LMFDB - Embedded newform 380.2.bh.a.357.9

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			357.9
Character	$\chi$	$=$	380.357
Dual form			380.2.bh.a.33.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.60791 - 2.29633i) q^{3} +(1.74139 + 1.40270i) q^{5} +(-0.546238 + 0.146364i) q^{7} +(-1.66171 - 4.56550i) q^{9} +O(q^{10})$	\(q+(1.60791 - 2.29633i) q^{3} +(1.74139 + 1.40270i) q^{5} +(-0.546238 + 0.146364i) q^{7} +(-1.66171 - 4.56550i) q^{9} +(0.973552 + 1.68624i) q^{11} +(4.44432 - 3.11195i) q^{13} +(6.02105 - 1.74340i) q^{15} +(0.656923 + 1.40878i) q^{17} +(-4.30338 - 0.693479i) q^{19} +(-0.542200 + 1.48968i) q^{21} +(-8.31664 + 0.727612i) q^{23} +(1.06488 + 4.88529i) q^{25} +(-5.03242 - 1.34843i) q^{27} +(1.88234 - 0.685117i) q^{29} +(-6.30203 - 3.63848i) q^{31} +(5.43755 + 0.475724i) q^{33} +(-1.15652 - 0.511330i) q^{35} +(4.89676 - 4.89676i) q^{37} -15.2094i q^{39} +(-5.71247 + 1.00726i) q^{41} +(-0.926985 + 10.5955i) q^{43} +(3.51034 - 10.2812i) q^{45} +(5.99419 + 2.79514i) q^{47} +(-5.78522 + 3.34010i) q^{49} +(4.29129 + 0.756670i) q^{51} +(0.198390 + 2.26761i) q^{53} +(-0.669954 + 4.30200i) q^{55} +(-8.51190 + 8.76694i) q^{57} +(3.62555 + 1.31959i) q^{59} +(3.63452 + 3.04972i) q^{61} +(1.57591 + 2.25063i) q^{63} +(12.1044 + 0.814927i) q^{65} +(0.894831 - 1.91897i) q^{67} +(-11.7016 + 20.2677i) q^{69} +(1.35617 + 1.61623i) q^{71} +(-0.728519 - 0.510115i) q^{73} +(12.9305 + 5.40978i) q^{75} +(-0.778595 - 0.778595i) q^{77} +(-2.16887 - 12.3003i) q^{79} +(-0.0226334 + 0.0189917i) q^{81} +(0.674124 + 2.51586i) q^{83} +(-0.832128 + 3.37469i) q^{85} +(1.45338 - 5.42409i) q^{87} +(-0.660318 + 3.74485i) q^{89} +(-1.97218 + 2.35035i) q^{91} +(-18.4882 + 8.62121i) q^{93} +(-6.52112 - 7.24396i) q^{95} +(-14.7372 + 6.87208i) q^{97} +(6.08078 - 7.24679i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	1.60791	−	2.29633i	0.928326	−	1.32579i	−0.0170667	−	0.999854i	$-0.505433\pi$
$3$	1.60791	−	2.29633i	0.928326	−	1.32579i	0.945393	−	0.325933i	$-0.105678\pi$
$4$		0			0
$5$	1.74139	+	1.40270i	0.778773	+	0.627306i
$5$	1.74139	+	1.40270i	0.778773	+	0.627306i
$6$		0			0
$7$	−0.546238	+	0.146364i	−0.206458	+	0.0553204i	−0.360566	−	0.932734i	$-0.617416\pi$
$7$	−0.546238	+	0.146364i	−0.206458	+	0.0553204i	0.154108	+	0.988054i	$0.450750\pi$
$8$		0			0
$9$	−1.66171	−	4.56550i	−0.553902	−	1.52183i
$10$		0			0
$11$	0.973552	+	1.68624i	0.293537	+	0.508421i	0.974643	−	0.223764i	$-0.0718343\pi$
$11$	0.973552	+	1.68624i	0.293537	+	0.508421i	−0.681107	+	0.732184i	$0.738501\pi$
$12$		0			0
$13$	4.44432	−	3.11195i	1.23263	−	0.863098i	0.238487	−	0.971146i	$-0.423349\pi$
$13$	4.44432	−	3.11195i	1.23263	−	0.863098i	0.994146	+	0.108047i	$0.0344598\pi$
$14$		0			0
$15$	6.02105	−	1.74340i	1.55463	−	0.450143i
$16$		0			0
$17$	0.656923	+	1.40878i	0.159327	+	0.341678i	0.969724	−	0.244203i	$-0.0785263\pi$
$17$	0.656923	+	1.40878i	0.159327	+	0.341678i	−0.810397	+	0.585881i	$0.800748\pi$
$18$		0			0
$19$	−4.30338	−	0.693479i	−0.987263	−	0.159095i
$19$	−4.30338	−	0.693479i	−0.987263	−	0.159095i
$20$		0			0
$21$	−0.542200	+	1.48968i	−0.118318	+	0.325075i
$22$		0			0
$23$	−8.31664	+	0.727612i	−1.73414	+	0.151718i	−0.909983	−	0.414645i	$-0.863906\pi$
$23$	−8.31664	+	0.727612i	−1.73414	+	0.151718i	−0.824157	+	0.566362i	$0.808350\pi$
$24$		0			0
$25$	1.06488	+	4.88529i	0.212975	+	0.977058i
$26$		0			0
$27$	−5.03242	−	1.34843i	−0.968490	−	0.259506i
$28$		0			0
$29$	1.88234	−	0.685117i	0.349542	−	0.127223i	−0.161281	−	0.986908i	$-0.551563\pi$
$29$	1.88234	−	0.685117i	0.349542	−	0.127223i	0.510824	+	0.859685i	$0.329340\pi$
$30$		0			0
$31$	−6.30203	−	3.63848i	−1.13188	−	0.653490i	−0.187472	−	0.982270i	$-0.560029\pi$
$31$	−6.30203	−	3.63848i	−1.13188	−	0.653490i	−0.944407	+	0.328780i	$0.893363\pi$
$32$		0			0
$33$	5.43755	+	0.475724i	0.946556	+	0.0828129i
$34$		0			0
$35$	−1.15652	−	0.511330i	−0.195487	−	0.0864305i
$36$		0			0
$37$	4.89676	−	4.89676i	0.805023	−	0.805023i	−0.178853	−	0.983876i	$-0.557239\pi$
$37$	4.89676	−	4.89676i	0.805023	−	0.805023i	0.983876	+	0.178853i	$0.0572386\pi$
$38$		0			0
$39$		−	15.2094i		−	2.43545i
$40$		0			0
$41$	−5.71247	+	1.00726i	−0.892138	+	0.157308i	−0.600883	−	0.799337i	$-0.705184\pi$
$41$	−5.71247	+	1.00726i	−0.892138	+	0.157308i	−0.291255	+	0.956645i	$0.594073\pi$
$42$		0			0
$43$	−0.926985	+	10.5955i	−0.141364	+	1.61580i	0.512160	+	0.858890i	$0.328846\pi$
$43$	−0.926985	+	10.5955i	−0.141364	+	1.61580i	−0.653523	+	0.756906i	$0.726710\pi$
$44$		0			0
$45$	3.51034	−	10.2812i	0.523290	−	1.53263i
$46$		0			0
$47$	5.99419	+	2.79514i	0.874342	+	0.407712i	0.807372	−	0.590043i	$-0.200889\pi$
$47$	5.99419	+	2.79514i	0.874342	+	0.407712i	0.0669699	+	0.997755i	$0.478667\pi$
$48$		0			0
$49$	−5.78522	+	3.34010i	−0.826461	+	0.477157i
$50$		0			0
$51$	4.29129	+	0.756670i	0.600901	+	0.105955i
$52$		0			0
$53$	0.198390	+	2.26761i	0.0272510	+	0.311480i	0.997571	+	0.0696561i	$0.0221902\pi$
$53$	0.198390	+	2.26761i	0.0272510	+	0.311480i	−0.970320	+	0.241824i	$0.922254\pi$
$54$		0			0
$55$	−0.669954	+	4.30200i	−0.0903365	+	0.580082i
$56$		0			0
$57$	−8.51190	+	8.76694i	−1.12743	+	1.16121i
$58$		0			0
$59$	3.62555	+	1.31959i	0.472006	+	0.171796i	0.567061	−	0.823676i	$-0.308080\pi$
$59$	3.62555	+	1.31959i	0.472006	+	0.171796i	−0.0950548	+	0.995472i	$0.530303\pi$
$60$		0			0
$61$	3.63452	+	3.04972i	0.465353	+	0.390477i	0.845096	−	0.534615i	$-0.179543\pi$
$61$	3.63452	+	3.04972i	0.465353	+	0.390477i	−0.379743	+	0.925092i	$0.623988\pi$
$62$		0			0
$63$	1.57591	+	2.25063i	0.198546	+	0.283553i
$64$		0			0
$65$	12.1044	+	0.814927i	1.50137	+	0.101079i
$66$		0			0
$67$	0.894831	−	1.91897i	0.109321	−	0.234440i	−0.844035	−	0.536288i	$-0.819826\pi$
$67$	0.894831	−	1.91897i	0.109321	−	0.234440i	0.953356	+	0.301849i	$0.0976037\pi$
$68$		0			0
$69$	−11.7016	+	20.2677i	−1.40870	+	2.43994i
$70$		0			0
$71$	1.35617	+	1.61623i	0.160948	+	0.191811i	0.840491	−	0.541825i	$-0.182266\pi$
$71$	1.35617	+	1.61623i	0.160948	+	0.191811i	−0.679543	+	0.733636i	$0.737822\pi$
$72$		0			0
$73$	−0.728519	−	0.510115i	−0.0852668	−	0.0597044i	0.530166	−	0.847894i	$-0.322130\pi$
$73$	−0.728519	−	0.510115i	−0.0852668	−	0.0597044i	−0.615432	+	0.788190i	$0.711019\pi$
$74$		0			0
$75$	12.9305	+	5.40978i	1.49308	+	0.624668i
$76$		0			0
$77$	−0.778595	−	0.778595i	−0.0887292	−	0.0887292i
$78$		0			0
$79$	−2.16887	−	12.3003i	−0.244017	−	1.38389i	−0.822765	−	0.568381i	$-0.807570\pi$
$79$	−2.16887	−	12.3003i	−0.244017	−	1.38389i	0.578749	−	0.815506i	$-0.303541\pi$
$80$		0			0
$81$	−0.0226334	+	0.0189917i	−0.00251482	+	0.00211019i
$82$		0			0
$83$	0.674124	+	2.51586i	0.0739947	+	0.276152i	0.993003	−	0.118085i	$-0.0376756\pi$
$83$	0.674124	+	2.51586i	0.0739947	+	0.276152i	−0.919009	+	0.394237i	$0.871009\pi$
$84$		0			0
$85$	−0.832128	+	3.37469i	−0.0902570	+	0.366037i
$86$		0			0
$87$	1.45338	−	5.42409i	0.155819	−	0.581523i
$88$		0			0
$89$	−0.660318	+	3.74485i	−0.0699935	+	0.396953i	0.929603	+	0.368562i	$0.120150\pi$
$89$	−0.660318	+	3.74485i	−0.0699935	+	0.396953i	−0.999597	+	0.0283915i	$0.990961\pi$
$90$		0			0
$91$	−1.97218	+	2.35035i	−0.206740	+	0.246384i
$92$		0			0
$93$	−18.4882	+	8.62121i	−1.91714	+	0.893978i
$94$		0			0
$95$	−6.52112	−	7.24396i	−0.669053	−	0.743215i
$96$		0			0
$97$	−14.7372	+	6.87208i	−1.49634	+	0.697754i	−0.986688	−	0.162627i	$-0.948003\pi$
$97$	−14.7372	+	6.87208i	−1.49634	+	0.697754i	−0.509651	+	0.860381i	$0.670225\pi$
$98$		0			0
$99$	6.08078	−	7.24679i	0.611141	−	0.728329i
$100$		0			0
$101$	1.91512	−	10.8612i	0.190562	−	1.08073i	−0.728037	−	0.685538i	$-0.759567\pi$
$101$	1.91512	−	10.8612i	0.190562	−	1.08073i	0.918599	−	0.395192i	$-0.129322\pi$
$102$		0			0
$103$	−3.15904	+	11.7897i	−0.311270	+	1.16167i	0.616143	+	0.787634i	$0.288694\pi$
$103$	−3.15904	+	11.7897i	−0.311270	+	1.16167i	−0.927413	+	0.374040i	$0.877972\pi$
$104$		0			0
$105$	−3.03376	+	1.83357i	−0.296064	+	0.178939i
$106$		0			0
$107$	1.11998	+	4.17982i	0.108272	+	0.404078i	0.998696	−	0.0510550i	$-0.0162584\pi$
$107$	1.11998	+	4.17982i	0.108272	+	0.404078i	−0.890423	+	0.455133i	$0.849592\pi$
$108$		0			0
$109$	−1.92234	+	1.61303i	−0.184126	+	0.154500i	−0.730192	−	0.683242i	$-0.760569\pi$
$109$	−1.92234	+	1.61303i	−0.184126	+	0.154500i	0.546066	+	0.837742i	$0.316125\pi$
$110$		0			0
$111$	−3.37104	−	19.1181i	−0.319965	−	1.81461i
$112$		0			0
$113$	14.2074	+	14.2074i	1.33652	+	1.33652i	0.899408	+	0.437110i	$0.143998\pi$
$113$	14.2074	+	14.2074i	1.33652	+	1.33652i	0.437110	+	0.899408i	$0.356002\pi$
$114$		0			0
$115$	−15.5031	−	10.3987i	−1.44568	−	0.969682i
$116$		0			0
$117$	−21.5927	−	15.1194i	−1.99625	−	1.39779i
$118$		0			0
$119$	−0.565030	−	0.673377i	−0.0517962	−	0.0617284i
$120$		0			0
$121$	3.60439	−	6.24299i	0.327672	−	0.567545i
$122$		0			0
$123$	−6.87212	+	14.7373i	−0.619638	+	1.32882i
$124$		0			0
$125$	−4.99822	+	10.0009i	−0.447054	+	0.894507i
$126$		0			0
$127$	−6.99567	−	9.99086i	−0.620766	−	0.886545i	0.378471	−	0.925613i	$-0.376450\pi$
$127$	−6.99567	−	9.99086i	−0.620766	−	0.886545i	−0.999237	+	0.0390679i	$0.987561\pi$
$128$		0			0
$129$	22.8402	+	19.1652i	2.01097	+	1.68740i
$130$		0			0
$131$	15.1437	+	5.51184i	1.32311	+	0.481572i	0.904453	−	0.426573i	$-0.140279\pi$
$131$	15.1437	+	5.51184i	1.32311	+	0.481572i	0.418655	+	0.908145i	$0.362502\pi$
$132$		0			0
$133$	2.45217	−	0.251056i	0.212630	−	0.0217693i
$134$		0			0
$135$	−6.87196	−	9.40712i	−0.591445	−	0.809636i
$136$		0			0
$137$	−0.188788	−	2.15785i	−0.0161292	−	0.184358i	−0.999985	−	0.00539709i	$-0.998282\pi$
$137$	−0.188788	−	2.15785i	−0.0161292	−	0.184358i	0.983856	−	0.178961i	$-0.0572735\pi$
$138$		0			0
$139$	−2.37766	−	0.419246i	−0.201671	−	0.0355600i	0.0719001	−	0.997412i	$-0.477094\pi$
$139$	−2.37766	−	0.419246i	−0.201671	−	0.0355600i	−0.273571	+	0.961852i	$0.588205\pi$
$140$		0			0
$141$	16.0567	−	9.27032i	1.35221	−	0.780701i
$142$		0			0
$143$	9.57426	+	4.46455i	0.800640	+	0.373345i
$144$		0			0
$145$	4.23891	+	1.44730i	0.352022	+	0.120192i
$146$		0			0
$147$	−1.63213	+	18.6554i	−0.134616	+	1.53867i
$148$		0			0
$149$	−16.7765	+	2.95815i	−1.37438	+	0.242341i	−0.811576	−	0.584247i	$-0.801390\pi$
$149$	−16.7765	+	2.95815i	−1.37438	+	0.242341i	−0.562807	+	0.826588i	$0.690279\pi$
$150$		0			0
$151$		−	16.0195i		−	1.30365i	−0.758371	−	0.651823i	$-0.774005\pi$
$151$		−	16.0195i		−	1.30365i	0.758371	−	0.651823i	$-0.225995\pi$
$152$		0			0
$153$	5.34016	−	5.34016i	0.431726	−	0.431726i
$154$		0			0
$155$	−5.87061	−	15.1759i	−0.471538	−	1.21895i
$156$		0			0
$157$	−16.0939	−	1.40804i	−1.28444	−	0.112374i	−0.575591	−	0.817738i	$-0.695228\pi$
$157$	−16.0939	−	1.40804i	−1.28444	−	0.112374i	−0.708845	+	0.705364i	$0.750784\pi$
$158$		0			0
$159$	5.52618	+	3.19054i	0.438254	+	0.253026i
$160$		0			0
$161$	4.43637	−	1.61471i	0.349635	−	0.127257i
$162$		0			0
$163$	−16.2220	−	4.34666i	−1.27060	−	0.340457i	−0.440341	−	0.897831i	$-0.645142\pi$
$163$	−16.2220	−	4.34666i	−1.27060	−	0.340457i	−0.830262	+	0.557374i	$0.811809\pi$
$164$		0			0
$165$	8.80159	+	8.45566i	0.685203	+	0.658272i
$166$		0			0
$167$	17.1208	−	1.49788i	1.32485	−	0.115909i	0.597329	−	0.801996i	$-0.296229\pi$
$167$	17.1208	−	1.49788i	1.32485	−	0.115909i	0.727520	+	0.686087i	$0.240673\pi$
$168$		0			0
$169$	5.62151	−	15.4450i	0.432423	−	1.18807i
$170$		0			0
$171$	3.98488	+	20.7994i	0.304731	+	1.59057i
$172$		0			0
$173$	−4.27205	−	9.16145i	−0.324798	−	0.696532i	0.674323	−	0.738436i	$-0.264435\pi$
$173$	−4.27205	−	9.16145i	−0.324798	−	0.696532i	−0.999122	+	0.0419041i	$0.986658\pi$
$174$		0			0
$175$	−1.29671	−	2.51267i	−0.0980218	−	0.189940i
$176$		0			0
$177$	8.85977	−	6.20368i	0.665941	−	0.466297i
$178$		0			0
$179$	−8.24265	−	14.2767i	−0.616084	−	1.06709i	−0.990193	−	0.139705i	$-0.955385\pi$
$179$	−8.24265	−	14.2767i	−0.616084	−	1.06709i	0.374109	−	0.927385i	$-0.377949\pi$
$180$		0			0
$181$	8.33707	+	22.9059i	0.619690	+	1.70258i	0.707745	+	0.706468i	$0.249713\pi$
$181$	8.33707	+	22.9059i	0.619690	+	1.70258i	−0.0880555	+	0.996116i	$0.528065\pi$
$182$		0			0
$183$	12.8471	−	3.44238i	0.949689	−	0.254468i
$184$		0			0
$185$	15.3959	−	1.65849i	1.13193	−	0.121935i
$186$		0			0
$187$	−1.73599	+	2.47925i	−0.126948	+	0.181301i
$188$		0			0
$189$	2.94626			0.214309
$190$		0			0
$191$	4.56136			0.330048			0.165024	−	0.986290i	$-0.447230\pi$
$191$	4.56136			0.330048			0.165024	+	0.986290i	$0.447230\pi$
$192$		0			0
$193$	3.86360	−	5.51779i	0.278108	−	0.397179i	−0.655661	−	0.755055i	$-0.727610\pi$
$193$	3.86360	−	5.51779i	0.278108	−	0.397179i	0.933769	+	0.357876i	$0.116499\pi$
$194$		0			0
$195$	21.3341	−	26.4854i	1.52777	−	1.89666i
$196$		0			0
$197$	22.2465	−	5.96092i	1.58499	−	0.424698i	0.644527	−	0.764581i	$-0.277054\pi$
$197$	22.2465	−	5.96092i	1.58499	−	0.424698i	0.940468	+	0.339883i	$0.110388\pi$
$198$		0			0
$199$	−1.74838	−	4.80365i	−0.123940	−	0.340521i	0.862169	−	0.506620i	$-0.169105\pi$
$199$	−1.74838	−	4.80365i	−0.123940	−	0.340521i	−0.986109	+	0.166098i	$0.946883\pi$
$200$		0			0
$201$	−2.96779	−	5.14036i	−0.209332	−	0.362573i
$202$		0			0
$203$	−0.927930	+	0.649744i	−0.0651279	+	0.0456031i
$204$		0			0
$205$	−11.3605	−	6.25883i	−0.793453	−	0.437136i
$206$		0			0
$207$	17.1417	+	36.7606i	1.19143	+	2.55504i
$208$		0			0
$209$	−3.02019	−	7.93167i	−0.208911	−	0.548645i
$210$		0			0
$211$	2.36520	−	6.49835i	0.162827	−	0.447365i	−0.831268	−	0.555871i	$-0.812385\pi$
$211$	2.36520	−	6.49835i	0.162827	−	0.447365i	0.994096	+	0.108507i	$0.0346069\pi$
$212$		0			0
$213$	5.89199	−	0.515483i	0.403713	−	0.0353203i
$214$		0			0
$215$	−16.4765	+	17.1506i	−1.12369	+	1.16966i
$216$		0			0
$217$	3.97495	+	1.06508i	0.269837	+	0.0723027i
$218$		0			0
$219$	−2.34278	+	0.852704i	−0.158311	+	0.0576204i
$220$		0			0
$221$	7.30361	+	4.21674i	0.491294	+	0.283649i
$222$		0			0
$223$	6.87693	+	0.601653i	0.460513	+	0.0402897i	0.315052	−	0.949074i	$-0.397978\pi$
$223$	6.87693	+	0.601653i	0.460513	+	0.0402897i	0.145461	+	0.989364i	$0.453534\pi$
$224$		0			0
$225$	20.5343	−	12.9796i	1.36895	−	0.865307i
$226$		0			0
$227$	12.9545	−	12.9545i	0.859819	−	0.859819i	−0.131498	−	0.991316i	$-0.541979\pi$
$227$	12.9545	−	12.9545i	0.859819	−	0.859819i	0.991316	+	0.131498i	$0.0419786\pi$
$228$		0			0
$229$		−	6.27031i		−	0.414354i	−0.978303	−	0.207177i	$-0.933572\pi$
$229$		−	6.27031i		−	0.414354i	0.978303	−	0.207177i	$-0.0664276\pi$
$230$		0			0
$231$	−3.03982	+	0.536003i	−0.200006	+	0.0352664i
$232$		0			0
$233$	0.626277	−	7.15838i	0.0410288	−	0.468961i	−0.947692	−	0.319188i	$-0.896590\pi$
$233$	0.626277	−	7.15838i	0.0410288	−	0.468961i	0.988720	−	0.149773i	$-0.0478544\pi$
$234$		0			0
$235$	6.51749	+	13.2755i	0.425154	+	0.865995i
$236$		0			0
$237$	−31.7328	−	14.7973i	−2.06127	−	0.961185i
$238$		0			0
$239$	1.98103	−	1.14375i	0.128142	−	0.0739830i	−0.434559	−	0.900644i	$-0.643096\pi$
$239$	1.98103	−	1.14375i	0.128142	−	0.0739830i	0.562701	+	0.826661i	$0.309762\pi$
$240$		0			0
$241$	−20.4019	−	3.59741i	−1.31420	−	0.231729i	−0.527760	−	0.849393i	$-0.676968\pi$
$241$	−20.4019	−	3.59741i	−1.31420	−	0.231729i	−0.786442	+	0.617664i	$0.788079\pi$
$242$		0			0
$243$	−1.35501	−	15.4879i	−0.0869240	−	0.993546i
$244$		0			0
$245$	−14.7595	−	2.29850i	−0.942949	−	0.146846i
$246$		0			0
$247$	−21.2837	+	10.3098i	−1.35425	+	0.656000i
$248$		0			0
$249$	6.86119	+	2.49727i	0.434810	+	0.158258i
$250$		0			0
$251$	−21.4529	−	18.0011i	−1.35409	−	1.13622i	−0.977758	−	0.209735i	$-0.932740\pi$
$251$	−21.4529	−	18.0011i	−1.35409	−	1.13622i	−0.376335	−	0.926484i	$-0.622816\pi$
$252$		0			0
$253$	−9.32361	−	13.3155i	−0.586170	−	0.837138i
$254$		0			0
$255$	6.41143	+	7.33704i	0.401499	+	0.459463i
$256$		0			0
$257$	2.85369	−	6.11975i	0.178008	−	0.381740i	−0.796977	−	0.604010i	$-0.793569\pi$
$257$	2.85369	−	6.11975i	0.178008	−	0.381740i	0.974985	+	0.222270i	$0.0713467\pi$
$258$		0			0
$259$	−1.95809	+	3.39151i	−0.121670	+	0.210738i
$260$		0			0
$261$	−6.25580	−	7.45537i	−0.387224	−	0.461476i
$262$		0			0
$263$	10.7403	+	7.52042i	0.662274	+	0.463729i	0.855759	−	0.517374i	$-0.173090\pi$
$263$	10.7403	+	7.52042i	0.662274	+	0.463729i	−0.193486	+	0.981103i	$0.561979\pi$
$264$		0			0
$265$	−2.83530	+	4.22708i	−0.174171	+	0.259667i
$266$		0			0
$267$	7.53768	+	7.53768i	0.461298	+	0.461298i
$268$		0			0
$269$	−3.83980	−	21.7766i	−0.234117	−	1.32774i	−0.844465	−	0.535610i	$-0.820082\pi$
$269$	−3.83980	−	21.7766i	−0.234117	−	1.32774i	0.610348	−	0.792133i	$-0.291029\pi$
$270$		0			0
$271$	−13.4605	+	11.2947i	−0.817665	+	0.686102i	−0.952424	−	0.304776i	$-0.901418\pi$
$271$	−13.4605	+	11.2947i	−0.817665	+	0.686102i	0.134759	+	0.990878i	$0.456974\pi$
$272$		0			0
$273$	2.22610	+	8.30792i	0.134730	+	0.502818i
$274$		0			0
$275$	−7.20106	+	6.55172i	−0.434240	+	0.395084i
$276$		0			0
$277$	7.34661	−	27.4179i	0.441415	−	1.64738i	−0.283818	−	0.958878i	$-0.591601\pi$
$277$	7.34661	−	27.4179i	0.441415	−	1.64738i	0.725233	−	0.688504i	$-0.241732\pi$
$278$		0			0
$279$	−6.13935	+	34.8180i	−0.367554	+	2.08450i
$280$		0			0
$281$	−7.97279	+	9.50160i	−0.475617	+	0.566818i	−0.949499	−	0.313770i	$-0.898408\pi$
$281$	−7.97279	+	9.50160i	−0.475617	+	0.566818i	0.473882	+	0.880588i	$0.342852\pi$
$282$		0			0
$283$	5.66899	−	2.64349i	0.336987	−	0.157139i	−0.246757	−	0.969077i	$-0.579365\pi$
$283$	5.66899	−	2.64349i	0.336987	−	0.157139i	0.583744	+	0.811938i	$0.301587\pi$
$284$		0			0
$285$	−27.1199	+	3.32703i	−1.60644	+	0.197076i
$286$		0			0
$287$	2.97294	−	1.38630i	0.175487	−	0.0818310i
$288$		0			0
$289$	9.37429	−	11.1718i	0.551429	−	0.657167i
$290$		0			0
$291$	−7.91553	+	44.8912i	−0.464017	+	2.63157i
$292$		0			0
$293$	−0.358571	+	1.33820i	−0.0209479	+	0.0781788i	−0.975609	−	0.219518i	$-0.929552\pi$
$293$	−0.358571	+	1.33820i	−0.0209479	+	0.0781788i	0.954661	+	0.297696i	$0.0962183\pi$
$294$		0			0
$295$	4.46250	+	7.38347i	0.259817	+	0.429882i
$296$		0			0
$297$	−2.62554	−	9.79865i	−0.152349	−	0.568575i
$298$		0			0
$299$	−34.6975	+	29.1147i	−2.00661	+	1.68375i
$300$		0			0
$301$	−1.04444	−	5.92333i	−0.0602007	−	0.341415i
$302$		0			0
$303$	−21.8616	−	21.8616i	−1.25591	−	1.25591i
$304$		0			0
$305$	2.05127	+	10.4089i	0.117456	+	0.596011i
$306$		0			0
$307$	15.5890	+	10.9155i	0.889709	+	0.622981i	0.926480	−	0.376343i	$-0.122819\pi$
$307$	15.5890	+	10.9155i	0.889709	+	0.622981i	−0.0367718	+	0.999324i	$0.511707\pi$
$308$		0			0
$309$	21.9936	+	26.2110i	1.25117	+	1.49109i
$310$		0			0
$311$	−2.39221	+	4.14342i	−0.135650	+	0.234952i	−0.925845	−	0.377903i	$-0.876645\pi$
$311$	−2.39221	+	4.14342i	−0.135650	+	0.234952i	0.790196	+	0.612854i	$0.209979\pi$
$312$		0			0
$313$	5.28008	−	11.3232i	0.298448	−	0.640023i	−0.698707	−	0.715408i	$-0.746241\pi$
$313$	5.28008	−	11.3232i	0.298448	−	0.640023i	0.997155	+	0.0753849i	$0.0240185\pi$
$314$		0			0
$315$	−0.412684	+	6.12976i	−0.0232521	+	0.345373i
$316$		0			0
$317$	8.62083	+	12.3118i	0.484194	+	0.691501i	0.984705	−	0.174229i	$-0.0557434\pi$
$317$	8.62083	+	12.3118i	0.484194	+	0.691501i	−0.500511	+	0.865730i	$0.666855\pi$
$318$		0			0
$319$	2.98783	+	2.50709i	0.167286	+	0.140370i
$320$		0			0
$321$	11.3991	+	4.14892i	0.636234	+	0.231570i
$322$		0			0
$323$	−1.85003	−	6.51806i	−0.102939	−	0.362675i
$324$		0			0
$325$	19.9354	+	18.3979i	1.10582	+	1.02053i
$326$		0			0
$327$	0.613114	+	7.00793i	0.0339053	+	0.387539i
$328$		0			0
$329$	−3.68336	−	0.649475i	−0.203070	−	0.0358067i
$330$		0			0
$331$	7.93671	−	4.58226i	0.436241	−	0.251864i	−0.265761	−	0.964039i	$-0.585623\pi$
$331$	7.93671	−	4.58226i	0.436241	−	0.251864i	0.702002	+	0.712175i	$0.252290\pi$
$332$		0			0
$333$	−30.4932	−	14.2192i	−1.67101	−	0.779207i
$334$		0			0
$335$	4.24999	−	2.08650i	0.232202	−	0.113998i
$336$		0			0
$337$	−0.361463	+	4.13154i	−0.0196901	+	0.225059i	0.979974	+	0.199127i	$0.0638108\pi$
$337$	−0.361463	+	4.13154i	−0.0196901	+	0.225059i	−0.999664	+	0.0259316i	$0.991745\pi$
$338$		0			0
$339$	55.4690	−	9.78068i	3.01266	−	0.531214i
$340$		0			0
$341$		−	14.1690i		−	0.767294i
$342$		0			0
$343$	5.47035	−	5.47035i	0.295371	−	0.295371i
$344$		0			0
$345$	−48.8064	+	18.8802i	−2.62765	+	1.01648i
$346$		0			0
$347$	−15.8300	−	1.38495i	−0.849800	−	0.0743479i	−0.346070	−	0.938209i	$-0.612484\pi$
$347$	−15.8300	−	1.38495i	−0.849800	−	0.0743479i	−0.503730	+	0.863861i	$0.668040\pi$
$348$		0			0
$349$	−17.1203	−	9.88441i	−0.916428	−	0.529100i	−0.0339345	−	0.999424i	$-0.510804\pi$
$349$	−17.1203	−	9.88441i	−0.916428	−	0.529100i	−0.882494	+	0.470324i	$0.844137\pi$
$350$		0			0
$351$	−26.5619	+	9.66776i	−1.41777	+	0.516027i
$352$		0			0
$353$	7.88893	+	2.11383i	0.419885	+	0.112508i	0.462574	−	0.886580i	$-0.346926\pi$
$353$	7.88893	+	2.11383i	0.419885	+	0.112508i	−0.0426890	+	0.999088i	$0.513592\pi$
$354$		0			0
$355$	0.0945519	+	4.71678i	0.00501829	+	0.250341i
$356$		0			0
$357$	−2.45481	+	0.214768i	−0.129922	+	0.0113667i
$358$		0			0
$359$	8.48419	−	23.3101i	0.447778	−	1.23026i	−0.486489	−	0.873687i	$-0.661723\pi$
$359$	8.48419	−	23.3101i	0.447778	−	1.23026i	0.934267	−	0.356574i	$-0.116055\pi$
$360$		0			0
$361$	18.0382	+	5.96860i	0.949378	+	0.314137i
$362$		0			0
$363$	−8.54045	−	18.3150i	−0.448257	−	0.961291i
$364$		0			0
$365$	−0.553099	−	1.91020i	−0.0289505	−	0.0999845i
$366$		0			0
$367$	0.643886	−	0.450854i	0.0336106	−	0.0235344i	−0.556650	−	0.830747i	$-0.687914\pi$
$367$	0.643886	−	0.450854i	0.0336106	−	0.0235344i	0.590261	+	0.807212i	$0.299025\pi$
$368$		0			0
$369$	14.0911	+	24.4065i	0.733554	+	1.27055i
$370$		0			0
$371$	−0.440265	−	1.20962i	−0.0228574	−	0.0628002i
$372$		0			0
$373$	32.5792	−	8.72958i	1.68689	−	0.452001i	0.717305	−	0.696759i	$-0.245375\pi$
$373$	32.5792	−	8.72958i	1.68689	−	0.452001i	0.969584	+	0.244759i	$0.0787088\pi$
$374$		0			0
$375$	14.9287	+	27.5581i	0.770914	+	1.42309i
$376$		0			0
$377$	6.23369	−	8.90263i	0.321051	−	0.458509i
$378$		0			0
$379$	−30.1605			−1.54924			−0.774620	−	0.632427i	$-0.782059\pi$
$379$	−30.1605			−1.54924			−0.774620	+	0.632427i	$0.782059\pi$
$380$		0			0
$381$	−34.1907			−1.75164
$382$		0			0
$383$	−20.8065	+	29.7148i	−1.06316	+	1.51836i	−0.223914	+	0.974609i	$0.571883\pi$
$383$	−20.8065	+	29.7148i	−1.06316	+	1.51836i	−0.839250	+	0.543746i	$0.817005\pi$
$384$		0			0
$385$	−0.263704	−	2.44797i	−0.0134396	−	0.124760i
$386$		0			0
$387$	49.9141	−	13.3744i	2.53727	−	0.679861i
$388$		0			0
$389$	−1.72044	−	4.72688i	−0.0872299	−	0.239662i	0.888406	−	0.459059i	$-0.151813\pi$
$389$	−1.72044	−	4.72688i	−0.0872299	−	0.239662i	−0.975636	+	0.219397i	$0.929591\pi$
$390$		0			0
$391$	−6.48844	−	11.2383i	−0.328134	−	0.568346i
$392$		0			0
$393$	37.0066	−	25.9123i	1.86674	−	1.30710i
$394$		0			0
$395$	13.4767	−	24.4618i	0.678087	−	1.23081i
$396$		0			0
$397$	6.09277	+	13.0660i	0.305787	+	0.655763i	0.997812	−	0.0661106i	$-0.0210590\pi$
$397$	6.09277	+	13.0660i	0.305787	+	0.655763i	−0.692025	+	0.721873i	$0.743281\pi$
$398$		0			0
$399$	3.36636	−	6.03467i	0.168529	−	0.302111i
$400$		0			0
$401$	−10.6933	+	29.3797i	−0.534000	+	1.46715i	0.320272	+	0.947326i	$0.396226\pi$
$401$	−10.6933	+	29.3797i	−0.534000	+	1.46715i	−0.854272	+	0.519827i	$0.825997\pi$
$402$		0			0
$403$	−39.3310	+	3.44102i	−1.95922	+	0.171409i
$404$		0			0
$405$	−0.0660531	+	0.00132409i	−0.00328221	+	6.57946e-5i
$406$		0			0
$407$	13.0244	+	3.48987i	0.645594	+	0.172986i
$408$		0			0
$409$	−13.1710	+	4.79385i	−0.651264	+	0.237041i	−0.646460	−	0.762948i	$-0.723751\pi$
$409$	−13.1710	+	4.79385i	−0.651264	+	0.237041i	−0.00480363	+	0.999988i	$0.501529\pi$
$410$		0			0
$411$	−5.25870	−	3.03611i	−0.259392	−	0.149760i
$412$		0			0
$413$	−2.17355	−	0.190161i	−0.106953	−	0.00935722i
$414$		0			0
$415$	−2.35509	+	5.32669i	−0.115607	+	0.261477i
$416$		0			0
$417$	−4.78579	+	4.78579i	−0.234361	+	0.234361i
$418$		0			0
$419$			32.1362i			1.56996i	0.619523	+	0.784979i	$0.287326\pi$
$419$			32.1362i			1.56996i	−0.619523	+	0.784979i	$0.712674\pi$
$420$		0			0
$421$	−14.5428	+	2.56429i	−0.708773	+	0.124976i	−0.516402	−	0.856346i	$-0.672729\pi$
$421$	−14.5428	+	2.56429i	−0.708773	+	0.124976i	−0.192371	+	0.981322i	$0.561618\pi$
$422$		0			0
$423$	2.80061	−	32.0112i	0.136170	−	1.55644i
$424$		0			0
$425$	−6.18274	+	4.70943i	−0.299907	+	0.228441i
$426$		0			0
$427$	−2.43168	−	1.13391i	−0.117677	−	0.0548738i
$428$		0			0
$429$	25.6466	−	14.8071i	1.23823	−	0.714893i
$430$		0			0
$431$	15.1442	+	2.67033i	0.729471	+	0.128625i	0.526035	−	0.850463i	$-0.323678\pi$
$431$	15.1442	+	2.67033i	0.729471	+	0.128625i	0.203436	+	0.979088i	$0.434789\pi$
$432$		0			0
$433$	0.313643	+	3.58496i	0.0150727	+	0.172282i	1.00000		0.000688216i	$-0.000219066\pi$
$433$	0.313643	+	3.58496i	0.0150727	+	0.172282i	−0.984927	+	0.172970i	$0.944664\pi$
$434$		0			0
$435$	10.1393	−	7.40680i	0.486140	−	0.355129i
$436$		0			0
$437$	36.2943	+	2.63622i	1.73619	+	0.126108i
$438$		0			0
$439$	6.34143	+	2.30809i	0.302660	+	0.110159i	0.488886	−	0.872348i	$-0.337403\pi$
$439$	6.34143	+	2.30809i	0.302660	+	0.110159i	−0.186226	+	0.982507i	$0.559626\pi$
$440$		0			0
$441$	24.8626	+	20.8622i	1.18393	+	0.993437i
$442$		0			0
$443$	16.8461	+	24.0587i	0.800382	+	1.14306i	0.987014	+	0.160634i	$0.0513538\pi$
$443$	16.8461	+	24.0587i	0.800382	+	1.14306i	−0.186632	+	0.982430i	$0.559757\pi$
$444$		0			0
$445$	−6.40276	+	5.59501i	−0.303520	+	0.265229i
$446$		0			0
$447$	−20.1822	+	43.2808i	−0.954583	+	2.04711i
$448$		0			0
$449$	−6.74086	+	11.6755i	−0.318121	+	0.551002i	−0.980096	−	0.198524i	$-0.936385\pi$
$449$	−6.74086	+	11.6755i	−0.318121	+	0.551002i	0.661975	+	0.749526i	$0.269718\pi$
$450$		0			0
$451$	−7.25987	−	8.65198i	−0.341854	−	0.407406i
$452$		0			0
$453$	−36.7860	−	25.7578i	−1.72836	−	1.21021i
$454$		0			0
$455$	−6.73116	+	1.32651i	−0.315562	+	0.0621876i
$456$		0			0
$457$	12.8668	+	12.8668i	0.601883	+	0.601883i	0.940812	−	0.338929i	$-0.110065\pi$
$457$	12.8668	+	12.8668i	0.601883	+	0.601883i	−0.338929	+	0.940812i	$0.610065\pi$
$458$		0			0
$459$	−1.40627	−	7.97538i	−0.0656392	−	0.372259i
$460$		0			0
$461$	−29.5673	+	24.8099i	−1.37709	+	1.15551i	−0.406813	+	0.913512i	$0.633360\pi$
$461$	−29.5673	+	24.8099i	−1.37709	+	1.15551i	−0.970276	+	0.242003i	$0.922196\pi$
$462$		0			0
$463$	5.50376	+	20.5403i	0.255781	+	0.954589i	0.967654	+	0.252281i	$0.0811806\pi$
$463$	5.50376	+	20.5403i	0.255781	+	0.954589i	−0.711873	+	0.702309i	$0.752153\pi$
$464$		0			0
$465$	−44.2882	−	10.9205i	−2.05382	−	0.506428i
$466$		0			0
$467$	10.1138	−	37.7454i	0.468013	−	1.74665i	−0.178690	−	0.983905i	$-0.557186\pi$
$467$	10.1138	−	37.7454i	0.468013	−	1.74665i	0.646703	−	0.762742i	$-0.276148\pi$
$468$		0			0
$469$	−0.207922	+	1.17919i	−0.00960096	+	0.0544497i
$470$		0			0
$471$	−29.1109	+	34.6930i	−1.34136	+	1.59857i
$472$		0			0
$473$	−18.7690	+	8.75213i	−0.863000	+	0.402424i
$474$		0			0
$475$	−1.19473	−	21.7617i	−0.0548180	−	0.998496i
$476$		0			0
$477$	10.0231	−	4.67385i	0.458927	−	0.214001i
$478$		0			0
$479$	24.5459	−	29.2526i	1.12153	−	1.33659i	0.186321	−	0.982489i	$-0.440344\pi$
$479$	24.5459	−	29.2526i	1.12153	−	1.33659i	0.935208	−	0.354098i	$-0.115212\pi$
$480$		0			0
$481$	6.52432	−	37.0012i	0.297483	−	1.68711i
$482$		0			0
$483$	3.42537	−	12.7837i	0.155860	−	0.581677i
$484$		0			0
$485$	−35.3027	−	8.70490i	−1.60301	−	0.395269i
$486$		0			0
$487$	−1.49664	−	5.58555i	−0.0678194	−	0.253105i	0.923690	−	0.383141i	$-0.125158\pi$
$487$	−1.49664	−	5.58555i	−0.0678194	−	0.253105i	−0.991509	+	0.130035i	$0.958491\pi$
$488$		0			0
$489$	−36.0648	+	30.2620i	−1.63091	+	1.36849i
$490$		0			0
$491$	2.63264	+	14.9304i	0.118809	+	0.673801i	0.984793	+	0.173729i	$0.0555818\pi$
$491$	2.63264	+	14.9304i	0.118809	+	0.673801i	−0.865984	+	0.500071i	$0.833307\pi$
$492$		0			0
$493$	2.20173	+	2.20173i	0.0991610	+	0.0991610i
$494$		0			0
$495$	20.7541	−	4.08999i	0.932825	−	0.183831i
$496$		0			0
$497$	−0.977351	−	0.684348i	−0.0438402	−	0.0306972i
$498$		0			0
$499$	17.1282	+	20.4126i	0.766765	+	0.913795i	0.998255	−	0.0590422i	$-0.0188047\pi$
$499$	17.1282	+	20.4126i	0.766765	+	0.913795i	−0.231490	+	0.972837i	$0.574360\pi$
$500$		0			0
$501$	24.0891	−	41.7235i	1.07622	−	1.86407i
$502$		0			0
$503$	14.7741	−	31.6832i	0.658745	−	1.41268i	−0.238496	−	0.971143i	$-0.576654\pi$
$503$	14.7741	−	31.6832i	0.658745	−	1.41268i	0.897241	−	0.441540i	$-0.145568\pi$
$504$		0			0
$505$	18.5700	−	16.2272i	0.826352	−	0.722103i
$506$		0			0
$507$	−26.4279	−	37.7429i	−1.17370	−	1.67622i
$508$		0			0
$509$	−16.1871	−	13.5826i	−0.717479	−	0.602036i	0.209208	−	0.977871i	$-0.432911\pi$
$509$	−16.1871	−	13.5826i	−0.717479	−	0.602036i	−0.926687	+	0.375835i	$0.877356\pi$
$510$		0			0
$511$	0.472607	+	0.172015i	0.0209069	+	0.00760949i
$512$		0			0
$513$	20.7213	+	9.29270i	0.914869	+	0.410283i
$514$		0			0
$515$	−22.0385	+	16.0993i	−0.971133	+	0.709419i
$516$		0			0
$517$	1.12238	+	12.8289i	0.0493622	+	0.564212i
$518$		0			0
$519$	−27.9068	−	4.92072i	−1.22497	−	0.215996i
$520$		0			0
$521$	9.21756	−	5.32176i	0.403829	−	0.233151i	−0.284306	−	0.958734i	$-0.591763\pi$
$521$	9.21756	−	5.32176i	0.403829	−	0.233151i	0.688135	+	0.725583i	$0.258430\pi$
$522$		0			0
$523$	−24.6979	−	11.5168i	−1.07996	−	0.503596i	−0.200565	−	0.979680i	$-0.564278\pi$
$523$	−24.6979	−	11.5168i	−1.07996	−	0.503596i	−0.879399	+	0.476085i	$0.842056\pi$
$524$		0			0
$525$	−7.85490	−	1.06247i	−0.342816	−	0.0463702i
$526$		0			0
$527$	0.985853	−	11.2684i	0.0429445	−	0.490857i
$528$		0			0
$529$	45.9866	−	8.10867i	1.99942	−	0.352551i
$530$		0			0
$531$		−	18.7452i		−	0.813473i
$532$		0			0
$533$	−22.2535	+	22.2535i	−0.963906	+	0.963906i
$534$		0			0
$535$	−3.91270	+	8.84968i	−0.169161	+	0.382605i
$536$		0			0
$537$	−46.0374	−	4.02775i	−1.98666	−	0.173810i
$538$		0			0
$539$	−11.2644	−	6.50352i	−0.485193	−	0.280126i
$540$		0			0
$541$	35.0592	−	12.7605i	1.50731	−	0.548618i	0.549372	−	0.835578i	$-0.314867\pi$
$541$	35.0592	−	12.7605i	1.50731	−	0.548618i	0.957942	+	0.286960i	$0.0926448\pi$
$542$		0			0
$543$	66.0048	+	17.6859i	2.83254	+	0.758976i
$544$		0			0
$545$	−5.61013	+	0.112460i	−0.240312	+	0.00481725i
$546$		0			0
$547$	0.987335	−	0.0863806i	0.0422154	−	0.00369337i	−0.0660285	−	0.997818i	$-0.521033\pi$
$547$	0.987335	−	0.0863806i	0.0422154	−	0.00369337i	0.108244	+	0.994124i	$0.465477\pi$
$548$		0			0
$549$	7.88401	−	21.6611i	0.336481	−	0.924475i
$550$		0			0
$551$	−8.57555	+	1.64295i	−0.365331	+	0.0699922i
$552$		0			0
$553$	2.98503	+	6.40142i	0.126936	+	0.272216i
$554$		0			0
$555$	20.9467	−	38.0207i	0.889136	−	1.61389i
$556$		0			0
$557$	−24.7602	+	17.3373i	−1.04912	+	0.734605i	−0.965106	−	0.261859i	$-0.915664\pi$
$557$	−24.7602	+	17.3373i	−1.04912	+	0.734605i	−0.0840186	+	0.996464i	$0.526776\pi$
$558$		0			0
$559$	28.8528	+	49.9745i	1.22034	+	2.11369i
$560$		0			0
$561$	2.90186	+	7.97280i	0.122517	+	0.336612i
$562$		0			0
$563$	6.03075	−	1.61593i	0.254166	−	0.0681035i	−0.129486	−	0.991581i	$-0.541333\pi$
$563$	6.03075	−	1.61593i	0.254166	−	0.0681035i	0.383652	+	0.923478i	$0.374666\pi$
$564$		0			0
$565$	4.81192	+	44.6692i	0.202439	+	1.87925i
$566$		0			0
$567$	0.00958352	−	0.0136867i	0.000402470	−	0.000574787i
$568$		0			0
$569$	−9.00137			−0.377357			−0.188679	−	0.982039i	$-0.560420\pi$
$569$	−9.00137			−0.377357			−0.188679	+	0.982039i	$0.560420\pi$
$570$		0			0
$571$	25.6850			1.07488			0.537442	−	0.843301i	$-0.319391\pi$
$571$	25.6850			1.07488			0.537442	+	0.843301i	$0.319391\pi$
$572$		0			0
$573$	7.33424	−	10.4744i	0.306392	−	0.437574i
$574$		0			0
$575$	−12.4108	−	39.8544i	−0.517566	−	1.66204i
$576$		0			0
$577$	26.4244	−	7.08039i	1.10006	−	0.294761i	0.337272	−	0.941407i	$-0.390496\pi$
$577$	26.4244	−	7.08039i	1.10006	−	0.294761i	0.762790	+	0.646647i	$0.223829\pi$
$578$		0			0
$579$	−6.45836	−	17.7442i	−0.268400	−	0.737423i
$580$		0			0
$581$	−0.736464	−	1.27559i	−0.0305537	−	0.0529205i
$582$		0			0
$583$	−3.63060	+	2.54217i	−0.150364	+	0.105286i
$584$		0			0
$585$	−16.3934	−	56.6169i	−0.677785	−	2.34082i
$586$		0			0
$587$	6.60971	+	14.1746i	0.272812	+	0.585047i	0.994208	−	0.107476i	$-0.0342769\pi$
$587$	6.60971	+	14.1746i	0.272812	+	0.585047i	−0.721396	+	0.692523i	$0.756499\pi$
$588$		0			0
$589$	24.5968	+	20.0281i	1.01350	+	0.825243i
$590$		0			0
$591$	22.0820	−	60.6698i	0.908333	−	2.49562i
$592$		0			0
$593$	6.53586	−	0.571813i	0.268395	−	0.0234816i	0.0478364	−	0.998855i	$-0.484767\pi$
$593$	6.53586	−	0.571813i	0.268395	−	0.0234816i	0.220559	+	0.975374i	$0.429212\pi$
$594$		0			0
$595$	−0.0393937	−	1.96518i	−0.00161498	−	0.0805645i
$596$		0			0
$597$	−13.8420	−	3.70895i	−0.566515	−	0.151797i
$598$		0			0
$599$	32.4410	−	11.8076i	1.32551	−	0.482444i	0.420287	−	0.907391i	$-0.361929\pi$
$599$	32.4410	−	11.8076i	1.32551	−	0.482444i	0.905218	+	0.424947i	$0.139707\pi$
$600$		0			0
$601$	18.1802	+	10.4964i	0.741587	+	0.428155i	0.822646	−	0.568554i	$-0.192497\pi$
$601$	18.1802	+	10.4964i	0.741587	+	0.428155i	−0.0810591	+	0.996709i	$0.525830\pi$
$602$		0			0
$603$	−10.2480	−	0.896585i	−0.417331	−	0.0365118i
$604$		0			0
$605$	15.0337	−	5.81561i	0.611206	−	0.236438i
$606$		0			0
$607$	4.59260	−	4.59260i	0.186408	−	0.186408i	−0.607733	−	0.794141i	$-0.707921\pi$
$607$	4.59260	−	4.59260i	0.186408	−	0.186408i	0.794141	+	0.607733i	$0.207921\pi$
$608$		0			0
$609$			3.17556i			0.128680i
$610$		0			0
$611$	35.3384	−	6.23111i	1.42964	−	0.252084i
$612$		0			0
$613$	0.952513	−	10.8873i	0.0384716	−	0.439733i	−0.952393	−	0.304873i	$-0.901386\pi$
$613$	0.952513	−	10.8873i	0.0384716	−	0.439733i	0.990865	−	0.134860i	$-0.0430584\pi$
$614$		0			0
$615$	−32.6390	+	16.0239i	−1.31613	+	0.646146i
$616$		0			0
$617$	8.72745	+	4.06968i	0.351354	+	0.163839i	0.590280	−	0.807199i	$-0.299017\pi$
$617$	8.72745	+	4.06968i	0.351354	+	0.163839i	−0.238926	+	0.971038i	$0.576795\pi$
$618$		0			0
$619$	−22.3619	+	12.9106i	−0.898800	+	0.518923i	−0.876811	−	0.480836i	$-0.840333\pi$
$619$	−22.3619	+	12.9106i	−0.898800	+	0.518923i	−0.0219894	+	0.999758i	$0.507000\pi$
$620$		0			0
$621$	42.8340	+	7.55279i	1.71887	+	0.303083i
$622$		0			0
$623$	−0.187420	−	2.14222i	−0.00750884	−	0.0858264i
$624$		0			0
$625$	−22.7321	+	10.4045i	−0.909283	+	0.416178i
$626$		0			0
$627$	−23.0699	−	5.81804i	−0.921325	−	0.232350i
$628$		0			0
$629$	10.1152	+	3.68165i	0.403321	+	0.146797i
$630$		0			0
$631$	−13.6482	−	11.4522i	−0.543327	−	0.455906i	0.329347	−	0.944209i	$-0.393172\pi$
$631$	−13.6482	−	11.4522i	−0.543327	−	0.455906i	−0.872674	+	0.488303i	$0.837616\pi$
$632$		0			0
$633$	−11.1193	−	15.8800i	−0.441953	−	0.631175i
$634$		0			0
$635$	1.83196	−	27.2108i	0.0726991	−	1.07983i
$636$		0			0
$637$	−15.3172	+	32.8478i	−0.606888	+	1.30148i
$638$		0			0
$639$	5.12531	−	8.87731i	0.202754	−	0.351181i
$640$		0			0
$641$	23.5459	+	28.0609i	0.930008	+	1.10834i	0.993889	+	0.110383i	$0.0352078\pi$
$641$	23.5459	+	28.0609i	0.930008	+	1.10834i	−0.0638810	+	0.997958i	$0.520348\pi$
$642$		0			0
$643$	9.52067	+	6.66644i	0.375458	+	0.262899i	0.746040	−	0.665901i	$-0.231953\pi$
$643$	9.52067	+	6.66644i	0.375458	+	0.262899i	−0.370582	+	0.928800i	$0.620842\pi$
$644$		0			0
$645$	12.8907	+	65.4121i	0.507572	+	2.57560i
$646$		0			0
$647$	10.6708	+	10.6708i	0.419513	+	0.419513i	0.885036	−	0.465523i	$-0.154134\pi$
$647$	10.6708	+	10.6708i	0.419513	+	0.419513i	−0.465523	+	0.885036i	$0.654134\pi$
$648$		0			0
$649$	1.30451	+	7.39824i	0.0512065	+	0.290406i
$650$		0			0
$651$	8.83714	−	7.41524i	0.346355	−	0.290626i
$652$		0			0
$653$	0.278988	+	1.04120i	0.0109176	+	0.0407452i	0.971170	−	0.238389i	$-0.0766193\pi$
$653$	0.278988	+	1.04120i	0.0109176	+	0.0407452i	−0.960252	+	0.279134i	$0.909953\pi$
$654$		0			0
$655$	18.6396	+	30.8403i	0.728309	+	1.20503i
$656$		0			0
$657$	−1.11834	+	4.17372i	−0.0436308	+	0.162832i
$658$		0			0
$659$	−5.83010	+	33.0642i	−0.227109	+	1.28800i	0.631504	+	0.775372i	$0.282438\pi$
$659$	−5.83010	+	33.0642i	−0.227109	+	1.28800i	−0.858613	+	0.512624i	$0.828673\pi$
$660$		0			0
$661$	17.9656	−	21.4106i	0.698781	−	0.832774i	−0.293607	−	0.955926i	$-0.594856\pi$
$661$	17.9656	−	21.4106i	0.698781	−	0.832774i	0.992388	+	0.123152i	$0.0393003\pi$
$662$		0			0
$663$	21.4266	−	9.99138i	0.832139	−	0.388033i
$664$		0			0
$665$	4.62234	+	3.00247i	0.179247	+	0.116431i
$666$		0			0
$667$	−15.1563	+	7.06749i	−0.586853	+	0.273654i
$668$		0			0
$669$	12.4391	−	14.8243i	0.480922	−	0.573140i
$670$		0			0
$671$	−1.60418	+	9.09774i	−0.0619286	+	0.351214i
$672$		0			0
$673$	8.92012	−	33.2904i	0.343846	−	1.28325i	−0.550110	−	0.835092i	$-0.685414\pi$
$673$	8.92012	−	33.2904i	0.343846	−	1.28325i	0.893955	−	0.448156i	$-0.147919\pi$
$674$		0			0
$675$	1.22857	−	26.0207i	0.0472879	−	1.00154i
$676$		0			0
$677$	−11.7610	−	43.8927i	−0.452012	−	1.68693i	−0.696726	−	0.717337i	$-0.745361\pi$
$677$	−11.7610	−	43.8927i	−0.452012	−	1.68693i	0.244714	−	0.969595i	$-0.421306\pi$
$678$		0			0
$679$	7.04420	−	5.91079i	0.270332	−	0.226835i
$680$		0			0
$681$	−8.91815	−	50.5774i	−0.341744	−	1.93813i
$682$		0			0
$683$	−8.67621	−	8.67621i	−0.331986	−	0.331986i	0.521354	−	0.853340i	$-0.325427\pi$
$683$	−8.67621	−	8.67621i	−0.331986	−	0.331986i	−0.853340	+	0.521354i	$0.825427\pi$
$684$		0			0
$685$	2.69806	−	4.02248i	0.103088	−	0.153691i
$686$		0			0
$687$	−14.3987	−	10.0821i	−0.549345	−	0.384656i
$688$		0			0
$689$	7.93839	+	9.46061i	0.302429	+	0.360420i
$690$		0			0
$691$	−4.42238	+	7.65978i	−0.168235	+	0.291392i	−0.937799	−	0.347177i	$-0.887140\pi$
$691$	−4.42238	+	7.65978i	−0.168235	+	0.291392i	0.769564	+	0.638569i	$0.220473\pi$
$692$		0			0
$693$	−2.26088	+	4.84847i	−0.0858838	+	0.184178i
$694$		0			0
$695$	−3.55236	−	4.06522i	−0.134749	−	0.154202i
$696$		0			0
$697$	−5.17166	−	7.38590i	−0.195891	−	0.279761i
$698$		0			0
$699$	−15.4310	−	12.9482i	−0.583654	−	0.489744i
$700$		0			0
$701$	3.14341	+	1.14411i	0.118725	+	0.0432124i	0.400700	−	0.916210i	$-0.368767\pi$
$701$	3.14341	+	1.14411i	0.118725	+	0.0432124i	−0.281974	+	0.959422i	$0.590989\pi$
$702$		0			0
$703$	−24.4684	+	17.6768i	−0.922845	+	0.666695i
$704$		0			0
$705$	40.9644	+	6.37941i	1.54281	+	0.240262i
$706$		0			0
$707$	0.543576	+	6.21310i	0.0204433	+	0.233668i
$708$		0			0
$709$	−9.47050	−	1.66990i	−0.355672	−	0.0627146i	−0.00704250	−	0.999975i	$-0.502242\pi$
$709$	−9.47050	−	1.66990i	−0.355672	−	0.0627146i	−0.348629	+	0.937261i	$0.613353\pi$
$710$		0			0
$711$	−52.5528	+	30.3414i	−1.97088	+	1.13789i
$712$		0			0
$713$	55.0592	+	25.6745i	2.06198	+	0.961518i
$714$		0			0
$715$	10.4101	+	21.2043i	0.389316	+	0.792997i
$716$		0			0
$717$	0.558890	−	6.38815i	0.0208721	−	0.238570i
$718$		0			0
$719$	−17.5942	+	3.10234i	−0.656154	+	0.115698i	−0.491806	−	0.870705i	$-0.663663\pi$
$719$	−17.5942	+	3.10234i	−0.656154	+	0.115698i	−0.164348	+	0.986402i	$0.552552\pi$
$720$		0			0
$721$		−	6.90235i		−	0.257057i
$722$		0			0
$723$	−41.0652	+	41.0652i	−1.52723	+	1.52723i
$724$		0			0
$725$	5.35146	+	8.46622i	0.198748	+	0.314428i
$726$		0			0
$727$	28.5905	+	2.50134i	1.06036	+	0.0927696i	0.603968	−	0.797008i	$-0.293585\pi$
$727$	28.5905	+	2.50134i	1.06036	+	0.0927696i	0.456393	+	0.889778i	$0.349141\pi$
$728$		0			0
$729$	−37.8207	−	21.8358i	−1.40077	−	0.808734i
$730$		0			0
$731$	−15.5356	+	5.65451i	−0.574606	+	0.209139i
$732$		0			0
$733$	−5.21597	−	1.39762i	−0.192656	−	0.0516221i	0.161201	−	0.986922i	$-0.448463\pi$
$733$	−5.21597	−	1.39762i	−0.192656	−	0.0516221i	−0.353857	+	0.935300i	$0.615130\pi$
$734$		0			0
$735$	−29.0100	+	30.1969i	−1.07005	+	1.11383i
$736$		0			0
$737$	4.10701	−	0.359317i	0.151284	−	0.0132356i
$738$		0			0
$739$	−5.46375	+	15.0115i	−0.200987	+	0.552208i	−0.998708	−	0.0508195i	$-0.983817\pi$
$739$	−5.46375	+	15.0115i	−0.200987	+	0.552208i	0.797721	+	0.603027i	$0.206039\pi$
$740$		0			0
$741$	−10.5474	+	65.4516i	−0.387467	+	2.40443i
$742$		0			0
$743$	10.7020	+	22.9504i	0.392617	+	0.841969i	0.998908	+	0.0467262i	$0.0148788\pi$
$743$	10.7020	+	22.9504i	0.392617	+	0.841969i	−0.606291	+	0.795243i	$0.707343\pi$
$744$		0			0
$745$	−33.3638	−	18.3811i	−1.22235	−	0.673430i
$746$		0			0
$747$	10.3660	−	7.25834i	0.379271	−	0.265569i
$748$		0			0
$749$	−1.22355	−	2.11925i	−0.0447075	−	0.0774356i
$750$		0			0
$751$	8.14322	+	22.3733i	0.297150	+	0.816414i	0.994973	+	0.100143i	$0.0319301\pi$
$751$	8.14322	+	22.3733i	0.297150	+	0.816414i	−0.697823	+	0.716270i	$0.745848\pi$
$752$		0			0
$753$	−75.8307	+	20.3188i	−2.76342	+	0.740457i
$754$		0			0
$755$	22.4705	−	27.8961i	0.817784	−	1.01524i
$756$		0			0
$757$	−11.5952	+	16.5597i	−0.421435	+	0.601872i	−0.972589	−	0.232532i	$-0.925299\pi$
$757$	−11.5952	+	16.5597i	−0.421435	+	0.601872i	0.551153	+	0.834404i	$0.314188\pi$
$758$		0			0
$759$	−45.5683			−1.65402
$760$		0			0
$761$	−45.0706			−1.63381			−0.816904	−	0.576774i	$-0.804311\pi$
$761$	−45.0706			−1.63381			−0.816904	+	0.576774i	$0.804311\pi$
$762$		0			0
$763$	0.813963	−	1.16246i	0.0294674	−	0.0420839i
$764$		0			0
$765$	16.7899	−	1.80867i	0.607041	−	0.0653925i
$766$		0			0
$767$	20.2196	−	5.41782i	0.730087	−	0.195626i
$768$		0			0
$769$	−9.43096	−	25.9114i	−0.340089	−	0.934388i	−0.985368	−	0.170440i	$-0.945481\pi$
$769$	−9.43096	−	25.9114i	−0.340089	−	0.934388i	0.645279	−	0.763947i	$-0.276741\pi$
$770$		0			0
$771$	−9.46451	−	16.3930i	−0.340856	−	0.590380i
$772$		0			0
$773$	−30.4826	+	21.3441i	−1.09638	+	0.767695i	−0.974396	−	0.224837i	$-0.927815\pi$
$773$	−30.4826	+	21.3441i	−1.09638	+	0.767695i	−0.121986	+	0.992532i	$0.538926\pi$
$774$		0			0
$775$	11.0641	−	34.6618i	0.397435	−	1.24509i
$776$		0			0
$777$	4.63960	+	9.94965i	0.166445	+	0.356942i
$778$		0			0
$779$	25.2815	−	0.373159i	0.905802	−	0.0133698i
$780$		0			0
$781$	−1.40504	+	3.86032i	−0.0502763	+	0.138133i
$782$		0			0
$783$	−10.3966	+	0.909583i	−0.371543	+	0.0325058i
$784$		0			0
$785$	−26.0508	−	25.0269i	−0.929792	−	0.893248i
$786$		0			0
$787$	9.49698	+	2.54471i	0.338531	+	0.0907090i	0.424080	−	0.905625i	$-0.360598\pi$
$787$	9.49698	+	2.54471i	0.338531	+	0.0907090i	−0.0855488	+	0.996334i	$0.527264\pi$
$788$		0			0
$789$	34.5387	−	12.5711i	1.22961	−	0.447542i
$790$		0			0
$791$	−9.84006	−	5.68116i	−0.349872	−	0.201999i
$792$		0			0
$793$	25.6435	+	2.24352i	0.910629	+	0.0796697i
$794$		0			0
$795$	5.14787	+	13.3075i	0.182576	+	0.471970i
$796$		0			0
$797$	16.9122	−	16.9122i	0.599062	−	0.599062i	−0.341001	−	0.940063i	$-0.610766\pi$
$797$	16.9122	−	16.9122i	0.599062	−	0.599062i	0.940063	+	0.341001i	$0.110766\pi$
$798$		0			0
$799$			10.2807i			0.363704i
$800$		0			0
$801$	18.1944	−	3.20816i	0.642866	−	0.113355i
$802$		0			0
$803$	0.150925	−	1.72508i	0.00532603	−	0.0608768i
$804$		0			0
$805$	9.99039	+	3.41105i	0.352115	+	0.120224i
$806$		0			0
$807$	−56.1804	−	26.1973i	−1.97764	−	0.922190i
$808$		0			0
$809$	−35.5738	+	20.5385i	−1.25071	+	0.722096i	−0.971250	−	0.238063i	$-0.923488\pi$
$809$	−35.5738	+	20.5385i	−1.25071	+	0.722096i	−0.279457	+	0.960158i	$0.590154\pi$
$810$		0			0
$811$	2.33829	+	0.412304i	0.0821086	+	0.0144780i	0.214552	−	0.976713i	$-0.431171\pi$
$811$	2.33829	+	0.412304i	0.0821086	+	0.0144780i	−0.132443	+	0.991191i	$0.542282\pi$
$812$		0			0
$813$	4.29311	+	49.0705i	0.150566	+	1.72098i
$814$		0			0
$815$	−22.1517	−	30.3238i	−0.775941	−	1.06219i
$816$		0			0
$817$	11.3369	−	44.9536i	0.396628	−	1.57273i
$818$		0			0
$819$	14.0077	+	5.09839i	0.489469	+	0.178152i
$820$		0			0
$821$	−13.3996	−	11.2436i	−0.467649	−	0.392404i	0.378287	−	0.925688i	$-0.376513\pi$
$821$	−13.3996	−	11.2436i	−0.467649	−	0.392404i	−0.845936	+	0.533284i	$0.820958\pi$
$822$		0			0
$823$	−1.53121	−	2.18680i	−0.0533748	−	0.0762271i	0.791577	−	0.611069i	$-0.209260\pi$
$823$	−1.53121	−	2.18680i	−0.0533748	−	0.0762271i	−0.844952	+	0.534842i	$0.820371\pi$
$824$		0			0
$825$	3.46627	+	27.0706i	0.120680	+	0.942476i
$826$		0			0
$827$	−16.9029	+	36.2485i	−0.587773	+	1.26048i	0.357412	+	0.933947i	$0.383659\pi$
$827$	−16.9029	+	36.2485i	−0.587773	+	1.26048i	−0.945185	+	0.326536i	$0.894118\pi$
$828$		0			0
$829$	7.85131	−	13.5989i	0.272687	−	0.472308i	−0.696862	−	0.717206i	$-0.745421\pi$
$829$	7.85131	−	13.5989i	0.272687	−	0.472308i	0.969549	+	0.244897i	$0.0787542\pi$
$830$		0			0
$831$	−51.1479	−	60.9557i	−1.77430	−	2.11453i
$832$		0			0
$833$	−8.50590	−	5.95590i	−0.294712	−	0.206360i
$834$		0			0
$835$	31.9151	+	21.4070i	1.10447	+	0.740818i
$836$		0			0
$837$	26.8082	+	26.8082i	0.926628	+	0.926628i
$838$		0			0
$839$	−2.39204	−	13.5659i	−0.0825824	−	0.468348i	−0.997852	−	0.0655066i	$-0.979134\pi$
$839$	−2.39204	−	13.5659i	−0.0825824	−	0.468348i	0.915270	−	0.402842i	$-0.131977\pi$
$840$		0			0
$841$	−19.1415	+	16.0616i	−0.660050	+	0.553848i
$842$		0			0
$843$	8.99931	+	33.5859i	0.309953	+	1.15676i
$844$		0			0
$845$	31.4538	−	19.0104i	1.08205	−	0.653978i
$846$		0			0
$847$	−1.05511	+	3.93771i	−0.0362539	+	0.135301i
$848$		0			0
$849$	3.04488	−	17.2684i	0.104500	−	0.592649i
$850$		0			0
$851$	−37.1617	+	44.2876i	−1.27389	+	1.51816i
$852$		0			0
$853$	−31.3419	+	14.6149i	−1.07312	+	0.500406i	−0.877157	−	0.480204i	$-0.840563\pi$
$853$	−31.3419	+	14.6149i	−1.07312	+	0.500406i	−0.195968	+	0.980610i	$0.562785\pi$
$854$		0			0
$855$	−22.2361	+	41.8095i	−0.760459	+	1.42986i
$856$		0			0
$857$	−28.6677	+	13.3680i	−0.979269	+	0.456641i	−0.845269	−	0.534341i	$-0.820560\pi$
$857$	−28.6677	+	13.3680i	−0.979269	+	0.456641i	−0.134000	+	0.990981i	$0.542782\pi$
$858$		0			0
$859$	2.57689	−	3.07102i	0.0879223	−	0.104782i	−0.720290	−	0.693673i	$-0.755991\pi$
$859$	2.57689	−	3.07102i	0.0879223	−	0.104782i	0.808212	+	0.588892i	$0.200436\pi$
$860$		0			0
$861$	1.59680	−	9.05590i	0.0544188	−	0.308624i
$862$		0			0
$863$	8.48135	−	31.6528i	0.288708	−	1.07747i	−0.657378	−	0.753561i	$-0.728335\pi$
$863$	8.48135	−	31.6528i	0.288708	−	1.07747i	0.946087	−	0.323914i	$-0.104999\pi$
$864$		0			0
$865$	5.41143	−	21.9461i	0.183994	−	0.746188i
$866$		0			0
$867$	−10.5812	−	39.4898i	−0.359358	−	1.34114i
$868$		0			0
$869$	18.6297	−	15.6322i	0.631969	−	0.530285i
$870$		0			0
$871$	−1.99482	−	11.3132i	−0.0675919	−	0.383333i
$872$		0			0
$873$	55.8634	+	55.8634i	1.89069	+	1.89069i
$874$		0			0
$875$	1.26644	−	6.19442i	0.0428136	−	0.209410i
$876$		0			0
$877$	5.17514	+	3.62367i	0.174752	+	0.122363i	0.657680	−	0.753297i	$-0.271538\pi$
$877$	5.17514	+	3.62367i	0.174752	+	0.122363i	−0.482928	+	0.875660i	$0.660427\pi$
$878$		0			0
$879$	2.49641	+	2.97511i	0.0842019	+	0.100348i
$880$		0			0
$881$	−10.0488	+	17.4050i	−0.338552	+	0.586389i	−0.984161	−	0.177280i	$-0.943270\pi$
$881$	−10.0488	+	17.4050i	−0.338552	+	0.586389i	0.645609	+	0.763668i	$0.276604\pi$
$882$		0			0
$883$	0.279670	−	0.599754i	0.00941164	−	0.0201833i	−0.901546	−	0.432684i	$-0.857567\pi$
$883$	0.279670	−	0.599754i	0.00941164	−	0.0201833i	0.910957	+	0.412500i	$0.135344\pi$
$884$		0			0
$885$	24.1302	+	1.62456i	0.811127	+	0.0546090i
$886$		0			0
$887$	−10.4759	−	14.9611i	−0.351746	−	0.502346i	0.603820	−	0.797120i	$-0.293644\pi$
$887$	−10.4759	−	14.9611i	−0.351746	−	0.502346i	−0.955567	+	0.294774i	$0.904755\pi$
$888$		0			0
$889$	5.28360	+	4.43347i	0.177206	+	0.148694i
$890$		0			0
$891$	−0.0540593	−	0.0196760i	−0.00181105	−	0.000659170i
$892$		0			0
$893$	−23.8569	−	16.1854i	−0.798341	−	0.541623i
$894$		0			0
$895$	5.67221	−	36.4232i	0.189601	−	1.21749i
$896$		0			0
$897$	11.0665	+	126.491i	0.369500	+	4.22340i
$898$		0			0
$899$	−14.3554	−	2.53124i	−0.478778	−	0.0844216i
$900$		0			0
$901$	−3.06423	+	1.76913i	−0.102084	+	0.0589384i
$902$		0			0
$903$	−15.2813	−	7.12579i	−0.508530	−	0.237131i
$904$		0			0
$905$	−17.6120	+	51.5825i	−0.585442	+	1.71466i
$906$		0			0
$907$	−1.66458	+	19.0262i	−0.0552714	+	0.631755i	0.917153	+	0.398536i	$0.130482\pi$
$907$	−1.66458	+	19.0262i	−0.0552714	+	0.631755i	−0.972424	+	0.233219i	$0.925074\pi$
$908$		0			0
$909$	−52.7692	+	9.30463i	−1.75024	+	0.308615i
$910$		0			0
$911$		−	22.4508i		−	0.743829i	−0.928267	−	0.371915i	$-0.878701\pi$
$911$		−	22.4508i		−	0.743829i	0.928267	−	0.371915i	$-0.121299\pi$
$912$		0			0
$913$	−3.58606	+	3.58606i	−0.118681	+	0.118681i
$914$		0			0
$915$	27.2005	+	12.0261i	0.899221	+	0.397572i
$916$		0			0
$917$	−9.07878	−	0.794290i	−0.299808	−	0.0262298i
$918$		0			0
$919$	10.9875	+	6.34363i	0.362444	+	0.209257i	0.670152	−	0.742224i	$-0.266229\pi$
$919$	10.9875	+	6.34363i	0.362444	+	0.209257i	−0.307708	+	0.951481i	$0.599562\pi$
$920$		0			0
$921$	50.1312	−	18.2463i	1.65188	−	0.601235i
$922$		0			0
$923$	11.0569	+	2.96268i	0.363942	+	0.0975179i
$924$		0			0
$925$	29.1365	+	18.7076i	0.958004	+	0.615104i
$926$		0			0
$927$	59.0753	−	5.16842i	1.94029	−	0.169753i
$928$		0			0
$929$	−13.3640	+	36.7172i	−0.438458	+	1.20465i	0.502038	+	0.864846i	$0.332584\pi$
$929$	−13.3640	+	36.7172i	−0.438458	+	1.20465i	−0.940495	+	0.339807i	$0.889638\pi$
$930$		0			0
$931$	27.2123	−	10.3618i	0.891848	−	0.339594i
$932$		0			0
$933$	5.66822	+	12.1555i	0.185569	+	0.397954i
$934$		0			0
$935$	−6.50067	+	1.88227i	−0.212595	+	0.0615568i
$936$		0			0
$937$	−2.80599	+	1.96478i	−0.0916678	+	0.0641865i	−0.618512	−	0.785776i	$-0.712264\pi$
$937$	−2.80599	+	1.96478i	−0.0916678	+	0.0641865i	0.526844	+	0.849962i	$0.323375\pi$
$938$		0			0
$939$	−17.5119	−	30.3314i	−0.571478	−	0.989829i
$940$		0			0
$941$	−2.99658	−	8.23305i	−0.0976858	−	0.268390i	0.881218	−	0.472709i	$-0.156724\pi$
$941$	−2.99658	−	8.23305i	−0.0976858	−	0.268390i	−0.978904	+	0.204320i	$0.934502\pi$
$942$		0			0
$943$	46.7757	−	12.5335i	1.52323	−	0.408147i
$944$		0			0
$945$	5.13059	+	4.13271i	0.166898	+	0.134437i
$946$		0			0
$947$	−12.4336	+	17.7571i	−0.404039	+	0.577027i	−0.968681	−	0.248309i	$-0.920125\pi$
$947$	−12.4336	+	17.7571i	−0.404039	+	0.577027i	0.564642	+	0.825336i	$0.309014\pi$
$948$		0			0
$949$	−4.82522			−0.156633
$950$		0			0
$951$	42.1335			1.36627
$952$		0			0
$953$	5.37596	−	7.67767i	0.174145	−	0.248704i	−0.722586	−	0.691281i	$-0.757047\pi$
$953$	5.37596	−	7.67767i	0.174145	−	0.248704i	0.896731	+	0.442577i	$0.145936\pi$
$954$		0			0
$955$	7.94310	+	6.39820i	0.257033	+	0.207041i
$956$		0			0
$957$	10.5613	−	2.82988i	0.341397	−	0.0914770i
$958$		0			0
$959$	0.418955	+	1.15107i	0.0135288	+	0.0371700i
$960$		0			0
$961$	10.9771	+	19.0128i	0.354099	+	0.613318i
$962$		0			0
$963$	17.2219	−	12.0589i	0.554967	−	0.388592i
$964$		0			0
$965$	14.4678	−	4.18916i	0.465735	−	0.134854i
$966$		0			0
$967$	−1.83782	−	3.94122i	−0.0591004	−	0.126741i	0.874539	−	0.484954i	$-0.161164\pi$
$967$	−1.83782	−	3.94122i	−0.0591004	−	0.126741i	−0.933640	+	0.358213i	$0.883386\pi$
$968$		0			0
$969$	−17.9423	−	6.23216i	−0.576390	−	0.200206i
$970$		0			0
$971$	−11.4064	+	31.3387i	−0.366047	+	1.00571i	0.610803	+	0.791783i	$0.290847\pi$
$971$	−11.4064	+	31.3387i	−0.366047	+	1.00571i	−0.976850	+	0.213924i	$0.931376\pi$
$972$		0			0
$973$	1.36013	−	0.118996i	0.0436038	−	0.00381484i
$974$		0			0
$975$	74.3021	−	16.1961i	2.37957	−	0.518690i
$976$		0			0
$977$	−14.9384	−	4.00274i	−0.477923	−	0.128059i	0.0118126	−	0.999930i	$-0.496240\pi$
$977$	−14.9384	−	4.00274i	−0.477923	−	0.128059i	−0.489735	+	0.871871i	$0.662907\pi$
$978$		0			0
$979$	−6.95757	+	2.53235i	−0.222365	+	0.0809342i
$980$		0			0
$981$	10.5587	+	6.09604i	0.337112	+	0.194632i
$982$		0			0
$983$	−26.5960	−	2.32684i	−0.848279	−	0.0742148i	−0.345278	−	0.938500i	$-0.612215\pi$
$983$	−26.5960	−	2.32684i	−0.848279	−	0.0742148i	−0.503001	+	0.864286i	$0.667771\pi$
$984$		0			0
$985$	47.1011	+	20.8248i	1.50077	+	0.663533i
$986$		0			0
$987$	−7.41391	+	7.41391i	−0.235987	+	0.235987i
$988$		0			0
$989$		−	88.7934i		−	2.82346i
$990$		0			0
$991$	20.0972	−	3.54368i	0.638409	−	0.112569i	0.154931	−	0.987925i	$-0.450485\pi$
$991$	20.0972	−	3.54368i	0.638409	−	0.112569i	0.483478	+	0.875357i	$0.339373\pi$
$992$		0			0
$993$	2.23911	−	25.5932i	0.0710561	−	0.812174i
$994$		0			0
$995$	3.69345	−	10.8175i	0.117090	−	0.342937i
$996$		0			0
$997$	14.9826	+	6.98648i	0.474502	+	0.221264i	0.645132	−	0.764071i	$-0.276802\pi$
$997$	14.9826	+	6.98648i	0.474502	+	0.221264i	−0.170630	+	0.985335i	$0.554580\pi$
$998$		0			0
$999$	−31.2455	+	18.0396i	−0.988565	+	0.570748i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bh.a.357.9	yes	120
5.3	odd	4	inner	380.2.bh.a.53.9	yes	120
19.14	odd	18	inner	380.2.bh.a.337.9	yes	120
95.33	even	36	inner	380.2.bh.a.33.9	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bh.a.33.9	✓	120	95.33	even	36	inner
380.2.bh.a.53.9	yes	120	5.3	odd	4	inner
380.2.bh.a.337.9	yes	120	19.14	odd	18	inner
380.2.bh.a.357.9	yes	120	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(1.60791 - 2.29633i) q^{3} +(1.74139 + 1.40270i) q^{5} +(-0.546238 + 0.146364i) q^{7} +(-1.66171 - 4.56550i) q^{9} +O(q^{10})\)	\(q+(1.60791 - 2.29633i) q^{3} +(1.74139 + 1.40270i) q^{5} +(-0.546238 + 0.146364i) q^{7} +(-1.66171 - 4.56550i) q^{9} +(0.973552 + 1.68624i) q^{11} +(4.44432 - 3.11195i) q^{13} +(6.02105 - 1.74340i) q^{15} +(0.656923 + 1.40878i) q^{17} +(-4.30338 - 0.693479i) q^{19} +(-0.542200 + 1.48968i) q^{21} +(-8.31664 + 0.727612i) q^{23} +(1.06488 + 4.88529i) q^{25} +(-5.03242 - 1.34843i) q^{27} +(1.88234 - 0.685117i) q^{29} +(-6.30203 - 3.63848i) q^{31} +(5.43755 + 0.475724i) q^{33} +(-1.15652 - 0.511330i) q^{35} +(4.89676 - 4.89676i) q^{37} -15.2094i q^{39} +(-5.71247 + 1.00726i) q^{41} +(-0.926985 + 10.5955i) q^{43} +(3.51034 - 10.2812i) q^{45} +(5.99419 + 2.79514i) q^{47} +(-5.78522 + 3.34010i) q^{49} +(4.29129 + 0.756670i) q^{51} +(0.198390 + 2.26761i) q^{53} +(-0.669954 + 4.30200i) q^{55} +(-8.51190 + 8.76694i) q^{57} +(3.62555 + 1.31959i) q^{59} +(3.63452 + 3.04972i) q^{61} +(1.57591 + 2.25063i) q^{63} +(12.1044 + 0.814927i) q^{65} +(0.894831 - 1.91897i) q^{67} +(-11.7016 + 20.2677i) q^{69} +(1.35617 + 1.61623i) q^{71} +(-0.728519 - 0.510115i) q^{73} +(12.9305 + 5.40978i) q^{75} +(-0.778595 - 0.778595i) q^{77} +(-2.16887 - 12.3003i) q^{79} +(-0.0226334 + 0.0189917i) q^{81} +(0.674124 + 2.51586i) q^{83} +(-0.832128 + 3.37469i) q^{85} +(1.45338 - 5.42409i) q^{87} +(-0.660318 + 3.74485i) q^{89} +(-1.97218 + 2.35035i) q^{91} +(-18.4882 + 8.62121i) q^{93} +(-6.52112 - 7.24396i) q^{95} +(-14.7372 + 6.87208i) q^{97} +(6.08078 - 7.24679i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 6 q^{7}+O(q^{10}) \) 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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