Properties

 Label 225.4.b.g.199.2 Level $225$ Weight $4$ Character 225.199 Analytic conductor $13.275$ Analytic rank $0$ Dimension $2$ CM discriminant -3 Inner twists $4$

Related objects

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(199,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("225.199");

S:= CuspForms(chi, 4);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$225 = 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 225.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: $$13.2754297513$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} + 1$$ x^2 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$2\cdot 5$$ Twist minimal: no (minimal twist has level 9) Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

 Embedding label 199.2 Root $$1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 225.199 Dual form 225.4.b.g.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+8.00000 q^{4} +20.0000i q^{7} +O(q^{10})$$ $$q+8.00000 q^{4} +20.0000i q^{7} +70.0000i q^{13} +64.0000 q^{16} -56.0000 q^{19} +160.000i q^{28} +308.000 q^{31} +110.000i q^{37} +520.000i q^{43} -57.0000 q^{49} +560.000i q^{52} +182.000 q^{61} +512.000 q^{64} -880.000i q^{67} -1190.00i q^{73} -448.000 q^{76} -884.000 q^{79} -1400.00 q^{91} -1330.00i q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 16 q^{4}+O(q^{10})$$ 2 * q + 16 * q^4 $$2 q + 16 q^{4} + 128 q^{16} - 112 q^{19} + 616 q^{31} - 114 q^{49} + 364 q^{61} + 1024 q^{64} - 896 q^{76} - 1768 q^{79} - 2800 q^{91}+O(q^{100})$$ 2 * q + 16 * q^4 + 128 * q^16 - 112 * q^19 + 616 * q^31 - 114 * q^49 + 364 * q^61 + 1024 * q^64 - 896 * q^76 - 1768 * q^79 - 2800 * q^91

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$127$$ $$\chi(n)$$ $$1$$ $$-1$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$3$$ 0 0
$$4$$ 8.00000 1.00000
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 20.0000i 1.07990i 0.841698 + 0.539949i $$0.181557\pi$$
−0.841698 + 0.539949i $$0.818443\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ 0 0
$$13$$ 70.0000i 1.49342i 0.665148 + 0.746712i $$0.268369\pi$$
−0.665148 + 0.746712i $$0.731631\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 64.0000 1.00000
$$17$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$18$$ 0 0
$$19$$ −56.0000 −0.676173 −0.338086 0.941115i $$-0.609780\pi$$
−0.338086 + 0.941115i $$0.609780\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 160.000i 1.07990i
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0 0
$$31$$ 308.000 1.78447 0.892233 0.451576i $$-0.149138\pi$$
0.892233 + 0.451576i $$0.149138\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 110.000i 0.488754i 0.969680 + 0.244377i $$0.0785834\pi$$
−0.969680 + 0.244377i $$0.921417\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ 520.000i 1.84417i 0.386989 + 0.922084i $$0.373515\pi$$
−0.386989 + 0.922084i $$0.626485\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$48$$ 0 0
$$49$$ −57.0000 −0.166181
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 560.000i 1.49342i
$$53$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$54$$ 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
$$61$$ 182.000 0.382012 0.191006 0.981589i $$-0.438825\pi$$
0.191006 + 0.981589i $$0.438825\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 512.000 1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ − 880.000i − 1.60461i −0.596912 0.802307i $$-0.703606\pi$$
0.596912 0.802307i $$-0.296394\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ − 1190.00i − 1.90793i −0.299916 0.953966i $$-0.596959\pi$$
0.299916 0.953966i $$-0.403041\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ −448.000 −0.676173
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −884.000 −1.25896 −0.629480 0.777017i $$-0.716732\pi$$
−0.629480 + 0.777017i $$0.716732\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$90$$ 0 0
$$91$$ −1400.00 −1.61275
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ − 1330.00i − 1.39218i −0.717957 0.696088i $$-0.754922\pi$$
0.717957 0.696088i $$-0.245078\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ 0 0
$$103$$ − 1820.00i − 1.74107i −0.492109 0.870534i $$-0.663774\pi$$
0.492109 0.870534i $$-0.336226\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$108$$ 0 0
$$109$$ 646.000 0.567666 0.283833 0.958874i $$-0.408394\pi$$
0.283833 + 0.958874i $$0.408394\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 1280.00i 1.07990i
$$113$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −1331.00 −1.00000
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 2464.00 1.78447
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 380.000i 0.265508i 0.991149 + 0.132754i $$0.0423821\pi$$
−0.991149 + 0.132754i $$0.957618\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ 0 0
$$133$$ − 1120.00i − 0.730198i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$138$$ 0 0
$$139$$ −2576.00 −1.57190 −0.785948 0.618293i $$-0.787825\pi$$
−0.785948 + 0.618293i $$0.787825\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 880.000i 0.488754i
$$149$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$150$$ 0 0
$$151$$ 1748.00 0.942054 0.471027 0.882119i $$-0.343883\pi$$
0.471027 + 0.882119i $$0.343883\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ − 3850.00i − 1.95709i −0.206028 0.978546i $$-0.566054\pi$$
0.206028 0.978546i $$-0.433946\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 3400.00i 1.63379i 0.576783 + 0.816897i $$0.304308\pi$$
−0.576783 + 0.816897i $$0.695692\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$168$$ 0 0
$$169$$ −2703.00 −1.23031
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 4160.00i 1.84417i
$$173$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ 0 0
$$181$$ 3458.00 1.42006 0.710031 0.704171i $$-0.248681\pi$$
0.710031 + 0.704171i $$0.248681\pi$$
$$182$$ 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
$$193$$ 1150.00i 0.428906i 0.976734 + 0.214453i $$0.0687968\pi$$
−0.976734 + 0.214453i $$0.931203\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ −456.000 −0.166181
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 0 0
$$199$$ 5236.00 1.86518 0.932588 0.360942i $$-0.117545\pi$$
0.932588 + 0.360942i $$0.117545\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 4480.00i 1.49342i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 6032.00 1.96806 0.984028 0.178011i $$-0.0569664\pi$$
0.984028 + 0.178011i $$0.0569664\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 6160.00i 1.92704i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 3220.00i 0.966938i 0.875362 + 0.483469i $$0.160623\pi$$
−0.875362 + 0.483469i $$0.839377\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$228$$ 0 0
$$229$$ −4466.00 −1.28874 −0.644370 0.764714i $$-0.722880\pi$$
−0.644370 + 0.764714i $$0.722880\pi$$
$$230$$ 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
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ −7378.00 −1.97203 −0.986014 0.166662i $$-0.946701\pi$$
−0.986014 + 0.166662i $$0.946701\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 1456.00 0.382012
$$245$$ 0 0
$$246$$ 0 0
$$247$$ − 3920.00i − 1.00981i
$$248$$ 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
$$256$$ 4096.00 1.00000
$$257$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$258$$ 0 0
$$259$$ −2200.00 −0.527804
$$260$$ 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
$$268$$ − 7040.00i − 1.60461i
$$269$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$270$$ 0 0
$$271$$ 812.000 0.182013 0.0910064 0.995850i $$-0.470992\pi$$
0.0910064 + 0.995850i $$0.470992\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ − 4030.00i − 0.874149i −0.899425 0.437074i $$-0.856015\pi$$
0.899425 0.437074i $$-0.143985\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$282$$ 0 0
$$283$$ − 5600.00i − 1.17627i −0.808761 0.588137i $$-0.799862\pi$$
0.808761 0.588137i $$-0.200138\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 4913.00 1.00000
$$290$$ 0 0
$$291$$ 0 0
$$292$$ − 9520.00i − 1.90793i
$$293$$ 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
$$301$$ −10400.0 −1.99152
$$302$$ 0 0
$$303$$ 0 0
$$304$$ −3584.00 −0.676173
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 10640.0i 1.97804i 0.147797 + 0.989018i $$0.452782\pi$$
−0.147797 + 0.989018i $$0.547218\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$312$$ 0 0
$$313$$ − 10010.0i − 1.80766i −0.427888 0.903832i $$-0.640742\pi$$
0.427888 0.903832i $$-0.359258\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ −7072.00 −1.25896
$$317$$ 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
$$331$$ 992.000 0.164729 0.0823644 0.996602i $$-0.473753\pi$$
0.0823644 + 0.996602i $$0.473753\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ − 4930.00i − 0.796897i −0.917191 0.398448i $$-0.869549\pi$$
0.917191 0.398448i $$-0.130451\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 5720.00i 0.900440i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$348$$ 0 0
$$349$$ 11914.0 1.82734 0.913670 0.406456i $$-0.133236\pi$$
0.913670 + 0.406456i $$0.133236\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 0 0
$$361$$ −3723.00 −0.542790
$$362$$ 0 0
$$363$$ 0 0
$$364$$ −11200.0 −1.61275
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 4340.00i 0.617292i 0.951177 + 0.308646i $$0.0998758\pi$$
−0.951177 + 0.308646i $$0.900124\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ − 12350.0i − 1.71437i −0.515011 0.857183i $$-0.672212\pi$$
0.515011 0.857183i $$-0.327788\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 8584.00 1.16340 0.581702 0.813402i $$-0.302387\pi$$
0.581702 + 0.813402i $$0.302387\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ − 10640.0i − 1.39218i
$$389$$ 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
$$397$$ 1190.00i 0.150439i 0.997167 + 0.0752196i $$0.0239658\pi$$
−0.997167 + 0.0752196i $$0.976034\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$402$$ 0 0
$$403$$ 21560.0i 2.66496i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −8246.00 −0.996916 −0.498458 0.866914i $$-0.666100\pi$$
−0.498458 + 0.866914i $$0.666100\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ − 14560.0i − 1.74107i
$$413$$ 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
$$421$$ 17138.0 1.98398 0.991989 0.126322i $$-0.0403172\pi$$
0.991989 + 0.126322i $$0.0403172\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 3640.00i 0.412534i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ 0 0
$$433$$ 2590.00i 0.287454i 0.989617 + 0.143727i $$0.0459087\pi$$
−0.989617 + 0.143727i $$0.954091\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 5168.00 0.567666
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −14924.0 −1.62251 −0.811257 0.584690i $$-0.801216\pi$$
−0.811257 + 0.584690i $$0.801216\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 10240.0i 1.07990i
$$449$$ 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
$$457$$ 12710.0i 1.30098i 0.759514 + 0.650491i $$0.225437\pi$$
−0.759514 + 0.650491i $$0.774563\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$462$$ 0 0
$$463$$ 19780.0i 1.98543i 0.120482 + 0.992716i $$0.461556\pi$$
−0.120482 + 0.992716i $$0.538444\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$468$$ 0 0
$$469$$ 17600.0 1.73282
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ −7700.00 −0.729916
$$482$$ 0 0
$$483$$ 0 0
$$484$$ −10648.0 −1.00000
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 20900.0i 1.94470i 0.233526 + 0.972351i $$0.424974\pi$$
−0.233526 + 0.972351i $$0.575026\pi$$
$$488$$ 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
$$496$$ 19712.0 1.78447
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 15136.0 1.35788 0.678938 0.734195i $$-0.262440\pi$$
0.678938 + 0.734195i $$0.262440\pi$$
$$500$$ 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
$$507$$ 0 0
$$508$$ 3040.00i 0.265508i
$$509$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$510$$ 0 0
$$511$$ 23800.0 2.06037
$$512$$ 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
$$523$$ 12040.0i 1.00664i 0.864100 + 0.503320i $$0.167888\pi$$
−0.864100 + 0.503320i $$0.832112\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 12167.0 1.00000
$$530$$ 0 0
$$531$$ 0 0
$$532$$ − 8960.00i − 0.730198i
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −22678.0 −1.80222 −0.901112 0.433586i $$-0.857248\pi$$
−0.901112 + 0.433586i $$0.857248\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 1640.00i 0.128193i 0.997944 + 0.0640963i $$0.0204165\pi$$
−0.997944 + 0.0640963i $$0.979584\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ − 17680.0i − 1.35955i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ −20608.0 −1.57190
$$557$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$558$$ 0 0
$$559$$ −36400.0 −2.75413
$$560$$ 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
$$568$$ 0 0
$$569$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$570$$ 0 0
$$571$$ 23312.0 1.70854 0.854270 0.519829i $$-0.174004\pi$$
0.854270 + 0.519829i $$0.174004\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ − 17710.0i − 1.27778i −0.769300 0.638888i $$-0.779395\pi$$
0.769300 0.638888i $$-0.220605\pi$$
$$578$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$588$$ 0 0
$$589$$ −17248.0 −1.20661
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 7040.00i 0.488754i
$$593$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 0 0
$$601$$ −29302.0 −1.98877 −0.994387 0.105801i $$-0.966259\pi$$
−0.994387 + 0.105801i $$0.966259\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 13984.0 0.942054
$$605$$ 0 0
$$606$$ 0 0
$$607$$ − 28420.0i − 1.90038i −0.311667 0.950191i $$-0.600887\pi$$
0.311667 0.950191i $$-0.399113\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ − 17390.0i − 1.14580i −0.819625 0.572900i $$-0.805818\pi$$
0.819625 0.572900i $$-0.194182\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$618$$ 0 0
$$619$$ 26656.0 1.73085 0.865424 0.501040i $$-0.167049\pi$$
0.865424 + 0.501040i $$0.167049\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 0 0
$$628$$ − 30800.0i − 1.95709i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 1892.00 0.119365 0.0596825 0.998217i $$-0.480991\pi$$
0.0596825 + 0.998217i $$0.480991\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ − 3990.00i − 0.248178i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$642$$ 0 0
$$643$$ − 13160.0i − 0.807122i −0.914953 0.403561i $$-0.867772\pi$$
0.914953 0.403561i $$-0.132228\pi$$
$$644$$ 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
$$652$$ 27200.0i 1.63379i
$$653$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ 0 0
$$661$$ −20482.0 −1.20523 −0.602615 0.798032i $$-0.705875\pi$$
−0.602615 + 0.798032i $$0.705875\pi$$
$$662$$ 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
$$673$$ − 24050.0i − 1.37750i −0.724998 0.688751i $$-0.758159\pi$$
0.724998 0.688751i $$-0.241841\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ −21624.0 −1.23031
$$677$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$678$$ 0 0
$$679$$ 26600.0 1.50341
$$680$$ 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
$$688$$ 33280.0i 1.84417i
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −16072.0 −0.884816 −0.442408 0.896814i $$-0.645876\pi$$
−0.442408 + 0.896814i $$0.645876\pi$$
$$692$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$702$$ 0 0
$$703$$ − 6160.00i − 0.330482i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −36146.0 −1.91466 −0.957328 0.289003i $$-0.906676\pi$$
−0.957328 + 0.289003i $$0.906676\pi$$
$$710$$ 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
$$721$$ 36400.0 1.88018
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 27664.0 1.42006
$$725$$ 0 0
$$726$$ 0 0
$$727$$ − 10780.0i − 0.549942i −0.961452 0.274971i $$-0.911332\pi$$
0.961452 0.274971i $$-0.0886683\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ − 15050.0i − 0.758369i −0.925321 0.379184i $$-0.876205\pi$$
0.925321 0.379184i $$-0.123795\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −31376.0 −1.56182 −0.780910 0.624644i $$-0.785244\pi$$
−0.780910 + 0.624644i $$0.785244\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 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
$$751$$ −23452.0 −1.13951 −0.569757 0.821813i $$-0.692963\pi$$
−0.569757 + 0.821813i $$0.692963\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ − 41470.0i − 1.99109i −0.0943039 0.995543i $$-0.530063\pi$$
0.0943039 0.995543i $$-0.469937\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$762$$ 0 0
$$763$$ 12920.0i 0.613022i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 4606.00 0.215990 0.107995 0.994151i $$-0.465557\pi$$
0.107995 + 0.994151i $$0.465557\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 9200.00i 0.428906i
$$773$$ 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
$$784$$ −3648.00 −0.166181
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 43400.0i 1.96575i 0.184281 + 0.982874i $$0.441004\pi$$
−0.184281 + 0.982874i $$0.558996\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 12740.0i 0.570505i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 41888.0 1.86518
$$797$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$810$$ 0 0
$$811$$ 39368.0 1.70456 0.852280 0.523087i $$-0.175220\pi$$
0.852280 + 0.523087i $$0.175220\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ − 29120.0i − 1.24698i
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$822$$ 0 0
$$823$$ 12220.0i 0.517573i 0.965935 + 0.258786i $$0.0833226\pi$$
−0.965935 + 0.258786i $$0.916677\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$828$$ 0 0
$$829$$ −17066.0 −0.714990 −0.357495 0.933915i $$-0.616369\pi$$
−0.357495 + 0.933915i $$0.616369\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 35840.0i 1.49342i
$$833$$ 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
$$841$$ −24389.0 −1.00000
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 48256.0 1.96806
$$845$$ 0 0
$$846$$ 0 0
$$847$$ − 26620.0i − 1.07990i
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 46690.0i 1.87413i 0.349151 + 0.937066i $$0.386470\pi$$
−0.349151 + 0.937066i $$0.613530\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$858$$ 0 0
$$859$$ −31304.0 −1.24340 −0.621699 0.783256i $$-0.713557\pi$$
−0.621699 + 0.783256i $$0.713557\pi$$
$$860$$ 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
$$867$$ 0 0
$$868$$ 49280.0i 1.92704i
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 61600.0 2.39637
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 50150.0i 1.93095i 0.260491 + 0.965476i $$0.416115\pi$$
−0.260491 + 0.965476i $$0.583885\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$882$$ 0 0
$$883$$ 20680.0i 0.788151i 0.919078 + 0.394076i $$0.128935\pi$$
−0.919078 + 0.394076i $$0.871065\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$888$$ 0 0
$$889$$ −7600.00 −0.286722
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 25760.0i 0.966938i
$$893$$ 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
$$907$$ 44840.0i 1.64155i 0.571250 + 0.820776i $$0.306459\pi$$
−0.571250 + 0.820776i $$0.693541\pi$$
$$908$$ 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
$$916$$ −35728.0 −1.28874
$$917$$ 0 0
$$918$$ 0 0
$$919$$ −2756.00 −0.0989250 −0.0494625 0.998776i $$-0.515751\pi$$
−0.0494625 + 0.998776i $$0.515751\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$930$$ 0 0
$$931$$ 3192.00 0.112367
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ − 55510.0i − 1.93536i −0.252181 0.967680i $$-0.581148\pi$$
0.252181 0.967680i $$-0.418852\pi$$
$$938$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$948$$ 0 0
$$949$$ 83300.0 2.84935
$$950$$ 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
$$961$$ 65073.0 2.18432
$$962$$ 0 0
$$963$$ 0 0
$$964$$ −59024.0 −1.97203
$$965$$ 0 0
$$966$$ 0 0
$$967$$ − 50020.0i − 1.66343i −0.555204 0.831714i $$-0.687360\pi$$
0.555204 0.831714i $$-0.312640\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$972$$ 0 0
$$973$$ − 51520.0i − 1.69749i
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 11648.0 0.382012
$$977$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ − 31360.0i − 1.00981i
$$989$$ 0 0
$$990$$ 0 0
$$991$$ −45628.0 −1.46258 −0.731292 0.682064i $$-0.761082\pi$$
−0.731292 + 0.682064i $$0.761082\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 28910.0i 0.918344i 0.888347 + 0.459172i $$0.151854\pi$$
−0.888347 + 0.459172i $$0.848146\pi$$
$$998$$ 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 225.4.b.g.199.2 2
3.2 odd 2 CM 225.4.b.g.199.2 2
5.2 odd 4 225.4.a.d.1.1 1
5.3 odd 4 9.4.a.a.1.1 1
5.4 even 2 inner 225.4.b.g.199.1 2
15.2 even 4 225.4.a.d.1.1 1
15.8 even 4 9.4.a.a.1.1 1
15.14 odd 2 inner 225.4.b.g.199.1 2
20.3 even 4 144.4.a.d.1.1 1
35.3 even 12 441.4.e.j.226.1 2
35.13 even 4 441.4.a.f.1.1 1
35.18 odd 12 441.4.e.i.226.1 2
35.23 odd 12 441.4.e.i.361.1 2
35.33 even 12 441.4.e.j.361.1 2
40.3 even 4 576.4.a.l.1.1 1
40.13 odd 4 576.4.a.m.1.1 1
45.13 odd 12 81.4.c.b.55.1 2
45.23 even 12 81.4.c.b.55.1 2
45.38 even 12 81.4.c.b.28.1 2
45.43 odd 12 81.4.c.b.28.1 2
55.43 even 4 1089.4.a.g.1.1 1
60.23 odd 4 144.4.a.d.1.1 1
65.38 odd 4 1521.4.a.g.1.1 1
105.23 even 12 441.4.e.i.361.1 2
105.38 odd 12 441.4.e.j.226.1 2
105.53 even 12 441.4.e.i.226.1 2
105.68 odd 12 441.4.e.j.361.1 2
105.83 odd 4 441.4.a.f.1.1 1
120.53 even 4 576.4.a.m.1.1 1
120.83 odd 4 576.4.a.l.1.1 1
165.98 odd 4 1089.4.a.g.1.1 1
195.38 even 4 1521.4.a.g.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
9.4.a.a.1.1 1 5.3 odd 4
9.4.a.a.1.1 1 15.8 even 4
81.4.c.b.28.1 2 45.38 even 12
81.4.c.b.28.1 2 45.43 odd 12
81.4.c.b.55.1 2 45.13 odd 12
81.4.c.b.55.1 2 45.23 even 12
144.4.a.d.1.1 1 20.3 even 4
144.4.a.d.1.1 1 60.23 odd 4
225.4.a.d.1.1 1 5.2 odd 4
225.4.a.d.1.1 1 15.2 even 4
225.4.b.g.199.1 2 5.4 even 2 inner
225.4.b.g.199.1 2 15.14 odd 2 inner
225.4.b.g.199.2 2 1.1 even 1 trivial
225.4.b.g.199.2 2 3.2 odd 2 CM
441.4.a.f.1.1 1 35.13 even 4
441.4.a.f.1.1 1 105.83 odd 4
441.4.e.i.226.1 2 35.18 odd 12
441.4.e.i.226.1 2 105.53 even 12
441.4.e.i.361.1 2 35.23 odd 12
441.4.e.i.361.1 2 105.23 even 12
441.4.e.j.226.1 2 35.3 even 12
441.4.e.j.226.1 2 105.38 odd 12
441.4.e.j.361.1 2 35.33 even 12
441.4.e.j.361.1 2 105.68 odd 12
576.4.a.l.1.1 1 40.3 even 4
576.4.a.l.1.1 1 120.83 odd 4
576.4.a.m.1.1 1 40.13 odd 4
576.4.a.m.1.1 1 120.53 even 4
1089.4.a.g.1.1 1 55.43 even 4
1089.4.a.g.1.1 1 165.98 odd 4
1521.4.a.g.1.1 1 65.38 odd 4
1521.4.a.g.1.1 1 195.38 even 4