LMFDB - Embedded newform 2394.2.f.b.2015.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2394,2,Mod(2015,2394)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2394, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("2394.2015");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2394.f (of order $2$, degree $1$, 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:	$19.1161862439$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2015.9
Character	$\chi$	$=$	2394.2015
Dual form			2394.2.f.b.2015.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} -1.42576 q^{5} +(2.62657 + 0.317999i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} -1.42576 q^{5} +(2.62657 + 0.317999i) q^{7} +1.00000i q^{8} +1.42576i q^{10} -1.96426i q^{11} +5.57912i q^{13} +(0.317999 - 2.62657i) q^{14} +1.00000 q^{16} -1.24731 q^{17} -1.00000i q^{19} +1.42576 q^{20} -1.96426 q^{22} -0.582257i q^{23} -2.96720 q^{25} +5.57912 q^{26} +(-2.62657 - 0.317999i) q^{28} +0.497667i q^{29} +6.46942i q^{31} -1.00000i q^{32} +1.24731i q^{34} +(-3.74487 - 0.453391i) q^{35} +4.52011 q^{37} -1.00000 q^{38} -1.42576i q^{40} +1.13024 q^{41} -9.71565 q^{43} +1.96426i q^{44} -0.582257 q^{46} -3.38468 q^{47} +(6.79775 + 1.67049i) q^{49} +2.96720i q^{50} -5.57912i q^{52} +9.99558i q^{53} +2.80058i q^{55} +(-0.317999 + 2.62657i) q^{56} +0.497667 q^{58} -5.26327 q^{59} +11.8401i q^{61} +6.46942 q^{62} -1.00000 q^{64} -7.95450i q^{65} -2.22053 q^{67} +1.24731 q^{68} +(-0.453391 + 3.74487i) q^{70} +4.00707i q^{71} -1.22215i q^{73} -4.52011i q^{74} +1.00000i q^{76} +(0.624634 - 5.15928i) q^{77} +3.74743 q^{79} -1.42576 q^{80} -1.13024i q^{82} -6.23791 q^{83} +1.77837 q^{85} +9.71565i q^{86} +1.96426 q^{88} +15.8345 q^{89} +(-1.77415 + 14.6540i) q^{91} +0.582257i q^{92} +3.38468i q^{94} +1.42576i q^{95} +4.51004i q^{97} +(1.67049 - 6.79775i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} + 4 q^{7}+O(q^{10}) $ 24 * q - 24 * q^4 + 4 * q^7	$ 24 q - 24 q^{4} + 4 q^{7} + 4 q^{14} + 24 q^{16} - 32 q^{17} - 8 q^{22} + 16 q^{25} - 4 q^{28} + 24 q^{35} - 24 q^{38} + 8 q^{41} + 16 q^{43} - 8 q^{46} - 16 q^{49} - 4 q^{56} + 16 q^{58} - 16 q^{59} + 16 q^{62} - 24 q^{64} - 24 q^{67} + 32 q^{68} - 16 q^{70} - 8 q^{77} - 40 q^{79} + 64 q^{83} + 40 q^{85} + 8 q^{88} + 64 q^{89} + 8 q^{91} + 16 q^{98}+O(q^{100}) $ 24 * q - 24 * q^4 + 4 * q^7 + 4 * q^14 + 24 * q^16 - 32 * q^17 - 8 * q^22 + 16 * q^25 - 4 * q^28 + 24 * q^35 - 24 * q^38 + 8 * q^41 + 16 * q^43 - 8 * q^46 - 16 * q^49 - 4 * q^56 + 16 * q^58 - 16 * q^59 + 16 * q^62 - 24 * q^64 - 24 * q^67 + 32 * q^68 - 16 * q^70 - 8 * q^77 - 40 * q^79 + 64 * q^83 + 40 * q^85 + 8 * q^88 + 64 * q^89 + 8 * q^91 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times$.

$n$	$533$	$1009$	$1711$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−1.42576			−0.637620			−0.318810	−	0.947819i	$-0.603283\pi$
$5$	−1.42576			−0.637620			−0.318810	+	0.947819i	$0.603283\pi$
$6$		0			0
$7$	2.62657	+	0.317999i	0.992751	+	0.120192i
$7$	2.62657	+	0.317999i	0.992751	+	0.120192i
$8$			1.00000i			0.353553i
$9$		0			0
$10$			1.42576i			0.450866i
$11$		−	1.96426i		−	0.592248i	−0.955149	−	0.296124i	$-0.904306\pi$
$11$		−	1.96426i		−	0.592248i	0.955149	−	0.296124i	$-0.0956942\pi$
$12$		0			0
$13$			5.57912i			1.54737i	0.633571	+	0.773685i	$0.281588\pi$
$13$			5.57912i			1.54737i	−0.633571	+	0.773685i	$0.718412\pi$
$14$	0.317999	−	2.62657i	0.0849888	−	0.701981i
$15$		0			0
$16$	1.00000			0.250000
$17$	−1.24731			−0.302517			−0.151258	−	0.988494i	$-0.548333\pi$
$17$	−1.24731			−0.302517			−0.151258	+	0.988494i	$0.548333\pi$
$18$		0			0
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	1.42576			0.318810
$21$		0			0
$22$	−1.96426			−0.418783
$23$		−	0.582257i		−	0.121409i	−0.998156	−	0.0607045i	$-0.980665\pi$
$23$		−	0.582257i		−	0.121409i	0.998156	−	0.0607045i	$-0.0193347\pi$
$24$		0			0
$25$	−2.96720			−0.593440
$26$	5.57912			1.09416
$27$		0			0
$28$	−2.62657	−	0.317999i	−0.496375	−	0.0600962i
$29$			0.497667i			0.0924144i	0.998932	+	0.0462072i	$0.0147134\pi$
$29$			0.497667i			0.0924144i	−0.998932	+	0.0462072i	$0.985287\pi$
$30$		0			0
$31$			6.46942i			1.16194i	0.813924	+	0.580971i	$0.197327\pi$
$31$			6.46942i			1.16194i	−0.813924	+	0.580971i	$0.802673\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$			1.24731i			0.213912i
$35$	−3.74487	−	0.453391i	−0.632998	−	0.0766371i
$36$		0			0
$37$	4.52011			0.743101			0.371551	−	0.928413i	$-0.378826\pi$
$37$	4.52011			0.743101			0.371551	+	0.928413i	$0.378826\pi$
$38$	−1.00000			−0.162221
$39$		0			0
$40$		−	1.42576i		−	0.225433i
$41$	1.13024			0.176515			0.0882573	−	0.996098i	$-0.471870\pi$
$41$	1.13024			0.176515			0.0882573	+	0.996098i	$0.471870\pi$
$42$		0			0
$43$	−9.71565			−1.48162			−0.740811	−	0.671713i	$-0.765559\pi$
$43$	−9.71565			−1.48162			−0.740811	+	0.671713i	$0.765559\pi$
$44$			1.96426i			0.296124i
$45$		0			0
$46$	−0.582257			−0.0858491
$47$	−3.38468			−0.493706			−0.246853	−	0.969053i	$-0.579397\pi$
$47$	−3.38468			−0.493706			−0.246853	+	0.969053i	$0.579397\pi$
$48$		0			0
$49$	6.79775	+	1.67049i	0.971108	+	0.238642i
$50$			2.96720i			0.419626i
$51$		0			0
$52$		−	5.57912i		−	0.773685i
$53$			9.99558i			1.37300i	0.727131	+	0.686499i	$0.240853\pi$
$53$			9.99558i			1.37300i	−0.727131	+	0.686499i	$0.759147\pi$
$54$		0			0
$55$			2.80058i			0.377629i
$56$	−0.317999	+	2.62657i	−0.0424944	+	0.350990i
$57$		0			0
$58$	0.497667			0.0653468
$59$	−5.26327			−0.685219			−0.342610	−	0.939478i	$-0.611311\pi$
$59$	−5.26327			−0.685219			−0.342610	+	0.939478i	$0.611311\pi$
$60$		0			0
$61$			11.8401i			1.51597i	0.652269	+	0.757987i	$0.273817\pi$
$61$			11.8401i			1.51597i	−0.652269	+	0.757987i	$0.726183\pi$
$62$	6.46942			0.821617
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	7.95450i		−	0.986634i
$66$		0			0
$67$	−2.22053			−0.271280			−0.135640	−	0.990758i	$-0.543309\pi$
$67$	−2.22053			−0.271280			−0.135640	+	0.990758i	$0.543309\pi$
$68$	1.24731			0.151258
$69$		0			0
$70$	−0.453391	+	3.74487i	−0.0541906	+	0.447597i
$71$			4.00707i			0.475552i	0.971320	+	0.237776i	$0.0764184\pi$
$71$			4.00707i			0.475552i	−0.971320	+	0.237776i	$0.923582\pi$
$72$		0			0
$73$		−	1.22215i		−	0.143042i	−0.997439	−	0.0715212i	$-0.977215\pi$
$73$		−	1.22215i		−	0.143042i	0.997439	−	0.0715212i	$-0.0227854\pi$
$74$		−	4.52011i		−	0.525452i
$75$		0			0
$76$			1.00000i			0.114708i
$77$	0.624634	−	5.15928i	0.0711837	−	0.587955i
$78$		0			0
$79$	3.74743			0.421619			0.210810	−	0.977527i	$-0.432390\pi$
$79$	3.74743			0.421619			0.210810	+	0.977527i	$0.432390\pi$
$80$	−1.42576			−0.159405
$81$		0			0
$82$		−	1.13024i		−	0.124815i
$83$	−6.23791			−0.684700			−0.342350	−	0.939573i	$-0.611223\pi$
$83$	−6.23791			−0.684700			−0.342350	+	0.939573i	$0.611223\pi$
$84$		0			0
$85$	1.77837			0.192891
$86$			9.71565i			1.04767i
$87$		0			0
$88$	1.96426			0.209391
$89$	15.8345			1.67845			0.839225	−	0.543785i	$-0.183009\pi$
$89$	15.8345			1.67845			0.839225	+	0.543785i	$0.183009\pi$
$90$		0			0
$91$	−1.77415	+	14.6540i	−0.185982	+	1.53615i
$92$			0.582257i			0.0607045i
$93$		0			0
$94$			3.38468i			0.349103i
$95$			1.42576i			0.146280i
$96$		0			0
$97$			4.51004i			0.457925i	0.973435	+	0.228963i	$0.0735334\pi$
$97$			4.51004i			0.457925i	−0.973435	+	0.228963i	$0.926467\pi$
$98$	1.67049	−	6.79775i	0.168745	−	0.686677i
$99$		0			0
$100$	2.96720			0.296720
$101$	−17.5394			−1.74524			−0.872620	−	0.488400i	$-0.837581\pi$
$101$	−17.5394			−1.74524			−0.872620	+	0.488400i	$0.837581\pi$
$102$		0			0
$103$			17.0744i			1.68239i	0.540730	+	0.841196i	$0.318148\pi$
$103$			17.0744i			1.68239i	−0.540730	+	0.841196i	$0.681852\pi$
$104$	−5.57912			−0.547078
$105$		0			0
$106$	9.99558			0.970856
$107$		−	2.35103i		−	0.227282i	−0.993522	−	0.113641i	$-0.963749\pi$
$107$		−	2.35103i		−	0.227282i	0.993522	−	0.113641i	$-0.0362514\pi$
$108$		0			0
$109$	11.1008			1.06326			0.531632	−	0.846975i	$-0.321579\pi$
$109$	11.1008			1.06326			0.531632	+	0.846975i	$0.321579\pi$
$110$	2.80058			0.267024
$111$		0			0
$112$	2.62657	+	0.317999i	0.248188	+	0.0300481i
$113$		−	15.0950i		−	1.42002i	−0.704194	−	0.710008i	$-0.748691\pi$
$113$		−	15.0950i		−	1.42002i	0.704194	−	0.710008i	$-0.251309\pi$
$114$		0			0
$115$			0.830160i			0.0774129i
$116$		−	0.497667i		−	0.0462072i
$117$		0			0
$118$			5.26327i			0.484523i
$119$	−3.27615	−	0.396643i	−0.300324	−	0.0363602i
$120$		0			0
$121$	7.14166			0.649242
$122$	11.8401			1.07196
$123$		0			0
$124$		−	6.46942i		−	0.580971i
$125$	11.3593			1.01601
$126$		0			0
$127$	9.89609			0.878136			0.439068	−	0.898454i	$-0.355309\pi$
$127$	9.89609			0.878136			0.439068	+	0.898454i	$0.355309\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	−7.95450			−0.697656
$131$	16.1032			1.40694			0.703472	−	0.710723i	$-0.251632\pi$
$131$	16.1032			1.40694			0.703472	+	0.710723i	$0.251632\pi$
$132$		0			0
$133$	0.317999	−	2.62657i	0.0275740	−	0.227753i
$134$			2.22053i			0.191824i
$135$		0			0
$136$		−	1.24731i		−	0.106956i
$137$			16.4268i			1.40344i	0.712453	+	0.701720i	$0.247584\pi$
$137$			16.4268i			1.40344i	−0.712453	+	0.701720i	$0.752416\pi$
$138$		0			0
$139$			3.65237i			0.309790i	0.987931	+	0.154895i	$0.0495040\pi$
$139$			3.65237i			0.309790i	−0.987931	+	0.154895i	$0.950496\pi$
$140$	3.74487	+	0.453391i	0.316499	+	0.0383185i
$141$		0			0
$142$	4.00707			0.336266
$143$	10.9589			0.916426
$144$		0			0
$145$		−	0.709555i		−	0.0589253i
$146$	−1.22215			−0.101146
$147$		0			0
$148$	−4.52011			−0.371551
$149$			22.2442i			1.82232i	0.412057	+	0.911158i	$0.364811\pi$
$149$			22.2442i			1.82232i	−0.412057	+	0.911158i	$0.635189\pi$
$150$		0			0
$151$	−11.7890			−0.959378			−0.479689	−	0.877439i	$-0.659251\pi$
$151$	−11.7890			−0.959378			−0.479689	+	0.877439i	$0.659251\pi$
$152$	1.00000			0.0811107
$153$		0			0
$154$	−5.15928	−	0.624634i	−0.415747	−	0.0503345i
$155$		−	9.22385i		−	0.740878i
$156$		0			0
$157$			11.5034i			0.918073i	0.888418	+	0.459036i	$0.151805\pi$
$157$			11.5034i			0.918073i	−0.888418	+	0.459036i	$0.848195\pi$
$158$		−	3.74743i		−	0.298130i
$159$		0			0
$160$			1.42576i			0.112716i
$161$	0.185157	−	1.52934i	0.0145924	−	0.120529i
$162$		0			0
$163$	−2.96476			−0.232218			−0.116109	−	0.993236i	$-0.537042\pi$
$163$	−2.96476			−0.232218			−0.116109	+	0.993236i	$0.537042\pi$
$164$	−1.13024			−0.0882573
$165$		0			0
$166$			6.23791i			0.484156i
$167$	−0.931442			−0.0720771			−0.0360386	−	0.999350i	$-0.511474\pi$
$167$	−0.931442			−0.0720771			−0.0360386	+	0.999350i	$0.511474\pi$
$168$		0			0
$169$	−18.1266			−1.39435
$170$		−	1.77837i		−	0.136395i
$171$		0			0
$172$	9.71565			0.740811
$173$	16.5879			1.26115			0.630576	−	0.776127i	$-0.282819\pi$
$173$	16.5879			1.26115			0.630576	+	0.776127i	$0.282819\pi$
$174$		0			0
$175$	−7.79356	−	0.943567i	−0.589138	−	0.0713270i
$176$		−	1.96426i		−	0.148062i
$177$		0			0
$178$		−	15.8345i		−	1.18684i
$179$		−	5.84819i		−	0.437114i	−0.975824	−	0.218557i	$-0.929865\pi$
$179$		−	5.84819i		−	0.437114i	0.975824	−	0.218557i	$-0.0701350\pi$
$180$		0			0
$181$			17.4712i			1.29863i	0.760521	+	0.649313i	$0.224943\pi$
$181$			17.4712i			1.29863i	−0.760521	+	0.649313i	$0.775057\pi$
$182$	14.6540	+	1.77415i	1.08622	+	0.131509i
$183$		0			0
$184$	0.582257			0.0429246
$185$	−6.44460			−0.473817
$186$		0			0
$187$			2.45005i			0.179165i
$188$	3.38468			0.246853
$189$		0			0
$190$	1.42576			0.103436
$191$			16.3917i			1.18606i	0.805180	+	0.593030i	$0.202069\pi$
$191$			16.3917i			1.18606i	−0.805180	+	0.593030i	$0.797931\pi$
$192$		0			0
$193$	12.2355			0.880732			0.440366	−	0.897818i	$-0.354849\pi$
$193$	12.2355			0.880732			0.440366	+	0.897818i	$0.354849\pi$
$194$	4.51004			0.323802
$195$		0			0
$196$	−6.79775	−	1.67049i	−0.485554	−	0.119321i
$197$		−	12.2839i		−	0.875193i	−0.899171	−	0.437596i	$-0.855830\pi$
$197$		−	12.2839i		−	0.875193i	0.899171	−	0.437596i	$-0.144170\pi$
$198$		0			0
$199$		−	15.6228i		−	1.10747i	−0.832694	−	0.553734i	$-0.813203\pi$
$199$		−	15.6228i		−	1.10747i	0.832694	−	0.553734i	$-0.186797\pi$
$200$		−	2.96720i		−	0.209813i
$201$		0			0
$202$			17.5394i			1.23407i
$203$	−0.158258	+	1.30716i	−0.0111075	+	0.0917444i
$204$		0			0
$205$	−1.61146			−0.112549
$206$	17.0744			1.18963
$207$		0			0
$208$			5.57912i			0.386842i
$209$	−1.96426			−0.135871
$210$		0			0
$211$	−6.77429			−0.466361			−0.233181	−	0.972433i	$-0.574913\pi$
$211$	−6.77429			−0.466361			−0.233181	+	0.972433i	$0.574913\pi$
$212$		−	9.99558i		−	0.686499i
$213$		0			0
$214$	−2.35103			−0.160713
$215$	13.8522			0.944713
$216$		0			0
$217$	−2.05727	+	16.9924i	−0.139656	+	1.15352i
$218$		−	11.1008i		−	0.751841i
$219$		0			0
$220$		−	2.80058i		−	0.188815i
$221$		−	6.95889i		−	0.468105i
$222$		0			0
$223$		−	8.83614i		−	0.591711i	−0.955233	−	0.295856i	$-0.904395\pi$
$223$		−	8.83614i		−	0.591711i	0.955233	−	0.295856i	$-0.0956048\pi$
$224$	0.317999	−	2.62657i	0.0212472	−	0.175495i
$225$		0			0
$226$	−15.0950			−1.00410
$227$	11.1345			0.739024			0.369512	−	0.929226i	$-0.379525\pi$
$227$	11.1345			0.739024			0.369512	+	0.929226i	$0.379525\pi$
$228$		0			0
$229$			0.853847i			0.0564238i	0.999602	+	0.0282119i	$0.00898132\pi$
$229$			0.853847i			0.0564238i	−0.999602	+	0.0282119i	$0.991019\pi$
$230$	0.830160			0.0547392
$231$		0			0
$232$	−0.497667			−0.0326734
$233$		−	7.41375i		−	0.485691i	−0.970065	−	0.242845i	$-0.921919\pi$
$233$		−	7.41375i		−	0.485691i	0.970065	−	0.242845i	$-0.0780808\pi$
$234$		0			0
$235$	4.82575			0.314797
$236$	5.26327			0.342610
$237$		0			0
$238$	−0.396643	+	3.27615i	−0.0257106	+	0.212361i
$239$			9.57474i			0.619339i	0.950844	+	0.309669i	$0.100218\pi$
$239$			9.57474i			0.619339i	−0.950844	+	0.309669i	$0.899782\pi$
$240$		0			0
$241$			2.70889i			0.174495i	0.996187	+	0.0872476i	$0.0278071\pi$
$241$			2.70889i			0.174495i	−0.996187	+	0.0872476i	$0.972193\pi$
$242$		−	7.14166i		−	0.459084i
$243$		0			0
$244$		−	11.8401i		−	0.757987i
$245$	−9.69198	−	2.38173i	−0.619198	−	0.152163i
$246$		0			0
$247$	5.57912			0.354991
$248$	−6.46942			−0.410808
$249$		0			0
$250$		−	11.3593i		−	0.718428i
$251$	−1.20239			−0.0758942			−0.0379471	−	0.999280i	$-0.512082\pi$
$251$	−1.20239			−0.0758942			−0.0379471	+	0.999280i	$0.512082\pi$
$252$		0			0
$253$	−1.14371			−0.0719043
$254$		−	9.89609i		−	0.620936i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−17.1573			−1.07024			−0.535120	−	0.844776i	$-0.679734\pi$
$257$	−17.1573			−1.07024			−0.535120	+	0.844776i	$0.679734\pi$
$258$		0			0
$259$	11.8724	+	1.43739i	0.737714	+	0.0893151i
$260$			7.95450i			0.493317i
$261$		0			0
$262$		−	16.1032i		−	0.994860i
$263$			8.95780i			0.552362i	0.961106	+	0.276181i	$0.0890689\pi$
$263$			8.95780i			0.552362i	−0.961106	+	0.276181i	$0.910931\pi$
$264$		0			0
$265$		−	14.2513i		−	0.875452i
$266$	−2.62657	−	0.317999i	−0.161045	−	0.0194978i
$267$		0			0
$268$	2.22053			0.135640
$269$	−29.3911			−1.79201			−0.896003	−	0.444049i	$-0.853542\pi$
$269$	−29.3911			−1.79201			−0.896003	+	0.444049i	$0.853542\pi$
$270$		0			0
$271$		−	1.30679i		−	0.0793821i	−0.999212	−	0.0396910i	$-0.987363\pi$
$271$		−	1.30679i		−	0.0793821i	0.999212	−	0.0396910i	$-0.0126374\pi$
$272$	−1.24731			−0.0756292
$273$		0			0
$274$	16.4268			0.992382
$275$			5.82837i			0.351464i
$276$		0			0
$277$	7.87237			0.473005			0.236502	−	0.971631i	$-0.423999\pi$
$277$	7.87237			0.473005			0.236502	+	0.971631i	$0.423999\pi$
$278$	3.65237			0.219055
$279$		0			0
$280$	0.453391	−	3.74487i	0.0270953	−	0.223799i
$281$			6.78719i			0.404890i	0.979294	+	0.202445i	$0.0648887\pi$
$281$			6.78719i			0.404890i	−0.979294	+	0.202445i	$0.935111\pi$
$282$		0			0
$283$		−	23.3771i		−	1.38962i	−0.719191	−	0.694812i	$-0.755488\pi$
$283$		−	23.3771i		−	1.38962i	0.719191	−	0.694812i	$-0.244512\pi$
$284$		−	4.00707i		−	0.237776i
$285$		0			0
$286$		−	10.9589i		−	0.648011i
$287$	2.96867	+	0.359417i	0.175235	+	0.0212157i
$288$		0			0
$289$	−15.4442			−0.908483
$290$	−0.709555			−0.0416665
$291$		0			0
$292$			1.22215i			0.0715212i
$293$	−21.6679			−1.26585			−0.632926	−	0.774212i	$-0.718146\pi$
$293$	−21.6679			−1.26585			−0.632926	+	0.774212i	$0.718146\pi$
$294$		0			0
$295$	7.50417			0.436910
$296$			4.52011i			0.262726i
$297$		0			0
$298$	22.2442			1.28857
$299$	3.24848			0.187865
$300$		0			0
$301$	−25.5188	−	3.08957i	−1.47088	−	0.178080i
$302$			11.7890i			0.678383i
$303$		0			0
$304$		−	1.00000i		−	0.0573539i
$305$		−	16.8812i		−	0.966616i
$306$		0			0
$307$			6.05980i			0.345851i	0.984935	+	0.172926i	$0.0553220\pi$
$307$			6.05980i			0.345851i	−0.984935	+	0.172926i	$0.944678\pi$
$308$	−0.624634	+	5.15928i	−0.0355918	+	0.293977i
$309$		0			0
$310$	−9.22385			−0.523880
$311$	−19.5209			−1.10693			−0.553464	−	0.832873i	$-0.686694\pi$
$311$	−19.5209			−1.10693			−0.553464	+	0.832873i	$0.686694\pi$
$312$		0			0
$313$		−	9.86252i		−	0.557463i	−0.960369	−	0.278731i	$-0.910086\pi$
$313$		−	9.86252i		−	0.557463i	0.960369	−	0.278731i	$-0.0899139\pi$
$314$	11.5034			0.649175
$315$		0			0
$316$	−3.74743			−0.210810
$317$		−	27.1853i		−	1.52688i	−0.645881	−	0.763438i	$-0.723510\pi$
$317$		−	27.1853i		−	1.52688i	0.645881	−	0.763438i	$-0.276490\pi$
$318$		0			0
$319$	0.977549			0.0547322
$320$	1.42576			0.0797026
$321$		0			0
$322$	−1.52934	−	0.185157i	−0.0852268	−	0.0103184i
$323$			1.24731i			0.0694022i
$324$		0			0
$325$		−	16.5544i		−	0.918271i
$326$			2.96476i			0.164203i
$327$		0			0
$328$			1.13024i			0.0624073i
$329$	−8.89010	−	1.07632i	−0.490127	−	0.0593397i
$330$		0			0
$331$	−7.87179			−0.432673			−0.216336	−	0.976319i	$-0.569411\pi$
$331$	−7.87179			−0.432673			−0.216336	+	0.976319i	$0.569411\pi$
$332$	6.23791			0.342350
$333$		0			0
$334$			0.931442i			0.0509662i
$335$	3.16594			0.172974
$336$		0			0
$337$	−19.1354			−1.04237			−0.521186	−	0.853443i	$-0.674510\pi$
$337$	−19.1354			−1.04237			−0.521186	+	0.853443i	$0.674510\pi$
$338$			18.1266i			0.985955i
$339$		0			0
$340$	−1.77837			−0.0964455
$341$	12.7076			0.688158
$342$		0			0
$343$	17.3236	+	6.54935i	0.935385	+	0.353632i
$344$		−	9.71565i		−	0.523833i
$345$		0			0
$346$		−	16.5879i		−	0.891769i
$347$		−	16.9122i		−	0.907892i	−0.891029	−	0.453946i	$-0.850016\pi$
$347$		−	16.9122i		−	0.907892i	0.891029	−	0.453946i	$-0.149984\pi$
$348$		0			0
$349$			7.42090i			0.397232i	0.980077	+	0.198616i	$0.0636446\pi$
$349$			7.42090i			0.397232i	−0.980077	+	0.198616i	$0.936355\pi$
$350$	−0.943567	+	7.79356i	−0.0504358	+	0.416584i
$351$		0			0
$352$	−1.96426			−0.104696
$353$	−18.6163			−0.990847			−0.495423	−	0.868652i	$-0.664987\pi$
$353$	−18.6163			−0.990847			−0.495423	+	0.868652i	$0.664987\pi$
$354$		0			0
$355$		−	5.71313i		−	0.303222i
$356$	−15.8345			−0.839225
$357$		0			0
$358$	−5.84819			−0.309086
$359$			1.76055i			0.0929180i	0.998920	+	0.0464590i	$0.0147937\pi$
$359$			1.76055i			0.0929180i	−0.998920	+	0.0464590i	$0.985206\pi$
$360$		0			0
$361$	−1.00000			−0.0526316
$362$	17.4712			0.918267
$363$		0			0
$364$	1.77415	−	14.6540i	0.0929910	−	0.768076i
$365$			1.74250i			0.0912067i
$366$		0			0
$367$		−	33.2171i		−	1.73392i	−0.498378	−	0.866960i	$-0.666071\pi$
$367$		−	33.2171i		−	1.73392i	0.498378	−	0.866960i	$-0.333929\pi$
$368$		−	0.582257i		−	0.0303523i
$369$		0			0
$370$			6.44460i			0.335039i
$371$	−3.17858	+	26.2541i	−0.165024	+	1.36304i
$372$		0			0
$373$	6.92083			0.358347			0.179173	−	0.983817i	$-0.442658\pi$
$373$	6.92083			0.358347			0.179173	+	0.983817i	$0.442658\pi$
$374$	2.45005			0.126689
$375$		0			0
$376$		−	3.38468i		−	0.174551i
$377$	−2.77654			−0.142999
$378$		0			0
$379$	4.30526			0.221146			0.110573	−	0.993868i	$-0.464731\pi$
$379$	4.30526			0.221146			0.110573	+	0.993868i	$0.464731\pi$
$380$		−	1.42576i		−	0.0731401i
$381$		0			0
$382$	16.3917			0.838671
$383$	1.95694			0.0999949			0.0499975	−	0.998749i	$-0.484079\pi$
$383$	1.95694			0.0999949			0.0499975	+	0.998749i	$0.484079\pi$
$384$		0			0
$385$	−0.890580	+	7.35591i	−0.0453882	+	0.374892i
$386$		−	12.2355i		−	0.622771i
$387$		0			0
$388$		−	4.51004i		−	0.228963i
$389$			17.9228i			0.908720i	0.890818	+	0.454360i	$0.150132\pi$
$389$			17.9228i			0.908720i	−0.890818	+	0.454360i	$0.849868\pi$
$390$		0			0
$391$			0.726255i			0.0367283i
$392$	−1.67049	+	6.79775i	−0.0843727	+	0.343338i
$393$		0			0
$394$	−12.2839			−0.618855
$395$	−5.34295			−0.268833
$396$		0			0
$397$			8.62358i			0.432805i	0.976304	+	0.216403i	$0.0694323\pi$
$397$			8.62358i			0.432805i	−0.976304	+	0.216403i	$0.930568\pi$
$398$	−15.6228			−0.783098
$399$		0			0
$400$	−2.96720			−0.148360
$401$		−	8.37201i		−	0.418078i	−0.977907	−	0.209039i	$-0.932966\pi$
$401$		−	8.37201i		−	0.418078i	0.977907	−	0.209039i	$-0.0670336\pi$
$402$		0			0
$403$	−36.0937			−1.79795
$404$	17.5394			0.872620
$405$		0			0
$406$	1.30716	+	0.158258i	0.0648731	+	0.00785419i
$407$		−	8.87869i		−	0.440100i
$408$		0			0
$409$		−	35.3801i		−	1.74943i	−0.484634	−	0.874717i	$-0.661047\pi$
$409$		−	35.3801i		−	1.74943i	0.484634	−	0.874717i	$-0.338953\pi$
$410$			1.61146i			0.0795844i
$411$		0			0
$412$		−	17.0744i		−	0.841196i
$413$	−13.8243	−	1.67371i	−0.680252	−	0.0823581i
$414$		0			0
$415$	8.89378			0.436579
$416$	5.57912			0.273539
$417$		0			0
$418$			1.96426i			0.0960753i
$419$	−27.3033			−1.33385			−0.666926	−	0.745124i	$-0.732390\pi$
$419$	−27.3033			−1.33385			−0.666926	+	0.745124i	$0.732390\pi$
$420$		0			0
$421$	38.1108			1.85741			0.928703	−	0.370824i	$-0.120925\pi$
$421$	38.1108			1.85741			0.928703	+	0.370824i	$0.120925\pi$
$422$			6.77429i			0.329767i
$423$		0			0
$424$	−9.99558			−0.485428
$425$	3.70102			0.179526
$426$		0			0
$427$	−3.76515	+	31.0990i	−0.182209	+	1.50498i
$428$			2.35103i			0.113641i
$429$		0			0
$430$		−	13.8522i		−	0.668013i
$431$		−	6.40501i		−	0.308519i	−0.988030	−	0.154259i	$-0.950701\pi$
$431$		−	6.40501i		−	0.308519i	0.988030	−	0.154259i	$-0.0492991\pi$
$432$		0			0
$433$		−	4.91673i		−	0.236283i	−0.992997	−	0.118141i	$-0.962306\pi$
$433$		−	4.91673i		−	0.236283i	0.992997	−	0.118141i	$-0.0376936\pi$
$434$	16.9924	+	2.05727i	0.815661	+	0.0987520i
$435$		0			0
$436$	−11.1008			−0.531632
$437$	−0.582257			−0.0278531
$438$		0			0
$439$		−	13.8656i		−	0.661767i	−0.943672	−	0.330883i	$-0.892653\pi$
$439$		−	13.8656i		−	0.661767i	0.943672	−	0.330883i	$-0.107347\pi$
$440$	−2.80058			−0.133512
$441$		0			0
$442$	−6.95889			−0.331001
$443$			35.9632i			1.70866i	0.519729	+	0.854331i	$0.326033\pi$
$443$			35.9632i			1.70866i	−0.519729	+	0.854331i	$0.673967\pi$
$444$		0			0
$445$	−22.5762			−1.07021
$446$	−8.83614			−0.418403
$447$		0			0
$448$	−2.62657	−	0.317999i	−0.124094	−	0.0150240i
$449$			20.8523i			0.984082i	0.870572	+	0.492041i	$0.163749\pi$
$449$			20.8523i			0.984082i	−0.870572	+	0.492041i	$0.836251\pi$
$450$		0			0
$451$		−	2.22010i		−	0.104540i
$452$			15.0950i			0.710008i
$453$		0			0
$454$		−	11.1345i		−	0.522569i
$455$	2.52952	−	20.8931i	0.118586	−	0.979482i
$456$		0			0
$457$	17.6898			0.827493			0.413747	−	0.910392i	$-0.364220\pi$
$457$	17.6898			0.827493			0.413747	+	0.910392i	$0.364220\pi$
$458$	0.853847			0.0398977
$459$		0			0
$460$		−	0.830160i		−	0.0387064i
$461$	−22.8916			−1.06617			−0.533084	−	0.846062i	$-0.678967\pi$
$461$	−22.8916			−1.06617			−0.533084	+	0.846062i	$0.678967\pi$
$462$		0			0
$463$	29.1151			1.35310			0.676548	−	0.736399i	$-0.263475\pi$
$463$	29.1151			1.35310			0.676548	+	0.736399i	$0.263475\pi$
$464$			0.497667i			0.0231036i
$465$		0			0
$466$	−7.41375			−0.343435
$467$	32.0610			1.48361			0.741803	−	0.670618i	$-0.233971\pi$
$467$	32.0610			1.48361			0.741803	+	0.670618i	$0.233971\pi$
$468$		0			0
$469$	−5.83237	−	0.706125i	−0.269314	−	0.0326058i
$470$		−	4.82575i		−	0.222595i
$471$		0			0
$472$		−	5.26327i		−	0.242262i
$473$			19.0841i			0.877488i
$474$		0			0
$475$			2.96720i			0.136145i
$476$	3.27615	+	0.396643i	0.150162	+	0.0181801i
$477$		0			0
$478$	9.57474			0.437939
$479$	25.7191			1.17513			0.587567	−	0.809176i	$-0.300086\pi$
$479$	25.7191			1.17513			0.587567	+	0.809176i	$0.300086\pi$
$480$		0			0
$481$			25.2182i			1.14985i
$482$	2.70889			0.123387
$483$		0			0
$484$	−7.14166			−0.324621
$485$		−	6.43025i		−	0.291983i
$486$		0			0
$487$	−6.19476			−0.280712			−0.140356	−	0.990101i	$-0.544825\pi$
$487$	−6.19476			−0.280712			−0.140356	+	0.990101i	$0.544825\pi$
$488$	−11.8401			−0.535978
$489$		0			0
$490$	−2.38173	+	9.69198i	−0.107596	+	0.437839i
$491$			8.56079i			0.386343i	0.981165	+	0.193172i	$0.0618774\pi$
$491$			8.56079i			0.386343i	−0.981165	+	0.193172i	$0.938123\pi$
$492$		0			0
$493$		−	0.620744i		−	0.0279569i
$494$		−	5.57912i		−	0.251016i
$495$		0			0
$496$			6.46942i			0.290485i
$497$	−1.27424	+	10.5249i	−0.0571577	+	0.472104i
$498$		0			0
$499$	−8.11428			−0.363245			−0.181623	−	0.983368i	$-0.558135\pi$
$499$	−8.11428			−0.363245			−0.181623	+	0.983368i	$0.558135\pi$
$500$	−11.3593			−0.508005
$501$		0			0
$502$			1.20239i			0.0536653i
$503$	13.6902			0.610416			0.305208	−	0.952286i	$-0.401274\pi$
$503$	13.6902			0.610416			0.305208	+	0.952286i	$0.401274\pi$
$504$		0			0
$505$	25.0071			1.11280
$506$			1.14371i			0.0508440i
$507$		0			0
$508$	−9.89609			−0.439068
$509$	−18.2360			−0.808297			−0.404149	−	0.914693i	$-0.632432\pi$
$509$	−18.2360			−0.808297			−0.404149	+	0.914693i	$0.632432\pi$
$510$		0			0
$511$	0.388644	−	3.21008i	0.0171926	−	0.142005i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$			17.1573i			0.756774i
$515$		−	24.3441i		−	1.07273i
$516$		0			0
$517$			6.64841i			0.292397i
$518$	1.43739	−	11.8724i	0.0631553	−	0.521643i
$519$		0			0
$520$	7.95450			0.348828
$521$	−8.67794			−0.380188			−0.190094	−	0.981766i	$-0.560879\pi$
$521$	−8.67794			−0.380188			−0.190094	+	0.981766i	$0.560879\pi$
$522$		0			0
$523$		−	12.8974i		−	0.563962i	−0.959420	−	0.281981i	$-0.909008\pi$
$523$		−	12.8974i		−	0.563962i	0.959420	−	0.281981i	$-0.0909915\pi$
$524$	−16.1032			−0.703472
$525$		0			0
$526$	8.95780			0.390579
$527$		−	8.06937i		−	0.351507i
$528$		0			0
$529$	22.6610			0.985260
$530$	−14.2513			−0.619038
$531$		0			0
$532$	−0.317999	+	2.62657i	−0.0137870	+	0.113876i
$533$			6.30577i			0.273133i
$534$		0			0
$535$			3.35201i			0.144920i
$536$		−	2.22053i		−	0.0959121i
$537$		0			0
$538$			29.3911i			1.26714i
$539$	3.28129	−	13.3526i	0.141335	−	0.575137i
$540$		0			0
$541$	4.29031			0.184455			0.0922274	−	0.995738i	$-0.470601\pi$
$541$	4.29031			0.184455			0.0922274	+	0.995738i	$0.470601\pi$
$542$	−1.30679			−0.0561316
$543$		0			0
$544$			1.24731i			0.0534780i
$545$	−15.8271			−0.677959
$546$		0			0
$547$	−28.6465			−1.22483			−0.612417	−	0.790535i	$-0.709803\pi$
$547$	−28.6465			−1.22483			−0.612417	+	0.790535i	$0.709803\pi$
$548$		−	16.4268i		−	0.701720i
$549$		0			0
$550$	5.82837			0.248522
$551$	0.497667			0.0212013
$552$		0			0
$553$	9.84290	+	1.19168i	0.418563	+	0.0506754i
$554$		−	7.87237i		−	0.334465i
$555$		0			0
$556$		−	3.65237i		−	0.154895i
$557$			12.5701i			0.532613i	0.963888	+	0.266306i	$0.0858033\pi$
$557$			12.5701i			0.532613i	−0.963888	+	0.266306i	$0.914197\pi$
$558$		0			0
$559$		−	54.2047i		−	2.29262i
$560$	−3.74487	−	0.453391i	−0.158250	−	0.0191593i
$561$		0			0
$562$	6.78719			0.286300
$563$	−42.5495			−1.79325			−0.896624	−	0.442794i	$-0.853987\pi$
$563$	−42.5495			−1.79325			−0.896624	+	0.442794i	$0.853987\pi$
$564$		0			0
$565$			21.5218i			0.905431i
$566$	−23.3771			−0.982613
$567$		0			0
$568$	−4.00707			−0.168133
$569$		−	19.9702i		−	0.837194i	−0.908172	−	0.418597i	$-0.862522\pi$
$569$		−	19.9702i		−	0.837194i	0.908172	−	0.418597i	$-0.137478\pi$
$570$		0			0
$571$	23.1122			0.967214			0.483607	−	0.875285i	$-0.339326\pi$
$571$	23.1122			0.967214			0.483607	+	0.875285i	$0.339326\pi$
$572$	−10.9589			−0.458213
$573$		0			0
$574$	0.359417	−	2.96867i	0.0150018	−	0.123910i
$575$			1.72767i			0.0720490i
$576$		0			0
$577$		−	10.9492i		−	0.455822i	−0.973682	−	0.227911i	$-0.926811\pi$
$577$		−	10.9492i		−	0.455822i	0.973682	−	0.227911i	$-0.0731895\pi$
$578$			15.4442i			0.642395i
$579$		0			0
$580$			0.709555i			0.0294627i
$581$	−16.3843	−	1.98365i	−0.679736	−	0.0822957i
$582$		0			0
$583$	19.6340			0.813155
$584$	1.22215			0.0505731
$585$		0			0
$586$			21.6679i			0.895093i
$587$	27.9618			1.15411			0.577053	−	0.816707i	$-0.304203\pi$
$587$	27.9618			1.15411			0.577053	+	0.816707i	$0.304203\pi$
$588$		0			0
$589$	6.46942			0.266568
$590$		−	7.50417i		−	0.308942i
$591$		0			0
$592$	4.52011			0.185775
$593$	−4.16660			−0.171102			−0.0855509	−	0.996334i	$-0.527265\pi$
$593$	−4.16660			−0.171102			−0.0855509	+	0.996334i	$0.527265\pi$
$594$		0			0
$595$	4.67101	+	0.565519i	0.191493	+	0.0231840i
$596$		−	22.2442i		−	0.911158i
$597$		0			0
$598$		−	3.24848i		−	0.132840i
$599$			16.1851i			0.661307i	0.943752	+	0.330654i	$0.107269\pi$
$599$			16.1851i			0.661307i	−0.943752	+	0.330654i	$0.892731\pi$
$600$		0			0
$601$		−	10.6390i		−	0.433973i	−0.976175	−	0.216986i	$-0.930377\pi$
$601$		−	10.6390i		−	0.433973i	0.976175	−	0.216986i	$-0.0696228\pi$
$602$	−3.08957	+	25.5188i	−0.125921	+	1.04007i
$603$		0			0
$604$	11.7890			0.479689
$605$	−10.1823			−0.413970
$606$		0			0
$607$		−	24.7128i		−	1.00306i	−0.865140	−	0.501531i	$-0.832770\pi$
$607$		−	24.7128i		−	1.00306i	0.865140	−	0.501531i	$-0.167230\pi$
$608$	−1.00000			−0.0405554
$609$		0			0
$610$	−16.8812			−0.683501
$611$		−	18.8835i		−	0.763946i
$612$		0			0
$613$	−27.7181			−1.11952			−0.559762	−	0.828653i	$-0.689108\pi$
$613$	−27.7181			−1.11952			−0.559762	+	0.828653i	$0.689108\pi$
$614$	6.05980			0.244554
$615$		0			0
$616$	5.15928	+	0.624634i	0.207873	+	0.0251672i
$617$			40.1400i			1.61598i	0.589198	+	0.807989i	$0.299444\pi$
$617$			40.1400i			1.61598i	−0.589198	+	0.807989i	$0.700556\pi$
$618$		0			0
$619$		−	44.2152i		−	1.77716i	−0.458724	−	0.888579i	$-0.651693\pi$
$619$		−	44.2152i		−	1.77716i	0.458724	−	0.888579i	$-0.348307\pi$
$620$			9.22385i			0.370439i
$621$		0			0
$622$			19.5209i			0.782717i
$623$	41.5903	+	5.03534i	1.66628	+	0.201737i
$624$		0			0
$625$	−1.35971			−0.0543885
$626$	−9.86252			−0.394186
$627$		0			0
$628$		−	11.5034i		−	0.459036i
$629$	−5.63797			−0.224801
$630$		0			0
$631$	−17.2912			−0.688353			−0.344176	−	0.938905i	$-0.611842\pi$
$631$	−17.2912			−0.688353			−0.344176	+	0.938905i	$0.611842\pi$
$632$			3.74743i			0.149065i
$633$		0			0
$634$	−27.1853			−1.07966
$635$	−14.1095			−0.559918
$636$		0			0
$637$	−9.31989	+	37.9255i	−0.369267	+	1.50266i
$638$		−	0.977549i		−	0.0387015i
$639$		0			0
$640$		−	1.42576i		−	0.0563582i
$641$			4.04175i			0.159640i	0.996809	+	0.0798198i	$0.0254345\pi$
$641$			4.04175i			0.159640i	−0.996809	+	0.0798198i	$0.974566\pi$
$642$		0			0
$643$		−	14.8862i		−	0.587054i	−0.955951	−	0.293527i	$-0.905171\pi$
$643$		−	14.8862i		−	0.587054i	0.955951	−	0.293527i	$-0.0948291\pi$
$644$	−0.185157	+	1.52934i	−0.00729622	+	0.0602644i
$645$		0			0
$646$	1.24731			0.0490747
$647$	−8.91346			−0.350424			−0.175212	−	0.984531i	$-0.556061\pi$
$647$	−8.91346			−0.350424			−0.175212	+	0.984531i	$0.556061\pi$
$648$		0			0
$649$			10.3385i			0.405820i
$650$	−16.5544			−0.649316
$651$		0			0
$652$	2.96476			0.116109
$653$		−	24.8350i		−	0.971868i	−0.873996	−	0.485934i	$-0.838480\pi$
$653$		−	24.8350i		−	0.971868i	0.873996	−	0.485934i	$-0.161520\pi$
$654$		0			0
$655$	−22.9594			−0.897096
$656$	1.13024			0.0441286
$657$		0			0
$658$	−1.07632	+	8.89010i	−0.0419595	+	0.346572i
$659$		−	25.4616i		−	0.991843i	−0.868367	−	0.495922i	$-0.834830\pi$
$659$		−	25.4616i		−	0.991843i	0.868367	−	0.495922i	$-0.165170\pi$
$660$		0			0
$661$			49.7936i			1.93675i	0.249508	+	0.968373i	$0.419731\pi$
$661$			49.7936i			1.93675i	−0.249508	+	0.968373i	$0.580269\pi$
$662$			7.87179i			0.305946i
$663$		0			0
$664$		−	6.23791i		−	0.242078i
$665$	−0.453391	+	3.74487i	−0.0175818	+	0.145220i
$666$		0			0
$667$	0.289770			0.0112199
$668$	0.931442			0.0360386
$669$		0			0
$670$		−	3.16594i		−	0.122311i
$671$	23.2572			0.897833
$672$		0			0
$673$	−12.3837			−0.477358			−0.238679	−	0.971098i	$-0.576714\pi$
$673$	−12.3837			−0.477358			−0.238679	+	0.971098i	$0.576714\pi$
$674$			19.1354i			0.737068i
$675$		0			0
$676$	18.1266			0.697176
$677$	−18.6753			−0.717752			−0.358876	−	0.933385i	$-0.616840\pi$
$677$	−18.6753			−0.717752			−0.358876	+	0.933385i	$0.616840\pi$
$678$		0			0
$679$	−1.43419	+	11.8459i	−0.0550391	+	0.454606i
$680$			1.77837i			0.0681973i
$681$		0			0
$682$		−	12.7076i		−	0.486601i
$683$		−	17.5157i		−	0.670221i	−0.942179	−	0.335110i	$-0.891226\pi$
$683$		−	17.5157i		−	0.670221i	0.942179	−	0.335110i	$-0.108774\pi$
$684$		0			0
$685$		−	23.4208i		−	0.894862i
$686$	6.54935	−	17.3236i	0.250055	−	0.661417i
$687$		0			0
$688$	−9.71565			−0.370406
$689$	−55.7665			−2.12453
$690$		0			0
$691$			0.509304i			0.0193748i	0.999953	+	0.00968741i	$0.00308365\pi$
$691$			0.509304i			0.0193748i	−0.999953	+	0.00968741i	$0.996916\pi$
$692$	−16.5879			−0.630576
$693$		0			0
$694$	−16.9122			−0.641977
$695$		−	5.20742i		−	0.197529i
$696$		0			0
$697$	−1.40976			−0.0533987
$698$	7.42090			0.280885
$699$		0			0
$700$	7.79356	+	0.943567i	0.294569	+	0.0356635i
$701$			41.3810i			1.56294i	0.623944	+	0.781469i	$0.285529\pi$
$701$			41.3810i			1.56294i	−0.623944	+	0.781469i	$0.714471\pi$
$702$		0			0
$703$		−	4.52011i		−	0.170479i
$704$			1.96426i			0.0740310i
$705$		0			0
$706$			18.6163i			0.700635i
$707$	−46.0686	−	5.57753i	−1.73259	−	0.209764i
$708$		0			0
$709$	22.5731			0.847751			0.423876	−	0.905720i	$-0.360669\pi$
$709$	22.5731			0.847751			0.423876	+	0.905720i	$0.360669\pi$
$710$	−5.71313			−0.214410
$711$		0			0
$712$			15.8345i			0.593421i
$713$	3.76686			0.141070
$714$		0			0
$715$	−15.6247			−0.584332
$716$			5.84819i			0.218557i
$717$		0			0
$718$	1.76055			0.0657030
$719$	38.8225			1.44783			0.723917	−	0.689887i	$-0.242340\pi$
$719$	38.8225			1.44783			0.723917	+	0.689887i	$0.242340\pi$
$720$		0			0
$721$	−5.42965	+	44.8472i	−0.202211	+	1.67020i
$722$			1.00000i			0.0372161i
$723$		0			0
$724$		−	17.4712i		−	0.649313i
$725$		−	1.47668i		−	0.0548424i
$726$		0			0
$727$		−	30.4747i		−	1.13025i	−0.825007	−	0.565123i	$-0.808829\pi$
$727$		−	30.4747i		−	1.13025i	0.825007	−	0.565123i	$-0.191171\pi$
$728$	−14.6540	−	1.77415i	−0.543112	−	0.0657545i
$729$		0			0
$730$	1.74250			0.0644929
$731$	12.1184			0.448216
$732$		0			0
$733$		−	39.4867i		−	1.45847i	−0.684261	−	0.729237i	$-0.739875\pi$
$733$		−	39.4867i		−	1.45847i	0.684261	−	0.729237i	$-0.260125\pi$
$734$	−33.2171			−1.22607
$735$		0			0
$736$	−0.582257			−0.0214623
$737$			4.36170i			0.160665i
$738$		0			0
$739$	−27.4043			−1.00808			−0.504042	−	0.863679i	$-0.668154\pi$
$739$	−27.4043			−1.00808			−0.504042	+	0.863679i	$0.668154\pi$
$740$	6.44460			0.236908
$741$		0			0
$742$	26.2541	+	3.17858i	0.963818	+	0.116689i
$743$			0.377004i			0.0138309i	0.999976	+	0.00691546i	$0.00220128\pi$
$743$			0.377004i			0.0138309i	−0.999976	+	0.00691546i	$0.997799\pi$
$744$		0			0
$745$		−	31.7150i		−	1.16195i
$746$		−	6.92083i		−	0.253390i
$747$		0			0
$748$		−	2.45005i		−	0.0895825i
$749$	0.747625	−	6.17514i	0.0273176	−	0.225635i
$750$		0			0
$751$	−28.2058			−1.02924			−0.514622	−	0.857417i	$-0.672068\pi$
$751$	−28.2058			−1.02924			−0.514622	+	0.857417i	$0.672068\pi$
$752$	−3.38468			−0.123427
$753$		0			0
$754$			2.77654i			0.101116i
$755$	16.8084			0.611719
$756$		0			0
$757$	−20.8231			−0.756827			−0.378414	−	0.925637i	$-0.623530\pi$
$757$	−20.8231			−0.756827			−0.378414	+	0.925637i	$0.623530\pi$
$758$		−	4.30526i		−	0.156374i
$759$		0			0
$760$	−1.42576			−0.0517178
$761$	24.5620			0.890370			0.445185	−	0.895439i	$-0.353138\pi$
$761$	24.5620			0.890370			0.445185	+	0.895439i	$0.353138\pi$
$762$		0			0
$763$	29.1571	+	3.53005i	1.05556	+	0.127796i
$764$		−	16.3917i		−	0.593030i
$765$		0			0
$766$		−	1.95694i		−	0.0707071i
$767$		−	29.3644i		−	1.06029i
$768$		0			0
$769$		−	40.8363i		−	1.47259i	−0.676659	−	0.736297i	$-0.736573\pi$
$769$		−	40.8363i		−	1.47259i	0.676659	−	0.736297i	$-0.263427\pi$
$770$	7.35591	+	0.890580i	0.265089	+	0.0320943i
$771$		0			0
$772$	−12.2355			−0.440366
$773$	−38.7214			−1.39271			−0.696355	−	0.717697i	$-0.745196\pi$
$773$	−38.7214			−1.39271			−0.696355	+	0.717697i	$0.745196\pi$
$774$		0			0
$775$		−	19.1961i		−	0.689543i
$776$	−4.51004			−0.161901
$777$		0			0
$778$	17.9228			0.642562
$779$		−	1.13024i		−	0.0404952i
$780$		0			0
$781$	7.87095			0.281645
$782$	0.726255			0.0259708
$783$		0			0
$784$	6.79775	+	1.67049i	0.242777	+	0.0596605i
$785$		−	16.4011i		−	0.585382i
$786$		0			0
$787$			3.71088i			0.132279i	0.997810	+	0.0661393i	$0.0210682\pi$
$787$			3.71088i			0.132279i	−0.997810	+	0.0661393i	$0.978932\pi$
$788$			12.2839i			0.437596i
$789$		0			0
$790$			5.34295i			0.190094i
$791$	4.80019	−	39.6480i	0.170675	−	1.40972i
$792$		0			0
$793$	−66.0576			−2.34577
$794$	8.62358			0.306039
$795$		0			0
$796$			15.6228i			0.553734i
$797$	−37.2983			−1.32117			−0.660586	−	0.750750i	$-0.729692\pi$
$797$	−37.2983			−1.32117			−0.660586	+	0.750750i	$0.729692\pi$
$798$		0			0
$799$	4.22174			0.149355
$800$			2.96720i			0.104906i
$801$		0			0
$802$	−8.37201			−0.295626
$803$	−2.40063			−0.0847166
$804$		0			0
$805$	−0.263990	+	2.18048i	−0.00930443	+	0.0768517i
$806$			36.0937i			1.27134i
$807$		0			0
$808$		−	17.5394i		−	0.617036i
$809$			13.8647i			0.487456i	0.969844	+	0.243728i	$0.0783705\pi$
$809$			13.8647i			0.487456i	−0.969844	+	0.243728i	$0.921630\pi$
$810$		0			0
$811$		−	38.9731i		−	1.36853i	−0.729234	−	0.684265i	$-0.760123\pi$
$811$		−	38.9731i		−	1.36853i	0.729234	−	0.684265i	$-0.239877\pi$
$812$	0.158258	−	1.30716i	0.00555375	−	0.0458722i
$813$		0			0
$814$	−8.87869			−0.311198
$815$	4.22705			0.148067
$816$		0			0
$817$			9.71565i			0.339907i
$818$	−35.3801			−1.23704
$819$		0			0
$820$	1.61146			0.0562746
$821$			30.5615i			1.06660i	0.845925	+	0.533302i	$0.179049\pi$
$821$			30.5615i			1.06660i	−0.845925	+	0.533302i	$0.820951\pi$
$822$		0			0
$823$	25.0795			0.874218			0.437109	−	0.899409i	$-0.356002\pi$
$823$	25.0795			0.874218			0.437109	+	0.899409i	$0.356002\pi$
$824$	−17.0744			−0.594815
$825$		0			0
$826$	−1.67371	+	13.8243i	−0.0582360	+	0.481011i
$827$			25.2941i			0.879561i	0.898105	+	0.439781i	$0.144944\pi$
$827$			25.2941i			0.879561i	−0.898105	+	0.439781i	$0.855056\pi$
$828$		0			0
$829$		−	30.4625i		−	1.05801i	−0.848620	−	0.529003i	$-0.822566\pi$
$829$		−	30.4625i		−	1.05801i	0.848620	−	0.529003i	$-0.177434\pi$
$830$		−	8.89378i		−	0.308708i
$831$		0			0
$832$		−	5.57912i		−	0.193421i
$833$	−8.47890	−	2.08362i	−0.293777	−	0.0721933i
$834$		0			0
$835$	1.32801			0.0459578
$836$	1.96426			0.0679355
$837$		0			0
$838$			27.3033i			0.943176i
$839$	53.5764			1.84966			0.924832	−	0.380375i	$-0.124205\pi$
$839$	53.5764			1.84966			0.924832	+	0.380375i	$0.124205\pi$
$840$		0			0
$841$	28.7523			0.991460
$842$		−	38.1108i		−	1.31338i
$843$		0			0
$844$	6.77429			0.233181
$845$	25.8442			0.889067
$846$		0			0
$847$	18.7581	+	2.27104i	0.644536	+	0.0780339i
$848$			9.99558i			0.343250i
$849$		0			0
$850$		−	3.70102i		−	0.126944i
$851$		−	2.63187i		−	0.0902192i
$852$		0			0
$853$			34.8403i			1.19291i	0.802647	+	0.596454i	$0.203424\pi$
$853$			34.8403i			1.19291i	−0.802647	+	0.596454i	$0.796576\pi$
$854$	31.0990	+	3.76515i	1.06418	+	0.128841i
$855$		0			0
$856$	2.35103			0.0803565
$857$	−14.2920			−0.488206			−0.244103	−	0.969749i	$-0.578493\pi$
$857$	−14.2920			−0.488206			−0.244103	+	0.969749i	$0.578493\pi$
$858$		0			0
$859$			48.6201i			1.65890i	0.558583	+	0.829449i	$0.311345\pi$
$859$			48.6201i			1.65890i	−0.558583	+	0.829449i	$0.688655\pi$
$860$	−13.8522			−0.472356
$861$		0			0
$862$	−6.40501			−0.218156
$863$			1.43297i			0.0487788i	0.999703	+	0.0243894i	$0.00776416\pi$
$863$			1.43297i			0.0487788i	−0.999703	+	0.0243894i	$0.992236\pi$
$864$		0			0
$865$	−23.6504			−0.804136
$866$	−4.91673			−0.167077
$867$		0			0
$868$	2.05727	−	16.9924i	0.0698282	−	0.576759i
$869$		−	7.36095i		−	0.249703i
$870$		0			0
$871$		−	12.3886i		−	0.419771i
$872$			11.1008i			0.375921i
$873$		0			0
$874$			0.582257i			0.0196951i
$875$	29.8361	+	3.61226i	1.00864	+	0.122117i
$876$		0			0
$877$	36.2583			1.22436			0.612178	−	0.790720i	$-0.290294\pi$
$877$	36.2583			1.22436			0.612178	+	0.790720i	$0.290294\pi$
$878$	−13.8656			−0.467940
$879$		0			0
$880$			2.80058i			0.0944074i
$881$	40.8485			1.37622			0.688111	−	0.725605i	$-0.258440\pi$
$881$	40.8485			1.37622			0.688111	+	0.725605i	$0.258440\pi$
$882$		0			0
$883$	21.6277			0.727829			0.363914	−	0.931432i	$-0.381440\pi$
$883$	21.6277			0.727829			0.363914	+	0.931432i	$0.381440\pi$
$884$			6.95889i			0.234053i
$885$		0			0
$886$	35.9632			1.20821
$887$	24.7041			0.829481			0.414741	−	0.909940i	$-0.363872\pi$
$887$	24.7041			0.829481			0.414741	+	0.909940i	$0.363872\pi$
$888$		0			0
$889$	25.9928	+	3.14695i	0.871770	+	0.105545i
$890$			22.5762i			0.756755i
$891$		0			0
$892$			8.83614i			0.295856i
$893$			3.38468i			0.113264i
$894$		0			0
$895$			8.33813i			0.278713i
$896$	−0.317999	+	2.62657i	−0.0106236	+	0.0877476i
$897$		0			0
$898$	20.8523			0.695851
$899$	−3.21961			−0.107380
$900$		0			0
$901$		−	12.4676i		−	0.415355i
$902$	−2.22010			−0.0739212
$903$		0			0
$904$	15.0950			0.502051
$905$		−	24.9098i		−	0.828030i
$906$		0			0
$907$	−41.6299			−1.38230			−0.691149	−	0.722712i	$-0.742895\pi$
$907$	−41.6299			−1.38230			−0.691149	+	0.722712i	$0.742895\pi$
$908$	−11.1345			−0.369512
$909$		0			0
$910$	−20.8931	−	2.52952i	−0.692598	−	0.0838529i
$911$		−	45.5764i		−	1.51001i	−0.655718	−	0.755006i	$-0.727634\pi$
$911$		−	45.5764i		−	1.51001i	0.655718	−	0.755006i	$-0.272366\pi$
$912$		0			0
$913$			12.2529i			0.405512i
$914$		−	17.6898i		−	0.585126i
$915$		0			0
$916$		−	0.853847i		−	0.0282119i
$917$	42.2962	+	5.12080i	1.39674	+	0.169104i
$918$		0			0
$919$	−43.7107			−1.44188			−0.720941	−	0.692996i	$-0.756290\pi$
$919$	−43.7107			−1.44188			−0.720941	+	0.692996i	$0.756290\pi$
$920$	−0.830160			−0.0273696
$921$		0			0
$922$			22.8916i			0.753895i
$923$	−22.3559			−0.735854
$924$		0			0
$925$	−13.4121			−0.440986
$926$		−	29.1151i		−	0.956783i
$927$		0			0
$928$	0.497667			0.0163367
$929$	36.5659			1.19969			0.599844	−	0.800117i	$-0.295229\pi$
$929$	36.5659			1.19969			0.599844	+	0.800117i	$0.295229\pi$
$930$		0			0
$931$	1.67049	−	6.79775i	0.0547482	−	0.222787i
$932$			7.41375i			0.242845i
$933$		0			0
$934$		−	32.0610i		−	1.04907i
$935$		−	3.49318i		−	0.114239i
$936$		0			0
$937$			24.2263i			0.791439i	0.918371	+	0.395720i	$0.129505\pi$
$937$			24.2263i			0.791439i	−0.918371	+	0.395720i	$0.870495\pi$
$938$	−0.706125	+	5.83237i	−0.0230558	+	0.190434i
$939$		0			0
$940$	−4.82575			−0.157399
$941$	−4.62238			−0.150685			−0.0753426	−	0.997158i	$-0.524005\pi$
$941$	−4.62238			−0.150685			−0.0753426	+	0.997158i	$0.524005\pi$
$942$		0			0
$943$		−	0.658093i		−	0.0214305i
$944$	−5.26327			−0.171305
$945$		0			0
$946$	19.0841			0.620478
$947$			3.17190i			0.103073i	0.998671	+	0.0515365i	$0.0164118\pi$
$947$			3.17190i			0.103073i	−0.998671	+	0.0515365i	$0.983588\pi$
$948$		0			0
$949$	6.81855			0.221339
$950$	2.96720			0.0962687
$951$		0			0
$952$	0.396643	−	3.27615i	0.0128553	−	0.106181i
$953$			21.6833i			0.702392i	0.936302	+	0.351196i	$0.114225\pi$
$953$			21.6833i			0.702392i	−0.936302	+	0.351196i	$0.885775\pi$
$954$		0			0
$955$		−	23.3706i		−	0.756256i
$956$		−	9.57474i		−	0.309669i
$957$		0			0
$958$		−	25.7191i		−	0.830945i
$959$	−5.22372	+	43.1463i	−0.168683	+	1.39327i
$960$		0			0
$961$	−10.8534			−0.350109
$962$	25.2182			0.813068
$963$		0			0
$964$		−	2.70889i		−	0.0872476i
$965$	−17.4449			−0.561573
$966$		0			0
$967$	−29.2623			−0.941012			−0.470506	−	0.882397i	$-0.655929\pi$
$967$	−29.2623			−0.941012			−0.470506	+	0.882397i	$0.655929\pi$
$968$			7.14166i			0.229542i
$969$		0			0
$970$	−6.43025			−0.206463
$971$	17.3512			0.556828			0.278414	−	0.960461i	$-0.410191\pi$
$971$	17.3512			0.556828			0.278414	+	0.960461i	$0.410191\pi$
$972$		0			0
$973$	−1.16145	+	9.59322i	−0.0372344	+	0.307544i
$974$			6.19476i			0.198493i
$975$		0			0
$976$			11.8401i			0.378994i
$977$		−	10.7790i		−	0.344850i	−0.985023	−	0.172425i	$-0.944840\pi$
$977$		−	10.7790i		−	0.344850i	0.985023	−	0.172425i	$-0.0551603\pi$
$978$		0			0
$979$		−	31.1031i		−	0.994058i
$980$	9.69198	+	2.38173i	0.309599	+	0.0760815i
$981$		0			0
$982$	8.56079			0.273186
$983$	6.39854			0.204082			0.102041	−	0.994780i	$-0.467463\pi$
$983$	6.39854			0.204082			0.102041	+	0.994780i	$0.467463\pi$
$984$		0			0
$985$			17.5140i			0.558041i
$986$	−0.620744			−0.0197685
$987$		0			0
$988$	−5.57912			−0.177495
$989$			5.65700i			0.179882i
$990$		0			0
$991$	60.3778			1.91796			0.958981	−	0.283469i	$-0.0914855\pi$
$991$	60.3778			1.91796			0.958981	+	0.283469i	$0.0914855\pi$
$992$	6.46942			0.205404
$993$		0			0
$994$	10.5249	+	1.27424i	0.333828	+	0.0404166i
$995$			22.2743i			0.706144i
$996$		0			0
$997$			36.9197i			1.16926i	0.811300	+	0.584630i	$0.198760\pi$
$997$			36.9197i			1.16926i	−0.811300	+	0.584630i	$0.801240\pi$
$998$			8.11428i			0.256853i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2394.2.f.b.2015.9	yes	24
3.2	odd	2		2394.2.f.a.2015.10	yes	24
7.6	odd	2		2394.2.f.a.2015.9	✓	24
21.20	even	2	inner	2394.2.f.b.2015.10	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2394.2.f.a.2015.9	✓	24	7.6	odd	2
2394.2.f.a.2015.10	yes	24	3.2	odd	2
2394.2.f.b.2015.9	yes	24	1.1	even	1	trivial
2394.2.f.b.2015.10	yes	24	21.20	even	2	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:	\( N \)	\(=\)	\( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2394.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} -1.42576 q^{5} +(2.62657 + 0.317999i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} -1.42576 q^{5} +(2.62657 + 0.317999i) q^{7} +1.00000i q^{8} +1.42576i q^{10} -1.96426i q^{11} +5.57912i q^{13} +(0.317999 - 2.62657i) q^{14} +1.00000 q^{16} -1.24731 q^{17} -1.00000i q^{19} +1.42576 q^{20} -1.96426 q^{22} -0.582257i q^{23} -2.96720 q^{25} +5.57912 q^{26} +(-2.62657 - 0.317999i) q^{28} +0.497667i q^{29} +6.46942i q^{31} -1.00000i q^{32} +1.24731i q^{34} +(-3.74487 - 0.453391i) q^{35} +4.52011 q^{37} -1.00000 q^{38} -1.42576i q^{40} +1.13024 q^{41} -9.71565 q^{43} +1.96426i q^{44} -0.582257 q^{46} -3.38468 q^{47} +(6.79775 + 1.67049i) q^{49} +2.96720i q^{50} -5.57912i q^{52} +9.99558i q^{53} +2.80058i q^{55} +(-0.317999 + 2.62657i) q^{56} +0.497667 q^{58} -5.26327 q^{59} +11.8401i q^{61} +6.46942 q^{62} -1.00000 q^{64} -7.95450i q^{65} -2.22053 q^{67} +1.24731 q^{68} +(-0.453391 + 3.74487i) q^{70} +4.00707i q^{71} -1.22215i q^{73} -4.52011i q^{74} +1.00000i q^{76} +(0.624634 - 5.15928i) q^{77} +3.74743 q^{79} -1.42576 q^{80} -1.13024i q^{82} -6.23791 q^{83} +1.77837 q^{85} +9.71565i q^{86} +1.96426 q^{88} +15.8345 q^{89} +(-1.77415 + 14.6540i) q^{91} +0.582257i q^{92} +3.38468i q^{94} +1.42576i q^{95} +4.51004i q^{97} +(1.67049 - 6.79775i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} + 4 q^{7}+O(q^{10}) \) 24 * q - 24 * q^4 + 4 * q^7	\( 24 q - 24 q^{4} + 4 q^{7} + 4 q^{14} + 24 q^{16} - 32 q^{17} - 8 q^{22} + 16 q^{25} - 4 q^{28} + 24 q^{35} - 24 q^{38} + 8 q^{41} + 16 q^{43} - 8 q^{46} - 16 q^{49} - 4 q^{56} + 16 q^{58} - 16 q^{59} + 16 q^{62} - 24 q^{64} - 24 q^{67} + 32 q^{68} - 16 q^{70} - 8 q^{77} - 40 q^{79} + 64 q^{83} + 40 q^{85} + 8 q^{88} + 64 q^{89} + 8 q^{91} + 16 q^{98}+O(q^{100}) \) 24 * q - 24 * q^4 + 4 * q^7 + 4 * q^14 + 24 * q^16 - 32 * q^17 - 8 * q^22 + 16 * q^25 - 4 * q^28 + 24 * q^35 - 24 * q^38 + 8 * q^41 + 16 * q^43 - 8 * q^46 - 16 * q^49 - 4 * q^56 + 16 * q^58 - 16 * q^59 + 16 * q^62 - 24 * q^64 - 24 * q^67 + 32 * q^68 - 16 * q^70 - 8 * q^77 - 40 * q^79 + 64 * q^83 + 40 * q^85 + 8 * q^88 + 64 * q^89 + 8 * q^91 + 16 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more