# Properties

 Label 9.22.a.b.1.1 Level $9$ Weight $22$ Character 9.1 Self dual yes Analytic conductor $25.153$ Analytic rank $1$ Dimension $1$ CM discriminant -3 Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,22,Mod(1,9)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 22);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$9 = 3^{2}$$ Weight: $$k$$ $$=$$ $$22$$ Character orbit: $$[\chi]$$ $$=$$ 9.a (trivial)

## 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: $$25.1529609858$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: yes Fricke sign: $$+1$$ Sato-Tate group: $N(\mathrm{U}(1))$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 9.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-2.09715e6 q^{4} +1.12398e9 q^{7} +O(q^{10})$$ $$q-2.09715e6 q^{4} +1.12398e9 q^{7} -3.70077e11 q^{13} +4.39805e12 q^{16} -3.55406e13 q^{19} -4.76837e14 q^{25} -2.35716e15 q^{28} -9.04007e15 q^{31} -5.77763e16 q^{37} +2.65258e17 q^{43} +7.04792e17 q^{49} +7.76107e17 q^{52} -1.08607e19 q^{61} -9.22337e18 q^{64} +6.94433e18 q^{67} -3.90986e19 q^{73} +7.45341e19 q^{76} +1.68068e20 q^{79} -4.15960e20 q^{91} -1.13207e21 q^{97} +O(q^{100})$$

## 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$3$$ 0 0
$$4$$ −2.09715e6 −1.00000
$$5$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$6$$ 0 0
$$7$$ 1.12398e9 1.50394 0.751970 0.659198i $$-0.229104\pi$$
0.751970 + 0.659198i $$0.229104\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ 0 0
$$13$$ −3.70077e11 −0.744538 −0.372269 0.928125i $$-0.621420\pi$$
−0.372269 + 0.928125i $$0.621420\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 4.39805e12 1.00000
$$17$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ 0 0
$$19$$ −3.55406e13 −1.32988 −0.664940 0.746897i $$-0.731543\pi$$
−0.664940 + 0.746897i $$0.731543\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ 0 0
$$25$$ −4.76837e14 −1.00000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ −2.35716e15 −1.50394
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0 0
$$31$$ −9.04007e15 −1.98095 −0.990476 0.137683i $$-0.956035\pi$$
−0.990476 + 0.137683i $$0.956035\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −5.77763e16 −1.97529 −0.987647 0.156694i $$-0.949916\pi$$
−0.987647 + 0.156694i $$0.949916\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ 2.65258e17 1.87176 0.935881 0.352317i $$-0.114606\pi$$
0.935881 + 0.352317i $$0.114606\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ 7.04792e17 1.26183
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 7.76107e17 0.744538
$$53$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ −1.08607e19 −1.94937 −0.974685 0.223583i $$-0.928225\pi$$
−0.974685 + 0.223583i $$0.928225\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ −9.22337e18 −1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 6.94433e18 0.465420 0.232710 0.972546i $$-0.425241\pi$$
0.232710 + 0.972546i $$0.425241\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ −3.90986e19 −1.06481 −0.532404 0.846490i $$-0.678711\pi$$
−0.532404 + 0.846490i $$0.678711\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 7.45341e19 1.32988
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 1.68068e20 1.99711 0.998553 0.0537677i $$-0.0171231\pi$$
0.998553 + 0.0537677i $$0.0171231\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$90$$ 0 0
$$91$$ −4.15960e20 −1.11974
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −1.13207e21 −1.55872 −0.779362 0.626573i $$-0.784457\pi$$
−0.779362 + 0.626573i $$0.784457\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 1.00000e21 1.00000
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ 0 0
$$103$$ −2.44432e21 −1.79212 −0.896060 0.443932i $$-0.853583\pi$$
−0.896060 + 0.443932i $$0.853583\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$108$$ 0 0
$$109$$ 4.46449e21 1.80632 0.903158 0.429309i $$-0.141243\pi$$
0.903158 + 0.429309i $$0.141243\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 4.94333e21 1.50394
$$113$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −7.40025e21 −1.00000
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 1.89584e22 1.98095
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −1.97512e22 −1.60566 −0.802832 0.596205i $$-0.796674\pi$$
−0.802832 + 0.596205i $$0.796674\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ 0 0
$$133$$ −3.99471e22 −2.00006
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$138$$ 0 0
$$139$$ −2.94518e21 −0.0927804 −0.0463902 0.998923i $$-0.514772\pi$$
−0.0463902 + 0.998923i $$0.514772\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 1.21166e23 1.97529
$$149$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$150$$ 0 0
$$151$$ 4.35403e22 0.574954 0.287477 0.957787i $$-0.407183\pi$$
0.287477 + 0.957787i $$0.407183\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −2.68883e22 −0.235840 −0.117920 0.993023i $$-0.537623\pi$$
−0.117920 + 0.993023i $$0.537623\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 1.34412e23 0.795188 0.397594 0.917561i $$-0.369845\pi$$
0.397594 + 0.917561i $$0.369845\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ −1.10108e23 −0.445664
$$170$$ 0 0
$$171$$ 0 0
$$172$$ −5.56287e23 −1.87176
$$173$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$174$$ 0 0
$$175$$ −5.35957e23 −1.50394
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ 0 0
$$181$$ 6.96900e23 1.37260 0.686302 0.727317i $$-0.259233\pi$$
0.686302 + 0.727317i $$0.259233\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 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
$$193$$ 1.98909e24 1.99665 0.998326 0.0578425i $$-0.0184221\pi$$
0.998326 + 0.0578425i $$0.0184221\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ −1.47806e24 −1.26183
$$197$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$198$$ 0 0
$$199$$ 2.33297e24 1.69806 0.849029 0.528346i $$-0.177188\pi$$
0.849029 + 0.528346i $$0.177188\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ −1.62762e24 −0.744538
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 1.58903e24 0.625412 0.312706 0.949850i $$-0.398764\pi$$
0.312706 + 0.949850i $$0.398764\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −1.01609e25 −2.97923
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −3.45915e24 −0.761672 −0.380836 0.924643i $$-0.624364\pi$$
−0.380836 + 0.924643i $$0.624364\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$228$$ 0 0
$$229$$ 1.17896e25 1.96438 0.982191 0.187884i $$-0.0601630\pi$$
0.982191 + 0.187884i $$0.0601630\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ −7.96668e24 −0.776423 −0.388212 0.921570i $$-0.626907\pi$$
−0.388212 + 0.921570i $$0.626907\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 2.27765e25 1.94937
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 1.31528e25 0.990146
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 1.93428e25 1.00000
$$257$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$258$$ 0 0
$$259$$ −6.49396e25 −2.97072
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −1.45633e25 −0.465420
$$269$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$270$$ 0 0
$$271$$ −4.18902e25 −1.19106 −0.595532 0.803332i $$-0.703059\pi$$
−0.595532 + 0.803332i $$0.703059\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −2.19618e24 −0.0496169 −0.0248085 0.999692i $$-0.507898\pi$$
−0.0248085 + 0.999692i $$0.507898\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$282$$ 0 0
$$283$$ 1.05541e26 1.90398 0.951992 0.306122i $$-0.0990315\pi$$
0.951992 + 0.306122i $$0.0990315\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −6.90919e25 −1.00000
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 8.19958e25 1.06481
$$293$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 2.98146e26 2.81502
$$302$$ 0 0
$$303$$ 0 0
$$304$$ −1.56309e26 −1.32988
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 1.32287e26 1.01523 0.507614 0.861585i $$-0.330528\pi$$
0.507614 + 0.861585i $$0.330528\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$312$$ 0 0
$$313$$ −3.18989e26 −1.99784 −0.998919 0.0464917i $$-0.985196\pi$$
−0.998919 + 0.0464917i $$0.985196\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ −3.52465e26 −1.99711
$$317$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 1.76466e26 0.744538
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −3.13448e26 −1.09137 −0.545684 0.837991i $$-0.683730\pi$$
−0.545684 + 0.837991i $$0.683730\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 1.86905e26 0.538898 0.269449 0.963015i $$-0.413158\pi$$
0.269449 + 0.963015i $$0.413158\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 1.64378e26 0.393782
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$348$$ 0 0
$$349$$ 9.79269e26 1.95540 0.977699 0.210012i $$-0.0673503\pi$$
0.977699 + 0.210012i $$0.0673503\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 0 0
$$361$$ 5.48927e26 0.768580
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 8.72331e26 1.11974
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −1.37670e27 −1.62124 −0.810619 0.585574i $$-0.800869\pi$$
−0.810619 + 0.585574i $$0.800869\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −1.60839e27 −1.59753 −0.798767 0.601641i $$-0.794514\pi$$
−0.798767 + 0.601641i $$0.794514\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −2.22265e27 −1.86707 −0.933534 0.358488i $$-0.883292\pi$$
−0.933534 + 0.358488i $$0.883292\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 2.37412e27 1.55872
$$389$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −1.94928e27 −1.00595 −0.502973 0.864302i $$-0.667761\pi$$
−0.502973 + 0.864302i $$0.667761\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ −2.09715e27 −1.00000
$$401$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$402$$ 0 0
$$403$$ 3.34552e27 1.47489
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 2.59171e27 0.978343 0.489171 0.872188i $$-0.337299\pi$$
0.489171 + 0.872188i $$0.337299\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 5.12611e27 1.79212
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 0 0
$$421$$ 4.53662e27 1.26407 0.632034 0.774940i $$-0.282220\pi$$
0.632034 + 0.774940i $$0.282220\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −1.22072e28 −2.93173
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ 0 0
$$433$$ 8.16275e27 1.69322 0.846611 0.532213i $$-0.178639\pi$$
0.846611 + 0.532213i $$0.178639\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −9.36271e27 −1.80632
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −3.72475e27 −0.668683 −0.334341 0.942452i $$-0.608514\pi$$
−0.334341 + 0.942452i $$0.608514\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ −1.03669e28 −1.50394
$$449$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 1.64801e28 1.94017 0.970083 0.242775i $$-0.0780577\pi$$
0.970083 + 0.242775i $$0.0780577\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$462$$ 0 0
$$463$$ −1.29245e28 −1.32682 −0.663411 0.748255i $$-0.730892\pi$$
−0.663411 + 0.748255i $$0.730892\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$468$$ 0 0
$$469$$ 7.80531e27 0.699964
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 1.69471e28 1.32988
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ 2.13817e28 1.47068
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 1.55194e28 1.00000
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −2.61774e27 −0.158078 −0.0790391 0.996872i $$-0.525185\pi$$
−0.0790391 + 0.996872i $$0.525185\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −3.97587e28 −1.98095
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −3.72846e28 −1.74371 −0.871855 0.489765i $$-0.837083\pi$$
−0.871855 + 0.489765i $$0.837083\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 4.14213e28 1.60566
$$509$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$510$$ 0 0
$$511$$ −4.39462e28 −1.60141
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$522$$ 0 0
$$523$$ −3.66325e28 −1.04616 −0.523081 0.852283i $$-0.675217\pi$$
−0.523081 + 0.852283i $$0.675217\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −3.94716e28 −1.00000
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 8.37751e28 2.00006
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 9.99080e28 1.99999 0.999997 0.00231282i $$-0.000736194\pi$$
0.999997 + 0.00231282i $$0.000736194\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −4.86895e28 −0.868097 −0.434048 0.900890i $$-0.642915\pi$$
−0.434048 + 0.900890i $$0.642915\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 1.88906e29 3.00353
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 6.17649e27 0.0927804
$$557$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$558$$ 0 0
$$559$$ −9.81660e28 −1.39360
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$570$$ 0 0
$$571$$ −1.36364e29 −1.54889 −0.774443 0.632643i $$-0.781970\pi$$
−0.774443 + 0.632643i $$0.781970\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −1.94611e29 −1.98072 −0.990358 0.138529i $$-0.955763\pi$$
−0.990358 + 0.138529i $$0.955763\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$588$$ 0 0
$$589$$ 3.21290e29 2.63443
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −2.54103e29 −1.97529
$$593$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 0 0
$$601$$ −2.22203e29 −1.47424 −0.737119 0.675762i $$-0.763815\pi$$
−0.737119 + 0.675762i $$0.763815\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −9.13106e28 −0.574954
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 2.01911e29 1.20692 0.603461 0.797392i $$-0.293788\pi$$
0.603461 + 0.797392i $$0.293788\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 3.35322e29 1.80770 0.903851 0.427848i $$-0.140728\pi$$
0.903851 + 0.427848i $$0.140728\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$618$$ 0 0
$$619$$ 3.54147e29 1.72358 0.861790 0.507264i $$-0.169343\pi$$
0.861790 + 0.507264i $$0.169343\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 2.27374e29 1.00000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 5.63888e28 0.235840
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −2.04089e29 −0.811914 −0.405957 0.913892i $$-0.633062\pi$$
−0.405957 + 0.913892i $$0.633062\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −2.60827e29 −0.939483
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$642$$ 0 0
$$643$$ −1.41918e29 −0.463259 −0.231629 0.972804i $$-0.574406\pi$$
−0.231629 + 0.972804i $$0.574406\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −2.81883e29 −0.795188
$$653$$ 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
$$661$$ −8.04773e29 −1.96588 −0.982942 0.183916i $$-0.941123\pi$$
−0.982942 + 0.183916i $$0.941123\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 8.12894e29 1.64390 0.821951 0.569559i $$-0.192886\pi$$
0.821951 + 0.569559i $$0.192886\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 2.30913e29 0.445664
$$677$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$678$$ 0 0
$$679$$ −1.27243e30 −2.34423
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 1.16662e30 1.87176
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −8.65504e28 −0.132663 −0.0663314 0.997798i $$-0.521129\pi$$
−0.0663314 + 0.997798i $$0.521129\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 1.12398e30 1.50394
$$701$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$702$$ 0 0
$$703$$ 2.05341e30 2.62690
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −7.91584e29 −0.926214 −0.463107 0.886302i $$-0.653265\pi$$
−0.463107 + 0.886302i $$0.653265\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 0 0
$$721$$ −2.74737e30 −2.69524
$$722$$ 0 0
$$723$$ 0 0
$$724$$ −1.46151e30 −1.37260
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 2.06610e30 1.85798 0.928990 0.370105i $$-0.120678\pi$$
0.928990 + 0.370105i $$0.120678\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −9.86819e29 −0.814040 −0.407020 0.913419i $$-0.633432\pi$$
−0.407020 + 0.913419i $$0.633432\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 2.73020e28 0.0206742 0.0103371 0.999947i $$-0.496710\pi$$
0.0103371 + 0.999947i $$0.496710\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −2.79025e30 −1.78412 −0.892059 0.451918i $$-0.850740\pi$$
−0.892059 + 0.451918i $$0.850740\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −2.68402e30 −1.57862 −0.789311 0.613993i $$-0.789562\pi$$
−0.789311 + 0.613993i $$0.789562\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$762$$ 0 0
$$763$$ 5.01801e30 2.71659
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 2.75585e30 1.37413 0.687066 0.726595i $$-0.258898\pi$$
0.687066 + 0.726595i $$0.258898\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −4.17142e30 −1.99665
$$773$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$774$$ 0 0
$$775$$ 4.31064e30 1.98095
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 3.09971e30 1.26183
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 1.38088e30 0.540035 0.270018 0.962855i $$-0.412970\pi$$
0.270018 + 0.962855i $$0.412970\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 4.01929e30 1.45138
$$794$$ 0 0
$$795$$ 0 0
$$796$$ −4.89260e30 −1.69806
$$797$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$798$$ 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
$$811$$ −5.30878e30 −1.51452 −0.757261 0.653112i $$-0.773463\pi$$
−0.757261 + 0.653112i $$0.773463\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −9.42745e30 −2.48922
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$822$$ 0 0
$$823$$ 7.90132e30 1.93197 0.965987 0.258591i $$-0.0832580\pi$$
0.965987 + 0.258591i $$0.0832580\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$828$$ 0 0
$$829$$ −4.85631e30 −1.10023 −0.550116 0.835088i $$-0.685416\pi$$
−0.550116 + 0.835088i $$0.685416\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 3.41336e30 0.744538
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$840$$ 0 0
$$841$$ −5.13284e30 −1.00000
$$842$$ 0 0
$$843$$ 0 0
$$844$$ −3.33244e30 −0.625412
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −8.31776e30 −1.50394
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 9.51956e30 1.59828 0.799139 0.601147i $$-0.205289\pi$$
0.799139 + 0.601147i $$0.205289\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$858$$ 0 0
$$859$$ 1.28204e31 1.99974 0.999872 0.0160193i $$-0.00509933\pi$$
0.999872 + 0.0160193i $$0.00509933\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 2.13089e31 2.97923
$$869$$ 0 0
$$870$$ 0 0
$$871$$ −2.56994e30 −0.346523
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −4.31229e30 −0.541019 −0.270509 0.962717i $$-0.587192\pi$$
−0.270509 + 0.962717i $$0.587192\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$882$$ 0 0
$$883$$ 5.16131e30 0.602799 0.301400 0.953498i $$-0.402546\pi$$
0.301400 + 0.953498i $$0.402546\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$888$$ 0 0
$$889$$ −2.22000e31 −2.41482
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 7.25436e30 0.761672
$$893$$ 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
$$907$$ −9.99735e30 −0.881066 −0.440533 0.897736i $$-0.645210\pi$$
−0.440533 + 0.897736i $$0.645210\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 0 0
$$916$$ −2.47246e31 −1.96438
$$917$$ 0 0
$$918$$ 0 0
$$919$$ −8.84453e30 −0.678988 −0.339494 0.940608i $$-0.610256\pi$$
−0.339494 + 0.940608i $$0.610256\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 2.75499e31 1.97529
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$930$$ 0 0
$$931$$ −2.50488e31 −1.67809
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 6.77423e30 0.424223 0.212111 0.977245i $$-0.431966\pi$$
0.212111 + 0.977245i $$0.431966\pi$$
$$938$$ 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
$$949$$ 1.44695e31 0.792790
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 6.08974e31 2.92417
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 1.67073e31 0.776423
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 2.48166e31 1.11626 0.558128 0.829755i $$-0.311520\pi$$
0.558128 + 0.829755i $$0.311520\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$972$$ 0 0
$$973$$ −3.31033e30 −0.139536
$$974$$ 0 0
$$975$$ 0 0
$$976$$ −4.77658e31 −1.94937
$$977$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ −2.75833e31 −0.990146
$$989$$ 0 0
$$990$$ 0 0
$$991$$ −2.96550e31 −1.03116 −0.515579 0.856842i $$-0.672423\pi$$
−0.515579 + 0.856842i $$0.672423\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 1.20454e31 0.393118 0.196559 0.980492i $$-0.437023\pi$$
0.196559 + 0.980492i $$0.437023\pi$$
$$998$$ 0 0
$$999$$ 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 9.22.a.b.1.1 1
3.2 odd 2 CM 9.22.a.b.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
9.22.a.b.1.1 1 1.1 even 1 trivial
9.22.a.b.1.1 1 3.2 odd 2 CM