# Properties

 Label 300.9.g.a.101.1 Level $300$ Weight $9$ Character 300.101 Self dual yes Analytic conductor $122.214$ Analytic rank $0$ 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] = [300,9,Mod(101,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("300.101");

S:= CuspForms(chi, 9);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$300 = 2^{2} \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 300.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: $$122.213583018$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 12) Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

## Embedding invariants

 Embedding label 101.1 Character $$\chi$$ $$=$$ 300.101

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-81.0000 q^{3} -4034.00 q^{7} +6561.00 q^{9} +O(q^{10})$$ $$q-81.0000 q^{3} -4034.00 q^{7} +6561.00 q^{9} +35806.0 q^{13} -258526. q^{19} +326754. q^{21} -531441. q^{27} -1.80941e6 q^{31} -503522. q^{37} -2.90029e6 q^{39} -3.49219e6 q^{43} +1.05084e7 q^{49} +2.09406e7 q^{57} -2.38265e7 q^{61} -2.64671e7 q^{63} +5.42141e6 q^{67} -1.61693e7 q^{73} -1.88870e7 q^{79} +4.30467e7 q^{81} -1.44441e8 q^{91} +1.46562e8 q^{93} -1.76908e8 q^{97} +O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$151$$ $$277$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −81.0000 −1.00000
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −4034.00 −1.68013 −0.840067 0.542483i $$-0.817484\pi$$
−0.840067 + 0.542483i $$0.817484\pi$$
$$8$$ 0 0
$$9$$ 6561.00 1.00000
$$10$$ 0 0
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 0 0
$$13$$ 35806.0 1.25367 0.626834 0.779153i $$-0.284350\pi$$
0.626834 + 0.779153i $$0.284350\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$18$$ 0 0
$$19$$ −258526. −1.98376 −0.991882 0.127165i $$-0.959412\pi$$
−0.991882 + 0.127165i $$0.959412\pi$$
$$20$$ 0 0
$$21$$ 326754. 1.68013
$$22$$ 0 0
$$23$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −531441. −1.00000
$$28$$ 0 0
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ 0 0
$$31$$ −1.80941e6 −1.95925 −0.979624 0.200842i $$-0.935632\pi$$
−0.979624 + 0.200842i $$0.935632\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −503522. −0.268665 −0.134333 0.990936i $$-0.542889\pi$$
−0.134333 + 0.990936i $$0.542889\pi$$
$$38$$ 0 0
$$39$$ −2.90029e6 −1.25367
$$40$$ 0 0
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ −3.49219e6 −1.02147 −0.510734 0.859739i $$-0.670626\pi$$
−0.510734 + 0.859739i $$0.670626\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$48$$ 0 0
$$49$$ 1.05084e7 1.82285
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 2.09406e7 1.98376
$$58$$ 0 0
$$59$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$60$$ 0 0
$$61$$ −2.38265e7 −1.72084 −0.860422 0.509583i $$-0.829800\pi$$
−0.860422 + 0.509583i $$0.829800\pi$$
$$62$$ 0 0
$$63$$ −2.64671e7 −1.68013
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 5.42141e6 0.269037 0.134519 0.990911i $$-0.457051\pi$$
0.134519 + 0.990911i $$0.457051\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0 0
$$73$$ −1.61693e7 −0.569376 −0.284688 0.958620i $$-0.591890\pi$$
−0.284688 + 0.958620i $$0.591890\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −1.88870e7 −0.484904 −0.242452 0.970163i $$-0.577952\pi$$
−0.242452 + 0.970163i $$0.577952\pi$$
$$80$$ 0 0
$$81$$ 4.30467e7 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
$$88$$ 0 0
$$89$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$90$$ 0 0
$$91$$ −1.44441e8 −2.10633
$$92$$ 0 0
$$93$$ 1.46562e8 1.95925
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −1.76908e8 −1.99830 −0.999150 0.0412262i $$-0.986874\pi$$
−0.999150 + 0.0412262i $$0.986874\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$102$$ 0 0
$$103$$ −4.44490e7 −0.394923 −0.197462 0.980311i $$-0.563270\pi$$
−0.197462 + 0.980311i $$0.563270\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$108$$ 0 0
$$109$$ 2.03181e8 1.43938 0.719692 0.694293i $$-0.244283\pi$$
0.719692 + 0.694293i $$0.244283\pi$$
$$110$$ 0 0
$$111$$ 4.07853e7 0.268665
$$112$$ 0 0
$$113$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 2.34923e8 1.25367
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 2.14359e8 1.00000
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 4.00562e8 1.53977 0.769883 0.638185i $$-0.220314\pi$$
0.769883 + 0.638185i $$0.220314\pi$$
$$128$$ 0 0
$$129$$ 2.82868e8 1.02147
$$130$$ 0 0
$$131$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$132$$ 0 0
$$133$$ 1.04289e9 3.33299
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$138$$ 0 0
$$139$$ 7.09431e8 1.90043 0.950213 0.311602i $$-0.100865\pi$$
0.950213 + 0.311602i $$0.100865\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −8.51177e8 −1.82285
$$148$$ 0 0
$$149$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$150$$ 0 0
$$151$$ 2.70234e8 0.519796 0.259898 0.965636i $$-0.416311\pi$$
0.259898 + 0.965636i $$0.416311\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −3.61735e7 −0.0595376 −0.0297688 0.999557i $$-0.509477\pi$$
−0.0297688 + 0.999557i $$0.509477\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 1.17139e9 1.65940 0.829698 0.558212i $$-0.188512\pi$$
0.829698 + 0.558212i $$0.188512\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$168$$ 0 0
$$169$$ 4.66339e8 0.571682
$$170$$ 0 0
$$171$$ −1.69619e9 −1.98376
$$172$$ 0 0
$$173$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$180$$ 0 0
$$181$$ −1.05268e9 −0.980801 −0.490400 0.871497i $$-0.663149\pi$$
−0.490400 + 0.871497i $$0.663149\pi$$
$$182$$ 0 0
$$183$$ 1.92995e9 1.72084
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 2.14383e9 1.68013
$$190$$ 0 0
$$191$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$192$$ 0 0
$$193$$ −2.32670e9 −1.67691 −0.838457 0.544968i $$-0.816542\pi$$
−0.838457 + 0.544968i $$0.816542\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 0 0
$$199$$ 1.73472e9 1.10616 0.553080 0.833128i $$-0.313452\pi$$
0.553080 + 0.833128i $$0.313452\pi$$
$$200$$ 0 0
$$201$$ −4.39134e8 −0.269037
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −1.83711e8 −0.0926840 −0.0463420 0.998926i $$-0.514756\pi$$
−0.0463420 + 0.998926i $$0.514756\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 7.29914e9 3.29180
$$218$$ 0 0
$$219$$ 1.30971e9 0.569376
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 4.72732e9 1.91159 0.955797 0.294027i $$-0.0949957\pi$$
0.955797 + 0.294027i $$0.0949957\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$228$$ 0 0
$$229$$ 5.35877e9 1.94860 0.974302 0.225247i $$-0.0723189\pi$$
0.974302 + 0.225247i $$0.0723189\pi$$
$$230$$ 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
$$237$$ 1.52985e9 0.484904
$$238$$ 0 0
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ 0 0
$$241$$ −5.56578e9 −1.64990 −0.824951 0.565204i $$-0.808797\pi$$
−0.824951 + 0.565204i $$0.808797\pi$$
$$242$$ 0 0
$$243$$ −3.48678e9 −1.00000
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −9.25678e9 −2.48698
$$248$$ 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
$$256$$ 0 0
$$257$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$258$$ 0 0
$$259$$ 2.03121e9 0.451393
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$264$$ 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
$$271$$ −2.98709e9 −0.553824 −0.276912 0.960895i $$-0.589311\pi$$
−0.276912 + 0.960895i $$0.589311\pi$$
$$272$$ 0 0
$$273$$ 1.16998e10 2.10633
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −7.42807e9 −1.26170 −0.630852 0.775904i $$-0.717294\pi$$
−0.630852 + 0.775904i $$0.717294\pi$$
$$278$$ 0 0
$$279$$ −1.18715e10 −1.95925
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ 1.03697e10 1.61667 0.808335 0.588723i $$-0.200369\pi$$
0.808335 + 0.588723i $$0.200369\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 6.97576e9 1.00000
$$290$$ 0 0
$$291$$ 1.43296e10 1.99830
$$292$$ 0 0
$$293$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 1.40875e10 1.71620
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 1.41256e10 1.59020 0.795101 0.606478i $$-0.207418\pi$$
0.795101 + 0.606478i $$0.207418\pi$$
$$308$$ 0 0
$$309$$ 3.60037e9 0.394923
$$310$$ 0 0
$$311$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$312$$ 0 0
$$313$$ −1.17006e10 −1.21908 −0.609541 0.792755i $$-0.708646\pi$$
−0.609541 + 0.792755i $$0.708646\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 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
$$327$$ −1.64576e10 −1.43938
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −1.62495e10 −1.35372 −0.676858 0.736113i $$-0.736659\pi$$
−0.676858 + 0.736113i $$0.736659\pi$$
$$332$$ 0 0
$$333$$ −3.30361e9 −0.268665
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 2.57689e10 1.99791 0.998957 0.0456520i $$-0.0145365\pi$$
0.998957 + 0.0456520i $$0.0145365\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ −1.91355e10 −1.38249
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$348$$ 0 0
$$349$$ −2.96004e10 −1.99524 −0.997621 0.0689403i $$-0.978038\pi$$
−0.997621 + 0.0689403i $$0.978038\pi$$
$$350$$ 0 0
$$351$$ −1.90288e10 −1.25367
$$352$$ 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
$$359$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$360$$ 0 0
$$361$$ 4.98521e10 2.93532
$$362$$ 0 0
$$363$$ −1.73631e10 −1.00000
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −2.43056e10 −1.33981 −0.669903 0.742448i $$-0.733664\pi$$
−0.669903 + 0.742448i $$0.733664\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −4.94467e9 −0.255448 −0.127724 0.991810i $$-0.540767\pi$$
−0.127724 + 0.991810i $$0.540767\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −3.49200e9 −0.169245 −0.0846227 0.996413i $$-0.526968\pi$$
−0.0846227 + 0.996413i $$0.526968\pi$$
$$380$$ 0 0
$$381$$ −3.24455e10 −1.53977
$$382$$ 0 0
$$383$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −2.29123e10 −1.02147
$$388$$ 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
$$397$$ 1.57611e10 0.634491 0.317245 0.948343i $$-0.397242\pi$$
0.317245 + 0.948343i $$0.397242\pi$$
$$398$$ 0 0
$$399$$ −8.44744e10 −3.33299
$$400$$ 0 0
$$401$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ 0 0
$$403$$ −6.47876e10 −2.45624
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −5.26810e10 −1.88261 −0.941305 0.337556i $$-0.890400\pi$$
−0.941305 + 0.337556i $$0.890400\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −5.74639e10 −1.90043
$$418$$ 0 0
$$419$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$420$$ 0 0
$$421$$ −1.16089e10 −0.369541 −0.184771 0.982782i $$-0.559154\pi$$
−0.184771 + 0.982782i $$0.559154\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 9.61162e10 2.89125
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ 0 0
$$433$$ −6.51683e10 −1.85389 −0.926947 0.375192i $$-0.877577\pi$$
−0.926947 + 0.375192i $$0.877577\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 6.75493e10 1.81871 0.909354 0.416024i $$-0.136577\pi$$
0.909354 + 0.416024i $$0.136577\pi$$
$$440$$ 0 0
$$441$$ 6.89453e10 1.82285
$$442$$ 0 0
$$443$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ −2.18890e10 −0.519796
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 2.72608e10 0.624991 0.312495 0.949919i $$-0.398835\pi$$
0.312495 + 0.949919i $$0.398835\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ 6.87853e10 1.49683 0.748413 0.663232i $$-0.230816\pi$$
0.748413 + 0.663232i $$0.230816\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$468$$ 0 0
$$469$$ −2.18700e10 −0.452019
$$470$$ 0 0
$$471$$ 2.93005e9 0.0595376
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$480$$ 0 0
$$481$$ −1.80291e10 −0.336817
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −9.09984e10 −1.61777 −0.808887 0.587965i $$-0.799929\pi$$
−0.808887 + 0.587965i $$0.799929\pi$$
$$488$$ 0 0
$$489$$ −9.48824e10 −1.65940
$$490$$ 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
$$499$$ 1.23330e11 1.98915 0.994574 0.104032i $$-0.0331743\pi$$
0.994574 + 0.104032i $$0.0331743\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −3.77735e10 −0.571682
$$508$$ 0 0
$$509$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$510$$ 0 0
$$511$$ 6.52269e10 0.956628
$$512$$ 0 0
$$513$$ 1.37391e11 1.98376
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ 0 0
$$523$$ −2.44747e10 −0.327122 −0.163561 0.986533i $$-0.552298\pi$$
−0.163561 + 0.986533i $$0.552298\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 7.83110e10 1.00000
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 6.27323e10 0.732322 0.366161 0.930551i $$-0.380672\pi$$
0.366161 + 0.930551i $$0.380672\pi$$
$$542$$ 0 0
$$543$$ 8.52668e10 0.980801
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 6.18266e10 0.690599 0.345300 0.938492i $$-0.387777\pi$$
0.345300 + 0.938492i $$0.387777\pi$$
$$548$$ 0 0
$$549$$ −1.56326e11 −1.72084
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 7.61903e10 0.814703
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$558$$ 0 0
$$559$$ −1.25041e11 −1.28058
$$560$$ 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
$$567$$ −1.73650e11 −1.68013
$$568$$ 0 0
$$569$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$570$$ 0 0
$$571$$ −1.94939e11 −1.83381 −0.916907 0.399102i $$-0.869322\pi$$
−0.916907 + 0.399102i $$0.869322\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 1.54299e11 1.39206 0.696031 0.718012i $$-0.254948\pi$$
0.696031 + 0.718012i $$0.254948\pi$$
$$578$$ 0 0
$$579$$ 1.88462e11 1.67691
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$588$$ 0 0
$$589$$ 4.67778e11 3.88668
$$590$$ 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
$$597$$ −1.40513e11 −1.10616
$$598$$ 0 0
$$599$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$600$$ 0 0
$$601$$ −6.22607e10 −0.477217 −0.238608 0.971116i $$-0.576691\pi$$
−0.238608 + 0.971116i $$0.576691\pi$$
$$602$$ 0 0
$$603$$ 3.55698e10 0.269037
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 2.65989e11 1.95933 0.979666 0.200634i $$-0.0643001\pi$$
0.979666 + 0.200634i $$0.0643001\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 1.57998e10 0.111894 0.0559472 0.998434i $$-0.482182\pi$$
0.0559472 + 0.998434i $$0.482182\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$618$$ 0 0
$$619$$ 2.25533e11 1.53620 0.768100 0.640330i $$-0.221203\pi$$
0.768100 + 0.640330i $$0.221203\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −2.00069e11 −1.26201 −0.631004 0.775780i $$-0.717357\pi$$
−0.631004 + 0.775780i $$0.717357\pi$$
$$632$$ 0 0
$$633$$ 1.48806e10 0.0926840
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 3.76262e11 2.28525
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$642$$ 0 0
$$643$$ −1.88544e11 −1.10298 −0.551490 0.834181i $$-0.685941\pi$$
−0.551490 + 0.834181i $$0.685941\pi$$
$$644$$ 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
$$651$$ −5.91231e11 −3.29180
$$652$$ 0 0
$$653$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −1.06087e11 −0.569376
$$658$$ 0 0
$$659$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$660$$ 0 0
$$661$$ 3.56009e11 1.86490 0.932449 0.361302i $$-0.117668\pi$$
0.932449 + 0.361302i $$0.117668\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ −3.82913e11 −1.91159
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 2.28934e11 1.11597 0.557983 0.829853i $$-0.311576\pi$$
0.557983 + 0.829853i $$0.311576\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$678$$ 0 0
$$679$$ 7.13647e11 3.35741
$$680$$ 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
$$687$$ −4.34061e11 −1.94860
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 1.55801e11 0.683374 0.341687 0.939814i $$-0.389002\pi$$
0.341687 + 0.939814i $$0.389002\pi$$
$$692$$ 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
$$703$$ 1.30174e11 0.532968
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −4.87686e11 −1.92999 −0.964995 0.262268i $$-0.915530\pi$$
−0.964995 + 0.262268i $$0.915530\pi$$
$$710$$ 0 0
$$711$$ −1.23918e11 −0.484904
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$720$$ 0 0
$$721$$ 1.79307e11 0.663524
$$722$$ 0 0
$$723$$ 4.50828e11 1.64990
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −1.21500e11 −0.434951 −0.217475 0.976066i $$-0.569782\pi$$
−0.217475 + 0.976066i $$0.569782\pi$$
$$728$$ 0 0
$$729$$ 2.82430e11 1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 5.77330e11 1.99990 0.999949 0.0100913i $$-0.00321221\pi$$
0.999949 + 0.0100913i $$0.00321221\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −4.35662e11 −1.46074 −0.730368 0.683054i $$-0.760651\pi$$
−0.730368 + 0.683054i $$0.760651\pi$$
$$740$$ 0 0
$$741$$ 7.49799e11 2.48698
$$742$$ 0 0
$$743$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −5.35831e11 −1.68449 −0.842244 0.539097i $$-0.818766\pi$$
−0.842244 + 0.539097i $$0.818766\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 4.59764e11 1.40008 0.700038 0.714106i $$-0.253167\pi$$
0.700038 + 0.714106i $$0.253167\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$762$$ 0 0
$$763$$ −8.19631e11 −2.41836
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 6.70500e11 1.91732 0.958658 0.284562i $$-0.0918483\pi$$
0.958658 + 0.284562i $$0.0918483\pi$$
$$770$$ 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
$$777$$ −1.64528e11 −0.451393
$$778$$ 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
$$787$$ −6.75420e11 −1.76066 −0.880329 0.474364i $$-0.842678\pi$$
−0.880329 + 0.474364i $$0.842678\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −8.53133e11 −2.15737
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$798$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$810$$ 0 0
$$811$$ 8.88545e10 0.205398 0.102699 0.994712i $$-0.467252\pi$$
0.102699 + 0.994712i $$0.467252\pi$$
$$812$$ 0 0
$$813$$ 2.41954e11 0.553824
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 9.02823e11 2.02635
$$818$$ 0 0
$$819$$ −9.47680e11 −2.10633
$$820$$ 0 0
$$821$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$822$$ 0 0
$$823$$ 8.62186e11 1.87932 0.939662 0.342105i $$-0.111140\pi$$
0.939662 + 0.342105i $$0.111140\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$828$$ 0 0
$$829$$ 4.11968e11 0.872258 0.436129 0.899884i $$-0.356349\pi$$
0.436129 + 0.899884i $$0.356349\pi$$
$$830$$ 0 0
$$831$$ 6.01674e11 1.26170
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 9.61593e11 1.95925
$$838$$ 0 0
$$839$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$840$$ 0 0
$$841$$ 5.00246e11 1.00000
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −8.64724e11 −1.68013
$$848$$ 0 0
$$849$$ −8.39948e11 −1.61667
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ −6.14949e11 −1.16156 −0.580782 0.814059i $$-0.697253\pi$$
−0.580782 + 0.814059i $$0.697253\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$858$$ 0 0
$$859$$ −8.02752e11 −1.47438 −0.737189 0.675686i $$-0.763847\pi$$
−0.737189 + 0.675686i $$0.763847\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ −5.65036e11 −1.00000
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 1.94119e11 0.337284
$$872$$ 0 0
$$873$$ −1.16069e12 −1.99830
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −2.10825e11 −0.356389 −0.178194 0.983995i $$-0.557026\pi$$
−0.178194 + 0.983995i $$0.557026\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$882$$ 0 0
$$883$$ −5.72878e11 −0.942366 −0.471183 0.882035i $$-0.656173\pi$$
−0.471183 + 0.882035i $$0.656173\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$888$$ 0 0
$$889$$ −1.61587e12 −2.58701
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 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
$$903$$ −1.14109e12 −1.71620
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −1.20490e12 −1.78042 −0.890212 0.455547i $$-0.849444\pi$$
−0.890212 + 0.455547i $$0.849444\pi$$
$$908$$ 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
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ −5.44534e11 −0.763419 −0.381709 0.924282i $$-0.624664\pi$$
−0.381709 + 0.924282i $$0.624664\pi$$
$$920$$ 0 0
$$921$$ −1.14417e12 −1.59020
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ −2.91630e11 −0.394923
$$928$$ 0 0
$$929$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$930$$ 0 0
$$931$$ −2.71668e12 −3.61610
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 1.43879e12 1.86655 0.933273 0.359168i $$-0.116939\pi$$
0.933273 + 0.359168i $$0.116939\pi$$
$$938$$ 0 0
$$939$$ 9.47753e11 1.21908
$$940$$ 0 0
$$941$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$948$$ 0 0
$$949$$ −5.78957e11 −0.713808
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 2.42106e12 2.83865
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 1.51552e12 1.73322 0.866611 0.498984i $$-0.166293\pi$$
0.866611 + 0.498984i $$0.166293\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$972$$ 0 0
$$973$$ −2.86184e12 −3.19297
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 1.33307e12 1.43938
$$982$$ 0 0
$$983$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 1.92066e12 1.99139 0.995693 0.0927105i $$-0.0295531\pi$$
0.995693 + 0.0927105i $$0.0295531\pi$$
$$992$$ 0 0
$$993$$ 1.31621e12 1.35372
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ −5.81390e11 −0.588420 −0.294210 0.955741i $$-0.595056\pi$$
−0.294210 + 0.955741i $$0.595056\pi$$
$$998$$ 0 0
$$999$$ 2.67592e11 0.268665
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 300.9.g.a.101.1 1
3.2 odd 2 CM 300.9.g.a.101.1 1
5.2 odd 4 300.9.b.b.149.2 2
5.3 odd 4 300.9.b.b.149.1 2
5.4 even 2 12.9.c.a.5.1 1
15.2 even 4 300.9.b.b.149.2 2
15.8 even 4 300.9.b.b.149.1 2
15.14 odd 2 12.9.c.a.5.1 1
20.19 odd 2 48.9.e.a.17.1 1
40.19 odd 2 192.9.e.b.65.1 1
40.29 even 2 192.9.e.a.65.1 1
45.4 even 6 324.9.g.a.269.1 2
45.14 odd 6 324.9.g.a.269.1 2
45.29 odd 6 324.9.g.a.53.1 2
45.34 even 6 324.9.g.a.53.1 2
60.59 even 2 48.9.e.a.17.1 1
120.29 odd 2 192.9.e.a.65.1 1
120.59 even 2 192.9.e.b.65.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
12.9.c.a.5.1 1 5.4 even 2
12.9.c.a.5.1 1 15.14 odd 2
48.9.e.a.17.1 1 20.19 odd 2
48.9.e.a.17.1 1 60.59 even 2
192.9.e.a.65.1 1 40.29 even 2
192.9.e.a.65.1 1 120.29 odd 2
192.9.e.b.65.1 1 40.19 odd 2
192.9.e.b.65.1 1 120.59 even 2
300.9.b.b.149.1 2 5.3 odd 4
300.9.b.b.149.1 2 15.8 even 4
300.9.b.b.149.2 2 5.2 odd 4
300.9.b.b.149.2 2 15.2 even 4
300.9.g.a.101.1 1 1.1 even 1 trivial
300.9.g.a.101.1 1 3.2 odd 2 CM
324.9.g.a.53.1 2 45.29 odd 6
324.9.g.a.53.1 2 45.34 even 6
324.9.g.a.269.1 2 45.4 even 6
324.9.g.a.269.1 2 45.14 odd 6