# Properties

 Label 1216.3.e.a.1025.1 Level $1216$ Weight $3$ Character 1216.1025 Self dual yes Analytic conductor $33.134$ Analytic rank $0$ Dimension $1$ CM discriminant -19 Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1216,3,Mod(1025,1216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1216, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1216.1025");

S:= CuspForms(chi, 3);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1216 = 2^{6} \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1216.e (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: yes Analytic conductor: $$33.1336001462$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 19) Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

## Embedding invariants

 Embedding label 1025.1 Character $$\chi$$ $$=$$ 1216.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+9.00000 q^{5} -5.00000 q^{7} +9.00000 q^{9} +O(q^{10})$$ $$q+9.00000 q^{5} -5.00000 q^{7} +9.00000 q^{9} -3.00000 q^{11} +15.0000 q^{17} +19.0000 q^{19} -30.0000 q^{23} +56.0000 q^{25} -45.0000 q^{35} +85.0000 q^{43} +81.0000 q^{45} +75.0000 q^{47} -24.0000 q^{49} -27.0000 q^{55} -103.000 q^{61} -45.0000 q^{63} -25.0000 q^{73} +15.0000 q^{77} +81.0000 q^{81} -90.0000 q^{83} +135.000 q^{85} +171.000 q^{95} -27.0000 q^{99} +O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$705$$ $$837$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$

## 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
$$3$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$4$$ 0 0
$$5$$ 9.00000 1.80000 0.900000 0.435890i $$-0.143566\pi$$
0.900000 + 0.435890i $$0.143566\pi$$
$$6$$ 0 0
$$7$$ −5.00000 −0.714286 −0.357143 0.934050i $$-0.616249\pi$$
−0.357143 + 0.934050i $$0.616249\pi$$
$$8$$ 0 0
$$9$$ 9.00000 1.00000
$$10$$ 0 0
$$11$$ −3.00000 −0.272727 −0.136364 0.990659i $$-0.543542\pi$$
−0.136364 + 0.990659i $$0.543542\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 15.0000 0.882353 0.441176 0.897420i $$-0.354561\pi$$
0.441176 + 0.897420i $$0.354561\pi$$
$$18$$ 0 0
$$19$$ 19.0000 1.00000
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −30.0000 −1.30435 −0.652174 0.758069i $$-0.726143\pi$$
−0.652174 + 0.758069i $$0.726143\pi$$
$$24$$ 0 0
$$25$$ 56.0000 2.24000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −45.0000 −1.28571
$$36$$ 0 0
$$37$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ 85.0000 1.97674 0.988372 0.152055i $$-0.0485890\pi$$
0.988372 + 0.152055i $$0.0485890\pi$$
$$44$$ 0 0
$$45$$ 81.0000 1.80000
$$46$$ 0 0
$$47$$ 75.0000 1.59574 0.797872 0.602826i $$-0.205959\pi$$
0.797872 + 0.602826i $$0.205959\pi$$
$$48$$ 0 0
$$49$$ −24.0000 −0.489796
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$54$$ 0 0
$$55$$ −27.0000 −0.490909
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$60$$ 0 0
$$61$$ −103.000 −1.68852 −0.844262 0.535930i $$-0.819961\pi$$
−0.844262 + 0.535930i $$0.819961\pi$$
$$62$$ 0 0
$$63$$ −45.0000 −0.714286
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0 0
$$73$$ −25.0000 −0.342466 −0.171233 0.985231i $$-0.554775\pi$$
−0.171233 + 0.985231i $$0.554775\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 15.0000 0.194805
$$78$$ 0 0
$$79$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$80$$ 0 0
$$81$$ 81.0000 1.00000
$$82$$ 0 0
$$83$$ −90.0000 −1.08434 −0.542169 0.840270i $$-0.682397\pi$$
−0.542169 + 0.840270i $$0.682397\pi$$
$$84$$ 0 0
$$85$$ 135.000 1.58824
$$86$$ 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
$$95$$ 171.000 1.80000
$$96$$ 0 0
$$97$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$98$$ 0 0
$$99$$ −27.0000 −0.272727
$$100$$ 0 0
$$101$$ 102.000 1.00990 0.504950 0.863148i $$-0.331511\pi$$
0.504950 + 0.863148i $$0.331511\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$108$$ 0 0
$$109$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$114$$ 0 0
$$115$$ −270.000 −2.34783
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −75.0000 −0.630252
$$120$$ 0 0
$$121$$ −112.000 −0.925620
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 279.000 2.23200
$$126$$ 0 0
$$127$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 213.000 1.62595 0.812977 0.582296i $$-0.197845\pi$$
0.812977 + 0.582296i $$0.197845\pi$$
$$132$$ 0 0
$$133$$ −95.0000 −0.714286
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 255.000 1.86131 0.930657 0.365893i $$-0.119236\pi$$
0.930657 + 0.365893i $$0.119236\pi$$
$$138$$ 0 0
$$139$$ 197.000 1.41727 0.708633 0.705577i $$-0.249312\pi$$
0.708633 + 0.705577i $$0.249312\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 177.000 1.18792 0.593960 0.804495i $$-0.297564\pi$$
0.593960 + 0.804495i $$0.297564\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ 0 0
$$153$$ 135.000 0.882353
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −10.0000 −0.0636943 −0.0318471 0.999493i $$-0.510139\pi$$
−0.0318471 + 0.999493i $$0.510139\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 150.000 0.931677
$$162$$ 0 0
$$163$$ −250.000 −1.53374 −0.766871 0.641801i $$-0.778187\pi$$
−0.766871 + 0.641801i $$0.778187\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$168$$ 0 0
$$169$$ 169.000 1.00000
$$170$$ 0 0
$$171$$ 171.000 1.00000
$$172$$ 0 0
$$173$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$174$$ 0 0
$$175$$ −280.000 −1.60000
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −45.0000 −0.240642
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −93.0000 −0.486911 −0.243455 0.969912i $$-0.578281\pi$$
−0.243455 + 0.969912i $$0.578281\pi$$
$$192$$ 0 0
$$193$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −90.0000 −0.456853 −0.228426 0.973561i $$-0.573358\pi$$
−0.228426 + 0.973561i $$0.573358\pi$$
$$198$$ 0 0
$$199$$ 227.000 1.14070 0.570352 0.821401i $$-0.306807\pi$$
0.570352 + 0.821401i $$0.306807\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −270.000 −1.30435
$$208$$ 0 0
$$209$$ −57.0000 −0.272727
$$210$$ 0 0
$$211$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 765.000 3.55814
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$224$$ 0 0
$$225$$ 504.000 2.24000
$$226$$ 0 0
$$227$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$228$$ 0 0
$$229$$ 17.0000 0.0742358 0.0371179 0.999311i $$-0.488182\pi$$
0.0371179 + 0.999311i $$0.488182\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −465.000 −1.99571 −0.997854 0.0654770i $$-0.979143\pi$$
−0.997854 + 0.0654770i $$0.979143\pi$$
$$234$$ 0 0
$$235$$ 675.000 2.87234
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −453.000 −1.89540 −0.947699 0.319166i $$-0.896597\pi$$
−0.947699 + 0.319166i $$0.896597\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −216.000 −0.881633
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −27.0000 −0.107570 −0.0537849 0.998553i $$-0.517129\pi$$
−0.0537849 + 0.998553i $$0.517129\pi$$
$$252$$ 0 0
$$253$$ 90.0000 0.355731
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −405.000 −1.53992 −0.769962 0.638090i $$-0.779725\pi$$
−0.769962 + 0.638090i $$0.779725\pi$$
$$264$$ 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
$$271$$ −142.000 −0.523985 −0.261993 0.965070i $$-0.584380\pi$$
−0.261993 + 0.965070i $$0.584380\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −168.000 −0.610909
$$276$$ 0 0
$$277$$ −535.000 −1.93141 −0.965704 0.259646i $$-0.916394\pi$$
−0.965704 + 0.259646i $$0.916394\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ −395.000 −1.39576 −0.697880 0.716215i $$-0.745873\pi$$
−0.697880 + 0.716215i $$0.745873\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −64.0000 −0.221453
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 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
$$301$$ −425.000 −1.41196
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −927.000 −3.03934
$$306$$ 0 0
$$307$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 603.000 1.93891 0.969453 0.245276i $$-0.0788785\pi$$
0.969453 + 0.245276i $$0.0788785\pi$$
$$312$$ 0 0
$$313$$ −590.000 −1.88498 −0.942492 0.334229i $$-0.891524\pi$$
−0.942492 + 0.334229i $$0.891524\pi$$
$$314$$ 0 0
$$315$$ −405.000 −1.28571
$$316$$ 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
$$323$$ 285.000 0.882353
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −375.000 −1.13982
$$330$$ 0 0
$$331$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 365.000 1.06414
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −675.000 −1.94524 −0.972622 0.232391i $$-0.925345\pi$$
−0.972622 + 0.232391i $$0.925345\pi$$
$$348$$ 0 0
$$349$$ −527.000 −1.51003 −0.755014 0.655708i $$-0.772370\pi$$
−0.755014 + 0.655708i $$0.772370\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −510.000 −1.44476 −0.722380 0.691497i $$-0.756952\pi$$
−0.722380 + 0.691497i $$0.756952\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 243.000 0.676880 0.338440 0.940988i $$-0.390101\pi$$
0.338440 + 0.940988i $$0.390101\pi$$
$$360$$ 0 0
$$361$$ 361.000 1.00000
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −225.000 −0.616438
$$366$$ 0 0
$$367$$ 50.0000 0.136240 0.0681199 0.997677i $$-0.478300\pi$$
0.0681199 + 0.997677i $$0.478300\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$384$$ 0 0
$$385$$ 135.000 0.350649
$$386$$ 0 0
$$387$$ 765.000 1.97674
$$388$$ 0 0
$$389$$ 153.000 0.393316 0.196658 0.980472i $$-0.436991\pi$$
0.196658 + 0.980472i $$0.436991\pi$$
$$390$$ 0 0
$$391$$ −450.000 −1.15090
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 745.000 1.87657 0.938287 0.345857i $$-0.112412\pi$$
0.938287 + 0.345857i $$0.112412\pi$$
$$398$$ 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
$$405$$ 729.000 1.80000
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 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
$$415$$ −810.000 −1.95181
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −762.000 −1.81862 −0.909308 0.416124i $$-0.863388\pi$$
−0.909308 + 0.416124i $$0.863388\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$422$$ 0 0
$$423$$ 675.000 1.59574
$$424$$ 0 0
$$425$$ 840.000 1.97647
$$426$$ 0 0
$$427$$ 515.000 1.20609
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ 0 0
$$433$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −570.000 −1.30435
$$438$$ 0 0
$$439$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$440$$ 0 0
$$441$$ −216.000 −0.489796
$$442$$ 0 0
$$443$$ 45.0000 0.101580 0.0507901 0.998709i $$-0.483826\pi$$
0.0507901 + 0.998709i $$0.483826\pi$$
$$444$$ 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
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −625.000 −1.36761 −0.683807 0.729663i $$-0.739677\pi$$
−0.683807 + 0.729663i $$0.739677\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −447.000 −0.969631 −0.484816 0.874616i $$-0.661113\pi$$
−0.484816 + 0.874616i $$0.661113\pi$$
$$462$$ 0 0
$$463$$ 755.000 1.63067 0.815335 0.578990i $$-0.196553\pi$$
0.815335 + 0.578990i $$0.196553\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −915.000 −1.95931 −0.979657 0.200677i $$-0.935686\pi$$
−0.979657 + 0.200677i $$0.935686\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −255.000 −0.539112
$$474$$ 0 0
$$475$$ 1064.00 2.24000
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −942.000 −1.96660 −0.983299 0.182000i $$-0.941743\pi$$
−0.983299 + 0.182000i $$0.941743\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 918.000 1.86965 0.934827 0.355104i $$-0.115554\pi$$
0.934827 + 0.355104i $$0.115554\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ −243.000 −0.490909
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −523.000 −1.04810 −0.524048 0.851689i $$-0.675579\pi$$
−0.524048 + 0.851689i $$0.675579\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 930.000 1.84891 0.924453 0.381295i $$-0.124522\pi$$
0.924453 + 0.381295i $$0.124522\pi$$
$$504$$ 0 0
$$505$$ 918.000 1.81782
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$510$$ 0 0
$$511$$ 125.000 0.244618
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −225.000 −0.435203
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ 0 0
$$523$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 371.000 0.701323
$$530$$ 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
$$539$$ 72.0000 0.133581
$$540$$ 0 0
$$541$$ 457.000 0.844732 0.422366 0.906425i $$-0.361200\pi$$
0.422366 + 0.906425i $$0.361200\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$548$$ 0 0
$$549$$ −927.000 −1.68852
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −1095.00 −1.96589 −0.982944 0.183903i $$-0.941127\pi$$
−0.982944 + 0.183903i $$0.941127\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −405.000 −0.714286
$$568$$ 0 0
$$569$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$570$$ 0 0
$$571$$ −458.000 −0.802102 −0.401051 0.916056i $$-0.631355\pi$$
−0.401051 + 0.916056i $$0.631355\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −1680.00 −2.92174
$$576$$ 0 0
$$577$$ −1145.00 −1.98440 −0.992201 0.124648i $$-0.960220\pi$$
−0.992201 + 0.124648i $$0.960220\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 450.000 0.774527
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 1125.00 1.91652 0.958262 0.285890i $$-0.0922893\pi$$
0.958262 + 0.285890i $$0.0922893\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −30.0000 −0.0505902 −0.0252951 0.999680i $$-0.508053\pi$$
−0.0252951 + 0.999680i $$0.508053\pi$$
$$594$$ 0 0
$$595$$ −675.000 −1.13445
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$600$$ 0 0
$$601$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −1008.00 −1.66612
$$606$$ 0 0
$$607$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −295.000 −0.481240 −0.240620 0.970619i $$-0.577351\pi$$
−0.240620 + 0.970619i $$0.577351\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −1065.00 −1.72609 −0.863047 0.505124i $$-0.831447\pi$$
−0.863047 + 0.505124i $$0.831447\pi$$
$$618$$ 0 0
$$619$$ 662.000 1.06947 0.534733 0.845021i $$-0.320412\pi$$
0.534733 + 0.845021i $$0.320412\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 1111.00 1.77760
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −1037.00 −1.64342 −0.821712 0.569904i $$-0.806981\pi$$
−0.821712 + 0.569904i $$0.806981\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$642$$ 0 0
$$643$$ −1115.00 −1.73406 −0.867030 0.498257i $$-0.833974\pi$$
−0.867030 + 0.498257i $$0.833974\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −1005.00 −1.55332 −0.776662 0.629918i $$-0.783088\pi$$
−0.776662 + 0.629918i $$0.783088\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −375.000 −0.574273 −0.287136 0.957890i $$-0.592703\pi$$
−0.287136 + 0.957890i $$0.592703\pi$$
$$654$$ 0 0
$$655$$ 1917.00 2.92672
$$656$$ 0 0
$$657$$ −225.000 −0.342466
$$658$$ 0 0
$$659$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$660$$ 0 0
$$661$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −855.000 −1.28571
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 309.000 0.460507
$$672$$ 0 0
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$684$$ 0 0
$$685$$ 2295.00 3.35036
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 157.000 0.227207 0.113603 0.993526i $$-0.463761\pi$$
0.113603 + 0.993526i $$0.463761\pi$$
$$692$$ 0 0
$$693$$ 135.000 0.194805
$$694$$ 0 0
$$695$$ 1773.00 2.55108
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −1098.00 −1.56633 −0.783167 0.621812i $$-0.786397\pi$$
−0.783167 + 0.621812i $$0.786397\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −510.000 −0.721358
$$708$$ 0 0
$$709$$ 1318.00 1.85896 0.929478 0.368877i $$-0.120258\pi$$
0.929478 + 0.368877i $$0.120258\pi$$
$$710$$ 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
$$719$$ 963.000 1.33936 0.669680 0.742650i $$-0.266431\pi$$
0.669680 + 0.742650i $$0.266431\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −85.0000 −0.116919 −0.0584594 0.998290i $$-0.518619\pi$$
−0.0584594 + 0.998290i $$0.518619\pi$$
$$728$$ 0 0
$$729$$ 729.000 1.00000
$$730$$ 0 0
$$731$$ 1275.00 1.74419
$$732$$ 0 0
$$733$$ 1270.00 1.73261 0.866303 0.499519i $$-0.166490\pi$$
0.866303 + 0.499519i $$0.166490\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −547.000 −0.740189 −0.370095 0.928994i $$-0.620675\pi$$
−0.370095 + 0.928994i $$0.620675\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$744$$ 0 0
$$745$$ 1593.00 2.13826
$$746$$ 0 0
$$747$$ −810.000 −1.08434
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 785.000 1.03699 0.518494 0.855081i $$-0.326493\pi$$
0.518494 + 0.855081i $$0.326493\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 1503.00 1.97503 0.987516 0.157516i $$-0.0503486\pi$$
0.987516 + 0.157516i $$0.0503486\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 1215.00 1.58824
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 1063.00 1.38231 0.691157 0.722704i $$-0.257101\pi$$
0.691157 + 0.722704i $$0.257101\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −90.0000 −0.114650
$$786$$ 0 0
$$787$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$798$$ 0 0
$$799$$ 1125.00 1.40801
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 75.0000 0.0933998
$$804$$ 0 0
$$805$$ 1350.00 1.67702
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −1593.00 −1.96910 −0.984549 0.175110i $$-0.943972\pi$$
−0.984549 + 0.175110i $$0.943972\pi$$
$$810$$ 0 0
$$811$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −2250.00 −2.76074
$$816$$ 0 0
$$817$$ 1615.00 1.97674
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −1167.00 −1.42144 −0.710719 0.703476i $$-0.751630\pi$$
−0.710719 + 0.703476i $$0.751630\pi$$
$$822$$ 0 0
$$823$$ −1565.00 −1.90158 −0.950790 0.309837i $$-0.899726\pi$$
−0.950790 + 0.309837i $$0.899726\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$828$$ 0 0
$$829$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −360.000 −0.432173
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$840$$ 0 0
$$841$$ 841.000 1.00000
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 1521.00 1.80000
$$846$$ 0 0
$$847$$ 560.000 0.661157
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 1030.00 1.20750 0.603751 0.797173i $$-0.293672\pi$$
0.603751 + 0.797173i $$0.293672\pi$$
$$854$$ 0 0
$$855$$ 1539.00 1.80000
$$856$$ 0 0
$$857$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$858$$ 0 0
$$859$$ 1493.00 1.73807 0.869034 0.494753i $$-0.164741\pi$$
0.869034 + 0.494753i $$0.164741\pi$$
$$860$$ 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
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ −1395.00 −1.59429
$$876$$ 0 0
$$877$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −537.000 −0.609535 −0.304767 0.952427i $$-0.598579\pi$$
−0.304767 + 0.952427i $$0.598579\pi$$
$$882$$ 0 0
$$883$$ −835.000 −0.945640 −0.472820 0.881159i $$-0.656764\pi$$
−0.472820 + 0.881159i $$0.656764\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ −243.000 −0.272727
$$892$$ 0 0
$$893$$ 1425.00 1.59574
$$894$$ 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
$$907$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$908$$ 0 0
$$909$$ 918.000 1.00990
$$910$$ 0 0
$$911$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$912$$ 0 0
$$913$$ 270.000 0.295728
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −1065.00 −1.16140
$$918$$ 0 0
$$919$$ 1762.00 1.91730 0.958651 0.284585i $$-0.0918559\pi$$
0.958651 + 0.284585i $$0.0918559\pi$$
$$920$$ 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
$$929$$ 642.000 0.691066 0.345533 0.938407i $$-0.387698\pi$$
0.345533 + 0.938407i $$0.387698\pi$$
$$930$$ 0 0
$$931$$ −456.000 −0.489796
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −405.000 −0.433155
$$936$$ 0 0
$$937$$ 335.000 0.357524 0.178762 0.983892i $$-0.442791\pi$$
0.178762 + 0.983892i $$0.442791\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 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
$$947$$ 1830.00 1.93242 0.966209 0.257760i $$-0.0829843\pi$$
0.966209 + 0.257760i $$0.0829843\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$954$$ 0 0
$$955$$ −837.000 −0.876440
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ −1275.00 −1.32951
$$960$$ 0 0
$$961$$ 961.000 1.00000
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −1790.00 −1.85109 −0.925543 0.378643i $$-0.876391\pi$$
−0.925543 + 0.378643i $$0.876391\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$972$$ 0 0
$$973$$ −985.000 −1.01233
$$974$$ 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
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$984$$ 0 0
$$985$$ −810.000 −0.822335
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −2550.00 −2.57836
$$990$$ 0 0
$$991$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 2043.00 2.05327
$$996$$ 0 0
$$997$$ −1975.00 −1.98094 −0.990471 0.137718i $$-0.956023\pi$$
−0.990471 + 0.137718i $$0.956023\pi$$
$$998$$ 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 1216.3.e.a.1025.1 1
4.3 odd 2 1216.3.e.b.1025.1 1
8.3 odd 2 304.3.e.a.113.1 1
8.5 even 2 19.3.b.a.18.1 1
19.18 odd 2 CM 1216.3.e.a.1025.1 1
24.5 odd 2 171.3.c.a.37.1 1
24.11 even 2 2736.3.o.a.721.1 1
40.13 odd 4 475.3.d.a.474.2 2
40.29 even 2 475.3.c.a.151.1 1
40.37 odd 4 475.3.d.a.474.1 2
76.75 even 2 1216.3.e.b.1025.1 1
152.5 even 18 361.3.f.a.127.1 6
152.13 odd 18 361.3.f.a.116.1 6
152.21 odd 18 361.3.f.a.262.1 6
152.29 odd 18 361.3.f.a.299.1 6
152.37 odd 2 19.3.b.a.18.1 1
152.45 even 6 361.3.d.a.293.1 2
152.53 odd 18 361.3.f.a.307.1 6
152.61 even 18 361.3.f.a.307.1 6
152.69 odd 6 361.3.d.a.293.1 2
152.75 even 2 304.3.e.a.113.1 1
152.85 even 18 361.3.f.a.299.1 6
152.93 even 18 361.3.f.a.262.1 6
152.101 even 18 361.3.f.a.116.1 6
152.109 odd 18 361.3.f.a.127.1 6
152.117 odd 18 361.3.f.a.333.1 6
152.125 even 6 361.3.d.a.69.1 2
152.141 odd 6 361.3.d.a.69.1 2
152.149 even 18 361.3.f.a.333.1 6
456.227 odd 2 2736.3.o.a.721.1 1
456.341 even 2 171.3.c.a.37.1 1
760.37 even 4 475.3.d.a.474.1 2
760.189 odd 2 475.3.c.a.151.1 1
760.493 even 4 475.3.d.a.474.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
19.3.b.a.18.1 1 8.5 even 2
19.3.b.a.18.1 1 152.37 odd 2
171.3.c.a.37.1 1 24.5 odd 2
171.3.c.a.37.1 1 456.341 even 2
304.3.e.a.113.1 1 8.3 odd 2
304.3.e.a.113.1 1 152.75 even 2
361.3.d.a.69.1 2 152.125 even 6
361.3.d.a.69.1 2 152.141 odd 6
361.3.d.a.293.1 2 152.45 even 6
361.3.d.a.293.1 2 152.69 odd 6
361.3.f.a.116.1 6 152.13 odd 18
361.3.f.a.116.1 6 152.101 even 18
361.3.f.a.127.1 6 152.5 even 18
361.3.f.a.127.1 6 152.109 odd 18
361.3.f.a.262.1 6 152.21 odd 18
361.3.f.a.262.1 6 152.93 even 18
361.3.f.a.299.1 6 152.29 odd 18
361.3.f.a.299.1 6 152.85 even 18
361.3.f.a.307.1 6 152.53 odd 18
361.3.f.a.307.1 6 152.61 even 18
361.3.f.a.333.1 6 152.117 odd 18
361.3.f.a.333.1 6 152.149 even 18
475.3.c.a.151.1 1 40.29 even 2
475.3.c.a.151.1 1 760.189 odd 2
475.3.d.a.474.1 2 40.37 odd 4
475.3.d.a.474.1 2 760.37 even 4
475.3.d.a.474.2 2 40.13 odd 4
475.3.d.a.474.2 2 760.493 even 4
1216.3.e.a.1025.1 1 1.1 even 1 trivial
1216.3.e.a.1025.1 1 19.18 odd 2 CM
1216.3.e.b.1025.1 1 4.3 odd 2
1216.3.e.b.1025.1 1 76.75 even 2
2736.3.o.a.721.1 1 24.11 even 2
2736.3.o.a.721.1 1 456.227 odd 2