Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4140,3,Mod(2161,4140)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4140, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4140.2161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 4140.d (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: | \(112.806829445\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2161.17 | ||
Character | \(\chi\) | \(=\) | 4140.2161 |
Dual form | 4140.3.d.b.2161.16 |
$q$-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 \(\left(\mathbb{Z}/4140\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(2071\) | \(3961\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 13.2033i | − | 1.88618i | −0.332535 | − | 0.943091i | \(-0.607904\pi\) | ||
0.332535 | − | 0.943091i | \(-0.392096\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.2113i | 1.01921i | 0.860409 | + | 0.509604i | \(0.170208\pi\) | ||||
−0.860409 | + | 0.509604i | \(0.829792\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −17.4654 | −1.34349 | −0.671746 | − | 0.740782i | \(-0.734455\pi\) | ||||
−0.671746 | + | 0.740782i | \(0.734455\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 22.0956i | − | 1.29974i | −0.760044 | − | 0.649871i | \(-0.774823\pi\) | ||
0.760044 | − | 0.649871i | \(-0.225177\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.38843i | 0.336233i | 0.985767 | + | 0.168117i | \(0.0537685\pi\) | ||||
−0.985767 | + | 0.168117i | \(0.946232\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −22.3859 | − | 5.27944i | −0.973299 | − | 0.229541i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 26.6662 | 0.919524 | 0.459762 | − | 0.888042i | \(-0.347935\pi\) | ||||
0.459762 | + | 0.888042i | \(0.347935\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −17.2415 | −0.556178 | −0.278089 | − | 0.960555i | \(-0.589701\pi\) | ||||
−0.278089 | + | 0.960555i | \(0.589701\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 29.5234 | 0.843526 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 33.5497i | 0.906747i | 0.891321 | + | 0.453374i | \(0.149780\pi\) | ||||
−0.891321 | + | 0.453374i | \(0.850220\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.39969 | 0.229261 | 0.114630 | − | 0.993408i | \(-0.463432\pi\) | ||||
0.114630 | + | 0.993408i | \(0.463432\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 34.5042i | − | 0.802424i | −0.915985 | − | 0.401212i | \(-0.868589\pi\) | ||
0.915985 | − | 0.401212i | \(-0.131411\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.525339 | 0.0111774 | 0.00558872 | − | 0.999984i | \(-0.498221\pi\) | ||||
0.00558872 | + | 0.999984i | \(0.498221\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −125.326 | −2.55768 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1.66679i | − | 0.0314488i | −0.999876 | − | 0.0157244i | \(-0.994995\pi\) | ||
0.999876 | − | 0.0157244i | \(-0.00500543\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −25.0692 | −0.455803 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.8063 | 0.217057 | 0.108528 | − | 0.994093i | \(-0.465386\pi\) | ||||
0.108528 | + | 0.994093i | \(0.465386\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 74.9031i | 1.22792i | 0.789337 | + | 0.613960i | \(0.210424\pi\) | ||||
−0.789337 | + | 0.613960i | \(0.789576\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 39.0538i | − | 0.600828i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 42.5332i | − | 0.634824i | −0.948288 | − | 0.317412i | \(-0.897186\pi\) | ||
0.948288 | − | 0.317412i | \(-0.102814\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 30.9853 | 0.436412 | 0.218206 | − | 0.975903i | \(-0.429979\pi\) | ||||
0.218206 | + | 0.975903i | \(0.429979\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −21.1091 | −0.289166 | −0.144583 | − | 0.989493i | \(-0.546184\pi\) | ||||
−0.144583 | + | 0.989493i | \(0.546184\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 148.026 | 1.92241 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 25.5678i | 0.323643i | 0.986820 | + | 0.161821i | \(0.0517369\pi\) | ||||
−0.986820 | + | 0.161821i | \(0.948263\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 31.7749i | 0.382830i | 0.981509 | + | 0.191415i | \(0.0613076\pi\) | ||||
−0.981509 | + | 0.191415i | \(0.938692\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 49.4073 | 0.581263 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 90.7583i | 1.01976i | 0.860247 | + | 0.509878i | \(0.170310\pi\) | ||||
−0.860247 | + | 0.509878i | \(0.829690\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 230.600i | 2.53407i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −14.2850 | −0.150368 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 51.5745i | 0.531696i | 0.964015 | + | 0.265848i | \(0.0856520\pi\) | ||||
−0.964015 | + | 0.265848i | \(0.914348\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.4508 | −0.152979 | −0.0764893 | − | 0.997070i | \(-0.524371\pi\) | ||||
−0.0764893 | + | 0.997070i | \(0.524371\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.31402i | 0.0904274i | 0.998977 | + | 0.0452137i | \(0.0143969\pi\) | ||||
−0.998977 | + | 0.0452137i | \(0.985603\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 157.134i | 1.46855i | 0.678854 | + | 0.734273i | \(0.262477\pi\) | ||||
−0.678854 | + | 0.734273i | \(0.737523\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 117.792i | 1.08066i | 0.841453 | + | 0.540330i | \(0.181701\pi\) | ||||
−0.841453 | + | 0.540330i | \(0.818299\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 221.153i | − | 1.95710i | −0.206004 | − | 0.978551i | \(-0.566046\pi\) | ||
0.206004 | − | 0.978551i | \(-0.433954\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.8052 | − | 50.0563i | 0.102654 | − | 0.435273i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −291.735 | −2.45155 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.69276 | −0.0387832 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 35.6835 | 0.280973 | 0.140486 | − | 0.990083i | \(-0.455133\pi\) | ||||
0.140486 | + | 0.990083i | \(0.455133\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.5344 | 0.118583 | 0.0592917 | − | 0.998241i | \(-0.481116\pi\) | ||||
0.0592917 | + | 0.998241i | \(0.481116\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 84.3482 | 0.634197 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 104.295i | − | 0.761278i | −0.924724 | − | 0.380639i | \(-0.875704\pi\) | ||
0.924724 | − | 0.380639i | \(-0.124296\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 109.260 | 0.786047 | 0.393023 | − | 0.919528i | \(-0.371429\pi\) | ||||
0.393023 | + | 0.919528i | \(0.371429\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 195.809i | − | 1.36930i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 59.6275i | 0.411224i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 28.2723i | 0.189747i | 0.995489 | + | 0.0948734i | \(0.0302446\pi\) | ||||
−0.995489 | + | 0.0948734i | \(0.969755\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 193.433 | 1.28102 | 0.640508 | − | 0.767951i | \(-0.278724\pi\) | ||||
0.640508 | + | 0.767951i | \(0.278724\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 38.5532i | − | 0.248730i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 69.1919i | − | 0.440713i | −0.975419 | − | 0.220356i | \(-0.929278\pi\) | ||
0.975419 | − | 0.220356i | \(-0.0707221\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −69.7059 | + | 295.567i | −0.432956 | + | 1.83582i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −37.3290 | −0.229013 | −0.114506 | − | 0.993423i | \(-0.536529\pi\) | ||||
−0.114506 | + | 0.993423i | \(0.536529\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 73.2056 | 0.438357 | 0.219178 | − | 0.975685i | \(-0.429662\pi\) | ||||
0.219178 | + | 0.975685i | \(0.429662\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 136.040 | 0.804970 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −209.810 | −1.21277 | −0.606387 | − | 0.795170i | \(-0.707382\pi\) | ||||
−0.606387 | + | 0.795170i | \(0.707382\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 66.0164i | 0.377236i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −125.483 | −0.701022 | −0.350511 | − | 0.936559i | \(-0.613992\pi\) | ||||
−0.350511 | + | 0.936559i | \(0.613992\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 236.495i | 1.30660i | 0.757098 | + | 0.653301i | \(0.226616\pi\) | ||||
−0.757098 | + | 0.653301i | \(0.773384\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −75.0193 | −0.405510 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 247.720 | 1.32471 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 219.291i | 1.14812i | 0.818813 | + | 0.574061i | \(0.194633\pi\) | ||||
−0.818813 | + | 0.574061i | \(0.805367\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −177.218 | −0.918227 | −0.459114 | − | 0.888378i | \(-0.651833\pi\) | ||||
−0.459114 | + | 0.888378i | \(0.651833\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 323.818 | 1.64375 | 0.821873 | − | 0.569671i | \(-0.192929\pi\) | ||||
0.821873 | + | 0.569671i | \(0.192929\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 135.346i | − | 0.680132i | −0.940402 | − | 0.340066i | \(-0.889551\pi\) | ||
0.940402 | − | 0.340066i | \(-0.110449\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 352.081i | − | 1.73439i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 21.0183i | 0.102528i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −71.6225 | −0.342691 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 345.381 | 1.63688 | 0.818438 | − | 0.574594i | \(-0.194840\pi\) | ||||
0.818438 | + | 0.574594i | \(0.194840\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 77.1538 | 0.358855 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 227.644i | 1.04905i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 385.909i | 1.74619i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 300.887 | 1.34927 | 0.674634 | − | 0.738153i | \(-0.264302\pi\) | ||||
0.674634 | + | 0.738153i | \(0.264302\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 349.586i | 1.54003i | 0.638028 | + | 0.770013i | \(0.279750\pi\) | ||||
−0.638028 | + | 0.770013i | \(0.720250\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.84200i | 0.0298777i | 0.999888 | + | 0.0149389i | \(0.00475537\pi\) | ||||
−0.999888 | + | 0.0149389i | \(0.995245\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −115.673 | −0.496449 | −0.248224 | − | 0.968703i | \(-0.579847\pi\) | ||||
−0.248224 | + | 0.968703i | \(0.579847\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.17469i | 0.00499870i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 147.933 | 0.618966 | 0.309483 | − | 0.950905i | \(-0.399844\pi\) | ||||
0.309483 | + | 0.950905i | \(0.399844\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 249.228i | 1.03414i | 0.855942 | + | 0.517071i | \(0.172978\pi\) | ||||
−0.855942 | + | 0.517071i | \(0.827022\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 280.238i | − | 1.14383i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 111.576i | − | 0.451726i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 41.4671i | − | 0.165208i | −0.996582 | − | 0.0826038i | \(-0.973676\pi\) | ||
0.996582 | − | 0.0826038i | \(-0.0263236\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 59.1893 | − | 250.974i | 0.233950 | − | 0.991993i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 220.328 | 0.857309 | 0.428654 | − | 0.903469i | \(-0.358988\pi\) | ||||
0.428654 | + | 0.903469i | \(0.358988\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 442.965 | 1.71029 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 319.837i | − | 1.21611i | −0.793895 | − | 0.608054i | \(-0.791950\pi\) | ||
0.793895 | − | 0.608054i | \(-0.208050\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.72705 | 0.0140643 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 355.239 | 1.32059 | 0.660295 | − | 0.751006i | \(-0.270431\pi\) | ||||
0.660295 | + | 0.751006i | \(0.270431\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −140.163 | −0.517208 | −0.258604 | − | 0.965983i | \(-0.583263\pi\) | ||||
−0.258604 | + | 0.965983i | \(0.583263\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 56.0564i | − | 0.203841i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −349.667 | −1.26234 | −0.631169 | − | 0.775646i | \(-0.717424\pi\) | ||||
−0.631169 | + | 0.775646i | \(0.717424\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 155.570i | 0.553631i | 0.960923 | + | 0.276815i | \(0.0892790\pi\) | ||||
−0.960923 | + | 0.276815i | \(0.910721\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 430.828i | 1.52236i | 0.648540 | + | 0.761181i | \(0.275380\pi\) | ||||
−0.648540 | + | 0.761181i | \(0.724620\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 124.107i | − | 0.432427i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −199.217 | −0.689331 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 30.1358i | − | 0.102853i | −0.998677 | − | 0.0514263i | \(-0.983623\pi\) | ||
0.998677 | − | 0.0514263i | \(-0.0163767\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 28.6359i | 0.0970707i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 390.978 | + | 92.2075i | 1.30762 | + | 0.308386i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −455.569 | −1.51352 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −167.488 | −0.549142 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −170.383 | −0.554994 | −0.277497 | − | 0.960726i | \(-0.589505\pi\) | ||||
−0.277497 | + | 0.960726i | \(0.589505\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −300.372 | −0.965826 | −0.482913 | − | 0.875668i | \(-0.660421\pi\) | ||||
−0.482913 | + | 0.875668i | \(0.660421\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 320.778i | 1.02485i | 0.858732 | + | 0.512424i | \(0.171253\pi\) | ||||
−0.858732 | + | 0.512424i | \(0.828747\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −488.337 | −1.54050 | −0.770248 | − | 0.637744i | \(-0.779868\pi\) | ||||
−0.770248 | + | 0.637744i | \(0.779868\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 298.962i | 0.937186i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 141.156 | 0.437017 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 87.3270 | 0.268698 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 6.93620i | − | 0.0210827i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −117.006 | −0.353492 | −0.176746 | − | 0.984257i | \(-0.556557\pi\) | ||||
−0.176746 | + | 0.984257i | \(0.556557\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 95.1071 | 0.283902 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 190.806i | 0.566190i | 0.959092 | + | 0.283095i | \(0.0913612\pi\) | ||||
−0.959092 | + | 0.283095i | \(0.908639\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 193.299i | − | 0.566860i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1007.76i | 2.93807i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 633.222 | 1.82485 | 0.912424 | − | 0.409246i | \(-0.134208\pi\) | ||||
0.912424 | + | 0.409246i | \(0.134208\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 353.303 | 1.01233 | 0.506165 | − | 0.862437i | \(-0.331063\pi\) | ||||
0.506165 | + | 0.862437i | \(0.331063\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −615.486 | −1.74359 | −0.871793 | − | 0.489875i | \(-0.837042\pi\) | ||||
−0.871793 | + | 0.489875i | \(0.837042\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 69.2852i | 0.195169i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 503.984i | − | 1.40385i | −0.712249 | − | 0.701927i | \(-0.752323\pi\) | ||
0.712249 | − | 0.701927i | \(-0.247677\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 320.188 | 0.886947 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 47.2013i | − | 0.129319i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 491.044i | 1.33800i | 0.743264 | + | 0.668998i | \(0.233276\pi\) | ||||
−0.743264 | + | 0.668998i | \(0.766724\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.0070 | −0.0593181 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 251.072i | − | 0.673116i | −0.941663 | − | 0.336558i | \(-0.890737\pi\) | ||
0.941663 | − | 0.336558i | \(-0.109263\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −465.736 | −1.23537 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 680.011i | 1.79422i | 0.441804 | + | 0.897112i | \(0.354339\pi\) | ||||
−0.441804 | + | 0.897112i | \(0.645661\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 70.9926i | 0.185359i | 0.995696 | + | 0.0926796i | \(0.0295432\pi\) | ||||
−0.995696 | + | 0.0926796i | \(0.970457\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 330.995i | 0.859728i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 161.082i | 0.414092i | 0.978331 | + | 0.207046i | \(0.0663850\pi\) | ||||
−0.978331 | + | 0.207046i | \(0.933615\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −116.653 | + | 494.630i | −0.298344 | + | 1.26504i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −57.1713 | −0.144738 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −644.249 | −1.62279 | −0.811397 | − | 0.584496i | \(-0.801292\pi\) | ||||
−0.811397 | + | 0.584496i | \(0.801292\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 341.135i | 0.850711i | 0.905026 | + | 0.425356i | \(0.139851\pi\) | ||||
−0.905026 | + | 0.425356i | \(0.860149\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 301.130 | 0.747220 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −376.134 | −0.924163 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −234.203 | −0.572623 | −0.286312 | − | 0.958137i | \(-0.592429\pi\) | ||||
−0.286312 | + | 0.958137i | \(0.592429\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 169.086i | − | 0.409409i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −71.0508 | −0.171207 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 381.051i | 0.909429i | 0.890637 | + | 0.454714i | \(0.150259\pi\) | ||||
−0.890637 | + | 0.454714i | \(0.849741\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 524.072i | − | 1.24483i | −0.782689 | − | 0.622413i | \(-0.786152\pi\) | ||
0.782689 | − | 0.622413i | \(-0.213848\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 110.478i | 0.259949i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 988.966 | 2.31608 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 589.078i | 1.36677i | 0.730058 | + | 0.683385i | \(0.239493\pi\) | ||||
−0.730058 | + | 0.683385i | \(0.760507\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 433.074i | 1.00017i | 0.865976 | + | 0.500085i | \(0.166698\pi\) | ||||
−0.865976 | + | 0.500085i | \(0.833302\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 33.7273 | − | 143.011i | 0.0771792 | − | 0.327255i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −843.550 | −1.92153 | −0.960763 | − | 0.277371i | \(-0.910537\pi\) | ||||
−0.960763 | + | 0.277371i | \(0.910537\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 765.775 | 1.72861 | 0.864305 | − | 0.502967i | \(-0.167758\pi\) | ||||
0.864305 | + | 0.502967i | \(0.167758\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −202.942 | −0.456049 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −773.319 | −1.72231 | −0.861157 | − | 0.508339i | \(-0.830260\pi\) | ||||
−0.861157 | + | 0.508339i | \(0.830260\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 105.383i | 0.233664i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −515.638 | −1.13327 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 598.517i | 1.30966i | 0.755774 | + | 0.654832i | \(0.227261\pi\) | ||||
−0.755774 | + | 0.654832i | \(0.772739\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −58.1169 | −0.126067 | −0.0630335 | − | 0.998011i | \(-0.520077\pi\) | ||||
−0.0630335 | + | 0.998011i | \(0.520077\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −583.571 | −1.26041 | −0.630207 | − | 0.776427i | \(-0.717030\pi\) | ||||
−0.630207 | + | 0.776427i | \(0.717030\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 671.076i | 1.43699i | 0.695531 | + | 0.718496i | \(0.255169\pi\) | ||||
−0.695531 | + | 0.718496i | \(0.744831\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −561.577 | −1.19739 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 386.837 | 0.817836 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 31.9421i | − | 0.0672466i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 162.207i | 0.338637i | 0.985561 | + | 0.169318i | \(0.0541566\pi\) | ||||
−0.985561 | + | 0.169318i | \(0.945843\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 585.958i | − | 1.21821i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −115.324 | −0.237782 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −428.312 | −0.879490 | −0.439745 | − | 0.898123i | \(-0.644931\pi\) | ||||
−0.439745 | + | 0.898123i | \(0.644931\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −324.673 | −0.661248 | −0.330624 | − | 0.943763i | \(-0.607259\pi\) | ||||
−0.330624 | + | 0.943763i | \(0.607259\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 589.207i | − | 1.19515i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 409.107i | − | 0.823153i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 332.157 | 0.665646 | 0.332823 | − | 0.942989i | \(-0.391999\pi\) | ||||
0.332823 | + | 0.942989i | \(0.391999\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 135.734i | − | 0.269849i | −0.990856 | − | 0.134924i | \(-0.956921\pi\) | ||
0.990856 | − | 0.134924i | \(-0.0430792\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 34.5491i | − | 0.0684141i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 822.660 | 1.61623 | 0.808114 | − | 0.589026i | \(-0.200488\pi\) | ||||
0.808114 | + | 0.589026i | \(0.200488\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 278.709i | 0.545419i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −20.8268 | −0.0404403 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.88973i | 0.0113921i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 707.690i | − | 1.35833i | −0.733985 | − | 0.679165i | \(-0.762342\pi\) | ||
0.733985 | − | 0.679165i | \(-0.237658\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 889.599i | 1.70095i | 0.526013 | + | 0.850477i | \(0.323686\pi\) | ||||
−0.526013 | + | 0.850477i | \(0.676314\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 380.962i | 0.722888i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 473.255 | + | 236.370i | 0.894622 | + | 0.446824i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −164.169 | −0.308010 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −351.363 | −0.656754 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1405.07i | − | 2.60681i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −217.745 | −0.402486 | −0.201243 | − | 0.979541i | \(-0.564498\pi\) | ||||
−0.201243 | + | 0.979541i | \(0.564498\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −263.391 | −0.483286 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 523.617 | 0.957252 | 0.478626 | − | 0.878019i | \(-0.341135\pi\) | ||||
0.478626 | + | 0.878019i | \(0.341135\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 170.355i | 0.309175i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 337.579 | 0.610449 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 609.072i | 1.09349i | 0.837300 | + | 0.546743i | \(0.184133\pi\) | ||||
−0.837300 | + | 0.546743i | \(0.815867\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 602.630i | 1.07805i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 547.226i | − | 0.971982i | −0.873964 | − | 0.485991i | \(-0.838459\pi\) | ||
0.873964 | − | 0.485991i | \(-0.161541\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 494.512 | 0.875243 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 960.993i | 1.68892i | 0.535621 | + | 0.844458i | \(0.320077\pi\) | ||||
−0.535621 | + | 0.844458i | \(0.679923\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 28.4911i | − | 0.0498969i | −0.999689 | − | 0.0249484i | \(-0.992058\pi\) | ||
0.999689 | − | 0.0249484i | \(-0.00794216\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 111.929 | + | 26.3972i | 0.194660 | + | 0.0459082i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 324.840 | 0.562980 | 0.281490 | − | 0.959564i | \(-0.409171\pi\) | ||||
0.281490 | + | 0.959564i | \(0.409171\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 419.532 | 0.722086 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.6868 | 0.0320528 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 399.193 | 0.680055 | 0.340028 | − | 0.940415i | \(-0.389564\pi\) | ||||
0.340028 | + | 0.940415i | \(0.389564\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 110.146i | − | 0.187005i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 475.610 | 0.802041 | 0.401021 | − | 0.916069i | \(-0.368656\pi\) | ||||
0.401021 | + | 0.916069i | \(0.368656\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 652.338i | − | 1.09637i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 327.989 | 0.547561 | 0.273780 | − | 0.961792i | \(-0.411726\pi\) | ||||
0.273780 | + | 0.961792i | \(0.411726\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 396.256 | 0.659328 | 0.329664 | − | 0.944098i | \(-0.393065\pi\) | ||||
0.329664 | + | 0.944098i | \(0.393065\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 10.4933i | − | 0.0173444i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −811.377 | −1.33670 | −0.668350 | − | 0.743847i | \(-0.732999\pi\) | ||||
−0.668350 | + | 0.743847i | \(0.732999\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.17526 | −0.0150168 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 133.195i | 0.217284i | 0.994081 | + | 0.108642i | \(0.0346502\pi\) | ||||
−0.994081 | + | 0.108642i | \(0.965350\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 960.566i | − | 1.55683i | −0.627748 | − | 0.778417i | \(-0.716023\pi\) | ||
0.627748 | − | 0.778417i | \(-0.283977\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 213.414i | − | 0.344771i | −0.985030 | − | 0.172386i | \(-0.944852\pi\) | ||
0.985030 | − | 0.172386i | \(-0.0551475\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1198.31 | 1.92345 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 741.301 | 1.17854 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 263.928i | − | 0.418269i | −0.977887 | − | 0.209134i | \(-0.932935\pi\) | ||
0.977887 | − | 0.209134i | \(-0.0670646\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 79.7908i | 0.125655i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2188.88 | 3.43622 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 185.770i | − | 0.289813i | −0.989445 | − | 0.144906i | \(-0.953712\pi\) | ||
0.989445 | − | 0.144906i | \(-0.0462881\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 50.0241i | − | 0.0777979i | −0.999243 | − | 0.0388990i | \(-0.987615\pi\) | ||
0.999243 | − | 0.0388990i | \(-0.0123850\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 686.937 | 1.06173 | 0.530863 | − | 0.847458i | \(-0.321868\pi\) | ||||
0.530863 | + | 0.847458i | \(0.321868\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 143.576i | 0.221226i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1218.00 | −1.86524 | −0.932620 | − | 0.360859i | \(-0.882484\pi\) | ||||
−0.932620 | + | 0.360859i | \(0.882484\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 34.7360i | 0.0530321i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 716.541i | − | 1.08732i | −0.839307 | − | 0.543658i | \(-0.817039\pi\) | ||
0.839307 | − | 0.543658i | \(-0.182961\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 786.925i | − | 1.19051i | −0.803538 | − | 0.595253i | \(-0.797052\pi\) | ||
0.803538 | − | 0.595253i | \(-0.202948\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 188.608i | 0.283621i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −596.946 | − | 140.783i | −0.894972 | − | 0.211068i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −839.759 | −1.25150 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 794.006 | 1.17980 | 0.589900 | − | 0.807476i | \(-0.299167\pi\) | ||||
0.589900 | + | 0.807476i | \(0.299167\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 689.897i | − | 1.01905i | −0.860456 | − | 0.509525i | \(-0.829821\pi\) | ||
0.860456 | − | 0.509525i | \(-0.170179\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 680.953 | 1.00288 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −172.107 | −0.251987 | −0.125993 | − | 0.992031i | \(-0.540212\pi\) | ||||
−0.125993 | + | 0.992031i | \(0.540212\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 233.211 | 0.340454 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 29.1111i | 0.0422512i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 117.871 | 0.170580 | 0.0852900 | − | 0.996356i | \(-0.472818\pi\) | ||||
0.0852900 | + | 0.996356i | \(0.472818\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 244.314i | 0.351531i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 207.692i | − | 0.297980i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 48.6907i | 0.0694590i | 0.999397 | + | 0.0347295i | \(0.0110570\pi\) | ||||
−0.999397 | + | 0.0347295i | \(0.988943\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −214.330 | −0.304878 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 204.002i | 0.288546i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 356.209i | − | 0.502411i | −0.967934 | − | 0.251205i | \(-0.919173\pi\) | ||
0.967934 | − | 0.251205i | \(-0.0808269\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 385.966 | + | 91.0255i | 0.541327 | + | 0.127665i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 437.843 | 0.612368 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 654.975 | 0.910953 | 0.455477 | − | 0.890248i | \(-0.349469\pi\) | ||||
0.455477 | + | 0.890248i | \(0.349469\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 122.976 | 0.170562 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −133.331 | −0.183905 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 498.965i | 0.686334i | 0.939274 | + | 0.343167i | \(0.111500\pi\) | ||||
−0.939274 | + | 0.343167i | \(0.888500\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −762.393 | −1.04294 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 612.320i | − | 0.835362i | −0.908594 | − | 0.417681i | \(-0.862843\pi\) | ||
0.908594 | − | 0.417681i | \(-0.137157\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 476.851 | 0.647017 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −772.436 | −1.04524 | −0.522622 | − | 0.852564i | \(-0.675046\pi\) | ||||
−0.522622 | + | 0.852564i | \(0.675046\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 919.192i | 1.23714i | 0.785731 | + | 0.618568i | \(0.212287\pi\) | ||||
−0.785731 | + | 0.618568i | \(0.787713\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −63.2187 | −0.0848573 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2074.69 | 2.76995 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 910.779i | 1.21276i | 0.795177 | + | 0.606378i | \(0.207378\pi\) | ||||
−0.795177 | + | 0.606378i | \(0.792622\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 432.530i | 0.572888i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 303.316i | 0.400681i | 0.979726 | + | 0.200341i | \(0.0642049\pi\) | ||||
−0.979726 | + | 0.200341i | \(0.935795\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 722.666 | 0.949627 | 0.474814 | − | 0.880086i | \(-0.342515\pi\) | ||||
0.474814 | + | 0.880086i | \(0.342515\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1555.24 | 2.03832 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −223.668 | −0.291614 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1281.01i | 1.66582i | 0.553411 | + | 0.832909i | \(0.313326\pi\) | ||||
−0.553411 | + | 0.832909i | \(0.686674\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 713.668i | 0.923245i | 0.887076 | + | 0.461623i | \(0.152733\pi\) | ||||
−0.887076 | + | 0.461623i | \(0.847267\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 86.2075 | 0.111236 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 60.0492i | 0.0770850i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 347.384i | 0.444794i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 154.718 | 0.197093 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 788.604i | 1.00204i | 0.865436 | + | 0.501019i | \(0.167041\pi\) | ||||
−0.865436 | + | 0.501019i | \(0.832959\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2919.94 | −3.69145 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1308.21i | − | 1.64970i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1090.39i | − | 1.36812i | −0.729426 | − | 0.684060i | \(-0.760213\pi\) | ||
0.729426 | − | 0.684060i | \(-0.239787\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 11.6077i | − | 0.0145278i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 236.660i | − | 0.294720i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −660.908 | − | 155.867i | −0.821003 | − | 0.193624i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −986.070 | −1.21887 | −0.609437 | − | 0.792834i | \(-0.708605\pi\) | ||||
−0.609437 | + | 0.792834i | \(0.708605\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 751.844 | 0.927057 | 0.463529 | − | 0.886082i | \(-0.346583\pi\) | ||||
0.463529 | + | 0.886082i | \(0.346583\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 83.4703i | − | 0.102418i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 220.428 | 0.269802 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1298.45 | −1.58155 | −0.790773 | − | 0.612110i | \(-0.790321\pi\) | ||||
−0.790773 | + | 0.612110i | \(0.790321\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −664.003 | −0.806808 | −0.403404 | − | 0.915022i | \(-0.632173\pi\) | ||||
−0.403404 | + | 0.915022i | \(0.632173\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 204.075i | − | 0.246766i | −0.992359 | − | 0.123383i | \(-0.960626\pi\) | ||
0.992359 | − | 0.123383i | \(-0.0393743\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1234.50 | 1.48914 | 0.744570 | − | 0.667544i | \(-0.232655\pi\) | ||||
0.744570 | + | 0.667544i | \(0.232655\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2769.17i | 3.32433i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 163.693i | 0.196039i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 218.644i | 0.260600i | 0.991475 | + | 0.130300i | \(0.0415941\pi\) | ||||
−0.991475 | + | 0.130300i | \(0.958406\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −129.913 | −0.154475 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 304.195i | 0.359994i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 61.9598i | 0.0731521i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 177.123 | − | 751.038i | 0.208136 | − | 0.882536i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1546.19 | −1.81264 | −0.906322 | − | 0.422587i | \(-0.861122\pi\) | ||||
−0.906322 | + | 0.422587i | \(0.861122\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1093.05 | 1.27544 | 0.637718 | − | 0.770270i | \(-0.279879\pi\) | ||||
0.637718 | + | 0.770270i | \(0.279879\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 784.906 | 0.913744 | 0.456872 | − | 0.889532i | \(-0.348970\pi\) | ||||
0.456872 | + | 0.889532i | \(0.348970\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −703.565 | −0.815255 | −0.407627 | − | 0.913148i | \(-0.633644\pi\) | ||||
−0.407627 | + | 0.913148i | \(0.633644\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 469.149i | − | 0.542369i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −286.648 | −0.329859 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 742.859i | 0.852880i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −147.617 | −0.168705 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 575.512 | 0.656228 | 0.328114 | − | 0.944638i | \(-0.393587\pi\) | ||||
0.328114 | + | 0.944638i | \(0.393587\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 362.368i | − | 0.411314i | −0.978624 | − | 0.205657i | \(-0.934067\pi\) | ||
0.978624 | − | 0.205657i | \(-0.0659331\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1312.15 | −1.48602 | −0.743008 | − | 0.669283i | \(-0.766602\pi\) | ||||
−0.743008 | + | 0.669283i | \(0.766602\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 692.301 | 0.780498 | 0.390249 | − | 0.920709i | \(-0.372389\pi\) | ||||
0.390249 | + | 0.920709i | \(0.372389\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 471.139i | − | 0.529966i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.35609i | 0.00375822i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 280.588i | − | 0.313507i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −459.766 | −0.511419 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.8287 | −0.0408753 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −528.819 | −0.584330 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 982.356i | 1.08308i | 0.840674 | + | 0.541541i | \(0.182159\pi\) | ||||
−0.840674 | + | 0.541541i | \(0.817841\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1321.66i | − | 1.45078i | −0.688338 | − | 0.725390i | \(-0.741659\pi\) | ||
0.688338 | − | 0.725390i | \(-0.258341\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −356.237 | −0.390183 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 205.105i | − | 0.223670i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 953.812i | − | 1.03788i | −0.854811 | − | 0.518940i | \(-0.826327\pi\) | ||
0.854811 | − | 0.518940i | \(-0.173673\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −541.170 | −0.586316 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 167.748i | − | 0.181349i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −322.827 | −0.347499 | −0.173749 | − | 0.984790i | \(-0.555588\pi\) | ||||
−0.173749 | + | 0.984790i | \(0.555588\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 800.639i | − | 0.859977i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 553.919i | 0.592427i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1159.90i | − | 1.23789i | −0.785434 | − | 0.618946i | \(-0.787560\pi\) | ||
0.785434 | − | 0.618946i | \(-0.212440\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 400.394i | − | 0.425499i | −0.977107 | − | 0.212749i | \(-0.931758\pi\) | ||
0.977107 | − | 0.212749i | \(-0.0682418\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −210.420 | − | 49.6251i | −0.223139 | − | 0.0526247i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.0706711 | 7.46263e−5 | 3.73132e−5 | − | 1.00000i | \(-0.499988\pi\) | ||||
3.73132e−5 | 1.00000i | \(0.499988\pi\) | ||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 368.678 | 0.388492 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 377.286i | 0.395893i | 0.980213 | + | 0.197947i | \(0.0634272\pi\) | ||||
−0.980213 | + | 0.197947i | \(0.936573\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −490.350 | −0.513455 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1377.04 | −1.43591 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −663.730 | −0.690666 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 396.271i | − | 0.410644i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −979.222 | −1.01264 | −0.506319 | − | 0.862346i | \(-0.668994\pi\) | ||||
−0.506319 | + | 0.862346i | \(0.668994\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 204.360i | 0.210463i | 0.994448 | + | 0.105232i | \(0.0335584\pi\) | ||||
−0.994448 | + | 0.105232i | \(0.966442\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1442.60i | − | 1.48263i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1474.62i | − | 1.50934i | −0.656106 | − | 0.754669i | \(-0.727798\pi\) | ||
0.656106 | − | 0.754669i | \(-0.272202\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1017.52 | −1.03934 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 462.209i | 0.470203i | 0.971971 | + | 0.235101i | \(0.0755422\pi\) | ||||
−0.971971 | + | 0.235101i | \(0.924458\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 724.079i | 0.735106i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −182.163 | + | 772.408i | −0.184189 | + | 0.780999i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1470.31 | −1.48366 | −0.741830 | − | 0.670587i | \(-0.766042\pi\) | ||||
−0.741830 | + | 0.670587i | \(0.766042\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 302.643 | 0.304164 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1599.83 | −1.60465 | −0.802324 | − | 0.596889i | \(-0.796403\pi\) | ||||
−0.802324 | + | 0.596889i | \(0.796403\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 4140.3.d.b.2161.17 | yes | 32 | |
3.2 | odd | 2 | inner | 4140.3.d.b.2161.1 | ✓ | 32 | |
23.22 | odd | 2 | inner | 4140.3.d.b.2161.16 | yes | 32 | |
69.68 | even | 2 | inner | 4140.3.d.b.2161.32 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4140.3.d.b.2161.1 | ✓ | 32 | 3.2 | odd | 2 | inner | |
4140.3.d.b.2161.16 | yes | 32 | 23.22 | odd | 2 | inner | |
4140.3.d.b.2161.17 | yes | 32 | 1.1 | even | 1 | trivial | |
4140.3.d.b.2161.32 | yes | 32 | 69.68 | even | 2 | inner |