# Properties

 Label 3332.1.g.e.883.1 Level $3332$ Weight $1$ Character 3332.883 Self dual yes Analytic conductor $1.663$ Analytic rank $0$ Dimension $1$ Projective image $D_{3}$ CM discriminant -68 Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3332,1,Mod(883,3332)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3332, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("3332.883");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$3332 = 2^{2} \cdot 7^{2} \cdot 17$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3332.g (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: yes Analytic conductor: $$1.66288462209$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 476) Projective image: $$D_{3}$$ Projective field: Galois closure of 3.1.3332.1 Artin image: $D_6$ Artin field: Galois closure of 6.0.44408896.1

## Embedding invariants

 Embedding label 883.1 Character $$\chi$$ $$=$$ 3332.88

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +1.00000 q^{8} +O(q^{10})$$ $$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{11} +1.00000 q^{12} -1.00000 q^{13} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{22} -2.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -1.00000 q^{26} -1.00000 q^{27} -2.00000 q^{31} +1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} -1.00000 q^{39} +1.00000 q^{44} -2.00000 q^{46} +1.00000 q^{48} +1.00000 q^{50} +1.00000 q^{51} -1.00000 q^{52} -1.00000 q^{53} -1.00000 q^{54} -2.00000 q^{62} +1.00000 q^{64} +1.00000 q^{66} +1.00000 q^{68} -2.00000 q^{69} +1.00000 q^{71} +1.00000 q^{75} -1.00000 q^{78} +1.00000 q^{79} -1.00000 q^{81} +1.00000 q^{88} -1.00000 q^{89} -2.00000 q^{92} -2.00000 q^{93} +1.00000 q^{96} +O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3332\mathbb{Z}\right)^\times$$.

 $$n$$ $$785$$ $$885$$ $$1667$$ $$\chi(n)$$ $$-1$$ $$1$$ $$-1$$

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 1.00000
$$3$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$4$$ 1.00000 1.00000
$$5$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$6$$ 1.00000 1.00000
$$7$$ 0 0
$$8$$ 1.00000 1.00000
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$12$$ 1.00000 1.00000
$$13$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.00000 1.00000
$$17$$ 1.00000 1.00000
$$18$$ 0 0
$$19$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 1.00000 1.00000
$$23$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$24$$ 1.00000 1.00000
$$25$$ 1.00000 1.00000
$$26$$ −1.00000 −1.00000
$$27$$ −1.00000 −1.00000
$$28$$ 0 0
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ 0 0
$$31$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$32$$ 1.00000 1.00000
$$33$$ 1.00000 1.00000
$$34$$ 1.00000 1.00000
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$38$$ 0 0
$$39$$ −1.00000 −1.00000
$$40$$ 0 0
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$44$$ 1.00000 1.00000
$$45$$ 0 0
$$46$$ −2.00000 −2.00000
$$47$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$48$$ 1.00000 1.00000
$$49$$ 0 0
$$50$$ 1.00000 1.00000
$$51$$ 1.00000 1.00000
$$52$$ −1.00000 −1.00000
$$53$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$54$$ −1.00000 −1.00000
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$60$$ 0 0
$$61$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$62$$ −2.00000 −2.00000
$$63$$ 0 0
$$64$$ 1.00000 1.00000
$$65$$ 0 0
$$66$$ 1.00000 1.00000
$$67$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$68$$ 1.00000 1.00000
$$69$$ −2.00000 −2.00000
$$70$$ 0 0
$$71$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$72$$ 0 0
$$73$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$74$$ 0 0
$$75$$ 1.00000 1.00000
$$76$$ 0 0
$$77$$ 0 0
$$78$$ −1.00000 −1.00000
$$79$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$80$$ 0 0
$$81$$ −1.00000 −1.00000
$$82$$ 0 0
$$83$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 1.00000 1.00000
$$89$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −2.00000 −2.00000
$$93$$ −2.00000 −2.00000
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 1.00000 1.00000
$$97$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 1.00000 1.00000
$$101$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$102$$ 1.00000 1.00000
$$103$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$104$$ −1.00000 −1.00000
$$105$$ 0 0
$$106$$ −1.00000 −1.00000
$$107$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$108$$ −1.00000 −1.00000
$$109$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 0 0
$$122$$ 0 0
$$123$$ 0 0
$$124$$ −2.00000 −2.00000
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$128$$ 1.00000 1.00000
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$132$$ 1.00000 1.00000
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 1.00000 1.00000
$$137$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$138$$ −2.00000 −2.00000
$$139$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 1.00000 1.00000
$$143$$ −1.00000 −1.00000
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$150$$ 1.00000 1.00000
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −1.00000 −1.00000
$$157$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$158$$ 1.00000 1.00000
$$159$$ −1.00000 −1.00000
$$160$$ 0 0
$$161$$ 0 0
$$162$$ −1.00000 −1.00000
$$163$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$168$$ 0 0
$$169$$ 0 0
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 1.00000 1.00000
$$177$$ 0 0
$$178$$ −1.00000 −1.00000
$$179$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −2.00000 −2.00000
$$185$$ 0 0
$$186$$ −2.00000 −2.00000
$$187$$ 1.00000 1.00000
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$192$$ 1.00000 1.00000
$$193$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 0 0
$$199$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$200$$ 1.00000 1.00000
$$201$$ 0 0
$$202$$ 2.00000 2.00000
$$203$$ 0 0
$$204$$ 1.00000 1.00000
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ −1.00000 −1.00000
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$212$$ −1.00000 −1.00000
$$213$$ 1.00000 1.00000
$$214$$ 1.00000 1.00000
$$215$$ 0 0
$$216$$ −1.00000 −1.00000
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −1.00000 −1.00000
$$222$$ 0 0
$$223$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$228$$ 0 0
$$229$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 1.00000 1.00000
$$238$$ 0 0
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ −2.00000 −2.00000
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$252$$ 0 0
$$253$$ −2.00000 −2.00000
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 1.00000 1.00000
$$257$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −2.00000 −2.00000
$$263$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$264$$ 1.00000 1.00000
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −1.00000 −1.00000
$$268$$ 0 0
$$269$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ 1.00000 1.00000
$$273$$ 0 0
$$274$$ −1.00000 −1.00000
$$275$$ 1.00000 1.00000
$$276$$ −2.00000 −2.00000
$$277$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$278$$ 1.00000 1.00000
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$282$$ 0 0
$$283$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$284$$ 1.00000 1.00000
$$285$$ 0 0
$$286$$ −1.00000 −1.00000
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 1.00000 1.00000
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −1.00000 −1.00000
$$298$$ −1.00000 −1.00000
$$299$$ 2.00000 2.00000
$$300$$ 1.00000 1.00000
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 2.00000 2.00000
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$312$$ −1.00000 −1.00000
$$313$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$314$$ −1.00000 −1.00000
$$315$$ 0 0
$$316$$ 1.00000 1.00000
$$317$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$318$$ −1.00000 −1.00000
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 1.00000 1.00000
$$322$$ 0 0
$$323$$ 0 0
$$324$$ −1.00000 −1.00000
$$325$$ −1.00000 −1.00000
$$326$$ −2.00000 −2.00000
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 1.00000 1.00000
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −2.00000 −2.00000
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$348$$ 0 0
$$349$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$350$$ 0 0
$$351$$ 1.00000 1.00000
$$352$$ 1.00000 1.00000
$$353$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −1.00000 −1.00000
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$360$$ 0 0
$$361$$ 1.00000 1.00000
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$368$$ −2.00000 −2.00000
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ −2.00000 −2.00000
$$373$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$374$$ 1.00000 1.00000
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$384$$ 1.00000 1.00000
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$390$$ 0 0
$$391$$ −2.00000 −2.00000
$$392$$ 0 0
$$393$$ −2.00000 −2.00000
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$398$$ 1.00000 1.00000
$$399$$ 0 0
$$400$$ 1.00000 1.00000
$$401$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ 0 0
$$403$$ 2.00000 2.00000
$$404$$ 2.00000 2.00000
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 1.00000 1.00000
$$409$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$410$$ 0 0
$$411$$ −1.00000 −1.00000
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ −1.00000 −1.00000
$$417$$ 1.00000 1.00000
$$418$$ 0 0
$$419$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$420$$ 0 0
$$421$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$422$$ −2.00000 −2.00000
$$423$$ 0 0
$$424$$ −1.00000 −1.00000
$$425$$ 1.00000 1.00000
$$426$$ 1.00000 1.00000
$$427$$ 0 0
$$428$$ 1.00000 1.00000
$$429$$ −1.00000 −1.00000
$$430$$ 0 0
$$431$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$432$$ −1.00000 −1.00000
$$433$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ −1.00000 −1.00000
$$443$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ −1.00000 −1.00000
$$448$$ 0 0
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 1.00000 1.00000
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$458$$ 2.00000 2.00000
$$459$$ −1.00000 −1.00000
$$460$$ 0 0
$$461$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −1.00000 −1.00000
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 1.00000 1.00000
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$488$$ 0 0
$$489$$ −2.00000 −2.00000
$$490$$ 0 0
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −2.00000 −2.00000
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$500$$ 0 0
$$501$$ 1.00000 1.00000
$$502$$ 0 0
$$503$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ −2.00000 −2.00000
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 1.00000 1.00000
$$513$$ 0 0
$$514$$ −1.00000 −1.00000
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ 0 0
$$523$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$524$$ −2.00000 −2.00000
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −2.00000 −2.00000
$$528$$ 1.00000 1.00000
$$529$$ 3.00000 3.00000
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ −1.00000 −1.00000
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 1.00000 1.00000
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$548$$ −1.00000 −1.00000
$$549$$ 0 0
$$550$$ 1.00000 1.00000
$$551$$ 0 0
$$552$$ −2.00000 −2.00000
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 1.00000 1.00000
$$557$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 1.00000 1.00000
$$562$$ −1.00000 −1.00000
$$563$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 1.00000 1.00000
$$567$$ 0 0
$$568$$ 1.00000 1.00000
$$569$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$570$$ 0 0
$$571$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$572$$ −1.00000 −1.00000
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −2.00000 −2.00000
$$576$$ 0 0
$$577$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$578$$ 1.00000 1.00000
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −1.00000 −1.00000
$$584$$ 0 0
$$585$$ 0 0
$$586$$ −1.00000 −1.00000
$$587$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$594$$ −1.00000 −1.00000
$$595$$ 0 0
$$596$$ −1.00000 −1.00000
$$597$$ 1.00000 1.00000
$$598$$ 2.00000 2.00000
$$599$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$600$$ 1.00000 1.00000
$$601$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 2.00000 2.00000
$$607$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$618$$ 0 0
$$619$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$620$$ 0 0
$$621$$ 2.00000 2.00000
$$622$$ 1.00000 1.00000
$$623$$ 0 0
$$624$$ −1.00000 −1.00000
$$625$$ 1.00000 1.00000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ −1.00000 −1.00000
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$632$$ 1.00000 1.00000
$$633$$ −2.00000 −2.00000
$$634$$ 0 0
$$635$$ 0 0
$$636$$ −1.00000 −1.00000
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$642$$ 1.00000 1.00000
$$643$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$648$$ −1.00000 −1.00000
$$649$$ 0 0
$$650$$ −1.00000 −1.00000
$$651$$ 0 0
$$652$$ −2.00000 −2.00000
$$653$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$660$$ 0 0
$$661$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$662$$ 0 0
$$663$$ −1.00000 −1.00000
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 1.00000 1.00000
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ 0 0
$$675$$ −1.00000 −1.00000
$$676$$ 0 0
$$677$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 1.00000 1.00000
$$682$$ −2.00000 −2.00000
$$683$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 2.00000 2.00000
$$688$$ 0 0
$$689$$ 1.00000 1.00000
$$690$$ 0 0
$$691$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ −2.00000 −2.00000
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 2.00000 2.00000
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$702$$ 1.00000 1.00000
$$703$$ 0 0
$$704$$ 1.00000 1.00000
$$705$$ 0 0
$$706$$ −1.00000 −1.00000
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −1.00000 −1.00000
$$713$$ 4.00000 4.00000
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 1.00000 1.00000
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$728$$ 0 0
$$729$$ 1.00000 1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$734$$ 1.00000 1.00000
$$735$$ 0 0
$$736$$ −2.00000 −2.00000
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$744$$ −2.00000 −2.00000
$$745$$ 0 0
$$746$$ −1.00000 −1.00000
$$747$$ 0 0
$$748$$ 1.00000 1.00000
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$758$$ 1.00000 1.00000
$$759$$ −2.00000 −2.00000
$$760$$ 0 0
$$761$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 1.00000 1.00000
$$769$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$770$$ 0 0
$$771$$ −1.00000 −1.00000
$$772$$ 0 0
$$773$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$774$$ 0 0
$$775$$ −2.00000 −2.00000
$$776$$ 0 0
$$777$$ 0 0
$$778$$ −1.00000 −1.00000
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 1.00000 1.00000
$$782$$ −2.00000 −2.00000
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ −2.00000 −2.00000
$$787$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 1.00000 1.00000
$$797$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 1.00000 1.00000
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 2.00000 2.00000
$$807$$ 0 0
$$808$$ 2.00000 2.00000
$$809$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$810$$ 0 0
$$811$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 1.00000 1.00000
$$817$$ 0 0
$$818$$ −1.00000 −1.00000
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$822$$ −1.00000 −1.00000
$$823$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$824$$ 0 0
$$825$$ 1.00000 1.00000
$$826$$ 0 0
$$827$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$828$$ 0 0
$$829$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ −1.00000 −1.00000
$$833$$ 0 0
$$834$$ 1.00000 1.00000
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 2.00000 2.00000
$$838$$ 1.00000 1.00000
$$839$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$840$$ 0 0
$$841$$ 1.00000 1.00000
$$842$$ 2.00000 2.00000
$$843$$ −1.00000 −1.00000
$$844$$ −2.00000 −2.00000
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 0 0
$$848$$ −1.00000 −1.00000
$$849$$ 1.00000 1.00000
$$850$$ 1.00000 1.00000
$$851$$ 0 0
$$852$$ 1.00000 1.00000
$$853$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 1.00000 1.00000
$$857$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$858$$ −1.00000 −1.00000
$$859$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 1.00000 1.00000
$$863$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$864$$ −1.00000 −1.00000
$$865$$ 0 0
$$866$$ 2.00000 2.00000
$$867$$ 1.00000 1.00000
$$868$$ 0 0
$$869$$ 1.00000 1.00000
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$878$$ 1.00000 1.00000
$$879$$ −1.00000 −1.00000
$$880$$ 0 0
$$881$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$882$$ 0 0
$$883$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$884$$ −1.00000 −1.00000
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ −1.00000 −1.00000
$$892$$ 0 0
$$893$$ 0 0
$$894$$ −1.00000 −1.00000
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 2.00000 2.00000
$$898$$ 0 0
$$899$$ 0 0
$$900$$ 0 0
$$901$$ −1.00000 −1.00000
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$908$$ 1.00000 1.00000
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 2.00000 2.00000
$$915$$ 0 0
$$916$$ 2.00000 2.00000
$$917$$ 0 0
$$918$$ −1.00000 −1.00000
$$919$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ −1.00000 −1.00000
$$923$$ −1.00000 −1.00000
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ 1.00000 1.00000
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$942$$ −1.00000 −1.00000
$$943$$ 0 0
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$948$$ 1.00000 1.00000
$$949$$ 0 0
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ −2.00000 −2.00000
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 3.00000 3.00000
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 1.00000 1.00000
$$975$$ −1.00000 −1.00000
$$976$$ 0 0
$$977$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$978$$ −2.00000 −2.00000
$$979$$ −1.00000 −1.00000
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$992$$ −2.00000 −2.00000
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$998$$ 1.00000 1.00000
$$999$$ 0 0
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 3332.1.g.e.883.1 1
4.3 odd 2 3332.1.g.b.883.1 1
7.2 even 3 476.1.o.a.67.1 2
7.3 odd 6 3332.1.o.b.2039.1 2
7.4 even 3 476.1.o.a.135.1 yes 2
7.5 odd 6 3332.1.o.b.67.1 2
7.6 odd 2 3332.1.g.c.883.1 1
17.16 even 2 3332.1.g.b.883.1 1
28.3 even 6 3332.1.o.a.2039.1 2
28.11 odd 6 476.1.o.b.135.1 yes 2
28.19 even 6 3332.1.o.a.67.1 2
28.23 odd 6 476.1.o.b.67.1 yes 2
28.27 even 2 3332.1.g.d.883.1 1
68.67 odd 2 CM 3332.1.g.e.883.1 1
119.16 even 6 476.1.o.b.67.1 yes 2
119.33 odd 6 3332.1.o.a.67.1 2
119.67 even 6 476.1.o.b.135.1 yes 2
119.101 odd 6 3332.1.o.a.2039.1 2
119.118 odd 2 3332.1.g.d.883.1 1
476.67 odd 6 476.1.o.a.135.1 yes 2
476.135 odd 6 476.1.o.a.67.1 2
476.271 even 6 3332.1.o.b.67.1 2
476.339 even 6 3332.1.o.b.2039.1 2
476.475 even 2 3332.1.g.c.883.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
476.1.o.a.67.1 2 7.2 even 3
476.1.o.a.67.1 2 476.135 odd 6
476.1.o.a.135.1 yes 2 7.4 even 3
476.1.o.a.135.1 yes 2 476.67 odd 6
476.1.o.b.67.1 yes 2 28.23 odd 6
476.1.o.b.67.1 yes 2 119.16 even 6
476.1.o.b.135.1 yes 2 28.11 odd 6
476.1.o.b.135.1 yes 2 119.67 even 6
3332.1.g.b.883.1 1 4.3 odd 2
3332.1.g.b.883.1 1 17.16 even 2
3332.1.g.c.883.1 1 7.6 odd 2
3332.1.g.c.883.1 1 476.475 even 2
3332.1.g.d.883.1 1 28.27 even 2
3332.1.g.d.883.1 1 119.118 odd 2
3332.1.g.e.883.1 1 1.1 even 1 trivial
3332.1.g.e.883.1 1 68.67 odd 2 CM
3332.1.o.a.67.1 2 28.19 even 6
3332.1.o.a.67.1 2 119.33 odd 6
3332.1.o.a.2039.1 2 28.3 even 6
3332.1.o.a.2039.1 2 119.101 odd 6
3332.1.o.b.67.1 2 7.5 odd 6
3332.1.o.b.67.1 2 476.271 even 6
3332.1.o.b.2039.1 2 7.3 odd 6
3332.1.o.b.2039.1 2 476.339 even 6