Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(113,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.113");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.ba (of order \(10\), degree \(4\), 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: | \(80\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 701.14 | ||
Character | \(\chi\) | \(=\) | 1148.701 |
Dual form | 1148.2.ba.a.113.7 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{10}\right)\) |
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 | ||||||||
\(3\) | 1.15530i | 0.667013i | 0.942748 | + | 0.333506i | \(0.108232\pi\) | ||||
−0.942748 | + | 0.333506i | \(0.891768\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.04872 | + | 3.22763i | −0.469002 | + | 1.44344i | 0.384878 | + | 0.922968i | \(0.374244\pi\) |
−0.853879 | + | 0.520471i | \(0.825756\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.587785 | + | 0.809017i | −0.222162 | + | 0.305780i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.66528 | 0.555094 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.79368 | + | 1.55756i | −1.44535 | + | 0.469623i | −0.923561 | − | 0.383452i | \(-0.874735\pi\) |
−0.521789 | + | 0.853074i | \(0.674735\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.242673 | − | 0.334011i | −0.0673054 | − | 0.0926379i | 0.774037 | − | 0.633140i | \(-0.218234\pi\) |
−0.841343 | + | 0.540502i | \(0.818234\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.72888 | − | 1.21159i | −0.962792 | − | 0.312830i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.09880 | − | 1.33178i | 0.994105 | − | 0.323004i | 0.233597 | − | 0.972333i | \(-0.424950\pi\) |
0.760507 | + | 0.649329i | \(0.224950\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.03463 | + | 5.55319i | −0.925608 | + | 1.27399i | 0.0359405 | + | 0.999354i | \(0.488557\pi\) |
−0.961548 | + | 0.274636i | \(0.911443\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.934658 | − | 0.679068i | −0.203959 | − | 0.148185i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.71308 | − | 1.97117i | 0.565717 | − | 0.411017i | −0.267830 | − | 0.963466i | \(-0.586307\pi\) |
0.833547 | + | 0.552449i | \(0.186307\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.27268 | − | 3.83082i | −1.05454 | − | 0.766165i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.38980i | 1.03727i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.54178 | − | 1.80063i | −1.02908 | − | 0.334369i | −0.254655 | − | 0.967032i | \(-0.581962\pi\) |
−0.774427 | + | 0.632663i | \(0.781962\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.17885 | + | 3.62811i | 0.211727 | + | 0.651628i | 0.999370 | + | 0.0354964i | \(0.0113012\pi\) |
−0.787643 | + | 0.616132i | \(0.788699\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.79945 | − | 5.53814i | −0.313244 | − | 0.964067i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.99478 | − | 2.74558i | −0.337180 | − | 0.464088i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.51545 | − | 4.66407i | 0.249138 | − | 0.766768i | −0.745790 | − | 0.666181i | \(-0.767928\pi\) |
0.994928 | − | 0.100587i | \(-0.0320720\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.385883 | − | 0.280360i | 0.0617907 | − | 0.0448936i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.10916 | − | 6.04578i | −0.329395 | − | 0.944192i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.08403 | − | 1.51413i | 0.317811 | − | 0.230903i | −0.417430 | − | 0.908709i | \(-0.637069\pi\) |
0.735241 | + | 0.677806i | \(0.237069\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.74641 | + | 5.37491i | −0.260340 | + | 0.801244i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.14962 | − | 2.95870i | −0.313554 | − | 0.431570i | 0.622931 | − | 0.782276i | \(-0.285942\pi\) |
−0.936486 | + | 0.350706i | \(0.885942\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.309017 | − | 0.951057i | −0.0441453 | − | 0.135865i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.53861 | + | 4.73534i | 0.215448 | + | 0.663081i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.59927 | − | 1.49439i | −0.631758 | − | 0.205271i | −0.0244041 | − | 0.999702i | \(-0.507769\pi\) |
−0.607354 | + | 0.794432i | \(0.707769\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 17.1057i | − | 2.30653i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.41561 | − | 4.66121i | −0.849768 | − | 0.617392i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.76662 | − | 2.01006i | 0.360183 | − | 0.261688i | −0.392946 | − | 0.919562i | \(-0.628544\pi\) |
0.753128 | + | 0.657874i | \(0.228544\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.57199 | + | 6.95446i | 1.22557 | + | 0.890427i | 0.996550 | − | 0.0829951i | \(-0.0264486\pi\) |
0.229018 | + | 0.973422i | \(0.426449\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.978828 | + | 1.34724i | −0.123321 | + | 0.169736i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.33256 | − | 0.432974i | 0.165283 | − | 0.0537038i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00013 | − | 1.29972i | −0.488693 | − | 0.158786i | 0.0542973 | − | 0.998525i | \(-0.482708\pi\) |
−0.542991 | + | 0.839739i | \(0.682708\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.27729 | + | 3.13442i | 0.274154 | + | 0.377340i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.48844 | + | 1.13346i | −0.414002 | + | 0.134517i | −0.508610 | − | 0.860997i | \(-0.669840\pi\) |
0.0946077 | + | 0.995515i | \(0.469840\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −16.2956 | −1.90725 | −0.953627 | − | 0.300991i | \(-0.902682\pi\) | ||||
−0.953627 | + | 0.300991i | \(0.902682\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.42575 | − | 6.09152i | 0.511042 | − | 0.703389i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.55756 | − | 4.79368i | 0.177501 | − | 0.546291i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.78329i | 0.650671i | 0.945599 | + | 0.325336i | \(0.105477\pi\) | ||||
−0.945599 | + | 0.325336i | \(0.894523\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.23099 | −0.136777 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.92404 | −0.979541 | −0.489770 | − | 0.871851i | \(-0.662919\pi\) | ||||
−0.489770 | + | 0.871851i | \(0.662919\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.6261i | 1.58642i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.08027 | − | 6.40242i | 0.223029 | − | 0.686411i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.55641 | − | 6.27135i | 0.482978 | − | 0.664762i | −0.496096 | − | 0.868268i | \(-0.665234\pi\) |
0.979074 | + | 0.203506i | \(0.0652335\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.412860 | 0.0432795 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.19156 | + | 1.36192i | −0.434645 | + | 0.141225i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −13.6924 | − | 18.8460i | −1.40481 | − | 1.93356i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.934792 | + | 0.303732i | 0.0949138 | + | 0.0308394i | 0.356089 | − | 0.934452i | \(-0.384110\pi\) |
−0.261175 | + | 0.965291i | \(0.584110\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.98283 | + | 2.59378i | −0.802305 | + | 0.260685i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.0408997 | + | 0.0562936i | −0.00406967 | + | 0.00560142i | −0.811047 | − | 0.584981i | \(-0.801102\pi\) |
0.806977 | + | 0.590582i | \(0.201102\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.9785 | + | 10.8825i | 1.47588 | + | 1.07229i | 0.978857 | + | 0.204546i | \(0.0655717\pi\) |
0.497018 | + | 0.867740i | \(0.334428\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.17197 | − | 2.30457i | 0.309553 | − | 0.224903i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.04598 | − | 5.11920i | −0.681160 | − | 0.494892i | 0.192582 | − | 0.981281i | \(-0.438314\pi\) |
−0.873742 | + | 0.486389i | \(0.838314\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.2495i | 1.17329i | 0.809844 | + | 0.586645i | \(0.199552\pi\) | ||||
−0.809844 | + | 0.586645i | \(0.800448\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.38840 | + | 1.75080i | 0.511444 | + | 0.166178i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.01600 | + | 3.12691i | 0.0955768 | + | 0.294155i | 0.987404 | − | 0.158222i | \(-0.0505761\pi\) |
−0.891827 | + | 0.452377i | \(0.850576\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.51694 | + | 10.8240i | 0.327956 | + | 1.00934i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.404119 | − | 0.556222i | −0.0373608 | − | 0.0514227i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.33178 | + | 4.09880i | −0.122084 | + | 0.375736i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.6542 | − | 8.46729i | 1.05947 | − | 0.769753i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.98469 | − | 2.43671i | 0.629788 | − | 0.219711i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.16611 | − | 3.02685i | 0.372628 | − | 0.270730i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.85134 | + | 18.0086i | −0.519222 | + | 1.59800i | 0.256244 | + | 0.966612i | \(0.417515\pi\) |
−0.775466 | + | 0.631390i | \(0.782485\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.74928 | + | 2.40768i | 0.154016 | + | 0.211984i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.90333 | + | 5.85786i | 0.166295 | + | 0.511803i | 0.999129 | − | 0.0417190i | \(-0.0132834\pi\) |
−0.832834 | + | 0.553522i | \(0.813283\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.12113 | − | 6.52817i | −0.183925 | − | 0.566064i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −17.3963 | − | 5.65239i | −1.49723 | − | 0.486480i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.52526i | 0.728362i | 0.931328 | + | 0.364181i | \(0.118651\pi\) | ||||
−0.931328 | + | 0.364181i | \(0.881349\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.6500 | + | 9.91729i | 1.15778 | + | 0.841174i | 0.989495 | − | 0.144565i | \(-0.0461783\pi\) |
0.168281 | + | 0.985739i | \(0.446178\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.41818 | − | 2.48345i | 0.287863 | − | 0.209145i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.68354 | + | 1.22316i | 0.140785 | + | 0.102286i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.6235 | − | 15.9984i | 0.965283 | − | 1.32860i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.09876 | − | 0.357007i | 0.0906239 | − | 0.0294455i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.5183 | − | 3.74252i | −0.943615 | − | 0.306599i | −0.203497 | − | 0.979076i | \(-0.565231\pi\) |
−0.740118 | + | 0.672477i | \(0.765231\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.96279 | + | 8.20708i | 0.485245 | + | 0.667882i | 0.979502 | − | 0.201433i | \(-0.0645599\pi\) |
−0.494257 | + | 0.869316i | \(0.664560\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.82565 | − | 2.21779i | 0.551821 | − | 0.179298i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.9465 | −1.03989 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.29599 | − | 3.16016i | 0.183240 | − | 0.252209i | −0.707508 | − | 0.706705i | \(-0.750181\pi\) |
0.890749 | + | 0.454496i | \(0.150181\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.72647 | − | 5.31353i | 0.136918 | − | 0.421391i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.35355i | 0.264297i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.83646 | 0.457147 | 0.228573 | − | 0.973527i | \(-0.426594\pi\) | ||||
0.228573 | + | 0.973527i | \(0.426594\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 19.7622 | 1.53848 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.5723i | 1.05026i | 0.851023 | + | 0.525128i | \(0.175983\pi\) | ||||
−0.851023 | + | 0.525128i | \(0.824017\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.96455 | − | 12.2016i | 0.304965 | − | 0.938586i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.71880 | + | 9.24763i | −0.513799 | + | 0.707184i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.5650 | 1.41147 | 0.705734 | − | 0.708477i | \(-0.250617\pi\) | ||||
0.705734 | + | 0.708477i | \(0.250617\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.19840 | − | 2.01398i | 0.468555 | − | 0.152243i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.32223 | + | 3.19627i | 0.174549 | + | 0.240247i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.6874 | − | 6.72174i | −1.54625 | − | 0.502406i | −0.593155 | − | 0.805088i | \(-0.702118\pi\) |
−0.953092 | + | 0.302682i | \(0.902118\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.1455 | + | 5.57091i | −1.27441 | + | 0.414082i | −0.866609 | − | 0.498987i | \(-0.833706\pi\) |
−0.407805 | + | 0.913069i | \(0.633706\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.03449 | + | 11.0585i | −0.593926 | + | 0.817470i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 13.4646 | + | 9.78259i | 0.989936 | + | 0.719230i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.5740 | + | 12.7683i | −1.28514 | + | 0.933708i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.36044 | − | 3.16805i | −0.317175 | − | 0.230441i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.75897i | 0.416704i | 0.978054 | + | 0.208352i | \(0.0668100\pi\) | ||||
−0.978054 | + | 0.208352i | \(0.933190\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.59712 | − | 3.11829i | −0.690816 | − | 0.224460i | −0.0574914 | − | 0.998346i | \(-0.518310\pi\) |
−0.633325 | + | 0.773886i | \(0.718310\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.500215 | + | 1.53950i | 0.0358212 | + | 0.110246i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.66718 | + | 14.3641i | 0.332523 | + | 1.02340i | 0.967929 | + | 0.251223i | \(0.0808327\pi\) |
−0.635406 | + | 0.772178i | \(0.719167\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.12212 | + | 2.92085i | 0.150433 | + | 0.207054i | 0.877582 | − | 0.479426i | \(-0.159155\pi\) |
−0.727149 | + | 0.686480i | \(0.759155\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.50157 | − | 4.62135i | 0.105912 | − | 0.325965i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.71412 | − | 3.42501i | 0.330866 | − | 0.240388i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 21.7254 | − | 0.467247i | 1.51737 | − | 0.0326339i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.51804 | − | 3.28255i | 0.314026 | − | 0.228153i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.6913 | − | 32.9044i | 0.739533 | − | 2.27605i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.6477 | − | 14.6553i | −0.733017 | − | 1.00891i | −0.998990 | − | 0.0449311i | \(-0.985693\pi\) |
0.265973 | − | 0.963981i | \(-0.414307\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.30949 | − | 4.03020i | −0.0897248 | − | 0.276145i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.70150 | + | 8.31436i | 0.184241 | + | 0.567035i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.62811 | − | 1.17885i | −0.246292 | − | 0.0800253i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 18.8263i | − | 1.27216i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.43950 | − | 1.04586i | −0.0968310 | − | 0.0703518i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.11339 | + | 0.808922i | −0.0745579 | + | 0.0541695i | −0.624440 | − | 0.781073i | \(-0.714673\pi\) |
0.549882 | + | 0.835242i | \(0.314673\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.78049 | − | 6.37940i | −0.585366 | − | 0.425293i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.87373 | − | 8.08449i | 0.389853 | − | 0.536587i | −0.568308 | − | 0.822816i | \(-0.692402\pi\) |
0.958161 | + | 0.286229i | \(0.0924019\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.2691 | − | 6.26092i | 1.27334 | − | 0.413733i | 0.407110 | − | 0.913379i | \(-0.366536\pi\) |
0.866230 | + | 0.499646i | \(0.166536\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.53814 | + | 1.79945i | 0.364383 | + | 0.118395i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.03542 | + | 9.68342i | 0.460905 | + | 0.634382i | 0.974696 | − | 0.223534i | \(-0.0717592\pi\) |
−0.513791 | + | 0.857916i | \(0.671759\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.8039 | − | 3.83532i | 0.770002 | − | 0.250189i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.68144 | −0.434006 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.02745 | + | 5.54331i | −0.260514 | + | 0.358567i | −0.919159 | − | 0.393887i | \(-0.871130\pi\) |
0.658645 | + | 0.752454i | \(0.271130\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.114728 | − | 0.353096i | 0.00739028 | − | 0.0227449i | −0.947293 | − | 0.320367i | \(-0.896194\pi\) |
0.954684 | + | 0.297622i | \(0.0961936\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.7472i | 0.946036i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.39373 | 0.216817 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.83392 | 0.180318 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 10.3099i | − | 0.653366i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.428825 | − | 1.31979i | 0.0270672 | − | 0.0833043i | −0.936610 | − | 0.350373i | \(-0.886055\pi\) |
0.963678 | + | 0.267068i | \(0.0860550\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.93544 | + | 13.6750i | −0.624636 | + | 0.859737i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −16.8975 | −1.05816 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.36241 | − | 1.74235i | 0.334498 | − | 0.108685i | −0.136952 | − | 0.990578i | \(-0.543731\pi\) |
0.471450 | + | 0.881893i | \(0.343731\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.88255 | + | 3.96749i | 0.179113 | + | 0.246528i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.22862 | − | 2.99856i | −0.571237 | − | 0.185606i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 25.0333 | − | 8.13381i | 1.54362 | − | 0.501552i | 0.591247 | − | 0.806491i | \(-0.298636\pi\) |
0.952372 | + | 0.304938i | \(0.0986359\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.64668 | − | 13.2775i | 0.592591 | − | 0.815631i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.24530 | + | 5.26402i | 0.443405 | + | 0.322153i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.14563 | + | 3.01197i | −0.252763 | + | 0.183643i | −0.706951 | − | 0.707263i | \(-0.749930\pi\) |
0.454187 | + | 0.890906i | \(0.349930\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.7992 | − | 17.2911i | −1.44570 | − | 1.05036i | −0.986813 | − | 0.161865i | \(-0.948249\pi\) |
−0.458885 | − | 0.888496i | \(-0.651751\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.476977i | 0.0288680i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 31.2423 | + | 10.1512i | 1.88398 | + | 0.612142i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.91362 | + | 30.5110i | 0.595652 | + | 1.83323i | 0.551454 | + | 0.834205i | \(0.314073\pi\) |
0.0441978 | + | 0.999023i | \(0.485927\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.96311 | + | 6.04183i | 0.117528 | + | 0.361715i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.4782 | + | 25.4330i | 1.10232 | + | 1.51721i | 0.832280 | + | 0.554356i | \(0.187035\pi\) |
0.270036 | + | 0.962850i | \(0.412965\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.429565 | + | 1.32207i | −0.0255350 | + | 0.0785886i | −0.963012 | − | 0.269459i | \(-0.913155\pi\) |
0.937477 | + | 0.348047i | \(0.113155\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 21.7728 | − | 15.8189i | 1.28971 | − | 0.937029i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.13087 | + | 1.84728i | 0.361894 | + | 0.109041i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.27322 | − | 0.925049i | 0.0748954 | − | 0.0544147i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.350902 | + | 1.07997i | −0.0205702 | + | 0.0633087i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.54333 | + | 10.3825i | 0.440686 | + | 0.606552i | 0.970364 | − | 0.241646i | \(-0.0776874\pi\) |
−0.529678 | + | 0.848199i | \(0.677687\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.58633 | + | 11.0376i | 0.208804 | + | 0.642634i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.39495 | − | 25.8370i | −0.487124 | − | 1.49922i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.31678 | − | 0.427849i | −0.0761515 | − | 0.0247431i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.57600i | 0.148478i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.0650360 | − | 0.0472514i | −0.00373622 | − | 0.00271452i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −32.4847 | + | 23.6015i | −1.86007 | + | 1.35142i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.9952 | + | 13.8008i | 1.08411 | + | 0.787653i | 0.978395 | − | 0.206744i | \(-0.0662867\pi\) |
0.105716 | + | 0.994396i | \(0.466287\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.5726 | + | 17.3047i | −0.715229 | + | 0.984428i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.5910 | + | 3.76614i | −0.657265 | + | 0.213558i | −0.618615 | − | 0.785694i | \(-0.712306\pi\) |
−0.0386503 | + | 0.999253i | \(0.512306\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.4243 | + | 8.26086i | 1.43707 | + | 0.466931i | 0.920982 | − | 0.389606i | \(-0.127389\pi\) |
0.516085 | + | 0.856537i | \(0.327389\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.32187 | − | 4.57217i | −0.187166 | − | 0.257612i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.65607 | + | 2.48761i | −0.430008 | + | 0.139718i | −0.516021 | − | 0.856576i | \(-0.672587\pi\) |
0.0860130 | + | 0.996294i | \(0.472587\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 29.3701 | 1.64441 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.91422 | − | 8.14022i | 0.330099 | − | 0.454343i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.14151 | + | 28.1347i | −0.508647 | + | 1.56545i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.69077i | 0.149257i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.1519 | −0.782600 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.65715 | 0.201625 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 16.3613i | − | 0.899300i | −0.893205 | − | 0.449650i | \(-0.851549\pi\) | ||
0.893205 | − | 0.449650i | \(-0.148451\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.52364 | − | 7.76698i | 0.138295 | − | 0.425628i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.39002 | − | 11.5479i | 0.458396 | − | 0.630928i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.1433 | 1.15175 | 0.575875 | − | 0.817538i | \(-0.304662\pi\) | ||||
0.575875 | + | 0.817538i | \(0.304662\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.61252 | + | 1.17378i | −0.196205 | + | 0.0637510i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.3020 | − | 15.5559i | −0.612039 | − | 0.842400i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.951057 | + | 0.309017i | 0.0513522 | + | 0.0166853i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12.5050 | + | 4.06312i | −0.673246 | + | 0.218751i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.89619 | + | 13.6209i | −0.531255 | + | 0.731210i | −0.987321 | − | 0.158736i | \(-0.949258\pi\) |
0.456066 | + | 0.889946i | \(0.349258\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.1720 | + | 13.2028i | 0.972727 | + | 0.706727i | 0.956071 | − | 0.293134i | \(-0.0946982\pi\) |
0.0166552 | + | 0.999861i | \(0.494698\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.80025 | − | 1.30796i | 0.0960903 | − | 0.0698137i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.0279 | − | 13.0981i | −0.959530 | − | 0.697139i | −0.00648827 | − | 0.999979i | \(-0.502065\pi\) |
−0.953041 | + | 0.302840i | \(0.902065\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 12.4481i | − | 0.660675i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.73534 | − | 1.53861i | −0.250621 | − | 0.0814317i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.87799 | + | 5.77986i | 0.0991166 | + | 0.305049i | 0.988305 | − | 0.152492i | \(-0.0487300\pi\) |
−0.889188 | + | 0.457542i | \(0.848730\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.68838 | − | 26.7401i | −0.457283 | − | 1.40737i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.78226 | + | 13.4641i | 0.513435 | + | 0.706683i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 17.0895 | − | 52.5961i | 0.894505 | − | 2.75300i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.6647 | + | 12.8342i | −0.922089 | + | 0.669937i | −0.944043 | − | 0.329822i | \(-0.893011\pi\) |
0.0219537 | + | 0.999759i | \(0.493011\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.51234 | − | 10.0679i | −0.182845 | − | 0.524115i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.91237 | − | 2.84250i | 0.203120 | − | 0.147575i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.12547 | − | 3.46385i | 0.0582748 | − | 0.179351i | −0.917682 | − | 0.397316i | \(-0.869942\pi\) |
0.975957 | + | 0.217964i | \(0.0699417\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.49693 | + | 4.81310i | 0.180580 | + | 0.248548i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.743409 | + | 2.28798i | 0.0382875 | + | 0.117837i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.02114 | − | 15.4535i | −0.257918 | − | 0.793791i | −0.993241 | − | 0.116074i | \(-0.962969\pi\) |
0.735322 | − | 0.677718i | \(-0.237031\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −20.8053 | − | 6.76005i | −1.06589 | − | 0.346328i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.9579i | 1.42858i | 0.699848 | + | 0.714292i | \(0.253251\pi\) | ||||
−0.699848 | + | 0.714292i | \(0.746749\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.8388 | + | 10.0545i | 0.705289 | + | 0.512423i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.47049 | − | 2.52146i | 0.176415 | − | 0.128173i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.8202 | + | 10.7675i | 0.751416 | + | 0.545935i | 0.896265 | − | 0.443518i | \(-0.146270\pi\) |
−0.144850 | + | 0.989454i | \(0.546270\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.49521 | − | 11.6927i | 0.429621 | − | 0.591323i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.76758 | + | 2.19892i | −0.341379 | + | 0.110921i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −18.6663 | − | 6.06505i | −0.939204 | − | 0.305166i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.3115 | − | 15.5689i | −0.567706 | − | 0.781381i | 0.424574 | − | 0.905393i | \(-0.360424\pi\) |
−0.992281 | + | 0.124012i | \(0.960424\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.54200 | − | 2.45054i | 0.377572 | − | 0.122681i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.2859 | 0.863215 | 0.431607 | − | 0.902062i | \(-0.357947\pi\) | ||||
0.431607 | + | 0.902062i | \(0.357947\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.925755 | − | 1.27419i | 0.0461151 | − | 0.0634720i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.29097 | − | 3.97319i | 0.0641487 | − | 0.197429i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.7185i | 1.22525i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.4513 | −1.35738 | −0.678689 | − | 0.734426i | \(-0.737452\pi\) | ||||
−0.678689 | + | 0.734426i | \(0.737452\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.84923 | −0.485827 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.41973i | 0.168274i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.35881 | − | 28.8035i | 0.459406 | − | 1.41391i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.4575 | + | 15.7698i | −0.561074 | + | 0.772252i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.7604 | −0.721091 | −0.360546 | − | 0.932742i | \(-0.617409\pi\) | ||||
−0.360546 | + | 0.932742i | \(0.617409\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.3618 | + | 4.34150i | −0.651212 | + | 0.211592i | −0.615949 | − | 0.787786i | \(-0.711227\pi\) |
−0.0352636 | + | 0.999378i | \(0.511227\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.57972 | − | 4.92706i | −0.174052 | − | 0.239562i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −26.7134 | − | 8.67973i | −1.29579 | − | 0.421029i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.2525 | + | 3.65618i | −0.544549 | + | 0.176935i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.41312 | + | 1.94499i | −0.0682261 | + | 0.0939052i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.96353 | − | 2.87968i | −0.190917 | − | 0.138709i | 0.488221 | − | 0.872720i | \(-0.337646\pi\) |
−0.679138 | + | 0.734011i | \(0.737646\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.96971 | − | 1.43108i | 0.0946583 | − | 0.0687733i | −0.539449 | − | 0.842018i | \(-0.681368\pi\) |
0.634108 | + | 0.773245i | \(0.281368\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 18.4830 | + | 13.4287i | 0.886192 | + | 0.643856i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 23.0192i | 1.10116i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.3307 | + | 11.1547i | 1.63852 | + | 0.532386i | 0.976206 | − | 0.216844i | \(-0.0695763\pi\) |
0.662310 | + | 0.749230i | \(0.269576\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.514600 | − | 1.58378i | −0.0245048 | − | 0.0754179i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.3084 | − | 37.8815i | −0.584792 | − | 1.79980i | −0.600106 | − | 0.799921i | \(-0.704875\pi\) |
0.0153139 | − | 0.999883i | \(-0.495125\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.4632 | + | 21.2833i | 0.733026 | + | 1.00892i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.32373 | − | 13.3071i | 0.204506 | − | 0.629403i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.10203 | − | 2.98030i | 0.193587 | − | 0.140649i | −0.486770 | − | 0.873530i | \(-0.661825\pi\) |
0.680357 | + | 0.732881i | \(0.261825\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.5273 | + | 25.6964i | 0.919505 | + | 1.21000i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.48164 | + | 6.88881i | −0.445486 | + | 0.323665i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.432974 | + | 1.33256i | −0.0202981 | + | 0.0624713i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.68451 | + | 3.69492i | 0.125576 | + | 0.172841i | 0.867176 | − | 0.498002i | \(-0.165933\pi\) |
−0.741600 | + | 0.670843i | \(0.765933\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.17803 | + | 22.0917i | 0.335042 | + | 1.03115i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.6223 | − | 38.8475i | −0.587880 | − | 1.80931i | −0.587385 | − | 0.809307i | \(-0.699843\pi\) |
−0.000494251 | − | 1.00000i | \(-0.500157\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.48043 | − | 1.78070i | −0.254697 | − | 0.0827562i | 0.178886 | − | 0.983870i | \(-0.442751\pi\) |
−0.433583 | + | 0.901114i | \(0.642751\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 14.9571i | − | 0.693617i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.1600 | − | 12.4675i | −0.794072 | − | 0.576927i | 0.115097 | − | 0.993354i | \(-0.463282\pi\) |
−0.909169 | + | 0.416427i | \(0.863282\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.40271 | − | 2.47222i | 0.157123 | − | 0.114156i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.65094 | + | 2.65256i | 0.168226 | + | 0.122224i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.63181 | + | 10.5043i | −0.350911 | + | 0.482988i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 42.5466 | − | 13.8242i | 1.95217 | − | 0.634299i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.65907 | − | 2.48858i | −0.350685 | − | 0.113944i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.5858 | − | 17.3228i | −0.575058 | − | 0.791500i | 0.418085 | − | 0.908408i | \(-0.362702\pi\) |
−0.993143 | + | 0.116909i | \(0.962702\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.92561 | + | 0.625667i | −0.0878001 | + | 0.0285280i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.87436 | −0.176290 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.96067 | + | 2.69863i | −0.0890294 | + | 0.122538i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.50329 | − | 16.9374i | 0.249378 | − | 0.767506i | −0.745508 | − | 0.666497i | \(-0.767793\pi\) |
0.994886 | − | 0.101009i | \(-0.0322071\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.74286i | 0.304923i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −43.1063 | −1.94536 | −0.972681 | − | 0.232147i | \(-0.925425\pi\) | ||||
−0.972681 | + | 0.232147i | \(0.925425\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −25.1127 | −1.13102 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 28.4858i | − | 1.28034i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.13346 | − | 3.48844i | 0.0508428 | − | 0.156478i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.83093 | + | 2.52006i | −0.0819636 | + | 0.112813i | −0.848030 | − | 0.529948i | \(-0.822211\pi\) |
0.766066 | + | 0.642761i | \(0.222211\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.6801 | −0.700535 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.34227 | − | 3.03549i | 0.416551 | − | 0.135346i | −0.0932404 | − | 0.995644i | \(-0.529723\pi\) |
0.509792 | + | 0.860298i | \(0.329723\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.138802 | − | 0.191045i | −0.00617662 | − | 0.00850139i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 14.0965 | + | 4.58024i | 0.626049 | + | 0.203416i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.3169 | − | 7.57613i | 1.03351 | − | 0.335806i | 0.257330 | − | 0.966324i | \(-0.417157\pi\) |
0.776175 | + | 0.630517i | \(0.217157\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.57830 | − | 13.1834i | 0.423719 | − | 0.583199i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −29.9306 | − | 21.7459i | −1.32147 | − | 0.960103i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −50.8329 | + | 36.9323i | −2.23997 | + | 1.62743i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.9129 | + | 10.8349i | 0.655871 | + | 0.476518i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.4481i | 0.941468i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.4453 | − | 8.91750i | −1.20240 | − | 0.390683i | −0.361756 | − | 0.932273i | \(-0.617823\pi\) |
−0.840643 | + | 0.541590i | \(0.817823\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.20554 | − | 3.71028i | −0.0527147 | − | 0.162239i | 0.921233 | − | 0.389010i | \(-0.127183\pi\) |
−0.973948 | + | 0.226771i | \(0.927183\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.32675 | + | 7.16102i | 0.101548 | + | 0.312532i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.66370 | + | 13.3009i | 0.420957 | + | 0.579398i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.63209 | + | 11.1784i | −0.157917 | + | 0.486018i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.60719 | − | 3.34732i | 0.199935 | − | 0.145261i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.50752 | + | 2.17163i | −0.0652979 | + | 0.0940637i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.9121 | − | 17.3732i | 1.03381 | − | 0.751108i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.76562 | − | 23.9001i | 0.335111 | − | 1.03137i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.96266 | + | 4.07775i | 0.127611 | + | 0.175641i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.35324 | + | 22.6310i | 0.316141 | + | 0.972981i | 0.975282 | + | 0.220962i | \(0.0709197\pi\) |
−0.659142 | + | 0.752019i | \(0.729080\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.43607 | − | 19.8082i | −0.276198 | − | 0.850051i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −39.5368 | − | 12.8463i | −1.69357 | − | 0.550275i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.4613i | 0.746590i | 0.927713 | + | 0.373295i | \(0.121772\pi\) | ||||
−0.927713 | + | 0.373295i | \(0.878228\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.9401 | + | 11.5811i | 0.680305 | + | 0.494271i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 32.3583 | − | 23.5097i | 1.37851 | − | 1.00155i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.67878 | − | 3.39933i | −0.198962 | − | 0.144554i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11.3018 | + | 15.5556i | −0.479736 | + | 0.660300i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.91316 | + | 0.621625i | −0.0810634 | + | 0.0263391i | −0.349268 | − | 0.937023i | \(-0.613570\pi\) |
0.268205 | + | 0.963362i | \(0.413570\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.01147 | − | 0.328648i | −0.0427808 | − | 0.0139003i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.7512 | − | 20.3033i | −0.622796 | − | 0.857204i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.0919 | − | 4.25381i | 0.551757 | − | 0.179277i | −0.0198518 | − | 0.999803i | \(-0.506319\pi\) |
0.571609 | + | 0.820526i | \(0.306319\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.1580 | −0.469421 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.723560 | − | 0.995895i | 0.0303867 | − | 0.0418237i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.33035 | − | 13.3274i | 0.181538 | − | 0.558715i | −0.818334 | − | 0.574743i | \(-0.805102\pi\) |
0.999872 | + | 0.0160279i | \(0.00510204\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 12.1249i | − | 0.507412i | −0.967281 | − | 0.253706i | \(-0.918351\pi\) | ||
0.967281 | − | 0.253706i | \(-0.0816495\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.65334 | −0.277947 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −21.8564 | −0.911475 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 45.6732i | 1.90140i | 0.310109 | + | 0.950701i | \(0.399635\pi\) | ||||
−0.310109 | + | 0.950701i | \(0.600365\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.60257 | − | 11.0876i | 0.149718 | − | 0.460783i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.24542 | − | 7.21970i | 0.217617 | − | 0.299524i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.3750 | 1.00951 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.21908 | − | 0.721024i | 0.0917478 | − | 0.0298107i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.92364 | + | 5.40043i | 0.161946 | + | 0.222900i | 0.882277 | − | 0.470731i | \(-0.156010\pi\) |
−0.720331 | + | 0.693631i | \(0.756010\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.9038 | − | 8.09174i | −1.02614 | − | 0.333414i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.5949 | + | 5.39200i | −0.682622 | + | 0.221797i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.3908 | + | 17.0545i | −0.508831 | + | 0.700346i | −0.983722 | − | 0.179699i | \(-0.942488\pi\) |
0.474891 | + | 0.880045i | \(0.342488\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.8327 | − | 8.59698i | −0.485094 | − | 0.352442i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.37446 | + | 2.45169i | −0.138108 | + | 0.100341i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.6596 | − | 12.8304i | −0.721551 | − | 0.524238i | 0.165328 | − | 0.986239i | \(-0.447132\pi\) |
−0.886879 | + | 0.462001i | \(0.847132\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.602524i | 0.0245775i | 0.999924 | + | 0.0122887i | \(0.00391172\pi\) | ||||
−0.999924 | + | 0.0122887i | \(0.996088\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.66134 | − | 2.16440i | −0.271271 | − | 0.0881412i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.1072 | + | 46.4953i | 0.614196 | + | 1.89030i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.85120 | + | 5.69740i | 0.0751377 | + | 0.231250i | 0.981571 | − | 0.191100i | \(-0.0612054\pi\) |
−0.906433 | + | 0.422350i | \(0.861205\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.95691 | + | 5.44622i | 0.160342 | + | 0.220692i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.466582 | + | 1.43599i | −0.0188759 | + | 0.0580940i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.40076 | − | 1.01771i | 0.0565762 | − | 0.0411050i | −0.559138 | − | 0.829075i | \(-0.688868\pi\) |
0.615714 | + | 0.787970i | \(0.288868\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.539811 | + | 25.0994i | 0.0217673 | + | 1.01211i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.0097 | + | 15.2644i | −0.845819 | + | 0.614524i | −0.923990 | − | 0.382416i | \(-0.875092\pi\) |
0.0781710 | + | 0.996940i | \(0.475092\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.7261 | + | 42.2446i | −0.551698 | + | 1.69795i | 0.152809 | + | 0.988256i | \(0.451168\pi\) |
−0.704507 | + | 0.709697i | \(0.748832\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.6242 | + | 14.6230i | 0.426335 | + | 0.586799i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.39544 | + | 7.37242i | 0.0959714 | + | 0.295370i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.66944 | − | 14.3710i | −0.186777 | − | 0.574842i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 38.0145 | + | 12.3517i | 1.51815 | + | 0.493278i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 21.1353i | − | 0.842720i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.0201 | − | 17.4516i | −0.956224 | − | 0.694737i | −0.00395328 | − | 0.999992i | \(-0.501258\pi\) |
−0.952271 | + | 0.305255i | \(0.901258\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.9313 | − | 12.3013i | 0.672957 | − | 0.488932i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −51.9885 | − | 37.7719i | −2.06310 | − | 1.49893i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.242673 | + | 0.334011i | −0.00961505 | + | 0.0132340i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.80924 | + | 1.88754i | −0.229810 | + | 0.0746697i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.9307 | − | 7.45065i | −0.905710 | − | 0.294283i | −0.181118 | − | 0.983461i | \(-0.557972\pi\) |
−0.724592 | + | 0.689178i | \(0.757972\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.9189 | − | 15.0285i | −0.430598 | − | 0.592667i | 0.537492 | − | 0.843269i | \(-0.319372\pi\) |
−0.968090 | + | 0.250601i | \(0.919372\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.60559 | + | 3.12104i | −0.378220 | + | 0.122891i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 46.6864 | 1.83543 | 0.917717 | − | 0.397236i | \(-0.130031\pi\) | ||||
0.917717 | + | 0.397236i | \(0.130031\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.1315 | + | 13.9448i | −0.397696 | + | 0.547381i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.36192 | − | 4.19156i | 0.0533779 | − | 0.164280i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 45.6865i | 1.78785i | 0.448215 | + | 0.893926i | \(0.352060\pi\) | ||||
−0.448215 | + | 0.893926i | \(0.647940\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.9030 | −0.816749 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −27.1367 | −1.05870 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.5351i | 0.644118i | 0.946720 | + | 0.322059i | \(0.104375\pi\) | ||||
−0.946720 | + | 0.322059i | \(0.895625\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.9357 | − | 33.6566i | 0.425349 | − | 1.30909i | −0.477311 | − | 0.878735i | \(-0.658388\pi\) |
0.902660 | − | 0.430355i | \(-0.141612\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.20828 | − | 1.66305i | 0.0469256 | − | 0.0645875i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 23.2950 | 0.903340 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.5847 | + | 6.03852i | −0.719601 | + | 0.233812i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.934548 | − | 1.28630i | −0.0361317 | − | 0.0497311i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −56.7171 | − | 18.4285i | −2.18954 | − | 0.711425i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −34.3566 | + | 11.1631i | −1.32435 | + | 0.430307i | −0.883986 | − | 0.467513i | \(-0.845150\pi\) |
−0.440362 | + | 0.897820i | \(0.645150\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 20.6474 | − | 28.4187i | 0.794718 | − | 1.09384i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.0289 | + | 16.7315i | 0.885073 | + | 0.643043i | 0.934589 | − | 0.355730i | \(-0.115768\pi\) |
−0.0495155 | + | 0.998773i | \(0.515768\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.795182 | + | 0.577733i | −0.0305163 | + | 0.0221714i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.34002 | + | 6.78592i | 0.357910 | + | 0.260037i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 51.6711i | − | 1.97714i | −0.150763 | − | 0.988570i | \(-0.548173\pi\) | ||
0.150763 | − | 0.988570i | \(-0.451827\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −27.5163 | − | 8.94060i | −1.05135 | − | 0.341603i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.23324 | + | 22.2616i | 0.275965 | + | 0.849334i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.616975 | + | 1.89885i | 0.0235049 | + | 0.0723405i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.1495 | − | 23.6043i | −0.652398 | − | 0.897949i | 0.346802 | − | 0.937938i | \(-0.387268\pi\) |
−0.999200 | + | 0.0399893i | \(0.987268\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.59378 | − | 7.98283i | 0.0985295 | − | 0.303243i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −46.3243 | + | 33.6566i | −1.75718 | + | 1.27667i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.6967 | − | 21.9715i | −0.632431 | − | 0.832230i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.1873 | + | 8.12802i | −0.423141 | + | 0.307430i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.6497 | − | 38.9317i | 0.477771 | − | 1.47043i | −0.364412 | − | 0.931238i | \(-0.618730\pi\) |
0.842183 | − | 0.539191i | \(-0.181270\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.7862 | + | 27.2333i | 0.746250 | + | 1.02713i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.43095 | + | 13.6371i | 0.166879 | + | 0.513602i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.0215022 | − | 0.0661771i | −0.000808675 | − | 0.00248884i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 39.8172 | + | 12.9374i | 1.49537 | + | 0.485874i | 0.938663 | − | 0.344836i | \(-0.112065\pi\) |
0.556705 | + | 0.830710i | \(0.312065\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.63081i | 0.361183i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.3499 | + | 7.51966i | 0.387608 | + | 0.281614i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.71348 | + | 4.15108i | −0.213672 | + | 0.155242i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.40419 | − | 4.65292i | −0.239169 | − | 0.173766i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.09406 | + | 12.5169i | −0.339151 | + | 0.466802i | −0.944193 | − | 0.329392i | \(-0.893156\pi\) |
0.605042 | + | 0.796194i | \(0.293156\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.6083 | + | 5.72128i | −0.655767 | + | 0.213071i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.407932 | + | 0.132545i | 0.0151712 | + | 0.00492941i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22.3221 | + | 30.7237i | 0.829022 | + | 1.14105i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.96990 | + | 1.28990i | −0.147235 | + | 0.0478397i | −0.381708 | − | 0.924283i | \(-0.624664\pi\) |
0.234472 | + | 0.972123i | \(0.424664\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.7305 | −0.767795 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.52551 | − | 8.98160i | 0.241355 | − | 0.332196i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.30718 | − | 4.02308i | 0.0482817 | − | 0.148596i | −0.924009 | − | 0.382370i | \(-0.875108\pi\) |
0.972291 | + | 0.233775i | \(0.0751078\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.92077i | 0.144620i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21.1997 | 0.780903 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.8473 | 1.35545 | 0.677725 | − | 0.735315i | \(-0.262966\pi\) | ||||
0.677725 | + | 0.735315i | \(0.262966\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.27403i | 0.120275i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.67553 | + | 20.5452i | −0.244902 | + | 0.753730i | 0.750751 | + | 0.660585i | \(0.229692\pi\) |
−0.995653 | + | 0.0931444i | \(0.970308\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.1589 | − | 33.2519i | 0.885114 | − | 1.21825i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.8610 | −0.543737 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.28304 | − | 2.69132i | 0.302656 | − | 0.0983389i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.1236 | − | 19.4394i | −0.515377 | − | 0.709355i | 0.469438 | − | 0.882966i | \(-0.344457\pi\) |
−0.984814 | + | 0.173610i | \(0.944457\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.52475 | + | 0.495422i | 0.0555650 | + | 0.0180542i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −32.7427 | + | 10.6387i | −1.19163 | + | 0.387183i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.0107 | − | 22.0368i | 0.581918 | − | 0.800942i | −0.411986 | − | 0.911190i | \(-0.635165\pi\) |
0.993904 | + | 0.110248i | \(0.0351646\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −15.7987 | − | 11.4784i | −0.573456 | − | 0.416640i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.60970 | + | 2.62260i | −0.130852 | + | 0.0950693i | −0.651286 | − | 0.758832i | \(-0.725770\pi\) |
0.520434 | + | 0.853902i | \(0.325770\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.91006 | − | 7.20008i | −0.358768 | − | 0.260660i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 24.3565i | 0.880611i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.34277 | − | 0.436291i | −0.0484845 | − | 0.0157536i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.4993 | + | 47.7021i | 0.558920 | + | 1.72018i | 0.685359 | + | 0.728205i | \(0.259645\pi\) |
−0.126439 | + | 0.991974i | \(0.540355\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.01294 | + | 6.19520i | 0.0724943 | + | 0.223115i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.75841 | − | 10.6785i | −0.279051 | − | 0.384080i | 0.646369 | − | 0.763025i | \(-0.276287\pi\) |
−0.925419 | + | 0.378945i | \(0.876287\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.68299 | − | 23.6458i | 0.275981 | − | 0.849383i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.58364 | + | 3.33021i | −0.164437 | + | 0.119471i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 42.0831 | + | 12.6799i | 1.50778 | + | 0.454306i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.9570 | − | 10.8669i | 0.535205 | − | 0.388849i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.70505 | − | 29.8691i | 0.346830 | − | 1.06743i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.79198 | + | 10.7247i | 0.278108 | + | 0.382782i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.96943 | + | 15.2943i | 0.177141 | + | 0.545184i | 0.999725 | − | 0.0234597i | \(-0.00746815\pi\) |
−0.822584 | + | 0.568644i | \(0.807468\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.39699 | + | 28.9210i | 0.334542 | + | 1.02961i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.12691 | − | 1.01600i | −0.111180 | − | 0.0361246i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 4.88481i | − | 0.173465i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15.3395 | + | 11.1448i | 0.544037 | + | 0.395266i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.90392 | − | 4.28945i | 0.209127 | − | 0.151940i | −0.478291 | − | 0.878201i | \(-0.658744\pi\) |
0.687419 | + | 0.726261i | \(0.258744\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.7512 | − | 9.26428i | −0.451105 | − | 0.327747i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.58770 | − | 10.4436i | 0.268098 | − | 0.369005i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 78.1159 | − | 25.3814i | 2.75665 | − | 0.895690i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.8240 | − | 3.51694i | −0.381496 | − | 0.123956i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.47973 | − | 4.78944i | −0.122492 | − | 0.168596i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 42.6321 | − | 13.8520i | 1.49887 | − | 0.487011i | 0.559179 | − | 0.829047i | \(-0.311116\pi\) |
0.939687 | + | 0.342035i | \(0.111116\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.8416 | 1.53949 | 0.769743 | − | 0.638354i | \(-0.220385\pi\) | ||||
0.769743 | + | 0.638354i | \(0.220385\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.9764 | − | 27.4952i | 0.700604 | − | 0.964299i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.12081 | + | 18.8379i | −0.214403 | + | 0.659863i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17.6820i | 0.618614i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.687528 | 0.0240242 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.5083 | 0.994947 | 0.497473 | − | 0.867479i | \(-0.334261\pi\) | ||||
0.497473 | + | 0.867479i | \(0.334261\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 37.7141i | − | 1.31463i | −0.753615 | − | 0.657316i | \(-0.771692\pi\) | ||
0.753615 | − | 0.657316i | \(-0.228308\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11.7277 | + | 36.0942i | −0.408307 | + | 1.25664i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.7140 | − | 39.5215i | 0.998485 | − | 1.37430i | 0.0722347 | − | 0.997388i | \(-0.476987\pi\) |
0.926250 | − | 0.376909i | \(-0.123013\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 47.3630 | 1.64499 | 0.822493 | − | 0.568775i | \(-0.192582\pi\) | ||||
0.822493 | + | 0.568775i | \(0.192582\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −35.2494 | + | 11.4532i | −1.22279 | + | 0.397308i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.53320 | − | 3.48665i | −0.0877701 | − | 0.120805i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −43.8064 | − | 14.2335i | −1.51598 | − | 0.492572i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −19.5548 | + | 6.35374i | −0.675913 | + | 0.219617i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.6343 | + | 29.7771i | −0.746900 | + | 1.02802i | 0.251292 | + | 0.967911i | \(0.419145\pi\) |
−0.998192 | + | 0.0601085i | \(0.980855\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.00755 | + | 2.91165i | 0.138191 | + | 0.100402i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −29.3828 | + | 21.3478i | −1.01200 | + | 0.735258i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 35.2246 | + | 25.5922i | 1.21176 | + | 0.880397i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.4054i | 0.494976i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.52738 | − | 0.496277i | −0.0524196 | − | 0.0170322i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.08213 | − | 15.6412i | −0.174213 | − | 0.536173i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.03889 | + | 15.5081i | 0.172528 | + | 0.530987i | 0.999512 | − | 0.0312386i | \(-0.00994518\pi\) |
−0.826984 | + | 0.562226i | \(0.809945\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −22.8018 | − | 31.3839i | −0.779804 | − | 1.07331i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.17343 | + | 25.1552i | −0.279199 | + | 0.859286i | 0.708879 | + | 0.705330i | \(0.249201\pi\) |
−0.988078 | + | 0.153956i | \(0.950799\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.1388 | − | 18.2644i | 0.857723 | − | 0.623173i | −0.0695413 | − | 0.997579i | \(-0.522154\pi\) |
0.927265 | + | 0.374407i | \(0.122154\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.13416 | + | 7.08300i | −0.0727319 | + | 0.241388i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.673959 | + | 0.489660i | −0.0229418 | + | 0.0166682i | −0.599197 | − | 0.800602i | \(-0.704513\pi\) |
0.576255 | + | 0.817270i | \(0.304513\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.4694 | + | 59.9208i | −0.661981 | + | 2.03737i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.06871 | + | 1.47095i | 0.0362953 | + | 0.0499562i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.00784 | − | 27.7233i | −0.305570 | − | 0.940447i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.536602 | + | 1.65149i | 0.0181821 | + | 0.0559587i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.55669 | + | 0.505800i | 0.0526860 | + | 0.0171187i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.14959i | 0.174088i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.1121 | − | 32.7758i | −1.52333 | − | 1.10676i | −0.959808 | − | 0.280657i | \(-0.909448\pi\) |
−0.563518 | − | 0.826104i | \(-0.690552\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −11.9949 | + | 8.71481i | −0.404578 | + | 0.293943i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41.9270 | − | 30.4617i | −1.41256 | − | 1.02628i | −0.992945 | − | 0.118577i | \(-0.962167\pi\) |
−0.419611 | − | 0.907704i | \(-0.637833\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.3207 | − | 33.4745i | 0.818455 | − | 1.12651i | −0.171508 | − | 0.985183i | \(-0.554864\pi\) |
0.989963 | − | 0.141324i | \(-0.0451360\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.7517 | + | 4.14329i | −0.428645 | + | 0.139275i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.8496 | − | 6.44954i | −0.666485 | − | 0.216554i | −0.0438164 | − | 0.999040i | \(-0.513952\pi\) |
−0.622669 | + | 0.782485i | \(0.713952\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.1299 | − | 15.3190i | −0.373285 | − | 0.513783i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.90100 | − | 1.91735i | 0.197691 | − | 0.0642337i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 25.1031 | 0.840044 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 43.3905 | − | 59.7219i | 1.45038 | − | 1.99628i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.494294 | − | 1.52128i | 0.0165040 | − | 0.0507941i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 22.2289i | − | 0.741374i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.8417 | −0.694336 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.97605 | −0.0990368 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 61.1815i | − | 2.03374i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.32287 | − | 19.4598i | 0.209947 | − | 0.646152i | −0.789526 | − | 0.613717i | \(-0.789674\pi\) |
0.999474 | − | 0.0324352i | \(-0.0103263\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.0681095 | + | 0.0937446i | −0.00225905 | + | 0.00310931i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.0535 | 0.697534 | 0.348767 | − | 0.937209i | \(-0.386600\pi\) | ||||
0.348767 | + | 0.937209i | \(0.386600\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 42.7790 | − | 13.8997i | 1.41578 | − | 0.460015i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −27.2669 | − | 37.5296i | −0.901415 | − | 1.24069i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.85786 | − | 1.90333i | −0.193443 | − | 0.0628536i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.5944 | − | 10.9155i | 1.10818 | − | 0.360069i | 0.302933 | − | 0.953012i | \(-0.402034\pi\) |
0.805245 | + | 0.592943i | \(0.202034\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.9441 | + | 21.9451i | −0.525374 | + | 0.723116i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.22514 | + | 0.890116i | 0.0403260 | + | 0.0292985i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.8577 | + | 18.7867i | −0.850195 | + | 0.617703i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 24.9434 | + | 18.1224i | 0.819249 | + | 0.595219i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.68947i | 0.186665i | 0.995635 | + | 0.0933327i | \(0.0297520\pi\) | ||||
−0.995635 | + | 0.0933327i | \(0.970248\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.52817 | + | 2.12113i | 0.213952 | + | 0.0695173i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.35103 | − | 13.3911i | −0.142446 | − | 0.438404i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −22.7810 | − | 70.1127i | −0.745018 | − | 2.29293i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.748614 | + | 1.03038i | 0.0244562 | + | 0.0336610i | 0.821070 | − | 0.570828i | \(-0.193378\pi\) |
−0.796614 | + | 0.604489i | \(0.793378\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.54377 | + | 29.3727i | −0.311449 | + | 0.958542i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.987921 | + | 0.717766i | −0.0322053 | + | 0.0233985i | −0.603771 | − | 0.797157i | \(-0.706336\pi\) |
0.571566 | + | 0.820556i | \(0.306336\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17.6396 | − | 12.2452i | −0.574423 | − | 0.398758i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 14.7981 | − | 10.7515i | 0.481384 | − | 0.349746i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.6281 | + | 48.0984i | −0.507845 | + | 1.56299i | 0.288089 | + | 0.957604i | \(0.406980\pi\) |
−0.795934 | + | 0.605383i | \(0.793020\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.95450 | + | 5.44290i | 0.128368 | + | 0.176684i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.87394 | − | 8.84506i | −0.0931937 | − | 0.286821i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.13279 | − | 15.7971i | −0.166267 | − | 0.511719i | 0.832860 | − | 0.553484i | \(-0.186702\pi\) |
−0.999127 | + | 0.0417651i | \(0.986702\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.5878 | − | 6.03954i | −0.601487 | − | 0.195435i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 33.9313i | 1.09684i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.89708 | − | 5.01102i | −0.222718 | − | 0.161814i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.3060 | − | 9.66737i | 0.429226 | − | 0.311851i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.7335 | − | 8.52491i | −0.378108 | − | 0.274711i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 20.1294 | − | 27.7057i | 0.647988 | − | 0.891878i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.8346 | − | 10.0188i | 0.991572 | − | 0.322181i | 0.232079 | − | 0.972697i | \(-0.425447\pi\) |
0.759493 | + | 0.650515i | \(0.225447\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −32.5040 | − | 10.5612i | −1.04418 | − | 0.339274i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.3727 | + | 22.5351i | 0.525425 | + | 0.723185i | 0.986425 | − | 0.164215i | \(-0.0525091\pi\) |
−0.461000 | + | 0.887400i | \(0.652509\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.0465 | + | 5.21383i | −0.514428 | + | 0.167148i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.10864 | −0.0995563 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.79274 | − | 9.34940i | 0.217319 | − | 0.299114i | −0.686414 | − | 0.727211i | \(-0.740816\pi\) |
0.903733 | + | 0.428097i | \(0.140816\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.0739 | + | 37.1598i | −0.385885 | + | 1.18763i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.3989i | 0.651286i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.1481 | −0.674519 | −0.337259 | − | 0.941412i | \(-0.609500\pi\) | ||||
−0.337259 | + | 0.941412i | \(0.609500\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −51.2566 | −1.63317 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.22511i | 0.134487i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.66952 | − | 8.21594i | 0.0848858 | − | 0.261252i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.13119 | − | 4.30971i | 0.0994655 | − | 0.136903i | −0.756383 | − | 0.654129i | \(-0.773035\pi\) |
0.855849 | + | 0.517226i | \(0.173035\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.9023 | 0.599845 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.6529 | + | 3.78627i | −0.369423 | + | 0.120033i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.6314 | + | 29.7730i | 0.685073 | + | 0.942921i | 0.999981 | − | 0.00620068i | \(-0.00197375\pi\) |
−0.314908 | + | 0.949122i | \(0.601974\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 25.1384 | + | 8.16796i | 0.795343 | + | 0.258423i |
(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.ba.a.701.14 | yes | 80 | |
41.31 | even | 10 | inner | 1148.2.ba.a.113.7 | ✓ | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.ba.a.113.7 | ✓ | 80 | 41.31 | even | 10 | inner | |
1148.2.ba.a.701.14 | yes | 80 | 1.1 | even | 1 | trivial |