LMFDB - Embedded newform 608.2.y.b.161.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [608,2,Mod(161,608)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(608, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("608.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 608 = 2^{5} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	608.y (of order $9$, degree $6$, 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:	$4.85490444289$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			161.4
Character	$\chi$	$=$	608.161
Dual form			608.2.y.b.321.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.08700 - 0.912100i) q^{3} +(-1.73765 - 0.632454i) q^{5} +(-0.766882 + 1.32828i) q^{7} +(-0.171305 + 0.971520i) q^{9} +O(q^{10})$	\(q+(1.08700 - 0.912100i) q^{3} +(-1.73765 - 0.632454i) q^{5} +(-0.766882 + 1.32828i) q^{7} +(-0.171305 + 0.971520i) q^{9} +(-2.67514 - 4.63347i) q^{11} +(-3.64069 - 3.05490i) q^{13} +(-2.46569 + 0.897438i) q^{15} +(-1.28429 - 7.28355i) q^{17} +(3.93481 - 1.87543i) q^{19} +(0.377923 + 2.14331i) q^{21} +(3.20063 - 1.16494i) q^{23} +(-1.21078 - 1.01596i) q^{25} +(2.82838 + 4.89890i) q^{27} +(0.487075 - 2.76234i) q^{29} +(-2.42051 + 4.19244i) q^{31} +(-7.13406 - 2.59658i) q^{33} +(2.17265 - 1.82307i) q^{35} -11.4400 q^{37} -6.74380 q^{39} +(0.484896 - 0.406876i) q^{41} +(4.05282 + 1.47511i) q^{43} +(0.912112 - 1.57982i) q^{45} +(-0.991588 + 5.62358i) q^{47} +(2.32378 + 4.02491i) q^{49} +(-8.03934 - 6.74581i) q^{51} +(6.31642 - 2.29899i) q^{53} +(1.71800 + 9.74327i) q^{55} +(2.56656 - 5.62753i) q^{57} +(1.45440 + 8.24828i) q^{59} +(4.69497 - 1.70883i) q^{61} +(-1.15908 - 0.972583i) q^{63} +(4.39417 + 7.61093i) q^{65} +(0.984932 - 5.58583i) q^{67} +(2.41655 - 4.18558i) q^{69} +(0.885715 + 0.322374i) q^{71} +(-9.76369 + 8.19271i) q^{73} -2.24277 q^{75} +8.20605 q^{77} +(8.68173 - 7.28484i) q^{79} +(4.76169 + 1.73311i) q^{81} +(7.25428 - 12.5648i) q^{83} +(-2.37487 + 13.4685i) q^{85} +(-1.99008 - 3.44692i) q^{87} +(-3.25584 - 2.73198i) q^{89} +(6.84974 - 2.49310i) q^{91} +(1.19284 + 6.76493i) q^{93} +(-8.02347 + 0.770260i) q^{95} +(-0.769831 - 4.36593i) q^{97} +(4.95978 - 1.80521i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} + 12 q^{7} + 3 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 + 12 * q^7 + 3 * q^9	$ 30 q - 3 q^{3} + 12 q^{7} + 3 q^{9} + 6 q^{11} - 6 q^{13} - 24 q^{15} - 6 q^{17} - 12 q^{19} - 6 q^{21} - 6 q^{23} - 12 q^{25} + 39 q^{27} + 12 q^{29} + 39 q^{33} - 12 q^{35} + 36 q^{37} - 24 q^{39} + 9 q^{41} + 18 q^{43} + 18 q^{45} + 12 q^{47} - 9 q^{49} + 51 q^{51} + 6 q^{53} + 24 q^{55} + 12 q^{57} - 9 q^{59} + 18 q^{61} - 132 q^{63} + 18 q^{65} - 51 q^{67} - 24 q^{69} + 36 q^{71} - 30 q^{73} + 48 q^{75} + 36 q^{77} + 60 q^{79} - 3 q^{81} + 30 q^{83} - 12 q^{85} - 24 q^{89} - 60 q^{91} + 30 q^{93} - 36 q^{95} - 9 q^{97} + 27 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 + 12 * q^7 + 3 * q^9 + 6 * q^11 - 6 * q^13 - 24 * q^15 - 6 * q^17 - 12 * q^19 - 6 * q^21 - 6 * q^23 - 12 * q^25 + 39 * q^27 + 12 * q^29 + 39 * q^33 - 12 * q^35 + 36 * q^37 - 24 * q^39 + 9 * q^41 + 18 * q^43 + 18 * q^45 + 12 * q^47 - 9 * q^49 + 51 * q^51 + 6 * q^53 + 24 * q^55 + 12 * q^57 - 9 * q^59 + 18 * q^61 - 132 * q^63 + 18 * q^65 - 51 * q^67 - 24 * q^69 + 36 * q^71 - 30 * q^73 + 48 * q^75 + 36 * q^77 + 60 * q^79 - 3 * q^81 + 30 * q^83 - 12 * q^85 - 24 * q^89 - 60 * q^91 + 30 * q^93 - 36 * q^95 - 9 * q^97 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/608\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (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
$2$		0			0
$3$	1.08700	−	0.912100i	0.627579	−	0.526601i	−0.272597	−	0.962128i	$-0.587882\pi$
$3$	1.08700	−	0.912100i	0.627579	−	0.526601i	0.900176	+	0.435527i	$0.143438\pi$
$4$		0			0
$5$	−1.73765	−	0.632454i	−0.777103	−	0.282842i	−0.0771387	−	0.997020i	$-0.524578\pi$
$5$	−1.73765	−	0.632454i	−0.777103	−	0.282842i	−0.699964	+	0.714178i	$0.746801\pi$
$6$		0			0
$7$	−0.766882	+	1.32828i	−0.289854	+	0.502042i	−0.973775	−	0.227514i	$-0.926940\pi$
$7$	−0.766882	+	1.32828i	−0.289854	+	0.502042i	0.683921	+	0.729557i	$0.260273\pi$
$8$		0			0
$9$	−0.171305	+	0.971520i	−0.0571018	+	0.323840i
$10$		0			0
$11$	−2.67514	−	4.63347i	−0.806584	−	1.39704i	−0.915217	−	0.402962i	$-0.867981\pi$
$11$	−2.67514	−	4.63347i	−0.806584	−	1.39704i	0.108633	−	0.994082i	$-0.465353\pi$
$12$		0			0
$13$	−3.64069	−	3.05490i	−1.00975	−	0.847277i	−0.0214407	−	0.999770i	$-0.506825\pi$
$13$	−3.64069	−	3.05490i	−1.00975	−	0.847277i	−0.988305	+	0.152493i	$0.951270\pi$
$14$		0			0
$15$	−2.46569	+	0.897438i	−0.636638	+	0.231717i
$16$		0			0
$17$	−1.28429	−	7.28355i	−0.311485	−	1.76652i	−0.591286	−	0.806462i	$-0.701380\pi$
$17$	−1.28429	−	7.28355i	−0.311485	−	1.76652i	0.279801	−	0.960058i	$-0.409732\pi$
$18$		0			0
$19$	3.93481	−	1.87543i	0.902708	−	0.430253i
$19$	3.93481	−	1.87543i	0.902708	−	0.430253i
$20$		0			0
$21$	0.377923	+	2.14331i	0.0824697	+	0.467709i
$22$		0			0
$23$	3.20063	−	1.16494i	0.667378	−	0.242906i	0.0139595	−	0.999903i	$-0.495556\pi$
$23$	3.20063	−	1.16494i	0.667378	−	0.242906i	0.653419	+	0.756997i	$0.273334\pi$
$24$		0			0
$25$	−1.21078	−	1.01596i	−0.242156	−	0.203193i
$26$		0			0
$27$	2.82838	+	4.89890i	0.544322	+	0.942793i
$28$		0			0
$29$	0.487075	−	2.76234i	0.0904475	−	0.512953i	−0.905600	−	0.424132i	$-0.860579\pi$
$29$	0.487075	−	2.76234i	0.0904475	−	0.512953i	0.996048	−	0.0888206i	$-0.0283098\pi$
$30$		0			0
$31$	−2.42051	+	4.19244i	−0.434736	+	0.752985i	−0.997274	−	0.0737862i	$-0.976492\pi$
$31$	−2.42051	+	4.19244i	−0.434736	+	0.752985i	0.562538	+	0.826772i	$0.309825\pi$
$32$		0			0
$33$	−7.13406	−	2.59658i	−1.24188	−	0.452007i
$34$		0			0
$35$	2.17265	−	1.82307i	0.367245	−	0.308155i
$36$		0			0
$37$	−11.4400			−1.88073			−0.940365	−	0.340167i	$-0.889516\pi$
$37$	−11.4400			−1.88073			−0.940365	+	0.340167i	$0.889516\pi$
$38$		0			0
$39$	−6.74380			−1.07987
$40$		0			0
$41$	0.484896	−	0.406876i	0.0757281	−	0.0635434i	−0.604138	−	0.796880i	$-0.706482\pi$
$41$	0.484896	−	0.406876i	0.0757281	−	0.0635434i	0.679866	+	0.733336i	$0.262038\pi$
$42$		0			0
$43$	4.05282	+	1.47511i	0.618049	+	0.224952i	0.632021	−	0.774951i	$-0.282225\pi$
$43$	4.05282	+	1.47511i	0.618049	+	0.224952i	−0.0139723	+	0.999902i	$0.504448\pi$
$44$		0			0
$45$	0.912112	−	1.57982i	0.135970	−	0.235506i
$46$		0			0
$47$	−0.991588	+	5.62358i	−0.144638	+	0.820283i	0.823019	+	0.568014i	$0.192288\pi$
$47$	−0.991588	+	5.62358i	−0.144638	+	0.820283i	−0.967657	+	0.252269i	$0.918823\pi$
$48$		0			0
$49$	2.32378	+	4.02491i	0.331969	+	0.574987i
$50$		0			0
$51$	−8.03934	−	6.74581i	−1.12573	−	0.944602i
$52$		0			0
$53$	6.31642	−	2.29899i	0.867627	−	0.315790i	0.130421	−	0.991459i	$-0.458367\pi$
$53$	6.31642	−	2.29899i	0.867627	−	0.315790i	0.737206	+	0.675668i	$0.236145\pi$
$54$		0			0
$55$	1.71800	+	9.74327i	0.231655	+	1.31378i
$56$		0			0
$57$	2.56656	−	5.62753i	0.339949	−	0.745385i
$58$		0			0
$59$	1.45440	+	8.24828i	0.189346	+	1.07384i	0.920243	+	0.391347i	$0.127991\pi$
$59$	1.45440	+	8.24828i	0.189346	+	1.07384i	−0.730897	+	0.682488i	$0.760898\pi$
$60$		0			0
$61$	4.69497	−	1.70883i	0.601130	−	0.218793i	−0.0234878	−	0.999724i	$-0.507477\pi$
$61$	4.69497	−	1.70883i	0.601130	−	0.218793i	0.624618	+	0.780931i	$0.285255\pi$
$62$		0			0
$63$	−1.15908	−	0.972583i	−0.146030	−	0.122534i
$64$		0			0
$65$	4.39417	+	7.61093i	0.545030	+	0.944020i
$66$		0			0
$67$	0.984932	−	5.58583i	0.120329	−	0.682417i	−0.863645	−	0.504101i	$-0.831824\pi$
$67$	0.984932	−	5.58583i	0.120329	−	0.682417i	0.983973	−	0.178316i	$-0.0570650\pi$
$68$		0			0
$69$	2.41655	−	4.18558i	0.290918	−	0.503885i
$70$		0			0
$71$	0.885715	+	0.322374i	0.105115	+	0.0382587i	0.394042	−	0.919092i	$-0.371076\pi$
$71$	0.885715	+	0.322374i	0.105115	+	0.0382587i	−0.288927	+	0.957351i	$0.593299\pi$
$72$		0			0
$73$	−9.76369	+	8.19271i	−1.14275	+	0.958884i	−0.999525	−	0.0308060i	$-0.990193\pi$
$73$	−9.76369	+	8.19271i	−1.14275	+	0.958884i	−0.143228	+	0.989690i	$0.545748\pi$
$74$		0			0
$75$	−2.24277			−0.258973
$76$		0			0
$77$	8.20605			0.935167
$78$		0			0
$79$	8.68173	−	7.28484i	0.976771	−	0.819608i	−0.00682829	−	0.999977i	$-0.502174\pi$
$79$	8.68173	−	7.28484i	0.976771	−	0.819608i	0.983599	+	0.180369i	$0.0577291\pi$
$80$		0			0
$81$	4.76169	+	1.73311i	0.529076	+	0.192568i
$82$		0			0
$83$	7.25428	−	12.5648i	0.796261	−	1.37916i	−0.125775	−	0.992059i	$-0.540142\pi$
$83$	7.25428	−	12.5648i	0.796261	−	1.37916i	0.922036	−	0.387105i	$-0.126525\pi$
$84$		0			0
$85$	−2.37487	+	13.4685i	−0.257591	+	1.46087i
$86$		0			0
$87$	−1.99008	−	3.44692i	−0.213359	−	0.369548i
$88$		0			0
$89$	−3.25584	−	2.73198i	−0.345119	−	0.289589i	0.453708	−	0.891151i	$-0.350101\pi$
$89$	−3.25584	−	2.73198i	−0.345119	−	0.289589i	−0.798826	+	0.601562i	$0.794545\pi$
$90$		0			0
$91$	6.84974	−	2.49310i	0.718048	−	0.261348i
$92$		0			0
$93$	1.19284	+	6.76493i	0.123692	+	0.701490i
$94$		0			0
$95$	−8.02347	+	0.770260i	−0.823191	+	0.0790270i
$96$		0			0
$97$	−0.769831	−	4.36593i	−0.0781645	−	0.443293i	−0.998623	−	0.0524535i	$-0.983296\pi$
$97$	−0.769831	−	4.36593i	−0.0781645	−	0.443293i	0.920459	−	0.390839i	$-0.127815\pi$
$98$		0			0
$99$	4.95978	−	1.80521i	0.498476	−	0.181430i
$100$		0			0
$101$	−5.87762	−	4.93191i	−0.584845	−	0.490743i	0.301689	−	0.953406i	$-0.402450\pi$
$101$	−5.87762	−	4.93191i	−0.584845	−	0.490743i	−0.886534	+	0.462663i	$0.846894\pi$
$102$		0			0
$103$	−7.01144	−	12.1442i	−0.690858	−	1.19660i	−0.971557	−	0.236805i	$-0.923900\pi$
$103$	−7.01144	−	12.1442i	−0.690858	−	1.19660i	0.280699	−	0.959796i	$-0.409434\pi$
$104$		0			0
$105$	0.698846	−	3.96335i	0.0682004	−	0.386784i
$106$		0			0
$107$	−4.28231	+	7.41718i	−0.413987	+	0.717046i	−0.995322	−	0.0966183i	$-0.969197\pi$
$107$	−4.28231	+	7.41718i	−0.413987	+	0.717046i	0.581335	+	0.813665i	$0.302531\pi$
$108$		0			0
$109$	3.35021	+	1.21938i	0.320892	+	0.116795i	0.497444	−	0.867496i	$-0.334272\pi$
$109$	3.35021	+	1.21938i	0.320892	+	0.116795i	−0.176552	+	0.984291i	$0.556494\pi$
$110$		0			0
$111$	−12.4353	+	10.4345i	−1.18031	+	0.990395i
$112$		0			0
$113$	11.9292			1.12220			0.561101	−	0.827748i	$-0.310378\pi$
$113$	11.9292			1.12220			0.561101	+	0.827748i	$0.310378\pi$
$114$		0			0
$115$	−6.29836			−0.587325
$116$		0			0
$117$	3.59157	−	3.01368i	0.332040	−	0.278615i
$118$		0			0
$119$	10.6595	+	3.87973i	0.977153	+	0.355655i
$120$		0			0
$121$	−8.81270	+	15.2640i	−0.801154	+	1.38764i
$122$		0			0
$123$	0.155970	−	0.884548i	0.0140633	−	0.0797570i
$124$		0			0
$125$	6.08430	+	10.5383i	0.544196	+	0.942575i
$126$		0			0
$127$	6.79090	+	5.69824i	0.602595	+	0.505637i	0.892278	−	0.451485i	$-0.149106\pi$
$127$	6.79090	+	5.69824i	0.602595	+	0.505637i	−0.289684	+	0.957122i	$0.593550\pi$
$128$		0			0
$129$	5.75085	−	2.09314i	0.506334	−	0.184291i
$130$		0			0
$131$	−0.922512	−	5.23183i	−0.0806003	−	0.457107i	−0.998220	−	0.0596464i	$-0.981003\pi$
$131$	−0.922512	−	5.23183i	−0.0806003	−	0.457107i	0.917619	−	0.397460i	$-0.130108\pi$
$132$		0			0
$133$	−0.526444	+	6.66476i	−0.0456484	+	0.577908i
$134$		0			0
$135$	−1.81642	−	10.3014i	−0.156332	−	0.886604i
$136$		0			0
$137$	0.0952647	−	0.0346735i	0.00813902	−	0.00296236i	−0.337947	−	0.941165i	$-0.609733\pi$
$137$	0.0952647	−	0.0346735i	0.00813902	−	0.00296236i	0.346086	+	0.938203i	$0.387510\pi$
$138$		0			0
$139$	−10.2636	−	8.61217i	−0.870546	−	0.730475i	0.0936671	−	0.995604i	$-0.470141\pi$
$139$	−10.2636	−	8.61217i	−0.870546	−	0.730475i	−0.964213	+	0.265129i	$0.914586\pi$
$140$		0			0
$141$	4.05141	+	7.01725i	0.341190	+	0.590959i
$142$		0			0
$143$	−4.41545	+	25.0413i	−0.369239	+	2.09406i
$144$		0			0
$145$	−2.59342	+	4.49193i	−0.215372	+	0.373035i
$146$		0			0
$147$	6.19707	+	2.25555i	0.511126	+	0.186035i
$148$		0			0
$149$	10.0582	−	8.43981i	0.823998	−	0.691416i	−0.129907	−	0.991526i	$-0.541468\pi$
$149$	10.0582	−	8.43981i	0.823998	−	0.691416i	0.953905	+	0.300110i	$0.0970233\pi$
$150$		0			0
$151$	−1.97618			−0.160820			−0.0804098	−	0.996762i	$-0.525623\pi$
$151$	−1.97618			−0.160820			−0.0804098	+	0.996762i	$0.525623\pi$
$152$		0			0
$153$	7.29612			0.589856
$154$		0			0
$155$	6.85754	−	5.75416i	0.550811	−	0.462185i
$156$		0			0
$157$	−3.37534	−	1.22852i	−0.269382	−	0.0980469i	0.203798	−	0.979013i	$-0.434672\pi$
$157$	−3.37534	−	1.22852i	−0.269382	−	0.0980469i	−0.473179	+	0.880966i	$0.656894\pi$
$158$		0			0
$159$	4.76903	−	8.26021i	0.378209	−	0.655077i
$160$		0			0
$161$	−0.907150	+	5.14470i	−0.0714934	+	0.405459i
$162$		0			0
$163$	2.30630	+	3.99462i	0.180643	+	0.312883i	0.942100	−	0.335333i	$-0.108849\pi$
$163$	2.30630	+	3.99462i	0.180643	+	0.312883i	−0.761457	+	0.648216i	$0.775515\pi$
$164$		0			0
$165$	10.7543	+	9.02393i	0.837221	+	0.702512i
$166$		0			0
$167$	15.0068	−	5.46203i	1.16126	−	0.422665i	0.311714	−	0.950176i	$-0.399097\pi$
$167$	15.0068	−	5.46203i	1.16126	−	0.422665i	0.849548	+	0.527511i	$0.176875\pi$
$168$		0			0
$169$	1.66477	+	9.44138i	0.128059	+	0.726260i
$170$		0			0
$171$	1.14796	+	4.14402i	0.0877871	+	0.316901i
$172$		0			0
$173$	−4.12228	−	23.3786i	−0.313411	−	1.77744i	−0.580995	−	0.813907i	$-0.697336\pi$
$173$	−4.12228	−	23.3786i	−0.313411	−	1.77744i	0.267584	−	0.963535i	$-0.413775\pi$
$174$		0			0
$175$	2.27801	−	0.829127i	0.172201	−	0.0626761i
$176$		0			0
$177$	9.10419	+	7.63932i	0.684312	+	0.574206i
$178$		0			0
$179$	0.880099	+	1.52438i	0.0657817	+	0.113937i	0.897040	−	0.441948i	$-0.145713\pi$
$179$	0.880099	+	1.52438i	0.0657817	+	0.113937i	−0.831259	+	0.555886i	$0.812379\pi$
$180$		0			0
$181$	−0.573930	+	3.25492i	−0.0426599	+	0.241936i	−0.998680	−	0.0513651i	$-0.983643\pi$
$181$	−0.573930	+	3.25492i	−0.0426599	+	0.241936i	0.956020	+	0.293301i	$0.0947539\pi$
$182$		0			0
$183$	3.54480	−	6.13978i	0.262040	−	0.453866i
$184$		0			0
$185$	19.8788	+	7.23530i	1.46152	+	0.531950i
$186$		0			0
$187$	−30.3125	+	25.4352i	−2.21667	+	1.86000i
$188$		0			0
$189$	−8.67613			−0.631096
$190$		0			0
$191$	−2.61309			−0.189077			−0.0945384	−	0.995521i	$-0.530138\pi$
$191$	−2.61309			−0.189077			−0.0945384	+	0.995521i	$0.530138\pi$
$192$		0			0
$193$	6.68801	−	5.61191i	0.481413	−	0.403954i	−0.369524	−	0.929221i	$-0.620479\pi$
$193$	6.68801	−	5.61191i	0.481413	−	0.403954i	0.850937	+	0.525267i	$0.176035\pi$
$194$		0			0
$195$	11.7184	+	4.26514i	0.839171	+	0.305433i
$196$		0			0
$197$	−7.61620	+	13.1916i	−0.542631	+	0.939865i	0.456120	+	0.889918i	$0.349239\pi$
$197$	−7.61620	+	13.1916i	−0.542631	+	0.939865i	−0.998752	+	0.0499472i	$0.984095\pi$
$198$		0			0
$199$	2.87608	−	16.3111i	0.203880	−	1.15626i	−0.695313	−	0.718707i	$-0.744734\pi$
$199$	2.87608	−	16.3111i	0.203880	−	1.15626i	0.899193	−	0.437553i	$-0.144155\pi$
$200$		0			0
$201$	−4.02421	−	6.97014i	−0.283846	−	0.491636i
$202$		0			0
$203$	3.29563	+	2.76536i	0.231308	+	0.194090i
$204$		0			0
$205$	−1.09991	+	0.400336i	−0.0768213	+	0.0279607i
$206$		0			0
$207$	0.583473	+	3.30904i	0.0405542	+	0.229994i
$208$		0			0
$209$	−19.2159	−	13.2148i	−1.32919	−	0.914088i
$210$		0			0
$211$	3.65041	+	20.7025i	0.251304	+	1.42522i	0.805384	+	0.592754i	$0.201959\pi$
$211$	3.65041	+	20.7025i	0.251304	+	1.42522i	−0.554079	+	0.832464i	$0.686930\pi$
$212$		0			0
$213$	1.25681	−	0.457441i	0.0861150	−	0.0313433i
$214$		0			0
$215$	−6.10946	−	5.12645i	−0.416662	−	0.349621i
$216$		0			0
$217$	−3.71249	−	6.43022i	−0.252020	−	0.436512i
$218$		0			0
$219$	−3.14055	+	17.8109i	−0.212218	+	1.20355i
$220$		0			0
$221$	−17.5748	+	30.4405i	−1.18221	+	2.04765i
$222$		0			0
$223$	4.44581	+	1.61814i	0.297713	+	0.108359i	0.486558	−	0.873648i	$-0.338252\pi$
$223$	4.44581	+	1.61814i	0.297713	+	0.108359i	−0.188845	+	0.982007i	$0.560474\pi$
$224$		0			0
$225$	1.19444	−	1.00226i	0.0796295	−	0.0668171i
$226$		0			0
$227$	−27.7975			−1.84498			−0.922491	−	0.386019i	$-0.873850\pi$
$227$	−27.7975			−1.84498			−0.922491	+	0.386019i	$0.873850\pi$
$228$		0			0
$229$	8.62256			0.569795			0.284898	−	0.958558i	$-0.408040\pi$
$229$	8.62256			0.569795			0.284898	+	0.958558i	$0.408040\pi$
$230$		0			0
$231$	8.91997	−	7.48474i	0.586891	−	0.492460i
$232$		0			0
$233$	17.2604	+	6.28228i	1.13077	+	0.411566i	0.838571	−	0.544793i	$-0.183392\pi$
$233$	17.2604	+	6.28228i	1.13077	+	0.411566i	0.292197	+	0.956358i	$0.405614\pi$
$234$		0			0
$235$	5.27969	−	9.14470i	0.344409	−	0.596534i
$236$		0			0
$237$	2.79253	−	15.8372i	0.181394	−	1.02874i
$238$		0			0
$239$	−8.21304	−	14.2254i	−0.531258	−	0.920165i	−0.999334	−	0.0364774i	$-0.988386\pi$
$239$	−8.21304	−	14.2254i	−0.531258	−	0.920165i	0.468077	−	0.883688i	$-0.344947\pi$
$240$		0			0
$241$	−6.99933	−	5.87313i	−0.450866	−	0.378322i	0.388891	−	0.921284i	$-0.372858\pi$
$241$	−6.99933	−	5.87313i	−0.450866	−	0.378322i	−0.839757	+	0.542962i	$0.817303\pi$
$242$		0			0
$243$	−9.19012	+	3.34493i	−0.589547	+	0.214577i
$244$		0			0
$245$	−1.49236	−	8.46359i	−0.0953433	−	0.540719i
$246$		0			0
$247$	−20.0547	−	5.19260i	−1.27605	−	0.330398i
$248$		0			0
$249$	−3.57495	−	20.2745i	−0.226553	−	1.28485i
$250$		0			0
$251$	7.52935	−	2.74046i	0.475248	−	0.172976i	−0.0932801	−	0.995640i	$-0.529735\pi$
$251$	7.52935	−	2.74046i	0.475248	−	0.172976i	0.568528	+	0.822664i	$0.307513\pi$
$252$		0			0
$253$	−13.9598	−	11.7137i	−0.877646	−	0.736433i
$254$		0			0
$255$	9.70318	+	16.8064i	0.607637	+	1.05246i
$256$		0			0
$257$	0.284719	−	1.61472i	0.0177603	−	0.100724i	−0.974639	−	0.223783i	$-0.928159\pi$
$257$	0.284719	−	1.61472i	0.0177603	−	0.100724i	0.992399	+	0.123059i	$0.0392705\pi$
$258$		0			0
$259$	8.77316	−	15.1956i	0.545138	−	0.944206i
$260$		0			0
$261$	2.60023	+	0.946406i	0.160950	+	0.0585810i
$262$		0			0
$263$	22.4066	−	18.8014i	1.38165	−	1.15934i	0.413056	−	0.910706i	$-0.364461\pi$
$263$	22.4066	−	18.8014i	1.38165	−	1.15934i	0.968596	−	0.248639i	$-0.0799831\pi$
$264$		0			0
$265$	−12.4298			−0.763554
$266$		0			0
$267$	−6.03094			−0.369087
$268$		0			0
$269$	2.76560	−	2.32062i	0.168622	−	0.141491i	−0.554572	−	0.832136i	$-0.687118\pi$
$269$	2.76560	−	2.32062i	0.168622	−	0.141491i	0.723194	+	0.690645i	$0.242673\pi$
$270$		0			0
$271$	29.1084	+	10.5946i	1.76821	+	0.643575i	0.999994	+	0.00338286i	$0.00107680\pi$
$271$	29.1084	+	10.5946i	1.76821	+	0.643575i	0.768215	+	0.640193i	$0.221145\pi$
$272$		0			0
$273$	5.17170	−	8.95764i	0.313005	−	0.542141i
$274$		0			0
$275$	−1.46844	+	8.32794i	−0.0885503	+	0.502194i
$276$		0			0
$277$	−16.1848	−	28.0329i	−0.972452	−	1.68434i	−0.688100	−	0.725616i	$-0.741555\pi$
$277$	−16.1848	−	28.0329i	−0.972452	−	1.68434i	−0.284352	−	0.958720i	$-0.591778\pi$
$278$		0			0
$279$	−3.65840	−	3.06976i	−0.219023	−	0.183782i
$280$		0			0
$281$	−1.41176	+	0.513838i	−0.0842184	+	0.0306530i	−0.383786	−	0.923422i	$-0.625380\pi$
$281$	−1.41176	+	0.513838i	−0.0842184	+	0.0306530i	0.299567	+	0.954075i	$0.403158\pi$
$282$		0			0
$283$	2.92877	+	16.6099i	0.174097	+	0.987354i	0.939181	+	0.343423i	$0.111587\pi$
$283$	2.92877	+	16.6099i	0.174097	+	0.987354i	−0.765083	+	0.643931i	$0.777302\pi$
$284$		0			0
$285$	−8.01895	+	8.15548i	−0.475001	+	0.483089i
$286$		0			0
$287$	0.168587	+	0.956104i	0.00995137	+	0.0564370i
$288$		0			0
$289$	−35.4259	+	12.8940i	−2.08388	+	0.758469i
$290$		0			0
$291$	−4.81897	−	4.04360i	−0.282493	−	0.237040i
$292$		0			0
$293$	−3.08589	−	5.34491i	−0.180279	−	0.312253i	0.761696	−	0.647934i	$-0.224367\pi$
$293$	−3.08589	−	5.34491i	−0.180279	−	0.312253i	−0.941976	+	0.335681i	$0.891034\pi$
$294$		0			0
$295$	2.68943	−	15.2525i	0.156585	−	0.888035i
$296$		0			0
$297$	15.1326	−	26.2104i	0.878082	−	1.52088i
$298$		0			0
$299$	−15.2113	−	5.53645i	−0.879690	−	0.320181i
$300$		0			0
$301$	−5.06739	+	4.25204i	−0.292079	+	0.245084i
$302$		0			0
$303$	−10.8874			−0.625463
$304$		0			0
$305$	−9.23900			−0.529024
$306$		0			0
$307$	9.02766	−	7.57511i	0.515236	−	0.432334i	−0.347731	−	0.937594i	$-0.613048\pi$
$307$	9.02766	−	7.57511i	0.515236	−	0.432334i	0.862967	+	0.505260i	$0.168603\pi$
$308$		0			0
$309$	−18.6981	−	6.80556i	−1.06370	−	0.387155i
$310$		0			0
$311$	7.86503	−	13.6226i	0.445985	−	0.772469i	−0.552135	−	0.833755i	$-0.686187\pi$
$311$	7.86503	−	13.6226i	0.445985	−	0.772469i	0.998120	+	0.0612857i	$0.0195201\pi$
$312$		0			0
$313$	−2.57800	+	14.6205i	−0.145717	+	0.826402i	0.821072	+	0.570825i	$0.193377\pi$
$313$	−2.57800	+	14.6205i	−0.145717	+	0.826402i	−0.966789	+	0.255577i	$0.917735\pi$
$314$		0			0
$315$	1.39896	+	2.42308i	0.0788227	+	0.136525i
$316$		0			0
$317$	−7.25312	−	6.08609i	−0.407376	−	0.341829i	0.415960	−	0.909383i	$-0.363445\pi$
$317$	−7.25312	−	6.08609i	−0.407376	−	0.341829i	−0.823336	+	0.567554i	$0.807890\pi$
$318$		0			0
$319$	−14.1022	+	5.13278i	−0.789571	+	0.287380i
$320$		0			0
$321$	2.11035	+	11.9684i	0.117788	+	0.668009i
$322$		0			0
$323$	−18.7132	−	26.2508i	−1.04123	−	1.46063i
$324$		0			0
$325$	1.30440	+	7.39761i	0.0723550	+	0.410346i
$326$		0			0
$327$	4.75387	−	1.73027i	0.262890	−	0.0956840i
$328$		0			0
$329$	−6.70925	−	5.62973i	−0.369893	−	0.310377i
$330$		0			0
$331$	9.38160	+	16.2494i	0.515659	+	0.893148i	0.999835	+	0.0181773i	$0.00578633\pi$
$331$	9.38160	+	16.2494i	0.515659	+	0.893148i	−0.484175	+	0.874971i	$0.660880\pi$
$332$		0			0
$333$	1.95974	−	11.1142i	0.107393	−	0.609056i
$334$		0			0
$335$	−5.24425	+	9.08331i	−0.286524	+	0.496274i
$336$		0			0
$337$	5.21245	+	1.89718i	0.283940	+	0.103346i	0.480064	−	0.877233i	$-0.340613\pi$
$337$	5.21245	+	1.89718i	0.283940	+	0.103346i	−0.196124	+	0.980579i	$0.562836\pi$
$338$		0			0
$339$	12.9670	−	10.8806i	0.704270	−	0.590952i
$340$		0			0
$341$	25.9008			1.40260
$342$		0			0
$343$	−17.8646			−0.964599
$344$		0			0
$345$	−6.84631	+	5.74474i	−0.368593	+	0.309286i
$346$		0			0
$347$	−13.7015	−	4.98693i	−0.735534	−	0.267712i	−0.0530284	−	0.998593i	$-0.516887\pi$
$347$	−13.7015	−	4.98693i	−0.735534	−	0.267712i	−0.682505	+	0.730881i	$0.739110\pi$
$348$		0			0
$349$	4.12854	−	7.15084i	0.220996	−	0.382776i	−0.734115	−	0.679025i	$-0.762403\pi$
$349$	4.12854	−	7.15084i	0.220996	−	0.382776i	0.955111	+	0.296250i	$0.0957360\pi$
$350$		0			0
$351$	4.66839	−	26.4758i	0.249180	−	1.41317i
$352$		0			0
$353$	−3.69832	−	6.40567i	−0.196841	−	0.340939i	0.750661	−	0.660687i	$-0.229735\pi$
$353$	−3.69832	−	6.40567i	−0.196841	−	0.340939i	−0.947503	+	0.319748i	$0.896402\pi$
$354$		0			0
$355$	−1.33518	−	1.12035i	−0.0708639	−	0.0594619i
$356$		0			0
$357$	15.1255	−	5.50525i	0.800529	−	0.291369i
$358$		0			0
$359$	3.47951	+	19.7333i	0.183642	+	1.04148i	0.927688	+	0.373355i	$0.121793\pi$
$359$	3.47951	+	19.7333i	0.183642	+	1.04148i	−0.744047	+	0.668127i	$0.767096\pi$
$360$		0			0
$361$	11.9655	−	14.7589i	0.629764	−	0.776786i
$362$		0			0
$363$	4.34294	+	24.6300i	0.227945	+	1.29274i
$364$		0			0
$365$	22.1474	−	8.06100i	1.15925	−	0.421932i
$366$		0			0
$367$	−24.2657	−	20.3614i	−1.26666	−	1.06285i	−0.994939	−	0.100479i	$-0.967963\pi$
$367$	−24.2657	−	20.3614i	−1.26666	−	1.06285i	−0.271722	−	0.962376i	$-0.587593\pi$
$368$		0			0
$369$	0.312223	+	0.540787i	0.0162537	+	0.0281522i
$370$		0			0
$371$	−1.79025	+	10.1530i	−0.0929453	+	0.527119i
$372$		0			0
$373$	−14.0210	+	24.2850i	−0.725977	+	1.25743i	0.232593	+	0.972574i	$0.425279\pi$
$373$	−14.0210	+	24.2850i	−0.725977	+	1.25743i	−0.958570	+	0.284855i	$0.908054\pi$
$374$		0			0
$375$	16.2256	+	5.90564i	0.837887	+	0.304966i
$376$		0			0
$377$	−10.2119	+	8.56884i	−0.525942	+	0.441318i
$378$		0			0
$379$	15.7255			0.807762			0.403881	−	0.914811i	$-0.367661\pi$
$379$	15.7255			0.807762			0.403881	+	0.914811i	$0.367661\pi$
$380$		0			0
$381$	12.5791			0.644445
$382$		0			0
$383$	19.5269	−	16.3851i	0.997780	−	0.837237i	0.0111048	−	0.999938i	$-0.496465\pi$
$383$	19.5269	−	16.3851i	0.997780	−	0.837237i	0.986675	+	0.162701i	$0.0520207\pi$
$384$		0			0
$385$	−14.2593	−	5.18996i	−0.726720	−	0.264505i
$386$		0			0
$387$	−2.12736	+	3.68470i	−0.108140	+	0.187304i
$388$		0			0
$389$	5.58225	−	31.6585i	0.283031	−	1.60515i	−0.429203	−	0.903208i	$-0.641206\pi$
$389$	5.58225	−	31.6585i	0.283031	−	1.60515i	0.712234	−	0.701942i	$-0.247683\pi$
$390$		0			0
$391$	−12.5954	−	21.8159i	−0.636976	−	1.10328i
$392$		0			0
$393$	−5.77472	−	4.84557i	−0.291296	−	0.244426i
$394$		0			0
$395$	−19.6932	+	7.16773i	−0.990871	+	0.360648i
$396$		0			0
$397$	0.896131	+	5.08221i	0.0449755	+	0.255069i	0.999003	−	0.0446514i	$-0.0142177\pi$
$397$	0.896131	+	5.08221i	0.0449755	+	0.255069i	−0.954027	+	0.299720i	$0.903107\pi$
$398$		0			0
$399$	5.50669	+	7.72476i	0.275679	+	0.386722i
$400$		0			0
$401$	2.51277	+	14.2506i	0.125482	+	0.711643i	0.981020	+	0.193904i	$0.0621151\pi$
$401$	2.51277	+	14.2506i	0.125482	+	0.711643i	−0.855539	+	0.517739i	$0.826774\pi$
$402$		0			0
$403$	21.6198	−	7.86897i	1.07696	−	0.391981i
$404$		0			0
$405$	−7.17805	−	6.02310i	−0.356680	−	0.299290i
$406$		0			0
$407$	30.6036	+	53.0071i	1.51697	+	2.62746i
$408$		0			0
$409$	2.84780	−	16.1507i	0.140814	−	0.798599i	−0.829819	−	0.558033i	$-0.811556\pi$
$409$	2.84780	−	16.1507i	0.140814	−	0.798599i	0.970633	−	0.240565i	$-0.0773328\pi$
$410$		0			0
$411$	0.0719269	−	0.124581i	0.00354789	−	0.00614513i
$412$		0			0
$413$	−12.0714	−	4.39362i	−0.593993	−	0.216196i
$414$		0			0
$415$	−20.5521	+	17.2452i	−1.00886	+	0.846536i
$416$		0			0
$417$	−19.0117			−0.931005
$418$		0			0
$419$	3.21866			0.157242			0.0786208	−	0.996905i	$-0.474948\pi$
$419$	3.21866			0.157242			0.0786208	+	0.996905i	$0.474948\pi$
$420$		0			0
$421$	−24.2300	+	20.3314i	−1.18090	+	0.990892i	−0.180927	+	0.983497i	$0.557910\pi$
$421$	−24.2300	+	20.3314i	−1.18090	+	0.990892i	−0.999973	+	0.00739596i	$0.997646\pi$
$422$		0			0
$423$	−5.29356	−	1.92670i	−0.257382	−	0.0936792i
$424$		0			0
$425$	−5.84483	+	10.1236i	−0.283516	+	0.491064i
$426$		0			0
$427$	−1.33069	+	7.54671i	−0.0643965	+	0.365211i
$428$		0			0
$429$	18.0406	+	31.2472i	0.871007	+	1.50863i
$430$		0			0
$431$	22.5060	+	18.8848i	1.08408	+	0.909649i	0.996253	−	0.0864868i	$-0.0275641\pi$
$431$	22.5060	+	18.8848i	1.08408	+	0.909649i	0.0878246	+	0.996136i	$0.472008\pi$
$432$		0			0
$433$	−13.4487	+	4.89494i	−0.646305	+	0.235236i	−0.644313	−	0.764762i	$-0.722856\pi$
$433$	−13.4487	+	4.89494i	−0.646305	+	0.235236i	−0.00199228	+	0.999998i	$0.500634\pi$
$434$		0			0
$435$	1.27805	+	7.24818i	0.0612778	+	0.347524i
$436$		0			0
$437$	10.4091	−	10.5864i	0.497937	−	0.506415i
$438$		0			0
$439$	6.31807	+	35.8316i	0.301545	+	1.71015i	0.639337	+	0.768926i	$0.279209\pi$
$439$	6.31807	+	35.8316i	0.301545	+	1.71015i	−0.337792	+	0.941221i	$0.609680\pi$
$440$		0			0
$441$	−4.30836	+	1.56811i	−0.205160	+	0.0746721i
$442$		0			0
$443$	−21.6366	−	18.1552i	−1.02798	−	0.862581i	−0.0373743	−	0.999301i	$-0.511899\pi$
$443$	−21.6366	−	18.1552i	−1.02798	−	0.862581i	−0.990610	+	0.136720i	$0.956344\pi$
$444$		0			0
$445$	3.92968	+	6.80641i	0.186285	+	0.322655i
$446$		0			0
$447$	3.23527	−	18.3481i	0.153023	−	0.867837i
$448$		0			0
$449$	14.0079	−	24.2623i	0.661072	−	1.14501i	−0.319263	−	0.947666i	$-0.603435\pi$
$449$	14.0079	−	24.2623i	0.661072	−	1.14501i	0.980334	−	0.197343i	$-0.0632314\pi$
$450$		0			0
$451$	−3.18241	−	1.15830i	−0.149854	−	0.0545424i
$452$		0			0
$453$	−2.14811	+	1.80248i	−0.100927	+	0.0846878i
$454$		0			0
$455$	−13.4793			−0.631917
$456$		0			0
$457$	−2.39211			−0.111898			−0.0559492	−	0.998434i	$-0.517818\pi$
$457$	−2.39211			−0.111898			−0.0559492	+	0.998434i	$0.517818\pi$
$458$		0			0
$459$	32.0489	−	26.8922i	1.49591	−	1.25522i
$460$		0			0
$461$	2.11543	+	0.769955i	0.0985256	+	0.0358604i	0.390813	−	0.920470i	$-0.372194\pi$
$461$	2.11543	+	0.769955i	0.0985256	+	0.0358604i	−0.292287	+	0.956331i	$0.594416\pi$
$462$		0			0
$463$	−5.17068	+	8.95589i	−0.240302	+	0.416215i	−0.960800	−	0.277241i	$-0.910580\pi$
$463$	−5.17068	+	8.95589i	−0.240302	+	0.416215i	0.720498	+	0.693457i	$0.243913\pi$
$464$		0			0
$465$	2.20577	−	12.5095i	0.102290	−	0.580115i
$466$		0			0
$467$	−8.89242	−	15.4021i	−0.411492	−	0.712726i	0.583561	−	0.812069i	$-0.301659\pi$
$467$	−8.89242	−	15.4021i	−0.411492	−	0.712726i	−0.995053	+	0.0993438i	$0.968326\pi$
$468$		0			0
$469$	6.66421	+	5.59194i	0.307725	+	0.258212i
$470$		0			0
$471$	−4.78953	+	1.74325i	−0.220690	+	0.0803245i
$472$		0			0
$473$	−4.00698	−	22.7247i	−0.184241	−	1.04488i
$474$		0			0
$475$	−6.66956	−	1.72690i	−0.306020	−	0.0792355i
$476$		0			0
$477$	1.15148	+	6.53036i	0.0527226	+	0.299005i
$478$		0			0
$479$	−36.8020	+	13.3948i	−1.68153	+	0.612026i	−0.993518	−	0.113675i	$-0.963738\pi$
$479$	−36.8020	+	13.3948i	−1.68153	+	0.612026i	−0.688010	+	0.725701i	$0.741516\pi$
$480$		0			0
$481$	41.6496	+	34.9482i	1.89906	+	1.59350i
$482$		0			0
$483$	3.70641	+	6.41969i	0.168648	+	0.292106i
$484$		0			0
$485$	−1.42355	+	8.07336i	−0.0646401	+	0.366592i
$486$		0			0
$487$	7.13779	−	12.3630i	0.323444	−	0.560221i	−0.657752	−	0.753234i	$-0.728493\pi$
$487$	7.13779	−	12.3630i	0.323444	−	0.560221i	0.981196	+	0.193013i	$0.0618259\pi$
$488$		0			0
$489$	6.15043	+	2.23857i	0.278132	+	0.101232i
$490$		0			0
$491$	−15.7330	+	13.2016i	−0.710021	+	0.595778i	−0.924605	−	0.380927i	$-0.875605\pi$
$491$	−15.7330	+	13.2016i	−0.710021	+	0.595778i	0.214584	+	0.976705i	$0.431160\pi$
$492$		0			0
$493$	−20.7452			−0.934315
$494$		0			0
$495$	−9.76009			−0.438683
$496$		0			0
$497$	−1.10744	+	0.929253i	−0.0496755	+	0.0416827i
$498$		0			0
$499$	1.01367	+	0.368944i	0.0453779	+	0.0165162i	0.364609	−	0.931161i	$-0.381203\pi$
$499$	1.01367	+	0.368944i	0.0453779	+	0.0165162i	−0.319231	+	0.947677i	$0.603425\pi$
$500$		0			0
$501$	11.3305	−	19.6249i	0.506208	−	0.876777i
$502$		0			0
$503$	−0.306899	+	1.74051i	−0.0136840	+	0.0776056i	−0.990885	−	0.134711i	$-0.956990\pi$
$503$	−0.306899	+	1.74051i	−0.0136840	+	0.0776056i	0.977201	+	0.212316i	$0.0681007\pi$
$504$		0			0
$505$	7.09407	+	12.2873i	0.315682	+	0.546777i
$506$		0			0
$507$	10.4211	+	8.74433i	0.462817	+	0.388349i
$508$		0			0
$509$	−7.79585	+	2.83746i	−0.345545	+	0.125768i	−0.508962	−	0.860789i	$-0.669971\pi$
$509$	−7.79585	+	2.83746i	−0.345545	+	0.125768i	0.163417	+	0.986557i	$0.447748\pi$
$510$		0			0
$511$	−3.39460	−	19.2517i	−0.150168	−	0.851647i
$512$		0			0
$513$	20.3167	+	13.9718i	0.897004	+	0.616871i
$514$		0			0
$515$	4.50283	+	25.5368i	0.198418	+	1.12529i
$516$		0			0
$517$	28.7093	−	10.4493i	1.26263	−	0.459561i
$518$		0			0
$519$	−25.8045	−	21.6526i	−1.13269	−	0.950443i
$520$		0			0
$521$	10.3658	+	17.9541i	0.454134	+	0.786584i	0.998638	−	0.0521747i	$-0.0166153\pi$
$521$	10.3658	+	17.9541i	0.454134	+	0.786584i	−0.544504	+	0.838759i	$0.683282\pi$
$522$		0			0
$523$	−3.85107	+	21.8405i	−0.168396	+	0.955019i	0.777098	+	0.629379i	$0.216691\pi$
$523$	−3.85107	+	21.8405i	−0.168396	+	0.955019i	−0.945494	+	0.325640i	$0.894420\pi$
$524$		0			0
$525$	1.71994	−	2.97903i	0.0750645	−	0.130016i
$526$		0			0
$527$	33.6445	+	12.2456i	1.46558	+	0.533427i
$528$		0			0
$529$	−8.73205	+	7.32706i	−0.379654	+	0.318568i
$530$		0			0
$531$	−8.26252			−0.358563
$532$		0			0
$533$	−3.00832			−0.130305
$534$		0			0
$535$	12.1322	−	10.1801i	0.524521	−	0.440126i
$536$		0			0
$537$	2.34705	+	0.854256i	0.101283	+	0.0368639i
$538$		0			0
$539$	12.4329	−	21.5344i	0.535522	−	0.927551i
$540$		0			0
$541$	−5.48845	+	31.1266i	−0.235967	+	1.33824i	0.604600	+	0.796529i	$0.293333\pi$
$541$	−5.48845	+	31.1266i	−0.235967	+	1.33824i	−0.840567	+	0.541707i	$0.817778\pi$
$542$		0			0
$543$	2.34495	+	4.06157i	0.100631	+	0.174299i
$544$		0			0
$545$	−5.05031	−	4.23771i	−0.216332	−	0.181524i
$546$		0			0
$547$	11.8022	−	4.29566i	0.504627	−	0.183669i	−0.0771470	−	0.997020i	$-0.524581\pi$
$547$	11.8022	−	4.29566i	0.504627	−	0.183669i	0.581774	+	0.813351i	$0.302359\pi$
$548$		0			0
$549$	0.855890	+	4.85399i	0.0365285	+	0.207163i
$550$		0			0
$551$	−3.26402	−	11.7828i	−0.139052	−	0.501962i
$552$		0			0
$553$	3.01843	+	17.1184i	0.128357	+	0.727947i
$554$		0			0
$555$	28.2076	−	10.2667i	1.19734	−	0.435798i
$556$		0			0
$557$	−16.9277	−	14.2041i	−0.717251	−	0.601845i	0.209372	−	0.977836i	$-0.432858\pi$
$557$	−16.9277	−	14.2041i	−0.717251	−	0.601845i	−0.926623	+	0.375991i	$0.877302\pi$
$558$		0			0
$559$	−10.2488	−	17.7514i	−0.433476	−	0.750802i
$560$		0			0
$561$	−9.75018	+	55.2960i	−0.411653	+	2.33460i
$562$		0			0
$563$	13.4589	−	23.3116i	0.567227	−	0.982465i	−0.429612	−	0.903014i	$-0.641350\pi$
$563$	13.4589	−	23.3116i	0.567227	−	0.982465i	0.996839	−	0.0794519i	$-0.0253170\pi$
$564$		0			0
$565$	−20.7288	−	7.54465i	−0.872065	−	0.317406i
$566$		0			0
$567$	−5.95371	+	4.99575i	−0.250032	+	0.209802i
$568$		0			0
$569$	32.4635			1.36094			0.680470	−	0.732776i	$-0.261776\pi$
$569$	32.4635			1.36094			0.680470	+	0.732776i	$0.261776\pi$
$570$		0			0
$571$	15.8562			0.663562			0.331781	−	0.943356i	$-0.392350\pi$
$571$	15.8562			0.663562			0.331781	+	0.943356i	$0.392350\pi$
$572$		0			0
$573$	−2.84043	+	2.38340i	−0.118661	+	0.0995681i
$574$		0			0
$575$	−5.05879	−	1.84125i	−0.210966	−	0.0767854i
$576$		0			0
$577$	17.5676	−	30.4281i	0.731351	−	1.26674i	−0.224955	−	0.974369i	$-0.572224\pi$
$577$	17.5676	−	30.4281i	0.731351	−	1.26674i	0.956306	−	0.292368i	$-0.0944431\pi$
$578$		0			0
$579$	2.15124	−	12.2003i	0.0894023	−	0.507026i
$580$		0			0
$581$	11.1264	+	19.2714i	0.461599	+	0.799513i
$582$		0			0
$583$	−27.5496	−	23.1168i	−1.14099	−	0.957402i
$584$		0			0
$585$	−8.14692	+	2.96524i	−0.336834	+	0.122597i
$586$		0			0
$587$	−3.63024	−	20.5881i	−0.149836	−	0.849761i	−0.963356	−	0.268225i	$-0.913563\pi$
$587$	−3.63024	−	20.5881i	−0.149836	−	0.849761i	0.813520	−	0.581536i	$-0.197548\pi$
$588$		0			0
$589$	−1.66161	+	21.0360i	−0.0684656	+	0.866773i
$590$		0			0
$591$	3.75330	+	21.2860i	0.154390	+	0.875590i
$592$		0			0
$593$	27.1765	−	9.89143i	1.11600	−	0.406192i	0.282812	−	0.959175i	$-0.408733\pi$
$593$	27.1765	−	9.89143i	1.11600	−	0.406192i	0.833192	+	0.552983i	$0.186511\pi$
$594$		0			0
$595$	−16.0687	−	13.4833i	−0.658754	−	0.552760i
$596$		0			0
$597$	−11.7510	−	20.3534i	−0.480937	−	0.833008i
$598$		0			0
$599$	−5.90825	+	33.5074i	−0.241405	+	1.36907i	0.587291	+	0.809376i	$0.300194\pi$
$599$	−5.90825	+	33.5074i	−0.241405	+	1.36907i	−0.828696	+	0.559699i	$0.810917\pi$
$600$		0			0
$601$	0.783785	−	1.35756i	0.0319713	−	0.0553759i	−0.849597	−	0.527432i	$-0.823155\pi$
$601$	0.783785	−	1.35756i	0.0319713	−	0.0553759i	0.881568	+	0.472056i	$0.156488\pi$
$602$		0			0
$603$	5.25802	+	1.91376i	0.214123	+	0.0779344i
$604$		0			0
$605$	24.9672	−	20.9500i	1.01506	−	0.851738i
$606$		0			0
$607$	41.3263			1.67738			0.838692	−	0.544606i	$-0.183321\pi$
$607$	41.3263			1.67738			0.838692	+	0.544606i	$0.183321\pi$
$608$		0			0
$609$	6.10462			0.247372
$610$		0			0
$611$	20.7895	−	17.4445i	0.841054	−	0.705729i
$612$		0			0
$613$	31.4512	+	11.4473i	1.27030	+	0.462352i	0.887213	−	0.461359i	$-0.152638\pi$
$613$	31.4512	+	11.4473i	1.27030	+	0.462352i	0.383089	+	0.923712i	$0.374860\pi$
$614$		0			0
$615$	−0.830458	+	1.43840i	−0.0334873	+	0.0580017i
$616$		0			0
$617$	−2.25471	+	12.7871i	−0.0907713	+	0.514790i	0.905190	+	0.425007i	$0.139728\pi$
$617$	−2.25471	+	12.7871i	−0.0907713	+	0.514790i	−0.995961	+	0.0897827i	$0.971383\pi$
$618$		0			0
$619$	4.25533	+	7.37045i	0.171036	+	0.296244i	0.938782	−	0.344511i	$-0.111955\pi$
$619$	4.25533	+	7.37045i	0.171036	+	0.296244i	−0.767746	+	0.640754i	$0.778622\pi$
$620$		0			0
$621$	14.7595	+	12.3847i	0.592278	+	0.496980i
$622$		0			0
$623$	6.12568	−	2.22956i	0.245420	−	0.0893256i
$624$		0			0
$625$	−2.53510	−	14.3772i	−0.101404	−	0.575090i
$626$		0			0
$627$	−32.9409	+	3.16235i	−1.31553	+	0.126292i
$628$		0			0
$629$	14.6923	+	83.3241i	0.585819	+	3.32235i
$630$		0			0
$631$	−21.5366	+	7.83867i	−0.857357	+	0.312052i	−0.733036	−	0.680190i	$-0.761897\pi$
$631$	−21.5366	+	7.83867i	−0.857357	+	0.312052i	−0.124321	+	0.992242i	$0.539675\pi$
$632$		0			0
$633$	22.8507	+	19.1740i	0.908235	+	0.762099i
$634$		0			0
$635$	−8.19636	−	14.1965i	−0.325262	−	0.563371i
$636$		0			0
$637$	3.83553	−	21.7524i	0.151969	−	0.861860i
$638$		0			0
$639$	−0.464920	+	0.805265i	−0.0183920	+	0.0318558i
$640$		0			0
$641$	16.1115	+	5.86410i	0.636366	+	0.231618i	0.640000	−	0.768375i	$-0.278934\pi$
$641$	16.1115	+	5.86410i	0.636366	+	0.231618i	−0.00363388	+	0.999993i	$0.501157\pi$
$642$		0			0
$643$	−11.2113	+	9.40741i	−0.442131	+	0.370992i	−0.836506	−	0.547958i	$-0.815406\pi$
$643$	−11.2113	+	9.40741i	−0.442131	+	0.370992i	0.394375	+	0.918950i	$0.370961\pi$
$644$		0			0
$645$	−11.3168			−0.445599
$646$		0			0
$647$	−24.2845			−0.954722			−0.477361	−	0.878707i	$-0.658407\pi$
$647$	−24.2845			−0.954722			−0.477361	+	0.878707i	$0.658407\pi$
$648$		0			0
$649$	34.3275	−	28.8042i	1.34747	−	1.13066i
$650$		0			0
$651$	−9.90048	−	3.60348i	−0.388030	−	0.141231i
$652$		0			0
$653$	−0.136782	+	0.236914i	−0.00535270	+	0.00927115i	−0.868689	−	0.495357i	$-0.835037\pi$
$653$	−0.136782	+	0.236914i	−0.00535270	+	0.00927115i	0.863337	+	0.504628i	$0.168370\pi$
$654$		0			0
$655$	−1.70589	+	9.67456i	−0.0666544	+	0.378016i
$656$		0			0
$657$	−6.28681	−	10.8891i	−0.245272	−	0.424823i
$658$		0			0
$659$	3.89352	+	3.26705i	0.151670	+	0.127266i	0.715465	−	0.698648i	$-0.246215\pi$
$659$	3.89352	+	3.26705i	0.151670	+	0.127266i	−0.563795	+	0.825915i	$0.690659\pi$
$660$		0			0
$661$	−6.24026	+	2.27127i	−0.242718	+	0.0883421i	−0.460515	−	0.887652i	$-0.652335\pi$
$661$	−6.24026	+	2.27127i	−0.242718	+	0.0883421i	0.217797	+	0.975994i	$0.430113\pi$
$662$		0			0
$663$	8.66097	+	49.1188i	0.336364	+	1.90762i
$664$		0			0
$665$	5.12994	−	11.2481i	0.198930	−	0.436183i
$666$		0			0
$667$	−1.65900	−	9.40864i	−0.0642366	−	0.364304i
$668$		0			0
$669$	6.30849	−	2.29610i	0.243900	−	0.0887725i
$670$		0			0
$671$	−20.4775	−	17.1827i	−0.790525	−	0.663329i
$672$		0			0
$673$	−8.66947	−	15.0160i	−0.334183	−	0.578823i	0.649144	−	0.760665i	$-0.275127\pi$
$673$	−8.66947	−	15.0160i	−0.334183	−	0.578823i	−0.983328	+	0.181843i	$0.941794\pi$
$674$		0			0
$675$	1.55256	−	8.80501i	0.0597581	−	0.338905i
$676$		0			0
$677$	0.925236	−	1.60256i	0.0355597	−	0.0615912i	−0.847698	−	0.530479i	$-0.822012\pi$
$677$	0.925236	−	1.60256i	0.0355597	−	0.0615912i	0.883258	+	0.468888i	$0.155345\pi$
$678$		0			0
$679$	6.38954	+	2.32560i	0.245208	+	0.0892485i
$680$		0			0
$681$	−30.2158	+	25.3541i	−1.15787	+	0.971570i
$682$		0			0
$683$	−12.2286			−0.467913			−0.233956	−	0.972247i	$-0.575167\pi$
$683$	−12.2286			−0.467913			−0.233956	+	0.972247i	$0.575167\pi$
$684$		0			0
$685$	−0.187467			−0.00716273
$686$		0			0
$687$	9.37272	−	7.86464i	0.357591	−	0.300055i
$688$		0			0
$689$	−30.0193	−	10.9261i	−1.14364	−	0.416253i
$690$		0			0
$691$	8.39778	−	14.5454i	0.319467	−	0.553333i	−0.660910	−	0.750465i	$-0.729830\pi$
$691$	8.39778	−	14.5454i	0.319467	−	0.553333i	0.980377	+	0.197132i	$0.0631629\pi$
$692$		0			0
$693$	−1.40574	+	7.97235i	−0.0533997	+	0.302844i
$694$		0			0
$695$	12.3878	+	21.4562i	0.469894	+	0.813881i
$696$		0			0
$697$	−3.58625	−	3.00922i	−0.135839	−	0.113982i
$698$		0			0
$699$	24.4921	−	8.91440i	0.926377	−	0.337174i
$700$		0			0
$701$	1.83157	+	10.3874i	0.0691775	+	0.392325i	0.999662	+	0.0259941i	$0.00827511\pi$
$701$	1.83157	+	10.3874i	0.0691775	+	0.392325i	−0.930485	+	0.366331i	$0.880614\pi$
$702$		0			0
$703$	−45.0144	+	21.4550i	−1.69775	+	0.809190i
$704$		0			0
$705$	−2.60186	−	14.7559i	−0.0979917	−	0.555739i
$706$		0			0
$707$	11.0584	−	4.02493i	0.415894	−	0.151373i
$708$		0			0
$709$	−4.55485	−	3.82198i	−0.171061	−	0.143537i	0.553238	−	0.833023i	$-0.313392\pi$
$709$	−4.55485	−	3.82198i	−0.171061	−	0.143537i	−0.724299	+	0.689486i	$0.757836\pi$
$710$		0			0
$711$	5.59014	+	9.68241i	0.209647	+	0.363119i
$712$		0			0
$713$	−2.86323	+	16.2382i	−0.107229	+	0.608126i
$714$		0			0
$715$	23.5100	−	40.7205i	0.879225	−	1.52286i
$716$		0			0
$717$	−21.9026	−	7.97188i	−0.817966	−	0.297715i
$718$		0			0
$719$	−10.9235	+	9.16589i	−0.407377	+	0.341830i	−0.823337	−	0.567553i	$-0.807890\pi$
$719$	−10.9235	+	9.16589i	−0.407377	+	0.341830i	0.415960	+	0.909383i	$0.363446\pi$
$720$		0			0
$721$	21.5078			0.800992
$722$		0			0
$723$	−12.9651			−0.482179
$724$		0			0
$725$	−3.39617	+	2.84973i	−0.126131	+	0.105836i
$726$		0			0
$727$	16.8560	+	6.13508i	0.625154	+	0.227538i	0.635121	−	0.772413i	$-0.280950\pi$
$727$	16.8560	+	6.13508i	0.625154	+	0.227538i	−0.00996657	+	0.999950i	$0.503173\pi$
$728$		0			0
$729$	−14.5397	+	25.1834i	−0.538506	+	0.932720i
$730$		0			0
$731$	5.53902	−	31.4134i	0.204868	−	1.16187i
$732$		0			0
$733$	−13.6637	−	23.6663i	−0.504682	−	0.874134i	−0.999985	−	0.00541423i	$-0.998277\pi$
$733$	−13.6637	−	23.6663i	−0.504682	−	0.874134i	0.495304	−	0.868720i	$-0.335057\pi$
$734$		0			0
$735$	−9.34183	−	7.83873i	−0.344579	−	0.289136i
$736$		0			0
$737$	−28.5166	+	10.3792i	−1.05042	+	0.382322i
$738$		0			0
$739$	6.60447	+	37.4558i	0.242949	+	1.37783i	0.825208	+	0.564830i	$0.191058\pi$
$739$	6.60447	+	37.4558i	0.242949	+	1.37783i	−0.582258	+	0.813004i	$0.697831\pi$
$740$		0			0
$741$	−26.5356	+	12.6475i	−0.974809	+	0.464618i
$742$		0			0
$743$	1.29193	+	7.32692i	0.0473965	+	0.268799i	0.999292	−	0.0376242i	$-0.0119790\pi$
$743$	1.29193	+	7.32692i	0.0473965	+	0.268799i	−0.951896	+	0.306423i	$0.900868\pi$
$744$		0			0
$745$	−22.8154	+	8.30414i	−0.835893	+	0.304240i
$746$		0			0
$747$	10.9642	+	9.20009i	0.401161	+	0.336614i
$748$		0			0
$749$	−6.56806	−	11.3762i	−0.239992	−	0.415678i
$750$		0			0
$751$	−5.68332	+	32.2317i	−0.207387	+	1.17615i	0.686251	+	0.727365i	$0.259255\pi$
$751$	−5.68332	+	32.2317i	−0.207387	+	1.17615i	−0.893638	+	0.448788i	$0.851856\pi$
$752$		0			0
$753$	5.68482	−	9.84639i	0.207166	−	0.358823i
$754$		0			0
$755$	3.43393	+	1.24985i	0.124973	+	0.0454866i
$756$		0			0
$757$	33.3415	−	27.9768i	1.21182	−	1.01683i	0.212604	−	0.977138i	$-0.431805\pi$
$757$	33.3415	−	27.9768i	1.21182	−	1.01683i	0.999212	−	0.0396962i	$-0.0126390\pi$
$758$		0			0
$759$	−25.8583			−0.938598
$760$		0			0
$761$	−41.4407			−1.50223			−0.751113	−	0.660174i	$-0.770483\pi$
$761$	−41.4407			−1.50223			−0.751113	+	0.660174i	$0.770483\pi$
$762$		0			0
$763$	−4.18889	+	3.51490i	−0.151648	+	0.127248i
$764$		0			0
$765$	−12.6781	−	4.61446i	−0.458379	−	0.166836i
$766$		0			0
$767$	19.9027	−	34.4725i	0.718644	−	1.24473i
$768$		0			0
$769$	2.97472	−	16.8705i	0.107271	−	0.608365i	−0.883018	−	0.469340i	$-0.844492\pi$
$769$	2.97472	−	16.8705i	0.107271	−	0.608365i	0.990289	−	0.139025i	$-0.0443969\pi$
$770$		0			0
$771$	−1.16330	−	2.01489i	−0.0418952	−	0.0725645i
$772$		0			0
$773$	12.5023	+	10.4906i	0.449675	+	0.377322i	0.839315	−	0.543645i	$-0.182956\pi$
$773$	12.5023	+	10.4906i	0.449675	+	0.377322i	−0.389640	+	0.920967i	$0.627401\pi$
$774$		0			0
$775$	7.19007	−	2.61697i	0.258275	−	0.0940044i
$776$		0			0
$777$	−4.32346	−	24.5195i	−0.155103	−	0.879634i
$778$		0			0
$779$	1.14491	−	2.51037i	0.0410206	−	0.0899434i
$780$		0			0
$781$	−0.875697	−	4.96632i	−0.0313349	−	0.177709i
$782$		0			0
$783$	14.9100	−	5.42681i	0.532841	−	0.193938i
$784$		0			0
$785$	5.08819	+	4.26950i	0.181605	+	0.152385i
$786$		0			0
$787$	13.8127	+	23.9244i	0.492371	+	0.852812i	0.999961	−	0.00878661i	$-0.00279690\pi$
$787$	13.8127	+	23.9244i	0.492371	+	0.852812i	−0.507590	+	0.861599i	$0.669464\pi$
$788$		0			0
$789$	7.20722	−	40.8742i	0.256584	−	1.45516i
$790$		0			0
$791$	−9.14826	+	15.8453i	−0.325275	+	0.563392i
$792$		0			0
$793$	−22.3132	−	8.12136i	−0.792366	−	0.288398i
$794$		0			0
$795$	−13.5111	+	11.3372i	−0.479191	+	0.402089i
$796$		0			0
$797$	−1.82403			−0.0646104			−0.0323052	−	0.999478i	$-0.510285\pi$
$797$	−1.82403			−0.0646104			−0.0323052	+	0.999478i	$0.510285\pi$
$798$		0			0
$799$	42.2331			1.49410
$800$		0			0
$801$	3.21192	−	2.69512i	0.113487	−	0.0952273i
$802$		0			0
$803$	64.0798	+	23.3232i	2.26133	+	0.823056i
$804$		0			0
$805$	4.83010	−	8.36598i	0.170239	−	0.294862i
$806$		0			0
$807$	0.889573	−	5.04502i	0.0313144	−	0.177593i
$808$		0			0
$809$	−2.77501	−	4.80646i	−0.0975641	−	0.168986i	0.813112	−	0.582108i	$-0.197772\pi$
$809$	−2.77501	−	4.80646i	−0.0975641	−	0.168986i	−0.910676	+	0.413122i	$0.864438\pi$
$810$		0			0
$811$	−2.29564	−	1.92627i	−0.0806107	−	0.0676404i	0.601592	−	0.798804i	$-0.294533\pi$
$811$	−2.29564	−	1.92627i	−0.0806107	−	0.0676404i	−0.682203	+	0.731163i	$0.738978\pi$
$812$		0			0
$813$	41.3041	−	15.0335i	1.44860	−	0.527247i
$814$		0			0
$815$	−1.48113	−	8.39990i	−0.0518817	−	0.294236i
$816$		0			0
$817$	18.7135	−	1.79652i	0.654704	−	0.0628521i
$818$		0			0
$819$	1.24870	+	7.08174i	0.0436332	+	0.247456i
$820$		0			0
$821$	−39.0032	+	14.1960i	−1.36122	+	0.495443i	−0.916431	−	0.400192i	$-0.868943\pi$
$821$	−39.0032	+	14.1960i	−1.36122	+	0.495443i	−0.444788	+	0.895636i	$0.646721\pi$
$822$		0			0
$823$	7.26094	+	6.09265i	0.253100	+	0.212377i	0.760506	−	0.649331i	$-0.224951\pi$
$823$	7.26094	+	6.09265i	0.253100	+	0.212377i	−0.507406	+	0.861707i	$0.669395\pi$
$824$		0			0
$825$	5.99972	+	10.3918i	0.208884	+	0.361797i
$826$		0			0
$827$	1.93086	−	10.9505i	0.0671427	−	0.380785i	−0.932657	−	0.360765i	$-0.882516\pi$
$827$	1.93086	−	10.9505i	0.0671427	−	0.380785i	0.999800	−	0.0200206i	$-0.00637317\pi$
$828$		0			0
$829$	15.5613	−	26.9530i	0.540467	−	0.936117i	−0.458410	−	0.888741i	$-0.651581\pi$
$829$	15.5613	−	26.9530i	0.540467	−	0.936117i	0.998877	−	0.0473757i	$-0.0150858\pi$
$830$		0			0
$831$	−43.1617	−	15.7096i	−1.49726	−	0.544959i
$832$		0			0
$833$	26.3312	−	22.0945i	0.912323	−	0.765530i
$834$		0			0
$835$	−29.5311			−1.02197
$836$		0			0
$837$	−27.3845			−0.946546
$838$		0			0
$839$	2.03799	−	1.71007i	0.0703591	−	0.0590383i	−0.606930	−	0.794755i	$-0.707599\pi$
$839$	2.03799	−	1.71007i	0.0703591	−	0.0590383i	0.677289	+	0.735717i	$0.263155\pi$
$840$		0			0
$841$	19.8578	+	7.22766i	0.684753	+	0.249230i
$842$		0			0
$843$	−1.06591	+	1.84621i	−0.0367118	+	0.0635867i
$844$		0			0
$845$	3.07845	−	17.4587i	0.105902	−	0.600599i
$846$		0			0
$847$	−13.5166	−	23.4114i	−0.464436	−	0.804426i
$848$		0			0
$849$	18.3334	+	15.3836i	0.629202	+	0.527963i
$850$		0			0
$851$	−36.6153	+	13.3269i	−1.25516	+	0.456840i
$852$		0			0
$853$	8.35651	+	47.3921i	0.286122	+	1.62268i	0.701251	+	0.712914i	$0.252625\pi$
$853$	8.35651	+	47.3921i	0.286122	+	1.62268i	−0.415130	+	0.909762i	$0.636264\pi$
$854$		0			0
$855$	0.626140	−	7.92692i	0.0214135	−	0.271095i
$856$		0			0
$857$	−6.87862	−	39.0106i	−0.234969	−	1.33258i	−0.842678	−	0.538417i	$-0.819022\pi$
$857$	−6.87862	−	39.0106i	−0.234969	−	1.33258i	0.607709	−	0.794160i	$-0.292089\pi$
$858$		0			0
$859$	−21.6818	+	7.89153i	−0.739774	+	0.269256i	−0.684296	−	0.729204i	$-0.739890\pi$
$859$	−21.6818	+	7.89153i	−0.739774	+	0.269256i	−0.0554778	+	0.998460i	$0.517668\pi$
$860$		0			0
$861$	1.05532	+	0.885515i	0.0359651	+	0.0301783i
$862$		0			0
$863$	−1.42640	−	2.47059i	−0.0485551	−	0.0840999i	0.840726	−	0.541460i	$-0.182128\pi$
$863$	−1.42640	−	2.47059i	−0.0485551	−	0.0840999i	−0.889281	+	0.457360i	$0.848795\pi$
$864$		0			0
$865$	−7.62281	+	43.2311i	−0.259183	+	1.46990i
$866$		0			0
$867$	−26.7473	+	46.3277i	−0.908387	+	1.57337i
$868$		0			0
$869$	−56.9789	−	20.7386i	−1.93288	−	0.703509i
$870$		0			0
$871$	−20.6500	+	17.3274i	−0.699698	+	0.587116i
$872$		0			0
$873$	4.37347			0.148019
$874$		0			0
$875$	−18.6638			−0.630950
$876$		0			0
$877$	−8.58114	+	7.20043i	−0.289765	+	0.243141i	−0.776069	−	0.630648i	$-0.782789\pi$
$877$	−8.58114	+	7.20043i	−0.289765	+	0.243141i	0.486304	+	0.873790i	$0.338345\pi$
$878$		0			0
$879$	−8.22945	−	2.99527i	−0.277572	−	0.101028i
$880$		0			0
$881$	2.55731	−	4.42939i	0.0861580	−	0.149230i	−0.819726	−	0.572756i	$-0.805874\pi$
$881$	2.55731	−	4.42939i	0.0861580	−	0.149230i	0.905884	+	0.423526i	$0.139208\pi$
$882$		0			0
$883$	5.95509	−	33.7730i	0.200405	−	1.13655i	−0.704104	−	0.710097i	$-0.748651\pi$
$883$	5.95509	−	33.7730i	0.200405	−	1.13655i	0.904509	−	0.426455i	$-0.140238\pi$
$884$		0			0
$885$	−10.9884	−	19.0325i	−0.369371	−	0.639770i
$886$		0			0
$887$	39.3169	+	32.9908i	1.32013	+	1.10772i	0.986277	+	0.165098i	$0.0527942\pi$
$887$	39.3169	+	32.9908i	1.32013	+	1.10772i	0.333855	+	0.942624i	$0.391650\pi$
$888$		0			0
$889$	−12.7767	+	4.65033i	−0.428516	+	0.155967i
$890$		0			0
$891$	−4.70783	−	26.6994i	−0.157718	−	0.894465i
$892$		0			0
$893$	6.64491	+	23.9874i	0.222364	+	0.802707i
$894$		0			0
$895$	−0.565209	−	3.20546i	−0.0188929	−	0.107147i
$896$		0			0
$897$	−21.5844	+	7.85609i	−0.720683	+	0.262307i
$898$		0			0
$899$	10.4020	+	8.72829i	0.346925	+	0.291105i
$900$		0			0
$901$	−24.8569	−	43.0534i	−0.828103	−	1.43432i
$902$		0			0
$903$	−1.62995	+	9.24393i	−0.0542415	+	0.307619i
$904$		0			0
$905$	3.05588	−	5.29294i	0.101581	−	0.175943i
$906$		0			0
$907$	2.80385	+	1.02052i	0.0931005	+	0.0338858i	0.388150	−	0.921596i	$-0.373114\pi$
$907$	2.80385	+	1.02052i	0.0931005	+	0.0338858i	−0.295050	+	0.955482i	$0.595336\pi$
$908$		0			0
$909$	5.79832	−	4.86537i	0.192318	−	0.161374i
$910$		0			0
$911$	−14.4793			−0.479720			−0.239860	−	0.970808i	$-0.577101\pi$
$911$	−14.4793			−0.479720			−0.239860	+	0.970808i	$0.577101\pi$
$912$		0			0
$913$	−77.6247			−2.56900
$914$		0			0
$915$	−10.0428	+	8.42689i	−0.332004	+	0.278584i
$916$		0			0
$917$	7.65678	+	2.78684i	0.252849	+	0.0920296i
$918$		0			0
$919$	−1.61854	+	2.80340i	−0.0533908	+	0.0924755i	−0.891486	−	0.453049i	$-0.850336\pi$
$919$	−1.61854	+	2.80340i	−0.0533908	+	0.0924755i	0.838095	+	0.545525i	$0.183670\pi$
$920$		0			0
$921$	2.90380	−	16.4683i	0.0956835	−	0.542648i
$922$		0			0
$923$	−2.23979	−	3.87943i	−0.0737236	−	0.127693i
$924$		0			0
$925$	13.8513	+	11.6227i	0.455429	+	0.382151i
$926$		0			0
$927$	12.9994	−	4.73140i	0.426957	−	0.155400i
$928$		0			0
$929$	−8.28362	−	46.9787i	−0.271777	−	1.54132i	−0.749018	−	0.662550i	$-0.769474\pi$
$929$	−8.28362	−	46.9787i	−0.271777	−	1.54132i	0.477241	−	0.878772i	$-0.341637\pi$
$930$		0			0
$931$	16.6921	+	11.4792i	0.547061	+	0.376215i
$932$		0			0
$933$	−3.87593	−	21.9815i	−0.126892	−	0.719641i
$934$		0			0
$935$	68.7592	−	25.0263i	2.24867	−	0.818447i
$936$		0			0
$937$	−7.08114	−	5.94178i	−0.231331	−	0.194110i	0.519753	−	0.854317i	$-0.326024\pi$
$937$	−7.08114	−	5.94178i	−0.231331	−	0.194110i	−0.751084	+	0.660207i	$0.770469\pi$
$938$		0			0
$939$	10.5331	+	18.2439i	0.343735	+	0.595367i
$940$		0			0
$941$	−1.16327	+	6.59722i	−0.0379214	+	0.215063i	−0.997880	−	0.0650784i	$-0.979270\pi$
$941$	−1.16327	+	6.59722i	−0.0379214	+	0.215063i	0.959959	+	0.280141i	$0.0903814\pi$
$942$		0			0
$943$	1.07799	−	1.86713i	0.0351042	−	0.0608023i
$944$		0			0
$945$	15.0761	+	5.48726i	0.490426	+	0.178501i
$946$		0			0
$947$	2.80307	−	2.35206i	0.0910876	−	0.0764316i	−0.596107	−	0.802905i	$-0.703287\pi$
$947$	2.80307	−	2.35206i	0.0910876	−	0.0764316i	0.687194	+	0.726474i	$0.258842\pi$
$948$		0			0
$949$	60.5744			1.96633
$950$		0			0
$951$	−13.4353			−0.435668
$952$		0			0
$953$	−21.4967	+	18.0378i	−0.696345	+	0.584303i	−0.920731	−	0.390197i	$-0.872407\pi$
$953$	−21.4967	+	18.0378i	−0.696345	+	0.584303i	0.224386	+	0.974500i	$0.427962\pi$
$954$		0			0
$955$	4.54066	+	1.65266i	0.146932	+	0.0534789i
$956$		0			0
$957$	−10.6475	+	18.4419i	−0.344183	+	0.596143i
$958$		0			0
$959$	−0.0270007	+	0.153129i	−0.000871899	+	0.00494478i
$960$		0			0
$961$	3.78227	+	6.55109i	0.122009	+	0.211325i
$962$		0			0
$963$	−6.47236	−	5.43096i	−0.208569	−	0.175010i
$964$		0			0
$965$	−15.1707	+	5.52169i	−0.488363	+	0.177750i
$966$		0			0
$967$	−4.49326	−	25.4826i	−0.144494	−	0.819464i	−0.967772	−	0.251827i	$-0.918969\pi$
$967$	−4.49326	−	25.4826i	−0.144494	−	0.819464i	0.823279	−	0.567637i	$-0.192142\pi$
$968$		0			0
$969$	−44.2846	−	11.4663i	−1.42263	−	0.368350i
$970$		0			0
$971$	−4.76567	−	27.0275i	−0.152938	−	0.867352i	−0.960647	−	0.277772i	$-0.910404\pi$
$971$	−4.76567	−	27.0275i	−0.152938	−	0.867352i	0.807709	−	0.589581i	$-0.200707\pi$
$972$		0			0
$973$	19.3103	−	7.02838i	0.619061	−	0.225320i
$974$		0			0
$975$	8.16524	+	6.85145i	0.261497	+	0.219422i
$976$		0			0
$977$	6.40065	+	11.0863i	0.204775	+	0.354681i	0.950061	−	0.312064i	$-0.101020\pi$
$977$	6.40065	+	11.0863i	0.204775	+	0.354681i	−0.745286	+	0.666745i	$0.767687\pi$
$978$		0			0
$979$	−3.94871	+	22.3943i	−0.126201	+	0.715724i
$980$		0			0
$981$	−1.75856	+	3.04591i	−0.0561465	+	0.0972485i
$982$		0			0
$983$	−18.4353	−	6.70990i	−0.587995	−	0.214013i	0.0308525	−	0.999524i	$-0.490178\pi$
$983$	−18.4353	−	6.70990i	−0.587995	−	0.214013i	−0.618847	+	0.785511i	$0.712400\pi$
$984$		0			0
$985$	21.5774	−	18.1056i	0.687514	−	0.576893i
$986$		0			0
$987$	−12.4278			−0.395582
$988$		0			0
$989$	14.6900			0.467114
$990$		0			0
$991$	34.7798	−	29.1837i	1.10482	−	0.927050i	0.107076	−	0.994251i	$-0.465851\pi$
$991$	34.7798	−	29.1837i	1.10482	−	0.927050i	0.997739	+	0.0672005i	$0.0214067\pi$
$992$		0			0
$993$	25.0189	+	9.10612i	0.793950	+	0.288974i
$994$		0			0
$995$	−15.3136	+	26.5240i	−0.485475	+	0.840867i
$996$		0			0
$997$	4.50858	−	25.5694i	0.142788	−	0.809792i	−0.826328	−	0.563189i	$-0.809574\pi$
$997$	4.50858	−	25.5694i	0.142788	−	0.809792i	0.969117	−	0.246603i	$-0.0793145\pi$
$998$		0			0
$999$	−32.3568	−	56.0435i	−1.02372	−	1.77314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	608.2.y.b.161.4	✓	30
4.3	odd	2		608.2.y.c.161.2	yes	30
19.17	even	9	inner	608.2.y.b.321.4	yes	30
76.55	odd	18		608.2.y.c.321.2	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
608.2.y.b.161.4	✓	30	1.1	even	1	trivial
608.2.y.b.321.4	yes	30	19.17	even	9	inner
608.2.y.c.161.2	yes	30	4.3	odd	2
608.2.y.c.321.2	yes	30	76.55	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 608 = 2^{5} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	608.y (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.08700 - 0.912100i) q^{3} +(-1.73765 - 0.632454i) q^{5} +(-0.766882 + 1.32828i) q^{7} +(-0.171305 + 0.971520i) q^{9} +O(q^{10})\)	\(q+(1.08700 - 0.912100i) q^{3} +(-1.73765 - 0.632454i) q^{5} +(-0.766882 + 1.32828i) q^{7} +(-0.171305 + 0.971520i) q^{9} +(-2.67514 - 4.63347i) q^{11} +(-3.64069 - 3.05490i) q^{13} +(-2.46569 + 0.897438i) q^{15} +(-1.28429 - 7.28355i) q^{17} +(3.93481 - 1.87543i) q^{19} +(0.377923 + 2.14331i) q^{21} +(3.20063 - 1.16494i) q^{23} +(-1.21078 - 1.01596i) q^{25} +(2.82838 + 4.89890i) q^{27} +(0.487075 - 2.76234i) q^{29} +(-2.42051 + 4.19244i) q^{31} +(-7.13406 - 2.59658i) q^{33} +(2.17265 - 1.82307i) q^{35} -11.4400 q^{37} -6.74380 q^{39} +(0.484896 - 0.406876i) q^{41} +(4.05282 + 1.47511i) q^{43} +(0.912112 - 1.57982i) q^{45} +(-0.991588 + 5.62358i) q^{47} +(2.32378 + 4.02491i) q^{49} +(-8.03934 - 6.74581i) q^{51} +(6.31642 - 2.29899i) q^{53} +(1.71800 + 9.74327i) q^{55} +(2.56656 - 5.62753i) q^{57} +(1.45440 + 8.24828i) q^{59} +(4.69497 - 1.70883i) q^{61} +(-1.15908 - 0.972583i) q^{63} +(4.39417 + 7.61093i) q^{65} +(0.984932 - 5.58583i) q^{67} +(2.41655 - 4.18558i) q^{69} +(0.885715 + 0.322374i) q^{71} +(-9.76369 + 8.19271i) q^{73} -2.24277 q^{75} +8.20605 q^{77} +(8.68173 - 7.28484i) q^{79} +(4.76169 + 1.73311i) q^{81} +(7.25428 - 12.5648i) q^{83} +(-2.37487 + 13.4685i) q^{85} +(-1.99008 - 3.44692i) q^{87} +(-3.25584 - 2.73198i) q^{89} +(6.84974 - 2.49310i) q^{91} +(1.19284 + 6.76493i) q^{93} +(-8.02347 + 0.770260i) q^{95} +(-0.769831 - 4.36593i) q^{97} +(4.95978 - 1.80521i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} + 12 q^{7} + 3 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 + 12 * q^7 + 3 * q^9	\( 30 q - 3 q^{3} + 12 q^{7} + 3 q^{9} + 6 q^{11} - 6 q^{13} - 24 q^{15} - 6 q^{17} - 12 q^{19} - 6 q^{21} - 6 q^{23} - 12 q^{25} + 39 q^{27} + 12 q^{29} + 39 q^{33} - 12 q^{35} + 36 q^{37} - 24 q^{39} + 9 q^{41} + 18 q^{43} + 18 q^{45} + 12 q^{47} - 9 q^{49} + 51 q^{51} + 6 q^{53} + 24 q^{55} + 12 q^{57} - 9 q^{59} + 18 q^{61} - 132 q^{63} + 18 q^{65} - 51 q^{67} - 24 q^{69} + 36 q^{71} - 30 q^{73} + 48 q^{75} + 36 q^{77} + 60 q^{79} - 3 q^{81} + 30 q^{83} - 12 q^{85} - 24 q^{89} - 60 q^{91} + 30 q^{93} - 36 q^{95} - 9 q^{97} + 27 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 + 12 * q^7 + 3 * q^9 + 6 * q^11 - 6 * q^13 - 24 * q^15 - 6 * q^17 - 12 * q^19 - 6 * q^21 - 6 * q^23 - 12 * q^25 + 39 * q^27 + 12 * q^29 + 39 * q^33 - 12 * q^35 + 36 * q^37 - 24 * q^39 + 9 * q^41 + 18 * q^43 + 18 * q^45 + 12 * q^47 - 9 * q^49 + 51 * q^51 + 6 * q^53 + 24 * q^55 + 12 * q^57 - 9 * q^59 + 18 * q^61 - 132 * q^63 + 18 * q^65 - 51 * q^67 - 24 * q^69 + 36 * q^71 - 30 * q^73 + 48 * q^75 + 36 * q^77 + 60 * q^79 - 3 * q^81 + 30 * q^83 - 12 * q^85 - 24 * q^89 - 60 * q^91 + 30 * q^93 - 36 * q^95 - 9 * q^97 + 27 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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