# Properties

 Label 3040.1.b.a.1329.3 Level $3040$ Weight $1$ Character 3040.1329 Analytic conductor $1.517$ Analytic rank $0$ Dimension $8$ Projective image $D_{8}$ CM discriminant -95 Inner twists $8$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3040,1,Mod(1329,3040)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3040, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3040.1329");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$3040 = 2^{5} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3040.b (of order $$2$$, degree $$1$$, 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: $$1.51715763840$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: $$\Q(\zeta_{16})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{8} + 1$$ x^8 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{3}$$ Twist minimal: no (minimal twist has level 760) Projective image: $$D_{8}$$ Projective field: Galois closure of 8.0.66724352000.2

## Embedding invariants

 Embedding label 1329.3 Root $$-0.382683 - 0.923880i$$ of defining polynomial Character $$\chi$$ $$=$$ 3040.1329 Dual form 3040.1.b.a.1329.6

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-0.765367i q^{3} -1.00000i q^{5} +0.414214 q^{9} +O(q^{10})$$ $$q-0.765367i q^{3} -1.00000i q^{5} +0.414214 q^{9} +1.41421i q^{11} -1.84776i q^{13} -0.765367 q^{15} -1.00000i q^{19} -1.00000 q^{25} -1.08239i q^{27} +1.08239 q^{33} +0.765367i q^{37} -1.41421 q^{39} -0.414214i q^{45} +1.00000 q^{49} -0.765367i q^{53} +1.41421 q^{55} -0.765367 q^{57} +1.41421i q^{61} -1.84776 q^{65} -1.84776i q^{67} +0.765367i q^{75} -0.414214 q^{81} -1.00000 q^{95} -1.84776 q^{97} +0.585786i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q - 8 q^{9}+O(q^{10})$$ 8 * q - 8 * q^9 $$8 q - 8 q^{9} - 8 q^{25} + 8 q^{49} + 8 q^{81} - 8 q^{95}+O(q^{100})$$ 8 * q - 8 * q^9 - 8 * q^25 + 8 * q^49 + 8 * q^81 - 8 * q^95

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3040\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$1217$$ $$1921$$ $$2661$$ $$\chi(n)$$ $$1$$ $$-1$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ − 0.765367i − 0.765367i −0.923880 0.382683i $$-0.875000\pi$$
0.923880 0.382683i $$-0.125000\pi$$
$$4$$ 0 0
$$5$$ − 1.00000i − 1.00000i
$$6$$ 0 0
$$7$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$8$$ 0 0
$$9$$ 0.414214 0.414214
$$10$$ 0 0
$$11$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$12$$ 0 0
$$13$$ − 1.84776i − 1.84776i −0.382683 0.923880i $$-0.625000\pi$$
0.382683 0.923880i $$-0.375000\pi$$
$$14$$ 0 0
$$15$$ −0.765367 −0.765367
$$16$$ 0 0
$$17$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$18$$ 0 0
$$19$$ − 1.00000i − 1.00000i
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$24$$ 0 0
$$25$$ −1.00000 −1.00000
$$26$$ 0 0
$$27$$ − 1.08239i − 1.08239i
$$28$$ 0 0
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ 0 0
$$33$$ 1.08239 1.08239
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 0.765367i 0.765367i 0.923880 + 0.382683i $$0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$38$$ 0 0
$$39$$ −1.41421 −1.41421
$$40$$ 0 0
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$44$$ 0 0
$$45$$ − 0.414214i − 0.414214i
$$46$$ 0 0
$$47$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$48$$ 0 0
$$49$$ 1.00000 1.00000
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ − 0.765367i − 0.765367i −0.923880 0.382683i $$-0.875000\pi$$
0.923880 0.382683i $$-0.125000\pi$$
$$54$$ 0 0
$$55$$ 1.41421 1.41421
$$56$$ 0 0
$$57$$ −0.765367 −0.765367
$$58$$ 0 0
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −1.84776 −1.84776
$$66$$ 0 0
$$67$$ − 1.84776i − 1.84776i −0.382683 0.923880i $$-0.625000\pi$$
0.382683 0.923880i $$-0.375000\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0 0
$$73$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$74$$ 0 0
$$75$$ 0.765367i 0.765367i
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$80$$ 0 0
$$81$$ −0.414214 −0.414214
$$82$$ 0 0
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −1.00000 −1.00000
$$96$$ 0 0
$$97$$ −1.84776 −1.84776 −0.923880 0.382683i $$-0.875000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$98$$ 0 0
$$99$$ 0.585786i 0.585786i
$$100$$ 0 0
$$101$$ − 1.41421i − 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$102$$ 0 0
$$103$$ −0.765367 −0.765367 −0.382683 0.923880i $$-0.625000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 1.84776i 1.84776i 0.382683 + 0.923880i $$0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$108$$ 0 0
$$109$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$110$$ 0 0
$$111$$ 0.585786 0.585786
$$112$$ 0 0
$$113$$ 0.765367 0.765367 0.382683 0.923880i $$-0.375000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ − 0.765367i − 0.765367i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −1.00000 −1.00000
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 1.00000i 1.00000i
$$126$$ 0 0
$$127$$ −1.84776 −1.84776 −0.923880 0.382683i $$-0.875000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ −1.08239 −1.08239
$$136$$ 0 0
$$137$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$138$$ 0 0
$$139$$ − 1.41421i − 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 2.61313 2.61313
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ − 0.765367i − 0.765367i
$$148$$ 0 0
$$149$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$158$$ 0 0
$$159$$ −0.585786 −0.585786
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$164$$ 0 0
$$165$$ − 1.08239i − 1.08239i
$$166$$ 0 0
$$167$$ 1.84776 1.84776 0.923880 0.382683i $$-0.125000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$168$$ 0 0
$$169$$ −2.41421 −2.41421
$$170$$ 0 0
$$171$$ − 0.414214i − 0.414214i
$$172$$ 0 0
$$173$$ 1.84776i 1.84776i 0.382683 + 0.923880i $$0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$182$$ 0 0
$$183$$ 1.08239 1.08239
$$184$$ 0 0
$$185$$ 0.765367 0.765367
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ 0 0
$$193$$ 1.84776 1.84776 0.923880 0.382683i $$-0.125000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$194$$ 0 0
$$195$$ 1.41421i 1.41421i
$$196$$ 0 0
$$197$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$200$$ 0 0
$$201$$ −1.41421 −1.41421
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 1.41421 1.41421
$$210$$ 0 0
$$211$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 1.84776 1.84776 0.923880 0.382683i $$-0.125000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$224$$ 0 0
$$225$$ −0.414214 −0.414214
$$226$$ 0 0
$$227$$ 1.84776i 1.84776i 0.382683 + 0.923880i $$0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$228$$ 0 0
$$229$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$230$$ 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
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$240$$ 0 0
$$241$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$242$$ 0 0
$$243$$ − 0.765367i − 0.765367i
$$244$$ 0 0
$$245$$ − 1.00000i − 1.00000i
$$246$$ 0 0
$$247$$ −1.84776 −1.84776
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 1.84776 1.84776 0.923880 0.382683i $$-0.125000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$264$$ 0 0
$$265$$ −0.765367 −0.765367
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$270$$ 0 0
$$271$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ − 1.41421i − 1.41421i
$$276$$ 0 0
$$277$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$284$$ 0 0
$$285$$ 0.765367i 0.765367i
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 1.00000 1.00000
$$290$$ 0 0
$$291$$ 1.41421i 1.41421i
$$292$$ 0 0
$$293$$ 0.765367i 0.765367i 0.923880 + 0.382683i $$0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 1.53073 1.53073
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ −1.08239 −1.08239
$$304$$ 0 0
$$305$$ 1.41421 1.41421
$$306$$ 0 0
$$307$$ 1.84776i 1.84776i 0.382683 + 0.923880i $$0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$308$$ 0 0
$$309$$ 0.585786i 0.585786i
$$310$$ 0 0
$$311$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$312$$ 0 0
$$313$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 1.84776i 1.84776i 0.382683 + 0.923880i $$0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 1.41421 1.41421
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 1.84776i 1.84776i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$332$$ 0 0
$$333$$ 0.317025i 0.317025i
$$334$$ 0 0
$$335$$ −1.84776 −1.84776
$$336$$ 0 0
$$337$$ −0.765367 −0.765367 −0.382683 0.923880i $$-0.625000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$338$$ 0 0
$$339$$ − 0.585786i − 0.585786i
$$340$$ 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
$$349$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$350$$ 0 0
$$351$$ −2.00000 −2.00000
$$352$$ 0 0
$$353$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$360$$ 0 0
$$361$$ −1.00000 −1.00000
$$362$$ 0 0
$$363$$ 0.765367i 0.765367i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ − 0.765367i − 0.765367i −0.923880 0.382683i $$-0.875000\pi$$
0.923880 0.382683i $$-0.125000\pi$$
$$374$$ 0 0
$$375$$ 0.765367 0.765367
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$380$$ 0 0
$$381$$ 1.41421i 1.41421i
$$382$$ 0 0
$$383$$ 0.765367 0.765367 0.382683 0.923880i $$-0.375000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$384$$ 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
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0.414214i 0.414214i
$$406$$ 0 0
$$407$$ −1.08239 −1.08239
$$408$$ 0 0
$$409$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −1.08239 −1.08239
$$418$$ 0 0
$$419$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ − 2.00000i − 2.00000i
$$430$$ 0 0
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ 0 0
$$433$$ 0.765367 0.765367 0.382683 0.923880i $$-0.375000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$440$$ 0 0
$$441$$ 0.414214 0.414214
$$442$$ 0 0
$$443$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 1.08239 1.08239
$$448$$ 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 $$\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 1.00000i 1.00000i
$$476$$ 0 0
$$477$$ − 0.317025i − 0.317025i
$$478$$ 0 0
$$479$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$480$$ 0 0
$$481$$ 1.41421 1.41421
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 1.84776i 1.84776i
$$486$$ 0 0
$$487$$ 0.765367 0.765367 0.382683 0.923880i $$-0.375000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0.585786 0.585786
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$500$$ 0 0
$$501$$ − 1.41421i − 1.41421i
$$502$$ 0 0
$$503$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$504$$ 0 0
$$505$$ −1.41421 −1.41421
$$506$$ 0 0
$$507$$ 1.84776i 1.84776i
$$508$$ 0 0
$$509$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ −1.08239 −1.08239
$$514$$ 0 0
$$515$$ 0.765367i 0.765367i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 1.41421 1.41421
$$520$$ 0 0
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ 0 0
$$523$$ − 0.765367i − 0.765367i −0.923880 0.382683i $$-0.875000\pi$$
0.923880 0.382683i $$-0.125000\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 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
$$535$$ 1.84776 1.84776
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 1.41421i 1.41421i
$$540$$ 0 0
$$541$$ − 1.41421i − 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0.765367i 0.765367i 0.923880 + 0.382683i $$0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$548$$ 0 0
$$549$$ 0.585786i 0.585786i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ − 0.585786i − 0.585786i
$$556$$ 0 0
$$557$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0.765367i 0.765367i 0.923880 + 0.382683i $$0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$564$$ 0 0
$$565$$ − 0.765367i − 0.765367i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$570$$ 0 0
$$571$$ − 1.41421i − 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$578$$ 0 0
$$579$$ − 1.41421i − 1.41421i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 1.08239 1.08239
$$584$$ 0 0
$$585$$ −0.765367 −0.765367
$$586$$ 0 0
$$587$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$594$$ 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
$$603$$ − 0.765367i − 0.765367i
$$604$$ 0 0
$$605$$ 1.00000i 1.00000i
$$606$$ 0 0
$$607$$ −0.765367 −0.765367 −0.382683 0.923880i $$-0.625000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$618$$ 0 0
$$619$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 1.00000 1.00000
$$626$$ 0 0
$$627$$ − 1.08239i − 1.08239i
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 1.84776i 1.84776i
$$636$$ 0 0
$$637$$ − 1.84776i − 1.84776i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$642$$ 0 0
$$643$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ 0 0
$$661$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ − 1.41421i − 1.41421i
$$670$$ 0 0
$$671$$ −2.00000 −2.00000
$$672$$ 0 0
$$673$$ −0.765367 −0.765367 −0.382683 0.923880i $$-0.625000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$674$$ 0 0
$$675$$ 1.08239i 1.08239i
$$676$$ 0 0
$$677$$ 0.765367i 0.765367i 0.923880 + 0.382683i $$0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 1.41421 1.41421
$$682$$ 0 0
$$683$$ − 0.765367i − 0.765367i −0.923880 0.382683i $$-0.875000\pi$$
0.923880 0.382683i $$-0.125000\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 1.08239 1.08239
$$688$$ 0 0
$$689$$ −1.41421 −1.41421
$$690$$ 0 0
$$691$$ − 1.41421i − 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −1.41421 −1.41421
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ − 1.41421i − 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$702$$ 0 0
$$703$$ 0.765367 0.765367
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ − 2.61313i − 2.61313i
$$716$$ 0 0
$$717$$ − 1.53073i − 1.53073i
$$718$$ 0 0
$$719$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 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
$$733$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$734$$ 0 0
$$735$$ −0.765367 −0.765367
$$736$$ 0 0
$$737$$ 2.61313 2.61313
$$738$$ 0 0
$$739$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$740$$ 0 0
$$741$$ 1.41421i 1.41421i
$$742$$ 0 0
$$743$$ −1.84776 −1.84776 −0.923880 0.382683i $$-0.875000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$744$$ 0 0
$$745$$ 1.41421 1.41421
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$752$$ 0 0
$$753$$ −1.53073 −1.53073
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$770$$ 0 0
$$771$$ − 1.41421i − 1.41421i
$$772$$ 0 0
$$773$$ 1.84776i 1.84776i 0.382683 + 0.923880i $$0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$774$$ 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
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 0.765367i 0.765367i 0.923880 + 0.382683i $$0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 2.61313 2.61313
$$794$$ 0 0
$$795$$ 0.585786i 0.585786i
$$796$$ 0 0
$$797$$ − 0.765367i − 0.765367i −0.923880 0.382683i $$-0.875000\pi$$
0.923880 0.382683i $$-0.125000\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$810$$ 0 0
$$811$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$812$$ 0 0
$$813$$ − 1.08239i − 1.08239i
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$822$$ 0 0
$$823$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$824$$ 0 0
$$825$$ −1.08239 −1.08239
$$826$$ 0 0
$$827$$ − 0.765367i − 0.765367i −0.923880 0.382683i $$-0.875000\pi$$
0.923880 0.382683i $$-0.125000\pi$$
$$828$$ 0 0
$$829$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ − 1.84776i − 1.84776i
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$840$$ 0 0
$$841$$ −1.00000 −1.00000
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 2.41421i 2.41421i
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$854$$ 0 0
$$855$$ −0.414214 −0.414214
$$856$$ 0 0
$$857$$ −1.84776 −1.84776 −0.923880 0.382683i $$-0.875000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$858$$ 0 0
$$859$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −1.84776 −1.84776 −0.923880 0.382683i $$-0.875000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$864$$ 0 0
$$865$$ 1.84776 1.84776
$$866$$ 0 0
$$867$$ − 0.765367i − 0.765367i
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ −3.41421 −3.41421
$$872$$ 0 0
$$873$$ −0.765367 −0.765367
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 0.765367i 0.765367i 0.923880 + 0.382683i $$0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$878$$ 0 0
$$879$$ 0.585786 0.585786
$$880$$ 0 0
$$881$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$882$$ 0 0
$$883$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 0.765367 0.765367 0.382683 0.923880i $$-0.375000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ − 0.585786i − 0.585786i
$$892$$ 0 0
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 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
$$907$$ − 1.84776i − 1.84776i −0.382683 0.923880i $$-0.625000\pi$$
0.382683 0.923880i $$-0.375000\pi$$
$$908$$ 0 0
$$909$$ − 0.585786i − 0.585786i
$$910$$ 0 0
$$911$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ − 1.08239i − 1.08239i
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$920$$ 0 0
$$921$$ 1.41421 1.41421
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ − 0.765367i − 0.765367i
$$926$$ 0 0
$$927$$ −0.317025 −0.317025
$$928$$ 0 0
$$929$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$930$$ 0 0
$$931$$ − 1.00000i − 1.00000i
$$932$$ 0 0
$$933$$ − 1.08239i − 1.08239i
$$934$$ 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
$$941$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0 0
$$951$$ 1.41421 1.41421
$$952$$ 0 0
$$953$$ 1.84776 1.84776 0.923880 0.382683i $$-0.125000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$954$$ 0 0
$$955$$ 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
$$963$$ 0.765367i 0.765367i
$$964$$ 0 0
$$965$$ − 1.84776i − 1.84776i
$$966$$ 0 0
$$967$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 1.41421 1.41421
$$976$$ 0 0
$$977$$ −0.765367 −0.765367 −0.382683 0.923880i $$-0.625000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −0.765367 −0.765367 −0.382683 0.923880i $$-0.625000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$984$$ 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
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$998$$ 0 0
$$999$$ 0.828427 0.828427
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 3040.1.b.a.1329.3 8
4.3 odd 2 760.1.b.a.189.4 yes 8
5.4 even 2 inner 3040.1.b.a.1329.5 8
8.3 odd 2 760.1.b.a.189.3 8
8.5 even 2 inner 3040.1.b.a.1329.6 8
19.18 odd 2 inner 3040.1.b.a.1329.5 8
20.3 even 4 3800.1.o.g.1101.8 8
20.7 even 4 3800.1.o.g.1101.1 8
20.19 odd 2 760.1.b.a.189.5 yes 8
40.3 even 4 3800.1.o.g.1101.2 8
40.19 odd 2 760.1.b.a.189.6 yes 8
40.27 even 4 3800.1.o.g.1101.7 8
40.29 even 2 inner 3040.1.b.a.1329.4 8
76.75 even 2 760.1.b.a.189.5 yes 8
95.94 odd 2 CM 3040.1.b.a.1329.3 8
152.37 odd 2 inner 3040.1.b.a.1329.4 8
152.75 even 2 760.1.b.a.189.6 yes 8
380.227 odd 4 3800.1.o.g.1101.8 8
380.303 odd 4 3800.1.o.g.1101.1 8
380.379 even 2 760.1.b.a.189.4 yes 8
760.189 odd 2 inner 3040.1.b.a.1329.6 8
760.227 odd 4 3800.1.o.g.1101.2 8
760.379 even 2 760.1.b.a.189.3 8
760.683 odd 4 3800.1.o.g.1101.7 8

By twisted newform
Twist Min Dim Char Parity Ord Type
760.1.b.a.189.3 8 8.3 odd 2
760.1.b.a.189.3 8 760.379 even 2
760.1.b.a.189.4 yes 8 4.3 odd 2
760.1.b.a.189.4 yes 8 380.379 even 2
760.1.b.a.189.5 yes 8 20.19 odd 2
760.1.b.a.189.5 yes 8 76.75 even 2
760.1.b.a.189.6 yes 8 40.19 odd 2
760.1.b.a.189.6 yes 8 152.75 even 2
3040.1.b.a.1329.3 8 1.1 even 1 trivial
3040.1.b.a.1329.3 8 95.94 odd 2 CM
3040.1.b.a.1329.4 8 40.29 even 2 inner
3040.1.b.a.1329.4 8 152.37 odd 2 inner
3040.1.b.a.1329.5 8 5.4 even 2 inner
3040.1.b.a.1329.5 8 19.18 odd 2 inner
3040.1.b.a.1329.6 8 8.5 even 2 inner
3040.1.b.a.1329.6 8 760.189 odd 2 inner
3800.1.o.g.1101.1 8 20.7 even 4
3800.1.o.g.1101.1 8 380.303 odd 4
3800.1.o.g.1101.2 8 40.3 even 4
3800.1.o.g.1101.2 8 760.227 odd 4
3800.1.o.g.1101.7 8 40.27 even 4
3800.1.o.g.1101.7 8 760.683 odd 4
3800.1.o.g.1101.8 8 20.3 even 4
3800.1.o.g.1101.8 8 380.227 odd 4