# Properties

 Label 3332.1.g.f.883.1 Level $3332$ Weight $1$ Character 3332.883 Self dual yes Analytic conductor $1.663$ Analytic rank $0$ Dimension $2$ Projective image $D_{6}$ CM discriminant -68 Inner twists $4$

# 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: $$2$$ Coefficient field: $$\Q(\zeta_{12})^+$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} - 3$$ x^2 - 3 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 476) Projective image: $$D_{6}$$ Projective field: Galois closure of 6.2.188737808.1

## Embedding invariants

 Embedding label 883.1 Root $$1.73205$$ of defining polynomial Character $$\chi$$ $$=$$ 3332.883

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} -1.73205 q^{3} +1.00000 q^{4} +1.73205 q^{6} -1.00000 q^{8} +2.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} -1.73205 q^{3} +1.00000 q^{4} +1.73205 q^{6} -1.00000 q^{8} +2.00000 q^{9} -1.73205 q^{11} -1.73205 q^{12} -1.00000 q^{13} +1.00000 q^{16} -1.00000 q^{17} -2.00000 q^{18} +1.73205 q^{22} +1.73205 q^{24} +1.00000 q^{25} +1.00000 q^{26} -1.73205 q^{27} -1.00000 q^{32} +3.00000 q^{33} +1.00000 q^{34} +2.00000 q^{36} +1.73205 q^{39} -1.73205 q^{44} -1.73205 q^{48} -1.00000 q^{50} +1.73205 q^{51} -1.00000 q^{52} -1.00000 q^{53} +1.73205 q^{54} +1.00000 q^{64} -3.00000 q^{66} -1.00000 q^{68} +1.73205 q^{71} -2.00000 q^{72} -1.73205 q^{75} -1.73205 q^{78} -1.73205 q^{79} +1.00000 q^{81} +1.73205 q^{88} -1.00000 q^{89} +1.73205 q^{96} -3.46410 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 2 q^{2} + 2 q^{4} - 2 q^{8} + 4 q^{9}+O(q^{10})$$ 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^8 + 4 * q^9 $$2 q - 2 q^{2} + 2 q^{4} - 2 q^{8} + 4 q^{9} - 2 q^{13} + 2 q^{16} - 2 q^{17} - 4 q^{18} + 2 q^{25} + 2 q^{26} - 2 q^{32} + 6 q^{33} + 2 q^{34} + 4 q^{36} - 2 q^{50} - 2 q^{52} - 2 q^{53} + 2 q^{64} - 6 q^{66} - 2 q^{68} - 4 q^{72} + 2 q^{81} - 2 q^{89}+O(q^{100})$$ 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^8 + 4 * q^9 - 2 * q^13 + 2 * q^16 - 2 * q^17 - 4 * q^18 + 2 * q^25 + 2 * q^26 - 2 * q^32 + 6 * q^33 + 2 * q^34 + 4 * q^36 - 2 * q^50 - 2 * q^52 - 2 * q^53 + 2 * q^64 - 6 * q^66 - 2 * q^68 - 4 * q^72 + 2 * q^81 - 2 * q^89

## 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
$$3$$ −1.73205 −1.73205 −0.866025 0.500000i $$-0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$4$$ 1.00000 1.00000
$$5$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$6$$ 1.73205 1.73205
$$7$$ 0 0
$$8$$ −1.00000 −1.00000
$$9$$ 2.00000 2.00000
$$10$$ 0 0
$$11$$ −1.73205 −1.73205 −0.866025 0.500000i $$-0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$12$$ −1.73205 −1.73205
$$13$$ −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
$$18$$ −2.00000 −2.00000
$$19$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 1.73205 1.73205
$$23$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ 1.73205 1.73205
$$25$$ 1.00000 1.00000
$$26$$ 1.00000 1.00000
$$27$$ −1.73205 −1.73205
$$28$$ 0 0
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ −1.00000 −1.00000
$$33$$ 3.00000 3.00000
$$34$$ 1.00000 1.00000
$$35$$ 0 0
$$36$$ 2.00000 2.00000
$$37$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$38$$ 0 0
$$39$$ 1.73205 1.73205
$$40$$ 0 0
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$44$$ −1.73205 −1.73205
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$48$$ −1.73205 −1.73205
$$49$$ 0 0
$$50$$ −1.00000 −1.00000
$$51$$ 1.73205 1.73205
$$52$$ −1.00000 −1.00000
$$53$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$54$$ 1.73205 1.73205
$$55$$ 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 $$\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 1.00000 1.00000
$$65$$ 0 0
$$66$$ −3.00000 −3.00000
$$67$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$68$$ −1.00000 −1.00000
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 1.73205 1.73205 0.866025 0.500000i $$-0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$72$$ −2.00000 −2.00000
$$73$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$74$$ 0 0
$$75$$ −1.73205 −1.73205
$$76$$ 0 0
$$77$$ 0 0
$$78$$ −1.73205 −1.73205
$$79$$ −1.73205 −1.73205 −0.866025 0.500000i $$-0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$80$$ 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
$$88$$ 1.73205 1.73205
$$89$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 1.73205 1.73205
$$97$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$98$$ 0 0
$$99$$ −3.46410 −3.46410
$$100$$ 1.00000 1.00000
$$101$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$102$$ −1.73205 −1.73205
$$103$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$104$$ 1.00000 1.00000
$$105$$ 0 0
$$106$$ 1.00000 1.00000
$$107$$ 1.73205 1.73205 0.866025 0.500000i $$-0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$108$$ −1.73205 −1.73205
$$109$$ 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
$$117$$ −2.00000 −2.00000
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 2.00000 2.00000
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 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
$$131$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ 3.00000 3.00000
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 1.00000 1.00000
$$137$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$138$$ 0 0
$$139$$ 1.73205 1.73205 0.866025 0.500000i $$-0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −1.73205 −1.73205
$$143$$ 1.73205 1.73205
$$144$$ 2.00000 2.00000
$$145$$ 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 $$0.666667\pi$$
$$150$$ 1.73205 1.73205
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ 0 0
$$153$$ −2.00000 −2.00000
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 1.73205 1.73205
$$157$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$158$$ 1.73205 1.73205
$$159$$ 1.73205 1.73205
$$160$$ 0 0
$$161$$ 0 0
$$162$$ −1.00000 −1.00000
$$163$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 1.73205 1.73205 0.866025 0.500000i $$-0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$168$$ 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
$$176$$ −1.73205 −1.73205
$$177$$ 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
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 1.73205 1.73205
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$192$$ −1.73205 −1.73205
$$193$$ 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 $$\pi$$
$$198$$ 3.46410 3.46410
$$199$$ 1.73205 1.73205 0.866025 0.500000i $$-0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$200$$ −1.00000 −1.00000
$$201$$ 0 0
$$202$$ −2.00000 −2.00000
$$203$$ 0 0
$$204$$ 1.73205 1.73205
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ −1.00000 −1.00000
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$212$$ −1.00000 −1.00000
$$213$$ −3.00000 −3.00000
$$214$$ −1.73205 −1.73205
$$215$$ 0 0
$$216$$ 1.73205 1.73205
$$217$$ 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
$$225$$ 2.00000 2.00000
$$226$$ 0 0
$$227$$ 1.73205 1.73205 0.866025 0.500000i $$-0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$228$$ 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 $$\pi$$
$$234$$ 2.00000 2.00000
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 3.00000 3.00000
$$238$$ 0 0
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$242$$ −2.00000 −2.00000
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 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
$$262$$ 0 0
$$263$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$264$$ −3.00000 −3.00000
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 1.73205 1.73205
$$268$$ 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
$$275$$ −1.73205 −1.73205
$$276$$ 0 0
$$277$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$278$$ −1.73205 −1.73205
$$279$$ 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
$$283$$ −1.73205 −1.73205 −0.866025 0.500000i $$-0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$284$$ 1.73205 1.73205
$$285$$ 0 0
$$286$$ −1.73205 −1.73205
$$287$$ 0 0
$$288$$ −2.00000 −2.00000
$$289$$ 1.00000 1.00000
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 3.00000 3.00000
$$298$$ 1.00000 1.00000
$$299$$ 0 0
$$300$$ −1.73205 −1.73205
$$301$$ 0 0
$$302$$ 0 0
$$303$$ −3.46410 −3.46410
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 2.00000 2.00000
$$307$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −1.73205 −1.73205 −0.866025 0.500000i $$-0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$312$$ −1.73205 −1.73205
$$313$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$314$$ −1.00000 −1.00000
$$315$$ 0 0
$$316$$ −1.73205 −1.73205
$$317$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$318$$ −1.73205 −1.73205
$$319$$ 0 0
$$320$$ 0 0
$$321$$ −3.00000 −3.00000
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 1.00000 1.00000
$$325$$ −1.00000 −1.00000
$$326$$ 0 0
$$327$$ 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
$$334$$ −1.73205 −1.73205
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$348$$ 0 0
$$349$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$350$$ 0 0
$$351$$ 1.73205 1.73205
$$352$$ 1.73205 1.73205
$$353$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$354$$ 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
$$363$$ −3.46410 −3.46410
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 1.73205 1.73205 0.866025 0.500000i $$-0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$374$$ −1.73205 −1.73205
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 1.73205 1.73205 0.866025 0.500000i $$-0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$384$$ 1.73205 1.73205
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ −3.46410 −3.46410
$$397$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$398$$ −1.73205 −1.73205
$$399$$ 0 0
$$400$$ 1.00000 1.00000
$$401$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 2.00000 2.00000
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ −1.73205 −1.73205
$$409$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$410$$ 0 0
$$411$$ −1.73205 −1.73205
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 1.00000 1.00000
$$417$$ −3.00000 −3.00000
$$418$$ 0 0
$$419$$ 1.73205 1.73205 0.866025 0.500000i $$-0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$420$$ 0 0
$$421$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 1.00000 1.00000
$$425$$ −1.00000 −1.00000
$$426$$ 3.00000 3.00000
$$427$$ 0 0
$$428$$ 1.73205 1.73205
$$429$$ −3.00000 −3.00000
$$430$$ 0 0
$$431$$ 1.73205 1.73205 0.866025 0.500000i $$-0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$432$$ −1.73205 −1.73205
$$433$$ 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
$$439$$ −1.73205 −1.73205 −0.866025 0.500000i $$-0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$440$$ 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
$$447$$ 1.73205 1.73205
$$448$$ 0 0
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ −2.00000 −2.00000
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ −1.73205 −1.73205
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$458$$ −2.00000 −2.00000
$$459$$ 1.73205 1.73205
$$460$$ 0 0
$$461$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$462$$ 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 $$\pi$$
$$468$$ −2.00000 −2.00000
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −1.73205 −1.73205
$$472$$ 0 0
$$473$$ 0 0
$$474$$ −3.00000 −3.00000
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −2.00000 −2.00000
$$478$$ 0 0
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 2.00000 2.00000
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −1.73205 −1.73205 −0.866025 0.500000i $$-0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 1.73205 1.73205 0.866025 0.500000i $$-0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$500$$ 0 0
$$501$$ −3.00000 −3.00000
$$502$$ 0 0
$$503$$ −1.73205 −1.73205 −0.866025 0.500000i $$-0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$510$$ 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 $$\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 3.00000 3.00000
$$529$$ −1.00000 −1.00000
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ −1.73205 −1.73205
$$535$$ 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
$$547$$ −1.73205 −1.73205 −0.866025 0.500000i $$-0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$548$$ 1.00000 1.00000
$$549$$ 0 0
$$550$$ 1.73205 1.73205
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 1.73205 1.73205
$$557$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ −3.00000 −3.00000
$$562$$ 1.00000 1.00000
$$563$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 1.73205 1.73205
$$567$$ 0 0
$$568$$ −1.73205 −1.73205
$$569$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$570$$ 0 0
$$571$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$572$$ 1.73205 1.73205
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 2.00000 2.00000
$$577$$ −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
$$583$$ 1.73205 1.73205
$$584$$ 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 $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$594$$ −3.00000 −3.00000
$$595$$ 0 0
$$596$$ −1.00000 −1.00000
$$597$$ −3.00000 −3.00000
$$598$$ 0 0
$$599$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$600$$ 1.73205 1.73205
$$601$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 3.46410 3.46410
$$607$$ 1.73205 1.73205 0.866025 0.500000i $$-0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ −2.00000 −2.00000
$$613$$ −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
$$619$$ −1.73205 −1.73205 −0.866025 0.500000i $$-0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 1.73205 1.73205
$$623$$ 0 0
$$624$$ 1.73205 1.73205
$$625$$ 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 $$\pi$$
$$632$$ 1.73205 1.73205
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 1.73205 1.73205
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 3.46410 3.46410
$$640$$ 0 0
$$641$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$642$$ 3.00000 3.00000
$$643$$ 1.73205 1.73205 0.866025 0.500000i $$-0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$644$$ 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
$$652$$ 0 0
$$653$$ 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 $$\pi$$
−1.00000 $$\pi$$
$$662$$ 0 0
$$663$$ −1.73205 −1.73205
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 1.73205 1.73205
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ 0 0
$$675$$ −1.73205 −1.73205
$$676$$ 0 0
$$677$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −3.00000 −3.00000
$$682$$ 0 0
$$683$$ −1.73205 −1.73205 −0.866025 0.500000i $$-0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −3.46410 −3.46410
$$688$$ 0 0
$$689$$ 1.00000 1.00000
$$690$$ 0 0
$$691$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 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 $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$702$$ −1.73205 −1.73205
$$703$$ 0 0
$$704$$ −1.73205 −1.73205
$$705$$ 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
$$711$$ −3.46410 −3.46410
$$712$$ 1.00000 1.00000
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 1.73205 1.73205 0.866025 0.500000i $$-0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −1.00000 −1.00000
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 3.46410 3.46410
$$727$$ 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 $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$734$$ −1.73205 −1.73205
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −1.73205 −1.73205 −0.866025 0.500000i $$-0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −1.00000 −1.00000
$$747$$ 0 0
$$748$$ 1.73205 1.73205
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 1.73205 1.73205 0.866025 0.500000i $$-0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$758$$ −1.73205 −1.73205
$$759$$ 0 0
$$760$$ 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
$$768$$ −1.73205 −1.73205
$$769$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$770$$ 0 0
$$771$$ 1.73205 1.73205
$$772$$ 0 0
$$773$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ −1.00000 −1.00000
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −3.00000 −3.00000
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 3.46410 3.46410
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 1.73205 1.73205
$$797$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ −1.00000 −1.00000
$$801$$ −2.00000 −2.00000
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ −2.00000 −2.00000
$$809$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$810$$ 0 0
$$811$$ −1.73205 −1.73205 −0.866025 0.500000i $$-0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 1.73205 1.73205
$$817$$ 0 0
$$818$$ −1.00000 −1.00000
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$822$$ 1.73205 1.73205
$$823$$ 1.73205 1.73205 0.866025 0.500000i $$-0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$824$$ 0 0
$$825$$ 3.00000 3.00000
$$826$$ 0 0
$$827$$ −1.73205 −1.73205 −0.866025 0.500000i $$-0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$828$$ 0 0
$$829$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ −1.00000 −1.00000
$$833$$ 0 0
$$834$$ 3.00000 3.00000
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ −1.73205 −1.73205
$$839$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$840$$ 0 0
$$841$$ 1.00000 1.00000
$$842$$ 2.00000 2.00000
$$843$$ 1.73205 1.73205
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 0 0
$$848$$ −1.00000 −1.00000
$$849$$ 3.00000 3.00000
$$850$$ 1.00000 1.00000
$$851$$ 0 0
$$852$$ −3.00000 −3.00000
$$853$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ −1.73205 −1.73205
$$857$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$858$$ 3.00000 3.00000
$$859$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ −1.73205 −1.73205
$$863$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$864$$ 1.73205 1.73205
$$865$$ 0 0
$$866$$ −2.00000 −2.00000
$$867$$ −1.73205 −1.73205
$$868$$ 0 0
$$869$$ 3.00000 3.00000
$$870$$ 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 $$\pi$$
$$878$$ 1.73205 1.73205
$$879$$ −1.73205 −1.73205
$$880$$ 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
$$887$$ 1.73205 1.73205 0.866025 0.500000i $$-0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ −1.73205 −1.73205
$$892$$ 0 0
$$893$$ 0 0
$$894$$ −1.73205 −1.73205
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 0 0
$$900$$ 2.00000 2.00000
$$901$$ 1.00000 1.00000
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$908$$ 1.73205 1.73205
$$909$$ 4.00000 4.00000
$$910$$ 0 0
$$911$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 2.00000 2.00000
$$915$$ 0 0
$$916$$ 2.00000 2.00000
$$917$$ 0 0
$$918$$ −1.73205 −1.73205
$$919$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ −1.00000 −1.00000
$$923$$ −1.73205 −1.73205
$$924$$ 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
$$933$$ 3.00000 3.00000
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 2.00000 2.00000
$$937$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$942$$ 1.73205 1.73205
$$943$$ 0 0
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 1.73205 1.73205 0.866025 0.500000i $$-0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$948$$ 3.00000 3.00000
$$949$$ 0 0
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$954$$ 2.00000 2.00000
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −1.00000 −1.00000
$$962$$ 0 0
$$963$$ 3.46410 3.46410
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$968$$ −2.00000 −2.00000
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 1.73205 1.73205
$$975$$ 1.73205 1.73205
$$976$$ 0 0
$$977$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$978$$ 0 0
$$979$$ 1.73205 1.73205
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −1.73205 −1.73205 −0.866025 0.500000i $$-0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ −1.73205 −1.73205 −0.866025 0.500000i $$-0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$998$$ −1.73205 −1.73205
$$999$$ 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.f.883.1 2
4.3 odd 2 inner 3332.1.g.f.883.2 2
7.2 even 3 3332.1.o.f.67.2 4
7.3 odd 6 476.1.o.c.135.1 yes 4
7.4 even 3 3332.1.o.f.2039.2 4
7.5 odd 6 476.1.o.c.67.1 4
7.6 odd 2 3332.1.g.g.883.2 2
17.16 even 2 inner 3332.1.g.f.883.2 2
28.3 even 6 476.1.o.c.135.2 yes 4
28.11 odd 6 3332.1.o.f.2039.1 4
28.19 even 6 476.1.o.c.67.2 yes 4
28.23 odd 6 3332.1.o.f.67.1 4
28.27 even 2 3332.1.g.g.883.1 2
68.67 odd 2 CM 3332.1.g.f.883.1 2
119.16 even 6 3332.1.o.f.67.1 4
119.33 odd 6 476.1.o.c.67.2 yes 4
119.67 even 6 3332.1.o.f.2039.1 4
119.101 odd 6 476.1.o.c.135.2 yes 4
119.118 odd 2 3332.1.g.g.883.1 2
476.67 odd 6 3332.1.o.f.2039.2 4
476.135 odd 6 3332.1.o.f.67.2 4
476.271 even 6 476.1.o.c.67.1 4
476.339 even 6 476.1.o.c.135.1 yes 4
476.475 even 2 3332.1.g.g.883.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
476.1.o.c.67.1 4 7.5 odd 6
476.1.o.c.67.1 4 476.271 even 6
476.1.o.c.67.2 yes 4 28.19 even 6
476.1.o.c.67.2 yes 4 119.33 odd 6
476.1.o.c.135.1 yes 4 7.3 odd 6
476.1.o.c.135.1 yes 4 476.339 even 6
476.1.o.c.135.2 yes 4 28.3 even 6
476.1.o.c.135.2 yes 4 119.101 odd 6
3332.1.g.f.883.1 2 1.1 even 1 trivial
3332.1.g.f.883.1 2 68.67 odd 2 CM
3332.1.g.f.883.2 2 4.3 odd 2 inner
3332.1.g.f.883.2 2 17.16 even 2 inner
3332.1.g.g.883.1 2 28.27 even 2
3332.1.g.g.883.1 2 119.118 odd 2
3332.1.g.g.883.2 2 7.6 odd 2
3332.1.g.g.883.2 2 476.475 even 2
3332.1.o.f.67.1 4 28.23 odd 6
3332.1.o.f.67.1 4 119.16 even 6
3332.1.o.f.67.2 4 7.2 even 3
3332.1.o.f.67.2 4 476.135 odd 6
3332.1.o.f.2039.1 4 28.11 odd 6
3332.1.o.f.2039.1 4 119.67 even 6
3332.1.o.f.2039.2 4 7.4 even 3
3332.1.o.f.2039.2 4 476.67 odd 6