LMFDB - Embedded newform 380.2.bh.a.117.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(13,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 27, 10]))

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

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

chi := DirichletCharacter("380.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bh (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			117.3
Character	$\chi$	$=$	380.117
Dual form			380.2.bh.a.13.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41596 - 0.660272i) q^{3} +(-0.949889 - 2.02428i) q^{5} +(-1.12143 + 4.18524i) q^{7} +(-0.359387 - 0.428300i) q^{9} +O(q^{10})$	\(q+(-1.41596 - 0.660272i) q^{3} +(-0.949889 - 2.02428i) q^{5} +(-1.12143 + 4.18524i) q^{7} +(-0.359387 - 0.428300i) q^{9} +(-0.627484 + 1.08683i) q^{11} +(1.92393 + 4.12588i) q^{13} +(0.00842766 + 3.49348i) q^{15} +(0.0727101 + 0.831080i) q^{17} +(3.83747 + 2.06733i) q^{19} +(4.35129 - 5.18567i) q^{21} +(0.587706 + 0.411516i) q^{23} +(-3.19542 + 3.84568i) q^{25} +(1.43917 + 5.37105i) q^{27} +(-3.22929 + 2.70969i) q^{29} +(-6.47928 + 3.74082i) q^{31} +(1.60610 - 1.12460i) q^{33} +(9.53733 - 1.70542i) q^{35} +(1.31792 - 1.31792i) q^{37} -7.11239i q^{39} +(-2.83535 - 7.79006i) q^{41} +(6.72347 + 9.60211i) q^{43} +(-0.525622 + 1.13434i) q^{45} +(-9.51062 - 0.832071i) q^{47} +(-10.1964 - 5.88691i) q^{49} +(0.445784 - 1.22478i) q^{51} +(-5.49098 + 7.84194i) q^{53} +(2.79610 + 0.237831i) q^{55} +(-4.06869 - 5.46102i) q^{57} +(-2.93676 - 2.46424i) q^{59} +(-1.31237 - 7.44285i) q^{61} +(2.19557 - 1.02381i) q^{63} +(6.52442 - 7.81370i) q^{65} +(0.616682 - 7.04871i) q^{67} +(-0.560454 - 0.970734i) q^{69} +(11.6384 + 2.05217i) q^{71} +(1.19747 - 2.56798i) q^{73} +(7.06378 - 3.33548i) q^{75} +(-3.84498 - 3.84498i) q^{77} +(-5.16648 + 1.88045i) q^{79} +(1.21729 - 6.90358i) q^{81} +(7.22139 + 1.93497i) q^{83} +(1.61327 - 0.936620i) q^{85} +(6.36167 - 1.70460i) q^{87} +(3.31376 + 1.20611i) q^{89} +(-19.4253 + 3.42521i) q^{91} +(11.6443 - 1.01875i) q^{93} +(0.539677 - 9.73184i) q^{95} +(-5.44825 + 0.476660i) q^{97} +(0.691001 - 0.121842i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 6 q^{7}+O(q^{10}) $ 120 * q + 6 * q^7	$ 120 q + 6 q^{7} + 18 q^{15} - 18 q^{17} + 48 q^{21} - 36 q^{23} - 24 q^{25} - 60 q^{33} - 18 q^{35} - 12 q^{41} - 36 q^{43} + 18 q^{45} - 24 q^{47} + 96 q^{51} - 18 q^{53} + 72 q^{55} - 6 q^{57} - 24 q^{61} + 36 q^{63} + 90 q^{65} - 24 q^{67} + 18 q^{73} - 36 q^{77} - 30 q^{83} - 24 q^{85} - 72 q^{87} - 144 q^{91} - 132 q^{93} - 12 q^{95} - 60 q^{97}+O(q^{100}) $ 120 * q + 6 * q^7 + 18 * q^15 - 18 * q^17 + 48 * q^21 - 36 * q^23 - 24 * q^25 - 60 * q^33 - 18 * q^35 - 12 * q^41 - 36 * q^43 + 18 * q^45 - 24 * q^47 + 96 * q^51 - 18 * q^53 + 72 * q^55 - 6 * q^57 - 24 * q^61 + 36 * q^63 + 90 * q^65 - 24 * q^67 + 18 * q^73 - 36 * q^77 - 30 * q^83 - 24 * q^85 - 72 * q^87 - 144 * q^91 - 132 * q^93 - 12 * q^95 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.41596	−	0.660272i	−0.817503	−	0.381208i	−0.0315563	−	0.999502i	$-0.510046\pi$
$3$	−1.41596	−	0.660272i	−0.817503	−	0.381208i	−0.785947	+	0.618294i	$0.787824\pi$
$4$		0			0
$5$	−0.949889	−	2.02428i	−0.424803	−	0.905286i
$5$	−0.949889	−	2.02428i	−0.424803	−	0.905286i
$6$		0			0
$7$	−1.12143	+	4.18524i	−0.423861	+	1.58187i	0.342536	+	0.939505i	$0.388714\pi$
$7$	−1.12143	+	4.18524i	−0.423861	+	1.58187i	−0.766397	+	0.642367i	$0.777953\pi$
$8$		0			0
$9$	−0.359387	−	0.428300i	−0.119796	−	0.142767i
$10$		0			0
$11$	−0.627484	+	1.08683i	−0.189194	+	0.327693i	−0.944982	−	0.327123i	$-0.893921\pi$
$11$	−0.627484	+	1.08683i	−0.189194	+	0.327693i	0.755788	+	0.654816i	$0.227254\pi$
$12$		0			0
$13$	1.92393	+	4.12588i	0.533602	+	1.14431i	0.969674	+	0.244402i	$0.0785915\pi$
$13$	1.92393	+	4.12588i	0.533602	+	1.14431i	−0.436072	+	0.899912i	$0.643631\pi$
$14$		0			0
$15$	0.00842766	+	3.49348i	0.00217601	+	0.902012i
$16$		0			0
$17$	0.0727101	+	0.831080i	0.0176348	+	0.201567i	0.999901	+	0.0140747i	$0.00448027\pi$
$17$	0.0727101	+	0.831080i	0.0176348	+	0.201567i	−0.982266	+	0.187492i	$0.939964\pi$
$18$		0			0
$19$	3.83747	+	2.06733i	0.880376	+	0.474277i
$19$	3.83747	+	2.06733i	0.880376	+	0.474277i
$20$		0			0
$21$	4.35129	−	5.18567i	0.949530	−	1.13161i
$22$		0			0
$23$	0.587706	+	0.411516i	0.122545	+	0.0858070i	0.633242	−	0.773954i	$-0.281724\pi$
$23$	0.587706	+	0.411516i	0.122545	+	0.0858070i	−0.510697	+	0.859761i	$0.670613\pi$
$24$		0			0
$25$	−3.19542	+	3.84568i	−0.639084	+	0.769137i
$26$		0			0
$27$	1.43917	+	5.37105i	0.276968	+	1.03366i
$28$		0			0
$29$	−3.22929	+	2.70969i	−0.599664	+	0.503177i	−0.891337	−	0.453340i	$-0.850232\pi$
$29$	−3.22929	+	2.70969i	−0.599664	+	0.503177i	0.291674	+	0.956518i	$0.405788\pi$
$30$		0			0
$31$	−6.47928	+	3.74082i	−1.16371	+	0.671870i	−0.952191	−	0.305503i	$-0.901175\pi$
$31$	−6.47928	+	3.74082i	−1.16371	+	0.671870i	−0.211522	+	0.977373i	$0.567842\pi$
$32$		0			0
$33$	1.60610	−	1.12460i	0.279586	−	0.195768i
$34$		0			0
$35$	9.53733	−	1.70542i	1.61210	−	0.288269i
$36$		0			0
$37$	1.31792	−	1.31792i	0.216665	−	0.216665i	−0.590427	−	0.807091i	$-0.701040\pi$
$37$	1.31792	−	1.31792i	0.216665	−	0.216665i	0.807091	+	0.590427i	$0.201040\pi$
$38$		0			0
$39$		−	7.11239i		−	1.13889i
$40$		0			0
$41$	−2.83535	−	7.79006i	−0.442807	−	1.21660i	−0.937638	−	0.347613i	$-0.886992\pi$
$41$	−2.83535	−	7.79006i	−0.442807	−	1.21660i	0.494831	−	0.868989i	$-0.335230\pi$
$42$		0			0
$43$	6.72347	+	9.60211i	1.02532	+	1.46431i	0.880030	+	0.474919i	$0.157523\pi$
$43$	6.72347	+	9.60211i	1.02532	+	1.46431i	0.145290	+	0.989389i	$0.453589\pi$
$44$		0			0
$45$	−0.525622	+	1.13434i	−0.0783552	+	0.169097i
$46$		0			0
$47$	−9.51062	−	0.832071i	−1.38727	−	0.121370i	−0.631076	−	0.775721i	$-0.717386\pi$
$47$	−9.51062	−	0.832071i	−1.38727	−	0.121370i	−0.756191	+	0.654351i	$0.772942\pi$
$48$		0			0
$49$	−10.1964	−	5.88691i	−1.45663	−	0.840988i
$50$		0			0
$51$	0.445784	−	1.22478i	0.0624223	−	0.171504i
$52$		0			0
$53$	−5.49098	+	7.84194i	−0.754245	+	1.07717i	0.240077	+	0.970754i	$0.422827\pi$
$53$	−5.49098	+	7.84194i	−0.754245	+	1.07717i	−0.994321	+	0.106419i	$0.966062\pi$
$54$		0			0
$55$	2.79610	+	0.237831i	0.377026	+	0.0320692i
$56$		0			0
$57$	−4.06869	−	5.46102i	−0.538912	−	0.723329i
$58$		0			0
$59$	−2.93676	−	2.46424i	−0.382334	−	0.320816i	0.431284	−	0.902216i	$-0.358061\pi$
$59$	−2.93676	−	2.46424i	−0.382334	−	0.320816i	−0.813618	+	0.581400i	$0.802505\pi$
$60$		0			0
$61$	−1.31237	−	7.44285i	−0.168032	−	0.952959i	−0.945883	−	0.324509i	$-0.894801\pi$
$61$	−1.31237	−	7.44285i	−0.168032	−	0.952959i	0.777850	−	0.628450i	$-0.216310\pi$
$62$		0			0
$63$	2.19557	−	1.02381i	0.276615	−	0.128988i
$64$		0			0
$65$	6.52442	−	7.81370i	0.809254	−	0.969170i
$66$		0			0
$67$	0.616682	−	7.04871i	0.0753398	−	0.861137i	−0.860670	−	0.509163i	$-0.829955\pi$
$67$	0.616682	−	7.04871i	0.0753398	−	0.861137i	0.936010	−	0.351974i	$-0.114489\pi$
$68$		0			0
$69$	−0.560454	−	0.970734i	−0.0674707	−	0.116863i
$70$		0			0
$71$	11.6384	+	2.05217i	1.38123	+	0.243548i	0.814408	−	0.580293i	$-0.197062\pi$
$71$	11.6384	+	2.05217i	1.38123	+	0.243548i	0.566821	+	0.823841i	$0.308173\pi$
$72$		0			0
$73$	1.19747	−	2.56798i	0.140153	−	0.300560i	−0.823685	−	0.567048i	$-0.808085\pi$
$73$	1.19747	−	2.56798i	0.140153	−	0.300560i	0.963838	+	0.266488i	$0.0858632\pi$
$74$		0			0
$75$	7.06378	−	3.33548i	0.815655	−	0.385148i
$76$		0			0
$77$	−3.84498	−	3.84498i	−0.438176	−	0.438176i
$78$		0			0
$79$	−5.16648	+	1.88045i	−0.581275	+	0.211567i	−0.615888	−	0.787834i	$-0.711202\pi$
$79$	−5.16648	+	1.88045i	−0.581275	+	0.211567i	0.0346128	+	0.999401i	$0.488980\pi$
$80$		0			0
$81$	1.21729	−	6.90358i	0.135254	−	0.767065i
$82$		0			0
$83$	7.22139	+	1.93497i	0.792651	+	0.212390i	0.632355	−	0.774679i	$-0.282088\pi$
$83$	7.22139	+	1.93497i	0.792651	+	0.212390i	0.160296	+	0.987069i	$0.448755\pi$
$84$		0			0
$85$	1.61327	−	0.936620i	0.174984	−	0.101591i
$86$		0			0
$87$	6.36167	−	1.70460i	0.682042	−	0.182753i
$88$		0			0
$89$	3.31376	+	1.20611i	0.351258	+	0.127847i	0.511622	−	0.859210i	$-0.329045\pi$
$89$	3.31376	+	1.20611i	0.351258	+	0.127847i	−0.160364	+	0.987058i	$0.551267\pi$
$90$		0			0
$91$	−19.4253	+	3.42521i	−2.03633	+	0.359060i
$92$		0			0
$93$	11.6443	−	1.01875i	1.20746	−	0.105639i
$94$		0			0
$95$	0.539677	−	9.73184i	0.0553697	−	0.998466i
$96$		0			0
$97$	−5.44825	+	0.476660i	−0.553186	+	0.0483975i	−0.360322	−	0.932828i	$-0.617333\pi$
$97$	−5.44825	+	0.476660i	−0.553186	+	0.0483975i	−0.192864	+	0.981225i	$0.561778\pi$
$98$		0			0
$99$	0.691001	−	0.121842i	0.0694482	−	0.0122456i
$100$		0			0
$101$	18.7117	+	6.81050i	1.86188	+	0.677670i	0.977511	+	0.210886i	$0.0676349\pi$
$101$	18.7117	+	6.81050i	1.86188	+	0.677670i	0.884372	+	0.466784i	$0.154587\pi$
$102$		0			0
$103$	−11.3695	+	3.04646i	−1.12027	+	0.300176i	−0.770994	−	0.636842i	$-0.780240\pi$
$103$	−11.3695	+	3.04646i	−1.12027	+	0.300176i	−0.349279	+	0.937019i	$0.613574\pi$
$104$		0			0
$105$	−14.6305	−	3.88243i	−1.42779	−	0.378886i
$106$		0			0
$107$	−9.44173	−	2.52990i	−0.912767	−	0.244575i	−0.228276	−	0.973597i	$-0.573309\pi$
$107$	−9.44173	−	2.52990i	−0.912767	−	0.244575i	−0.684491	+	0.729021i	$0.739975\pi$
$108$		0			0
$109$	0.626255	−	3.55167i	0.0599843	−	0.340188i	−0.940015	−	0.341132i	$-0.889190\pi$
$109$	0.626255	−	3.55167i	0.0599843	−	0.340188i	1.00000		0.000944474i	$0.000300635\pi$
$110$		0			0
$111$	−2.73631	+	0.995934i	−0.259719	+	0.0945298i
$112$		0			0
$113$	−2.42630	−	2.42630i	−0.228248	−	0.228248i	0.583713	−	0.811960i	$-0.301599\pi$
$113$	−2.42630	−	2.42630i	−0.228248	−	0.228248i	−0.811960	+	0.583713i	$0.801599\pi$
$114$		0			0
$115$	0.274768	−	1.58058i	0.0256223	−	0.147389i
$116$		0			0
$117$	1.07568	−	2.30681i	0.0994468	−	0.213264i
$118$		0			0
$119$	−3.55981	−	0.627690i	−0.326327	−	0.0575403i
$120$		0			0
$121$	4.71253	+	8.16234i	0.428412	+	0.742031i
$122$		0			0
$123$	−1.12882	+	12.9025i	−0.101782	+	1.16338i
$124$		0			0
$125$	10.8200	+	2.81545i	0.967774	+	0.251822i
$126$		0			0
$127$	−14.6210	+	6.81787i	−1.29740	+	0.604988i	−0.943834	−	0.330421i	$-0.892809\pi$
$127$	−14.6210	+	6.81787i	−1.29740	+	0.604988i	−0.353568	+	0.935409i	$0.615032\pi$
$128$		0			0
$129$	−3.18014	−	18.0355i	−0.279996	−	1.58794i
$130$		0			0
$131$	−6.12211	−	5.13706i	−0.534891	−	0.448827i	0.334895	−	0.942255i	$-0.391299\pi$
$131$	−6.12211	−	5.13706i	−0.534891	−	0.448827i	−0.869786	+	0.493428i	$0.835743\pi$
$132$		0			0
$133$	−12.9557	+	13.7424i	−1.12340	+	1.19161i
$134$		0			0
$135$	9.50546	−	8.01518i	0.818100	−	0.689837i
$136$		0			0
$137$	−2.56871	+	3.66850i	−0.219460	+	0.313421i	−0.913752	−	0.406272i	$-0.866829\pi$
$137$	−2.56871	+	3.66850i	−0.219460	+	0.313421i	0.694292	+	0.719693i	$0.255718\pi$
$138$		0			0
$139$	0.806465	−	2.21574i	0.0684034	−	0.187937i	−0.900781	−	0.434274i	$-0.857005\pi$
$139$	0.806465	−	2.21574i	0.0684034	−	0.187937i	0.969184	+	0.246337i	$0.0792271\pi$
$140$		0			0
$141$	12.9172	+	7.45777i	1.08783	+	0.628057i
$142$		0			0
$143$	−5.69138	−	0.497932i	−0.475937	−	0.0416391i
$144$		0			0
$145$	8.55264	+	3.96307i	0.710258	+	0.329115i
$146$		0			0
$147$	10.5508	+	15.0680i	0.870211	+	1.24279i
$148$		0			0
$149$	5.59712	+	15.3780i	0.458534	+	1.25981i	0.926577	+	0.376106i	$0.122737\pi$
$149$	5.59712	+	15.3780i	0.458534	+	1.25981i	−0.468042	+	0.883706i	$0.655041\pi$
$150$		0			0
$151$		−	0.517855i		−	0.0421424i	−0.999778	−	0.0210712i	$-0.993292\pi$
$151$		−	0.517855i		−	0.0421424i	0.999778	−	0.0210712i	$-0.00670767\pi$
$152$		0			0
$153$	0.329821	−	0.329821i	0.0266644	−	0.0266644i
$154$		0			0
$155$	13.7271	+	9.56252i	1.10258	+	0.768080i
$156$		0			0
$157$	11.3740	−	7.96413i	0.907740	−	0.635607i	−0.0236140	−	0.999721i	$-0.507517\pi$
$157$	11.3740	−	7.96413i	0.907740	−	0.635607i	0.931354	+	0.364115i	$0.118628\pi$
$158$		0			0
$159$	12.9528	−	7.47831i	1.02722	−	0.593068i
$160$		0			0
$161$	−2.38136	+	1.99820i	−0.187678	+	0.157480i
$162$		0			0
$163$	−1.30493	−	4.87008i	−0.102210	−	0.381454i	0.895803	−	0.444450i	$-0.146601\pi$
$163$	−1.30493	−	4.87008i	−0.102210	−	0.381454i	−0.998014	+	0.0629965i	$0.979934\pi$
$164$		0			0
$165$	−3.80212	−	2.18294i	−0.295995	−	0.169942i
$166$		0			0
$167$	5.42628	+	3.79952i	0.419898	+	0.294016i	0.764366	−	0.644782i	$-0.223052\pi$
$167$	5.42628	+	3.79952i	0.419898	+	0.294016i	−0.344468	+	0.938798i	$0.611941\pi$
$168$		0			0
$169$	−4.96514	+	5.91723i	−0.381934	+	0.455171i
$170$		0			0
$171$	−0.493699	−	2.38656i	−0.0377541	−	0.182505i
$172$		0			0
$173$	−1.61153	−	18.4199i	−0.122523	−	1.40044i	−0.769849	−	0.638226i	$-0.779669\pi$
$173$	−1.61153	−	18.4199i	−0.122523	−	1.40044i	0.647327	−	0.762213i	$-0.275887\pi$
$174$		0			0
$175$	−12.5117	−	17.6863i	−0.945793	−	1.33696i
$176$		0			0
$177$	2.53126	+	5.42831i	0.190261	+	0.408017i
$178$		0			0
$179$	−5.66803	+	9.81732i	−0.423649	+	0.733781i	−0.996293	−	0.0860227i	$-0.972584\pi$
$179$	−5.66803	+	9.81732i	−0.423649	+	0.733781i	0.572644	+	0.819804i	$0.305918\pi$
$180$		0			0
$181$	−0.118595	−	0.141336i	−0.00881508	−	0.0105054i	0.761619	−	0.648025i	$-0.224405\pi$
$181$	−0.118595	−	0.141336i	−0.00881508	−	0.0105054i	−0.770434	+	0.637520i	$0.779960\pi$
$182$		0			0
$183$	−3.05604	+	11.4053i	−0.225909	+	0.843102i
$184$		0			0
$185$	−3.91972	−	1.41596i	−0.288184	−	0.104104i
$186$		0			0
$187$	−0.948871	−	0.442466i	−0.0693883	−	0.0323563i
$188$		0			0
$189$	−24.0931			−1.75251
$190$		0			0
$191$	25.1481			1.81965			0.909826	−	0.414990i	$-0.136215\pi$
$191$	25.1481			1.81965			0.909826	+	0.414990i	$0.136215\pi$
$192$		0			0
$193$	24.2689	+	11.3168i	1.74691	+	0.814599i	0.986210	+	0.165501i	$0.0529241\pi$
$193$	24.2689	+	11.3168i	1.74691	+	0.814599i	0.760704	+	0.649098i	$0.224854\pi$
$194$		0			0
$195$	−14.3975	+	6.75598i	−1.03102	+	0.483806i
$196$		0			0
$197$	−6.29283	+	23.4852i	−0.448346	+	1.67325i	0.258602	+	0.965984i	$0.416738\pi$
$197$	−6.29283	+	23.4852i	−0.448346	+	1.67325i	−0.706948	+	0.707266i	$0.749929\pi$
$198$		0			0
$199$	7.12400	+	8.49005i	0.505007	+	0.601844i	0.956968	−	0.290194i	$-0.0937198\pi$
$199$	7.12400	+	8.49005i	0.505007	+	0.601844i	−0.451961	+	0.892038i	$0.649275\pi$
$200$		0			0
$201$	−5.52726	+	9.57350i	−0.389863	+	0.675262i
$202$		0			0
$203$	−7.71929	−	16.5541i	−0.541788	−	1.16187i
$204$		0			0
$205$	−13.0760	+	13.1392i	−0.913267	+	0.917684i
$206$		0			0
$207$	−0.0349612	−	0.399608i	−0.00242997	−	0.0277747i
$208$		0			0
$209$	−4.65479	+	2.87348i	−0.321979	+	0.198763i
$210$		0			0
$211$	−4.97867	+	5.93334i	−0.342746	+	0.408468i	−0.909690	−	0.415288i	$-0.863681\pi$
$211$	−4.97867	+	5.93334i	−0.342746	+	0.408468i	0.566945	+	0.823756i	$0.308125\pi$
$212$		0			0
$213$	−15.1245	−	10.5903i	−1.03632	−	0.725636i
$214$		0			0
$215$	13.0508	−	22.7311i	0.890058	−	1.55025i
$216$		0			0
$217$	−8.39013	−	31.3124i	−0.569559	−	2.12562i
$218$		0			0
$219$	−3.39114	+	2.84550i	−0.229152	+	0.192281i
$220$		0			0
$221$	−3.28905	+	1.89893i	−0.221245	+	0.127736i
$222$		0			0
$223$	−12.9568	+	9.07244i	−0.867651	+	0.607536i	−0.920359	−	0.391074i	$-0.872104\pi$
$223$	−12.9568	+	9.07244i	−0.867651	+	0.607536i	0.0527082	+	0.998610i	$0.483215\pi$
$224$		0			0
$225$	2.79550	−	0.0134878i	0.186367	−	0.000899186i
$226$		0			0
$227$	2.21321	−	2.21321i	0.146896	−	0.146896i	−0.629834	−	0.776730i	$-0.716877\pi$
$227$	2.21321	−	2.21321i	0.146896	−	0.146896i	0.776730	+	0.629834i	$0.216877\pi$
$228$		0			0
$229$			23.5566i			1.55667i	0.627851	+	0.778334i	$0.283935\pi$
$229$			23.5566i			1.55667i	−0.627851	+	0.778334i	$0.716065\pi$
$230$		0			0
$231$	2.90560	+	7.98306i	0.191174	+	0.525247i
$232$		0			0
$233$	0.916232	+	1.30851i	0.0600243	+	0.0857236i	0.848042	−	0.529929i	$-0.177781\pi$
$233$	0.916232	+	1.30851i	0.0600243	+	0.0857236i	−0.788018	+	0.615653i	$0.788893\pi$
$234$		0			0
$235$	7.34969	+	20.0425i	0.479441	+	1.30743i
$236$		0			0
$237$	8.55712	+	0.748651i	0.555845	+	0.0486301i
$238$		0			0
$239$	−3.75395	−	2.16735i	−0.242823	−	0.140194i	0.373651	−	0.927570i	$-0.378106\pi$
$239$	−3.75395	−	2.16735i	−0.242823	−	0.140194i	−0.616474	+	0.787376i	$0.711439\pi$
$240$		0			0
$241$	5.13813	−	14.1169i	0.330976	−	0.909349i	−0.656883	−	0.753993i	$-0.728125\pi$
$241$	5.13813	−	14.1169i	0.330976	−	0.909349i	0.987859	−	0.155356i	$-0.0496525\pi$
$242$		0			0
$243$	3.28628	−	4.69330i	0.210815	−	0.301075i
$244$		0			0
$245$	−2.23128	+	26.2324i	−0.142551	+	1.67592i
$246$		0			0
$247$	−1.14652	+	19.8103i	−0.0729513	+	1.26050i
$248$		0			0
$249$	−8.94758	−	7.50791i	−0.567030	−	0.475795i
$250$		0			0
$251$	−4.89620	−	27.7677i	−0.309045	−	1.75268i	−0.603824	−	0.797117i	$-0.706357\pi$
$251$	−4.89620	−	27.7677i	−0.309045	−	1.75268i	0.294779	−	0.955565i	$-0.404754\pi$
$252$		0			0
$253$	−0.816026	+	0.380519i	−0.0513031	+	0.0239230i
$254$		0			0
$255$	−2.90275	+	0.261015i	−0.181777	+	0.0163454i
$256$		0			0
$257$	0.855227	−	9.77528i	0.0533476	−	0.609765i	−0.921720	−	0.387856i	$-0.873216\pi$
$257$	0.855227	−	9.77528i	0.0533476	−	0.609765i	0.975067	−	0.221909i	$-0.0712288\pi$
$258$		0			0
$259$	4.03786	+	6.99377i	0.250900	+	0.434572i
$260$		0			0
$261$	2.32113	+	0.409277i	0.143674	+	0.0253336i
$262$		0			0
$263$	−3.78126	+	8.10893i	−0.233162	+	0.500018i	−0.987724	−	0.156211i	$-0.950072\pi$
$263$	−3.78126	+	8.10893i	−0.233162	+	0.500018i	0.754561	+	0.656229i	$0.227850\pi$
$264$		0			0
$265$	21.0901	+	3.66632i	1.29555	+	0.225220i
$266$		0			0
$267$	−3.89578	−	3.89578i	−0.238418	−	0.238418i
$268$		0			0
$269$	8.17730	−	2.97629i	0.498579	−	0.181468i	−0.0804758	−	0.996757i	$-0.525644\pi$
$269$	8.17730	−	2.97629i	0.498579	−	0.181468i	0.579055	+	0.815289i	$0.303422\pi$
$270$		0			0
$271$	2.80096	−	15.8850i	0.170146	−	0.964948i	−0.773452	−	0.633855i	$-0.781472\pi$
$271$	2.80096	−	15.8850i	0.170146	−	0.964948i	0.943598	−	0.331093i	$-0.107417\pi$
$272$		0			0
$273$	29.7670	+	7.97605i	1.80158	+	0.482733i
$274$		0			0
$275$	−2.17455	−	5.88600i	−0.131130	−	0.354939i
$276$		0			0
$277$	16.0550	−	4.30192i	0.964650	−	0.258477i	0.258083	−	0.966123i	$-0.416909\pi$
$277$	16.0550	−	4.30192i	0.964650	−	0.258477i	0.706568	+	0.707646i	$0.250243\pi$
$278$		0			0
$279$	3.93076	+	1.43068i	0.235328	+	0.0856526i
$280$		0			0
$281$	−26.2583	+	4.63004i	−1.56644	+	0.276205i	−0.888486	−	0.458903i	$-0.848243\pi$
$281$	−26.2583	+	4.63004i	−1.56644	+	0.276205i	−0.677950	+	0.735108i	$0.737131\pi$
$282$		0			0
$283$	24.7322	−	2.16379i	1.47018	−	0.128624i	0.676266	−	0.736657i	$-0.263597\pi$
$283$	24.7322	−	2.16379i	1.47018	−	0.128624i	0.793911	+	0.608034i	$0.208041\pi$
$284$		0			0
$285$	−7.18982	+	13.4235i	−0.425888	+	0.795142i
$286$		0			0
$287$	35.7829	−	3.13060i	2.11220	−	0.184793i
$288$		0			0
$289$	16.0563	−	2.83116i	0.944490	−	0.166539i
$290$		0			0
$291$	8.02922	+	2.92240i	0.470681	+	0.171314i
$292$		0			0
$293$	9.06575	−	2.42916i	0.529627	−	0.141913i	0.0159107	−	0.999873i	$-0.494935\pi$
$293$	9.06575	−	2.42916i	0.529627	−	0.141913i	0.513716	+	0.857960i	$0.328269\pi$
$294$		0			0
$295$	−2.19870	+	8.28558i	−0.128014	+	0.482405i
$296$		0			0
$297$	−6.74050	−	1.80611i	−0.391123	−	0.104801i
$298$		0			0
$299$	−0.567161	+	3.21653i	−0.0327998	+	0.186017i
$300$		0			0
$301$	−47.7270	+	17.3712i	−2.75094	+	1.00126i
$302$		0			0
$303$	−21.9982	−	21.9982i	−1.26376	−	1.26376i
$304$		0			0
$305$	−13.8198	+	9.72650i	−0.791319	+	0.556938i
$306$		0			0
$307$	0.819462	−	1.75734i	0.0467692	−	0.100297i	−0.881535	−	0.472119i	$-0.843489\pi$
$307$	0.819462	−	1.75734i	0.0467692	−	0.100297i	0.928304	+	0.371822i	$0.121267\pi$
$308$		0			0
$309$	18.1103	+	3.19333i	1.03026	+	0.181662i
$310$		0			0
$311$	−5.27241	−	9.13209i	−0.298971	−	0.517833i	0.676930	−	0.736048i	$-0.263310\pi$
$311$	−5.27241	−	9.13209i	−0.298971	−	0.517833i	−0.975901	+	0.218215i	$0.929977\pi$
$312$		0			0
$313$	0.322366	−	3.68466i	0.0182212	−	0.208269i	−0.981626	−	0.190813i	$-0.938888\pi$
$313$	0.322366	−	3.68466i	0.0182212	−	0.208269i	0.999848	−	0.0174565i	$-0.00555685\pi$
$314$		0			0
$315$	−4.15802	−	3.47194i	−0.234278	−	0.195621i
$316$		0			0
$317$	5.08844	−	2.37278i	0.285795	−	0.133268i	−0.274435	−	0.961606i	$-0.588491\pi$
$317$	5.08844	−	2.37278i	0.285795	−	0.133268i	0.560230	+	0.828337i	$0.310713\pi$
$318$		0			0
$319$	−0.918662	−	5.20999i	−0.0514352	−	0.291703i
$320$		0			0
$321$	11.6987	+	9.81634i	0.652956	+	0.547895i
$322$		0			0
$323$	−1.43909	+	3.33956i	−0.0800732	+	0.185818i
$324$		0			0
$325$	−22.0146	−	5.78510i	−1.22115	−	0.320899i
$326$		0			0
$327$	−3.23182	+	4.61551i	−0.178720	+	0.255238i
$328$		0			0
$329$	14.1479	−	38.8711i	0.780000	−	2.14303i
$330$		0			0
$331$	−2.07238	−	1.19649i	−0.113908	−	0.0657650i	0.441963	−	0.897033i	$-0.354282\pi$
$331$	−2.07238	−	1.19649i	−0.113908	−	0.0657650i	−0.555872	+	0.831268i	$0.687615\pi$
$332$		0			0
$333$	−1.03811	−	0.0908228i	−0.0568880	−	0.00497706i
$334$		0			0
$335$	−14.8543	+	5.44716i	−0.811580	+	0.297610i
$336$		0			0
$337$	−18.2235	−	26.0259i	−0.992700	−	1.41772i	−0.906869	−	0.421412i	$-0.861535\pi$
$337$	−18.2235	−	26.0259i	−0.992700	−	1.41772i	−0.0858304	−	0.996310i	$-0.527354\pi$
$338$		0			0
$339$	1.83352	+	5.03756i	0.0995833	+	0.273603i
$340$		0			0
$341$		−	9.38921i		−	0.508454i
$342$		0			0
$343$	14.6261	−	14.6261i	0.789735	−	0.789735i
$344$		0			0
$345$	−1.43267	+	2.05661i	−0.0771323	+	0.110724i
$346$		0			0
$347$	−18.2967	+	12.8115i	−0.982217	+	0.687756i	−0.950171	−	0.311730i	$-0.899091\pi$
$347$	−18.2967	+	12.8115i	−0.982217	+	0.687756i	−0.0320466	+	0.999486i	$0.510203\pi$
$348$		0			0
$349$	7.19692	−	4.15514i	0.385242	−	0.222420i	−0.294854	−	0.955542i	$-0.595271\pi$
$349$	7.19692	−	4.15514i	0.385242	−	0.222420i	0.680097	+	0.733122i	$0.261938\pi$
$350$		0			0
$351$	−19.3914	+	16.2714i	−1.03504	+	0.868501i
$352$		0			0
$353$	−5.28430	−	19.7213i	−0.281255	−	1.04966i	−0.951533	−	0.307547i	$-0.900492\pi$
$353$	−5.28430	−	19.7213i	−0.281255	−	1.04966i	0.670278	−	0.742110i	$-0.266175\pi$
$354$		0			0
$355$	−6.90106	−	25.5088i	−0.366270	−	1.35387i
$356$		0			0
$357$	4.62609	+	3.23922i	0.244839	+	0.171438i
$358$		0			0
$359$	15.2531	−	18.1780i	0.805030	−	0.959397i	−0.194740	−	0.980855i	$-0.562386\pi$
$359$	15.2531	−	18.1780i	0.805030	−	0.959397i	0.999770	+	0.0214576i	$0.00683068\pi$
$360$		0			0
$361$	10.4523	+	15.8666i	0.550123	+	0.835084i
$362$		0			0
$363$	−1.28338	−	14.6691i	−0.0673598	−	0.769926i
$364$		0			0
$365$	−6.33579	+	0.0152844i	−0.331630	+	0.000800023i
$366$		0			0
$367$	7.24722	+	15.5417i	0.378302	+	0.811271i	0.999616	+	0.0277092i	$0.00882124\pi$
$367$	7.24722	+	15.5417i	0.378302	+	0.811271i	−0.621314	+	0.783561i	$0.713401\pi$
$368$		0			0
$369$	−2.31750	+	4.01402i	−0.120644	+	0.208962i
$370$		0			0
$371$	−26.6626	−	31.7753i	−1.38425	−	1.64969i
$372$		0			0
$373$	7.47949	−	27.9138i	0.387273	−	1.44532i	−0.447279	−	0.894394i	$-0.647607\pi$
$373$	7.47949	−	27.9138i	0.387273	−	1.44532i	0.834552	−	0.550929i	$-0.185726\pi$
$374$		0			0
$375$	−13.4617	−	11.1307i	−0.695162	−	0.574788i
$376$		0			0
$377$	−17.3928	−	8.11039i	−0.895774	−	0.417706i
$378$		0			0
$379$	5.08838			0.261372			0.130686	−	0.991424i	$-0.458282\pi$
$379$	5.08838			0.261372			0.130686	+	0.991424i	$0.458282\pi$
$380$		0			0
$381$	25.2043			1.29126
$382$		0			0
$383$	−5.29678	−	2.46993i	−0.270653	−	0.126207i	0.282554	−	0.959251i	$-0.408818\pi$
$383$	−5.29678	−	2.46993i	−0.270653	−	0.126207i	−0.553207	+	0.833044i	$0.686596\pi$
$384$		0			0
$385$	−4.13101	+	11.4356i	−0.210536	+	0.582813i
$386$		0			0
$387$	1.69626	−	6.33053i	0.0862258	−	0.321799i
$388$		0			0
$389$	7.46433	+	8.89565i	0.378457	+	0.451027i	0.921327	−	0.388790i	$-0.127107\pi$
$389$	7.46433	+	8.89565i	0.378457	+	0.451027i	−0.542870	+	0.839817i	$0.682662\pi$
$390$		0			0
$391$	−0.299271	+	0.518352i	−0.0151348	+	0.0262142i
$392$		0			0
$393$	5.27679	+	11.3161i	0.266179	+	0.570822i
$394$		0			0
$395$	8.71414	+	8.67219i	0.438456	+	0.436345i
$396$		0			0
$397$	−0.652608	−	7.45934i	−0.0327534	−	0.374373i	−0.994827	−	0.101583i	$-0.967609\pi$
$397$	−0.652608	−	7.45934i	−0.0327534	−	0.374373i	0.962074	−	0.272790i	$-0.0879464\pi$
$398$		0			0
$399$	27.4184	−	10.9043i	1.37264	−	0.545898i
$400$		0			0
$401$	16.8666	−	20.1008i	0.842276	−	1.00379i	−0.157591	−	0.987504i	$-0.550373\pi$
$401$	16.8666	−	20.1008i	0.842276	−	1.00379i	0.999867	−	0.0162813i	$-0.00518271\pi$
$402$		0			0
$403$	−27.8998	−	19.5357i	−1.38979	−	0.973141i
$404$		0			0
$405$	−15.1311	+	4.09351i	−0.751869	+	0.203408i
$406$		0			0
$407$	0.605387	+	2.25934i	0.0300079	+	0.111991i
$408$		0			0
$409$	−20.4951	+	17.1975i	−1.01342	+	0.850359i	−0.988786	−	0.149337i	$-0.952286\pi$
$409$	−20.4951	+	17.1975i	−1.01342	+	0.850359i	−0.0246326	+	0.999697i	$0.507842\pi$
$410$		0			0
$411$	6.05940	−	3.49840i	0.298888	−	0.172563i
$412$		0			0
$413$	13.6068	−	9.52757i	0.669546	−	0.468821i
$414$		0			0
$415$	−2.94261	−	16.4561i	−0.144447	−	0.807800i
$416$		0			0
$417$	−2.60491	+	2.60491i	−0.127563	+	0.127563i
$418$		0			0
$419$		−	38.9944i		−	1.90500i	−0.304538	−	0.952500i	$-0.598502\pi$
$419$		−	38.9944i		−	1.90500i	0.304538	−	0.952500i	$-0.401498\pi$
$420$		0			0
$421$	11.1837	+	30.7270i	0.545061	+	1.49754i	0.840301	+	0.542120i	$0.182378\pi$
$421$	11.1837	+	30.7270i	0.545061	+	1.49754i	−0.295240	+	0.955423i	$0.595399\pi$
$422$		0			0
$423$	3.06161	+	4.37244i	0.148861	+	0.212595i
$424$		0			0
$425$	−3.42841	−	2.37603i	−0.166302	−	0.115254i
$426$		0			0
$427$	32.6218	+	2.85404i	1.57868	+	0.138117i
$428$		0			0
$429$	7.72999	+	4.46291i	0.373207	+	0.215471i
$430$		0			0
$431$	−6.59218	+	18.1119i	−0.317534	+	0.872418i	0.673545	+	0.739146i	$0.264771\pi$
$431$	−6.59218	+	18.1119i	−0.317534	+	0.872418i	−0.991079	+	0.133272i	$0.957452\pi$
$432$		0			0
$433$	−9.46607	+	13.5190i	−0.454910	+	0.649679i	−0.979445	−	0.201709i	$-0.935350\pi$
$433$	−9.46607	+	13.5190i	−0.454910	+	0.649679i	0.524535	+	0.851389i	$0.324239\pi$
$434$		0			0
$435$	−9.49347	−	11.2586i	−0.455177	−	0.539809i
$436$		0			0
$437$	1.40456	+	2.79416i	0.0671894	+	0.133663i
$438$		0			0
$439$	−9.58352	−	8.04153i	−0.457396	−	0.383801i	0.384776	−	0.923010i	$-0.374279\pi$
$439$	−9.58352	−	8.04153i	−0.457396	−	0.383801i	−0.842172	+	0.539209i	$0.818723\pi$
$440$		0			0
$441$	1.14310	+	6.48282i	0.0544331	+	0.308706i
$442$		0			0
$443$	−16.7204	+	7.79683i	−0.794408	+	0.370439i	−0.777072	−	0.629411i	$-0.783296\pi$
$443$	−16.7204	+	7.79683i	−0.794408	+	0.370439i	−0.0173356	+	0.999850i	$0.505518\pi$
$444$		0			0
$445$	−0.706201	−	7.85365i	−0.0334771	−	0.372299i
$446$		0			0
$447$	2.22835	−	25.4702i	0.105397	−	1.20470i
$448$		0			0
$449$	20.3319	+	35.2159i	0.959523	+	1.66194i	0.723661	+	0.690156i	$0.242458\pi$
$449$	20.3319	+	35.2159i	0.959523	+	1.66194i	0.235862	+	0.971787i	$0.424209\pi$
$450$		0			0
$451$	10.2456	+	1.80658i	0.482448	+	0.0850686i
$452$		0			0
$453$	−0.341925	+	0.733260i	−0.0160650	+	0.0344516i
$454$		0			0
$455$	25.3855	+	36.0688i	1.19009	+	1.69093i
$456$		0			0
$457$	7.81003	+	7.81003i	0.365338	+	0.365338i	0.865774	−	0.500436i	$-0.166827\pi$
$457$	7.81003	+	7.81003i	0.365338	+	0.365338i	−0.500436	+	0.865774i	$0.666827\pi$
$458$		0			0
$459$	−4.35913	+	1.58659i	−0.203467	+	0.0740559i
$460$		0			0
$461$	−3.06108	+	17.3603i	−0.142569	+	0.808548i	0.826718	+	0.562616i	$0.190205\pi$
$461$	−3.06108	+	17.3603i	−0.142569	+	0.808548i	−0.969287	+	0.245932i	$0.920906\pi$
$462$		0			0
$463$	−9.39003	−	2.51605i	−0.436392	−	0.116931i	0.0339334	−	0.999424i	$-0.489197\pi$
$463$	−9.39003	−	2.51605i	−0.436392	−	0.116931i	−0.470325	+	0.882493i	$0.655863\pi$
$464$		0			0
$465$	−13.1231	−	22.6037i	−0.608568	−	1.04822i
$466$		0			0
$467$	16.8773	−	4.52226i	0.780989	−	0.209265i	0.153768	−	0.988107i	$-0.450859\pi$
$467$	16.8773	−	4.52226i	0.780989	−	0.209265i	0.627221	+	0.778842i	$0.284192\pi$
$468$		0			0
$469$	28.8090	+	10.4856i	1.33027	+	0.484180i
$470$		0			0
$471$	−21.3635	+	3.76696i	−0.984379	+	0.173573i
$472$		0			0
$473$	−14.6548	+	1.28213i	−0.673827	+	0.0589522i
$474$		0			0
$475$	−20.2126	+	8.15172i	−0.927418	+	0.374026i
$476$		0			0
$477$	5.33209	−	0.466497i	0.244140	−	0.0213595i
$478$		0			0
$479$	1.45945	−	0.257341i	0.0666840	−	0.0117582i	−0.140207	−	0.990122i	$-0.544777\pi$
$479$	1.45945	−	0.257341i	0.0666840	−	0.0117582i	0.206891	+	0.978364i	$0.433666\pi$
$480$		0			0
$481$	7.97317	+	2.90200i	0.363545	+	0.132320i
$482$		0			0
$483$	4.69126	−	1.25702i	0.213460	−	0.0571964i
$484$		0			0
$485$	6.14013	+	10.5760i	0.278809	+	0.480232i
$486$		0			0
$487$	−7.05747	−	1.89104i	−0.319804	−	0.0856913i	0.0953458	−	0.995444i	$-0.469604\pi$
$487$	−7.05747	−	1.89104i	−0.319804	−	0.0856913i	−0.415150	+	0.909753i	$0.636271\pi$
$488$		0			0
$489$	−1.36784	+	7.75743i	−0.0618561	+	0.350803i
$490$		0			0
$491$	−17.1404	+	6.23861i	−0.773538	+	0.281545i	−0.698475	−	0.715634i	$-0.746138\pi$
$491$	−17.1404	+	6.23861i	−0.773538	+	0.281545i	−0.0750624	+	0.997179i	$0.523916\pi$
$492$		0			0
$493$	−2.48677	−	2.48677i	−0.111999	−	0.111999i
$494$		0			0
$495$	−0.903017	−	1.28304i	−0.0405876	−	0.0576685i
$496$		0			0
$497$	−21.6405	+	46.4083i	−0.970710	+	2.08170i
$498$		0			0
$499$	−9.23009	−	1.62751i	−0.413195	−	0.0728575i	−0.0368136	−	0.999322i	$-0.511721\pi$
$499$	−9.23009	−	1.62751i	−0.413195	−	0.0728575i	−0.376382	+	0.926465i	$0.622832\pi$
$500$		0			0
$501$	−5.17466	−	8.96278i	−0.231187	−	0.400427i
$502$		0			0
$503$	−1.00360	+	11.4712i	−0.0447483	+	0.511475i	0.940435	+	0.339973i	$0.110418\pi$
$503$	−1.00360	+	11.4712i	−0.0447483	+	0.511475i	−0.985184	+	0.171503i	$0.945138\pi$
$504$		0			0
$505$	−3.98768	−	44.3469i	−0.177449	−	1.97341i
$506$		0			0
$507$	10.9374	−	5.10020i	0.485747	−	0.226508i
$508$		0			0
$509$	7.60010	+	43.1023i	0.336869	+	1.91048i	0.407946	+	0.913006i	$0.366245\pi$
$509$	7.60010	+	43.1023i	0.336869	+	1.91048i	−0.0710777	+	0.997471i	$0.522644\pi$
$510$		0			0
$511$	9.40475	+	7.89152i	0.416042	+	0.349100i
$512$		0			0
$513$	−5.58095	+	23.5865i	−0.246405	+	1.04137i
$514$		0			0
$515$	16.9667	+	20.1213i	0.747641	+	0.886651i
$516$		0			0
$517$	6.87209	−	9.81435i	0.302234	−	0.431635i
$518$		0			0
$519$	−9.88028	+	27.1458i	−0.433696	+	1.19157i
$520$		0			0
$521$	0.242872	+	0.140222i	0.0106404	+	0.00614324i	0.505311	−	0.862937i	$-0.331378\pi$
$521$	0.242872	+	0.140222i	0.0106404	+	0.00614324i	−0.494670	+	0.869081i	$0.664711\pi$
$522$		0			0
$523$	1.99335	+	0.174395i	0.0871629	+	0.00762577i	0.130654	−	0.991428i	$-0.458292\pi$
$523$	1.99335	+	0.174395i	0.0871629	+	0.00762577i	−0.0434908	+	0.999054i	$0.513848\pi$
$524$		0			0
$525$	6.03823	+	33.3041i	0.263530	+	1.45351i
$526$		0			0
$527$	−3.58003	−	5.11281i	−0.155948	−	0.222717i
$528$		0			0
$529$	−7.69041	−	21.1292i	−0.334366	−	0.918662i
$530$		0			0
$531$			2.14343i			0.0930169i
$532$		0			0
$533$	26.6858	−	26.6858i	1.15589	−	1.15589i
$534$		0			0
$535$	3.84736	+	21.5158i	0.166336	+	0.930211i
$536$		0			0
$537$	14.5078	−	10.1585i	0.626057	−	0.438370i
$538$		0			0
$539$	12.7962	−	7.38789i	0.551171	−	0.318219i
$540$		0			0
$541$	10.2788	−	8.62496i	0.441921	−	0.370816i	−0.394507	−	0.918893i	$-0.629084\pi$
$541$	10.2788	−	8.62496i	0.441921	−	0.370816i	0.836428	+	0.548077i	$0.184640\pi$
$542$		0			0
$543$	0.0746051	+	0.278430i	0.00320161	+	0.0119486i
$544$		0			0
$545$	−7.78444	+	2.10598i	−0.333449	+	0.0902101i
$546$		0			0
$547$	11.3886	+	7.97438i	0.486941	+	0.340960i	0.791126	−	0.611653i	$-0.209495\pi$
$547$	11.3886	+	7.97438i	0.486941	+	0.340960i	−0.304185	+	0.952613i	$0.598384\pi$
$548$		0			0
$549$	−2.71612	+	3.23695i	−0.115921	+	0.138150i
$550$		0			0
$551$	−17.9941	+	3.72237i	−0.766575	+	0.158579i
$552$		0			0
$553$	−2.07626	−	23.7318i	−0.0882915	−	1.00918i
$554$		0			0
$555$	4.61524	+	4.59302i	0.195906	+	0.194963i
$556$		0			0
$557$	12.1311	+	26.0152i	0.514011	+	1.10230i	0.976469	+	0.215658i	$0.0691897\pi$
$557$	12.1311	+	26.0152i	0.514011	+	1.10230i	−0.462458	+	0.886641i	$0.653033\pi$
$558$		0			0
$559$	−26.6817	+	46.2140i	−1.12851	+	1.95464i
$560$		0			0
$561$	1.05141	+	1.25303i	0.0443907	+	0.0529028i
$562$		0			0
$563$	9.21873	−	34.4048i	0.388523	−	1.44999i	−0.444014	−	0.896020i	$-0.646446\pi$
$563$	9.21873	−	34.4048i	0.388523	−	1.44999i	0.832537	−	0.553969i	$-0.186887\pi$
$564$		0			0
$565$	−2.60680	+	7.21624i	−0.109669	+	0.303590i
$566$		0			0
$567$	27.5280	+	12.8365i	1.15607	+	0.539084i
$568$		0			0
$569$	−0.0950399			−0.00398428			−0.00199214	−	0.999998i	$-0.500634\pi$
$569$	−0.0950399			−0.00398428			−0.00199214	+	0.999998i	$0.500634\pi$
$570$		0			0
$571$	23.5973			0.987515			0.493757	−	0.869600i	$-0.335623\pi$
$571$	23.5973			0.987515			0.493757	+	0.869600i	$0.335623\pi$
$572$		0			0
$573$	−35.6086	−	16.6046i	−1.48757	−	0.693666i
$574$		0			0
$575$	−3.46053	+	0.945164i	−0.144314	+	0.0394161i
$576$		0			0
$577$	3.27264	−	12.2136i	0.136242	−	0.508461i	−0.863748	−	0.503924i	$-0.831889\pi$
$577$	3.27264	−	12.2136i	0.136242	−	0.508461i	0.999990	−	0.00453685i	$-0.00144413\pi$
$578$		0			0
$579$	−26.8916	−	32.0481i	−1.11758	−	1.33188i
$580$		0			0
$581$	−16.1966	+	28.0533i	−0.671948	+	1.16385i
$582$		0			0
$583$	−5.07738	−	10.8885i	−0.210284	−	0.450955i
$584$		0			0
$585$	−5.69140	+	0.0137299i	−0.235310	+	0.000567662i
$586$		0			0
$587$	1.55082	+	17.7260i	0.0640093	+	0.731629i	0.958602	+	0.284748i	$0.0919098\pi$
$587$	1.55082	+	17.7260i	0.0640093	+	0.731629i	−0.894593	+	0.446881i	$0.852535\pi$
$588$		0			0
$589$	−32.5975	+	0.960473i	−1.34316	+	0.0395756i
$590$		0			0
$591$	24.4170	−	29.0990i	1.00438	−	1.19697i
$592$		0			0
$593$	3.53786	+	2.47723i	0.145282	+	0.101728i	0.643958	−	0.765061i	$-0.277291\pi$
$593$	3.53786	+	2.47723i	0.145282	+	0.101728i	−0.498676	+	0.866789i	$0.666180\pi$
$594$		0			0
$595$	2.11080	+	7.80229i	0.0865345	+	0.319863i
$596$		0			0
$597$	−4.48154	−	16.7253i	−0.183417	−	0.684522i
$598$		0			0
$599$	−34.4065	+	28.8705i	−1.40581	+	1.17962i	−0.447364	+	0.894352i	$0.647637\pi$
$599$	−34.4065	+	28.8705i	−1.40581	+	1.17962i	−0.958449	+	0.285265i	$0.907918\pi$
$600$		0			0
$601$	14.6787	−	8.47474i	0.598756	−	0.345692i	−0.169796	−	0.985479i	$-0.554311\pi$
$601$	14.6787	−	8.47474i	0.598756	−	0.345692i	0.768552	+	0.639787i	$0.220978\pi$
$602$		0			0
$603$	−3.24059	+	2.26909i	−0.131967	+	0.0924044i
$604$		0			0
$605$	12.0465	−	17.2928i	0.489759	−	0.703052i
$606$		0			0
$607$	−2.96963	+	2.96963i	−0.120533	+	0.120533i	−0.764801	−	0.644267i	$-0.777163\pi$
$607$	−2.96963	+	2.96963i	−0.120533	+	0.120533i	0.644267	+	0.764801i	$0.277163\pi$
$608$		0			0
$609$			28.5367i			1.15636i
$610$		0			0
$611$	−14.8647	−	40.8405i	−0.601363	−	1.65223i
$612$		0			0
$613$	20.9803	+	29.9630i	0.847386	+	1.21019i	0.975842	+	0.218478i	$0.0701091\pi$
$613$	20.9803	+	29.9630i	0.847386	+	1.21019i	−0.128456	+	0.991715i	$0.541002\pi$
$614$		0			0
$615$	27.1905	−	9.97088i	1.09643	−	0.402065i
$616$		0			0
$617$	−33.5844	−	2.93825i	−1.35206	−	0.118290i	−0.612012	−	0.790848i	$-0.709640\pi$
$617$	−33.5844	−	2.93825i	−1.35206	−	0.118290i	−0.740044	+	0.672559i	$0.765195\pi$
$618$		0			0
$619$	−11.6155	−	6.70623i	−0.466868	−	0.269546i	0.248060	−	0.968745i	$-0.420207\pi$
$619$	−11.6155	−	6.70623i	−0.466868	−	0.269546i	−0.714928	+	0.699199i	$0.753540\pi$
$620$		0			0
$621$	−1.36447	+	3.74884i	−0.0547541	+	0.150436i
$622$		0			0
$623$	−8.76401	+	12.5163i	−0.351123	+	0.501455i
$624$		0			0
$625$	−4.57857	−	24.5772i	−0.183143	−	0.983086i
$626$		0			0
$627$	8.48826	−	0.995296i	0.338989	−	0.0397483i
$628$		0			0
$629$	1.19112	+	0.999472i	0.0474932	+	0.0398516i
$630$		0			0
$631$	4.13445	+	23.4477i	0.164590	+	0.933436i	0.949486	+	0.313809i	$0.101605\pi$
$631$	4.13445	+	23.4477i	0.164590	+	0.933436i	−0.784896	+	0.619627i	$0.787284\pi$
$632$		0			0
$633$	10.9672	−	5.11409i	0.435907	−	0.203267i
$634$		0			0
$635$	27.6896	+	23.1207i	1.09883	+	0.917518i
$636$		0			0
$637$	4.67148	−	53.3953i	0.185091	−	2.11560i
$638$		0			0
$639$	−3.30375	−	5.72227i	−0.130694	−	0.226369i
$640$		0			0
$641$	−6.56316	−	1.15726i	−0.259229	−	0.0457091i	0.0425231	−	0.999095i	$-0.486460\pi$
$641$	−6.56316	−	1.15726i	−0.259229	−	0.0457091i	−0.301752	+	0.953386i	$0.597572\pi$
$642$		0			0
$643$	−10.8110	+	23.1843i	−0.426344	+	0.914298i	0.569393	+	0.822065i	$0.307178\pi$
$643$	−10.8110	+	23.1843i	−0.426344	+	0.914298i	−0.995737	+	0.0922329i	$0.970600\pi$
$644$		0			0
$645$	−33.4881	+	23.5692i	−1.31859	+	0.928037i
$646$		0			0
$647$	−3.24357	−	3.24357i	−0.127518	−	0.127518i	0.640467	−	0.767985i	$-0.278741\pi$
$647$	−3.24357	−	3.24357i	−0.127518	−	0.127518i	−0.767985	+	0.640467i	$0.778741\pi$
$648$		0			0
$649$	4.52099	−	1.64550i	0.177464	−	0.0645917i
$650$		0			0
$651$	−8.79462	+	49.8768i	−0.344689	+	1.95483i
$652$		0			0
$653$	−45.0049	−	12.0590i	−1.76118	−	0.471906i	−0.774224	−	0.632911i	$-0.781860\pi$
$653$	−45.0049	−	12.0590i	−1.76118	−	0.471906i	−0.986954	+	0.161005i	$0.948526\pi$
$654$		0			0
$655$	−4.58352	+	17.2725i	−0.179093	+	0.674892i
$656$		0			0
$657$	−1.53022	+	0.410022i	−0.0596997	+	0.0159965i
$658$		0			0
$659$	33.6242	+	12.2382i	1.30981	+	0.476734i	0.900181	−	0.435516i	$-0.143434\pi$
$659$	33.6242	+	12.2382i	1.30981	+	0.476734i	0.409634	+	0.912250i	$0.365656\pi$
$660$		0			0
$661$	37.6347	−	6.63602i	1.46382	−	0.258111i	0.615728	−	0.787958i	$-0.288862\pi$
$661$	37.6347	−	6.63602i	1.46382	−	0.258111i	0.848093	+	0.529847i	$0.177751\pi$
$662$		0			0
$663$	5.91096	−	0.517142i	0.229563	−	0.0200841i
$664$		0			0
$665$	40.1249	+	13.1723i	1.55598	+	0.510799i
$666$		0			0
$667$	−3.01295	+	0.263599i	−0.116662	+	0.0102066i
$668$		0			0
$669$	24.3365	−	4.29119i	0.940905	−	0.165907i
$670$		0			0
$671$	8.91264	+	3.24393i	0.344069	+	0.125231i
$672$		0			0
$673$	11.7288	−	3.14274i	0.452114	−	0.121144i	−0.0255745	−	0.999673i	$-0.508141\pi$
$673$	11.7288	−	3.14274i	0.452114	−	0.121144i	0.477688	+	0.878529i	$0.341475\pi$
$674$		0			0
$675$	−25.2541	−	11.6282i	−0.972031	−	0.447569i
$676$		0			0
$677$	−37.7262	−	10.1087i	−1.44993	−	0.388509i	−0.553933	−	0.832561i	$-0.686874\pi$
$677$	−37.7262	−	10.1087i	−1.44993	−	0.388509i	−0.896001	+	0.444053i	$0.853540\pi$
$678$		0			0
$679$	4.11490	−	23.3368i	0.157915	−	0.895583i
$680$		0			0
$681$	−4.59513	+	1.67249i	−0.176086	+	0.0640900i
$682$		0			0
$683$	15.8482	+	15.8482i	0.606413	+	0.606413i	0.942007	−	0.335594i	$-0.108937\pi$
$683$	15.8482	+	15.8482i	0.606413	+	0.606413i	−0.335594	+	0.942007i	$0.608937\pi$
$684$		0			0
$685$	9.86607	+	1.71512i	0.376963	+	0.0655315i
$686$		0			0
$687$	15.5538	−	33.3552i	0.593414	−	1.27258i
$688$		0			0
$689$	−42.9192	−	7.56780i	−1.63509	−	0.288310i
$690$		0			0
$691$	6.94745	+	12.0333i	0.264294	+	0.457770i	0.967378	−	0.253336i	$-0.0815279\pi$
$691$	6.94745	+	12.0333i	0.264294	+	0.457770i	−0.703085	+	0.711106i	$0.748195\pi$
$692$		0			0
$693$	−0.264972	+	3.02864i	−0.0100654	+	0.115049i
$694$		0			0
$695$	−5.25134	+	0.472200i	−0.199195	+	0.0179116i
$696$		0			0
$697$	6.26800	−	2.92282i	0.237418	−	0.110710i
$698$		0			0
$699$	−0.433370	−	2.45776i	−0.0163915	−	0.0929611i
$700$		0			0
$701$	−1.98247	−	1.66349i	−0.0748767	−	0.0628290i	0.604581	−	0.796544i	$-0.293341\pi$
$701$	−1.98247	−	1.66349i	−0.0748767	−	0.0628290i	−0.679458	+	0.733715i	$0.737785\pi$
$702$		0			0
$703$	7.78205	−	2.33291i	0.293506	−	0.0879873i
$704$		0			0
$705$	2.82667	−	33.2322i	0.106459	−	1.25160i
$706$		0			0
$707$	−49.4874	+	70.6754i	−1.86117	+	2.65802i
$708$		0			0
$709$	10.1015	−	27.7536i	0.379369	−	1.04231i	−0.592250	−	0.805755i	$-0.701760\pi$
$709$	10.1015	−	27.7536i	0.379369	−	1.04231i	0.971619	−	0.236553i	$-0.0760177\pi$
$710$		0			0
$711$	2.66216	+	1.53700i	0.0998388	+	0.0576420i
$712$		0			0
$713$	−5.34732	−	0.467829i	−0.200259	−	0.0175204i
$714$		0			0
$715$	4.39823	+	11.9939i	0.164485	+	0.448548i
$716$		0			0
$717$	3.88440	+	5.54750i	0.145066	+	0.207175i
$718$		0			0
$719$	4.71649	+	12.9585i	0.175895	+	0.483269i	0.996042	−	0.0888849i	$-0.0283303\pi$
$719$	4.71649	+	12.9585i	0.175895	+	0.483269i	−0.820146	+	0.572154i	$0.806108\pi$
$720$		0			0
$721$		−	51.0006i		−	1.89936i
$722$		0			0
$723$	−16.5964	+	16.5964i	−0.617225	+	0.617225i
$724$		0			0
$725$	−0.101695	−	21.0774i	−0.00377685	−	0.782796i
$726$		0			0
$727$	17.9695	−	12.5824i	0.666450	−	0.466654i	−0.190749	−	0.981639i	$-0.561092\pi$
$727$	17.9695	−	12.5824i	0.666450	−	0.466654i	0.857199	+	0.514985i	$0.172203\pi$
$728$		0			0
$729$	−25.9648	+	14.9908i	−0.961660	+	0.555214i
$730$		0			0
$731$	−7.49126	+	6.28591i	−0.277074	+	0.232493i
$732$		0			0
$733$	0.320929	+	1.19772i	0.0118538	+	0.0442389i	0.971599	−	0.236632i	$-0.0760435\pi$
$733$	0.320929	+	1.19772i	0.0118538	+	0.0442389i	−0.959746	+	0.280871i	$0.909377\pi$
$734$		0			0
$735$	20.4799	−	35.6706i	0.755412	−	1.31573i
$736$		0			0
$737$	7.27382	+	5.09319i	0.267935	+	0.187610i
$738$		0			0
$739$	7.20842	−	8.59067i	0.265166	−	0.316013i	−0.616989	−	0.786972i	$-0.711648\pi$
$739$	7.20842	−	8.59067i	0.265166	−	0.316013i	0.882155	+	0.470959i	$0.156092\pi$
$740$		0			0
$741$	14.7036	−	27.2936i	0.540151	−	1.00265i
$742$		0			0
$743$	3.04364	+	34.7890i	0.111660	+	1.27628i	0.820800	+	0.571216i	$0.193528\pi$
$743$	3.04364	+	34.7890i	0.111660	+	1.27628i	−0.709139	+	0.705068i	$0.750916\pi$
$744$		0			0
$745$	25.8127	−	25.9375i	0.945703	−	0.950277i
$746$		0			0
$747$	−1.76653	−	3.78833i	−0.0646338	−	0.138608i
$748$		0			0
$749$	21.1765	−	36.6788i	0.773773	−	1.34021i
$750$		0			0
$751$	17.3523	+	20.6797i	0.633196	+	0.754614i	0.983279	−	0.182105i	$-0.0582911\pi$
$751$	17.3523	+	20.6797i	0.633196	+	0.754614i	−0.350083	+	0.936719i	$0.613847\pi$
$752$		0			0
$753$	−11.4014	+	42.5507i	−0.415491	+	1.55063i
$754$		0			0
$755$	−1.04828	+	0.491905i	−0.0381509	+	0.0179022i
$756$		0			0
$757$	9.20704	+	4.29331i	0.334635	+	0.156043i	0.582672	−	0.812708i	$-0.302007\pi$
$757$	9.20704	+	4.29331i	0.334635	+	0.156043i	−0.248036	+	0.968751i	$0.579785\pi$
$758$		0			0
$759$	1.40670			0.0510601
$760$		0			0
$761$	−16.4509			−0.596344			−0.298172	−	0.954512i	$-0.596377\pi$
$761$	−16.4509			−0.596344			−0.298172	+	0.954512i	$0.596377\pi$
$762$		0			0
$763$	14.1623	+	6.60398i	0.512709	+	0.239080i
$764$		0			0
$765$	−0.980944	−	0.354357i	−0.0354661	−	0.0128118i
$766$		0			0
$767$	4.51702	−	16.8577i	0.163100	−	0.608698i
$768$		0			0
$769$	22.4354	+	26.7375i	0.809041	+	0.964177i	0.999848	−	0.0174502i	$-0.00555484\pi$
$769$	22.4354	+	26.7375i	0.809041	+	0.964177i	−0.190807	+	0.981628i	$0.561110\pi$
$770$		0			0
$771$	−7.66531	+	13.2767i	−0.276059	+	0.478149i
$772$		0			0
$773$	−12.2468	−	26.2634i	−0.440488	−	0.944630i	−0.993751	−	0.111623i	$-0.964395\pi$
$773$	−12.2468	−	26.2634i	−0.440488	−	0.944630i	0.553262	−	0.833007i	$-0.313383\pi$
$774$		0			0
$775$	6.31804	−	36.8707i	0.226951	−	1.32444i
$776$		0			0
$777$	−1.09964	−	12.5690i	−0.0394494	−	0.450909i
$778$		0			0
$779$	5.22402	−	35.7557i	0.187170	−	1.28108i
$780$		0			0
$781$	−9.53330	+	11.3613i	−0.341128	+	0.406541i
$782$		0			0
$783$	−19.2014	−	13.4450i	−0.686202	−	0.480484i
$784$		0			0
$785$	−26.9256	−	15.4590i	−0.961017	−	0.551756i
$786$		0			0
$787$	7.59968	+	28.3624i	0.270899	+	1.01101i	0.958540	+	0.284959i	$0.0919799\pi$
$787$	7.59968	+	28.3624i	0.270899	+	1.01101i	−0.687640	+	0.726051i	$0.741353\pi$
$788$		0			0
$789$	10.7082	−	8.98524i	0.381222	−	0.319883i
$790$		0			0
$791$	12.8756	−	7.43373i	0.457804	−	0.264313i
$792$		0			0
$793$	28.1834	−	19.7342i	1.00082	−	0.700783i
$794$		0			0
$795$	−27.4419	−	19.1165i	−0.973265	−	0.677994i
$796$		0			0
$797$	−12.2345	+	12.2345i	−0.433369	+	0.433369i	−0.889773	−	0.456404i	$-0.849137\pi$
$797$	−12.2345	+	12.2345i	−0.433369	+	0.433369i	0.456404	+	0.889773i	$0.349137\pi$
$798$		0			0
$799$		−	7.96459i		−	0.281767i
$800$		0			0
$801$	−0.674344	−	1.85274i	−0.0238268	−	0.0654635i
$802$		0			0
$803$	2.03958	+	2.91282i	0.0719752	+	0.102791i
$804$		0			0
$805$	6.30695	+	2.92248i	0.222291	+	0.103004i
$806$		0			0
$807$	−13.5439	−	1.18494i	−0.476767	−	0.0417117i
$808$		0			0
$809$	21.8651	+	12.6238i	0.768735	+	0.443829i	0.832423	−	0.554141i	$-0.186953\pi$
$809$	21.8651	+	12.6238i	0.768735	+	0.443829i	−0.0636884	+	0.997970i	$0.520286\pi$
$810$		0			0
$811$	−11.3886	+	31.2899i	−0.399908	+	1.09874i	0.562421	+	0.826851i	$0.309870\pi$
$811$	−11.3886	+	31.2899i	−0.399908	+	1.09874i	−0.962329	+	0.271888i	$0.912352\pi$
$812$		0			0
$813$	−14.4545	+	20.6431i	−0.506941	+	0.723987i
$814$		0			0
$815$	−8.61886	+	7.26758i	−0.301905	+	0.254572i
$816$		0			0
$817$	5.95041	+	50.7474i	0.208179	+	1.77543i
$818$		0			0
$819$	8.44823	+	7.08891i	0.295205	+	0.247706i
$820$		0			0
$821$	−5.87203	−	33.3019i	−0.204935	−	1.16225i	−0.897542	−	0.440930i	$-0.854649\pi$
$821$	−5.87203	−	33.3019i	−0.204935	−	1.16225i	0.692607	−	0.721316i	$-0.256462\pi$
$822$		0			0
$823$	11.3119	−	5.27484i	0.394309	−	0.183869i	−0.215343	−	0.976538i	$-0.569087\pi$
$823$	11.3119	−	5.27484i	0.394309	−	0.183869i	0.609652	+	0.792669i	$0.291309\pi$
$824$		0			0
$825$	−0.807294	+	9.77011i	−0.0281064	+	0.340152i
$826$		0			0
$827$	3.46251	−	39.5767i	0.120403	−	1.37622i	−0.660153	−	0.751131i	$-0.729509\pi$
$827$	3.46251	−	39.5767i	0.120403	−	1.37622i	0.780557	−	0.625085i	$-0.214936\pi$
$828$		0			0
$829$	−13.5185	−	23.4147i	−0.469516	−	0.813225i	0.529877	−	0.848075i	$-0.322238\pi$
$829$	−13.5185	−	23.4147i	−0.469516	−	0.813225i	−0.999393	+	0.0348494i	$0.988905\pi$
$830$		0			0
$831$	−25.5736	−	4.50932i	−0.887138	−	0.156426i
$832$		0			0
$833$	4.15112	−	8.90210i	0.143828	−	0.308439i
$834$		0			0
$835$	2.53693	−	14.5934i	0.0877942	−	0.505027i
$836$		0			0
$837$	−29.4169	−	29.4169i	−1.01680	−	1.01680i
$838$		0			0
$839$	29.4014	−	10.7012i	1.01505	−	0.369448i	0.219679	−	0.975572i	$-0.429499\pi$
$839$	29.4014	−	10.7012i	1.01505	−	0.369448i	0.795370	+	0.606125i	$0.207277\pi$
$840$		0			0
$841$	−1.94994	+	11.0587i	−0.0672394	+	0.381333i
$842$		0			0
$843$	40.2377	+	10.7816i	1.38586	+	0.371340i
$844$		0			0
$845$	16.6945	+	4.43013i	0.574307	+	0.152401i
$846$		0			0
$847$	−39.4461	+	10.5696i	−1.35538	+	0.363174i
$848$		0			0
$849$	−36.4484	−	13.2661i	−1.25091	−	0.455293i
$850$		0			0
$851$	1.31689	−	0.232204i	0.0451426	−	0.00795985i
$852$		0			0
$853$	6.42314	−	0.561952i	0.219924	−	0.0192409i	0.0233390	−	0.999728i	$-0.492570\pi$
$853$	6.42314	−	0.561952i	0.219924	−	0.0192409i	0.196585	+	0.980487i	$0.437015\pi$
$854$		0			0
$855$	−4.36210	+	3.26635i	−0.149181	+	0.111707i
$856$		0			0
$857$	−1.58196	+	0.138403i	−0.0540387	+	0.00472777i	−0.114143	−	0.993464i	$-0.536412\pi$
$857$	−1.58196	+	0.138403i	−0.0540387	+	0.00472777i	0.0601043	+	0.998192i	$0.480857\pi$
$858$		0			0
$859$	23.5305	−	4.14905i	0.802849	−	0.141564i	0.242857	−	0.970062i	$-0.421915\pi$
$859$	23.5305	−	4.14905i	0.802849	−	0.141564i	0.559992	+	0.828498i	$0.310804\pi$
$860$		0			0
$861$	−52.7341	−	19.1936i	−1.79717	−	0.654117i
$862$		0			0
$863$	23.3688	−	6.26164i	0.795482	−	0.213149i	0.161882	−	0.986810i	$-0.448243\pi$
$863$	23.3688	−	6.26164i	0.795482	−	0.213149i	0.633599	+	0.773661i	$0.281577\pi$
$864$		0			0
$865$	−35.7563	+	20.7591i	−1.21575	+	0.705829i
$866$		0			0
$867$	−24.6044	−	6.59273i	−0.835609	−	0.223901i
$868$		0			0
$869$	1.19815	−	6.79506i	0.0406445	−	0.230507i
$870$		0			0
$871$	30.2686	−	11.0169i	1.02561	−	0.373292i
$872$		0			0
$873$	2.16218	+	2.16218i	0.0731788	+	0.0731788i
$874$		0			0
$875$	−23.9173	+	42.1271i	−0.808551	+	1.42416i
$876$		0			0
$877$	−3.22036	+	6.90609i	−0.108744	+	0.233202i	−0.953148	−	0.302505i	$-0.902177\pi$
$877$	−3.22036	+	6.90609i	−0.108744	+	0.233202i	0.844404	+	0.535707i	$0.179955\pi$
$878$		0			0
$879$	−14.4406	−	2.54627i	−0.487070	−	0.0858835i
$880$		0			0
$881$	−2.06523	−	3.57708i	−0.0695792	−	0.120515i	0.829137	−	0.559046i	$-0.188832\pi$
$881$	−2.06523	−	3.57708i	−0.0695792	−	0.120515i	−0.898716	+	0.438531i	$0.855499\pi$
$882$		0			0
$883$	−0.631179	+	7.21441i	−0.0212409	+	0.242784i	0.978150	+	0.207898i	$0.0666623\pi$
$883$	−0.631179	+	7.21441i	−0.0212409	+	0.242784i	−0.999391	+	0.0348859i	$0.988893\pi$
$884$		0			0
$885$	8.58400	−	10.2803i	0.288548	−	0.345568i
$886$		0			0
$887$	−27.5263	+	12.8357i	−0.924242	+	0.430981i	−0.825673	−	0.564149i	$-0.809204\pi$
$887$	−27.5263	+	12.8357i	−0.924242	+	0.430981i	−0.0985691	+	0.995130i	$0.531427\pi$
$888$		0			0
$889$	−12.1380	−	68.8380i	−0.407096	−	2.30875i
$890$		0			0
$891$	6.73922	+	5.65488i	0.225772	+	0.189446i
$892$		0			0
$893$	−34.7765	−	22.8546i	−1.16375	−	0.764800i
$894$		0			0
$895$	25.2570	+	2.14832i	0.844249	+	0.0718104i
$896$		0			0
$897$	2.92686	−	4.17999i	0.0977250	−	0.139566i
$898$		0			0
$899$	10.7870	−	29.6370i	0.359767	−	0.988450i
$900$		0			0
$901$	−6.91653	−	3.99326i	−0.230423	−	0.133035i
$902$		0			0
$903$	79.0491	+	6.91590i	2.63059	+	0.230147i
$904$		0			0
$905$	−0.173451	+	0.374322i	−0.00576572	+	0.0124429i
$906$		0			0
$907$	−7.63768	−	10.9077i	−0.253605	−	0.362185i	0.672081	−	0.740477i	$-0.265400\pi$
$907$	−7.63768	−	10.9077i	−0.253605	−	0.362185i	−0.925686	+	0.378292i	$0.876512\pi$
$908$		0			0
$909$	−3.80779	−	10.4618i	−0.126296	−	0.346997i
$910$		0			0
$911$		−	40.3027i		−	1.33529i	−0.744480	−	0.667644i	$-0.767303\pi$
$911$		−	40.3027i		−	1.33529i	0.744480	−	0.667644i	$-0.232697\pi$
$912$		0			0
$913$	−6.63430	+	6.63430i	−0.219563	+	0.219563i
$914$		0			0
$915$	25.9904	−	4.64748i	0.859215	−	0.153641i
$916$		0			0
$917$	28.3653	−	19.8616i	0.936706	−	0.655889i
$918$		0			0
$919$	−25.3573	+	14.6400i	−0.836460	+	0.482931i	−0.856060	−	0.516877i	$-0.827094\pi$
$919$	−25.3573	+	14.6400i	−0.836460	+	0.482931i	0.0195991	+	0.999808i	$0.493761\pi$
$920$		0			0
$921$	−2.32065	+	1.94725i	−0.0764679	+	0.0641642i
$922$		0			0
$923$	13.9245	+	51.9670i	0.458331	+	1.71052i
$924$		0			0
$925$	0.856996	+	9.27962i	0.0281778	+	0.305112i
$926$		0			0
$927$	5.39086	+	3.77472i	0.177059	+	0.123978i
$928$		0			0
$929$	−13.9922	+	16.6752i	−0.459068	+	0.547096i	−0.945073	−	0.326860i	$-0.894009\pi$
$929$	−13.9922	+	16.6752i	−0.459068	+	0.547096i	0.486004	+	0.873956i	$0.338454\pi$
$930$		0			0
$931$	−26.9583	−	43.6702i	−0.883524	−	1.43123i
$932$		0			0
$933$	1.43585	+	16.4119i	0.0470077	+	0.537300i
$934$		0			0
$935$	0.00564760	+	2.34107i	0.000184696	+	0.0765613i
$936$		0			0
$937$	4.51043	+	9.67264i	0.147349	+	0.315991i	0.966105	−	0.258151i	$-0.0831133\pi$
$937$	4.51043	+	9.67264i	0.147349	+	0.315991i	−0.818755	+	0.574143i	$0.805335\pi$
$938$		0			0
$939$	−2.88934	+	5.00448i	−0.0942899	+	0.163315i
$940$		0			0
$941$	31.6809	+	37.7559i	1.03277	+	1.23081i	0.972568	+	0.232620i	$0.0747300\pi$
$941$	31.6809	+	37.7559i	1.03277	+	1.23081i	0.0602017	+	0.998186i	$0.480826\pi$
$942$		0			0
$943$	1.53938	−	5.74505i	0.0501292	−	0.187085i
$944$		0			0
$945$	22.8857	+	48.7711i	0.744473	+	1.58652i
$946$		0			0
$947$	20.7066	+	9.65566i	0.672875	+	0.313767i	0.728858	−	0.684665i	$-0.240051\pi$
$947$	20.7066	+	9.65566i	0.672875	+	0.313767i	−0.0559830	+	0.998432i	$0.517829\pi$
$948$		0			0
$949$	12.8990			0.418721
$950$		0			0
$951$	−8.77169			−0.284442
$952$		0			0
$953$	23.1050	+	10.7740i	0.748444	+	0.349005i	0.759131	−	0.650938i	$-0.225624\pi$
$953$	23.1050	+	10.7740i	0.748444	+	0.349005i	−0.0106871	+	0.999943i	$0.503402\pi$
$954$		0			0
$955$	−23.8879	−	50.9068i	−0.772994	−	1.64730i
$956$		0			0
$957$	−2.13922	+	7.98369i	−0.0691513	+	0.258076i
$958$		0			0
$959$	−12.4729	−	14.8647i	−0.402772	−	0.480005i
$960$		0			0
$961$	12.4874	−	21.6288i	0.402819	−	0.697703i
$962$		0			0
$963$	2.30967	+	4.95311i	0.0744282	+	0.159612i
$964$		0			0
$965$	−0.144446	−	59.8768i	−0.00464990	−	1.92750i
$966$		0			0
$967$	−2.85693	−	32.6549i	−0.0918728	−	1.05011i	−0.892530	−	0.450988i	$-0.851072\pi$
$967$	−2.85693	−	32.6549i	−0.0918728	−	1.05011i	0.800657	−	0.599123i	$-0.204484\pi$
$968$		0			0
$969$	4.24271	−	3.77848i	0.136295	−	0.121382i
$970$		0			0
$971$	22.5024	−	26.8173i	0.722136	−	0.860608i	−0.272700	−	0.962099i	$-0.587917\pi$
$971$	22.5024	−	26.8173i	0.722136	−	0.860608i	0.994836	+	0.101491i	$0.0323612\pi$
$972$		0			0
$973$	8.36902	+	5.86005i	0.268298	+	0.187865i
$974$		0			0
$975$	27.3520	+	22.7271i	0.875965	+	0.727849i
$976$		0			0
$977$	−2.09436	−	7.81625i	−0.0670045	−	0.250064i	0.924297	−	0.381674i	$-0.124652\pi$
$977$	−2.09436	−	7.81625i	−0.0670045	−	0.250064i	−0.991302	+	0.131610i	$0.957985\pi$
$978$		0			0
$979$	−3.39017	+	2.84469i	−0.108350	+	0.0909168i
$980$		0			0
$981$	−1.74625	+	1.00820i	−0.0557534	+	0.0321892i
$982$		0			0
$983$	−46.3287	+	32.4397i	−1.47766	+	1.03467i	−0.491127	+	0.871088i	$0.663415\pi$
$983$	−46.3287	+	32.4397i	−1.47766	+	1.03467i	−0.986530	+	0.163579i	$0.947696\pi$
$984$		0			0
$985$	53.5181	−	9.56986i	1.70523	−	0.304921i
$986$		0			0
$987$	−45.6983	+	45.6983i	−1.45459	+	1.45459i
$988$		0			0
$989$			8.41003i			0.267423i
$990$		0			0
$991$	−15.5383	−	42.6910i	−0.493589	−	1.35612i	−0.897374	−	0.441271i	$-0.854528\pi$
$991$	−15.5383	−	42.6910i	−0.493589	−	1.35612i	0.403785	−	0.914854i	$-0.367694\pi$
$992$		0			0
$993$	2.14439	+	3.06251i	0.0680503	+	0.0971859i
$994$		0			0
$995$	10.4192	−	22.4856i	0.330312	−	0.712841i
$996$		0			0
$997$	42.7540	+	3.74049i	1.35403	+	0.118462i	0.740952	−	0.671558i	$-0.234375\pi$
$997$	42.7540	+	3.74049i	1.35403	+	0.118462i	0.613081	+	0.790020i	$0.289930\pi$
$998$		0			0
$999$	8.97533	+	5.18191i	0.283967	+	0.163948i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bh.a.117.3	yes	120
5.3	odd	4	inner	380.2.bh.a.193.8	yes	120
19.13	odd	18	inner	380.2.bh.a.317.8	yes	120
95.13	even	36	inner	380.2.bh.a.13.3	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bh.a.13.3	✓	120	95.13	even	36	inner
380.2.bh.a.117.3	yes	120	1.1	even	1	trivial
380.2.bh.a.193.8	yes	120	5.3	odd	4	inner
380.2.bh.a.317.8	yes	120	19.13	odd	18	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bh (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41596 - 0.660272i) q^{3} +(-0.949889 - 2.02428i) q^{5} +(-1.12143 + 4.18524i) q^{7} +(-0.359387 - 0.428300i) q^{9} +O(q^{10})\)	\(q+(-1.41596 - 0.660272i) q^{3} +(-0.949889 - 2.02428i) q^{5} +(-1.12143 + 4.18524i) q^{7} +(-0.359387 - 0.428300i) q^{9} +(-0.627484 + 1.08683i) q^{11} +(1.92393 + 4.12588i) q^{13} +(0.00842766 + 3.49348i) q^{15} +(0.0727101 + 0.831080i) q^{17} +(3.83747 + 2.06733i) q^{19} +(4.35129 - 5.18567i) q^{21} +(0.587706 + 0.411516i) q^{23} +(-3.19542 + 3.84568i) q^{25} +(1.43917 + 5.37105i) q^{27} +(-3.22929 + 2.70969i) q^{29} +(-6.47928 + 3.74082i) q^{31} +(1.60610 - 1.12460i) q^{33} +(9.53733 - 1.70542i) q^{35} +(1.31792 - 1.31792i) q^{37} -7.11239i q^{39} +(-2.83535 - 7.79006i) q^{41} +(6.72347 + 9.60211i) q^{43} +(-0.525622 + 1.13434i) q^{45} +(-9.51062 - 0.832071i) q^{47} +(-10.1964 - 5.88691i) q^{49} +(0.445784 - 1.22478i) q^{51} +(-5.49098 + 7.84194i) q^{53} +(2.79610 + 0.237831i) q^{55} +(-4.06869 - 5.46102i) q^{57} +(-2.93676 - 2.46424i) q^{59} +(-1.31237 - 7.44285i) q^{61} +(2.19557 - 1.02381i) q^{63} +(6.52442 - 7.81370i) q^{65} +(0.616682 - 7.04871i) q^{67} +(-0.560454 - 0.970734i) q^{69} +(11.6384 + 2.05217i) q^{71} +(1.19747 - 2.56798i) q^{73} +(7.06378 - 3.33548i) q^{75} +(-3.84498 - 3.84498i) q^{77} +(-5.16648 + 1.88045i) q^{79} +(1.21729 - 6.90358i) q^{81} +(7.22139 + 1.93497i) q^{83} +(1.61327 - 0.936620i) q^{85} +(6.36167 - 1.70460i) q^{87} +(3.31376 + 1.20611i) q^{89} +(-19.4253 + 3.42521i) q^{91} +(11.6443 - 1.01875i) q^{93} +(0.539677 - 9.73184i) q^{95} +(-5.44825 + 0.476660i) q^{97} +(0.691001 - 0.121842i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 6 q^{7}+O(q^{10}) \) 120 * q + 6 * q^7	\( 120 q + 6 q^{7} + 18 q^{15} - 18 q^{17} + 48 q^{21} - 36 q^{23} - 24 q^{25} - 60 q^{33} - 18 q^{35} - 12 q^{41} - 36 q^{43} + 18 q^{45} - 24 q^{47} + 96 q^{51} - 18 q^{53} + 72 q^{55} - 6 q^{57} - 24 q^{61} + 36 q^{63} + 90 q^{65} - 24 q^{67} + 18 q^{73} - 36 q^{77} - 30 q^{83} - 24 q^{85} - 72 q^{87} - 144 q^{91} - 132 q^{93} - 12 q^{95} - 60 q^{97}+O(q^{100}) \) 120 * q + 6 * q^7 + 18 * q^15 - 18 * q^17 + 48 * q^21 - 36 * q^23 - 24 * q^25 - 60 * q^33 - 18 * q^35 - 12 * q^41 - 36 * q^43 + 18 * q^45 - 24 * q^47 + 96 * q^51 - 18 * q^53 + 72 * q^55 - 6 * q^57 - 24 * q^61 + 36 * q^63 + 90 * q^65 - 24 * q^67 + 18 * q^73 - 36 * q^77 - 30 * q^83 - 24 * q^85 - 72 * q^87 - 144 * q^91 - 132 * q^93 - 12 * q^95 - 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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