# Properties

 Label 639.1.d.a.496.3 Level $639$ Weight $1$ Character 639.496 Self dual yes Analytic conductor $0.319$ Analytic rank $0$ Dimension $3$ Projective image $D_{7}$ CM discriminant -71 Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [639,1,Mod(496,639)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(639, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("639.496");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$639 = 3^{2} \cdot 71$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 639.d (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

comment: select newform

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

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

 Self dual: yes Analytic conductor: $$0.318902543072$$ Analytic rank: $$0$$ Dimension: $$3$$ Coefficient field: $$\Q(\zeta_{14})^+$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{3} - x^{2} - 2x + 1$$ x^3 - x^2 - 2*x + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 71) Projective image: $$D_{7}$$ Projective field: Galois closure of 7.1.357911.1 Artin image: $D_{14}$ Artin field: Galois closure of 14.0.280155320935227.1

## Embedding invariants

 Embedding label 496.3 Root $$1.80194$$ of defining polynomial Character $$\chi$$ $$=$$ 639.496

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+1.80194 q^{2} +2.24698 q^{4} -1.24698 q^{5} +2.24698 q^{8} +O(q^{10})$$ $$q+1.80194 q^{2} +2.24698 q^{4} -1.24698 q^{5} +2.24698 q^{8} -2.24698 q^{10} +1.80194 q^{16} -1.80194 q^{19} -2.80194 q^{20} +0.554958 q^{25} +0.445042 q^{29} +1.00000 q^{32} -1.80194 q^{37} -3.24698 q^{38} -2.80194 q^{40} +1.24698 q^{43} +1.00000 q^{49} +1.00000 q^{50} +0.801938 q^{58} -1.00000 q^{71} +1.24698 q^{73} -3.24698 q^{74} -4.04892 q^{76} +1.24698 q^{79} -2.24698 q^{80} +1.80194 q^{83} +2.24698 q^{86} +0.445042 q^{89} +2.24698 q^{95} +1.80194 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$3 q + q^{2} + 2 q^{4} + q^{5} + 2 q^{8}+O(q^{10})$$ 3 * q + q^2 + 2 * q^4 + q^5 + 2 * q^8 $$3 q + q^{2} + 2 q^{4} + q^{5} + 2 q^{8} - 2 q^{10} + q^{16} - q^{19} - 4 q^{20} + 2 q^{25} + q^{29} + 3 q^{32} - q^{37} - 5 q^{38} - 4 q^{40} - q^{43} + 3 q^{49} + 3 q^{50} - 2 q^{58} - 3 q^{71} - q^{73} - 5 q^{74} - 3 q^{76} - q^{79} - 2 q^{80} + q^{83} + 2 q^{86} + q^{89} + 2 q^{95} + q^{98}+O(q^{100})$$ 3 * q + q^2 + 2 * q^4 + q^5 + 2 * q^8 - 2 * q^10 + q^16 - q^19 - 4 * q^20 + 2 * q^25 + q^29 + 3 * q^32 - q^37 - 5 * q^38 - 4 * q^40 - q^43 + 3 * q^49 + 3 * q^50 - 2 * q^58 - 3 * q^71 - q^73 - 5 * q^74 - 3 * q^76 - q^79 - 2 * q^80 + q^83 + 2 * q^86 + q^89 + 2 * q^95 + q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/639\mathbb{Z}\right)^\times$$.

 $$n$$ $$433$$ $$569$$ $$\chi(n)$$ $$-1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.80194 1.80194 0.900969 0.433884i $$-0.142857\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$3$$ 0 0
$$4$$ 2.24698 2.24698
$$5$$ −1.24698 −1.24698 −0.623490 0.781831i $$-0.714286\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$6$$ 0 0
$$7$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$8$$ 2.24698 2.24698
$$9$$ 0 0
$$10$$ −2.24698 −2.24698
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.80194 1.80194
$$17$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$18$$ 0 0
$$19$$ −1.80194 −1.80194 −0.900969 0.433884i $$-0.857143\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$20$$ −2.80194 −2.80194
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$24$$ 0 0
$$25$$ 0.554958 0.554958
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 0.445042 0.445042 0.222521 0.974928i $$-0.428571\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ 1.00000 1.00000
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −1.80194 −1.80194 −0.900969 0.433884i $$-0.857143\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$38$$ −3.24698 −3.24698
$$39$$ 0 0
$$40$$ −2.80194 −2.80194
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ 1.24698 1.24698 0.623490 0.781831i $$-0.285714\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$48$$ 0 0
$$49$$ 1.00000 1.00000
$$50$$ 1.00000 1.00000
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0.801938 0.801938
$$59$$ 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
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −1.00000 −1.00000
$$72$$ 0 0
$$73$$ 1.24698 1.24698 0.623490 0.781831i $$-0.285714\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$74$$ −3.24698 −3.24698
$$75$$ 0 0
$$76$$ −4.04892 −4.04892
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 1.24698 1.24698 0.623490 0.781831i $$-0.285714\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$80$$ −2.24698 −2.24698
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 1.80194 1.80194 0.900969 0.433884i $$-0.142857\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 2.24698 2.24698
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0.445042 0.445042 0.222521 0.974928i $$-0.428571\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 2.24698 2.24698
$$96$$ 0 0
$$97$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$98$$ 1.80194 1.80194
$$99$$ 0 0
$$100$$ 1.24698 1.24698
$$101$$ 1.80194 1.80194 0.900969 0.433884i $$-0.142857\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$102$$ 0 0
$$103$$ −0.445042 −0.445042 −0.222521 0.974928i $$-0.571429\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$108$$ 0 0
$$109$$ −0.445042 −0.445042 −0.222521 0.974928i $$-0.571429\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 1.00000 1.00000
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 1.00000 1.00000
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0.554958 0.554958
$$126$$ 0 0
$$127$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$128$$ −1.00000 −1.00000
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −1.24698 −1.24698 −0.623490 0.781831i $$-0.714286\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −1.80194 −1.80194
$$143$$ 0 0
$$144$$ 0 0
$$145$$ −0.554958 −0.554958
$$146$$ 2.24698 2.24698
$$147$$ 0 0
$$148$$ −4.04892 −4.04892
$$149$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$150$$ 0 0
$$151$$ −0.445042 −0.445042 −0.222521 0.974928i $$-0.571429\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$152$$ −4.04892 −4.04892
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −0.445042 −0.445042 −0.222521 0.974928i $$-0.571429\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$158$$ 2.24698 2.24698
$$159$$ 0 0
$$160$$ −1.24698 −1.24698
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 3.24698 3.24698
$$167$$ −1.24698 −1.24698 −0.623490 0.781831i $$-0.714286\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$168$$ 0 0
$$169$$ 1.00000 1.00000
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 2.80194 2.80194
$$173$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0.801938 0.801938
$$179$$ −1.24698 −1.24698 −0.623490 0.781831i $$-0.714286\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 2.24698 2.24698
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 4.04892 4.04892
$$191$$ 0.445042 0.445042 0.222521 0.974928i $$-0.428571\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$192$$ 0 0
$$193$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 2.24698 2.24698
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 0 0
$$199$$ −1.80194 −1.80194 −0.900969 0.433884i $$-0.857143\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$200$$ 1.24698 1.24698
$$201$$ 0 0
$$202$$ 3.24698 3.24698
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ −0.801938 −0.801938
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ −3.60388 −3.60388
$$215$$ −1.55496 −1.55496
$$216$$ 0 0
$$217$$ 0 0
$$218$$ −0.801938 −0.801938
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −1.80194 −1.80194 −0.900969 0.433884i $$-0.857143\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$228$$ 0 0
$$229$$ 1.24698 1.24698 0.623490 0.781831i $$-0.285714\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 1.00000 1.00000
$$233$$ 1.80194 1.80194 0.900969 0.433884i $$-0.142857\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$242$$ 1.80194 1.80194
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −1.24698 −1.24698
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 1.00000 1.00000
$$251$$ 1.80194 1.80194 0.900969 0.433884i $$-0.142857\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ −1.80194 −1.80194
$$257$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −2.24698 −2.24698
$$263$$ −1.24698 −1.24698 −0.623490 0.781831i $$-0.714286\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$270$$ 0 0
$$271$$ −0.445042 −0.445042 −0.222521 0.974928i $$-0.571429\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −1.80194 −1.80194 −0.900969 0.433884i $$-0.857143\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$284$$ −2.24698 −2.24698
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 1.00000 1.00000
$$290$$ −1.00000 −1.00000
$$291$$ 0 0
$$292$$ 2.80194 2.80194
$$293$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ −4.04892 −4.04892
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −0.801938 −0.801938
$$303$$ 0 0
$$304$$ −3.24698 −3.24698
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 1.80194 1.80194 0.900969 0.433884i $$-0.142857\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$312$$ 0 0
$$313$$ −1.80194 −1.80194 −0.900969 0.433884i $$-0.857143\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$314$$ −0.801938 −0.801938
$$315$$ 0 0
$$316$$ 2.80194 2.80194
$$317$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$332$$ 4.04892 4.04892
$$333$$ 0 0
$$334$$ −2.24698 −2.24698
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$338$$ 1.80194 1.80194
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 2.80194 2.80194
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$348$$ 0 0
$$349$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$354$$ 0 0
$$355$$ 1.24698 1.24698
$$356$$ 1.00000 1.00000
$$357$$ 0 0
$$358$$ −2.24698 −2.24698
$$359$$ −1.24698 −1.24698 −0.623490 0.781831i $$-0.714286\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$360$$ 0 0
$$361$$ 2.24698 2.24698
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −1.55496 −1.55496
$$366$$ 0 0
$$367$$ 1.24698 1.24698 0.623490 0.781831i $$-0.285714\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 4.04892 4.04892
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 1.24698 1.24698 0.623490 0.781831i $$-0.285714\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −0.445042 −0.445042 −0.222521 0.974928i $$-0.571429\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$380$$ 5.04892 5.04892
$$381$$ 0 0
$$382$$ 0.801938 0.801938
$$383$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 2.24698 2.24698
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −1.55496 −1.55496
$$396$$ 0 0
$$397$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$398$$ −3.24698 −3.24698
$$399$$ 0 0
$$400$$ 1.00000 1.00000
$$401$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 4.04892 4.04892
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −0.445042 −0.445042 −0.222521 0.974928i $$-0.571429\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −1.00000 −1.00000
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −2.24698 −2.24698
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0.445042 0.445042 0.222521 0.974928i $$-0.428571\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −4.49396 −4.49396
$$429$$ 0 0
$$430$$ −2.80194 −2.80194
$$431$$ 1.80194 1.80194 0.900969 0.433884i $$-0.142857\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$432$$ 0 0
$$433$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −1.00000 −1.00000
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$444$$ 0 0
$$445$$ −0.554958 −0.554958
$$446$$ −3.24698 −3.24698
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$458$$ 2.24698 2.24698
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ −1.80194 −1.80194 −0.900969 0.433884i $$-0.857143\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$464$$ 0.801938 0.801938
$$465$$ 0 0
$$466$$ 3.24698 3.24698
$$467$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ −1.00000 −1.00000
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 2.24698 2.24698
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ −2.24698 −2.24698
$$491$$ 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
$$499$$ −0.445042 −0.445042 −0.222521 0.974928i $$-0.571429\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$500$$ 1.24698 1.24698
$$501$$ 0 0
$$502$$ 3.24698 3.24698
$$503$$ 0.445042 0.445042 0.222521 0.974928i $$-0.428571\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$504$$ 0 0
$$505$$ −2.24698 −2.24698
$$506$$ 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
$$512$$ −2.24698 −2.24698
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0.554958 0.554958
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −1.24698 −1.24698 −0.623490 0.781831i $$-0.714286\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$522$$ 0 0
$$523$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$524$$ −2.80194 −2.80194
$$525$$ 0 0
$$526$$ −2.24698 −2.24698
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 1.00000 1.00000
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 2.49396 2.49396
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$542$$ −0.801938 −0.801938
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0.554958 0.554958
$$546$$ 0 0
$$547$$ −1.80194 −1.80194 −0.900969 0.433884i $$-0.857143\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −0.801938 −0.801938
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −3.24698 −3.24698
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 0.445042 0.445042 0.222521 0.974928i $$-0.428571\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ −2.24698 −2.24698
$$569$$ −1.24698 −1.24698 −0.623490 0.781831i $$-0.714286\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$570$$ 0 0
$$571$$ −1.80194 −1.80194 −0.900969 0.433884i $$-0.857143\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 1.24698 1.24698 0.623490 0.781831i $$-0.285714\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$578$$ 1.80194 1.80194
$$579$$ 0 0
$$580$$ −1.24698 −1.24698
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 2.80194 2.80194
$$585$$ 0 0
$$586$$ −3.60388 −3.60388
$$587$$ 0.445042 0.445042 0.222521 0.974928i $$-0.428571\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −3.24698 −3.24698
$$593$$ 0.445042 0.445042 0.222521 0.974928i $$-0.428571\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$600$$ 0 0
$$601$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −1.00000 −1.00000
$$605$$ −1.24698 −1.24698
$$606$$ 0 0
$$607$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$608$$ −1.80194 −1.80194
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −0.445042 −0.445042 −0.222521 0.974928i $$-0.571429\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −1.24698 −1.24698 −0.623490 0.781831i $$-0.714286\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$618$$ 0 0
$$619$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 3.24698 3.24698
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −1.24698 −1.24698
$$626$$ −3.24698 −3.24698
$$627$$ 0 0
$$628$$ −1.00000 −1.00000
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$632$$ 2.80194 2.80194
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 1.24698 1.24698
$$641$$ 1.80194 1.80194 0.900969 0.433884i $$-0.142857\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$642$$ 0 0
$$643$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$654$$ 0 0
$$655$$ 1.55496 1.55496
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0.445042 0.445042 0.222521 0.974928i $$-0.428571\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$660$$ 0 0
$$661$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 4.04892 4.04892
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ −2.80194 −2.80194
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 2.24698 2.24698
$$677$$ 0.445042 0.445042 0.222521 0.974928i $$-0.428571\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 2.24698 2.24698
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ 0 0
$$703$$ 3.24698 3.24698
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$710$$ 2.24698 2.24698
$$711$$ 0 0
$$712$$ 1.00000 1.00000
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −2.80194 −2.80194
$$717$$ 0 0
$$718$$ −2.24698 −2.24698
$$719$$ 1.80194 1.80194 0.900969 0.433884i $$-0.142857\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 4.04892 4.04892
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0.246980 0.246980
$$726$$ 0 0
$$727$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ −2.80194 −2.80194
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$734$$ 2.24698 2.24698
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$740$$ 5.04892 5.04892
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 2.24698 2.24698
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0.554958 0.554958
$$756$$ 0 0
$$757$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$758$$ −0.801938 −0.801938
$$759$$ 0 0
$$760$$ 5.04892 5.04892
$$761$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 1.00000 1.00000
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 1.80194 1.80194
$$785$$ 0.554958 0.554958
$$786$$ 0 0
$$787$$ −0.445042 −0.445042 −0.222521 0.974928i $$-0.571429\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ −2.80194 −2.80194
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ −4.04892 −4.04892
$$797$$ 1.80194 1.80194 0.900969 0.433884i $$-0.142857\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0.554958 0.554958
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 4.04892 4.04892
$$809$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$810$$ 0 0
$$811$$ 1.24698 1.24698 0.623490 0.781831i $$-0.285714\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −2.24698 −2.24698
$$818$$ −0.801938 −0.801938
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 1.80194 1.80194 0.900969 0.433884i $$-0.142857\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$822$$ 0 0
$$823$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$824$$ −1.00000 −1.00000
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$828$$ 0 0
$$829$$ −1.80194 −1.80194 −0.900969 0.433884i $$-0.857143\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$830$$ −4.04892 −4.04892
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 1.55496 1.55496
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0.801938 0.801938
$$839$$ 1.80194 1.80194 0.900969 0.433884i $$-0.142857\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$840$$ 0 0
$$841$$ −0.801938 −0.801938
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ −1.24698 −1.24698
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ −0.445042 −0.445042 −0.222521 0.974928i $$-0.571429\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ −4.49396 −4.49396
$$857$$ 0.445042 0.445042 0.222521 0.974928i $$-0.428571\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$858$$ 0 0
$$859$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$860$$ −3.49396 −3.49396
$$861$$ 0 0
$$862$$ 3.24698 3.24698
$$863$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ −1.00000 −1.00000
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 1.24698 1.24698 0.623490 0.781831i $$-0.285714\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −1.24698 −1.24698 −0.623490 0.781831i $$-0.714286\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$882$$ 0 0
$$883$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ −1.00000 −1.00000
$$891$$ 0 0
$$892$$ −4.04892 −4.04892
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 1.55496 1.55496
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 0 0
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 2.80194 2.80194
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ −1.00000 −1.00000
$$926$$ −3.24698 −3.24698
$$927$$ 0 0
$$928$$ 0.445042 0.445042
$$929$$ 1.80194 1.80194 0.900969 0.433884i $$-0.142857\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$930$$ 0 0
$$931$$ −1.80194 −1.80194
$$932$$ 4.04892 4.04892
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 1.80194 1.80194 0.900969 0.433884i $$-0.142857\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −1.24698 −1.24698 −0.623490 0.781831i $$-0.714286\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ −1.80194 −1.80194
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −1.24698 −1.24698 −0.623490 0.781831i $$-0.714286\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$954$$ 0 0
$$955$$ −0.554958 −0.554958
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 1.00000 1.00000
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$968$$ 2.24698 2.24698
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 0.445042 0.445042 0.222521 0.974928i $$-0.428571\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ −2.80194 −2.80194
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 1.80194 1.80194 0.900969 0.433884i $$-0.142857\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 2.24698 2.24698
$$996$$ 0 0
$$997$$ 1.24698 1.24698 0.623490 0.781831i $$-0.285714\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$998$$ −0.801938 −0.801938
$$999$$ 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 639.1.d.a.496.3 3
3.2 odd 2 71.1.b.a.70.1 3
12.11 even 2 1136.1.h.a.993.2 3
15.2 even 4 1775.1.c.a.1774.1 6
15.8 even 4 1775.1.c.a.1774.6 6
15.14 odd 2 1775.1.d.b.851.3 3
21.2 odd 6 3479.1.g.e.851.3 6
21.5 even 6 3479.1.g.d.851.3 6
21.11 odd 6 3479.1.g.e.1206.3 6
21.17 even 6 3479.1.g.d.1206.3 6
21.20 even 2 3479.1.d.e.638.1 3
71.70 odd 2 CM 639.1.d.a.496.3 3
213.212 even 2 71.1.b.a.70.1 3
852.851 odd 2 1136.1.h.a.993.2 3
1065.212 odd 4 1775.1.c.a.1774.1 6
1065.638 odd 4 1775.1.c.a.1774.6 6
1065.1064 even 2 1775.1.d.b.851.3 3
1491.212 even 6 3479.1.g.e.851.3 6
1491.425 odd 6 3479.1.g.d.851.3 6
1491.851 even 6 3479.1.g.e.1206.3 6
1491.1277 odd 6 3479.1.g.d.1206.3 6
1491.1490 odd 2 3479.1.d.e.638.1 3

By twisted newform
Twist Min Dim Char Parity Ord Type
71.1.b.a.70.1 3 3.2 odd 2
71.1.b.a.70.1 3 213.212 even 2
639.1.d.a.496.3 3 1.1 even 1 trivial
639.1.d.a.496.3 3 71.70 odd 2 CM
1136.1.h.a.993.2 3 12.11 even 2
1136.1.h.a.993.2 3 852.851 odd 2
1775.1.c.a.1774.1 6 15.2 even 4
1775.1.c.a.1774.1 6 1065.212 odd 4
1775.1.c.a.1774.6 6 15.8 even 4
1775.1.c.a.1774.6 6 1065.638 odd 4
1775.1.d.b.851.3 3 15.14 odd 2
1775.1.d.b.851.3 3 1065.1064 even 2
3479.1.d.e.638.1 3 21.20 even 2
3479.1.d.e.638.1 3 1491.1490 odd 2
3479.1.g.d.851.3 6 21.5 even 6
3479.1.g.d.851.3 6 1491.425 odd 6
3479.1.g.d.1206.3 6 21.17 even 6
3479.1.g.d.1206.3 6 1491.1277 odd 6
3479.1.g.e.851.3 6 21.2 odd 6
3479.1.g.e.851.3 6 1491.212 even 6
3479.1.g.e.1206.3 6 21.11 odd 6
3479.1.g.e.1206.3 6 1491.851 even 6