LMFDB - Embedded newform 920.2.bv.a.217.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(17,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))

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

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

chi := DirichletCharacter("920.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bv (of order $44$, degree $20$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			217.9
Character	$\chi$	$=$	920.217
Dual form			920.2.bv.a.513.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00586 + 0.436349i) q^{3} +(-2.22483 - 0.223911i) q^{5} +(1.76620 - 0.964419i) q^{7} +(1.10420 - 0.504269i) q^{9} +O(q^{10})$	\(q+(-2.00586 + 0.436349i) q^{3} +(-2.22483 - 0.223911i) q^{5} +(1.76620 - 0.964419i) q^{7} +(1.10420 - 0.504269i) q^{9} +(-2.16172 - 1.87314i) q^{11} +(-0.486300 + 0.890592i) q^{13} +(4.56041 - 0.521666i) q^{15} +(-2.26722 - 1.69722i) q^{17} +(-0.358983 + 2.49678i) q^{19} +(-3.12194 + 2.70517i) q^{21} +(4.78098 - 0.377125i) q^{23} +(4.89973 + 0.996329i) q^{25} +(2.93517 - 2.19724i) q^{27} +(-4.90193 + 0.704791i) q^{29} +(5.20042 - 3.34211i) q^{31} +(5.15346 + 2.81400i) q^{33} +(-4.14544 + 1.75019i) q^{35} +(-0.250674 - 0.0934964i) q^{37} +(0.586843 - 1.99860i) q^{39} +(-3.31991 + 7.26958i) q^{41} +(2.41613 + 11.1068i) q^{43} +(-2.56956 + 0.874671i) q^{45} +(5.27335 + 5.27335i) q^{47} +(-1.59512 + 2.48206i) q^{49} +(5.28831 + 2.41509i) q^{51} +(5.81428 + 10.6481i) q^{53} +(4.39004 + 4.65145i) q^{55} +(-0.369397 - 5.16485i) q^{57} +(-1.07505 - 3.66127i) q^{59} +(1.34223 + 2.08855i) q^{61} +(1.46391 - 1.95555i) q^{63} +(1.28135 - 1.87253i) q^{65} +(12.7324 + 0.910642i) q^{67} +(-9.42544 + 2.84264i) q^{69} +(0.925958 + 1.06861i) q^{71} +(5.68532 + 7.59470i) q^{73} +(-10.2629 + 0.139491i) q^{75} +(-5.62452 - 1.22354i) q^{77} +(2.74811 - 0.806917i) q^{79} +(-7.31358 + 8.44032i) q^{81} +(3.30878 - 8.87118i) q^{83} +(4.66414 + 4.28367i) q^{85} +(9.52507 - 3.55267i) q^{87} +(1.88862 + 1.21375i) q^{89} +2.04196i q^{91} +(-8.97302 + 8.97302i) q^{93} +(1.35773 - 5.47453i) q^{95} +(-2.68355 - 7.19488i) q^{97} +(-3.33153 - 0.978225i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q+O(q^{10}) $ 720 * q	$ 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) $ 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{3}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−2.00586	+	0.436349i	−1.15809	+	0.251926i	−0.750266	−	0.661136i	$-0.770075\pi$
$3$	−2.00586	+	0.436349i	−1.15809	+	0.251926i	−0.407820	+	0.913062i	$0.633711\pi$
$4$		0			0
$5$	−2.22483	−	0.223911i	−0.994974	−	0.100136i
$5$	−2.22483	−	0.223911i	−0.994974	−	0.100136i
$6$		0			0
$7$	1.76620	−	0.964419i	0.667561	−	0.364516i	−0.109459	−	0.993991i	$-0.534912\pi$
$7$	1.76620	−	0.964419i	0.667561	−	0.364516i	0.777021	+	0.629475i	$0.216730\pi$
$8$		0			0
$9$	1.10420	−	0.504269i	0.368065	−	0.168090i
$10$		0			0
$11$	−2.16172	−	1.87314i	−0.651783	−	0.564773i	0.264956	−	0.964260i	$-0.414643\pi$
$11$	−2.16172	−	1.87314i	−0.651783	−	0.564773i	−0.916739	+	0.399488i	$0.869188\pi$
$12$		0			0
$13$	−0.486300	+	0.890592i	−0.134875	+	0.247006i	−0.936384	−	0.350978i	$-0.885849\pi$
$13$	−0.486300	+	0.890592i	−0.134875	+	0.247006i	0.801508	+	0.597983i	$0.204031\pi$
$14$		0			0
$15$	4.56041	−	0.521666i	1.17749	−	0.134694i
$16$		0			0
$17$	−2.26722	−	1.69722i	−0.549881	−	0.411636i	0.287885	−	0.957665i	$-0.407048\pi$
$17$	−2.26722	−	1.69722i	−0.549881	−	0.411636i	−0.837766	+	0.546029i	$0.816139\pi$
$18$		0			0
$19$	−0.358983	+	2.49678i	−0.0823564	+	0.572801i	0.906303	+	0.422628i	$0.138892\pi$
$19$	−0.358983	+	2.49678i	−0.0823564	+	0.572801i	−0.988660	+	0.150173i	$0.952017\pi$
$20$		0			0
$21$	−3.12194	+	2.70517i	−0.681263	+	0.590317i
$22$		0			0
$23$	4.78098	−	0.377125i	0.996903	−	0.0786361i
$23$	4.78098	−	0.377125i	0.996903	−	0.0786361i
$24$		0			0
$25$	4.89973	+	0.996329i	0.979945	+	0.199266i
$26$		0			0
$27$	2.93517	−	2.19724i	0.564873	−	0.422859i
$28$		0			0
$29$	−4.90193	+	0.704791i	−0.910265	+	0.130876i	−0.581511	−	0.813539i	$-0.697538\pi$
$29$	−4.90193	+	0.704791i	−0.910265	+	0.130876i	−0.328755	+	0.944415i	$0.606629\pi$
$30$		0			0
$31$	5.20042	−	3.34211i	0.934023	−	0.600260i	0.0173292	−	0.999850i	$-0.494484\pi$
$31$	5.20042	−	3.34211i	0.934023	−	0.600260i	0.916694	+	0.399589i	$0.130847\pi$
$32$		0			0
$33$	5.15346	+	2.81400i	0.897102	+	0.489855i
$34$		0			0
$35$	−4.14544	+	1.75019i	−0.700707	+	0.295837i
$36$		0			0
$37$	−0.250674	−	0.0934964i	−0.0412105	−	0.0153707i	0.328774	−	0.944408i	$-0.393364\pi$
$37$	−0.250674	−	0.0934964i	−0.0412105	−	0.0153707i	−0.369985	+	0.929038i	$0.620637\pi$
$38$		0			0
$39$	0.586843	−	1.99860i	0.0939701	−	0.320033i
$40$		0			0
$41$	−3.31991	+	7.26958i	−0.518482	+	1.13532i	0.451529	+	0.892257i	$0.350879\pi$
$41$	−3.31991	+	7.26958i	−0.518482	+	1.13532i	−0.970011	+	0.243061i	$0.921848\pi$
$42$		0			0
$43$	2.41613	+	11.1068i	0.368457	+	1.69377i	0.671675	+	0.740846i	$0.265575\pi$
$43$	2.41613	+	11.1068i	0.368457	+	1.69377i	−0.303218	+	0.952921i	$0.598061\pi$
$44$		0			0
$45$	−2.56956	+	0.874671i	−0.383047	+	0.130388i
$46$		0			0
$47$	5.27335	+	5.27335i	0.769197	+	0.769197i	0.977965	−	0.208768i	$-0.0669455\pi$
$47$	5.27335	+	5.27335i	0.769197	+	0.769197i	−0.208768	+	0.977965i	$0.566945\pi$
$48$		0			0
$49$	−1.59512	+	2.48206i	−0.227875	+	0.354580i
$50$		0			0
$51$	5.28831	+	2.41509i	0.740511	+	0.338180i
$52$		0			0
$53$	5.81428	+	10.6481i	0.798653	+	1.46262i	0.884613	+	0.466326i	$0.154422\pi$
$53$	5.81428	+	10.6481i	0.798653	+	1.46262i	−0.0859599	+	0.996299i	$0.527396\pi$
$54$		0			0
$55$	4.39004	+	4.65145i	0.591952	+	0.627201i
$56$		0			0
$57$	−0.369397	−	5.16485i	−0.0489279	−	0.684101i
$58$		0			0
$59$	−1.07505	−	3.66127i	−0.139959	−	0.476657i	0.859443	−	0.511232i	$-0.170811\pi$
$59$	−1.07505	−	3.66127i	−0.139959	−	0.476657i	−0.999402	+	0.0345745i	$0.988992\pi$
$60$		0			0
$61$	1.34223	+	2.08855i	0.171855	+	0.267412i	0.916488	−	0.400063i	$-0.131012\pi$
$61$	1.34223	+	2.08855i	0.171855	+	0.267412i	−0.744633	+	0.667474i	$0.767375\pi$
$62$		0			0
$63$	1.46391	−	1.95555i	0.184435	−	0.246376i
$64$		0			0
$65$	1.28135	−	1.87253i	0.158932	−	0.232258i
$66$		0			0
$67$	12.7324	+	0.910642i	1.55552	+	0.111253i	0.822423	−	0.568876i	$-0.192622\pi$
$67$	12.7324	+	0.910642i	1.55552	+	0.111253i	0.733093	+	0.680129i	$0.238076\pi$
$68$		0			0
$69$	−9.42544	+	2.84264i	−1.13469	+	0.342214i
$70$		0			0
$71$	0.925958	+	1.06861i	0.109891	+	0.126821i	0.808030	−	0.589141i	$-0.200534\pi$
$71$	0.925958	+	1.06861i	0.109891	+	0.126821i	−0.698139	+	0.715962i	$0.745988\pi$
$72$		0			0
$73$	5.68532	+	7.59470i	0.665417	+	0.888893i	0.998541	−	0.0539899i	$-0.0171939\pi$
$73$	5.68532	+	7.59470i	0.665417	+	0.888893i	−0.333125	+	0.942883i	$0.608103\pi$
$74$		0			0
$75$	−10.2629	+	0.139491i	−1.18506	+	0.0161070i
$76$		0			0
$77$	−5.62452	−	1.22354i	−0.640974	−	0.139435i
$78$		0			0
$79$	2.74811	−	0.806917i	0.309186	−	0.0907852i	−0.123459	−	0.992350i	$-0.539399\pi$
$79$	2.74811	−	0.806917i	0.309186	−	0.0907852i	0.432645	+	0.901565i	$0.357580\pi$
$80$		0			0
$81$	−7.31358	+	8.44032i	−0.812620	+	0.937813i
$82$		0			0
$83$	3.30878	−	8.87118i	0.363186	−	0.973738i	−0.618928	−	0.785448i	$-0.712433\pi$
$83$	3.30878	−	8.87118i	0.363186	−	0.973738i	0.982113	−	0.188290i	$-0.0602946\pi$
$84$		0			0
$85$	4.66414	+	4.28367i	0.505897	+	0.464629i
$86$		0			0
$87$	9.52507	−	3.55267i	1.02119	−	0.380886i
$88$		0			0
$89$	1.88862	+	1.21375i	0.200194	+	0.128657i	0.636897	−	0.770949i	$-0.280218\pi$
$89$	1.88862	+	1.21375i	0.200194	+	0.128657i	−0.436703	+	0.899606i	$0.643854\pi$
$90$		0			0
$91$			2.04196i			0.214056i
$92$		0			0
$93$	−8.97302	+	8.97302i	−0.930458	+	0.930458i
$94$		0			0
$95$	1.35773	−	5.47453i	0.139301	−	0.561675i
$96$		0			0
$97$	−2.68355	−	7.19488i	−0.272473	−	0.730529i	−0.999056	−	0.0434499i	$-0.986165\pi$
$97$	−2.68355	−	7.19488i	−0.272473	−	0.730529i	0.726582	−	0.687080i	$-0.241108\pi$
$98$		0			0
$99$	−3.33153	−	0.978225i	−0.334831	−	0.0983153i
$100$		0			0
$101$	−0.168784	−	0.369585i	−0.0167946	−	0.0367750i	0.901049	−	0.433718i	$-0.142798\pi$
$101$	−0.168784	−	0.369585i	−0.0167946	−	0.0367750i	−0.917843	+	0.396943i	$0.870071\pi$
$102$		0			0
$103$	−8.04197	+	0.575173i	−0.792399	+	0.0566735i	−0.461669	−	0.887052i	$-0.652749\pi$
$103$	−8.04197	+	0.575173i	−0.792399	+	0.0566735i	−0.330729	+	0.943726i	$0.607295\pi$
$104$		0			0
$105$	7.55150	−	5.31951i	0.736951	−	0.519131i
$106$		0			0
$107$	1.13024	−	5.19564i	0.109265	−	0.502281i	−0.889690	−	0.456565i	$-0.849079\pi$
$107$	1.13024	−	5.19564i	0.109265	−	0.502281i	0.998954	−	0.0457160i	$-0.0145569\pi$
$108$		0			0
$109$	0.440279	+	3.06221i	0.0421711	+	0.293307i	0.999983	+	0.00590912i	$0.00188094\pi$
$109$	0.440279	+	3.06221i	0.0421711	+	0.293307i	−0.957811	+	0.287397i	$0.907210\pi$
$110$		0			0
$111$	0.543614	+	0.0781599i	0.0515976	+	0.00741861i
$112$		0			0
$113$	0.311341	−	4.35311i	0.0292885	−	0.409506i	−0.961566	−	0.274573i	$-0.911463\pi$
$113$	0.311341	−	4.35311i	0.0292885	−	0.409506i	0.990855	−	0.134933i	$-0.0430820\pi$
$114$		0			0
$115$	−10.7213	−	0.231477i	−0.999767	−	0.0215853i
$116$		0			0
$117$	−0.0878723	+	1.22861i	−0.00812379	+	0.113585i
$118$		0			0
$119$	−5.64119	−	0.811080i	−0.517127	−	0.0743516i
$120$		0			0
$121$	−0.401089	−	2.78964i	−0.0364627	−	0.253603i
$122$		0			0
$123$	3.48721	−	16.0304i	0.314431	−	1.44542i
$124$		0			0
$125$	−10.6780	−	3.31377i	−0.955066	−	0.296392i
$126$		0			0
$127$	10.6824	−	0.764020i	0.947910	−	0.0677959i	0.411184	−	0.911552i	$-0.365115\pi$
$127$	10.6824	−	0.764020i	0.947910	−	0.0677959i	0.536726	+	0.843757i	$0.319661\pi$
$128$		0			0
$129$	−9.69286	−	21.2244i	−0.853409	−	1.86871i
$130$		0			0
$131$	−13.6775	−	4.01608i	−1.19501	−	0.350886i	−0.377066	−	0.926186i	$-0.623067\pi$
$131$	−13.6775	−	4.01608i	−1.19501	−	0.350886i	−0.817942	+	0.575300i	$0.804885\pi$
$132$		0			0
$133$	1.77391	+	4.75603i	0.153817	+	0.412400i
$134$		0			0
$135$	−7.02223	+	4.23126i	−0.604378	+	0.364169i
$136$		0			0
$137$	16.4338	−	16.4338i	1.40403	−	1.40403i	0.617332	−	0.786703i	$-0.288214\pi$
$137$	16.4338	−	16.4338i	1.40403	−	1.40403i	0.786703	−	0.617332i	$-0.211786\pi$
$138$		0			0
$139$			9.60071i			0.814321i	0.913357	+	0.407161i	$0.133481\pi$
$139$			9.60071i			0.814321i	−0.913357	+	0.407161i	$0.866519\pi$
$140$		0			0
$141$	−12.8786	−	8.27660i	−1.08458	−	0.697015i
$142$		0			0
$143$	2.71945	−	1.01430i	0.227412	−	0.0848202i
$144$		0			0
$145$	11.0638	−	0.470442i	0.918796	−	0.0390681i
$146$		0			0
$147$	2.11655	−	5.67470i	0.174571	−	0.468042i
$148$		0			0
$149$	−3.83225	+	4.42265i	−0.313950	+	0.362317i	−0.890691	−	0.454610i	$-0.849779\pi$
$149$	−3.83225	+	4.42265i	−0.313950	+	0.362317i	0.576741	+	0.816927i	$0.304324\pi$
$150$		0			0
$151$	−0.177598	+	0.0521475i	−0.0144527	+	0.00424371i	−0.288951	−	0.957344i	$-0.593306\pi$
$151$	−0.177598	+	0.0521475i	−0.0144527	+	0.00424371i	0.274498	+	0.961588i	$0.411488\pi$
$152$		0			0
$153$	−3.35931	−	0.730772i	−0.271584	−	0.0590794i
$154$		0			0
$155$	−12.3184	+	6.27119i	−0.989437	+	0.503714i
$156$		0			0
$157$	0.666649	+	0.890539i	0.0532044	+	0.0710728i	0.826354	−	0.563151i	$-0.190411\pi$
$157$	0.666649	+	0.890539i	0.0532044	+	0.0710728i	−0.773150	+	0.634223i	$0.781320\pi$
$158$		0			0
$159$	−16.3089	−	18.8215i	−1.29338	−	1.49264i
$160$		0			0
$161$	8.08047	−	5.27695i	0.636830	−	0.415882i
$162$		0			0
$163$	−2.50466	−	0.179137i	−0.196180	−	0.0140311i	−0.0270968	−	0.999633i	$-0.508626\pi$
$163$	−2.50466	−	0.179137i	−0.196180	−	0.0140311i	−0.169084	+	0.985602i	$0.554081\pi$
$164$		0			0
$165$	−10.8355	−	7.41459i	−0.843540	−	0.577225i
$166$		0			0
$167$	−7.18160	+	9.59349i	−0.555729	+	0.742366i	−0.987152	−	0.159783i	$-0.948921\pi$
$167$	−7.18160	+	9.59349i	−0.555729	+	0.742366i	0.431424	+	0.902149i	$0.358011\pi$
$168$		0			0
$169$	6.47166	+	10.0701i	0.497820	+	0.774623i
$170$		0			0
$171$	0.862663	+	2.93796i	0.0659695	+	0.224671i
$172$		0			0
$173$	−0.262818	−	3.67467i	−0.0199817	−	0.279380i	−0.997613	−	0.0690539i	$-0.978002\pi$
$173$	−0.262818	−	3.67467i	−0.0199817	−	0.279380i	0.977631	−	0.210326i	$-0.0674526\pi$
$174$		0			0
$175$	9.61478	−	2.96567i	0.726809	−	0.224184i
$176$		0			0
$177$	3.75399	+	6.87492i	0.282167	+	0.516751i
$178$		0			0
$179$	7.61039	+	3.47555i	0.568827	+	0.259775i	0.679001	−	0.734138i	$-0.262413\pi$
$179$	7.61039	+	3.47555i	0.568827	+	0.259775i	−0.110173	+	0.993912i	$0.535141\pi$
$180$		0			0
$181$	7.72517	−	12.0206i	0.574207	−	0.893484i	−0.425728	−	0.904851i	$-0.639982\pi$
$181$	7.72517	−	12.0206i	0.574207	−	0.893484i	0.999935	+	0.0113672i	$0.00361838\pi$
$182$		0			0
$183$	−3.60367	−	3.60367i	−0.266391	−	0.266391i
$184$		0			0
$185$	0.536771	+	0.264142i	0.0394642	+	0.0194201i
$186$		0			0
$187$	1.72196	+	7.91572i	0.125922	+	0.578854i
$188$		0			0
$189$	3.06504	−	6.71150i	0.222949	−	0.488190i
$190$		0			0
$191$	−5.24799	+	17.8730i	−0.379731	+	1.29324i	0.519011	+	0.854767i	$0.326300\pi$
$191$	−5.24799	+	17.8730i	−0.379731	+	1.29324i	−0.898742	+	0.438478i	$0.855518\pi$
$192$		0			0
$193$	18.3137	+	6.83064i	1.31825	+	0.491681i	0.907494	−	0.420066i	$-0.137993\pi$
$193$	18.3137	+	6.83064i	1.31825	+	0.491681i	0.410753	+	0.911747i	$0.365266\pi$
$194$		0			0
$195$	−1.75314	+	4.31515i	−0.125545	+	0.309014i
$196$		0			0
$197$	9.28113	+	5.06788i	0.661253	+	0.361072i	0.774571	−	0.632487i	$-0.217966\pi$
$197$	9.28113	+	5.06788i	0.661253	+	0.361072i	−0.113318	+	0.993559i	$0.536148\pi$
$198$		0			0
$199$	−9.16900	+	5.89256i	−0.649974	+	0.417713i	−0.823657	−	0.567089i	$-0.808070\pi$
$199$	−9.16900	+	5.89256i	−0.649974	+	0.417713i	0.173683	+	0.984802i	$0.444433\pi$
$200$		0			0
$201$	−25.9369	+	3.72917i	−1.82945	+	0.263035i
$202$		0			0
$203$	−7.97808	+	5.97232i	−0.559951	+	0.419174i
$204$		0			0
$205$	9.01397	−	15.4302i	0.629563	−	1.07769i
$206$		0			0
$207$	5.08897	−	2.82732i	0.353708	−	0.196512i
$208$		0			0
$209$	5.45284	−	4.72491i	0.377181	−	0.326829i
$210$		0			0
$211$	1.42072	−	9.88134i	0.0978066	−	0.680260i	−0.880644	−	0.473779i	$-0.842890\pi$
$211$	1.42072	−	9.88134i	0.0978066	−	0.680260i	0.978451	−	0.206481i	$-0.0662012\pi$
$212$		0			0
$213$	−2.32363	−	1.73945i	−0.159213	−	0.119185i
$214$		0			0
$215$	−2.88855	−	25.2517i	−0.196997	−	1.72215i
$216$		0			0
$217$	5.96180	−	10.9182i	0.404713	−	0.741177i
$218$		0			0
$219$	−14.7179	−	12.7532i	−0.994546	−	0.861779i
$220$		0			0
$221$	2.61408	−	1.19381i	0.175842	−	0.0803042i
$222$		0			0
$223$	−21.2832	+	11.6215i	−1.42523	+	0.778233i	−0.992378	−	0.123233i	$-0.960674\pi$
$223$	−21.2832	+	11.6215i	−1.42523	+	0.778233i	−0.432850	+	0.901466i	$0.642492\pi$
$224$		0			0
$225$	5.91268	−	1.37064i	0.394178	−	0.0913760i
$226$		0			0
$227$	18.4292	−	4.00903i	1.22319	−	0.266089i	0.445815	−	0.895125i	$-0.352914\pi$
$227$	18.4292	−	4.00903i	1.22319	−	0.266089i	0.777376	+	0.629036i	$0.216550\pi$
$228$		0			0
$229$	−16.2684			−1.07505			−0.537523	−	0.843249i	$-0.680640\pi$
$229$	−16.2684			−1.07505			−0.537523	+	0.843249i	$0.680640\pi$
$230$		0			0
$231$	11.8159			0.777430
$232$		0			0
$233$	−22.7507	+	4.94911i	−1.49045	+	0.324227i	−0.882713	−	0.469913i	$-0.844285\pi$
$233$	−22.7507	+	4.94911i	−1.49045	+	0.324227i	−0.607735	+	0.794140i	$0.707922\pi$
$234$		0			0
$235$	−10.5515	−	12.9131i	−0.688306	−	0.842355i
$236$		0			0
$237$	−5.16023	+	2.81770i	−0.335193	+	0.183029i
$238$		0			0
$239$	25.0134	−	11.4232i	1.61798	−	0.738907i	0.619059	−	0.785345i	$-0.287514\pi$
$239$	25.0134	−	11.4232i	1.61798	−	0.738907i	0.998921	+	0.0464380i	$0.0147870\pi$
$240$		0			0
$241$	−5.08624	−	4.40725i	−0.327634	−	0.283896i	0.475474	−	0.879730i	$-0.342276\pi$
$241$	−5.08624	−	4.40725i	−0.327634	−	0.283896i	−0.803108	+	0.595833i	$0.796822\pi$
$242$		0			0
$243$	5.71565	−	10.4674i	0.366659	−	0.671486i
$244$		0			0
$245$	4.10464	−	5.16499i	0.262236	−	0.329979i
$246$		0			0
$247$	−2.04904	−	1.53389i	−0.130377	−	0.0975993i
$248$		0			0
$249$	−2.76603	+	19.2382i	−0.175290	+	1.21917i
$250$		0			0
$251$	−8.49991	+	7.36521i	−0.536509	+	0.464888i	−0.880474	−	0.474095i	$-0.842775\pi$
$251$	−8.49991	+	7.36521i	−0.536509	+	0.464888i	0.343965	+	0.938983i	$0.388230\pi$
$252$		0			0
$253$	−11.0415	−	8.14020i	−0.694176	−	0.511770i
$254$		0			0
$255$	−11.2248	−	6.55727i	−0.702925	−	0.410632i
$256$		0			0
$257$	−20.3065	+	15.2013i	−1.26669	+	0.948229i	−0.999880	−	0.0155214i	$-0.995059\pi$
$257$	−20.3065	+	15.2013i	−1.26669	+	0.948229i	−0.266806	+	0.963750i	$0.585968\pi$
$258$		0			0
$259$	−0.532910	+	0.0766208i	−0.0331134	+	0.00476099i
$260$		0			0
$261$	−5.05729	+	3.25012i	−0.313038	+	0.201177i
$262$		0			0
$263$	8.98139	+	4.90421i	0.553816	+	0.302406i	0.731680	−	0.681649i	$-0.238737\pi$
$263$	8.98139	+	4.90421i	0.553816	+	0.302406i	−0.177864	+	0.984055i	$0.556919\pi$
$264$		0			0
$265$	−10.5516	−	24.9920i	−0.648177	−	1.53525i
$266$		0			0
$267$	−4.31794	−	1.61051i	−0.264254	−	0.0985615i
$268$		0			0
$269$	−3.50993	+	11.9537i	−0.214004	+	0.728830i	0.780595	+	0.625037i	$0.214916\pi$
$269$	−3.50993	+	11.9537i	−0.214004	+	0.728830i	−0.994599	+	0.103793i	$0.966902\pi$
$270$		0			0
$271$	0.986248	−	2.15958i	0.0599103	−	0.131185i	−0.877309	−	0.479926i	$-0.840663\pi$
$271$	0.986248	−	2.15958i	0.0599103	−	0.131185i	0.937219	+	0.348741i	$0.113391\pi$
$272$		0			0
$273$	−0.891009	−	4.09590i	−0.0539263	−	0.247895i
$274$		0			0
$275$	−8.72557	−	11.3317i	−0.526171	−	0.683324i
$276$		0			0
$277$	5.58968	+	5.58968i	0.335852	+	0.335852i	0.854803	−	0.518952i	$-0.173678\pi$
$277$	5.58968	+	5.58968i	0.335852	+	0.335852i	−0.518952	+	0.854803i	$0.673678\pi$
$278$		0			0
$279$	4.05696	−	6.31276i	0.242884	−	0.377935i
$280$		0			0
$281$	21.1377	+	9.65328i	1.26097	+	0.575867i	0.929926	−	0.367748i	$-0.119871\pi$
$281$	21.1377	+	9.65328i	1.26097	+	0.575867i	0.331046	+	0.943614i	$0.392598\pi$
$282$		0			0
$283$	10.7320	+	19.6542i	0.637952	+	1.16832i	0.974015	+	0.226482i	$0.0727225\pi$
$283$	10.7320	+	19.6542i	0.637952	+	1.16832i	−0.336063	+	0.941839i	$0.609096\pi$
$284$		0			0
$285$	−0.334623	+	11.5736i	−0.0198213	+	0.685562i
$286$		0			0
$287$	1.14730	+	16.0413i	0.0677229	+	0.946890i
$288$		0			0
$289$	−2.52973	−	8.61547i	−0.148808	−	0.506792i
$290$		0			0
$291$	8.52232	+	13.2610i	0.499587	+	0.777373i
$292$		0			0
$293$	4.19531	−	5.60427i	0.245092	−	0.327405i	−0.661079	−	0.750317i	$-0.729901\pi$
$293$	4.19531	−	5.60427i	0.245092	−	0.327405i	0.906171	+	0.422912i	$0.138992\pi$
$294$		0			0
$295$	1.57199	+	8.38642i	0.0915251	+	0.488276i
$296$		0			0
$297$	−10.4607	−	0.748167i	−0.606994	−	0.0434130i
$298$		0			0
$299$	−1.98913	+	4.44130i	−0.115034	+	0.256847i
$300$		0			0
$301$	14.9790	+	17.2866i	0.863373	+	0.996385i
$302$		0			0
$303$	0.499825	+	0.667688i	0.0287142	+	0.0383577i
$304$		0			0
$305$	−2.51858	−	4.94721i	−0.144214	−	0.283277i
$306$		0			0
$307$	17.3366	+	3.77134i	0.989450	+	0.215242i	0.678033	−	0.735032i	$-0.262833\pi$
$307$	17.3366	+	3.77134i	0.989450	+	0.215242i	0.311417	+	0.950273i	$0.399196\pi$
$308$		0			0
$309$	15.8801	−	4.66282i	0.903389	−	0.265259i
$310$		0			0
$311$	7.55333	−	8.71701i	0.428310	−	0.494296i	−0.500040	−	0.866002i	$-0.666682\pi$
$311$	7.55333	−	8.71701i	0.428310	−	0.494296i	0.928351	+	0.371706i	$0.121227\pi$
$312$		0			0
$313$	10.6933	−	28.6699i	0.604422	−	1.62052i	−0.168273	−	0.985740i	$-0.553819\pi$
$313$	10.6933	−	28.6699i	0.604422	−	1.62052i	0.772695	−	0.634777i	$-0.218908\pi$
$314$		0			0
$315$	−3.69481	+	4.02298i	−0.208179	+	0.226669i
$316$		0			0
$317$	−27.1140	+	10.1130i	−1.52287	+	0.568003i	−0.965075	−	0.261973i	$-0.915627\pi$
$317$	−27.1140	+	10.1130i	−1.52287	+	0.568003i	−0.557799	+	0.829976i	$0.688354\pi$
$318$		0			0
$319$	11.9168	+	7.65844i	0.667211	+	0.428790i
$320$		0			0
$321$			10.9149i			0.609212i
$322$		0			0
$323$	5.05147	−	5.05147i	0.281071	−	0.281071i
$324$		0			0
$325$	−3.27006	+	3.87914i	−0.181390	+	0.215176i
$326$		0			0
$327$	−2.21933	−	5.95026i	−0.122729	−	0.329050i
$328$		0			0
$329$	14.3995	+	4.22808i	0.793871	+	0.233101i
$330$		0			0
$331$	4.90392	+	10.7381i	0.269544	+	0.590218i	0.995203	−	0.0978364i	$-0.0311922\pi$
$331$	4.90392	+	10.7381i	0.269544	+	0.590218i	−0.725659	+	0.688055i	$0.758465\pi$
$332$		0			0
$333$	−0.323940	+	0.0231687i	−0.0177518	+	0.00126963i
$334$		0			0
$335$	−28.1236	−	4.87696i	−1.53656	−	0.266457i
$336$		0			0
$337$	1.13838	−	5.23304i	0.0620114	−	0.285062i	−0.935690	−	0.352823i	$-0.885222\pi$
$337$	1.13838	−	5.23304i	0.0620114	−	0.285062i	0.997702	+	0.0677609i	$0.0215855\pi$
$338$		0			0
$339$	1.27497	+	8.86760i	0.0692468	+	0.481622i
$340$		0			0
$341$	−17.5021	−	2.51642i	−0.947791	−	0.136272i
$342$		0			0
$343$	−1.42848	+	19.9728i	−0.0771307	+	1.07843i
$344$		0			0
$345$	21.6065	−	4.21392i	1.16325	−	0.226870i
$346$		0			0
$347$	1.76663	−	24.7008i	0.0948379	−	1.32601i	−0.697791	−	0.716302i	$-0.745833\pi$
$347$	1.76663	−	24.7008i	0.0948379	−	1.32601i	0.792628	−	0.609705i	$-0.208712\pi$
$348$		0			0
$349$	−3.02956	−	0.435586i	−0.162169	−	0.0233164i	0.0607521	−	0.998153i	$-0.480650\pi$
$349$	−3.02956	−	0.435586i	−0.162169	−	0.0233164i	−0.222921	+	0.974837i	$0.571559\pi$
$350$		0			0
$351$	0.529472	+	3.68256i	0.0282611	+	0.196560i
$352$		0			0
$353$	−3.42242	+	15.7326i	−0.182157	+	0.837362i	0.791827	+	0.610745i	$0.209130\pi$
$353$	−3.42242	+	15.7326i	−0.182157	+	0.837362i	−0.973984	+	0.226617i	$0.927234\pi$
$354$		0			0
$355$	−1.82082	−	2.58481i	−0.0966392	−	0.137188i
$356$		0			0
$357$	11.6694	−	0.834610i	0.617609	−	0.0441722i
$358$		0			0
$359$	−4.81800	−	10.5500i	−0.254284	−	0.556805i	0.738838	−	0.673883i	$-0.235375\pi$
$359$	−4.81800	−	10.5500i	−0.254284	−	0.556805i	−0.993123	+	0.117077i	$0.962647\pi$
$360$		0			0
$361$	12.1253	+	3.56031i	0.638174	+	0.187385i
$362$		0			0
$363$	2.02179	+	5.42062i	0.106116	+	0.284509i
$364$		0			0
$365$	−10.9483	−	18.1699i	−0.573062	−	0.951057i
$366$		0			0
$367$	−5.85074	+	5.85074i	−0.305406	+	0.305406i	−0.843125	−	0.537718i	$-0.819286\pi$
$367$	−5.85074	+	5.85074i	−0.305406	+	0.305406i	0.537718	+	0.843125i	$0.319286\pi$
$368$		0			0
$369$			9.70117i			0.505023i
$370$		0			0
$371$	20.5384	+	13.1992i	1.06630	+	0.685269i
$372$		0			0
$373$	8.28593	−	3.09049i	0.429029	−	0.160020i	−0.125667	−	0.992072i	$-0.540107\pi$
$373$	8.28593	−	3.09049i	0.429029	−	0.160020i	0.554696	+	0.832053i	$0.312834\pi$
$374$		0			0
$375$	22.8645	+	1.98764i	1.18072	+	0.102642i
$376$		0			0
$377$	1.75613	−	4.70836i	0.0904452	−	0.242493i
$378$		0			0
$379$	0.944087	−	1.08953i	0.0484945	−	0.0559656i	−0.730984	−	0.682394i	$-0.760939\pi$
$379$	0.944087	−	1.08953i	0.0484945	−	0.0559656i	0.779479	+	0.626429i	$0.215484\pi$
$380$		0			0
$381$	−21.0941	+	6.19378i	−1.08068	+	0.317317i
$382$		0			0
$383$	−14.3422	−	3.11995i	−0.732850	−	0.159422i	−0.169371	−	0.985552i	$-0.554174\pi$
$383$	−14.3422	−	3.11995i	−0.732850	−	0.159422i	−0.563479	+	0.826131i	$0.690537\pi$
$384$		0			0
$385$	12.2396	+	3.98156i	0.623789	+	0.202919i
$386$		0			0
$387$	8.26869	+	11.0457i	0.420321	+	0.561483i
$388$		0			0
$389$	17.0582	+	19.6862i	0.864883	+	0.998129i	0.999973	+	0.00729519i	$0.00232215\pi$
$389$	17.0582	+	19.6862i	0.864883	+	0.998129i	−0.135090	+	0.990833i	$0.543132\pi$
$390$		0			0
$391$	−11.4796	−	7.25934i	−0.580547	−	0.367120i
$392$		0			0
$393$	29.1876	+	2.08754i	1.47232	+	0.105302i
$394$		0			0
$395$	−6.29474	+	1.17992i	−0.316723	+	0.0593682i
$396$		0			0
$397$	−2.98238	+	3.98399i	−0.149681	+	0.199951i	−0.869115	−	0.494611i	$-0.835311\pi$
$397$	−2.98238	+	3.98399i	−0.149681	+	0.199951i	0.719433	+	0.694561i	$0.244402\pi$
$398$		0			0
$399$	−5.63351	−	8.76591i	−0.282028	−	0.438844i
$400$		0			0
$401$	5.46151	+	18.6002i	0.272735	+	0.928850i	0.975972	+	0.217895i	$0.0699190\pi$
$401$	5.46151	+	18.6002i	0.272735	+	0.928850i	−0.703237	+	0.710955i	$0.748263\pi$
$402$		0			0
$403$	0.447490	+	6.25672i	0.0222911	+	0.311670i
$404$		0			0
$405$	18.1613	−	17.1407i	0.902444	−	0.851727i
$406$		0			0
$407$	0.366754	+	0.671659i	0.0181793	+	0.0332929i
$408$		0			0
$409$	13.3024	+	6.07501i	0.657762	+	0.300390i	0.716194	−	0.697901i	$-0.245883\pi$
$409$	13.3024	+	6.07501i	0.657762	+	0.300390i	−0.0584315	+	0.998291i	$0.518610\pi$
$410$		0			0
$411$	−25.7931	+	40.1349i	−1.27228	+	1.97971i
$412$		0			0
$413$	−5.42975	−	5.42975i	−0.267181	−	0.267181i
$414$		0			0
$415$	−9.34782	+	18.9960i	−0.458867	+	0.932476i
$416$		0			0
$417$	−4.18926	−	19.2577i	−0.205149	−	0.943055i
$418$		0			0
$419$	10.5941	−	23.1979i	0.517557	−	1.13329i	−0.452799	−	0.891613i	$-0.649574\pi$
$419$	10.5941	−	23.1979i	0.517557	−	1.13329i	0.970356	−	0.241680i	$-0.0776983\pi$
$420$		0			0
$421$	−1.08407	+	3.69199i	−0.0528341	+	0.179936i	−0.981683	−	0.190523i	$-0.938982\pi$
$421$	−1.08407	+	3.69199i	−0.0528341	+	0.179936i	0.928849	+	0.370460i	$0.120800\pi$
$422$		0			0
$423$	8.48200	+	3.16362i	0.412409	+	0.153821i
$424$		0			0
$425$	−9.41775	−	10.5748i	−0.456828	−	0.512953i
$426$		0			0
$427$	4.38489	+	2.39433i	0.212200	+	0.115870i
$428$		0			0
$429$	−5.01225	+	3.22118i	−0.241994	+	0.155520i
$430$		0			0
$431$	−26.5878	+	3.82275i	−1.28069	+	0.184135i	−0.748867	−	0.662721i	$-0.769402\pi$
$431$	−26.5878	+	3.82275i	−1.28069	+	0.184135i	−0.531822	+	0.846856i	$0.678493\pi$
$432$		0			0
$433$	−25.4987	+	19.0881i	−1.22539	+	0.917316i	−0.998398	−	0.0565808i	$-0.981980\pi$
$433$	−25.4987	+	19.0881i	−1.22539	+	0.917316i	−0.226992	+	0.973897i	$0.572889\pi$
$434$		0			0
$435$	−21.9871	+	5.77131i	−1.05420	+	0.276713i
$436$		0			0
$437$	−0.774691	+	12.0724i	−0.0370585	+	0.577504i
$438$		0			0
$439$	3.51793	−	3.04831i	0.167902	−	0.145488i	−0.566857	−	0.823816i	$-0.691841\pi$
$439$	3.51793	−	3.04831i	0.167902	−	0.145488i	0.734759	+	0.678328i	$0.237295\pi$
$440$		0			0
$441$	−0.509701	+	3.54505i	−0.0242715	+	0.168812i
$442$		0			0
$443$	9.75529	+	7.30272i	0.463488	+	0.346963i	0.805362	−	0.592783i	$-0.201971\pi$
$443$	9.75529	+	7.30272i	0.463488	+	0.346963i	−0.341874	+	0.939746i	$0.611062\pi$
$444$		0			0
$445$	−3.93009	−	3.12326i	−0.186304	−	0.148057i
$446$		0			0
$447$	5.75715	−	10.5434i	0.272304	−	0.498687i
$448$		0			0
$449$	−4.26937	−	3.69943i	−0.201484	−	0.174587i	0.548275	−	0.836298i	$-0.315285\pi$
$449$	−4.26937	−	3.69943i	−0.201484	−	0.174587i	−0.749759	+	0.661712i	$0.769830\pi$
$450$		0			0
$451$	20.7936	−	9.49614i	0.979135	−	0.447156i
$452$		0			0
$453$	0.333483	−	0.182096i	0.0156684	−	0.00855560i
$454$		0			0
$455$	0.457219	−	4.54302i	0.0214347	−	0.212980i
$456$		0			0
$457$	38.0077	−	8.26807i	1.77792	−	0.386764i	0.800716	−	0.599045i	$-0.204453\pi$
$457$	38.0077	−	8.26807i	1.77792	−	0.386764i	0.977209	+	0.212281i	$0.0680891\pi$
$458$		0			0
$459$	−10.3839			−0.484677
$460$		0			0
$461$	−3.70952			−0.172770			−0.0863848	−	0.996262i	$-0.527531\pi$
$461$	−3.70952			−0.172770			−0.0863848	+	0.996262i	$0.527531\pi$
$462$		0			0
$463$	−33.7828	+	7.34901i	−1.57002	+	0.341537i	−0.911589	−	0.411102i	$-0.865144\pi$
$463$	−33.7828	+	7.34901i	−1.57002	+	0.341537i	−0.658433	+	0.752640i	$0.728780\pi$
$464$		0			0
$465$	21.9726	−	17.9543i	1.01895	−	0.832609i
$466$		0			0
$467$	12.5740	−	6.86591i	0.581854	−	0.317716i	−0.161228	−	0.986917i	$-0.551545\pi$
$467$	12.5740	−	6.86591i	0.581854	−	0.317716i	0.743081	+	0.669201i	$0.233363\pi$
$468$		0			0
$469$	23.3663	−	10.6710i	1.07896	−	0.492742i
$470$		0			0
$471$	−1.72579	−	1.49541i	−0.0795204	−	0.0689048i
$472$		0			0
$473$	15.5815	−	28.5355i	0.716440	−	1.31206i
$474$		0			0
$475$	−4.24654	+	11.8759i	−0.194844	+	0.544903i
$476$		0			0
$477$	11.7896	+	8.82559i	0.539809	+	0.404096i
$478$		0			0
$479$	2.06343	−	14.3515i	0.0942805	−	0.655735i	−0.886803	−	0.462148i	$-0.847079\pi$
$479$	2.06343	−	14.3515i	0.0942805	−	0.655735i	0.981083	−	0.193587i	$-0.0620121\pi$
$480$		0			0
$481$	0.205170	−	0.177781i	0.00935494	−	0.00810610i
$482$		0			0
$483$	−13.9057	+	14.1107i	−0.632733	+	0.642061i
$484$		0			0
$485$	4.35943	+	16.6083i	0.197951	+	0.754142i
$486$		0			0
$487$	−17.5527	+	13.1398i	−0.795388	+	0.595420i	−0.917793	−	0.397060i	$-0.870030\pi$
$487$	−17.5527	+	13.1398i	−0.795388	+	0.595420i	0.122405	+	0.992480i	$0.460939\pi$
$488$		0			0
$489$	5.10218	−	0.733583i	0.230729	−	0.0331738i
$490$		0			0
$491$	15.5989	−	10.0248i	0.703966	−	0.452412i	−0.139060	−	0.990284i	$-0.544408\pi$
$491$	15.5989	−	10.0248i	0.703966	−	0.452412i	0.843026	+	0.537872i	$0.180772\pi$
$492$		0			0
$493$	12.3099	+	6.72172i	0.554411	+	0.302731i
$494$		0			0
$495$	7.19304	+	2.92235i	0.323303	+	0.131350i
$496$		0			0
$497$	2.66602	+	0.994373i	0.119587	+	0.0446037i
$498$		0			0
$499$	9.06129	−	30.8599i	0.405639	−	1.38148i	−0.463143	−	0.886284i	$-0.653278\pi$
$499$	9.06129	−	30.8599i	0.405639	−	1.38148i	0.868782	−	0.495195i	$-0.164904\pi$
$500$		0			0
$501$	10.2192	−	22.3769i	0.456560	−	0.999727i
$502$		0			0
$503$	6.92352	+	31.8269i	0.308704	+	1.41909i	0.826186	+	0.563397i	$0.190506\pi$
$503$	6.92352	+	31.8269i	0.308704	+	1.41909i	−0.517482	+	0.855694i	$0.673130\pi$
$504$		0			0
$505$	0.292761	+	0.860055i	0.0130277	+	0.0382719i
$506$		0			0
$507$	−17.3754	−	17.3754i	−0.771667	−	0.771667i
$508$		0			0
$509$	−19.4379	+	30.2460i	−0.861572	+	1.34063i	0.0775289	+	0.996990i	$0.475297\pi$
$509$	−19.4379	+	30.2460i	−0.861572	+	1.34063i	−0.939101	+	0.343642i	$0.888339\pi$
$510$		0			0
$511$	17.3659	+	7.93074i	0.768222	+	0.350835i
$512$		0			0
$513$	4.43235	+	8.11725i	0.195693	+	0.358385i
$514$		0			0
$515$	18.0208	+	0.521027i	0.794091	+	0.0229592i
$516$		0			0
$517$	−1.52178	−	21.2772i	−0.0669276	−	0.935770i
$518$		0			0
$519$	2.13062	+	7.25621i	0.0935237	+	0.318512i
$520$		0			0
$521$	−11.4990	−	17.8927i	−0.503778	−	0.783894i	0.492480	−	0.870324i	$-0.336091\pi$
$521$	−11.4990	−	17.8927i	−0.503778	−	0.783894i	−0.996258	+	0.0864298i	$0.972454\pi$
$522$		0			0
$523$	2.79508	−	3.73379i	0.122220	−	0.163267i	−0.735258	−	0.677787i	$-0.762939\pi$
$523$	2.79508	−	3.73379i	0.122220	−	0.163267i	0.857478	+	0.514520i	$0.172030\pi$
$524$		0			0
$525$	−17.9919	+	10.1441i	−0.785230	+	0.442727i
$526$		0			0
$527$	−17.4628	−	1.24896i	−0.760690	−	0.0544056i
$528$		0			0
$529$	22.7156	−	3.60606i	0.987633	−	0.156785i
$530$		0			0
$531$	−3.03333	−	3.50065i	−0.131635	−	0.151915i
$532$		0			0
$533$	−4.85976	−	6.49188i	−0.210500	−	0.281195i
$534$		0			0
$535$	−3.67796	+	11.3063i	−0.159012	+	0.488815i
$536$		0			0
$537$	−16.7820	−	3.65069i	−0.724195	−	0.157539i
$538$		0			0
$539$	8.09745	−	2.37762i	0.348782	−	0.102412i
$540$		0			0
$541$	−17.4141	+	20.0970i	−0.748692	+	0.864037i	−0.994441	−	0.105297i	$-0.966421\pi$
$541$	−17.4141	+	20.0970i	−0.748692	+	0.864037i	0.245748	+	0.969334i	$0.420966\pi$
$542$		0			0
$543$	−10.2505	+	27.4826i	−0.439890	+	1.17939i
$544$		0			0
$545$	−0.293883	−	6.91148i	−0.0125885	−	0.296055i
$546$		0			0
$547$	−8.21280	+	3.06322i	−0.351154	+	0.130974i	−0.518850	−	0.854865i	$-0.673640\pi$
$547$	−8.21280	+	3.06322i	−0.351154	+	0.130974i	0.167696	+	0.985839i	$0.446367\pi$
$548$		0			0
$549$	2.53528	+	1.62932i	0.108203	+	0.0695379i
$550$		0			0
$551$		−	12.4921i		−	0.532180i
$552$		0			0
$553$	4.07550	−	4.07550i	0.173308	−	0.173308i
$554$		0			0
$555$	−1.19195	−	0.295614i	−0.0505954	−	0.0125481i
$556$		0			0
$557$	−2.60201	−	6.97626i	−0.110251	−	0.295594i	0.870094	−	0.492886i	$-0.164058\pi$
$557$	−2.60201	−	6.97626i	−0.110251	−	0.295594i	−0.980345	+	0.197292i	$0.936785\pi$
$558$		0			0
$559$	−11.0666	−	3.24944i	−0.468066	−	0.137437i
$560$		0			0
$561$	−6.90803	−	15.1265i	−0.291657	−	0.638640i
$562$		0			0
$563$	27.7150	−	1.98221i	1.16805	−	0.0835404i	0.526192	−	0.850366i	$-0.323619\pi$
$563$	27.7150	−	1.98221i	1.16805	−	0.0835404i	0.641855	+	0.766826i	$0.278165\pi$
$564$		0			0
$565$	−1.66739	+	9.61521i	−0.0701476	+	0.404515i
$566$		0			0
$567$	−4.77725	+	21.9607i	−0.200626	+	0.922261i
$568$		0			0
$569$	4.47342	+	31.1133i	0.187536	+	1.30434i	0.838363	+	0.545113i	$0.183513\pi$
$569$	4.47342	+	31.1133i	0.187536	+	1.30434i	−0.650827	+	0.759226i	$0.725578\pi$
$570$		0			0
$571$	12.4673	+	1.79253i	0.521740	+	0.0750149i	0.398153	−	0.917319i	$-0.369651\pi$
$571$	12.4673	+	1.79253i	0.521740	+	0.0750149i	0.123587	+	0.992334i	$0.460560\pi$
$572$		0			0
$573$	2.72788	−	38.1408i	0.113959	−	1.59335i
$574$		0			0
$575$	23.8012	+	2.91562i	0.992580	+	0.121590i
$576$		0			0
$577$	0.196455	−	2.74680i	0.00817854	−	0.114351i	−0.991723	−	0.128397i	$-0.959017\pi$
$577$	0.196455	−	2.74680i	0.00817854	−	0.114351i	0.999901	+	0.0140464i	$0.00447127\pi$
$578$		0			0
$579$	−39.7153	−	5.71020i	−1.65051	−	0.237308i
$580$		0			0
$581$	−2.71156	−	18.8593i	−0.112495	−	0.782417i
$582$		0			0
$583$	7.37647	−	33.9091i	0.305502	−	1.40437i
$584$		0			0
$585$	0.470602	−	2.71378i	0.0194570	−	0.112201i
$586$		0			0
$587$	−36.0936	+	2.58147i	−1.48974	+	0.106549i	−0.792318	−	0.610109i	$-0.791126\pi$
$587$	−36.0936	+	2.58147i	−1.48974	+	0.106549i	−0.697426	+	0.716657i	$0.745671\pi$
$588$		0			0
$589$	6.47765	+	14.1841i	0.266907	+	0.584445i
$590$		0			0
$591$	−20.8281	−	6.11567i	−0.856752	−	0.251565i
$592$		0			0
$593$	−8.25271	−	22.1264i	−0.338898	−	0.908622i	−0.988886	−	0.148677i	$-0.952499\pi$
$593$	−8.25271	−	22.1264i	−0.338898	−	0.908622i	0.649988	−	0.759945i	$-0.274774\pi$
$594$		0			0
$595$	12.3691	+	3.06764i	0.507082	+	0.125761i
$596$		0			0
$597$	15.8206	−	15.8206i	0.647493	−	0.647493i
$598$		0			0
$599$			6.31347i			0.257961i	0.991647	+	0.128981i	$0.0411705\pi$
$599$			6.31347i			0.257961i	−0.991647	+	0.128981i	$0.958829\pi$
$600$		0			0
$601$	24.3323	+	15.6374i	0.992536	+	0.637864i	0.932817	−	0.360351i	$-0.117343\pi$
$601$	24.3323	+	15.6374i	0.992536	+	0.637864i	0.0597192	+	0.998215i	$0.480979\pi$
$602$		0			0
$603$	14.5183	−	5.41505i	0.591232	−	0.220518i
$604$		0			0
$605$	0.267724	+	6.29627i	0.0108845	+	0.255980i
$606$		0			0
$607$	−16.1771	+	43.3724i	−0.656607	+	1.76043i	−0.00721744	+	0.999974i	$0.502297\pi$
$607$	−16.1771	+	43.3724i	−0.656607	+	1.76043i	−0.649389	+	0.760456i	$0.724975\pi$
$608$		0			0
$609$	13.3969	−	15.4609i	0.542871	−	0.626507i
$610$		0			0
$611$	−7.26083	+	2.13197i	−0.293742	+	0.0862504i
$612$		0			0
$613$	−27.2879	−	5.93612i	−1.10215	−	0.239758i	−0.375537	−	0.926807i	$-0.622542\pi$
$613$	−27.2879	−	5.93612i	−1.10215	−	0.239758i	−0.726610	+	0.687050i	$0.758905\pi$
$614$		0			0
$615$	−11.3478	+	34.8842i	−0.457589	+	1.40666i
$616$		0			0
$617$	14.6400	+	19.5568i	0.589384	+	0.787325i	0.991755	−	0.128152i	$-0.0409045\pi$
$617$	14.6400	+	19.5568i	0.589384	+	0.787325i	−0.402370	+	0.915477i	$0.631814\pi$
$618$		0			0
$619$	−5.14375	−	5.93620i	−0.206745	−	0.238596i	0.642902	−	0.765948i	$-0.277730\pi$
$619$	−5.14375	−	5.93620i	−0.206745	−	0.238596i	−0.849647	+	0.527352i	$0.823185\pi$
$620$		0			0
$621$	13.2043	−	11.6119i	0.529872	−	0.465969i
$622$		0			0
$623$	4.50625	+	0.322293i	0.180539	+	0.0129124i
$624$		0			0
$625$	23.0147	+	9.76348i	0.920586	+	0.390539i
$626$		0			0
$627$	−8.87595	+	11.8569i	−0.354471	+	0.473518i
$628$		0			0
$629$	0.409647	+	0.637424i	0.0163337	+	0.0254158i
$630$		0			0
$631$	−9.89663	−	33.7048i	−0.393979	−	1.34177i	−0.882949	−	0.469468i	$-0.844446\pi$
$631$	−9.89663	−	33.7048i	−0.393979	−	1.34177i	0.488971	−	0.872300i	$-0.337373\pi$
$632$		0			0
$633$	1.46194	+	20.4406i	0.0581068	+	0.812440i
$634$		0			0
$635$	−23.9376	−	0.692096i	−0.949934	−	0.0274650i
$636$		0			0
$637$	−1.43479	−	2.62763i	−0.0568486	−	0.104110i
$638$		0			0
$639$	1.56131	+	0.713025i	0.0617644	+	0.0282068i
$640$		0			0
$641$	−15.5107	+	24.1351i	−0.612635	+	0.953279i	0.386879	+	0.922130i	$0.373553\pi$
$641$	−15.5107	+	24.1351i	−0.612635	+	0.953279i	−0.999515	+	0.0311490i	$0.990083\pi$
$642$		0			0
$643$	24.5459	+	24.5459i	0.967996	+	0.967996i	0.999504	−	0.0315076i	$-0.0100308\pi$
$643$	24.5459	+	24.5459i	0.967996	+	0.967996i	−0.0315076	+	0.999504i	$0.510031\pi$
$644$		0			0
$645$	16.8126	+	49.3910i	0.661995	+	1.94477i
$646$		0			0
$647$	4.67449	+	21.4883i	0.183773	+	0.844792i	0.973021	+	0.230717i	$0.0741072\pi$
$647$	4.67449	+	21.4883i	0.183773	+	0.844792i	−0.789248	+	0.614075i	$0.789529\pi$
$648$		0			0
$649$	−4.53413	+	9.92835i	−0.177980	+	0.389722i
$650$		0			0
$651$	−7.19441	+	24.5019i	−0.281971	+	0.960305i
$652$		0			0
$653$	42.8076	+	15.9664i	1.67519	+	0.624814i	0.994207	−	0.107484i	$-0.0342794\pi$
$653$	42.8076	+	15.9664i	1.67519	+	0.624814i	0.680984	+	0.732298i	$0.261552\pi$
$654$		0			0
$655$	29.5308	+	11.9976i	1.15387	+	0.468786i
$656$		0			0
$657$	10.1075	+	5.51911i	0.394331	+	0.215321i
$658$		0			0
$659$	−17.0070	+	10.9298i	−0.662501	+	0.425763i	−0.828215	−	0.560411i	$-0.810643\pi$
$659$	−17.0070	+	10.9298i	−0.662501	+	0.425763i	0.165714	+	0.986174i	$0.447007\pi$
$660$		0			0
$661$	43.3573	−	6.23383i	1.68640	−	0.242468i	0.768663	−	0.639653i	$-0.220922\pi$
$661$	43.3573	−	6.23383i	1.68640	−	0.242468i	0.917738	+	0.397185i	$0.130013\pi$
$662$		0			0
$663$	−4.72256	+	3.53527i	−0.183409	+	0.137298i
$664$		0			0
$665$	−2.88171	−	10.9786i	−0.111748	−	0.425730i
$666$		0			0
$667$	−23.1702	+	5.21823i	−0.897155	+	0.202051i
$668$		0			0
$669$	37.6202	−	32.5980i	1.45448	−	1.26031i
$670$		0			0
$671$	1.01062	−	7.02905i	0.0390147	−	0.271353i
$672$		0			0
$673$	−23.2444	−	17.4005i	−0.896005	−	0.670741i	0.0486470	−	0.998816i	$-0.484509\pi$
$673$	−23.2444	−	17.4005i	−0.896005	−	0.670741i	−0.944652	+	0.328075i	$0.893600\pi$
$674$		0			0
$675$	16.5707	−	7.84148i	0.637806	−	0.301819i
$676$		0			0
$677$	1.59939	−	2.92907i	0.0614697	−	0.112573i	−0.845137	−	0.534549i	$-0.820481\pi$
$677$	1.59939	−	2.92907i	0.0614697	−	0.112573i	0.906607	+	0.421976i	$0.138663\pi$
$678$		0			0
$679$	−11.6786	−	10.1195i	−0.448182	−	0.388352i
$680$		0			0
$681$	−35.2172	+	16.0832i	−1.34953	+	0.616308i
$682$		0			0
$683$	−12.7593	+	6.96710i	−0.488220	+	0.266588i	−0.704449	−	0.709754i	$-0.748806\pi$
$683$	−12.7593	+	6.96710i	−0.488220	+	0.266588i	0.216229	+	0.976343i	$0.430624\pi$
$684$		0			0
$685$	−40.2421	+	32.8827i	−1.53757	+	1.25638i
$686$		0			0
$687$	32.6322	−	7.09870i	1.24500	−	0.270832i
$688$		0			0
$689$	−12.3106			−0.468995
$690$		0			0
$691$	42.3775			1.61212			0.806058	−	0.591836i	$-0.201597\pi$
$691$	42.3775			1.61212			0.806058	+	0.591836i	$0.201597\pi$
$692$		0			0
$693$	−6.82757	+	1.48525i	−0.259358	+	0.0564198i
$694$		0			0
$695$	2.14971	−	21.3599i	0.0815431	−	0.810228i
$696$		0			0
$697$	19.8650	−	10.8471i	0.752441	−	0.410864i
$698$		0			0
$699$	43.4753	−	19.8545i	1.64439	−	0.750966i
$700$		0			0
$701$	−32.6203	−	28.2657i	−1.23205	−	1.06758i	−0.995382	−	0.0959906i	$-0.969398\pi$
$701$	−32.6203	−	28.2657i	−1.23205	−	1.06758i	−0.236671	−	0.971590i	$-0.576056\pi$
$702$		0			0
$703$	0.323428	−	0.592314i	0.0121983	−	0.0223395i
$704$		0			0
$705$	26.7995	+	21.2977i	1.00933	+	0.802117i
$706$		0			0
$707$	−0.654540	−	0.489983i	−0.0246165	−	0.0184277i
$708$		0			0
$709$	−5.98137	+	41.6014i	−0.224635	+	1.56237i	0.495543	+	0.868583i	$0.334969\pi$
$709$	−5.98137	+	41.6014i	−0.224635	+	1.56237i	−0.720178	+	0.693789i	$0.755940\pi$
$710$		0			0
$711$	2.62754	−	2.27678i	0.0985406	−	0.0853859i
$712$		0			0
$713$	23.6027	−	17.9398i	0.883929	−	0.671850i
$714$		0			0
$715$	−6.27742	+	1.64773i	−0.234762	+	0.0616217i
$716$		0			0
$717$	−45.1889	+	33.8280i	−1.68761	+	1.26333i
$718$		0			0
$719$	−19.0727	+	2.74224i	−0.711292	+	0.102268i	−0.488457	−	0.872588i	$-0.662440\pi$
$719$	−19.0727	+	2.74224i	−0.711292	+	0.102268i	−0.222835	+	0.974856i	$0.571531\pi$
$720$		0			0
$721$	−13.6490	+	8.77170i	−0.508316	+	0.326675i
$722$		0			0
$723$	12.1254	+	6.62098i	0.450949	+	0.246237i
$724$		0			0
$725$	−24.7203	−	1.43065i	−0.918090	−	0.0531330i
$726$		0			0
$727$	31.2110	+	11.6411i	1.15755	+	0.431745i	0.853593	−	0.520940i	$-0.174419\pi$
$727$	31.2110	+	11.6411i	1.15755	+	0.431745i	0.303959	+	0.952685i	$0.401691\pi$
$728$		0			0
$729$	2.54192	−	8.65699i	0.0941452	−	0.320629i
$730$		0			0
$731$	13.3727	−	29.2822i	0.494608	−	1.08304i
$732$		0			0
$733$	−7.57532	−	34.8232i	−0.279801	−	1.28622i	−0.875579	−	0.483075i	$-0.839520\pi$
$733$	−7.57532	−	34.8232i	−0.279801	−	1.28622i	0.595778	−	0.803149i	$-0.296844\pi$
$734$		0			0
$735$	−5.97960	+	12.1513i	−0.220561	+	0.448208i
$736$		0			0
$737$	−25.8182	−	25.8182i	−0.951025	−	0.951025i
$738$		0			0
$739$	−18.6476	+	29.0163i	−0.685964	+	1.06738i	0.307312	+	0.951609i	$0.400571\pi$
$739$	−18.6476	+	29.0163i	−0.685964	+	1.06738i	−0.993276	+	0.115772i	$0.963066\pi$
$740$		0			0
$741$	4.77941	+	2.18268i	0.175576	+	0.0801829i
$742$		0			0
$743$	−15.5766	−	28.5264i	−0.571449	−	1.04653i	−0.990362	−	0.138504i	$-0.955771\pi$
$743$	−15.5766	−	28.5264i	−0.571449	−	1.04653i	0.418913	−	0.908026i	$-0.362411\pi$
$744$		0			0
$745$	9.51637	−	8.98155i	0.348653	−	0.329059i
$746$		0			0
$747$	−0.819924	−	11.4640i	−0.0299995	−	0.419447i
$748$		0			0
$749$	−3.01454	−	10.2666i	−0.110149	−	0.375132i
$750$		0			0
$751$	−15.7813	−	24.5562i	−0.575869	−	0.896070i	0.424085	−	0.905622i	$-0.360596\pi$
$751$	−15.7813	−	24.5562i	−0.575869	−	0.896070i	−0.999954	+	0.00955224i	$0.996959\pi$
$752$		0			0
$753$	13.8359	−	18.4825i	0.504207	−	0.673541i
$754$		0			0
$755$	0.406802	−	0.0762531i	0.0148050	−	0.00277513i
$756$		0			0
$757$	−12.8342	−	0.917919i	−0.466466	−	0.0333623i	−0.163872	−	0.986482i	$-0.552398\pi$
$757$	−12.8342	−	0.917919i	−0.466466	−	0.0333623i	−0.302595	+	0.953119i	$0.597853\pi$
$758$		0			0
$759$	25.6998	+	11.5102i	0.932844	+	0.417793i
$760$		0			0
$761$	23.6590	+	27.3040i	0.857639	+	0.989768i	1.00000		4.64077e-5i	$-1.47720e-5\pi$
$761$	23.6590	+	27.3040i	0.857639	+	0.989768i	−0.142361	+	0.989815i	$0.545469\pi$
$762$		0			0
$763$	3.73088	+	4.98387i	0.135067	+	0.180428i
$764$		0			0
$765$	7.31025	+	2.37803i	0.264303	+	0.0859778i
$766$		0			0
$767$	3.78350	+	0.823050i	0.136614	+	0.0297186i
$768$		0			0
$769$	−44.0666	+	12.9391i	−1.58908	+	0.466596i	−0.952481	−	0.304598i	$-0.901478\pi$
$769$	−44.0666	+	12.9391i	−1.58908	+	0.466596i	−0.636600	+	0.771194i	$0.719660\pi$
$770$		0			0
$771$	34.0991	−	39.3524i	1.22805	−	1.41724i
$772$		0			0
$773$	−9.76707	+	26.1865i	−0.351297	+	0.941864i	0.634350	+	0.773046i	$0.281268\pi$
$773$	−9.76707	+	26.1865i	−0.351297	+	0.941864i	−0.985647	+	0.168818i	$0.946005\pi$
$774$		0			0
$775$	28.8105	−	11.1941i	1.03490	−	0.402104i
$776$		0			0
$777$	1.03551	−	0.386226i	0.0371488	−	0.0138558i
$778$		0			0
$779$	−16.9588	−	10.8987i	−0.607611	−	0.390488i
$780$		0			0
$781$		−	4.04449i		−	0.144723i
$782$		0			0
$783$	−12.8394	+	12.8394i	−0.458842	+	0.458842i
$784$		0			0
$785$	−1.28378	−	2.13057i	−0.0458200	−	0.0760432i
$786$		0			0
$787$	−10.6203	−	28.4741i	−0.378573	−	1.01499i	−0.976892	−	0.213735i	$-0.931437\pi$
$787$	−10.6203	−	28.4741i	−0.378573	−	1.01499i	0.598319	−	0.801258i	$-0.295835\pi$
$788$		0			0
$789$	−20.1554	−	5.91816i	−0.717551	−	0.210692i
$790$		0			0
$791$	−3.64833	−	7.98873i	−0.129720	−	0.284047i
$792$		0			0
$793$	−2.51278	+	0.179717i	−0.0892313	+	0.00638195i
$794$		0			0
$795$	32.0702	+	45.5264i	1.13741	+	1.61466i
$796$		0			0
$797$	−4.60165	+	21.1534i	−0.162999	+	0.749294i	0.820973	+	0.570968i	$0.193432\pi$
$797$	−4.60165	+	21.1534i	−0.162999	+	0.749294i	−0.983971	+	0.178326i	$0.942932\pi$
$798$		0			0
$799$	−3.00580	−	20.9058i	−0.106338	−	0.739595i
$800$		0			0
$801$	2.69747	+	0.387837i	0.0953103	+	0.0137035i
$802$		0			0
$803$	1.93587	−	27.0670i	0.0683154	−	0.955174i
$804$		0			0
$805$	−19.1592	+	9.93100i	−0.675274	+	0.350022i
$806$		0			0
$807$	1.82444	−	25.5091i	0.0642235	−	0.897962i
$808$		0			0
$809$	−44.3382	−	6.37487i	−1.55885	−	0.224129i	−0.691702	−	0.722183i	$-0.743139\pi$
$809$	−44.3382	−	6.37487i	−1.55885	−	0.224129i	−0.867146	+	0.498054i	$0.834048\pi$
$810$		0			0
$811$	−4.69489	−	32.6537i	−0.164860	−	1.14663i	−0.889312	−	0.457301i	$-0.848816\pi$
$811$	−4.69489	−	32.6537i	−0.164860	−	1.14663i	0.724452	−	0.689325i	$-0.242093\pi$
$812$		0			0
$813$	−1.03595	+	4.76218i	−0.0363323	+	0.167017i
$814$		0			0
$815$	5.53234	+	0.959372i	0.193789	+	0.0336053i
$816$		0			0
$817$	−28.5985	+	2.04541i	−1.00054	+	0.0715598i
$818$		0			0
$819$	1.02970	+	2.25473i	0.0359806	+	0.0787865i
$820$		0			0
$821$	−19.8992	−	5.84293i	−0.694487	−	0.203920i	−0.0846079	−	0.996414i	$-0.526964\pi$
$821$	−19.8992	−	5.84293i	−0.694487	−	0.203920i	−0.609879	+	0.792495i	$0.708782\pi$
$822$		0			0
$823$	−5.73338	−	15.3718i	−0.199853	−	0.535826i	0.797903	−	0.602786i	$-0.205943\pi$
$823$	−5.73338	−	15.3718i	−0.199853	−	0.535826i	−0.997756	+	0.0669597i	$0.978670\pi$
$824$		0			0
$825$	22.4469	+	18.9224i	0.781499	+	0.658792i
$826$		0			0
$827$	16.4424	−	16.4424i	0.571759	−	0.571759i	−0.360861	−	0.932620i	$-0.617517\pi$
$827$	16.4424	−	16.4424i	0.571759	−	0.571759i	0.932620	+	0.360861i	$0.117517\pi$
$828$		0			0
$829$			37.4134i			1.29942i	0.760182	+	0.649710i	$0.225110\pi$
$829$			37.4134i			1.29942i	−0.760182	+	0.649710i	$0.774890\pi$
$830$		0			0
$831$	−13.6512	−	8.77309i	−0.473555	−	0.304335i
$832$		0			0
$833$	7.82908	−	2.92010i	0.271261	−	0.101175i
$834$		0			0
$835$	18.1259	−	19.7358i	0.627273	−	0.682987i
$836$		0			0
$837$	7.92070	−	21.2362i	0.273779	−	0.734031i
$838$		0			0
$839$	−12.7171	+	14.6763i	−0.439042	+	0.506681i	−0.931543	−	0.363630i	$-0.881537\pi$
$839$	−12.7171	+	14.6763i	−0.439042	+	0.506681i	0.492502	+	0.870312i	$0.336083\pi$
$840$		0			0
$841$	−4.29312	+	1.26057i	−0.148039	+	0.0434680i
$842$		0			0
$843$	−46.6117	−	10.1397i	−1.60539	−	0.349231i
$844$		0			0
$845$	−12.1435	−	23.8533i	−0.417750	−	0.820580i
$846$		0			0
$847$	−3.39878	−	4.54024i	−0.116784	−	0.156005i
$848$		0			0
$849$	−30.1031	−	34.7408i	−1.03313	−	1.19230i
$850$		0			0
$851$	−1.23373	−	0.352469i	−0.0422916	−	0.0120825i
$852$		0			0
$853$	34.4469	+	2.46369i	1.17944	+	0.0843551i	0.647255	−	0.762274i	$-0.275917\pi$
$853$	34.4469	+	2.46369i	1.17944	+	0.0843551i	0.532184	+	0.846629i	$0.321372\pi$
$854$		0			0
$855$	−1.26144	−	6.72962i	−0.0431402	−	0.230148i
$856$		0			0
$857$	18.0789	−	24.1506i	0.617565	−	0.824970i	−0.377310	−	0.926087i	$-0.623151\pi$
$857$	18.0789	−	24.1506i	0.617565	−	0.824970i	0.994875	+	0.101117i	$0.0322417\pi$
$858$		0			0
$859$	−8.66856	−	13.4885i	−0.295767	−	0.460223i	0.661286	−	0.750134i	$-0.270011\pi$
$859$	−8.66856	−	13.4885i	−0.295767	−	0.460223i	−0.957054	+	0.289911i	$0.906374\pi$
$860$		0			0
$861$	−9.30094	−	31.6761i	−0.316975	−	1.07952i
$862$		0			0
$863$	−3.58306	−	50.0977i	−0.121969	−	1.70535i	−0.578536	−	0.815657i	$-0.696376\pi$
$863$	−3.58306	−	50.0977i	−0.121969	−	1.70535i	0.456567	−	0.889689i	$-0.349079\pi$
$864$		0			0
$865$	−0.238076	+	8.23436i	−0.00809483	+	0.279977i
$866$		0			0
$867$	8.83364	+	16.1776i	0.300006	+	0.549421i
$868$		0			0
$869$	−7.45210	−	3.40326i	−0.252795	−	0.115448i
$870$		0			0
$871$	−7.00280	+	10.8966i	−0.237281	+	0.369216i
$872$		0			0
$873$	−6.59132	−	6.59132i	−0.223083	−	0.223083i
$874$		0			0
$875$	−22.0553	+	4.44525i	−0.745605	+	0.150277i
$876$		0			0
$877$	2.46426	+	11.3280i	0.0832122	+	0.382520i	0.999852	−	0.0171935i	$-0.00547315\pi$
$877$	2.46426	+	11.3280i	0.0832122	+	0.382520i	−0.916640	+	0.399714i	$0.869110\pi$
$878$		0			0
$879$	−5.96980	+	13.0720i	−0.201356	+	0.440909i
$880$		0			0
$881$	10.0354	−	34.1776i	0.338102	−	1.15147i	−0.598513	−	0.801113i	$-0.704242\pi$
$881$	10.0354	−	34.1776i	0.338102	−	1.15147i	0.936616	−	0.350358i	$-0.113940\pi$
$882$		0			0
$883$	−17.0987	−	6.37747i	−0.575416	−	0.214619i	0.0448728	−	0.998993i	$-0.485712\pi$
$883$	−17.0987	−	6.37747i	−0.575416	−	0.214619i	−0.620288	+	0.784374i	$0.712984\pi$
$884$		0			0
$885$	−6.81262	−	16.1361i	−0.229004	−	0.542409i
$886$		0			0
$887$	1.91360	+	1.04490i	0.0642523	+	0.0350844i	0.511054	−	0.859549i	$-0.329255\pi$
$887$	1.91360	+	1.04490i	0.0642523	+	0.0350844i	−0.446802	+	0.894633i	$0.647437\pi$
$888$		0			0
$889$	18.1304	−	11.6517i	0.608075	−	0.390786i
$890$		0			0
$891$	31.6198	−	4.54624i	1.05930	−	0.152305i
$892$		0			0
$893$	−15.0594	+	11.2734i	−0.503945	+	0.377249i
$894$		0			0
$895$	−16.1536	−	9.43655i	−0.539955	−	0.315429i
$896$		0			0
$897$	2.05196	−	9.77660i	0.0685130	−	0.326431i
$898$		0			0
$899$	−23.1366	+	20.0480i	−0.771649	+	0.668638i
$900$		0			0
$901$	4.88984	−	34.0096i	0.162904	−	1.13302i
$902$		0			0
$903$	−37.5888	−	28.1386i	−1.25088	−	0.936394i
$904$		0			0
$905$	−19.8787	+	25.0140i	−0.660791	+	0.831494i
$906$		0			0
$907$	20.0479	−	36.7150i	0.665680	−	1.21910i	−0.298641	−	0.954366i	$-0.596533\pi$
$907$	20.0479	−	36.7150i	0.665680	−	1.21910i	0.964321	−	0.264737i	$-0.0852850\pi$
$908$		0			0
$909$	−0.372740	−	0.322981i	−0.0123630	−	0.0107126i
$910$		0			0
$911$	17.7344	−	8.09904i	0.587568	−	0.268333i	−0.0993686	−	0.995051i	$-0.531682\pi$
$911$	17.7344	−	8.09904i	0.587568	−	0.268333i	0.686937	+	0.726717i	$0.258955\pi$
$912$		0			0
$913$	−23.7696	+	12.9792i	−0.786659	+	0.429548i
$914$		0			0
$915$	7.21065	+	8.82445i	0.238377	+	0.291727i
$916$		0			0
$917$	−28.0304	+	6.09764i	−0.925645	+	0.201362i
$918$		0			0
$919$	39.1083			1.29006			0.645031	−	0.764156i	$-0.276844\pi$
$919$	39.1083			1.29006			0.645031	+	0.764156i	$0.276844\pi$
$920$		0			0
$921$	−36.4204			−1.20009
$922$		0			0
$923$	−1.40199	+	0.304985i	−0.0461471	+	0.0100387i
$924$		0			0
$925$	−1.13508	−	0.707860i	−0.0373212	−	0.0232743i
$926$		0			0
$927$	−8.58987	+	4.69042i	−0.282128	+	0.154054i
$928$		0			0
$929$	−19.7911	+	9.03828i	−0.649324	+	0.296536i	−0.712716	−	0.701452i	$-0.752535\pi$
$929$	−19.7911	+	9.03828i	−0.649324	+	0.296536i	0.0633923	+	0.997989i	$0.479808\pi$
$930$		0			0
$931$	−5.62454	−	4.87369i	−0.184337	−	0.159729i
$932$		0			0
$933$	−11.3473	+	20.7810i	−0.371494	+	0.680341i
$934$		0			0
$935$	−2.05864	−	17.9967i	−0.0673249	−	0.588554i
$936$		0			0
$937$	−41.9059	−	31.3704i	−1.36901	−	1.02483i	−0.995255	−	0.0972962i	$-0.968981\pi$
$937$	−41.9059	−	31.3704i	−1.36901	−	1.02483i	−0.373751	−	0.927529i	$-0.621929\pi$
$938$		0			0
$939$	−8.93926	+	62.1739i	−0.291722	+	2.02897i
$940$		0			0
$941$	14.4003	−	12.4779i	0.469435	−	0.406768i	−0.387759	−	0.921761i	$-0.626751\pi$
$941$	14.4003	−	12.4779i	0.469435	−	0.406768i	0.857195	+	0.514993i	$0.172205\pi$
$942$		0			0
$943$	−13.1309	+	36.0078i	−0.427600	+	1.17257i
$944$		0			0
$945$	−8.32197	+	14.2456i	−0.270714	+	0.463411i
$946$		0			0
$947$	30.9580	−	23.1749i	1.00600	−	0.753083i	0.0367917	−	0.999323i	$-0.488286\pi$
$947$	30.9580	−	23.1749i	1.00600	−	0.753083i	0.969209	+	0.246240i	$0.0791953\pi$
$948$		0			0
$949$	−9.52856	+	1.37000i	−0.309310	+	0.0444721i
$950$		0			0
$951$	49.9742	−	32.1165i	1.62053	−	1.04145i
$952$		0			0
$953$	−23.1566	−	12.6445i	−0.750116	−	0.409595i	0.0582288	−	0.998303i	$-0.481455\pi$
$953$	−23.1566	−	12.6445i	−0.750116	−	0.409595i	−0.808345	+	0.588709i	$0.799637\pi$
$954$		0			0
$955$	15.6778	−	38.5893i	0.507323	−	1.24872i
$956$		0			0
$957$	−27.2452	−	10.1619i	−0.880711	−	0.328488i
$958$		0			0
$959$	13.1763	−	44.8745i	0.425486	−	1.44907i
$960$		0			0
$961$	2.99684	−	6.56216i	0.0966722	−	0.211683i
$962$		0			0
$963$	−1.37199	−	6.30695i	−0.0442119	−	0.203239i
$964$		0			0
$965$	−39.2153	−	19.2977i	−1.26239	−	0.621213i
$966$		0			0
$967$	19.2060	+	19.2060i	0.617624	+	0.617624i	0.944921	−	0.327297i	$-0.106138\pi$
$967$	19.2060	+	19.2060i	0.617624	+	0.617624i	−0.327297	+	0.944921i	$0.606138\pi$
$968$		0			0
$969$	−7.92836	+	12.3368i	−0.254696	+	0.396314i
$970$		0			0
$971$	−12.9636	−	5.92028i	−0.416022	−	0.189991i	0.196397	−	0.980525i	$-0.437076\pi$
$971$	−12.9636	−	5.92028i	−0.416022	−	0.189991i	−0.612418	+	0.790534i	$0.709803\pi$
$972$		0			0
$973$	9.25910	+	16.9568i	0.296833	+	0.543610i
$974$		0			0
$975$	4.86664	−	9.20793i	0.155857	−	0.294890i
$976$		0			0
$977$	2.78305	+	38.9121i	0.0890377	+	1.24491i	0.823917	+	0.566711i	$0.191784\pi$
$977$	2.78305	+	38.9121i	0.0890377	+	1.24491i	−0.734879	+	0.678198i	$0.762761\pi$
$978$		0			0
$979$	−1.80916	−	6.16143i	−0.0578210	−	0.196920i
$980$		0			0
$981$	2.03033	+	3.15926i	0.0648236	+	0.100867i
$982$		0			0
$983$	22.6185	−	30.2148i	0.721417	−	0.963701i	−0.278577	−	0.960414i	$-0.589863\pi$
$983$	22.6185	−	30.2148i	0.721417	−	0.963701i	0.999995	−	0.00328702i	$-0.00104629\pi$
$984$		0			0
$985$	−19.5142	−	13.3533i	−0.621773	−	0.425472i
$986$		0			0
$987$	−30.7284	−	2.19774i	−0.978095	−	0.0699547i
$988$		0			0
$989$	15.7401	+	52.1901i	0.500507	+	1.65955i
$990$		0			0
$991$	−34.9650	−	40.3517i	−1.11070	−	1.28182i	−0.955843	−	0.293878i	$-0.905054\pi$
$991$	−34.9650	−	40.3517i	−1.11070	−	1.28182i	−0.154856	−	0.987937i	$-0.549491\pi$
$992$		0			0
$993$	−14.5221	−	19.3993i	−0.460846	−	0.615619i
$994$		0			0
$995$	21.7189	−	11.0569i	0.688535	−	0.350527i
$996$		0			0
$997$	−27.7177	−	6.02961i	−0.877827	−	0.190960i	−0.248999	−	0.968504i	$-0.580102\pi$
$997$	−27.7177	−	6.02961i	−0.877827	−	0.190960i	−0.628828	+	0.777544i	$0.716465\pi$
$998$		0			0
$999$	−0.941203	+	0.276362i	−0.0297783	+	0.00874371i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.217.9	yes	720
5.3	odd	4	inner	920.2.bv.a.33.9	✓	720
23.7	odd	22	inner	920.2.bv.a.697.9	yes	720
115.53	even	44	inner	920.2.bv.a.513.9	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.33.9	✓	720	5.3	odd	4	inner
920.2.bv.a.217.9	yes	720	1.1	even	1	trivial
920.2.bv.a.513.9	yes	720	115.53	even	44	inner
920.2.bv.a.697.9	yes	720	23.7	odd	22	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:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bv (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00586 + 0.436349i) q^{3} +(-2.22483 - 0.223911i) q^{5} +(1.76620 - 0.964419i) q^{7} +(1.10420 - 0.504269i) q^{9} +O(q^{10})\)	\(q+(-2.00586 + 0.436349i) q^{3} +(-2.22483 - 0.223911i) q^{5} +(1.76620 - 0.964419i) q^{7} +(1.10420 - 0.504269i) q^{9} +(-2.16172 - 1.87314i) q^{11} +(-0.486300 + 0.890592i) q^{13} +(4.56041 - 0.521666i) q^{15} +(-2.26722 - 1.69722i) q^{17} +(-0.358983 + 2.49678i) q^{19} +(-3.12194 + 2.70517i) q^{21} +(4.78098 - 0.377125i) q^{23} +(4.89973 + 0.996329i) q^{25} +(2.93517 - 2.19724i) q^{27} +(-4.90193 + 0.704791i) q^{29} +(5.20042 - 3.34211i) q^{31} +(5.15346 + 2.81400i) q^{33} +(-4.14544 + 1.75019i) q^{35} +(-0.250674 - 0.0934964i) q^{37} +(0.586843 - 1.99860i) q^{39} +(-3.31991 + 7.26958i) q^{41} +(2.41613 + 11.1068i) q^{43} +(-2.56956 + 0.874671i) q^{45} +(5.27335 + 5.27335i) q^{47} +(-1.59512 + 2.48206i) q^{49} +(5.28831 + 2.41509i) q^{51} +(5.81428 + 10.6481i) q^{53} +(4.39004 + 4.65145i) q^{55} +(-0.369397 - 5.16485i) q^{57} +(-1.07505 - 3.66127i) q^{59} +(1.34223 + 2.08855i) q^{61} +(1.46391 - 1.95555i) q^{63} +(1.28135 - 1.87253i) q^{65} +(12.7324 + 0.910642i) q^{67} +(-9.42544 + 2.84264i) q^{69} +(0.925958 + 1.06861i) q^{71} +(5.68532 + 7.59470i) q^{73} +(-10.2629 + 0.139491i) q^{75} +(-5.62452 - 1.22354i) q^{77} +(2.74811 - 0.806917i) q^{79} +(-7.31358 + 8.44032i) q^{81} +(3.30878 - 8.87118i) q^{83} +(4.66414 + 4.28367i) q^{85} +(9.52507 - 3.55267i) q^{87} +(1.88862 + 1.21375i) q^{89} +2.04196i q^{91} +(-8.97302 + 8.97302i) q^{93} +(1.35773 - 5.47453i) q^{95} +(-2.68355 - 7.19488i) q^{97} +(-3.33153 - 0.978225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q+O(q^{10}) \) 720 * q	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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