LMFDB - Embedded newform 1620.4.i.v.541.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1620,4,Mod(541,1620)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1620, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1620.541");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1620 = 2^{2} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1620.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$95.5830942093$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 91x^{4} + 570x^{3} + 7860x^{2} + 21600x + 57600 $ x^6 - x^5 + 91x^4 + 570x^3 + 7860x^2 + 21600x + 57600
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.3
Root			$5.53944 + 9.59460i$ of defining polynomial
Character	$\chi$	$=$	1620.541
Dual form			1620.4.i.v.1081.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.50000 + 4.33013i) q^{5} +(13.4157 - 23.2367i) q^{7} +O(q^{10})$	$q+(2.50000 + 4.33013i) q^{5} +(13.4157 - 23.2367i) q^{7} +(-23.3210 + 40.3931i) q^{11} +(-0.605219 - 1.04827i) q^{13} +87.2838 q^{17} -125.136 q^{19} +(3.58429 + 6.20818i) q^{23} +(-12.5000 + 21.6506i) q^{25} +(-21.9157 + 37.9591i) q^{29} +(-70.1733 - 121.544i) q^{31} +134.157 q^{35} -187.030 q^{37} +(119.952 + 207.764i) q^{41} +(-228.778 + 396.255i) q^{43} +(12.8053 - 22.1795i) q^{47} +(-188.462 - 326.426i) q^{49} -82.8314 q^{53} -233.210 q^{55} +(-369.787 - 640.490i) q^{59} +(14.3153 - 24.7949i) q^{61} +(3.02610 - 5.24135i) q^{65} +(63.1046 + 109.300i) q^{67} -611.336 q^{71} +983.531 q^{73} +(625.734 + 1083.80i) q^{77} +(-186.369 + 322.800i) q^{79} +(-346.640 + 600.398i) q^{83} +(218.210 + 377.950i) q^{85} -873.848 q^{89} -32.4778 q^{91} +(-312.840 - 541.855i) q^{95} +(41.3769 - 71.6669i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 15 q^{5} + 3 q^{7}+O(q^{10}) $ 6 * q + 15 * q^5 + 3 * q^7	$ 6 q + 15 q^{5} + 3 q^{7} - 24 q^{11} - 3 q^{13} + 60 q^{17} - 54 q^{19} + 99 q^{23} - 75 q^{25} - 54 q^{29} - 72 q^{31} + 30 q^{35} - 36 q^{37} + 411 q^{41} - 444 q^{43} - 75 q^{47} - 204 q^{49} - 342 q^{53} - 240 q^{55} + 297 q^{59} - 684 q^{61} + 15 q^{65} - 12 q^{67} - 1284 q^{71} - 132 q^{73} + 1044 q^{77} - 1122 q^{79} + 90 q^{83} + 150 q^{85} - 1512 q^{89} - 3306 q^{91} - 135 q^{95} - 1536 q^{97}+O(q^{100}) $ 6 * q + 15 * q^5 + 3 * q^7 - 24 * q^11 - 3 * q^13 + 60 * q^17 - 54 * q^19 + 99 * q^23 - 75 * q^25 - 54 * q^29 - 72 * q^31 + 30 * q^35 - 36 * q^37 + 411 * q^41 - 444 * q^43 - 75 * q^47 - 204 * q^49 - 342 * q^53 - 240 * q^55 + 297 * q^59 - 684 * q^61 + 15 * q^65 - 12 * q^67 - 1284 * q^71 - 132 * q^73 + 1044 * q^77 - 1122 * q^79 + 90 * q^83 + 150 * q^85 - 1512 * q^89 - 3306 * q^91 - 135 * q^95 - 1536 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$6$		0			0
$7$	13.4157	−	23.2367i	0.724380	−	1.25466i	−0.234849	−	0.972032i	$-0.575459\pi$
$7$	13.4157	−	23.2367i	0.724380	−	1.25466i	0.959229	−	0.282631i	$-0.0912072\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−23.3210	+	40.3931i	−0.639230	+	1.10718i	0.346372	+	0.938097i	$0.387414\pi$
$11$	−23.3210	+	40.3931i	−0.639230	+	1.10718i	−0.985602	+	0.169082i	$0.945920\pi$
$12$		0			0
$13$	−0.605219	−	1.04827i	−0.0129121	−	0.0223645i	0.859497	−	0.511141i	$-0.170777\pi$
$13$	−0.605219	−	1.04827i	−0.0129121	−	0.0223645i	−0.872409	+	0.488776i	$0.837444\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	87.2838			1.24526			0.622630	−	0.782516i	$-0.286064\pi$
$17$	87.2838			1.24526			0.622630	+	0.782516i	$0.286064\pi$
$18$		0			0
$19$	−125.136			−1.51096			−0.755479	−	0.655173i	$-0.772596\pi$
$19$	−125.136			−1.51096			−0.755479	+	0.655173i	$0.772596\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.58429	+	6.20818i	0.0324946	+	0.0562824i	0.881815	−	0.471595i	$-0.156321\pi$
$23$	3.58429	+	6.20818i	0.0324946	+	0.0562824i	−0.849321	+	0.527877i	$0.822988\pi$
$24$		0			0
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−21.9157	+	37.9591i	−0.140333	+	0.243063i	−0.927622	−	0.373521i	$-0.878151\pi$
$29$	−21.9157	+	37.9591i	−0.140333	+	0.243063i	0.787289	+	0.616584i	$0.211484\pi$
$30$		0			0
$31$	−70.1733	−	121.544i	−0.406564	−	0.704190i	0.587938	−	0.808906i	$-0.299940\pi$
$31$	−70.1733	−	121.544i	−0.406564	−	0.704190i	−0.994502	+	0.104716i	$0.966607\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	134.157			0.647905
$36$		0			0
$37$	−187.030			−0.831016			−0.415508	−	0.909589i	$-0.636396\pi$
$37$	−187.030			−0.831016			−0.415508	+	0.909589i	$0.636396\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	119.952	+	207.764i	0.456913	+	0.791396i	0.998796	−	0.0490579i	$-0.0156219\pi$
$41$	119.952	+	207.764i	0.456913	+	0.791396i	−0.541883	+	0.840454i	$0.682289\pi$
$42$		0			0
$43$	−228.778	+	396.255i	−0.811356	+	1.40531i	0.100559	+	0.994931i	$0.467937\pi$
$43$	−228.778	+	396.255i	−0.811356	+	1.40531i	−0.911915	+	0.410379i	$0.865396\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	12.8053	−	22.1795i	0.0397414	−	0.0688342i	−0.845471	−	0.534022i	$-0.820680\pi$
$47$	12.8053	−	22.1795i	0.0397414	−	0.0688342i	0.885212	+	0.465188i	$0.154013\pi$
$48$		0			0
$49$	−188.462	−	326.426i	−0.549453	−	0.951681i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−82.8314			−0.214675			−0.107337	−	0.994223i	$-0.534233\pi$
$53$	−82.8314			−0.214675			−0.107337	+	0.994223i	$0.534233\pi$
$54$		0			0
$55$	−233.210			−0.571745
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−369.787	−	640.490i	−0.815969	−	1.41330i	−0.908630	−	0.417602i	$-0.862871\pi$
$59$	−369.787	−	640.490i	−0.815969	−	1.41330i	0.0926612	−	0.995698i	$-0.470463\pi$
$60$		0			0
$61$	14.3153	−	24.7949i	0.0300474	−	0.0520435i	−0.850611	−	0.525796i	$-0.823768\pi$
$61$	14.3153	−	24.7949i	0.0300474	−	0.0520435i	0.880658	+	0.473752i	$0.157101\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.02610	−	5.24135i	0.00577448	−	0.0100017i
$66$		0			0
$67$	63.1046	+	109.300i	0.115067	+	0.199301i	0.917806	−	0.397028i	$-0.129959\pi$
$67$	63.1046	+	109.300i	0.115067	+	0.199301i	−0.802740	+	0.596329i	$0.796625\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−611.336			−1.02186			−0.510931	−	0.859622i	$-0.670699\pi$
$71$	−611.336			−1.02186			−0.510931	+	0.859622i	$0.670699\pi$
$72$		0			0
$73$	983.531			1.57690			0.788449	−	0.615100i	$-0.210884\pi$
$73$	983.531			1.57690			0.788449	+	0.615100i	$0.210884\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	625.734	+	1083.80i	0.926091	+	1.60404i
$78$		0			0
$79$	−186.369	+	322.800i	−0.265419	+	0.459720i	−0.967673	−	0.252207i	$-0.918844\pi$
$79$	−186.369	+	322.800i	−0.265419	+	0.459720i	0.702254	+	0.711926i	$0.252177\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−346.640	+	600.398i	−0.458418	+	0.794003i	−0.998878	−	0.0473672i	$-0.984917\pi$
$83$	−346.640	+	600.398i	−0.458418	+	0.794003i	0.540460	+	0.841370i	$0.318250\pi$
$84$		0			0
$85$	218.210	+	377.950i	0.278449	+	0.482287i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−873.848			−1.04076			−0.520380	−	0.853935i	$-0.674210\pi$
$89$	−873.848			−1.04076			−0.520380	+	0.853935i	$0.674210\pi$
$90$		0			0
$91$	−32.4778			−0.0374131
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−312.840	−	541.855i	−0.337860	−	0.585191i
$96$		0			0
$97$	41.3769	−	71.6669i	0.0433112	−	0.0750173i	−0.843557	−	0.537039i	$-0.819543\pi$
$97$	41.3769	−	71.6669i	0.0433112	−	0.0750173i	0.886868	+	0.462022i	$0.152876\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	663.155	−	1148.62i	0.653331	−	1.13160i	−0.328979	−	0.944337i	$-0.606704\pi$
$101$	663.155	−	1148.62i	0.653331	−	1.13160i	0.982309	−	0.187265i	$-0.0599623\pi$
$102$		0			0
$103$	834.307	+	1445.06i	0.798124	+	1.38239i	0.920837	+	0.389948i	$0.127507\pi$
$103$	834.307	+	1445.06i	0.798124	+	1.38239i	−0.122713	+	0.992442i	$0.539160\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−192.253			−0.173699			−0.0868495	−	0.996221i	$-0.527680\pi$
$107$	−192.253			−0.173699			−0.0868495	+	0.996221i	$0.527680\pi$
$108$		0			0
$109$	−1645.59			−1.44605			−0.723025	−	0.690822i	$-0.757249\pi$
$109$	−1645.59			−1.44605			−0.723025	+	0.690822i	$0.757249\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	778.479	+	1348.37i	0.648081	+	1.12251i	0.983581	+	0.180469i	$0.0577616\pi$
$113$	778.479	+	1348.37i	0.648081	+	1.12251i	−0.335499	+	0.942040i	$0.608905\pi$
$114$		0			0
$115$	−17.9215	+	31.0409i	−0.0145320	+	0.0251702i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1170.97	−	2028.19i	0.902042	−	1.56238i
$120$		0			0
$121$	−422.233	−	731.330i	−0.317230	−	0.549459i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−125.000			−0.0894427
$126$		0			0
$127$	−409.005			−0.285774			−0.142887	−	0.989739i	$-0.545639\pi$
$127$	−409.005			−0.285774			−0.142887	+	0.989739i	$0.545639\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	1453.16	+	2516.95i	0.969186	+	1.67868i	0.697921	+	0.716174i	$0.254109\pi$
$131$	1453.16	+	2516.95i	0.969186	+	1.67868i	0.271265	+	0.962505i	$0.412558\pi$
$132$		0			0
$133$	−1678.79	+	2907.75i	−1.09451	+	1.89574i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	944.999	−	1636.79i	0.589319	−	1.02073i	−0.405002	−	0.914316i	$-0.632729\pi$
$137$	944.999	−	1636.79i	0.589319	−	1.02073i	0.994322	−	0.106415i	$-0.0339373\pi$
$138$		0			0
$139$	1354.77	+	2346.53i	0.826693	+	1.43187i	0.900619	+	0.434610i	$0.143114\pi$
$139$	1354.77	+	2346.53i	0.826693	+	1.43187i	−0.0739261	+	0.997264i	$0.523553\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	56.4572			0.0330153
$144$		0			0
$145$	−219.157			−0.125517
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−682.194	−	1181.59i	−0.375084	−	0.649664i	0.615256	−	0.788327i	$-0.289053\pi$
$149$	−682.194	−	1181.59i	−0.375084	−	0.649664i	−0.990340	+	0.138663i	$0.955719\pi$
$150$		0			0
$151$	−441.446	+	764.607i	−0.237910	+	0.412072i	−0.960114	−	0.279608i	$-0.909796\pi$
$151$	−441.446	+	764.607i	−0.237910	+	0.412072i	0.722204	+	0.691680i	$0.243129\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	350.866	−	607.719i	0.181821	−	0.314923i
$156$		0			0
$157$	−598.169	−	1036.06i	−0.304071	−	0.526666i	0.672983	−	0.739658i	$-0.265013\pi$
$157$	−598.169	−	1036.06i	−0.304071	−	0.526666i	−0.977054	+	0.212992i	$0.931679\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	192.343			0.0941539
$162$		0			0
$163$	−2328.91			−1.11910			−0.559552	−	0.828795i	$-0.689027\pi$
$163$	−2328.91			−1.11910			−0.559552	+	0.828795i	$0.689027\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−774.846	−	1342.07i	−0.359038	−	0.621873i	0.628762	−	0.777598i	$-0.283562\pi$
$167$	−774.846	−	1342.07i	−0.359038	−	0.621873i	−0.987800	+	0.155725i	$0.950229\pi$
$168$		0			0
$169$	1097.77	−	1901.39i	0.499667	−	0.865448i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1203.07	+	2083.77i	−0.528714	+	0.915759i	0.470725	+	0.882280i	$0.343992\pi$
$173$	−1203.07	+	2083.77i	−0.528714	+	0.915759i	−0.999439	+	0.0334797i	$0.989341\pi$
$174$		0			0
$175$	335.393	+	580.917i	0.144876	+	0.250933i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	115.757			0.0483358			0.0241679	−	0.999708i	$-0.492306\pi$
$179$	115.757			0.0483358			0.0241679	+	0.999708i	$0.492306\pi$
$180$		0			0
$181$	−2214.21			−0.909285			−0.454643	−	0.890674i	$-0.650233\pi$
$181$	−2214.21			−0.909285			−0.454643	+	0.890674i	$0.650233\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−467.576	−	809.865i	−0.185821	−	0.321851i
$186$		0			0
$187$	−2035.54	+	3525.66i	−0.796008	+	1.37873i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1355.40	+	2347.63i	−0.513474	+	0.889364i	0.486403	+	0.873734i	$0.338309\pi$
$191$	−1355.40	+	2347.63i	−0.513474	+	0.889364i	−0.999878	+	0.0156295i	$0.995025\pi$
$192$		0			0
$193$	−2168.38	−	3755.74i	−0.808721	−	1.40075i	−0.913750	−	0.406277i	$-0.866827\pi$
$193$	−2168.38	−	3755.74i	−0.808721	−	1.40075i	0.105029	−	0.994469i	$-0.466506\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−4840.88			−1.75075			−0.875376	−	0.483443i	$-0.839386\pi$
$197$	−4840.88			−1.75075			−0.875376	+	0.483443i	$0.839386\pi$
$198$		0			0
$199$	−4580.41			−1.63164			−0.815820	−	0.578306i	$-0.803714\pi$
$199$	−4580.41			−1.63164			−0.815820	+	0.578306i	$0.803714\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	588.029	+	1018.50i	0.203308	+	0.352140i
$204$		0			0
$205$	−599.762	+	1038.82i	−0.204338	+	0.353923i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2918.29	−	5054.63i	0.965850	−	1.67290i
$210$		0			0
$211$	−985.215	−	1706.44i	−0.321445	−	0.556760i	0.659341	−	0.751844i	$-0.270835\pi$
$211$	−985.215	−	1706.44i	−0.321445	−	0.556760i	−0.980787	+	0.195084i	$0.937502\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−2287.78			−0.725699
$216$		0			0
$217$	−3765.70			−1.17803
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−52.8258	−	91.4970i	−0.0160790	−	0.0278496i
$222$		0			0
$223$	−2564.10	+	4441.15i	−0.769977	+	1.33364i	0.167598	+	0.985855i	$0.446399\pi$
$223$	−2564.10	+	4441.15i	−0.769977	+	1.33364i	−0.937575	+	0.347784i	$0.886934\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1581.81	+	2739.78i	−0.462505	+	0.801082i	−0.999085	−	0.0427674i	$-0.986383\pi$
$227$	−1581.81	+	2739.78i	−0.462505	+	0.801082i	0.536580	+	0.843849i	$0.319716\pi$
$228$		0			0
$229$	1977.57	+	3425.25i	0.570662	+	0.988415i	0.996498	+	0.0836149i	$0.0266466\pi$
$229$	1977.57	+	3425.25i	0.570662	+	0.988415i	−0.425836	+	0.904800i	$0.640020\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−111.366			−0.0313126			−0.0156563	−	0.999877i	$-0.504984\pi$
$233$	−111.366			−0.0313126			−0.0156563	+	0.999877i	$0.504984\pi$
$234$		0			0
$235$	128.053			0.0355458
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1309.17	+	2267.55i	0.354322	+	0.613705i	0.987002	−	0.160709i	$-0.0513782\pi$
$239$	1309.17	+	2267.55i	0.354322	+	0.613705i	−0.632679	+	0.774414i	$0.718045\pi$
$240$		0			0
$241$	−2743.28	+	4751.50i	−0.733237	+	1.27000i	0.222255	+	0.974989i	$0.428658\pi$
$241$	−2743.28	+	4751.50i	−0.733237	+	1.27000i	−0.955492	+	0.295016i	$0.904675\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	942.312	−	1632.13i	0.245723	−	0.425604i
$246$		0			0
$247$	75.7348	+	131.177i	0.0195097	+	0.0337917i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−517.287			−0.130083			−0.0650416	−	0.997883i	$-0.520718\pi$
$251$	−517.287			−0.130083			−0.0650416	+	0.997883i	$0.520718\pi$
$252$		0			0
$253$	−334.356			−0.0830862
$254$		0			0
$255$		0			0
$256$		0			0
$257$	2187.00	+	3787.99i	0.530822	+	0.919410i	0.999353	+	0.0359634i	$0.0114500\pi$
$257$	2187.00	+	3787.99i	0.530822	+	0.919410i	−0.468531	+	0.883447i	$0.655217\pi$
$258$		0			0
$259$	−2509.14	+	4345.97i	−0.601972	+	1.04265i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	1502.91	−	2603.12i	0.352371	−	0.610324i	−0.634293	−	0.773092i	$-0.718709\pi$
$263$	1502.91	−	2603.12i	0.352371	−	0.610324i	0.986664	+	0.162768i	$0.0520422\pi$
$264$		0			0
$265$	−207.079	−	358.671i	−0.0480028	−	0.0831432i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−3265.82			−0.740224			−0.370112	−	0.928987i	$-0.620681\pi$
$269$	−3265.82			−0.740224			−0.370112	+	0.928987i	$0.620681\pi$
$270$		0			0
$271$	−6523.97			−1.46237			−0.731186	−	0.682178i	$-0.761033\pi$
$271$	−6523.97			−1.46237			−0.731186	+	0.682178i	$0.761033\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−583.024	−	1009.83i	−0.127846	−	0.221436i
$276$		0			0
$277$	−2008.58	+	3478.97i	−0.435683	+	0.754624i	−0.997351	−	0.0727381i	$-0.976826\pi$
$277$	−2008.58	+	3478.97i	−0.435683	+	0.754624i	0.561669	+	0.827362i	$0.310160\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	2204.16	−	3817.72i	0.467933	−	0.810484i	−0.531395	−	0.847124i	$-0.678332\pi$
$281$	2204.16	−	3817.72i	0.467933	−	0.810484i	0.999329	+	0.0366399i	$0.0116654\pi$
$282$		0			0
$283$	−2896.85	−	5017.48i	−0.608479	−	1.05392i	−0.991491	−	0.130173i	$-0.958447\pi$
$283$	−2896.85	−	5017.48i	−0.608479	−	1.05392i	0.383012	−	0.923743i	$-0.374887\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	6436.98			1.32391
$288$		0			0
$289$	2705.46			0.550674
$290$		0			0
$291$		0			0
$292$		0			0
$293$	3517.64	+	6092.73i	0.701375	+	1.21482i	0.967984	+	0.251012i	$0.0807633\pi$
$293$	3517.64	+	6092.73i	0.701375	+	1.21482i	−0.266609	+	0.963805i	$0.585903\pi$
$294$		0			0
$295$	1848.93	−	3202.45i	0.364912	−	0.632047i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	4.33857	−	7.51462i	0.000839150	−	0.00145345i
$300$		0			0
$301$	6138.44	+	10632.1i	1.17546	+	2.03596i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	143.153			0.0268752
$306$		0			0
$307$	2744.60			0.510236			0.255118	−	0.966910i	$-0.417886\pi$
$307$	2744.60			0.510236			0.255118	+	0.966910i	$0.417886\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	3818.79	+	6614.33i	0.696281	+	1.20599i	0.969747	+	0.244113i	$0.0784967\pi$
$311$	3818.79	+	6614.33i	0.696281	+	1.20599i	−0.273466	+	0.961882i	$0.588170\pi$
$312$		0			0
$313$	1562.93	−	2707.08i	0.282243	−	0.488859i	−0.689694	−	0.724101i	$-0.742255\pi$
$313$	1562.93	−	2707.08i	0.282243	−	0.488859i	0.971937	+	0.235242i	$0.0755882\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2400.29	−	4157.42i	0.425280	−	0.736606i	−0.571167	−	0.820834i	$-0.693509\pi$
$317$	2400.29	−	4157.42i	0.425280	−	0.736606i	0.996447	+	0.0842278i	$0.0268424\pi$
$318$		0			0
$319$	−1022.19	−	1770.49i	−0.179410	−	0.310747i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−10922.4			−1.88154
$324$		0			0
$325$	30.2610			0.00516485
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−343.585	−	595.106i	−0.0575758	−	0.0997242i
$330$		0			0
$331$	−1034.38	+	1791.60i	−0.171766	+	0.297508i	−0.939037	−	0.343815i	$-0.888281\pi$
$331$	−1034.38	+	1791.60i	−0.171766	+	0.297508i	0.767271	+	0.641323i	$0.221614\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−315.523	+	546.502i	−0.0514593	+	0.0891302i
$336$		0			0
$337$	4961.92	+	8594.30i	0.802057	+	1.38920i	0.918260	+	0.395978i	$0.129594\pi$
$337$	4961.92	+	8594.30i	0.802057	+	1.38920i	−0.116203	+	0.993225i	$0.537072\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	6546.03			1.03955
$342$		0			0
$343$	−910.250			−0.143291
$344$		0			0
$345$		0			0
$346$		0			0
$347$	2815.82	+	4877.14i	0.435623	+	0.754520i	0.997346	−	0.0728045i	$-0.0231949\pi$
$347$	2815.82	+	4877.14i	0.435623	+	0.754520i	−0.561724	+	0.827325i	$0.689862\pi$
$348$		0			0
$349$	−1433.29	+	2482.52i	−0.219834	+	0.380763i	−0.954757	−	0.297387i	$-0.903885\pi$
$349$	−1433.29	+	2482.52i	−0.219834	+	0.380763i	0.734923	+	0.678150i	$0.237218\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1238.27	−	2144.75i	0.186704	−	0.323381i	−0.757445	−	0.652899i	$-0.773553\pi$
$353$	1238.27	−	2144.75i	0.186704	−	0.323381i	0.944149	+	0.329518i	$0.106886\pi$
$354$		0			0
$355$	−1528.34	−	2647.16i	−0.228495	−	0.395765i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−5526.01			−0.812400			−0.406200	−	0.913784i	$-0.633146\pi$
$359$	−5526.01			−0.812400			−0.406200	+	0.913784i	$0.633146\pi$
$360$		0			0
$361$	8800.05			1.28299
$362$		0			0
$363$		0			0
$364$		0			0
$365$	2458.83	+	4258.82i	0.352605	+	0.610730i
$366$		0			0
$367$	1473.29	−	2551.81i	0.209551	−	0.362952i	−0.742022	−	0.670375i	$-0.766133\pi$
$367$	1473.29	−	2551.81i	0.209551	−	0.362952i	0.951573	+	0.307423i	$0.0994666\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−1111.24	+	1924.73i	−0.155506	+	0.269345i
$372$		0			0
$373$	2449.29	+	4242.29i	0.339998	+	0.588894i	0.984432	−	0.175766i	$-0.0562401\pi$
$373$	2449.29	+	4242.29i	0.339998	+	0.588894i	−0.644434	+	0.764660i	$0.722907\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	53.0552			0.00724797
$378$		0			0
$379$	−4680.57			−0.634366			−0.317183	−	0.948364i	$-0.602737\pi$
$379$	−4680.57			−0.634366			−0.317183	+	0.948364i	$0.602737\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−4516.45	−	7822.73i	−0.602559	−	1.04366i	−0.992432	−	0.122794i	$-0.960815\pi$
$383$	−4516.45	−	7822.73i	−0.602559	−	1.04366i	0.389874	−	0.920868i	$-0.372519\pi$
$384$		0			0
$385$	−3128.67	+	5419.02i	−0.414161	+	0.717347i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−4300.13	+	7448.05i	−0.560477	+	0.970774i	0.436978	+	0.899472i	$0.356049\pi$
$389$	−4300.13	+	7448.05i	−0.560477	+	0.970774i	−0.997455	+	0.0713019i	$0.977285\pi$
$390$		0			0
$391$	312.851	+	541.873i	0.0404643	+	0.0700862i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−1863.69			−0.237398
$396$		0			0
$397$	−12355.8			−1.56201			−0.781006	−	0.624523i	$-0.785293\pi$
$397$	−12355.8			−1.56201			−0.781006	+	0.624523i	$0.785293\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2246.11	−	3890.37i	−0.279714	−	0.484479i	0.691600	−	0.722281i	$-0.256906\pi$
$401$	−2246.11	−	3890.37i	−0.279714	−	0.484479i	−0.971314	+	0.237802i	$0.923573\pi$
$402$		0			0
$403$	−84.9404	+	147.121i	−0.0104992	+	0.0181852i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	4361.73	−	7554.73i	0.531211	−	0.920084i
$408$		0			0
$409$	−3045.26	−	5274.55i	−0.368163	−	0.637677i	0.621116	−	0.783719i	$-0.286680\pi$
$409$	−3045.26	−	5274.55i	−0.368163	−	0.637677i	−0.989278	+	0.146042i	$0.953346\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−19843.8			−2.36429
$414$		0			0
$415$	−3466.40			−0.410021
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−1091.38	−	1890.32i	−0.127249	−	0.220402i	0.795361	−	0.606136i	$-0.207281\pi$
$419$	−1091.38	−	1890.32i	−0.127249	−	0.220402i	−0.922610	+	0.385735i	$0.873948\pi$
$420$		0			0
$421$	−1708.38	+	2959.01i	−0.197771	+	0.342549i	−0.947805	−	0.318850i	$-0.896703\pi$
$421$	−1708.38	+	2959.01i	−0.197771	+	0.342549i	0.750035	+	0.661399i	$0.230037\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1091.05	+	1889.75i	−0.124526	+	0.215685i
$426$		0			0
$427$	−384.100	−	665.281i	−0.0435314	−	0.0753986i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1697.09			−0.189665			−0.0948327	−	0.995493i	$-0.530232\pi$
$431$	−1697.09			−0.189665			−0.0948327	+	0.995493i	$0.530232\pi$
$432$		0			0
$433$	8934.22			0.991574			0.495787	−	0.868444i	$-0.334880\pi$
$433$	8934.22			0.991574			0.495787	+	0.868444i	$0.334880\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−448.525	−	776.867i	−0.0490980	−	0.0850403i
$438$		0			0
$439$	−5740.37	+	9942.61i	−0.624084	+	1.08095i	0.364633	+	0.931151i	$0.381194\pi$
$439$	−5740.37	+	9942.61i	−0.624084	+	1.08095i	−0.988717	+	0.149794i	$0.952139\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	5800.74	−	10047.2i	0.622125	−	1.07755i	−0.366964	−	0.930235i	$-0.619603\pi$
$443$	5800.74	−	10047.2i	0.622125	−	1.07755i	0.989089	−	0.147317i	$-0.0470638\pi$
$444$		0			0
$445$	−2184.62	−	3783.87i	−0.232721	−	0.403085i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	11918.6			1.25273			0.626364	−	0.779531i	$-0.284543\pi$
$449$	11918.6			1.25273			0.626364	+	0.779531i	$0.284543\pi$
$450$		0			0
$451$	−11189.6			−1.16829
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−81.1944	−	140.633i	−0.00836583	−	0.0144900i
$456$		0			0
$457$	1535.06	−	2658.80i	0.157127	−	0.272152i	−0.776704	−	0.629865i	$-0.783110\pi$
$457$	1535.06	−	2658.80i	0.157127	−	0.272152i	0.933832	+	0.357713i	$0.116443\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	2978.63	−	5159.14i	0.300930	−	0.521226i	−0.675417	−	0.737436i	$-0.736036\pi$
$461$	2978.63	−	5159.14i	0.300930	−	0.521226i	0.976347	+	0.216210i	$0.0693696\pi$
$462$		0			0
$463$	−3995.99	−	6921.27i	−0.401101	−	0.694727i	0.592758	−	0.805380i	$-0.298039\pi$
$463$	−3995.99	−	6921.27i	−0.401101	−	0.694727i	−0.993859	+	0.110654i	$0.964706\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	13084.9			1.29657			0.648283	−	0.761400i	$-0.275487\pi$
$467$	13084.9			1.29657			0.648283	+	0.761400i	$0.275487\pi$
$468$		0			0
$469$	3386.37			0.333408
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−10670.6	−	18482.1i	−1.03729	−	1.79663i
$474$		0			0
$475$	1564.20	−	2709.28i	0.151096	−	0.261706i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−3374.59	+	5844.96i	−0.321897	+	0.557543i	−0.980880	−	0.194616i	$-0.937654\pi$
$479$	−3374.59	+	5844.96i	−0.321897	+	0.557543i	0.658982	+	0.752159i	$0.270987\pi$
$480$		0			0
$481$	113.194	+	196.058i	0.0107302	+	0.0185852i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	413.769			0.0387387
$486$		0			0
$487$	1764.54			0.164187			0.0820936	−	0.996625i	$-0.473839\pi$
$487$	1764.54			0.164187			0.0820936	+	0.996625i	$0.473839\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−2714.07	−	4700.91i	−0.249459	−	0.432076i	0.713917	−	0.700230i	$-0.246919\pi$
$491$	−2714.07	−	4700.91i	−0.249459	−	0.432076i	−0.963376	+	0.268155i	$0.913586\pi$
$492$		0			0
$493$	−1912.89	+	3313.22i	−0.174751	+	0.302677i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−8201.50	+	14205.4i	−0.740216	+	1.28209i
$498$		0			0
$499$	−8843.00	−	15316.5i	−0.793321	−	1.37407i	−0.923900	−	0.382635i	$-0.875017\pi$
$499$	−8843.00	−	15316.5i	−0.793321	−	1.37407i	0.130579	−	0.991438i	$-0.458317\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	4258.96			0.377530			0.188765	−	0.982022i	$-0.439552\pi$
$503$	4258.96			0.377530			0.188765	+	0.982022i	$0.439552\pi$
$504$		0			0
$505$	6631.55			0.584357
$506$		0			0
$507$		0			0
$508$		0			0
$509$	8509.75	+	14739.3i	0.741038	+	1.28352i	0.952023	+	0.306026i	$0.0989994\pi$
$509$	8509.75	+	14739.3i	0.741038	+	1.28352i	−0.210985	+	0.977489i	$0.567667\pi$
$510$		0			0
$511$	13194.8	−	22854.0i	1.14227	−	1.97848i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−4171.54	+	7225.31i	−0.356932	+	0.618224i
$516$		0			0
$517$	597.264	+	1034.49i	0.0508078	+	0.0880018i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	17688.5			1.48742			0.743712	−	0.668500i	$-0.233063\pi$
$521$	17688.5			1.48742			0.743712	+	0.668500i	$0.233063\pi$
$522$		0			0
$523$	−8952.32			−0.748485			−0.374242	−	0.927331i	$-0.622097\pi$
$523$	−8952.32			−0.748485			−0.374242	+	0.927331i	$0.622097\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−6124.99	−	10608.8i	−0.506279	−	0.876900i
$528$		0			0
$529$	6057.81	−	10492.4i	0.497888	−	0.862368i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	145.195	−	251.485i	0.0117994	−	0.0204372i
$534$		0			0
$535$	−480.632	−	832.480i	−0.0388403	−	0.0672733i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	17580.5			1.40491
$540$		0			0
$541$	−10010.9			−0.795570			−0.397785	−	0.917479i	$-0.630221\pi$
$541$	−10010.9			−0.795570			−0.397785	+	0.917479i	$0.630221\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−4113.99	−	7125.63i	−0.323347	−	0.560053i
$546$		0			0
$547$	6015.68	−	10419.5i	0.470223	−	0.814451i	−0.529197	−	0.848499i	$-0.677507\pi$
$547$	6015.68	−	10419.5i	0.470223	−	0.814451i	0.999420	+	0.0340485i	$0.0108401\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	2742.45	−	4750.06i	0.212037	−	0.367258i
$552$		0			0
$553$	5000.54	+	8661.18i	0.384529	+	0.666023i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−19557.6			−1.48776			−0.743878	−	0.668315i	$-0.767016\pi$
$557$	−19557.6			−1.48776			−0.743878	+	0.668315i	$0.767016\pi$
$558$		0			0
$559$	553.843			0.0419053
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−11149.7	−	19311.8i	−0.834642	−	1.44564i	−0.894322	−	0.447424i	$-0.852341\pi$
$563$	−11149.7	−	19311.8i	−0.834642	−	1.44564i	0.0596804	−	0.998218i	$-0.480992\pi$
$564$		0			0
$565$	−3892.40	+	6741.83i	−0.289831	+	0.502002i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−9694.64	+	16791.6i	−0.714271	+	1.23715i	0.248969	+	0.968512i	$0.419908\pi$
$569$	−9694.64	+	16791.6i	−0.714271	+	1.23715i	−0.963240	+	0.268643i	$0.913425\pi$
$570$		0			0
$571$	8894.47	+	15405.7i	0.651877	+	1.12908i	0.982667	+	0.185380i	$0.0593516\pi$
$571$	8894.47	+	15405.7i	0.651877	+	1.12908i	−0.330790	+	0.943704i	$0.607315\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−179.215			−0.0129979
$576$		0			0
$577$	13034.2			0.940420			0.470210	−	0.882555i	$-0.344178\pi$
$577$	13034.2			0.940420			0.470210	+	0.882555i	$0.344178\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	9300.84	+	16109.5i	0.664137	+	1.15032i
$582$		0			0
$583$	1931.71	−	3345.82i	0.137227	−	0.237684i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1448.59	−	2509.04i	0.101857	−	0.176421i	−0.810593	−	0.585610i	$-0.800855\pi$
$587$	1448.59	−	2509.04i	0.101857	−	0.176421i	0.912450	+	0.409189i	$0.134188\pi$
$588$		0			0
$589$	8781.22	+	15209.5i	0.614302	+	1.06400i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	9064.89			0.627741			0.313871	−	0.949466i	$-0.398374\pi$
$593$	9064.89			0.627741			0.313871	+	0.949466i	$0.398374\pi$
$594$		0			0
$595$	11709.7			0.806811
$596$		0			0
$597$		0			0
$598$		0			0
$599$	13064.3	+	22628.0i	0.891138	+	1.54350i	0.838513	+	0.544882i	$0.183426\pi$
$599$	13064.3	+	22628.0i	0.891138	+	1.54350i	0.0526252	+	0.998614i	$0.483241\pi$
$600$		0			0
$601$	10771.2	−	18656.3i	0.731060	−	1.26623i	−0.225370	−	0.974273i	$-0.572359\pi$
$601$	10771.2	−	18656.3i	0.731060	−	1.26623i	0.956431	−	0.291960i	$-0.0943074\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	2111.17	−	3656.65i	0.141870	−	0.245726i
$606$		0			0
$607$	−9594.12	−	16617.5i	−0.641538	−	1.11118i	−0.985090	−	0.172042i	$-0.944963\pi$
$607$	−9594.12	−	16617.5i	−0.641538	−	1.11118i	0.343552	−	0.939134i	$-0.388370\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−31.0001			−0.00205259
$612$		0			0
$613$	19212.5			1.26588			0.632942	−	0.774199i	$-0.281847\pi$
$613$	19212.5			1.26588			0.632942	+	0.774199i	$0.281847\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	11212.9	+	19421.4i	0.731630	+	1.26722i	0.956186	+	0.292759i	$0.0945734\pi$
$617$	11212.9	+	19421.4i	0.731630	+	1.26722i	−0.224556	+	0.974461i	$0.572093\pi$
$618$		0			0
$619$	363.047	−	628.816i	0.0235736	−	0.0408308i	−0.853998	−	0.520276i	$-0.825829\pi$
$619$	363.047	−	628.816i	0.0235736	−	0.0408308i	0.877572	+	0.479446i	$0.159162\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−11723.3	+	20305.3i	−0.753906	+	1.30580i
$624$		0			0
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−16324.7			−1.03483
$630$		0			0
$631$	−11350.8			−0.716116			−0.358058	−	0.933699i	$-0.616561\pi$
$631$	−11350.8			−0.716116			−0.358058	+	0.933699i	$0.616561\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1022.51	−	1771.04i	−0.0639010	−	0.110680i
$636$		0			0
$637$	−228.122	+	395.119i	−0.0141892	+	0.0245764i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	6698.91	−	11602.9i	0.412779	−	0.714953i	−0.582414	−	0.812892i	$-0.697892\pi$
$641$	6698.91	−	11602.9i	0.412779	−	0.714953i	0.995192	+	0.0979390i	$0.0312250\pi$
$642$		0			0
$643$	1635.27	+	2832.37i	0.100294	+	0.173713i	0.911806	−	0.410622i	$-0.134688\pi$
$643$	1635.27	+	2832.37i	0.100294	+	0.173713i	−0.811512	+	0.584336i	$0.801355\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	24464.4			1.48655			0.743273	−	0.668989i	$-0.233273\pi$
$647$	24464.4			1.48655			0.743273	+	0.668989i	$0.233273\pi$
$648$		0			0
$649$	34495.1			2.08637
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−13996.5	−	24242.6i	−0.838783	−	1.45281i	−0.890913	−	0.454174i	$-0.849934\pi$
$653$	−13996.5	−	24242.6i	−0.838783	−	1.45281i	0.0521299	−	0.998640i	$-0.483399\pi$
$654$		0			0
$655$	−7265.81	+	12584.8i	−0.433433	+	0.750728i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	6665.90	−	11545.7i	0.394031	−	0.682482i	−0.598946	−	0.800790i	$-0.704414\pi$
$659$	6665.90	−	11545.7i	0.394031	−	0.682482i	0.992977	+	0.118308i	$0.0377469\pi$
$660$		0			0
$661$	−11078.9	−	19189.1i	−0.651917	−	1.12915i	−0.982657	−	0.185432i	$-0.940632\pi$
$661$	−11078.9	−	19189.1i	−0.651917	−	1.12915i	0.330740	−	0.943722i	$-0.392702\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−16787.9			−0.978958
$666$		0			0
$667$	−314.209			−0.0182402
$668$		0			0
$669$		0			0
$670$		0			0
$671$	667.694	+	1156.48i	0.0384143	+	0.0665356i
$672$		0			0
$673$	3144.67	−	5446.74i	0.180116	−	0.311971i	−0.761804	−	0.647808i	$-0.775686\pi$
$673$	3144.67	−	5446.74i	0.180116	−	0.311971i	0.941920	+	0.335837i	$0.109019\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	4781.57	−	8281.92i	0.271448	−	0.470162i	−0.697785	−	0.716308i	$-0.745831\pi$
$677$	4781.57	−	8281.92i	0.271448	−	0.470162i	0.969233	+	0.246145i	$0.0791640\pi$
$678$		0			0
$679$	−1110.20	−	1922.92i	−0.0627476	−	0.108682i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−10285.5			−0.576226			−0.288113	−	0.957596i	$-0.593028\pi$
$683$	−10285.5			−0.576226			−0.288113	+	0.957596i	$0.593028\pi$
$684$		0			0
$685$	9449.99			0.527103
$686$		0			0
$687$		0			0
$688$		0			0
$689$	50.1312	+	86.8297i	0.00277191	+	0.00480109i
$690$		0			0
$691$	6877.60	−	11912.3i	0.378634	−	0.655813i	−0.612230	−	0.790680i	$-0.709727\pi$
$691$	6877.60	−	11912.3i	0.378634	−	0.655813i	0.990864	+	0.134867i	$0.0430606\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−6773.86	+	11732.7i	−0.369708	+	0.640353i
$696$		0			0
$697$	10469.9	+	18134.4i	0.568975	+	0.985494i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	24564.4			1.32352			0.661758	−	0.749717i	$-0.269810\pi$
$701$	24564.4			1.32352			0.661758	+	0.749717i	$0.269810\pi$
$702$		0			0
$703$	23404.3			1.25563
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−17793.4	−	30819.1i	−0.946520	−	1.63942i
$708$		0			0
$709$	16871.6	−	29222.4i	0.893689	−	1.54791i	0.0582696	−	0.998301i	$-0.481442\pi$
$709$	16871.6	−	29222.4i	0.893689	−	1.54791i	0.835419	−	0.549613i	$-0.185225\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	503.043	−	871.297i	0.0264223	−	0.0457648i
$714$		0			0
$715$	141.143	+	244.467i	0.00738244	+	0.0127868i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	20159.9			1.04567			0.522837	−	0.852433i	$-0.324874\pi$
$719$	20159.9			1.04567			0.522837	+	0.852433i	$0.324874\pi$
$720$		0			0
$721$	44771.3			2.31258
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−547.893	−	948.978i	−0.0280665	−	0.0486126i
$726$		0			0
$727$	8374.59	−	14505.2i	0.427230	−	0.739985i	−0.569395	−	0.822064i	$-0.692823\pi$
$727$	8374.59	−	14505.2i	0.427230	−	0.739985i	0.996626	+	0.0820791i	$0.0261560\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−19968.6	+	34586.7i	−1.01035	+	1.74998i
$732$		0			0
$733$	−4071.57	−	7052.16i	−0.205166	−	0.355358i	0.745020	−	0.667043i	$-0.232440\pi$
$733$	−4071.57	−	7052.16i	−0.205166	−	0.355358i	−0.950186	+	0.311684i	$0.899107\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5886.64			−0.294216
$738$		0			0
$739$	26837.1			1.33588			0.667942	−	0.744213i	$-0.267175\pi$
$739$	26837.1			1.33588			0.667942	+	0.744213i	$0.267175\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−8399.10	−	14547.7i	−0.414715	−	0.718307i	0.580684	−	0.814129i	$-0.302785\pi$
$743$	−8399.10	−	14547.7i	−0.414715	−	0.718307i	−0.995398	+	0.0958222i	$0.969452\pi$
$744$		0			0
$745$	3410.97	−	5907.97i	0.167743	−	0.290539i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−2579.21	+	4467.32i	−0.125824	+	0.217934i
$750$		0			0
$751$	−4951.87	−	8576.89i	−0.240607	−	0.416744i	0.720280	−	0.693683i	$-0.244013\pi$
$751$	−4951.87	−	8576.89i	−0.240607	−	0.416744i	−0.960887	+	0.276939i	$0.910680\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−4414.46			−0.212793
$756$		0			0
$757$	20197.0			0.969713			0.484856	−	0.874594i	$-0.338872\pi$
$757$	20197.0			0.969713			0.484856	+	0.874594i	$0.338872\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	14091.6	+	24407.4i	0.671248	+	1.16264i	0.977550	+	0.210702i	$0.0675749\pi$
$761$	14091.6	+	24407.4i	0.671248	+	1.16264i	−0.306302	+	0.951934i	$0.599092\pi$
$762$		0			0
$763$	−22076.8	+	38238.2i	−1.04749	+	1.81431i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−447.604	+	775.274i	−0.0210718	+	0.0364974i
$768$		0			0
$769$	5919.64	+	10253.1i	0.277591	+	0.480803i	0.970786	−	0.239948i	$-0.0771305\pi$
$769$	5919.64	+	10253.1i	0.277591	+	0.480803i	−0.693194	+	0.720751i	$0.743797\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−38537.8			−1.79316			−0.896578	−	0.442886i	$-0.853955\pi$
$773$	−38537.8			−1.79316			−0.896578	+	0.442886i	$0.853955\pi$
$774$		0			0
$775$	3508.66			0.162626
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−15010.4	−	25998.7i	−0.690376	−	1.19577i
$780$		0			0
$781$	14256.9	−	24693.7i	0.653205	−	1.13138i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	2990.84	−	5180.29i	0.135984	−	0.235532i
$786$		0			0
$787$	−8997.07	−	15583.4i	−0.407511	−	0.705829i	0.587100	−	0.809515i	$-0.300270\pi$
$787$	−8997.07	−	15583.4i	−0.407511	−	0.705829i	−0.994610	+	0.103686i	$0.966936\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	41775.4			1.87783
$792$		0			0
$793$	−34.6556			−0.00155190
$794$		0			0
$795$		0			0
$796$		0			0
$797$	12624.1	+	21865.6i	0.561065	+	0.971794i	0.997404	+	0.0720111i	$0.0229417\pi$
$797$	12624.1	+	21865.6i	0.561065	+	0.971794i	−0.436338	+	0.899783i	$0.643725\pi$
$798$		0			0
$799$	1117.70	−	1935.91i	0.0494885	−	0.0857165i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−22936.9	+	39727.8i	−1.00800	+	1.74591i
$804$		0			0
$805$	480.858	+	832.871i	0.0210534	+	0.0364656i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1766.26			−0.0767595			−0.0383798	−	0.999263i	$-0.512220\pi$
$809$	−1766.26			−0.0767595			−0.0383798	+	0.999263i	$0.512220\pi$
$810$		0			0
$811$	−41618.0			−1.80198			−0.900990	−	0.433840i	$-0.857158\pi$
$811$	−41618.0			−1.80198			−0.900990	+	0.433840i	$0.857158\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−5822.26	−	10084.5i	−0.250239	−	0.433427i
$816$		0			0
$817$	28628.4	−	49585.8i	1.22593	−	2.12337i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	22500.9	−	38972.7i	0.956501	−	1.65671i	0.225606	−	0.974219i	$-0.427564\pi$
$821$	22500.9	−	38972.7i	0.956501	−	1.65671i	0.730895	−	0.682490i	$-0.239103\pi$
$822$		0			0
$823$	−20306.9	−	35172.6i	−0.860091	−	1.48972i	−0.871840	−	0.489790i	$-0.837073\pi$
$823$	−20306.9	−	35172.6i	−0.860091	−	1.48972i	0.0117495	−	0.999931i	$-0.496260\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	25678.5			1.07972			0.539861	−	0.841754i	$-0.318477\pi$
$827$	25678.5			1.07972			0.539861	+	0.841754i	$0.318477\pi$
$828$		0			0
$829$	−28161.7			−1.17985			−0.589925	−	0.807458i	$-0.700843\pi$
$829$	−28161.7			−1.17985			−0.589925	+	0.807458i	$0.700843\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−16449.7	−	28491.7i	−0.684212	−	1.18509i
$834$		0			0
$835$	3874.23	−	6710.37i	0.160567	−	0.278110i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−2002.51	+	3468.45i	−0.0824008	+	0.142722i	−0.904281	−	0.426938i	$-0.859592\pi$
$839$	−2002.51	+	3468.45i	−0.0824008	+	0.142722i	0.821880	+	0.569661i	$0.192925\pi$
$840$		0			0
$841$	11233.9	+	19457.7i	0.460614	+	0.797806i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	10977.7			0.446915
$846$		0			0
$847$	−22658.2			−0.919181
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−670.372	−	1161.12i	−0.0270036	−	0.0467716i
$852$		0			0
$853$	3907.87	−	6768.63i	0.156862	−	0.271692i	−0.776874	−	0.629656i	$-0.783196\pi$
$853$	3907.87	−	6768.63i	0.156862	−	0.271692i	0.933735	+	0.357964i	$0.116529\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−21526.3	+	37284.6i	−0.858021	+	1.48614i	0.0157934	+	0.999875i	$0.494973\pi$
$857$	−21526.3	+	37284.6i	−0.858021	+	1.48614i	−0.873814	+	0.486260i	$0.838361\pi$
$858$		0			0
$859$	−5789.83	−	10028.3i	−0.229973	−	0.398324i	0.727827	−	0.685761i	$-0.240530\pi$
$859$	−5789.83	−	10028.3i	−0.229973	−	0.398324i	−0.957800	+	0.287436i	$0.907197\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−9555.34			−0.376903			−0.188452	−	0.982082i	$-0.560347\pi$
$863$	−9555.34			−0.376903			−0.188452	+	0.982082i	$0.560347\pi$
$864$		0			0
$865$	−12030.7			−0.472896
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−8692.59	−	15056.0i	−0.339328	−	0.587733i
$870$		0			0
$871$	76.3843	−	132.301i	0.00297151	−	0.00514680i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1676.96	+	2904.59i	−0.0647905	+	0.112220i
$876$		0			0
$877$	10446.0	+	18092.9i	0.402206	+	0.696641i	0.993992	−	0.109454i	$-0.0349102\pi$
$877$	10446.0	+	18092.9i	0.402206	+	0.696641i	−0.591786	+	0.806095i	$0.701577\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	11671.3			0.446327			0.223164	−	0.974781i	$-0.428362\pi$
$881$	11671.3			0.446327			0.223164	+	0.974781i	$0.428362\pi$
$882$		0			0
$883$	34959.3			1.33236			0.666181	−	0.745790i	$-0.267928\pi$
$883$	34959.3			1.33236			0.666181	+	0.745790i	$0.267928\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	17852.7	+	30921.9i	0.675802	+	1.17052i	0.976234	+	0.216720i	$0.0695359\pi$
$887$	17852.7	+	30921.9i	0.675802	+	1.17052i	−0.300432	+	0.953803i	$0.597131\pi$
$888$		0			0
$889$	−5487.09	+	9503.92i	−0.207009	+	0.358550i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1602.41	+	2775.45i	−0.0600476	+	0.104006i
$894$		0			0
$895$	289.393	+	501.244i	0.0108082	+	0.0187204i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	6151.59			0.228217
$900$		0			0
$901$	−7229.84			−0.267326
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−5535.52	−	9587.79i	−0.203322	−	0.352165i
$906$		0			0
$907$	−5460.78	+	9458.35i	−0.199914	+	0.346262i	−0.948500	−	0.316776i	$-0.897400\pi$
$907$	−5460.78	+	9458.35i	−0.199914	+	0.346262i	0.748586	+	0.663038i	$0.230733\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−22845.3	+	39569.2i	−0.830842	+	1.43906i	0.0665291	+	0.997784i	$0.478807\pi$
$911$	−22845.3	+	39569.2i	−0.830842	+	1.43906i	−0.897371	+	0.441276i	$0.854526\pi$
$912$		0			0
$913$	−16167.9	−	28003.7i	−0.586069	−	1.01510i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	77980.8			2.80824
$918$		0			0
$919$	−46123.5			−1.65558			−0.827788	−	0.561041i	$-0.810401\pi$
$919$	−46123.5			−1.65558			−0.827788	+	0.561041i	$0.810401\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	369.992	+	640.845i	0.0131944	+	0.0228534i
$924$		0			0
$925$	2337.88	−	4049.33i	0.0831016	−	0.143936i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	20826.2	−	36072.0i	0.735506	−	1.27393i	−0.218994	−	0.975726i	$-0.570278\pi$
$929$	20826.2	−	36072.0i	0.735506	−	1.27393i	0.954501	−	0.298208i	$-0.0963891\pi$
$930$		0			0
$931$	23583.5	+	40847.7i	0.830200	+	1.43795i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−20355.4			−0.711971
$936$		0			0
$937$	−26210.8			−0.913841			−0.456920	−	0.889508i	$-0.651048\pi$
$937$	−26210.8			−0.913841			−0.456920	+	0.889508i	$0.651048\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	4284.52	+	7421.01i	0.148429	+	0.257086i	0.930647	−	0.365919i	$-0.119245\pi$
$941$	4284.52	+	7421.01i	0.148429	+	0.257086i	−0.782218	+	0.623005i	$0.785912\pi$
$942$		0			0
$943$	−859.889	+	1489.37i	−0.0296944	+	0.0514322i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	17193.6	−	29780.2i	0.589986	−	1.02189i	−0.404247	−	0.914650i	$-0.632467\pi$
$947$	17193.6	−	29780.2i	0.589986	−	1.02189i	0.994234	−	0.107236i	$-0.0342001\pi$
$948$		0			0
$949$	−595.252	−	1031.01i	−0.0203611	−	0.0352665i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−48075.9			−1.63414			−0.817068	−	0.576541i	$-0.804402\pi$
$953$	−48075.9			−1.63414			−0.817068	+	0.576541i	$0.804402\pi$
$954$		0			0
$955$	−13554.0			−0.459266
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−25355.7	−	43917.3i	−0.853782	−	1.47879i
$960$		0			0
$961$	5046.92	−	8741.52i	0.169411	−	0.293428i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	10841.9	−	18778.7i	0.361671	−	0.626433i
$966$		0			0
$967$	7834.77	+	13570.2i	0.260547	+	0.451281i	0.966387	−	0.257090i	$-0.0827637\pi$
$967$	7834.77	+	13570.2i	0.260547	+	0.451281i	−0.705840	+	0.708371i	$0.749430\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	42128.0			1.39233			0.696165	−	0.717881i	$-0.254888\pi$
$971$	42128.0			1.39233			0.696165	+	0.717881i	$0.254888\pi$
$972$		0			0
$973$	72700.9			2.39536
$974$		0			0
$975$		0			0
$976$		0			0
$977$	2428.50	+	4206.28i	0.0795236	+	0.137739i	0.903044	−	0.429547i	$-0.141327\pi$
$977$	2428.50	+	4206.28i	0.0795236	+	0.137739i	−0.823521	+	0.567286i	$0.807993\pi$
$978$		0			0
$979$	20379.0	−	35297.4i	0.665285	−	1.15231i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	2302.32	−	3987.74i	0.0747026	−	0.129389i	−0.826254	−	0.563297i	$-0.809533\pi$
$983$	2302.32	−	3987.74i	0.0747026	−	0.129389i	0.900957	+	0.433909i	$0.142866\pi$
$984$		0			0
$985$	−12102.2	−	20961.6i	−0.391480	−	0.678063i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−3280.03			−0.105459
$990$		0			0
$991$	4082.46			0.130861			0.0654307	−	0.997857i	$-0.479158\pi$
$991$	4082.46			0.130861			0.0654307	+	0.997857i	$0.479158\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−11451.0	−	19833.7i	−0.364846	−	0.631931i
$996$		0			0
$997$	−17034.8	+	29505.1i	−0.541121	+	0.937249i	0.457719	+	0.889097i	$0.348666\pi$
$997$	−17034.8	+	29505.1i	−0.541121	+	0.937249i	−0.998840	+	0.0481519i	$0.984667\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.4.i.v.541.3		6
3.2	odd	2		1620.4.i.t.541.3		6
9.2	odd	6		1620.4.a.e.1.1	yes	3
9.4	even	3	inner	1620.4.i.v.1081.3		6
9.5	odd	6		1620.4.i.t.1081.3		6
9.7	even	3		1620.4.a.c.1.1	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1620.4.a.c.1.1	✓	3	9.7	even	3
1620.4.a.e.1.1	yes	3	9.2	odd	6
1620.4.i.t.541.3		6	3.2	odd	2
1620.4.i.t.1081.3		6	9.5	odd	6
1620.4.i.v.541.3		6	1.1	even	1	trivial
1620.4.i.v.1081.3		6	9.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1620.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.50000 + 4.33013i) q^{5} +(13.4157 - 23.2367i) q^{7} +O(q^{10})\)	\(q+(2.50000 + 4.33013i) q^{5} +(13.4157 - 23.2367i) q^{7} +(-23.3210 + 40.3931i) q^{11} +(-0.605219 - 1.04827i) q^{13} +87.2838 q^{17} -125.136 q^{19} +(3.58429 + 6.20818i) q^{23} +(-12.5000 + 21.6506i) q^{25} +(-21.9157 + 37.9591i) q^{29} +(-70.1733 - 121.544i) q^{31} +134.157 q^{35} -187.030 q^{37} +(119.952 + 207.764i) q^{41} +(-228.778 + 396.255i) q^{43} +(12.8053 - 22.1795i) q^{47} +(-188.462 - 326.426i) q^{49} -82.8314 q^{53} -233.210 q^{55} +(-369.787 - 640.490i) q^{59} +(14.3153 - 24.7949i) q^{61} +(3.02610 - 5.24135i) q^{65} +(63.1046 + 109.300i) q^{67} -611.336 q^{71} +983.531 q^{73} +(625.734 + 1083.80i) q^{77} +(-186.369 + 322.800i) q^{79} +(-346.640 + 600.398i) q^{83} +(218.210 + 377.950i) q^{85} -873.848 q^{89} -32.4778 q^{91} +(-312.840 - 541.855i) q^{95} +(41.3769 - 71.6669i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 15 q^{5} + 3 q^{7}+O(q^{10}) \) 6 * q + 15 * q^5 + 3 * q^7	\( 6 q + 15 q^{5} + 3 q^{7} - 24 q^{11} - 3 q^{13} + 60 q^{17} - 54 q^{19} + 99 q^{23} - 75 q^{25} - 54 q^{29} - 72 q^{31} + 30 q^{35} - 36 q^{37} + 411 q^{41} - 444 q^{43} - 75 q^{47} - 204 q^{49} - 342 q^{53} - 240 q^{55} + 297 q^{59} - 684 q^{61} + 15 q^{65} - 12 q^{67} - 1284 q^{71} - 132 q^{73} + 1044 q^{77} - 1122 q^{79} + 90 q^{83} + 150 q^{85} - 1512 q^{89} - 3306 q^{91} - 135 q^{95} - 1536 q^{97}+O(q^{100}) \) 6 * q + 15 * q^5 + 3 * q^7 - 24 * q^11 - 3 * q^13 + 60 * q^17 - 54 * q^19 + 99 * q^23 - 75 * q^25 - 54 * q^29 - 72 * q^31 + 30 * q^35 - 36 * q^37 + 411 * q^41 - 444 * q^43 - 75 * q^47 - 204 * q^49 - 342 * q^53 - 240 * q^55 + 297 * q^59 - 684 * q^61 + 15 * q^65 - 12 * q^67 - 1284 * q^71 - 132 * q^73 + 1044 * q^77 - 1122 * q^79 + 90 * q^83 + 150 * q^85 - 1512 * q^89 - 3306 * q^91 - 135 * q^95 - 1536 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more