Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(337,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.k (of order \(4\), degree \(2\), 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: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 337.12 | ||
Character | \(\chi\) | \(=\) | 1148.337 |
Dual form | 1148.2.k.b.729.12 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | 0.805830 | + | 0.805830i | 0.465246 | + | 0.465246i | 0.900370 | − | 0.435124i | \(-0.143296\pi\) |
−0.435124 | + | 0.900370i | \(0.643296\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 0.251332i | − | 0.112399i | −0.998420 | − | 0.0561996i | \(-0.982102\pi\) | ||
0.998420 | − | 0.0561996i | \(-0.0178983\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.707107 | + | 0.707107i | 0.267261 | + | 0.267261i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.70128i | − | 0.567092i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.93936 | − | 2.93936i | −0.886251 | − | 0.886251i | 0.107910 | − | 0.994161i | \(-0.465584\pi\) |
−0.994161 | + | 0.107910i | \(0.965584\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.89283 | + | 1.89283i | 0.524977 | + | 0.524977i | 0.919070 | − | 0.394094i | \(-0.128941\pi\) |
−0.394094 | + | 0.919070i | \(0.628941\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.202531 | − | 0.202531i | 0.0522933 | − | 0.0522933i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.33562 | − | 2.33562i | 0.566472 | − | 0.566472i | −0.364667 | − | 0.931138i | \(-0.618817\pi\) |
0.931138 | + | 0.364667i | \(0.118817\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.33917 | − | 1.33917i | 0.307227 | − | 0.307227i | −0.536606 | − | 0.843833i | \(-0.680294\pi\) |
0.843833 | + | 0.536606i | \(0.180294\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.13962i | 0.248685i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.67279 | 1.39137 | 0.695687 | − | 0.718345i | \(-0.255100\pi\) | ||||
0.695687 | + | 0.718345i | \(0.255100\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.93683 | 0.987366 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.78843 | − | 3.78843i | 0.729084 | − | 0.729084i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.0155144 | − | 0.0155144i | −0.00288095 | − | 0.00288095i | 0.705665 | − | 0.708546i | \(-0.250648\pi\) |
−0.708546 | + | 0.705665i | \(0.750648\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.61614 | −0.649478 | −0.324739 | − | 0.945804i | \(-0.605276\pi\) | ||||
−0.324739 | + | 0.945804i | \(0.605276\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 4.73725i | − | 0.824650i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.177719 | − | 0.177719i | 0.0300399 | − | 0.0300399i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.22196 | 1.51608 | 0.758040 | − | 0.652208i | \(-0.226157\pi\) | ||||
0.758040 | + | 0.652208i | \(0.226157\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.05060i | 0.488487i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.16529 | + | 1.72894i | −0.962856 | + | 0.270015i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.97318i | − | 0.300908i | −0.988617 | − | 0.150454i | \(-0.951927\pi\) | ||
0.988617 | − | 0.150454i | \(-0.0480735\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.427585 | −0.0637407 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.41064 | + | 2.41064i | −0.351628 | + | 0.351628i | −0.860715 | − | 0.509087i | \(-0.829983\pi\) |
0.509087 | + | 0.860715i | \(0.329983\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.76423 | 0.527098 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.16272 | + | 3.16272i | 0.434434 | + | 0.434434i | 0.890133 | − | 0.455700i | \(-0.150611\pi\) |
−0.455700 | + | 0.890133i | \(0.650611\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.738756 | + | 0.738756i | −0.0996139 | + | 0.0996139i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.15829 | 0.285873 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.91005 | −0.639234 | −0.319617 | − | 0.947547i | \(-0.603554\pi\) | ||||
−0.319617 | + | 0.947547i | \(0.603554\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.53072i | 1.22028i | 0.792292 | + | 0.610142i | \(0.208888\pi\) | ||||
−0.792292 | + | 0.610142i | \(0.791112\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.20298 | − | 1.20298i | 0.151562 | − | 0.151562i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.475729 | − | 0.475729i | 0.0590070 | − | 0.0590070i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.59321 | − | 8.59321i | 1.04983 | − | 1.04983i | 0.0511362 | − | 0.998692i | \(-0.483716\pi\) |
0.998692 | − | 0.0511362i | \(-0.0162843\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.37714 | + | 5.37714i | 0.647332 | + | 0.647332i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.30998 | − | 9.30998i | −1.10489 | − | 1.10489i | −0.993811 | − | 0.111080i | \(-0.964569\pi\) |
−0.111080 | − | 0.993811i | \(-0.535431\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.52711i | 0.646899i | 0.946245 | + | 0.323449i | \(0.104843\pi\) | ||||
−0.946245 | + | 0.323449i | \(0.895157\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.97825 | + | 3.97825i | 0.459369 | + | 0.459369i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 4.15689i | − | 0.473721i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.22270 | + | 4.22270i | 0.475091 | + | 0.475091i | 0.903557 | − | 0.428467i | \(-0.140946\pi\) |
−0.428467 | + | 0.903557i | \(0.640946\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00184 | 0.111315 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.78231 | 0.744455 | 0.372227 | − | 0.928142i | \(-0.378594\pi\) | ||||
0.372227 | + | 0.928142i | \(0.378594\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.587017 | − | 0.587017i | −0.0636709 | − | 0.0636709i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 0.0250039i | − | 0.00268070i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.72662 | − | 1.72662i | −0.183022 | − | 0.183022i | 0.609649 | − | 0.792671i | \(-0.291310\pi\) |
−0.792671 | + | 0.609649i | \(0.791310\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.67687i | 0.280612i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.91399 | − | 2.91399i | −0.302167 | − | 0.302167i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.336577 | − | 0.336577i | −0.0345321 | − | 0.0345321i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.76074 | + | 2.76074i | −0.280311 | + | 0.280311i | −0.833233 | − | 0.552922i | \(-0.813513\pi\) |
0.552922 | + | 0.833233i | \(0.313513\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.00066 | + | 5.00066i | −0.502586 | + | 0.502586i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.9870 | − | 11.9870i | 1.19275 | − | 1.19275i | 0.216454 | − | 0.976293i | \(-0.430551\pi\) |
0.976293 | − | 0.216454i | \(-0.0694491\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 2.76891i | − | 0.272829i | −0.990652 | − | 0.136414i | \(-0.956442\pi\) | ||
0.990652 | − | 0.136414i | \(-0.0435579\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.286422 | 0.0279520 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.25137 | −0.314322 | −0.157161 | − | 0.987573i | \(-0.550234\pi\) | ||||
−0.157161 | + | 0.987573i | \(0.550234\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.32806 | + | 3.32806i | −0.318770 | + | 0.318770i | −0.848295 | − | 0.529524i | \(-0.822370\pi\) |
0.529524 | + | 0.848295i | \(0.322370\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.43133 | + | 7.43133i | 0.705351 | + | 0.705351i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.47898 | −0.609491 | −0.304745 | − | 0.952434i | \(-0.598571\pi\) | ||||
−0.304745 | + | 0.952434i | \(0.598571\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1.67709i | − | 0.156389i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.22023 | − | 3.22023i | 0.297710 | − | 0.297710i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.30307 | 0.302792 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.27970i | 0.570881i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.36141 | − | 3.57494i | −0.573589 | − | 0.322342i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 2.49745i | − | 0.223378i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.7703 | −1.31065 | −0.655327 | − | 0.755345i | \(-0.727469\pi\) | ||||
−0.655327 | + | 0.755345i | \(0.727469\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.59005 | − | 1.59005i | 0.139996 | − | 0.139996i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.39527i | 0.820869i | 0.911890 | + | 0.410434i | \(0.134623\pi\) | ||||
−0.911890 | + | 0.410434i | \(0.865377\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.89388 | 0.164220 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.952155 | − | 0.952155i | −0.0819484 | − | 0.0819484i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.34033 | − | 8.34033i | 0.712562 | − | 0.712562i | −0.254508 | − | 0.967071i | \(-0.581914\pi\) |
0.967071 | + | 0.254508i | \(0.0819137\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.27568 | 0.277839 | 0.138920 | − | 0.990304i | \(-0.455637\pi\) | ||||
0.138920 | + | 0.990304i | \(0.455637\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.88514 | −0.327188 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 11.1274i | − | 0.930522i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.00389927 | + | 0.00389927i | −0.000323817 | + | 0.000323817i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.805830 | + | 0.805830i | −0.0664638 | + | 0.0664638i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.0335973 | + | 0.0335973i | −0.00275239 | + | 0.00275239i | −0.708482 | − | 0.705729i | \(-0.750620\pi\) |
0.705729 | + | 0.708482i | \(0.250620\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.45616 | − | 1.45616i | −0.118501 | − | 0.118501i | 0.645370 | − | 0.763870i | \(-0.276703\pi\) |
−0.763870 | + | 0.645370i | \(0.776703\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.97354 | − | 3.97354i | −0.321241 | − | 0.321241i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.908852i | 0.0730008i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.76143 | + | 6.76143i | 0.539621 | + | 0.539621i | 0.923418 | − | 0.383797i | \(-0.125384\pi\) |
−0.383797 | + | 0.923418i | \(0.625384\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.09724i | 0.404237i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.71838 | + | 4.71838i | 0.371860 | + | 0.371860i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.6072 | −1.30078 | −0.650388 | − | 0.759602i | \(-0.725394\pi\) | ||||
−0.650388 | + | 0.759602i | \(0.725394\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.19062 | −0.0926900 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.56993 | − | 5.56993i | −0.431014 | − | 0.431014i | 0.457959 | − | 0.888973i | \(-0.348581\pi\) |
−0.888973 | + | 0.457959i | \(0.848581\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 5.83438i | − | 0.448799i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.27830 | − | 2.27830i | −0.174226 | − | 0.174226i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.6379i | 1.56907i | 0.620082 | + | 0.784537i | \(0.287099\pi\) | ||||
−0.620082 | + | 0.784537i | \(0.712901\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.49087 | + | 3.49087i | 0.263885 | + | 0.263885i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.95667 | − | 3.95667i | −0.297401 | − | 0.297401i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.8890 | + | 13.8890i | −1.03811 | + | 1.03811i | −0.0388691 | + | 0.999244i | \(0.512376\pi\) |
−0.999244 | + | 0.0388691i | \(0.987624\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.658651 | − | 0.658651i | 0.0489572 | − | 0.0489572i | −0.682204 | − | 0.731162i | \(-0.738979\pi\) |
0.731162 | + | 0.682204i | \(0.238979\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.68015 | + | 7.68015i | −0.567733 | + | 0.567733i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 2.31778i | − | 0.170406i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.7305 | −1.00407 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.35765 | 0.389712 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.280520 | − | 0.280520i | 0.0202977 | − | 0.0202977i | −0.696885 | − | 0.717183i | \(-0.745431\pi\) |
0.717183 | + | 0.696885i | \(0.245431\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.497202 | + | 0.497202i | 0.0357894 | + | 0.0357894i | 0.724775 | − | 0.688986i | \(-0.241944\pi\) |
−0.688986 | + | 0.724775i | \(0.741944\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.766714 | 0.0549056 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 20.6787i | − | 1.47329i | −0.676277 | − | 0.736647i | \(-0.736408\pi\) | ||
0.676277 | − | 0.736647i | \(-0.263592\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.3611 | + | 18.3611i | −1.30159 | + | 1.30159i | −0.374262 | + | 0.927323i | \(0.622104\pi\) |
−0.927323 | + | 0.374262i | \(0.877896\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.8493 | 0.976857 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 0.0219407i | − | 0.00153993i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.434539 | + | 1.54954i | 0.0303495 | + | 0.108224i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 11.3523i | − | 0.789037i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.87263 | −0.544561 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.29562 | + | 9.29562i | −0.639937 | + | 0.639937i | −0.950540 | − | 0.310603i | \(-0.899469\pi\) |
0.310603 | + | 0.950540i | \(0.399469\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 15.0045i | − | 1.02809i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.495925 | −0.0338218 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.55700 | − | 2.55700i | −0.173580 | − | 0.173580i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.45391 | + | 4.45391i | −0.300967 | + | 0.300967i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.84188 | 0.594769 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.8455 | 1.12805 | 0.564027 | − | 0.825756i | \(-0.309251\pi\) | ||||
0.564027 | + | 0.825756i | \(0.309251\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | − | 8.39891i | − | 0.559927i | ||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.51778 | − | 3.51778i | 0.233483 | − | 0.233483i | −0.580662 | − | 0.814145i | \(-0.697206\pi\) |
0.814145 | + | 0.580662i | \(0.197206\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.4731 | − | 18.4731i | 1.22074 | − | 1.22074i | 0.253365 | − | 0.967371i | \(-0.418463\pi\) |
0.967371 | − | 0.253365i | \(-0.0815374\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.34974 | − | 3.34974i | 0.220397 | − | 0.220397i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.7275 | + | 18.7275i | 1.22688 | + | 1.22688i | 0.965138 | + | 0.261740i | \(0.0842962\pi\) |
0.261740 | + | 0.965138i | \(0.415704\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.605872 | + | 0.605872i | 0.0395228 | + | 0.0395228i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.80555i | 0.442068i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.4946 | − | 18.4946i | −1.19631 | − | 1.19631i | −0.975262 | − | 0.221051i | \(-0.929051\pi\) |
−0.221051 | − | 0.975262i | \(-0.570949\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 4.82354i | − | 0.310711i | −0.987859 | − | 0.155356i | \(-0.950348\pi\) | ||
0.987859 | − | 0.155356i | \(-0.0496524\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.5580 | − | 10.5580i | −0.677295 | − | 0.677295i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.251332 | 0.0160570 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.06966 | 0.322575 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.46539 | + | 5.46539i | 0.346355 | + | 0.346355i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.48952i | 0.220256i | 0.993917 | + | 0.110128i | \(0.0351261\pi\) | ||||
−0.993917 | + | 0.110128i | \(0.964874\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.6138 | − | 19.6138i | −1.23311 | − | 1.23311i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 0.946072i | − | 0.0592453i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.97950 | − | 1.97950i | −0.123478 | − | 0.123478i | 0.642668 | − | 0.766145i | \(-0.277828\pi\) |
−0.766145 | + | 0.642668i | \(0.777828\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.52091 | + | 6.52091i | 0.405190 | + | 0.405190i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.0263943 | + | 0.0263943i | −0.00163376 | + | 0.00163376i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.28189 | + | 8.28189i | −0.510683 | + | 0.510683i | −0.914736 | − | 0.404053i | \(-0.867601\pi\) |
0.404053 | + | 0.914736i | \(0.367601\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.794895 | − | 0.794895i | 0.0488300 | − | 0.0488300i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 2.78273i | − | 0.170300i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.6204 | −0.647536 | −0.323768 | − | 0.946136i | \(-0.604950\pi\) | ||||
−0.323768 | + | 0.946136i | \(0.604950\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.9253 | −0.785157 | −0.392578 | − | 0.919719i | \(-0.628417\pi\) | ||||
−0.392578 | + | 0.919719i | \(0.628417\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.15710 | + | 2.15710i | −0.130554 | + | 0.130554i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.5111 | − | 14.5111i | −0.875054 | − | 0.875054i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.9179 | −1.61734 | −0.808671 | − | 0.588261i | \(-0.799813\pi\) | ||||
−0.808671 | + | 0.588261i | \(0.799813\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.15205i | 0.368313i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.65940 | + | 8.65940i | −0.516576 | + | 0.516576i | −0.916534 | − | 0.399957i | \(-0.869025\pi\) |
0.399957 | + | 0.916534i | \(0.369025\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.0160 | −0.892610 | −0.446305 | − | 0.894881i | \(-0.647260\pi\) | ||||
−0.446305 | + | 0.894881i | \(0.647260\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 0.542449i | − | 0.0321319i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.58206 | − | 3.13697i | −0.329499 | − | 0.185169i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.08974i | 0.358220i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.44938 | −0.260827 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.60587 | − | 1.60587i | 0.0938161 | − | 0.0938161i | −0.658641 | − | 0.752457i | \(-0.728868\pi\) |
0.752457 | + | 0.658641i | \(0.228868\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.23405i | 0.0718494i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −22.2711 | −1.29230 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.6305 | + | 12.6305i | 0.730439 | + | 0.730439i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.39525 | − | 1.39525i | 0.0804210 | − | 0.0804210i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 19.3189 | 1.10984 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.39538 | 0.137159 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.4083i | 1.84964i | 0.380406 | + | 0.924820i | \(0.375784\pi\) | ||||
−0.380406 | + | 0.924820i | \(0.624216\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.23127 | − | 2.23127i | 0.126933 | − | 0.126933i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.87863 | − | 5.87863i | 0.333346 | − | 0.333346i | −0.520509 | − | 0.853856i | \(-0.674258\pi\) |
0.853856 | + | 0.520509i | \(0.174258\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.7559 | + | 14.7559i | −0.834051 | + | 0.834051i | −0.988068 | − | 0.154017i | \(-0.950779\pi\) |
0.154017 | + | 0.988068i | \(0.450779\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.302348 | − | 0.302348i | −0.0170354 | − | 0.0170354i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.4241 | + | 15.4241i | 0.866306 | + | 0.866306i | 0.992061 | − | 0.125755i | \(-0.0401353\pi\) |
−0.125755 | + | 0.992061i | \(0.540135\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.0912049i | 0.00510649i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.62005 | − | 2.62005i | −0.146237 | − | 0.146237i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 6.25561i | − | 0.348071i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.34459 | + | 9.34459i | 0.518344 | + | 0.518344i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.36370 | −0.296613 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.40916 | −0.187953 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.74721 | + | 2.74721i | 0.151001 | + | 0.151001i | 0.778565 | − | 0.627564i | \(-0.215948\pi\) |
−0.627564 | + | 0.778565i | \(0.715948\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 15.6891i | − | 0.859757i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.15975 | − | 2.15975i | −0.118000 | − | 0.118000i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.03529i | 0.0563957i | 0.999602 | + | 0.0281978i | \(0.00897684\pi\) | ||||
−0.999602 | + | 0.0281978i | \(0.991023\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.22096 | − | 5.22096i | −0.283563 | − | 0.283563i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.6291 | + | 10.6291i | 0.575600 | + | 0.575600i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.707107 | + | 0.707107i | −0.0381802 | + | 0.0381802i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.35145 | − | 1.35145i | 0.0727596 | − | 0.0727596i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.4454 | + | 19.4454i | −1.04389 | + | 1.04389i | −0.0448940 | + | 0.998992i | \(0.514295\pi\) |
−0.998992 | + | 0.0448940i | \(0.985705\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.7361i | 0.574692i | 0.957827 | + | 0.287346i | \(0.0927729\pi\) | ||||
−0.957827 | + | 0.287346i | \(0.907227\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.3417 | 0.765504 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −28.7630 | −1.53090 | −0.765450 | − | 0.643495i | \(-0.777484\pi\) | ||||
−0.765450 | + | 0.643495i | \(0.777484\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.33990 | + | 2.33990i | −0.124189 | + | 0.124189i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.66171 | + | 2.66171i | 0.140873 | + | 0.140873i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.6893 | −0.880830 | −0.440415 | − | 0.897794i | \(-0.645169\pi\) | ||||
−0.440415 | + | 0.897794i | \(0.645169\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.4132i | 0.811223i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.06037 | + | 5.06037i | −0.265600 | + | 0.265600i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.38914 | 0.0727109 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.5495i | 0.759478i | 0.925094 | + | 0.379739i | \(0.123986\pi\) | ||||
−0.925094 | + | 0.379739i | \(0.876014\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.94141 | + | 10.4888i | 0.153123 | + | 0.546028i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.47277i | 0.232215i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 36.4059 | 1.88502 | 0.942512 | − | 0.334172i | \(-0.108457\pi\) | ||||
0.942512 | + | 0.334172i | \(0.108457\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.01252 | − | 2.01252i | 0.103926 | − | 0.103926i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 0.0587323i | − | 0.00302487i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.6143 | −1.05889 | −0.529443 | − | 0.848346i | \(-0.677599\pi\) | ||||
−0.529443 | + | 0.848346i | \(0.677599\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.9024 | − | 11.9024i | −0.609777 | − | 0.609777i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.1886 | − | 15.1886i | 0.776101 | − | 0.776101i | −0.203065 | − | 0.979165i | \(-0.565090\pi\) |
0.979165 | + | 0.203065i | \(0.0650902\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.04476 | −0.0532459 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.35693 | −0.170642 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 15.8359i | − | 0.802911i | −0.915879 | − | 0.401456i | \(-0.868504\pi\) | ||
0.915879 | − | 0.401456i | \(-0.131496\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.5851 | − | 15.5851i | 0.788174 | − | 0.788174i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.57099 | + | 7.57099i | −0.381906 | + | 0.381906i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.06130 | − | 1.06130i | 0.0533998 | − | 0.0533998i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.2558 | + | 21.2558i | 1.06680 | + | 1.06680i | 0.997603 | + | 0.0691953i | \(0.0220432\pi\) |
0.0691953 | + | 0.997603i | \(0.477957\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.52614 | + | 1.52614i | 0.0764027 | + | 0.0764027i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 9.85414i | − | 0.492092i | −0.969258 | − | 0.246046i | \(-0.920869\pi\) | ||
0.969258 | − | 0.246046i | \(-0.0791315\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.84474 | − | 6.84474i | −0.340961 | − | 0.340961i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 0.251794i | − | 0.0125117i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −27.1067 | − | 27.1067i | −1.34363 | − | 1.34363i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −35.0043 | −1.73085 | −0.865426 | − | 0.501037i | \(-0.832952\pi\) | ||||
−0.865426 | + | 0.501037i | \(0.832952\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.4418 | 0.663034 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.47193 | − | 3.47193i | −0.170843 | − | 0.170843i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 1.70461i | − | 0.0836761i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.63964 | + | 2.63964i | 0.129264 | + | 0.129264i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 10.1050i | − | 0.493660i | −0.969059 | − | 0.246830i | \(-0.920611\pi\) | ||
0.969059 | − | 0.246830i | \(-0.0793889\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.4472 | + | 12.4472i | 0.606642 | + | 0.606642i | 0.942067 | − | 0.335425i | \(-0.108880\pi\) |
−0.335425 | + | 0.942067i | \(0.608880\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.10117 | + | 4.10117i | 0.199406 | + | 0.199406i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.5306 | − | 11.5306i | 0.559315 | − | 0.559315i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.73924 | + | 6.73924i | −0.326135 | + | 0.326135i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.96682 | − | 8.96682i | 0.432922 | − | 0.432922i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 28.9838i | − | 1.39610i | −0.716048 | − | 0.698051i | \(-0.754051\pi\) | ||
0.716048 | − | 0.698051i | \(-0.245949\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.54664 | 0.458782 | 0.229391 | − | 0.973334i | \(-0.426327\pi\) | ||||
0.229391 | + | 0.973334i | \(0.426327\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.00628430 | −0.000301309 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.93603 | − | 8.93603i | 0.427468 | − | 0.427468i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.1559 | + | 18.1559i | 0.866534 | + | 0.866534i | 0.992087 | − | 0.125553i | \(-0.0400704\pi\) |
−0.125553 | + | 0.992087i | \(0.540070\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.70128 | 0.0810131 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.77375i | 0.464365i | 0.972672 | + | 0.232182i | \(0.0745866\pi\) | ||||
−0.972672 | + | 0.232182i | \(0.925413\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.433956 | + | 0.433956i | −0.0205715 | + | 0.0205715i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.0541474 | −0.00256108 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 5.24705i | − | 0.247624i | −0.992306 | − | 0.123812i | \(-0.960488\pi\) | ||
0.992306 | − | 0.123812i | \(-0.0395119\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.2040 | + | 13.0400i | 1.09263 | + | 0.614031i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 2.34684i | − | 0.110264i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.672783 | 0.0315406 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.36459 | + | 5.36459i | −0.250945 | + | 0.250945i | −0.821358 | − | 0.570413i | \(-0.806783\pi\) |
0.570413 | + | 0.821358i | \(0.306783\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 17.6967i | − | 0.826010i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.2557 | 1.17627 | 0.588137 | − | 0.808762i | \(-0.299862\pi\) | ||||
0.588137 | + | 0.808762i | \(0.299862\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.71331 | + | 2.71331i | 0.126098 | + | 0.126098i | 0.767339 | − | 0.641241i | \(-0.221580\pi\) |
−0.641241 | + | 0.767339i | \(0.721580\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.732381 | + | 0.732381i | −0.0339633 | + | 0.0339633i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.12402 | −0.422209 | −0.211105 | − | 0.977463i | \(-0.567706\pi\) | ||||
−0.211105 | + | 0.977463i | \(0.567706\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.1526 | 0.561157 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.8971i | 0.502113i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.79990 | + | 5.79990i | −0.266680 | + | 0.266680i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.61127 | − | 6.61127i | 0.303346 | − | 0.303346i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.38066 | − | 5.38066i | 0.246364 | − | 0.246364i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.86377 | − | 3.86377i | −0.176540 | − | 0.176540i | 0.613306 | − | 0.789846i | \(-0.289839\pi\) |
−0.789846 | + | 0.613306i | \(0.789839\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.4556 | + | 17.4556i | 0.795907 | + | 0.795907i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.60442i | 0.346013i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.693863 | + | 0.693863i | 0.0315067 | + | 0.0315067i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 4.69099i | − | 0.212569i | −0.994336 | − | 0.106285i | \(-0.966105\pi\) | ||
0.994336 | − | 0.106285i | \(-0.0338955\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.3826 | − | 13.3826i | −0.605182 | − | 0.605182i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.5610 | 0.476609 | 0.238305 | − | 0.971190i | \(-0.423408\pi\) | ||||
0.238305 | + | 0.971190i | \(0.423408\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.0724715 | −0.00326395 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.25683 | + | 1.25683i | 0.0564902 | + | 0.0564902i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 13.1663i | − | 0.590589i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.375630 | + | 0.375630i | 0.0168155 | + | 0.0168155i | 0.715465 | − | 0.698649i | \(-0.246215\pi\) |
−0.698649 | + | 0.715465i | \(0.746215\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 8.97684i | − | 0.401055i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.0124 | + | 16.0124i | 0.713959 | + | 0.713959i | 0.967361 | − | 0.253402i | \(-0.0815495\pi\) |
−0.253402 | + | 0.967361i | \(0.581550\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.01271 | − | 3.01271i | −0.134064 | − | 0.134064i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.70152 | − | 4.70152i | 0.208802 | − | 0.208802i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.8161 | − | 12.8161i | 0.568065 | − | 0.568065i | −0.363521 | − | 0.931586i | \(-0.618425\pi\) |
0.931586 | + | 0.363521i | \(0.118425\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.90825 | + | 3.90825i | −0.172891 | + | 0.172891i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 10.1467i | − | 0.447989i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.695916 | −0.0306657 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.1715 | 0.623262 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.6307 | + | 16.6307i | −0.730006 | + | 0.730006i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.9848 | − | 25.9848i | −1.13841 | − | 1.13841i | −0.988735 | − | 0.149678i | \(-0.952176\pi\) |
−0.149678 | − | 0.988735i | \(-0.547824\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.4566 | 0.632142 | 0.316071 | − | 0.948736i | \(-0.397636\pi\) | ||||
0.316071 | + | 0.948736i | \(0.397636\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.62609i | 0.245543i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.44593 | + | 8.44593i | −0.367911 | + | 0.367911i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.5262 | 0.935921 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.35335i | 0.362504i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.9424 | − | 8.39725i | −0.647229 | − | 0.363725i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.817174i | 0.0353295i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −22.3844 | −0.965957 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.93936 | − | 2.93936i | 0.126607 | − | 0.126607i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 15.2484i | − | 0.655578i | −0.944751 | − | 0.327789i | \(-0.893696\pi\) | ||
0.944751 | − | 0.327789i | \(-0.106304\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.06152 | 0.0455543 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.836449 | + | 0.836449i | 0.0358295 | + | 0.0358295i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.9756 | − | 27.9756i | 1.19615 | − | 1.19615i | 0.220839 | − | 0.975310i | \(-0.429120\pi\) |
0.975310 | − | 0.220839i | \(-0.0708795\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 16.2144 | 0.692013 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.0415529 | −0.00177021 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.97180i | 0.253947i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.86773 | − | 1.86773i | 0.0792809 | − | 0.0792809i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.14092 | − | 3.14092i | 0.133085 | − | 0.133085i | −0.637426 | − | 0.770511i | \(-0.720001\pi\) |
0.770511 | + | 0.637426i | \(0.220001\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.73490 | − | 3.73490i | 0.157970 | − | 0.157970i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.0644 | − | 11.0644i | −0.467141 | − | 0.467141i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 26.3968 | + | 26.3968i | 1.11249 | + | 1.11249i | 0.992812 | + | 0.119681i | \(0.0381871\pi\) |
0.119681 | + | 0.992812i | \(0.461813\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.62838i | 0.0685063i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.708406 | + | 0.708406i | 0.0297502 | + | 0.0297502i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.73462i | 0.198486i | 0.995063 | + | 0.0992429i | \(0.0316421\pi\) | ||||
−0.995063 | + | 0.0992429i | \(0.968358\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.339810 | + | 0.339810i | 0.0142206 | + | 0.0142206i | 0.714181 | − | 0.699961i | \(-0.246799\pi\) |
−0.699961 | + | 0.714181i | \(0.746799\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.452103 | 0.0188869 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 32.9425 | 1.37380 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.2352 | + | 17.2352i | 0.717511 | + | 0.717511i | 0.968095 | − | 0.250584i | \(-0.0806225\pi\) |
−0.250584 | + | 0.968095i | \(0.580623\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.801321i | 0.0333018i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.79581 | + | 4.79581i | 0.198964 | + | 0.198964i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 18.5928i | − | 0.770034i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.809347 | − | 0.809347i | −0.0334624 | − | 0.0334624i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 29.5688 | + | 29.5688i | 1.22043 | + | 1.22043i | 0.967478 | + | 0.252955i | \(0.0814025\pi\) |
0.252955 | + | 0.967478i | \(0.418598\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.84264 | + | 4.84264i | −0.199537 | + | 0.199537i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.6635 | − | 16.6635i | 0.685445 | − | 0.685445i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.7699 | − | 20.7699i | 0.852918 | − | 0.852918i | −0.137573 | − | 0.990492i | \(-0.543930\pi\) |
0.990492 | + | 0.137573i | \(0.0439303\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 0.830168i | − | 0.0340336i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −29.5919 | −1.21112 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.18039 | −0.252524 | −0.126262 | − | 0.991997i | \(-0.540298\pi\) | ||||
−0.126262 | + | 0.991997i | \(0.540298\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.2543 | + | 15.2543i | −0.622236 | + | 0.622236i | −0.946103 | − | 0.323867i | \(-0.895017\pi\) |
0.323867 | + | 0.946103i | \(0.395017\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.6194 | − | 14.6194i | −0.595349 | − | 0.595349i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.57829 | 0.0641666 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 24.5297i | − | 0.995631i | −0.867283 | − | 0.497815i | \(-0.834136\pi\) | ||
0.867283 | − | 0.497815i | \(-0.165864\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.0176805 | − | 0.0176805i | 0.000716448 | − | 0.000716448i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.12588 | −0.369194 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.7130i | 1.24049i | 0.784409 | + | 0.620244i | \(0.212966\pi\) | ||||
−0.784409 | + | 0.620244i | \(0.787034\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.898498 | + | 1.59883i | −0.0362309 | + | 0.0644709i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.0231327i | 0.000931289i | 1.00000 | 0.000465645i | \(0.000148219\pi\) | |||||
−1.00000 | 0.000465645i | \(0.999852\pi\) | ||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.6769 | −0.790882 | −0.395441 | − | 0.918491i | \(-0.629408\pi\) | ||||
−0.395441 | + | 0.918491i | \(0.629408\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 25.2794 | − | 25.2794i | 1.01443 | − | 1.01443i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 2.44181i | − | 0.0978293i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.0565 | 0.962259 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.34400 | − | 6.34400i | −0.253355 | − | 0.253355i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.5390 | − | 21.5390i | 0.858816 | − | 0.858816i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.80666 | 0.0719221 | 0.0359610 | − | 0.999353i | \(-0.488551\pi\) | ||||
0.0359610 | + | 0.999353i | \(0.488551\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.9814 | −0.595456 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.71226i | 0.147316i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.89283 | + | 1.89283i | −0.0749967 | + | 0.0749967i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.8388 | + | 15.8388i | −0.626575 | + | 0.626575i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.2949 | − | 24.2949i | 0.959592 | − | 0.959592i | −0.0396225 | − | 0.999215i | \(-0.512616\pi\) |
0.999215 | + | 0.0396225i | \(0.0126155\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.3547 | + | 12.3547i | 0.487223 | + | 0.487223i | 0.907429 | − | 0.420206i | \(-0.138042\pi\) |
−0.420206 | + | 0.907429i | \(0.638042\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.399631 | − | 0.399631i | −0.0157355 | − | 0.0157355i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.8408i | 0.544136i | 0.962278 | + | 0.272068i | \(0.0877076\pi\) | ||||
−0.962278 | + | 0.272068i | \(0.912292\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.4324 | + | 14.4324i | 0.566522 | + | 0.566522i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 4.12101i | − | 0.161515i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.41607 | + | 7.41607i | 0.290213 | + | 0.290213i | 0.837164 | − | 0.546951i | \(-0.184212\pi\) |
−0.546951 | + | 0.837164i | \(0.684212\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.36133 | 0.0922650 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.40313 | 0.366851 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.5341 | − | 12.5341i | −0.488258 | − | 0.488258i | 0.419498 | − | 0.907756i | \(-0.362206\pi\) |
−0.907756 | + | 0.419498i | \(0.862206\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 17.7094i | − | 0.688815i | −0.938820 | − | 0.344408i | \(-0.888080\pi\) | ||
0.938820 | − | 0.344408i | \(-0.111920\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.12505 | + | 7.12505i | 0.276714 | + | 0.276714i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 0.475992i | − | 0.0184582i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.103524 | − | 0.103524i | −0.00400848 | − | 0.00400848i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.5746 | + | 13.5746i | 0.524823 | + | 0.524823i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28.0142 | − | 28.0142i | 1.08148 | − | 1.08148i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.3633 | + | 11.3633i | −0.438024 | + | 0.438024i | −0.891347 | − | 0.453322i | \(-0.850239\pi\) |
0.453322 | + | 0.891347i | \(0.350239\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 18.7028 | − | 18.7028i | 0.719873 | − | 0.719873i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 2.90980i | − | 0.111833i | −0.998435 | − | 0.0559164i | \(-0.982192\pi\) | ||
0.998435 | − | 0.0559164i | \(-0.0178080\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.90428 | −0.149832 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.66947 | 0.217254 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.92137 | + | 1.92137i | −0.0735191 | + | 0.0735191i | −0.742910 | − | 0.669391i | \(-0.766555\pi\) |
0.669391 | + | 0.742910i | \(0.266555\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.09619 | − | 2.09619i | −0.0800914 | − | 0.0800914i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 29.7723 | 1.13589 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.9730i | 0.456135i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.1912 | − | 27.1912i | 1.03440 | − | 1.03440i | 0.0350170 | − | 0.999387i | \(-0.488851\pi\) |
0.999387 | − | 0.0350170i | \(-0.0111485\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.07201 | −0.268643 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 0.823283i | − | 0.0312289i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.3616 | + | 18.4379i | −0.392475 | + | 0.698387i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 30.1823i | 1.14160i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.7290 | −0.594076 | −0.297038 | − | 0.954866i | \(-0.595999\pi\) | ||||
−0.297038 | + | 0.954866i | \(0.595999\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.3498 | − | 12.3498i | 0.465781 | − | 0.465781i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.976461i | 0.0367756i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16.9521 | 0.637550 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.87844 | + | 1.87844i | 0.0705463 | + | 0.0705463i | 0.741500 | − | 0.670953i | \(-0.234115\pi\) |
−0.670953 | + | 0.741500i | \(0.734115\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.18397 | − | 7.18397i | 0.269420 | − | 0.269420i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24.1298 | −0.903666 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.79668 | −0.104590 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 29.8069i | − | 1.11316i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.04723 | + | 3.04723i | −0.113642 | + | 0.113642i | −0.761641 | − | 0.647999i | \(-0.775606\pi\) |
0.647999 | + | 0.761641i | \(0.275606\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.95792 | − | 1.95792i | 0.0729166 | − | 0.0729166i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.88695 | − | 3.88695i | 0.144557 | − | 0.144557i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.0765920 | − | 0.0765920i | −0.00284455 | − | 0.00284455i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.14245 | + | 8.14245i | 0.301987 | + | 0.301987i | 0.841791 | − | 0.539804i | \(-0.181502\pi\) |
−0.539804 | + | 0.841791i | \(0.681502\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 20.0214i | − | 0.741533i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.60861 | − | 4.60861i | −0.170456 | − | 0.170456i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 48.1604i | 1.77884i | 0.457087 | + | 0.889422i | \(0.348893\pi\) | ||||
−0.457087 | + | 0.889422i | \(0.651107\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.202531 | + | 0.202531i | 0.00747047 | + | 0.00747047i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −50.5171 | −1.86082 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −39.0976 | −1.43823 | −0.719114 | − | 0.694892i | \(-0.755452\pi\) | ||||
−0.719114 | + | 0.694892i | \(0.755452\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.08528 | + | 4.08528i | 0.150077 | + | 0.150077i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 41.5962i | 1.52602i | 0.646389 | + | 0.763008i | \(0.276278\pi\) | ||||
−0.646389 | + | 0.763008i | \(0.723722\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.00844407 | + | 0.00844407i | 0.000309367 | + | 0.000309367i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 11.5386i | − | 0.422174i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.29907 | − | 2.29907i | −0.0840061 | − | 0.0840061i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.4849 | + | 37.4849i | 1.36784 | + | 1.36784i | 0.863507 | + | 0.504337i | \(0.168263\pi\) |
0.504337 | + | 0.863507i | \(0.331737\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.81196 | + | 2.81196i | −0.102473 | + | 0.102473i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.365981 | + | 0.365981i | −0.0133194 | + | 0.0133194i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.22630 | + | 7.22630i | −0.262644 | + | 0.262644i | −0.826128 | − | 0.563483i | \(-0.809461\pi\) |
0.563483 | + | 0.826128i | \(0.309461\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 31.6107i | − | 1.14740i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 41.1038 | 1.49001 | 0.745005 | − | 0.667059i | \(-0.232447\pi\) | ||||
0.745005 | + | 0.667059i | \(0.232447\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.70659 | −0.170390 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.998678 | + | 0.998678i | −0.0361073 | + | 0.0361073i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.29390 | − | 9.29390i | −0.335583 | − | 0.335583i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.5557 | −1.24611 | −0.623055 | − | 0.782178i | \(-0.714109\pi\) | ||||
−0.623055 | + | 0.782178i | \(0.714109\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 3.19028i | − | 0.114895i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.8386 | + | 15.8386i | −0.569673 | + | 0.569673i | −0.932037 | − | 0.362364i | \(-0.881970\pi\) |
0.362364 | + | 0.932037i | \(0.381970\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.8523 | −0.641273 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.5095i | 0.377026i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.94103 | + | 10.5717i | −0.212860 | + | 0.378772i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 54.7308i | 1.95842i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.117550 | −0.00420091 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.69936 | − | 1.69936i | 0.0606529 | − | 0.0606529i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 13.9193i | − | 0.496171i | −0.968738 | − | 0.248085i | \(-0.920199\pi\) | ||
0.968738 | − | 0.248085i | \(-0.0798014\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.3476 | −0.475187 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.58133 | − | 4.58133i | −0.162893 | − | 0.162893i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.0400 | + | 18.0400i | −0.640621 | + | 0.640621i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.28110 | 0.0454359 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −54.7723 | −1.94014 | −0.970068 | − | 0.242834i | \(-0.921923\pi\) | ||||
−0.970068 | + | 0.242834i | \(0.921923\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.2607i | 0.398375i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.93746 | + | 2.93746i | −0.103790 | + | 0.103790i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.2462 | − | 16.2462i | 0.573315 | − | 0.573315i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.18588 | − | 1.18588i | 0.0417968 | − | 0.0417968i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.55823 | − | 8.55823i | −0.301264 | − | 0.301264i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.5463 | + | 13.5463i | 0.476263 | + | 0.476263i | 0.903934 | − | 0.427671i | \(-0.140666\pi\) |
−0.427671 | + | 0.903934i | \(0.640666\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 52.7075i | − | 1.85081i | −0.378979 | − | 0.925405i | \(-0.623725\pi\) | ||
0.378979 | − | 0.925405i | \(-0.376275\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.4156 | − | 10.4156i | −0.365291 | − | 0.365291i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.17393i | 0.146206i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.64244 | − | 2.64244i | −0.0924471 | − | 0.0924471i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.55409 | 0.159133 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.1616 | 1.40165 | 0.700825 | − | 0.713333i | \(-0.252815\pi\) | ||||
0.700825 | + | 0.713333i | \(0.252815\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.8151 | − | 16.8151i | −0.586138 | − | 0.586138i | 0.350445 | − | 0.936583i | \(-0.386030\pi\) |
−0.936583 | + | 0.350445i | \(0.886030\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 23.3870i | − | 0.814232i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.7356 | + | 11.7356i | 0.408087 | + | 0.408087i | 0.881071 | − | 0.472984i | \(-0.156823\pi\) |
−0.472984 | + | 0.881071i | \(0.656823\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 51.1586i | 1.77681i | 0.459057 | + | 0.888407i | \(0.348187\pi\) | ||||
−0.459057 | + | 0.888407i | \(0.651813\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21.6913 | − | 21.6913i | −0.752463 | − | 0.752463i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.33562 | + | 2.33562i | 0.0809245 | + | 0.0809245i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.39990 | + | 1.39990i | −0.0484456 | + | 0.0484456i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13.6995 | + | 13.6995i | −0.473524 | + | 0.473524i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.71879 | + | 5.71879i | −0.197434 | + | 0.197434i | −0.798899 | − | 0.601465i | \(-0.794584\pi\) |
0.601465 | + | 0.798899i | \(0.294584\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 28.9995i | − | 0.999983i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.9560 | −0.480671 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.46637 | −0.0504446 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.44042 | + | 4.44042i | −0.152574 | + | 0.152574i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.1004 | − | 12.1004i | −0.415283 | − | 0.415283i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 61.5362 | 2.10943 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 11.5830i | − | 0.396593i | −0.980142 | − | 0.198297i | \(-0.936459\pi\) | ||
0.980142 | − | 0.198297i | \(-0.0635409\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.572611 | + | 0.572611i | −0.0195829 | + | 0.0195829i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.9897 | −0.375402 | −0.187701 | − | 0.982226i | \(-0.560104\pi\) | ||||
−0.187701 | + | 0.982226i | \(0.560104\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 56.4252i | 1.92520i | 0.270920 | + | 0.962602i | \(0.412672\pi\) | ||||
−0.270920 | + | 0.962602i | \(0.587328\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.97033 | − | 7.02606i | −0.0671486 | − | 0.239447i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 16.0485i | − | 0.546296i | −0.961972 | − | 0.273148i | \(-0.911935\pi\) | ||
0.961972 | − | 0.273148i | \(-0.0880648\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.18698 | 0.176363 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.90730 | + | 4.90730i | −0.166661 | + | 0.166661i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 24.8241i | − | 0.842099i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.5310 | 1.10227 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.69678 | + | 4.69678i | 0.158962 | + | 0.158962i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.76596 | − | 1.76596i | 0.0597004 | − | 0.0597004i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.1322 | −0.848655 | −0.424327 | − | 0.905509i | \(-0.639489\pi\) | ||||
−0.424327 | + | 0.905509i | \(0.639489\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.58812 | 0.0872952 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.9285i | 0.873555i | 0.899570 | + | 0.436777i | \(0.143880\pi\) | ||||
−0.899570 | + | 0.436777i | \(0.856120\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.3964 | − | 26.3964i | 0.888309 | − | 0.888309i | −0.106052 | − | 0.994361i | \(-0.533821\pi\) |
0.994361 | + | 0.106052i | \(0.0338209\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.994438 | + | 0.994438i | −0.0334277 | + | 0.0334277i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15.8761 | + | 15.8761i | −0.533066 | + | 0.533066i | −0.921484 | − | 0.388417i | \(-0.873022\pi\) |
0.388417 | + | 0.921484i | \(0.373022\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.4442 | − | 10.4442i | −0.350287 | − | 0.350287i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.94476 | − | 2.94476i | −0.0986532 | − | 0.0986532i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.45654i | 0.216060i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.49076 | + | 3.49076i | 0.116683 | + | 0.116683i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 20.3560i | 0.679668i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.0561022 | + | 0.0561022i | 0.00187111 | + | 0.00187111i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.7739 | 0.492189 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.24867 | 0.0748311 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.165540 | − | 0.165540i | −0.00550275 | − | 0.00550275i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 38.8133i | − | 1.28877i | −0.764700 | − | 0.644387i | \(-0.777113\pi\) | ||
0.764700 | − | 0.644387i | \(-0.222887\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −20.3931 | − | 20.3931i | −0.676397 | − | 0.676397i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.4491i | 1.27388i | 0.770915 | + | 0.636938i | \(0.219799\pi\) | ||||
−0.770915 | + | 0.636938i | \(0.780201\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19.9356 | − | 19.9356i | −0.659774 | − | 0.659774i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.93027 | + | 1.93027i | 0.0638127 | + | 0.0638127i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.64346 | + | 6.64346i | −0.219386 | + | 0.219386i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.3680 | − | 23.3680i | 0.770838 | − | 0.770838i | −0.207415 | − | 0.978253i | \(-0.566505\pi\) |
0.978253 | + | 0.207415i | \(0.0665050\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26.1156 | + | 26.1156i | −0.860538 | + | 0.860538i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 35.2444i | − | 1.16008i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 45.5273 | 1.49693 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.71068 | −0.154719 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.0547 | + | 19.0547i | −0.625165 | + | 0.625165i | −0.946848 | − | 0.321682i | \(-0.895752\pi\) |
0.321682 | + | 0.946848i | \(0.395752\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.33917 | + | 1.33917i | 0.0438896 | + | 0.0438896i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.47436 | 0.310176 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.45091i | 0.112857i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.000932308 | 0 | 0.000932308i | 3.04572e−5 | 0 | 3.04572e-5i | −0.707092 | − | 0.707122i | \(-0.749993\pi\) |
0.707122 | + | 0.707092i | \(0.249993\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23.7814 | −0.776078 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.6335i | 1.16162i | 0.814039 | + | 0.580810i | \(0.197264\pi\) | ||||
−0.814039 | + | 0.580810i | \(0.802736\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −41.1397 | + | 11.5369i | −1.33969 | + | 0.375692i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 1.34655i | − | 0.0438033i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.2183 | 0.657006 | 0.328503 | − | 0.944503i | \(-0.393456\pi\) | ||||
0.328503 | + | 0.944503i | \(0.393456\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.4619 | + | 10.4619i | −0.339607 | + | 0.339607i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.8585i | 0.806092i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −48.9387 | −1.58528 | −0.792641 | − | 0.609689i | \(-0.791294\pi\) | ||||
−0.792641 | + | 0.609689i | \(0.791294\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.0705038 | − | 0.0705038i | −0.00228145 | − | 0.00228145i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.0734956 | + | 0.0734956i | −0.00237578 | + | 0.00237578i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.7950 | 0.380880 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.9235 | −0.578179 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.53148i | 0.178249i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.124963 | − | 0.124963i | 0.00402270 | − | 0.00402270i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.8816 | − | 12.8816i | 0.414245 | − | 0.414245i | −0.468969 | − | 0.883214i | \(-0.655375\pi\) |
0.883214 | + | 0.468969i | \(0.155375\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.04096 | − | 5.04096i | 0.161939 | − | 0.161939i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.40187 | − | 9.40187i | −0.301720 | − | 0.301720i | 0.539966 | − | 0.841687i | \(-0.318437\pi\) |
−0.841687 | + | 0.539966i | \(0.818437\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.31625 | + | 2.31625i | 0.0742557 | + | 0.0742557i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 15.0603i | 0.482316i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −33.7732 | − | 33.7732i | −1.08050 | − | 1.08050i | −0.996463 | − | 0.0840367i | \(-0.973219\pi\) |
−0.0840367 | − | 0.996463i | \(-0.526781\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.1503i | 0.324406i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.66194 | + | 5.66194i | 0.180772 | + | 0.180772i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.3461 | 0.393779 | 0.196890 | − | 0.980426i | \(-0.436916\pi\) | ||||
0.196890 | + | 0.980426i | \(0.436916\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.19722 | −0.165597 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.74721 | − | 2.74721i | −0.0874446 | − | 0.0874446i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 13.1667i | − | 0.418675i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.2467 | − | 32.2467i | −1.02435 | − | 1.02435i | −0.999696 | − | 0.0246531i | \(-0.992152\pi\) |
−0.0246531 | − | 0.999696i | \(-0.507848\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.42758i | 0.140505i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.61474 | + | 4.61474i | 0.146297 | + | 0.146297i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.32451 | + | 7.32451i | 0.231970 | + | 0.231970i | 0.813514 | − | 0.581545i | \(-0.197552\pi\) |
−0.581545 | + | 0.813514i | \(0.697552\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 34.9367 | − | 34.9367i | 1.10535 | − | 1.10535i |
(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 | 1148.2.k.b.337.12 | ✓ | 36 | |
41.32 | even | 4 | inner | 1148.2.k.b.729.12 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.k.b.337.12 | ✓ | 36 | 1.1 | even | 1 | trivial | |
1148.2.k.b.729.12 | yes | 36 | 41.32 | even | 4 | inner |