LMFDB - Embedded newform 2850.2.d.a.799.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2850,2,Mod(799,2850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2850, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2850.799");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2850.d (of order $2$, degree $1$, not 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:	$22.7573645761$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			799.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	2850.799
Dual form			2850.2.d.a.799.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +4.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +4.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} -4.00000 q^{11} -1.00000i q^{12} -6.00000i q^{13} -4.00000 q^{14} +1.00000 q^{16} +6.00000i q^{17} -1.00000i q^{18} +1.00000 q^{19} -4.00000 q^{21} -4.00000i q^{22} +4.00000i q^{23} +1.00000 q^{24} +6.00000 q^{26} -1.00000i q^{27} -4.00000i q^{28} -6.00000 q^{29} -8.00000 q^{31} +1.00000i q^{32} -4.00000i q^{33} -6.00000 q^{34} +1.00000 q^{36} -2.00000i q^{37} +1.00000i q^{38} +6.00000 q^{39} +10.0000 q^{41} -4.00000i q^{42} -8.00000i q^{43} +4.00000 q^{44} -4.00000 q^{46} -12.0000i q^{47} +1.00000i q^{48} -9.00000 q^{49} -6.00000 q^{51} +6.00000i q^{52} +2.00000i q^{53} +1.00000 q^{54} +4.00000 q^{56} +1.00000i q^{57} -6.00000i q^{58} +4.00000 q^{59} -2.00000 q^{61} -8.00000i q^{62} -4.00000i q^{63} -1.00000 q^{64} +4.00000 q^{66} +12.0000i q^{67} -6.00000i q^{68} -4.00000 q^{69} -16.0000 q^{71} +1.00000i q^{72} -14.0000i q^{73} +2.00000 q^{74} -1.00000 q^{76} -16.0000i q^{77} +6.00000i q^{78} -8.00000 q^{79} +1.00000 q^{81} +10.0000i q^{82} +4.00000 q^{84} +8.00000 q^{86} -6.00000i q^{87} +4.00000i q^{88} +6.00000 q^{89} +24.0000 q^{91} -4.00000i q^{92} -8.00000i q^{93} +12.0000 q^{94} -1.00000 q^{96} -14.0000i q^{97} -9.00000i q^{98} +4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^4 - 2 * q^6 - 2 * q^9	$ 2 q - 2 q^{4} - 2 q^{6} - 2 q^{9} - 8 q^{11} - 8 q^{14} + 2 q^{16} + 2 q^{19} - 8 q^{21} + 2 q^{24} + 12 q^{26} - 12 q^{29} - 16 q^{31} - 12 q^{34} + 2 q^{36} + 12 q^{39} + 20 q^{41} + 8 q^{44} - 8 q^{46} - 18 q^{49} - 12 q^{51} + 2 q^{54} + 8 q^{56} + 8 q^{59} - 4 q^{61} - 2 q^{64} + 8 q^{66} - 8 q^{69} - 32 q^{71} + 4 q^{74} - 2 q^{76} - 16 q^{79} + 2 q^{81} + 8 q^{84} + 16 q^{86} + 12 q^{89} + 48 q^{91} + 24 q^{94} - 2 q^{96} + 8 q^{99}+O(q^{100}) $ 2 * q - 2 * q^4 - 2 * q^6 - 2 * q^9 - 8 * q^11 - 8 * q^14 + 2 * q^16 + 2 * q^19 - 8 * q^21 + 2 * q^24 + 12 * q^26 - 12 * q^29 - 16 * q^31 - 12 * q^34 + 2 * q^36 + 12 * q^39 + 20 * q^41 + 8 * q^44 - 8 * q^46 - 18 * q^49 - 12 * q^51 + 2 * q^54 + 8 * q^56 + 8 * q^59 - 4 * q^61 - 2 * q^64 + 8 * q^66 - 8 * q^69 - 32 * q^71 + 4 * q^74 - 2 * q^76 - 16 * q^79 + 2 * q^81 + 8 * q^84 + 16 * q^86 + 12 * q^89 + 48 * q^91 + 24 * q^94 - 2 * q^96 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2850\mathbb{Z}\right)^\times$.

$n$	$1027$	$1351$	$1901$
$\chi(n)$	$-1$	$1$	$1$

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
$3$	1.00000i	0.577350i
$3$	1.00000i	0.577350i
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	4.00000i	1.51186i	0.654654	+	0.755929i	$0.272814\pi$
$7$	4.00000i	1.51186i	−0.654654	+	0.755929i	$0.727186\pi$
$8$	− 1.00000i	− 0.353553i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	− 1.00000i	− 0.288675i
$13$	− 6.00000i	− 1.66410i	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	− 6.00000i	− 1.66410i	0.554700	−	0.832050i	$-0.312833\pi$
$14$	−4.00000	−1.06904
$15$	0	0
$16$	1.00000	0.250000
$17$	6.00000i	1.45521i	0.685994	+	0.727607i	$0.259367\pi$
$17$	6.00000i	1.45521i	−0.685994	+	0.727607i	$0.740633\pi$
$18$	− 1.00000i	− 0.235702i
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	−4.00000	−0.872872
$22$	− 4.00000i	− 0.852803i
$23$	4.00000i	0.834058i	0.908893	+	0.417029i	$0.136929\pi$
$23$	4.00000i	0.834058i	−0.908893	+	0.417029i	$0.863071\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	6.00000	1.17670
$27$	− 1.00000i	− 0.192450i
$28$	− 4.00000i	− 0.755929i
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	0	0
$31$	−8.00000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	1.00000i	0.176777i
$33$	− 4.00000i	− 0.696311i
$34$	−6.00000	−1.02899
$35$	0	0
$36$	1.00000	0.166667
$37$	− 2.00000i	− 0.328798i	−0.986394	−	0.164399i	$-0.947432\pi$
$37$	− 2.00000i	− 0.328798i	0.986394	−	0.164399i	$-0.0525685\pi$
$38$	1.00000i	0.162221i
$39$	6.00000	0.960769
$40$	0	0
$41$	10.0000	1.56174	0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000	1.56174	0.780869	+	0.624695i	$0.214777\pi$
$42$	− 4.00000i	− 0.617213i
$43$	− 8.00000i	− 1.21999i	−0.792406	−	0.609994i	$-0.791172\pi$
$43$	− 8.00000i	− 1.21999i	0.792406	−	0.609994i	$-0.208828\pi$
$44$	4.00000	0.603023
$45$	0	0
$46$	−4.00000	−0.589768
$47$	− 12.0000i	− 1.75038i	−0.483779	−	0.875190i	$-0.660736\pi$
$47$	− 12.0000i	− 1.75038i	0.483779	−	0.875190i	$-0.339264\pi$
$48$	1.00000i	0.144338i
$49$	−9.00000	−1.28571
$50$	0	0
$51$	−6.00000	−0.840168
$52$	6.00000i	0.832050i
$53$	2.00000i	0.274721i	0.990521	+	0.137361i	$0.0438619\pi$
$53$	2.00000i	0.274721i	−0.990521	+	0.137361i	$0.956138\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	4.00000	0.534522
$57$	1.00000i	0.132453i
$58$	− 6.00000i	− 0.787839i
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	0	0
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	− 8.00000i	− 1.01600i
$63$	− 4.00000i	− 0.503953i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	4.00000	0.492366
$67$	12.0000i	1.46603i	0.680211	+	0.733017i	$0.261888\pi$
$67$	12.0000i	1.46603i	−0.680211	+	0.733017i	$0.738112\pi$
$68$	− 6.00000i	− 0.727607i
$69$	−4.00000	−0.481543
$70$	0	0
$71$	−16.0000	−1.89885	−0.949425	−	0.313993i	$-0.898333\pi$
$71$	−16.0000	−1.89885	−0.949425	+	0.313993i	$0.898333\pi$
$72$	1.00000i	0.117851i
$73$	− 14.0000i	− 1.63858i	−0.573382	−	0.819288i	$-0.694369\pi$
$73$	− 14.0000i	− 1.63858i	0.573382	−	0.819288i	$-0.305631\pi$
$74$	2.00000	0.232495
$75$	0	0
$76$	−1.00000	−0.114708
$77$	− 16.0000i	− 1.82337i
$78$	6.00000i	0.679366i
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	10.0000i	1.10432i
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	4.00000	0.436436
$85$	0	0
$86$	8.00000	0.862662
$87$	− 6.00000i	− 0.643268i
$88$	4.00000i	0.426401i
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	0	0
$91$	24.0000	2.51588
$92$	− 4.00000i	− 0.417029i
$93$	− 8.00000i	− 0.829561i
$94$	12.0000	1.23771
$95$	0	0
$96$	−1.00000	−0.102062
$97$	− 14.0000i	− 1.42148i	−0.703452	−	0.710742i	$-0.748359\pi$
$97$	− 14.0000i	− 1.42148i	0.703452	−	0.710742i	$-0.251641\pi$
$98$	− 9.00000i	− 0.909137i
$99$	4.00000	0.402015
$100$	0	0
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	− 6.00000i	− 0.594089i
$103$	8.00000i	0.788263i	0.919054	+	0.394132i	$0.128955\pi$
$103$	8.00000i	0.788263i	−0.919054	+	0.394132i	$0.871045\pi$
$104$	−6.00000	−0.588348
$105$	0	0
$106$	−2.00000	−0.194257
$107$	12.0000i	1.16008i	0.814587	+	0.580042i	$0.196964\pi$
$107$	12.0000i	1.16008i	−0.814587	+	0.580042i	$0.803036\pi$
$108$	1.00000i	0.0962250i
$109$	−6.00000	−0.574696	−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000	−0.574696	−0.287348	+	0.957826i	$0.592774\pi$
$110$	0	0
$111$	2.00000	0.189832
$112$	4.00000i	0.377964i
$113$	− 10.0000i	− 0.940721i	−0.882474	−	0.470360i	$-0.844124\pi$
$113$	− 10.0000i	− 0.940721i	0.882474	−	0.470360i	$-0.155876\pi$
$114$	−1.00000	−0.0936586
$115$	0	0
$116$	6.00000	0.557086
$117$	6.00000i	0.554700i
$118$	4.00000i	0.368230i
$119$	−24.0000	−2.20008
$120$	0	0
$121$	5.00000	0.454545
$122$	− 2.00000i	− 0.181071i
$123$	10.0000i	0.901670i
$124$	8.00000	0.718421
$125$	0	0
$126$	4.00000	0.356348
$127$	16.0000i	1.41977i	0.704317	+	0.709885i	$0.251253\pi$
$127$	16.0000i	1.41977i	−0.704317	+	0.709885i	$0.748747\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	8.00000	0.704361
$130$	0	0
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	4.00000i	0.348155i
$133$	4.00000i	0.346844i
$134$	−12.0000	−1.03664
$135$	0	0
$136$	6.00000	0.514496
$137$	− 2.00000i	− 0.170872i	−0.996344	−	0.0854358i	$-0.972772\pi$
$137$	− 2.00000i	− 0.170872i	0.996344	−	0.0854358i	$-0.0272282\pi$
$138$	− 4.00000i	− 0.340503i
$139$	−12.0000	−1.01783	−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000	−1.01783	−0.508913	+	0.860818i	$0.669953\pi$
$140$	0	0
$141$	12.0000	1.01058
$142$	− 16.0000i	− 1.34269i
$143$	24.0000i	2.00698i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	14.0000	1.15865
$147$	− 9.00000i	− 0.742307i
$148$	2.00000i	0.164399i
$149$	10.0000	0.819232	0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000	0.819232	0.409616	+	0.912258i	$0.365663\pi$
$150$	0	0
$151$	8.00000	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	− 1.00000i	− 0.0811107i
$153$	− 6.00000i	− 0.485071i
$154$	16.0000	1.28932
$155$	0	0
$156$	−6.00000	−0.480384
$157$	− 22.0000i	− 1.75579i	−0.478852	−	0.877896i	$-0.658947\pi$
$157$	− 22.0000i	− 1.75579i	0.478852	−	0.877896i	$-0.341053\pi$
$158$	− 8.00000i	− 0.636446i
$159$	−2.00000	−0.158610
$160$	0	0
$161$	−16.0000	−1.26098
$162$	1.00000i	0.0785674i
$163$	− 16.0000i	− 1.25322i	−0.779334	−	0.626608i	$-0.784443\pi$
$163$	− 16.0000i	− 1.25322i	0.779334	−	0.626608i	$-0.215557\pi$
$164$	−10.0000	−0.780869
$165$	0	0
$166$	0	0
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	4.00000i	0.308607i
$169$	−23.0000	−1.76923
$170$	0	0
$171$	−1.00000	−0.0764719
$172$	8.00000i	0.609994i
$173$	− 6.00000i	− 0.456172i	−0.973641	−	0.228086i	$-0.926753\pi$
$173$	− 6.00000i	− 0.456172i	0.973641	−	0.228086i	$-0.0732467\pi$
$174$	6.00000	0.454859
$175$	0	0
$176$	−4.00000	−0.301511
$177$	4.00000i	0.300658i
$178$	6.00000i	0.449719i
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	0	0
$181$	−2.00000	−0.148659	−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000	−0.148659	−0.0743294	+	0.997234i	$0.523682\pi$
$182$	24.0000i	1.77900i
$183$	− 2.00000i	− 0.147844i
$184$	4.00000	0.294884
$185$	0	0
$186$	8.00000	0.586588
$187$	− 24.0000i	− 1.75505i
$188$	12.0000i	0.875190i
$189$	4.00000	0.290957
$190$	0	0
$191$	−8.00000	−0.578860	−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000	−0.578860	−0.289430	+	0.957199i	$0.593466\pi$
$192$	− 1.00000i	− 0.0721688i
$193$	− 2.00000i	− 0.143963i	−0.997406	−	0.0719816i	$-0.977068\pi$
$193$	− 2.00000i	− 0.143963i	0.997406	−	0.0719816i	$-0.0229323\pi$
$194$	14.0000	1.00514
$195$	0	0
$196$	9.00000	0.642857
$197$	− 6.00000i	− 0.427482i	−0.976890	−	0.213741i	$-0.931435\pi$
$197$	− 6.00000i	− 0.427482i	0.976890	−	0.213741i	$-0.0685649\pi$
$198$	4.00000i	0.284268i
$199$	16.0000	1.13421	0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000	1.13421	0.567105	+	0.823646i	$0.308063\pi$
$200$	0	0
$201$	−12.0000	−0.846415
$202$	6.00000i	0.422159i
$203$	− 24.0000i	− 1.68447i
$204$	6.00000	0.420084
$205$	0	0
$206$	−8.00000	−0.557386
$207$	− 4.00000i	− 0.278019i
$208$	− 6.00000i	− 0.416025i
$209$	−4.00000	−0.276686
$210$	0	0
$211$	−20.0000	−1.37686	−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000	−1.37686	−0.688428	+	0.725304i	$0.741699\pi$
$212$	− 2.00000i	− 0.137361i
$213$	− 16.0000i	− 1.09630i
$214$	−12.0000	−0.820303
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	− 32.0000i	− 2.17230i
$218$	− 6.00000i	− 0.406371i
$219$	14.0000	0.946032
$220$	0	0
$221$	36.0000	2.42162
$222$	2.00000i	0.134231i
$223$	− 16.0000i	− 1.07144i	−0.844396	−	0.535720i	$-0.820040\pi$
$223$	− 16.0000i	− 1.07144i	0.844396	−	0.535720i	$-0.179960\pi$
$224$	−4.00000	−0.267261
$225$	0	0
$226$	10.0000	0.665190
$227$	4.00000i	0.265489i	0.991150	+	0.132745i	$0.0423790\pi$
$227$	4.00000i	0.265489i	−0.991150	+	0.132745i	$0.957621\pi$
$228$	− 1.00000i	− 0.0662266i
$229$	−6.00000	−0.396491	−0.198246	−	0.980152i	$-0.563524\pi$
$229$	−6.00000	−0.396491	−0.198246	+	0.980152i	$0.563524\pi$
$230$	0	0
$231$	16.0000	1.05272
$232$	6.00000i	0.393919i
$233$	10.0000i	0.655122i	0.944830	+	0.327561i	$0.106227\pi$
$233$	10.0000i	0.655122i	−0.944830	+	0.327561i	$0.893773\pi$
$234$	−6.00000	−0.392232
$235$	0	0
$236$	−4.00000	−0.260378
$237$	− 8.00000i	− 0.519656i
$238$	− 24.0000i	− 1.55569i
$239$	−16.0000	−1.03495	−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000	−1.03495	−0.517477	+	0.855697i	$0.673129\pi$
$240$	0	0
$241$	−22.0000	−1.41714	−0.708572	−	0.705638i	$-0.750660\pi$
$241$	−22.0000	−1.41714	−0.708572	+	0.705638i	$0.750660\pi$
$242$	5.00000i	0.321412i
$243$	1.00000i	0.0641500i
$244$	2.00000	0.128037
$245$	0	0
$246$	−10.0000	−0.637577
$247$	− 6.00000i	− 0.381771i
$248$	8.00000i	0.508001i
$249$	0	0
$250$	0	0
$251$	4.00000	0.252478	0.126239	−	0.992000i	$-0.459709\pi$
$251$	4.00000	0.252478	0.126239	+	0.992000i	$0.459709\pi$
$252$	4.00000i	0.251976i
$253$	− 16.0000i	− 1.00591i
$254$	−16.0000	−1.00393
$255$	0	0
$256$	1.00000	0.0625000
$257$	18.0000i	1.12281i	0.827541	+	0.561405i	$0.189739\pi$
$257$	18.0000i	1.12281i	−0.827541	+	0.561405i	$0.810261\pi$
$258$	8.00000i	0.498058i
$259$	8.00000	0.497096
$260$	0	0
$261$	6.00000	0.371391
$262$	12.0000i	0.741362i
$263$	20.0000i	1.23325i	0.787256	+	0.616626i	$0.211501\pi$
$263$	20.0000i	1.23325i	−0.787256	+	0.616626i	$0.788499\pi$
$264$	−4.00000	−0.246183
$265$	0	0
$266$	−4.00000	−0.245256
$267$	6.00000i	0.367194i
$268$	− 12.0000i	− 0.733017i
$269$	−14.0000	−0.853595	−0.426798	−	0.904347i	$-0.640358\pi$
$269$	−14.0000	−0.853595	−0.426798	+	0.904347i	$0.640358\pi$
$270$	0	0
$271$	−8.00000	−0.485965	−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000	−0.485965	−0.242983	+	0.970031i	$0.578126\pi$
$272$	6.00000i	0.363803i
$273$	24.0000i	1.45255i
$274$	2.00000	0.120824
$275$	0	0
$276$	4.00000	0.240772
$277$	2.00000i	0.120168i	0.998193	+	0.0600842i	$0.0191369\pi$
$277$	2.00000i	0.120168i	−0.998193	+	0.0600842i	$0.980863\pi$
$278$	− 12.0000i	− 0.719712i
$279$	8.00000	0.478947
$280$	0	0
$281$	−22.0000	−1.31241	−0.656205	−	0.754583i	$-0.727839\pi$
$281$	−22.0000	−1.31241	−0.656205	+	0.754583i	$0.727839\pi$
$282$	12.0000i	0.714590i
$283$	− 16.0000i	− 0.951101i	−0.879688	−	0.475551i	$-0.842249\pi$
$283$	− 16.0000i	− 0.951101i	0.879688	−	0.475551i	$-0.157751\pi$
$284$	16.0000	0.949425
$285$	0	0
$286$	−24.0000	−1.41915
$287$	40.0000i	2.36113i
$288$	− 1.00000i	− 0.0589256i
$289$	−19.0000	−1.11765
$290$	0	0
$291$	14.0000	0.820695
$292$	14.0000i	0.819288i
$293$	2.00000i	0.116841i	0.998292	+	0.0584206i	$0.0186065\pi$
$293$	2.00000i	0.116841i	−0.998292	+	0.0584206i	$0.981394\pi$
$294$	9.00000	0.524891
$295$	0	0
$296$	−2.00000	−0.116248
$297$	4.00000i	0.232104i
$298$	10.0000i	0.579284i
$299$	24.0000	1.38796
$300$	0	0
$301$	32.0000	1.84445
$302$	8.00000i	0.460348i
$303$	6.00000i	0.344691i
$304$	1.00000	0.0573539
$305$	0	0
$306$	6.00000	0.342997
$307$	20.0000i	1.14146i	0.821138	+	0.570730i	$0.193340\pi$
$307$	20.0000i	1.14146i	−0.821138	+	0.570730i	$0.806660\pi$
$308$	16.0000i	0.911685i
$309$	−8.00000	−0.455104
$310$	0	0
$311$	−8.00000	−0.453638	−0.226819	−	0.973937i	$-0.572833\pi$
$311$	−8.00000	−0.453638	−0.226819	+	0.973937i	$0.572833\pi$
$312$	− 6.00000i	− 0.339683i
$313$	− 6.00000i	− 0.339140i	−0.985518	−	0.169570i	$-0.945762\pi$
$313$	− 6.00000i	− 0.339140i	0.985518	−	0.169570i	$-0.0542379\pi$
$314$	22.0000	1.24153
$315$	0	0
$316$	8.00000	0.450035
$317$	14.0000i	0.786318i	0.919470	+	0.393159i	$0.128618\pi$
$317$	14.0000i	0.786318i	−0.919470	+	0.393159i	$0.871382\pi$
$318$	− 2.00000i	− 0.112154i
$319$	24.0000	1.34374
$320$	0	0
$321$	−12.0000	−0.669775
$322$	− 16.0000i	− 0.891645i
$323$	6.00000i	0.333849i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	16.0000	0.886158
$327$	− 6.00000i	− 0.331801i
$328$	− 10.0000i	− 0.552158i
$329$	48.0000	2.64633
$330$	0	0
$331$	4.00000	0.219860	0.109930	−	0.993939i	$-0.464937\pi$
$331$	4.00000	0.219860	0.109930	+	0.993939i	$0.464937\pi$
$332$	0	0
$333$	2.00000i	0.109599i
$334$	0	0
$335$	0	0
$336$	−4.00000	−0.218218
$337$	− 14.0000i	− 0.762629i	−0.924445	−	0.381314i	$-0.875472\pi$
$337$	− 14.0000i	− 0.762629i	0.924445	−	0.381314i	$-0.124528\pi$
$338$	− 23.0000i	− 1.25104i
$339$	10.0000	0.543125
$340$	0	0
$341$	32.0000	1.73290
$342$	− 1.00000i	− 0.0540738i
$343$	− 8.00000i	− 0.431959i
$344$	−8.00000	−0.431331
$345$	0	0
$346$	6.00000	0.322562
$347$	− 32.0000i	− 1.71785i	−0.512101	−	0.858925i	$-0.671133\pi$
$347$	− 32.0000i	− 1.71785i	0.512101	−	0.858925i	$-0.328867\pi$
$348$	6.00000i	0.321634i
$349$	2.00000	0.107058	0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000	0.107058	0.0535288	+	0.998566i	$0.482953\pi$
$350$	0	0
$351$	−6.00000	−0.320256
$352$	− 4.00000i	− 0.213201i
$353$	26.0000i	1.38384i	0.721974	+	0.691920i	$0.243235\pi$
$353$	26.0000i	1.38384i	−0.721974	+	0.691920i	$0.756765\pi$
$354$	−4.00000	−0.212598
$355$	0	0
$356$	−6.00000	−0.317999
$357$	− 24.0000i	− 1.27021i
$358$	12.0000i	0.634220i
$359$	16.0000	0.844448	0.422224	−	0.906492i	$-0.361250\pi$
$359$	16.0000	0.844448	0.422224	+	0.906492i	$0.361250\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	− 2.00000i	− 0.105118i
$363$	5.00000i	0.262432i
$364$	−24.0000	−1.25794
$365$	0	0
$366$	2.00000	0.104542
$367$	− 4.00000i	− 0.208798i	−0.994535	−	0.104399i	$-0.966708\pi$
$367$	− 4.00000i	− 0.208798i	0.994535	−	0.104399i	$-0.0332919\pi$
$368$	4.00000i	0.208514i
$369$	−10.0000	−0.520579
$370$	0	0
$371$	−8.00000	−0.415339
$372$	8.00000i	0.414781i
$373$	10.0000i	0.517780i	0.965907	+	0.258890i	$0.0833568\pi$
$373$	10.0000i	0.517780i	−0.965907	+	0.258890i	$0.916643\pi$
$374$	24.0000	1.24101
$375$	0	0
$376$	−12.0000	−0.618853
$377$	36.0000i	1.85409i
$378$	4.00000i	0.205738i
$379$	−4.00000	−0.205466	−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000	−0.205466	−0.102733	+	0.994709i	$0.532759\pi$
$380$	0	0
$381$	−16.0000	−0.819705
$382$	− 8.00000i	− 0.409316i
$383$	24.0000i	1.22634i	0.789950	+	0.613171i	$0.210106\pi$
$383$	24.0000i	1.22634i	−0.789950	+	0.613171i	$0.789894\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	2.00000	0.101797
$387$	8.00000i	0.406663i
$388$	14.0000i	0.710742i
$389$	26.0000	1.31825	0.659126	−	0.752032i	$-0.270926\pi$
$389$	26.0000	1.31825	0.659126	+	0.752032i	$0.270926\pi$
$390$	0	0
$391$	−24.0000	−1.21373
$392$	9.00000i	0.454569i
$393$	12.0000i	0.605320i
$394$	6.00000	0.302276
$395$	0	0
$396$	−4.00000	−0.201008
$397$	− 22.0000i	− 1.10415i	−0.833795	−	0.552074i	$-0.813837\pi$
$397$	− 22.0000i	− 1.10415i	0.833795	−	0.552074i	$-0.186163\pi$
$398$	16.0000i	0.802008i
$399$	−4.00000	−0.200250
$400$	0	0
$401$	−22.0000	−1.09863	−0.549314	−	0.835616i	$-0.685111\pi$
$401$	−22.0000	−1.09863	−0.549314	+	0.835616i	$0.685111\pi$
$402$	− 12.0000i	− 0.598506i
$403$	48.0000i	2.39105i
$404$	−6.00000	−0.298511
$405$	0	0
$406$	24.0000	1.19110
$407$	8.00000i	0.396545i
$408$	6.00000i	0.297044i
$409$	6.00000	0.296681	0.148340	−	0.988936i	$-0.452607\pi$
$409$	6.00000	0.296681	0.148340	+	0.988936i	$0.452607\pi$
$410$	0	0
$411$	2.00000	0.0986527
$412$	− 8.00000i	− 0.394132i
$413$	16.0000i	0.787309i
$414$	4.00000	0.196589
$415$	0	0
$416$	6.00000	0.294174
$417$	− 12.0000i	− 0.587643i
$418$	− 4.00000i	− 0.195646i
$419$	−20.0000	−0.977064	−0.488532	−	0.872546i	$-0.662467\pi$
$419$	−20.0000	−0.977064	−0.488532	+	0.872546i	$0.662467\pi$
$420$	0	0
$421$	−26.0000	−1.26716	−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−26.0000	−1.26716	−0.633581	+	0.773676i	$0.718416\pi$
$422$	− 20.0000i	− 0.973585i
$423$	12.0000i	0.583460i
$424$	2.00000	0.0971286
$425$	0	0
$426$	16.0000	0.775203
$427$	− 8.00000i	− 0.387147i
$428$	− 12.0000i	− 0.580042i
$429$	−24.0000	−1.15873
$430$	0	0
$431$	−32.0000	−1.54139	−0.770693	−	0.637207i	$-0.780090\pi$
$431$	−32.0000	−1.54139	−0.770693	+	0.637207i	$0.780090\pi$
$432$	− 1.00000i	− 0.0481125i
$433$	14.0000i	0.672797i	0.941720	+	0.336399i	$0.109209\pi$
$433$	14.0000i	0.672797i	−0.941720	+	0.336399i	$0.890791\pi$
$434$	32.0000	1.53605
$435$	0	0
$436$	6.00000	0.287348
$437$	4.00000i	0.191346i
$438$	14.0000i	0.668946i
$439$	−32.0000	−1.52728	−0.763638	−	0.645644i	$-0.776589\pi$
$439$	−32.0000	−1.52728	−0.763638	+	0.645644i	$0.776589\pi$
$440$	0	0
$441$	9.00000	0.428571
$442$	36.0000i	1.71235i
$443$	8.00000i	0.380091i	0.981775	+	0.190046i	$0.0608636\pi$
$443$	8.00000i	0.380091i	−0.981775	+	0.190046i	$0.939136\pi$
$444$	−2.00000	−0.0949158
$445$	0	0
$446$	16.0000	0.757622
$447$	10.0000i	0.472984i
$448$	− 4.00000i	− 0.188982i
$449$	−10.0000	−0.471929	−0.235965	−	0.971762i	$-0.575825\pi$
$449$	−10.0000	−0.471929	−0.235965	+	0.971762i	$0.575825\pi$
$450$	0	0
$451$	−40.0000	−1.88353
$452$	10.0000i	0.470360i
$453$	8.00000i	0.375873i
$454$	−4.00000	−0.187729
$455$	0	0
$456$	1.00000	0.0468293
$457$	− 10.0000i	− 0.467780i	−0.972263	−	0.233890i	$-0.924854\pi$
$457$	− 10.0000i	− 0.467780i	0.972263	−	0.233890i	$-0.0751456\pi$
$458$	− 6.00000i	− 0.280362i
$459$	6.00000	0.280056
$460$	0	0
$461$	−18.0000	−0.838344	−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000	−0.838344	−0.419172	+	0.907907i	$0.637680\pi$
$462$	16.0000i	0.744387i
$463$	20.0000i	0.929479i	0.885448	+	0.464739i	$0.153852\pi$
$463$	20.0000i	0.929479i	−0.885448	+	0.464739i	$0.846148\pi$
$464$	−6.00000	−0.278543
$465$	0	0
$466$	−10.0000	−0.463241
$467$	8.00000i	0.370196i	0.982720	+	0.185098i	$0.0592602\pi$
$467$	8.00000i	0.370196i	−0.982720	+	0.185098i	$0.940740\pi$
$468$	− 6.00000i	− 0.277350i
$469$	−48.0000	−2.21643
$470$	0	0
$471$	22.0000	1.01371
$472$	− 4.00000i	− 0.184115i
$473$	32.0000i	1.47136i
$474$	8.00000	0.367452
$475$	0	0
$476$	24.0000	1.10004
$477$	− 2.00000i	− 0.0915737i
$478$	− 16.0000i	− 0.731823i
$479$	−24.0000	−1.09659	−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000	−1.09659	−0.548294	+	0.836286i	$0.684723\pi$
$480$	0	0
$481$	−12.0000	−0.547153
$482$	− 22.0000i	− 1.00207i
$483$	− 16.0000i	− 0.728025i
$484$	−5.00000	−0.227273
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	16.0000i	0.725029i	0.931978	+	0.362515i	$0.118082\pi$
$487$	16.0000i	0.725029i	−0.931978	+	0.362515i	$0.881918\pi$
$488$	2.00000i	0.0905357i
$489$	16.0000	0.723545
$490$	0	0
$491$	−12.0000	−0.541552	−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000	−0.541552	−0.270776	+	0.962642i	$0.587280\pi$
$492$	− 10.0000i	− 0.450835i
$493$	− 36.0000i	− 1.62136i
$494$	6.00000	0.269953
$495$	0	0
$496$	−8.00000	−0.359211
$497$	− 64.0000i	− 2.87079i
$498$	0	0
$499$	28.0000	1.25345	0.626726	−	0.779240i	$-0.284395\pi$
$499$	28.0000	1.25345	0.626726	+	0.779240i	$0.284395\pi$
$500$	0	0
$501$	0	0
$502$	4.00000i	0.178529i
$503$	− 12.0000i	− 0.535054i	−0.963550	−	0.267527i	$-0.913794\pi$
$503$	− 12.0000i	− 0.535054i	0.963550	−	0.267527i	$-0.0862064\pi$
$504$	−4.00000	−0.178174
$505$	0	0
$506$	16.0000	0.711287
$507$	− 23.0000i	− 1.02147i
$508$	− 16.0000i	− 0.709885i
$509$	−6.00000	−0.265945	−0.132973	−	0.991120i	$-0.542452\pi$
$509$	−6.00000	−0.265945	−0.132973	+	0.991120i	$0.542452\pi$
$510$	0	0
$511$	56.0000	2.47729
$512$	1.00000i	0.0441942i
$513$	− 1.00000i	− 0.0441511i
$514$	−18.0000	−0.793946
$515$	0	0
$516$	−8.00000	−0.352180
$517$	48.0000i	2.11104i
$518$	8.00000i	0.351500i
$519$	6.00000	0.263371
$520$	0	0
$521$	−14.0000	−0.613351	−0.306676	−	0.951814i	$-0.599217\pi$
$521$	−14.0000	−0.613351	−0.306676	+	0.951814i	$0.599217\pi$
$522$	6.00000i	0.262613i
$523$	20.0000i	0.874539i	0.899331	+	0.437269i	$0.144054\pi$
$523$	20.0000i	0.874539i	−0.899331	+	0.437269i	$0.855946\pi$
$524$	−12.0000	−0.524222
$525$	0	0
$526$	−20.0000	−0.872041
$527$	− 48.0000i	− 2.09091i
$528$	− 4.00000i	− 0.174078i
$529$	7.00000	0.304348
$530$	0	0
$531$	−4.00000	−0.173585
$532$	− 4.00000i	− 0.173422i
$533$	− 60.0000i	− 2.59889i
$534$	−6.00000	−0.259645
$535$	0	0
$536$	12.0000	0.518321
$537$	12.0000i	0.517838i
$538$	− 14.0000i	− 0.603583i
$539$	36.0000	1.55063
$540$	0	0
$541$	−34.0000	−1.46177	−0.730887	−	0.682498i	$-0.760893\pi$
$541$	−34.0000	−1.46177	−0.730887	+	0.682498i	$0.760893\pi$
$542$	− 8.00000i	− 0.343629i
$543$	− 2.00000i	− 0.0858282i
$544$	−6.00000	−0.257248
$545$	0	0
$546$	−24.0000	−1.02711
$547$	36.0000i	1.53925i	0.638497	+	0.769624i	$0.279557\pi$
$547$	36.0000i	1.53925i	−0.638497	+	0.769624i	$0.720443\pi$
$548$	2.00000i	0.0854358i
$549$	2.00000	0.0853579
$550$	0	0
$551$	−6.00000	−0.255609
$552$	4.00000i	0.170251i
$553$	− 32.0000i	− 1.36078i
$554$	−2.00000	−0.0849719
$555$	0	0
$556$	12.0000	0.508913
$557$	26.0000i	1.10166i	0.834619	+	0.550828i	$0.185688\pi$
$557$	26.0000i	1.10166i	−0.834619	+	0.550828i	$0.814312\pi$
$558$	8.00000i	0.338667i
$559$	−48.0000	−2.03018
$560$	0	0
$561$	24.0000	1.01328
$562$	− 22.0000i	− 0.928014i
$563$	− 20.0000i	− 0.842900i	−0.906852	−	0.421450i	$-0.861521\pi$
$563$	− 20.0000i	− 0.842900i	0.906852	−	0.421450i	$-0.138479\pi$
$564$	−12.0000	−0.505291
$565$	0	0
$566$	16.0000	0.672530
$567$	4.00000i	0.167984i
$568$	16.0000i	0.671345i
$569$	−34.0000	−1.42535	−0.712677	−	0.701492i	$-0.752517\pi$
$569$	−34.0000	−1.42535	−0.712677	+	0.701492i	$0.752517\pi$
$570$	0	0
$571$	4.00000	0.167395	0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000	0.167395	0.0836974	+	0.996491i	$0.473327\pi$
$572$	− 24.0000i	− 1.00349i
$573$	− 8.00000i	− 0.334205i
$574$	−40.0000	−1.66957
$575$	0	0
$576$	1.00000	0.0416667
$577$	− 18.0000i	− 0.749350i	−0.927156	−	0.374675i	$-0.877754\pi$
$577$	− 18.0000i	− 0.749350i	0.927156	−	0.374675i	$-0.122246\pi$
$578$	− 19.0000i	− 0.790296i
$579$	2.00000	0.0831172
$580$	0	0
$581$	0	0
$582$	14.0000i	0.580319i
$583$	− 8.00000i	− 0.331326i
$584$	−14.0000	−0.579324
$585$	0	0
$586$	−2.00000	−0.0826192
$587$	− 32.0000i	− 1.32078i	−0.750922	−	0.660391i	$-0.770391\pi$
$587$	− 32.0000i	− 1.32078i	0.750922	−	0.660391i	$-0.229609\pi$
$588$	9.00000i	0.371154i
$589$	−8.00000	−0.329634
$590$	0	0
$591$	6.00000	0.246807
$592$	− 2.00000i	− 0.0821995i
$593$	34.0000i	1.39621i	0.715994	+	0.698106i	$0.245974\pi$
$593$	34.0000i	1.39621i	−0.715994	+	0.698106i	$0.754026\pi$
$594$	−4.00000	−0.164122
$595$	0	0
$596$	−10.0000	−0.409616
$597$	16.0000i	0.654836i
$598$	24.0000i	0.981433i
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	0	0
$601$	2.00000	0.0815817	0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000	0.0815817	0.0407909	+	0.999168i	$0.487012\pi$
$602$	32.0000i	1.30422i
$603$	− 12.0000i	− 0.488678i
$604$	−8.00000	−0.325515
$605$	0	0
$606$	−6.00000	−0.243733
$607$	− 24.0000i	− 0.974130i	−0.873366	−	0.487065i	$-0.838067\pi$
$607$	− 24.0000i	− 0.974130i	0.873366	−	0.487065i	$-0.161933\pi$
$608$	1.00000i	0.0405554i
$609$	24.0000	0.972529
$610$	0	0
$611$	−72.0000	−2.91281
$612$	6.00000i	0.242536i
$613$	46.0000i	1.85792i	0.370177	+	0.928961i	$0.379297\pi$
$613$	46.0000i	1.85792i	−0.370177	+	0.928961i	$0.620703\pi$
$614$	−20.0000	−0.807134
$615$	0	0
$616$	−16.0000	−0.644658
$617$	14.0000i	0.563619i	0.959470	+	0.281809i	$0.0909346\pi$
$617$	14.0000i	0.563619i	−0.959470	+	0.281809i	$0.909065\pi$
$618$	− 8.00000i	− 0.321807i
$619$	20.0000	0.803868	0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000	0.803868	0.401934	+	0.915669i	$0.368338\pi$
$620$	0	0
$621$	4.00000	0.160514
$622$	− 8.00000i	− 0.320771i
$623$	24.0000i	0.961540i
$624$	6.00000	0.240192
$625$	0	0
$626$	6.00000	0.239808
$627$	− 4.00000i	− 0.159745i
$628$	22.0000i	0.877896i
$629$	12.0000	0.478471
$630$	0	0
$631$	−32.0000	−1.27390	−0.636950	−	0.770905i	$-0.719804\pi$
$631$	−32.0000	−1.27390	−0.636950	+	0.770905i	$0.719804\pi$
$632$	8.00000i	0.318223i
$633$	− 20.0000i	− 0.794929i
$634$	−14.0000	−0.556011
$635$	0	0
$636$	2.00000	0.0793052
$637$	54.0000i	2.13956i
$638$	24.0000i	0.950169i
$639$	16.0000	0.632950
$640$	0	0
$641$	−14.0000	−0.552967	−0.276483	−	0.961019i	$-0.589169\pi$
$641$	−14.0000	−0.552967	−0.276483	+	0.961019i	$0.589169\pi$
$642$	− 12.0000i	− 0.473602i
$643$	− 40.0000i	− 1.57745i	−0.614749	−	0.788723i	$-0.710743\pi$
$643$	− 40.0000i	− 1.57745i	0.614749	−	0.788723i	$-0.289257\pi$
$644$	16.0000	0.630488
$645$	0	0
$646$	−6.00000	−0.236067
$647$	− 12.0000i	− 0.471769i	−0.971781	−	0.235884i	$-0.924201\pi$
$647$	− 12.0000i	− 0.471769i	0.971781	−	0.235884i	$-0.0757987\pi$
$648$	− 1.00000i	− 0.0392837i
$649$	−16.0000	−0.628055
$650$	0	0
$651$	32.0000	1.25418
$652$	16.0000i	0.626608i
$653$	6.00000i	0.234798i	0.993085	+	0.117399i	$0.0374557\pi$
$653$	6.00000i	0.234798i	−0.993085	+	0.117399i	$0.962544\pi$
$654$	6.00000	0.234619
$655$	0	0
$656$	10.0000	0.390434
$657$	14.0000i	0.546192i
$658$	48.0000i	1.87123i
$659$	12.0000	0.467454	0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000	0.467454	0.233727	+	0.972302i	$0.424908\pi$
$660$	0	0
$661$	−10.0000	−0.388955	−0.194477	−	0.980907i	$-0.562301\pi$
$661$	−10.0000	−0.388955	−0.194477	+	0.980907i	$0.562301\pi$
$662$	4.00000i	0.155464i
$663$	36.0000i	1.39812i
$664$	0	0
$665$	0	0
$666$	−2.00000	−0.0774984
$667$	− 24.0000i	− 0.929284i
$668$	0	0
$669$	16.0000	0.618596
$670$	0	0
$671$	8.00000	0.308837
$672$	− 4.00000i	− 0.154303i
$673$	22.0000i	0.848038i	0.905653	+	0.424019i	$0.139381\pi$
$673$	22.0000i	0.848038i	−0.905653	+	0.424019i	$0.860619\pi$
$674$	14.0000	0.539260
$675$	0	0
$676$	23.0000	0.884615
$677$	30.0000i	1.15299i	0.817099	+	0.576497i	$0.195581\pi$
$677$	30.0000i	1.15299i	−0.817099	+	0.576497i	$0.804419\pi$
$678$	10.0000i	0.384048i
$679$	56.0000	2.14908
$680$	0	0
$681$	−4.00000	−0.153280
$682$	32.0000i	1.22534i
$683$	− 12.0000i	− 0.459167i	−0.973289	−	0.229584i	$-0.926264\pi$
$683$	− 12.0000i	− 0.459167i	0.973289	−	0.229584i	$-0.0737364\pi$
$684$	1.00000	0.0382360
$685$	0	0
$686$	8.00000	0.305441
$687$	− 6.00000i	− 0.228914i
$688$	− 8.00000i	− 0.304997i
$689$	12.0000	0.457164
$690$	0	0
$691$	−20.0000	−0.760836	−0.380418	−	0.924815i	$-0.624220\pi$
$691$	−20.0000	−0.760836	−0.380418	+	0.924815i	$0.624220\pi$
$692$	6.00000i	0.228086i
$693$	16.0000i	0.607790i
$694$	32.0000	1.21470
$695$	0	0
$696$	−6.00000	−0.227429
$697$	60.0000i	2.27266i
$698$	2.00000i	0.0757011i
$699$	−10.0000	−0.378235
$700$	0	0
$701$	−18.0000	−0.679851	−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000	−0.679851	−0.339925	+	0.940452i	$0.610402\pi$
$702$	− 6.00000i	− 0.226455i
$703$	− 2.00000i	− 0.0754314i
$704$	4.00000	0.150756
$705$	0	0
$706$	−26.0000	−0.978523
$707$	24.0000i	0.902613i
$708$	− 4.00000i	− 0.150329i
$709$	−6.00000	−0.225335	−0.112667	−	0.993633i	$-0.535939\pi$
$709$	−6.00000	−0.225335	−0.112667	+	0.993633i	$0.535939\pi$
$710$	0	0
$711$	8.00000	0.300023
$712$	− 6.00000i	− 0.224860i
$713$	− 32.0000i	− 1.19841i
$714$	24.0000	0.898177
$715$	0	0
$716$	−12.0000	−0.448461
$717$	− 16.0000i	− 0.597531i
$718$	16.0000i	0.597115i
$719$	−24.0000	−0.895049	−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000	−0.895049	−0.447524	+	0.894272i	$0.647694\pi$
$720$	0	0
$721$	−32.0000	−1.19174
$722$	1.00000i	0.0372161i
$723$	− 22.0000i	− 0.818189i
$724$	2.00000	0.0743294
$725$	0	0
$726$	−5.00000	−0.185567
$727$	− 28.0000i	− 1.03846i	−0.854634	−	0.519231i	$-0.826218\pi$
$727$	− 28.0000i	− 1.03846i	0.854634	−	0.519231i	$-0.173782\pi$
$728$	− 24.0000i	− 0.889499i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	48.0000	1.77534
$732$	2.00000i	0.0739221i
$733$	− 50.0000i	− 1.84679i	−0.383849	−	0.923396i	$-0.625402\pi$
$733$	− 50.0000i	− 1.84679i	0.383849	−	0.923396i	$-0.374598\pi$
$734$	4.00000	0.147643
$735$	0	0
$736$	−4.00000	−0.147442
$737$	− 48.0000i	− 1.76810i
$738$	− 10.0000i	− 0.368105i
$739$	−44.0000	−1.61857	−0.809283	−	0.587419i	$-0.800144\pi$
$739$	−44.0000	−1.61857	−0.809283	+	0.587419i	$0.800144\pi$
$740$	0	0
$741$	6.00000	0.220416
$742$	− 8.00000i	− 0.293689i
$743$	16.0000i	0.586983i	0.955962	+	0.293492i	$0.0948173\pi$
$743$	16.0000i	0.586983i	−0.955962	+	0.293492i	$0.905183\pi$
$744$	−8.00000	−0.293294
$745$	0	0
$746$	−10.0000	−0.366126
$747$	0	0
$748$	24.0000i	0.877527i
$749$	−48.0000	−1.75388
$750$	0	0
$751$	−32.0000	−1.16770	−0.583848	−	0.811863i	$-0.698454\pi$
$751$	−32.0000	−1.16770	−0.583848	+	0.811863i	$0.698454\pi$
$752$	− 12.0000i	− 0.437595i
$753$	4.00000i	0.145768i
$754$	−36.0000	−1.31104
$755$	0	0
$756$	−4.00000	−0.145479
$757$	10.0000i	0.363456i	0.983349	+	0.181728i	$0.0581691\pi$
$757$	10.0000i	0.363456i	−0.983349	+	0.181728i	$0.941831\pi$
$758$	− 4.00000i	− 0.145287i
$759$	16.0000	0.580763
$760$	0	0
$761$	−6.00000	−0.217500	−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000	−0.217500	−0.108750	+	0.994069i	$0.534685\pi$
$762$	− 16.0000i	− 0.579619i
$763$	− 24.0000i	− 0.868858i
$764$	8.00000	0.289430
$765$	0	0
$766$	−24.0000	−0.867155
$767$	− 24.0000i	− 0.866590i
$768$	1.00000i	0.0360844i
$769$	−18.0000	−0.649097	−0.324548	−	0.945869i	$-0.605212\pi$
$769$	−18.0000	−0.649097	−0.324548	+	0.945869i	$0.605212\pi$
$770$	0	0
$771$	−18.0000	−0.648254
$772$	2.00000i	0.0719816i
$773$	10.0000i	0.359675i	0.983696	+	0.179838i	$0.0575572\pi$
$773$	10.0000i	0.359675i	−0.983696	+	0.179838i	$0.942443\pi$
$774$	−8.00000	−0.287554
$775$	0	0
$776$	−14.0000	−0.502571
$777$	8.00000i	0.286998i
$778$	26.0000i	0.932145i
$779$	10.0000	0.358287
$780$	0	0
$781$	64.0000	2.29010
$782$	− 24.0000i	− 0.858238i
$783$	6.00000i	0.214423i
$784$	−9.00000	−0.321429
$785$	0	0
$786$	−12.0000	−0.428026
$787$	52.0000i	1.85360i	0.375555	+	0.926800i	$0.377452\pi$
$787$	52.0000i	1.85360i	−0.375555	+	0.926800i	$0.622548\pi$
$788$	6.00000i	0.213741i
$789$	−20.0000	−0.712019
$790$	0	0
$791$	40.0000	1.42224
$792$	− 4.00000i	− 0.142134i
$793$	12.0000i	0.426132i
$794$	22.0000	0.780751
$795$	0	0
$796$	−16.0000	−0.567105
$797$	38.0000i	1.34603i	0.739629	+	0.673015i	$0.235001\pi$
$797$	38.0000i	1.34603i	−0.739629	+	0.673015i	$0.764999\pi$
$798$	− 4.00000i	− 0.141598i
$799$	72.0000	2.54718
$800$	0	0
$801$	−6.00000	−0.212000
$802$	− 22.0000i	− 0.776847i
$803$	56.0000i	1.97620i
$804$	12.0000	0.423207
$805$	0	0
$806$	−48.0000	−1.69073
$807$	− 14.0000i	− 0.492823i
$808$	− 6.00000i	− 0.211079i
$809$	−42.0000	−1.47664	−0.738321	−	0.674450i	$-0.764381\pi$
$809$	−42.0000	−1.47664	−0.738321	+	0.674450i	$0.764381\pi$
$810$	0	0
$811$	28.0000	0.983213	0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000	0.983213	0.491606	+	0.870817i	$0.336410\pi$
$812$	24.0000i	0.842235i
$813$	− 8.00000i	− 0.280572i
$814$	−8.00000	−0.280400
$815$	0	0
$816$	−6.00000	−0.210042
$817$	− 8.00000i	− 0.279885i
$818$	6.00000i	0.209785i
$819$	−24.0000	−0.838628
$820$	0	0
$821$	6.00000	0.209401	0.104701	−	0.994504i	$-0.466612\pi$
$821$	6.00000	0.209401	0.104701	+	0.994504i	$0.466612\pi$
$822$	2.00000i	0.0697580i
$823$	4.00000i	0.139431i	0.997567	+	0.0697156i	$0.0222092\pi$
$823$	4.00000i	0.139431i	−0.997567	+	0.0697156i	$0.977791\pi$
$824$	8.00000	0.278693
$825$	0	0
$826$	−16.0000	−0.556711
$827$	− 12.0000i	− 0.417281i	−0.977992	−	0.208640i	$-0.933096\pi$
$827$	− 12.0000i	− 0.417281i	0.977992	−	0.208640i	$-0.0669038\pi$
$828$	4.00000i	0.139010i
$829$	26.0000	0.903017	0.451509	−	0.892267i	$-0.350886\pi$
$829$	26.0000	0.903017	0.451509	+	0.892267i	$0.350886\pi$
$830$	0	0
$831$	−2.00000	−0.0693792
$832$	6.00000i	0.208013i
$833$	− 54.0000i	− 1.87099i
$834$	12.0000	0.415526
$835$	0	0
$836$	4.00000	0.138343
$837$	8.00000i	0.276520i
$838$	− 20.0000i	− 0.690889i
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	− 26.0000i	− 0.896019i
$843$	− 22.0000i	− 0.757720i
$844$	20.0000	0.688428
$845$	0	0
$846$	−12.0000	−0.412568
$847$	20.0000i	0.687208i
$848$	2.00000i	0.0686803i
$849$	16.0000	0.549119
$850$	0	0
$851$	8.00000	0.274236
$852$	16.0000i	0.548151i
$853$	− 10.0000i	− 0.342393i	−0.985237	−	0.171197i	$-0.945237\pi$
$853$	− 10.0000i	− 0.342393i	0.985237	−	0.171197i	$-0.0547634\pi$
$854$	8.00000	0.273754
$855$	0	0
$856$	12.0000	0.410152
$857$	− 6.00000i	− 0.204956i	−0.994735	−	0.102478i	$-0.967323\pi$
$857$	− 6.00000i	− 0.204956i	0.994735	−	0.102478i	$-0.0326771\pi$
$858$	− 24.0000i	− 0.819346i
$859$	44.0000	1.50126	0.750630	−	0.660722i	$-0.229750\pi$
$859$	44.0000	1.50126	0.750630	+	0.660722i	$0.229750\pi$
$860$	0	0
$861$	−40.0000	−1.36320
$862$	− 32.0000i	− 1.08992i
$863$	24.0000i	0.816970i	0.912765	+	0.408485i	$0.133943\pi$
$863$	24.0000i	0.816970i	−0.912765	+	0.408485i	$0.866057\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	−14.0000	−0.475739
$867$	− 19.0000i	− 0.645274i
$868$	32.0000i	1.08615i
$869$	32.0000	1.08553
$870$	0	0
$871$	72.0000	2.43963
$872$	6.00000i	0.203186i
$873$	14.0000i	0.473828i
$874$	−4.00000	−0.135302
$875$	0	0
$876$	−14.0000	−0.473016
$877$	− 18.0000i	− 0.607817i	−0.952701	−	0.303908i	$-0.901708\pi$
$877$	− 18.0000i	− 0.607817i	0.952701	−	0.303908i	$-0.0982917\pi$
$878$	− 32.0000i	− 1.07995i
$879$	−2.00000	−0.0674583
$880$	0	0
$881$	−14.0000	−0.471672	−0.235836	−	0.971793i	$-0.575783\pi$
$881$	−14.0000	−0.471672	−0.235836	+	0.971793i	$0.575783\pi$
$882$	9.00000i	0.303046i
$883$	− 16.0000i	− 0.538443i	−0.963078	−	0.269221i	$-0.913234\pi$
$883$	− 16.0000i	− 0.538443i	0.963078	−	0.269221i	$-0.0867663\pi$
$884$	−36.0000	−1.21081
$885$	0	0
$886$	−8.00000	−0.268765
$887$	8.00000i	0.268614i	0.990940	+	0.134307i	$0.0428808\pi$
$887$	8.00000i	0.268614i	−0.990940	+	0.134307i	$0.957119\pi$
$888$	− 2.00000i	− 0.0671156i
$889$	−64.0000	−2.14649
$890$	0	0
$891$	−4.00000	−0.134005
$892$	16.0000i	0.535720i
$893$	− 12.0000i	− 0.401565i
$894$	−10.0000	−0.334450
$895$	0	0
$896$	4.00000	0.133631
$897$	24.0000i	0.801337i
$898$	− 10.0000i	− 0.333704i
$899$	48.0000	1.60089
$900$	0	0
$901$	−12.0000	−0.399778
$902$	− 40.0000i	− 1.33185i
$903$	32.0000i	1.06489i
$904$	−10.0000	−0.332595
$905$	0	0
$906$	−8.00000	−0.265782
$907$	12.0000i	0.398453i	0.979953	+	0.199227i	$0.0638430\pi$
$907$	12.0000i	0.398453i	−0.979953	+	0.199227i	$0.936157\pi$
$908$	− 4.00000i	− 0.132745i
$909$	−6.00000	−0.199007
$910$	0	0
$911$	16.0000	0.530104	0.265052	−	0.964234i	$-0.414611\pi$
$911$	16.0000	0.530104	0.265052	+	0.964234i	$0.414611\pi$
$912$	1.00000i	0.0331133i
$913$	0	0
$914$	10.0000	0.330771
$915$	0	0
$916$	6.00000	0.198246
$917$	48.0000i	1.58510i
$918$	6.00000i	0.198030i
$919$	0	0		−	1.00000i	$-0.5\pi$
$919$	0	0			1.00000i	$0.5\pi$
$920$	0	0
$921$	−20.0000	−0.659022
$922$	− 18.0000i	− 0.592798i
$923$	96.0000i	3.15988i
$924$	−16.0000	−0.526361
$925$	0	0
$926$	−20.0000	−0.657241
$927$	− 8.00000i	− 0.262754i
$928$	− 6.00000i	− 0.196960i
$929$	14.0000	0.459325	0.229663	−	0.973270i	$-0.426238\pi$
$929$	14.0000	0.459325	0.229663	+	0.973270i	$0.426238\pi$
$930$	0	0
$931$	−9.00000	−0.294963
$932$	− 10.0000i	− 0.327561i
$933$	− 8.00000i	− 0.261908i
$934$	−8.00000	−0.261768
$935$	0	0
$936$	6.00000	0.196116
$937$	30.0000i	0.980057i	0.871706	+	0.490029i	$0.163014\pi$
$937$	30.0000i	0.980057i	−0.871706	+	0.490029i	$0.836986\pi$
$938$	− 48.0000i	− 1.56726i
$939$	6.00000	0.195803
$940$	0	0
$941$	46.0000	1.49956	0.749779	−	0.661689i	$-0.230160\pi$
$941$	46.0000	1.49956	0.749779	+	0.661689i	$0.230160\pi$
$942$	22.0000i	0.716799i
$943$	40.0000i	1.30258i
$944$	4.00000	0.130189
$945$	0	0
$946$	−32.0000	−1.04041
$947$	24.0000i	0.779895i	0.920837	+	0.389948i	$0.127507\pi$
$947$	24.0000i	0.779895i	−0.920837	+	0.389948i	$0.872493\pi$
$948$	8.00000i	0.259828i
$949$	−84.0000	−2.72676
$950$	0	0
$951$	−14.0000	−0.453981
$952$	24.0000i	0.777844i
$953$	− 42.0000i	− 1.36051i	−0.732974	−	0.680257i	$-0.761868\pi$
$953$	− 42.0000i	− 1.36051i	0.732974	−	0.680257i	$-0.238132\pi$
$954$	2.00000	0.0647524
$955$	0	0
$956$	16.0000	0.517477
$957$	24.0000i	0.775810i
$958$	− 24.0000i	− 0.775405i
$959$	8.00000	0.258333
$960$	0	0
$961$	33.0000	1.06452
$962$	− 12.0000i	− 0.386896i
$963$	− 12.0000i	− 0.386695i
$964$	22.0000	0.708572
$965$	0	0
$966$	16.0000	0.514792
$967$	− 52.0000i	− 1.67221i	−0.548572	−	0.836104i	$-0.684828\pi$
$967$	− 52.0000i	− 1.67221i	0.548572	−	0.836104i	$-0.315172\pi$
$968$	− 5.00000i	− 0.160706i
$969$	−6.00000	−0.192748
$970$	0	0
$971$	28.0000	0.898563	0.449281	−	0.893390i	$-0.351680\pi$
$971$	28.0000	0.898563	0.449281	+	0.893390i	$0.351680\pi$
$972$	− 1.00000i	− 0.0320750i
$973$	− 48.0000i	− 1.53881i
$974$	−16.0000	−0.512673
$975$	0	0
$976$	−2.00000	−0.0640184
$977$	2.00000i	0.0639857i	0.999488	+	0.0319928i	$0.0101854\pi$
$977$	2.00000i	0.0639857i	−0.999488	+	0.0319928i	$0.989815\pi$
$978$	16.0000i	0.511624i
$979$	−24.0000	−0.767043
$980$	0	0
$981$	6.00000	0.191565
$982$	− 12.0000i	− 0.382935i
$983$	0	0	1.00000			$0$
$983$	0	0	−1.00000			$\pi$
$984$	10.0000	0.318788
$985$	0	0
$986$	36.0000	1.14647
$987$	48.0000i	1.52786i
$988$	6.00000i	0.190885i
$989$	32.0000	1.01754
$990$	0	0
$991$	16.0000	0.508257	0.254128	−	0.967170i	$-0.418211\pi$
$991$	16.0000	0.508257	0.254128	+	0.967170i	$0.418211\pi$
$992$	− 8.00000i	− 0.254000i
$993$	4.00000i	0.126936i
$994$	64.0000	2.02996
$995$	0	0
$996$	0	0
$997$	− 46.0000i	− 1.45683i	−0.685134	−	0.728417i	$-0.740256\pi$
$997$	− 46.0000i	− 1.45683i	0.685134	−	0.728417i	$-0.259744\pi$
$998$	28.0000i	0.886325i
$999$	−2.00000	−0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2850.2.d.a.799.2		2
5.2	odd	4		570.2.a.e.1.1	✓	1
5.3	odd	4		2850.2.a.v.1.1		1
5.4	even	2	inner	2850.2.d.a.799.1		2
15.2	even	4		1710.2.a.l.1.1		1
15.8	even	4		8550.2.a.r.1.1		1
20.7	even	4		4560.2.a.q.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.a.e.1.1	✓	1	5.2	odd	4
1710.2.a.l.1.1		1	15.2	even	4
2850.2.a.v.1.1		1	5.3	odd	4
2850.2.d.a.799.1		2	5.4	even	2	inner
2850.2.d.a.799.2		2	1.1	even	1	trivial
4560.2.a.q.1.1		1	20.7	even	4
8550.2.a.r.1.1		1	15.8	even	4

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:	\( N \)	\(=\)	\( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2850.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +4.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +4.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} -4.00000 q^{11} -1.00000i q^{12} -6.00000i q^{13} -4.00000 q^{14} +1.00000 q^{16} +6.00000i q^{17} -1.00000i q^{18} +1.00000 q^{19} -4.00000 q^{21} -4.00000i q^{22} +4.00000i q^{23} +1.00000 q^{24} +6.00000 q^{26} -1.00000i q^{27} -4.00000i q^{28} -6.00000 q^{29} -8.00000 q^{31} +1.00000i q^{32} -4.00000i q^{33} -6.00000 q^{34} +1.00000 q^{36} -2.00000i q^{37} +1.00000i q^{38} +6.00000 q^{39} +10.0000 q^{41} -4.00000i q^{42} -8.00000i q^{43} +4.00000 q^{44} -4.00000 q^{46} -12.0000i q^{47} +1.00000i q^{48} -9.00000 q^{49} -6.00000 q^{51} +6.00000i q^{52} +2.00000i q^{53} +1.00000 q^{54} +4.00000 q^{56} +1.00000i q^{57} -6.00000i q^{58} +4.00000 q^{59} -2.00000 q^{61} -8.00000i q^{62} -4.00000i q^{63} -1.00000 q^{64} +4.00000 q^{66} +12.0000i q^{67} -6.00000i q^{68} -4.00000 q^{69} -16.0000 q^{71} +1.00000i q^{72} -14.0000i q^{73} +2.00000 q^{74} -1.00000 q^{76} -16.0000i q^{77} +6.00000i q^{78} -8.00000 q^{79} +1.00000 q^{81} +10.0000i q^{82} +4.00000 q^{84} +8.00000 q^{86} -6.00000i q^{87} +4.00000i q^{88} +6.00000 q^{89} +24.0000 q^{91} -4.00000i q^{92} -8.00000i q^{93} +12.0000 q^{94} -1.00000 q^{96} -14.0000i q^{97} -9.00000i q^{98} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^4 - 2 * q^6 - 2 * q^9	\( 2 q - 2 q^{4} - 2 q^{6} - 2 q^{9} - 8 q^{11} - 8 q^{14} + 2 q^{16} + 2 q^{19} - 8 q^{21} + 2 q^{24} + 12 q^{26} - 12 q^{29} - 16 q^{31} - 12 q^{34} + 2 q^{36} + 12 q^{39} + 20 q^{41} + 8 q^{44} - 8 q^{46} - 18 q^{49} - 12 q^{51} + 2 q^{54} + 8 q^{56} + 8 q^{59} - 4 q^{61} - 2 q^{64} + 8 q^{66} - 8 q^{69} - 32 q^{71} + 4 q^{74} - 2 q^{76} - 16 q^{79} + 2 q^{81} + 8 q^{84} + 16 q^{86} + 12 q^{89} + 48 q^{91} + 24 q^{94} - 2 q^{96} + 8 q^{99}+O(q^{100}) \) 2 * q - 2 * q^4 - 2 * q^6 - 2 * q^9 - 8 * q^11 - 8 * q^14 + 2 * q^16 + 2 * q^19 - 8 * q^21 + 2 * q^24 + 12 * q^26 - 12 * q^29 - 16 * q^31 - 12 * q^34 + 2 * q^36 + 12 * q^39 + 20 * q^41 + 8 * q^44 - 8 * q^46 - 18 * q^49 - 12 * q^51 + 2 * q^54 + 8 * q^56 + 8 * q^59 - 4 * q^61 - 2 * q^64 + 8 * q^66 - 8 * q^69 - 32 * q^71 + 4 * q^74 - 2 * q^76 - 16 * q^79 + 2 * q^81 + 8 * q^84 + 16 * q^86 + 12 * q^89 + 48 * q^91 + 24 * q^94 - 2 * q^96 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more