LMFDB - Embedded newform 768.2.o.b.671.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(95,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, 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("768.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.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:	$6.13251087523$
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			671.4
Character	$\chi$	$=$	768.671
Dual form			768.2.o.b.95.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18890 - 1.25957i) q^{3} +(-1.06973 - 0.443098i) q^{5} +(2.37247 - 2.37247i) q^{7} +(-0.173046 + 2.99501i) q^{9} +O(q^{10})$	\(q+(-1.18890 - 1.25957i) q^{3} +(-1.06973 - 0.443098i) q^{5} +(2.37247 - 2.37247i) q^{7} +(-0.173046 + 2.99501i) q^{9} +(5.50127 + 2.27870i) q^{11} +(-0.346353 - 0.836171i) q^{13} +(0.713689 + 1.87421i) q^{15} +0.685064 q^{17} +(3.35074 - 1.38792i) q^{19} +(-5.80891 - 0.167674i) q^{21} +(-2.05133 + 2.05133i) q^{23} +(-2.58754 - 2.58754i) q^{25} +(3.97816 - 3.34279i) q^{27} +(-1.98869 - 4.80112i) q^{29} -6.36503i q^{31} +(-3.67025 - 9.63838i) q^{33} +(-3.58914 + 1.48667i) q^{35} +(-0.112738 + 0.272172i) q^{37} +(-0.641440 + 1.43038i) q^{39} +(3.26585 + 3.26585i) q^{41} +(0.993018 - 2.39736i) q^{43} +(1.51219 - 3.12718i) q^{45} -11.7975i q^{47} -4.25719i q^{49} +(-0.814471 - 0.862888i) q^{51} +(-1.56192 + 3.77080i) q^{53} +(-4.87520 - 4.87520i) q^{55} +(-5.73187 - 2.57040i) q^{57} +(-2.20815 + 5.33094i) q^{59} +(1.53549 - 0.636020i) q^{61} +(6.69500 + 7.51609i) q^{63} +1.04795i q^{65} +(-4.69605 - 11.3373i) q^{67} +(5.02262 + 0.144978i) q^{69} +(7.99150 + 7.99150i) q^{71} +(-2.34760 + 2.34760i) q^{73} +(-0.182875 + 6.33551i) q^{75} +(18.4577 - 7.64543i) q^{77} +8.91043 q^{79} +(-8.94011 - 1.03655i) q^{81} +(-3.06920 - 7.40970i) q^{83} +(-0.732836 - 0.303551i) q^{85} +(-3.68301 + 8.21294i) q^{87} +(1.99332 - 1.99332i) q^{89} +(-2.80550 - 1.16208i) q^{91} +(-8.01722 + 7.56737i) q^{93} -4.19938 q^{95} +8.66510 q^{97} +(-7.77669 + 16.0820i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{3} - 8 q^{7} - 4 q^{9}+O(q^{10}) $ 56 * q + 4 * q^3 - 8 * q^7 - 4 * q^9	$ 56 q + 4 q^{3} - 8 q^{7} - 4 q^{9} + 8 q^{13} - 8 q^{15} + 8 q^{19} + 4 q^{21} - 8 q^{25} + 28 q^{27} - 8 q^{33} + 8 q^{37} - 28 q^{39} + 8 q^{43} + 4 q^{45} + 16 q^{51} + 24 q^{55} - 4 q^{57} + 40 q^{61} - 56 q^{67} + 4 q^{69} - 8 q^{73} - 16 q^{75} + 16 q^{79} + 48 q^{85} + 52 q^{87} - 40 q^{91} - 8 q^{93} - 16 q^{97} - 60 q^{99}+O(q^{100}) $ 56 * q + 4 * q^3 - 8 * q^7 - 4 * q^9 + 8 * q^13 - 8 * q^15 + 8 * q^19 + 4 * q^21 - 8 * q^25 + 28 * q^27 - 8 * q^33 + 8 * q^37 - 28 * q^39 + 8 * q^43 + 4 * q^45 + 16 * q^51 + 24 * q^55 - 4 * q^57 + 40 * q^61 - 56 * q^67 + 4 * q^69 - 8 * q^73 - 16 * q^75 + 16 * q^79 + 48 * q^85 + 52 * q^87 - 40 * q^91 - 8 * q^93 - 16 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{8}\right)$

Coefficient data

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

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
$3$	−1.18890	−	1.25957i	−0.686410	−	0.727215i
$3$	−1.18890	−	1.25957i	−0.686410	−	0.727215i
$4$		0			0
$5$	−1.06973	−	0.443098i	−0.478400	−	0.198160i	0.130435	−	0.991457i	$-0.458363\pi$
$5$	−1.06973	−	0.443098i	−0.478400	−	0.198160i	−0.608834	+	0.793297i	$0.708363\pi$
$6$		0			0
$7$	2.37247	−	2.37247i	0.896708	−	0.896708i	−0.0984354	−	0.995143i	$-0.531384\pi$
$7$	2.37247	−	2.37247i	0.896708	−	0.896708i	0.995143	+	0.0984354i	$0.0313838\pi$
$8$		0			0
$9$	−0.173046	+	2.99501i	−0.0576820	+	0.998335i
$10$		0			0
$11$	5.50127	+	2.27870i	1.65869	+	0.687054i	0.997977	−	0.0635809i	$-0.0202521\pi$
$11$	5.50127	+	2.27870i	1.65869	+	0.687054i	0.660718	+	0.750635i	$0.270252\pi$
$12$		0			0
$13$	−0.346353	−	0.836171i	−0.0960612	−	0.231912i	0.868543	−	0.495613i	$-0.165057\pi$
$13$	−0.346353	−	0.836171i	−0.0960612	−	0.231912i	−0.964604	+	0.263701i	$0.915057\pi$
$14$		0			0
$15$	0.713689	+	1.87421i	0.184274	+	0.483918i
$16$		0			0
$17$	0.685064			0.166152			0.0830762	−	0.996543i	$-0.473526\pi$
$17$	0.685064			0.166152			0.0830762	+	0.996543i	$0.473526\pi$
$18$		0			0
$19$	3.35074	−	1.38792i	0.768712	−	0.318411i	0.0363614	−	0.999339i	$-0.488423\pi$
$19$	3.35074	−	1.38792i	0.768712	−	0.318411i	0.732351	+	0.680928i	$0.238423\pi$
$20$		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	$-0.847805\pi$
$23$	−2.05133	+	2.05133i	−0.427732	+	0.427732i	0.460123	+	0.887855i	$0.347805\pi$
$24$		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	−0.993867	−	0.110582i	$-0.964728\pi$
$29$	−1.98869	−	4.80112i	−0.369291	−	0.891546i	0.624576	−	0.780964i	$-0.285272\pi$
$30$		0			0
$31$		−	6.36503i		−	1.14319i	−0.820535	−	0.571596i	$-0.806324\pi$
$31$		−	6.36503i		−	1.14319i	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	$-0.882709\pi$
$37$	−0.112738	+	0.272172i	−0.0185339	+	0.0447449i	0.914342	+	0.404944i	$0.132709\pi$
$38$		0			0
$39$	−0.641440	+	1.43038i	−0.102713	+	0.229044i
$40$		0			0
$41$	3.26585	+	3.26585i	0.510040	+	0.510040i	0.914539	−	0.404499i	$-0.132554\pi$
$41$	3.26585	+	3.26585i	0.510040	+	0.510040i	−0.404499	+	0.914539i	$0.632554\pi$
$42$		0			0
$43$	0.993018	−	2.39736i	0.151434	−	0.365594i	−0.829898	−	0.557915i	$-0.811602\pi$
$43$	0.993018	−	2.39736i	0.151434	−	0.365594i	0.981332	+	0.192321i	$0.0616016\pi$
$44$		0			0
$45$	1.51219	−	3.12718i	0.225425	−	0.466173i
$46$		0			0
$47$		−	11.7975i		−	1.72084i	−0.509589	−	0.860418i	$-0.670203\pi$
$47$		−	11.7975i		−	1.72084i	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	$-0.965440\pi$
$53$	−1.56192	+	3.77080i	−0.214546	+	0.517959i	0.779566	+	0.626320i	$0.215440\pi$
$54$		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	−0.999971	−	0.00764882i	$-0.997565\pi$
$59$	−2.20815	+	5.33094i	−0.287476	+	0.694029i	0.712495	+	0.701678i	$0.247565\pi$
$60$		0			0
$61$	1.53549	−	0.636020i	0.196599	−	0.0814341i	−0.282212	−	0.959352i	$-0.591068\pi$
$61$	1.53549	−	0.636020i	0.196599	−	0.0814341i	0.478811	+	0.877918i	$0.341068\pi$
$62$		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	−0.898371	−	0.439237i	$-0.855249\pi$
$67$	−4.69605	−	11.3373i	−0.573714	−	1.38507i	0.324657	−	0.945832i	$-0.394751\pi$
$68$		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	$-0.0160232\pi$
$71$	7.99150	+	7.99150i	0.948416	+	0.948416i	−0.0503173	+	0.998733i	$0.516023\pi$
$72$		0			0
$73$	−2.34760	+	2.34760i	−0.274766	+	0.274766i	−0.831015	−	0.556250i	$-0.812240\pi$
$73$	−2.34760	+	2.34760i	−0.274766	+	0.274766i	0.556250	+	0.831015i	$0.312240\pi$
$74$		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	$-0.332873\pi$
$79$	8.91043			1.00250			0.501251	+	0.865302i	$0.332873\pi$
$80$		0			0
$81$	−8.94011	−	1.03655i	−0.993346	−	0.115172i
$82$		0			0
$83$	−3.06920	−	7.40970i	−0.336888	−	0.813320i	−0.998011	−	0.0630420i	$-0.979920\pi$
$83$	−3.06920	−	7.40970i	−0.336888	−	0.813320i	0.661123	−	0.750278i	$-0.270080\pi$
$84$		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	−0.593525	−	0.804816i	$-0.702264\pi$
$89$	1.99332	−	1.99332i	0.211291	−	0.211291i	0.804816	+	0.593525i	$0.202264\pi$
$90$		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	$-0.355013\pi$
$97$	8.66510			0.879807			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	$-0.695417\pi$
$101$	−15.6920	−	6.49983i	−1.56141	−	0.646758i	−0.985334	+	0.170637i	$0.945417\pi$
$102$		0			0
$103$	−5.39788	+	5.39788i	−0.531869	+	0.531869i	−0.921128	−	0.389259i	$-0.872731\pi$
$103$	−5.39788	+	5.39788i	−0.531869	+	0.531869i	0.389259	+	0.921128i	$0.372731\pi$
$104$		0			0
$105$	6.13969	+	2.75329i	0.599173	+	0.268693i
$106$		0			0
$107$	0.0169596	+	0.00702491i	0.00163955	+	0.000679124i	0.383503	−	0.923540i	$-0.374718\pi$
$107$	0.0169596	+	0.00702491i	0.00163955	+	0.000679124i	−0.381864	+	0.924219i	$0.624718\pi$
$108$		0			0
$109$	4.94357	+	11.9348i	0.473508	+	1.14315i	0.962602	+	0.270919i	$0.0873276\pi$
$109$	4.94357	+	11.9348i	0.473508	+	1.14315i	−0.489094	+	0.872231i	$0.662672\pi$
$110$		0			0
$111$	0.476854	−	0.181584i	0.0452610	−	0.0172352i
$112$		0			0
$113$	−10.4984			−0.987609			−0.493804	−	0.869573i	$-0.664394\pi$
$113$	−10.4984			−0.987609			−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	$0.0112046\pi$
$127$			0.793212i			0.0703862i	−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	0.0674502	−	0.997723i	$-0.478514\pi$
$131$	9.39267	−	3.89057i	0.820641	−	0.339921i	0.753191	+	0.657802i	$0.228514\pi$
$132$		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	0.569280	−	0.822144i	$-0.307222\pi$
$137$	−2.95969	−	2.95969i	−0.252863	−	0.252863i	−0.822144	+	0.569280i	$0.807222\pi$
$138$		0			0
$139$	1.91155	−	4.61488i	0.162135	−	0.391429i	−0.821844	−	0.569713i	$-0.807054\pi$
$139$	1.91155	−	4.61488i	0.162135	−	0.391429i	0.983979	+	0.178284i	$0.0570545\pi$
$140$		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	0.517614	+	0.855614i	$0.326820\pi$
$149$	−5.53451	+	13.3615i	−0.453405	+	1.09462i	−0.971019	+	0.239002i	$0.923180\pi$
$150$		0			0
$151$	2.96063	+	2.96063i	0.240932	+	0.240932i	0.817236	−	0.576303i	$-0.195505\pi$
$151$	2.96063	+	2.96063i	0.240932	+	0.240932i	−0.576303	+	0.817236i	$0.695505\pi$
$152$		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	$-0.379822\pi$
$157$	16.1213	−	6.67768i	1.28662	−	0.532937i	0.917977	+	0.396633i	$0.129822\pi$
$158$		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	0.995007	+	0.0998018i	$0.0318209\pi$
$163$	4.62172	+	11.1578i	0.362001	+	0.873949i	−0.633006	+	0.774147i	$0.718179\pi$
$164$		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	$-0.227583\pi$
$167$	1.28603	+	1.28603i	0.0995157	+	0.0995157i	−0.655596	+	0.755112i	$0.727583\pi$
$168$		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	$-0.624259\pi$
$173$	0.0565964	−	0.0234430i	0.00430295	−	0.00178234i	0.384834	+	0.922986i	$0.374259\pi$
$174$		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	0.961678	−	0.274180i	$-0.0884064\pi$
$179$	1.17461	+	2.83576i	0.0877946	+	0.211955i	−0.873884	+	0.486135i	$0.838406\pi$
$180$		0			0
$181$	20.8334	+	8.62949i	1.54854	+	0.641425i	0.983051	−	0.183334i	$-0.0586889\pi$
$181$	20.8334	+	8.62949i	1.54854	+	0.641425i	0.565485	+	0.824758i	$0.308689\pi$
$182$		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	$-0.814046\pi$
$191$	−23.0566			−1.66832			−0.834158	+	0.551525i	$0.814046\pi$
$192$		0			0
$193$	7.52832			0.541900			0.270950	−	0.962593i	$-0.412662\pi$
$193$	7.52832			0.541900			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	$-0.348612\pi$
$197$	2.14750	+	0.889524i	0.153003	+	0.0633760i	−0.304868	+	0.952395i	$0.598612\pi$
$198$		0			0
$199$	7.46994	−	7.46994i	0.529530	−	0.529530i	−0.390902	−	0.920432i	$-0.627837\pi$
$199$	7.46994	−	7.46994i	0.529530	−	0.529530i	0.920432	+	0.390902i	$0.127837\pi$
$200$		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	−0.857567	−	0.514372i	$-0.828025\pi$
$211$	−15.9819	+	6.61994i	−1.10024	+	0.455735i	−0.242676	+	0.970107i	$0.578025\pi$
$212$		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	$0.208910\pi$
$223$			18.2244i			1.22040i	−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	0.00747022	−	0.999972i	$-0.497622\pi$
$227$	10.8455	−	4.49234i	0.719840	−	0.298167i	0.712369	+	0.701805i	$0.247622\pi$
$228$		0			0
$229$	−5.20986	+	12.5777i	−0.344277	+	0.831159i	0.652996	+	0.757362i	$0.273512\pi$
$229$	−5.20986	+	12.5777i	−0.344277	+	0.831159i	−0.997273	+	0.0737978i	$0.976488\pi$
$230$		0			0
$231$	−31.5743	−	14.1592i	−2.07744	−	0.931606i
$232$		0			0
$233$	−11.7233	−	11.7233i	−0.768016	−	0.768016i	0.209741	−	0.977757i	$-0.432738\pi$
$233$	−11.7233	−	11.7233i	−0.768016	−	0.768016i	−0.977757	+	0.209741i	$0.932738\pi$
$234$		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	$0.246117\pi$
$239$			21.5949i			1.39685i	−0.715681	+	0.698427i	$0.753883\pi$
$240$		0			0
$241$			14.6095i			0.941078i	0.882379	+	0.470539i	$0.155941\pi$
$241$			14.6095i			0.941078i	−0.882379	+	0.470539i	$0.844059\pi$
$242$		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	−0.885900	−	0.463876i	$-0.846458\pi$
$251$	1.08581	−	2.62137i	0.0685355	−	0.165459i	0.954436	+	0.298416i	$0.0964584\pi$
$252$		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	$0.0134498\pi$
$257$			1.35436i			0.0844827i	−0.999107	+	0.0422414i	$0.986550\pi$
$258$		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	$-0.200900\pi$
$263$	3.52372	+	3.52372i	0.217282	+	0.217282i	−0.590070	+	0.807352i	$0.700900\pi$
$264$		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	$-0.807940\pi$
$269$	−16.4741	+	6.82380i	−1.00444	+	0.416055i	−0.181020	+	0.983479i	$0.557940\pi$
$270$		0			0
$271$	−8.50293			−0.516516			−0.258258	−	0.966076i	$-0.583149\pi$
$271$	−8.50293			−0.516516			−0.258258	+	0.966076i	$0.583149\pi$
$272$		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	$-0.603150\pi$
$277$	−20.2028	−	8.36828i	−1.21387	−	0.502801i	−0.895456	+	0.445150i	$0.853150\pi$
$278$		0			0
$279$	19.0633	+	1.10144i	1.14129	+	0.0659416i
$280$		0			0
$281$	10.3342	−	10.3342i	0.616487	−	0.616487i	−0.328142	−	0.944629i	$-0.606422\pi$
$281$	10.3342	−	10.3342i	0.616487	−	0.616487i	0.944629	+	0.328142i	$0.106422\pi$
$282$		0			0
$283$	−8.67342	−	3.59265i	−0.515581	−	0.213561i	0.109694	−	0.993965i	$-0.465013\pi$
$283$	−8.67342	−	3.59265i	−0.515581	−	0.213561i	−0.625275	+	0.780405i	$0.715013\pi$
$284$		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	$-0.257827\pi$
$293$	11.3816	+	4.71442i	0.664922	+	0.275420i	−0.0245862	+	0.999698i	$0.507827\pi$
$294$		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	0.00753514	−	0.999972i	$-0.497601\pi$
$307$	12.6145	−	5.22511i	0.719950	−	0.298213i	0.712415	+	0.701759i	$0.247601\pi$
$308$		0			0
$309$	13.2166	+	0.381496i	0.751863	+	0.0217025i
$310$		0			0
$311$	18.8020	−	18.8020i	1.06617	−	1.06617i	0.0685162	−	0.997650i	$-0.478174\pi$
$311$	18.8020	−	18.8020i	1.06617	−	1.06617i	0.997650	−	0.0685162i	$-0.0218265\pi$
$312$		0			0
$313$	4.30835	+	4.30835i	0.243522	+	0.243522i	0.818306	−	0.574783i	$-0.194914\pi$
$313$	4.30835	+	4.30835i	0.243522	+	0.243522i	−0.574783	+	0.818306i	$0.694914\pi$
$314$		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	$-0.112303\pi$
$317$	0.543402	+	1.31189i	0.0305205	+	0.0736830i	−0.907884	+	0.419221i	$0.862303\pi$
$318$		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	−0.714774	−	0.699356i	$-0.753470\pi$
$331$	5.18815	−	12.5253i	0.285167	−	0.688453i	0.999941	+	0.0109024i	$0.00347041\pi$
$332$		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	$-0.816756\pi$
$337$		−	19.9878i		−	1.08881i	0.838824	−	0.544403i	$-0.183244\pi$
$338$		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	0.685707	+	0.727877i	$0.259493\pi$
$347$	−5.84634	+	14.1143i	−0.313848	+	0.757696i	−0.999555	+	0.0298187i	$0.990507\pi$
$348$		0			0
$349$	−7.90170	+	3.27299i	−0.422969	+	0.175199i	−0.584007	−	0.811749i	$-0.698516\pi$
$349$	−7.90170	+	3.27299i	−0.422969	+	0.175199i	0.161038	+	0.986948i	$0.448516\pi$
$350$		0			0
$351$	−4.17299	−	2.16864i	−0.222738	−	0.115753i
$352$		0			0
$353$			28.4566i			1.51459i	0.653072	+	0.757296i	$0.273480\pi$
$353$			28.4566i			1.51459i	−0.653072	+	0.757296i	$0.726520\pi$
$354$		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	$-0.208473\pi$
$359$	3.48589	+	3.48589i	0.183978	+	0.183978i	−0.609109	+	0.793087i	$0.708473\pi$
$360$		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	$-0.438353\pi$
$367$	7.37411			0.384925			0.192463	+	0.981304i	$0.438353\pi$
$368$		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	$-0.305512\pi$
$373$	7.72861	+	3.20130i	0.400172	+	0.165757i	−0.173515	+	0.984831i	$0.555512\pi$
$374$		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	0.879465	−	0.475963i	$-0.157900\pi$
$379$	22.6759	+	9.39268i	1.16478	+	0.482470i	0.285319	+	0.958433i	$0.407900\pi$
$380$		0			0
$381$	0.999108	−	0.943047i	0.0511858	−	0.0483138i
$382$		0			0
$383$	11.3729			0.581129			0.290565	−	0.956855i	$-0.406157\pi$
$383$	11.3729			0.581129			0.290565	+	0.956855i	$0.406157\pi$
$384$		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	$-0.274983\pi$
$389$	11.2635	+	4.66550i	0.571083	+	0.236550i	−0.0784059	+	0.996922i	$0.524983\pi$
$390$		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	$-0.201985\pi$
$397$	−3.65241	−	8.81769i	−0.183309	−	0.442547i	−0.988645	+	0.150272i	$0.951985\pi$
$398$		0			0
$399$	−19.6969	+	7.50048i	−0.986076	+	0.375494i
$400$		0			0
$401$	−5.46170			−0.272744			−0.136372	−	0.990658i	$-0.543544\pi$
$401$	−5.46170			−0.272744			−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	−0.997327	−	0.0730670i	$-0.976721\pi$
$409$	−21.6474	−	21.6474i	−1.07039	−	1.07039i	−0.0730670	−	0.997327i	$-0.523279\pi$
$410$		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	0.0471519	−	0.998888i	$-0.484986\pi$
$419$	16.1057	−	6.67119i	0.786814	−	0.325909i	0.739662	+	0.672979i	$0.234986\pi$
$420$		0			0
$421$	−11.0865	+	26.7651i	−0.540321	+	1.30445i	0.384176	+	0.923260i	$0.374486\pi$
$421$	−11.0865	+	26.7651i	−0.540321	+	1.30445i	−0.924497	+	0.381190i	$0.875514\pi$
$422$		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	$-0.835834\pi$
$431$		−	20.4774i		−	0.986361i	0.869927	−	0.493180i	$-0.164166\pi$
$432$		0			0
$433$		−	14.6756i		−	0.705262i	−0.935762	−	0.352631i	$-0.885287\pi$
$433$		−	14.6756i		−	0.705262i	0.935762	−	0.352631i	$-0.114713\pi$
$434$		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	$-0.197465\pi$
$439$	4.86825	+	4.86825i	0.232349	+	0.232349i	−0.581324	+	0.813672i	$0.697465\pi$
$440$		0			0
$441$	12.7503	+	0.736690i	0.607158	+	0.0350805i
$442$		0			0
$443$	−6.00738	+	14.5031i	−0.285419	+	0.689063i	−0.999944	−	0.0105468i	$-0.996643\pi$
$443$	−6.00738	+	14.5031i	−0.285419	+	0.689063i	0.714525	+	0.699610i	$0.246643\pi$
$444$		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	$0.0132691\pi$
$449$			1.76611i			0.0833480i	−0.999131	+	0.0416740i	$0.986731\pi$
$450$		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	−0.0469601	+	0.998897i	$0.514953\pi$
$457$	−22.3579	+	22.3579i	−1.04586	+	1.04586i	−0.998897	+	0.0469601i	$0.985047\pi$
$458$		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	$-0.618485\pi$
$461$	0.811938	−	0.336316i	0.0378157	−	0.0156638i	0.401511	+	0.915854i	$0.368485\pi$
$462$		0			0
$463$	14.0009			0.650678			0.325339	−	0.945597i	$-0.394522\pi$
$463$	14.0009			0.650678			0.325339	+	0.945597i	$0.394522\pi$
$464$		0			0
$465$	11.9294	−	4.54265i	0.553211	−	0.210661i
$466$		0			0
$467$	5.94695	+	14.3572i	0.275192	+	0.664373i	0.999690	−	0.0249045i	$-0.00792818\pi$
$467$	5.94695	+	14.3572i	0.275192	+	0.664373i	−0.724498	+	0.689277i	$0.757928\pi$
$468$		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	$-0.788627\pi$
$479$	−34.4708			−1.57501			−0.787505	+	0.616309i	$0.788627\pi$
$480$		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	$-0.894329\pi$
$487$	−13.6710	+	13.6710i	−0.619490	+	0.619490i	0.325911	+	0.945401i	$0.394329\pi$
$488$		0			0
$489$	8.55934	−	19.0869i	0.387067	−	0.863140i
$490$		0			0
$491$	−16.0034	−	6.62882i	−0.722223	−	0.299154i	−0.00887095	−	0.999961i	$-0.502824\pi$
$491$	−16.0034	−	6.62882i	−0.722223	−	0.299154i	−0.713352	+	0.700806i	$0.752824\pi$
$492$		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	−0.235717	−	0.971822i	$-0.575744\pi$
$499$	6.36166	−	2.63509i	0.284787	−	0.117963i	0.520504	+	0.853859i	$0.325744\pi$
$500$		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	$-0.928291\pi$
$503$	−16.8510	+	16.8510i	−0.751350	+	0.751350i	0.223381	+	0.974731i	$0.428291\pi$
$504$		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	−0.999977	−	0.00678764i	$-0.997839\pi$
$509$	−6.71610	−	16.2141i	−0.297686	−	0.718678i	0.702291	−	0.711890i	$-0.252161\pi$
$510$		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	0.982765	−	0.184858i	$-0.0591824\pi$
$521$	18.2126	+	18.2126i	0.797908	+	0.797908i	−0.184858	+	0.982765i	$0.559182\pi$
$522$		0			0
$523$	0.472480	−	1.14067i	0.0206601	−	0.0498779i	−0.913213	−	0.407483i	$-0.866407\pi$
$523$	0.472480	−	1.14067i	0.0206601	−	0.0498779i	0.933873	+	0.357605i	$0.116407\pi$
$524$		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	$-0.732418\pi$
$541$	−14.2297	+	5.89412i	−0.611781	+	0.253408i	0.0552087	+	0.998475i	$0.482418\pi$
$542$		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	0.999336	−	0.0364266i	$-0.0115975\pi$
$547$	6.24323	+	15.0725i	0.266941	+	0.644453i	−0.732395	+	0.680880i	$0.761598\pi$
$548$		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	$-0.573001\pi$
$557$	7.09223	−	2.93770i	0.300507	−	0.124474i	0.527842	+	0.849342i	$0.323001\pi$
$558$		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	0.934400	−	0.356226i	$-0.115937\pi$
$563$	0.517007	+	1.24817i	0.0217892	+	0.0526039i	−0.912610	+	0.408830i	$0.865937\pi$
$564$		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	−0.793296	−	0.608836i	$-0.791637\pi$
$569$	−4.40004	+	4.40004i	−0.184459	+	0.184459i	0.608836	+	0.793296i	$0.291637\pi$
$570$		0			0
$571$	−23.9135	−	9.90528i	−1.00075	−	0.414523i	−0.178676	−	0.983908i	$-0.557181\pi$
$571$	−23.9135	−	9.90528i	−1.00075	−	0.414523i	−0.822071	+	0.569385i	$0.807181\pi$
$572$		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	$-0.549578\pi$
$577$	−7.45244			−0.310249			−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	0.993420	−	0.114526i	$-0.0365349\pi$
$587$	39.1257	+	16.2064i	1.61489	+	0.668910i	0.621472	+	0.783436i	$0.286535\pi$
$588$		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	$-0.841232\pi$
$593$	−42.7694			−1.75633			−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	$-0.538829\pi$
$599$	21.3145	−	21.3145i	0.870885	−	0.870885i	0.992569	+	0.121684i	$0.0388294\pi$
$600$		0			0
$601$	−4.26621	−	4.26621i	−0.174022	−	0.174022i	0.614722	−	0.788744i	$-0.289268\pi$
$601$	−4.26621	−	4.26621i	−0.174022	−	0.174022i	−0.788744	+	0.614722i	$0.789268\pi$
$602$		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	$0.212915\pi$
$607$			30.5562i			1.24024i	−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	0.378584	+	0.925567i	$0.376411\pi$
$613$	−13.4587	+	32.4921i	−0.543590	+	1.31234i	−0.922174	+	0.386775i	$0.873589\pi$
$614$		0			0
$615$	−3.79007	+	8.45168i	−0.152830	+	0.340804i
$616$		0			0
$617$	32.1395	+	32.1395i	1.29389	+	1.29389i	0.932363	+	0.361524i	$0.117743\pi$
$617$	32.1395	+	32.1395i	1.29389	+	1.29389i	0.361524	+	0.932363i	$0.382257\pi$
$618$		0			0
$619$	−14.9456	+	36.0820i	−0.600716	+	1.45026i	0.272129	+	0.962261i	$0.412272\pi$
$619$	−14.9456	+	36.0820i	−0.600716	+	1.45026i	−0.872846	+	0.487996i	$0.837728\pi$
$620$		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	$-0.0531442\pi$
$631$	20.5960	+	20.5960i	0.819912	+	0.819912i	−0.166183	+	0.986095i	$0.553144\pi$
$632$		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	$0.0806426\pi$
$641$			12.6916i			0.501289i	−0.968079	+	0.250645i	$0.919357\pi$
$642$		0			0
$643$	−0.974363	−	2.35232i	−0.0384251	−	0.0927665i	0.903502	−	0.428584i	$-0.140987\pi$
$643$	−0.974363	−	2.35232i	−0.0384251	−	0.0927665i	−0.941927	+	0.335818i	$0.890987\pi$
$644$		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	$-0.463766\pi$
$647$	−22.3823	−	22.3823i	−0.879941	−	0.879941i	−0.993528	+	0.113587i	$0.963766\pi$
$648$		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	$-0.638666\pi$
$653$	−2.02663	+	0.839459i	−0.0793083	+	0.0328506i	0.342677	+	0.939453i	$0.388666\pi$
$654$		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	0.988224	−	0.153011i	$-0.0488971\pi$
$659$	4.65284	+	11.2330i	0.181249	+	0.437574i	−0.806975	+	0.590585i	$0.798897\pi$
$660$		0			0
$661$	22.0472	+	9.13226i	0.857538	+	0.355204i	0.767744	−	0.640757i	$-0.221379\pi$
$661$	22.0472	+	9.13226i	0.857538	+	0.355204i	0.0897938	+	0.995960i	$0.471379\pi$
$662$		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	$-0.489129\pi$
$673$	1.77155			0.0682883			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	$-0.598929\pi$
$677$	−31.1005	−	12.8822i	−1.19529	−	0.495105i	−0.889474	+	0.456986i	$0.848929\pi$
$678$		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	0.334000	−	0.942573i	$-0.391601\pi$
$683$	−2.51740	−	1.04274i	−0.0963256	−	0.0398994i	−0.430326	+	0.902674i	$0.641601\pi$
$684$		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	−0.942000	−	0.335614i	$-0.891056\pi$
$691$	−36.0335	+	14.9256i	−1.37078	+	0.567795i	−0.428779	+	0.903409i	$0.641056\pi$
$692$		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	$-0.103079\pi$
$701$	1.39440	+	3.36638i	0.0526658	+	0.127147i	−0.895357	+	0.445350i	$0.853079\pi$
$702$		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	0.655708	+	0.755015i	$0.272370\pi$
$709$	−9.10175	+	21.9736i	−0.341824	+	0.825235i	−0.997531	+	0.0702205i	$0.977630\pi$
$710$		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	$0.118744\pi$
$719$			19.5450i			0.728907i	−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	$-0.434565\pi$
$727$	−20.8914	−	20.8914i	−0.774821	−	0.774821i	−0.978945	+	0.204124i	$0.934565\pi$
$728$		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	$-0.566777\pi$
$733$	9.09957	−	3.76916i	0.336100	−	0.139217i	0.544350	+	0.838859i	$0.316777\pi$
$734$		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	−0.999992	−	0.00394665i	$-0.998744\pi$
$739$	−8.03797	−	19.4054i	−0.295682	−	0.713839i	0.704311	−	0.709892i	$-0.251256\pi$
$740$		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	$-0.123830\pi$
$743$	14.8827	+	14.8827i	0.545995	+	0.545995i	−0.379285	+	0.925280i	$0.623830\pi$
$744$		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	$-0.839582\pi$
$751$	−47.9945			−1.75135			−0.875673	+	0.482905i	$0.839582\pi$
$752$		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	$-0.346070\pi$
$757$	4.61422	+	1.91127i	0.167707	+	0.0694663i	−0.297251	+	0.954799i	$0.596070\pi$
$758$		0			0
$759$	27.3004	+	12.2426i	0.990943	+	0.444379i
$760$		0			0
$761$	−35.4112	+	35.4112i	−1.28365	+	1.28365i	−0.345081	+	0.938573i	$0.612149\pi$
$761$	−35.4112	+	35.4112i	−1.28365	+	1.28365i	−0.938573	+	0.345081i	$0.887851\pi$
$762$		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	$-0.153578\pi$
$769$	49.1306			1.77169			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	0.996535	+	0.0831696i	$0.0265043\pi$
$773$	48.9331	+	20.2688i	1.76000	+	0.729017i	0.763467	+	0.645847i	$0.223496\pi$
$774$		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	0.593681	−	0.804701i	$-0.297674\pi$
$787$	44.3943	−	18.3887i	1.58249	−	0.655487i	0.988805	+	0.149214i	$0.0476743\pi$
$788$		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	0.992899	+	0.118961i	$0.0379562\pi$
$797$	10.5848	+	25.5539i	0.374931	+	0.905164i	−0.617968	+	0.786203i	$0.712044\pi$
$798$		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	0.997647	−	0.0685638i	$-0.0218417\pi$
$809$	26.4258	+	26.4258i	0.929083	+	0.929083i	−0.0685638	+	0.997647i	$0.521842\pi$
$810$		0			0
$811$	−10.2190	+	24.6709i	−0.358838	+	0.866311i	0.636626	+	0.771173i	$0.280329\pi$
$811$	−10.2190	+	24.6709i	−0.358838	+	0.866311i	−0.995464	+	0.0951387i	$0.969671\pi$
$812$		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	0.357146	+	0.934048i	$0.383750\pi$
$821$	−15.9273	+	38.4519i	−0.555866	+	1.34198i	−0.913013	+	0.407932i	$0.866250\pi$
$822$		0			0
$823$	−27.1818	−	27.1818i	−0.947499	−	0.947499i	0.0511904	−	0.998689i	$-0.483698\pi$
$823$	−27.1818	−	27.1818i	−0.947499	−	0.947499i	−0.998689	+	0.0511904i	$0.983698\pi$
$824$		0			0
$825$	−15.4428	+	34.4366i	−0.537648	+	1.19893i
$826$		0			0
$827$	12.6297	−	30.4907i	0.439176	−	1.06027i	−0.537058	−	0.843546i	$-0.680464\pi$
$827$	12.6297	−	30.4907i	0.439176	−	1.06027i	0.976234	−	0.216720i	$-0.0695358\pi$
$828$		0			0
$829$	34.6568	−	14.3553i	1.20368	−	0.498581i	0.311494	−	0.950248i	$-0.399171\pi$
$829$	34.6568	−	14.3553i	1.20368	−	0.498581i	0.892187	+	0.451667i	$0.149171\pi$
$830$		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	$-0.290025\pi$
$839$	−5.13731	−	5.13731i	−0.177360	−	0.177360i	−0.790204	+	0.612844i	$0.790025\pi$
$840$		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	$-0.547077\pi$
$853$	−27.7734	−	11.5041i	−0.950943	−	0.393893i	−0.803585	+	0.595190i	$0.797077\pi$
$854$		0			0
$855$	0.726686	−	12.5772i	0.0248521	−	0.430130i
$856$		0			0
$857$	−23.9037	+	23.9037i	−0.816536	+	0.816536i	−0.985604	−	0.169069i	$-0.945924\pi$
$857$	−23.9037	+	23.9037i	−0.816536	+	0.816536i	0.169069	+	0.985604i	$0.445924\pi$
$858$		0			0
$859$	−36.4970	−	15.1176i	−1.24526	−	0.515805i	−0.339907	−	0.940459i	$-0.610396\pi$
$859$	−36.4970	−	15.1176i	−1.24526	−	0.515805i	−0.905356	+	0.424654i	$0.860396\pi$
$860$		0			0
$861$	−18.4234	−	19.5186i	−0.627869	−	0.665193i
$862$		0			0
$863$	48.7809			1.66052			0.830260	−	0.557377i	$-0.188192\pi$
$863$	48.7809			1.66052			0.830260	+	0.557377i	$0.188192\pi$
$864$		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	$-0.00332930\pi$
$877$	8.45430	+	20.4105i	0.285481	+	0.689213i	−0.714464	+	0.699672i	$0.753329\pi$
$878$		0			0
$879$	−7.59343	−	19.9410i	−0.256120	−	0.672592i
$880$		0			0
$881$	−25.8223			−0.869976			−0.434988	−	0.900436i	$-0.643247\pi$
$881$	−25.8223			−0.869976			−0.434988	+	0.900436i	$0.643247\pi$
$882$		0			0
$883$	−33.3809	+	13.8268i	−1.12336	+	0.465310i	−0.865518	−	0.500878i	$-0.833010\pi$
$883$	−33.3809	+	13.8268i	−1.12336	+	0.465310i	−0.257839	+	0.966188i	$0.583010\pi$
$884$		0			0
$885$	−11.5672	−	0.333887i	−0.388827	−	0.0112235i
$886$		0			0
$887$	−34.6997	+	34.6997i	−1.16510	+	1.16510i	−0.181760	+	0.983343i	$0.558180\pi$
$887$	−34.6997	+	34.6997i	−1.16510	+	1.16510i	−0.983343	+	0.181760i	$0.941820\pi$
$888$		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	−0.751392	−	0.659856i	$-0.770617\pi$
$907$	7.42403	−	17.9232i	0.246511	−	0.595130i	0.997903	+	0.0647258i	$0.0206173\pi$
$908$		0			0
$909$	22.1825	−	45.8728i	0.735746	−	1.52151i
$910$		0			0
$911$		−	37.5930i		−	1.24551i	−0.782416	−	0.622756i	$-0.786013\pi$
$911$		−	37.5930i		−	1.24551i	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	$-0.0202936\pi$
$919$	28.3220	+	28.3220i	0.934258	+	0.934258i	−0.0637109	+	0.997968i	$0.520294\pi$
$920$		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	$-0.922855\pi$
$929$		−	14.6297i		−	0.479986i	0.970775	−	0.239993i	$-0.0771452\pi$
$930$		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	−0.609541	−	0.792754i	$-0.708646\pi$
$937$	5.60824	−	5.60824i	0.183213	−	0.183213i	0.792754	+	0.609541i	$0.208646\pi$
$938$		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	$-0.565536\pi$
$941$	10.5273	−	4.36054i	0.343180	−	0.142150i	0.547615	+	0.836730i	$0.315536\pi$
$942$		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	−0.654711	−	0.755879i	$-0.727210\pi$
$947$	−22.3491	−	53.9555i	−0.726248	−	1.75332i	−0.0715370	−	0.997438i	$-0.522790\pi$
$948$		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	0.0673750	−	0.997728i	$-0.478538\pi$
$953$	32.8805	−	32.8805i	1.06510	−	1.06510i	0.997728	−	0.0673750i	$-0.0214624\pi$
$954$		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	$-0.642124\pi$
$967$	14.6204	−	14.6204i	0.470160	−	0.470160i	0.901966	+	0.431807i	$0.142124\pi$
$968$		0			0
$969$	−3.92670	−	1.76089i	−0.126144	−	0.0565679i
$970$		0			0
$971$	−39.9825	−	16.5613i	−1.28310	−	0.531477i	−0.366178	−	0.930545i	$-0.619334\pi$
$971$	−39.9825	−	16.5613i	−1.28310	−	0.531477i	−0.916921	+	0.399068i	$0.869334\pi$
$972$		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	$-0.427286\pi$
$977$	14.1567			0.452912			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	$-0.536506\pi$
$983$	27.5590	−	27.5590i	0.878995	−	0.878995i	0.993431	+	0.114436i	$0.0365060\pi$
$984$		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	$0.0760734\pi$
$991$			14.9042i			0.473446i	−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	$-0.813180\pi$
$997$	4.66402	−	11.2599i	0.147711	−	0.356606i	0.980366	+	0.197186i	$0.0631804\pi$
$998$		0			0
$999$	0.461327	+	1.45960i	0.0145958	+	0.0461798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.o.b.671.4		56
3.2	odd	2	inner	768.2.o.b.671.7		56
4.3	odd	2		768.2.o.a.671.11		56
8.3	odd	2		384.2.o.a.335.4		56
8.5	even	2		96.2.o.a.11.6	✓	56
12.11	even	2		768.2.o.a.671.8		56
24.5	odd	2		96.2.o.a.11.9	yes	56
24.11	even	2		384.2.o.a.335.7		56
32.3	odd	8	inner	768.2.o.b.95.7		56
32.13	even	8		384.2.o.a.47.7		56
32.19	odd	8		96.2.o.a.35.9	yes	56
32.29	even	8		768.2.o.a.95.8		56
96.29	odd	8		768.2.o.a.95.11		56
96.35	even	8	inner	768.2.o.b.95.4		56
96.77	odd	8		384.2.o.a.47.4		56
96.83	even	8		96.2.o.a.35.6	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.o.a.11.6	✓	56	8.5	even	2
96.2.o.a.11.9	yes	56	24.5	odd	2
96.2.o.a.35.6	yes	56	96.83	even	8
96.2.o.a.35.9	yes	56	32.19	odd	8
384.2.o.a.47.4		56	96.77	odd	8
384.2.o.a.47.7		56	32.13	even	8
384.2.o.a.335.4		56	8.3	odd	2
384.2.o.a.335.7		56	24.11	even	2
768.2.o.a.95.8		56	32.29	even	8
768.2.o.a.95.11		56	96.29	odd	8
768.2.o.a.671.8		56	12.11	even	2
768.2.o.a.671.11		56	4.3	odd	2
768.2.o.b.95.4		56	96.35	even	8	inner
768.2.o.b.95.7		56	32.3	odd	8	inner
768.2.o.b.671.4		56	1.1	even	1	trivial
768.2.o.b.671.7		56	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.o (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.18890 - 1.25957i) q^{3} +(-1.06973 - 0.443098i) q^{5} +(2.37247 - 2.37247i) q^{7} +(-0.173046 + 2.99501i) q^{9} +O(q^{10})\)	\(q+(-1.18890 - 1.25957i) q^{3} +(-1.06973 - 0.443098i) q^{5} +(2.37247 - 2.37247i) q^{7} +(-0.173046 + 2.99501i) q^{9} +(5.50127 + 2.27870i) q^{11} +(-0.346353 - 0.836171i) q^{13} +(0.713689 + 1.87421i) q^{15} +0.685064 q^{17} +(3.35074 - 1.38792i) q^{19} +(-5.80891 - 0.167674i) q^{21} +(-2.05133 + 2.05133i) q^{23} +(-2.58754 - 2.58754i) q^{25} +(3.97816 - 3.34279i) q^{27} +(-1.98869 - 4.80112i) q^{29} -6.36503i q^{31} +(-3.67025 - 9.63838i) q^{33} +(-3.58914 + 1.48667i) q^{35} +(-0.112738 + 0.272172i) q^{37} +(-0.641440 + 1.43038i) q^{39} +(3.26585 + 3.26585i) q^{41} +(0.993018 - 2.39736i) q^{43} +(1.51219 - 3.12718i) q^{45} -11.7975i q^{47} -4.25719i q^{49} +(-0.814471 - 0.862888i) q^{51} +(-1.56192 + 3.77080i) q^{53} +(-4.87520 - 4.87520i) q^{55} +(-5.73187 - 2.57040i) q^{57} +(-2.20815 + 5.33094i) q^{59} +(1.53549 - 0.636020i) q^{61} +(6.69500 + 7.51609i) q^{63} +1.04795i q^{65} +(-4.69605 - 11.3373i) q^{67} +(5.02262 + 0.144978i) q^{69} +(7.99150 + 7.99150i) q^{71} +(-2.34760 + 2.34760i) q^{73} +(-0.182875 + 6.33551i) q^{75} +(18.4577 - 7.64543i) q^{77} +8.91043 q^{79} +(-8.94011 - 1.03655i) q^{81} +(-3.06920 - 7.40970i) q^{83} +(-0.732836 - 0.303551i) q^{85} +(-3.68301 + 8.21294i) q^{87} +(1.99332 - 1.99332i) q^{89} +(-2.80550 - 1.16208i) q^{91} +(-8.01722 + 7.56737i) q^{93} -4.19938 q^{95} +8.66510 q^{97} +(-7.77669 + 16.0820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{3} - 8 q^{7} - 4 q^{9}+O(q^{10}) \) 56 * q + 4 * q^3 - 8 * q^7 - 4 * q^9	\( 56 q + 4 q^{3} - 8 q^{7} - 4 q^{9} + 8 q^{13} - 8 q^{15} + 8 q^{19} + 4 q^{21} - 8 q^{25} + 28 q^{27} - 8 q^{33} + 8 q^{37} - 28 q^{39} + 8 q^{43} + 4 q^{45} + 16 q^{51} + 24 q^{55} - 4 q^{57} + 40 q^{61} - 56 q^{67} + 4 q^{69} - 8 q^{73} - 16 q^{75} + 16 q^{79} + 48 q^{85} + 52 q^{87} - 40 q^{91} - 8 q^{93} - 16 q^{97} - 60 q^{99}+O(q^{100}) \) 56 * q + 4 * q^3 - 8 * q^7 - 4 * q^9 + 8 * q^13 - 8 * q^15 + 8 * q^19 + 4 * q^21 - 8 * q^25 + 28 * q^27 - 8 * q^33 + 8 * q^37 - 28 * q^39 + 8 * q^43 + 4 * q^45 + 16 * q^51 + 24 * q^55 - 4 * q^57 + 40 * q^61 - 56 * q^67 + 4 * q^69 - 8 * q^73 - 16 * q^75 + 16 * q^79 + 48 * q^85 + 52 * q^87 - 40 * q^91 - 8 * q^93 - 16 * q^97 - 60 * q^99

Introduction

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