Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,2,Mod(47,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.o (of order \(8\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.06625543762\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 96) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 47.4 | ||
Character | \(\chi\) | \(=\) | 384.47 |
Dual form | 384.2.o.a.335.4 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{8}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.18890 | + | 1.25957i | −0.686410 | + | 0.727215i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.06973 | − | 0.443098i | 0.478400 | − | 0.198160i | −0.130435 | − | 0.991457i | \(-0.541637\pi\) |
0.608834 | + | 0.793297i | \(0.291637\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.37247 | − | 2.37247i | −0.896708 | − | 0.896708i | 0.0984354 | − | 0.995143i | \(-0.468616\pi\) |
−0.995143 | + | 0.0984354i | \(0.968616\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.173046 | − | 2.99501i | −0.0576820 | − | 0.998335i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.50127 | − | 2.27870i | 1.65869 | − | 0.687054i | 0.660718 | − | 0.750635i | \(-0.270252\pi\) |
0.997977 | + | 0.0635809i | \(0.0202521\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.346353 | − | 0.836171i | 0.0960612 | − | 0.231912i | −0.868543 | − | 0.495613i | \(-0.834943\pi\) |
0.964604 | + | 0.263701i | \(0.0849433\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.713689 | + | 1.87421i | −0.184274 | + | 0.483918i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.685064 | 0.166152 | 0.0830762 | − | 0.996543i | \(-0.473526\pi\) | ||||
0.0830762 | + | 0.996543i | \(0.473526\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.35074 | + | 1.38792i | 0.768712 | + | 0.318411i | 0.732351 | − | 0.680928i | \(-0.238423\pi\) |
0.0363614 | + | 0.999339i | \(0.488423\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.80891 | − | 0.167674i | 1.26761 | − | 0.0365895i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.05133 | + | 2.05133i | 0.427732 | + | 0.427732i | 0.887855 | − | 0.460123i | \(-0.152195\pi\) |
−0.460123 | + | 0.887855i | \(0.652195\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.58754 | + | 2.58754i | −0.517508 | + | 0.517508i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.97816 | + | 3.34279i | 0.765597 | + | 0.643320i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.98869 | − | 4.80112i | 0.369291 | − | 0.891546i | −0.624576 | − | 0.780964i | \(-0.714728\pi\) |
0.993867 | − | 0.110582i | \(-0.0352716\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.36503i | − | 1.14319i | −0.820535 | − | 0.571596i | \(-0.806324\pi\) | ||
0.820535 | − | 0.571596i | \(-0.193676\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.67025 | + | 9.63838i | −0.638909 | + | 1.67783i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.58914 | − | 1.48667i | −0.606676 | − | 0.251293i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.112738 | + | 0.272172i | 0.0185339 | + | 0.0447449i | 0.932876 | − | 0.360199i | \(-0.117291\pi\) |
−0.914342 | + | 0.404944i | \(0.867291\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.641440 | + | 1.43038i | 0.102713 | + | 0.229044i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.26585 | − | 3.26585i | 0.510040 | − | 0.510040i | −0.404499 | − | 0.914539i | \(-0.632554\pi\) |
0.914539 | + | 0.404499i | \(0.132554\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.993018 | + | 2.39736i | 0.151434 | + | 0.365594i | 0.981332 | − | 0.192321i | \(-0.0616016\pi\) |
−0.829898 | + | 0.557915i | \(0.811602\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.51219 | − | 3.12718i | −0.225425 | − | 0.466173i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 11.7975i | − | 1.72084i | −0.509589 | − | 0.860418i | \(-0.670203\pi\) | ||
0.509589 | − | 0.860418i | \(-0.329797\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.25719i | 0.608171i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.814471 | + | 0.862888i | −0.114049 | + | 0.120828i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.56192 | + | 3.77080i | 0.214546 | + | 0.517959i | 0.994112 | − | 0.108361i | \(-0.0345602\pi\) |
−0.779566 | + | 0.626320i | \(0.784560\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.87520 | − | 4.87520i | 0.657372 | − | 0.657372i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.73187 | + | 2.57040i | −0.759205 | + | 0.340458i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.20815 | − | 5.33094i | −0.287476 | − | 0.694029i | 0.712495 | − | 0.701678i | \(-0.247565\pi\) |
−0.999971 | + | 0.00764882i | \(0.997565\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.53549 | − | 0.636020i | −0.196599 | − | 0.0814341i | 0.282212 | − | 0.959352i | \(-0.408932\pi\) |
−0.478811 | + | 0.877918i | \(0.658932\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.69500 | + | 7.51609i | −0.843491 | + | 0.946939i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 1.04795i | − | 0.129982i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.69605 | + | 11.3373i | −0.573714 | + | 1.38507i | 0.324657 | + | 0.945832i | \(0.394751\pi\) |
−0.898371 | + | 0.439237i | \(0.855249\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.02262 | + | 0.144978i | −0.604653 | + | 0.0174533i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.99150 | + | 7.99150i | −0.948416 | + | 0.948416i | −0.998733 | − | 0.0503173i | \(-0.983977\pi\) |
0.0503173 | + | 0.998733i | \(0.483977\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.34760 | − | 2.34760i | −0.274766 | − | 0.274766i | 0.556250 | − | 0.831015i | \(-0.312240\pi\) |
−0.831015 | + | 0.556250i | \(0.812240\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.182875 | − | 6.33551i | −0.0211165 | − | 0.731562i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −18.4577 | − | 7.64543i | −2.10345 | − | 0.871278i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.91043 | −1.00250 | −0.501251 | − | 0.865302i | \(-0.667127\pi\) | ||||
−0.501251 | + | 0.865302i | \(0.667127\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.94011 | + | 1.03655i | −0.993346 | + | 0.115172i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.06920 | + | 7.40970i | −0.336888 | + | 0.813320i | 0.661123 | + | 0.750278i | \(0.270080\pi\) |
−0.998011 | + | 0.0630420i | \(0.979920\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.732836 | − | 0.303551i | 0.0794872 | − | 0.0329247i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.68301 | + | 8.21294i | 0.394861 | + | 0.880520i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.99332 | + | 1.99332i | 0.211291 | + | 0.211291i | 0.804816 | − | 0.593525i | \(-0.202264\pi\) |
−0.593525 | + | 0.804816i | \(0.702264\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.80550 | + | 1.16208i | −0.294096 | + | 0.121819i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.01722 | + | 7.56737i | 0.831347 | + | 0.784699i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.19938 | 0.430848 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.66510 | 0.879807 | 0.439904 | − | 0.898045i | \(-0.355013\pi\) | ||||
0.439904 | + | 0.898045i | \(0.355013\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.77669 | − | 16.0820i | −0.781586 | − | 1.61630i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.6920 | − | 6.49983i | 1.56141 | − | 0.646758i | 0.576077 | − | 0.817395i | \(-0.304583\pi\) |
0.985334 | + | 0.170637i | \(0.0545827\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.39788 | + | 5.39788i | 0.531869 | + | 0.531869i | 0.921128 | − | 0.389259i | \(-0.127269\pi\) |
−0.389259 | + | 0.921128i | \(0.627269\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.13969 | − | 2.75329i | 0.599173 | − | 0.268693i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.0169596 | − | 0.00702491i | 0.00163955 | − | 0.000679124i | −0.381864 | − | 0.924219i | \(-0.624718\pi\) |
0.383503 | + | 0.923540i | \(0.374718\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.94357 | + | 11.9348i | −0.473508 | + | 1.14315i | 0.489094 | + | 0.872231i | \(0.337328\pi\) |
−0.962602 | + | 0.270919i | \(0.912672\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.476854 | − | 0.181584i | −0.0452610 | − | 0.0172352i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.4984 | −0.987609 | −0.493804 | − | 0.869573i | \(-0.664394\pi\) | ||||
−0.493804 | + | 0.869573i | \(0.664394\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.10332 | + | 1.28544i | 0.289386 | + | 0.119868i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.56427 | − | 0.892634i | −0.237067 | − | 0.0825241i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.62529 | − | 1.62529i | −0.148990 | − | 0.148990i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.2933 | − | 17.2933i | 1.57212 | − | 1.57212i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.230814 | + | 7.99633i | 0.0208118 | + | 0.721005i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.83694 | + | 9.26318i | −0.343186 | + | 0.828524i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.793212i | 0.0703862i | 0.999381 | + | 0.0351931i | \(0.0112046\pi\) | ||||
−0.999381 | + | 0.0351931i | \(0.988795\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.20024 | − | 1.59943i | −0.369811 | − | 0.140822i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.39267 | + | 3.89057i | 0.820641 | + | 0.339921i | 0.753191 | − | 0.657802i | \(-0.228514\pi\) |
0.0674502 | + | 0.997723i | \(0.478514\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.65672 | − | 11.2423i | −0.403789 | − | 0.974832i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.73676 | + | 1.81318i | 0.493741 | + | 0.156054i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.95969 | + | 2.95969i | −0.252863 | + | 0.252863i | −0.822144 | − | 0.569280i | \(-0.807222\pi\) |
0.569280 | + | 0.822144i | \(0.307222\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.91155 | + | 4.61488i | 0.162135 | + | 0.391429i | 0.983979 | − | 0.178284i | \(-0.0570545\pi\) |
−0.821844 | + | 0.569713i | \(0.807054\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 14.8597 | + | 14.0260i | 1.25142 | + | 1.18120i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 5.38924i | − | 0.450671i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 6.01711i | − | 0.499694i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.36224 | − | 5.06137i | −0.442270 | − | 0.417455i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.53451 | + | 13.3615i | 0.453405 | + | 1.09462i | 0.971019 | + | 0.239002i | \(0.0768202\pi\) |
−0.517614 | + | 0.855614i | \(0.673180\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.96063 | + | 2.96063i | −0.240932 | + | 0.240932i | −0.817236 | − | 0.576303i | \(-0.804495\pi\) |
0.576303 | + | 0.817236i | \(0.304495\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.118548 | − | 2.05177i | −0.00958400 | − | 0.165876i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.82033 | − | 6.80889i | −0.226535 | − | 0.546903i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.1213 | − | 6.67768i | −1.28662 | − | 0.532937i | −0.368646 | − | 0.929570i | \(-0.620178\pi\) |
−0.917977 | + | 0.396633i | \(0.870178\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.60656 | − | 2.51575i | −0.523934 | − | 0.199512i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 9.73343i | − | 0.767102i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.62172 | − | 11.1578i | 0.362001 | − | 0.873949i | −0.633006 | − | 0.774147i | \(-0.718179\pi\) |
0.995007 | − | 0.0998018i | \(-0.0318209\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.344556 | + | 11.9368i | 0.0268236 | + | 0.929278i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.28603 | + | 1.28603i | −0.0995157 | + | 0.0995157i | −0.755112 | − | 0.655596i | \(-0.772417\pi\) |
0.655596 | + | 0.755112i | \(0.272417\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.61317 | + | 8.61317i | 0.662551 | + | 0.662551i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.57700 | − | 10.2756i | 0.273540 | − | 0.785799i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.0565964 | − | 0.0234430i | −0.00430295 | − | 0.00178234i | 0.380531 | − | 0.924768i | \(-0.375741\pi\) |
−0.384834 | + | 0.922986i | \(0.625741\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.2777 | 0.928107 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.33996 | + | 3.55662i | 0.702034 | + | 0.267332i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.17461 | − | 2.83576i | 0.0877946 | − | 0.211955i | −0.873884 | − | 0.486135i | \(-0.838406\pi\) |
0.961678 | + | 0.274180i | \(0.0884064\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.8334 | + | 8.62949i | −1.54854 | + | 0.641425i | −0.983051 | − | 0.183334i | \(-0.941311\pi\) |
−0.565485 | + | 0.824758i | \(0.691311\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.62665 | − | 1.17790i | 0.194168 | − | 0.0870726i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.241198 | + | 0.241198i | 0.0177333 | + | 0.0177333i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.76872 | − | 1.56105i | 0.275596 | − | 0.114156i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.50739 | − | 17.3687i | −0.109647 | − | 1.26339i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.0566 | 1.66832 | 0.834158 | − | 0.551525i | \(-0.185954\pi\) | ||||
0.834158 | + | 0.551525i | \(0.185954\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.52832 | 0.541900 | 0.270950 | − | 0.962593i | \(-0.412662\pi\) | ||||
0.270950 | + | 0.962593i | \(0.412662\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.31997 | + | 1.24590i | 0.0945249 | + | 0.0892211i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.14750 | + | 0.889524i | −0.153003 | + | 0.0633760i | −0.457871 | − | 0.889019i | \(-0.651388\pi\) |
0.304868 | + | 0.952395i | \(0.401388\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.46994 | − | 7.46994i | −0.529530 | − | 0.529530i | 0.390902 | − | 0.920432i | \(-0.372163\pi\) |
−0.920432 | + | 0.390902i | \(0.872163\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.69699 | − | 19.3939i | −0.613439 | − | 1.36794i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.1086 | + | 6.67240i | −1.13060 | + | 0.468311i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.04650 | − | 4.94068i | 0.142934 | − | 0.345072i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.78877 | − | 6.49872i | 0.402348 | − | 0.451692i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.5960 | 1.49382 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.9819 | − | 6.61994i | −1.10024 | − | 0.455735i | −0.242676 | − | 0.970107i | \(-0.578025\pi\) |
−0.857567 | + | 0.514372i | \(0.828025\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.564800 | − | 19.5669i | −0.0386994 | − | 1.34070i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.12453 | + | 2.12453i | 0.144892 | + | 0.144892i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.1008 | + | 15.1008i | −1.02511 | + | 1.02511i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.74803 | − | 0.165917i | 0.388416 | − | 0.0112116i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.237274 | − | 0.572831i | 0.0159608 | − | 0.0385328i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.2244i | 1.22040i | 0.792248 | + | 0.610199i | \(0.208910\pi\) | ||||
−0.792248 | + | 0.610199i | \(0.791090\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.19746 | + | 7.30193i | 0.546497 | + | 0.486795i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.8455 | + | 4.49234i | 0.719840 | + | 0.298167i | 0.712369 | − | 0.701805i | \(-0.247622\pi\) |
0.00747022 | + | 0.999972i | \(0.497622\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.20986 | + | 12.5777i | 0.344277 | + | 0.831159i | 0.997273 | + | 0.0737978i | \(0.0235119\pi\) |
−0.652996 | + | 0.757362i | \(0.726488\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 31.5743 | − | 14.1592i | 2.07744 | − | 0.931606i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.7233 | + | 11.7233i | −0.768016 | + | 0.768016i | −0.977757 | − | 0.209741i | \(-0.932738\pi\) |
0.209741 | + | 0.977757i | \(0.432738\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.22743 | − | 12.6201i | −0.341000 | − | 0.823247i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.5936 | − | 11.2233i | 0.688128 | − | 0.729034i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.5949i | 1.39685i | 0.715681 | + | 0.698427i | \(0.246117\pi\) | ||||
−0.715681 | + | 0.698427i | \(0.753883\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 14.6095i | − | 0.941078i | −0.882379 | − | 0.470539i | \(-0.844059\pi\) | ||
0.882379 | − | 0.470539i | \(-0.155941\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.32327 | − | 12.4931i | 0.598088 | − | 0.801430i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.88636 | + | 4.55406i | 0.120515 | + | 0.290949i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.32108 | − | 2.32108i | 0.147687 | − | 0.147687i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.68409 | − | 12.6752i | −0.360215 | − | 0.803261i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.08581 | + | 2.62137i | 0.0685355 | + | 0.165459i | 0.954436 | − | 0.298416i | \(-0.0964584\pi\) |
−0.885900 | + | 0.463876i | \(0.846458\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.9593 | + | 6.61055i | 1.00335 | + | 0.415602i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.488923 | + | 1.28395i | −0.0306175 | + | 0.0804041i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1.35436i | − | 0.0844827i | −0.999107 | − | 0.0422414i | \(-0.986550\pi\) | ||
0.999107 | − | 0.0422414i | \(-0.0134498\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.378254 | − | 0.913186i | 0.0235036 | − | 0.0567426i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −14.7235 | − | 5.12532i | −0.911363 | − | 0.317250i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.52372 | + | 3.52372i | −0.217282 | + | 0.217282i | −0.807352 | − | 0.590070i | \(-0.799100\pi\) |
0.590070 | + | 0.807352i | \(0.299100\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.34167 | + | 3.34167i | 0.205277 | + | 0.205277i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.88057 | + | 0.140878i | −0.298686 | + | 0.00862158i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.4741 | + | 6.82380i | 1.00444 | + | 0.416055i | 0.823425 | − | 0.567425i | \(-0.192060\pi\) |
0.181020 | + | 0.983479i | \(0.442060\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.50293 | 0.516516 | 0.258258 | − | 0.966076i | \(-0.416851\pi\) | ||||
0.258258 | + | 0.966076i | \(0.416851\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.87173 | − | 4.91532i | 0.113282 | − | 0.297489i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.33852 | + | 20.1310i | −0.502832 | + | 1.21394i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.2028 | − | 8.36828i | 1.21387 | − | 0.502801i | 0.318414 | − | 0.947952i | \(-0.396850\pi\) |
0.895456 | + | 0.445150i | \(0.146850\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −19.0633 | + | 1.10144i | −1.14129 | + | 0.0659416i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.3342 | + | 10.3342i | 0.616487 | + | 0.616487i | 0.944629 | − | 0.328142i | \(-0.106422\pi\) |
−0.328142 | + | 0.944629i | \(0.606422\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.67342 | + | 3.59265i | −0.515581 | + | 0.213561i | −0.625275 | − | 0.780405i | \(-0.715013\pi\) |
0.109694 | + | 0.993965i | \(0.465013\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.99264 | + | 5.28943i | −0.295738 | + | 0.313319i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.4962 | −0.914714 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5307 | −0.972393 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.3019 | + | 10.9143i | −0.603909 | + | 0.639809i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.3816 | + | 4.71442i | −0.664922 | + | 0.275420i | −0.689508 | − | 0.724278i | \(-0.742173\pi\) |
0.0245862 | + | 0.999698i | \(0.492173\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.72426 | − | 4.72426i | −0.275057 | − | 0.275057i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 29.5021 | + | 9.32455i | 1.71189 | + | 0.541065i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.42575 | − | 1.00478i | 0.140285 | − | 0.0581078i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.33175 | − | 8.04355i | 0.192039 | − | 0.463623i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.4692 | + | 27.4928i | −0.601437 | + | 1.57942i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.92438 | −0.110190 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.6145 | + | 5.22511i | 0.719950 | + | 0.298213i | 0.712415 | − | 0.701759i | \(-0.247601\pi\) |
0.00753514 | + | 0.999972i | \(0.497601\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.2166 | + | 0.381496i | −0.751863 | + | 0.0217025i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.8020 | − | 18.8020i | −1.06617 | − | 1.06617i | −0.997650 | − | 0.0685162i | \(-0.978174\pi\) |
−0.0685162 | − | 0.997650i | \(-0.521826\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.30835 | − | 4.30835i | 0.243522 | − | 0.243522i | −0.574783 | − | 0.818306i | \(-0.694914\pi\) |
0.818306 | + | 0.574783i | \(0.194914\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.83150 | + | 11.0068i | −0.215881 | + | 0.620161i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.543402 | + | 1.31189i | −0.0305205 | + | 0.0736830i | −0.938405 | − | 0.345538i | \(-0.887697\pi\) |
0.907884 | + | 0.419221i | \(0.137697\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 30.9439i | − | 1.73252i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.0113149 | + | 0.0297138i | −0.000631535 | + | 0.00165846i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.29547 | + | 0.950815i | 0.127723 | + | 0.0529047i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.26742 | + | 3.05983i | 0.0703040 | + | 0.169729i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.15540 | − | 20.4161i | −0.506295 | − | 1.12901i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −27.9891 | + | 27.9891i | −1.54309 | + | 1.54309i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.18815 | + | 12.5253i | 0.285167 | + | 0.688453i | 0.999941 | − | 0.0109024i | \(-0.00347041\pi\) |
−0.714774 | + | 0.699356i | \(0.753470\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.795649 | − | 0.384748i | 0.0436013 | − | 0.0210840i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.2087i | 0.776303i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.9878i | 1.08881i | 0.838824 | + | 0.544403i | \(0.183244\pi\) | ||||
−0.838824 | + | 0.544403i | \(0.816756\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.4815 | − | 13.2235i | 0.677905 | − | 0.718203i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.5040 | − | 35.0157i | −0.785435 | − | 1.89621i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.50721 | + | 6.50721i | −0.351357 | + | 0.351357i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.30863 | + | 2.38060i | −0.285807 | + | 0.128167i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.84634 | − | 14.1143i | −0.313848 | − | 0.757696i | −0.999555 | − | 0.0298187i | \(-0.990507\pi\) |
0.685707 | − | 0.727877i | \(-0.259493\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.90170 | + | 3.27299i | 0.422969 | + | 0.175199i | 0.584007 | − | 0.811749i | \(-0.301484\pi\) |
−0.161038 | + | 0.986948i | \(0.551484\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.17299 | − | 2.16864i | 0.222738 | − | 0.115753i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 28.4566i | − | 1.51459i | −0.653072 | − | 0.757296i | \(-0.726520\pi\) | ||
0.653072 | − | 0.757296i | \(-0.273480\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.00776 | + | 12.0898i | −0.265784 | + | 0.641659i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.97948 | − | 0.114868i | 0.210616 | − | 0.00607944i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.48589 | + | 3.48589i | −0.183978 | + | 0.183978i | −0.793087 | − | 0.609109i | \(-0.791527\pi\) |
0.609109 | + | 0.793087i | \(0.291527\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.13391 | − | 4.13391i | −0.217574 | − | 0.217574i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.22221 | + | 42.3421i | 0.0641491 | + | 2.22238i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.55152 | − | 1.47109i | −0.185895 | − | 0.0770003i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.37411 | −0.384925 | −0.192463 | − | 0.981304i | \(-0.561647\pi\) | ||||
−0.192463 | + | 0.981304i | \(0.561647\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.3464 | − | 9.21609i | −0.538611 | − | 0.479771i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.24050 | − | 12.6517i | 0.272073 | − | 0.656843i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.72861 | + | 3.20130i | −0.400172 | + | 0.165757i | −0.573687 | − | 0.819074i | \(-0.694488\pi\) |
0.173515 | + | 0.984831i | \(0.444488\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.10593 | − | 15.8459i | −0.366948 | − | 0.818277i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.32577 | − | 3.32577i | −0.171286 | − | 0.171286i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.6759 | − | 9.39268i | 1.16478 | − | 0.482470i | 0.285319 | − | 0.958433i | \(-0.407900\pi\) |
0.879465 | + | 0.475963i | \(0.157900\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.999108 | − | 0.943047i | −0.0511858 | − | 0.0483138i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.3729 | −0.581129 | −0.290565 | − | 0.956855i | \(-0.593843\pi\) | ||||
−0.290565 | + | 0.956855i | \(0.593843\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −23.1325 | −1.17894 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.00826 | − | 3.38895i | 0.356250 | − | 0.172270i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.2635 | + | 4.66550i | −0.571083 | + | 0.236550i | −0.649489 | − | 0.760371i | \(-0.725017\pi\) |
0.0784059 | + | 0.996922i | \(0.475017\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.40529 | + | 1.40529i | 0.0710687 | + | 0.0710687i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.0674 | + | 7.20526i | −0.810492 | + | 0.363457i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.53179 | + | 3.94820i | −0.479596 | + | 0.198655i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.65241 | − | 8.81769i | 0.183309 | − | 0.442547i | −0.805336 | − | 0.592819i | \(-0.798015\pi\) |
0.988645 | + | 0.150272i | \(0.0480149\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 19.6969 | + | 7.50048i | 0.986076 | + | 0.375494i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.46170 | −0.272744 | −0.136372 | − | 0.990658i | \(-0.543544\pi\) | ||||
−0.136372 | + | 0.990658i | \(0.543544\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.32225 | − | 2.20455i | −0.265120 | − | 0.109816i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.10425 | + | 5.07018i | −0.452394 | + | 0.251939i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.24040 | + | 1.24040i | 0.0614843 | + | 0.0614843i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.6474 | + | 21.6474i | −1.07039 | + | 1.07039i | −0.0730670 | + | 0.997327i | \(0.523279\pi\) |
−0.997327 | + | 0.0730670i | \(0.976721\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.209176 | − | 7.24671i | −0.0103179 | − | 0.357454i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.40871 | + | 17.8862i | −0.364559 | + | 0.880123i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.28636i | 0.455849i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.08541 | − | 3.07889i | −0.395944 | − | 0.150774i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.1057 | + | 6.67119i | 0.786814 | + | 0.325909i | 0.739662 | − | 0.672979i | \(-0.234986\pi\) |
0.0471519 | + | 0.998888i | \(0.484986\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.0865 | + | 26.7651i | 0.540321 | + | 1.30445i | 0.924497 | + | 0.381190i | \(0.124486\pi\) |
−0.384176 | + | 0.923260i | \(0.625514\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −35.3334 | + | 2.04150i | −1.71797 | + | 0.0992612i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.77263 | + | 1.77263i | −0.0859852 | + | 0.0859852i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.13396 | + | 5.15183i | 0.103270 | + | 0.249315i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.78813 | + | 6.40725i | 0.327734 | + | 0.309345i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 20.4774i | − | 0.986361i | −0.869927 | − | 0.493180i | \(-0.835834\pi\) | ||
0.869927 | − | 0.493180i | \(-0.164166\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.6756i | 0.705262i | 0.935762 | + | 0.352631i | \(0.114713\pi\) | ||||
−0.935762 | + | 0.352631i | \(0.885287\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.57899 | + | 7.15373i | 0.363385 | + | 0.342995i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.02639 | + | 9.72056i | 0.192608 | + | 0.464997i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.86825 | + | 4.86825i | −0.232349 | + | 0.232349i | −0.813672 | − | 0.581324i | \(-0.802535\pi\) |
0.581324 | + | 0.813672i | \(0.302535\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.7503 | − | 0.736690i | 0.607158 | − | 0.0350805i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.00738 | − | 14.5031i | −0.285419 | − | 0.689063i | 0.714525 | − | 0.699610i | \(-0.246643\pi\) |
−0.999944 | + | 0.0105468i | \(0.996643\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.01555 | + | 1.24908i | 0.142951 | + | 0.0592122i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −23.4097 | − | 8.91432i | −1.10724 | − | 0.421633i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 1.76611i | − | 0.0833480i | −0.999131 | − | 0.0416740i | \(-0.986731\pi\) | ||
0.999131 | − | 0.0416740i | \(-0.0132691\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.5244 | − | 25.4082i | 0.495576 | − | 1.19643i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.209243 | − | 7.24901i | −0.00983108 | − | 0.340588i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.48622 | + | 2.48622i | −0.116556 | + | 0.116556i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.3579 | − | 22.3579i | −1.04586 | − | 1.04586i | −0.998897 | − | 0.0469601i | \(-0.985047\pi\) |
−0.0469601 | − | 0.998897i | \(-0.514953\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.72529 | + | 2.29003i | 0.127206 | + | 0.106889i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.811938 | − | 0.336316i | −0.0378157 | − | 0.0156638i | 0.363695 | − | 0.931518i | \(-0.381515\pi\) |
−0.401511 | + | 0.915854i | \(0.631515\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.0009 | −0.650678 | −0.325339 | − | 0.945597i | \(-0.605478\pi\) | ||||
−0.325339 | + | 0.945597i | \(0.605478\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 11.9294 | + | 4.54265i | 0.553211 | + | 0.210661i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.94695 | − | 14.3572i | 0.275192 | − | 0.664373i | −0.724498 | − | 0.689277i | \(-0.757928\pi\) |
0.999690 | + | 0.0249045i | \(0.00792818\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 38.0385 | − | 15.7561i | 1.75646 | − | 0.727548i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 27.5776 | − | 12.3669i | 1.27071 | − | 0.569838i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.9257 | + | 10.9257i | 0.502365 | + | 0.502365i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.2615 | + | 5.07887i | −0.562595 | + | 0.233034i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.0233 | − | 5.33047i | 0.504722 | − | 0.244066i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 34.4708 | 1.57501 | 0.787505 | − | 0.616309i | \(-0.211373\pi\) | ||||
0.787505 | + | 0.616309i | \(0.211373\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.266630 | 0.0121573 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.2600 | + | 11.5720i | 0.557847 | + | 0.526546i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.26935 | − | 3.83949i | 0.420899 | − | 0.174342i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.6710 | + | 13.6710i | 0.619490 | + | 0.619490i | 0.945401 | − | 0.325911i | \(-0.105671\pi\) |
−0.325911 | + | 0.945401i | \(0.605671\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.55934 | + | 19.0869i | 0.387067 | + | 0.863140i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.0034 | + | 6.62882i | −0.722223 | + | 0.299154i | −0.713352 | − | 0.700806i | \(-0.752824\pi\) |
−0.00887095 | + | 0.999961i | \(0.502824\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.36238 | − | 3.28908i | 0.0613585 | − | 0.148133i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −15.4449 | − | 13.7576i | −0.694196 | − | 0.618359i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 37.9191 | 1.70090 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.36166 | + | 2.63509i | 0.284787 | + | 0.117963i | 0.520504 | − | 0.853859i | \(-0.325744\pi\) |
−0.235717 | + | 0.971822i | \(0.575744\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.0908900 | − | 3.14880i | −0.00406067 | − | 0.140678i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.8510 | + | 16.8510i | 0.751350 | + | 0.751350i | 0.974731 | − | 0.223381i | \(-0.0717095\pi\) |
−0.223381 | + | 0.974731i | \(0.571709\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.9062 | − | 13.9062i | 0.618817 | − | 0.618817i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −21.0891 | + | 0.608736i | −0.936599 | + | 0.0270349i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.71610 | − | 16.2141i | 0.297686 | − | 0.718678i | −0.702291 | − | 0.711890i | \(-0.747839\pi\) |
0.999977 | − | 0.00678764i | \(-0.00216059\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.1392i | 0.492769i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.69024 | + | 16.7222i | 0.383684 | + | 0.738302i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.16609 | + | 3.38250i | 0.359841 | + | 0.149051i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26.8828 | − | 64.9009i | −1.18231 | − | 2.85434i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.0968155 | − | 0.0434160i | 0.00424973 | − | 0.00190575i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.2126 | − | 18.2126i | 0.797908 | − | 0.797908i | −0.184858 | − | 0.982765i | \(-0.559182\pi\) |
0.982765 | + | 0.184858i | \(0.0591824\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.472480 | + | 1.14067i | 0.0206601 | + | 0.0498779i | 0.933873 | − | 0.357605i | \(-0.116407\pi\) |
−0.913213 | + | 0.407483i | \(0.866407\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −14.5969 | + | 15.4647i | −0.637062 | + | 0.674933i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 4.36045i | − | 0.189944i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 14.5841i | − | 0.634090i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −15.5841 | + | 7.53590i | −0.676291 | + | 0.327030i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.59967 | − | 3.86195i | −0.0692895 | − | 0.167280i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.0150296 | − | 0.0150296i | 0.000649785 | − | 0.000649785i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.17536 | + | 4.85094i | 0.0938735 | + | 0.209333i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.70087 | + | 23.4200i | 0.417846 | + | 1.00877i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.2297 | + | 5.89412i | 0.611781 | + | 0.253408i | 0.666990 | − | 0.745067i | \(-0.267582\pi\) |
−0.0552087 | + | 0.998475i | \(0.517582\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.8993 | − | 36.5008i | 0.596478 | − | 1.56640i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.9576i | 0.640713i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.24323 | − | 15.0725i | 0.266941 | − | 0.644453i | −0.732395 | − | 0.680880i | \(-0.761598\pi\) |
0.999336 | + | 0.0364266i | \(0.0115975\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.63917 | + | 4.70886i | −0.0699582 | + | 0.200969i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.3272 | − | 13.3272i | 0.567756 | − | 0.567756i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 21.1397 | + | 21.1397i | 0.898952 | + | 0.898952i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.590567 | + | 0.0170467i | −0.0250682 | + | 0.000723593i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.09223 | − | 2.93770i | −0.300507 | − | 0.124474i | 0.227335 | − | 0.973817i | \(-0.426999\pi\) |
−0.527842 | + | 0.849342i | \(0.676999\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.34854 | 0.0993325 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.51436 | + | 6.60291i | −0.106156 | + | 0.278775i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.517007 | − | 1.24817i | 0.0217892 | − | 0.0526039i | −0.912610 | − | 0.408830i | \(-0.865937\pi\) |
0.934400 | + | 0.356226i | \(0.115937\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.2305 | + | 4.65183i | −0.472471 | + | 0.195704i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.6693 | + | 18.7509i | 0.994016 | + | 0.787465i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.40004 | − | 4.40004i | −0.184459 | − | 0.184459i | 0.608836 | − | 0.793296i | \(-0.291637\pi\) |
−0.793296 | + | 0.608836i | \(0.791637\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.9135 | + | 9.90528i | −1.00075 | + | 0.414523i | −0.822071 | − | 0.569385i | \(-0.807181\pi\) |
−0.178676 | + | 0.983908i | \(0.557181\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −27.4119 | + | 29.0415i | −1.14515 | + | 1.21322i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.6158 | −0.442709 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.45244 | −0.310249 | −0.155124 | − | 0.987895i | \(-0.549578\pi\) | ||||
−0.155124 | + | 0.987895i | \(0.549578\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.95040 | + | 9.48246i | −0.371966 | + | 0.394078i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.8608 | − | 10.2977i | 1.03140 | − | 0.427220i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.1850 | + | 17.1850i | 0.711732 | + | 0.711732i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.13861 | + | 0.181343i | −0.129766 | + | 0.00749762i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 39.1257 | − | 16.2064i | 1.61489 | − | 0.668910i | 0.621472 | − | 0.783436i | \(-0.286535\pi\) |
0.993420 | + | 0.114526i | \(0.0365349\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.83416 | − | 21.3275i | 0.364005 | − | 0.878786i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.43274 | − | 3.76249i | 0.0589350 | − | 0.154768i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −42.7694 | −1.75633 | −0.878164 | − | 0.478359i | \(-0.841232\pi\) | ||||
−0.878164 | + | 0.478359i | \(0.841232\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.45879 | − | 1.01847i | −0.100801 | − | 0.0417530i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.2899 | − | 0.527938i | 0.748556 | − | 0.0216071i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.3145 | − | 21.3145i | −0.870885 | − | 0.870885i | 0.121684 | − | 0.992569i | \(-0.461171\pi\) |
−0.992569 | + | 0.121684i | \(0.961171\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.26621 | + | 4.26621i | −0.174022 | + | 0.174022i | −0.788744 | − | 0.614722i | \(-0.789268\pi\) |
0.614722 | + | 0.788744i | \(0.289268\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 34.7678 | + | 12.1028i | 1.41586 | + | 0.492865i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.8366 | − | 26.1618i | 0.440570 | − | 1.06363i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.5562i | 1.24024i | 0.784508 | + | 0.620118i | \(0.212915\pi\) | ||||
−0.784508 | + | 0.620118i | \(0.787085\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.7471 | − | 28.2228i | 0.435495 | − | 1.14364i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.86469 | − | 4.08609i | −0.399083 | − | 0.165305i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.4587 | + | 32.4921i | 0.543590 | + | 1.31234i | 0.922174 | + | 0.386775i | \(0.126411\pi\) |
−0.378584 | + | 0.925567i | \(0.623589\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.79007 | + | 8.45168i | 0.152830 | + | 0.340804i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.1395 | − | 32.1395i | 1.29389 | − | 1.29389i | 0.361524 | − | 0.932363i | \(-0.382257\pi\) |
0.932363 | − | 0.361524i | \(-0.117743\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.9456 | − | 36.0820i | −0.600716 | − | 1.45026i | −0.872846 | − | 0.487996i | \(-0.837728\pi\) |
0.272129 | − | 0.962261i | \(-0.412272\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.30335 | + | 15.0177i | 0.0523018 | + | 0.602639i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 9.45815i | − | 0.378933i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 6.68739i | − | 0.267496i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −25.6754 | + | 27.2017i | −1.02538 | + | 1.08633i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.0772324 | + | 0.186456i | 0.00307946 | + | 0.00743447i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.5960 | + | 20.5960i | −0.819912 | + | 0.819912i | −0.986095 | − | 0.166183i | \(-0.946856\pi\) |
0.166183 | + | 0.986095i | \(0.446856\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 27.3392 | − | 12.2600i | 1.08664 | − | 0.487291i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.351471 | + | 0.848526i | 0.0139477 | + | 0.0336727i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.55974 | + | 1.47449i | 0.141042 | + | 0.0584216i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 25.3175 | + | 22.5517i | 1.00154 | + | 0.892130i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 12.6916i | − | 0.501289i | −0.968079 | − | 0.250645i | \(-0.919357\pi\) | ||
0.968079 | − | 0.250645i | \(-0.0806426\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.974363 | + | 2.35232i | −0.0384251 | + | 0.0927665i | −0.941927 | − | 0.335818i | \(-0.890987\pi\) |
0.903502 | + | 0.428584i | \(0.140987\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.20185 | + | 0.150151i | −0.204823 | + | 0.00591221i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.3823 | − | 22.3823i | 0.879941 | − | 0.879941i | −0.113587 | − | 0.993528i | \(-0.536234\pi\) |
0.993528 | + | 0.113587i | \(0.0362341\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.2952 | − | 24.2952i | −0.953670 | − | 0.953670i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.06725 | − | 36.9739i | −0.0418289 | − | 1.44912i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.02663 | + | 0.839459i | 0.0793083 | + | 0.0328506i | 0.421985 | − | 0.906603i | \(-0.361334\pi\) |
−0.342677 | + | 0.939453i | \(0.611334\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.7716 | 0.459953 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.62483 | + | 7.43731i | −0.258459 | + | 0.290157i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.65284 | − | 11.2330i | 0.181249 | − | 0.437574i | −0.806975 | − | 0.590585i | \(-0.798897\pi\) |
0.988224 | + | 0.153011i | \(0.0488971\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.0472 | + | 9.13226i | −0.857538 | + | 0.355204i | −0.767744 | − | 0.640757i | \(-0.778621\pi\) |
−0.0897938 | + | 0.995960i | \(0.528621\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.439427 | + | 0.979901i | 0.0170659 | + | 0.0380562i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.96289 | − | 9.96289i | −0.386344 | − | 0.386344i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.9282 | − | 5.76923i | 0.539300 | − | 0.223386i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −22.9550 | − | 21.6670i | −0.887491 | − | 0.837694i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.89643 | −0.382048 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.77155 | 0.0682883 | 0.0341441 | − | 0.999417i | \(-0.489129\pi\) | ||||
0.0341441 | + | 0.999417i | \(0.489129\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −18.9432 | + | 1.64404i | −0.729126 | + | 0.0632793i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.1005 | − | 12.8822i | 1.19529 | − | 0.495105i | 0.305815 | − | 0.952091i | \(-0.401071\pi\) |
0.889474 | + | 0.456986i | \(0.151071\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.5577 | − | 20.5577i | −0.788930 | − | 0.788930i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.5526 | + | 8.31973i | −0.710937 | + | 0.318813i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.51740 | + | 1.04274i | −0.0963256 | + | 0.0398994i | −0.430326 | − | 0.902674i | \(-0.641601\pi\) |
0.334000 | + | 0.942573i | \(0.391601\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.85465 | + | 4.47752i | −0.0708624 | + | 0.171077i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −22.0365 | − | 8.39142i | −0.840747 | − | 0.320153i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.69401 | 0.140731 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.0335 | − | 14.9256i | −1.37078 | − | 0.567795i | −0.428779 | − | 0.903409i | \(-0.641056\pi\) |
−0.942000 | + | 0.335614i | \(0.891056\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −19.7041 | + | 56.6039i | −0.748496 | + | 2.15021i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.08969 | + | 4.08969i | 0.155131 | + | 0.155131i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.23732 | − | 2.23732i | 0.0847444 | − | 0.0847444i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.828543 | − | 28.7040i | −0.0313384 | − | 1.08569i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.39440 | + | 3.36638i | −0.0526658 | + | 0.127147i | −0.948023 | − | 0.318203i | \(-0.896921\pi\) |
0.895357 | + | 0.445350i | \(0.146921\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.06845i | 0.0402973i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 22.1109 | + | 8.41972i | 0.832743 | + | 0.317105i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −52.6494 | − | 21.8081i | −1.98008 | − | 0.820177i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.10175 | + | 21.9736i | 0.341824 | + | 0.825235i | 0.997531 | + | 0.0702205i | \(0.0223703\pi\) |
−0.655708 | + | 0.755015i | \(0.727630\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.54191 | + | 26.6868i | 0.0578263 | + | 1.00083i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.0568 | − | 13.0568i | 0.488980 | − | 0.488980i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.38796 | − | 5.76505i | −0.0893047 | − | 0.215601i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −27.2003 | − | 25.6741i | −1.01581 | − | 0.958816i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.5450i | 0.728907i | 0.931222 | + | 0.364453i | \(0.118744\pi\) | ||||
−0.931222 | + | 0.364453i | \(0.881256\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 25.6126i | − | 0.953863i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.4017 | + | 17.3692i | 0.684366 | + | 0.645966i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.27728 | + | 17.5689i | 0.270271 | + | 0.652493i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.8914 | − | 20.8914i | 0.774821 | − | 0.774821i | −0.204124 | − | 0.978945i | \(-0.565435\pi\) |
0.978945 | + | 0.204124i | \(0.0654347\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.65151 | + | 26.5963i | 0.172278 | + | 0.985048i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.680281 | + | 1.64234i | 0.0251611 | + | 0.0607443i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.09957 | − | 3.76916i | −0.336100 | − | 0.139217i | 0.208249 | − | 0.978076i | \(-0.433223\pi\) |
−0.544350 | + | 0.838859i | \(0.683223\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.97886 | − | 3.03831i | −0.294305 | − | 0.112070i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 73.0703i | 2.69158i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.03797 | + | 19.4054i | −0.295682 | + | 0.713839i | 0.704311 | + | 0.709892i | \(0.251256\pi\) |
−0.999992 | + | 0.00394665i | \(0.998744\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.164043 | + | 5.68309i | 0.00602625 | + | 0.208774i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.8827 | + | 14.8827i | −0.545995 | + | 0.545995i | −0.925280 | − | 0.379285i | \(-0.876170\pi\) |
0.379285 | + | 0.925280i | \(0.376170\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.8409 | + | 11.8409i | 0.433817 | + | 0.433817i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 22.7232 | + | 7.91004i | 0.831398 | + | 0.289413i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.0569026 | − | 0.0235698i | −0.00207917 | − | 0.000861222i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 47.9945 | 1.75135 | 0.875673 | − | 0.482905i | \(-0.160418\pi\) | ||||
0.875673 | + | 0.482905i | \(0.160418\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.59272 | − | 1.74889i | −0.167368 | − | 0.0637330i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.85523 | + | 4.47893i | −0.0675189 | + | 0.163005i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.61422 | + | 1.91127i | −0.167707 | + | 0.0694663i | −0.464957 | − | 0.885333i | \(-0.653930\pi\) |
0.297251 | + | 0.954799i | \(0.403930\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −27.3004 | + | 12.2426i | −0.990943 | + | 0.444379i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −35.4112 | − | 35.4112i | −1.28365 | − | 1.28365i | −0.938573 | − | 0.345081i | \(-0.887851\pi\) |
−0.345081 | − | 0.938573i | \(-0.612149\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 40.0435 | − | 16.5865i | 1.44967 | − | 0.600473i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.03595 | − | 2.14232i | −0.0374549 | − | 0.0774557i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.22237 | −0.188569 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 49.1306 | 1.77169 | 0.885847 | − | 0.463978i | \(-0.153578\pi\) | ||||
0.885847 | + | 0.463978i | \(0.153578\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.70592 | + | 1.61020i | 0.0614371 | + | 0.0579898i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −48.9331 | + | 20.2688i | −1.76000 | + | 0.729017i | −0.763467 | + | 0.645847i | \(0.776504\pi\) |
−0.996535 | + | 0.0831696i | \(0.973496\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16.4698 | + | 16.4698i | 0.591611 | + | 0.591611i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.700519 | + | 1.56212i | 0.0251310 | + | 0.0560408i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15.4757 | − | 6.41026i | 0.554476 | − | 0.229672i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25.7531 | + | 62.1736i | −0.921520 | + | 2.22474i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 23.9605 | − | 12.4519i | 0.856277 | − | 0.444993i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.2044 | −0.721126 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 44.3943 | + | 18.3887i | 1.58249 | + | 0.655487i | 0.988805 | − | 0.149214i | \(-0.0476743\pi\) |
0.593681 | + | 0.804701i | \(0.297674\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.249039 | − | 8.62771i | −0.00886602 | − | 0.307155i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.9072 | + | 24.9072i | 0.885597 | + | 0.885597i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.06364 | + | 1.06364i | −0.0377711 | + | 0.0377711i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.18198 | + | 0.236173i | −0.290185 | + | 0.00837619i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.5848 | + | 25.5539i | −0.374931 | + | 0.905164i | 0.617968 | + | 0.786203i | \(0.287956\pi\) |
−0.992899 | + | 0.118961i | \(0.962044\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 8.08201i | − | 0.285921i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.62505 | − | 6.31492i | 0.198752 | − | 0.223127i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.2642 | − | 7.56530i | −0.644531 | − | 0.266974i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.31287 | − | 10.4122i | −0.152009 | − | 0.366981i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −28.1811 | + | 12.6375i | −0.992022 | + | 0.444863i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.4258 | − | 26.4258i | 0.929083 | − | 0.929083i | −0.0685638 | − | 0.997647i | \(-0.521842\pi\) |
0.997647 | + | 0.0685638i | \(0.0218417\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.2190 | − | 24.6709i | −0.358838 | − | 0.866311i | −0.995464 | − | 0.0951387i | \(-0.969671\pi\) |
0.636626 | − | 0.771173i | \(-0.280329\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.1091 | + | 10.7101i | −0.354542 | + | 0.375618i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 13.9838i | − | 0.489831i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.41115i | 0.329254i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.96590 | + | 8.20140i | 0.138580 | + | 0.286580i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.9273 | + | 38.4519i | 0.555866 | + | 1.34198i | 0.913013 | + | 0.407932i | \(0.133750\pi\) |
−0.357146 | + | 0.934048i | \(0.616250\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.1818 | − | 27.1818i | 0.947499 | − | 0.947499i | −0.0511904 | − | 0.998689i | \(-0.516302\pi\) |
0.998689 | + | 0.0511904i | \(0.0163015\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −15.4428 | − | 34.4366i | −0.537648 | − | 1.19893i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.6297 | + | 30.4907i | 0.439176 | + | 1.06027i | 0.976234 | + | 0.216720i | \(0.0695358\pi\) |
−0.537058 | + | 0.843546i | \(0.680464\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.6568 | − | 14.3553i | −1.20368 | − | 0.498581i | −0.311494 | − | 0.950248i | \(-0.600829\pi\) |
−0.892187 | + | 0.451667i | \(0.850829\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.4786 | + | 35.3960i | −0.467568 | + | 1.22787i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.91645i | 0.101049i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.805870 | + | 1.94554i | −0.0278883 | + | 0.0673282i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 21.2770 | − | 25.3211i | 0.735439 | − | 0.875225i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.13731 | − | 5.13731i | 0.177360 | − | 0.177360i | −0.612844 | − | 0.790204i | \(-0.709975\pi\) |
0.790204 | + | 0.612844i | \(0.209975\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.41020 | + | 1.41020i | 0.0486277 | + | 0.0486277i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −25.3030 | + | 0.730371i | −0.871481 | + | 0.0251553i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.0303 | + | 5.39732i | 0.448255 | + | 0.185673i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −82.0555 | −2.81946 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.78660 | − | 15.1961i | 0.198596 | − | 0.521528i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.327054 | + | 0.789578i | −0.0112113 | + | 0.0270664i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.7734 | − | 11.5041i | 0.950943 | − | 0.393893i | 0.147358 | − | 0.989083i | \(-0.452923\pi\) |
0.803585 | + | 0.595190i | \(0.202923\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.726686 | − | 12.5772i | −0.0248521 | − | 0.430130i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.9037 | − | 23.9037i | −0.816536 | − | 0.816536i | 0.169069 | − | 0.985604i | \(-0.445924\pi\) |
−0.985604 | + | 0.169069i | \(0.945924\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.4970 | + | 15.1176i | −1.24526 | + | 0.515805i | −0.905356 | − | 0.424654i | \(-0.860396\pi\) |
−0.339907 | + | 0.940459i | \(0.610396\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.4234 | − | 19.5186i | 0.627869 | − | 0.665193i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −48.7809 | −1.66052 | −0.830260 | − | 0.557377i | \(-0.811808\pi\) | ||||
−0.830260 | + | 0.557377i | \(0.811808\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.0709307 | −0.00241172 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 19.6533 | − | 20.8216i | 0.667461 | − | 0.707139i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −49.0187 | + | 20.3042i | −1.66284 | + | 0.688773i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.85341 | + | 7.85341i | 0.266103 | + | 0.266103i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.49946 | − | 25.9520i | −0.0507490 | − | 0.878342i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 31.0796 | − | 12.8736i | 1.05068 | − | 0.435207i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.45430 | + | 20.4105i | −0.285481 | + | 0.689213i | −0.999945 | − | 0.0104591i | \(-0.996671\pi\) |
0.714464 | + | 0.699672i | \(0.246671\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.59343 | − | 19.9410i | 0.256120 | − | 0.672592i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.8223 | −0.869976 | −0.434988 | − | 0.900436i | \(-0.643247\pi\) | ||||
−0.434988 | + | 0.900436i | \(0.643247\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.3809 | − | 13.8268i | −1.12336 | − | 0.465310i | −0.257839 | − | 0.966188i | \(-0.583010\pi\) |
−0.865518 | + | 0.500878i | \(0.833010\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.5672 | − | 0.333887i | 0.388827 | − | 0.0112235i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34.6997 | + | 34.6997i | 1.16510 | + | 1.16510i | 0.983343 | + | 0.181760i | \(0.0581796\pi\) |
0.181760 | + | 0.983343i | \(0.441820\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.88187 | − | 1.88187i | 0.0631158 | − | 0.0631158i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −46.8200 | + | 26.0741i | −1.56853 | + | 0.873517i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.3739 | − | 39.5302i | 0.547933 | − | 1.32283i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 3.55398i | − | 0.118796i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.61838 | + | 4.24999i | −0.0540360 | + | 0.141903i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −30.5593 | − | 12.6581i | −1.01921 | − | 0.422170i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.07001 | + | 2.58324i | 0.0356473 | + | 0.0860602i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.17033 | + | 13.7595i | 0.205336 | + | 0.457889i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.4625 | + | 18.4625i | −0.613715 | + | 0.613715i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.42403 | + | 17.9232i | 0.246511 | + | 0.595130i | 0.997903 | − | 0.0647258i | \(-0.0206173\pi\) |
−0.751392 | + | 0.659856i | \(0.770617\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −22.1825 | − | 45.8728i | −0.735746 | − | 1.52151i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 37.5930i | − | 1.24551i | −0.782416 | − | 0.622756i | \(-0.786013\pi\) | ||
0.782416 | − | 0.622756i | \(-0.213987\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 47.7565i | 1.58051i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.28790 | − | 2.42390i | 0.0756355 | − | 0.0801317i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.0535 | − | 31.5140i | −0.431066 | − | 1.04069i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.3220 | + | 28.3220i | −0.934258 | + | 0.934258i | −0.997968 | − | 0.0637109i | \(-0.979706\pi\) |
0.0637109 | + | 0.997968i | \(0.479706\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.5788 | + | 9.67681i | −0.711046 | + | 0.318862i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.91438 | + | 9.45014i | 0.128843 | + | 0.311055i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.995970 | − | 0.412544i | −0.0327473 | − | 0.0135644i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.2326 | − | 17.1008i | 0.500304 | − | 0.561663i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.6297i | 0.479986i | 0.970775 | + | 0.239993i | \(0.0771452\pi\) | ||||
−0.970775 | + | 0.239993i | \(0.922855\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.90865 | + | 14.2647i | −0.193648 | + | 0.467508i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 46.0362 | − | 1.32884i | 1.50716 | − | 0.0435042i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.33983 | − | 3.33983i | 0.109224 | − | 0.109224i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.60824 | + | 5.60824i | 0.183213 | + | 0.183213i | 0.792754 | − | 0.609541i | \(-0.208646\pi\) |
−0.609541 | + | 0.792754i | \(0.708646\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.304493 | + | 10.5489i | 0.00993676 | + | 0.344249i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.5273 | − | 4.36054i | −0.343180 | − | 0.142150i | 0.204435 | − | 0.978880i | \(-0.434464\pi\) |
−0.547615 | + | 0.836730i | \(0.684464\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.3987 | 0.436321 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.30855 | − | 17.9120i | −0.302807 | − | 0.582676i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.3491 | + | 53.9555i | −0.726248 | + | 1.75332i | −0.0715370 | + | 0.997438i | \(0.522790\pi\) |
−0.654711 | + | 0.755879i | \(0.727210\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.77609 | + | 1.14990i | −0.0901158 | + | 0.0373272i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.00637 | − | 2.24416i | −0.0326338 | − | 0.0727718i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.8805 | + | 32.8805i | 1.06510 | + | 1.06510i | 0.997728 | + | 0.0673750i | \(0.0214624\pi\) |
0.0673750 | + | 0.997728i | \(0.478538\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.6644 | − | 10.2163i | 0.798122 | − | 0.330593i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 38.9761 | + | 36.7891i | 1.25992 | + | 1.18922i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.0435 | 0.453489 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.51359 | −0.306890 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.0239745 | − | 0.0495786i | −0.000772566 | − | 0.00159765i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.05330 | − | 3.33578i | 0.259245 | − | 0.107383i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.6204 | − | 14.6204i | −0.470160 | − | 0.470160i | 0.431807 | − | 0.901966i | \(-0.357876\pi\) |
−0.901966 | + | 0.431807i | \(0.857876\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.92670 | + | 1.76089i | −0.126144 | + | 0.0565679i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39.9825 | + | 16.5613i | −1.28310 | + | 0.531477i | −0.916921 | − | 0.399068i | \(-0.869334\pi\) |
−0.366178 | + | 0.930545i | \(0.619334\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.41357 | − | 15.4837i | 0.205610 | − | 0.496386i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.36091 | − | 2.04141i | −0.171687 | − | 0.0653775i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.1567 | 0.452912 | 0.226456 | − | 0.974021i | \(-0.427286\pi\) | ||||
0.226456 | + | 0.974021i | \(0.427286\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.5079 | + | 6.42359i | 0.495635 | + | 0.205299i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 36.6004 | + | 12.7408i | 1.16856 | + | 0.406781i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.5590 | − | 27.5590i | −0.878995 | − | 0.878995i | 0.114436 | − | 0.993431i | \(-0.463494\pi\) |
−0.993431 | + | 0.114436i | \(0.963494\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.90311 | + | 1.90311i | −0.0606381 | + | 0.0606381i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.97813 | − | 68.5304i | −0.0629646 | − | 2.18135i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.88077 | + | 6.95478i | −0.0916030 | + | 0.221149i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.9042i | 0.473446i | 0.971577 | + | 0.236723i | \(0.0760734\pi\) | ||||
−0.971577 | + | 0.236723i | \(0.923927\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −21.9447 | − | 8.35645i | −0.696395 | − | 0.265184i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.3008 | − | 4.68093i | −0.358258 | − | 0.148395i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.66402 | − | 11.2599i | −0.147711 | − | 0.356606i | 0.832655 | − | 0.553792i | \(-0.186820\pi\) |
−0.980366 | + | 0.197186i | \(0.936820\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.461327 | + | 1.45960i | −0.0145958 | + | 0.0461798i |
(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 | 384.2.o.a.47.4 | 56 | ||
3.2 | odd | 2 | inner | 384.2.o.a.47.7 | 56 | ||
4.3 | odd | 2 | 96.2.o.a.35.6 | yes | 56 | ||
8.3 | odd | 2 | 768.2.o.b.95.4 | 56 | |||
8.5 | even | 2 | 768.2.o.a.95.11 | 56 | |||
12.11 | even | 2 | 96.2.o.a.35.9 | yes | 56 | ||
24.5 | odd | 2 | 768.2.o.a.95.8 | 56 | |||
24.11 | even | 2 | 768.2.o.b.95.7 | 56 | |||
32.5 | even | 8 | 768.2.o.b.671.7 | 56 | |||
32.11 | odd | 8 | inner | 384.2.o.a.335.7 | 56 | ||
32.21 | even | 8 | 96.2.o.a.11.9 | yes | 56 | ||
32.27 | odd | 8 | 768.2.o.a.671.8 | 56 | |||
96.5 | odd | 8 | 768.2.o.b.671.4 | 56 | |||
96.11 | even | 8 | inner | 384.2.o.a.335.4 | 56 | ||
96.53 | odd | 8 | 96.2.o.a.11.6 | ✓ | 56 | ||
96.59 | even | 8 | 768.2.o.a.671.11 | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.2.o.a.11.6 | ✓ | 56 | 96.53 | odd | 8 | ||
96.2.o.a.11.9 | yes | 56 | 32.21 | even | 8 | ||
96.2.o.a.35.6 | yes | 56 | 4.3 | odd | 2 | ||
96.2.o.a.35.9 | yes | 56 | 12.11 | even | 2 | ||
384.2.o.a.47.4 | 56 | 1.1 | even | 1 | trivial | ||
384.2.o.a.47.7 | 56 | 3.2 | odd | 2 | inner | ||
384.2.o.a.335.4 | 56 | 96.11 | even | 8 | inner | ||
384.2.o.a.335.7 | 56 | 32.11 | odd | 8 | inner | ||
768.2.o.a.95.8 | 56 | 24.5 | odd | 2 | |||
768.2.o.a.95.11 | 56 | 8.5 | even | 2 | |||
768.2.o.a.671.8 | 56 | 32.27 | odd | 8 | |||
768.2.o.a.671.11 | 56 | 96.59 | even | 8 | |||
768.2.o.b.95.4 | 56 | 8.3 | odd | 2 | |||
768.2.o.b.95.7 | 56 | 24.11 | even | 2 | |||
768.2.o.b.671.4 | 56 | 96.5 | odd | 8 | |||
768.2.o.b.671.7 | 56 | 32.5 | even | 8 |