LMFDB - Embedded newform 380.2.bh.a.357.8

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			357.8
Character	$\chi$	$=$	380.357
Dual form			380.2.bh.a.33.8

$q$-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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

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

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
$3$	0.935220	−	1.33563i	0.539949	−	0.771128i	−0.452764	−	0.891631i	$-0.649562\pi$
$3$	0.935220	−	1.33563i	0.539949	−	0.771128i	0.992713	+	0.120503i	$0.0384508\pi$
$4$		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	−0.930471	−	0.366364i	$-0.880602\pi$
$7$	−4.10912	+	1.10104i	−1.55310	+	0.416152i	−0.622630	+	0.782517i	$0.713936\pi$
$8$		0			0
$9$	0.116783	+	0.320859i	0.0389277	+	0.106953i
$10$		0			0
$11$	−3.07824	−	5.33167i	−0.928125	−	1.60756i	−0.786457	−	0.617645i	$-0.788087\pi$
$11$	−3.07824	−	5.33167i	−0.928125	−	1.60756i	−0.141667	−	0.989914i	$-0.545246\pi$
$12$		0			0
$13$	4.00743	−	2.80603i	1.11146	−	0.778253i	0.134339	−	0.990935i	$-0.457109\pi$
$13$	4.00743	−	2.80603i	1.11146	−	0.778253i	0.977121	+	0.212682i	$0.0682199\pi$
$14$		0			0
$15$	−3.27785	−	1.59639i	−0.846337	−	0.412186i
$16$		0			0
$17$	−1.67016	−	3.58167i	−0.405073	−	0.868682i	−0.997987	−	0.0634164i	$-0.979800\pi$
$17$	−1.67016	−	3.58167i	−0.405073	−	0.868682i	0.592914	−	0.805266i	$-0.297977\pi$
$18$		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	−0.476336	−	0.879263i	$-0.658035\pi$
$23$	−3.80191	+	0.332624i	−0.792753	+	0.0693569i	−0.316417	+	0.948620i	$0.602480\pi$
$24$		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	−0.528524	−	0.848918i	$-0.677254\pi$
$29$	−2.08795	+	0.759952i	−0.387723	+	0.141120i	0.140801	+	0.990038i	$0.455032\pi$
$30$		0			0
$31$	2.56290	+	1.47969i	0.460311	+	0.265761i	0.712175	−	0.702002i	$-0.247710\pi$
$31$	2.56290	+	1.47969i	0.460311	+	0.265761i	−0.251864	+	0.967763i	$0.581044\pi$
$32$		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	−0.423174	−	0.906048i	$-0.639084\pi$
$37$	2.93721	−	2.93721i	0.482875	−	0.482875i	0.906048	+	0.423174i	$0.139084\pi$
$38$		0			0
$39$		−	7.97671i		−	1.27730i
$40$		0			0
$41$	11.8292	−	2.08580i	1.84741	−	0.325748i	0.863489	−	0.504368i	$-0.168275\pi$
$41$	11.8292	−	2.08580i	1.84741	−	0.325748i	0.983918	+	0.178621i	$0.0571635\pi$
$42$		0			0
$43$	0.317560	−	3.62973i	0.0484275	−	0.553529i	−0.932763	−	0.360489i	$-0.882610\pi$
$43$	0.317560	−	3.62973i	0.0484275	−	0.553529i	0.981191	−	0.193040i	$-0.0618347\pi$
$44$		0			0
$45$	0.667567	−	0.370539i	0.0995150	−	0.0552366i
$46$		0			0
$47$	−5.68035	−	2.64879i	−0.828564	−	0.386366i	−0.0384011	−	0.999262i	$-0.512226\pi$
$47$	−5.68035	−	2.64879i	−0.828564	−	0.386366i	−0.790163	+	0.612897i	$0.790004\pi$
$48$		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	0.987366	+	0.158456i	$0.0506516\pi$
$53$	0.309521	+	3.53784i	0.0425159	+	0.485959i	−0.944850	+	0.327503i	$0.893793\pi$
$54$		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	0.910609	−	0.413269i	$-0.135613\pi$
$59$	10.3122	+	3.75333i	1.34253	+	0.488642i	0.431923	+	0.901910i	$0.357835\pi$
$60$		0			0
$61$	2.42752	+	2.03693i	0.310813	+	0.260803i	0.784828	−	0.619714i	$-0.212751\pi$
$61$	2.42752	+	2.03693i	0.310813	+	0.260803i	−0.474015	+	0.880517i	$0.657196\pi$
$62$		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	−0.846102	−	0.533020i	$-0.821057\pi$
$67$	0.868295	−	1.86206i	0.106079	−	0.227487i	0.952181	+	0.305533i	$0.0988347\pi$
$68$		0			0
$69$	−3.11136	+	5.38903i	−0.374564	+	0.648763i
$70$		0			0
$71$	−1.80576	−	2.15203i	−0.214305	−	0.255399i	0.648173	−	0.761493i	$-0.275533\pi$
$71$	−1.80576	−	2.15203i	−0.214305	−	0.255399i	−0.862478	+	0.506094i	$0.831089\pi$
$72$		0			0
$73$	0.0922302	+	0.0645803i	0.0107947	+	0.00755855i	0.578961	−	0.815355i	$-0.303458\pi$
$73$	0.0922302	+	0.0645803i	0.0107947	+	0.00755855i	−0.568167	+	0.822914i	$0.692347\pi$
$74$		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	0.871682	+	0.490073i	$0.163030\pi$
$79$	1.95703	+	11.0989i	0.220184	+	1.24872i	−0.651498	+	0.758650i	$0.725859\pi$
$80$		0			0
$81$	6.02039	−	5.05170i	0.668932	−	0.561301i
$82$		0			0
$83$	−2.25226	−	8.40553i	−0.247217	−	0.922627i	−0.972256	−	0.233919i	$-0.924845\pi$
$83$	−2.25226	−	8.40553i	−0.247217	−	0.922627i	0.725039	−	0.688708i	$-0.241822\pi$
$84$		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	−0.991716	−	0.128446i	$-0.959001\pi$
$89$	−0.149779	+	0.849439i	−0.0158765	+	0.0900403i	0.975840	+	0.218487i	$0.0701121\pi$
$90$		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	0.296077	−	0.955164i	$-0.404322\pi$
$97$	11.9968	−	5.59420i	1.21809	−	0.568004i	0.922013	+	0.387160i	$0.126544\pi$
$98$		0			0
$99$	1.35123	−	1.61033i	0.135804	−	0.161844i
$100$		0			0
$101$	1.09573	−	6.21419i	0.109029	−	0.618335i	−0.880505	−	0.474037i	$-0.842796\pi$
$101$	1.09573	−	6.21419i	0.109029	−	0.618335i	0.989534	−	0.144298i	$-0.0460925\pi$
$102$		0			0
$103$	−2.53468	+	9.45957i	−0.249750	+	0.932079i	0.721187	+	0.692741i	$0.243597\pi$
$103$	−2.53468	+	9.45957i	−0.249750	+	0.932079i	−0.970936	+	0.239338i	$0.923070\pi$
$104$		0			0
$105$	15.2267	+	2.95073i	1.48598	+	0.287961i
$106$		0			0
$107$	−3.99406	−	14.9061i	−0.386121	−	1.44102i	−0.836393	−	0.548131i	$-0.815340\pi$
$107$	−3.99406	−	14.9061i	−0.386121	−	1.44102i	0.450272	−	0.892892i	$-0.351327\pi$
$108$		0			0
$109$	−2.63062	+	2.20735i	−0.251967	+	0.211426i	−0.760019	−	0.649901i	$-0.774810\pi$
$109$	−2.63062	+	2.20735i	−0.251967	+	0.211426i	0.508052	+	0.861327i	$0.330366\pi$
$110$		0			0
$111$	−1.17610	−	6.66997i	−0.111630	−	0.633086i
$112$		0			0
$113$	3.86404	+	3.86404i	0.363498	+	0.363498i	0.865099	−	0.501601i	$-0.167255\pi$
$113$	3.86404	+	3.86404i	0.363498	+	0.363498i	−0.501601	+	0.865099i	$0.667255\pi$
$114$		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	0.404790	−	0.914410i	$-0.367345\pi$
$127$	−6.68188	−	9.54271i	−0.592921	−	0.846779i	−0.997710	+	0.0676311i	$0.978456\pi$
$128$		0			0
$129$	−4.55100	−	3.81874i	−0.400693	−	0.336221i
$130$		0			0
$131$	4.64450	+	1.69046i	0.405791	+	0.147696i	0.536848	−	0.843679i	$-0.319615\pi$
$131$	4.64450	+	1.69046i	0.405791	+	0.147696i	−0.131057	+	0.991375i	$0.541837\pi$
$132$		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	0.927961	+	0.372677i	$0.121560\pi$
$137$	0.922477	+	10.5440i	0.0788125	+	0.900831i	−0.849149	+	0.528154i	$0.822884\pi$
$138$		0			0
$139$	−12.0785	−	2.12977i	−1.02449	−	0.180645i	−0.363935	−	0.931424i	$-0.618567\pi$
$139$	−12.0785	−	2.12977i	−1.02449	−	0.180645i	−0.660553	+	0.750779i	$0.729678\pi$
$140$		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	0.285936	−	0.958249i	$-0.407695\pi$
$149$	10.7707	−	1.89916i	0.882369	−	0.155585i	0.596432	+	0.802663i	$0.296584\pi$
$150$		0			0
$151$			22.0807i			1.79690i	0.439074	+	0.898451i	$0.355307\pi$
$151$			22.0807i			1.79690i	−0.439074	+	0.898451i	$0.644693\pi$
$152$		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	−0.681968	−	0.731382i	$-0.738876\pi$
$157$	−18.5516	−	1.62305i	−1.48058	−	0.129534i	−0.798610	+	0.601848i	$0.794431\pi$
$158$		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	0.515735	−	0.856748i	$-0.327519\pi$
$163$	6.81767	+	1.82679i	0.534001	+	0.143085i	0.0182660	+	0.999833i	$0.494185\pi$
$164$		0			0
$165$	1.57859	+	22.3905i	0.122893	+	1.74310i
$166$		0			0
$167$	−0.466372	+	0.0408023i	−0.0360889	+	0.00315737i	−0.105186	−	0.994453i	$-0.533544\pi$
$167$	−0.466372	+	0.0408023i	−0.0360889	+	0.00315737i	0.0690970	+	0.997610i	$0.477988\pi$
$168$		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	−0.986802	−	0.161930i	$-0.948228\pi$
$173$	−6.26796	−	13.4417i	−0.476544	−	1.02195i	0.510258	−	0.860021i	$-0.329550\pi$
$174$		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	0.922454	−	0.386107i	$-0.126181\pi$
$179$	1.69711	+	2.93948i	0.126848	+	0.219707i	−0.795606	+	0.605815i	$0.792847\pi$
$180$		0			0
$181$	−0.565054	−	1.55247i	−0.0420001	−	0.115394i	0.916920	−	0.399072i	$-0.130668\pi$
$181$	−0.565054	−	1.55247i	−0.0420001	−	0.115394i	−0.958920	+	0.283678i	$0.908445\pi$
$182$		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	−0.588011	−	0.808853i	$-0.700089\pi$
$193$	5.18430	−	7.40395i	0.373174	−	0.532948i	0.961185	+	0.275905i	$0.0889776\pi$
$194$		0			0
$195$	−17.6153	+	2.80033i	−1.26145	+	0.200536i
$196$		0			0
$197$	1.41494	−	0.379131i	0.100810	−	0.0270120i	−0.208061	−	0.978116i	$-0.566715\pi$
$197$	1.41494	−	0.379131i	0.100810	−	0.0270120i	0.308871	+	0.951104i	$0.400049\pi$
$198$		0			0
$199$	−5.25239	−	14.4308i	−0.372332	−	1.02297i	−0.974457	−	0.224573i	$-0.927901\pi$
$199$	−5.25239	−	14.4308i	−0.372332	−	1.02297i	0.602125	−	0.798402i	$-0.294321\pi$
$200$		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	−0.371240	−	0.928537i	$-0.621067\pi$
$211$	7.40816	−	20.3537i	0.509998	−	1.40121i	0.881238	−	0.472672i	$-0.156711\pi$
$212$		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	0.717876	−	0.696170i	$-0.245114\pi$
$223$	19.4722	+	1.70360i	1.30396	+	0.114082i	0.586082	+	0.810252i	$0.300670\pi$
$224$		0			0
$225$	−1.05263	−	1.34413i	−0.0701755	−	0.0896087i
$226$		0			0
$227$	−3.26415	+	3.26415i	−0.216649	+	0.216649i	−0.807085	−	0.590436i	$-0.798956\pi$
$227$	−3.26415	+	3.26415i	−0.216649	+	0.216649i	0.590436	+	0.807085i	$0.298956\pi$
$228$		0			0
$229$		−	4.99206i		−	0.329884i	−0.986303	−	0.164942i	$-0.947256\pi$
$229$		−	4.99206i		−	0.329884i	0.986303	−	0.164942i	$-0.0527438\pi$
$230$		0			0
$231$	42.0544	−	7.41532i	2.76698	−	0.487893i
$232$		0			0
$233$	−0.826433	+	9.44617i	−0.0541414	+	0.618839i	0.919852	+	0.392265i	$0.128308\pi$
$233$	−0.826433	+	9.44617i	−0.0541414	+	0.618839i	−0.973994	+	0.226575i	$0.927247\pi$
$234$		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	−0.655251	−	0.755411i	$-0.727437\pi$
$239$	−5.08115	+	2.93360i	−0.328672	+	0.189759i	0.326579	+	0.945170i	$0.394104\pi$
$240$		0			0
$241$	−26.1187	−	4.60543i	−1.68245	−	0.296662i	−0.750940	−	0.660371i	$-0.770399\pi$
$241$	−26.1187	−	4.60543i	−1.68245	−	0.296662i	−0.931513	+	0.363709i	$0.881510\pi$
$242$		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	0.969749	−	0.244105i	$-0.0784943\pi$
$251$	14.2230	+	11.9345i	0.897747	+	0.753299i	−0.0720018	+	0.997405i	$0.522939\pi$
$252$		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	−0.999999	−	0.00168322i	$-0.999464\pi$
$257$	−5.70587	+	12.2363i	−0.355922	+	0.763278i	0.644076	+	0.764961i	$0.277242\pi$
$258$		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	0.783187	−	0.621786i	$-0.213593\pi$
$263$	7.56965	+	5.30033i	0.466765	+	0.326832i	−0.316422	+	0.948618i	$0.602482\pi$
$264$		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	0.986601	−	0.163151i	$-0.0521659\pi$
$269$	0.0606558	+	0.343996i	0.00369825	+	0.0209738i	−0.982903	+	0.184125i	$0.941055\pi$
$270$		0			0
$271$	12.2387	−	10.2695i	0.743449	−	0.623828i	−0.190313	−	0.981724i	$-0.560950\pi$
$271$	12.2387	−	10.2695i	0.743449	−	0.623828i	0.933762	+	0.357896i	$0.116506\pi$
$272$		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	−0.991158	−	0.132690i	$-0.957639\pi$
$277$	−1.10587	+	4.12716i	−0.0664452	+	0.247977i	0.924712	+	0.380666i	$0.124305\pi$
$278$		0			0
$279$	−0.175469	+	0.995135i	−0.0105051	+	0.0595771i
$280$		0			0
$281$	−6.18716	+	7.37357i	−0.369095	+	0.439870i	−0.918341	−	0.395791i	$-0.870471\pi$
$281$	−6.18716	+	7.37357i	−0.369095	+	0.439870i	0.549246	+	0.835661i	$0.314915\pi$
$282$		0			0
$283$	−21.6840	+	10.1114i	−1.28898	+	0.601061i	−0.941622	−	0.336672i	$-0.890699\pi$
$283$	−21.6840	+	10.1114i	−1.28898	+	0.601061i	−0.347357	+	0.937733i	$0.612921\pi$
$284$		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	0.773607	+	0.633666i	$0.218451\pi$
$293$	−3.64921	+	13.6190i	−0.213189	+	0.795633i	−0.986796	+	0.161967i	$0.948216\pi$
$294$		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	0.926169	−	0.377108i	$-0.123081\pi$
$307$	15.5691	+	10.9016i	0.888573	+	0.622185i	−0.0375967	+	0.999293i	$0.511970\pi$
$308$		0			0
$309$	10.2640	+	12.2322i	0.583899	+	0.695864i
$310$		0			0
$311$	1.87691	−	3.25090i	0.106430	−	0.184341i	−0.807892	−	0.589331i	$-0.799391\pi$
$311$	1.87691	−	3.25090i	0.106430	−	0.184341i	0.914321	+	0.404989i	$0.132725\pi$
$312$		0			0
$313$	−0.738313	+	1.58332i	−0.0417319	+	0.0894944i	−0.926068	−	0.377356i	$-0.876833\pi$
$313$	−0.738313	+	1.58332i	−0.0417319	+	0.0894944i	0.884336	+	0.466850i	$0.154611\pi$
$314$		0			0
$315$	−2.33514	+	2.25760i	−0.131570	+	0.127201i
$316$		0			0
$317$	3.20502	+	4.57724i	0.180012	+	0.257084i	0.899010	−	0.437929i	$-0.144288\pi$
$317$	3.20502	+	4.57724i	0.180012	+	0.257084i	−0.718998	+	0.695012i	$0.755399\pi$
$318$		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	−0.419990	−	0.907529i	$-0.637966\pi$
$331$	2.83740	−	1.63817i	0.155958	−	0.0900422i	0.575948	+	0.817486i	$0.304633\pi$
$332$		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	−0.914565	−	0.404440i	$-0.867466\pi$
$337$	1.03419	−	11.8209i	0.0563360	−	0.643923i	0.970900	−	0.239483i	$-0.0769780\pi$
$338$		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	−0.0575026	−	0.998345i	$-0.518314\pi$
$347$	−5.35539	−	0.468536i	−0.287492	−	0.0251523i	−0.229990	+	0.973193i	$0.573869\pi$
$348$		0			0
$349$	−17.3820	−	10.0355i	−0.930436	−	0.537187i	−0.0434863	−	0.999054i	$-0.513846\pi$
$349$	−17.3820	−	10.0355i	−0.930436	−	0.537187i	−0.886949	+	0.461867i	$0.847180\pi$
$350$		0			0
$351$	25.0464	−	9.11613i	1.33688	−	0.486583i
$352$		0			0
$353$	28.2204	+	7.56165i	1.50202	+	0.402466i	0.913777	−	0.406216i	$-0.133152\pi$
$353$	28.2204	+	7.56165i	1.50202	+	0.402466i	0.588246	+	0.808682i	$0.299819\pi$
$354$		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	−0.430901	−	0.902399i	$-0.641804\pi$
$359$	9.08029	−	24.9479i	0.479239	−	1.31670i	0.910140	−	0.414300i	$-0.135974\pi$
$360$		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	−0.590627	−	0.806945i	$-0.701119\pi$
$367$	−0.658107	+	0.460812i	−0.0343529	+	0.0240542i	0.556274	+	0.830999i	$0.312231\pi$
$368$		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	−0.391334	−	0.920249i	$-0.627986\pi$
$373$	−5.21679	+	1.39783i	−0.270115	+	0.0723771i	0.121219	+	0.992626i	$0.461320\pi$
$374$		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	−0.601350	−	0.798986i	$-0.705370\pi$
$383$	6.94993	−	9.92553i	0.355125	−	0.507171i	0.956475	+	0.291815i	$0.0942591\pi$
$384$		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	0.806433	+	0.591326i	$0.201395\pi$
$389$	11.2178	+	30.8207i	0.568766	+	1.56267i	−0.237667	+	0.971347i	$0.576383\pi$
$390$		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	0.998315	−	0.0580241i	$-0.0184800\pi$
$397$	6.21977	+	13.3383i	0.312161	+	0.669432i	−0.686154	+	0.727457i	$0.740702\pi$
$398$		0			0
$399$	−26.0464	+	15.3530i	−1.30395	+	0.768610i
$400$		0			0
$401$	5.99205	−	16.4630i	0.299229	−	0.822124i	−0.695401	−	0.718622i	$-0.744773\pi$
$401$	5.99205	−	16.4630i	0.299229	−	0.822124i	0.994629	−	0.103502i	$-0.0330048\pi$
$402$		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	−0.555184	−	0.831728i	$-0.687352\pi$
$409$	−9.01686	+	3.28187i	−0.445855	+	0.162278i	0.109329	+	0.994006i	$0.465130\pi$
$410$		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	$-0.933430\pi$
$419$		−	8.49953i		−	0.415229i	0.978211	−	0.207615i	$-0.0665700\pi$
$420$		0			0
$421$	18.9233	−	3.33669i	0.922267	−	0.162621i	0.307698	−	0.951484i	$-0.400441\pi$
$421$	18.9233	−	3.33669i	0.922267	−	0.162621i	0.614569	+	0.788863i	$0.289330\pi$
$422$		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	0.485989	−	0.873965i	$-0.338459\pi$
$431$	13.3647	+	2.35656i	0.643757	+	0.113512i	0.157767	+	0.987476i	$0.449570\pi$
$432$		0			0
$433$	3.08921	+	35.3099i	0.148458	+	1.69688i	0.596292	+	0.802768i	$0.296640\pi$
$433$	3.08921	+	35.3099i	0.148458	+	1.69688i	−0.447834	+	0.894117i	$0.647804\pi$
$434$		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	0.977890	−	0.209121i	$-0.0670603\pi$
$439$	33.3682	+	12.1450i	1.59258	+	0.579650i	0.614687	+	0.788772i	$0.289283\pi$
$440$		0			0
$441$	2.90264	+	2.43561i	0.138221	+	0.115981i
$442$		0			0
$443$	2.71132	+	3.87217i	0.128819	+	0.183972i	0.878380	−	0.477962i	$-0.158624\pi$
$443$	2.71132	+	3.87217i	0.128819	+	0.183972i	−0.749562	+	0.661935i	$0.769736\pi$
$444$		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	−0.716333	−	0.697759i	$-0.754181\pi$
$449$	5.21499	−	9.03263i	0.246111	−	0.426276i	0.962443	+	0.271483i	$0.0875140\pi$
$450$		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	−0.999706	−	0.0242509i	$-0.992280\pi$
$457$	−21.8897	−	21.8897i	−1.02396	−	1.02396i	−0.0242509	−	0.999706i	$-0.507720\pi$
$458$		0			0
$459$	−3.73884	−	21.2040i	−0.174514	−	0.989720i
$460$		0			0
$461$	−23.8271	+	19.9933i	−1.10974	+	0.931180i	−0.998041	−	0.0625622i	$-0.980073\pi$
$461$	−23.8271	+	19.9933i	−1.10974	+	0.931180i	−0.111696	+	0.993742i	$0.535628\pi$
$462$		0			0
$463$	3.56144	+	13.2915i	0.165514	+	0.617708i	0.997974	+	0.0636221i	$0.0202652\pi$
$463$	3.56144	+	13.2915i	0.165514	+	0.617708i	−0.832460	+	0.554085i	$0.813068\pi$
$464$		0			0
$465$	−6.03864	−	8.94160i	−0.280035	−	0.414657i
$466$		0			0
$467$	−1.47897	+	5.51958i	−0.0684385	+	0.255416i	−0.991666	−	0.128839i	$-0.958875\pi$
$467$	−1.47897	+	5.51958i	−0.0684385	+	0.255416i	0.923227	+	0.384255i	$0.125542\pi$
$468$		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	−0.723607	−	0.690212i	$-0.757517\pi$
$479$	1.78967	−	2.13284i	0.0817719	−	0.0974520i	0.805379	+	0.592760i	$0.201962\pi$
$480$		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	0.875509	+	0.483202i	$0.160526\pi$
$487$	7.92017	+	29.5585i	0.358897	+	1.33942i	−0.516612	+	0.856220i	$0.672807\pi$
$488$		0			0
$489$	8.81594	−	7.39745i	0.398671	−	0.334524i
$490$		0			0
$491$	−0.652704	−	3.70167i	−0.0294561	−	0.167054i	0.966531	−	0.256549i	$-0.0825857\pi$
$491$	−0.652704	−	3.70167i	−0.0294561	−	0.167054i	−0.995987	+	0.0894954i	$0.971475\pi$
$492$		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	0.762967	−	0.646437i	$-0.223742\pi$
$499$	−0.137101	−	0.163390i	−0.00613746	−	0.00731435i	−0.769104	+	0.639123i	$0.779297\pi$
$500$		0			0
$501$	−0.381663	+	0.661060i	−0.0170515	+	0.0295340i
$502$		0			0
$503$	5.13886	−	11.0203i	0.229130	−	0.491372i	−0.757806	−	0.652480i	$-0.773729\pi$
$503$	5.13886	−	11.0203i	0.229130	−	0.491372i	0.986937	+	0.161108i	$0.0515066\pi$
$504$		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	0.280534	−	0.959844i	$-0.409488\pi$
$509$	−13.8979	−	11.6617i	−0.616014	−	0.516897i	−0.896548	+	0.442947i	$0.853933\pi$
$510$		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	−0.536109	−	0.844149i	$-0.680106\pi$
$521$	−1.66873	+	0.963444i	−0.0731086	+	0.0422092i	0.463000	+	0.886358i	$0.346773\pi$
$522$		0			0
$523$	11.9082	+	5.55289i	0.520709	+	0.242811i	0.665160	−	0.746701i	$-0.268364\pi$
$523$	11.9082	+	5.55289i	0.520709	+	0.242811i	−0.144450	+	0.989512i	$0.546141\pi$
$524$		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	−0.188182	−	0.982134i	$-0.560260\pi$
$541$	6.95375	−	2.53096i	0.298965	−	0.108814i	0.487148	+	0.873320i	$0.338037\pi$
$542$		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	−0.148296	−	0.988943i	$-0.547379\pi$
$547$	−2.86763	+	0.250885i	−0.122611	+	0.0107271i	0.0256851	+	0.999670i	$0.491823\pi$
$548$		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	−0.716707	−	0.697375i	$-0.754351\pi$
$557$	−7.23405	+	5.06534i	−0.306517	+	0.214625i	0.410190	+	0.912000i	$0.365462\pi$
$558$		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	−0.236816	−	0.971555i	$-0.576104\pi$
$563$	1.04101	−	0.278939i	0.0438735	−	0.0117559i	0.280689	+	0.959799i	$0.409437\pi$
$564$		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	0.221978	−	0.975052i	$-0.428749\pi$
$577$	21.6606	−	5.80394i	0.901742	−	0.241621i	0.679764	+	0.733431i	$0.262082\pi$
$578$		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	0.872804	+	0.488071i	$0.162299\pi$
$587$	16.6122	+	35.6251i	0.685660	+	1.47040i	−0.187144	+	0.982333i	$0.559923\pi$
$588$		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	−0.948945	−	0.315442i	$-0.897847\pi$
$593$	−44.5317	+	3.89602i	−1.82870	+	0.159990i	−0.879752	+	0.475432i	$0.842292\pi$
$594$		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	0.248027	−	0.968753i	$-0.420218\pi$
$599$	25.9608	−	9.44895i	1.06073	−	0.386074i	0.812702	+	0.582679i	$0.197996\pi$
$600$		0			0
$601$	31.0150	+	17.9065i	1.26513	+	0.730423i	0.974062	−	0.226279i	$-0.0726562\pi$
$601$	31.0150	+	17.9065i	1.26513	+	0.730423i	0.291068	+	0.956702i	$0.405990\pi$
$602$		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	0.165229	−	0.986255i	$-0.447164\pi$
$607$	28.3695	−	28.3695i	1.15148	−	1.15148i	0.986255	−	0.165229i	$-0.0528363\pi$
$608$		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	−0.788545	−	0.614978i	$-0.789165\pi$
$613$	2.34738	−	26.8307i	0.0948100	−	1.08368i	0.883355	−	0.468705i	$-0.155279\pi$
$614$		0			0
$615$	−42.1040	−	12.0470i	−1.69780	−	0.485783i
$616$		0			0
$617$	18.1404	+	8.45900i	0.730304	+	0.340546i	0.751951	−	0.659219i	$-0.229113\pi$
$617$	18.1404	+	8.45900i	0.730304	+	0.340546i	−0.0216467	+	0.999766i	$0.506891\pi$
$618$		0			0
$619$	19.2344	−	11.1050i	0.773095	−	0.446347i	−0.0608824	−	0.998145i	$-0.519391\pi$
$619$	19.2344	−	11.1050i	0.773095	−	0.446347i	0.833978	+	0.551798i	$0.186058\pi$
$620$		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	0.646002	−	0.763336i	$-0.276440\pi$
$631$	0.161770	+	0.135741i	0.00643997	+	0.00540377i	−0.639562	+	0.768740i	$0.720884\pi$
$632$		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	0.507958	−	0.861382i	$-0.330401\pi$
$641$	−10.8499	−	12.9304i	−0.428544	−	0.510719i	−0.936502	+	0.350663i	$0.885956\pi$
$642$		0			0
$643$	−32.1531	−	22.5139i	−1.26800	−	0.887860i	−0.270795	−	0.962637i	$-0.587287\pi$
$643$	−32.1531	−	22.5139i	−1.26800	−	0.887860i	−0.997200	+	0.0747770i	$0.976175\pi$
$644$		0			0
$645$	−6.83538	+	11.3908i	−0.269143	+	0.448511i
$646$		0			0
$647$	−0.922638	−	0.922638i	−0.0362726	−	0.0362726i	0.688738	−	0.725010i	$-0.258165\pi$
$647$	−0.922638	−	0.922638i	−0.0362726	−	0.0362726i	−0.725010	+	0.688738i	$0.758165\pi$
$648$		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	0.953189	+	0.302375i	$0.0977796\pi$
$653$	7.12674	+	26.5973i	0.278891	+	1.04083i	−0.674298	+	0.738459i	$0.735554\pi$
$654$		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	−0.951241	−	0.308448i	$-0.900191\pi$
$659$	1.23550	−	7.00689i	0.0481284	−	0.272950i	0.999370	+	0.0354978i	$0.0113017\pi$
$660$		0			0
$661$	14.5776	−	17.3729i	0.567002	−	0.675727i	−0.404010	−	0.914754i	$-0.632384\pi$
$661$	14.5776	−	17.3729i	0.567002	−	0.675727i	0.971013	+	0.239027i	$0.0768285\pi$
$662$		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	−0.984692	−	0.174303i	$-0.944233\pi$
$673$	−1.16149	+	4.33474i	−0.0447722	+	0.167092i	0.939920	+	0.341395i	$0.110899\pi$
$674$		0			0
$675$	−27.2023	+	1.45688i	−1.04702	+	0.0560752i
$676$		0			0
$677$	3.58347	+	13.3737i	0.137724	+	0.513993i	0.999972	+	0.00750657i	$0.00238944\pi$
$677$	3.58347	+	13.3737i	0.137724	+	0.513993i	−0.862248	+	0.506487i	$0.830944\pi$
$678$		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	0.953992	−	0.299833i	$-0.0969311\pi$
$683$	17.0959	+	17.0959i	0.654158	+	0.654158i	−0.299833	+	0.953992i	$0.596931\pi$
$684$		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	−0.991671	−	0.128793i	$-0.958890\pi$
$691$	−10.1020	+	17.4972i	−0.384298	+	0.665623i	0.607374	+	0.794416i	$0.292223\pi$
$692$		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	0.575392	−	0.817877i	$-0.304849\pi$
$701$	12.9853	+	4.72625i	0.490447	+	0.178508i	−0.0849454	+	0.996386i	$0.527072\pi$
$702$		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	0.410556	−	0.911835i	$-0.365335\pi$
$709$	12.9004	+	2.27470i	0.484486	+	0.0854280i	0.0739303	+	0.997263i	$0.476446\pi$
$710$		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	−0.267019	−	0.963691i	$-0.586039\pi$
$719$	−5.05000	+	0.890451i	−0.188333	+	0.0332082i	0.0786859	+	0.996899i	$0.474928\pi$
$720$		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	0.365288	−	0.930895i	$-0.380971\pi$
$727$	15.1903	+	1.32898i	0.563377	+	0.0492891i	0.198090	+	0.980184i	$0.436526\pi$
$728$		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	0.593680	−	0.804701i	$-0.297674\pi$
$733$	19.0999	+	5.11781i	0.705472	+	0.189031i	0.111791	+	0.993732i	$0.464341\pi$
$734$		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	−0.991645	−	0.129000i	$-0.958823\pi$
$739$	−4.05271	+	11.1347i	−0.149081	+	0.409597i	0.842563	+	0.538597i	$0.181046\pi$
$740$		0			0
$741$	22.1082	−	26.8357i	0.812166	−	0.985834i
$742$		0			0
$743$	−1.42642	−	3.05896i	−0.0523301	−	0.112222i	0.878404	−	0.477919i	$-0.158609\pi$
$743$	−1.42642	−	3.05896i	−0.0523301	−	0.112222i	−0.930734	+	0.365696i	$0.880831\pi$
$744$		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	0.992559	+	0.121761i	$0.0388543\pi$
$751$	8.50855	+	23.3771i	0.310481	+	0.853041i	−0.682078	+	0.731280i	$0.738924\pi$
$752$		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	−0.974940	−	0.222469i	$-0.928588\pi$
$757$	−11.8979	+	16.9920i	−0.432438	+	0.617585i	0.542502	+	0.840055i	$0.317477\pi$
$758$		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	0.998052	−	0.0623797i	$-0.0198690\pi$
$769$	5.36323	+	14.7354i	0.193403	+	0.531370i	−0.804649	+	0.593750i	$0.797647\pi$
$770$		0			0
$771$	11.0069	+	19.0646i	0.396405	+	0.686593i
$772$		0			0
$773$	−1.81583	+	1.27145i	−0.0653107	+	0.0457310i	−0.605776	−	0.795635i	$-0.707137\pi$
$773$	−1.81583	+	1.27145i	−0.0653107	+	0.0457310i	0.540465	+	0.841366i	$0.318248\pi$
$774$		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	0.0178245	−	0.999841i	$-0.494326\pi$
$787$	−13.0914	−	3.50784i	−0.466660	−	0.125041i	−0.484484	+	0.874800i	$0.660993\pi$
$788$		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	−0.831813	−	0.555056i	$-0.812697\pi$
$797$	−7.81316	+	7.81316i	−0.276756	+	0.276756i	0.555056	+	0.831813i	$0.312697\pi$
$798$		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	−0.878058	−	0.478555i	$-0.841161\pi$
$809$	−25.6739	+	14.8228i	−0.902646	+	0.521143i	−0.0245880	+	0.999698i	$0.507827\pi$
$810$		0			0
$811$	41.5313	+	7.32310i	1.45836	+	0.257149i	0.845896	−	0.533348i	$-0.179066\pi$
$811$	41.5313	+	7.32310i	1.45836	+	0.257149i	0.612467	+	0.790497i	$0.290177\pi$
$812$		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	−0.148035	−	0.988982i	$-0.547295\pi$
$821$	−32.8851	−	27.5939i	−1.14770	−	0.963033i	−0.999663	+	0.0259486i	$0.991739\pi$
$822$		0			0
$823$	−2.16592	−	3.09325i	−0.0754992	−	0.107824i	0.779626	−	0.626245i	$-0.215409\pi$
$823$	−2.16592	−	3.09325i	−0.0754992	−	0.107824i	−0.855126	+	0.518421i	$0.826520\pi$
$824$		0			0
$825$	48.8915	−	11.3465i	1.70218	−	0.395036i
$826$		0			0
$827$	−16.2958	+	34.9465i	−0.566661	+	1.21521i	0.389136	+	0.921180i	$0.372774\pi$
$827$	−16.2958	+	34.9465i	−0.566661	+	1.21521i	−0.955797	+	0.294028i	$0.905004\pi$
$828$		0			0
$829$	−21.7208	+	37.6215i	−0.754393	+	1.30665i	0.191282	+	0.981535i	$0.438735\pi$
$829$	−21.7208	+	37.6215i	−0.754393	+	1.30665i	−0.945675	+	0.325112i	$0.894598\pi$
$830$		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	0.724989	+	0.688761i	$0.241845\pi$
$839$	8.08984	+	45.8798i	0.279292	+	1.58395i	−0.445696	+	0.895184i	$0.647044\pi$
$840$		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	0.468735	−	0.883339i	$-0.344710\pi$
$853$	42.2528	−	19.7028i	1.44671	−	0.674612i	0.977974	+	0.208727i	$0.0669320\pi$
$854$		0			0
$855$	3.27285	+	0.603640i	0.111929	+	0.0206441i
$856$		0			0
$857$	0.377599	−	0.176077i	0.0128985	−	0.00601469i	−0.416158	−	0.909292i	$-0.636624\pi$
$857$	0.377599	−	0.176077i	0.0128985	−	0.00601469i	0.429057	+	0.903277i	$0.358846\pi$
$858$		0			0
$859$	19.1057	−	22.7693i	0.651879	−	0.776879i	−0.334317	−	0.942461i	$-0.608506\pi$
$859$	19.1057	−	22.7693i	0.651879	−	0.776879i	0.986196	+	0.165582i	$0.0529501\pi$
$860$		0			0
$861$	−14.4677	+	82.0506i	−0.493059	+	2.79628i
$862$		0			0
$863$	0.879081	−	3.28077i	0.0299243	−	0.111679i	−0.949348	−	0.314226i	$-0.898255\pi$
$863$	0.879081	−	3.28077i	0.0299243	−	0.111679i	0.979273	+	0.202547i	$0.0649218\pi$
$864$		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	0.999986	+	0.00525616i	$0.00167310\pi$
$877$	39.8886	+	27.9303i	1.34694	+	0.943138i	0.346955	+	0.937882i	$0.387216\pi$
$878$		0			0
$879$	14.7772	+	17.6108i	0.498423	+	0.593998i
$880$		0			0
$881$	−9.67864	+	16.7639i	−0.326082	+	0.564790i	−0.981731	−	0.190276i	$-0.939062\pi$
$881$	−9.67864	+	16.7639i	−0.326082	+	0.564790i	0.655649	+	0.755066i	$0.272395\pi$
$882$		0			0
$883$	−6.14600	+	13.1801i	−0.206829	+	0.443547i	−0.982170	−	0.187997i	$-0.939801\pi$
$883$	−6.14600	+	13.1801i	−0.206829	+	0.443547i	0.775340	+	0.631544i	$0.217578\pi$
$884$		0			0
$885$	−27.8100	−	28.7651i	−0.934823	−	0.966928i
$886$		0			0
$887$	−21.8051	−	31.1408i	−0.732142	−	1.04561i	−0.996695	−	0.0812359i	$-0.974113\pi$
$887$	−21.8051	−	31.1408i	−0.732142	−	1.04561i	0.264553	−	0.964371i	$-0.414776\pi$
$888$		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	0.726721	+	0.686933i	$0.241043\pi$
$907$	−3.25993	+	37.2611i	−0.108244	+	1.23724i	−0.834965	+	0.550303i	$0.814512\pi$
$908$		0			0
$909$	2.12184	−	0.374138i	0.0703771	−	0.0124094i
$910$		0			0
$911$		−	50.7989i		−	1.68304i	−0.540225	−	0.841521i	$-0.681661\pi$
$911$		−	50.7989i		−	1.68304i	0.540225	−	0.841521i	$-0.318339\pi$
$912$		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	−0.398489	−	0.917173i	$-0.630465\pi$
$919$	−42.1994	−	24.3638i	−1.39203	−	0.803688i	−0.993540	+	0.113485i	$0.963798\pi$
$920$		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	−0.615917	−	0.787811i	$-0.711214\pi$
$929$	11.0427	−	30.3395i	0.362298	−	0.995405i	0.978215	−	0.207594i	$-0.0665634\pi$
$930$		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	−0.222988	−	0.974821i	$-0.571581\pi$
$937$	18.8798	−	13.2198i	0.616777	−	0.431872i	0.839766	+	0.542949i	$0.182692\pi$
$938$		0			0
$939$	1.42425	+	2.46687i	0.0464785	+	0.0805031i
$940$		0			0
$941$	−11.8218	−	32.4802i	−0.385380	−	1.05882i	−0.969057	−	0.246837i	$-0.920609\pi$
$941$	−11.8218	−	32.4802i	−0.385380	−	1.05882i	0.583677	−	0.811986i	$-0.301613\pi$
$942$		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	−0.926076	−	0.377338i	$-0.876839\pi$
$947$	−7.83974	+	11.1963i	−0.254757	+	0.363831i	0.671318	+	0.741169i	$0.265728\pi$
$948$		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	−0.853137	−	0.521687i	$-0.825303\pi$
$953$	−2.19555	+	3.13557i	−0.0711209	+	0.101571i	0.782016	+	0.623259i	$0.214192\pi$
$954$		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	0.943398	−	0.331663i	$-0.107610\pi$
$967$	2.57869	+	5.53002i	0.0829251	+	0.177833i	−0.860473	+	0.509496i	$0.829832\pi$
$968$		0			0
$969$	−18.2475	−	21.3523i	−0.586196	−	0.685933i
$970$		0			0
$971$	1.34949	−	3.70770i	0.0433073	−	0.118986i	−0.916154	−	0.400827i	$-0.868723\pi$
$971$	1.34949	−	3.70770i	0.0433073	−	0.118986i	0.959461	+	0.281841i	$0.0909451\pi$
$972$		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	0.497575	−	0.867421i	$-0.334224\pi$
$977$	15.4653	+	4.14390i	0.494777	+	0.132575i	−0.00279779	+	0.999996i	$0.500891\pi$
$978$		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	0.0544510	−	0.998516i	$-0.482659\pi$
$983$	−2.04783	−	0.179162i	−0.0653157	−	0.00571438i	−0.119767	+	0.992802i	$0.538215\pi$
$984$		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	−0.109860	−	0.993947i	$-0.535040\pi$
$991$	3.99342	−	0.704147i	0.126855	−	0.0223680i	0.236715	+	0.971579i	$0.423929\pi$
$992$		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	0.232811	−	0.972522i	$-0.425208\pi$
$997$	−11.4472	−	5.33792i	−0.362536	−	0.169054i	−0.595347	+	0.803469i	$0.702985\pi$
$998$		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.357.8	yes	120
5.3	odd	4	inner	380.2.bh.a.53.8	yes	120
19.14	odd	18	inner	380.2.bh.a.337.8	yes	120
95.33	even	36	inner	380.2.bh.a.33.8	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bh.a.33.8	✓	120	95.33	even	36	inner
380.2.bh.a.53.8	yes	120	5.3	odd	4	inner
380.2.bh.a.337.8	yes	120	19.14	odd	18	inner
380.2.bh.a.357.8	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)

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