LMFDB - Embedded newform 380.2.bh.a.33.8

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			33.8
Character	$\chi$	$=$	380.33
Dual form			380.2.bh.a.357.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.935220 + 1.33563i) q^{3} +(-0.351064 + 2.20834i) q^{5} +(-4.10912 - 1.10104i) q^{7} +(0.116783 - 0.320859i) q^{9} +O(q^{10})$	\(q+(0.935220 + 1.33563i) q^{3} +(-0.351064 + 2.20834i) q^{5} +(-4.10912 - 1.10104i) q^{7} +(0.116783 - 0.320859i) q^{9} +(-3.07824 + 5.33167i) q^{11} +(4.00743 + 2.80603i) q^{13} +(-3.27785 + 1.59639i) q^{15} +(-1.67016 + 3.58167i) q^{17} +(3.36426 - 2.77160i) q^{19} +(-2.37235 - 6.51798i) q^{21} +(-3.80191 - 0.332624i) q^{23} +(-4.75351 - 1.55053i) q^{25} +(5.26261 - 1.41011i) q^{27} +(-2.08795 - 0.759952i) q^{29} +(2.56290 - 1.47969i) q^{31} +(-9.99998 + 0.874885i) q^{33} +(3.87402 - 8.68779i) q^{35} +(2.93721 + 2.93721i) q^{37} +7.97671i q^{39} +(11.8292 + 2.08580i) q^{41} +(0.317560 + 3.62973i) q^{43} +(0.667567 + 0.370539i) q^{45} +(-5.68035 + 2.64879i) q^{47} +(9.61040 + 5.54857i) q^{49} +(-6.34576 + 1.11893i) q^{51} +(0.309521 - 3.53784i) q^{53} +(-10.6935 - 8.66955i) q^{55} +(6.84816 + 1.90136i) q^{57} +(10.3122 - 3.75333i) q^{59} +(2.42752 - 2.03693i) q^{61} +(-0.833153 + 1.18987i) q^{63} +(-7.60353 + 7.86466i) q^{65} +(0.868295 + 1.86206i) q^{67} +(-3.11136 - 5.38903i) q^{69} +(-1.80576 + 2.15203i) q^{71} +(0.0922302 - 0.0645803i) q^{73} +(-2.37463 - 7.79903i) q^{75} +(18.5192 - 18.5192i) q^{77} +(1.95703 - 11.0989i) q^{79} +(6.02039 + 5.05170i) q^{81} +(-2.25226 + 8.40553i) q^{83} +(-7.32320 - 4.94567i) q^{85} +(-0.937677 - 3.49946i) q^{87} +(-0.149779 - 0.849439i) q^{89} +(-13.3775 - 15.9426i) q^{91} +(4.37320 + 2.03926i) q^{93} +(4.93956 + 8.40243i) q^{95} +(11.9968 + 5.59420i) q^{97} +(1.35123 + 1.61033i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	0.935220	+	1.33563i	0.539949	+	0.771128i	0.992713	−	0.120503i	$-0.0384508\pi$
$3$	0.935220	+	1.33563i	0.539949	+	0.771128i	−0.452764	+	0.891631i	$0.649562\pi$
$4$		0			0
$5$	−0.351064	+	2.20834i	−0.157000	+	0.987599i
$5$	−0.351064	+	2.20834i	−0.157000	+	0.987599i
$6$		0			0
$7$	−4.10912	−	1.10104i	−1.55310	−	0.416152i	−0.622630	−	0.782517i	$-0.713936\pi$
$7$	−4.10912	−	1.10104i	−1.55310	−	0.416152i	−0.930471	+	0.366364i	$0.880602\pi$
$8$		0			0
$9$	0.116783	−	0.320859i	0.0389277	−	0.106953i
$10$		0			0
$11$	−3.07824	+	5.33167i	−0.928125	+	1.60756i	−0.141667	+	0.989914i	$0.545246\pi$
$11$	−3.07824	+	5.33167i	−0.928125	+	1.60756i	−0.786457	+	0.617645i	$0.788087\pi$
$12$		0			0
$13$	4.00743	+	2.80603i	1.11146	+	0.778253i	0.977121	−	0.212682i	$-0.0682199\pi$
$13$	4.00743	+	2.80603i	1.11146	+	0.778253i	0.134339	+	0.990935i	$0.457109\pi$
$14$		0			0
$15$	−3.27785	+	1.59639i	−0.846337	+	0.412186i
$16$		0			0
$17$	−1.67016	+	3.58167i	−0.405073	+	0.868682i	0.592914	+	0.805266i	$0.297977\pi$
$17$	−1.67016	+	3.58167i	−0.405073	+	0.868682i	−0.997987	+	0.0634164i	$0.979800\pi$
$18$		0			0
$19$	3.36426	−	2.77160i	0.771814	−	0.635849i
$19$	3.36426	−	2.77160i	0.771814	−	0.635849i
$20$		0			0
$21$	−2.37235	−	6.51798i	−0.517689	−	1.42234i
$22$		0			0
$23$	−3.80191	−	0.332624i	−0.792753	−	0.0693569i	−0.316417	−	0.948620i	$-0.602480\pi$
$23$	−3.80191	−	0.332624i	−0.792753	−	0.0693569i	−0.476336	+	0.879263i	$0.658035\pi$
$24$		0			0
$25$	−4.75351	−	1.55053i	−0.950702	−	0.310107i
$26$		0			0
$27$	5.26261	−	1.41011i	1.01279	−	0.271376i
$28$		0			0
$29$	−2.08795	−	0.759952i	−0.387723	−	0.141120i	0.140801	−	0.990038i	$-0.455032\pi$
$29$	−2.08795	−	0.759952i	−0.387723	−	0.141120i	−0.528524	+	0.848918i	$0.677254\pi$
$30$		0			0
$31$	2.56290	−	1.47969i	0.460311	−	0.265761i	−0.251864	−	0.967763i	$-0.581044\pi$
$31$	2.56290	−	1.47969i	0.460311	−	0.265761i	0.712175	+	0.702002i	$0.247710\pi$
$32$		0			0
$33$	−9.99998	+	0.874885i	−1.74077	+	0.152298i
$34$		0			0
$35$	3.87402	−	8.68779i	0.654829	−	1.46850i
$36$		0			0
$37$	2.93721	+	2.93721i	0.482875	+	0.482875i	0.906048	−	0.423174i	$-0.139084\pi$
$37$	2.93721	+	2.93721i	0.482875	+	0.482875i	−0.423174	+	0.906048i	$0.639084\pi$
$38$		0			0
$39$			7.97671i			1.27730i
$40$		0			0
$41$	11.8292	+	2.08580i	1.84741	+	0.325748i	0.983918	−	0.178621i	$-0.0571635\pi$
$41$	11.8292	+	2.08580i	1.84741	+	0.325748i	0.863489	+	0.504368i	$0.168275\pi$
$42$		0			0
$43$	0.317560	+	3.62973i	0.0484275	+	0.553529i	0.981191	+	0.193040i	$0.0618347\pi$
$43$	0.317560	+	3.62973i	0.0484275	+	0.553529i	−0.932763	+	0.360489i	$0.882610\pi$
$44$		0			0
$45$	0.667567	+	0.370539i	0.0995150	+	0.0552366i
$46$		0			0
$47$	−5.68035	+	2.64879i	−0.828564	+	0.386366i	−0.790163	−	0.612897i	$-0.790004\pi$
$47$	−5.68035	+	2.64879i	−0.828564	+	0.386366i	−0.0384011	+	0.999262i	$0.512226\pi$
$48$		0			0
$49$	9.61040	+	5.54857i	1.37291	+	0.792653i
$50$		0			0
$51$	−6.34576	+	1.11893i	−0.888584	+	0.156681i
$52$		0			0
$53$	0.309521	−	3.53784i	0.0425159	−	0.485959i	−0.944850	−	0.327503i	$-0.893793\pi$
$53$	0.309521	−	3.53784i	0.0425159	−	0.485959i	0.987366	−	0.158456i	$-0.0506516\pi$
$54$		0			0
$55$	−10.6935	−	8.66955i	−1.44191	−	1.16900i
$56$		0			0
$57$	6.84816	+	1.90136i	0.907061	+	0.251841i
$58$		0			0
$59$	10.3122	−	3.75333i	1.34253	−	0.488642i	0.431923	−	0.901910i	$-0.357835\pi$
$59$	10.3122	−	3.75333i	1.34253	−	0.488642i	0.910609	+	0.413269i	$0.135613\pi$
$60$		0			0
$61$	2.42752	−	2.03693i	0.310813	−	0.260803i	−0.474015	−	0.880517i	$-0.657196\pi$
$61$	2.42752	−	2.03693i	0.310813	−	0.260803i	0.784828	+	0.619714i	$0.212751\pi$
$62$		0			0
$63$	−0.833153	+	1.18987i	−0.104967	+	0.149909i
$64$		0			0
$65$	−7.60353	+	7.86466i	−0.943101	+	0.975491i
$66$		0			0
$67$	0.868295	+	1.86206i	0.106079	+	0.227487i	0.952181	−	0.305533i	$-0.0988347\pi$
$67$	0.868295	+	1.86206i	0.106079	+	0.227487i	−0.846102	+	0.533020i	$0.821057\pi$
$68$		0			0
$69$	−3.11136	−	5.38903i	−0.374564	−	0.648763i
$70$		0			0
$71$	−1.80576	+	2.15203i	−0.214305	+	0.255399i	−0.862478	−	0.506094i	$-0.831089\pi$
$71$	−1.80576	+	2.15203i	−0.214305	+	0.255399i	0.648173	+	0.761493i	$0.275533\pi$
$72$		0			0
$73$	0.0922302	−	0.0645803i	0.0107947	−	0.00755855i	−0.568167	−	0.822914i	$-0.692347\pi$
$73$	0.0922302	−	0.0645803i	0.0107947	−	0.00755855i	0.578961	+	0.815355i	$0.303458\pi$
$74$		0			0
$75$	−2.37463	−	7.79903i	−0.274199	−	0.900554i
$76$		0			0
$77$	18.5192	−	18.5192i	2.11046	−	2.11046i
$78$		0			0
$79$	1.95703	−	11.0989i	0.220184	−	1.24872i	−0.651498	−	0.758650i	$-0.725859\pi$
$79$	1.95703	−	11.0989i	0.220184	−	1.24872i	0.871682	−	0.490073i	$-0.163030\pi$
$80$		0			0
$81$	6.02039	+	5.05170i	0.668932	+	0.561301i
$82$		0			0
$83$	−2.25226	+	8.40553i	−0.247217	+	0.922627i	0.725039	+	0.688708i	$0.241822\pi$
$83$	−2.25226	+	8.40553i	−0.247217	+	0.922627i	−0.972256	+	0.233919i	$0.924845\pi$
$84$		0			0
$85$	−7.32320	−	4.94567i	−0.794313	−	0.536433i
$86$		0			0
$87$	−0.937677	−	3.49946i	−0.100529	−	0.375181i
$88$		0			0
$89$	−0.149779	−	0.849439i	−0.0158765	−	0.0900403i	0.975840	−	0.218487i	$-0.0701121\pi$
$89$	−0.149779	−	0.849439i	−0.0158765	−	0.0900403i	−0.991716	+	0.128446i	$0.959001\pi$
$90$		0			0
$91$	−13.3775	−	15.9426i	−1.40234	−	1.67124i
$92$		0			0
$93$	4.37320	+	2.03926i	0.453480	+	0.211461i
$94$		0			0
$95$	4.93956	+	8.40243i	0.506788	+	0.862071i
$96$		0			0
$97$	11.9968	+	5.59420i	1.21809	+	0.568004i	0.922013	−	0.387160i	$-0.126544\pi$
$97$	11.9968	+	5.59420i	1.21809	+	0.568004i	0.296077	+	0.955164i	$0.404322\pi$
$98$		0			0
$99$	1.35123	+	1.61033i	0.135804	+	0.161844i
$100$		0			0
$101$	1.09573	+	6.21419i	0.109029	+	0.618335i	0.989534	+	0.144298i	$0.0460925\pi$
$101$	1.09573	+	6.21419i	0.109029	+	0.618335i	−0.880505	+	0.474037i	$0.842796\pi$
$102$		0			0
$103$	−2.53468	−	9.45957i	−0.249750	−	0.932079i	−0.970936	−	0.239338i	$-0.923070\pi$
$103$	−2.53468	−	9.45957i	−0.249750	−	0.932079i	0.721187	−	0.692741i	$-0.243597\pi$
$104$		0			0
$105$	15.2267	−	2.95073i	1.48598	−	0.287961i
$106$		0			0
$107$	−3.99406	+	14.9061i	−0.386121	+	1.44102i	0.450272	+	0.892892i	$0.351327\pi$
$107$	−3.99406	+	14.9061i	−0.386121	+	1.44102i	−0.836393	+	0.548131i	$0.815340\pi$
$108$		0			0
$109$	−2.63062	−	2.20735i	−0.251967	−	0.211426i	0.508052	−	0.861327i	$-0.330366\pi$
$109$	−2.63062	−	2.20735i	−0.251967	−	0.211426i	−0.760019	+	0.649901i	$0.774810\pi$
$110$		0			0
$111$	−1.17610	+	6.66997i	−0.111630	+	0.633086i
$112$		0			0
$113$	3.86404	−	3.86404i	0.363498	−	0.363498i	−0.501601	−	0.865099i	$-0.667255\pi$
$113$	3.86404	−	3.86404i	0.363498	−	0.363498i	0.865099	+	0.501601i	$0.167255\pi$
$114$		0			0
$115$	2.06926	−	8.27913i	0.192959	−	0.772033i
$116$		0			0
$117$	1.36834	−	0.958123i	0.126503	−	0.0885785i
$118$		0			0
$119$	10.8064	−	12.8786i	0.990623	−	1.18058i
$120$		0			0
$121$	−13.4511	−	23.2981i	−1.22283	−	2.11801i
$122$		0			0
$123$	8.27701	+	17.7501i	0.746313	+	1.60047i
$124$		0			0
$125$	5.09289	−	9.95301i	0.455522	−	0.890225i
$126$		0			0
$127$	−6.68188	+	9.54271i	−0.592921	+	0.846779i	−0.997710	−	0.0676311i	$-0.978456\pi$
$127$	−6.68188	+	9.54271i	−0.592921	+	0.846779i	0.404790	+	0.914410i	$0.367345\pi$
$128$		0			0
$129$	−4.55100	+	3.81874i	−0.400693	+	0.336221i
$130$		0			0
$131$	4.64450	−	1.69046i	0.405791	−	0.147696i	−0.131057	−	0.991375i	$-0.541837\pi$
$131$	4.64450	−	1.69046i	0.405791	−	0.147696i	0.536848	+	0.843679i	$0.319615\pi$
$132$		0			0
$133$	−16.8758	+	7.68467i	−1.46331	+	0.666345i
$134$		0			0
$135$	1.26649	+	12.1167i	0.109002	+	1.04284i
$136$		0			0
$137$	0.922477	−	10.5440i	0.0788125	−	0.900831i	−0.849149	−	0.528154i	$-0.822884\pi$
$137$	0.922477	−	10.5440i	0.0788125	−	0.900831i	0.927961	−	0.372677i	$-0.121560\pi$
$138$		0			0
$139$	−12.0785	+	2.12977i	−1.02449	+	0.180645i	−0.660553	−	0.750779i	$-0.729678\pi$
$139$	−12.0785	+	2.12977i	−1.02449	+	0.180645i	−0.363935	+	0.931424i	$0.618567\pi$
$140$		0			0
$141$	−8.85018	−	5.10966i	−0.745320	−	0.430311i
$142$		0			0
$143$	−27.2967	+	12.7286i	−2.28266	+	1.06442i
$144$		0			0
$145$	2.41123	−	4.34411i	0.200242	−	0.360759i
$146$		0			0
$147$	1.57699	+	18.0251i	0.130068	+	1.48668i
$148$		0			0
$149$	10.7707	+	1.89916i	0.882369	+	0.155585i	0.596432	−	0.802663i	$-0.296584\pi$
$149$	10.7707	+	1.89916i	0.882369	+	0.155585i	0.285936	+	0.958249i	$0.407695\pi$
$150$		0			0
$151$		−	22.0807i		−	1.79690i	−0.439074	−	0.898451i	$-0.644693\pi$
$151$		−	22.0807i		−	1.79690i	0.439074	−	0.898451i	$-0.355307\pi$
$152$		0			0
$153$	0.954164	+	0.954164i	0.0771396	+	0.0771396i
$154$		0			0
$155$	2.36792	+	6.17922i	0.190196	+	0.496327i
$156$		0			0
$157$	−18.5516	+	1.62305i	−1.48058	+	0.129534i	−0.798610	−	0.601848i	$-0.794431\pi$
$157$	−18.5516	+	1.62305i	−1.48058	+	0.129534i	−0.681968	+	0.731382i	$0.738876\pi$
$158$		0			0
$159$	5.01472	−	2.89525i	0.397693	−	0.229608i
$160$		0			0
$161$	15.2563	+	5.55283i	1.20236	+	0.437624i
$162$		0			0
$163$	6.81767	−	1.82679i	0.534001	−	0.143085i	0.0182660	−	0.999833i	$-0.494185\pi$
$163$	6.81767	−	1.82679i	0.534001	−	0.143085i	0.515735	+	0.856748i	$0.327519\pi$
$164$		0			0
$165$	1.57859	−	22.3905i	0.122893	−	1.74310i
$166$		0			0
$167$	−0.466372	−	0.0408023i	−0.0360889	−	0.00315737i	0.0690970	−	0.997610i	$-0.477988\pi$
$167$	−0.466372	−	0.0408023i	−0.0360889	−	0.00315737i	−0.105186	+	0.994453i	$0.533544\pi$
$168$		0			0
$169$	3.73941	+	10.2739i	0.287647	+	0.790303i
$170$		0			0
$171$	−0.496404	−	1.40313i	−0.0379610	−	0.107300i
$172$		0			0
$173$	−6.26796	+	13.4417i	−0.476544	+	1.02195i	0.510258	+	0.860021i	$0.329550\pi$
$173$	−6.26796	+	13.4417i	−0.476544	+	1.02195i	−0.986802	+	0.161930i	$0.948228\pi$
$174$		0			0
$175$	17.8255	+	11.6051i	1.34748	+	0.877264i
$176$		0			0
$177$	14.6572	+	10.2631i	1.10170	+	0.771422i
$178$		0			0
$179$	1.69711	−	2.93948i	0.126848	−	0.219707i	−0.795606	−	0.605815i	$-0.792847\pi$
$179$	1.69711	−	2.93948i	0.126848	−	0.219707i	0.922454	+	0.386107i	$0.126181\pi$
$180$		0			0
$181$	−0.565054	+	1.55247i	−0.0420001	+	0.115394i	−0.958920	−	0.283678i	$-0.908445\pi$
$181$	−0.565054	+	1.55247i	−0.0420001	+	0.115394i	0.916920	+	0.399072i	$0.130668\pi$
$182$		0			0
$183$	4.99086	+	1.33730i	0.368935	+	0.0988559i
$184$		0			0
$185$	−7.51750	+	5.45521i	−0.552698	+	0.401075i
$186$		0			0
$187$	−13.9551	−	19.9300i	−1.02050	−	1.45742i
$188$		0			0
$189$	−23.1773			−1.68590
$190$		0			0
$191$	−10.4096			−0.753214			−0.376607	−	0.926373i	$-0.622909\pi$
$191$	−10.4096			−0.753214			−0.376607	+	0.926373i	$0.622909\pi$
$192$		0			0
$193$	5.18430	+	7.40395i	0.373174	+	0.532948i	0.961185	−	0.275905i	$-0.0889776\pi$
$193$	5.18430	+	7.40395i	0.373174	+	0.532948i	−0.588011	+	0.808853i	$0.700089\pi$
$194$		0			0
$195$	−17.6153	−	2.80033i	−1.26145	−	0.200536i
$196$		0			0
$197$	1.41494	+	0.379131i	0.100810	+	0.0270120i	0.308871	−	0.951104i	$-0.400049\pi$
$197$	1.41494	+	0.379131i	0.100810	+	0.0270120i	−0.208061	+	0.978116i	$0.566715\pi$
$198$		0			0
$199$	−5.25239	+	14.4308i	−0.372332	+	1.02297i	0.602125	+	0.798402i	$0.294321\pi$
$199$	−5.25239	+	14.4308i	−0.372332	+	1.02297i	−0.974457	+	0.224573i	$0.927901\pi$
$200$		0			0
$201$	−1.67499	+	2.90116i	−0.118144	+	0.204632i
$202$		0			0
$203$	7.74291	+	5.42164i	0.543445	+	0.380525i
$204$		0			0
$205$	−8.75895	+	25.3906i	−0.611752	+	1.77335i
$206$		0			0
$207$	−0.550725	+	1.18103i	−0.0382780	+	0.0820875i
$208$		0			0
$209$	4.42125	+	26.4688i	0.305825	+	1.83088i
$210$		0			0
$211$	7.40816	+	20.3537i	0.509998	+	1.40121i	0.881238	+	0.472672i	$0.156711\pi$
$211$	7.40816	+	20.3537i	0.509998	+	1.40121i	−0.371240	+	0.928537i	$0.621067\pi$
$212$		0			0
$213$	−4.56310	−	0.399220i	−0.312659	−	0.0273541i
$214$		0			0
$215$	−8.12716	−	0.572987i	−0.554268	−	0.0390774i
$216$		0			0
$217$	−12.1605	+	3.25839i	−0.825507	+	0.221194i
$218$		0			0
$219$	0.172511	+	0.0627889i	0.0116572	+	0.00424288i
$220$		0			0
$221$	−16.7433	+	9.66676i	−1.12628	+	0.650257i
$222$		0			0
$223$	19.4722	−	1.70360i	1.30396	−	0.114082i	0.586082	−	0.810252i	$-0.300670\pi$
$223$	19.4722	−	1.70360i	1.30396	−	0.114082i	0.717876	+	0.696170i	$0.245114\pi$
$224$		0			0
$225$	−1.05263	+	1.34413i	−0.0701755	+	0.0896087i
$226$		0			0
$227$	−3.26415	−	3.26415i	−0.216649	−	0.216649i	0.590436	−	0.807085i	$-0.298956\pi$
$227$	−3.26415	−	3.26415i	−0.216649	−	0.216649i	−0.807085	+	0.590436i	$0.798956\pi$
$228$		0			0
$229$			4.99206i			0.329884i	0.986303	+	0.164942i	$0.0527438\pi$
$229$			4.99206i			0.329884i	−0.986303	+	0.164942i	$0.947256\pi$
$230$		0			0
$231$	42.0544	+	7.41532i	2.76698	+	0.487893i
$232$		0			0
$233$	−0.826433	−	9.44617i	−0.0541414	−	0.618839i	−0.973994	−	0.226575i	$-0.927247\pi$
$233$	−0.826433	−	9.44617i	−0.0541414	−	0.618839i	0.919852	−	0.392265i	$-0.128308\pi$
$234$		0			0
$235$	−3.85526	−	13.4740i	−0.251489	−	0.878948i
$236$		0			0
$237$	16.6543	−	7.76603i	1.08181	−	0.504458i
$238$		0			0
$239$	−5.08115	−	2.93360i	−0.328672	−	0.189759i	0.326579	−	0.945170i	$-0.394104\pi$
$239$	−5.08115	−	2.93360i	−0.328672	−	0.189759i	−0.655251	+	0.755411i	$0.727437\pi$
$240$		0			0
$241$	−26.1187	+	4.60543i	−1.68245	+	0.296662i	−0.931513	−	0.363709i	$-0.881510\pi$
$241$	−26.1187	+	4.60543i	−1.68245	+	0.296662i	−0.750940	+	0.660371i	$0.770399\pi$
$242$		0			0
$243$	0.307706	−	3.51709i	0.0197393	−	0.225622i
$244$		0			0
$245$	−15.6270	+	19.2751i	−0.998371	+	1.23144i
$246$		0			0
$247$	21.2592	−	1.66677i	1.35269	−	0.106054i
$248$		0			0
$249$	−13.3330	+	4.85283i	−0.844948	+	0.307536i
$250$		0			0
$251$	14.2230	−	11.9345i	0.897747	−	0.753299i	−0.0720018	−	0.997405i	$-0.522939\pi$
$251$	14.2230	−	11.9345i	0.897747	−	0.753299i	0.969749	+	0.244105i	$0.0784943\pi$
$252$		0			0
$253$	13.4766	−	19.2466i	0.847269	−	1.21003i
$254$		0			0
$255$	−0.243206	−	14.4064i	−0.0152302	−	0.902163i
$256$		0			0
$257$	−5.70587	−	12.2363i	−0.355922	−	0.763278i	0.644076	−	0.764961i	$-0.277242\pi$
$257$	−5.70587	−	12.2363i	−0.355922	−	0.763278i	−0.999999	+	0.00168322i	$0.999464\pi$
$258$		0			0
$259$	−8.83538	−	15.3033i	−0.549004	−	0.950902i
$260$		0			0
$261$	−0.487675	+	0.581189i	−0.0301863	+	0.0359747i
$262$		0			0
$263$	7.56965	−	5.30033i	0.466765	−	0.326832i	−0.316422	−	0.948618i	$-0.602482\pi$
$263$	7.56965	−	5.30033i	0.466765	−	0.326832i	0.783187	+	0.621786i	$0.213593\pi$
$264$		0			0
$265$	7.70407	+	1.92553i	0.473258	+	0.118284i
$266$		0			0
$267$	0.994461	−	0.994461i	0.0608601	−	0.0608601i
$268$		0			0
$269$	0.0606558	−	0.343996i	0.00369825	−	0.0209738i	−0.982903	−	0.184125i	$-0.941055\pi$
$269$	0.0606558	−	0.343996i	0.00369825	−	0.0209738i	0.986601	+	0.163151i	$0.0521659\pi$
$270$		0			0
$271$	12.2387	+	10.2695i	0.743449	+	0.623828i	0.933762	−	0.357896i	$-0.116506\pi$
$271$	12.2387	+	10.2695i	0.743449	+	0.623828i	−0.190313	+	0.981724i	$0.560950\pi$
$272$		0			0
$273$	8.78263	−	32.7772i	0.531549	−	1.98377i
$274$		0			0
$275$	22.8994	−	20.5712i	1.38088	−	1.24049i
$276$		0			0
$277$	−1.10587	−	4.12716i	−0.0664452	−	0.247977i	0.924712	−	0.380666i	$-0.124305\pi$
$277$	−1.10587	−	4.12716i	−0.0664452	−	0.247977i	−0.991158	+	0.132690i	$0.957639\pi$
$278$		0			0
$279$	−0.175469	−	0.995135i	−0.0105051	−	0.0595771i
$280$		0			0
$281$	−6.18716	−	7.37357i	−0.369095	−	0.439870i	0.549246	−	0.835661i	$-0.314915\pi$
$281$	−6.18716	−	7.37357i	−0.369095	−	0.439870i	−0.918341	+	0.395791i	$0.870471\pi$
$282$		0			0
$283$	−21.6840	−	10.1114i	−1.28898	−	0.601061i	−0.347357	−	0.937733i	$-0.612921\pi$
$283$	−21.6840	−	10.1114i	−1.28898	−	0.601061i	−0.941622	+	0.336672i	$0.890699\pi$
$284$		0			0
$285$	−6.60298	+	14.4555i	−0.391127	+	0.856273i
$286$		0			0
$287$	−46.3109	−	21.5951i	−2.73365	−	1.27472i
$288$		0			0
$289$	0.888475	+	1.05884i	0.0522632	+	0.0622849i
$290$		0			0
$291$	3.74785	+	21.2551i	0.219703	+	1.24600i
$292$		0			0
$293$	−3.64921	−	13.6190i	−0.213189	−	0.795633i	−0.986796	−	0.161967i	$-0.948216\pi$
$293$	−3.64921	−	13.6190i	−0.213189	−	0.795633i	0.773607	−	0.633666i	$-0.218451\pi$
$294$		0			0
$295$	4.66838	+	24.0904i	0.271804	+	1.40260i
$296$		0			0
$297$	−8.68133	+	32.3992i	−0.503742	+	1.87999i
$298$		0			0
$299$	−14.3025	−	12.0012i	−0.827137	−	0.694050i
$300$		0			0
$301$	2.69157	−	15.2646i	0.155139	−	0.879840i
$302$		0			0
$303$	−7.27512	+	7.27512i	−0.417945	+	0.417945i
$304$		0			0
$305$	3.64602	+	6.07588i	0.208771	+	0.347904i
$306$		0			0
$307$	15.5691	−	10.9016i	0.888573	−	0.622185i	−0.0375967	−	0.999293i	$-0.511970\pi$
$307$	15.5691	−	10.9016i	0.888573	−	0.622185i	0.926169	+	0.377108i	$0.123081\pi$
$308$		0			0
$309$	10.2640	−	12.2322i	0.583899	−	0.695864i
$310$		0			0
$311$	1.87691	+	3.25090i	0.106430	+	0.184341i	0.914321	−	0.404989i	$-0.132725\pi$
$311$	1.87691	+	3.25090i	0.106430	+	0.184341i	−0.807892	+	0.589331i	$0.799391\pi$
$312$		0			0
$313$	−0.738313	−	1.58332i	−0.0417319	−	0.0894944i	0.884336	−	0.466850i	$-0.154611\pi$
$313$	−0.738313	−	1.58332i	−0.0417319	−	0.0894944i	−0.926068	+	0.377356i	$0.876833\pi$
$314$		0			0
$315$	−2.33514	−	2.25760i	−0.131570	−	0.127201i
$316$		0			0
$317$	3.20502	−	4.57724i	0.180012	−	0.257084i	−0.718998	−	0.695012i	$-0.755399\pi$
$317$	3.20502	−	4.57724i	0.180012	−	0.257084i	0.899010	+	0.437929i	$0.144288\pi$
$318$		0			0
$319$	10.4790	−	8.79295i	0.586713	−	0.492311i
$320$		0			0
$321$	−23.6443	+	8.60583i	−1.31970	+	0.480331i
$322$		0			0
$323$	4.30810	+	16.6787i	0.239709	+	0.928026i
$324$		0			0
$325$	−14.6985	−	19.5521i	−0.815326	−	1.08456i
$326$		0			0
$327$	0.488003	−	5.57789i	0.0269866	−	0.308458i
$328$		0			0
$329$	26.2576	−	4.62993i	1.44763	−	0.255256i
$330$		0			0
$331$	2.83740	+	1.63817i	0.155958	+	0.0900422i	0.575948	−	0.817486i	$-0.304633\pi$
$331$	2.83740	+	1.63817i	0.155958	+	0.0900422i	−0.419990	+	0.907529i	$0.637966\pi$
$332$		0			0
$333$	1.28545	−	0.599414i	0.0704421	−	0.0328477i
$334$		0			0
$335$	−4.41689	+	1.26378i	−0.241321	+	0.0690479i
$336$		0			0
$337$	1.03419	+	11.8209i	0.0563360	+	0.643923i	0.970900	+	0.239483i	$0.0769780\pi$
$337$	1.03419	+	11.8209i	0.0563360	+	0.643923i	−0.914565	+	0.404440i	$0.867466\pi$
$338$		0			0
$339$	8.77465	+	1.54721i	0.476574	+	0.0840328i
$340$		0			0
$341$			18.2194i			0.986637i
$342$		0			0
$343$	−12.3245	−	12.3245i	−0.665462	−	0.665462i
$344$		0			0
$345$	12.9931	−	4.97904i	0.699524	−	0.268062i
$346$		0			0
$347$	−5.35539	+	0.468536i	−0.287492	+	0.0251523i	−0.229990	−	0.973193i	$-0.573869\pi$
$347$	−5.35539	+	0.468536i	−0.287492	+	0.0251523i	−0.0575026	+	0.998345i	$0.518314\pi$
$348$		0			0
$349$	−17.3820	+	10.0355i	−0.930436	+	0.537187i	−0.886949	−	0.461867i	$-0.847180\pi$
$349$	−17.3820	+	10.0355i	−0.930436	+	0.537187i	−0.0434863	+	0.999054i	$0.513846\pi$
$350$		0			0
$351$	25.0464	+	9.11613i	1.33688	+	0.486583i
$352$		0			0
$353$	28.2204	−	7.56165i	1.50202	−	0.402466i	0.588246	−	0.808682i	$-0.299819\pi$
$353$	28.2204	−	7.56165i	1.50202	−	0.402466i	0.913777	+	0.406216i	$0.133152\pi$
$354$		0			0
$355$	−4.11846	−	4.74324i	−0.218585	−	0.251745i
$356$		0			0
$357$	27.3074	+	2.38909i	1.44526	+	0.126444i
$358$		0			0
$359$	9.08029	+	24.9479i	0.479239	+	1.31670i	0.910140	+	0.414300i	$0.135974\pi$
$359$	9.08029	+	24.9479i	0.479239	+	1.31670i	−0.430901	+	0.902399i	$0.641804\pi$
$360$		0			0
$361$	3.63647	−	18.6488i	0.191393	−	0.981513i
$362$		0			0
$363$	18.5379	−	39.7546i	0.972985	−	2.08657i
$364$		0			0
$365$	0.110236	+	0.226347i	0.00577003	+	0.0118476i
$366$		0			0
$367$	−0.658107	−	0.460812i	−0.0343529	−	0.0240542i	0.556274	−	0.830999i	$-0.312231\pi$
$367$	−0.658107	−	0.460812i	−0.0343529	−	0.0240542i	−0.590627	+	0.806945i	$0.701119\pi$
$368$		0			0
$369$	2.05070	−	3.55191i	0.106755	−	0.184905i
$370$		0			0
$371$	−5.16714	+	14.1966i	−0.268264	+	0.737051i
$372$		0			0
$373$	−5.21679	−	1.39783i	−0.270115	−	0.0723771i	0.121219	−	0.992626i	$-0.461320\pi$
$373$	−5.21679	−	1.39783i	−0.270115	−	0.0723771i	−0.391334	+	0.920249i	$0.627986\pi$
$374$		0			0
$375$	18.0565	−	2.50603i	0.932435	−	0.129411i
$376$		0			0
$377$	−6.23486	−	8.90431i	−0.321112	−	0.458595i
$378$		0			0
$379$	8.12668			0.417440			0.208720	−	0.977975i	$-0.433070\pi$
$379$	8.12668			0.417440			0.208720	+	0.977975i	$0.433070\pi$
$380$		0			0
$381$	−18.9946			−0.973122
$382$		0			0
$383$	6.94993	+	9.92553i	0.355125	+	0.507171i	0.956475	−	0.291815i	$-0.0942591\pi$
$383$	6.94993	+	9.92553i	0.355125	+	0.507171i	−0.601350	+	0.798986i	$0.705370\pi$
$384$		0			0
$385$	34.3953	+	47.3981i	1.75294	+	2.41563i
$386$		0			0
$387$	1.20172	+	0.322000i	0.0610868	+	0.0163682i
$388$		0			0
$389$	11.2178	−	30.8207i	0.568766	−	1.56267i	−0.237667	−	0.971347i	$-0.576383\pi$
$389$	11.2178	−	30.8207i	0.568766	−	1.56267i	0.806433	−	0.591326i	$-0.201395\pi$
$390$		0			0
$391$	7.54115	−	13.0616i	0.381372	−	0.660556i
$392$		0			0
$393$	6.60145	+	4.62239i	0.332999	+	0.233169i
$394$		0			0
$395$	23.8231	+	8.21821i	1.19867	+	0.413503i
$396$		0			0
$397$	6.21977	−	13.3383i	0.312161	−	0.669432i	−0.686154	−	0.727457i	$-0.740702\pi$
$397$	6.21977	−	13.3383i	0.312161	−	0.669432i	0.998315	+	0.0580241i	$0.0184800\pi$
$398$		0			0
$399$	−26.0464	−	15.3530i	−1.30395	−	0.768610i
$400$		0			0
$401$	5.99205	+	16.4630i	0.299229	+	0.822124i	0.994629	+	0.103502i	$0.0330048\pi$
$401$	5.99205	+	16.4630i	0.299229	+	0.822124i	−0.695401	+	0.718622i	$0.744773\pi$
$402$		0			0
$403$	14.4227	+	1.26182i	0.718447	+	0.0628560i
$404$		0			0
$405$	−13.2694	+	11.5216i	−0.659362	+	0.572512i
$406$		0			0
$407$	−24.7017	+	6.61880i	−1.22442	+	0.328082i
$408$		0			0
$409$	−9.01686	−	3.28187i	−0.445855	−	0.162278i	0.109329	−	0.994006i	$-0.465130\pi$
$409$	−9.01686	−	3.28187i	−0.445855	−	0.162278i	−0.555184	+	0.831728i	$0.687352\pi$
$410$		0			0
$411$	14.9456	−	8.62883i	0.737211	−	0.425629i
$412$		0			0
$413$	−46.5066	+	4.06880i	−2.28844	+	0.200212i
$414$		0			0
$415$	−17.7716	−	7.92462i	−0.872372	−	0.389004i
$416$		0			0
$417$	−14.1407	−	14.1407i	−0.692472	−	0.692472i
$418$		0			0
$419$			8.49953i			0.415229i	0.978211	+	0.207615i	$0.0665700\pi$
$419$			8.49953i			0.415229i	−0.978211	+	0.207615i	$0.933430\pi$
$420$		0			0
$421$	18.9233	+	3.33669i	0.922267	+	0.162621i	0.614569	−	0.788863i	$-0.289330\pi$
$421$	18.9233	+	3.33669i	0.922267	+	0.162621i	0.307698	+	0.951484i	$0.400441\pi$
$422$		0			0
$423$	0.186519	+	2.13193i	0.00906888	+	0.103658i
$424$		0			0
$425$	13.4926	−	14.4359i	0.654488	−	0.700242i
$426$		0			0
$427$	−12.2177	+	5.69722i	−0.591257	+	0.275708i
$428$		0			0
$429$	−42.5292	−	24.5542i	−2.05333	−	1.18549i
$430$		0			0
$431$	13.3647	−	2.35656i	0.643757	−	0.113512i	0.157767	−	0.987476i	$-0.449570\pi$
$431$	13.3647	−	2.35656i	0.643757	−	0.113512i	0.485989	+	0.873965i	$0.338459\pi$
$432$		0			0
$433$	3.08921	−	35.3099i	0.148458	−	1.69688i	−0.447834	−	0.894117i	$-0.647804\pi$
$433$	3.08921	−	35.3099i	0.148458	−	1.69688i	0.596292	−	0.802768i	$-0.296640\pi$
$434$		0			0
$435$	8.05716	−	0.842174i	0.386311	−	0.0403792i
$436$		0			0
$437$	−13.7125	+	9.41834i	−0.655958	+	0.450540i
$438$		0			0
$439$	33.3682	−	12.1450i	1.59258	−	0.579650i	0.614687	−	0.788772i	$-0.289283\pi$
$439$	33.3682	−	12.1450i	1.59258	−	0.579650i	0.977890	+	0.209121i	$0.0670603\pi$
$440$		0			0
$441$	2.90264	−	2.43561i	0.138221	−	0.115981i
$442$		0			0
$443$	2.71132	−	3.87217i	0.128819	−	0.183972i	−0.749562	−	0.661935i	$-0.769736\pi$
$443$	2.71132	−	3.87217i	0.128819	−	0.183972i	0.878380	+	0.477962i	$0.158624\pi$
$444$		0			0
$445$	1.92843	−	0.0325554i	0.0914163	−	0.00154327i
$446$		0			0
$447$	7.53637	+	16.1618i	0.356458	+	0.764427i
$448$		0			0
$449$	5.21499	+	9.03263i	0.246111	+	0.426276i	0.962443	−	0.271483i	$-0.0875140\pi$
$449$	5.21499	+	9.03263i	0.246111	+	0.426276i	−0.716333	+	0.697759i	$0.754181\pi$
$450$		0			0
$451$	−47.5339	+	56.6487i	−2.23828	+	2.66748i
$452$		0			0
$453$	29.4917	−	20.6503i	1.38564	−	0.970236i
$454$		0			0
$455$	39.9031	−	23.9451i	1.87068	−	1.12256i
$456$		0			0
$457$	−21.8897	+	21.8897i	−1.02396	+	1.02396i	−0.0242509	+	0.999706i	$0.507720\pi$
$457$	−21.8897	+	21.8897i	−1.02396	+	1.02396i	−0.999706	+	0.0242509i	$0.992280\pi$
$458$		0			0
$459$	−3.73884	+	21.2040i	−0.174514	+	0.989720i
$460$		0			0
$461$	−23.8271	−	19.9933i	−1.10974	−	0.931180i	−0.111696	−	0.993742i	$-0.535628\pi$
$461$	−23.8271	−	19.9933i	−1.10974	−	0.931180i	−0.998041	+	0.0625622i	$0.980073\pi$
$462$		0			0
$463$	3.56144	−	13.2915i	0.165514	−	0.617708i	−0.832460	−	0.554085i	$-0.813068\pi$
$463$	3.56144	−	13.2915i	0.165514	−	0.617708i	0.997974	−	0.0636221i	$-0.0202652\pi$
$464$		0			0
$465$	−6.03864	+	8.94160i	−0.280035	+	0.414657i
$466$		0			0
$467$	−1.47897	−	5.51958i	−0.0684385	−	0.255416i	0.923227	−	0.384255i	$-0.125542\pi$
$467$	−1.47897	−	5.51958i	−0.0684385	−	0.255416i	−0.991666	+	0.128839i	$0.958875\pi$
$468$		0			0
$469$	−1.51773	−	8.60747i	−0.0700822	−	0.397456i
$470$		0			0
$471$	−19.5176	−	23.2602i	−0.899324	−	1.07177i
$472$		0			0
$473$	−20.3301	−	9.48007i	−0.934777	−	0.435894i
$474$		0			0
$475$	−20.2895	+	7.95842i	−0.930946	+	0.365158i
$476$		0			0
$477$	−1.09900	−	0.512472i	−0.0503198	−	0.0234645i
$478$		0			0
$479$	1.78967	+	2.13284i	0.0817719	+	0.0974520i	0.805379	−	0.592760i	$-0.201962\pi$
$479$	1.78967	+	2.13284i	0.0817719	+	0.0974520i	−0.723607	+	0.690212i	$0.757517\pi$
$480$		0			0
$481$	3.52876	+	20.0126i	0.160897	+	0.912495i
$482$		0			0
$483$	6.85143	+	25.5699i	0.311751	+	1.16347i
$484$		0			0
$485$	−16.5655	+	24.5290i	−0.752201	+	1.11381i
$486$		0			0
$487$	7.92017	−	29.5585i	0.358897	−	1.33942i	−0.516612	−	0.856220i	$-0.672807\pi$
$487$	7.92017	−	29.5585i	0.358897	−	1.33942i	0.875509	−	0.483202i	$-0.160526\pi$
$488$		0			0
$489$	8.81594	+	7.39745i	0.398671	+	0.334524i
$490$		0			0
$491$	−0.652704	+	3.70167i	−0.0294561	+	0.167054i	−0.995987	−	0.0894954i	$-0.971475\pi$
$491$	−0.652704	+	3.70167i	−0.0294561	+	0.167054i	0.966531	+	0.256549i	$0.0825857\pi$
$492$		0			0
$493$	6.20911	−	6.20911i	0.279644	−	0.279644i
$494$		0			0
$495$	−4.03052	+	2.41864i	−0.181158	+	0.108710i
$496$		0			0
$497$	9.78956	−	6.85472i	0.439122	−	0.307476i
$498$		0			0
$499$	−0.137101	+	0.163390i	−0.00613746	+	0.00731435i	−0.769104	−	0.639123i	$-0.779297\pi$
$499$	−0.137101	+	0.163390i	−0.00613746	+	0.00731435i	0.762967	+	0.646437i	$0.223742\pi$
$500$		0			0
$501$	−0.381663	−	0.661060i	−0.0170515	−	0.0295340i
$502$		0			0
$503$	5.13886	+	11.0203i	0.229130	+	0.491372i	0.986937	−	0.161108i	$-0.0515066\pi$
$503$	5.13886	+	11.0203i	0.229130	+	0.491372i	−0.757806	+	0.652480i	$0.773729\pi$
$504$		0			0
$505$	−14.1077	+	0.238164i	−0.627784	+	0.0105981i
$506$		0			0
$507$	−10.2250	+	14.6029i	−0.454109	+	0.648536i
$508$		0			0
$509$	−13.8979	+	11.6617i	−0.616014	+	0.516897i	−0.896548	−	0.442947i	$-0.853933\pi$
$509$	−13.8979	+	11.6617i	−0.616014	+	0.516897i	0.280534	+	0.959844i	$0.409488\pi$
$510$		0			0
$511$	−0.450090	+	0.163819i	−0.0199108	+	0.00724694i
$512$		0			0
$513$	13.7965	−	19.3298i	0.609131	−	0.853433i
$514$		0			0
$515$	21.7797	−	2.27653i	0.959730	−	0.100316i
$516$		0			0
$517$	3.36301	−	38.4394i	0.147905	−	1.69056i
$518$		0			0
$519$	−23.8150	+	4.19924i	−1.04536	+	0.184326i
$520$		0			0
$521$	−1.66873	−	0.963444i	−0.0731086	−	0.0422092i	0.463000	−	0.886358i	$-0.346773\pi$
$521$	−1.66873	−	0.963444i	−0.0731086	−	0.0422092i	−0.536109	+	0.844149i	$0.680106\pi$
$522$		0			0
$523$	11.9082	−	5.55289i	0.520709	−	0.242811i	−0.144450	−	0.989512i	$-0.546141\pi$
$523$	11.9082	−	5.55289i	0.520709	−	0.242811i	0.665160	+	0.746701i	$0.268364\pi$
$524$		0			0
$525$	1.17064	+	34.6617i	0.0510908	+	1.51276i
$526$		0			0
$527$	1.01931	+	11.6508i	0.0444020	+	0.507517i
$528$		0			0
$529$	−8.30669	−	1.46469i	−0.361160	−	0.0636823i
$530$		0			0
$531$		−	3.74708i		−	0.162610i
$532$		0			0
$533$	41.5517	+	41.5517i	1.79981	+	1.79981i
$534$		0			0
$535$	−31.5154	−	14.0532i	−1.36253	−	0.607574i
$536$		0			0
$537$	5.51324	−	0.482346i	0.237914	−	0.0208148i
$538$		0			0
$539$	−59.1663	+	34.1597i	−2.54847	+	1.47136i
$540$		0			0
$541$	6.95375	+	2.53096i	0.298965	+	0.108814i	0.487148	−	0.873320i	$-0.338037\pi$
$541$	6.95375	+	2.53096i	0.298965	+	0.108814i	−0.188182	+	0.982134i	$0.560260\pi$
$542$		0			0
$543$	−2.60198	+	0.697199i	−0.111662	+	0.0299197i
$544$		0			0
$545$	5.79809	−	5.03437i	0.248363	−	0.215649i
$546$		0			0
$547$	−2.86763	−	0.250885i	−0.122611	−	0.0107271i	0.0256851	−	0.999670i	$-0.491823\pi$
$547$	−2.86763	−	0.250885i	−0.122611	−	0.0107271i	−0.148296	+	0.988943i	$0.547379\pi$
$548$		0			0
$549$	−0.370075	−	1.01677i	−0.0157944	−	0.0433948i
$550$		0			0
$551$	−9.13069	+	3.23029i	−0.388980	+	0.137615i
$552$		0			0
$553$	−20.2620	+	43.4519i	−0.861626	+	1.84776i
$554$		0			0
$555$	−14.3167	−	4.93880i	−0.607708	−	0.209640i
$556$		0			0
$557$	−7.23405	−	5.06534i	−0.306517	−	0.214625i	0.410190	−	0.912000i	$-0.365462\pi$
$557$	−7.23405	−	5.06534i	−0.306517	−	0.214625i	−0.716707	+	0.697375i	$0.754351\pi$
$558$		0			0
$559$	−8.91254	+	15.4370i	−0.376960	+	0.652915i
$560$		0			0
$561$	13.5680	−	37.2778i	0.572842	−	1.57387i
$562$		0			0
$563$	1.04101	+	0.278939i	0.0438735	+	0.0117559i	0.280689	−	0.959799i	$-0.409437\pi$
$563$	1.04101	+	0.278939i	0.0438735	+	0.0117559i	−0.236816	+	0.971555i	$0.576104\pi$
$564$		0			0
$565$	7.17657	+	9.88962i	0.301921	+	0.416059i
$566$		0			0
$567$	−19.1764	−	27.3867i	−0.805332	−	1.15013i
$568$		0			0
$569$	−32.1736			−1.34879			−0.674394	−	0.738372i	$-0.735595\pi$
$569$	−32.1736			−1.34879			−0.674394	+	0.738372i	$0.735595\pi$
$570$		0			0
$571$	36.3716			1.52210			0.761052	−	0.648690i	$-0.224683\pi$
$571$	36.3716			1.52210			0.761052	+	0.648690i	$0.224683\pi$
$572$		0			0
$573$	−9.73529	−	13.9034i	−0.406697	−	0.580824i
$574$		0			0
$575$	17.5567	+	7.47613i	0.732164	+	0.311776i
$576$		0			0
$577$	21.6606	+	5.80394i	0.901742	+	0.241621i	0.679764	−	0.733431i	$-0.262082\pi$
$577$	21.6606	+	5.80394i	0.901742	+	0.241621i	0.221978	+	0.975052i	$0.428749\pi$
$578$		0			0
$579$	−5.04049	+	13.8486i	−0.209476	+	0.575530i
$580$		0			0
$581$	18.5096	−	32.0595i	0.767906	−	1.33005i
$582$		0			0
$583$	17.9098	+	12.5406i	0.741748	+	0.519378i
$584$		0			0
$585$	1.63548	+	3.35812i	0.0676189	+	0.138841i
$586$		0			0
$587$	16.6122	−	35.6251i	0.685660	−	1.47040i	−0.187144	−	0.982333i	$-0.559923\pi$
$587$	16.6122	−	35.6251i	0.685660	−	1.47040i	0.872804	−	0.488071i	$-0.162299\pi$
$588$		0			0
$589$	4.52116	−	12.0814i	0.186291	−	0.497806i
$590$		0			0
$591$	0.816897	+	2.24440i	0.0336026	+	0.0923225i
$592$		0			0
$593$	−44.5317	−	3.89602i	−1.82870	−	0.159990i	−0.879752	−	0.475432i	$-0.842292\pi$
$593$	−44.5317	−	3.89602i	−1.82870	−	0.159990i	−0.948945	+	0.315442i	$0.897847\pi$
$594$		0			0
$595$	24.6465	+	28.3854i	1.01041	+	1.16369i
$596$		0			0
$597$	−24.1864	+	6.48073i	−0.989885	+	0.265239i
$598$		0			0
$599$	25.9608	+	9.44895i	1.06073	+	0.386074i	0.812702	−	0.582679i	$-0.197996\pi$
$599$	25.9608	+	9.44895i	1.06073	+	0.386074i	0.248027	+	0.968753i	$0.420218\pi$
$600$		0			0
$601$	31.0150	−	17.9065i	1.26513	−	0.730423i	0.291068	−	0.956702i	$-0.405990\pi$
$601$	31.0150	−	17.9065i	1.26513	−	0.730423i	0.974062	+	0.226279i	$0.0726562\pi$
$602$		0			0
$603$	0.698862	−	0.0611425i	0.0284599	−	0.00248992i
$604$		0			0
$605$	56.1722	−	21.5256i	2.28372	−	0.875138i
$606$		0			0
$607$	28.3695	+	28.3695i	1.15148	+	1.15148i	0.986255	+	0.165229i	$0.0528363\pi$
$607$	28.3695	+	28.3695i	1.15148	+	1.15148i	0.165229	+	0.986255i	$0.447164\pi$
$608$		0			0
$609$			15.4121i			0.624530i
$610$		0			0
$611$	−30.1962	−	5.32440i	−1.22161	−	0.215402i
$612$		0			0
$613$	2.34738	+	26.8307i	0.0948100	+	1.08368i	0.883355	+	0.468705i	$0.155279\pi$
$613$	2.34738	+	26.8307i	0.0948100	+	1.08368i	−0.788545	+	0.614978i	$0.789165\pi$
$614$		0			0
$615$	−42.1040	+	12.0470i	−1.69780	+	0.485783i
$616$		0			0
$617$	18.1404	−	8.45900i	0.730304	−	0.340546i	−0.0216467	−	0.999766i	$-0.506891\pi$
$617$	18.1404	−	8.45900i	0.730304	−	0.340546i	0.751951	+	0.659219i	$0.229113\pi$
$618$		0			0
$619$	19.2344	+	11.1050i	0.773095	+	0.446347i	0.833978	−	0.551798i	$-0.186058\pi$
$619$	19.2344	+	11.1050i	0.773095	+	0.446347i	−0.0608824	+	0.998145i	$0.519391\pi$
$620$		0			0
$621$	−20.4770	+	3.61065i	−0.821714	+	0.144890i
$622$		0			0
$623$	−0.319802	+	3.65536i	−0.0128126	+	0.146449i
$624$		0			0
$625$	20.1917	+	14.7410i	0.807667	+	0.589638i
$626$		0			0
$627$	−31.2177	+	30.6593i	−1.24671	+	1.22441i
$628$		0			0
$629$	−15.4257	+	5.61451i	−0.615064	+	0.223865i
$630$		0			0
$631$	0.161770	−	0.135741i	0.00643997	−	0.00540377i	−0.639562	−	0.768740i	$-0.720884\pi$
$631$	0.161770	−	0.135741i	0.00643997	−	0.00540377i	0.646002	+	0.763336i	$0.276440\pi$
$632$		0			0
$633$	−20.2569	+	28.9298i	−0.805138	+	1.14986i
$634$		0			0
$635$	−18.7278	−	18.1059i	−0.743189	−	0.718512i
$636$		0			0
$637$	22.9435	+	49.2026i	0.909056	+	1.94948i
$638$		0			0
$639$	0.479614	+	0.830717i	0.0189733	+	0.0328626i
$640$		0			0
$641$	−10.8499	+	12.9304i	−0.428544	+	0.510719i	−0.936502	−	0.350663i	$-0.885956\pi$
$641$	−10.8499	+	12.9304i	−0.428544	+	0.510719i	0.507958	+	0.861382i	$0.330401\pi$
$642$		0			0
$643$	−32.1531	+	22.5139i	−1.26800	+	0.887860i	−0.997200	−	0.0747770i	$-0.976175\pi$
$643$	−32.1531	+	22.5139i	−1.26800	+	0.887860i	−0.270795	+	0.962637i	$0.587287\pi$
$644$		0			0
$645$	−6.83538	−	11.3908i	−0.269143	−	0.448511i
$646$		0			0
$647$	−0.922638	+	0.922638i	−0.0362726	+	0.0362726i	−0.725010	−	0.688738i	$-0.758165\pi$
$647$	−0.922638	+	0.922638i	−0.0362726	+	0.0362726i	0.688738	+	0.725010i	$0.258165\pi$
$648$		0			0
$649$	−11.7319	+	66.5348i	−0.460517	+	2.61172i
$650$		0			0
$651$	−15.7247	−	13.1946i	−0.616300	−	0.517137i
$652$		0			0
$653$	7.12674	−	26.5973i	0.278891	−	1.04083i	−0.674298	−	0.738459i	$-0.735554\pi$
$653$	7.12674	−	26.5973i	0.278891	−	1.04083i	0.953189	−	0.302375i	$-0.0977796\pi$
$654$		0			0
$655$	2.10259	+	10.8501i	0.0821549	+	0.423947i
$656$		0			0
$657$	−0.00995024	−	0.0371348i	−0.000388196	−	0.00144877i
$658$		0			0
$659$	1.23550	+	7.00689i	0.0481284	+	0.272950i	0.999370	−	0.0354978i	$-0.0113017\pi$
$659$	1.23550	+	7.00689i	0.0481284	+	0.272950i	−0.951241	+	0.308448i	$0.900191\pi$
$660$		0			0
$661$	14.5776	+	17.3729i	0.567002	+	0.675727i	0.971013	−	0.239027i	$-0.0768285\pi$
$661$	14.5776	+	17.3729i	0.567002	+	0.675727i	−0.404010	+	0.914754i	$0.632384\pi$
$662$		0			0
$663$	−28.5699	−	13.3224i	−1.10956	−	0.517398i
$664$		0			0
$665$	−11.0459	−	39.9652i	−0.428340	−	1.54978i
$666$		0			0
$667$	7.68543	+	3.58377i	0.297581	+	0.138764i
$668$		0			0
$669$	20.4862	+	24.4145i	0.792043	+	0.943920i
$670$		0			0
$671$	3.38776	+	19.2129i	0.130783	+	0.741707i
$672$		0			0
$673$	−1.16149	−	4.33474i	−0.0447722	−	0.167092i	0.939920	−	0.341395i	$-0.110899\pi$
$673$	−1.16149	−	4.33474i	−0.0447722	−	0.167092i	−0.984692	+	0.174303i	$0.944233\pi$
$674$		0			0
$675$	−27.2023	−	1.45688i	−1.04702	−	0.0560752i
$676$		0			0
$677$	3.58347	−	13.3737i	0.137724	−	0.513993i	−0.862248	−	0.506487i	$-0.830944\pi$
$677$	3.58347	−	13.3737i	0.137724	−	0.513993i	0.999972	−	0.00750657i	$-0.00238944\pi$
$678$		0			0
$679$	−43.1368	−	36.1961i	−1.65544	−	1.38908i
$680$		0			0
$681$	1.30700	−	7.41239i	0.0500845	−	0.284043i
$682$		0			0
$683$	17.0959	−	17.0959i	0.654158	−	0.654158i	−0.299833	−	0.953992i	$-0.596931\pi$
$683$	17.0959	−	17.0959i	0.654158	−	0.654158i	0.953992	+	0.299833i	$0.0969311\pi$
$684$		0			0
$685$	22.9608	+	5.73874i	0.877286	+	0.219266i
$686$		0			0
$687$	−6.66755	+	4.66867i	−0.254383	+	0.178121i
$688$		0			0
$689$	11.1677	−	13.3091i	0.425454	−	0.507036i
$690$		0			0
$691$	−10.1020	−	17.4972i	−0.384298	−	0.665623i	0.607374	−	0.794416i	$-0.292223\pi$
$691$	−10.1020	−	17.4972i	−0.384298	−	0.665623i	−0.991671	+	0.128793i	$0.958890\pi$
$692$		0			0
$693$	−3.77933	−	8.10479i	−0.143565	−	0.307876i
$694$		0			0
$695$	−0.462919	−	27.4212i	−0.0175595	−	1.04014i
$696$		0			0
$697$	−27.2273	+	38.8846i	−1.03131	+	1.47286i
$698$		0			0
$699$	11.8437	−	9.93805i	0.447970	−	0.375892i
$700$		0			0
$701$	12.9853	−	4.72625i	0.490447	−	0.178508i	−0.0849454	−	0.996386i	$-0.527072\pi$
$701$	12.9853	−	4.72625i	0.490447	−	0.178508i	0.575392	+	0.817877i	$0.304849\pi$
$702$		0			0
$703$	18.0223	+	1.74077i	0.679724	+	0.0656542i
$704$		0			0
$705$	14.3908	−	17.7504i	0.541990	−	0.668518i
$706$		0			0
$707$	2.33956	−	26.7413i	0.0879882	−	1.00571i
$708$		0			0
$709$	12.9004	−	2.27470i	0.484486	−	0.0854280i	0.0739303	−	0.997263i	$-0.476446\pi$
$709$	12.9004	−	2.27470i	0.484486	−	0.0854280i	0.410556	+	0.911835i	$0.365335\pi$
$710$		0			0
$711$	−3.33263	−	1.92410i	−0.124983	−	0.0721592i
$712$		0			0
$713$	−10.2361	+	4.77318i	−0.383346	+	0.178757i
$714$		0			0
$715$	−18.5263	−	64.7488i	−0.692843	−	2.42147i
$716$		0			0
$717$	−0.833776	−	9.53011i	−0.0311379	−	0.355908i
$718$		0			0
$719$	−5.05000	−	0.890451i	−0.188333	−	0.0332082i	0.0786859	−	0.996899i	$-0.474928\pi$
$719$	−5.05000	−	0.890451i	−0.188333	−	0.0332082i	−0.267019	+	0.963691i	$0.586039\pi$
$720$		0			0
$721$			41.6613i			1.55155i
$722$		0			0
$723$	−30.5779	−	30.5779i	−1.13720	−	1.13720i
$724$		0			0
$725$	8.74676	+	6.84988i	0.324847	+	0.254398i
$726$		0			0
$727$	15.1903	−	1.32898i	0.563377	−	0.0492891i	0.198090	−	0.980184i	$-0.436526\pi$
$727$	15.1903	−	1.32898i	0.563377	−	0.0492891i	0.365288	+	0.930895i	$0.380971\pi$
$728$		0			0
$729$	25.4037	−	14.6669i	0.940879	−	0.543217i
$730$		0			0
$731$	−13.5309	−	4.92484i	−0.500457	−	0.182152i
$732$		0			0
$733$	19.0999	−	5.11781i	0.705472	−	0.189031i	0.111791	−	0.993732i	$-0.464341\pi$
$733$	19.0999	−	5.11781i	0.705472	−	0.189031i	0.593680	+	0.804701i	$0.297674\pi$
$734$		0			0
$735$	−40.3591	−	2.84543i	−1.48867	−	0.104955i
$736$		0			0
$737$	−12.6007	−	1.10242i	−0.464154	−	0.0406082i
$738$		0			0
$739$	−4.05271	−	11.1347i	−0.149081	−	0.409597i	0.842563	−	0.538597i	$-0.181046\pi$
$739$	−4.05271	−	11.1347i	−0.149081	−	0.409597i	−0.991645	+	0.129000i	$0.958823\pi$
$740$		0			0
$741$	22.1082	+	26.8357i	0.812166	+	0.985834i
$742$		0			0
$743$	−1.42642	+	3.05896i	−0.0523301	+	0.112222i	−0.930734	−	0.365696i	$-0.880831\pi$
$743$	−1.42642	+	3.05896i	−0.0523301	+	0.112222i	0.878404	+	0.477919i	$0.158609\pi$
$744$		0			0
$745$	−7.97519	+	23.1186i	−0.292188	+	0.846999i
$746$		0			0
$747$	2.43397	+	1.70428i	0.0890541	+	0.0623564i
$748$		0			0
$749$	32.8242	−	56.8531i	1.19937	−	2.07737i
$750$		0			0
$751$	8.50855	−	23.3771i	0.310481	−	0.853041i	−0.682078	−	0.731280i	$-0.738924\pi$
$751$	8.50855	−	23.3771i	0.310481	−	0.853041i	0.992559	−	0.121761i	$-0.0388543\pi$
$752$		0			0
$753$	29.2417	+	7.83530i	1.06563	+	0.285534i
$754$		0			0
$755$	48.7616	+	7.75173i	1.77462	+	0.282114i
$756$		0			0
$757$	−11.8979	−	16.9920i	−0.432438	−	0.617585i	0.542502	−	0.840055i	$-0.317477\pi$
$757$	−11.8979	−	16.9920i	−0.432438	−	0.617585i	−0.974940	+	0.222469i	$0.928588\pi$
$758$		0			0
$759$	38.3101			1.39057
$760$		0			0
$761$	−36.1409			−1.31011			−0.655053	−	0.755583i	$-0.727354\pi$
$761$	−36.1409			−1.31011			−0.655053	+	0.755583i	$0.727354\pi$
$762$		0			0
$763$	8.37915	+	11.9667i	0.303346	+	0.433222i
$764$		0			0
$765$	−2.44209	+	1.77214i	−0.0882939	+	0.0640720i
$766$		0			0
$767$	51.8573	+	13.8951i	1.87246	+	0.501724i
$768$		0			0
$769$	5.36323	−	14.7354i	0.193403	−	0.531370i	−0.804649	−	0.593750i	$-0.797647\pi$
$769$	5.36323	−	14.7354i	0.193403	−	0.531370i	0.998052	+	0.0623797i	$0.0198690\pi$
$770$		0			0
$771$	11.0069	−	19.0646i	0.396405	−	0.686593i
$772$		0			0
$773$	−1.81583	−	1.27145i	−0.0653107	−	0.0457310i	0.540465	−	0.841366i	$-0.318248\pi$
$773$	−1.81583	−	1.27145i	−0.0653107	−	0.0457310i	−0.605776	+	0.795635i	$0.707137\pi$
$774$		0			0
$775$	−14.4771	+	3.05986i	−0.520033	+	0.109914i
$776$		0			0
$777$	12.1766	−	26.1128i	0.436833	−	0.936791i
$778$		0			0
$779$	45.5774	−	25.7686i	1.63298	−	0.923254i
$780$		0			0
$781$	−5.91532	−	16.2522i	−0.211667	−	0.581549i
$782$		0			0
$783$	−12.0597	−	1.05509i	−0.430978	−	0.0377057i
$784$		0			0
$785$	2.92854	−	41.5380i	0.104524	−	1.48255i
$786$		0			0
$787$	−13.0914	+	3.50784i	−0.466660	+	0.125041i	−0.484484	−	0.874800i	$-0.660993\pi$
$787$	−13.0914	+	3.50784i	−0.466660	+	0.125041i	0.0178245	+	0.999841i	$0.494326\pi$
$788$		0			0
$789$	14.1586	+	5.15330i	0.504059	+	0.183462i
$790$		0			0
$791$	−20.1322	+	11.6233i	−0.715820	+	0.413279i
$792$		0			0
$793$	15.4438	−	1.35116i	0.548426	−	0.0479811i
$794$		0			0
$795$	4.63320	+	12.0906i	0.164323	+	0.428810i
$796$		0			0
$797$	−7.81316	−	7.81316i	−0.276756	−	0.276756i	0.555056	−	0.831813i	$-0.312697\pi$
$797$	−7.81316	−	7.81316i	−0.276756	−	0.276756i	−0.831813	+	0.555056i	$0.812697\pi$
$798$		0			0
$799$		−	24.7690i		−	0.876265i
$800$		0			0
$801$	−0.290042	−	0.0511422i	−0.0102481	−	0.00180702i
$802$		0			0
$803$	0.0604139	+	0.690535i	0.00213196	+	0.0243684i
$804$		0			0
$805$	−17.6184	+	31.7416i	−0.620969	+	1.11874i
$806$		0			0
$807$	0.516179	−	0.240698i	0.0181703	−	0.00847297i
$808$		0			0
$809$	−25.6739	−	14.8228i	−0.902646	−	0.521143i	−0.0245880	−	0.999698i	$-0.507827\pi$
$809$	−25.6739	−	14.8228i	−0.902646	−	0.521143i	−0.878058	+	0.478555i	$0.841161\pi$
$810$		0			0
$811$	41.5313	−	7.32310i	1.45836	−	0.257149i	0.612467	−	0.790497i	$-0.290177\pi$
$811$	41.5313	−	7.32310i	1.45836	−	0.257149i	0.845896	+	0.533348i	$0.179066\pi$
$812$		0			0
$813$	−2.27039	+	25.9507i	−0.0796260	+	0.910129i
$814$		0			0
$815$	1.64073	+	15.6970i	0.0574723	+	0.549843i
$816$		0			0
$817$	11.1285	+	11.3312i	0.389338	+	0.396429i
$818$		0			0
$819$	−6.67760	+	2.43045i	−0.233334	+	0.0849267i
$820$		0			0
$821$	−32.8851	+	27.5939i	−1.14770	+	0.963033i	−0.999663	−	0.0259486i	$-0.991739\pi$
$821$	−32.8851	+	27.5939i	−1.14770	+	0.963033i	−0.148035	+	0.988982i	$0.547295\pi$
$822$		0			0
$823$	−2.16592	+	3.09325i	−0.0754992	+	0.107824i	−0.855126	−	0.518421i	$-0.826520\pi$
$823$	−2.16592	+	3.09325i	−0.0754992	+	0.107824i	0.779626	+	0.626245i	$0.215409\pi$
$824$		0			0
$825$	48.8915	+	11.3465i	1.70218	+	0.395036i
$826$		0			0
$827$	−16.2958	−	34.9465i	−0.566661	−	1.21521i	−0.955797	−	0.294028i	$-0.905004\pi$
$827$	−16.2958	−	34.9465i	−0.566661	−	1.21521i	0.389136	−	0.921180i	$-0.372774\pi$
$828$		0			0
$829$	−21.7208	−	37.6215i	−0.754393	−	1.30665i	−0.945675	−	0.325112i	$-0.894598\pi$
$829$	−21.7208	−	37.6215i	−0.754393	−	1.30665i	0.191282	−	0.981535i	$-0.438735\pi$
$830$		0			0
$831$	4.47813	−	5.33683i	0.155345	−	0.185133i
$832$		0			0
$833$	−35.9240	+	25.1543i	−1.24469	+	0.871544i
$834$		0			0
$835$	0.253831	−	1.01558i	0.00878420	−	0.0351457i
$836$		0			0
$837$	11.4010	−	11.4010i	0.394077	−	0.394077i
$838$		0			0
$839$	8.08984	−	45.8798i	0.279292	−	1.58395i	−0.445696	−	0.895184i	$-0.647044\pi$
$839$	8.08984	−	45.8798i	0.279292	−	1.58395i	0.724989	−	0.688761i	$-0.241845\pi$
$840$		0			0
$841$	−18.4333	−	15.4674i	−0.635630	−	0.533357i
$842$		0			0
$843$	4.06202	−	15.1597i	0.139904	−	0.522127i
$844$		0			0
$845$	−24.0011	+	4.65107i	−0.825662	+	0.160002i
$846$		0			0
$847$	29.6204	+	110.545i	1.01777	+	3.79836i
$848$		0			0
$849$	−6.77417	−	38.4182i	−0.232489	−	1.31851i
$850$		0			0
$851$	−10.1900	−	12.1440i	−0.349310	−	0.416291i
$852$		0			0
$853$	42.2528	+	19.7028i	1.44671	+	0.674612i	0.977974	−	0.208727i	$-0.0669320\pi$
$853$	42.2528	+	19.7028i	1.44671	+	0.674612i	0.468735	+	0.883339i	$0.344710\pi$
$854$		0			0
$855$	3.27285	−	0.603640i	0.111929	−	0.0206441i
$856$		0			0
$857$	0.377599	+	0.176077i	0.0128985	+	0.00601469i	0.429057	−	0.903277i	$-0.358846\pi$
$857$	0.377599	+	0.176077i	0.0128985	+	0.00601469i	−0.416158	+	0.909292i	$0.636624\pi$
$858$		0			0
$859$	19.1057	+	22.7693i	0.651879	+	0.776879i	0.986196	−	0.165582i	$-0.0529501\pi$
$859$	19.1057	+	22.7693i	0.651879	+	0.776879i	−0.334317	+	0.942461i	$0.608506\pi$
$860$		0			0
$861$	−14.4677	−	82.0506i	−0.493059	−	2.79628i
$862$		0			0
$863$	0.879081	+	3.28077i	0.0299243	+	0.111679i	0.979273	−	0.202547i	$-0.0649218\pi$
$863$	0.879081	+	3.28077i	0.0299243	+	0.111679i	−0.949348	+	0.314226i	$0.898255\pi$
$864$		0			0
$865$	−27.4833	−	18.5606i	−0.934460	−	0.631081i
$866$		0			0
$867$	−0.583306	+	2.17693i	−0.0198101	+	0.0739323i
$868$		0			0
$869$	53.1514	+	44.5993i	1.80304	+	1.51293i
$870$		0			0
$871$	−1.74538	+	9.89855i	−0.0591400	+	0.335400i
$872$		0			0
$873$	3.19597	−	3.19597i	0.108167	−	0.108167i
$874$		0			0
$875$	−31.8859	+	35.2907i	−1.07794	+	1.19304i
$876$		0			0
$877$	39.8886	−	27.9303i	1.34694	−	0.943138i	0.346955	−	0.937882i	$-0.387216\pi$
$877$	39.8886	−	27.9303i	1.34694	−	0.943138i	0.999986	−	0.00525616i	$-0.00167310\pi$
$878$		0			0
$879$	14.7772	−	17.6108i	0.498423	−	0.593998i
$880$		0			0
$881$	−9.67864	−	16.7639i	−0.326082	−	0.564790i	0.655649	−	0.755066i	$-0.272395\pi$
$881$	−9.67864	−	16.7639i	−0.326082	−	0.564790i	−0.981731	+	0.190276i	$0.939062\pi$
$882$		0			0
$883$	−6.14600	−	13.1801i	−0.206829	−	0.443547i	0.775340	−	0.631544i	$-0.217578\pi$
$883$	−6.14600	−	13.1801i	−0.206829	−	0.443547i	−0.982170	+	0.187997i	$0.939801\pi$
$884$		0			0
$885$	−27.8100	+	28.7651i	−0.934823	+	0.966928i
$886$		0			0
$887$	−21.8051	+	31.1408i	−0.732142	+	1.04561i	0.264553	+	0.964371i	$0.414776\pi$
$887$	−21.8051	+	31.1408i	−0.732142	+	1.04561i	−0.996695	+	0.0812359i	$0.974113\pi$
$888$		0			0
$889$	37.9635	−	31.8552i	1.27325	−	1.06839i
$890$		0			0
$891$	−45.4662	+	16.5484i	−1.52318	+	0.554391i
$892$		0			0
$893$	−11.7688	+	24.6549i	−0.393827	+	0.825044i
$894$		0			0
$895$	5.89558	+	4.77974i	0.197067	+	0.159769i
$896$		0			0
$897$	2.65324	−	30.3267i	0.0885893	−	1.01258i
$898$		0			0
$899$	−6.47571	+	1.14184i	−0.215977	+	0.0380826i
$900$		0			0
$901$	12.1544	+	7.01735i	0.404922	+	0.233782i
$902$		0			0
$903$	22.9052	−	10.6809i	0.762236	−	0.355437i
$904$		0			0
$905$	−3.23002	−	1.79285i	−0.107369	−	0.0595963i
$906$		0			0
$907$	−3.25993	−	37.2611i	−0.108244	−	1.23724i	−0.834965	−	0.550303i	$-0.814512\pi$
$907$	−3.25993	−	37.2611i	−0.108244	−	1.23724i	0.726721	−	0.686933i	$-0.241043\pi$
$908$		0			0
$909$	2.12184	+	0.374138i	0.0703771	+	0.0124094i
$910$		0			0
$911$			50.7989i			1.68304i	0.540225	+	0.841521i	$0.318339\pi$
$911$			50.7989i			1.68304i	−0.540225	+	0.841521i	$0.681661\pi$
$912$		0			0
$913$	−37.8825	−	37.8825i	−1.25373	−	1.25373i
$914$		0			0
$915$	−4.70531	+	10.5520i	−0.155553	+	0.348839i
$916$		0			0
$917$	−20.9460	+	1.83254i	−0.691699	+	0.0605158i
$918$		0			0
$919$	−42.1994	+	24.3638i	−1.39203	+	0.803688i	−0.993540	−	0.113485i	$-0.963798\pi$
$919$	−42.1994	+	24.3638i	−1.39203	+	0.803688i	−0.398489	+	0.917173i	$0.630465\pi$
$920$		0			0
$921$	29.1210	+	10.5992i	0.959568	+	0.349254i
$922$		0			0
$923$	−13.2751	+	3.55706i	−0.436956	+	0.117082i
$924$		0			0
$925$	−9.40781	−	18.5163i	−0.309327	−	0.608812i
$926$		0			0
$927$	−3.33120	−	0.291442i	−0.109411	−	0.00957221i
$928$		0			0
$929$	11.0427	+	30.3395i	0.362298	+	0.995405i	0.978215	+	0.207594i	$0.0665634\pi$
$929$	11.0427	+	30.3395i	0.362298	+	0.995405i	−0.615917	+	0.787811i	$0.711214\pi$
$930$		0			0
$931$	47.7103	−	7.96937i	1.56364	−	0.261185i
$932$		0			0
$933$	−2.58668	+	5.54716i	−0.0846842	+	0.181606i
$934$		0			0
$935$	48.9113	−	23.8209i	1.59957	−	0.779028i
$936$		0			0
$937$	18.8798	+	13.2198i	0.616777	+	0.431872i	0.839766	−	0.542949i	$-0.182692\pi$
$937$	18.8798	+	13.2198i	0.616777	+	0.431872i	−0.222988	+	0.974821i	$0.571581\pi$
$938$		0			0
$939$	1.42425	−	2.46687i	0.0464785	−	0.0805031i
$940$		0			0
$941$	−11.8218	+	32.4802i	−0.385380	+	1.05882i	0.583677	+	0.811986i	$0.301613\pi$
$941$	−11.8218	+	32.4802i	−0.385380	+	1.05882i	−0.969057	+	0.246837i	$0.920609\pi$
$942$		0			0
$943$	−44.2797	−	11.8647i	−1.44194	−	0.386368i
$944$		0			0
$945$	8.13670	−	51.1832i	0.264687	−	1.66499i
$946$		0			0
$947$	−7.83974	−	11.1963i	−0.254757	−	0.363831i	0.671318	−	0.741169i	$-0.265728\pi$
$947$	−7.83974	−	11.1963i	−0.254757	−	0.363831i	−0.926076	+	0.377338i	$0.876839\pi$
$948$		0			0
$949$	0.550820			0.0178804
$950$		0			0
$951$	9.11091			0.295441
$952$		0			0
$953$	−2.19555	−	3.13557i	−0.0711209	−	0.101571i	0.782016	−	0.623259i	$-0.214192\pi$
$953$	−2.19555	−	3.13557i	−0.0711209	−	0.101571i	−0.853137	+	0.521687i	$0.825303\pi$
$954$		0			0
$955$	3.65444	−	22.9880i	0.118255	−	0.743873i
$956$		0			0
$957$	21.5443	+	5.77279i	0.696430	+	0.186608i
$958$		0			0
$959$	−15.3998	+	42.3107i	−0.497287	+	1.36628i
$960$		0			0
$961$	−11.1210	+	19.2622i	−0.358742	+	0.621360i
$962$		0			0
$963$	4.31630	+	3.02231i	0.139091	+	0.0973925i
$964$		0			0
$965$	−18.1704	+	8.84943i	−0.584927	+	0.284873i
$966$		0			0
$967$	2.57869	−	5.53002i	0.0829251	−	0.177833i	−0.860473	−	0.509496i	$-0.829832\pi$
$967$	2.57869	−	5.53002i	0.0829251	−	0.177833i	0.943398	+	0.331663i	$0.107610\pi$
$968$		0			0
$969$	−18.2475	+	21.3523i	−0.586196	+	0.685933i
$970$		0			0
$971$	1.34949	+	3.70770i	0.0433073	+	0.118986i	0.959461	−	0.281841i	$-0.0909451\pi$
$971$	1.34949	+	3.70770i	0.0433073	+	0.118986i	−0.916154	+	0.400827i	$0.868723\pi$
$972$		0			0
$973$	51.9771	+	4.54741i	1.66631	+	0.145783i
$974$		0			0
$975$	12.3682	−	37.9173i	0.396098	−	1.21433i
$976$		0			0
$977$	15.4653	−	4.14390i	0.494777	−	0.132575i	−0.00279779	−	0.999996i	$-0.500891\pi$
$977$	15.4653	−	4.14390i	0.494777	−	0.132575i	0.497575	+	0.867421i	$0.334224\pi$
$978$		0			0
$979$	4.98998	+	1.81621i	0.159481	+	0.0580462i
$980$		0			0
$981$	−1.01546	+	0.586276i	−0.0324212	+	0.0187184i
$982$		0			0
$983$	−2.04783	+	0.179162i	−0.0653157	+	0.00571438i	−0.119767	−	0.992802i	$-0.538215\pi$
$983$	−2.04783	+	0.179162i	−0.0653157	+	0.00571438i	0.0544510	+	0.998516i	$0.482659\pi$
$984$		0			0
$985$	−1.33398	+	2.99156i	−0.0425042	+	0.0953189i
$986$		0			0
$987$	30.7406	+	30.7406i	0.978483	+	0.978483i
$988$		0			0
$989$		−	13.9055i		−	0.442171i
$990$		0			0
$991$	3.99342	+	0.704147i	0.126855	+	0.0223680i	0.236715	−	0.971579i	$-0.423929\pi$
$991$	3.99342	+	0.704147i	0.126855	+	0.0223680i	−0.109860	+	0.993947i	$0.535040\pi$
$992$		0			0
$993$	0.465595	+	5.32178i	0.0147752	+	0.168881i
$994$		0			0
$995$	−30.0242	−	16.6652i	−0.951832	−	0.528322i
$996$		0			0
$997$	−11.4472	+	5.33792i	−0.362536	+	0.169054i	−0.595347	−	0.803469i	$-0.702985\pi$
$997$	−11.4472	+	5.33792i	−0.362536	+	0.169054i	0.232811	+	0.972522i	$0.425208\pi$
$998$		0			0
$999$	19.5992	+	11.3156i	0.620091	+	0.358010i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bh.a.33.8	✓	120
5.2	odd	4	inner	380.2.bh.a.337.8	yes	120
19.15	odd	18	inner	380.2.bh.a.53.8	yes	120
95.72	even	36	inner	380.2.bh.a.357.8	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bh.a.33.8	✓	120	1.1	even	1	trivial
380.2.bh.a.53.8	yes	120	19.15	odd	18	inner
380.2.bh.a.337.8	yes	120	5.2	odd	4	inner
380.2.bh.a.357.8	yes	120	95.72	even	36	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)

\(f(q)\)	\(=\)	\(q+(0.935220 + 1.33563i) q^{3} +(-0.351064 + 2.20834i) q^{5} +(-4.10912 - 1.10104i) q^{7} +(0.116783 - 0.320859i) q^{9} +O(q^{10})\)	\(q+(0.935220 + 1.33563i) q^{3} +(-0.351064 + 2.20834i) q^{5} +(-4.10912 - 1.10104i) q^{7} +(0.116783 - 0.320859i) q^{9} +(-3.07824 + 5.33167i) q^{11} +(4.00743 + 2.80603i) q^{13} +(-3.27785 + 1.59639i) q^{15} +(-1.67016 + 3.58167i) q^{17} +(3.36426 - 2.77160i) q^{19} +(-2.37235 - 6.51798i) q^{21} +(-3.80191 - 0.332624i) q^{23} +(-4.75351 - 1.55053i) q^{25} +(5.26261 - 1.41011i) q^{27} +(-2.08795 - 0.759952i) q^{29} +(2.56290 - 1.47969i) q^{31} +(-9.99998 + 0.874885i) q^{33} +(3.87402 - 8.68779i) q^{35} +(2.93721 + 2.93721i) q^{37} +7.97671i q^{39} +(11.8292 + 2.08580i) q^{41} +(0.317560 + 3.62973i) q^{43} +(0.667567 + 0.370539i) q^{45} +(-5.68035 + 2.64879i) q^{47} +(9.61040 + 5.54857i) q^{49} +(-6.34576 + 1.11893i) q^{51} +(0.309521 - 3.53784i) q^{53} +(-10.6935 - 8.66955i) q^{55} +(6.84816 + 1.90136i) q^{57} +(10.3122 - 3.75333i) q^{59} +(2.42752 - 2.03693i) q^{61} +(-0.833153 + 1.18987i) q^{63} +(-7.60353 + 7.86466i) q^{65} +(0.868295 + 1.86206i) q^{67} +(-3.11136 - 5.38903i) q^{69} +(-1.80576 + 2.15203i) q^{71} +(0.0922302 - 0.0645803i) q^{73} +(-2.37463 - 7.79903i) q^{75} +(18.5192 - 18.5192i) q^{77} +(1.95703 - 11.0989i) q^{79} +(6.02039 + 5.05170i) q^{81} +(-2.25226 + 8.40553i) q^{83} +(-7.32320 - 4.94567i) q^{85} +(-0.937677 - 3.49946i) q^{87} +(-0.149779 - 0.849439i) q^{89} +(-13.3775 - 15.9426i) q^{91} +(4.37320 + 2.03926i) q^{93} +(4.93956 + 8.40243i) q^{95} +(11.9968 + 5.59420i) q^{97} +(1.35123 + 1.61033i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 6 q^{7}+O(q^{10}) \) 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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