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 | 2161.2 | ||
Character | \(\chi\) | \(=\) | 4140.2161 |
Dual form | 4140.3.d.b.2161.31 |
$q$-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 | ||||||||
\(7\) | − | 9.55915i | − | 1.36559i | −0.730609 | − | 0.682796i | \(-0.760764\pi\) | ||
0.730609 | − | 0.682796i | \(-0.239236\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 18.8089i | 1.70990i | 0.518714 | + | 0.854948i | \(0.326411\pi\) | ||||
−0.518714 | + | 0.854948i | \(0.673589\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 20.1043 | 1.54649 | 0.773244 | − | 0.634109i | \(-0.218633\pi\) | ||||
0.773244 | + | 0.634109i | \(0.218633\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 28.4427i | − | 1.67310i | −0.547892 | − | 0.836549i | \(-0.684570\pi\) | ||
0.547892 | − | 0.836549i | \(-0.315430\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 28.9585i | 1.52413i | 0.647501 | + | 0.762065i | \(0.275814\pi\) | ||||
−0.647501 | + | 0.762065i | \(0.724186\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 18.3876 | + | 13.8165i | 0.799461 | + | 0.600719i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.59078 | −0.0548544 | −0.0274272 | − | 0.999624i | \(-0.508731\pi\) | ||||
−0.0274272 | + | 0.999624i | \(0.508731\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −26.9023 | −0.867815 | −0.433907 | − | 0.900957i | \(-0.642866\pi\) | ||||
−0.433907 | + | 0.900957i | \(0.642866\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −21.3749 | −0.610712 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 51.7035i | 1.39739i | 0.715419 | + | 0.698695i | \(0.246236\pi\) | ||||
−0.715419 | + | 0.698695i | \(0.753764\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 54.4792 | 1.32876 | 0.664381 | − | 0.747394i | \(-0.268695\pi\) | ||||
0.664381 | + | 0.747394i | \(0.268695\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 81.2956i | 1.89060i | 0.326209 | + | 0.945298i | \(0.394229\pi\) | ||||
−0.326209 | + | 0.945298i | \(0.605771\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −27.5628 | −0.586443 | −0.293222 | − | 0.956045i | \(-0.594727\pi\) | ||||
−0.293222 | + | 0.956045i | \(0.594727\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −42.3773 | −0.864843 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 37.2235i | − | 0.702330i | −0.936314 | − | 0.351165i | \(-0.885786\pi\) | ||
0.936314 | − | 0.351165i | \(-0.114214\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 42.0579 | 0.764689 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −53.7093 | −0.910327 | −0.455164 | − | 0.890408i | \(-0.650419\pi\) | ||||
−0.455164 | + | 0.890408i | \(0.650419\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 39.8548i | − | 0.653357i | −0.945136 | − | 0.326679i | \(-0.894071\pi\) | ||
0.945136 | − | 0.326679i | \(-0.105929\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 44.9547i | − | 0.691611i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 42.9728i | 0.641385i | 0.947183 | + | 0.320693i | \(0.103916\pi\) | ||||
−0.947183 | + | 0.320693i | \(0.896084\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −84.4430 | −1.18934 | −0.594669 | − | 0.803970i | \(-0.702717\pi\) | ||||
−0.594669 | + | 0.803970i | \(0.702717\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −77.4277 | −1.06065 | −0.530327 | − | 0.847793i | \(-0.677931\pi\) | ||||
−0.530327 | + | 0.847793i | \(0.677931\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 179.797 | 2.33502 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 80.2412i | 1.01571i | 0.861442 | + | 0.507856i | \(0.169562\pi\) | ||||
−0.861442 | + | 0.507856i | \(0.830438\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 119.214i | 1.43632i | 0.695880 | + | 0.718158i | \(0.255015\pi\) | ||||
−0.695880 | + | 0.718158i | \(0.744985\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −63.5997 | −0.748232 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 22.1863i | 0.249285i | 0.992202 | + | 0.124642i | \(0.0397783\pi\) | ||||
−0.992202 | + | 0.124642i | \(0.960222\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 192.180i | − | 2.11187i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 64.7531 | 0.681612 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 99.9018i | − | 1.02992i | −0.857216 | − | 0.514958i | \(-0.827808\pi\) | ||
0.857216 | − | 0.514958i | \(-0.172192\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −65.3352 | −0.646884 | −0.323442 | − | 0.946248i | \(-0.604840\pi\) | ||||
−0.323442 | + | 0.946248i | \(0.604840\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 202.325i | 1.96432i | 0.188042 | + | 0.982161i | \(0.439786\pi\) | ||||
−0.188042 | + | 0.982161i | \(0.560214\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 168.608i | − | 1.57577i | −0.615820 | − | 0.787887i | \(-0.711175\pi\) | ||
0.615820 | − | 0.787887i | \(-0.288825\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 59.8713i | 0.549278i | 0.961547 | + | 0.274639i | \(0.0885583\pi\) | ||||
−0.961547 | + | 0.274639i | \(0.911442\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 105.020i | 0.929376i | 0.885474 | + | 0.464688i | \(0.153834\pi\) | ||||
−0.885474 | + | 0.464688i | \(0.846166\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 30.8947 | − | 41.1159i | 0.268650 | − | 0.357530i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −271.888 | −2.28477 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −232.773 | −1.92374 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 72.4497 | 0.570470 | 0.285235 | − | 0.958458i | \(-0.407928\pi\) | ||||
0.285235 | + | 0.958458i | \(0.407928\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −149.778 | −1.14335 | −0.571673 | − | 0.820482i | \(-0.693705\pi\) | ||||
−0.571673 | + | 0.820482i | \(0.693705\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 276.818 | 2.08134 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 112.515i | 0.821276i | 0.911798 | + | 0.410638i | \(0.134694\pi\) | ||||
−0.911798 | + | 0.410638i | \(0.865306\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 156.250 | 1.12410 | 0.562052 | − | 0.827102i | \(-0.310012\pi\) | ||||
0.562052 | + | 0.827102i | \(0.310012\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 378.140i | 2.64433i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.55709i | 0.0245317i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 113.365i | − | 0.760837i | −0.924814 | − | 0.380418i | \(-0.875780\pi\) | ||
0.924814 | − | 0.380418i | \(-0.124220\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −90.5230 | −0.599490 | −0.299745 | − | 0.954019i | \(-0.596902\pi\) | ||||
−0.299745 | + | 0.954019i | \(0.596902\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 60.1553i | 0.388099i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 79.0800i | 0.503694i | 0.967767 | + | 0.251847i | \(0.0810380\pi\) | ||||
−0.967767 | + | 0.251847i | \(0.918962\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 132.074 | − | 175.770i | 0.820337 | − | 1.09174i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 210.029 | 1.28852 | 0.644260 | − | 0.764807i | \(-0.277166\pi\) | ||||
0.644260 | + | 0.764807i | \(0.277166\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −162.144 | −0.970921 | −0.485461 | − | 0.874259i | \(-0.661348\pi\) | ||||
−0.485461 | + | 0.874259i | \(0.661348\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 235.185 | 1.39163 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 186.737 | 1.07940 | 0.539701 | − | 0.841857i | \(-0.318537\pi\) | ||||
0.539701 | + | 0.841857i | \(0.318537\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 47.7957i | 0.273119i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.54664 | −0.0254002 | −0.0127001 | − | 0.999919i | \(-0.504043\pi\) | ||||
−0.0127001 | + | 0.999919i | \(0.504043\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 69.4440i | − | 0.383669i | −0.981427 | − | 0.191834i | \(-0.938556\pi\) | ||
0.981427 | − | 0.191834i | \(-0.0614436\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 115.612 | 0.624932 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 534.974 | 2.86082 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 216.144i | 1.13164i | 0.824527 | + | 0.565822i | \(0.191441\pi\) | ||||
−0.824527 | + | 0.565822i | \(0.808559\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 238.065 | 1.23350 | 0.616748 | − | 0.787161i | \(-0.288450\pi\) | ||||
0.616748 | + | 0.787161i | \(0.288450\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −88.2296 | −0.447866 | −0.223933 | − | 0.974605i | \(-0.571890\pi\) | ||||
−0.223933 | + | 0.974605i | \(0.571890\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 74.1586i | − | 0.372656i | −0.982488 | − | 0.186328i | \(-0.940341\pi\) | ||
0.982488 | − | 0.186328i | \(-0.0596587\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.2065i | 0.0749088i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 121.819i | − | 0.594240i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −544.676 | −2.60610 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 150.488 | 0.713216 | 0.356608 | − | 0.934254i | \(-0.383933\pi\) | ||||
0.356608 | + | 0.934254i | \(0.383933\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 181.782 | 0.845500 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 257.163i | 1.18508i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 571.821i | − | 2.58743i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −98.5288 | −0.441833 | −0.220917 | − | 0.975293i | \(-0.570905\pi\) | ||||
−0.220917 | + | 0.975293i | \(0.570905\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 52.6756i | − | 0.232051i | −0.993246 | − | 0.116026i | \(-0.962985\pi\) | ||
0.993246 | − | 0.116026i | \(-0.0370155\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 372.613i | 1.62713i | 0.581473 | + | 0.813566i | \(0.302477\pi\) | ||||
−0.581473 | + | 0.813566i | \(0.697523\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 44.5159 | 0.191055 | 0.0955277 | − | 0.995427i | \(-0.469546\pi\) | ||||
0.0955277 | + | 0.995427i | \(0.469546\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 61.6324i | 0.262265i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 433.189 | 1.81251 | 0.906253 | − | 0.422736i | \(-0.138930\pi\) | ||||
0.906253 | + | 0.422736i | \(0.138930\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 212.470i | 0.881618i | 0.897601 | + | 0.440809i | \(0.145308\pi\) | ||||
−0.897601 | + | 0.440809i | \(0.854692\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 94.7586i | 0.386770i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 582.191i | 2.35705i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 468.549i | − | 1.86673i | −0.358932 | − | 0.933364i | \(-0.616859\pi\) | ||
0.358932 | − | 0.933364i | \(-0.383141\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −259.873 | + | 345.849i | −1.02717 | + | 1.36699i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 449.301 | 1.74825 | 0.874127 | − | 0.485697i | \(-0.161434\pi\) | ||||
0.874127 | + | 0.485697i | \(0.161434\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 494.241 | 1.90827 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 181.830i | − | 0.691369i | −0.938351 | − | 0.345685i | \(-0.887647\pi\) | ||
0.938351 | − | 0.345685i | \(-0.112353\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −83.2342 | −0.314091 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 214.110 | 0.795949 | 0.397975 | − | 0.917396i | \(-0.369713\pi\) | ||||
0.397975 | + | 0.917396i | \(0.369713\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −337.430 | −1.24513 | −0.622564 | − | 0.782569i | \(-0.713909\pi\) | ||||
−0.622564 | + | 0.782569i | \(0.713909\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 94.0443i | − | 0.341979i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −153.931 | −0.555708 | −0.277854 | − | 0.960623i | \(-0.589623\pi\) | ||||
−0.277854 | + | 0.960623i | \(0.589623\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 204.395i | 0.727386i | 0.931519 | + | 0.363693i | \(0.118484\pi\) | ||||
−0.931519 | + | 0.363693i | \(0.881516\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 372.530i | − | 1.31636i | −0.752861 | − | 0.658180i | \(-0.771327\pi\) | ||
0.752861 | − | 0.658180i | \(-0.228673\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 520.775i | − | 1.81455i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −519.985 | −1.79926 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 98.4000i | 0.335836i | 0.985801 | + | 0.167918i | \(0.0537044\pi\) | ||||
−0.985801 | + | 0.167918i | \(0.946296\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 120.098i | 0.407111i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 369.671 | + | 277.772i | 1.23636 | + | 0.929004i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 777.117 | 2.58178 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −89.1180 | −0.292190 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 290.060 | 0.944822 | 0.472411 | − | 0.881378i | \(-0.343384\pi\) | ||||
0.472411 | + | 0.881378i | \(0.343384\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 319.010 | 1.02576 | 0.512878 | − | 0.858462i | \(-0.328579\pi\) | ||||
0.512878 | + | 0.858462i | \(0.328579\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 52.6956i | − | 0.168356i | −0.996451 | − | 0.0841782i | \(-0.973174\pi\) | ||
0.996451 | − | 0.0841782i | \(-0.0268265\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −61.8574 | −0.195134 | −0.0975668 | − | 0.995229i | \(-0.531106\pi\) | ||||
−0.0975668 | + | 0.995229i | \(0.531106\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 29.9207i | − | 0.0937954i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 823.656 | 2.55002 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −100.522 | −0.309298 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 263.477i | 0.800842i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 616.092 | 1.86131 | 0.930653 | − | 0.365902i | \(-0.119240\pi\) | ||||
0.930653 | + | 0.365902i | \(0.119240\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 96.0901 | 0.286836 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 330.744i | 0.981436i | 0.871318 | + | 0.490718i | \(0.163265\pi\) | ||||
−0.871318 | + | 0.490718i | \(0.836735\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 506.001i | − | 1.48387i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 63.3072i | − | 0.184569i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −551.866 | −1.59039 | −0.795197 | − | 0.606352i | \(-0.792632\pi\) | ||||
−0.795197 | + | 0.606352i | \(0.792632\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.0766 | −0.0747181 | −0.0373590 | − | 0.999302i | \(-0.511895\pi\) | ||||
−0.0373590 | + | 0.999302i | \(0.511895\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −367.348 | −1.04064 | −0.520322 | − | 0.853970i | \(-0.674188\pi\) | ||||
−0.520322 | + | 0.853970i | \(0.674188\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 188.820i | 0.531888i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 666.079i | 1.85537i | 0.373359 | + | 0.927687i | \(0.378206\pi\) | ||||
−0.373359 | + | 0.927687i | \(0.621794\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −477.593 | −1.32297 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 173.134i | 0.474339i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 387.158i | 1.05493i | 0.849578 | + | 0.527463i | \(0.176857\pi\) | ||||
−0.849578 | + | 0.527463i | \(0.823143\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −355.825 | −0.959096 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 631.246i | 1.69235i | 0.532906 | + | 0.846174i | \(0.321100\pi\) | ||||
−0.532906 | + | 0.846174i | \(0.678900\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −31.9816 | −0.0848318 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 199.324i | 0.525920i | 0.964807 | + | 0.262960i | \(0.0846987\pi\) | ||||
−0.964807 | + | 0.262960i | \(0.915301\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 255.191i | − | 0.666294i | −0.942875 | − | 0.333147i | \(-0.891889\pi\) | ||
0.942875 | − | 0.333147i | \(-0.108111\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 402.037i | − | 1.04425i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 203.813i | − | 0.523940i | −0.965076 | − | 0.261970i | \(-0.915628\pi\) | ||
0.965076 | − | 0.261970i | \(-0.0843721\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 392.979 | − | 522.992i | 1.00506 | − | 1.33758i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 179.425 | 0.454240 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −33.1882 | −0.0835975 | −0.0417987 | − | 0.999126i | \(-0.513309\pi\) | ||||
−0.0417987 | + | 0.999126i | \(0.513309\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 55.4248i | − | 0.138216i | −0.997609 | − | 0.0691082i | \(-0.977985\pi\) | ||
0.997609 | − | 0.0691082i | \(-0.0220154\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −540.852 | −1.34207 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −972.482 | −2.38939 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.5349 | 0.0697675 | 0.0348838 | − | 0.999391i | \(-0.488894\pi\) | ||||
0.0348838 | + | 0.999391i | \(0.488894\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 513.415i | 1.24314i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 266.571 | 0.642340 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 271.192i | − | 0.647236i | −0.946188 | − | 0.323618i | \(-0.895101\pi\) | ||
0.946188 | − | 0.323618i | \(-0.104899\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 792.990i | 1.88359i | 0.336192 | + | 0.941793i | \(0.390861\pi\) | ||||
−0.336192 | + | 0.941793i | \(0.609139\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 142.213i | 0.334620i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −380.978 | −0.892220 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 583.988i | 1.35496i | 0.735540 | + | 0.677481i | \(0.236928\pi\) | ||||
−0.735540 | + | 0.677481i | \(0.763072\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 543.770i | − | 1.25582i | −0.778286 | − | 0.627910i | \(-0.783911\pi\) | ||
0.778286 | − | 0.627910i | \(-0.216089\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −400.105 | + | 532.477i | −0.915573 | + | 1.21848i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 554.291 | 1.26262 | 0.631311 | − | 0.775530i | \(-0.282517\pi\) | ||||
0.631311 | + | 0.775530i | \(0.282517\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −154.056 | −0.347756 | −0.173878 | − | 0.984767i | \(-0.555630\pi\) | ||||
−0.173878 | + | 0.984767i | \(0.555630\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 49.6102 | 0.111483 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 216.232 | 0.481586 | 0.240793 | − | 0.970576i | \(-0.422592\pi\) | ||||
0.240793 | + | 0.970576i | \(0.422592\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1024.69i | 2.27204i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −429.728 | −0.944458 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 368.540i | − | 0.806434i | −0.915104 | − | 0.403217i | \(-0.867892\pi\) | ||
0.915104 | − | 0.403217i | \(-0.132108\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −343.678 | −0.745506 | −0.372753 | − | 0.927931i | \(-0.621586\pi\) | ||||
−0.372753 | + | 0.927931i | \(0.621586\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.2165 | −0.0523033 | −0.0261517 | − | 0.999658i | \(-0.508325\pi\) | ||||
−0.0261517 | + | 0.999658i | \(0.508325\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.3382i | 0.0456921i | 0.999739 | + | 0.0228460i | \(0.00727275\pi\) | ||||
−0.999739 | + | 0.0228460i | \(0.992727\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 410.784 | 0.875871 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1529.08 | −3.23272 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 144.792i | − | 0.304826i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 353.583i | − | 0.738168i | −0.929396 | − | 0.369084i | \(-0.879671\pi\) | ||
0.929396 | − | 0.369084i | \(-0.120329\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1039.46i | 2.16105i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −223.387 | −0.460592 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −832.579 | −1.70961 | −0.854804 | − | 0.518951i | \(-0.826323\pi\) | ||||
−0.854804 | + | 0.518951i | \(0.826323\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 200.501 | 0.408352 | 0.204176 | − | 0.978934i | \(-0.434549\pi\) | ||||
0.204176 | + | 0.978934i | \(0.434549\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 45.2460i | 0.0917768i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 807.203i | 1.62415i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −790.773 | −1.58471 | −0.792357 | − | 0.610057i | \(-0.791146\pi\) | ||||
−0.792357 | + | 0.610057i | \(0.791146\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 207.441i | − | 0.412408i | −0.978509 | − | 0.206204i | \(-0.933889\pi\) | ||
0.978509 | − | 0.206204i | \(-0.0661110\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 146.094i | 0.289295i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −240.857 | −0.473197 | −0.236598 | − | 0.971608i | \(-0.576033\pi\) | ||||
−0.236598 | + | 0.971608i | \(0.576033\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 740.143i | 1.44842i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 452.413 | 0.878472 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 518.425i | − | 1.00276i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 549.887i | − | 1.05545i | −0.849417 | − | 0.527723i | \(-0.823046\pi\) | ||
0.849417 | − | 0.527723i | \(-0.176954\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 173.718i | − | 0.332156i | −0.986113 | − | 0.166078i | \(-0.946890\pi\) | ||
0.986113 | − | 0.166078i | \(-0.0531104\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 765.172i | 1.45194i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 147.207 | + | 508.105i | 0.278274 | + | 0.960502i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1095.27 | 2.05491 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −377.018 | −0.704707 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 797.069i | − | 1.47879i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 346.955 | 0.641322 | 0.320661 | − | 0.947194i | \(-0.396095\pi\) | ||||
0.320661 | + | 0.947194i | \(0.396095\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 133.876 | 0.245644 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 707.916 | 1.29418 | 0.647090 | − | 0.762414i | \(-0.275986\pi\) | ||||
0.647090 | + | 0.762414i | \(0.275986\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 46.0665i | − | 0.0836053i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 767.037 | 1.38705 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 688.947i | 1.23689i | 0.785829 | + | 0.618444i | \(0.212237\pi\) | ||||
−0.785829 | + | 0.618444i | \(0.787763\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1634.39i | 2.92378i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 373.375i | − | 0.663187i | −0.943422 | − | 0.331594i | \(-0.892414\pi\) | ||
0.943422 | − | 0.331594i | \(-0.107586\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 234.831 | 0.415630 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 133.254i | 0.234190i | 0.993121 | + | 0.117095i | \(0.0373582\pi\) | ||||
−0.993121 | + | 0.117095i | \(0.962642\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 83.6044i | 0.146418i | 0.997317 | + | 0.0732088i | \(0.0233239\pi\) | ||||
−0.997317 | + | 0.0732088i | \(0.976676\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −91.9380 | − | 69.0826i | −0.159892 | − | 0.120144i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 926.137 | 1.60509 | 0.802545 | − | 0.596591i | \(-0.203479\pi\) | ||||
0.802545 | + | 0.596591i | \(0.203479\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1139.59 | 1.96142 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 700.131 | 1.20091 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 588.228 | 1.00209 | 0.501046 | − | 0.865421i | \(-0.332949\pi\) | ||||
0.501046 | + | 0.865421i | \(0.332949\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 779.048i | − | 1.32266i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 832.912 | 1.40457 | 0.702287 | − | 0.711894i | \(-0.252162\pi\) | ||||
0.702287 | + | 0.711894i | \(0.252162\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 607.959i | 1.02178i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −594.374 | −0.992277 | −0.496139 | − | 0.868243i | \(-0.665249\pi\) | ||||
−0.496139 | + | 0.868243i | \(0.665249\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 180.418 | 0.300196 | 0.150098 | − | 0.988671i | \(-0.452041\pi\) | ||||
0.150098 | + | 0.988671i | \(0.452041\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 520.496i | 0.860324i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 854.913 | 1.40842 | 0.704212 | − | 0.709990i | \(-0.251300\pi\) | ||||
0.704212 | + | 0.709990i | \(0.251300\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −554.133 | −0.906927 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 637.880i | 1.04059i | 0.853987 | + | 0.520294i | \(0.174178\pi\) | ||||
−0.853987 | + | 0.520294i | \(0.825822\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 625.473i | − | 1.01373i | −0.862025 | − | 0.506866i | \(-0.830804\pi\) | ||
0.862025 | − | 0.506866i | \(-0.169196\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 330.557i | − | 0.534017i | −0.963694 | − | 0.267009i | \(-0.913965\pi\) | ||
0.963694 | − | 0.267009i | \(-0.0860352\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 212.082 | 0.340421 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1470.58 | 2.33797 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.1193i | 0.0604109i | 0.999544 | + | 0.0302055i | \(0.00961616\pi\) | ||||
−0.999544 | + | 0.0302055i | \(0.990384\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 162.003i | − | 0.255122i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −851.968 | −1.33747 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 133.794i | − | 0.208727i | −0.994539 | − | 0.104363i | \(-0.966720\pi\) | ||
0.994539 | − | 0.104363i | \(-0.0332805\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 195.216i | 0.303601i | 0.988411 | + | 0.151801i | \(0.0485072\pi\) | ||||
−0.988411 | + | 0.151801i | \(0.951493\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −973.923 | −1.50529 | −0.752645 | − | 0.658426i | \(-0.771223\pi\) | ||||
−0.752645 | + | 0.658426i | \(0.771223\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1010.21i | − | 1.55656i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −587.480 | −0.899663 | −0.449831 | − | 0.893114i | \(-0.648516\pi\) | ||||
−0.449831 | + | 0.893114i | \(0.648516\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 334.914i | 0.511320i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 322.810i | − | 0.489849i | −0.969542 | − | 0.244924i | \(-0.921237\pi\) | ||
0.969542 | − | 0.244924i | \(-0.0787631\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 463.530i | − | 0.701256i | −0.936515 | − | 0.350628i | \(-0.885968\pi\) | ||
0.936515 | − | 0.350628i | \(-0.114032\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 618.985i | − | 0.930804i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −29.2506 | − | 21.9790i | −0.0438540 | − | 0.0329521i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 749.623 | 1.11717 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 312.153 | 0.463823 | 0.231912 | − | 0.972737i | \(-0.425502\pi\) | ||||
0.231912 | + | 0.972737i | \(0.425502\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 386.425i | − | 0.570790i | −0.958410 | − | 0.285395i | \(-0.907875\pi\) | ||
0.958410 | − | 0.285395i | \(-0.0921249\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −954.976 | −1.40645 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 889.807 | 1.30279 | 0.651396 | − | 0.758738i | \(-0.274184\pi\) | ||||
0.651396 | + | 0.758738i | \(0.274184\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 251.591 | 0.367286 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 748.354i | − | 1.08614i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 211.397 | 0.305928 | 0.152964 | − | 0.988232i | \(-0.451118\pi\) | ||||
0.152964 | + | 0.988232i | \(0.451118\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 349.387i | − | 0.502714i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1549.53i | − | 2.22315i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1169.73i | − | 1.66865i | −0.551269 | − | 0.834327i | \(-0.685856\pi\) | ||
0.551269 | − | 0.834327i | \(-0.314144\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1497.25 | −2.12980 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 624.549i | 0.883379i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 16.6676i | − | 0.0235086i | −0.999931 | − | 0.0117543i | \(-0.996258\pi\) | ||
0.999931 | − | 0.0117543i | \(-0.00374160\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −494.668 | − | 371.696i | −0.693784 | − | 0.521312i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 845.546 | 1.18258 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −673.301 | −0.936442 | −0.468221 | − | 0.883612i | \(-0.655105\pi\) | ||||
−0.468221 | + | 0.883612i | \(0.655105\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1934.06 | 2.68246 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.95389 | 0.0109709 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 456.897i | − | 0.628469i | −0.949345 | − | 0.314235i | \(-0.898252\pi\) | ||
0.949345 | − | 0.314235i | \(-0.101748\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2312.26 | 3.16315 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 945.078i | 1.28933i | 0.764466 | + | 0.644664i | \(0.223003\pi\) | ||||
−0.764466 | + | 0.644664i | \(0.776997\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −808.269 | −1.09670 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1245.76 | 1.68574 | 0.842872 | − | 0.538114i | \(-0.180863\pi\) | ||||
0.842872 | + | 0.538114i | \(0.180863\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1452.42i | 1.95480i | 0.211401 | + | 0.977399i | \(0.432197\pi\) | ||||
−0.211401 | + | 0.977399i | \(0.567803\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −253.491 | −0.340257 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1611.75 | −2.15187 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 269.832i | − | 0.359297i | −0.983731 | − | 0.179649i | \(-0.942504\pi\) | ||
0.983731 | − | 0.179649i | \(-0.0574960\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 202.416i | 0.268100i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 624.541i | − | 0.825021i | −0.910953 | − | 0.412510i | \(-0.864652\pi\) | ||
0.910953 | − | 0.412510i | \(-0.135348\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 236.248 | 0.310445 | 0.155222 | − | 0.987880i | \(-0.450391\pi\) | ||||
0.155222 | + | 0.987880i | \(0.450391\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 572.318 | 0.750090 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1079.79 | −1.40781 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1361.59i | − | 1.77060i | −0.465023 | − | 0.885298i | \(-0.653954\pi\) | ||
0.465023 | − | 0.885298i | \(-0.346046\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 289.140i | 0.374049i | 0.982355 | + | 0.187025i | \(0.0598844\pi\) | ||||
−0.982355 | + | 0.187025i | \(0.940116\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 134.511 | 0.173563 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1577.63i | 2.02521i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 1588.28i | − | 2.03364i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 176.828 | 0.225259 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 958.162i | − | 1.21749i | −0.793367 | − | 0.608744i | \(-0.791674\pi\) | ||
0.793367 | − | 0.608744i | \(-0.208326\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1003.90 | 1.26915 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 801.254i | − | 1.01041i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 147.380i | 0.184919i | 0.995716 | + | 0.0924594i | \(0.0294728\pi\) | ||||
−0.995716 | + | 0.0924594i | \(0.970527\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 783.960i | 0.981177i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 1456.33i | − | 1.81361i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −393.033 | − | 295.327i | −0.488240 | − | 0.366866i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −339.448 | −0.419589 | −0.209795 | − | 0.977745i | \(-0.567280\pi\) | ||||
−0.209795 | + | 0.977745i | \(0.567280\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −763.230 | −0.941097 | −0.470548 | − | 0.882374i | \(-0.655944\pi\) | ||||
−0.470548 | + | 0.882374i | \(0.655944\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 469.638i | − | 0.576243i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2354.20 | −2.88151 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.5246 | 0.0323076 | 0.0161538 | − | 0.999870i | \(-0.494858\pi\) | ||||
0.0161538 | + | 0.999870i | \(0.494858\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 419.120 | 0.509259 | 0.254629 | − | 0.967039i | \(-0.418046\pi\) | ||||
0.254629 | + | 0.967039i | \(0.418046\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 131.070i | 0.158489i | 0.996855 | + | 0.0792443i | \(0.0252507\pi\) | ||||
−0.996855 | + | 0.0792443i | \(0.974749\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −570.854 | −0.688606 | −0.344303 | − | 0.938859i | \(-0.611885\pi\) | ||||
−0.344303 | + | 0.938859i | \(0.611885\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1205.32i | 1.44697i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 362.565i | 0.434209i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 419.908i | 0.500486i | 0.968183 | + | 0.250243i | \(0.0805106\pi\) | ||||
−0.968183 | + | 0.250243i | \(0.919489\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −838.469 | −0.996991 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 525.889i | − | 0.622354i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2225.11i | 2.62705i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −714.362 | + | 950.702i | −0.839438 | + | 1.11716i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1378.65 | 1.61624 | 0.808119 | − | 0.589020i | \(-0.200486\pi\) | ||||
0.808119 | + | 0.589020i | \(0.200486\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1310.60 | 1.52929 | 0.764646 | − | 0.644451i | \(-0.222914\pi\) | ||||
0.764646 | + | 0.644451i | \(0.222914\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 532.378 | 0.619765 | 0.309882 | − | 0.950775i | \(-0.399710\pi\) | ||||
0.309882 | + | 0.950775i | \(0.399710\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −904.616 | −1.04822 | −0.524111 | − | 0.851650i | \(-0.675602\pi\) | ||||
−0.524111 | + | 0.851650i | \(0.675602\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 417.556i | − | 0.482724i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1509.24 | −1.73676 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 863.940i | 0.991895i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 106.875 | 0.122142 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 750.929 | 0.856248 | 0.428124 | − | 0.903720i | \(-0.359175\pi\) | ||||
0.428124 | + | 0.903720i | \(0.359175\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 888.261i | 1.00824i | 0.863633 | + | 0.504121i | \(0.168183\pi\) | ||||
−0.863633 | + | 0.504121i | \(0.831817\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −96.1065 | −0.108841 | −0.0544205 | − | 0.998518i | \(-0.517331\pi\) | ||||
−0.0544205 | + | 0.998518i | \(0.517331\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −714.733 | −0.805787 | −0.402894 | − | 0.915247i | \(-0.631996\pi\) | ||||
−0.402894 | + | 0.915247i | \(0.631996\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 692.558i | − | 0.779030i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 798.177i | − | 0.893816i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.1666i | 0.0113593i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 42.7955 | 0.0476035 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1058.73 | −1.17507 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −155.282 | −0.171582 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 876.164i | − | 0.966003i | −0.875620 | − | 0.483001i | \(-0.839547\pi\) | ||
0.875620 | − | 0.483001i | \(-0.160453\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 286.256i | 0.314222i | 0.987581 | + | 0.157111i | \(0.0502180\pi\) | ||||
−0.987581 | + | 0.157111i | \(0.949782\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2242.28 | −2.45595 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1431.75i | 1.56134i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 701.426i | 0.763249i | 0.924317 | + | 0.381625i | \(0.124635\pi\) | ||||
−0.924317 | + | 0.381625i | \(0.875365\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1697.67 | −1.83930 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 258.517i | − | 0.279478i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 651.581 | 0.701379 | 0.350690 | − | 0.936492i | \(-0.385947\pi\) | ||||
0.350690 | + | 0.936492i | \(0.385947\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 1227.18i | − | 1.31813i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 1196.24i | − | 1.27940i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 81.1240i | 0.0865784i | 0.999063 | + | 0.0432892i | \(0.0137837\pi\) | ||||
−0.999063 | + | 0.0432892i | \(0.986216\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 158.773i | 0.168728i | 0.996435 | + | 0.0843641i | \(0.0268859\pi\) | ||||
−0.996435 | + | 0.0843641i | \(0.973114\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1001.74 | + | 752.714i | 1.06229 | + | 0.798212i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −557.127 | −0.588307 | −0.294154 | − | 0.955758i | \(-0.595038\pi\) | ||||
−0.294154 | + | 0.955758i | \(0.595038\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1556.63 | −1.64029 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 982.429i | − | 1.03088i | −0.856926 | − | 0.515440i | \(-0.827629\pi\) | ||
0.856926 | − | 0.515440i | \(-0.172371\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 483.313 | 0.506086 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1075.55 | 1.12153 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −237.268 | −0.246897 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 532.329i | − | 0.551636i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −993.341 | −1.02724 | −0.513620 | − | 0.858018i | \(-0.671696\pi\) | ||||
−0.513620 | + | 0.858018i | \(0.671696\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 903.976i | − | 0.930975i | −0.885055 | − | 0.465487i | \(-0.845879\pi\) | ||
0.885055 | − | 0.465487i | \(-0.154121\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1493.62i | − | 1.53507i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 681.912i | 0.697965i | 0.937129 | + | 0.348982i | \(0.113473\pi\) | ||||
−0.937129 | + | 0.348982i | \(0.886527\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −417.299 | −0.426251 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 849.167i | − | 0.863852i | −0.901909 | − | 0.431926i | \(-0.857834\pi\) | ||
0.901909 | − | 0.431926i | \(-0.142166\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 197.287i | 0.200292i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1123.22 | + | 1494.83i | −1.13572 | + | 1.51146i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −321.586 | −0.324507 | −0.162253 | − | 0.986749i | \(-0.551876\pi\) | ||||
−0.162253 | + | 0.986749i | \(0.551876\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −165.824 | −0.166657 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1057.30 | −1.06049 | −0.530243 | − | 0.847846i | \(-0.677899\pi\) | ||||
−0.530243 | + | 0.847846i | \(0.677899\pi\) | |||||||
\(998\) | 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.2161.2 | ✓ | 32 | |
3.2 | odd | 2 | inner | 4140.3.d.b.2161.18 | yes | 32 | |
23.22 | odd | 2 | inner | 4140.3.d.b.2161.31 | yes | 32 | |
69.68 | even | 2 | inner | 4140.3.d.b.2161.15 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4140.3.d.b.2161.2 | ✓ | 32 | 1.1 | even | 1 | trivial | |
4140.3.d.b.2161.15 | yes | 32 | 69.68 | even | 2 | inner | |
4140.3.d.b.2161.18 | yes | 32 | 3.2 | odd | 2 | inner | |
4140.3.d.b.2161.31 | yes | 32 | 23.22 | odd | 2 | inner |