Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1664,2,Mod(417,1664)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1664, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1664.417");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1664 = 2^{7} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1664.n (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.2871068963\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 208) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 417.8 | ||
Character | \(\chi\) | \(=\) | 1664.417 |
Dual form | 1664.2.n.b.1249.8 |
$q$-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 \(\left(\mathbb{Z}/1664\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(769\) | \(1535\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −0.902776 | − | 0.902776i | −0.521218 | − | 0.521218i | 0.396721 | − | 0.917939i | \(-0.370148\pi\) |
−0.917939 | + | 0.396721i | \(0.870148\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.29480 | − | 1.29480i | 0.579054 | − | 0.579054i | −0.355589 | − | 0.934643i | \(-0.615720\pi\) |
0.934643 | + | 0.355589i | \(0.115720\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.20594i | − | 1.21173i | −0.795567 | − | 0.605865i | \(-0.792827\pi\) | ||
0.795567 | − | 0.605865i | \(-0.207173\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.36999i | − | 0.456663i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.72143 | − | 2.72143i | 0.820543 | − | 0.820543i | −0.165642 | − | 0.986186i | \(-0.552970\pi\) |
0.986186 | + | 0.165642i | \(0.0529698\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.707107 | − | 0.707107i | −0.196116 | − | 0.196116i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.33784 | −0.603627 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.03671 | −1.46412 | −0.732058 | − | 0.681242i | \(-0.761440\pi\) | ||||
−0.732058 | + | 0.681242i | \(0.761440\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.89947 | − | 1.89947i | −0.435768 | − | 0.435768i | 0.454817 | − | 0.890585i | \(-0.349705\pi\) |
−0.890585 | + | 0.454817i | \(0.849705\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.89424 | + | 2.89424i | −0.631576 | + | 0.631576i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 8.67448i | − | 1.80875i | −0.426734 | − | 0.904377i | \(-0.640336\pi\) | ||
0.426734 | − | 0.904377i | \(-0.359664\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.64697i | 0.329393i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.94512 | + | 3.94512i | −0.759239 | + | 0.759239i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.82640 | + | 6.82640i | 1.26763 | + | 1.26763i | 0.947309 | + | 0.320321i | \(0.103791\pi\) |
0.320321 | + | 0.947309i | \(0.396209\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.23082 | 0.939484 | 0.469742 | − | 0.882804i | \(-0.344347\pi\) | ||||
0.469742 | + | 0.882804i | \(0.344347\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.91369 | −0.855364 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.15106 | − | 4.15106i | −0.701657 | − | 0.701657i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.208536 | − | 0.208536i | 0.0342830 | − | 0.0342830i | −0.689757 | − | 0.724041i | \(-0.742283\pi\) |
0.724041 | + | 0.689757i | \(0.242283\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.27672i | 0.204439i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.29774i | 1.45206i | 0.687662 | + | 0.726031i | \(0.258637\pi\) | ||||
−0.687662 | + | 0.726031i | \(0.741363\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.0416722 | + | 0.0416722i | −0.00635495 | + | 0.00635495i | −0.710277 | − | 0.703922i | \(-0.751430\pi\) |
0.703922 | + | 0.710277i | \(0.251430\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.77387 | − | 1.77387i | −0.264433 | − | 0.264433i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.16694 | 0.316081 | 0.158040 | − | 0.987433i | \(-0.449482\pi\) | ||||
0.158040 | + | 0.987433i | \(0.449482\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.27803 | −0.468290 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.44980 | + | 5.44980i | 0.763124 | + | 0.763124i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.38002 | − | 6.38002i | 0.876363 | − | 0.876363i | −0.116793 | − | 0.993156i | \(-0.537261\pi\) |
0.993156 | + | 0.116793i | \(0.0372614\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 7.04745i | − | 0.950278i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.42959i | 0.454260i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.38796 | + | 3.38796i | −0.441075 | + | 0.441075i | −0.892373 | − | 0.451298i | \(-0.850961\pi\) |
0.451298 | + | 0.892373i | \(0.350961\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.72743 | − | 1.72743i | −0.221175 | − | 0.221175i | 0.587818 | − | 0.808993i | \(-0.299987\pi\) |
−0.808993 | + | 0.587818i | \(0.799987\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.39210 | −0.553353 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.83113 | −0.227124 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.56033 | + | 1.56033i | 0.190624 | + | 0.190624i | 0.795966 | − | 0.605342i | \(-0.206963\pi\) |
−0.605342 | + | 0.795966i | \(0.706963\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.83111 | + | 7.83111i | −0.942755 | + | 0.942755i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.73843i | 1.15574i | 0.816129 | + | 0.577869i | \(0.196116\pi\) | ||||
−0.816129 | + | 0.577869i | \(0.803884\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.08728i | 0.712462i | 0.934398 | + | 0.356231i | \(0.115938\pi\) | ||||
−0.934398 | + | 0.356231i | \(0.884062\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.48684 | − | 1.48684i | 0.171686 | − | 0.171686i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.72475 | − | 8.72475i | −0.994277 | − | 0.994277i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.31445 | −0.597922 | −0.298961 | − | 0.954265i | \(-0.596640\pi\) | ||||
−0.298961 | + | 0.954265i | \(0.596640\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.01316 | 0.334795 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.71028 | − | 9.71028i | −1.06584 | − | 1.06584i | −0.997674 | − | 0.0681682i | \(-0.978285\pi\) |
−0.0681682 | − | 0.997674i | \(-0.521715\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.81635 | + | 7.81635i | −0.847802 | + | 0.847802i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 12.3254i | − | 1.32142i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 5.94615i | − | 0.630291i | −0.949043 | − | 0.315145i | \(-0.897947\pi\) | ||
0.949043 | − | 0.315145i | \(-0.102053\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.26694 | + | 2.26694i | −0.237640 | + | 0.237640i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.72226 | − | 4.72226i | −0.489676 | − | 0.489676i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.91887 | −0.504666 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.79055 | −0.994080 | −0.497040 | − | 0.867728i | \(-0.665580\pi\) | ||||
−0.497040 | + | 0.867728i | \(0.665580\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.72834 | − | 3.72834i | −0.374712 | − | 0.374712i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.75506 | − | 4.75506i | 0.473146 | − | 0.473146i | −0.429785 | − | 0.902931i | \(-0.641411\pi\) |
0.902931 | + | 0.429785i | \(0.141411\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 2.88844i | − | 0.284607i | −0.989823 | − | 0.142303i | \(-0.954549\pi\) | ||
0.989823 | − | 0.142303i | \(-0.0454509\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.49496i | 0.731433i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.70795 | + | 3.70795i | −0.358461 | + | 0.358461i | −0.863245 | − | 0.504785i | \(-0.831572\pi\) |
0.504785 | + | 0.863245i | \(0.331572\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.76524 | − | 2.76524i | −0.264862 | − | 0.264862i | 0.562164 | − | 0.827026i | \(-0.309969\pi\) |
−0.827026 | + | 0.562164i | \(0.809969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.376522 | −0.0357379 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.12934 | 0.858816 | 0.429408 | − | 0.903111i | \(-0.358722\pi\) | ||||
0.429408 | + | 0.903111i | \(0.358722\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.2317 | − | 11.2317i | −1.04737 | − | 1.04737i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.968729 | + | 0.968729i | −0.0895591 | + | 0.0895591i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 19.3533i | 1.77411i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 3.81241i | − | 0.346583i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.39378 | − | 8.39378i | 0.756841 | − | 0.756841i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.60652 | + | 8.60652i | 0.769790 | + | 0.769790i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.7097 | 1.12780 | 0.563901 | − | 0.825842i | \(-0.309300\pi\) | ||||
0.563901 | + | 0.825842i | \(0.309300\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.0752414 | 0.00662464 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.39425 | − | 6.39425i | −0.558668 | − | 0.558668i | 0.370260 | − | 0.928928i | \(-0.379269\pi\) |
−0.928928 | + | 0.370260i | \(0.879269\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.08957 | + | 6.08957i | −0.528033 | + | 0.528033i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10.2163i | 0.879281i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 19.8173i | − | 1.69310i | −0.532306 | − | 0.846552i | \(-0.678674\pi\) | ||
0.532306 | − | 0.846552i | \(-0.321326\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.81457 | − | 7.81457i | 0.662823 | − | 0.662823i | −0.293221 | − | 0.956045i | \(-0.594727\pi\) |
0.956045 | + | 0.293221i | \(0.0947273\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.95626 | − | 1.95626i | −0.164747 | − | 0.164747i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.84869 | −0.321844 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 17.6777 | 1.46805 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.95933 | + | 2.95933i | 0.244081 | + | 0.244081i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.86136 | + | 6.86136i | −0.562104 | + | 0.562104i | −0.929905 | − | 0.367800i | \(-0.880111\pi\) |
0.367800 | + | 0.929905i | \(0.380111\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 12.0002i | − | 0.976560i | −0.872687 | − | 0.488280i | \(-0.837624\pi\) | ||
0.872687 | − | 0.488280i | \(-0.162376\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.27023i | 0.668608i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.77289 | − | 6.77289i | 0.544012 | − | 0.544012i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.81214 | − | 1.81214i | −0.144625 | − | 0.144625i | 0.631087 | − | 0.775712i | \(-0.282609\pi\) |
−0.775712 | + | 0.631087i | \(0.782609\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.5195 | −0.913553 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −27.8098 | −2.19172 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.8786 | + | 13.8786i | 1.08706 | + | 1.08706i | 0.995830 | + | 0.0912264i | \(0.0290787\pi\) |
0.0912264 | + | 0.995830i | \(0.470921\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.36227 | + | 6.36227i | −0.495302 | + | 0.495302i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.99276i | 0.308969i | 0.987995 | + | 0.154485i | \(0.0493717\pi\) | ||||
−0.987995 | + | 0.154485i | \(0.950628\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000i | 0.0769231i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.60225 | + | 2.60225i | −0.198999 | + | 0.198999i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.5447 | − | 12.5447i | −0.953756 | − | 0.953756i | 0.0452212 | − | 0.998977i | \(-0.485601\pi\) |
−0.998977 | + | 0.0452212i | \(0.985601\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.28007 | 0.399136 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.11715 | 0.459793 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.56516 | + | 6.56516i | 0.490703 | + | 0.490703i | 0.908528 | − | 0.417825i | \(-0.137207\pi\) |
−0.417825 | + | 0.908528i | \(0.637207\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.91102 | + | 6.91102i | −0.513692 | + | 0.513692i | −0.915656 | − | 0.401964i | \(-0.868328\pi\) |
0.401964 | + | 0.915656i | \(0.368328\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.11897i | 0.230561i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 0.540025i | − | 0.0397035i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.4285 | + | 16.4285i | −1.20137 | + | 1.20137i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.6478 | + | 12.6478i | 0.919993 | + | 0.919993i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.2566 | −0.814502 | −0.407251 | − | 0.913316i | \(-0.633513\pi\) | ||||
−0.407251 | + | 0.913316i | \(0.633513\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.54609 | −0.183272 | −0.0916358 | − | 0.995793i | \(-0.529210\pi\) | ||||
−0.0916358 | + | 0.995793i | \(0.529210\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.65310 | + | 1.65310i | 0.118381 | + | 0.118381i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.30038 | + | 4.30038i | −0.306389 | + | 0.306389i | −0.843507 | − | 0.537118i | \(-0.819513\pi\) |
0.537118 | + | 0.843507i | \(0.319513\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 26.2885i | − | 1.86354i | −0.363048 | − | 0.931771i | \(-0.618264\pi\) | ||
0.363048 | − | 0.931771i | \(-0.381736\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 2.81725i | − | 0.198714i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 21.8850 | − | 21.8850i | 1.53603 | − | 1.53603i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.0387 | + | 12.0387i | 0.840823 | + | 0.840823i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −11.8840 | −0.825992 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.3385 | −0.715132 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.51991 | + | 7.51991i | 0.517692 | + | 0.517692i | 0.916872 | − | 0.399180i | \(-0.130705\pi\) |
−0.399180 | + | 0.916872i | \(0.630705\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.79162 | − | 8.79162i | 0.602392 | − | 0.602392i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.107915i | 0.00735972i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 16.7697i | − | 1.13840i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.49545 | − | 5.49545i | 0.371348 | − | 0.371348i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.26860 | + | 4.26860i | 0.287137 | + | 0.287137i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.7318 | −1.25438 | −0.627188 | − | 0.778868i | \(-0.715794\pi\) | ||||
−0.627188 | + | 0.778868i | \(0.715794\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.25633 | 0.150422 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.552713 | − | 0.552713i | −0.0366849 | − | 0.0366849i | 0.688526 | − | 0.725211i | \(-0.258258\pi\) |
−0.725211 | + | 0.688526i | \(0.758258\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.9481 | − | 14.9481i | 0.987798 | − | 0.987798i | −0.0121281 | − | 0.999926i | \(-0.503861\pi\) |
0.999926 | + | 0.0121281i | \(0.00386060\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 15.7530i | 1.03647i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 23.9526i | − | 1.56919i | −0.620009 | − | 0.784595i | \(-0.712871\pi\) | ||
0.620009 | − | 0.784595i | \(-0.287129\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.80576 | − | 2.80576i | 0.183028 | − | 0.183028i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.79776 | + | 4.79776i | 0.311648 | + | 0.311648i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.49140 | 0.0964709 | 0.0482354 | − | 0.998836i | \(-0.484640\pi\) | ||||
0.0482354 | + | 0.998836i | \(0.484640\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.0970048 | −0.00624863 | −0.00312431 | − | 0.999995i | \(-0.500995\pi\) | ||||
−0.00312431 | + | 0.999995i | \(0.500995\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.11516 | + | 9.11516i | 0.584738 | + | 0.584738i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.24441 | + | 4.24441i | −0.271165 | + | 0.271165i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.68625i | 0.170922i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17.5324i | 1.11107i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.32996 | + | 7.32996i | −0.462663 | + | 0.462663i | −0.899527 | − | 0.436864i | \(-0.856089\pi\) |
0.436864 | + | 0.899527i | \(0.356089\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −23.6070 | − | 23.6070i | −1.48416 | − | 1.48416i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 14.1128 | 0.883780 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 28.9029 | 1.80291 | 0.901457 | − | 0.432869i | \(-0.142499\pi\) | ||||
0.901457 | + | 0.432869i | \(0.142499\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.668552 | − | 0.668552i | −0.0415418 | − | 0.0415418i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.35210 | − | 9.35210i | 0.578880 | − | 0.578880i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.4287i | 1.07470i | 0.843360 | + | 0.537349i | \(0.180574\pi\) | ||||
−0.843360 | + | 0.537349i | \(0.819426\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 16.5217i | − | 1.01492i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.36804 | + | 5.36804i | −0.328519 | + | 0.328519i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.0262 | + | 12.0262i | 0.733248 | + | 0.733248i | 0.971262 | − | 0.238013i | \(-0.0764962\pi\) |
−0.238013 | + | 0.971262i | \(0.576496\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.79480 | 0.109026 | 0.0545131 | − | 0.998513i | \(-0.482639\pi\) | ||||
0.0545131 | + | 0.998513i | \(0.482639\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.09308 | 0.247724 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.48211 | + | 4.48211i | 0.270282 | + | 0.270282i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.31019 | − | 1.31019i | 0.0787215 | − | 0.0787215i | −0.666650 | − | 0.745371i | \(-0.732272\pi\) |
0.745371 | + | 0.666650i | \(0.232272\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 7.16618i | − | 0.429028i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.8404i | 1.60116i | 0.599225 | + | 0.800581i | \(0.295475\pi\) | ||||
−0.599225 | + | 0.800581i | \(0.704525\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.50326 | + | 1.50326i | −0.0893595 | + | 0.0893595i | −0.750374 | − | 0.661014i | \(-0.770126\pi\) |
0.661014 | + | 0.750374i | \(0.270126\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.44064 | + | 4.44064i | 0.263041 | + | 0.263041i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 29.8080 | 1.75951 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.4418 | 1.14364 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.83868 | + | 8.83868i | 0.518133 | + | 0.518133i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.58243 | − | 4.58243i | 0.267709 | − | 0.267709i | −0.560468 | − | 0.828176i | \(-0.689379\pi\) |
0.828176 | + | 0.560468i | \(0.189379\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.77350i | 0.510813i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 21.4728i | 1.24598i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.13378 | + | 6.13378i | −0.354726 | + | 0.354726i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.133599 | + | 0.133599i | 0.00770049 | + | 0.00770049i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.58551 | −0.493224 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.47337 | −0.256144 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.7315 | − | 13.7315i | −0.783699 | − | 0.783699i | 0.196754 | − | 0.980453i | \(-0.436960\pi\) |
−0.980453 | + | 0.196754i | \(0.936960\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.60762 | + | 2.60762i | −0.148342 | + | 0.148342i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.60913i | 0.0912455i | 0.998959 | + | 0.0456228i | \(0.0145272\pi\) | ||||
−0.998959 | + | 0.0456228i | \(0.985473\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 14.3857i | − | 0.813126i | −0.913623 | − | 0.406563i | \(-0.866727\pi\) | ||
0.913623 | − | 0.406563i | \(-0.133273\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.68691 | + | 5.68691i | −0.320421 | + | 0.320421i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.4126 | + | 12.4126i | 0.697160 | + | 0.697160i | 0.963797 | − | 0.266637i | \(-0.0859124\pi\) |
−0.266637 | + | 0.963797i | \(0.585912\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 37.1552 | 2.08029 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.69489 | 0.373673 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.4665 | + | 11.4665i | 0.638015 | + | 0.638015i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.16458 | − | 1.16458i | 0.0645994 | − | 0.0645994i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.99279i | 0.276102i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 6.94708i | − | 0.383005i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.1517 | − | 17.1517i | 0.942742 | − | 0.942742i | −0.0557049 | − | 0.998447i | \(-0.517741\pi\) |
0.998447 | + | 0.0557049i | \(0.0177406\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.285692 | − | 0.285692i | −0.0156558 | − | 0.0156558i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.04064 | 0.220764 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.8004 | 1.67781 | 0.838903 | − | 0.544281i | \(-0.183198\pi\) | ||||
0.838903 | + | 0.544281i | \(0.183198\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.24175 | − | 8.24175i | −0.447631 | − | 0.447631i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.2353 | − | 14.2353i | 0.770887 | − | 0.770887i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 11.9324i | − | 0.644289i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 20.2795i | 1.09181i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −22.1815 | + | 22.1815i | −1.19076 | + | 1.19076i | −0.213910 | + | 0.976853i | \(0.568620\pi\) |
−0.976853 | + | 0.213910i | \(0.931380\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.7484 | − | 15.7484i | −0.842990 | − | 0.842990i | 0.146256 | − | 0.989247i | \(-0.453278\pi\) |
−0.989247 | + | 0.146256i | \(0.953278\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.57925 | 0.297798 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.1232 | 1.49685 | 0.748424 | − | 0.663220i | \(-0.230811\pi\) | ||||
0.748424 | + | 0.663220i | \(0.230811\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.6094 | + | 12.6094i | 0.669235 | + | 0.669235i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 17.4717 | − | 17.4717i | 0.924701 | − | 0.924701i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 2.91495i | − | 0.153845i | −0.997037 | − | 0.0769225i | \(-0.975491\pi\) | ||
0.997037 | − | 0.0769225i | \(-0.0245094\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 11.7841i | − | 0.620213i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.44176 | + | 3.44176i | −0.180645 | + | 0.180645i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.88183 | + | 7.88183i | 0.412554 | + | 0.412554i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.29896 | −0.328803 | −0.164402 | − | 0.986394i | \(-0.552569\pi\) | ||||
−0.164402 | + | 0.986394i | \(0.552569\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12.7378 | 0.663104 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −20.4539 | − | 20.4539i | −1.06192 | − | 1.06192i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.7757 | − | 12.7757i | 0.661498 | − | 0.661498i | −0.294235 | − | 0.955733i | \(-0.595065\pi\) |
0.955733 | + | 0.294235i | \(0.0950648\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 15.5395i | − | 0.802457i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 9.65398i | − | 0.497205i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.8540 | − | 17.8540i | 0.917097 | − | 0.917097i | −0.0797198 | − | 0.996817i | \(-0.525403\pi\) |
0.996817 | + | 0.0797198i | \(0.0254026\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.4740 | − | 11.4740i | −0.587831 | − | 0.587831i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.20840 | 0.470527 | 0.235264 | − | 0.971932i | \(-0.424405\pi\) | ||||
0.235264 | + | 0.971932i | \(0.424405\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −22.5937 | −1.15148 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.0570905 | + | 0.0570905i | 0.00290208 | + | 0.00290208i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.1892 | − | 19.1892i | 0.972930 | − | 0.972930i | −0.0267131 | − | 0.999643i | \(-0.508504\pi\) |
0.999643 | + | 0.0267131i | \(0.00850406\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 52.3653i | 2.64823i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.5452i | 0.582376i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.88117 | + | 6.88117i | −0.346229 | + | 0.346229i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.2018 | + | 15.2018i | 0.762956 | + | 0.762956i | 0.976856 | − | 0.213900i | \(-0.0686165\pi\) |
−0.213900 | + | 0.976856i | \(0.568617\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.9950 | 0.550441 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.1785 | −0.907793 | −0.453897 | − | 0.891054i | \(-0.649966\pi\) | ||||
−0.453897 | + | 0.891054i | \(0.649966\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.69875 | − | 3.69875i | −0.184248 | − | 0.184248i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.90145 | − | 3.90145i | 0.193864 | − | 0.193864i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1.13503i | − | 0.0562615i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.29435i | 0.261789i | 0.991396 | + | 0.130894i | \(0.0417849\pi\) | ||||
−0.991396 | + | 0.130894i | \(0.958215\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.8906 | + | 17.8906i | −0.882477 | + | 0.882477i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.8616 | + | 10.8616i | 0.534464 | + | 0.534464i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −25.1458 | −1.23436 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.1096 | −0.690951 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.93469 | + | 1.93469i | 0.0945158 | + | 0.0945158i | 0.752784 | − | 0.658268i | \(-0.228711\pi\) |
−0.658268 | + | 0.752784i | \(0.728711\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.75321 | − | 7.75321i | 0.377868 | − | 0.377868i | −0.492464 | − | 0.870333i | \(-0.663904\pi\) |
0.870333 | + | 0.492464i | \(0.163904\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 2.96869i | − | 0.144343i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 9.94226i | − | 0.482270i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.53804 | + | 5.53804i | −0.268004 | + | 0.268004i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.47451 | + | 3.47451i | 0.167751 | + | 0.167751i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.1933 | −1.35802 | −0.679011 | − | 0.734128i | \(-0.737591\pi\) | ||||
−0.679011 | + | 0.734128i | \(0.737591\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.5535 | −1.37219 | −0.686097 | − | 0.727511i | \(-0.740677\pi\) | ||||
−0.686097 | + | 0.727511i | \(0.740677\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −15.9590 | − | 15.9590i | −0.765175 | − | 0.765175i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.4769 | + | 16.4769i | −0.788196 | + | 0.788196i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 0.436290i | − | 0.0208230i | −0.999946 | − | 0.0104115i | \(-0.996686\pi\) | ||
0.999946 | − | 0.0104115i | \(-0.00331414\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.49087i | 0.213851i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.4448 | + | 22.4448i | −1.06638 | + | 1.06638i | −0.0687507 | + | 0.997634i | \(0.521901\pi\) |
−0.997634 | + | 0.0687507i | \(0.978099\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.69910 | − | 7.69910i | −0.364972 | − | 0.364972i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.3885 | 0.585958 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.83048 | 0.0863856 | 0.0431928 | − | 0.999067i | \(-0.486247\pi\) | ||||
0.0431928 | + | 0.999067i | \(0.486247\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.3032 | + | 25.3032i | 1.19148 | + | 1.19148i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.8335 | + | 10.8335i | −0.509001 | + | 0.509001i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.87048i | 0.275213i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 18.3262i | − | 0.857264i | −0.903479 | − | 0.428632i | \(-0.858996\pi\) | ||
0.903479 | − | 0.428632i | \(-0.141004\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 23.8156 | − | 23.8156i | 1.11161 | − | 1.11161i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.1809 | + | 10.1809i | 0.474171 | + | 0.474171i | 0.903262 | − | 0.429090i | \(-0.141166\pi\) |
−0.429090 | + | 0.903262i | \(0.641166\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.8403 | 1.34032 | 0.670162 | − | 0.742215i | \(-0.266225\pi\) | ||||
0.670162 | + | 0.742215i | \(0.266225\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12.2288 | −0.567097 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.4431 | + | 11.4431i | 0.529526 | + | 0.529526i | 0.920431 | − | 0.390905i | \(-0.127838\pi\) |
−0.390905 | + | 0.920431i | \(0.627838\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.00231 | − | 5.00231i | 0.230985 | − | 0.230985i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.27192i | 0.150762i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.226816i | 0.0104290i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.12836 | − | 3.12836i | 0.143539 | − | 0.143539i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.74057 | − | 8.74057i | −0.400203 | − | 0.400203i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.9400 | 1.23092 | 0.615459 | − | 0.788169i | \(-0.288971\pi\) | ||||
0.615459 | + | 0.788169i | \(0.288971\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.294914 | −0.0134469 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 25.1061 | + | 25.1061i | 1.14237 | + | 1.14237i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.6768 | + | 12.6768i | −0.575626 | + | 0.575626i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 10.4127i | − | 0.471844i | −0.971772 | − | 0.235922i | \(-0.924189\pi\) | ||
0.971772 | − | 0.235922i | \(-0.0758110\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 25.0586i | − | 1.13319i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.32818 | + | 3.32818i | −0.150199 | + | 0.150199i | −0.778207 | − | 0.628008i | \(-0.783870\pi\) |
0.628008 | + | 0.778207i | \(0.283870\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −41.2090 | − | 41.2090i | −1.85596 | − | 1.85596i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.65493 | −0.433957 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 31.2208 | 1.40044 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.7043 | − | 12.7043i | −0.568720 | − | 0.568720i | 0.363049 | − | 0.931770i | \(-0.381736\pi\) |
−0.931770 | + | 0.363049i | \(0.881736\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.60457 | − | 3.60457i | 0.161040 | − | 0.161040i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.37422i | 0.195037i | 0.995234 | + | 0.0975184i | \(0.0310905\pi\) | ||||
−0.995234 | + | 0.0975184i | \(0.968910\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 12.3137i | − | 0.547954i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.902776 | − | 0.902776i | 0.0400937 | − | 0.0400937i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.4429 | + | 19.4429i | 0.861791 | + | 0.861791i | 0.991546 | − | 0.129755i | \(-0.0414192\pi\) |
−0.129755 | + | 0.991546i | \(0.541419\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.5154 | 0.863312 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14.9873 | 0.661704 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.73997 | − | 3.73997i | −0.164803 | − | 0.164803i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.89719 | − | 5.89719i | 0.259358 | − | 0.259358i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.6501i | 0.994230i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.9872i | 1.62044i | 0.586127 | + | 0.810219i | \(0.300652\pi\) | ||||
−0.586127 | + | 0.810219i | \(0.699348\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.80040 | − | 1.80040i | 0.0787260 | − | 0.0787260i | −0.666647 | − | 0.745373i | \(-0.732271\pi\) |
0.745373 | + | 0.666647i | \(0.232271\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.76672 | − | 4.76672i | −0.208037 | − | 0.208037i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −31.5770 | −1.37551 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −52.2466 | −2.27159 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.64148 | + | 4.64148i | 0.201423 | + | 0.201423i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.57449 | − | 6.57449i | 0.284773 | − | 0.284773i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.60213i | 0.415136i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 11.8537i | − | 0.511527i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.92095 | + | 8.92095i | −0.384253 | + | 0.384253i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.6616 | − | 13.6616i | −0.587357 | − | 0.587357i | 0.349558 | − | 0.936915i | \(-0.386332\pi\) |
−0.936915 | + | 0.349558i | \(0.886332\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.4782 | 0.535491 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.16089 | −0.306739 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.89436 | + | 5.89436i | 0.252025 | + | 0.252025i | 0.821800 | − | 0.569776i | \(-0.192970\pi\) |
−0.569776 | + | 0.821800i | \(0.692970\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.36656 | + | 2.36656i | −0.101003 | + | 0.101003i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 25.9330i | − | 1.10478i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.0378i | 0.724520i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.487522 | + | 0.487522i | −0.0206942 | + | 0.0206942i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.07239 | − | 9.07239i | −0.384409 | − | 0.384409i | 0.488278 | − | 0.872688i | \(-0.337625\pi\) |
−0.872688 | + | 0.488278i | \(0.837625\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.0589334 | 0.00249262 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 29.6625 | 1.25235 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.9168 | − | 17.9168i | −0.755104 | − | 0.755104i | 0.220323 | − | 0.975427i | \(-0.429289\pi\) |
−0.975427 | + | 0.220323i | \(0.929289\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.8207 | − | 11.8207i | 0.497301 | − | 0.497301i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 9.65999i | − | 0.405681i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.4121i | 0.646109i | 0.946380 | + | 0.323054i | \(0.104710\pi\) | ||||
−0.946380 | + | 0.323054i | \(0.895290\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.6916 | + | 15.6916i | −0.656673 | + | 0.656673i | −0.954591 | − | 0.297919i | \(-0.903708\pi\) |
0.297919 | + | 0.954591i | \(0.403708\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.1622 | + | 10.1622i | 0.424533 | + | 0.424533i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14.2866 | 0.595792 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.3626 | −0.722815 | −0.361407 | − | 0.932408i | \(-0.617704\pi\) | ||||
−0.361407 | + | 0.932408i | \(0.617704\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.29855 | + | 2.29855i | 0.0955244 | + | 0.0955244i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −31.1306 | + | 31.1306i | −1.29151 | + | 1.29151i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 34.7256i | − | 1.43819i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.50863i | 0.103719i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.0345 | + | 15.0345i | −0.620541 | + | 0.620541i | −0.945670 | − | 0.325129i | \(-0.894592\pi\) |
0.325129 | + | 0.945670i | \(0.394592\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.93577 | − | 9.93577i | −0.409396 | − | 0.409396i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.76456 | 0.319391 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −42.6498 | −1.75142 | −0.875709 | − | 0.482840i | \(-0.839605\pi\) | ||||
−0.875709 | + | 0.482840i | \(0.839605\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 25.0587 | + | 25.0587i | 1.02731 | + | 1.02731i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −23.7326 | + | 23.7326i | −0.971311 | + | 0.971311i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.7066i | 1.09120i | 0.838045 | + | 0.545602i | \(0.183699\pi\) | ||||
−0.838045 | + | 0.545602i | \(0.816301\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.30933i | 0.338944i | 0.985535 | + | 0.169472i | \(0.0542063\pi\) | ||||
−0.985535 | + | 0.169472i | \(0.945794\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.13763 | − | 2.13763i | 0.0870512 | − | 0.0870512i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.93633 | − | 4.93633i | −0.200690 | − | 0.200690i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.9913 | −0.933190 | −0.466595 | − | 0.884471i | \(-0.654519\pi\) | ||||
−0.466595 | + | 0.884471i | \(0.654519\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −39.5145 | −1.60121 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.53226 | − | 1.53226i | −0.0619886 | − | 0.0619886i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.71226 | − | 6.71226i | 0.271106 | − | 0.271106i | −0.558440 | − | 0.829545i | \(-0.688600\pi\) |
0.829545 | + | 0.558440i | \(0.188600\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 21.7366i | − | 0.876504i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.3150i | 0.415266i | 0.978207 | + | 0.207633i | \(0.0665760\pi\) | ||||
−0.978207 | + | 0.207633i | \(0.933424\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.94177 | − | 6.94177i | 0.279013 | − | 0.279013i | −0.553702 | − | 0.832715i | \(-0.686785\pi\) |
0.832715 | + | 0.553702i | \(0.186785\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 34.2219 | + | 34.2219i | 1.37328 | + | 1.37328i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −19.0630 | −0.763743 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.0527 | 0.562107 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.33340 | + | 9.33340i | 0.372740 | + | 0.372740i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.25887 | + | 1.25887i | −0.0501944 | + | 0.0501944i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 11.6081i | − | 0.462113i | −0.972940 | − | 0.231056i | \(-0.925782\pi\) | ||
0.972940 | − | 0.231056i | \(-0.0742182\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 13.5776i | − | 0.539661i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.4565 | − | 16.4565i | 0.653058 | − | 0.653058i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.31792 | + | 2.31792i | 0.0918393 | + | 0.0918393i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.3416 | 0.527784 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.0384 | 1.06795 | 0.533977 | − | 0.845499i | \(-0.320697\pi\) | ||||
0.533977 | + | 0.845499i | \(0.320697\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.7661 | + | 12.7661i | 0.503444 | + | 0.503444i | 0.912507 | − | 0.409062i | \(-0.134144\pi\) |
−0.409062 | + | 0.912507i | \(0.634144\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.0974228 | − | 0.0974228i | 0.00383602 | − | 0.00383602i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.0134i | 0.393667i | 0.980437 | + | 0.196833i | \(0.0630658\pi\) | ||||
−0.980437 | + | 0.196833i | \(0.936934\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.4402i | 0.723843i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.1393 | + | 15.1393i | −0.593355 | + | 0.593355i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.13213 | − | 9.13213i | −0.357368 | − | 0.357368i | 0.505474 | − | 0.862842i | \(-0.331318\pi\) |
−0.862842 | + | 0.505474i | \(0.831318\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.5586 | −0.646998 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.33951 | 0.325355 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26.5843 | − | 26.5843i | −1.03558 | − | 1.03558i | −0.999343 | − | 0.0362320i | \(-0.988464\pi\) |
−0.0362320 | − | 0.999343i | \(-0.511536\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.76639 | + | 1.76639i | −0.0687044 | + | 0.0687044i | −0.740624 | − | 0.671920i | \(-0.765470\pi\) |
0.671920 | + | 0.740624i | \(0.265470\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 7.70718i | − | 0.299322i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.7696i | 0.611519i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 59.2154 | − | 59.2154i | 2.29283 | − | 2.29283i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.9107 | + | 16.9107i | 0.653804 | + | 0.653804i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.40218 | −0.362967 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.1888 | 1.51062 | 0.755308 | − | 0.655370i | \(-0.227487\pi\) | ||||
0.755308 | + | 0.655370i | \(0.227487\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.49749 | − | 6.49749i | −0.250088 | − | 0.250088i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.8583 | − | 13.8583i | 0.532616 | − | 0.532616i | −0.388734 | − | 0.921350i | \(-0.627087\pi\) |
0.921350 | + | 0.388734i | \(0.127087\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 31.3879i | 1.20456i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.997953i | 0.0382416i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.54143 | − | 8.54143i | 0.326829 | − | 0.326829i | −0.524550 | − | 0.851379i | \(-0.675767\pi\) |
0.851379 | + | 0.524550i | \(0.175767\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25.6595 | − | 25.6595i | −0.980399 | − | 0.980399i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −26.9896 | −1.02972 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.02271 | −0.343738 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.55830 | + | 5.55830i | 0.211448 | + | 0.211448i | 0.804882 | − | 0.593435i | \(-0.202228\pi\) |
−0.593435 | + | 0.804882i | \(0.702228\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −11.9528 | + | 11.9528i | −0.454050 | + | 0.454050i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 20.2367i | − | 0.767621i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 56.1277i | − | 2.12599i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −21.6239 | + | 21.6239i | −0.817890 | + | 0.817890i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.3550 | + | 30.3550i | 1.14649 | + | 1.14649i | 0.987238 | + | 0.159253i | \(0.0509086\pi\) |
0.159253 | + | 0.987238i | \(0.449091\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.792213 | −0.0298789 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.06595 | −0.190795 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.2444 | − | 15.2444i | −0.573325 | − | 0.573325i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.0689 | − | 33.0689i | 1.24193 | − | 1.24193i | 0.282730 | − | 0.959199i | \(-0.408760\pi\) |
0.959199 | − | 0.282730i | \(-0.0912401\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.28074i | 0.273049i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 45.3747i | − | 1.69929i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.98330 | + | 4.98330i | −0.186365 | + | 0.186365i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.34640 | − | 1.34640i | −0.0502824 | − | 0.0502824i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.1360 | −0.900121 | −0.450060 | − | 0.892998i | \(-0.648598\pi\) | ||||
−0.450060 | + | 0.892998i | \(0.648598\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.26017 | −0.344867 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.0875736 | + | 0.0875736i | 0.00325690 | + | 0.00325690i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11.2428 | + | 11.2428i | −0.417549 | + | 0.417549i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 25.4413i | − | 0.943564i | −0.881715 | − | 0.471782i | \(-0.843611\pi\) | ||
0.881715 | − | 0.471782i | \(-0.156389\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 25.4974i | − | 0.944347i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.251563 | − | 0.251563i | 0.00930440 | − | 0.00930440i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.11861 | − | 1.11861i | −0.0413170 | − | 0.0413170i | 0.686146 | − | 0.727463i | \(-0.259301\pi\) |
−0.727463 | + | 0.686146i | \(0.759301\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.66350 | 0.282673 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.49266 | 0.312831 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27.9487 | − | 27.9487i | −1.02811 | − | 1.02811i | −0.999593 | − | 0.0285153i | \(-0.990922\pi\) |
−0.0285153 | − | 0.999593i | \(-0.509078\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.42508 | − | 2.42508i | 0.0890877 | − | 0.0890877i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 6.84243i | − | 0.251024i | −0.992092 | − | 0.125512i | \(-0.959943\pi\) | ||
0.992092 | − | 0.125512i | \(-0.0400574\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.7682i | 0.650977i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.3030 | + | 13.3030i | −0.486731 | + | 0.486731i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.8874 | + | 11.8874i | 0.434358 | + | 0.434358i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.3074 | −0.850500 | −0.425250 | − | 0.905076i | \(-0.639814\pi\) | ||||
−0.425250 | + | 0.905076i | \(0.639814\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.2346 | 0.482297 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.5379 | − | 15.5379i | −0.565481 | − | 0.565481i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.0617 | + | 10.0617i | −0.365700 | + | 0.365700i | −0.865906 | − | 0.500206i | \(-0.833258\pi\) |
0.500206 | + | 0.865906i | \(0.333258\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 42.6237i | 1.54714i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.4743i | 0.379695i | 0.981814 | + | 0.189847i | \(0.0607993\pi\) | ||||
−0.981814 | + | 0.189847i | \(0.939201\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.86519 | + | 8.86519i | −0.320941 | + | 0.320941i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10.7083 | + | 10.7083i | 0.387160 | + | 0.387160i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.79131 | 0.173004 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.4816 | 1.42374 | 0.711871 | − | 0.702310i | \(-0.247848\pi\) | ||||
0.711871 | + | 0.702310i | \(0.247848\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −26.0928 | − | 26.0928i | −0.939711 | − | 0.939711i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −22.4954 | + | 22.4954i | −0.809104 | + | 0.809104i | −0.984498 | − | 0.175394i | \(-0.943880\pi\) |
0.175394 | + | 0.984498i | \(0.443880\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.61499i | 0.309460i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.20711i | 0.0433047i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.6607 | − | 17.6607i | 0.632762 | − | 0.632762i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 26.5025 | + | 26.5025i | 0.948334 | + | 0.948334i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −53.8619 | −1.92487 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.69274 | −0.167491 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.2640 | − | 16.2640i | −0.579750 | − | 0.579750i | 0.355085 | − | 0.934834i | \(-0.384452\pi\) |
−0.934834 | + | 0.355085i | \(0.884452\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.7342 | − | 15.7342i | 0.560152 | − | 0.560152i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 29.2681i | − | 1.04065i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.44296i | 0.0867520i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14.9154 | + | 14.9154i | −0.528996 | + | 0.528996i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27.5649 | − | 27.5649i | −0.976398 | − | 0.976398i | 0.0233299 | − | 0.999728i | \(-0.492573\pi\) |
−0.999728 | + | 0.0233299i | \(0.992573\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.0812 | −0.462779 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.14617 | −0.287831 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.5661 | + | 16.5661i | 0.584606 | + | 0.584606i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −36.0083 | + | 36.0083i | −1.26913 | + | 1.26913i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 21.7139i | − | 0.764365i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 5.17865i | − | 0.182072i | −0.995848 | − | 0.0910358i | \(-0.970982\pi\) | ||
0.995848 | − | 0.0910358i | \(-0.0290178\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.6428 | − | 32.6428i | 1.14625 | − | 1.14625i | 0.158960 | − | 0.987285i | \(-0.449186\pi\) |
0.987285 | − | 0.158960i | \(-0.0508141\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.62030 | − | 1.62030i | −0.0568264 | − | 0.0568264i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 35.9401 | 1.25893 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.158310 | 0.00553857 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.10569 | + | 3.10569i | 0.108521 | + | 0.108521i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.1496 | + | 12.1496i | −0.424025 | + | 0.424025i | −0.886587 | − | 0.462562i | \(-0.846930\pi\) |
0.462562 | + | 0.886587i | \(0.346930\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 27.6976i | − | 0.965476i | −0.875765 | − | 0.482738i | \(-0.839642\pi\) | ||
0.875765 | − | 0.482738i | \(-0.160358\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 8.09269i | − | 0.281751i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21.8635 | − | 21.8635i | 0.760269 | − | 0.760269i | −0.216102 | − | 0.976371i | \(-0.569334\pi\) |
0.976371 | + | 0.216102i | \(0.0693343\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.7756 | − | 14.7756i | −0.513178 | − | 0.513178i | 0.402320 | − | 0.915499i | \(-0.368204\pi\) |
−0.915499 | + | 0.402320i | \(0.868204\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.36561 | −0.0820622 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19.7885 | 0.685632 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.16984 | + | 5.16984i | 0.178910 | + | 0.178910i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −20.6362 | + | 20.6362i | −0.713293 | + | 0.713293i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 0.625398i | − | 0.0215912i | −0.999942 | − | 0.0107956i | \(-0.996564\pi\) | ||
0.999942 | − | 0.0107956i | \(-0.00343641\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 64.1994i | 2.21377i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24.2308 | − | 24.2308i | 0.834554 | − | 0.834554i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.29480 | + | 1.29480i | 0.0445426 | + | 0.0445426i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.2224 | −0.419965 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.71421 | 0.0931516 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.80894 | − | 1.80894i | −0.0620096 | − | 0.0620096i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.2267 | + | 14.2267i | −0.487114 | + | 0.487114i | −0.907394 | − | 0.420280i | \(-0.861932\pi\) |
0.420280 | + | 0.907394i | \(0.361932\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.73881i | 0.230462i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 36.8671i | 1.25936i | 0.776857 | + | 0.629678i | \(0.216813\pi\) | ||||
−0.776857 | + | 0.629678i | \(0.783187\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.0958 | − | 11.0958i | 0.378584 | − | 0.378584i | −0.492007 | − | 0.870591i | \(-0.663737\pi\) |
0.870591 | + | 0.492007i | \(0.163737\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −26.9099 | − | 26.9099i | −0.917088 | − | 0.917088i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.79818 | 0.197372 | 0.0986862 | − | 0.995119i | \(-0.468536\pi\) | ||||
0.0986862 | + | 0.995119i | \(0.468536\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −32.4858 | −1.10455 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17.5516 | − | 17.5516i | −0.596085 | − | 0.596085i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.4629 | + | 14.4629i | −0.490621 | + | 0.490621i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 2.20664i | − | 0.0747690i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.4130i | 0.453960i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 27.5920 | − | 27.5920i | 0.932778 | − | 0.932778i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.4174 | + | 11.4174i | 0.385537 | + | 0.385537i | 0.873092 | − | 0.487555i | \(-0.162111\pi\) |
−0.487555 | + | 0.873092i | \(0.662111\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.27382 | −0.279069 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.6667 | 0.729971 | 0.364985 | − | 0.931013i | \(-0.381074\pi\) | ||||
0.364985 | + | 0.931013i | \(0.381074\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.37331 | − | 3.37331i | −0.113521 | − | 0.113521i | 0.648064 | − | 0.761585i | \(-0.275579\pi\) |
−0.761585 | + | 0.648064i | \(0.775579\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.92050 | − | 7.92050i | 0.266245 | − | 0.266245i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.0852i | 0.338628i | 0.985562 | + | 0.169314i | \(0.0541552\pi\) | ||||
−0.985562 | + | 0.169314i | \(0.945845\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 40.7465i | − | 1.36659i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.20011 | − | 8.20011i | 0.274714 | − | 0.274714i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.11603 | − | 4.11603i | −0.137738 | − | 0.137738i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.0012 | 0.568287 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.0749 | 0.369779 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 35.7077 | + | 35.7077i | 1.19092 | + | 1.19092i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −38.5143 | + | 38.5143i | −1.28310 | + | 1.28310i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 0.241219i | − | 0.00802727i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17.8968i | 0.594910i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.1727 | + | 14.1727i | −0.470597 | + | 0.470597i | −0.902108 | − | 0.431511i | \(-0.857981\pi\) |
0.431511 | + | 0.902108i | \(0.357981\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.51438 | − | 6.51438i | −0.216068 | − | 0.216068i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.12861 | 0.169919 | 0.0849593 | − | 0.996384i | \(-0.472924\pi\) | ||||
0.0849593 | + | 0.996384i | \(0.472924\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −52.8518 | −1.74914 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.03845 | + | 4.03845i | 0.133507 | + | 0.133507i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −20.4996 | + | 20.4996i | −0.676955 | + | 0.676955i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.74928i | 0.0577034i | 0.999584 | + | 0.0288517i | \(0.00918506\pi\) | ||||
−0.999584 | + | 0.0288517i | \(0.990815\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.7930i | 0.816956i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.88611 | − | 6.88611i | 0.226659 | − | 0.226659i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.343451 | + | 0.343451i | 0.0112926 | + | 0.0112926i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.95714 | −0.129969 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.8593 | −0.946844 | −0.473422 | − | 0.880836i | \(-0.656981\pi\) | ||||
−0.473422 | + | 0.880836i | \(0.656981\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.22652 | + | 6.22652i | 0.204066 | + | 0.204066i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.45269 | − | 1.45269i | 0.0475588 | − | 0.0475588i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 42.5434i | 1.39132i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.4959i | 0.408223i | 0.978948 | + | 0.204111i | \(0.0654304\pi\) | ||||
−0.978948 | + | 0.204111i | \(0.934570\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.9870 | + | 12.9870i | −0.423816 | + | 0.423816i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.93712 | + | 3.93712i | 0.128347 | + | 0.128347i | 0.768362 | − | 0.640015i | \(-0.221072\pi\) |
−0.640015 | + | 0.768362i | \(0.721072\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 80.6530 | 2.62642 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 32.7529 | 1.06545 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31.9342 | − | 31.9342i | −1.03772 | − | 1.03772i | −0.999260 | − | 0.0384618i | \(-0.987754\pi\) |
−0.0384618 | − | 0.999260i | \(-0.512246\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.30436 | − | 4.30436i | 0.139725 | − | 0.139725i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 22.4116i | − | 0.726745i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 28.7558i | − | 0.931492i | −0.884918 | − | 0.465746i | \(-0.845786\pi\) | ||
0.884918 | − | 0.465746i | \(-0.154214\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.5751 | + | 14.5751i | −0.471640 | + | 0.471640i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −33.5428 | − | 33.5428i | −1.08429 | − | 1.08429i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −63.5329 | −2.05159 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.63849 | −0.117371 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.07985 | + | 5.07985i | 0.163696 | + | 0.163696i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.29669 | + | 3.29669i | −0.106124 | + | 0.106124i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.77351i | 0.185664i | 0.995682 | + | 0.0928318i | \(0.0295919\pi\) | ||||
−0.995682 | + | 0.0928318i | \(0.970408\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 20.7034i | − | 0.665090i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.9091 | − | 17.9091i | 0.574729 | − | 0.574729i | −0.358717 | − | 0.933446i | \(-0.616786\pi\) |
0.933446 | + | 0.358717i | \(0.116786\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25.0530 | − | 25.0530i | −0.803163 | − | 0.803163i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.10271 | −0.0673407 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.82926 | −0.122509 | −0.0612544 | − | 0.998122i | \(-0.519510\pi\) | ||||
−0.0612544 | + | 0.998122i | \(0.519510\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.1821 | − | 16.1821i | −0.517181 | − | 0.517181i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.78835 | + | 3.78835i | −0.120953 | + | 0.120953i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 42.4136i | − | 1.35279i | −0.736541 | − | 0.676393i | \(-0.763542\pi\) | ||
0.736541 | − | 0.676393i | \(-0.236458\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.1363i | 0.354832i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.27166 | + | 6.27166i | −0.199629 | + | 0.199629i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.361485 | + | 0.361485i | 0.0114946 | + | 0.0114946i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 59.1239 | 1.87813 | 0.939066 | − | 0.343736i | \(-0.111693\pi\) | ||||
0.939066 | + | 0.343736i | \(0.111693\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −30.9683 | −0.982749 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −34.0384 | − | 34.0384i | −1.07909 | − | 1.07909i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35.9832 | − | 35.9832i | 1.13960 | − | 1.13960i | 0.151079 | − | 0.988522i | \(-0.451725\pi\) |
0.988522 | − | 0.151079i | \(-0.0482748\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.64540i | 0.0520581i |
(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 | 1664.2.n.b.417.8 | 48 | ||
4.3 | odd | 2 | 1664.2.n.a.417.17 | 48 | |||
8.3 | odd | 2 | 832.2.n.a.209.8 | 48 | |||
8.5 | even | 2 | 208.2.n.a.157.24 | yes | 48 | ||
16.3 | odd | 4 | 832.2.n.a.625.8 | 48 | |||
16.5 | even | 4 | inner | 1664.2.n.b.1249.8 | 48 | ||
16.11 | odd | 4 | 1664.2.n.a.1249.17 | 48 | |||
16.13 | even | 4 | 208.2.n.a.53.24 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
208.2.n.a.53.24 | ✓ | 48 | 16.13 | even | 4 | ||
208.2.n.a.157.24 | yes | 48 | 8.5 | even | 2 | ||
832.2.n.a.209.8 | 48 | 8.3 | odd | 2 | |||
832.2.n.a.625.8 | 48 | 16.3 | odd | 4 | |||
1664.2.n.a.417.17 | 48 | 4.3 | odd | 2 | |||
1664.2.n.a.1249.17 | 48 | 16.11 | odd | 4 | |||
1664.2.n.b.417.8 | 48 | 1.1 | even | 1 | trivial | ||
1664.2.n.b.1249.8 | 48 | 16.5 | even | 4 | inner |