LMFDB - Embedded newform 945.2.d.a.379.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(379,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, 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("945.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.d (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:	$7.54586299101$
Analytic rank:	$0$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	945.379
Dual form			945.2.d.a.379.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} -1.00000i q^{7} +3.00000i q^{8} +(2.00000 - 1.00000i) q^{10} -3.00000 q^{11} -7.00000i q^{13} +1.00000 q^{14} -1.00000 q^{16} -4.00000i q^{17} -3.00000 q^{19} +(-1.00000 - 2.00000i) q^{20} -3.00000i q^{22} +(-3.00000 + 4.00000i) q^{25} +7.00000 q^{26} -1.00000i q^{28} -2.00000 q^{29} +8.00000 q^{31} +5.00000i q^{32} +4.00000 q^{34} +(-2.00000 + 1.00000i) q^{35} -4.00000i q^{37} -3.00000i q^{38} +(6.00000 - 3.00000i) q^{40} -11.0000 q^{41} -5.00000i q^{43} -3.00000 q^{44} -9.00000i q^{47} -1.00000 q^{49} +(-4.00000 - 3.00000i) q^{50} -7.00000i q^{52} -3.00000i q^{53} +(3.00000 + 6.00000i) q^{55} +3.00000 q^{56} -2.00000i q^{58} +10.0000 q^{59} -2.00000 q^{61} +8.00000i q^{62} -7.00000 q^{64} +(-14.0000 + 7.00000i) q^{65} -7.00000i q^{67} -4.00000i q^{68} +(-1.00000 - 2.00000i) q^{70} +8.00000 q^{71} +15.0000i q^{73} +4.00000 q^{74} -3.00000 q^{76} +3.00000i q^{77} +14.0000 q^{79} +(1.00000 + 2.00000i) q^{80} -11.0000i q^{82} -1.00000i q^{83} +(-8.00000 + 4.00000i) q^{85} +5.00000 q^{86} -9.00000i q^{88} +15.0000 q^{89} -7.00000 q^{91} +9.00000 q^{94} +(3.00000 + 6.00000i) q^{95} -2.00000i q^{97} -1.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{4} - 2 q^{5} + 4 q^{10} - 6 q^{11} + 2 q^{14} - 2 q^{16} - 6 q^{19} - 2 q^{20} - 6 q^{25} + 14 q^{26} - 4 q^{29} + 16 q^{31} + 8 q^{34} - 4 q^{35} + 12 q^{40} - 22 q^{41} - 6 q^{44} - 2 q^{49}+ \cdots + 6 q^{95}+O(q^{100}) $ 2 * q + 2 * q^4 - 2 * q^5 + 4 * q^10 - 6 * q^11 + 2 * q^14 - 2 * q^16 - 6 * q^19 - 2 * q^20 - 6 * q^25 + 14 * q^26 - 4 * q^29 + 16 * q^31 + 8 * q^34 - 4 * q^35 + 12 * q^40 - 22 * q^41 - 6 * q^44 - 2 * q^49 - 8 * q^50 + 6 * q^55 + 6 * q^56 + 20 * q^59 - 4 * q^61 - 14 * q^64 - 28 * q^65 - 2 * q^70 + 16 * q^71 + 8 * q^74 - 6 * q^76 + 28 * q^79 + 2 * q^80 - 16 * q^85 + 10 * q^86 + 30 * q^89 - 14 * q^91 + 18 * q^94 + 6 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$1$	$1$	$-1$

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	0.935414	+	0.353553i	$0.115027\pi$
$2$			1.00000i			0.707107i	−0.935414	+	0.353553i	$0.884973\pi$
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−1.00000	−	2.00000i	−0.447214	−	0.894427i
$5$	−1.00000	−	2.00000i	−0.447214	−	0.894427i
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$			3.00000i			1.06066i
$9$		0			0
$10$	2.00000	−	1.00000i	0.632456	−	0.316228i
$11$	−3.00000			−0.904534			−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000			−0.904534			−0.452267	+	0.891883i	$0.649385\pi$
$12$		0			0
$13$		−	7.00000i		−	1.94145i	−0.240192	−	0.970725i	$-0.577210\pi$
$13$		−	7.00000i		−	1.94145i	0.240192	−	0.970725i	$-0.422790\pi$
$14$	1.00000			0.267261
$15$		0			0
$16$	−1.00000			−0.250000
$17$		−	4.00000i		−	0.970143i	−0.874475	−	0.485071i	$-0.838794\pi$
$17$		−	4.00000i		−	0.970143i	0.874475	−	0.485071i	$-0.161206\pi$
$18$		0			0
$19$	−3.00000			−0.688247			−0.344124	−	0.938924i	$-0.611824\pi$
$19$	−3.00000			−0.688247			−0.344124	+	0.938924i	$0.611824\pi$
$20$	−1.00000	−	2.00000i	−0.223607	−	0.447214i
$21$		0			0
$22$		−	3.00000i		−	0.639602i
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$		0			0
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$	7.00000			1.37281
$27$		0			0
$28$		−	1.00000i		−	0.188982i
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		0			0
$31$	8.00000			1.43684			0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000			1.43684			0.718421	+	0.695608i	$0.244865\pi$
$32$			5.00000i			0.883883i
$33$		0			0
$34$	4.00000			0.685994
$35$	−2.00000	+	1.00000i	−0.338062	+	0.169031i
$36$		0			0
$37$		−	4.00000i		−	0.657596i	−0.944400	−	0.328798i	$-0.893356\pi$
$37$		−	4.00000i		−	0.657596i	0.944400	−	0.328798i	$-0.106644\pi$
$38$		−	3.00000i		−	0.486664i
$39$		0			0
$40$	6.00000	−	3.00000i	0.948683	−	0.474342i
$41$	−11.0000			−1.71791			−0.858956	−	0.512050i	$-0.828886\pi$
$41$	−11.0000			−1.71791			−0.858956	+	0.512050i	$0.828886\pi$
$42$		0			0
$43$		−	5.00000i		−	0.762493i	−0.924473	−	0.381246i	$-0.875495\pi$
$43$		−	5.00000i		−	0.762493i	0.924473	−	0.381246i	$-0.124505\pi$
$44$	−3.00000			−0.452267
$45$		0			0
$46$		0			0
$47$		−	9.00000i		−	1.31278i	−0.754420	−	0.656392i	$-0.772082\pi$
$47$		−	9.00000i		−	1.31278i	0.754420	−	0.656392i	$-0.227918\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	−4.00000	−	3.00000i	−0.565685	−	0.424264i
$51$		0			0
$52$		−	7.00000i		−	0.970725i
$53$		−	3.00000i		−	0.412082i	−0.978543	−	0.206041i	$-0.933942\pi$
$53$		−	3.00000i		−	0.412082i	0.978543	−	0.206041i	$-0.0660580\pi$
$54$		0			0
$55$	3.00000	+	6.00000i	0.404520	+	0.809040i
$56$	3.00000			0.400892
$57$		0			0
$58$		−	2.00000i		−	0.262613i
$59$	10.0000			1.30189			0.650945	−	0.759125i	$-0.274373\pi$
$59$	10.0000			1.30189			0.650945	+	0.759125i	$0.274373\pi$
$60$		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
$63$		0			0
$64$	−7.00000			−0.875000
$65$	−14.0000	+	7.00000i	−1.73649	+	0.868243i
$66$		0			0
$67$		−	7.00000i		−	0.855186i	−0.903971	−	0.427593i	$-0.859362\pi$
$67$		−	7.00000i		−	0.855186i	0.903971	−	0.427593i	$-0.140638\pi$
$68$		−	4.00000i		−	0.485071i
$69$		0			0
$70$	−1.00000	−	2.00000i	−0.119523	−	0.239046i
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$		0			0
$73$			15.0000i			1.75562i	0.479012	+	0.877809i	$0.340995\pi$
$73$			15.0000i			1.75562i	−0.479012	+	0.877809i	$0.659005\pi$
$74$	4.00000			0.464991
$75$		0			0
$76$	−3.00000			−0.344124
$77$			3.00000i			0.341882i
$78$		0			0
$79$	14.0000			1.57512			0.787562	−	0.616236i	$-0.211343\pi$
$79$	14.0000			1.57512			0.787562	+	0.616236i	$0.211343\pi$
$80$	1.00000	+	2.00000i	0.111803	+	0.223607i
$81$		0			0
$82$		−	11.0000i		−	1.21475i
$83$		−	1.00000i		−	0.109764i	−0.998493	−	0.0548821i	$-0.982522\pi$
$83$		−	1.00000i		−	0.109764i	0.998493	−	0.0548821i	$-0.0174783\pi$
$84$		0			0
$85$	−8.00000	+	4.00000i	−0.867722	+	0.433861i
$86$	5.00000			0.539164
$87$		0			0
$88$		−	9.00000i		−	0.959403i
$89$	15.0000			1.59000			0.794998	−	0.606612i	$-0.207472\pi$
$89$	15.0000			1.59000			0.794998	+	0.606612i	$0.207472\pi$
$90$		0			0
$91$	−7.00000			−0.733799
$92$		0			0
$93$		0			0
$94$	9.00000			0.928279
$95$	3.00000	+	6.00000i	0.307794	+	0.615587i
$96$		0			0
$97$		−	2.00000i		−	0.203069i	−0.994832	−	0.101535i	$-0.967625\pi$
$97$		−	2.00000i		−	0.203069i	0.994832	−	0.101535i	$-0.0323753\pi$
$98$		−	1.00000i		−	0.101015i
$99$		0			0
$100$	−3.00000	+	4.00000i	−0.300000	+	0.400000i
$101$	−3.00000			−0.298511			−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000			−0.298511			−0.149256	+	0.988799i	$0.547688\pi$
$102$		0			0
$103$			10.0000i			0.985329i	0.870219	+	0.492665i	$0.163977\pi$
$103$			10.0000i			0.985329i	−0.870219	+	0.492665i	$0.836023\pi$
$104$	21.0000			2.05922
$105$		0			0
$106$	3.00000			0.291386
$107$			14.0000i			1.35343i	0.736245	+	0.676716i	$0.236597\pi$
$107$			14.0000i			1.35343i	−0.736245	+	0.676716i	$0.763403\pi$
$108$		0			0
$109$	7.00000			0.670478			0.335239	−	0.942133i	$-0.391183\pi$
$109$	7.00000			0.670478			0.335239	+	0.942133i	$0.391183\pi$
$110$	−6.00000	+	3.00000i	−0.572078	+	0.286039i
$111$		0			0
$112$			1.00000i			0.0944911i
$113$		−	3.00000i		−	0.282216i	−0.989994	−	0.141108i	$-0.954933\pi$
$113$		−	3.00000i		−	0.282216i	0.989994	−	0.141108i	$-0.0450665\pi$
$114$		0			0
$115$		0			0
$116$	−2.00000			−0.185695
$117$		0			0
$118$			10.0000i			0.920575i
$119$	−4.00000			−0.366679
$120$		0			0
$121$	−2.00000			−0.181818
$122$		−	2.00000i		−	0.181071i
$123$		0			0
$124$	8.00000			0.718421
$125$	11.0000	+	2.00000i	0.983870	+	0.178885i
$126$		0			0
$127$		−	7.00000i		−	0.621150i	−0.950549	−	0.310575i	$-0.899478\pi$
$127$		−	7.00000i		−	0.621150i	0.950549	−	0.310575i	$-0.100522\pi$
$128$			3.00000i			0.265165i
$129$		0			0
$130$	−7.00000	−	14.0000i	−0.613941	−	1.22788i
$131$	−4.00000			−0.349482			−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000			−0.349482			−0.174741	+	0.984614i	$0.555909\pi$
$132$		0			0
$133$			3.00000i			0.260133i
$134$	7.00000			0.604708
$135$		0			0
$136$	12.0000			1.02899
$137$		−	3.00000i		−	0.256307i	−0.991754	−	0.128154i	$-0.959095\pi$
$137$		−	3.00000i		−	0.256307i	0.991754	−	0.128154i	$-0.0409051\pi$
$138$		0			0
$139$	−20.0000			−1.69638			−0.848189	−	0.529694i	$-0.822307\pi$
$139$	−20.0000			−1.69638			−0.848189	+	0.529694i	$0.822307\pi$
$140$	−2.00000	+	1.00000i	−0.169031	+	0.0845154i
$141$		0			0
$142$			8.00000i			0.671345i
$143$			21.0000i			1.75611i
$144$		0			0
$145$	2.00000	+	4.00000i	0.166091	+	0.332182i
$146$	−15.0000			−1.24141
$147$		0			0
$148$		−	4.00000i		−	0.328798i
$149$	4.00000			0.327693			0.163846	−	0.986486i	$-0.447610\pi$
$149$	4.00000			0.327693			0.163846	+	0.986486i	$0.447610\pi$
$150$		0			0
$151$	−10.0000			−0.813788			−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000			−0.813788			−0.406894	+	0.913475i	$0.633388\pi$
$152$		−	9.00000i		−	0.729996i
$153$		0			0
$154$	−3.00000			−0.241747
$155$	−8.00000	−	16.0000i	−0.642575	−	1.28515i
$156$		0			0
$157$			18.0000i			1.43656i	0.695756	+	0.718278i	$0.255069\pi$
$157$			18.0000i			1.43656i	−0.695756	+	0.718278i	$0.744931\pi$
$158$			14.0000i			1.11378i
$159$		0			0
$160$	10.0000	−	5.00000i	0.790569	−	0.395285i
$161$		0			0
$162$		0			0
$163$		−	4.00000i		−	0.313304i	−0.987654	−	0.156652i	$-0.949930\pi$
$163$		−	4.00000i		−	0.313304i	0.987654	−	0.156652i	$-0.0500701\pi$
$164$	−11.0000			−0.858956
$165$		0			0
$166$	1.00000			0.0776151
$167$		−	12.0000i		−	0.928588i	−0.885681	−	0.464294i	$-0.846308\pi$
$167$		−	12.0000i		−	0.928588i	0.885681	−	0.464294i	$-0.153692\pi$
$168$		0			0
$169$	−36.0000			−2.76923
$170$	−4.00000	−	8.00000i	−0.306786	−	0.613572i
$171$		0			0
$172$		−	5.00000i		−	0.381246i
$173$		−	18.0000i		−	1.36851i	−0.729241	−	0.684257i	$-0.760127\pi$
$173$		−	18.0000i		−	1.36851i	0.729241	−	0.684257i	$-0.239873\pi$
$174$		0			0
$175$	4.00000	+	3.00000i	0.302372	+	0.226779i
$176$	3.00000			0.226134
$177$		0			0
$178$			15.0000i			1.12430i
$179$	13.0000			0.971666			0.485833	−	0.874052i	$-0.338516\pi$
$179$	13.0000			0.971666			0.485833	+	0.874052i	$0.338516\pi$
$180$		0			0
$181$	−6.00000			−0.445976			−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000			−0.445976			−0.222988	+	0.974821i	$0.571581\pi$
$182$		−	7.00000i		−	0.518875i
$183$		0			0
$184$		0			0
$185$	−8.00000	+	4.00000i	−0.588172	+	0.294086i
$186$		0			0
$187$			12.0000i			0.877527i
$188$		−	9.00000i		−	0.656392i
$189$		0			0
$190$	−6.00000	+	3.00000i	−0.435286	+	0.217643i
$191$	−9.00000			−0.651217			−0.325609	−	0.945505i	$-0.605569\pi$
$191$	−9.00000			−0.651217			−0.325609	+	0.945505i	$0.605569\pi$
$192$		0			0
$193$			26.0000i			1.87152i	0.352636	+	0.935760i	$0.385285\pi$
$193$			26.0000i			1.87152i	−0.352636	+	0.935760i	$0.614715\pi$
$194$	2.00000			0.143592
$195$		0			0
$196$	−1.00000			−0.0714286
$197$		−	11.0000i		−	0.783718i	−0.920025	−	0.391859i	$-0.871832\pi$
$197$		−	11.0000i		−	0.783718i	0.920025	−	0.391859i	$-0.128168\pi$
$198$		0			0
$199$	13.0000			0.921546			0.460773	−	0.887518i	$-0.347572\pi$
$199$	13.0000			0.921546			0.460773	+	0.887518i	$0.347572\pi$
$200$	−12.0000	−	9.00000i	−0.848528	−	0.636396i
$201$		0			0
$202$		−	3.00000i		−	0.211079i
$203$			2.00000i			0.140372i
$204$		0			0
$205$	11.0000	+	22.0000i	0.768273	+	1.53655i
$206$	−10.0000			−0.696733
$207$		0			0
$208$			7.00000i			0.485363i
$209$	9.00000			0.622543
$210$		0			0
$211$	2.00000			0.137686			0.0688428	−	0.997628i	$-0.478069\pi$
$211$	2.00000			0.137686			0.0688428	+	0.997628i	$0.478069\pi$
$212$		−	3.00000i		−	0.206041i
$213$		0			0
$214$	−14.0000			−0.957020
$215$	−10.0000	+	5.00000i	−0.681994	+	0.340997i
$216$		0			0
$217$		−	8.00000i		−	0.543075i
$218$			7.00000i			0.474100i
$219$		0			0
$220$	3.00000	+	6.00000i	0.202260	+	0.404520i
$221$	−28.0000			−1.88348
$222$		0			0
$223$			6.00000i			0.401790i	0.979613	+	0.200895i	$0.0643850\pi$
$223$			6.00000i			0.401790i	−0.979613	+	0.200895i	$0.935615\pi$
$224$	5.00000			0.334077
$225$		0			0
$226$	3.00000			0.199557
$227$			1.00000i			0.0663723i	0.999449	+	0.0331862i	$0.0105654\pi$
$227$			1.00000i			0.0663723i	−0.999449	+	0.0331862i	$0.989435\pi$
$228$		0			0
$229$	10.0000			0.660819			0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000			0.660819			0.330409	+	0.943838i	$0.392813\pi$
$230$		0			0
$231$		0			0
$232$		−	6.00000i		−	0.393919i
$233$			1.00000i			0.0655122i	0.999463	+	0.0327561i	$0.0104285\pi$
$233$			1.00000i			0.0655122i	−0.999463	+	0.0327561i	$0.989572\pi$
$234$		0			0
$235$	−18.0000	+	9.00000i	−1.17419	+	0.587095i
$236$	10.0000			0.650945
$237$		0			0
$238$		−	4.00000i		−	0.259281i
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$		0			0
$241$	22.0000			1.41714			0.708572	−	0.705638i	$-0.249340\pi$
$241$	22.0000			1.41714			0.708572	+	0.705638i	$0.249340\pi$
$242$		−	2.00000i		−	0.128565i
$243$		0			0
$244$	−2.00000			−0.128037
$245$	1.00000	+	2.00000i	0.0638877	+	0.127775i
$246$		0			0
$247$			21.0000i			1.33620i
$248$			24.0000i			1.52400i
$249$		0			0
$250$	−2.00000	+	11.0000i	−0.126491	+	0.695701i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$		0			0
$254$	7.00000			0.439219
$255$		0			0
$256$	−17.0000			−1.06250
$257$			20.0000i			1.24757i	0.781598	+	0.623783i	$0.214405\pi$
$257$			20.0000i			1.24757i	−0.781598	+	0.623783i	$0.785595\pi$
$258$		0			0
$259$	−4.00000			−0.248548
$260$	−14.0000	+	7.00000i	−0.868243	+	0.434122i
$261$		0			0
$262$		−	4.00000i		−	0.247121i
$263$			12.0000i			0.739952i	0.929041	+	0.369976i	$0.120634\pi$
$263$			12.0000i			0.739952i	−0.929041	+	0.369976i	$0.879366\pi$
$264$		0			0
$265$	−6.00000	+	3.00000i	−0.368577	+	0.184289i
$266$	−3.00000			−0.183942
$267$		0			0
$268$		−	7.00000i		−	0.427593i
$269$	22.0000			1.34136			0.670682	−	0.741745i	$-0.266002\pi$
$269$	22.0000			1.34136			0.670682	+	0.741745i	$0.266002\pi$
$270$		0			0
$271$	−23.0000			−1.39715			−0.698575	−	0.715537i	$-0.746182\pi$
$271$	−23.0000			−1.39715			−0.698575	+	0.715537i	$0.746182\pi$
$272$			4.00000i			0.242536i
$273$		0			0
$274$	3.00000			0.181237
$275$	9.00000	−	12.0000i	0.542720	−	0.723627i
$276$		0			0
$277$			8.00000i			0.480673i	0.970690	+	0.240337i	$0.0772579\pi$
$277$			8.00000i			0.480673i	−0.970690	+	0.240337i	$0.922742\pi$
$278$		−	20.0000i		−	1.19952i
$279$		0			0
$280$	−3.00000	−	6.00000i	−0.179284	−	0.358569i
$281$	2.00000			0.119310			0.0596550	−	0.998219i	$-0.481000\pi$
$281$	2.00000			0.119310			0.0596550	+	0.998219i	$0.481000\pi$
$282$		0			0
$283$		−	20.0000i		−	1.18888i	−0.804141	−	0.594438i	$-0.797374\pi$
$283$		−	20.0000i		−	1.18888i	0.804141	−	0.594438i	$-0.202626\pi$
$284$	8.00000			0.474713
$285$		0			0
$286$	−21.0000			−1.24176
$287$			11.0000i			0.649309i
$288$		0			0
$289$	1.00000			0.0588235
$290$	−4.00000	+	2.00000i	−0.234888	+	0.117444i
$291$		0			0
$292$			15.0000i			0.877809i
$293$		−	30.0000i		−	1.75262i	−0.481749	−	0.876309i	$-0.659998\pi$
$293$		−	30.0000i		−	1.75262i	0.481749	−	0.876309i	$-0.340002\pi$
$294$		0			0
$295$	−10.0000	−	20.0000i	−0.582223	−	1.16445i
$296$	12.0000			0.697486
$297$		0			0
$298$			4.00000i			0.231714i
$299$		0			0
$300$		0			0
$301$	−5.00000			−0.288195
$302$		−	10.0000i		−	0.575435i
$303$		0			0
$304$	3.00000			0.172062
$305$	2.00000	+	4.00000i	0.114520	+	0.229039i
$306$		0			0
$307$		−	14.0000i		−	0.799022i	−0.916728	−	0.399511i	$-0.869180\pi$
$307$		−	14.0000i		−	0.799022i	0.916728	−	0.399511i	$-0.130820\pi$
$308$			3.00000i			0.170941i
$309$		0			0
$310$	16.0000	−	8.00000i	0.908739	−	0.454369i
$311$	−30.0000			−1.70114			−0.850572	−	0.525859i	$-0.823744\pi$
$311$	−30.0000			−1.70114			−0.850572	+	0.525859i	$0.823744\pi$
$312$		0			0
$313$		−	15.0000i		−	0.847850i	−0.905697	−	0.423925i	$-0.860652\pi$
$313$		−	15.0000i		−	0.847850i	0.905697	−	0.423925i	$-0.139348\pi$
$314$	−18.0000			−1.01580
$315$		0			0
$316$	14.0000			0.787562
$317$			27.0000i			1.51647i	0.651981	+	0.758236i	$0.273938\pi$
$317$			27.0000i			1.51647i	−0.651981	+	0.758236i	$0.726062\pi$
$318$		0			0
$319$	6.00000			0.335936
$320$	7.00000	+	14.0000i	0.391312	+	0.782624i
$321$		0			0
$322$		0			0
$323$			12.0000i			0.667698i
$324$		0			0
$325$	28.0000	+	21.0000i	1.55316	+	1.16487i
$326$	4.00000			0.221540
$327$		0			0
$328$		−	33.0000i		−	1.82212i
$329$	−9.00000			−0.496186
$330$		0			0
$331$	12.0000			0.659580			0.329790	−	0.944054i	$-0.393022\pi$
$331$	12.0000			0.659580			0.329790	+	0.944054i	$0.393022\pi$
$332$		−	1.00000i		−	0.0548821i
$333$		0			0
$334$	12.0000			0.656611
$335$	−14.0000	+	7.00000i	−0.764902	+	0.382451i
$336$		0			0
$337$			30.0000i			1.63420i	0.576493	+	0.817102i	$0.304421\pi$
$337$			30.0000i			1.63420i	−0.576493	+	0.817102i	$0.695579\pi$
$338$		−	36.0000i		−	1.95814i
$339$		0			0
$340$	−8.00000	+	4.00000i	−0.433861	+	0.216930i
$341$	−24.0000			−1.29967
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	15.0000			0.808746
$345$		0			0
$346$	18.0000			0.967686
$347$		−	12.0000i		−	0.644194i	−0.946707	−	0.322097i	$-0.895612\pi$
$347$		−	12.0000i		−	0.644194i	0.946707	−	0.322097i	$-0.104388\pi$
$348$		0			0
$349$	−16.0000			−0.856460			−0.428230	−	0.903670i	$-0.640863\pi$
$349$	−16.0000			−0.856460			−0.428230	+	0.903670i	$0.640863\pi$
$350$	−3.00000	+	4.00000i	−0.160357	+	0.213809i
$351$		0			0
$352$		−	15.0000i		−	0.799503i
$353$		−	34.0000i		−	1.80964i	−0.425797	−	0.904819i	$-0.640006\pi$
$353$		−	34.0000i		−	1.80964i	0.425797	−	0.904819i	$-0.359994\pi$
$354$		0			0
$355$	−8.00000	−	16.0000i	−0.424596	−	0.849192i
$356$	15.0000			0.794998
$357$		0			0
$358$			13.0000i			0.687071i
$359$	31.0000			1.63612			0.818059	−	0.575135i	$-0.195050\pi$
$359$	31.0000			1.63612			0.818059	+	0.575135i	$0.195050\pi$
$360$		0			0
$361$	−10.0000			−0.526316
$362$		−	6.00000i		−	0.315353i
$363$		0			0
$364$	−7.00000			−0.366900
$365$	30.0000	−	15.0000i	1.57027	−	0.785136i
$366$		0			0
$367$			18.0000i			0.939592i	0.882775	+	0.469796i	$0.155673\pi$
$367$			18.0000i			0.939592i	−0.882775	+	0.469796i	$0.844327\pi$
$368$		0			0
$369$		0			0
$370$	−4.00000	−	8.00000i	−0.207950	−	0.415900i
$371$	−3.00000			−0.155752
$372$		0			0
$373$			18.0000i			0.932005i	0.884783	+	0.466002i	$0.154306\pi$
$373$			18.0000i			0.932005i	−0.884783	+	0.466002i	$0.845694\pi$
$374$	−12.0000			−0.620505
$375$		0			0
$376$	27.0000			1.39242
$377$			14.0000i			0.721037i
$378$		0			0
$379$	10.0000			0.513665			0.256833	−	0.966456i	$-0.417321\pi$
$379$	10.0000			0.513665			0.256833	+	0.966456i	$0.417321\pi$
$380$	3.00000	+	6.00000i	0.153897	+	0.307794i
$381$		0			0
$382$		−	9.00000i		−	0.460480i
$383$			16.0000i			0.817562i	0.912633	+	0.408781i	$0.134046\pi$
$383$			16.0000i			0.817562i	−0.912633	+	0.408781i	$0.865954\pi$
$384$		0			0
$385$	6.00000	−	3.00000i	0.305788	−	0.152894i
$386$	−26.0000			−1.32337
$387$		0			0
$388$		−	2.00000i		−	0.101535i
$389$	−10.0000			−0.507020			−0.253510	−	0.967333i	$-0.581585\pi$
$389$	−10.0000			−0.507020			−0.253510	+	0.967333i	$0.581585\pi$
$390$		0			0
$391$		0			0
$392$		−	3.00000i		−	0.151523i
$393$		0			0
$394$	11.0000			0.554172
$395$	−14.0000	−	28.0000i	−0.704416	−	1.40883i
$396$		0			0
$397$		−	14.0000i		−	0.702640i	−0.936255	−	0.351320i	$-0.885733\pi$
$397$		−	14.0000i		−	0.702640i	0.936255	−	0.351320i	$-0.114267\pi$
$398$			13.0000i			0.651631i
$399$		0			0
$400$	3.00000	−	4.00000i	0.150000	−	0.200000i
$401$	−6.00000			−0.299626			−0.149813	−	0.988714i	$-0.547867\pi$
$401$	−6.00000			−0.299626			−0.149813	+	0.988714i	$0.547867\pi$
$402$		0			0
$403$		−	56.0000i		−	2.78956i
$404$	−3.00000			−0.149256
$405$		0			0
$406$	−2.00000			−0.0992583
$407$			12.0000i			0.594818i
$408$		0			0
$409$	−14.0000			−0.692255			−0.346128	−	0.938187i	$-0.612504\pi$
$409$	−14.0000			−0.692255			−0.346128	+	0.938187i	$0.612504\pi$
$410$	−22.0000	+	11.0000i	−1.08650	+	0.543251i
$411$		0			0
$412$			10.0000i			0.492665i
$413$		−	10.0000i		−	0.492068i
$414$		0			0
$415$	−2.00000	+	1.00000i	−0.0981761	+	0.0490881i
$416$	35.0000			1.71602
$417$		0			0
$418$			9.00000i			0.440204i
$419$	6.00000			0.293119			0.146560	−	0.989202i	$-0.453180\pi$
$419$	6.00000			0.293119			0.146560	+	0.989202i	$0.453180\pi$
$420$		0			0
$421$	−27.0000			−1.31590			−0.657950	−	0.753062i	$-0.728576\pi$
$421$	−27.0000			−1.31590			−0.657950	+	0.753062i	$0.728576\pi$
$422$			2.00000i			0.0973585i
$423$		0			0
$424$	9.00000			0.437079
$425$	16.0000	+	12.0000i	0.776114	+	0.582086i
$426$		0			0
$427$			2.00000i			0.0967868i
$428$			14.0000i			0.676716i
$429$		0			0
$430$	−5.00000	−	10.0000i	−0.241121	−	0.482243i
$431$	23.0000			1.10787			0.553936	−	0.832560i	$-0.313125\pi$
$431$	23.0000			1.10787			0.553936	+	0.832560i	$0.313125\pi$
$432$		0			0
$433$		−	11.0000i		−	0.528626i	−0.964437	−	0.264313i	$-0.914855\pi$
$433$		−	11.0000i		−	0.528626i	0.964437	−	0.264313i	$-0.0851452\pi$
$434$	8.00000			0.384012
$435$		0			0
$436$	7.00000			0.335239
$437$		0			0
$438$		0			0
$439$	39.0000			1.86137			0.930684	−	0.365824i	$-0.119213\pi$
$439$	39.0000			1.86137			0.930684	+	0.365824i	$0.119213\pi$
$440$	−18.0000	+	9.00000i	−0.858116	+	0.429058i
$441$		0			0
$442$		−	28.0000i		−	1.33182i
$443$		−	4.00000i		−	0.190046i	−0.995475	−	0.0950229i	$-0.969708\pi$
$443$		−	4.00000i		−	0.190046i	0.995475	−	0.0950229i	$-0.0302924\pi$
$444$		0			0
$445$	−15.0000	−	30.0000i	−0.711068	−	1.42214i
$446$	−6.00000			−0.284108
$447$		0			0
$448$			7.00000i			0.330719i
$449$	10.0000			0.471929			0.235965	−	0.971762i	$-0.424175\pi$
$449$	10.0000			0.471929			0.235965	+	0.971762i	$0.424175\pi$
$450$		0			0
$451$	33.0000			1.55391
$452$		−	3.00000i		−	0.141108i
$453$		0			0
$454$	−1.00000			−0.0469323
$455$	7.00000	+	14.0000i	0.328165	+	0.656330i
$456$		0			0
$457$		−	2.00000i		−	0.0935561i	−0.998905	−	0.0467780i	$-0.985105\pi$
$457$		−	2.00000i		−	0.0935561i	0.998905	−	0.0467780i	$-0.0148953\pi$
$458$			10.0000i			0.467269i
$459$		0			0
$460$		0			0
$461$	33.0000			1.53696			0.768482	−	0.639872i	$-0.221013\pi$
$461$	33.0000			1.53696			0.768482	+	0.639872i	$0.221013\pi$
$462$		0			0
$463$		−	27.0000i		−	1.25480i	−0.778699	−	0.627398i	$-0.784120\pi$
$463$		−	27.0000i		−	1.25480i	0.778699	−	0.627398i	$-0.215880\pi$
$464$	2.00000			0.0928477
$465$		0			0
$466$	−1.00000			−0.0463241
$467$		−	12.0000i		−	0.555294i	−0.960683	−	0.277647i	$-0.910445\pi$
$467$		−	12.0000i		−	0.555294i	0.960683	−	0.277647i	$-0.0895545\pi$
$468$		0			0
$469$	−7.00000			−0.323230
$470$	−9.00000	−	18.0000i	−0.415139	−	0.830278i
$471$		0			0
$472$			30.0000i			1.38086i
$473$			15.0000i			0.689701i
$474$		0			0
$475$	9.00000	−	12.0000i	0.412948	−	0.550598i
$476$	−4.00000			−0.183340
$477$		0			0
$478$			12.0000i			0.548867i
$479$	42.0000			1.91903			0.959514	−	0.281659i	$-0.0908848\pi$
$479$	42.0000			1.91903			0.959514	+	0.281659i	$0.0908848\pi$
$480$		0			0
$481$	−28.0000			−1.27669
$482$			22.0000i			1.00207i
$483$		0			0
$484$	−2.00000			−0.0909091
$485$	−4.00000	+	2.00000i	−0.181631	+	0.0908153i
$486$		0			0
$487$		−	15.0000i		−	0.679715i	−0.940477	−	0.339857i	$-0.889621\pi$
$487$		−	15.0000i		−	0.679715i	0.940477	−	0.339857i	$-0.110379\pi$
$488$		−	6.00000i		−	0.271607i
$489$		0			0
$490$	−2.00000	+	1.00000i	−0.0903508	+	0.0451754i
$491$	−28.0000			−1.26362			−0.631811	−	0.775122i	$-0.717688\pi$
$491$	−28.0000			−1.26362			−0.631811	+	0.775122i	$0.717688\pi$
$492$		0			0
$493$			8.00000i			0.360302i
$494$	−21.0000			−0.944835
$495$		0			0
$496$	−8.00000			−0.359211
$497$		−	8.00000i		−	0.358849i
$498$		0			0
$499$	32.0000			1.43252			0.716258	−	0.697835i	$-0.245853\pi$
$499$	32.0000			1.43252			0.716258	+	0.697835i	$0.245853\pi$
$500$	11.0000	+	2.00000i	0.491935	+	0.0894427i
$501$		0			0
$502$		0			0
$503$		−	9.00000i		−	0.401290i	−0.979664	−	0.200645i	$-0.935696\pi$
$503$		−	9.00000i		−	0.401290i	0.979664	−	0.200645i	$-0.0643038\pi$
$504$		0			0
$505$	3.00000	+	6.00000i	0.133498	+	0.266996i
$506$		0			0
$507$		0			0
$508$		−	7.00000i		−	0.310575i
$509$	−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
$511$	15.0000			0.663561
$512$		−	11.0000i		−	0.486136i
$513$		0			0
$514$	−20.0000			−0.882162
$515$	20.0000	−	10.0000i	0.881305	−	0.440653i
$516$		0			0
$517$			27.0000i			1.18746i
$518$		−	4.00000i		−	0.175750i
$519$		0			0
$520$	−21.0000	−	42.0000i	−0.920911	−	1.84182i
$521$	25.0000			1.09527			0.547635	−	0.836717i	$-0.315528\pi$
$521$	25.0000			1.09527			0.547635	+	0.836717i	$0.315528\pi$
$522$		0			0
$523$		−	20.0000i		−	0.874539i	−0.899331	−	0.437269i	$-0.855946\pi$
$523$		−	20.0000i		−	0.874539i	0.899331	−	0.437269i	$-0.144054\pi$
$524$	−4.00000			−0.174741
$525$		0			0
$526$	−12.0000			−0.523225
$527$		−	32.0000i		−	1.39394i
$528$		0			0
$529$	23.0000			1.00000
$530$	−3.00000	−	6.00000i	−0.130312	−	0.260623i
$531$		0			0
$532$			3.00000i			0.130066i
$533$			77.0000i			3.33524i
$534$		0			0
$535$	28.0000	−	14.0000i	1.21055	−	0.605273i
$536$	21.0000			0.907062
$537$		0			0
$538$			22.0000i			0.948487i
$539$	3.00000			0.129219
$540$		0			0
$541$	15.0000			0.644900			0.322450	−	0.946586i	$-0.395494\pi$
$541$	15.0000			0.644900			0.322450	+	0.946586i	$0.395494\pi$
$542$		−	23.0000i		−	0.987935i
$543$		0			0
$544$	20.0000			0.857493
$545$	−7.00000	−	14.0000i	−0.299847	−	0.599694i
$546$		0			0
$547$		−	16.0000i		−	0.684111i	−0.939680	−	0.342055i	$-0.888877\pi$
$547$		−	16.0000i		−	0.684111i	0.939680	−	0.342055i	$-0.111123\pi$
$548$		−	3.00000i		−	0.128154i
$549$		0			0
$550$	12.0000	+	9.00000i	0.511682	+	0.383761i
$551$	6.00000			0.255609
$552$		0			0
$553$		−	14.0000i		−	0.595341i
$554$	−8.00000			−0.339887
$555$		0			0
$556$	−20.0000			−0.848189
$557$		−	2.00000i		−	0.0847427i	−0.999102	−	0.0423714i	$-0.986509\pi$
$557$		−	2.00000i		−	0.0847427i	0.999102	−	0.0423714i	$-0.0134913\pi$
$558$		0			0
$559$	−35.0000			−1.48034
$560$	2.00000	−	1.00000i	0.0845154	−	0.0422577i
$561$		0			0
$562$			2.00000i			0.0843649i
$563$			27.0000i			1.13791i	0.822367	+	0.568957i	$0.192653\pi$
$563$			27.0000i			1.13791i	−0.822367	+	0.568957i	$0.807347\pi$
$564$		0			0
$565$	−6.00000	+	3.00000i	−0.252422	+	0.126211i
$566$	20.0000			0.840663
$567$		0			0
$568$			24.0000i			1.00702i
$569$	−30.0000			−1.25767			−0.628833	−	0.777541i	$-0.716467\pi$
$569$	−30.0000			−1.25767			−0.628833	+	0.777541i	$0.716467\pi$
$570$		0			0
$571$	18.0000			0.753277			0.376638	−	0.926360i	$-0.377080\pi$
$571$	18.0000			0.753277			0.376638	+	0.926360i	$0.377080\pi$
$572$			21.0000i			0.878054i
$573$		0			0
$574$	−11.0000			−0.459131
$575$		0			0
$576$		0			0
$577$		−	13.0000i		−	0.541197i	−0.962692	−	0.270599i	$-0.912778\pi$
$577$		−	13.0000i		−	0.541197i	0.962692	−	0.270599i	$-0.0872216\pi$
$578$			1.00000i			0.0415945i
$579$		0			0
$580$	2.00000	+	4.00000i	0.0830455	+	0.166091i
$581$	−1.00000			−0.0414870
$582$		0			0
$583$			9.00000i			0.372742i
$584$	−45.0000			−1.86211
$585$		0			0
$586$	30.0000			1.23929
$587$			12.0000i			0.495293i	0.968850	+	0.247647i	$0.0796572\pi$
$587$			12.0000i			0.495293i	−0.968850	+	0.247647i	$0.920343\pi$
$588$		0			0
$589$	−24.0000			−0.988903
$590$	20.0000	−	10.0000i	0.823387	−	0.411693i
$591$		0			0
$592$			4.00000i			0.164399i
$593$			26.0000i			1.06769i	0.845582	+	0.533846i	$0.179254\pi$
$593$			26.0000i			1.06769i	−0.845582	+	0.533846i	$0.820746\pi$
$594$		0			0
$595$	4.00000	+	8.00000i	0.163984	+	0.327968i
$596$	4.00000			0.163846
$597$		0			0
$598$		0			0
$599$	7.00000			0.286012			0.143006	−	0.989722i	$-0.454323\pi$
$599$	7.00000			0.286012			0.143006	+	0.989722i	$0.454323\pi$
$600$		0			0
$601$	28.0000			1.14214			0.571072	−	0.820900i	$-0.306528\pi$
$601$	28.0000			1.14214			0.571072	+	0.820900i	$0.306528\pi$
$602$		−	5.00000i		−	0.203785i
$603$		0			0
$604$	−10.0000			−0.406894
$605$	2.00000	+	4.00000i	0.0813116	+	0.162623i
$606$		0			0
$607$		−	12.0000i		−	0.487065i	−0.969893	−	0.243532i	$-0.921694\pi$
$607$		−	12.0000i		−	0.487065i	0.969893	−	0.243532i	$-0.0783062\pi$
$608$		−	15.0000i		−	0.608330i
$609$		0			0
$610$	−4.00000	+	2.00000i	−0.161955	+	0.0809776i
$611$	−63.0000			−2.54871
$612$		0			0
$613$		−	4.00000i		−	0.161558i	−0.996732	−	0.0807792i	$-0.974259\pi$
$613$		−	4.00000i		−	0.161558i	0.996732	−	0.0807792i	$-0.0257409\pi$
$614$	14.0000			0.564994
$615$		0			0
$616$	−9.00000			−0.362620
$617$		−	10.0000i		−	0.402585i	−0.979531	−	0.201292i	$-0.935486\pi$
$617$		−	10.0000i		−	0.402585i	0.979531	−	0.201292i	$-0.0645141\pi$
$618$		0			0
$619$	35.0000			1.40677			0.703384	−	0.710810i	$-0.251671\pi$
$619$	35.0000			1.40677			0.703384	+	0.710810i	$0.251671\pi$
$620$	−8.00000	−	16.0000i	−0.321288	−	0.642575i
$621$		0			0
$622$		−	30.0000i		−	1.20289i
$623$		−	15.0000i		−	0.600962i
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	15.0000			0.599521
$627$		0			0
$628$			18.0000i			0.718278i
$629$	−16.0000			−0.637962
$630$		0			0
$631$	−2.00000			−0.0796187			−0.0398094	−	0.999207i	$-0.512675\pi$
$631$	−2.00000			−0.0796187			−0.0398094	+	0.999207i	$0.512675\pi$
$632$			42.0000i			1.67067i
$633$		0			0
$634$	−27.0000			−1.07231
$635$	−14.0000	+	7.00000i	−0.555573	+	0.277787i
$636$		0			0
$637$			7.00000i			0.277350i
$638$			6.00000i			0.237542i
$639$		0			0
$640$	6.00000	−	3.00000i	0.237171	−	0.118585i
$641$	38.0000			1.50091			0.750455	−	0.660922i	$-0.229834\pi$
$641$	38.0000			1.50091			0.750455	+	0.660922i	$0.229834\pi$
$642$		0			0
$643$			2.00000i			0.0788723i	0.999222	+	0.0394362i	$0.0125562\pi$
$643$			2.00000i			0.0788723i	−0.999222	+	0.0394362i	$0.987444\pi$
$644$		0			0
$645$		0			0
$646$	−12.0000			−0.472134
$647$		−	25.0000i		−	0.982851i	−0.870919	−	0.491426i	$-0.836476\pi$
$647$		−	25.0000i		−	0.982851i	0.870919	−	0.491426i	$-0.163524\pi$
$648$		0			0
$649$	−30.0000			−1.17760
$650$	−21.0000	+	28.0000i	−0.823688	+	1.09825i
$651$		0			0
$652$		−	4.00000i		−	0.156652i
$653$		−	34.0000i		−	1.33052i	−0.746611	−	0.665261i	$-0.768320\pi$
$653$		−	34.0000i		−	1.33052i	0.746611	−	0.665261i	$-0.231680\pi$
$654$		0			0
$655$	4.00000	+	8.00000i	0.156293	+	0.312586i
$656$	11.0000			0.429478
$657$		0			0
$658$		−	9.00000i		−	0.350857i
$659$	−36.0000			−1.40236			−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000			−1.40236			−0.701180	+	0.712984i	$0.747343\pi$
$660$		0			0
$661$		0			0			−	1.00000i	$-0.5\pi$
$661$		0			0				1.00000i	$0.5\pi$
$662$			12.0000i			0.466393i
$663$		0			0
$664$	3.00000			0.116423
$665$	6.00000	−	3.00000i	0.232670	−	0.116335i
$666$		0			0
$667$		0			0
$668$		−	12.0000i		−	0.464294i
$669$		0			0
$670$	−7.00000	−	14.0000i	−0.270434	−	0.540867i
$671$	6.00000			0.231627
$672$		0			0
$673$		−	36.0000i		−	1.38770i	−0.720121	−	0.693849i	$-0.755914\pi$
$673$		−	36.0000i		−	1.38770i	0.720121	−	0.693849i	$-0.244086\pi$
$674$	−30.0000			−1.15556
$675$		0			0
$676$	−36.0000			−1.38462
$677$			4.00000i			0.153732i	0.997041	+	0.0768662i	$0.0244914\pi$
$677$			4.00000i			0.153732i	−0.997041	+	0.0768662i	$0.975509\pi$
$678$		0			0
$679$	−2.00000			−0.0767530
$680$	−12.0000	−	24.0000i	−0.460179	−	0.920358i
$681$		0			0
$682$		−	24.0000i		−	0.919007i
$683$		−	44.0000i		−	1.68361i	−0.539779	−	0.841807i	$-0.681492\pi$
$683$		−	44.0000i		−	1.68361i	0.539779	−	0.841807i	$-0.318508\pi$
$684$		0			0
$685$	−6.00000	+	3.00000i	−0.229248	+	0.114624i
$686$	−1.00000			−0.0381802
$687$		0			0
$688$			5.00000i			0.190623i
$689$	−21.0000			−0.800036
$690$		0			0
$691$	−5.00000			−0.190209			−0.0951045	−	0.995467i	$-0.530319\pi$
$691$	−5.00000			−0.190209			−0.0951045	+	0.995467i	$0.530319\pi$
$692$		−	18.0000i		−	0.684257i
$693$		0			0
$694$	12.0000			0.455514
$695$	20.0000	+	40.0000i	0.758643	+	1.51729i
$696$		0			0
$697$			44.0000i			1.66662i
$698$		−	16.0000i		−	0.605609i
$699$		0			0
$700$	4.00000	+	3.00000i	0.151186	+	0.113389i
$701$	−8.00000			−0.302156			−0.151078	−	0.988522i	$-0.548274\pi$
$701$	−8.00000			−0.302156			−0.151078	+	0.988522i	$0.548274\pi$
$702$		0			0
$703$			12.0000i			0.452589i
$704$	21.0000			0.791467
$705$		0			0
$706$	34.0000			1.27961
$707$			3.00000i			0.112827i
$708$		0			0
$709$	1.00000			0.0375558			0.0187779	−	0.999824i	$-0.494022\pi$
$709$	1.00000			0.0375558			0.0187779	+	0.999824i	$0.494022\pi$
$710$	16.0000	−	8.00000i	0.600469	−	0.300235i
$711$		0			0
$712$			45.0000i			1.68645i
$713$		0			0
$714$		0			0
$715$	42.0000	−	21.0000i	1.57071	−	0.785355i
$716$	13.0000			0.485833
$717$		0			0
$718$			31.0000i			1.15691i
$719$	−6.00000			−0.223762			−0.111881	−	0.993722i	$-0.535688\pi$
$719$	−6.00000			−0.223762			−0.111881	+	0.993722i	$0.535688\pi$
$720$		0			0
$721$	10.0000			0.372419
$722$		−	10.0000i		−	0.372161i
$723$		0			0
$724$	−6.00000			−0.222988
$725$	6.00000	−	8.00000i	0.222834	−	0.297113i
$726$		0			0
$727$		−	22.0000i		−	0.815935i	−0.912996	−	0.407967i	$-0.866238\pi$
$727$		−	22.0000i		−	0.815935i	0.912996	−	0.407967i	$-0.133762\pi$
$728$		−	21.0000i		−	0.778312i
$729$		0			0
$730$	15.0000	+	30.0000i	0.555175	+	1.11035i
$731$	−20.0000			−0.739727
$732$		0			0
$733$		−	31.0000i		−	1.14501i	−0.819901	−	0.572506i	$-0.805971\pi$
$733$		−	31.0000i		−	1.14501i	0.819901	−	0.572506i	$-0.194029\pi$
$734$	−18.0000			−0.664392
$735$		0			0
$736$		0			0
$737$			21.0000i			0.773545i
$738$		0			0
$739$	44.0000			1.61857			0.809283	−	0.587419i	$-0.199856\pi$
$739$	44.0000			1.61857			0.809283	+	0.587419i	$0.199856\pi$
$740$	−8.00000	+	4.00000i	−0.294086	+	0.147043i
$741$		0			0
$742$		−	3.00000i		−	0.110133i
$743$			22.0000i			0.807102i	0.914957	+	0.403551i	$0.132224\pi$
$743$			22.0000i			0.807102i	−0.914957	+	0.403551i	$0.867776\pi$
$744$		0			0
$745$	−4.00000	−	8.00000i	−0.146549	−	0.293097i
$746$	−18.0000			−0.659027
$747$		0			0
$748$			12.0000i			0.438763i
$749$	14.0000			0.511549
$750$		0			0
$751$	6.00000			0.218943			0.109472	−	0.993990i	$-0.465084\pi$
$751$	6.00000			0.218943			0.109472	+	0.993990i	$0.465084\pi$
$752$			9.00000i			0.328196i
$753$		0			0
$754$	−14.0000			−0.509850
$755$	10.0000	+	20.0000i	0.363937	+	0.727875i
$756$		0			0
$757$			32.0000i			1.16306i	0.813525	+	0.581530i	$0.197546\pi$
$757$			32.0000i			1.16306i	−0.813525	+	0.581530i	$0.802454\pi$
$758$			10.0000i			0.363216i
$759$		0			0
$760$	−18.0000	+	9.00000i	−0.652929	+	0.326464i
$761$	−50.0000			−1.81250			−0.906249	−	0.422744i	$-0.861067\pi$
$761$	−50.0000			−1.81250			−0.906249	+	0.422744i	$0.861067\pi$
$762$		0			0
$763$		−	7.00000i		−	0.253417i
$764$	−9.00000			−0.325609
$765$		0			0
$766$	−16.0000			−0.578103
$767$		−	70.0000i		−	2.52755i
$768$		0			0
$769$	18.0000			0.649097			0.324548	−	0.945869i	$-0.394788\pi$
$769$	18.0000			0.649097			0.324548	+	0.945869i	$0.394788\pi$
$770$	3.00000	+	6.00000i	0.108112	+	0.216225i
$771$		0			0
$772$			26.0000i			0.935760i
$773$			6.00000i			0.215805i	0.994161	+	0.107903i	$0.0344134\pi$
$773$			6.00000i			0.215805i	−0.994161	+	0.107903i	$0.965587\pi$
$774$		0			0
$775$	−24.0000	+	32.0000i	−0.862105	+	1.14947i
$776$	6.00000			0.215387
$777$		0			0
$778$		−	10.0000i		−	0.358517i
$779$	33.0000			1.18235
$780$		0			0
$781$	−24.0000			−0.858788
$782$		0			0
$783$		0			0
$784$	1.00000			0.0357143
$785$	36.0000	−	18.0000i	1.28490	−	0.642448i
$786$		0			0
$787$		−	22.0000i		−	0.784215i	−0.919919	−	0.392108i	$-0.871746\pi$
$787$		−	22.0000i		−	0.784215i	0.919919	−	0.392108i	$-0.128254\pi$
$788$		−	11.0000i		−	0.391859i
$789$		0			0
$790$	28.0000	−	14.0000i	0.996195	−	0.498098i
$791$	−3.00000			−0.106668
$792$		0			0
$793$			14.0000i			0.497155i
$794$	14.0000			0.496841
$795$		0			0
$796$	13.0000			0.460773
$797$			16.0000i			0.566749i	0.959009	+	0.283375i	$0.0914540\pi$
$797$			16.0000i			0.566749i	−0.959009	+	0.283375i	$0.908546\pi$
$798$		0			0
$799$	−36.0000			−1.27359
$800$	−20.0000	−	15.0000i	−0.707107	−	0.530330i
$801$		0			0
$802$		−	6.00000i		−	0.211867i
$803$		−	45.0000i		−	1.58802i
$804$		0			0
$805$		0			0
$806$	56.0000			1.97252
$807$		0			0
$808$		−	9.00000i		−	0.316619i
$809$	−36.0000			−1.26569			−0.632846	−	0.774277i	$-0.718114\pi$
$809$	−36.0000			−1.26569			−0.632846	+	0.774277i	$0.718114\pi$
$810$		0			0
$811$	7.00000			0.245803			0.122902	−	0.992419i	$-0.460780\pi$
$811$	7.00000			0.245803			0.122902	+	0.992419i	$0.460780\pi$
$812$			2.00000i			0.0701862i
$813$		0			0
$814$	−12.0000			−0.420600
$815$	−8.00000	+	4.00000i	−0.280228	+	0.140114i
$816$		0			0
$817$			15.0000i			0.524784i
$818$		−	14.0000i		−	0.489499i
$819$		0			0
$820$	11.0000	+	22.0000i	0.384137	+	0.768273i
$821$	2.00000			0.0698005			0.0349002	−	0.999391i	$-0.488889\pi$
$821$	2.00000			0.0698005			0.0349002	+	0.999391i	$0.488889\pi$
$822$		0			0
$823$			1.00000i			0.0348578i	0.999848	+	0.0174289i	$0.00554807\pi$
$823$			1.00000i			0.0348578i	−0.999848	+	0.0174289i	$0.994452\pi$
$824$	−30.0000			−1.04510
$825$		0			0
$826$	10.0000			0.347945
$827$		−	6.00000i		−	0.208640i	−0.994544	−	0.104320i	$-0.966733\pi$
$827$		−	6.00000i		−	0.208640i	0.994544	−	0.104320i	$-0.0332667\pi$
$828$		0			0
$829$	−30.0000			−1.04194			−0.520972	−	0.853574i	$-0.674430\pi$
$829$	−30.0000			−1.04194			−0.520972	+	0.853574i	$0.674430\pi$
$830$	−1.00000	−	2.00000i	−0.0347105	−	0.0694210i
$831$		0			0
$832$			49.0000i			1.69877i
$833$			4.00000i			0.138592i
$834$		0			0
$835$	−24.0000	+	12.0000i	−0.830554	+	0.415277i
$836$	9.00000			0.311272
$837$		0			0
$838$			6.00000i			0.207267i
$839$	−42.0000			−1.45000			−0.725001	−	0.688748i	$-0.758161\pi$
$839$	−42.0000			−1.45000			−0.725001	+	0.688748i	$0.758161\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$		−	27.0000i		−	0.930481i
$843$		0			0
$844$	2.00000			0.0688428
$845$	36.0000	+	72.0000i	1.23844	+	2.47688i
$846$		0			0
$847$			2.00000i			0.0687208i
$848$			3.00000i			0.103020i
$849$		0			0
$850$	−12.0000	+	16.0000i	−0.411597	+	0.548795i
$851$		0			0
$852$		0			0
$853$			6.00000i			0.205436i	0.994711	+	0.102718i	$0.0327539\pi$
$853$			6.00000i			0.205436i	−0.994711	+	0.102718i	$0.967246\pi$
$854$	−2.00000			−0.0684386
$855$		0			0
$856$	−42.0000			−1.43553
$857$		−	12.0000i		−	0.409912i	−0.978771	−	0.204956i	$-0.934295\pi$
$857$		−	12.0000i		−	0.409912i	0.978771	−	0.204956i	$-0.0657052\pi$
$858$		0			0
$859$	−19.0000			−0.648272			−0.324136	−	0.946011i	$-0.605073\pi$
$859$	−19.0000			−0.648272			−0.324136	+	0.946011i	$0.605073\pi$
$860$	−10.0000	+	5.00000i	−0.340997	+	0.170499i
$861$		0			0
$862$			23.0000i			0.783383i
$863$		−	6.00000i		−	0.204242i	−0.994772	−	0.102121i	$-0.967437\pi$
$863$		−	6.00000i		−	0.204242i	0.994772	−	0.102121i	$-0.0325630\pi$
$864$		0			0
$865$	−36.0000	+	18.0000i	−1.22404	+	0.612018i
$866$	11.0000			0.373795
$867$		0			0
$868$		−	8.00000i		−	0.271538i
$869$	−42.0000			−1.42475
$870$		0			0
$871$	−49.0000			−1.66030
$872$			21.0000i			0.711150i
$873$		0			0
$874$		0			0
$875$	2.00000	−	11.0000i	0.0676123	−	0.371868i
$876$		0			0
$877$		−	22.0000i		−	0.742887i	−0.928456	−	0.371444i	$-0.878863\pi$
$877$		−	22.0000i		−	0.742887i	0.928456	−	0.371444i	$-0.121137\pi$
$878$			39.0000i			1.31619i
$879$		0			0
$880$	−3.00000	−	6.00000i	−0.101130	−	0.202260i
$881$	−14.0000			−0.471672			−0.235836	−	0.971793i	$-0.575783\pi$
$881$	−14.0000			−0.471672			−0.235836	+	0.971793i	$0.575783\pi$
$882$		0			0
$883$			12.0000i			0.403832i	0.979403	+	0.201916i	$0.0647168\pi$
$883$			12.0000i			0.403832i	−0.979403	+	0.201916i	$0.935283\pi$
$884$	−28.0000			−0.941742
$885$		0			0
$886$	4.00000			0.134383
$887$			55.0000i			1.84672i	0.383936	+	0.923360i	$0.374568\pi$
$887$			55.0000i			1.84672i	−0.383936	+	0.923360i	$0.625432\pi$
$888$		0			0
$889$	−7.00000			−0.234772
$890$	30.0000	−	15.0000i	1.00560	−	0.502801i
$891$		0			0
$892$			6.00000i			0.200895i
$893$			27.0000i			0.903521i
$894$		0			0
$895$	−13.0000	−	26.0000i	−0.434542	−	0.869084i
$896$	3.00000			0.100223
$897$		0			0
$898$			10.0000i			0.333704i
$899$	−16.0000			−0.533630
$900$		0			0
$901$	−12.0000			−0.399778
$902$			33.0000i			1.09878i
$903$		0			0
$904$	9.00000			0.299336
$905$	6.00000	+	12.0000i	0.199447	+	0.398893i
$906$		0			0
$907$			25.0000i			0.830111i	0.909796	+	0.415056i	$0.136238\pi$
$907$			25.0000i			0.830111i	−0.909796	+	0.415056i	$0.863762\pi$
$908$			1.00000i			0.0331862i
$909$		0			0
$910$	−14.0000	+	7.00000i	−0.464095	+	0.232048i
$911$	−15.0000			−0.496972			−0.248486	−	0.968635i	$-0.579933\pi$
$911$	−15.0000			−0.496972			−0.248486	+	0.968635i	$0.579933\pi$
$912$		0			0
$913$			3.00000i			0.0992855i
$914$	2.00000			0.0661541
$915$		0			0
$916$	10.0000			0.330409
$917$			4.00000i			0.132092i
$918$		0			0
$919$	−10.0000			−0.329870			−0.164935	−	0.986304i	$-0.552741\pi$
$919$	−10.0000			−0.329870			−0.164935	+	0.986304i	$0.552741\pi$
$920$		0			0
$921$		0			0
$922$			33.0000i			1.08680i
$923$		−	56.0000i		−	1.84326i
$924$		0			0
$925$	16.0000	+	12.0000i	0.526077	+	0.394558i
$926$	27.0000			0.887275
$927$		0			0
$928$		−	10.0000i		−	0.328266i
$929$	13.0000			0.426516			0.213258	−	0.976996i	$-0.431592\pi$
$929$	13.0000			0.426516			0.213258	+	0.976996i	$0.431592\pi$
$930$		0			0
$931$	3.00000			0.0983210
$932$			1.00000i			0.0327561i
$933$		0			0
$934$	12.0000			0.392652
$935$	24.0000	−	12.0000i	0.784884	−	0.392442i
$936$		0			0
$937$		−	7.00000i		−	0.228680i	−0.993442	−	0.114340i	$-0.963525\pi$
$937$		−	7.00000i		−	0.228680i	0.993442	−	0.114340i	$-0.0364753\pi$
$938$		−	7.00000i		−	0.228558i
$939$		0			0
$940$	−18.0000	+	9.00000i	−0.587095	+	0.293548i
$941$	15.0000			0.488986			0.244493	−	0.969651i	$-0.421378\pi$
$941$	15.0000			0.488986			0.244493	+	0.969651i	$0.421378\pi$
$942$		0			0
$943$		0			0
$944$	−10.0000			−0.325472
$945$		0			0
$946$	−15.0000			−0.487692
$947$			18.0000i			0.584921i	0.956278	+	0.292461i	$0.0944741\pi$
$947$			18.0000i			0.584921i	−0.956278	+	0.292461i	$0.905526\pi$
$948$		0			0
$949$	105.000			3.40844
$950$	12.0000	+	9.00000i	0.389331	+	0.291999i
$951$		0			0
$952$		−	12.0000i		−	0.388922i
$953$			42.0000i			1.36051i	0.732974	+	0.680257i	$0.238132\pi$
$953$			42.0000i			1.36051i	−0.732974	+	0.680257i	$0.761868\pi$
$954$		0			0
$955$	9.00000	+	18.0000i	0.291233	+	0.582466i
$956$	12.0000			0.388108
$957$		0			0
$958$			42.0000i			1.35696i
$959$	−3.00000			−0.0968751
$960$		0			0
$961$	33.0000			1.06452
$962$		−	28.0000i		−	0.902756i
$963$		0			0
$964$	22.0000			0.708572
$965$	52.0000	−	26.0000i	1.67394	−	0.836970i
$966$		0			0
$967$		−	5.00000i		−	0.160789i	−0.996763	−	0.0803946i	$-0.974382\pi$
$967$		−	5.00000i		−	0.160789i	0.996763	−	0.0803946i	$-0.0256180\pi$
$968$		−	6.00000i		−	0.192847i
$969$		0			0
$970$	−2.00000	−	4.00000i	−0.0642161	−	0.128432i
$971$	26.0000			0.834380			0.417190	−	0.908819i	$-0.363015\pi$
$971$	26.0000			0.834380			0.417190	+	0.908819i	$0.363015\pi$
$972$		0			0
$973$			20.0000i			0.641171i
$974$	15.0000			0.480631
$975$		0			0
$976$	2.00000			0.0640184
$977$		−	21.0000i		−	0.671850i	−0.941889	−	0.335925i	$-0.890951\pi$
$977$		−	21.0000i		−	0.671850i	0.941889	−	0.335925i	$-0.109049\pi$
$978$		0			0
$979$	−45.0000			−1.43821
$980$	1.00000	+	2.00000i	0.0319438	+	0.0638877i
$981$		0			0
$982$		−	28.0000i		−	0.893516i
$983$			24.0000i			0.765481i	0.923856	+	0.382741i	$0.125020\pi$
$983$			24.0000i			0.765481i	−0.923856	+	0.382741i	$0.874980\pi$
$984$		0			0
$985$	−22.0000	+	11.0000i	−0.700978	+	0.350489i
$986$	−8.00000			−0.254772
$987$		0			0
$988$			21.0000i			0.668099i
$989$		0			0
$990$		0			0
$991$	4.00000			0.127064			0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000			0.127064			0.0635321	+	0.997980i	$0.479763\pi$
$992$			40.0000i			1.27000i
$993$		0			0
$994$	8.00000			0.253745
$995$	−13.0000	−	26.0000i	−0.412128	−	0.824255i
$996$		0			0
$997$			50.0000i			1.58352i	0.610835	+	0.791758i	$0.290834\pi$
$997$			50.0000i			1.58352i	−0.610835	+	0.791758i	$0.709166\pi$
$998$			32.0000i			1.01294i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.d.a.379.2	yes	2
3.2	odd	2		945.2.d.b.379.1	yes	2
5.2	odd	4		4725.2.a.f.1.1		1
5.3	odd	4		4725.2.a.o.1.1		1
5.4	even	2	inner	945.2.d.a.379.1	✓	2
15.2	even	4		4725.2.a.p.1.1		1
15.8	even	4		4725.2.a.e.1.1		1
15.14	odd	2		945.2.d.b.379.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.d.a.379.1	✓	2	5.4	even	2	inner
945.2.d.a.379.2	yes	2	1.1	even	1	trivial
945.2.d.b.379.1	yes	2	3.2	odd	2
945.2.d.b.379.2	yes	2	15.14	odd	2
4725.2.a.e.1.1		1	15.8	even	4
4725.2.a.f.1.1		1	5.2	odd	4
4725.2.a.o.1.1		1	5.3	odd	4
4725.2.a.p.1.1		1	15.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} -1.00000i q^{7} +3.00000i q^{8} +(2.00000 - 1.00000i) q^{10} -3.00000 q^{11} -7.00000i q^{13} +1.00000 q^{14} -1.00000 q^{16} -4.00000i q^{17} -3.00000 q^{19} +(-1.00000 - 2.00000i) q^{20} -3.00000i q^{22} +(-3.00000 + 4.00000i) q^{25} +7.00000 q^{26} -1.00000i q^{28} -2.00000 q^{29} +8.00000 q^{31} +5.00000i q^{32} +4.00000 q^{34} +(-2.00000 + 1.00000i) q^{35} -4.00000i q^{37} -3.00000i q^{38} +(6.00000 - 3.00000i) q^{40} -11.0000 q^{41} -5.00000i q^{43} -3.00000 q^{44} -9.00000i q^{47} -1.00000 q^{49} +(-4.00000 - 3.00000i) q^{50} -7.00000i q^{52} -3.00000i q^{53} +(3.00000 + 6.00000i) q^{55} +3.00000 q^{56} -2.00000i q^{58} +10.0000 q^{59} -2.00000 q^{61} +8.00000i q^{62} -7.00000 q^{64} +(-14.0000 + 7.00000i) q^{65} -7.00000i q^{67} -4.00000i q^{68} +(-1.00000 - 2.00000i) q^{70} +8.00000 q^{71} +15.0000i q^{73} +4.00000 q^{74} -3.00000 q^{76} +3.00000i q^{77} +14.0000 q^{79} +(1.00000 + 2.00000i) q^{80} -11.0000i q^{82} -1.00000i q^{83} +(-8.00000 + 4.00000i) q^{85} +5.00000 q^{86} -9.00000i q^{88} +15.0000 q^{89} -7.00000 q^{91} +9.00000 q^{94} +(3.00000 + 6.00000i) q^{95} -2.00000i q^{97} -1.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{4} - 2 q^{5} + 4 q^{10} - 6 q^{11} + 2 q^{14} - 2 q^{16} - 6 q^{19} - 2 q^{20} - 6 q^{25} + 14 q^{26} - 4 q^{29} + 16 q^{31} + 8 q^{34} - 4 q^{35} + 12 q^{40} - 22 q^{41} - 6 q^{44} - 2 q^{49}+ \cdots + 6 q^{95}+O(q^{100}) \) 2 * q + 2 * q^4 - 2 * q^5 + 4 * q^10 - 6 * q^11 + 2 * q^14 - 2 * q^16 - 6 * q^19 - 2 * q^20 - 6 * q^25 + 14 * q^26 - 4 * q^29 + 16 * q^31 + 8 * q^34 - 4 * q^35 + 12 * q^40 - 22 * q^41 - 6 * q^44 - 2 * q^49 - 8 * q^50 + 6 * q^55 + 6 * q^56 + 20 * q^59 - 4 * q^61 - 14 * q^64 - 28 * q^65 - 2 * q^70 + 16 * q^71 + 8 * q^74 - 6 * q^76 + 28 * q^79 + 2 * q^80 - 16 * q^85 + 10 * q^86 + 30 * q^89 - 14 * q^91 + 18 * q^94 + 6 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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