LMFDB - Embedded newform 352.2.s.b.79.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [352,2,Mod(79,352)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(352, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 1]))

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

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

chi := DirichletCharacter("352.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 352 = 2^{5} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	352.s (of order $10$, 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:	$2.81073415115$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			79.6
Character	$\chi$	$=$	352.79
Dual form			352.2.s.b.303.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.903665 - 0.656551i) q^{3} +(3.74056 - 1.21538i) q^{5} +(2.25832 + 1.64076i) q^{7} +(-0.541500 + 1.66657i) q^{9} +(-3.00002 - 1.41418i) q^{11} +(-0.653051 + 2.00988i) q^{13} +(2.58225 - 3.55416i) q^{15} +(-4.42965 + 1.43928i) q^{17} +(-2.18382 - 3.00577i) q^{19} +3.11801 q^{21} -0.854640i q^{23} +(8.46953 - 6.15347i) q^{25} +(1.64036 + 5.04850i) q^{27} +(-4.36210 - 3.16925i) q^{29} +(0.796872 + 0.258919i) q^{31} +(-3.63949 + 0.691723i) q^{33} +(10.4415 + 3.39265i) q^{35} +(2.13456 - 2.93797i) q^{37} +(0.729452 + 2.24502i) q^{39} +(-2.17890 - 2.99900i) q^{41} +1.38448i q^{43} +6.89201i q^{45} +(0.799046 + 1.09979i) q^{47} +(0.244772 + 0.753330i) q^{49} +(-3.05796 + 4.20892i) q^{51} +(-4.01470 - 1.30446i) q^{53} +(-12.9405 - 1.64365i) q^{55} +(-3.94688 - 1.28242i) q^{57} +(-6.80468 - 4.94389i) q^{59} +(0.970728 + 2.98759i) q^{61} +(-3.95732 + 2.87516i) q^{63} +8.31179i q^{65} -3.45851 q^{67} +(-0.561115 - 0.772308i) q^{69} +(11.7395 - 3.81439i) q^{71} +(1.90829 - 2.62654i) q^{73} +(3.61355 - 11.1214i) q^{75} +(-4.45466 - 8.11598i) q^{77} +(-3.59997 + 11.0796i) q^{79} +(0.543938 + 0.395194i) q^{81} +(-0.870974 + 0.282997i) q^{83} +(-14.8201 + 10.7674i) q^{85} -6.02266 q^{87} +7.98458 q^{89} +(-4.77254 + 3.46745i) q^{91} +(0.890099 - 0.289211i) q^{93} +(-11.8218 - 8.58907i) q^{95} +(-3.44331 + 10.5974i) q^{97} +(3.98133 - 4.23395i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{3} - 10 q^{9} + 18 q^{11} - 10 q^{17} + 6 q^{25} + 32 q^{27} + 32 q^{33} + 10 q^{35} - 10 q^{41} - 18 q^{49} - 60 q^{51} - 80 q^{57} - 28 q^{59} + 28 q^{67} - 10 q^{73} - 4 q^{75} + 28 q^{81}+ \cdots - 122 q^{99}+O(q^{100}) $ 32 * q + 2 * q^3 - 10 * q^9 + 18 * q^11 - 10 * q^17 + 6 * q^25 + 32 * q^27 + 32 * q^33 + 10 * q^35 - 10 * q^41 - 18 * q^49 - 60 * q^51 - 80 * q^57 - 28 * q^59 + 28 * q^67 - 10 * q^73 - 4 * q^75 + 28 * q^81 + 20 * q^89 - 78 * q^91 - 52 * q^97 - 122 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/352\mathbb{Z}\right)^\times$.

$n$	$133$	$287$	$321$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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
$3$	0.903665	−	0.656551i	0.521731	−	0.379060i	−0.295525	−	0.955335i	$-0.595494\pi$
$3$	0.903665	−	0.656551i	0.521731	−	0.379060i	0.817256	+	0.576275i	$0.195494\pi$
$4$		0			0
$5$	3.74056	−	1.21538i	1.67283	−	0.543535i	0.689329	−	0.724448i	$-0.257905\pi$
$5$	3.74056	−	1.21538i	1.67283	−	0.543535i	0.983499	+	0.180914i	$0.0579055\pi$
$6$		0			0
$7$	2.25832	+	1.64076i	0.853564	+	0.620150i	0.926126	−	0.377214i	$-0.123118\pi$
$7$	2.25832	+	1.64076i	0.853564	+	0.620150i	−0.0725628	+	0.997364i	$0.523118\pi$
$8$		0			0
$9$	−0.541500	+	1.66657i	−0.180500	+	0.555522i
$10$		0			0
$11$	−3.00002	−	1.41418i	−0.904539	−	0.426390i
$11$	−3.00002	−	1.41418i	−0.904539	−	0.426390i
$12$		0			0
$13$	−0.653051	+	2.00988i	−0.181124	+	0.557441i	−0.999860	−	0.0167282i	$-0.994675\pi$
$13$	−0.653051	+	2.00988i	−0.181124	+	0.557441i	0.818736	+	0.574170i	$0.194675\pi$
$14$		0			0
$15$	2.58225	−	3.55416i	0.666734	−	0.917681i
$16$		0			0
$17$	−4.42965	+	1.43928i	−1.07435	+	0.349077i	−0.792180	−	0.610288i	$-0.791054\pi$
$17$	−4.42965	+	1.43928i	−1.07435	+	0.349077i	−0.282169	+	0.959365i	$0.591054\pi$
$18$		0			0
$19$	−2.18382	−	3.00577i	−0.501002	−	0.689570i	0.481368	−	0.876519i	$-0.340140\pi$
$19$	−2.18382	−	3.00577i	−0.501002	−	0.689570i	−0.982370	+	0.186949i	$0.940140\pi$
$20$		0			0
$21$	3.11801			0.680405
$22$		0			0
$23$		−	0.854640i		−	0.178205i	−0.996022	−	0.0891024i	$-0.971600\pi$
$23$		−	0.854640i		−	0.178205i	0.996022	−	0.0891024i	$-0.0283998\pi$
$24$		0			0
$25$	8.46953	−	6.15347i	1.69391	−	1.23069i
$26$		0			0
$27$	1.64036	+	5.04850i	0.315687	+	0.971585i
$28$		0			0
$29$	−4.36210	−	3.16925i	−0.810022	−	0.588516i	0.103815	−	0.994597i	$-0.466895\pi$
$29$	−4.36210	−	3.16925i	−0.810022	−	0.588516i	−0.913837	+	0.406081i	$0.866895\pi$
$30$		0			0
$31$	0.796872	+	0.258919i	0.143122	+	0.0465033i	0.379702	−	0.925109i	$-0.376026\pi$
$31$	0.796872	+	0.258919i	0.143122	+	0.0465033i	−0.236580	+	0.971612i	$0.576026\pi$
$32$		0			0
$33$	−3.63949	+	0.691723i	−0.633554	+	0.120413i
$34$		0			0
$35$	10.4415	+	3.39265i	1.76494	+	0.573463i
$36$		0			0
$37$	2.13456	−	2.93797i	0.350919	−	0.482999i	−0.596671	−	0.802486i	$-0.703510\pi$
$37$	2.13456	−	2.93797i	0.350919	−	0.482999i	0.947591	+	0.319487i	$0.103510\pi$
$38$		0			0
$39$	0.729452	+	2.24502i	0.116806	+	0.359491i
$40$		0			0
$41$	−2.17890	−	2.99900i	−0.340287	−	0.468365i	0.604238	−	0.796804i	$-0.293478\pi$
$41$	−2.17890	−	2.99900i	−0.340287	−	0.468365i	−0.944525	+	0.328439i	$0.893478\pi$
$42$		0			0
$43$			1.38448i			0.211131i	0.994412	+	0.105565i	$0.0336652\pi$
$43$			1.38448i			0.211131i	−0.994412	+	0.105565i	$0.966335\pi$
$44$		0			0
$45$			6.89201i			1.02740i
$46$		0			0
$47$	0.799046	+	1.09979i	0.116553	+	0.160421i	0.863307	−	0.504679i	$-0.168389\pi$
$47$	0.799046	+	1.09979i	0.116553	+	0.160421i	−0.746754	+	0.665100i	$0.768389\pi$
$48$		0			0
$49$	0.244772	+	0.753330i	0.0349674	+	0.107619i
$50$		0			0
$51$	−3.05796	+	4.20892i	−0.428200	+	0.589367i
$52$		0			0
$53$	−4.01470	−	1.30446i	−0.551462	−	0.179181i	0.0200141	−	0.999800i	$-0.493629\pi$
$53$	−4.01470	−	1.30446i	−0.551462	−	0.179181i	−0.571476	+	0.820619i	$0.693629\pi$
$54$		0			0
$55$	−12.9405	−	1.64365i	−1.74490	−	0.221629i
$56$		0			0
$57$	−3.94688	−	1.28242i	−0.522776	−	0.169860i
$58$		0			0
$59$	−6.80468	−	4.94389i	−0.885894	−	0.643640i	0.0489102	−	0.998803i	$-0.484425\pi$
$59$	−6.80468	−	4.94389i	−0.885894	−	0.643640i	−0.934804	+	0.355164i	$0.884425\pi$
$60$		0			0
$61$	0.970728	+	2.98759i	0.124289	+	0.382522i	0.993771	−	0.111443i	$-0.0355471\pi$
$61$	0.970728	+	2.98759i	0.124289	+	0.382522i	−0.869482	+	0.493965i	$0.835547\pi$
$62$		0			0
$63$	−3.95732	+	2.87516i	−0.498575	+	0.362236i
$64$		0			0
$65$			8.31179i			1.03095i
$66$		0			0
$67$	−3.45851			−0.422524			−0.211262	−	0.977429i	$-0.567757\pi$
$67$	−3.45851			−0.422524			−0.211262	+	0.977429i	$0.567757\pi$
$68$		0			0
$69$	−0.561115	−	0.772308i	−0.0675503	−	0.0929750i
$70$		0			0
$71$	11.7395	−	3.81439i	1.39322	−	0.452684i	0.486227	−	0.873832i	$-0.338373\pi$
$71$	11.7395	−	3.81439i	1.39322	−	0.452684i	0.906992	+	0.421148i	$0.138373\pi$
$72$		0			0
$73$	1.90829	−	2.62654i	0.223349	−	0.307413i	−0.682607	−	0.730786i	$-0.739154\pi$
$73$	1.90829	−	2.62654i	0.223349	−	0.307413i	0.905956	+	0.423373i	$0.139154\pi$
$74$		0			0
$75$	3.61355	−	11.1214i	0.417257	−	1.28418i
$76$		0			0
$77$	−4.45466	−	8.11598i	−0.507656	−	0.924901i
$78$		0			0
$79$	−3.59997	+	11.0796i	−0.405029	+	1.24655i	0.515843	+	0.856683i	$0.327479\pi$
$79$	−3.59997	+	11.0796i	−0.405029	+	1.24655i	−0.920871	+	0.389867i	$0.872521\pi$
$80$		0			0
$81$	0.543938	+	0.395194i	0.0604376	+	0.0439105i
$82$		0			0
$83$	−0.870974	+	0.282997i	−0.0956018	+	0.0310629i	−0.356427	−	0.934323i	$-0.616005\pi$
$83$	−0.870974	+	0.282997i	−0.0956018	+	0.0310629i	0.260826	+	0.965386i	$0.416005\pi$
$84$		0			0
$85$	−14.8201	+	10.7674i	−1.60746	+	1.16789i
$86$		0			0
$87$	−6.02266			−0.645697
$88$		0			0
$89$	7.98458			0.846363			0.423182	−	0.906045i	$-0.360913\pi$
$89$	7.98458			0.846363			0.423182	+	0.906045i	$0.360913\pi$
$90$		0			0
$91$	−4.77254	+	3.46745i	−0.500298	+	0.363488i
$92$		0			0
$93$	0.890099	−	0.289211i	0.0922990	−	0.0299898i
$94$		0			0
$95$	−11.8218	−	8.58907i	−1.21289	−	0.881220i
$96$		0			0
$97$	−3.44331	+	10.5974i	−0.349615	+	1.07600i	0.609451	+	0.792824i	$0.291390\pi$
$97$	−3.44331	+	10.5974i	−0.349615	+	1.07600i	−0.959066	+	0.283181i	$0.908610\pi$
$98$		0			0
$99$	3.98133	−	4.23395i	0.400138	−	0.425528i
$100$		0			0
$101$	−1.65660	+	5.09849i	−0.164838	+	0.507319i	−0.999024	−	0.0441635i	$-0.985938\pi$
$101$	−1.65660	+	5.09849i	−0.164838	+	0.507319i	0.834186	+	0.551483i	$0.185938\pi$
$102$		0			0
$103$	3.62026	−	4.98285i	0.356714	−	0.490975i	−0.592515	−	0.805559i	$-0.701865\pi$
$103$	3.62026	−	4.98285i	0.356714	−	0.490975i	0.949230	+	0.314584i	$0.101865\pi$
$104$		0			0
$105$	11.6631	−	3.78956i	1.13820	−	0.369824i
$106$		0			0
$107$	9.02248	+	12.4184i	0.872236	+	1.20053i	0.978511	+	0.206193i	$0.0661075\pi$
$107$	9.02248	+	12.4184i	0.872236	+	1.20053i	−0.106275	+	0.994337i	$0.533893\pi$
$108$		0			0
$109$	2.86723			0.274631			0.137315	−	0.990527i	$-0.456153\pi$
$109$	2.86723			0.274631			0.137315	+	0.990527i	$0.456153\pi$
$110$		0			0
$111$		−	4.05639i		−	0.385015i
$112$		0			0
$113$	−8.25780	+	5.99964i	−0.776828	+	0.564399i	−0.904025	−	0.427479i	$-0.859402\pi$
$113$	−8.25780	+	5.99964i	−0.776828	+	0.564399i	0.127197	+	0.991877i	$0.459402\pi$
$114$		0			0
$115$	−1.03871	−	3.19683i	−0.0968605	−	0.298106i
$116$		0			0
$117$	−2.99598	−	2.17670i	−0.276978	−	0.201236i
$118$		0			0
$119$	−12.3651	−	4.01766i	−1.13350	−	0.368298i
$120$		0			0
$121$	7.00021	+	8.48511i	0.636383	+	0.771374i
$122$		0			0
$123$	−3.93799	−	1.27953i	−0.355077	−	0.115371i
$124$		0			0
$125$	12.6430	−	17.4016i	1.13082	−	1.55645i
$126$		0			0
$127$	3.94256	+	12.1339i	0.349845	+	1.07671i	0.958938	+	0.283614i	$0.0915335\pi$
$127$	3.94256	+	12.1339i	0.349845	+	1.07671i	−0.609093	+	0.793099i	$0.708467\pi$
$128$		0			0
$129$	0.908979	+	1.25110i	0.0800312	+	0.110153i
$130$		0			0
$131$		−	10.8120i		−	0.944646i	−0.881426	−	0.472323i	$-0.843416\pi$
$131$		−	10.8120i		−	0.944646i	0.881426	−	0.472323i	$-0.156584\pi$
$132$		0			0
$133$		−	10.3711i		−	0.899288i
$134$		0			0
$135$	12.2717	+	16.8906i	1.05618	+	1.45371i
$136$		0			0
$137$	−6.64424	−	20.4489i	−0.567656	−	1.74707i	−0.659925	−	0.751332i	$-0.729412\pi$
$137$	−6.64424	−	20.4489i	−0.567656	−	1.74707i	0.0922685	−	0.995734i	$-0.470588\pi$
$138$		0			0
$139$	−4.01113	+	5.52085i	−0.340220	+	0.468273i	−0.944506	−	0.328495i	$-0.893459\pi$
$139$	−4.01113	+	5.52085i	−0.340220	+	0.468273i	0.604286	+	0.796768i	$0.293459\pi$
$140$		0			0
$141$	1.44414	+	0.469230i	0.121619	+	0.0395163i
$142$		0			0
$143$	4.80149	−	5.10616i	0.401521	−	0.426998i
$144$		0			0
$145$	−20.1686	−	6.55316i	−1.67491	−	0.544210i
$146$		0			0
$147$	0.715792	+	0.520053i	0.0590375	+	0.0428932i
$148$		0			0
$149$	3.50314	+	10.7816i	0.286989	+	0.883260i	0.985796	+	0.167950i	$0.0537147\pi$
$149$	3.50314	+	10.7816i	0.286989	+	0.883260i	−0.698807	+	0.715310i	$0.746285\pi$
$150$		0			0
$151$	1.11632	−	0.811053i	0.0908447	−	0.0660026i	−0.541436	−	0.840742i	$-0.682119\pi$
$151$	1.11632	−	0.811053i	0.0908447	−	0.0660026i	0.632280	+	0.774740i	$0.282119\pi$
$152$		0			0
$153$		−	8.16168i		−	0.659832i
$154$		0			0
$155$	3.29543			0.264695
$156$		0			0
$157$	11.3001	+	15.5532i	0.901843	+	1.24128i	0.969876	+	0.243598i	$0.0783277\pi$
$157$	11.3001	+	15.5532i	0.901843	+	1.24128i	−0.0680330	+	0.997683i	$0.521672\pi$
$158$		0			0
$159$	−4.48439	+	1.45707i	−0.355635	+	0.115553i
$160$		0			0
$161$	1.40226	−	1.93005i	0.110514	−	0.152109i
$162$		0			0
$163$	−3.44315	+	10.5969i	−0.269689	+	0.830016i	0.720887	+	0.693052i	$0.243734\pi$
$163$	−3.44315	+	10.5969i	−0.269689	+	0.830016i	−0.990576	+	0.136964i	$0.956266\pi$
$164$		0			0
$165$	−12.7730	+	7.01079i	−0.994378	+	0.545789i
$166$		0			0
$167$	6.27006	−	19.2973i	0.485192	−	1.49327i	−0.346510	−	0.938046i	$-0.612633\pi$
$167$	6.27006	−	19.2973i	0.485192	−	1.49327i	0.831702	−	0.555222i	$-0.187367\pi$
$168$		0			0
$169$	6.90406	+	5.01610i	0.531082	+	0.385854i
$170$		0			0
$171$	6.19184	−	2.01185i	0.473502	−	0.153850i
$172$		0			0
$173$	12.6022	−	9.15603i	0.958127	−	0.696120i	0.00541199	−	0.999985i	$-0.498277\pi$
$173$	12.6022	−	9.15603i	0.958127	−	0.696120i	0.952715	+	0.303865i	$0.0982773\pi$
$174$		0			0
$175$	29.2233			2.20907
$176$		0			0
$177$	−9.39507			−0.706176
$178$		0			0
$179$	−13.7239	+	9.97097i	−1.02577	+	0.745265i	−0.967458	−	0.253033i	$-0.918572\pi$
$179$	−13.7239	+	9.97097i	−1.02577	+	0.745265i	−0.0583123	+	0.998298i	$0.518572\pi$
$180$		0			0
$181$	12.6430	−	4.10796i	0.939746	−	0.305342i	0.201204	−	0.979549i	$-0.435515\pi$
$181$	12.6430	−	4.10796i	0.939746	−	0.305342i	0.738542	+	0.674207i	$0.235515\pi$
$182$		0			0
$183$	2.83872	+	2.06245i	0.209844	+	0.152461i
$184$		0			0
$185$	4.41369	−	13.5839i	0.324501	−	0.998711i
$186$		0			0
$187$	15.3244	+	1.94644i	1.12063	+	0.142338i
$188$		0			0
$189$	−4.57895	+	14.0926i	−0.333070	+	1.02508i
$190$		0			0
$191$	14.8778	−	20.4775i	1.07652	−	1.48170i	0.213224	−	0.977003i	$-0.431603\pi$
$191$	14.8778	−	20.4775i	1.07652	−	1.48170i	0.863295	−	0.504699i	$-0.168397\pi$
$192$		0			0
$193$	6.00552	−	1.95131i	0.432287	−	0.140458i	−0.0847876	−	0.996399i	$-0.527021\pi$
$193$	6.00552	−	1.95131i	0.432287	−	0.140458i	0.517074	+	0.855941i	$0.327021\pi$
$194$		0			0
$195$	5.45711	+	7.51107i	0.390792	+	0.537879i
$196$		0			0
$197$	10.8725			0.774631			0.387316	−	0.921947i	$-0.373402\pi$
$197$	10.8725			0.774631			0.387316	+	0.921947i	$0.373402\pi$
$198$		0			0
$199$			22.1838i			1.57257i	0.617866	+	0.786283i	$0.287997\pi$
$199$			22.1838i			1.57257i	−0.617866	+	0.786283i	$0.712003\pi$
$200$		0			0
$201$	−3.12533	+	2.27069i	−0.220444	+	0.160162i
$202$		0			0
$203$	−4.65102	−	14.3144i	−0.326437	−	1.00467i
$204$		0			0
$205$	−11.7952	−	8.56973i	−0.823814	−	0.598536i
$206$		0			0
$207$	1.42431	+	0.462788i	0.0989966	+	0.0321660i
$208$		0			0
$209$	2.30080	+	12.1056i	0.159150	+	0.837365i
$210$		0			0
$211$	−4.29344	−	1.39502i	−0.295572	−	0.0960373i	0.157477	−	0.987523i	$-0.449664\pi$
$211$	−4.29344	−	1.39502i	−0.295572	−	0.0960373i	−0.453050	+	0.891485i	$0.649664\pi$
$212$		0			0
$213$	8.10421	−	11.1545i	0.555291	−	0.764293i
$214$		0			0
$215$	1.68267	+	5.17871i	0.114757	+	0.353185i
$216$		0			0
$217$	1.37476	+	1.89220i	0.0933251	+	0.128451i
$218$		0			0
$219$		−	3.62640i		−	0.245049i
$220$		0			0
$221$		−	9.84301i		−	0.662112i
$222$		0			0
$223$	−9.00750	−	12.3978i	−0.603187	−	0.830216i	0.392808	−	0.919620i	$-0.371504\pi$
$223$	−9.00750	−	12.3978i	−0.603187	−	0.830216i	−0.995995	+	0.0894046i	$0.971504\pi$
$224$		0			0
$225$	5.66892	+	17.4471i	0.377928	+	1.16314i
$226$		0			0
$227$	11.9130	−	16.3968i	0.790692	−	1.08829i	−0.203329	−	0.979110i	$-0.565176\pi$
$227$	11.9130	−	16.3968i	0.790692	−	1.08829i	0.994022	−	0.109184i	$-0.0348238\pi$
$228$		0			0
$229$	−3.54360	−	1.15138i	−0.234168	−	0.0760856i	0.189583	−	0.981865i	$-0.439287\pi$
$229$	−3.54360	−	1.15138i	−0.234168	−	0.0760856i	−0.423750	+	0.905779i	$0.639287\pi$
$230$		0			0
$231$	−9.35407	−	4.40941i	−0.615453	−	0.290118i
$232$		0			0
$233$	23.3988	+	7.60272i	1.53290	+	0.498071i	0.949408	−	0.314045i	$-0.101684\pi$
$233$	23.3988	+	7.60272i	1.53290	+	0.498071i	0.583496	+	0.812116i	$0.301684\pi$
$234$		0			0
$235$	4.32555	+	3.14269i	0.282168	+	0.205007i
$236$		0			0
$237$	4.02114	+	12.3758i	0.261201	+	0.803894i
$238$		0			0
$239$	−14.0082	+	10.1775i	−0.906113	+	0.658330i	−0.940029	−	0.341095i	$-0.889202\pi$
$239$	−14.0082	+	10.1775i	−0.906113	+	0.658330i	0.0339157	+	0.999425i	$0.489202\pi$
$240$		0			0
$241$		−	12.0062i		−	0.773387i	−0.922208	−	0.386694i	$-0.873617\pi$
$241$		−	12.0062i		−	0.773387i	0.922208	−	0.386694i	$-0.126383\pi$
$242$		0			0
$243$	−15.1739			−0.973408
$244$		0			0
$245$	1.83117	+	2.52038i	0.116989	+	0.161021i
$246$		0			0
$247$	7.46738	−	2.42630i	0.475138	−	0.154382i
$248$		0			0
$249$	−0.601267	+	0.827573i	−0.0381037	+	0.0524453i
$250$		0			0
$251$	−0.828764	+	2.55067i	−0.0523111	+	0.160997i	−0.973799	−	0.227410i	$-0.926974\pi$
$251$	−0.828764	+	2.55067i	−0.0523111	+	0.160997i	0.921488	+	0.388407i	$0.126974\pi$
$252$		0			0
$253$	−1.20861	+	2.56393i	−0.0759848	+	0.161193i
$254$		0			0
$255$	−6.32303	+	19.4603i	−0.395964	+	1.21865i
$256$		0			0
$257$	−10.9160	−	7.93091i	−0.680919	−	0.494717i	0.192743	−	0.981249i	$-0.438261\pi$
$257$	−10.9160	−	7.93091i	−0.680919	−	0.494717i	−0.873662	+	0.486533i	$0.838261\pi$
$258$		0			0
$259$	9.64102	−	3.13256i	0.599064	−	0.194648i
$260$		0			0
$261$	7.64385	−	5.55358i	0.473142	−	0.343758i
$262$		0			0
$263$	0.593593			0.0366025			0.0183013	−	0.999833i	$-0.494174\pi$
$263$	0.593593			0.0366025			0.0183013	+	0.999833i	$0.494174\pi$
$264$		0			0
$265$	−16.6026			−1.01989
$266$		0			0
$267$	7.21538	−	5.24228i	0.441574	−	0.320822i
$268$		0			0
$269$	−18.5270	+	6.01978i	−1.12961	+	0.367032i	−0.813427	−	0.581666i	$-0.802401\pi$
$269$	−18.5270	+	6.01978i	−1.12961	+	0.367032i	−0.316182	+	0.948699i	$0.602401\pi$
$270$		0			0
$271$	−19.8565	−	14.4266i	−1.20619	−	0.876351i	−0.211314	−	0.977418i	$-0.567774\pi$
$271$	−19.8565	−	14.4266i	−1.20619	−	0.876351i	−0.994880	+	0.101067i	$0.967774\pi$
$272$		0			0
$273$	−2.03622	+	6.26683i	−0.123237	+	0.379286i
$274$		0			0
$275$	−34.1108	+	6.48312i	−2.05696	+	0.390947i
$276$		0			0
$277$	4.54208	−	13.9791i	0.272907	−	0.839921i	−0.716859	−	0.697219i	$-0.754421\pi$
$277$	4.54208	−	13.9791i	0.272907	−	0.839921i	0.989766	−	0.142703i	$-0.0455793\pi$
$278$		0			0
$279$	−0.863012	+	1.18783i	−0.0516672	+	0.0711138i
$280$		0			0
$281$	−21.9124	+	7.11976i	−1.30718	+	0.424729i	−0.878075	−	0.478524i	$-0.841172\pi$
$281$	−21.9124	+	7.11976i	−1.30718	+	0.424729i	−0.429108	+	0.903253i	$0.641172\pi$
$282$		0			0
$283$	−13.2652	−	18.2581i	−0.788537	−	1.08533i	−0.994289	−	0.106724i	$-0.965964\pi$
$283$	−13.2652	−	18.2581i	−0.788537	−	1.08533i	0.205751	−	0.978604i	$-0.434036\pi$
$284$		0			0
$285$	−16.3221			−0.966840
$286$		0			0
$287$		−	10.3477i		−	0.610808i
$288$		0			0
$289$	3.79700	−	2.75868i	0.223353	−	0.162275i
$290$		0			0
$291$	3.84615	+	11.8372i	0.225465	+	0.693910i
$292$		0			0
$293$	0.181791	+	0.132079i	0.0106203	+	0.00771613i	0.593083	−	0.805142i	$-0.297911\pi$
$293$	0.181791	+	0.132079i	0.0106203	+	0.00771613i	−0.582462	+	0.812858i	$0.697911\pi$
$294$		0			0
$295$	−31.4620	−	10.2226i	−1.83179	−	0.595184i
$296$		0			0
$297$	2.21837	−	17.4654i	0.128723	−	1.01344i
$298$		0			0
$299$	1.71773	+	0.558123i	0.0993387	+	0.0322771i
$300$		0			0
$301$	−2.27160	+	3.12659i	−0.130933	+	0.180213i
$302$		0			0
$303$	1.85041	+	5.69497i	0.106303	+	0.327168i
$304$		0			0
$305$	7.26213	+	9.99546i	0.415828	+	0.572339i
$306$		0			0
$307$		−	7.94263i		−	0.453310i	−0.973975	−	0.226655i	$-0.927221\pi$
$307$		−	7.94263i		−	0.453310i	0.973975	−	0.226655i	$-0.0727790\pi$
$308$		0			0
$309$		−	6.87971i		−	0.391373i
$310$		0			0
$311$	18.5030	+	25.4672i	1.04921	+	1.44411i	0.889491	+	0.456952i	$0.151059\pi$
$311$	18.5030	+	25.4672i	1.04921	+	1.44411i	0.159720	+	0.987162i	$0.448941\pi$
$312$		0			0
$313$	5.75907	+	17.7246i	0.325522	+	1.00185i	0.971204	+	0.238248i	$0.0765730\pi$
$313$	5.75907	+	17.7246i	0.325522	+	1.00185i	−0.645682	+	0.763606i	$0.723427\pi$
$314$		0			0
$315$	−11.3082	+	15.5643i	−0.637143	+	0.876952i
$316$		0			0
$317$	−21.9489	−	7.13164i	−1.23277	−	0.400553i	−0.381056	−	0.924552i	$-0.624439\pi$
$317$	−21.9489	−	7.13164i	−1.23277	−	0.400553i	−0.851719	+	0.523999i	$0.824439\pi$
$318$		0			0
$319$	8.60450	+	15.6766i	0.481760	+	0.877721i
$320$		0			0
$321$	16.3066	+	5.29833i	0.910145	+	0.295724i
$322$		0			0
$323$	13.9997	+	10.1714i	0.778963	+	0.565950i
$324$		0			0
$325$	6.83673	+	21.0413i	0.379234	+	1.16716i
$326$		0			0
$327$	2.59101	−	1.88248i	0.143283	−	0.104101i
$328$		0			0
$329$			3.79473i			0.209210i
$330$		0			0
$331$	19.9470			1.09639			0.548194	−	0.836351i	$-0.315316\pi$
$331$	19.9470			1.09639			0.548194	+	0.836351i	$0.315316\pi$
$332$		0			0
$333$	3.74045	+	5.14829i	0.204976	+	0.282125i
$334$		0			0
$335$	−12.9368	+	4.20341i	−0.706810	+	0.229657i
$336$		0			0
$337$	2.52155	−	3.47062i	0.137358	−	0.189056i	−0.734797	−	0.678287i	$-0.762722\pi$
$337$	2.52155	−	3.47062i	0.137358	−	0.189056i	0.872154	+	0.489231i	$0.162722\pi$
$338$		0			0
$339$	−3.52321	+	10.8433i	−0.191355	+	0.588929i
$340$		0			0
$341$	−2.02447	−	1.90368i	−0.109631	−	0.103090i
$342$		0			0
$343$	5.35494	−	16.4808i	0.289139	−	0.889880i
$344$		0			0
$345$	−3.03753	−	2.20689i	−0.163535	−	0.118815i
$346$		0			0
$347$	−13.9379	+	4.52870i	−0.748226	+	0.243113i	−0.658217	−	0.752828i	$-0.728689\pi$
$347$	−13.9379	+	4.52870i	−0.748226	+	0.243113i	−0.0900080	+	0.995941i	$0.528689\pi$
$348$		0			0
$349$	−27.4557	+	19.9477i	−1.46967	+	1.06778i	−0.488961	+	0.872306i	$0.662624\pi$
$349$	−27.4557	+	19.9477i	−1.46967	+	1.06778i	−0.980709	+	0.195472i	$0.937376\pi$
$350$		0			0
$351$	−11.2181			−0.598780
$352$		0			0
$353$	13.8039			0.734707			0.367353	−	0.930081i	$-0.380264\pi$
$353$	13.8039			0.734707			0.367353	+	0.930081i	$0.380264\pi$
$354$		0			0
$355$	39.2762	−	28.5359i	2.08457	−	1.51453i
$356$		0			0
$357$	−13.8117	+	4.48769i	−0.730992	+	0.237514i
$358$		0			0
$359$	−13.6648	−	9.92802i	−0.721198	−	0.523981i	0.165569	−	0.986198i	$-0.447054\pi$
$359$	−13.6648	−	9.92802i	−0.721198	−	0.523981i	−0.886767	+	0.462217i	$0.847054\pi$
$360$		0			0
$361$	1.60575	−	4.94200i	0.0845133	−	0.260105i
$362$		0			0
$363$	11.8967	+	3.07170i	0.624417	+	0.161222i
$364$		0			0
$365$	3.94583	−	12.1440i	0.206534	−	0.635646i
$366$		0			0
$367$	0.132390	−	0.182219i	0.00691070	−	0.00951176i	−0.805548	−	0.592531i	$-0.798129\pi$
$367$	0.132390	−	0.182219i	0.00691070	−	0.00951176i	0.812458	+	0.583019i	$0.198129\pi$
$368$		0			0
$369$	6.17790	−	2.00732i	0.321609	−	0.104497i
$370$		0			0
$371$	−6.92616	−	9.53305i	−0.359589	−	0.494931i
$372$		0			0
$373$	11.3347			0.586890			0.293445	−	0.955976i	$-0.405198\pi$
$373$	11.3347			0.586890			0.293445	+	0.955976i	$0.405198\pi$
$374$		0			0
$375$		−	24.0260i		−	1.24070i
$376$		0			0
$377$	9.21851	−	6.69764i	0.474777	−	0.344946i
$378$		0			0
$379$	1.61104	+	4.95826i	0.0827534	+	0.254689i	0.983869	−	0.178890i	$-0.0572506\pi$
$379$	1.61104	+	4.95826i	0.0827534	+	0.254689i	−0.901116	+	0.433579i	$0.857251\pi$
$380$		0			0
$381$	11.5293	+	8.37652i	0.590664	+	0.429142i
$382$		0			0
$383$	31.4132	+	10.2068i	1.60514	+	0.521541i	0.968371	−	0.249514i	$-0.0802710\pi$
$383$	31.4132	+	10.2068i	1.60514	+	0.521541i	0.636768	+	0.771056i	$0.280271\pi$
$384$		0			0
$385$	−26.5269	−	24.9442i	−1.35194	−	1.27127i
$386$		0			0
$387$	−2.30732	−	0.749694i	−0.117288	−	0.0381091i
$388$		0			0
$389$	−4.37628	+	6.02343i	−0.221886	+	0.305400i	−0.905418	−	0.424520i	$-0.860443\pi$
$389$	−4.37628	+	6.02343i	−0.221886	+	0.305400i	0.683532	+	0.729920i	$0.260443\pi$
$390$		0			0
$391$	1.23007	+	3.78576i	0.0622072	+	0.191454i
$392$		0			0
$393$	−7.09860	−	9.77039i	−0.358077	−	0.492851i
$394$		0			0
$395$			45.8191i			2.30541i
$396$		0			0
$397$			12.5755i			0.631147i	0.948901	+	0.315573i	$0.102197\pi$
$397$			12.5755i			0.631147i	−0.948901	+	0.315573i	$0.897803\pi$
$398$		0			0
$399$	−6.80915	−	9.37199i	−0.340884	−	0.469187i
$400$		0			0
$401$	−4.30402	−	13.2464i	−0.214933	−	0.661494i	−0.999158	−	0.0410189i	$-0.986940\pi$
$401$	−4.30402	−	13.2464i	−0.214933	−	0.661494i	0.784226	−	0.620476i	$-0.213060\pi$
$402$		0			0
$403$	−1.04080	+	1.43253i	−0.0518457	+	0.0713595i
$404$		0			0
$405$	2.51494	+	0.817155i	0.124969	+	0.0406047i
$406$		0			0
$407$	−10.5585	+	5.79531i	−0.523366	+	0.287263i
$408$		0			0
$409$	−1.47362	−	0.478807i	−0.0728657	−	0.0236755i	0.272357	−	0.962196i	$-0.412197\pi$
$409$	−1.47362	−	0.478807i	−0.0728657	−	0.0236755i	−0.345223	+	0.938521i	$0.612197\pi$
$410$		0			0
$411$	−19.4299	−	14.1167i	−0.958406	−	0.696323i
$412$		0			0
$413$	−7.25537	−	22.3297i	−0.357014	−	1.09877i
$414$		0			0
$415$	−2.91398	+	2.11713i	−0.143042	+	0.103926i
$416$		0			0
$417$			7.62252i			0.373276i
$418$		0			0
$419$	18.4122			0.899496			0.449748	−	0.893155i	$-0.351514\pi$
$419$	18.4122			0.899496			0.449748	+	0.893155i	$0.351514\pi$
$420$		0			0
$421$	−16.4415	−	22.6298i	−0.801311	−	1.10291i	−0.992606	−	0.121378i	$-0.961269\pi$
$421$	−16.4415	−	22.6298i	−0.801311	−	1.10291i	0.191295	−	0.981533i	$-0.438731\pi$
$422$		0			0
$423$	−2.26556	+	0.736125i	−0.110155	+	0.0357916i
$424$		0			0
$425$	−28.6605	+	39.4478i	−1.39024	+	1.91350i
$426$		0			0
$427$	−2.70972	+	8.33967i	−0.131133	+	0.403585i
$428$		0			0
$429$	0.986489	−	7.76668i	0.0476282	−	0.374979i
$430$		0			0
$431$	−9.07766	+	27.9382i	−0.437256	+	1.34573i	0.453502	+	0.891255i	$0.350175\pi$
$431$	−9.07766	+	27.9382i	−0.437256	+	1.34573i	−0.890758	+	0.454479i	$0.849825\pi$
$432$		0			0
$433$	−14.9096	−	10.8325i	−0.716509	−	0.520575i	0.168758	−	0.985658i	$-0.446024\pi$
$433$	−14.9096	−	10.8325i	−0.716509	−	0.520575i	−0.885267	+	0.465083i	$0.846024\pi$
$434$		0			0
$435$	−22.5281	+	7.31982i	−1.08014	+	0.350959i
$436$		0			0
$437$	−2.56885	+	1.86638i	−0.122885	+	0.0892809i
$438$		0			0
$439$	2.97316			0.141901			0.0709506	−	0.997480i	$-0.477397\pi$
$439$	2.97316			0.141901			0.0709506	+	0.997480i	$0.477397\pi$
$440$		0			0
$441$	−1.38802			−0.0660961
$442$		0			0
$443$	0.965497	−	0.701475i	0.0458722	−	0.0333281i	−0.564613	−	0.825356i	$-0.690975\pi$
$443$	0.965497	−	0.701475i	0.0458722	−	0.0333281i	0.610485	+	0.792028i	$0.290975\pi$
$444$		0			0
$445$	29.8668	−	9.70430i	1.41582	−	0.460028i
$446$		0			0
$447$	10.2443	+	7.44293i	0.484540	+	0.352039i
$448$		0			0
$449$	5.69852	−	17.5383i	0.268930	−	0.827681i	−0.721832	−	0.692068i	$-0.756700\pi$
$449$	5.69852	−	17.5383i	0.268930	−	0.827681i	0.990762	−	0.135613i	$-0.0433003\pi$
$450$		0			0
$451$	2.29562	+	12.0784i	0.108097	+	0.568750i
$452$		0			0
$453$	0.476280	−	1.46584i	0.0223776	−	0.0688712i
$454$		0			0
$455$	−13.6377	+	18.7707i	−0.639344	+	0.879982i
$456$		0			0
$457$	0.304061	−	0.0987953i	0.0142234	−	0.00462145i	−0.301897	−	0.953341i	$-0.597620\pi$
$457$	0.304061	−	0.0987953i	0.0142234	−	0.00462145i	0.316120	+	0.948719i	$0.397620\pi$
$458$		0			0
$459$	−14.5324	−	20.0022i	−0.678316	−	0.933622i
$460$		0			0
$461$	14.6804			0.683735			0.341868	−	0.939748i	$-0.388941\pi$
$461$	14.6804			0.683735			0.341868	+	0.939748i	$0.388941\pi$
$462$		0			0
$463$		−	16.1267i		−	0.749471i	−0.927132	−	0.374735i	$-0.877734\pi$
$463$		−	16.1267i		−	0.749471i	0.927132	−	0.374735i	$-0.122266\pi$
$464$		0			0
$465$	2.97797	−	2.16362i	0.138100	−	0.100335i
$466$		0			0
$467$	1.71292	+	5.27183i	0.0792645	+	0.243951i	0.982834	−	0.184489i	$-0.0590632\pi$
$467$	1.71292	+	5.27183i	0.0792645	+	0.243951i	−0.903570	+	0.428441i	$0.859063\pi$
$468$		0			0
$469$	−7.81041	−	5.67460i	−0.360651	−	0.262028i
$470$		0			0
$471$	20.4229	+	6.63582i	0.941040	+	0.305762i
$472$		0			0
$473$	1.95789	−	4.15345i	0.0900241	−	0.190976i
$474$		0			0
$475$	−36.9918	−	12.0194i	−1.69730	−	0.551486i
$476$		0			0
$477$	4.34792	−	5.98440i	0.199078	−	0.274007i
$478$		0			0
$479$	−1.04517	−	3.21671i	−0.0477551	−	0.146975i	0.924336	−	0.381581i	$-0.124620\pi$
$479$	−1.04517	−	3.21671i	−0.0477551	−	0.146975i	−0.972091	+	0.234606i	$0.924620\pi$
$480$		0			0
$481$	4.51100	+	6.20886i	0.205684	+	0.283100i
$482$		0			0
$483$		−	2.66477i		−	0.121251i
$484$		0			0
$485$			43.8252i			1.99000i
$486$		0			0
$487$	−17.9182	−	24.6623i	−0.811952	−	1.11756i	−0.991019	−	0.133719i	$-0.957308\pi$
$487$	−17.9182	−	24.6623i	−0.811952	−	1.11756i	0.179068	−	0.983837i	$-0.442692\pi$
$488$		0			0
$489$	3.84597	+	11.8367i	0.173921	+	0.535273i
$490$		0			0
$491$	19.3196	−	26.5912i	0.871882	−	1.20004i	−0.106721	−	0.994289i	$-0.534035\pi$
$491$	19.3196	−	26.5912i	0.871882	−	1.20004i	0.978604	−	0.205754i	$-0.0659647\pi$
$492$		0			0
$493$	23.8841	+	7.76040i	1.07568	+	0.349511i
$494$		0			0
$495$	9.74652	−	20.6762i	0.438074	−	0.929324i
$496$		0			0
$497$	32.7700	+	10.6476i	1.46993	+	0.477610i
$498$		0			0
$499$	8.74683	+	6.35494i	0.391562	+	0.284486i	0.766095	−	0.642727i	$-0.222197\pi$
$499$	8.74683	+	6.35494i	0.391562	+	0.284486i	−0.374533	+	0.927213i	$0.622197\pi$
$500$		0			0
$501$	−7.00361	−	21.5549i	−0.312898	−	0.963001i
$502$		0			0
$503$	20.9779	−	15.2413i	0.935357	−	0.679577i	−0.0119412	−	0.999929i	$-0.503801\pi$
$503$	20.9779	−	15.2413i	0.935357	−	0.679577i	0.947299	+	0.320352i	$0.103801\pi$
$504$		0			0
$505$			21.0846i			0.938253i
$506$		0			0
$507$	9.53228			0.423344
$508$		0			0
$509$	15.4298	+	21.2373i	0.683914	+	0.941327i	0.999973	−	0.00741265i	$-0.00235954\pi$
$509$	15.4298	+	21.2373i	0.683914	+	0.941327i	−0.316058	+	0.948740i	$0.602360\pi$
$510$		0			0
$511$	8.61905	−	2.80050i	0.381284	−	0.123887i
$512$		0			0
$513$	11.5924	−	15.9555i	0.511816	−	0.704454i
$514$		0			0
$515$	7.48571	−	23.0386i	0.329860	−	1.01520i
$516$		0			0
$517$	−0.841852	−	4.42939i	−0.0370246	−	0.194804i
$518$		0			0
$519$	5.37676	−	16.5480i	0.236014	−	0.726375i
$520$		0			0
$521$	9.15472	+	6.65129i	0.401076	+	0.291399i	0.769979	−	0.638069i	$-0.220267\pi$
$521$	9.15472	+	6.65129i	0.401076	+	0.291399i	−0.368903	+	0.929468i	$0.620267\pi$
$522$		0			0
$523$	21.7647	−	7.07178i	0.951704	−	0.309227i	0.208296	−	0.978066i	$-0.433208\pi$
$523$	21.7647	−	7.07178i	0.951704	−	0.309227i	0.743408	+	0.668838i	$0.233208\pi$
$524$		0			0
$525$	26.4080	−	19.1866i	1.15254	−	0.837371i
$526$		0			0
$527$	−3.90252			−0.169997
$528$		0			0
$529$	22.2696			0.968243
$530$		0			0
$531$	11.9241	−	8.66333i	0.517460	−	0.375957i
$532$		0			0
$533$	7.45057	−	2.42084i	0.322720	−	0.104858i
$534$		0			0
$535$	48.8421	+	35.4859i	2.11163	+	1.53419i
$536$		0			0
$537$	−5.85532	+	18.0208i	−0.252676	+	0.777656i
$538$		0			0
$539$	0.331022	−	2.60616i	0.0142581	−	0.112255i
$540$		0			0
$541$	5.01194	−	15.4252i	0.215480	−	0.663180i	−0.783639	−	0.621217i	$-0.786639\pi$
$541$	5.01194	−	15.4252i	0.215480	−	0.663180i	0.999119	−	0.0419633i	$-0.0133613\pi$
$542$		0			0
$543$	8.72795	−	12.0130i	0.374552	−	0.515527i
$544$		0			0
$545$	10.7250	−	3.48477i	0.459410	−	0.149271i
$546$		0			0
$547$	6.35466	+	8.74643i	0.271705	+	0.373970i	0.922965	−	0.384885i	$-0.125759\pi$
$547$	6.35466	+	8.74643i	0.271705	+	0.373970i	−0.651259	+	0.758855i	$0.725759\pi$
$548$		0			0
$549$	−5.50467			−0.234934
$550$		0			0
$551$			20.0325i			0.853415i
$552$		0			0
$553$	−26.3088	+	19.1145i	−1.11877	+	0.812831i
$554$		0			0
$555$	−4.93005	−	15.1731i	−0.209269	−	0.644064i
$556$		0			0
$557$	−3.64856	−	2.65084i	−0.154595	−	0.112320i	0.507799	−	0.861476i	$-0.330459\pi$
$557$	−3.64856	−	2.65084i	−0.154595	−	0.112320i	−0.662394	+	0.749156i	$0.730459\pi$
$558$		0			0
$559$	−2.78264	−	0.904133i	−0.117693	−	0.0382408i
$560$		0			0
$561$	15.1261	−	8.30234i	0.638624	−	0.350525i
$562$		0			0
$563$	0.590824	+	0.191970i	0.0249003	+	0.00809058i	0.321441	−	0.946930i	$-0.395833\pi$
$563$	0.590824	+	0.191970i	0.0249003	+	0.00809058i	−0.296540	+	0.955020i	$0.595833\pi$
$564$		0			0
$565$	−23.5969	+	32.4784i	−0.992730	+	1.36638i
$566$		0			0
$567$	0.579965	+	1.78495i	0.0243562	+	0.0749607i
$568$		0			0
$569$	−11.6083	−	15.9774i	−0.486644	−	0.669807i	0.493121	−	0.869961i	$-0.335856\pi$
$569$	−11.6083	−	15.9774i	−0.486644	−	0.669807i	−0.979765	+	0.200153i	$0.935856\pi$
$570$		0			0
$571$			28.2428i			1.18193i	0.806699	+	0.590963i	$0.201252\pi$
$571$			28.2428i			1.18193i	−0.806699	+	0.590963i	$0.798748\pi$
$572$		0			0
$573$		−	28.2729i		−	1.18112i
$574$		0			0
$575$	−5.25901	−	7.23840i	−0.219316	−	0.301862i
$576$		0			0
$577$	4.23700	+	13.0402i	0.176389	+	0.542869i	0.999694	−	0.0247297i	$-0.00787253\pi$
$577$	4.23700	+	13.0402i	0.176389	+	0.542869i	−0.823305	+	0.567599i	$0.807873\pi$
$578$		0			0
$579$	4.14584	−	5.70626i	0.172295	−	0.237144i
$580$		0			0
$581$	−2.43126	−	0.789966i	−0.100866	−	0.0327733i
$582$		0			0
$583$	10.1994	+	9.59089i	0.422418	+	0.397214i
$584$		0			0
$585$	−13.8521	−	4.50083i	−0.572716	−	0.186087i
$586$		0			0
$587$	−27.8108	−	20.2057i	−1.14788	−	0.833981i	−0.159679	−	0.987169i	$-0.551046\pi$
$587$	−27.8108	−	20.2057i	−1.14788	−	0.833981i	−0.988197	+	0.153188i	$0.951046\pi$
$588$		0			0
$589$	−0.961971	−	2.96064i	−0.0396373	−	0.121991i
$590$		0			0
$591$	9.82507	−	7.13833i	0.404149	−	0.293632i
$592$		0			0
$593$		−	18.6125i		−	0.764323i	−0.924096	−	0.382161i	$-0.875180\pi$
$593$		−	18.6125i		−	0.764323i	0.924096	−	0.382161i	$-0.124820\pi$
$594$		0			0
$595$	−51.1353			−2.09634
$596$		0			0
$597$	14.5648	+	20.0467i	0.596097	+	0.820457i
$598$		0			0
$599$	−14.6710	+	4.76689i	−0.599440	+	0.194770i	−0.592990	−	0.805209i	$-0.702053\pi$
$599$	−14.6710	+	4.76689i	−0.599440	+	0.194770i	−0.00644913	+	0.999979i	$0.502053\pi$
$600$		0			0
$601$	−6.78408	+	9.33748i	−0.276728	+	0.380884i	−0.924647	−	0.380826i	$-0.875640\pi$
$601$	−6.78408	+	9.33748i	−0.276728	+	0.380884i	0.647919	+	0.761710i	$0.275640\pi$
$602$		0			0
$603$	1.87278	−	5.76383i	0.0762656	−	0.234721i
$604$		0			0
$605$	36.4973	+	23.2311i	1.48383	+	0.944479i
$606$		0			0
$607$	−0.811344	+	2.49706i	−0.0329314	+	0.101353i	−0.966171	−	0.257902i	$-0.916969\pi$
$607$	−0.811344	+	2.49706i	−0.0329314	+	0.101353i	0.933240	+	0.359254i	$0.116969\pi$
$608$		0			0
$609$	−13.6011	−	9.88175i	−0.551143	−	0.400429i
$610$		0			0
$611$	−2.73227	+	0.887770i	−0.110536	+	0.0359153i
$612$		0			0
$613$	23.6605	−	17.1903i	0.955638	−	0.694311i	0.00350423	−	0.999994i	$-0.498885\pi$
$613$	23.6605	−	17.1903i	0.955638	−	0.694311i	0.952134	+	0.305682i	$0.0988846\pi$
$614$		0			0
$615$	−16.2854			−0.656691
$616$		0			0
$617$	−18.7736			−0.755798			−0.377899	−	0.925847i	$-0.623353\pi$
$617$	−18.7736			−0.755798			−0.377899	+	0.925847i	$0.623353\pi$
$618$		0			0
$619$	−35.7686	+	25.9874i	−1.43766	+	1.04452i	−0.449139	+	0.893462i	$0.648269\pi$
$619$	−35.7686	+	25.9874i	−1.43766	+	1.04452i	−0.988524	+	0.151061i	$0.951731\pi$
$620$		0			0
$621$	4.31465	−	1.40192i	0.173141	−	0.0562569i
$622$		0			0
$623$	18.0317	+	13.1008i	0.722425	+	0.524872i
$624$		0			0
$625$	9.96692	−	30.6750i	0.398677	−	1.22700i
$626$		0			0
$627$	10.0271	+	9.42885i	0.400445	+	0.376552i
$628$		0			0
$629$	−5.22679	+	16.0864i	−0.208406	+	0.641407i
$630$		0			0
$631$	3.44264	−	4.73839i	0.137049	−	0.188632i	−0.734976	−	0.678093i	$-0.762806\pi$
$631$	3.44264	−	4.73839i	0.137049	−	0.188632i	0.872025	+	0.489461i	$0.162806\pi$
$632$		0			0
$633$	−4.79573	+	1.55823i	−0.190613	+	0.0619340i
$634$		0			0
$635$	29.4947	+	40.5960i	1.17046	+	1.61100i
$636$		0			0
$637$	−1.67395			−0.0663245
$638$		0			0
$639$			21.6301i			0.855673i
$640$		0			0
$641$	−15.9169	+	11.5643i	−0.628680	+	0.456763i	−0.855943	−	0.517071i	$-0.827022\pi$
$641$	−15.9169	+	11.5643i	−0.628680	+	0.456763i	0.227263	+	0.973833i	$0.427022\pi$
$642$		0			0
$643$	−3.22855	−	9.93645i	−0.127322	−	0.391855i	0.866995	−	0.498316i	$-0.166048\pi$
$643$	−3.22855	−	9.93645i	−0.127322	−	0.391855i	−0.994317	+	0.106461i	$0.966048\pi$
$644$		0			0
$645$	4.92065	+	3.57506i	0.193751	+	0.140768i
$646$		0			0
$647$	6.43578	+	2.09111i	0.253017	+	0.0822101i	0.432779	−	0.901500i	$-0.357533\pi$
$647$	6.43578	+	2.09111i	0.253017	+	0.0822101i	−0.179763	+	0.983710i	$0.557533\pi$
$648$		0			0
$649$	13.4226	+	24.4548i	0.526884	+	0.959934i
$650$		0			0
$651$	2.48465	+	0.807312i	0.0973812	+	0.0316411i
$652$		0			0
$653$	−20.1960	+	27.7974i	−0.790332	+	1.08780i	0.203735	+	0.979026i	$0.434692\pi$
$653$	−20.1960	+	27.7974i	−0.790332	+	1.08780i	−0.994067	+	0.108772i	$0.965308\pi$
$654$		0			0
$655$	−13.1406	−	40.4428i	−0.513448	−	1.58023i
$656$		0			0
$657$	3.34396	+	4.60256i	0.130460	+	0.179563i
$658$		0			0
$659$		−	34.5518i		−	1.34595i	−0.739667	−	0.672973i	$-0.765017\pi$
$659$		−	34.5518i		−	1.34595i	0.739667	−	0.672973i	$-0.234983\pi$
$660$		0			0
$661$		−	17.3103i		−	0.673292i	−0.941631	−	0.336646i	$-0.890707\pi$
$661$		−	17.3103i		−	0.673292i	0.941631	−	0.336646i	$-0.109293\pi$
$662$		0			0
$663$	−6.46244	−	8.89478i	−0.250980	−	0.345445i
$664$		0			0
$665$	−12.6048	−	38.7937i	−0.488794	−	1.50435i
$666$		0			0
$667$	−2.70857	+	3.72803i	−0.104876	+	0.144350i
$668$		0			0
$669$	−16.2795	−	5.28954i	−0.629403	−	0.204505i
$670$		0			0
$671$	1.31278	−	10.3356i	0.0506795	−	0.399002i
$672$		0			0
$673$	−25.9975	−	8.44710i	−1.00213	−	0.325612i	−0.238413	−	0.971164i	$-0.576627\pi$
$673$	−25.9975	−	8.44710i	−1.00213	−	0.325612i	−0.763716	+	0.645552i	$0.776627\pi$
$674$		0			0
$675$	44.9589	+	32.6646i	1.73047	+	1.25726i
$676$		0			0
$677$	−8.46763	−	26.0607i	−0.325438	−	1.00159i	−0.971243	−	0.238091i	$-0.923478\pi$
$677$	−8.46763	−	26.0607i	−0.325438	−	1.00159i	0.645805	−	0.763502i	$-0.276522\pi$
$678$		0			0
$679$	−25.1639	+	18.2827i	−0.965703	+	0.701625i
$680$		0			0
$681$		−	22.6387i		−	0.867517i
$682$		0			0
$683$	19.0093			0.727370			0.363685	−	0.931522i	$-0.381518\pi$
$683$	19.0093			0.727370			0.363685	+	0.931522i	$0.381518\pi$
$684$		0			0
$685$	−49.7064	−	68.4149i	−1.89918	−	2.61400i
$686$		0			0
$687$	−3.95817	+	1.28609i	−0.151013	+	0.0490673i
$688$		0			0
$689$	5.24361	−	7.21721i	0.199766	−	0.274954i
$690$		0			0
$691$	−10.0374	+	30.8919i	−0.381840	+	1.17518i	0.556907	+	0.830575i	$0.311988\pi$
$691$	−10.0374	+	30.8919i	−0.381840	+	1.17518i	−0.938747	+	0.344607i	$0.888012\pi$
$692$		0			0
$693$	15.9380	−	3.02918i	0.605435	−	0.115069i
$694$		0			0
$695$	−8.29394	+	25.5261i	−0.314607	+	0.968261i
$696$		0			0
$697$	13.9682	+	10.1485i	0.529082	+	0.384401i
$698$		0			0
$699$	26.1362	−	8.49217i	0.988563	−	0.321203i
$700$		0			0
$701$	−34.5883	+	25.1299i	−1.30638	+	0.949142i	−0.999996	−	0.00276567i	$-0.999120\pi$
$701$	−34.5883	+	25.1299i	−1.30638	+	0.949142i	−0.306386	+	0.951908i	$0.599120\pi$
$702$		0			0
$703$	−13.4923			−0.508873
$704$		0			0
$705$	5.97218			0.224925
$706$		0			0
$707$	−12.1066	+	8.79593i	−0.455314	+	0.330805i
$708$		0			0
$709$	−6.59283	+	2.14214i	−0.247599	+	0.0804498i	−0.430187	−	0.902740i	$-0.641552\pi$
$709$	−6.59283	+	2.14214i	−0.247599	+	0.0804498i	0.182588	+	0.983189i	$0.441552\pi$
$710$		0			0
$711$	−16.5155	−	11.9992i	−0.619378	−	0.450005i
$712$		0			0
$713$	0.221283	−	0.681039i	0.00828711	−	0.0255051i
$714$		0			0
$715$	11.7543	−	24.9355i	0.439587	−	0.932535i
$716$		0			0
$717$	−5.97662	+	18.3942i	−0.223201	+	0.686942i
$718$		0			0
$719$	−29.1465	+	40.1168i	−1.08698	+	1.49610i	−0.235388	+	0.971901i	$0.575636\pi$
$719$	−29.1465	+	40.1168i	−1.08698	+	1.49610i	−0.851594	+	0.524202i	$0.824364\pi$
$720$		0			0
$721$	16.3514	−	5.31288i	0.608957	−	0.197862i
$722$		0			0
$723$	−7.88268	−	10.8496i	−0.293160	−	0.403500i
$724$		0			0
$725$	−56.4469			−2.09639
$726$		0			0
$727$		−	20.0972i		−	0.745365i	−0.927959	−	0.372683i	$-0.878438\pi$
$727$		−	20.0972i		−	0.745365i	0.927959	−	0.372683i	$-0.121562\pi$
$728$		0			0
$729$	−15.3440	+	11.1480i	−0.568295	+	0.412890i
$730$		0			0
$731$	−1.99265	−	6.13275i	−0.0737008	−	0.226828i
$732$		0			0
$733$	38.5016	+	27.9731i	1.42209	+	1.03321i	0.991422	+	0.130699i	$0.0417222\pi$
$733$	38.5016	+	27.9731i	1.42209	+	1.03321i	0.430669	+	0.902510i	$0.358278\pi$
$734$		0			0
$735$	3.30952	+	1.07533i	0.122074	+	0.0396641i
$736$		0			0
$737$	10.3756	+	4.89094i	0.382190	+	0.180160i
$738$		0			0
$739$	47.1991	+	15.3359i	1.73625	+	0.564140i	0.994329	−	0.106351i	$-0.0339168\pi$
$739$	47.1991	+	15.3359i	1.73625	+	0.564140i	0.741917	+	0.670492i	$0.233917\pi$
$740$		0			0
$741$	5.15502	−	7.09528i	0.189374	−	0.260651i
$742$		0			0
$743$	−11.3841	−	35.0366i	−0.417642	−	1.28537i	−0.909866	−	0.414901i	$-0.863816\pi$
$743$	−11.3841	−	35.0366i	−0.417642	−	1.28537i	0.492225	−	0.870468i	$-0.336184\pi$
$744$		0			0
$745$	26.2074	+	36.0714i	0.960166	+	1.32155i
$746$		0			0
$747$		−	1.60478i		−	0.0587157i
$748$		0			0
$749$			42.8484i			1.56565i
$750$		0			0
$751$	−3.19001	−	4.39067i	−0.116405	−	0.160218i	0.746839	−	0.665005i	$-0.231571\pi$
$751$	−3.19001	−	4.39067i	−0.116405	−	0.160218i	−0.863244	+	0.504788i	$0.831571\pi$
$752$		0			0
$753$	0.925722	+	2.84908i	0.0337352	+	0.103826i
$754$		0			0
$755$	3.18992	−	4.39054i	0.116093	−	0.159788i
$756$		0			0
$757$	18.5263	+	6.01955i	0.673348	+	0.218784i	0.625681	−	0.780079i	$-0.284821\pi$
$757$	18.5263	+	6.01955i	0.673348	+	0.218784i	0.0476675	+	0.998863i	$0.484821\pi$
$758$		0			0
$759$	0.591174	+	3.11045i	0.0214582	+	0.112902i
$760$		0			0
$761$	−11.3571	−	3.69015i	−0.411695	−	0.133768i	0.0958447	−	0.995396i	$-0.469445\pi$
$761$	−11.3571	−	3.69015i	−0.411695	−	0.133768i	−0.507539	+	0.861629i	$0.669445\pi$
$762$		0			0
$763$	6.47511	+	4.70444i	0.234415	+	0.170312i
$764$		0			0
$765$	−9.91954	−	30.5292i	−0.358642	−	1.10379i
$766$		0			0
$767$	14.3804	−	10.4480i	0.519248	−	0.377256i
$768$		0			0
$769$		−	42.9323i		−	1.54818i	−0.633077	−	0.774089i	$-0.718208\pi$
$769$		−	42.9323i		−	1.54818i	0.633077	−	0.774089i	$-0.281792\pi$
$770$		0			0
$771$	−15.0714			−0.542784
$772$		0			0
$773$	−5.52701	−	7.60728i	−0.198793	−	0.273615i	0.697969	−	0.716128i	$-0.254087\pi$
$773$	−5.52701	−	7.60728i	−0.198793	−	0.273615i	−0.896762	+	0.442513i	$0.854087\pi$
$774$		0			0
$775$	8.34239	−	2.71061i	0.299667	−	0.0973678i
$776$		0			0
$777$	6.65557	−	9.16060i	0.238767	−	0.328635i
$778$		0			0
$779$	−4.25597	+	13.0985i	−0.152486	+	0.469303i
$780$		0			0
$781$	−40.6128	−	5.15846i	−1.45324	−	0.184584i
$782$		0			0
$783$	8.84458	−	27.2208i	0.316079	−	0.972793i
$784$		0			0
$785$	61.1716	+	44.4438i	2.18331	+	1.58627i
$786$		0			0
$787$	−48.8038	+	15.8573i	−1.73967	+	0.565252i	−0.994790	−	0.101948i	$-0.967493\pi$
$787$	−48.8038	+	15.8573i	−1.73967	+	0.565252i	−0.744878	+	0.667200i	$0.767493\pi$
$788$		0			0
$789$	0.536409	−	0.389724i	0.0190967	−	0.0138745i
$790$		0			0
$791$	−28.4927			−1.01308
$792$		0			0
$793$	−6.63865			−0.235745
$794$		0			0
$795$	−15.0032	+	10.9005i	−0.532109	+	0.386600i
$796$		0			0
$797$	−20.8890	+	6.78723i	−0.739925	+	0.240416i	−0.654640	−	0.755941i	$-0.727180\pi$
$797$	−20.8890	+	6.78723i	−0.739925	+	0.240416i	−0.0852843	+	0.996357i	$0.527180\pi$
$798$		0			0
$799$	−5.12241	−	3.72165i	−0.181218	−	0.131662i
$800$		0			0
$801$	−4.32365	+	13.3068i	−0.152769	+	0.470173i
$802$		0			0
$803$	−9.43929	+	5.18100i	−0.333105	+	0.182833i
$804$		0			0
$805$	2.89950	−	8.92374i	0.102194	−	0.314520i
$806$		0			0
$807$	−12.7899	+	17.6038i	−0.450225	+	0.619682i
$808$		0			0
$809$	−44.5044	+	14.4604i	−1.56469	+	0.508399i	−0.958056	−	0.286580i	$-0.907482\pi$
$809$	−44.5044	+	14.4604i	−1.56469	+	0.508399i	−0.606636	+	0.794980i	$0.707482\pi$
$810$		0			0
$811$	1.59838	+	2.19998i	0.0561267	+	0.0772518i	0.836158	−	0.548489i	$-0.184797\pi$
$811$	1.59838	+	2.19998i	0.0561267	+	0.0772518i	−0.780031	+	0.625741i	$0.784797\pi$
$812$		0			0
$813$	−27.4153			−0.961498
$814$		0			0
$815$			43.8232i			1.53506i
$816$		0			0
$817$	4.16141	−	3.02344i	0.145589	−	0.105777i
$818$		0			0
$819$	−3.19441	−	9.83137i	−0.111622	−	0.343536i
$820$		0			0
$821$	35.2195	+	25.5884i	1.22917	+	0.893043i	0.996828	−	0.0795914i	$-0.0253616\pi$
$821$	35.2195	+	25.5884i	1.22917	+	0.893043i	0.232341	+	0.972634i	$0.425362\pi$
$822$		0			0
$823$	18.1038	+	5.88230i	0.631060	+	0.205044i	0.607045	−	0.794668i	$-0.292355\pi$
$823$	18.1038	+	5.88230i	0.631060	+	0.205044i	0.0240156	+	0.999712i	$0.492355\pi$
$824$		0			0
$825$	−26.5683	+	28.2541i	−0.924988	+	0.983680i
$826$		0			0
$827$	−36.6382	−	11.9045i	−1.27404	−	0.413959i	−0.407560	−	0.913179i	$-0.633620\pi$
$827$	−36.6382	−	11.9045i	−1.27404	−	0.413959i	−0.866476	+	0.499220i	$0.833620\pi$
$828$		0			0
$829$	−19.6824	+	27.0905i	−0.683597	+	0.940890i	−0.999970	−	0.00774447i	$-0.997535\pi$
$829$	−19.6824	+	27.0905i	−0.683597	+	0.940890i	0.316373	+	0.948635i	$0.397535\pi$
$830$		0			0
$831$	−5.07346	−	15.6145i	−0.175996	−	0.541661i
$832$		0			0
$833$	−2.16851	−	2.98470i	−0.0751344	−	0.103414i
$834$		0			0
$835$		−	79.8031i		−	2.76170i
$836$		0			0
$837$			4.44773i			0.153736i
$838$		0			0
$839$	3.48024	+	4.79014i	0.120151	+	0.165374i	0.864856	−	0.502020i	$-0.167410\pi$
$839$	3.48024	+	4.79014i	0.120151	+	0.165374i	−0.744705	+	0.667394i	$0.767410\pi$
$840$		0			0
$841$	0.0222891	+	0.0685987i	0.000768589	+	0.00236547i
$842$		0			0
$843$	−15.1270	+	20.8205i	−0.521000	+	0.717095i
$844$		0			0
$845$	31.9215	+	10.3719i	1.09813	+	0.356805i
$846$		0			0
$847$	1.88663	+	30.6477i	0.0648255	+	1.05307i
$848$		0			0
$849$	−23.9747	−	7.78985i	−0.822809	−	0.267347i
$850$		0			0
$851$	−2.51091	−	1.82428i	−0.0860727	−	0.0625355i
$852$		0			0
$853$	−2.67901	−	8.24514i	−0.0917275	−	0.282308i	0.894660	−	0.446749i	$-0.147418\pi$
$853$	−2.67901	−	8.24514i	−0.0917275	−	0.282308i	−0.986387	+	0.164440i	$0.947418\pi$
$854$		0			0
$855$	20.7158	−	15.0509i	0.708464	−	0.514730i
$856$		0			0
$857$			18.5127i			0.632382i	0.948695	+	0.316191i	$0.102404\pi$
$857$			18.5127i			0.632382i	−0.948695	+	0.316191i	$0.897596\pi$
$858$		0			0
$859$	0.218543			0.00745661			0.00372830	−	0.999993i	$-0.498813\pi$
$859$	0.218543			0.00745661			0.00372830	+	0.999993i	$0.498813\pi$
$860$		0			0
$861$	−6.79382	−	9.35090i	−0.231533	−	0.318678i
$862$		0			0
$863$	−5.38003	+	1.74808i	−0.183138	+	0.0595053i	−0.399151	−	0.916885i	$-0.630695\pi$
$863$	−5.38003	+	1.74808i	−0.183138	+	0.0595053i	0.216012	+	0.976391i	$0.430695\pi$
$864$		0			0
$865$	36.0112	−	49.5651i	1.22442	−	1.68526i
$866$		0			0
$867$	1.62000	−	4.98584i	0.0550180	−	0.169328i
$868$		0			0
$869$	26.4685	−	28.1479i	0.897881	−	0.954853i
$870$		0			0
$871$	2.25858	−	6.95120i	0.0765291	−	0.235532i
$872$		0			0
$873$	−15.7967	−	11.4770i	−0.534639	−	0.388438i
$874$		0			0
$875$	57.1038	−	18.5541i	1.93046	−	0.627244i
$876$		0			0
$877$	28.1771	−	20.4719i	0.951473	−	0.691286i	0.000318228	−	1.00000i	$-0.499899\pi$
$877$	28.1771	−	20.4719i	0.951473	−	0.691286i	0.951155	+	0.308714i	$0.0998987\pi$
$878$		0			0
$879$	0.250994			0.00846583
$880$		0			0
$881$	−29.7384			−1.00191			−0.500957	−	0.865472i	$-0.667018\pi$
$881$	−29.7384			−1.00191			−0.500957	+	0.865472i	$0.667018\pi$
$882$		0			0
$883$	−16.7903	+	12.1988i	−0.565038	+	0.410524i	−0.833299	−	0.552822i	$-0.813551\pi$
$883$	−16.7903	+	12.1988i	−0.565038	+	0.410524i	0.268262	+	0.963346i	$0.413551\pi$
$884$		0			0
$885$	−35.1428	+	11.4186i	−1.18131	+	0.383831i
$886$		0			0
$887$	−21.3255	−	15.4939i	−0.716042	−	0.520235i	0.169075	−	0.985603i	$-0.445922\pi$
$887$	−21.3255	−	15.4939i	−0.716042	−	0.520235i	−0.885117	+	0.465368i	$0.845922\pi$
$888$		0			0
$889$	−11.0054	+	33.8711i	−0.369109	+	1.13600i
$890$		0			0
$891$	−1.07295	−	1.95481i	−0.0359452	−	0.0654887i
$892$		0			0
$893$	1.56075	−	4.80349i	0.0522285	−	0.160743i
$894$		0			0
$895$	−39.2164	+	53.9767i	−1.31086	+	1.80424i
$896$		0			0
$897$	1.91869	−	0.623419i	0.0640630	−	0.0208153i
$898$		0			0
$899$	−2.65546	−	3.65492i	−0.0885645	−	0.121899i
$900$		0			0
$901$	19.6612			0.655010
$902$		0			0
$903$			4.31681i			0.143654i
$904$		0			0
$905$	42.2991	−	30.7321i	1.40607	−	1.02157i
$906$		0			0
$907$	−2.25055	−	6.92648i	−0.0747283	−	0.229990i	0.906715	−	0.421745i	$-0.138582\pi$
$907$	−2.25055	−	6.92648i	−0.0747283	−	0.229990i	−0.981443	+	0.191755i	$0.938582\pi$
$908$		0			0
$909$	−7.59993	−	5.52167i	−0.252074	−	0.183142i
$910$		0			0
$911$	−15.5732	−	5.06005i	−0.515964	−	0.167647i	0.0394488	−	0.999222i	$-0.487440\pi$
$911$	−15.5732	−	5.06005i	−0.515964	−	0.167647i	−0.555413	+	0.831575i	$0.687440\pi$
$912$		0			0
$913$	3.01314	+	0.382716i	0.0997205	+	0.0126661i
$914$		0			0
$915$	13.1251	+	4.26459i	0.433901	+	0.140983i
$916$		0			0
$917$	17.7399	−	24.4168i	0.585822	−	0.806315i
$918$		0			0
$919$	−1.67576	−	5.15747i	−0.0552783	−	0.170129i	0.919606	−	0.392843i	$-0.128508\pi$
$919$	−1.67576	−	5.15747i	−0.0552783	−	0.170129i	−0.974884	+	0.222714i	$0.928508\pi$
$920$		0			0
$921$	−5.21474	−	7.17748i	−0.171832	−	0.236506i
$922$		0			0
$923$			26.0860i			0.858630i
$924$		0			0
$925$		−	38.0182i		−	1.25003i
$926$		0			0
$927$	6.34389	+	8.73161i	0.208361	+	0.286784i
$928$		0			0
$929$	5.92577	+	18.2377i	0.194418	+	0.598358i	0.999983	+	0.00584999i	$0.00186212\pi$
$929$	5.92577	+	18.2377i	0.194418	+	0.598358i	−0.805565	+	0.592508i	$0.798138\pi$
$930$		0			0
$931$	1.72980	−	2.38086i	0.0566918	−	0.0780296i
$932$		0			0
$933$	33.4411	+	10.8657i	1.09481	+	0.355726i
$934$		0			0
$935$	59.6876	−	11.3442i	1.95199	−	0.370996i
$936$		0			0
$937$	29.5300	+	9.59489i	0.964705	+	0.313452i	0.748676	−	0.662936i	$-0.230690\pi$
$937$	29.5300	+	9.59489i	0.964705	+	0.313452i	0.216028	+	0.976387i	$0.430690\pi$
$938$		0			0
$939$	16.8414	+	12.2360i	0.549598	+	0.399306i
$940$		0			0
$941$	17.9943	+	55.3808i	0.586598	+	1.80536i	0.592756	+	0.805382i	$0.298040\pi$
$941$	17.9943	+	55.3808i	0.586598	+	1.80536i	−0.00615836	+	0.999981i	$0.501960\pi$
$942$		0			0
$943$	−2.56306	+	1.86218i	−0.0834649	+	0.0606408i
$944$		0			0
$945$			58.2792i			1.89582i
$946$		0			0
$947$	−3.35443			−0.109004			−0.0545022	−	0.998514i	$-0.517357\pi$
$947$	−3.35443			−0.109004			−0.0545022	+	0.998514i	$0.517357\pi$
$948$		0			0
$949$	4.03282	+	5.55070i	0.130911	+	0.180183i
$950$		0			0
$951$	−24.5168	+	7.96598i	−0.795010	+	0.258315i
$952$		0			0
$953$	10.8409	−	14.9213i	0.351173	−	0.483348i	−0.596490	−	0.802620i	$-0.703439\pi$
$953$	10.8409	−	14.9213i	0.351173	−	0.483348i	0.947663	+	0.319273i	$0.103439\pi$
$954$		0			0
$955$	30.7633	−	94.6796i	0.995476	−	3.06376i
$956$		0			0
$957$	18.0681	+	8.51710i	0.584058	+	0.275319i
$958$		0			0
$959$	18.5470	−	57.0817i	0.598913	−	1.84326i
$960$		0			0
$961$	−24.5116	−	17.8087i	−0.790696	−	0.574474i
$962$		0			0
$963$	−25.5817	+	8.31200i	−0.824359	+	0.267850i
$964$		0			0
$965$	20.0924	−	14.5980i	0.646797	−	0.469925i
$966$		0			0
$967$	48.1597			1.54871			0.774356	−	0.632750i	$-0.218074\pi$
$967$	48.1597			1.54871			0.774356	+	0.632750i	$0.218074\pi$
$968$		0			0
$969$	19.3290			0.620938
$970$		0			0
$971$	1.37224	−	0.996990i	0.0440372	−	0.0319949i	−0.565549	−	0.824715i	$-0.691336\pi$
$971$	1.37224	−	0.996990i	0.0440372	−	0.0319949i	0.609586	+	0.792720i	$0.291336\pi$
$972$		0			0
$973$	−18.1168	+	5.88651i	−0.580799	+	0.188713i
$974$		0			0
$975$	19.9928	+	14.5256i	0.640282	+	0.465192i
$976$		0			0
$977$	−13.9474	+	42.9258i	−0.446218	+	1.37332i	0.434925	+	0.900467i	$0.356775\pi$
$977$	−13.9474	+	42.9258i	−0.446218	+	1.37332i	−0.881143	+	0.472851i	$0.843225\pi$
$978$		0			0
$979$	−23.9539	−	11.2916i	−0.765569	−	0.360881i
$980$		0			0
$981$	−1.55260	+	4.77842i	−0.0495708	+	0.152563i
$982$		0			0
$983$	−9.96222	+	13.7118i	−0.317745	+	0.437339i	−0.937777	−	0.347238i	$-0.887120\pi$
$983$	−9.96222	+	13.7118i	−0.317745	+	0.437339i	0.620032	+	0.784577i	$0.287120\pi$
$984$		0			0
$985$	40.6691	−	13.2142i	1.29582	−	0.421039i
$986$		0			0
$987$	2.49143	+	3.42916i	0.0793031	+	0.109151i
$988$		0			0
$989$	1.18323			0.0376245
$990$		0			0
$991$		−	18.1908i		−	0.577849i	−0.957352	−	0.288925i	$-0.906702\pi$
$991$		−	18.1908i		−	0.577849i	0.957352	−	0.288925i	$-0.0932977\pi$
$992$		0			0
$993$	18.0254	−	13.0962i	0.572019	−	0.415596i
$994$		0			0
$995$	26.9617	+	82.9797i	0.854744	+	2.63063i
$996$		0			0
$997$	−9.00121	−	6.53976i	−0.285071	−	0.207116i	0.436055	−	0.899920i	$-0.356375\pi$
$997$	−9.00121	−	6.53976i	−0.285071	−	0.207116i	−0.721126	+	0.692804i	$0.756375\pi$
$998$		0			0
$999$	18.3338	+	5.95701i	0.580055	+	0.188471i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	352.2.s.b.79.6		32
4.3	odd	2		88.2.k.b.35.6	yes	32
8.3	odd	2	inner	352.2.s.b.79.5		32
8.5	even	2		88.2.k.b.35.4	✓	32
11.4	even	5		3872.2.g.d.1935.16		32
11.6	odd	10	inner	352.2.s.b.303.5		32
11.7	odd	10		3872.2.g.d.1935.14		32
12.11	even	2		792.2.bp.b.739.3		32
24.5	odd	2		792.2.bp.b.739.5		32
44.3	odd	10		968.2.k.i.403.3		32
44.7	even	10		968.2.g.e.483.1		32
44.15	odd	10		968.2.g.e.483.32		32
44.19	even	10		968.2.k.e.403.6		32
44.27	odd	10		968.2.k.h.699.5		32
44.31	odd	10		968.2.k.e.723.2		32
44.35	even	10		968.2.k.i.723.7		32
44.39	even	10		88.2.k.b.83.4	yes	32
44.43	even	2		968.2.k.h.475.3		32
88.5	even	10		968.2.k.h.699.3		32
88.13	odd	10		968.2.k.i.723.3		32
88.21	odd	2		968.2.k.h.475.5		32
88.29	odd	10		968.2.g.e.483.31		32
88.37	even	10		968.2.g.e.483.2		32
88.51	even	10		3872.2.g.d.1935.13		32
88.53	even	10		968.2.k.e.723.6		32
88.59	odd	10		3872.2.g.d.1935.15		32
88.61	odd	10		88.2.k.b.83.6	yes	32
88.69	even	10		968.2.k.i.403.7		32
88.83	even	10	inner	352.2.s.b.303.6		32
88.85	odd	10		968.2.k.e.403.2		32
132.83	odd	10		792.2.bp.b.523.5		32
264.149	even	10		792.2.bp.b.523.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.k.b.35.4	✓	32	8.5	even	2
88.2.k.b.35.6	yes	32	4.3	odd	2
88.2.k.b.83.4	yes	32	44.39	even	10
88.2.k.b.83.6	yes	32	88.61	odd	10
352.2.s.b.79.5		32	8.3	odd	2	inner
352.2.s.b.79.6		32	1.1	even	1	trivial
352.2.s.b.303.5		32	11.6	odd	10	inner
352.2.s.b.303.6		32	88.83	even	10	inner
792.2.bp.b.523.3		32	264.149	even	10
792.2.bp.b.523.5		32	132.83	odd	10
792.2.bp.b.739.3		32	12.11	even	2
792.2.bp.b.739.5		32	24.5	odd	2
968.2.g.e.483.1		32	44.7	even	10
968.2.g.e.483.2		32	88.37	even	10
968.2.g.e.483.31		32	88.29	odd	10
968.2.g.e.483.32		32	44.15	odd	10
968.2.k.e.403.2		32	88.85	odd	10
968.2.k.e.403.6		32	44.19	even	10
968.2.k.e.723.2		32	44.31	odd	10
968.2.k.e.723.6		32	88.53	even	10
968.2.k.h.475.3		32	44.43	even	2
968.2.k.h.475.5		32	88.21	odd	2
968.2.k.h.699.3		32	88.5	even	10
968.2.k.h.699.5		32	44.27	odd	10
968.2.k.i.403.3		32	44.3	odd	10
968.2.k.i.403.7		32	88.69	even	10
968.2.k.i.723.3		32	88.13	odd	10
968.2.k.i.723.7		32	44.35	even	10
3872.2.g.d.1935.13		32	88.51	even	10
3872.2.g.d.1935.14		32	11.7	odd	10
3872.2.g.d.1935.15		32	88.59	odd	10
3872.2.g.d.1935.16		32	11.4	even	5

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:	\( N \)	\(=\)	\( 352 = 2^{5} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	352.s (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.903665 - 0.656551i) q^{3} +(3.74056 - 1.21538i) q^{5} +(2.25832 + 1.64076i) q^{7} +(-0.541500 + 1.66657i) q^{9} +(-3.00002 - 1.41418i) q^{11} +(-0.653051 + 2.00988i) q^{13} +(2.58225 - 3.55416i) q^{15} +(-4.42965 + 1.43928i) q^{17} +(-2.18382 - 3.00577i) q^{19} +3.11801 q^{21} -0.854640i q^{23} +(8.46953 - 6.15347i) q^{25} +(1.64036 + 5.04850i) q^{27} +(-4.36210 - 3.16925i) q^{29} +(0.796872 + 0.258919i) q^{31} +(-3.63949 + 0.691723i) q^{33} +(10.4415 + 3.39265i) q^{35} +(2.13456 - 2.93797i) q^{37} +(0.729452 + 2.24502i) q^{39} +(-2.17890 - 2.99900i) q^{41} +1.38448i q^{43} +6.89201i q^{45} +(0.799046 + 1.09979i) q^{47} +(0.244772 + 0.753330i) q^{49} +(-3.05796 + 4.20892i) q^{51} +(-4.01470 - 1.30446i) q^{53} +(-12.9405 - 1.64365i) q^{55} +(-3.94688 - 1.28242i) q^{57} +(-6.80468 - 4.94389i) q^{59} +(0.970728 + 2.98759i) q^{61} +(-3.95732 + 2.87516i) q^{63} +8.31179i q^{65} -3.45851 q^{67} +(-0.561115 - 0.772308i) q^{69} +(11.7395 - 3.81439i) q^{71} +(1.90829 - 2.62654i) q^{73} +(3.61355 - 11.1214i) q^{75} +(-4.45466 - 8.11598i) q^{77} +(-3.59997 + 11.0796i) q^{79} +(0.543938 + 0.395194i) q^{81} +(-0.870974 + 0.282997i) q^{83} +(-14.8201 + 10.7674i) q^{85} -6.02266 q^{87} +7.98458 q^{89} +(-4.77254 + 3.46745i) q^{91} +(0.890099 - 0.289211i) q^{93} +(-11.8218 - 8.58907i) q^{95} +(-3.44331 + 10.5974i) q^{97} +(3.98133 - 4.23395i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{3} - 10 q^{9} + 18 q^{11} - 10 q^{17} + 6 q^{25} + 32 q^{27} + 32 q^{33} + 10 q^{35} - 10 q^{41} - 18 q^{49} - 60 q^{51} - 80 q^{57} - 28 q^{59} + 28 q^{67} - 10 q^{73} - 4 q^{75} + 28 q^{81}+ \cdots - 122 q^{99}+O(q^{100}) \) 32 * q + 2 * q^3 - 10 * q^9 + 18 * q^11 - 10 * q^17 + 6 * q^25 + 32 * q^27 + 32 * q^33 + 10 * q^35 - 10 * q^41 - 18 * q^49 - 60 * q^51 - 80 * q^57 - 28 * q^59 + 28 * q^67 - 10 * q^73 - 4 * q^75 + 28 * q^81 + 20 * q^89 - 78 * q^91 - 52 * q^97 - 122 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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