LMFDB - Embedded newform 2394.2.f.b.2015.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2394.2015");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2394.f (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$19.1161862439$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2015.14
Character	$\chi$	$=$	2394.2015
Dual form			2394.2.f.b.2015.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +0.335231 q^{5} +(-2.35234 - 1.21100i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +0.335231 q^{5} +(-2.35234 - 1.21100i) q^{7} -1.00000i q^{8} +0.335231i q^{10} -0.185254i q^{11} -0.757021i q^{13} +(1.21100 - 2.35234i) q^{14} +1.00000 q^{16} -0.456509 q^{17} +1.00000i q^{19} -0.335231 q^{20} +0.185254 q^{22} -1.64986i q^{23} -4.88762 q^{25} +0.757021 q^{26} +(2.35234 + 1.21100i) q^{28} +3.90862i q^{29} +9.21951i q^{31} +1.00000i q^{32} -0.456509i q^{34} +(-0.788575 - 0.405963i) q^{35} +5.23896 q^{37} -1.00000 q^{38} -0.335231i q^{40} +11.9325 q^{41} +5.93699 q^{43} +0.185254i q^{44} +1.64986 q^{46} +2.36902 q^{47} +(4.06698 + 5.69734i) q^{49} -4.88762i q^{50} +0.757021i q^{52} -4.49358i q^{53} -0.0621027i q^{55} +(-1.21100 + 2.35234i) q^{56} -3.90862 q^{58} -6.16386 q^{59} +4.83232i q^{61} -9.21951 q^{62} -1.00000 q^{64} -0.253777i q^{65} +11.6219 q^{67} +0.456509 q^{68} +(0.405963 - 0.788575i) q^{70} +5.10688i q^{71} +12.0776i q^{73} +5.23896i q^{74} -1.00000i q^{76} +(-0.224341 + 0.435779i) q^{77} +0.519106 q^{79} +0.335231 q^{80} +11.9325i q^{82} -8.81830 q^{83} -0.153036 q^{85} +5.93699i q^{86} -0.185254 q^{88} +3.20306 q^{89} +(-0.916750 + 1.78077i) q^{91} +1.64986i q^{92} +2.36902i q^{94} +0.335231i q^{95} +16.2754i q^{97} +(-5.69734 + 4.06698i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} + 4 q^{7}+O(q^{10}) $ 24 * q - 24 * q^4 + 4 * q^7	$ 24 q - 24 q^{4} + 4 q^{7} + 4 q^{14} + 24 q^{16} - 32 q^{17} - 8 q^{22} + 16 q^{25} - 4 q^{28} + 24 q^{35} - 24 q^{38} + 8 q^{41} + 16 q^{43} - 8 q^{46} - 16 q^{49} - 4 q^{56} + 16 q^{58} - 16 q^{59} + 16 q^{62} - 24 q^{64} - 24 q^{67} + 32 q^{68} - 16 q^{70} - 8 q^{77} - 40 q^{79} + 64 q^{83} + 40 q^{85} + 8 q^{88} + 64 q^{89} + 8 q^{91} + 16 q^{98}+O(q^{100}) $ 24 * q - 24 * q^4 + 4 * q^7 + 4 * q^14 + 24 * q^16 - 32 * q^17 - 8 * q^22 + 16 * q^25 - 4 * q^28 + 24 * q^35 - 24 * q^38 + 8 * q^41 + 16 * q^43 - 8 * q^46 - 16 * q^49 - 4 * q^56 + 16 * q^58 - 16 * q^59 + 16 * q^62 - 24 * q^64 - 24 * q^67 + 32 * q^68 - 16 * q^70 - 8 * q^77 - 40 * q^79 + 64 * q^83 + 40 * q^85 + 8 * q^88 + 64 * q^89 + 8 * q^91 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	0.335231			0.149920			0.0749599	−	0.997187i	$-0.476117\pi$
$5$	0.335231			0.149920			0.0749599	+	0.997187i	$0.476117\pi$
$6$		0			0
$7$	−2.35234	−	1.21100i	−0.889100	−	0.457714i
$7$	−2.35234	−	1.21100i	−0.889100	−	0.457714i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$			0.335231i			0.106009i
$11$		−	0.185254i		−	0.0558561i	−0.999610	−	0.0279280i	$-0.991109\pi$
$11$		−	0.185254i		−	0.0558561i	0.999610	−	0.0279280i	$-0.00889092\pi$
$12$		0			0
$13$		−	0.757021i		−	0.209960i	−0.994474	−	0.104980i	$-0.966522\pi$
$13$		−	0.757021i		−	0.209960i	0.994474	−	0.104980i	$-0.0334778\pi$
$14$	1.21100	−	2.35234i	0.323652	−	0.628688i
$15$		0			0
$16$	1.00000			0.250000
$17$	−0.456509			−0.110720			−0.0553598	−	0.998466i	$-0.517631\pi$
$17$	−0.456509			−0.110720			−0.0553598	+	0.998466i	$0.517631\pi$
$18$		0			0
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	−0.335231			−0.0749599
$21$		0			0
$22$	0.185254			0.0394962
$23$		−	1.64986i		−	0.344020i	−0.985095	−	0.172010i	$-0.944974\pi$
$23$		−	1.64986i		−	0.344020i	0.985095	−	0.172010i	$-0.0550261\pi$
$24$		0			0
$25$	−4.88762			−0.977524
$26$	0.757021			0.148464
$27$		0			0
$28$	2.35234	+	1.21100i	0.444550	+	0.228857i
$29$			3.90862i			0.725813i	0.931826	+	0.362907i	$0.118216\pi$
$29$			3.90862i			0.725813i	−0.931826	+	0.362907i	$0.881784\pi$
$30$		0			0
$31$			9.21951i			1.65587i	0.560823	+	0.827936i	$0.310485\pi$
$31$			9.21951i			1.65587i	−0.560823	+	0.827936i	$0.689515\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$		−	0.456509i		−	0.0782906i
$35$	−0.788575	−	0.405963i	−0.133294	−	0.0686203i
$36$		0			0
$37$	5.23896			0.861280			0.430640	−	0.902524i	$-0.358288\pi$
$37$	5.23896			0.861280			0.430640	+	0.902524i	$0.358288\pi$
$38$	−1.00000			−0.162221
$39$		0			0
$40$		−	0.335231i		−	0.0530046i
$41$	11.9325			1.86354			0.931771	−	0.363047i	$-0.118264\pi$
$41$	11.9325			1.86354			0.931771	+	0.363047i	$0.118264\pi$
$42$		0			0
$43$	5.93699			0.905382			0.452691	−	0.891668i	$-0.350464\pi$
$43$	5.93699			0.905382			0.452691	+	0.891668i	$0.350464\pi$
$44$			0.185254i			0.0279280i
$45$		0			0
$46$	1.64986			0.243259
$47$	2.36902			0.345557			0.172778	−	0.984961i	$-0.444726\pi$
$47$	2.36902			0.345557			0.172778	+	0.984961i	$0.444726\pi$
$48$		0			0
$49$	4.06698	+	5.69734i	0.580997	+	0.813906i
$50$		−	4.88762i		−	0.691214i
$51$		0			0
$52$			0.757021i			0.104980i
$53$		−	4.49358i		−	0.617241i	−0.951185	−	0.308620i	$-0.900133\pi$
$53$		−	4.49358i		−	0.617241i	0.951185	−	0.308620i	$-0.0998672\pi$
$54$		0			0
$55$		−	0.0621027i		−	0.00837392i
$56$	−1.21100	+	2.35234i	−0.161826	+	0.314344i
$57$		0			0
$58$	−3.90862			−0.513227
$59$	−6.16386			−0.802466			−0.401233	−	0.915976i	$-0.631418\pi$
$59$	−6.16386			−0.802466			−0.401233	+	0.915976i	$0.631418\pi$
$60$		0			0
$61$			4.83232i			0.618715i	0.950946	+	0.309357i	$0.100114\pi$
$61$			4.83232i			0.618715i	−0.950946	+	0.309357i	$0.899886\pi$
$62$	−9.21951			−1.17088
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	0.253777i		−	0.0314771i
$66$		0			0
$67$	11.6219			1.41985			0.709923	−	0.704279i	$-0.248730\pi$
$67$	11.6219			1.41985			0.709923	+	0.704279i	$0.248730\pi$
$68$	0.456509			0.0553598
$69$		0			0
$70$	0.405963	−	0.788575i	0.0485219	−	0.0942528i
$71$			5.10688i			0.606076i	0.952979	+	0.303038i	$0.0980008\pi$
$71$			5.10688i			0.606076i	−0.952979	+	0.303038i	$0.901999\pi$
$72$		0			0
$73$			12.0776i			1.41358i	0.707424	+	0.706789i	$0.249857\pi$
$73$			12.0776i			1.41358i	−0.707424	+	0.706789i	$0.750143\pi$
$74$			5.23896i			0.609017i
$75$		0			0
$76$		−	1.00000i		−	0.114708i
$77$	−0.224341	+	0.435779i	−0.0255661	+	0.0496616i
$78$		0			0
$79$	0.519106			0.0584040			0.0292020	−	0.999574i	$-0.490703\pi$
$79$	0.519106			0.0584040			0.0292020	+	0.999574i	$0.490703\pi$
$80$	0.335231			0.0374799
$81$		0			0
$82$			11.9325i			1.31772i
$83$	−8.81830			−0.967934			−0.483967	−	0.875086i	$-0.660805\pi$
$83$	−8.81830			−0.967934			−0.483967	+	0.875086i	$0.660805\pi$
$84$		0			0
$85$	−0.153036			−0.0165991
$86$			5.93699i			0.640202i
$87$		0			0
$88$	−0.185254			−0.0197481
$89$	3.20306			0.339523			0.169762	−	0.985485i	$-0.445700\pi$
$89$	3.20306			0.339523			0.169762	+	0.985485i	$0.445700\pi$
$90$		0			0
$91$	−0.916750	+	1.78077i	−0.0961015	+	0.186675i
$92$			1.64986i			0.172010i
$93$		0			0
$94$			2.36902i			0.244345i
$95$			0.335231i			0.0343939i
$96$		0			0
$97$			16.2754i			1.65252i	0.563291	+	0.826258i	$0.309535\pi$
$97$			16.2754i			1.65252i	−0.563291	+	0.826258i	$0.690465\pi$
$98$	−5.69734	+	4.06698i	−0.575518	+	0.410827i
$99$		0			0
$100$	4.88762			0.488762
$101$	−6.98657			−0.695190			−0.347595	−	0.937645i	$-0.613002\pi$
$101$	−6.98657			−0.695190			−0.347595	+	0.937645i	$0.613002\pi$
$102$		0			0
$103$			9.05580i			0.892294i	0.894960	+	0.446147i	$0.147204\pi$
$103$			9.05580i			0.892294i	−0.894960	+	0.446147i	$0.852796\pi$
$104$	−0.757021			−0.0742320
$105$		0			0
$106$	4.49358			0.436455
$107$			9.44558i			0.913139i	0.889688	+	0.456569i	$0.150922\pi$
$107$			9.44558i			0.913139i	−0.889688	+	0.456569i	$0.849078\pi$
$108$		0			0
$109$	12.7360			1.21988			0.609942	−	0.792446i	$-0.291193\pi$
$109$	12.7360			1.21988			0.609942	+	0.792446i	$0.291193\pi$
$110$	0.0621027			0.00592126
$111$		0			0
$112$	−2.35234	−	1.21100i	−0.222275	−	0.114428i
$113$		−	16.9974i		−	1.59898i	−0.600677	−	0.799492i	$-0.705102\pi$
$113$		−	16.9974i		−	1.59898i	0.600677	−	0.799492i	$-0.294898\pi$
$114$		0			0
$115$		−	0.553084i		−	0.0515754i
$116$		−	3.90862i		−	0.362907i
$117$		0			0
$118$		−	6.16386i		−	0.567429i
$119$	1.07386	+	0.552831i	0.0984408	+	0.0506779i
$120$		0			0
$121$	10.9657			0.996880
$122$	−4.83232			−0.437497
$123$		0			0
$124$		−	9.21951i		−	0.827936i
$125$	−3.31463			−0.296470
$126$		0			0
$127$	−4.39380			−0.389887			−0.194943	−	0.980815i	$-0.562452\pi$
$127$	−4.39380			−0.389887			−0.194943	+	0.980815i	$0.562452\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	0.253777			0.0222577
$131$	9.40934			0.822098			0.411049	−	0.911613i	$-0.365163\pi$
$131$	9.40934			0.822098			0.411049	+	0.911613i	$0.365163\pi$
$132$		0			0
$133$	1.21100	−	2.35234i	0.105007	−	0.203973i
$134$			11.6219i			1.00398i
$135$		0			0
$136$			0.456509i			0.0391453i
$137$		−	2.27085i		−	0.194012i	−0.995284	−	0.0970058i	$-0.969073\pi$
$137$		−	2.27085i		−	0.194012i	0.995284	−	0.0970058i	$-0.0309265\pi$
$138$		0			0
$139$			4.39303i			0.372612i	0.982492	+	0.186306i	$0.0596516\pi$
$139$			4.39303i			0.372612i	−0.982492	+	0.186306i	$0.940348\pi$
$140$	0.788575	+	0.405963i	0.0666468	+	0.0343101i
$141$		0			0
$142$	−5.10688			−0.428560
$143$	−0.140241			−0.0117275
$144$		0			0
$145$			1.31029i			0.108814i
$146$	−12.0776			−0.999551
$147$		0			0
$148$	−5.23896			−0.430640
$149$		−	2.44847i		−	0.200587i	−0.994958	−	0.100293i	$-0.968022\pi$
$149$		−	2.44847i		−	0.200587i	0.994958	−	0.100293i	$-0.0319781\pi$
$150$		0			0
$151$	−4.09905			−0.333576			−0.166788	−	0.985993i	$-0.553340\pi$
$151$	−4.09905			−0.333576			−0.166788	+	0.985993i	$0.553340\pi$
$152$	1.00000			0.0811107
$153$		0			0
$154$	−0.435779	−	0.224341i	−0.0351161	−	0.0180779i
$155$			3.09066i			0.248248i
$156$		0			0
$157$			11.6622i			0.930745i	0.885115	+	0.465372i	$0.154080\pi$
$157$			11.6622i			0.930745i	−0.885115	+	0.465372i	$0.845920\pi$
$158$			0.519106i			0.0412978i
$159$		0			0
$160$			0.335231i			0.0265023i
$161$	−1.99798	+	3.88103i	−0.157463	+	0.305868i
$162$		0			0
$163$	−17.5586			−1.37530			−0.687649	−	0.726044i	$-0.741357\pi$
$163$	−17.5586			−1.37530			−0.687649	+	0.726044i	$0.741357\pi$
$164$	−11.9325			−0.931771
$165$		0			0
$166$		−	8.81830i		−	0.684433i
$167$	−11.9515			−0.924831			−0.462416	−	0.886663i	$-0.653017\pi$
$167$	−11.9515			−0.924831			−0.462416	+	0.886663i	$0.653017\pi$
$168$		0			0
$169$	12.4269			0.955917
$170$		−	0.153036i		−	0.0117373i
$171$		0			0
$172$	−5.93699			−0.452691
$173$	19.0517			1.44847			0.724235	−	0.689553i	$-0.242193\pi$
$173$	19.0517			1.44847			0.724235	+	0.689553i	$0.242193\pi$
$174$		0			0
$175$	11.4973	+	5.91889i	0.869116	+	0.447426i
$176$		−	0.185254i		−	0.0139640i
$177$		0			0
$178$			3.20306i			0.240079i
$179$			12.9510i			0.968003i	0.875067	+	0.484002i	$0.160817\pi$
$179$			12.9510i			0.968003i	−0.875067	+	0.484002i	$0.839183\pi$
$180$		0			0
$181$			5.64615i			0.419675i	0.977736	+	0.209837i	$0.0672934\pi$
$181$			5.64615i			0.419675i	−0.977736	+	0.209837i	$0.932707\pi$
$182$	−1.78077	−	0.916750i	−0.131999	−	0.0679540i
$183$		0			0
$184$	−1.64986			−0.121629
$185$	1.75626			0.129123
$186$		0			0
$187$			0.0845699i			0.00618436i
$188$	−2.36902			−0.172778
$189$		0			0
$190$	−0.335231			−0.0243202
$191$		−	11.0980i		−	0.803026i	−0.915853	−	0.401513i	$-0.868484\pi$
$191$		−	11.0980i		−	0.803026i	0.915853	−	0.401513i	$-0.131516\pi$
$192$		0			0
$193$	−5.02100			−0.361419			−0.180710	−	0.983536i	$-0.557839\pi$
$193$	−5.02100			−0.361419			−0.180710	+	0.983536i	$0.557839\pi$
$194$	−16.2754			−1.16851
$195$		0			0
$196$	−4.06698	−	5.69734i	−0.290498	−	0.406953i
$197$		−	15.4710i		−	1.10226i	−0.834419	−	0.551130i	$-0.814197\pi$
$197$		−	15.4710i		−	1.10226i	0.834419	−	0.551130i	$-0.185803\pi$
$198$		0			0
$199$			5.21243i			0.369499i	0.982786	+	0.184750i	$0.0591474\pi$
$199$			5.21243i			0.369499i	−0.982786	+	0.184750i	$0.940853\pi$
$200$			4.88762i			0.345607i
$201$		0			0
$202$		−	6.98657i		−	0.491573i
$203$	4.73333	−	9.19440i	0.332215	−	0.645320i
$204$		0			0
$205$	4.00014			0.279382
$206$	−9.05580			−0.630947
$207$		0			0
$208$		−	0.757021i		−	0.0524900i
$209$	0.185254			0.0128143
$210$		0			0
$211$	−11.1551			−0.767950			−0.383975	−	0.923343i	$-0.625445\pi$
$211$	−11.1551			−0.767950			−0.383975	+	0.923343i	$0.625445\pi$
$212$			4.49358i			0.308620i
$213$		0			0
$214$	−9.44558			−0.645687
$215$	1.99026			0.135735
$216$		0			0
$217$	11.1648	−	21.6874i	0.757915	−	1.47224i
$218$			12.7360i			0.862588i
$219$		0			0
$220$			0.0621027i			0.00418696i
$221$			0.345587i			0.0232467i
$222$		0			0
$223$		−	27.3838i		−	1.83376i	−0.399166	−	0.916878i	$-0.630700\pi$
$223$		−	27.3838i		−	1.83376i	0.399166	−	0.916878i	$-0.369300\pi$
$224$	1.21100	−	2.35234i	0.0809131	−	0.157172i
$225$		0			0
$226$	16.9974			1.13065
$227$	−14.1354			−0.938202			−0.469101	−	0.883145i	$-0.655422\pi$
$227$	−14.1354			−0.938202			−0.469101	+	0.883145i	$0.655422\pi$
$228$		0			0
$229$			20.5265i			1.35643i	0.734863	+	0.678216i	$0.237247\pi$
$229$			20.5265i			1.35643i	−0.734863	+	0.678216i	$0.762753\pi$
$230$	0.553084			0.0364693
$231$		0			0
$232$	3.90862			0.256614
$233$		−	2.91114i		−	0.190715i	−0.995443	−	0.0953577i	$-0.969601\pi$
$233$		−	2.91114i		−	0.190715i	0.995443	−	0.0953577i	$-0.0303995\pi$
$234$		0			0
$235$	0.794167			0.0518058
$236$	6.16386			0.401233
$237$		0			0
$238$	−0.552831	+	1.07386i	−0.0358347	+	0.0696082i
$239$			16.1133i			1.04229i	0.853470	+	0.521143i	$0.174494\pi$
$239$			16.1133i			1.04229i	−0.853470	+	0.521143i	$0.825506\pi$
$240$		0			0
$241$			20.6759i			1.33185i	0.746019	+	0.665924i	$0.231963\pi$
$241$			20.6759i			1.33185i	−0.746019	+	0.665924i	$0.768037\pi$
$242$			10.9657i			0.704901i
$243$		0			0
$244$		−	4.83232i		−	0.309357i
$245$	1.36337	+	1.90992i	0.0871028	+	0.122021i
$246$		0			0
$247$	0.757021			0.0481681
$248$	9.21951			0.585439
$249$		0			0
$250$		−	3.31463i		−	0.209636i
$251$	−10.2039			−0.644065			−0.322032	−	0.946729i	$-0.604366\pi$
$251$	−10.2039			−0.644065			−0.322032	+	0.946729i	$0.604366\pi$
$252$		0			0
$253$	−0.305643			−0.0192156
$254$		−	4.39380i		−	0.275691i
$255$		0			0
$256$	1.00000			0.0625000
$257$	29.7388			1.85506			0.927528	−	0.373755i	$-0.121930\pi$
$257$	29.7388			1.85506			0.927528	+	0.373755i	$0.121930\pi$
$258$		0			0
$259$	−12.3238	−	6.34436i	−0.765764	−	0.394219i
$260$			0.253777i			0.0157386i
$261$		0			0
$262$			9.40934i			0.581311i
$263$			8.14216i			0.502067i	0.967978	+	0.251034i	$0.0807705\pi$
$263$			8.14216i			0.502067i	−0.967978	+	0.251034i	$0.919230\pi$
$264$		0			0
$265$		−	1.50639i		−	0.0925365i
$266$	2.35234	+	1.21100i	0.144231	+	0.0742509i
$267$		0			0
$268$	−11.6219			−0.709923
$269$	−25.9102			−1.57977			−0.789885	−	0.613255i	$-0.789860\pi$
$269$	−25.9102			−1.57977			−0.789885	+	0.613255i	$0.789860\pi$
$270$		0			0
$271$		−	15.2972i		−	0.929237i	−0.885511	−	0.464619i	$-0.846191\pi$
$271$		−	15.2972i		−	0.929237i	0.885511	−	0.464619i	$-0.153809\pi$
$272$	−0.456509			−0.0276799
$273$		0			0
$274$	2.27085			0.137187
$275$			0.905449i			0.0546006i
$276$		0			0
$277$	−6.68378			−0.401589			−0.200795	−	0.979633i	$-0.564352\pi$
$277$	−6.68378			−0.401589			−0.200795	+	0.979633i	$0.564352\pi$
$278$	−4.39303			−0.263477
$279$		0			0
$280$	−0.405963	+	0.788575i	−0.0242609	+	0.0471264i
$281$			10.3331i			0.616419i	0.951319	+	0.308209i	$0.0997297\pi$
$281$			10.3331i			0.616419i	−0.951319	+	0.308209i	$0.900270\pi$
$282$		0			0
$283$			3.39813i			0.201998i	0.994887	+	0.100999i	$0.0322039\pi$
$283$			3.39813i			0.201998i	−0.994887	+	0.100999i	$0.967796\pi$
$284$		−	5.10688i		−	0.303038i
$285$		0			0
$286$		−	0.140241i		−	0.00829262i
$287$	−28.0692	−	14.4502i	−1.65687	−	0.852968i
$288$		0			0
$289$	−16.7916			−0.987741
$290$	−1.31029			−0.0769429
$291$		0			0
$292$		−	12.0776i		−	0.706789i
$293$	32.4348			1.89486			0.947431	−	0.319961i	$-0.103670\pi$
$293$	32.4348			1.89486			0.947431	+	0.319961i	$0.103670\pi$
$294$		0			0
$295$	−2.06632			−0.120306
$296$		−	5.23896i		−	0.304508i
$297$		0			0
$298$	2.44847			0.141836
$299$	−1.24898			−0.0722304
$300$		0			0
$301$	−13.9658	−	7.18967i	−0.804975	−	0.414406i
$302$		−	4.09905i		−	0.235874i
$303$		0			0
$304$			1.00000i			0.0573539i
$305$			1.61994i			0.0927575i
$306$		0			0
$307$			13.6149i			0.777044i	0.921440	+	0.388522i	$0.127014\pi$
$307$			13.6149i			0.777044i	−0.921440	+	0.388522i	$0.872986\pi$
$308$	0.224341	−	0.435779i	0.0127830	−	0.0248308i
$309$		0			0
$310$	−3.09066			−0.175538
$311$	10.5231			0.596710			0.298355	−	0.954455i	$-0.403562\pi$
$311$	10.5231			0.596710			0.298355	+	0.954455i	$0.403562\pi$
$312$		0			0
$313$		−	21.6817i		−	1.22552i	−0.790269	−	0.612760i	$-0.790059\pi$
$313$		−	21.6817i		−	1.22552i	0.790269	−	0.612760i	$-0.209941\pi$
$314$	−11.6622			−0.658136
$315$		0			0
$316$	−0.519106			−0.0292020
$317$			16.2235i			0.911203i	0.890184	+	0.455602i	$0.150576\pi$
$317$			16.2235i			0.911203i	−0.890184	+	0.455602i	$0.849424\pi$
$318$		0			0
$319$	0.724087			0.0405411
$320$	−0.335231			−0.0187400
$321$		0			0
$322$	−3.88103	−	1.99798i	−0.216281	−	0.111343i
$323$		−	0.456509i		−	0.0254008i
$324$		0			0
$325$			3.70003i			0.205241i
$326$		−	17.5586i		−	0.972482i
$327$		0			0
$328$		−	11.9325i		−	0.658861i
$329$	−5.57273	−	2.86887i	−0.307234	−	0.158166i
$330$		0			0
$331$	11.2594			0.618872			0.309436	−	0.950920i	$-0.399860\pi$
$331$	11.2594			0.618872			0.309436	+	0.950920i	$0.399860\pi$
$332$	8.81830			0.483967
$333$		0			0
$334$		−	11.9515i		−	0.653954i
$335$	3.89603			0.212863
$336$		0			0
$337$	28.7008			1.56343			0.781717	−	0.623633i	$-0.214344\pi$
$337$	28.7008			1.56343			0.781717	+	0.623633i	$0.214344\pi$
$338$			12.4269i			0.675935i
$339$		0			0
$340$	0.153036			0.00829953
$341$	1.70795			0.0924905
$342$		0			0
$343$	−2.66744	−	18.3272i	−0.144028	−	0.989574i
$344$		−	5.93699i		−	0.320101i
$345$		0			0
$346$			19.0517i			1.02422i
$347$		−	29.7352i		−	1.59627i	−0.602480	−	0.798134i	$-0.705821\pi$
$347$		−	29.7352i		−	1.59627i	0.602480	−	0.798134i	$-0.294179\pi$
$348$		0			0
$349$		−	17.2667i		−	0.924263i	−0.886811	−	0.462131i	$-0.847085\pi$
$349$		−	17.2667i		−	0.924263i	0.886811	−	0.462131i	$-0.152915\pi$
$350$	−5.91889	+	11.4973i	−0.316378	+	0.614558i
$351$		0			0
$352$	0.185254			0.00987405
$353$	12.1035			0.644204			0.322102	−	0.946705i	$-0.395611\pi$
$353$	12.1035			0.644204			0.322102	+	0.946705i	$0.395611\pi$
$354$		0			0
$355$			1.71198i			0.0908627i
$356$	−3.20306			−0.169762
$357$		0			0
$358$	−12.9510			−0.684482
$359$			23.3990i			1.23495i	0.786591	+	0.617475i	$0.211844\pi$
$359$			23.3990i			1.23495i	−0.786591	+	0.617475i	$0.788156\pi$
$360$		0			0
$361$	−1.00000			−0.0526316
$362$	−5.64615			−0.296755
$363$		0			0
$364$	0.916750	−	1.78077i	0.0480507	−	0.0933376i
$365$			4.04879i			0.211923i
$366$		0			0
$367$			12.4496i			0.649865i	0.945737	+	0.324933i	$0.105342\pi$
$367$			12.4496i			0.649865i	−0.945737	+	0.324933i	$0.894658\pi$
$368$		−	1.64986i		−	0.0860050i
$369$		0			0
$370$			1.75626i			0.0913036i
$371$	−5.44171	+	10.5704i	−0.282519	+	0.548788i
$372$		0			0
$373$	2.78536			0.144220			0.0721102	−	0.997397i	$-0.477027\pi$
$373$	2.78536			0.144220			0.0721102	+	0.997397i	$0.477027\pi$
$374$	−0.0845699			−0.00437301
$375$		0			0
$376$		−	2.36902i		−	0.122173i
$377$	2.95891			0.152392
$378$		0			0
$379$	6.35912			0.326646			0.163323	−	0.986573i	$-0.447779\pi$
$379$	6.35912			0.326646			0.163323	+	0.986573i	$0.447779\pi$
$380$		−	0.335231i		−	0.0171970i
$381$		0			0
$382$	11.0980			0.567825
$383$	17.0337			0.870381			0.435190	−	0.900338i	$-0.356681\pi$
$383$	17.0337			0.870381			0.435190	+	0.900338i	$0.356681\pi$
$384$		0			0
$385$	−0.0752061	+	0.146086i	−0.00383286	+	0.00744525i
$386$		−	5.02100i		−	0.255562i
$387$		0			0
$388$		−	16.2754i		−	0.826258i
$389$		−	4.80916i		−	0.243834i	−0.992540	−	0.121917i	$-0.961096\pi$
$389$		−	4.80916i		−	0.243834i	0.992540	−	0.121917i	$-0.0389042\pi$
$390$		0			0
$391$			0.753176i			0.0380898i
$392$	5.69734	−	4.06698i	0.287759	−	0.205413i
$393$		0			0
$394$	15.4710			0.779416
$395$	0.174020			0.00875590
$396$		0			0
$397$		−	2.28472i		−	0.114667i	−0.998355	−	0.0573334i	$-0.981740\pi$
$397$		−	2.28472i		−	0.114667i	0.998355	−	0.0573334i	$-0.0182598\pi$
$398$	−5.21243			−0.261275
$399$		0			0
$400$	−4.88762			−0.244381
$401$		−	24.2802i		−	1.21249i	−0.795277	−	0.606247i	$-0.792674\pi$
$401$		−	24.2802i		−	1.21249i	0.795277	−	0.606247i	$-0.207326\pi$
$402$		0			0
$403$	6.97936			0.347667
$404$	6.98657			0.347595
$405$		0			0
$406$	9.19440	+	4.73333i	0.456310	+	0.234911i
$407$		−	0.970536i		−	0.0481077i
$408$		0			0
$409$		−	6.01833i		−	0.297587i	−0.988868	−	0.148794i	$-0.952461\pi$
$409$		−	6.01833i		−	0.297587i	0.988868	−	0.148794i	$-0.0475390\pi$
$410$			4.00014i			0.197553i
$411$		0			0
$412$		−	9.05580i		−	0.446147i
$413$	14.4995	+	7.46441i	0.713473	+	0.367300i
$414$		0			0
$415$	−2.95617			−0.145112
$416$	0.757021			0.0371160
$417$		0			0
$418$			0.185254i			0.00906105i
$419$	8.32697			0.406799			0.203400	−	0.979096i	$-0.434801\pi$
$419$	8.32697			0.406799			0.203400	+	0.979096i	$0.434801\pi$
$420$		0			0
$421$	−25.5208			−1.24381			−0.621905	−	0.783093i	$-0.713641\pi$
$421$	−25.5208			−1.24381			−0.621905	+	0.783093i	$0.713641\pi$
$422$		−	11.1551i		−	0.543023i
$423$		0			0
$424$	−4.49358			−0.218227
$425$	2.23124			0.108231
$426$		0			0
$427$	5.85192	−	11.3672i	0.283194	−	0.550099i
$428$		−	9.44558i		−	0.456569i
$429$		0			0
$430$			1.99026i			0.0959788i
$431$			0.484959i			0.0233596i	0.999932	+	0.0116798i	$0.00371789\pi$
$431$			0.484959i			0.0233596i	−0.999932	+	0.0116798i	$0.996282\pi$
$432$		0			0
$433$			13.0041i			0.624937i	0.949928	+	0.312469i	$0.101156\pi$
$433$			13.0041i			0.624937i	−0.949928	+	0.312469i	$0.898844\pi$
$434$	21.6874	+	11.1648i	1.04103	+	0.535927i
$435$		0			0
$436$	−12.7360			−0.609942
$437$	1.64986			0.0789236
$438$		0			0
$439$		−	20.0339i		−	0.956164i	−0.878315	−	0.478082i	$-0.841332\pi$
$439$		−	20.0339i		−	0.956164i	0.878315	−	0.478082i	$-0.158668\pi$
$440$	−0.0621027			−0.00296063
$441$		0			0
$442$	−0.345587			−0.0164379
$443$		−	13.3813i		−	0.635765i	−0.948130	−	0.317883i	$-0.897028\pi$
$443$		−	13.3813i		−	0.635765i	0.948130	−	0.317883i	$-0.102972\pi$
$444$		0			0
$445$	1.07376			0.0509012
$446$	27.3838			1.29666
$447$		0			0
$448$	2.35234	+	1.21100i	0.111137	+	0.0572142i
$449$		−	21.4895i		−	1.01415i	−0.861901	−	0.507076i	$-0.830726\pi$
$449$		−	21.4895i		−	1.01415i	0.861901	−	0.507076i	$-0.169274\pi$
$450$		0			0
$451$		−	2.21054i		−	0.104090i
$452$			16.9974i			0.799492i
$453$		0			0
$454$		−	14.1354i		−	0.663409i
$455$	−0.307323	+	0.596968i	−0.0144075	+	0.0279863i
$456$		0			0
$457$	−27.4559			−1.28433			−0.642167	−	0.766565i	$-0.721964\pi$
$457$	−27.4559			−1.28433			−0.642167	+	0.766565i	$0.721964\pi$
$458$	−20.5265			−0.959142
$459$		0			0
$460$			0.553084i			0.0257877i
$461$	−18.3684			−0.855502			−0.427751	−	0.903897i	$-0.640694\pi$
$461$	−18.3684			−0.855502			−0.427751	+	0.903897i	$0.640694\pi$
$462$		0			0
$463$	−6.44046			−0.299314			−0.149657	−	0.988738i	$-0.547817\pi$
$463$	−6.44046			−0.299314			−0.149657	+	0.988738i	$0.547817\pi$
$464$			3.90862i			0.181453i
$465$		0			0
$466$	2.91114			0.134856
$467$	25.6442			1.18667			0.593336	−	0.804955i	$-0.297811\pi$
$467$	25.6442			1.18667			0.593336	+	0.804955i	$0.297811\pi$
$468$		0			0
$469$	−27.3387	−	14.0741i	−1.26238	−	0.649883i
$470$			0.794167i			0.0366322i
$471$		0			0
$472$			6.16386i			0.283715i
$473$		−	1.09985i		−	0.0505711i
$474$		0			0
$475$		−	4.88762i		−	0.224259i
$476$	−1.07386	−	0.552831i	−0.0492204	−	0.0253389i
$477$		0			0
$478$	−16.1133			−0.737007
$479$	−11.5000			−0.525448			−0.262724	−	0.964871i	$-0.584621\pi$
$479$	−11.5000			−0.525448			−0.262724	+	0.964871i	$0.584621\pi$
$480$		0			0
$481$		−	3.96600i		−	0.180834i
$482$	−20.6759			−0.941759
$483$		0			0
$484$	−10.9657			−0.498440
$485$			5.45601i			0.247745i
$486$		0			0
$487$	−19.9663			−0.904761			−0.452380	−	0.891825i	$-0.649425\pi$
$487$	−19.9663			−0.904761			−0.452380	+	0.891825i	$0.649425\pi$
$488$	4.83232			0.218749
$489$		0			0
$490$	−1.90992	+	1.36337i	−0.0862816	+	0.0615910i
$491$		−	21.9310i		−	0.989730i	−0.868970	−	0.494865i	$-0.835217\pi$
$491$		−	21.9310i		−	0.989730i	0.868970	−	0.494865i	$-0.164783\pi$
$492$		0			0
$493$		−	1.78432i		−	0.0803618i
$494$			0.757021i			0.0340600i
$495$		0			0
$496$			9.21951i			0.413968i
$497$	6.18442	−	12.0131i	0.277409	−	0.538862i
$498$		0			0
$499$	−0.0948850			−0.00424764			−0.00212382	−	0.999998i	$-0.500676\pi$
$499$	−0.0948850			−0.00424764			−0.00212382	+	0.999998i	$0.500676\pi$
$500$	3.31463			0.148235
$501$		0			0
$502$		−	10.2039i		−	0.455422i
$503$	0.568508			0.0253485			0.0126743	−	0.999920i	$-0.495966\pi$
$503$	0.568508			0.0253485			0.0126743	+	0.999920i	$0.495966\pi$
$504$		0			0
$505$	−2.34211			−0.104223
$506$		−	0.305643i		−	0.0135875i
$507$		0			0
$508$	4.39380			0.194943
$509$	29.9561			1.32778			0.663889	−	0.747831i	$-0.268905\pi$
$509$	29.9561			1.32778			0.663889	+	0.747831i	$0.268905\pi$
$510$		0			0
$511$	14.6259	−	28.4106i	0.647014	−	1.25681i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$			29.7388i			1.31172i
$515$			3.03578i			0.133772i
$516$		0			0
$517$		−	0.438869i		−	0.0193014i
$518$	6.34436	−	12.3238i	0.278755	−	0.541477i
$519$		0			0
$520$	−0.253777			−0.0111288
$521$	−20.4964			−0.897962			−0.448981	−	0.893541i	$-0.648213\pi$
$521$	−20.4964			−0.897962			−0.448981	+	0.893541i	$0.648213\pi$
$522$		0			0
$523$		−	27.0668i		−	1.18355i	−0.806103	−	0.591775i	$-0.798428\pi$
$523$		−	27.0668i		−	1.18355i	0.806103	−	0.591775i	$-0.201572\pi$
$524$	−9.40934			−0.411049
$525$		0			0
$526$	−8.14216			−0.355015
$527$		−	4.20879i		−	0.183338i
$528$		0			0
$529$	20.2780			0.881650
$530$	1.50639			0.0654332
$531$		0			0
$532$	−1.21100	+	2.35234i	−0.0525033	+	0.101987i
$533$		−	9.03314i		−	0.391269i
$534$		0			0
$535$			3.16645i			0.136898i
$536$		−	11.6219i		−	0.501991i
$537$		0			0
$538$		−	25.9102i		−	1.11707i
$539$	1.05545	−	0.753422i	0.0454616	−	0.0324522i
$540$		0			0
$541$	30.4399			1.30871			0.654357	−	0.756186i	$-0.272939\pi$
$541$	30.4399			1.30871			0.654357	+	0.756186i	$0.272939\pi$
$542$	15.2972			0.657070
$543$		0			0
$544$		−	0.456509i		−	0.0195727i
$545$	4.26948			0.182885
$546$		0			0
$547$	−21.8784			−0.935451			−0.467725	−	0.883874i	$-0.654926\pi$
$547$	−21.8784			−0.935451			−0.467725	+	0.883874i	$0.654926\pi$
$548$			2.27085i			0.0970058i
$549$		0			0
$550$	−0.905449			−0.0386085
$551$	−3.90862			−0.166513
$552$		0			0
$553$	−1.22111	−	0.628635i	−0.0519269	−	0.0267323i
$554$		−	6.68378i		−	0.283967i
$555$		0			0
$556$		−	4.39303i		−	0.186306i
$557$			16.7695i			0.710548i	0.934762	+	0.355274i	$0.115612\pi$
$557$			16.7695i			0.710548i	−0.934762	+	0.355274i	$0.884388\pi$
$558$		0			0
$559$		−	4.49442i		−	0.190094i
$560$	−0.788575	−	0.405963i	−0.0333234	−	0.0171551i
$561$		0			0
$562$	−10.3331			−0.435874
$563$	13.5027			0.569072			0.284536	−	0.958665i	$-0.408160\pi$
$563$	13.5027			0.569072			0.284536	+	0.958665i	$0.408160\pi$
$564$		0			0
$565$		−	5.69806i		−	0.239719i
$566$	−3.39813			−0.142834
$567$		0			0
$568$	5.10688			0.214280
$569$		−	36.4004i		−	1.52599i	−0.646407	−	0.762993i	$-0.723729\pi$
$569$		−	36.4004i		−	1.52599i	0.646407	−	0.762993i	$-0.276271\pi$
$570$		0			0
$571$	−19.5493			−0.818115			−0.409057	−	0.912509i	$-0.634142\pi$
$571$	−19.5493			−0.818115			−0.409057	+	0.912509i	$0.634142\pi$
$572$	0.140241			0.00586377
$573$		0			0
$574$	14.4502	−	28.0692i	0.603140	−	1.17159i
$575$			8.06390i			0.336288i
$576$		0			0
$577$			19.3784i			0.806732i	0.915039	+	0.403366i	$0.132160\pi$
$577$			19.3784i			0.806732i	−0.915039	+	0.403366i	$0.867840\pi$
$578$		−	16.7916i		−	0.698438i
$579$		0			0
$580$		−	1.31029i		−	0.0544069i
$581$	20.7436	+	10.6789i	0.860590	+	0.443037i
$582$		0			0
$583$	−0.832452			−0.0344766
$584$	12.0776			0.499775
$585$		0			0
$586$			32.4348i			1.33987i
$587$	41.2573			1.70287			0.851435	−	0.524461i	$-0.175733\pi$
$587$	41.2573			1.70287			0.851435	+	0.524461i	$0.175733\pi$
$588$		0			0
$589$	−9.21951			−0.379883
$590$		−	2.06632i		−	0.0850689i
$591$		0			0
$592$	5.23896			0.215320
$593$	41.8374			1.71806			0.859028	−	0.511928i	$-0.171068\pi$
$593$	41.8374			1.71806			0.859028	+	0.511928i	$0.171068\pi$
$594$		0			0
$595$	0.359992	+	0.185326i	0.0147582	+	0.00759762i
$596$			2.44847i			0.100293i
$597$		0			0
$598$		−	1.24898i		−	0.0510746i
$599$			46.3554i			1.89403i	0.321191	+	0.947014i	$0.395917\pi$
$599$			46.3554i			1.89403i	−0.321191	+	0.947014i	$0.604083\pi$
$600$		0			0
$601$			25.1173i			1.02456i	0.858819	+	0.512279i	$0.171198\pi$
$601$			25.1173i			1.02456i	−0.858819	+	0.512279i	$0.828802\pi$
$602$	7.18967	−	13.9658i	0.293029	−	0.569203i
$603$		0			0
$604$	4.09905			0.166788
$605$	3.67603			0.149452
$606$		0			0
$607$			8.00166i			0.324777i	0.986727	+	0.162389i	$0.0519198\pi$
$607$			8.00166i			0.324777i	−0.986727	+	0.162389i	$0.948080\pi$
$608$	−1.00000			−0.0405554
$609$		0			0
$610$	−1.61994			−0.0655895
$611$		−	1.79340i		−	0.0725530i
$612$		0			0
$613$	0.0962021			0.00388557			0.00194278	−	0.999998i	$-0.499382\pi$
$613$	0.0962021			0.00388557			0.00194278	+	0.999998i	$0.499382\pi$
$614$	−13.6149			−0.549453
$615$		0			0
$616$	0.435779	+	0.224341i	0.0175580	+	0.00903897i
$617$			22.6139i			0.910403i	0.890389	+	0.455201i	$0.150433\pi$
$617$			22.6139i			0.910403i	−0.890389	+	0.455201i	$0.849567\pi$
$618$		0			0
$619$			28.8822i			1.16087i	0.814305	+	0.580437i	$0.197118\pi$
$619$			28.8822i			1.16087i	−0.814305	+	0.580437i	$0.802882\pi$
$620$		−	3.09066i		−	0.124124i
$621$		0			0
$622$			10.5231i			0.421938i
$623$	−7.53467	−	3.87889i	−0.301870	−	0.155404i
$624$		0			0
$625$	23.3269			0.933077
$626$	21.6817			0.866574
$627$		0			0
$628$		−	11.6622i		−	0.465372i
$629$	−2.39163			−0.0953606
$630$		0			0
$631$	−6.36072			−0.253216			−0.126608	−	0.991953i	$-0.540409\pi$
$631$	−6.36072			−0.253216			−0.126608	+	0.991953i	$0.540409\pi$
$632$		−	0.519106i		−	0.0206489i
$633$		0			0
$634$	−16.2235			−0.644318
$635$	−1.47294			−0.0584517
$636$		0			0
$637$	4.31301	−	3.07879i	0.170888	−	0.121986i
$638$			0.724087i			0.0286669i
$639$		0			0
$640$		−	0.335231i		−	0.0132512i
$641$		−	29.7991i		−	1.17699i	−0.808499	−	0.588497i	$-0.799720\pi$
$641$		−	29.7991i		−	1.17699i	0.808499	−	0.588497i	$-0.200280\pi$
$642$		0			0
$643$			5.46000i			0.215321i	0.994188	+	0.107661i	$0.0343360\pi$
$643$			5.46000i			0.215321i	−0.994188	+	0.107661i	$0.965664\pi$
$644$	1.99798	−	3.88103i	0.0787313	−	0.152934i
$645$		0			0
$646$	0.456509			0.0179611
$647$	−47.9433			−1.88485			−0.942424	−	0.334421i	$-0.891459\pi$
$647$	−47.9433			−1.88485			−0.942424	+	0.334421i	$0.891459\pi$
$648$		0			0
$649$			1.14188i			0.0448226i
$650$	−3.70003			−0.145127
$651$		0			0
$652$	17.5586			0.687649
$653$		−	25.1366i		−	0.983670i	−0.870689	−	0.491835i	$-0.836326\pi$
$653$		−	25.1366i		−	0.983670i	0.870689	−	0.491835i	$-0.163674\pi$
$654$		0			0
$655$	3.15430			0.123249
$656$	11.9325			0.465885
$657$		0			0
$658$	2.86887	−	5.57273i	0.111840	−	0.217247i
$659$		−	16.2227i		−	0.631946i	−0.948768	−	0.315973i	$-0.897669\pi$
$659$		−	16.2227i		−	0.631946i	0.948768	−	0.315973i	$-0.102331\pi$
$660$		0			0
$661$		−	0.874259i		−	0.0340047i	−0.999855	−	0.0170024i	$-0.994588\pi$
$661$		−	0.874259i		−	0.0340047i	0.999855	−	0.0170024i	$-0.00541228\pi$
$662$			11.2594i			0.437608i
$663$		0			0
$664$			8.81830i			0.342217i
$665$	0.405963	−	0.788575i	0.0157426	−	0.0305796i
$666$		0			0
$667$	6.44869			0.249694
$668$	11.9515			0.462416
$669$		0			0
$670$			3.89603i			0.150517i
$671$	0.895204			0.0345590
$672$		0			0
$673$	8.09769			0.312143			0.156072	−	0.987746i	$-0.450117\pi$
$673$	8.09769			0.312143			0.156072	+	0.987746i	$0.450117\pi$
$674$			28.7008i			1.10551i
$675$		0			0
$676$	−12.4269			−0.477958
$677$	6.73366			0.258796			0.129398	−	0.991593i	$-0.458696\pi$
$677$	6.73366			0.258796			0.129398	+	0.991593i	$0.458696\pi$
$678$		0			0
$679$	19.7095	−	38.2852i	0.756379	−	1.46925i
$680$			0.153036i			0.00586865i
$681$		0			0
$682$			1.70795i			0.0654007i
$683$		−	39.6495i		−	1.51715i	−0.651588	−	0.758573i	$-0.725897\pi$
$683$		−	39.6495i		−	1.51715i	0.651588	−	0.758573i	$-0.274103\pi$
$684$		0			0
$685$		−	0.761257i		−	0.0290861i
$686$	18.3272	−	2.66744i	0.699734	−	0.101843i
$687$		0			0
$688$	5.93699			0.226345
$689$	−3.40173			−0.129596
$690$		0			0
$691$		−	1.10834i		−	0.0421632i	−0.999778	−	0.0210816i	$-0.993289\pi$
$691$		−	1.10834i		−	0.0421632i	0.999778	−	0.0210816i	$-0.00671098\pi$
$692$	−19.0517			−0.724235
$693$		0			0
$694$	29.7352			1.12873
$695$			1.47268i			0.0558619i
$696$		0			0
$697$	−5.44729			−0.206331
$698$	17.2667			0.653552
$699$		0			0
$700$	−11.4973	−	5.91889i	−0.434558	−	0.223713i
$701$			45.6448i			1.72398i	0.506924	+	0.861991i	$0.330782\pi$
$701$			45.6448i			1.72398i	−0.506924	+	0.861991i	$0.669218\pi$
$702$		0			0
$703$			5.23896i			0.197591i
$704$			0.185254i			0.00698201i
$705$		0			0
$706$			12.1035i			0.455521i
$707$	16.4348	+	8.46071i	0.618093	+	0.318198i
$708$		0			0
$709$	−18.6506			−0.700439			−0.350220	−	0.936668i	$-0.613893\pi$
$709$	−18.6506			−0.700439			−0.350220	+	0.936668i	$0.613893\pi$
$710$	−1.71198			−0.0642496
$711$		0			0
$712$		−	3.20306i		−	0.120040i
$713$	15.2109			0.569653
$714$		0			0
$715$	−0.0470130			−0.00175819
$716$		−	12.9510i		−	0.484002i
$717$		0			0
$718$	−23.3990			−0.873242
$719$	−18.6947			−0.697195			−0.348598	−	0.937272i	$-0.613342\pi$
$719$	−18.6947			−0.697195			−0.348598	+	0.937272i	$0.613342\pi$
$720$		0			0
$721$	10.9665	−	21.3023i	0.408415	−	0.793338i
$722$		−	1.00000i		−	0.0372161i
$723$		0			0
$724$		−	5.64615i		−	0.209837i
$725$		−	19.1039i		−	0.709500i
$726$		0			0
$727$			25.5941i			0.949232i	0.880193	+	0.474616i	$0.157413\pi$
$727$			25.5941i			0.949232i	−0.880193	+	0.474616i	$0.842587\pi$
$728$	1.78077	+	0.916750i	0.0659997	+	0.0339770i
$729$		0			0
$730$	−4.04879			−0.149852
$731$	−2.71029			−0.100244
$732$		0			0
$733$			25.5018i			0.941930i	0.882152	+	0.470965i	$0.156094\pi$
$733$			25.5018i			0.941930i	−0.882152	+	0.470965i	$0.843906\pi$
$734$	−12.4496			−0.459524
$735$		0			0
$736$	1.64986			0.0608147
$737$		−	2.15301i		−	0.0793070i
$738$		0			0
$739$	11.0480			0.406408			0.203204	−	0.979136i	$-0.434865\pi$
$739$	11.0480			0.406408			0.203204	+	0.979136i	$0.434865\pi$
$740$	−1.75626			−0.0645614
$741$		0			0
$742$	−10.5704	−	5.44171i	−0.388052	−	0.199771i
$743$		−	33.6803i		−	1.23561i	−0.786331	−	0.617805i	$-0.788022\pi$
$743$		−	33.6803i		−	1.23561i	0.786331	−	0.617805i	$-0.211978\pi$
$744$		0			0
$745$		−	0.820803i		−	0.0300719i
$746$			2.78536i			0.101979i
$747$		0			0
$748$		−	0.0845699i		−	0.00309218i
$749$	11.4386	−	22.2192i	0.417956	−	0.811871i
$750$		0			0
$751$	25.4142			0.927376			0.463688	−	0.885999i	$-0.346526\pi$
$751$	25.4142			0.927376			0.463688	+	0.885999i	$0.346526\pi$
$752$	2.36902			0.0863892
$753$		0			0
$754$			2.95891i			0.107757i
$755$	−1.37413			−0.0500096
$756$		0			0
$757$	10.8036			0.392663			0.196332	−	0.980538i	$-0.437097\pi$
$757$	10.8036			0.392663			0.196332	+	0.980538i	$0.437097\pi$
$758$			6.35912i			0.230974i
$759$		0			0
$760$	0.335231			0.0121601
$761$	19.3196			0.700335			0.350168	−	0.936687i	$-0.386125\pi$
$761$	19.3196			0.700335			0.350168	+	0.936687i	$0.386125\pi$
$762$		0			0
$763$	−29.9593	−	15.4232i	−1.08460	−	0.558357i
$764$			11.0980i			0.401513i
$765$		0			0
$766$			17.0337i			0.615452i
$767$			4.66617i			0.168486i
$768$		0			0
$769$			16.1081i			0.580872i	0.956894	+	0.290436i	$0.0938003\pi$
$769$			16.1081i			0.580872i	−0.956894	+	0.290436i	$0.906200\pi$
$770$	−0.146086	−	0.0752061i	−0.00526459	−	0.00271024i
$771$		0			0
$772$	5.02100			0.180710
$773$	13.2644			0.477086			0.238543	−	0.971132i	$-0.423330\pi$
$773$	13.2644			0.477086			0.238543	+	0.971132i	$0.423330\pi$
$774$		0			0
$775$		−	45.0614i		−	1.61865i
$776$	16.2754			0.584253
$777$		0			0
$778$	4.80916			0.172417
$779$			11.9325i			0.427526i
$780$		0			0
$781$	0.946068			0.0338530
$782$	−0.753176			−0.0269335
$783$		0			0
$784$	4.06698	+	5.69734i	0.145249	+	0.203477i
$785$			3.90953i			0.139537i
$786$		0			0
$787$			3.18595i			0.113567i	0.998387	+	0.0567834i	$0.0180844\pi$
$787$			3.18595i			0.113567i	−0.998387	+	0.0567834i	$0.981916\pi$
$788$			15.4710i			0.551130i
$789$		0			0
$790$			0.174020i			0.00619136i
$791$	−20.5838	+	39.9837i	−0.731876	+	1.42166i
$792$		0			0
$793$	3.65817			0.129905
$794$	2.28472			0.0810817
$795$		0			0
$796$		−	5.21243i		−	0.184750i
$797$	−41.1036			−1.45596			−0.727982	−	0.685596i	$-0.759542\pi$
$797$	−41.1036			−1.45596			−0.727982	+	0.685596i	$0.759542\pi$
$798$		0			0
$799$	−1.08148			−0.0382599
$800$		−	4.88762i		−	0.172803i
$801$		0			0
$802$	24.2802			0.857362
$803$	2.23742			0.0789569
$804$		0			0
$805$	−0.669783	+	1.30104i	−0.0236067	+	0.0458556i
$806$			6.97936i			0.245837i
$807$		0			0
$808$			6.98657i			0.245787i
$809$			14.2230i			0.500053i	0.968239	+	0.250027i	$0.0804394\pi$
$809$			14.2230i			0.500053i	−0.968239	+	0.250027i	$0.919561\pi$
$810$		0			0
$811$			4.82019i			0.169260i	0.996412	+	0.0846299i	$0.0269708\pi$
$811$			4.82019i			0.169260i	−0.996412	+	0.0846299i	$0.973029\pi$
$812$	−4.73333	+	9.19440i	−0.166107	+	0.322660i
$813$		0			0
$814$	0.970536			0.0340173
$815$	−5.88619			−0.206184
$816$		0			0
$817$			5.93699i			0.207709i
$818$	6.01833			0.210426
$819$		0			0
$820$	−4.00014			−0.139691
$821$			45.9816i			1.60477i	0.596807	+	0.802385i	$0.296436\pi$
$821$			45.9816i			1.60477i	−0.596807	+	0.802385i	$0.703564\pi$
$822$		0			0
$823$	−37.6266			−1.31158			−0.655791	−	0.754943i	$-0.727665\pi$
$823$	−37.6266			−1.31158			−0.655791	+	0.754943i	$0.727665\pi$
$824$	9.05580			0.315474
$825$		0			0
$826$	−7.46441	+	14.4995i	−0.259720	+	0.504501i
$827$			21.9153i			0.762069i	0.924561	+	0.381035i	$0.124432\pi$
$827$			21.9153i			0.762069i	−0.924561	+	0.381035i	$0.875568\pi$
$828$		0			0
$829$		−	5.98931i		−	0.208017i	−0.994576	−	0.104009i	$-0.966833\pi$
$829$		−	5.98931i		−	0.208017i	0.994576	−	0.104009i	$-0.0331670\pi$
$830$		−	2.95617i		−	0.102610i
$831$		0			0
$832$			0.757021i			0.0262450i
$833$	−1.85661	−	2.60089i	−0.0643277	−	0.0901154i
$834$		0			0
$835$	−4.00649			−0.138650
$836$	−0.185254			−0.00640713
$837$		0			0
$838$			8.32697i			0.287650i
$839$	−42.0006			−1.45002			−0.725011	−	0.688737i	$-0.758165\pi$
$839$	−42.0006			−1.45002			−0.725011	+	0.688737i	$0.758165\pi$
$840$		0			0
$841$	13.7227			0.473195
$842$		−	25.5208i		−	0.879506i
$843$		0			0
$844$	11.1551			0.383975
$845$	4.16588			0.143311
$846$		0			0
$847$	−25.7950	−	13.2794i	−0.886326	−	0.456286i
$848$		−	4.49358i		−	0.154310i
$849$		0			0
$850$			2.23124i			0.0765310i
$851$		−	8.64356i		−	0.296297i
$852$		0			0
$853$		−	14.4255i		−	0.493919i	−0.969026	−	0.246960i	$-0.920569\pi$
$853$		−	14.4255i		−	0.493919i	0.969026	−	0.246960i	$-0.0794315\pi$
$854$	11.3672	+	5.85192i	0.388979	+	0.200249i
$855$		0			0
$856$	9.44558			0.322843
$857$	−9.25307			−0.316079			−0.158039	−	0.987433i	$-0.550517\pi$
$857$	−9.25307			−0.316079			−0.158039	+	0.987433i	$0.550517\pi$
$858$		0			0
$859$		−	37.7183i		−	1.28693i	−0.765474	−	0.643466i	$-0.777496\pi$
$859$		−	37.7183i		−	1.28693i	0.765474	−	0.643466i	$-0.222504\pi$
$860$	−1.99026			−0.0678673
$861$		0			0
$862$	−0.484959			−0.0165178
$863$		−	14.3315i		−	0.487851i	−0.969794	−	0.243926i	$-0.921565\pi$
$863$		−	14.3315i		−	0.487851i	0.969794	−	0.243926i	$-0.0784353\pi$
$864$		0			0
$865$	6.38670			0.217154
$866$	−13.0041			−0.441897
$867$		0			0
$868$	−11.1648	+	21.6874i	−0.378958	+	0.736118i
$869$		−	0.0961662i		−	0.00326222i
$870$		0			0
$871$		−	8.79806i		−	0.298111i
$872$		−	12.7360i		−	0.431294i
$873$		0			0
$874$			1.64986i			0.0558074i
$875$	7.79713	+	4.01401i	0.263591	+	0.135698i
$876$		0			0
$877$	−31.3302			−1.05795			−0.528973	−	0.848639i	$-0.677423\pi$
$877$	−31.3302			−1.05795			−0.528973	+	0.848639i	$0.677423\pi$
$878$	20.0339			0.676110
$879$		0			0
$880$		−	0.0621027i		−	0.00209348i
$881$	21.4228			0.721753			0.360876	−	0.932614i	$-0.382478\pi$
$881$	21.4228			0.721753			0.360876	+	0.932614i	$0.382478\pi$
$882$		0			0
$883$	33.1919			1.11700			0.558498	−	0.829506i	$-0.311378\pi$
$883$	33.1919			1.11700			0.558498	+	0.829506i	$0.311378\pi$
$884$		−	0.345587i		−	0.0116233i
$885$		0			0
$886$	13.3813			0.449554
$887$	−19.8206			−0.665512			−0.332756	−	0.943013i	$-0.607979\pi$
$887$	−19.8206			−0.665512			−0.332756	+	0.943013i	$0.607979\pi$
$888$		0			0
$889$	10.3357	+	5.32087i	0.346648	+	0.178456i
$890$			1.07376i			0.0359926i
$891$		0			0
$892$			27.3838i			0.916878i
$893$			2.36902i			0.0792761i
$894$		0			0
$895$			4.34157i			0.145123i
$896$	−1.21100	+	2.35234i	−0.0404565	+	0.0785861i
$897$		0			0
$898$	21.4895			0.717114
$899$	−36.0356			−1.20185
$900$		0			0
$901$			2.05136i			0.0683407i
$902$	2.21054			0.0736028
$903$		0			0
$904$	−16.9974			−0.565326
$905$			1.89276i			0.0629175i
$906$		0			0
$907$	47.5431			1.57864			0.789322	−	0.613980i	$-0.210432\pi$
$907$	47.5431			1.57864			0.789322	+	0.613980i	$0.210432\pi$
$908$	14.1354			0.469101
$909$		0			0
$910$	−0.596968	−	0.307323i	−0.0197893	−	0.0101876i
$911$		−	9.15848i		−	0.303434i	−0.988424	−	0.151717i	$-0.951520\pi$
$911$		−	9.15848i		−	0.303434i	0.988424	−	0.151717i	$-0.0484802\pi$
$912$		0			0
$913$			1.63362i			0.0540650i
$914$		−	27.4559i		−	0.908161i
$915$		0			0
$916$		−	20.5265i		−	0.678216i
$917$	−22.1339	−	11.3947i	−0.730927	−	0.376285i
$918$		0			0
$919$	−41.1704			−1.35809			−0.679043	−	0.734099i	$-0.737605\pi$
$919$	−41.1704			−1.35809			−0.679043	+	0.734099i	$0.737605\pi$
$920$	−0.553084			−0.0182346
$921$		0			0
$922$		−	18.3684i		−	0.604931i
$923$	3.86602			0.127252
$924$		0			0
$925$	−25.6061			−0.841922
$926$		−	6.44046i		−	0.211647i
$927$		0			0
$928$	−3.90862			−0.128307
$929$	5.86170			0.192316			0.0961581	−	0.995366i	$-0.469345\pi$
$929$	5.86170			0.192316			0.0961581	+	0.995366i	$0.469345\pi$
$930$		0			0
$931$	−5.69734	+	4.06698i	−0.186723	+	0.133290i
$932$			2.91114i			0.0953577i
$933$		0			0
$934$			25.6442i			0.839103i
$935$			0.0283504i			0.000927158i
$936$		0			0
$937$			21.9623i			0.717478i	0.933438	+	0.358739i	$0.116793\pi$
$937$			21.9623i			0.717478i	−0.933438	+	0.358739i	$0.883207\pi$
$938$	14.0741	−	27.3387i	0.459537	−	0.892641i
$939$		0			0
$940$	−0.794167			−0.0259029
$941$	−17.1006			−0.557462			−0.278731	−	0.960369i	$-0.589914\pi$
$941$	−17.1006			−0.557462			−0.278731	+	0.960369i	$0.589914\pi$
$942$		0			0
$943$		−	19.6870i		−	0.641095i
$944$	−6.16386			−0.200617
$945$		0			0
$946$	1.09985			0.0357591
$947$			55.3886i			1.79989i	0.436006	+	0.899944i	$0.356392\pi$
$947$			55.3886i			1.79989i	−0.436006	+	0.899944i	$0.643608\pi$
$948$		0			0
$949$	9.14301			0.296795
$950$	4.88762			0.158575
$951$		0			0
$952$	0.552831	−	1.07386i	0.0179173	−	0.0348041i
$953$		−	5.72474i		−	0.185442i	−0.995692	−	0.0927212i	$-0.970443\pi$
$953$		−	5.72474i		−	0.185442i	0.995692	−	0.0927212i	$-0.0295565\pi$
$954$		0			0
$955$		−	3.72040i		−	0.120389i
$956$		−	16.1133i		−	0.521143i
$957$		0			0
$958$		−	11.5000i		−	0.371548i
$959$	−2.74999	+	5.34180i	−0.0888017	+	0.172496i
$960$		0			0
$961$	−53.9993			−1.74191
$962$	3.96600			0.127869
$963$		0			0
$964$		−	20.6759i		−	0.665924i
$965$	−1.68319			−0.0541839
$966$		0			0
$967$	0.602657			0.0193801			0.00969007	−	0.999953i	$-0.496916\pi$
$967$	0.602657			0.0193801			0.00969007	+	0.999953i	$0.496916\pi$
$968$		−	10.9657i		−	0.352450i
$969$		0			0
$970$	−5.45601			−0.175182
$971$	−33.1846			−1.06494			−0.532472	−	0.846448i	$-0.678737\pi$
$971$	−33.1846			−1.06494			−0.532472	+	0.846448i	$0.678737\pi$
$972$		0			0
$973$	5.31995	−	10.3339i	0.170550	−	0.331289i
$974$		−	19.9663i		−	0.639763i
$975$		0			0
$976$			4.83232i			0.154679i
$977$			10.6340i			0.340211i	0.985426	+	0.170105i	$0.0544108\pi$
$977$			10.6340i			0.340211i	−0.985426	+	0.170105i	$0.945589\pi$
$978$		0			0
$979$		−	0.593378i		−	0.0189644i
$980$	−1.36337	−	1.90992i	−0.0435514	−	0.0610103i
$981$		0			0
$982$	21.9310			0.699845
$983$	−45.3442			−1.44626			−0.723128	−	0.690714i	$-0.757296\pi$
$983$	−45.3442			−1.44626			−0.723128	+	0.690714i	$0.757296\pi$
$984$		0			0
$985$		−	5.18634i		−	0.165250i
$986$	1.78432			0.0568244
$987$		0			0
$988$	−0.757021			−0.0240840
$989$		−	9.79520i		−	0.311469i
$990$		0			0
$991$	−37.9935			−1.20690			−0.603451	−	0.797400i	$-0.706208\pi$
$991$	−37.9935			−1.20690			−0.603451	+	0.797400i	$0.706208\pi$
$992$	−9.21951			−0.292720
$993$		0			0
$994$	12.0131	+	6.18442i	0.381033	+	0.196158i
$995$			1.74737i			0.0553952i
$996$		0			0
$997$		−	17.7690i		−	0.562748i	−0.959598	−	0.281374i	$-0.909210\pi$
$997$		−	17.7690i		−	0.562748i	0.959598	−	0.281374i	$-0.0907902\pi$
$998$		−	0.0948850i		−	0.00300353i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2394.2.f.b.2015.14	yes	24
3.2	odd	2		2394.2.f.a.2015.13	✓	24
7.6	odd	2		2394.2.f.a.2015.14	yes	24
21.20	even	2	inner	2394.2.f.b.2015.13	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2394.2.f.a.2015.13	✓	24	3.2	odd	2
2394.2.f.a.2015.14	yes	24	7.6	odd	2
2394.2.f.b.2015.13	yes	24	21.20	even	2	inner
2394.2.f.b.2015.14	yes	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2394.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +0.335231 q^{5} +(-2.35234 - 1.21100i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +0.335231 q^{5} +(-2.35234 - 1.21100i) q^{7} -1.00000i q^{8} +0.335231i q^{10} -0.185254i q^{11} -0.757021i q^{13} +(1.21100 - 2.35234i) q^{14} +1.00000 q^{16} -0.456509 q^{17} +1.00000i q^{19} -0.335231 q^{20} +0.185254 q^{22} -1.64986i q^{23} -4.88762 q^{25} +0.757021 q^{26} +(2.35234 + 1.21100i) q^{28} +3.90862i q^{29} +9.21951i q^{31} +1.00000i q^{32} -0.456509i q^{34} +(-0.788575 - 0.405963i) q^{35} +5.23896 q^{37} -1.00000 q^{38} -0.335231i q^{40} +11.9325 q^{41} +5.93699 q^{43} +0.185254i q^{44} +1.64986 q^{46} +2.36902 q^{47} +(4.06698 + 5.69734i) q^{49} -4.88762i q^{50} +0.757021i q^{52} -4.49358i q^{53} -0.0621027i q^{55} +(-1.21100 + 2.35234i) q^{56} -3.90862 q^{58} -6.16386 q^{59} +4.83232i q^{61} -9.21951 q^{62} -1.00000 q^{64} -0.253777i q^{65} +11.6219 q^{67} +0.456509 q^{68} +(0.405963 - 0.788575i) q^{70} +5.10688i q^{71} +12.0776i q^{73} +5.23896i q^{74} -1.00000i q^{76} +(-0.224341 + 0.435779i) q^{77} +0.519106 q^{79} +0.335231 q^{80} +11.9325i q^{82} -8.81830 q^{83} -0.153036 q^{85} +5.93699i q^{86} -0.185254 q^{88} +3.20306 q^{89} +(-0.916750 + 1.78077i) q^{91} +1.64986i q^{92} +2.36902i q^{94} +0.335231i q^{95} +16.2754i q^{97} +(-5.69734 + 4.06698i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} + 4 q^{7}+O(q^{10}) \) 24 * q - 24 * q^4 + 4 * q^7	\( 24 q - 24 q^{4} + 4 q^{7} + 4 q^{14} + 24 q^{16} - 32 q^{17} - 8 q^{22} + 16 q^{25} - 4 q^{28} + 24 q^{35} - 24 q^{38} + 8 q^{41} + 16 q^{43} - 8 q^{46} - 16 q^{49} - 4 q^{56} + 16 q^{58} - 16 q^{59} + 16 q^{62} - 24 q^{64} - 24 q^{67} + 32 q^{68} - 16 q^{70} - 8 q^{77} - 40 q^{79} + 64 q^{83} + 40 q^{85} + 8 q^{88} + 64 q^{89} + 8 q^{91} + 16 q^{98}+O(q^{100}) \) 24 * q - 24 * q^4 + 4 * q^7 + 4 * q^14 + 24 * q^16 - 32 * q^17 - 8 * q^22 + 16 * q^25 - 4 * q^28 + 24 * q^35 - 24 * q^38 + 8 * q^41 + 16 * q^43 - 8 * q^46 - 16 * q^49 - 4 * q^56 + 16 * q^58 - 16 * q^59 + 16 * q^62 - 24 * q^64 - 24 * q^67 + 32 * q^68 - 16 * q^70 - 8 * q^77 - 40 * q^79 + 64 * q^83 + 40 * q^85 + 8 * q^88 + 64 * q^89 + 8 * q^91 + 16 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more