Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(237,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4012.237");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.b (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: | \(32.0359812909\) |
Analytic rank: | \(0\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 237.3 | ||
Character | \(\chi\) | \(=\) | 4012.237 |
Dual form | 4012.2.b.b.237.44 |
$q$-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 \(\left(\mathbb{Z}/4012\mathbb{Z}\right)^\times\).
\(n\) | \(2007\) | \(3129\) | \(3777\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 3.18403i | − | 1.83830i | −0.393907 | − | 0.919150i | \(-0.628877\pi\) | ||
0.393907 | − | 0.919150i | \(-0.371123\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.45906i | − | 0.652512i | −0.945281 | − | 0.326256i | \(-0.894213\pi\) | ||
0.945281 | − | 0.326256i | \(-0.105787\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.23253i | − | 0.465854i | −0.972494 | − | 0.232927i | \(-0.925170\pi\) | ||
0.972494 | − | 0.232927i | \(-0.0748304\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −7.13805 | −2.37935 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.92877i | 1.78759i | 0.448474 | + | 0.893796i | \(0.351968\pi\) | ||||
−0.448474 | + | 0.893796i | \(0.648032\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.31160 | −0.918472 | −0.459236 | − | 0.888314i | \(-0.651877\pi\) | ||||
−0.459236 | + | 0.888314i | \(0.651877\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.64569 | −1.19951 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.08333 | + | 0.571297i | −0.990354 | + | 0.138560i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.44989 | −0.562044 | −0.281022 | − | 0.959701i | \(-0.590673\pi\) | ||||
−0.281022 | + | 0.959701i | \(0.590673\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.92443 | −0.856380 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.79101i | 0.998995i | 0.866315 | + | 0.499497i | \(0.166482\pi\) | ||||
−0.866315 | + | 0.499497i | \(0.833518\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.87114 | 0.574228 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 13.1757i | 2.53566i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.32008i | − | 0.430828i | −0.976523 | − | 0.215414i | \(-0.930890\pi\) | ||
0.976523 | − | 0.215414i | \(-0.0691101\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.94770i | − | 0.349817i | −0.984585 | − | 0.174908i | \(-0.944037\pi\) | ||
0.984585 | − | 0.174908i | \(-0.0559630\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 18.8774 | 3.28613 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.79834 | −0.303976 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3.37438i | − | 0.554745i | −0.960763 | − | 0.277372i | \(-0.910536\pi\) | ||
0.960763 | − | 0.277372i | \(-0.0894635\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.5442i | 1.68843i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 8.19338i | − | 1.27959i | −0.768545 | − | 0.639795i | \(-0.779019\pi\) | ||
0.768545 | − | 0.639795i | \(-0.220981\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.42601 | −1.13246 | −0.566228 | − | 0.824249i | \(-0.691598\pi\) | ||||
−0.566228 | + | 0.824249i | \(0.691598\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.4148i | 1.55255i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.88961 | 0.421493 | 0.210746 | − | 0.977541i | \(-0.432411\pi\) | ||||
0.210746 | + | 0.977541i | \(0.432411\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.48086 | 0.782980 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.81903 | + | 13.0015i | 0.254715 | + | 1.82057i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.48779 | 0.204364 | 0.102182 | − | 0.994766i | \(-0.467418\pi\) | ||||
0.102182 | + | 0.994766i | \(0.467418\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.65044 | 1.16643 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.80053i | 1.03321i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.0568i | 1.41568i | 0.706374 | + | 0.707838i | \(0.250329\pi\) | ||||
−0.706374 | + | 0.707838i | \(0.749671\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.79789i | 1.10843i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.83182i | 0.599314i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.4333 | 1.39679 | 0.698397 | − | 0.715710i | \(-0.253897\pi\) | ||||
0.698397 | + | 0.715710i | \(0.253897\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 15.2547 | 1.83645 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.97142i | − | 1.06471i | −0.846521 | − | 0.532356i | \(-0.821307\pi\) | ||
0.846521 | − | 0.532356i | \(-0.178693\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.1610i | 1.89151i | 0.324887 | + | 0.945753i | \(0.394674\pi\) | ||||
−0.324887 | + | 0.945753i | \(0.605326\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 9.14180i | − | 1.05560i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.30742 | 0.832758 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.60558i | 0.855694i | 0.903851 | + | 0.427847i | \(0.140728\pi\) | ||||
−0.903851 | + | 0.427847i | \(0.859272\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 20.5376 | 2.28195 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.36739 | 1.02820 | 0.514102 | − | 0.857729i | \(-0.328125\pi\) | ||||
0.514102 | + | 0.857729i | \(0.328125\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.833557 | + | 5.95783i | 0.0904119 | + | 0.646218i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.38721 | −0.791992 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.54564 | 0.481837 | 0.240919 | − | 0.970545i | \(-0.422551\pi\) | ||||
0.240919 | + | 0.970545i | \(0.422551\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.08166i | 0.427874i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.20153 | −0.643069 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.57454i | 0.366740i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.608891i | 0.0618235i | 0.999522 | + | 0.0309118i | \(0.00984109\pi\) | ||||
−0.999522 | + | 0.0309118i | \(0.990159\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 42.3199i | − | 4.25331i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.06408 | −0.702903 | −0.351451 | − | 0.936206i | \(-0.614312\pi\) | ||||
−0.351451 | + | 0.936206i | \(0.614312\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.85515 | 0.576925 | 0.288463 | − | 0.957491i | \(-0.406856\pi\) | ||||
0.288463 | + | 0.957491i | \(0.406856\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.72598i | 0.558798i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 18.6545i | − | 1.80340i | −0.432367 | − | 0.901698i | \(-0.642322\pi\) | ||
0.432367 | − | 0.901698i | \(-0.357678\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 20.3443i | 1.94863i | 0.225186 | + | 0.974316i | \(0.427701\pi\) | ||||
−0.225186 | + | 0.974316i | \(0.572299\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.7441 | −1.01979 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.86914i | − | 0.175834i | −0.996128 | − | 0.0879168i | \(-0.971979\pi\) | ||
0.996128 | − | 0.0879168i | \(-0.0280210\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.99038 | 0.651856 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 23.6383 | 2.18537 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.704143 | + | 5.03285i | 0.0645487 | + | 0.461361i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −24.1503 | −2.19549 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −26.0880 | −2.35227 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.4845i | − | 1.02720i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.86748 | −0.520654 | −0.260327 | − | 0.965520i | \(-0.583830\pi\) | ||||
−0.260327 | + | 0.965520i | \(0.583830\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 23.6446i | 2.08180i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21.4508i | 1.87417i | 0.349107 | + | 0.937083i | \(0.386485\pi\) | ||||
−0.349107 | + | 0.937083i | \(0.613515\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.01958i | 0.261831i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 19.2241 | 1.65455 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.62103 | 0.223930 | 0.111965 | − | 0.993712i | \(-0.464286\pi\) | ||||
0.111965 | + | 0.993712i | \(0.464286\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 0.836202i | − | 0.0709257i | −0.999371 | − | 0.0354629i | \(-0.988709\pi\) | ||
0.999371 | − | 0.0354629i | \(-0.0112906\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 9.20060i | − | 0.774831i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 19.6337i | − | 1.64185i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.38514 | −0.281121 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 17.4512i | − | 1.43935i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.2552 | −1.41361 | −0.706803 | − | 0.707411i | \(-0.749863\pi\) | ||||
−0.706803 | + | 0.707411i | \(0.749863\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.67871 | −0.462127 | −0.231064 | − | 0.972939i | \(-0.574221\pi\) | ||||
−0.231064 | + | 0.972939i | \(0.574221\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 29.1470 | − | 4.07794i | 2.35640 | − | 0.329682i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.84181 | −0.228260 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.89767 | −0.470685 | −0.235343 | − | 0.971912i | \(-0.575621\pi\) | ||||
−0.235343 | + | 0.971912i | \(0.575621\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 4.73717i | − | 0.375682i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.90509 | 0.465386 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.23741i | 0.566878i | 0.958990 | + | 0.283439i | \(0.0914753\pi\) | ||||
−0.958990 | + | 0.283439i | \(0.908525\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 27.5433i | − | 2.14424i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.9836i | 1.70114i | 0.525860 | + | 0.850571i | \(0.323744\pi\) | ||||
−0.525860 | + | 0.850571i | \(0.676256\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.03332 | −0.156409 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 17.4874 | 1.33730 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.50222i | 0.342297i | 0.985245 | + | 0.171149i | \(0.0547478\pi\) | ||||
−0.985245 | + | 0.171149i | \(0.945252\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3.53878i | − | 0.267507i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 3.18403i | − | 0.239326i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.15021 | 0.384945 | 0.192472 | − | 0.981302i | \(-0.438349\pi\) | ||||
0.192472 | + | 0.981302i | \(0.438349\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.67026i | − | 0.198479i | −0.995064 | − | 0.0992393i | \(-0.968359\pi\) | ||
0.995064 | − | 0.0992393i | \(-0.0316409\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 35.2051 | 2.60244 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.92343 | −0.361977 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.38709 | − | 24.2092i | −0.247688 | − | 1.77035i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 16.2395 | 1.18125 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.9344 | −1.73183 | −0.865917 | − | 0.500188i | \(-0.833264\pi\) | ||||
−0.865917 | + | 0.500188i | \(0.833264\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.3152i | 1.17439i | 0.809444 | + | 0.587197i | \(0.199769\pi\) | ||||
−0.809444 | + | 0.587197i | \(0.800231\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 15.3847 | 1.10172 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.6339i | 1.89759i | 0.315897 | + | 0.948793i | \(0.397694\pi\) | ||||
−0.315897 | + | 0.948793i | \(0.602306\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.39212i | 0.311349i | 0.987808 | + | 0.155674i | \(0.0497551\pi\) | ||||
−0.987808 | + | 0.155674i | \(0.950245\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 36.4038i | − | 2.56773i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.85958 | −0.200703 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.9546 | −0.834948 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 34.1985i | − | 2.37696i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 14.5248i | − | 1.00470i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 4.06297i | − | 0.279706i | −0.990172 | − | 0.139853i | \(-0.955337\pi\) | ||
0.990172 | − | 0.139853i | \(-0.0446630\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −28.5653 | −1.95726 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.8350i | 0.738941i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.40061 | −0.162964 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 51.4572 | 3.47716 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.5224 | − | 1.89190i | 0.909613 | − | 0.127263i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.1345 | 1.61617 | 0.808084 | − | 0.589067i | \(-0.200505\pi\) | ||||
0.808084 | + | 0.589067i | \(0.200505\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −20.4943 | −1.36629 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 6.76308i | − | 0.448882i | −0.974488 | − | 0.224441i | \(-0.927944\pi\) | ||
0.974488 | − | 0.224441i | \(-0.0720555\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.27977 | 0.414979 | 0.207489 | − | 0.978237i | \(-0.433471\pi\) | ||||
0.207489 | + | 0.978237i | \(0.433471\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 23.2670i | − | 1.53086i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 7.30784i | − | 0.478753i | −0.970927 | − | 0.239376i | \(-0.923057\pi\) | ||
0.970927 | − | 0.239376i | \(-0.0769430\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 4.21612i | − | 0.275029i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 24.2164 | 1.57302 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.6417 | −1.27051 | −0.635257 | − | 0.772301i | \(-0.719106\pi\) | ||||
−0.635257 | + | 0.772301i | \(0.719106\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 12.0508i | − | 0.776259i | −0.921605 | − | 0.388130i | \(-0.873121\pi\) | ||
0.921605 | − | 0.388130i | \(-0.126879\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 25.8652i | − | 1.65926i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 7.99691i | − | 0.510904i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.11306 | 0.516221 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 29.8260i | − | 1.89015i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.54963 | −0.413409 | −0.206705 | − | 0.978403i | \(-0.566274\pi\) | ||||
−0.206705 | + | 0.978403i | \(0.566274\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −28.4048 | −1.78580 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 18.9699 | − | 2.65407i | 1.18794 | − | 0.166204i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.8588 | −0.864486 | −0.432243 | − | 0.901757i | \(-0.642278\pi\) | ||||
−0.432243 | + | 0.901757i | \(0.642278\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.15904 | −0.258430 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16.5608i | 1.02509i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.2879 | 1.18934 | 0.594672 | − | 0.803968i | \(-0.297282\pi\) | ||||
0.594672 | + | 0.803968i | \(0.297282\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2.17078i | − | 0.133350i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 14.4735i | − | 0.885762i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.5692i | 1.31509i | 0.753413 | + | 0.657547i | \(0.228406\pi\) | ||||
−0.753413 | + | 0.657547i | \(0.771594\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.1592 | −0.860109 | −0.430054 | − | 0.902803i | \(-0.641506\pi\) | ||||
−0.430054 | + | 0.902803i | \(0.641506\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.9961 | 0.786561 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 17.0223i | 1.02649i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.541294i | 0.0325232i | 0.999868 | + | 0.0162616i | \(0.00517645\pi\) | ||||
−0.999868 | + | 0.0162616i | \(0.994824\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.9028i | 0.832337i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.83498 | −0.288431 | −0.144215 | − | 0.989546i | \(-0.546066\pi\) | ||||
−0.144215 | + | 0.989546i | \(0.546066\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.8603i | 1.53723i | 0.639709 | + | 0.768617i | \(0.279055\pi\) | ||||
−0.639709 | + | 0.768617i | \(0.720945\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 11.3814 | 0.674179 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.0986 | −0.596103 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.3472 | − | 4.66559i | 0.961602 | − | 0.274446i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.93873 | 0.113650 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −23.6848 | −1.38368 | −0.691840 | − | 0.722051i | \(-0.743200\pi\) | ||||
−0.691840 | + | 0.722051i | \(0.743200\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1.45906i | − | 0.0849498i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −78.1155 | −4.53272 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 15.8659i | − | 0.917549i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.15282i | 0.527560i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 22.4923i | 1.29215i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.1325 | 0.923746 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.4472 | 1.73771 | 0.868855 | − | 0.495066i | \(-0.164856\pi\) | ||||
0.868855 | + | 0.495066i | \(0.164856\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 18.6430i | − | 1.06056i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.55904i | 0.258519i | 0.991611 | + | 0.129260i | \(0.0412601\pi\) | ||||
−0.991611 | + | 0.129260i | \(0.958740\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.6866i | 0.886661i | 0.896358 | + | 0.443331i | \(0.146203\pi\) | ||||
−0.896358 | + | 0.443331i | \(0.853797\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 12.8367 | 0.723264 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 1.65225i | − | 0.0927993i | −0.998923 | − | 0.0463997i | \(-0.985225\pi\) | ||
0.998923 | − | 0.0463997i | \(-0.0147748\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.7552 | 0.770145 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −59.3964 | −3.31518 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.0037 | − | 1.39961i | 0.556622 | − | 0.0778766i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.50806 | −0.527412 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 64.7769 | 3.58217 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 3.56154i | − | 0.196354i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.1265 | −0.721498 | −0.360749 | − | 0.932663i | \(-0.617479\pi\) | ||||
−0.360749 | + | 0.932663i | \(0.617479\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 24.0865i | 1.31993i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 16.6818i | − | 0.911425i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.09349i | 0.0595662i | 0.999556 | + | 0.0297831i | \(0.00948165\pi\) | ||||
−0.999556 | + | 0.0297831i | \(0.990518\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.95139 | −0.323235 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.5475 | 0.625330 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 15.3831i | − | 0.830609i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 22.2576i | − | 1.19831i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.1509i | 1.29649i | 0.761432 | + | 0.648244i | \(0.224496\pi\) | ||||
−0.761432 | + | 0.648244i | \(0.775504\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.8561 | 1.16993 | 0.584964 | − | 0.811059i | \(-0.301108\pi\) | ||||
0.584964 | + | 0.811059i | \(0.301108\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 43.6325i | − | 2.32893i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.9809 | −1.11670 | −0.558351 | − | 0.829605i | \(-0.688566\pi\) | ||||
−0.558351 | + | 0.829605i | \(0.688566\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.0898 | −0.694737 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 16.0248 | − | 2.24201i | 0.848120 | − | 0.118660i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.4184 | −0.549861 | −0.274931 | − | 0.961464i | \(-0.588655\pi\) | ||||
−0.274931 | + | 0.961464i | \(0.588655\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.9980 | −0.684107 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 76.8954i | 4.03596i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 23.5799 | 1.23423 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 24.4045i | − | 1.27390i | −0.770904 | − | 0.636951i | \(-0.780195\pi\) | ||
0.770904 | − | 0.636951i | \(-0.219805\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 58.4847i | 3.04459i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 1.83375i | − | 0.0952037i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.5197 | 1.58025 | 0.790124 | − | 0.612947i | \(-0.210016\pi\) | ||||
0.790124 | + | 0.612947i | \(0.210016\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −36.5669 | −1.88831 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.68318i | 0.395704i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 5.24374i | − | 0.269353i | −0.990890 | − | 0.134677i | \(-0.957000\pi\) | ||
0.990890 | − | 0.134677i | \(-0.0429995\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.6822i | 0.957119i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.4888 | −0.893634 | −0.446817 | − | 0.894625i | \(-0.647442\pi\) | ||||
−0.446817 | + | 0.894625i | \(0.647442\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 10.6620i | − | 0.543384i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 53.0072 | 2.69451 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.6054 | 0.588417 | 0.294209 | − | 0.955741i | \(-0.404944\pi\) | ||||
0.294209 | + | 0.955741i | \(0.404944\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.73709 | − | 19.5633i | −0.138420 | − | 0.989359i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 68.3000 | 3.44528 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.0970 | 0.558351 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 39.0760i | 1.96117i | 0.196102 | + | 0.980584i | \(0.437172\pi\) | ||||
−0.196102 | + | 0.980584i | \(0.562828\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.61442 | 0.481323 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.1430i | 0.856080i | 0.903760 | + | 0.428040i | \(0.140796\pi\) | ||||
−0.903760 | + | 0.428040i | \(0.859204\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.44999i | 0.321297i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 29.9656i | − | 1.48900i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20.0059 | 0.991657 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.3558 | 1.15487 | 0.577435 | − | 0.816437i | \(-0.304054\pi\) | ||||
0.577435 | + | 0.816437i | \(0.304054\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 8.34544i | − | 0.411650i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 1.23253i | − | 0.0606491i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 13.6676i | − | 0.670916i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.66249 | −0.130383 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.1123i | 0.494020i | 0.969013 | + | 0.247010i | \(0.0794481\pi\) | ||||
−0.969013 | + | 0.247010i | \(0.920552\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.94430 | −0.387182 | −0.193591 | − | 0.981082i | \(-0.562013\pi\) | ||||
−0.193591 | + | 0.981082i | \(0.562013\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −20.6262 | −1.00288 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.7238 | + | 1.64027i | −0.568689 | + | 0.0795649i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.6279 | 0.659499 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −62.5143 | −3.01822 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 21.7853i | − | 1.04936i | −0.851299 | − | 0.524681i | \(-0.824185\pi\) | ||
0.851299 | − | 0.524681i | \(-0.175815\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.5810 | −0.892944 | −0.446472 | − | 0.894798i | \(-0.647320\pi\) | ||||
−0.446472 | + | 0.894798i | \(0.647320\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.7784i | 0.516784i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 11.7375i | − | 0.561479i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 34.4288i | − | 1.64320i | −0.570067 | − | 0.821598i | \(-0.693083\pi\) | ||
0.570067 | − | 0.821598i | \(-0.306917\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −39.1226 | −1.86298 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.7022 | −1.50622 | −0.753109 | − | 0.657896i | \(-0.771447\pi\) | ||||
−0.753109 | + | 0.657896i | \(0.771447\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 6.63237i | − | 0.314405i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 54.9412i | 2.59863i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.310627i | 0.0146594i | 0.999973 | + | 0.00732969i | \(0.00233314\pi\) | ||||
−0.999973 | + | 0.00732969i | \(0.997667\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 48.5767 | 2.28739 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.0812i | 0.849529i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.95539 | 0.279193 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.6630 | −0.732686 | −0.366343 | − | 0.930480i | \(-0.619390\pi\) | ||||
−0.366343 | + | 0.930480i | \(0.619390\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.52721 | − | 53.8006i | −0.351340 | − | 2.51120i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.35063 | 0.249204 | 0.124602 | − | 0.992207i | \(-0.460235\pi\) | ||||
0.124602 | + | 0.992207i | \(0.460235\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.79377 | −0.222785 | −0.111393 | − | 0.993776i | \(-0.535531\pi\) | ||||
−0.111393 | + | 0.993776i | \(0.535531\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.04841i | 0.419610i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 35.4649 | 1.64112 | 0.820560 | − | 0.571561i | \(-0.193662\pi\) | ||||
0.820560 | + | 0.571561i | \(0.193662\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 14.0919i | − | 0.650703i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.7784i | 0.865261i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 44.0271i | − | 2.02437i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.03398 | −0.322741 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.6199 | −0.486252 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 29.4834i | − | 1.34713i | −0.739128 | − | 0.673565i | \(-0.764762\pi\) | ||
0.739128 | − | 0.673565i | \(-0.235238\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.1746i | 0.509517i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 18.8020i | − | 0.855520i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.888409 | 0.0403406 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 30.1177i | − | 1.36476i | −0.730996 | − | 0.682382i | \(-0.760944\pi\) | ||
0.730996 | − | 0.682382i | \(-0.239056\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 23.0441 | 1.04209 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.5413 | −1.24292 | −0.621461 | − | 0.783445i | \(-0.713461\pi\) | ||||
−0.621461 | + | 0.783445i | \(0.713461\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.32545 | + | 9.47367i | 0.0596955 | + | 0.426673i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −61.7473 | −2.77533 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.0576 | −0.496000 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 20.6410i | − | 0.924016i | −0.886876 | − | 0.462008i | \(-0.847129\pi\) | ||
0.886876 | − | 0.462008i | \(-0.152871\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 69.9965 | 3.12721 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 29.7160i | 1.32497i | 0.749075 | + | 0.662485i | \(0.230498\pi\) | ||||
−0.749075 | + | 0.662485i | \(0.769502\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.3069i | 0.458652i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.47415i | 0.287527i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.45892 | 0.374935 | 0.187467 | − | 0.982271i | \(-0.439972\pi\) | ||||
0.187467 | + | 0.982271i | \(0.439972\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.9190 | 0.881166 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 32.2790i | − | 1.42515i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 8.54302i | − | 0.376451i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.1318i | 0.753457i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.3352 | 0.629245 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.2625i | 1.06296i | 0.847071 | + | 0.531480i | \(0.178364\pi\) | ||||
−0.847071 | + | 0.531480i | \(0.821636\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.31208 | 0.363462 | 0.181731 | − | 0.983348i | \(-0.441830\pi\) | ||||
0.181731 | + | 0.983348i | \(0.441830\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −11.2676 | −0.491758 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.11271 | + | 7.95310i | 0.0484706 | + | 0.346443i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.0462149 | 0.00200935 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.13805 | −0.309765 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 27.1332i | 1.17527i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −27.2180 | −1.17674 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 16.3984i | − | 0.707644i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 32.4948i | 1.39965i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 18.8560i | − | 0.810685i | −0.914165 | − | 0.405342i | \(-0.867152\pi\) | ||
0.914165 | − | 0.405342i | \(-0.132848\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.50218 | −0.364863 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 29.6836 | 1.27151 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.5805i | 1.60683i | 0.595421 | + | 0.803414i | \(0.296985\pi\) | ||||
−0.595421 | + | 0.803414i | \(0.703015\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 78.9239i | − | 3.36839i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.68395i | 0.242144i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.37414 | 0.398629 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 15.6763i | 0.665423i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −33.9610 | −1.43898 | −0.719488 | − | 0.694505i | \(-0.755623\pi\) | ||||
−0.719488 | + | 0.694505i | \(0.755623\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.5920 | 1.04013 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −77.0827 | + | 10.7846i | −3.25443 | + | 0.455326i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.2925 | −1.23453 | −0.617265 | − | 0.786755i | \(-0.711759\pi\) | ||||
−0.617265 | + | 0.786755i | \(0.711759\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.72718 | −0.114734 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 25.3133i | − | 1.06306i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.5056 | −0.566184 | −0.283092 | − | 0.959093i | \(-0.591360\pi\) | ||||
−0.283092 | + | 0.959093i | \(0.591360\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 4.26022i | − | 0.178285i | −0.996019 | − | 0.0891424i | \(-0.971587\pi\) | ||
0.996019 | − | 0.0891424i | \(-0.0284126\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 76.2079i | 3.18363i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.7557i | 0.573651i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.52454 | 0.396512 | 0.198256 | − | 0.980150i | \(-0.436472\pi\) | ||||
0.198256 | + | 0.980150i | \(0.436472\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 51.9481 | 2.15889 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 11.5456i | − | 0.478993i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.82076i | 0.365319i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 34.4898i | − | 1.42598i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 38.4819 | 1.58832 | 0.794160 | − | 0.607709i | \(-0.207911\pi\) | ||||
0.794160 | + | 0.607709i | \(0.207911\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.77165i | 0.196612i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 84.8031 | 3.48833 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −38.7928 | −1.59303 | −0.796515 | − | 0.604618i | \(-0.793326\pi\) | ||||
−0.796515 | + | 0.604618i | \(0.793326\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.34324 | − | 1.02739i | 0.301043 | − | 0.0421188i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.9846 | 0.572353 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.53260 | 0.307774 | 0.153887 | − | 0.988088i | \(-0.450821\pi\) | ||||
0.153887 | + | 0.988088i | \(0.450821\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.8971i | 1.54585i | 0.634494 | + | 0.772927i | \(0.281208\pi\) | ||||
−0.634494 | + | 0.772927i | \(0.718792\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −81.6111 | −3.32346 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 35.2368i | 1.43258i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.1958i | 0.779133i | 0.920998 | + | 0.389567i | \(0.127375\pi\) | ||||
−0.920998 | + | 0.389567i | \(0.872625\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.10499i | 0.368953i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.56922 | −0.387129 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.0662 | −1.13358 | −0.566792 | − | 0.823861i | \(-0.691816\pi\) | ||||
−0.566792 | + | 0.823861i | \(0.691816\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 38.0639i | 1.53489i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 20.2211i | − | 0.814072i | −0.913412 | − | 0.407036i | \(-0.866562\pi\) | ||
0.913412 | − | 0.407036i | \(-0.133438\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 40.1443i | − | 1.61354i | −0.590869 | − | 0.806768i | \(-0.701215\pi\) | ||
0.590869 | − | 0.806768i | \(-0.298785\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −63.1248 | −2.53311 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 5.60266i | − | 0.224466i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.40085 | −0.0960339 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −46.2476 | −1.84695 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.92777 | + | 13.7787i | 0.0768653 | + | 0.549394i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.1841 | 1.04237 | 0.521186 | − | 0.853443i | \(-0.325490\pi\) | ||||
0.521186 | + | 0.853443i | \(0.325490\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.9366 | −0.514184 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.56101i | 0.339733i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.1504 | −0.719145 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 64.0384i | 2.53332i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.0919i | 0.596096i | 0.954551 | + | 0.298048i | \(0.0963355\pi\) | ||||
−0.954551 | + | 0.298048i | \(0.903665\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 8.11859i | − | 0.320166i | −0.987104 | − | 0.160083i | \(-0.948824\pi\) | ||
0.987104 | − | 0.160083i | \(-0.0511762\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 34.4990 | 1.35840 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.93033 | 0.351088 | 0.175544 | − | 0.984472i | \(-0.443832\pi\) | ||||
0.175544 | + | 0.984472i | \(0.443832\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.92877i | 0.232725i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.64360i | 0.299576i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.8172i | 0.932040i | 0.884774 | + | 0.466020i | \(0.154312\pi\) | ||||
−0.884774 | + | 0.466020i | \(0.845688\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 31.2980 | 1.22292 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 115.358i | − | 4.50055i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.17063 | 0.279328 | 0.139664 | − | 0.990199i | \(-0.455398\pi\) | ||||
0.139664 | + | 0.990199i | \(0.455398\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.249180 | 0.00969197 | 0.00484599 | − | 0.999988i | \(-0.498457\pi\) | ||||
0.00484599 | + | 0.999988i | \(0.498457\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.02388 | − | 43.0556i | −0.233948 | − | 1.67214i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.40575 | 0.170848 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.1155 | 0.430395 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 76.8451i | − | 2.97100i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −65.5532 | −2.53065 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.92563i | 0.266964i | 0.991051 | + | 0.133482i | \(0.0426158\pi\) | ||||
−0.991051 | + | 0.133482i | \(0.957384\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 37.8292i | 1.45605i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 8.31848i | − | 0.319705i | −0.987141 | − | 0.159853i | \(-0.948898\pi\) | ||
0.987141 | − | 0.159853i | \(-0.0511019\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.750479 | 0.0288008 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21.5339 | −0.825179 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.6455i | 1.24914i | 0.780967 | + | 0.624572i | \(0.214726\pi\) | ||||
−0.780967 | + | 0.624572i | \(0.785274\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 3.82425i | − | 0.146117i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 19.9950i | − | 0.762856i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.92696 | −0.187702 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.2226i | 0.959513i | 0.877402 | + | 0.479756i | \(0.159275\pi\) | ||||
−0.877402 | + | 0.479756i | \(0.840725\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −52.1607 | −1.98142 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.22007 | −0.0462799 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.68085 | + | 33.4563i | 0.177300 | + | 1.26725i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.2684 | −0.880091 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33.1163 | −1.25079 | −0.625393 | − | 0.780310i | \(-0.715061\pi\) | ||||
−0.625393 | + | 0.780310i | \(0.715061\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.26686i | 0.311791i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.4242 | −0.505586 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.70673i | 0.327450i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.2206i | 1.09740i | 0.836019 | + | 0.548701i | \(0.184877\pi\) | ||||
−0.836019 | + | 0.548701i | \(0.815123\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 54.2890i | − | 2.03599i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.33144 | 0.349465 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −28.6468 | −1.07133 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 62.5396i | 2.33559i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 3.76832i | − | 0.140535i | −0.997528 | − | 0.0702673i | \(-0.977615\pi\) | ||
0.997528 | − | 0.0702673i | \(-0.0223852\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 7.21668i | − | 0.268763i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −38.3701 | −1.42700 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 6.66128i | − | 0.247394i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.8098 | −0.549265 | −0.274632 | − | 0.961549i | \(-0.588556\pi\) | ||||
−0.274632 | + | 0.961549i | \(0.588556\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.7430 | −0.768260 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.3229 | − | 4.24246i | 1.12153 | − | 0.156913i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −48.5122 | −1.79184 | −0.895920 | − | 0.444215i | \(-0.853483\pi\) | ||||
−0.895920 | + | 0.444215i | \(0.853483\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −25.4624 | −0.939194 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 67.7852i | 2.49690i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.0660 | −0.738141 | −0.369070 | − | 0.929401i | \(-0.620324\pi\) | ||||
−0.369070 | + | 0.929401i | \(0.620324\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 25.8322i | − | 0.948970i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 23.6271i | − | 0.866795i | −0.901203 | − | 0.433398i | \(-0.857315\pi\) | ||
0.901203 | − | 0.433398i | \(-0.142685\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 25.1765i | 0.922394i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −66.8648 | −2.44646 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −22.9923 | −0.840120 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 10.6929i | − | 0.390188i | −0.980785 | − | 0.195094i | \(-0.937499\pi\) | ||
0.980785 | − | 0.195094i | \(-0.0625012\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20.8542i | 0.759970i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.28559i | 0.301544i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.7900 | −1.19177 | −0.595886 | − | 0.803069i | \(-0.703199\pi\) | ||||
−0.595886 | + | 0.803069i | \(0.703199\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 90.4418i | 3.28283i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −35.3405 | −1.28109 | −0.640547 | − | 0.767919i | \(-0.721292\pi\) | ||||
−0.640547 | + | 0.767919i | \(0.721292\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.0751 | 0.907779 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.94997 | − | 42.5273i | −0.215121 | − | 1.53758i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.31160 | −0.119575 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 45.1200 | 1.62707 | 0.813534 | − | 0.581518i | \(-0.197541\pi\) | ||||
0.813534 | + | 0.581518i | \(0.197541\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 44.1267i | 1.58919i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.2692 | 1.12468 | 0.562338 | − | 0.826908i | \(-0.309902\pi\) | ||||
0.562338 | + | 0.826908i | \(0.309902\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 5.59212i | − | 0.200875i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 13.2425i | 0.475072i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.0729i | 0.719186i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 53.1895 | 1.90327 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 30.5686 | 1.09243 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.60506i | 0.307128i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.20289i | 0.292402i | 0.989255 | + | 0.146201i | \(0.0467046\pi\) | ||||
−0.989255 | + | 0.146201i | \(0.953295\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 61.4133i | − | 2.18637i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.30378 | −0.0819128 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 36.6156i | − | 1.30026i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.91181 | −0.245137 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.16816 | −0.183066 | −0.0915328 | − | 0.995802i | \(-0.529177\pi\) | ||||
−0.0915328 | + | 0.995802i | \(0.529177\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.7992 | + | 1.65082i | −0.417427 | + | 0.0584020i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −32.4470 | −1.14646 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −95.8151 | −3.38124 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 8.61588i | − | 0.303670i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 68.6768 | 2.41754 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 6.84255i | − | 0.240571i | −0.992739 | − | 0.120286i | \(-0.961619\pi\) | ||
0.992739 | − | 0.120286i | \(-0.0383810\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 17.7327i | − | 0.622679i | −0.950299 | − | 0.311340i | \(-0.899222\pi\) | ||
0.950299 | − | 0.311340i | \(-0.100778\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 45.0833i | 1.58114i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.5598 | 0.369895 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.1929 | 0.636490 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 29.1351i | − | 1.01806i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 25.9390i | − | 0.905277i | −0.891694 | − | 0.452638i | \(-0.850483\pi\) | ||
0.891694 | − | 0.452638i | \(-0.149517\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 29.4843i | − | 1.02776i | −0.857863 | − | 0.513879i | \(-0.828208\pi\) | ||
0.857863 | − | 0.513879i | \(-0.171792\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 54.1996 | 1.88699 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.2942i | 0.357966i | 0.983852 | + | 0.178983i | \(0.0572806\pi\) | ||||
−0.983852 | + | 0.178983i | \(0.942719\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.6829 | −0.579421 | −0.289711 | − | 0.957114i | \(-0.593559\pi\) | ||||
−0.289711 | + | 0.957114i | \(0.593559\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.72349 | 0.0597874 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −22.3802 | + | 3.13120i | −0.775427 | + | 0.108489i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 32.0754 | 1.11002 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 25.6622 | 0.887016 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 5.70771i | − | 0.197052i | −0.995134 | − | 0.0985261i | \(-0.968587\pi\) | ||
0.995134 | − | 0.0985261i | \(-0.0314128\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.6172 | 0.814387 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.3947i | 0.530222i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.96674i | 0.102059i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.7661i | 1.02278i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 82.3399 | 2.82590 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.1667 | 0.554187 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 37.1226i | − | 1.27105i | −0.772078 | − | 0.635527i | \(-0.780783\pi\) | ||
0.772078 | − | 0.635527i | \(-0.219217\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 25.5152i | − | 0.872603i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.9145i | 0.714426i | 0.934023 | + | 0.357213i | \(0.116273\pi\) | ||||
−0.934023 | + | 0.357213i | \(0.883727\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.37977 | −0.285914 | −0.142957 | − | 0.989729i | \(-0.545661\pi\) | ||||
−0.142957 | + | 0.989729i | \(0.545661\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 32.1543i | 1.09582i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.04249 | −0.137608 | −0.0688039 | − | 0.997630i | \(-0.521918\pi\) | ||||
−0.0688039 | + | 0.997630i | \(0.521918\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.56901 | 0.223353 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.8554 | − | 52.0501i | −0.504515 | − | 1.76771i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −45.0917 | −1.52963 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37.8623 | −1.28292 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 4.34629i | − | 0.147100i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −14.1550 | −0.478527 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.3720i | 0.687913i | 0.938986 | + | 0.343956i | \(0.111767\pi\) | ||||
−0.938986 | + | 0.343956i | \(0.888233\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 75.4131i | 2.54362i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.9500i | 0.739514i | 0.929128 | + | 0.369757i | \(0.120559\pi\) | ||||
−0.929128 | + | 0.369757i | \(0.879441\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.59273 | 0.154558 | 0.0772788 | − | 0.997010i | \(-0.475377\pi\) | ||||
0.0772788 | + | 0.997010i | \(0.475377\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.64569 | −0.156163 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.07477i | 0.203971i | 0.994786 | + | 0.101985i | \(0.0325195\pi\) | ||||
−0.994786 | + | 0.101985i | \(0.967481\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.23187i | 0.242549i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 121.763i | 4.07920i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.07923 | −0.236897 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 7.51447i | − | 0.251181i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −50.5175 | −1.68673 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.51882 | −0.150711 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.07514 | + | 0.849969i | −0.202392 | + | 0.0283166i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 29.1429 | 0.969813 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.89607 | −0.129510 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.2220i | 0.937098i | 0.883438 | + | 0.468549i | \(0.155223\pi\) | ||||
−0.883438 | + | 0.468549i | \(0.844777\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 50.4238 | 1.67245 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 26.1712i | − | 0.867091i | −0.901132 | − | 0.433546i | \(-0.857262\pi\) | ||
0.901132 | − | 0.433546i | \(-0.142738\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 55.5371i | 1.83801i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 51.3665i | − | 1.69812i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 26.4389 | 0.873088 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43.4222 | −1.43237 | −0.716184 | − | 0.697912i | \(-0.754113\pi\) | ||||
−0.716184 | + | 0.697912i | \(0.754113\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 96.9447i | − | 3.19444i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29.7097i | 0.977908i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 9.68832i | − | 0.318550i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −41.7943 | −1.37271 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 33.8956i | − | 1.11208i | −0.831156 | − | 0.556040i | \(-0.812320\pi\) | ||
0.831156 | − | 0.556040i | \(-0.187680\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.4275 | −0.440069 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.5161 | 0.475236 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −35.3226 | + | 4.94197i | −1.15517 | + | 0.161620i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.3949 | 1.35231 | 0.676157 | − | 0.736758i | \(-0.263644\pi\) | ||||
0.676157 | + | 0.736758i | \(0.263644\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 49.9467 | 1.62995 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 58.5036i | 1.90716i | 0.301138 | + | 0.953581i | \(0.402634\pi\) | ||||
−0.301138 | + | 0.953581i | \(0.597366\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 39.2546 | 1.27830 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 23.6944i | − | 0.770778i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 3.50635i | − | 0.113941i | −0.998376 | − | 0.0569705i | \(-0.981856\pi\) | ||
0.998376 | − | 0.0569705i | \(-0.0181441\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 53.5188i | − | 1.73729i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.26080 | −0.170593 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −47.1521 | −1.52741 | −0.763703 | − | 0.645568i | \(-0.776621\pi\) | ||||
−0.763703 | + | 0.645568i | \(0.776621\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 34.9218i | 1.13004i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 43.7971i | − | 1.41576i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 3.23051i | − | 0.104319i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.2065 | 0.877628 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 133.156i | 4.29091i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 23.8049 | 0.766306 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.0301269 | −0.000968815 | −0.000484408 | − | 1.00000i | \(-0.500154\pi\) | ||||
−0.000484408 | 1.00000i | \(0.500154\pi\) | ||||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.45642 | − | 31.8522i | −0.143161 | − | 1.02324i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.4249 | −0.591282 | −0.295641 | − | 0.955299i | \(-0.595533\pi\) | ||||
−0.295641 | + | 0.955299i | \(0.595533\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.03065 | −0.0330411 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 30.2740i | 0.969543i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.65741 | −0.0850182 | −0.0425091 | − | 0.999096i | \(-0.513535\pi\) | ||||
−0.0425091 | + | 0.999096i | \(0.513535\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26.9501i | 0.861328i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 145.219i | − | 4.63647i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 9.60071i | − | 0.306215i | −0.988210 | − | 0.153107i | \(-0.951072\pi\) | ||
0.988210 | − | 0.153107i | \(-0.0489281\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 38.8605 | 1.23820 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −11.3401 | −0.360958 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 35.5781i | − | 1.13132i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 43.6728i | − | 1.38731i | −0.720307 | − | 0.693655i | \(-0.755999\pi\) | ||
0.720307 | − | 0.693655i | \(-0.244001\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 41.7952i | 1.32633i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.40837 | 0.203159 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 58.9172i | 1.86593i | 0.359970 | + | 0.932964i | \(0.382787\pi\) | ||||
−0.359970 | + | 0.932964i | \(0.617213\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 44.4597 | 1.40664 |
(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 | 4012.2.b.b.237.3 | ✓ | 46 | |
17.16 | even | 2 | inner | 4012.2.b.b.237.44 | yes | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.b.b.237.3 | ✓ | 46 | 1.1 | even | 1 | trivial | |
4012.2.b.b.237.44 | yes | 46 | 17.16 | even | 2 | inner |