 0.231949i | ||||||||
\(91\) | − | 20.0907i | − | 0.220777i | ||||||
\(92\) | −28.6775 | − | 6.07106i | −0.311712 | − | 0.0659898i | ||||
\(93\) | 52.1864 | 0.561144 | ||||||||
\(94\) | −13.1255 | −0.139633 | ||||||||
\(95\) | 52.4534 | 0.552141 | ||||||||
\(96\) | 33.7994 | 0.352077 | ||||||||
\(97\) | − | 68.3863i | − | 0.705013i | −0.935809 | − | 0.352507i | \(-0.885329\pi\) | ||
0.935809 | − | 0.352507i | \(-0.114671\pi\) | |||||||
\(98\) | 11.5564 | 0.117922 | ||||||||
\(99\) | 13.6432i | 0.137810i | ||||||||
\(100\) | −9.22028 | −0.0922028 | ||||||||
\(101\) | −172.128 | −1.70423 | −0.852117 | − | 0.523352i | \(-0.824681\pi\) | ||||
−0.852117 | + | 0.523352i | \(0.824681\pi\) | |||||||
\(102\) | − | 8.88789i | − | 0.0871361i | ||||||
\(103\) | 109.279i | 1.06096i | 0.847697 | + | 0.530480i | \(0.177988\pi\) | ||||
−0.847697 | + | 0.530480i | \(0.822012\pi\) | |||||||
\(104\) | 66.1226 | 0.635794 | ||||||||
\(105\) | 19.3151 | 0.183954 | ||||||||
\(106\) | − | 40.4841i | − | 0.381926i | ||||||
\(107\) | 128.031i | 1.19655i | 0.801291 | + | 0.598274i | \(0.204147\pi\) | ||||
−0.801291 | + | 0.598274i | \(0.795853\pi\) | |||||||
\(108\) | 6.62240 | 0.0613185 | ||||||||
\(109\) | − | 47.1808i | − | 0.432852i | −0.976299 | − | 0.216426i | \(-0.930560\pi\) | ||
0.976299 | − | 0.216426i | \(-0.0694400\pi\) | |||||||
\(110\) | −31.6451 | −0.287683 | ||||||||
\(111\) | 107.754i | 0.970754i | ||||||||
\(112\) | 24.5467i | 0.219167i | ||||||||
\(113\) | − | 148.877i | − | 1.31749i | −0.752366 | − | 0.658746i | \(-0.771087\pi\) | ||
0.752366 | − | 0.658746i | \(-0.228913\pi\) | |||||||
\(114\) | 35.5853i | 0.312152i | ||||||||
\(115\) | 20.0780 | − | 94.8410i | 0.174591 | − | 0.824704i | ||||
\(116\) | 8.10115 | 0.0698375 | ||||||||
\(117\) | 22.7807 | 0.194707 | ||||||||
\(118\) | 53.9455 | 0.457166 | ||||||||
\(119\) | −8.22361 | −0.0691059 | ||||||||
\(120\) | 63.5702i | 0.529751i | ||||||||
\(121\) | 100.318 | 0.829077 | ||||||||
\(122\) | 135.192i | 1.10813i | ||||||||
\(123\) | −102.152 | −0.830506 | ||||||||
\(124\) | 38.3999 | 0.309677 | ||||||||
\(125\) | − | 135.866i | − | 1.08693i | ||||||
\(126\) | 13.1037i | 0.103998i | ||||||||
\(127\) | −175.275 | −1.38012 | −0.690060 | − | 0.723752i | \(-0.742416\pi\) | ||||
−0.690060 | + | 0.723752i | \(0.742416\pi\) | |||||||
\(128\) | −36.3969 | −0.284351 | ||||||||
\(129\) | 81.3251i | 0.630427i | ||||||||
\(130\) | 52.8394i | 0.406457i | ||||||||
\(131\) | 67.6253 | 0.516223 | 0.258112 | − | 0.966115i | \(-0.416900\pi\) | ||||
0.258112 | + | 0.966115i | \(0.416900\pi\) | |||||||
\(132\) | 10.0389i | 0.0760525i | ||||||||
\(133\) | 32.9257 | 0.247561 | ||||||||
\(134\) | 166.161i | 1.24001i | ||||||||
\(135\) | 21.9013i | 0.162232i | ||||||||
\(136\) | − | 27.0656i | − | 0.199012i | ||||||
\(137\) | − | 46.4504i | − | 0.339054i | −0.985526 | − | 0.169527i | \(-0.945776\pi\) | ||
0.985526 | − | 0.169527i | \(-0.0542240\pi\) | |||||||
\(138\) | 64.3417 | + | 13.6212i | 0.466245 | + | 0.0987046i | ||||
\(139\) | 30.8658 | 0.222056 | 0.111028 | − | 0.993817i | \(-0.464586\pi\) | ||||
0.111028 | + | 0.993817i | \(0.464586\pi\) | |||||||
\(140\) | 14.2125 | 0.101518 | ||||||||
\(141\) | −13.7706 | −0.0976639 | ||||||||
\(142\) | 67.1881 | 0.473156 | ||||||||
\(143\) | 34.5334i | 0.241492i | ||||||||
\(144\) | −27.8333 | −0.193287 | ||||||||
\(145\) | 26.7918i | 0.184771i | ||||||||
\(146\) | 94.5918 | 0.647889 | ||||||||
\(147\) | 12.1244 | 0.0824786 | ||||||||
\(148\) | 79.2876i | 0.535727i | ||||||||
\(149\) | 31.6314i | 0.212291i | 0.994351 | + | 0.106146i | \(0.0338510\pi\) | ||||
−0.994351 | + | 0.106146i | \(0.966149\pi\) | |||||||
\(150\) | 20.6869 | 0.137913 | ||||||||
\(151\) | −83.7183 | −0.554426 | −0.277213 | − | 0.960809i | \(-0.589411\pi\) | ||||
−0.277213 | + | 0.960809i | \(0.589411\pi\) | |||||||
\(152\) | 108.365i | 0.712929i | ||||||||
\(153\) | − | 9.32469i | − | 0.0609457i | ||||||
\(154\) | −19.8640 | −0.128987 | ||||||||
\(155\) | 126.994i | 0.819319i | ||||||||
\(156\) | 16.7625 | 0.107452 | ||||||||
\(157\) | 214.353i | 1.36531i | 0.730742 | + | 0.682654i | \(0.239174\pi\) | ||||
−0.730742 | + | 0.682654i | \(0.760826\pi\) | |||||||
\(158\) | 191.595i | 1.21263i | ||||||||
\(159\) | − | 42.4738i | − | 0.267131i | ||||||
\(160\) | 82.2500i | 0.514063i | ||||||||
\(161\) | 12.6032 | − | 59.5328i | 0.0782806 | − | 0.369769i | ||||
\(162\) | −14.8582 | −0.0917175 | ||||||||
\(163\) | 61.9299 | 0.379938 | 0.189969 | − | 0.981790i | \(-0.439161\pi\) | ||||
0.189969 | + | 0.981790i | \(0.439161\pi\) | |||||||
\(164\) | −75.1659 | −0.458329 | ||||||||
\(165\) | −33.2003 | −0.201214 | ||||||||
\(166\) | − | 63.4472i | − | 0.382212i | ||||||
\(167\) | 233.362 | 1.39738 | 0.698689 | − | 0.715425i | \(-0.253767\pi\) | ||||
0.698689 | + | 0.715425i | \(0.253767\pi\) | |||||||
\(168\) | 39.9038i | 0.237522i | ||||||||
\(169\) | −111.338 | −0.658804 | ||||||||
\(170\) | 21.6285 | 0.127226 | ||||||||
\(171\) | 37.3342i | 0.218329i | ||||||||
\(172\) | 59.8408i | 0.347912i | ||||||||
\(173\) | 25.7071 | 0.148596 | 0.0742978 | − | 0.997236i | \(-0.476328\pi\) | ||||
0.0742978 | + | 0.997236i | \(0.476328\pi\) | |||||||
\(174\) | −18.1760 | −0.104460 | ||||||||
\(175\) | − | 19.1408i | − | 0.109376i | ||||||
\(176\) | − | 42.1927i | − | 0.239731i | ||||||
\(177\) | 56.5968 | 0.319756 | ||||||||
\(178\) | − | 35.3017i | − | 0.198324i | ||||||
\(179\) | 128.100 | 0.715642 | 0.357821 | − | 0.933790i | \(-0.383520\pi\) | ||||
0.357821 | + | 0.933790i | \(0.383520\pi\) | |||||||
\(180\) | 16.1155i | 0.0895304i | ||||||||
\(181\) | − | 227.238i | − | 1.25546i | −0.778433 | − | 0.627728i | \(-0.783985\pi\) | ||
0.778433 | − | 0.627728i | \(-0.216015\pi\) | |||||||
\(182\) | 33.1680i | 0.182242i | ||||||||
\(183\) | 141.836i | 0.775063i | ||||||||
\(184\) | 195.935 | + | 41.4797i | 1.06486 | + | 0.225433i | ||||
\(185\) | −262.216 | −1.41739 | ||||||||
\(186\) | −86.1552 | −0.463200 | ||||||||
\(187\) | 14.1354 | 0.0755901 | ||||||||
\(188\) | −10.1327 | −0.0538974 | ||||||||
\(189\) | 13.7477i | 0.0727393i | ||||||||
\(190\) | −86.5961 | −0.455769 | ||||||||
\(191\) | − | 81.2083i | − | 0.425174i | −0.977142 | − | 0.212587i | \(-0.931811\pi\) | ||
0.977142 | − | 0.212587i | \(-0.0681889\pi\) | |||||||
\(192\) | −120.078 | −0.625407 | ||||||||
\(193\) | 6.86510 | 0.0355705 | 0.0177852 | − | 0.999842i | \(-0.494338\pi\) | ||||
0.0177852 | + | 0.999842i | \(0.494338\pi\) | |||||||
\(194\) | 112.900i | 0.581958i | ||||||||
\(195\) | 55.4363i | 0.284289i | ||||||||
\(196\) | 8.92137 | 0.0455172 | ||||||||
\(197\) | 163.498 | 0.829938 | 0.414969 | − | 0.909836i | \(-0.363792\pi\) | ||||
0.414969 | + | 0.909836i | \(0.363792\pi\) | |||||||
\(198\) | − | 22.5237i | − | 0.113756i | ||||||
\(199\) | 129.255i | 0.649521i | 0.945796 | + | 0.324760i | \(0.105284\pi\) | ||||
−0.945796 | + | 0.324760i | \(0.894716\pi\) | |||||||
\(200\) | 62.9963 | 0.314981 | ||||||||
\(201\) | 174.327i | 0.867298i | ||||||||
\(202\) | 284.168 | 1.40677 | ||||||||
\(203\) | 16.8175i | 0.0828450i | ||||||||
\(204\) | − | 6.86132i | − | 0.0336339i | ||||||
\(205\) | − | 248.585i | − | 1.21261i | ||||||
\(206\) | − | 180.410i | − | 0.875778i | ||||||
\(207\) | 67.5039 | + | 14.2907i | 0.326106 | + | 0.0690370i | ||||
\(208\) | −70.4513 | −0.338708 | ||||||||
\(209\) | −56.5951 | −0.270790 | ||||||||
\(210\) | −31.8876 | −0.151846 | ||||||||
\(211\) | −95.5511 | −0.452849 | −0.226424 | − | 0.974029i | \(-0.572704\pi\) | ||||
−0.226424 | + | 0.974029i | \(0.572704\pi\) | |||||||
\(212\) | − | 31.2532i | − | 0.147421i | ||||||
\(213\) | 70.4902 | 0.330940 | ||||||||
\(214\) | − | 211.368i | − | 0.987700i | ||||||
\(215\) | −197.903 | −0.920479 | ||||||||
\(216\) | −45.2466 | −0.209475 | ||||||||
\(217\) | 79.7160i | 0.367355i | ||||||||
\(218\) | 77.8915i | 0.357301i | ||||||||
\(219\) | 99.2407 | 0.453154 | ||||||||
\(220\) | −24.4295 | −0.111043 | ||||||||
\(221\) | − | 23.6025i | − | 0.106799i | ||||||
\(222\) | − | 177.892i | − | 0.801316i | ||||||
\(223\) | −160.057 | −0.717744 | −0.358872 | − | 0.933387i | \(-0.616839\pi\) | ||||
−0.358872 | + | 0.933387i | \(0.616839\pi\) | |||||||
\(224\) | 51.6294i | 0.230488i | ||||||||
\(225\) | 21.7036 | 0.0964605 | ||||||||
\(226\) | 245.782i | 1.08753i | ||||||||
\(227\) | − | 58.2831i | − | 0.256754i | −0.991725 | − | 0.128377i | \(-0.959023\pi\) | ||
0.991725 | − | 0.128377i | \(-0.0409767\pi\) | |||||||
\(228\) | 27.4713i | 0.120488i | ||||||||
\(229\) | − | 94.5361i | − | 0.412821i | −0.978465 | − | 0.206411i | \(-0.933822\pi\) | ||
0.978465 | − | 0.206411i | \(-0.0661783\pi\) | |||||||
\(230\) | −33.1470 | + | 156.574i | −0.144117 | + | 0.680758i | ||||
\(231\) | −20.8403 | −0.0902176 | ||||||||
\(232\) | −55.3500 | −0.238578 | ||||||||
\(233\) | 436.615 | 1.87388 | 0.936942 | − | 0.349485i | \(-0.113643\pi\) | ||||
0.936942 | + | 0.349485i | \(0.113643\pi\) | |||||||
\(234\) | −37.6089 | −0.160722 | ||||||||
\(235\) | − | 33.5105i | − | 0.142598i | ||||||
\(236\) | 41.6452 | 0.176463 | ||||||||
\(237\) | 201.012i | 0.848150i | ||||||||
\(238\) | 13.5765 | 0.0570440 | ||||||||
\(239\) | 140.417 | 0.587518 | 0.293759 | − | 0.955879i | \(-0.405094\pi\) | ||||
0.293759 | + | 0.955879i | \(0.405094\pi\) | |||||||
\(240\) | − | 67.7318i | − | 0.282216i | ||||||
\(241\) | − | 210.191i | − | 0.872164i | −0.899907 | − | 0.436082i | \(-0.856366\pi\) | ||
0.899907 | − | 0.436082i | \(-0.143634\pi\) | |||||||
\(242\) | −165.617 | −0.684367 | ||||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 104.366i | 0.427731i | ||||||||
\(245\) | 29.5044i | 0.120426i | ||||||||
\(246\) | 168.645 | 0.685547 | ||||||||
\(247\) | 94.4998i | 0.382590i | ||||||||
\(248\) | −262.362 | −1.05791 | ||||||||
\(249\) | − | 66.5654i | − | 0.267331i | ||||||
\(250\) | 224.303i | 0.897210i | ||||||||
\(251\) | − | 495.849i | − | 1.97549i | −0.156066 | − | 0.987747i | \(-0.549881\pi\) | ||
0.156066 | − | 0.987747i | \(-0.450119\pi\) | |||||||
\(252\) | 10.1159i | 0.0401424i | ||||||||
\(253\) | −21.6633 | + | 102.330i | −0.0856257 | + | 0.404465i | ||||
\(254\) | 289.364 | 1.13923 | ||||||||
\(255\) | 22.6914 | 0.0889861 | ||||||||
\(256\) | −217.220 | −0.848517 | ||||||||
\(257\) | −287.293 | −1.11787 | −0.558936 | − | 0.829211i | \(-0.688790\pi\) | ||||
−0.558936 | + | 0.829211i | \(0.688790\pi\) | |||||||
\(258\) | − | 134.261i | − | 0.520391i | ||||||
\(259\) | −164.597 | −0.635508 | ||||||||
\(260\) | 40.7913i | 0.156889i | ||||||||
\(261\) | −19.0693 | −0.0730624 | ||||||||
\(262\) | −111.644 | −0.426120 | ||||||||
\(263\) | − | 48.8657i | − | 0.185801i | −0.995675 | − | 0.0929005i | \(-0.970386\pi\) | ||
0.995675 | − | 0.0929005i | \(-0.0296139\pi\) | |||||||
\(264\) | − | 68.5896i | − | 0.259809i | ||||||
\(265\) | 103.359 | 0.390034 | ||||||||
\(266\) | −54.3574 | −0.204351 | ||||||||
\(267\) | − | 37.0366i | − | 0.138714i | ||||||
\(268\) | 128.274i | 0.478633i | ||||||||
\(269\) | −253.706 | −0.943147 | −0.471573 | − | 0.881827i | \(-0.656314\pi\) | ||||
−0.471573 | + | 0.881827i | \(0.656314\pi\) | |||||||
\(270\) | − | 36.1572i | − | 0.133916i | ||||||
\(271\) | −299.666 | −1.10578 | −0.552889 | − | 0.833255i | \(-0.686475\pi\) | ||||
−0.552889 | + | 0.833255i | \(0.686475\pi\) | |||||||
\(272\) | 28.8375i | 0.106020i | ||||||||
\(273\) | 34.7981i | 0.127465i | ||||||||
\(274\) | 76.6856i | 0.279874i | ||||||||
\(275\) | 32.9006i | 0.119639i | ||||||||
\(276\) | 49.6709 | + | 10.5154i | 0.179967 | + | 0.0380992i | ||||
\(277\) | 115.620 | 0.417402 | 0.208701 | − | 0.977980i | \(-0.433077\pi\) | ||||
0.208701 | + | 0.977980i | \(0.433077\pi\) | |||||||
\(278\) | −50.9568 | −0.183298 | ||||||||
\(279\) | −90.3894 | −0.323976 | ||||||||
\(280\) | −97.1050 | −0.346804 | ||||||||
\(281\) | − | 497.545i | − | 1.77062i | −0.464999 | − | 0.885311i | \(-0.653945\pi\) | ||
0.464999 | − | 0.885311i | \(-0.346055\pi\) | |||||||
\(282\) | 22.7341 | 0.0806173 | ||||||||
\(283\) | − | 198.565i | − | 0.701645i | −0.936442 | − | 0.350822i | \(-0.885902\pi\) | ||
0.936442 | − | 0.350822i | \(-0.114098\pi\) | |||||||
\(284\) | 51.8683 | 0.182635 | ||||||||
\(285\) | −90.8520 | −0.318779 | ||||||||
\(286\) | − | 57.0116i | − | 0.199341i | ||||||
\(287\) | − | 156.040i | − | 0.543694i | ||||||
\(288\) | −58.5422 | −0.203272 | ||||||||
\(289\) | 279.339 | 0.966571 | ||||||||
\(290\) | − | 44.2309i | − | 0.152520i | ||||||
\(291\) | 118.448i | 0.407040i | ||||||||
\(292\) | 73.0235 | 0.250080 | ||||||||
\(293\) | 72.3189i | 0.246822i | 0.992356 | + | 0.123411i | \(0.0393834\pi\) | ||||
−0.992356 | + | 0.123411i | \(0.960617\pi\) | |||||||
\(294\) | −20.0163 | −0.0680826 | ||||||||
\(295\) | 137.727i | 0.466871i | ||||||||
\(296\) | − | 541.721i | − | 1.83014i | ||||||
\(297\) | − | 23.6306i | − | 0.0795644i | ||||||
\(298\) | − | 52.2207i | − | 0.175237i | ||||||
\(299\) | 170.865 | + | 36.1723i | 0.571455 | + | 0.120978i | ||||
\(300\) | 15.9700 | 0.0532333 | ||||||||
\(301\) | −124.226 | −0.412712 | ||||||||
\(302\) | 138.212 | 0.457655 | ||||||||
\(303\) | 298.134 | 0.983940 | ||||||||
\(304\) | − | 115.459i | − | 0.379800i | ||||||
\(305\) | −345.156 | −1.13166 | ||||||||
\(306\) | 15.3943i | 0.0503081i | ||||||||
\(307\) | 168.067 | 0.547451 | 0.273725 | − | 0.961808i | \(-0.411744\pi\) | ||||
0.273725 | + | 0.961808i | \(0.411744\pi\) | |||||||
\(308\) | −15.3347 | −0.0497881 | ||||||||
\(309\) | − | 189.277i | − | 0.612546i | ||||||
\(310\) | − | 209.657i | − | 0.676313i | ||||||
\(311\) | 98.4333 | 0.316506 | 0.158253 | − | 0.987399i | \(-0.449414\pi\) | ||||
0.158253 | + | 0.987399i | \(0.449414\pi\) | |||||||
\(312\) | −114.528 | −0.367076 | ||||||||
\(313\) | − | 449.000i | − | 1.43450i | −0.696813 | − | 0.717252i | \(-0.745399\pi\) | ||
0.696813 | − | 0.717252i | \(-0.254601\pi\) | |||||||
\(314\) | − | 353.879i | − | 1.12700i | ||||||
\(315\) | −33.4548 | −0.106206 | ||||||||
\(316\) | 147.909i | 0.468066i | ||||||||
\(317\) | 64.7677 | 0.204314 | 0.102157 | − | 0.994768i | \(-0.467426\pi\) | ||||
0.102157 | + | 0.994768i | \(0.467426\pi\) | |||||||
\(318\) | 70.1206i | 0.220505i | ||||||||
\(319\) | − | 28.9072i | − | 0.0906183i | ||||||
\(320\) | − | 292.208i | − | 0.913149i | ||||||
\(321\) | − | 221.756i | − | 0.690828i | ||||||
\(322\) | −20.8068 | + | 98.2836i | −0.0646173 | + | 0.305229i | ||||
\(323\) | 38.6811 | 0.119756 | ||||||||
\(324\) | −11.4703 | −0.0354023 | ||||||||
\(325\) | 54.9358 | 0.169033 | ||||||||
\(326\) | −102.241 | −0.313622 | ||||||||
\(327\) | 81.7196i | 0.249907i | ||||||||
\(328\) | 513.560 | 1.56573 | ||||||||
\(329\) | − | 21.0349i | − | 0.0639360i | ||||||
\(330\) | 54.8109 | 0.166094 | ||||||||
\(331\) | 579.469 | 1.75066 | 0.875331 | − | 0.483524i | \(-0.160643\pi\) | ||||
0.875331 | + | 0.483524i | \(0.160643\pi\) | |||||||
\(332\) | − | 48.9803i | − | 0.147531i | ||||||
\(333\) | − | 186.635i | − | 0.560465i | ||||||
\(334\) | −385.261 | −1.15348 | ||||||||
\(335\) | −424.221 | −1.26633 | ||||||||
\(336\) | − | 42.5161i | − | 0.126536i | ||||||
\(337\) | − | 60.8832i | − | 0.180662i | −0.995912 | − | 0.0903312i | \(-0.971207\pi\) | ||
0.995912 | − | 0.0903312i | \(-0.0287926\pi\) | |||||||
\(338\) | 183.809 | 0.543815 | ||||||||
\(339\) | 257.862i | 0.760654i | ||||||||
\(340\) | 16.6969 | 0.0491084 | ||||||||
\(341\) | − | 137.022i | − | 0.401824i | ||||||
\(342\) | − | 61.6356i | − | 0.180221i | ||||||
\(343\) | 18.5203i | 0.0539949i | ||||||||
\(344\) | − | 408.854i | − | 1.18853i | ||||||
\(345\) | −34.7760 | + | 164.269i | −0.100800 | + | 0.476143i | ||||
\(346\) | −42.4401 | −0.122659 | ||||||||
\(347\) | −88.2666 | −0.254371 | −0.127185 | − | 0.991879i | \(-0.540594\pi\) | ||||
−0.127185 | + | 0.991879i | \(0.540594\pi\) | |||||||
\(348\) | −14.0316 | −0.0403207 | ||||||||
\(349\) | −18.0521 | −0.0517253 | −0.0258627 | − | 0.999666i | \(-0.508233\pi\) | ||||
−0.0258627 | + | 0.999666i | \(0.508233\pi\) | |||||||
\(350\) | 31.5998i | 0.0902851i | ||||||||
\(351\) | −39.4573 | −0.112414 | ||||||||
\(352\) | − | 88.7445i | − | 0.252115i | ||||||
\(353\) | −236.133 | −0.668932 | −0.334466 | − | 0.942408i | \(-0.608556\pi\) | ||||
−0.334466 | + | 0.942408i | \(0.608556\pi\) | |||||||
\(354\) | −93.4364 | −0.263945 | ||||||||
\(355\) | 171.536i | 0.483201i | ||||||||
\(356\) | − | 27.2524i | − | 0.0765516i | ||||||
\(357\) | 14.2437 | 0.0398983 | ||||||||
\(358\) | −211.482 | −0.590732 | ||||||||
\(359\) | 56.2854i | 0.156784i | 0.996923 | + | 0.0783919i | \(0.0249785\pi\) | ||||
−0.996923 | + | 0.0783919i | \(0.975021\pi\) | |||||||
\(360\) | − | 110.107i | − | 0.305852i | ||||||
\(361\) | 206.129 | 0.570994 | ||||||||
\(362\) | 375.150i | 1.03633i | ||||||||
\(363\) | −173.756 | −0.478668 | ||||||||
\(364\) | 25.6052i | 0.0703439i | ||||||||
\(365\) | 241.500i | 0.661644i | ||||||||
\(366\) | − | 234.160i | − | 0.639781i | ||||||
\(367\) | 360.108i | 0.981222i | 0.871379 | + | 0.490611i | \(0.163226\pi\) | ||||
−0.871379 | + | 0.490611i | \(0.836774\pi\) | |||||||
\(368\) | −208.762 | − | 44.1952i | −0.567288 | − | 0.120096i | ||||
\(369\) | 176.933 | 0.479493 | ||||||||
\(370\) | 432.897 | 1.16999 | ||||||||
\(371\) | 64.8798 | 0.174878 | ||||||||
\(372\) | −66.5106 | −0.178792 | ||||||||
\(373\) | − | 61.6038i | − | 0.165158i | −0.996585 | − | 0.0825788i | \(-0.973684\pi\) | ||
0.996585 | − | 0.0825788i | \(-0.0263156\pi\) | |||||||
\(374\) | −23.3363 | −0.0623964 | ||||||||
\(375\) | 235.326i | 0.627537i | ||||||||
\(376\) | 69.2304 | 0.184123 | ||||||||
\(377\) | −48.2679 | −0.128032 | ||||||||
\(378\) | − | 22.6963i | − | 0.0600432i | ||||||
\(379\) | 92.1888i | 0.243242i | 0.992577 | + | 0.121621i | \(0.0388093\pi\) | ||||
−0.992577 | + | 0.121621i | \(0.961191\pi\) | |||||||
\(380\) | −66.8509 | −0.175923 | ||||||||
\(381\) | 303.586 | 0.796813 | ||||||||
\(382\) | 134.068i | 0.350963i | ||||||||
\(383\) | 283.695i | 0.740719i | 0.928888 | + | 0.370360i | \(0.120766\pi\) | ||||
−0.928888 | + | 0.370360i | \(0.879234\pi\) | |||||||
\(384\) | 63.0413 | 0.164170 | ||||||||
\(385\) | − | 50.7143i | − | 0.131726i | ||||||
\(386\) | −11.3337 | −0.0293619 | ||||||||
\(387\) | − | 140.859i | − | 0.363977i | ||||||
\(388\) | 87.1570i | 0.224632i | ||||||||
\(389\) | − | 465.693i | − | 1.19715i | −0.801065 | − | 0.598577i | \(-0.795733\pi\) | ||
0.801065 | − | 0.598577i | \(-0.204267\pi\) | |||||||
\(390\) | − | 91.5206i | − | 0.234668i | ||||||
\(391\) | 14.8062 | − | 69.9392i | 0.0378676 | − | 0.178873i | ||||
\(392\) | −60.9540 | −0.155495 | ||||||||
\(393\) | −117.130 | −0.298042 | ||||||||
\(394\) | −269.921 | −0.685078 | ||||||||
\(395\) | −489.158 | −1.23837 | ||||||||
\(396\) | − | 17.3879i | − | 0.0439090i | ||||||
\(397\) | −478.271 | −1.20471 | −0.602356 | − | 0.798228i | \(-0.705771\pi\) | ||||
−0.602356 | + | 0.798228i | \(0.705771\pi\) | |||||||
\(398\) | − | 213.388i | − | 0.536152i | ||||||
\(399\) | −57.0289 | −0.142930 | ||||||||
\(400\) | −67.1203 | −0.167801 | ||||||||
\(401\) | − | 88.2014i | − | 0.219954i | −0.993934 | − | 0.109977i | \(-0.964922\pi\) | ||
0.993934 | − | 0.109977i | \(-0.0350776\pi\) | |||||||
\(402\) | − | 287.799i | − | 0.715918i | ||||||
\(403\) | −228.792 | −0.567723 | ||||||||
\(404\) | 219.373 | 0.543003 | ||||||||
\(405\) | − | 37.9342i | − | 0.0936647i | ||||||
\(406\) | − | 27.7643i | − | 0.0683850i | ||||||
\(407\) | 282.921 | 0.695137 | ||||||||
\(408\) | 46.8790i | 0.114899i | ||||||||
\(409\) | 380.561 | 0.930467 | 0.465233 | − | 0.885188i | \(-0.345970\pi\) | ||||
0.465233 | + | 0.885188i | \(0.345970\pi\) | |||||||
\(410\) | 410.393i | 1.00096i | ||||||||
\(411\) | 80.4544i | 0.195753i | ||||||||
\(412\) | − | 139.274i | − | 0.338044i | ||||||
\(413\) | 86.4530i | 0.209329i | ||||||||
\(414\) | −111.443 | − | 23.5927i | −0.269186 | − | 0.0569871i | ||||
\(415\) | 161.986 | 0.390327 | ||||||||
\(416\) | −148.181 | −0.356205 | ||||||||
\(417\) | −53.4611 | −0.128204 | ||||||||
\(418\) | 93.4337 | 0.223526 | ||||||||
\(419\) | 751.317i | 1.79312i | 0.442923 | + | 0.896560i | \(0.353942\pi\) | ||||
−0.442923 | + | 0.896560i | \(0.646058\pi\) | |||||||
\(420\) | −24.6168 | −0.0586114 | ||||||||
\(421\) | − | 734.354i | − | 1.74431i | −0.489231 | − | 0.872154i | \(-0.662722\pi\) | ||
0.489231 | − | 0.872154i | \(-0.337278\pi\) | |||||||
\(422\) | 157.747 | 0.373807 | ||||||||
\(423\) | 23.8514 | 0.0563863 | ||||||||
\(424\) | 213.533i | 0.503615i | ||||||||
\(425\) | − | 22.4866i | − | 0.0529097i | ||||||
\(426\) | −116.373 | −0.273177 | ||||||||
\(427\) | −216.659 | −0.507398 | ||||||||
\(428\) | − | 163.173i | − | 0.381245i | ||||||
\(429\) | − | 59.8135i | − | 0.139425i | ||||||
\(430\) | 326.721 | 0.759816 | ||||||||
\(431\) | 291.967i | 0.677417i | 0.940891 | + | 0.338708i | \(0.109990\pi\) | ||||
−0.940891 | + | 0.338708i | \(0.890010\pi\) | |||||||
\(432\) | 48.2087 | 0.111594 | ||||||||
\(433\) | 599.769i | 1.38515i | 0.721347 | + | 0.692573i | \(0.243523\pi\) | ||||
−0.721347 | + | 0.692573i | \(0.756477\pi\) | |||||||
\(434\) | − | 131.604i | − | 0.303236i | ||||||
\(435\) | − | 46.4047i | − | 0.106678i | ||||||
\(436\) | 60.1311i | 0.137915i | ||||||||
\(437\) | −59.2811 | + | 280.023i | −0.135655 | + | 0.640784i | ||||
\(438\) | −163.838 | −0.374059 | ||||||||
\(439\) | 43.1472 | 0.0982853 | 0.0491426 | − | 0.998792i | \(-0.484351\pi\) | ||||
0.0491426 | + | 0.998792i | \(0.484351\pi\) | |||||||
\(440\) | 166.911 | 0.379344 | ||||||||
\(441\) | −21.0000 | −0.0476190 | ||||||||
\(442\) | 38.9658i | 0.0881578i | ||||||||
\(443\) | 159.701 | 0.360498 | 0.180249 | − | 0.983621i | \(-0.442310\pi\) | ||||
0.180249 | + | 0.983621i | \(0.442310\pi\) | |||||||
\(444\) | − | 137.330i | − | 0.309302i | ||||||
\(445\) | 90.1279 | 0.202535 | ||||||||
\(446\) | 264.240 | 0.592467 | ||||||||
\(447\) | − | 54.7872i | − | 0.122566i | ||||||
\(448\) | − | 183.422i | − | 0.409425i | ||||||
\(449\) | 551.417 | 1.22810 | 0.614050 | − | 0.789267i | \(-0.289539\pi\) | ||||
0.614050 | + | 0.789267i | \(0.289539\pi\) | |||||||
\(450\) | −35.8308 | −0.0796240 | ||||||||
\(451\) | 268.214i | 0.594709i | ||||||||
\(452\) | 189.740i | 0.419780i | ||||||||
\(453\) | 145.004 | 0.320098 | ||||||||
\(454\) | 96.2205i | 0.211939i | ||||||||
\(455\) | −84.6803 | −0.186111 | ||||||||
\(456\) | − | 187.694i | − | 0.411610i | ||||||
\(457\) | 447.366i | 0.978918i | 0.872026 | + | 0.489459i | \(0.162806\pi\) | ||||
−0.872026 | + | 0.489459i | \(0.837194\pi\) | |||||||
\(458\) | 156.071i | 0.340766i | ||||||||
\(459\) | 16.1508i | 0.0351870i | ||||||||
\(460\) | −25.5890 | + | 120.873i | −0.0556282 | + | 0.262768i | ||||
\(461\) | −548.620 | −1.19006 | −0.595032 | − | 0.803702i | \(-0.702861\pi\) | ||||
−0.595032 | + | 0.803702i | \(0.702861\pi\) | |||||||
\(462\) | 34.4055 | 0.0744708 | ||||||||
\(463\) | −34.7666 | −0.0750899 | −0.0375450 | − | 0.999295i | \(-0.511954\pi\) | ||||
−0.0375450 | + | 0.999295i | \(0.511954\pi\) | |||||||
\(464\) | 58.9735 | 0.127098 | ||||||||
\(465\) | − | 219.961i | − | 0.473034i | ||||||
\(466\) | −720.814 | −1.54681 | ||||||||
\(467\) | 12.5545i | 0.0268833i | 0.999910 | + | 0.0134416i | \(0.00427874\pi\) | ||||
−0.999910 | + | 0.0134416i | \(0.995721\pi\) | |||||||
\(468\) | −29.0335 | −0.0620375 | ||||||||
\(469\) | −266.289 | −0.567780 | ||||||||
\(470\) | 55.3229i | 0.117708i | ||||||||
\(471\) | − | 371.271i | − | 0.788261i | ||||||
\(472\) | −284.535 | −0.602828 | ||||||||
\(473\) | 213.529 | 0.451436 | ||||||||
\(474\) | − | 331.853i | − | 0.700112i | ||||||
\(475\) | 90.0318i | 0.189541i | ||||||||
\(476\) | 10.4808 | 0.0220186 | ||||||||
\(477\) | 73.5668i | 0.154228i | ||||||||
\(478\) | −231.816 | −0.484971 | ||||||||
\(479\) | 404.310i | 0.844071i | 0.906579 | + | 0.422036i | \(0.138684\pi\) | ||||
−0.906579 | + | 0.422036i | \(0.861316\pi\) | |||||||
\(480\) | − | 142.461i | − | 0.296794i | ||||||
\(481\) | − | 472.408i | − | 0.982136i | ||||||
\(482\) | 347.008i | 0.719934i | ||||||||
\(483\) | −21.8293 | + | 103.114i | −0.0451953 | + | 0.213486i | ||||
\(484\) | −127.854 | −0.264161 | ||||||||
\(485\) | −288.242 | −0.594313 | ||||||||
\(486\) | 25.7352 | 0.0529531 | ||||||||
\(487\) | 694.784 | 1.42666 | 0.713331 | − | 0.700827i | \(-0.247186\pi\) | ||||
0.713331 | + | 0.700827i | \(0.247186\pi\) | |||||||
\(488\) | − | 713.069i | − | 1.46121i | ||||||
\(489\) | −107.266 | −0.219357 | ||||||||
\(490\) | − | 48.7092i | − | 0.0994065i | ||||||
\(491\) | 646.833 | 1.31738 | 0.658689 | − | 0.752415i | \(-0.271111\pi\) | ||||
0.658689 | + | 0.752415i | \(0.271111\pi\) | |||||||
\(492\) | 130.191 | 0.264616 | ||||||||
\(493\) | 19.7573i | 0.0400756i | ||||||||
\(494\) | − | 156.011i | − | 0.315812i | ||||||
\(495\) | 57.5047 | 0.116171 | ||||||||
\(496\) | 279.537 | 0.563584 | ||||||||
\(497\) | 107.676i | 0.216651i | ||||||||
\(498\) | 109.894i | 0.220670i | ||||||||
\(499\) | −909.018 | −1.82168 | −0.910839 | − | 0.412761i | \(-0.864565\pi\) | ||||
−0.910839 | + | 0.412761i | \(0.864565\pi\) | |||||||
\(500\) | 173.158i | 0.346317i | ||||||||
\(501\) | −404.195 | −0.806777 | ||||||||
\(502\) | 818.604i | 1.63069i | ||||||||
\(503\) | 589.607i | 1.17218i | 0.810246 | + | 0.586090i | \(0.199334\pi\) | ||||
−0.810246 | + | 0.586090i | \(0.800666\pi\) | |||||||
\(504\) | − | 69.1154i | − | 0.137134i | ||||||
\(505\) | 725.502i | 1.43664i | ||||||||
\(506\) | 35.7643 | − | 168.937i | 0.0706804 | − | 0.333868i | ||||
\(507\) | 192.843 | 0.380361 | ||||||||
\(508\) | 223.385 | 0.439734 | ||||||||
\(509\) | −703.954 | −1.38301 | −0.691507 | − | 0.722370i | \(-0.743053\pi\) | ||||
−0.691507 | + | 0.722370i | \(0.743053\pi\) | |||||||
\(510\) | −37.4616 | −0.0734542 | ||||||||
\(511\) | 151.593i | 0.296659i | ||||||||
\(512\) | 504.200 | 0.984765 | ||||||||
\(513\) | − | 64.6647i | − | 0.126052i | ||||||
\(514\) | 474.296 | 0.922755 | ||||||||
\(515\) | 460.601 | 0.894371 | ||||||||
\(516\) | − | 103.647i | − | 0.200867i | ||||||
\(517\) | 36.1565i | 0.0699351i | ||||||||
\(518\) | 271.735 | 0.524584 | ||||||||
\(519\) | −44.5259 | −0.0857918 | ||||||||
\(520\) | − | 278.701i | − | 0.535963i | ||||||
\(521\) | − | 201.467i | − | 0.386694i | −0.981130 | − | 0.193347i | \(-0.938066\pi\) | ||
0.981130 | − | 0.193347i | \(-0.0619343\pi\) | |||||||
\(522\) | 31.4818 | 0.0603099 | ||||||||
\(523\) | 875.330i | 1.67367i | 0.547455 | + | 0.836835i | \(0.315597\pi\) | ||||
−0.547455 | + | 0.836835i | \(0.684403\pi\) | |||||||
\(524\) | −86.1872 | −0.164479 | ||||||||
\(525\) | 33.1528i | 0.0631482i | ||||||||
\(526\) | 80.6730i | 0.153371i | ||||||||
\(527\) | 93.6504i | 0.177705i | ||||||||
\(528\) | 73.0799i | 0.138409i | ||||||||
\(529\) | 483.617 | + | 214.372i | 0.914210 | + | 0.405241i | ||||
\(530\) | −170.637 | −0.321957 | ||||||||
\(531\) | −98.0285 | −0.184611 | ||||||||
\(532\) | −41.9631 | −0.0788781 | ||||||||
\(533\) | 447.850 | 0.840244 | ||||||||
\(534\) | 61.1443i | 0.114502i | ||||||||
\(535\) | 539.638 | 1.00867 | ||||||||
\(536\) | − | 876.412i | − | 1.63510i | ||||||
\(537\) | −221.876 | −0.413176 | ||||||||
\(538\) | 418.848 | 0.778527 | ||||||||
\(539\) | − | 31.8340i | − | 0.0590613i | ||||||
\(540\) | − | 27.9128i | − | 0.0516904i | ||||||
\(541\) | −276.743 | −0.511539 | −0.255770 | − | 0.966738i | \(-0.582329\pi\) | ||||
−0.255770 | + | 0.966738i | \(0.582329\pi\) | |||||||
\(542\) | 494.723 | 0.912772 | ||||||||
\(543\) | 393.587i | 0.724838i | ||||||||
\(544\) | 60.6542i | 0.111497i | ||||||||
\(545\) | −198.863 | −0.364886 | ||||||||
\(546\) | − | 57.4486i | − | 0.105217i | ||||||
\(547\) | 381.964 | 0.698289 | 0.349145 | − | 0.937069i | \(-0.386472\pi\) | ||||
0.349145 | + | 0.937069i | \(0.386472\pi\) | |||||||
\(548\) | 59.2001i | 0.108029i | ||||||||
\(549\) | − | 245.668i | − | 0.447483i | ||||||
\(550\) | − | 54.3161i | − | 0.0987566i | ||||||
\(551\) | − | 79.1040i | − | 0.143565i | ||||||
\(552\) | −339.369 | − | 71.8449i | −0.614800 | − | 0.130154i | ||||
\(553\) | −307.050 | −0.555245 | ||||||||
\(554\) | −190.879 | −0.344547 | ||||||||
\(555\) | 454.172 | 0.818328 | ||||||||
\(556\) | −39.3379 | −0.0707516 | ||||||||
\(557\) | 627.049i | 1.12576i | 0.826538 | + | 0.562880i | \(0.190307\pi\) | ||||
−0.826538 | + | 0.562880i | \(0.809693\pi\) | |||||||
\(558\) | 149.225 | 0.267429 | ||||||||
\(559\) | − | 356.541i | − | 0.637819i | ||||||
\(560\) | 103.462 | 0.184754 | ||||||||
\(561\) | −24.4832 | −0.0436420 | ||||||||
\(562\) | 821.404i | 1.46157i | ||||||||
\(563\) | − | 6.12085i | − | 0.0108718i | −0.999985 | − | 0.00543592i | \(-0.998270\pi\) | ||
0.999985 | − | 0.00543592i | \(-0.00173032\pi\) | |||||||
\(564\) | 17.5504 | 0.0311177 | ||||||||
\(565\) | −627.501 | −1.11062 | ||||||||
\(566\) | 327.815i | 0.579178i | ||||||||
\(567\) | − | 23.8118i | − | 0.0419961i | ||||||
\(568\) | −354.383 | −0.623913 | ||||||||
\(569\) | 933.547i | 1.64068i | 0.571876 | + | 0.820340i | \(0.306216\pi\) | ||||
−0.571876 | + | 0.820340i | \(0.693784\pi\) | |||||||
\(570\) | 149.989 | 0.263138 | ||||||||
\(571\) | 123.163i | 0.215698i | 0.994167 | + | 0.107849i | \(0.0343963\pi\) | ||||
−0.994167 | + | 0.107849i | \(0.965604\pi\) | |||||||
\(572\) | − | 44.0121i | − | 0.0769443i | ||||||
\(573\) | 140.657i | 0.245474i | ||||||||
\(574\) | 257.609i | 0.448796i | ||||||||
\(575\) | 162.786 | + | 34.4621i | 0.283107 | + | 0.0599341i | ||||
\(576\) | 207.981 | 0.361079 | ||||||||
\(577\) | 686.069 | 1.18903 | 0.594514 | − | 0.804086i | \(-0.297345\pi\) | ||||
0.594514 | + | 0.804086i | \(0.297345\pi\) | |||||||
\(578\) | −461.165 | −0.797863 | ||||||||
\(579\) | −11.8907 | −0.0205366 | ||||||||
\(580\) | − | 34.1456i | − | 0.0588718i | ||||||
\(581\) | 101.680 | 0.175009 | ||||||||
\(582\) | − | 195.548i | − | 0.335994i | ||||||
\(583\) | −111.520 | −0.191287 | ||||||||
\(584\) | −498.923 | −0.854320 | ||||||||
\(585\) | − | 96.0185i | − | 0.164134i | ||||||
\(586\) | − | 119.392i | − | 0.203741i | ||||||
\(587\) | 424.082 | 0.722457 | 0.361228 | − | 0.932477i | \(-0.382358\pi\) | ||||
0.361228 | + | 0.932477i | \(0.382358\pi\) | |||||||
\(588\) | −15.4523 | −0.0262794 | ||||||||
\(589\) | − | 374.957i | − | 0.636600i | ||||||
\(590\) | − | 227.376i | − | 0.385382i | ||||||
\(591\) | −283.186 | −0.479165 | ||||||||
\(592\) | 577.185i | 0.974975i | ||||||||
\(593\) | 105.687 | 0.178224 | 0.0891118 | − | 0.996022i | \(-0.471597\pi\) | ||||
0.0891118 | + | 0.996022i | \(0.471597\pi\) | |||||||
\(594\) | 39.0122i | 0.0656770i | ||||||||
\(595\) | 34.6618i | 0.0582551i | ||||||||
\(596\) | − | 40.3136i | − | 0.0676403i | ||||||
\(597\) | − | 223.876i | − | 0.375001i | ||||||
\(598\) | −282.083 | − | 59.7174i | −0.471711 | − | 0.0998619i | ||||
\(599\) | 475.544 | 0.793897 | 0.396949 | − | 0.917841i | \(-0.370069\pi\) | ||||
0.396949 | + | 0.917841i | \(0.370069\pi\) | |||||||
\(600\) | −109.113 | −0.181855 | ||||||||
\(601\) | 271.584 | 0.451887 | 0.225944 | − | 0.974140i | \(-0.427453\pi\) | ||||
0.225944 | + | 0.974140i | \(0.427453\pi\) | |||||||
\(602\) | 205.087 | 0.340676 | ||||||||
\(603\) | − | 301.943i | − | 0.500735i | ||||||
\(604\) | 106.697 | 0.176651 | ||||||||
\(605\) | − | 422.832i | − | 0.698897i | ||||||
\(606\) | −492.193 | −0.812200 | ||||||||
\(607\) | −371.399 | −0.611861 | −0.305930 | − | 0.952054i | \(-0.598967\pi\) | ||||
−0.305930 | + | 0.952054i | \(0.598967\pi\) | |||||||
\(608\) | − | 242.847i | − | 0.399420i | ||||||
\(609\) | − | 29.1288i | − | 0.0478306i | ||||||
\(610\) | 569.823 | 0.934136 | ||||||||
\(611\) | 60.3723 | 0.0988090 | ||||||||
\(612\) | 11.8841i | 0.0194185i | ||||||||
\(613\) | 424.357i | 0.692263i | 0.938186 | + | 0.346131i | \(0.112505\pi\) | ||||
−0.938186 | + | 0.346131i | \(0.887495\pi\) | |||||||
\(614\) | −277.465 | −0.451897 | ||||||||
\(615\) | 430.562i | 0.700102i | ||||||||
\(616\) | 104.772 | 0.170085 | ||||||||
\(617\) | 721.025i | 1.16860i | 0.811539 | + | 0.584299i | \(0.198630\pi\) | ||||
−0.811539 | + | 0.584299i | \(0.801370\pi\) | |||||||
\(618\) | 312.480i | 0.505631i | ||||||||
\(619\) | − | 1121.60i | − | 1.81195i | −0.423326 | − | 0.905977i | \(-0.639137\pi\) | ||
0.423326 | − | 0.905977i | \(-0.360863\pi\) | |||||||
\(620\) | − | 161.852i | − | 0.261052i | ||||||
\(621\) | −116.920 | − | 24.7522i | −0.188277 | − | 0.0398585i | ||||
\(622\) | −162.505 | −0.261262 | ||||||||
\(623\) | 56.5744 | 0.0908096 | ||||||||
\(624\) | 122.025 | 0.195553 | ||||||||
\(625\) | −391.798 | −0.626877 | ||||||||
\(626\) | 741.261i | 1.18412i | ||||||||
\(627\) | 98.0256 | 0.156341 | ||||||||
\(628\) | − | 273.189i | − | 0.435015i | ||||||
\(629\) | −193.368 | −0.307421 | ||||||||
\(630\) | 55.2310 | 0.0876683 | ||||||||
\(631\) | 557.475i | 0.883478i | 0.897144 | + | 0.441739i | \(0.145638\pi\) | ||||
−0.897144 | + | 0.441739i | \(0.854362\pi\) | |||||||
\(632\) | − | 1010.57i | − | 1.59900i | ||||||
\(633\) | 165.499 | 0.261452 | ||||||||
\(634\) | −106.926 | −0.168653 | ||||||||
\(635\) | 738.769i | 1.16342i | ||||||||
\(636\) | 54.1321i | 0.0851133i | ||||||||
\(637\) | −53.1549 | −0.0834457 | ||||||||
\(638\) | 47.7234i | 0.0748016i | ||||||||
\(639\) | −122.093 | −0.191068 | ||||||||
\(640\) | 153.410i | 0.239703i | ||||||||
\(641\) | − | 984.048i | − | 1.53518i | −0.640944 | − | 0.767588i | \(-0.721457\pi\) | ||
0.640944 | − | 0.767588i | \(-0.278543\pi\) | |||||||
\(642\) | 366.100i | 0.570249i | ||||||||
\(643\) | − | 514.028i | − | 0.799422i | −0.916641 | − | 0.399711i | \(-0.869111\pi\) | ||
0.916641 | − | 0.399711i | \(-0.130889\pi\) | |||||||
\(644\) | −16.0625 | + | 75.8735i | −0.0249418 | + | 0.117816i | ||||
\(645\) | 342.778 | 0.531439 | ||||||||
\(646\) | −63.8592 | −0.0988532 | ||||||||
\(647\) | −590.304 | −0.912371 | −0.456186 | − | 0.889885i | \(-0.650785\pi\) | ||||
−0.456186 | + | 0.889885i | \(0.650785\pi\) | |||||||
\(648\) | 78.3695 | 0.120941 | ||||||||
\(649\) | − | 148.602i | − | 0.228971i | ||||||
\(650\) | −90.6944 | −0.139530 | ||||||||
\(651\) | − | 138.072i | − | 0.212092i | ||||||
\(652\) | −78.9285 | −0.121056 | ||||||||
\(653\) | −133.633 | −0.204644 | −0.102322 | − | 0.994751i | \(-0.532627\pi\) | ||||
−0.102322 | + | 0.994751i | \(0.532627\pi\) | |||||||
\(654\) | − | 134.912i | − | 0.206288i | ||||||
\(655\) | − | 285.034i | − | 0.435167i | ||||||
\(656\) | −547.181 | −0.834117 | ||||||||
\(657\) | −171.890 | −0.261628 | ||||||||
\(658\) | 34.7269i | 0.0527764i | ||||||||
\(659\) | − | 219.218i | − | 0.332652i | −0.986071 | − | 0.166326i | \(-0.946810\pi\) | ||
0.986071 | − | 0.166326i | \(-0.0531904\pi\) | |||||||
\(660\) | 42.3132 | 0.0641109 | ||||||||
\(661\) | 55.5775i | 0.0840809i | 0.999116 | + | 0.0420405i | \(0.0133858\pi\) | ||||
−0.999116 | + | 0.0420405i | \(0.986614\pi\) | |||||||
\(662\) | −956.654 | −1.44510 | ||||||||
\(663\) | 40.8808i | 0.0616603i | ||||||||
\(664\) | 334.651i | 0.503993i | ||||||||
\(665\) | − | 138.779i | − | 0.208690i | ||||||
\(666\) | 308.118i | 0.462640i | ||||||||
\(667\) | −143.028 | − | 30.2792i | −0.214435 | − | 0.0453961i | ||||
\(668\) | −297.416 | −0.445233 | ||||||||
\(669\) | 277.227 | 0.414390 | ||||||||
\(670\) | 700.353 | 1.04530 | ||||||||
\(671\) | 372.409 | 0.555007 | ||||||||
\(672\) | − | 89.4247i | − | 0.133072i | ||||||
\(673\) | −163.832 | −0.243435 | −0.121718 | − | 0.992565i | \(-0.538840\pi\) | ||||
−0.121718 | + | 0.992565i | \(0.538840\pi\) | |||||||
\(674\) | 100.513i | 0.149129i | ||||||||
\(675\) | −37.5917 | −0.0556915 | ||||||||
\(676\) | 141.898 | 0.209908 | ||||||||
\(677\) | − | 1154.10i | − | 1.70473i | −0.522949 | − | 0.852364i | \(-0.675168\pi\) | ||
0.522949 | − | 0.852364i | \(-0.324832\pi\) | |||||||
\(678\) | − | 425.708i | − | 0.627887i | ||||||
\(679\) | −180.933 | −0.266470 | ||||||||
\(680\) | −114.079 | −0.167763 | ||||||||
\(681\) | 100.949i | 0.148237i | ||||||||
\(682\) | 226.211i | 0.331688i | ||||||||
\(683\) | 791.579 | 1.15897 | 0.579487 | − | 0.814982i | \(-0.303253\pi\) | ||||
0.579487 | + | 0.814982i | \(0.303253\pi\) | |||||||
\(684\) | − | 47.5817i | − | 0.0695639i | ||||||
\(685\) | −195.784 | −0.285816 | ||||||||
\(686\) | − | 30.5754i | − | 0.0445705i | ||||||
\(687\) | 163.741i | 0.238342i | ||||||||
\(688\) | 435.620i | 0.633168i | ||||||||
\(689\) | 186.211i | 0.270263i | ||||||||
\(690\) | 57.4123 | − | 271.195i | 0.0832062 | − | 0.393036i | ||||
\(691\) | −637.514 | −0.922597 | −0.461298 | − | 0.887245i | \(-0.652616\pi\) | ||||
−0.461298 | + | 0.887245i | \(0.652616\pi\) | |||||||
\(692\) | −32.7632 | −0.0473456 | ||||||||
\(693\) | 36.0964 | 0.0520871 | ||||||||
\(694\) | 145.721 | 0.209972 | ||||||||
\(695\) | − | 130.096i | − | 0.187189i | ||||||
\(696\) | 95.8690 | 0.137743 | ||||||||
\(697\) | − | 183.316i | − | 0.263007i | ||||||
\(698\) | 29.8025 | 0.0426971 | ||||||||
\(699\) | −756.239 | −1.08189 | ||||||||
\(700\) | 24.3946i | 0.0348494i | ||||||||
\(701\) | − | 1124.94i | − | 1.60476i | −0.596811 | − | 0.802382i | \(-0.703566\pi\) | ||
0.596811 | − | 0.802382i | \(-0.296434\pi\) | |||||||
\(702\) | 65.1406 | 0.0927929 | ||||||||
\(703\) | 774.207 | 1.10129 | ||||||||
\(704\) | 315.280i | 0.447841i | ||||||||
\(705\) | 58.0419i | 0.0823289i | ||||||||
\(706\) | 389.835 | 0.552174 | ||||||||
\(707\) | 455.407i | 0.644140i | ||||||||
\(708\) | −72.1315 | −0.101881 | ||||||||
\(709\) | − | 313.320i | − | 0.441918i | −0.975283 | − | 0.220959i | \(-0.929081\pi\) | ||
0.975283 | − | 0.220959i | \(-0.0709187\pi\) | |||||||
\(710\) | − | 283.192i | − | 0.398862i | ||||||
\(711\) | − | 348.162i | − | 0.489680i | ||||||
\(712\) | 186.198i | 0.261514i | ||||||||
\(713\) | −677.960 | − | 143.525i | −0.950855 | − | 0.201297i | ||||
\(714\) | −23.5151 | −0.0329344 | ||||||||
\(715\) | 145.555 | 0.203573 | ||||||||
\(716\) | −163.261 | −0.228018 | ||||||||
\(717\) | −243.209 | −0.339204 | ||||||||
\(718\) | − | 92.9224i | − | 0.129418i | ||||||
\(719\) | −739.371 | −1.02833 | −0.514166 | − | 0.857691i | \(-0.671899\pi\) | ||||
−0.514166 | + | 0.857691i | \(0.671899\pi\) | |||||||
\(720\) | 117.315i | 0.162937i | ||||||||
\(721\) | 289.125 | 0.401006 | ||||||||
\(722\) | −340.301 | −0.471331 | ||||||||
\(723\) | 364.062i | 0.503544i | ||||||||
\(724\) | 289.610i | 0.400014i | ||||||||
\(725\) | −45.9858 | −0.0634287 | ||||||||
\(726\) | 286.857 | 0.395120 | ||||||||
\(727\) | − | 314.072i | − | 0.432010i | −0.976392 | − | 0.216005i | \(-0.930697\pi\) | ||
0.976392 | − | 0.216005i | \(-0.0693028\pi\) | |||||||
\(728\) | − | 174.944i | − | 0.240307i | ||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | − | 398.696i | − | 0.546159i | ||||||
\(731\) | −145.941 | −0.199646 | ||||||||
\(732\) | − | 180.768i | − | 0.246951i | ||||||
\(733\) | 1294.12i | 1.76552i | 0.469828 | + | 0.882758i | \(0.344316\pi\) | ||||
−0.469828 | + | 0.882758i | \(0.655684\pi\) | |||||||
\(734\) | − | 594.508i | − | 0.809956i | ||||||
\(735\) | − | 51.1031i | − | 0.0695280i | ||||||
\(736\) | −439.092 | − | 92.9563i | −0.596592 | − | 0.126299i | ||||
\(737\) | 457.717 | 0.621055 | ||||||||
\(738\) | −292.101 | −0.395801 | ||||||||
\(739\) | 816.696 | 1.10514 | 0.552568 | − | 0.833468i | \(-0.313648\pi\) | ||||
0.552568 | + | 0.833468i | \(0.313648\pi\) | |||||||
\(740\) | 334.190 | 0.451608 | ||||||||
\(741\) | − | 163.678i | − | 0.220889i | ||||||
\(742\) | −107.111 | −0.144354 | ||||||||
\(743\) | 983.833i | 1.32414i | 0.749444 | + | 0.662068i | \(0.230321\pi\) | ||||
−0.749444 | + | 0.662068i | \(0.769679\pi\) | |||||||
\(744\) | 454.424 | 0.610785 | ||||||||
\(745\) | 133.323 | 0.178958 | ||||||||
\(746\) | 101.703i | 0.136331i | ||||||||
\(747\) | 115.295i | 0.154344i | ||||||||
\(748\) | −18.0153 | −0.0240846 | ||||||||
\(749\) | 338.737 | 0.452253 | ||||||||
\(750\) | − | 388.503i | − | 0.518005i | ||||||
\(751\) | − | 209.234i | − | 0.278608i | −0.990250 | − | 0.139304i | \(-0.955514\pi\) | ||
0.990250 | − | 0.139304i | \(-0.0444864\pi\) | |||||||
\(752\) | −73.7626 | −0.0980885 | ||||||||
\(753\) | 858.835i | 1.14055i | ||||||||
\(754\) | 79.6862 | 0.105685 | ||||||||
\(755\) | 352.865i | 0.467371i | ||||||||
\(756\) | − | 17.5212i | − | 0.0231762i | ||||||
\(757\) | − | 780.239i | − | 1.03070i | −0.856980 | − | 0.515349i | \(-0.827662\pi\) | ||
0.856980 | − | 0.515349i | \(-0.172338\pi\) | |||||||
\(758\) | − | 152.196i | − | 0.200786i | ||||||
\(759\) | 37.5219 | − | 177.240i | 0.0494360 | − | 0.233518i | ||||
\(760\) | 456.750 | 0.600986 | ||||||||
\(761\) | 79.2597 | 0.104152 | 0.0520760 | − | 0.998643i | \(-0.483416\pi\) | ||||
0.0520760 | + | 0.998643i | \(0.483416\pi\) | |||||||
\(762\) | −501.194 | −0.657735 | ||||||||
\(763\) | −124.829 | −0.163603 | ||||||||
\(764\) | 103.498i | 0.135469i | ||||||||
\(765\) | −39.3027 | −0.0513761 | ||||||||
\(766\) | − | 468.357i | − | 0.611432i | ||||||
\(767\) | −248.128 | −0.323505 | ||||||||
\(768\) | 376.237 | 0.489892 | ||||||||
\(769\) | − | 648.022i | − | 0.842681i | −0.906902 | − | 0.421341i | \(-0.861560\pi\) | ||
0.906902 | − | 0.421341i | \(-0.138440\pi\) | |||||||
\(770\) | 83.7250i | 0.108734i | ||||||||
\(771\) | 497.606 | 0.645403 | ||||||||
\(772\) | −8.74944 | −0.0113335 | ||||||||
\(773\) | 485.666i | 0.628287i | 0.949376 | + | 0.314143i | \(0.101717\pi\) | ||||
−0.949376 | + | 0.314143i | \(0.898283\pi\) | |||||||
\(774\) | 232.547i | 0.300448i | ||||||||
\(775\) | −217.975 | −0.281258 | ||||||||
\(776\) | − | 595.488i | − | 0.767382i | ||||||
\(777\) | 285.090 | 0.366911 | ||||||||
\(778\) | 768.820i | 0.988200i | ||||||||
\(779\) | 733.961i | 0.942183i | ||||||||
\(780\) | − | 70.6525i | − | 0.0905802i | ||||||
\(781\) | − | 185.081i | − | 0.236979i | ||||||
\(782\) | −24.4438 | + | 115.464i | −0.0312581 | + | 0.147652i | ||||
\(783\) | 33.0290 | 0.0421826 | ||||||||
\(784\) | 64.9444 | 0.0828372 | ||||||||
\(785\) | 903.480 | 1.15093 | ||||||||
\(786\) | 193.372 | 0.246021 | ||||||||
\(787\) | 328.821i | 0.417816i | 0.977935 | + | 0.208908i | \(0.0669910\pi\) | ||||
−0.977935 | + | 0.208908i | \(0.933009\pi\) | |||||||
\(788\) | −208.375 | −0.264435 | ||||||||
\(789\) | 84.6378i | 0.107272i | ||||||||
\(790\) | 807.557 | 1.02222 | ||||||||
\(791\) | −393.890 | −0.497965 | ||||||||
\(792\) | 118.801i | 0.150001i | ||||||||
\(793\) | − | 621.831i | − | 0.784150i | ||||||
\(794\) | 789.584 | 0.994438 | ||||||||
\(795\) | −179.023 | −0.225186 | ||||||||
\(796\) | − | 164.733i | − | 0.206951i | ||||||
\(797\) | − | 210.642i | − | 0.264294i | −0.991230 | − | 0.132147i | \(-0.957813\pi\) | ||
0.991230 | − | 0.132147i | \(-0.0421871\pi\) | |||||||
\(798\) | 94.1499 | 0.117982 | ||||||||
\(799\) | − | 24.7119i | − | 0.0309285i | ||||||
\(800\) | −141.175 | −0.176469 | ||||||||
\(801\) | 64.1493i | 0.0800865i | ||||||||
\(802\) | 145.613i | 0.181562i | ||||||||
\(803\) | − | 260.569i | − | 0.324494i | ||||||
\(804\) | − | 222.176i | − | 0.276339i | ||||||
\(805\) | −250.926 | − | 53.1213i | −0.311709 | − | 0.0659892i | ||||
\(806\) | 377.717 | 0.468631 | ||||||||
\(807\) | 439.433 | 0.544526 | ||||||||
\(808\) | −1498.84 | −1.85500 | ||||||||
\(809\) | 970.805 | 1.20001 | 0.600003 | − | 0.799998i | \(-0.295166\pi\) | ||||
0.600003 | + | 0.799998i | \(0.295166\pi\) | |||||||
\(810\) | 62.6261i | 0.0773162i | ||||||||
\(811\) | 412.410 | 0.508521 | 0.254260 | − | 0.967136i | \(-0.418168\pi\) | ||||
0.254260 | + | 0.967136i | \(0.418168\pi\) | |||||||
\(812\) | − | 21.4336i | − | 0.0263961i | ||||||
\(813\) | 519.036 | 0.638421 | ||||||||
\(814\) | −467.078 | −0.573806 | ||||||||
\(815\) | − | 261.029i | − | 0.320281i | ||||||
\(816\) | − | 49.9479i | − | 0.0612107i | ||||||
\(817\) | 584.318 | 0.715200 | ||||||||
\(818\) | −628.273 | −0.768060 | ||||||||
\(819\) | − | 60.2720i | − | 0.0735922i | ||||||
\(820\) | 316.817i | 0.386363i | ||||||||
\(821\) | −1141.98 | −1.39097 | −0.695483 | − | 0.718543i | \(-0.744809\pi\) | ||||
−0.695483 | + | 0.718543i | \(0.744809\pi\) | |||||||
\(822\) | − | 132.823i | − | 0.161586i | ||||||
\(823\) | −238.245 | −0.289483 | −0.144742 | − | 0.989469i | \(-0.546235\pi\) | ||||
−0.144742 | + | 0.989469i | \(0.546235\pi\) | |||||||
\(824\) | 951.570i | 1.15482i | ||||||||
\(825\) | − | 56.9855i | − | 0.0690734i | ||||||
\(826\) | − | 142.726i | − | 0.172792i | ||||||
\(827\) | − | 878.553i | − | 1.06234i | −0.847266 | − | 0.531169i | \(-0.821753\pi\) | ||
0.847266 | − | 0.531169i | \(-0.178247\pi\) | |||||||
\(828\) | −86.0325 | − | 18.2132i | −0.103904 | − | 0.0219966i | ||||
\(829\) | −90.5985 | −0.109287 | −0.0546433 | − | 0.998506i | \(-0.517402\pi\) | ||||
−0.0546433 | + | 0.998506i | \(0.517402\pi\) | |||||||
\(830\) | −267.424 | −0.322198 | ||||||||
\(831\) | −200.260 | −0.240987 | ||||||||
\(832\) | 526.440 | 0.632740 | ||||||||
\(833\) | 21.7576i | 0.0261196i | ||||||||
\(834\) | 88.2597 | 0.105827 | ||||||||
\(835\) | − | 983.601i | − | 1.17796i | ||||||
\(836\) | 72.1294 | 0.0862792 | ||||||||
\(837\) | 156.559 | 0.187048 | ||||||||
\(838\) | − | 1240.36i | − | 1.48014i | ||||||
\(839\) | 1062.29i | 1.26614i | 0.774095 | + | 0.633069i | \(0.218205\pi\) | ||||
−0.774095 | + | 0.633069i | \(0.781795\pi\) | |||||||
\(840\) | 168.191 | 0.200227 | ||||||||
\(841\) | −800.596 | −0.951957 | ||||||||
\(842\) | 1212.36i | 1.43985i | ||||||||
\(843\) | 861.773i | 1.02227i | ||||||||
\(844\) | 121.778 | 0.144287 | ||||||||
\(845\) | 469.279i | 0.555360i | ||||||||
\(846\) | −39.3766 | −0.0465444 | ||||||||
\(847\) | − | 265.417i | − | 0.313361i | ||||||
\(848\) | − | 227.512i | − | 0.268292i | ||||||
\(849\) | 343.925i | 0.405095i | ||||||||
\(850\) | 37.1235i | 0.0436747i | ||||||||
\(851\) | 296.349 | − | 1399.84i | 0.348236 | − | 1.64494i | ||||
\(852\) | −89.8385 | −0.105444 | ||||||||
\(853\) | −21.3731 | −0.0250564 | −0.0125282 | − | 0.999922i | \(-0.503988\pi\) | ||||
−0.0125282 | + | 0.999922i | \(0.503988\pi\) | |||||||
\(854\) | 357.685 | 0.418835 | ||||||||
\(855\) | 157.360 | 0.184047 | ||||||||
\(856\) | 1114.86i | 1.30240i | ||||||||
\(857\) | −102.520 | −0.119627 | −0.0598133 | − | 0.998210i | \(-0.519051\pi\) | ||||
−0.0598133 | + | 0.998210i | \(0.519051\pi\) | |||||||
\(858\) | 98.7470i | 0.115090i | ||||||||
\(859\) | −454.836 | −0.529494 | −0.264747 | − | 0.964318i | \(-0.585289\pi\) | ||||
−0.264747 | + | 0.964318i | \(0.585289\pi\) | |||||||
\(860\) | 252.224 | 0.293283 | ||||||||
\(861\) | 270.269i | 0.313902i | ||||||||
\(862\) | − | 482.012i | − | 0.559178i | ||||||
\(863\) | −242.685 | −0.281211 | −0.140605 | − | 0.990066i | \(-0.544905\pi\) | ||||
−0.140605 | + | 0.990066i | \(0.544905\pi\) | |||||||
\(864\) | 101.398 | 0.117359 | ||||||||
\(865\) | − | 108.353i | − | 0.125263i | ||||||
\(866\) | − | 990.166i | − | 1.14338i | ||||||
\(867\) | −483.829 | −0.558050 | ||||||||
\(868\) | − | 101.597i | − | 0.117047i | ||||||
\(869\) | 527.781 | 0.607343 | ||||||||
\(870\) | 76.6102i | 0.0880577i | ||||||||
\(871\) | − | 764.274i | − | 0.877467i | ||||||
\(872\) | − | 410.837i | − | 0.471144i | ||||||
\(873\) | − | 205.159i | − | 0.235004i | ||||||
\(874\) | 97.8681 | − | 462.293i | 0.111977 | − | 0.528940i | ||||
\(875\) | −359.467 | −0.410819 | ||||||||
\(876\) | −126.480 | −0.144384 | ||||||||
\(877\) | −1002.21 | −1.14277 | −0.571386 | − | 0.820681i | \(-0.693594\pi\) | ||||
−0.571386 | + | 0.820681i | \(0.693594\pi\) | |||||||
\(878\) | −71.2324 | −0.0811303 | ||||||||
\(879\) | − | 125.260i | − | 0.142503i | ||||||
\(880\) | −177.838 | −0.202089 | ||||||||
\(881\) | − | 348.088i | − | 0.395105i | −0.980292 | − | 0.197553i | \(-0.936701\pi\) | ||
0.980292 | − | 0.197553i | \(-0.0632994\pi\) | |||||||
\(882\) | 34.6692 | 0.0393075 | ||||||||
\(883\) | −1154.44 | −1.30740 | −0.653701 | − | 0.756753i | \(-0.726784\pi\) | ||||
−0.653701 | + | 0.756753i | \(0.726784\pi\) | |||||||
\(884\) | 30.0810i | 0.0340283i | ||||||||
\(885\) | − | 238.550i | − | 0.269548i | ||||||
\(886\) | −263.652 | −0.297576 | ||||||||
\(887\) | 1473.62 | 1.66135 | 0.830676 | − | 0.556756i | \(-0.187954\pi\) | ||||
0.830676 | + | 0.556756i | \(0.187954\pi\) | |||||||
\(888\) | 938.289i | 1.05663i | ||||||||
\(889\) | 463.735i | 0.521636i | ||||||||
\(890\) | −148.793 | −0.167184 | ||||||||
\(891\) | 40.9295i | 0.0459365i | ||||||||
\(892\) | 203.990 | 0.228688 | ||||||||
\(893\) | 98.9414i | 0.110797i | ||||||||
\(894\) | 90.4490i | 0.101173i | ||||||||
\(895\) | − | 539.930i | − | 0.603273i | ||||||
\(896\) | 96.2972i | 0.107475i | ||||||||
\(897\) | −295.947 | − | 62.6523i | −0.329929 | − | 0.0698465i | ||||
\(898\) | −910.342 | −1.01374 | ||||||||
\(899\) | 191.518 | 0.213034 | ||||||||
\(900\) | −27.6608 | −0.0307343 | ||||||||
\(901\) | 76.2208 | 0.0845958 | ||||||||
\(902\) | − | 442.798i | − | 0.490907i | ||||||
\(903\) | 215.166 | 0.238279 | ||||||||
\(904\) | − | 1296.37i | − | 1.43404i | ||||||
\(905\) | −957.786 | −1.05833 | ||||||||
\(906\) | −239.390 | −0.264227 | ||||||||
\(907\) | − | 627.159i | − | 0.691466i | −0.938333 | − | 0.345733i | \(-0.887630\pi\) | ||
0.938333 | − | 0.345733i | \(-0.112370\pi\) | |||||||
\(908\) | 74.2808i | 0.0818070i | ||||||||
\(909\) | −516.383 | −0.568078 | ||||||||
\(910\) | 139.800 | 0.153626 | ||||||||
\(911\) | 1207.37i | 1.32532i | 0.748919 | + | 0.662662i | \(0.230573\pi\) | ||||
−0.748919 | + | 0.662662i | \(0.769427\pi\) | |||||||
\(912\) | 199.981i | 0.219278i | ||||||||
\(913\) | −174.776 | −0.191430 | ||||||||
\(914\) | − | 738.562i | − | 0.808055i | ||||||
\(915\) | 597.828 | 0.653364 | ||||||||
\(916\) | 120.484i | 0.131533i | ||||||||
\(917\) | − | 178.920i | − | 0.195114i | ||||||
\(918\) | − | 26.6637i | − | 0.0290454i | ||||||
\(919\) | 1055.99i | 1.14907i | 0.818481 | + | 0.574533i | \(0.194816\pi\) | ||||
−0.818481 | + | 0.574533i | \(0.805184\pi\) | |||||||
\(920\) | 174.833 | − | 825.848i | 0.190036 | − | 0.897661i | ||||
\(921\) | −291.101 | −0.316071 | ||||||||
\(922\) | 905.724 | 0.982347 | ||||||||
\(923\) | −309.039 | −0.334820 | ||||||||
\(924\) | 26.5605 | 0.0287452 | ||||||||
\(925\) | − | 450.072i | − | 0.486565i | ||||||
\(926\) | 57.3967 | 0.0619835 | ||||||||
\(927\) | 327.837i | 0.353654i | ||||||||
\(928\) | 124.040 | 0.133664 | ||||||||
\(929\) | −444.106 | −0.478048 | −0.239024 | − | 0.971014i | \(-0.576827\pi\) | ||||
−0.239024 | + | 0.971014i | \(0.576827\pi\) | |||||||
\(930\) | 363.136i | 0.390469i | ||||||||
\(931\) | − | 87.1131i | − | 0.0935694i | ||||||
\(932\) | −556.458 | −0.597058 | ||||||||
\(933\) | −170.492 | −0.182735 | ||||||||
\(934\) | − | 20.7264i | − | 0.0221910i | ||||||
\(935\) | − | 59.5793i | − | 0.0637211i | ||||||
\(936\) | 198.368 | 0.211931 | ||||||||
\(937\) | − | 378.621i | − | 0.404078i | −0.979377 | − | 0.202039i | \(-0.935243\pi\) | ||
0.979377 | − | 0.202039i | \(-0.0647567\pi\) | |||||||
\(938\) | 439.620 | 0.468678 | ||||||||
\(939\) | 777.691i | 0.828212i | ||||||||
\(940\) | 42.7085i | 0.0454346i | ||||||||
\(941\) | − | 1375.22i | − | 1.46145i | −0.682672 | − | 0.730725i | \(-0.739182\pi\) | ||
0.682672 | − | 0.730725i | \(-0.260818\pi\) | |||||||
\(942\) | 612.936i | 0.650675i | ||||||||
\(943\) | 1327.07 | + | 280.943i | 1.40729 | + | 0.297925i | ||||
\(944\) | 303.162 | 0.321146 | ||||||||
\(945\) | 57.9454 | 0.0613179 | ||||||||
\(946\) | −352.519 | −0.372641 | ||||||||
\(947\) | −1169.55 | −1.23501 | −0.617505 | − | 0.786567i | \(-0.711857\pi\) | ||||
−0.617505 | + | 0.786567i | \(0.711857\pi\) | |||||||
\(948\) | − | 256.186i | − | 0.270238i | ||||||
\(949\) | −435.085 | −0.458467 | ||||||||
\(950\) | − | 148.635i | − | 0.156458i | ||||||
\(951\) | −112.181 | −0.117961 | ||||||||
\(952\) | −71.6088 | −0.0752194 | ||||||||
\(953\) | 155.595i | 0.163269i | 0.996662 | + | 0.0816343i | \(0.0260139\pi\) | ||||
−0.996662 | + | 0.0816343i | \(0.973986\pi\) | |||||||
\(954\) | − | 121.452i | − | 0.127309i | ||||||
\(955\) | −342.286 | −0.358414 | ||||||||
\(956\) | −178.959 | −0.187195 | ||||||||
\(957\) | 50.0688i | 0.0523185i | ||||||||
\(958\) | − | 667.482i | − | 0.696745i | ||||||
\(959\) | −122.896 | −0.128150 | ||||||||
\(960\) | 506.118i | 0.527207i | ||||||||
\(961\) | −53.1946 | −0.0553534 | ||||||||
\(962\) | 779.905i | 0.810712i | ||||||||
\(963\) | 384.092i | 0.398850i | ||||||||
\(964\) | 267.885i | 0.277889i | ||||||||
\(965\) | − | 28.9358i | − | 0.0299853i | ||||||
\(966\) | 36.0384 | − | 170.232i | 0.0373068 | − | 0.176224i | ||||
\(967\) | −153.295 | −0.158526 | −0.0792630 | − | 0.996854i | \(-0.525257\pi\) | ||||
−0.0792630 | + | 0.996854i | \(0.525257\pi\) | |||||||
\(968\) | 873.543 | 0.902421 | ||||||||
\(969\) | −66.9976 | −0.0691410 | ||||||||
\(970\) | 475.863 | 0.490580 | ||||||||
\(971\) | − | 762.447i | − | 0.785218i | −0.919705 | − | 0.392609i | \(-0.871573\pi\) | ||
0.919705 | − | 0.392609i | \(-0.128427\pi\) | |||||||
\(972\) | 19.8672 | 0.0204395 | ||||||||
\(973\) | − | 81.6632i | − | 0.0839293i | ||||||
\(974\) | −1147.03 | −1.17765 | ||||||||
\(975\) | −95.1517 | −0.0975915 | ||||||||
\(976\) | 759.750i | 0.778433i | ||||||||
\(977\) | 862.652i | 0.882960i | 0.897271 | + | 0.441480i | \(0.145546\pi\) | ||||
−0.897271 | + | 0.441480i | \(0.854454\pi\) | |||||||
\(978\) | 177.086 | 0.181070 | ||||||||
\(979\) | −97.2443 | −0.0993303 | ||||||||
\(980\) | − | 37.6028i | − | 0.0383702i | ||||||
\(981\) | − | 141.543i | − | 0.144284i | ||||||
\(982\) | −1067.87 | −1.08744 | ||||||||
\(983\) | 510.011i | 0.518831i | 0.965766 | + | 0.259416i | \(0.0835300\pi\) | ||||
−0.965766 | + | 0.259416i | \(0.916470\pi\) | |||||||
\(984\) | −889.513 | −0.903976 | ||||||||
\(985\) | − | 689.128i | − | 0.699623i | ||||||
\(986\) | − | 32.6175i | − | 0.0330807i | ||||||
\(987\) | 36.4336i | 0.0369135i | ||||||||
\(988\) | − | 120.438i | − | 0.121901i | ||||||
\(989\) | 223.664 | − | 1056.51i | 0.226151 | − | 1.06826i | ||||
\(990\) | −94.9353 | −0.0958942 | ||||||||
\(991\) | −108.953 | −0.109942 | −0.0549710 | − | 0.998488i | \(-0.517507\pi\) | ||||
−0.0549710 | + | 0.998488i | \(0.517507\pi\) | |||||||
\(992\) | 587.955 | 0.592697 | ||||||||
\(993\) | −1003.67 | −1.01075 | ||||||||
\(994\) | − | 177.763i | − | 0.178836i | ||||||
\(995\) | 544.797 | 0.547534 | ||||||||
\(996\) | 84.8364i | 0.0851771i | ||||||||
\(997\) | 457.929 | 0.459307 | 0.229654 | − | 0.973272i | \(-0.426241\pi\) | ||||
0.229654 | + | 0.973272i | \(0.426241\pi\) | |||||||
\(998\) | 1500.71 | 1.50372 | ||||||||
\(999\) | 323.261i | 0.323585i |
(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 | 483.3.f.a.22.16 | yes | 48 | |
23.22 | odd | 2 | inner | 483.3.f.a.22.15 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.3.f.a.22.15 | ✓ | 48 | 23.22 | odd | 2 | inner | |
483.3.f.a.22.16 | yes | 48 | 1.1 | even | 1 | trivial |