# Properties

 Label 115.3.c.a.114.1 Level $115$ Weight $3$ Character 115.114 Self dual yes Analytic conductor $3.134$ Analytic rank $0$ Dimension $1$ CM discriminant -115 Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,3,Mod(114,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("115.114");

S:= CuspForms(chi, 3);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$115 = 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 115.c (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: $$3.13352304014$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

## Embedding invariants

 Embedding label 114.1 Character $$\chi$$ $$=$$ 115.114

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+4.00000 q^{4} -5.00000 q^{5} +9.00000 q^{7} +9.00000 q^{9} +O(q^{10})$$ $$q+4.00000 q^{4} -5.00000 q^{5} +9.00000 q^{7} +9.00000 q^{9} +16.0000 q^{16} -11.0000 q^{17} -20.0000 q^{20} +23.0000 q^{23} +25.0000 q^{25} +36.0000 q^{28} -57.0000 q^{29} -53.0000 q^{31} -45.0000 q^{35} +36.0000 q^{36} -51.0000 q^{37} -33.0000 q^{41} +6.00000 q^{43} -45.0000 q^{45} +32.0000 q^{49} +101.000 q^{53} +3.00000 q^{59} +81.0000 q^{63} +64.0000 q^{64} -111.000 q^{67} -44.0000 q^{68} +27.0000 q^{71} -80.0000 q^{80} +81.0000 q^{81} +41.0000 q^{83} +55.0000 q^{85} +92.0000 q^{92} +174.000 q^{97} +O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$$.

 $$n$$ $$47$$ $$51$$ $$\chi(n)$$ $$-1$$ $$-1$$

## 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$4$$ 4.00000 1.00000
$$5$$ −5.00000 −1.00000
$$6$$ 0 0
$$7$$ 9.00000 1.28571 0.642857 0.765986i $$-0.277749\pi$$
0.642857 + 0.765986i $$0.277749\pi$$
$$8$$ 0 0
$$9$$ 9.00000 1.00000
$$10$$ 0 0
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 16.0000 1.00000
$$17$$ −11.0000 −0.647059 −0.323529 0.946218i $$-0.604869\pi$$
−0.323529 + 0.946218i $$0.604869\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$20$$ −20.0000 −1.00000
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 23.0000 1.00000
$$24$$ 0 0
$$25$$ 25.0000 1.00000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 36.0000 1.28571
$$29$$ −57.0000 −1.96552 −0.982759 0.184893i $$-0.940806\pi$$
−0.982759 + 0.184893i $$0.940806\pi$$
$$30$$ 0 0
$$31$$ −53.0000 −1.70968 −0.854839 0.518894i $$-0.826344\pi$$
−0.854839 + 0.518894i $$0.826344\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −45.0000 −1.28571
$$36$$ 36.0000 1.00000
$$37$$ −51.0000 −1.37838 −0.689189 0.724581i $$-0.742033\pi$$
−0.689189 + 0.724581i $$0.742033\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −33.0000 −0.804878 −0.402439 0.915447i $$-0.631837\pi$$
−0.402439 + 0.915447i $$0.631837\pi$$
$$42$$ 0 0
$$43$$ 6.00000 0.139535 0.0697674 0.997563i $$-0.477774\pi$$
0.0697674 + 0.997563i $$0.477774\pi$$
$$44$$ 0 0
$$45$$ −45.0000 −1.00000
$$46$$ 0 0
$$47$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$48$$ 0 0
$$49$$ 32.0000 0.653061
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 101.000 1.90566 0.952830 0.303504i $$-0.0981565\pi$$
0.952830 + 0.303504i $$0.0981565\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 3.00000 0.0508475 0.0254237 0.999677i $$-0.491907\pi$$
0.0254237 + 0.999677i $$0.491907\pi$$
$$60$$ 0 0
$$61$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$62$$ 0 0
$$63$$ 81.0000 1.28571
$$64$$ 64.0000 1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −111.000 −1.65672 −0.828358 0.560199i $$-0.810725\pi$$
−0.828358 + 0.560199i $$0.810725\pi$$
$$68$$ −44.0000 −0.647059
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 27.0000 0.380282 0.190141 0.981757i $$-0.439106\pi$$
0.190141 + 0.981757i $$0.439106\pi$$
$$72$$ 0 0
$$73$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$80$$ −80.0000 −1.00000
$$81$$ 81.0000 1.00000
$$82$$ 0 0
$$83$$ 41.0000 0.493976 0.246988 0.969019i $$-0.420559\pi$$
0.246988 + 0.969019i $$0.420559\pi$$
$$84$$ 0 0
$$85$$ 55.0000 0.647059
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 92.0000 1.00000
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 174.000 1.79381 0.896907 0.442219i $$-0.145809\pi$$
0.896907 + 0.442219i $$0.145809\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 100.000 1.00000
$$101$$ 87.0000 0.861386 0.430693 0.902498i $$-0.358269\pi$$
0.430693 + 0.902498i $$0.358269\pi$$
$$102$$ 0 0
$$103$$ −114.000 −1.10680 −0.553398 0.832917i $$-0.686669\pi$$
−0.553398 + 0.832917i $$0.686669\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −191.000 −1.78505 −0.892523 0.451001i $$-0.851067\pi$$
−0.892523 + 0.451001i $$0.851067\pi$$
$$108$$ 0 0
$$109$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 144.000 1.28571
$$113$$ −19.0000 −0.168142 −0.0840708 0.996460i $$-0.526792\pi$$
−0.0840708 + 0.996460i $$0.526792\pi$$
$$114$$ 0 0
$$115$$ −115.000 −1.00000
$$116$$ −228.000 −1.96552
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −99.0000 −0.831933
$$120$$ 0 0
$$121$$ 121.000 1.00000
$$122$$ 0 0
$$123$$ 0 0
$$124$$ −212.000 −1.70968
$$125$$ −125.000 −1.00000
$$126$$ 0 0
$$127$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −198.000 −1.51145 −0.755725 0.654889i $$-0.772715\pi$$
−0.755725 + 0.654889i $$0.772715\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 94.0000 0.686131 0.343066 0.939311i $$-0.388535\pi$$
0.343066 + 0.939311i $$0.388535\pi$$
$$138$$ 0 0
$$139$$ 163.000 1.17266 0.586331 0.810072i $$-0.300572\pi$$
0.586331 + 0.810072i $$0.300572\pi$$
$$140$$ −180.000 −1.28571
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 144.000 1.00000
$$145$$ 285.000 1.96552
$$146$$ 0 0
$$147$$ 0 0
$$148$$ −204.000 −1.37838
$$149$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$150$$ 0 0
$$151$$ −158.000 −1.04636 −0.523179 0.852223i $$-0.675254\pi$$
−0.523179 + 0.852223i $$0.675254\pi$$
$$152$$ 0 0
$$153$$ −99.0000 −0.647059
$$154$$ 0 0
$$155$$ 265.000 1.70968
$$156$$ 0 0
$$157$$ −291.000 −1.85350 −0.926752 0.375675i $$-0.877411\pi$$
−0.926752 + 0.375675i $$0.877411\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 207.000 1.28571
$$162$$ 0 0
$$163$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$164$$ −132.000 −0.804878
$$165$$ 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
$$171$$ 0 0
$$172$$ 24.0000 0.139535
$$173$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$174$$ 0 0
$$175$$ 225.000 1.28571
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −102.000 −0.569832 −0.284916 0.958552i $$-0.591966\pi$$
−0.284916 + 0.958552i $$0.591966\pi$$
$$180$$ −180.000 −1.00000
$$181$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 255.000 1.37838
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$192$$ 0 0
$$193$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 128.000 0.653061
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −513.000 −2.52709
$$204$$ 0 0
$$205$$ 165.000 0.804878
$$206$$ 0 0
$$207$$ 207.000 1.00000
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 307.000 1.45498 0.727488 0.686120i $$-0.240688\pi$$
0.727488 + 0.686120i $$0.240688\pi$$
$$212$$ 404.000 1.90566
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −30.0000 −0.139535
$$216$$ 0 0
$$217$$ −477.000 −2.19816
$$218$$ 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
$$225$$ 225.000 1.00000
$$226$$ 0 0
$$227$$ 374.000 1.64758 0.823789 0.566897i $$-0.191856\pi$$
0.823789 + 0.566897i $$0.191856\pi$$
$$228$$ 0 0
$$229$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 12.0000 0.0508475
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 363.000 1.51883 0.759414 0.650607i $$-0.225486\pi$$
0.759414 + 0.650607i $$0.225486\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −160.000 −0.653061
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$252$$ 324.000 1.28571
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 256.000 1.00000
$$257$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$258$$ 0 0
$$259$$ −459.000 −1.77220
$$260$$ 0 0
$$261$$ −513.000 −1.96552
$$262$$ 0 0
$$263$$ −319.000 −1.21293 −0.606464 0.795111i $$-0.707413\pi$$
−0.606464 + 0.795111i $$0.707413\pi$$
$$264$$ 0 0
$$265$$ −505.000 −1.90566
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −444.000 −1.65672
$$269$$ 423.000 1.57249 0.786245 0.617914i $$-0.212022\pi$$
0.786245 + 0.617914i $$0.212022\pi$$
$$270$$ 0 0
$$271$$ −493.000 −1.81919 −0.909594 0.415498i $$-0.863607\pi$$
−0.909594 + 0.415498i $$0.863607\pi$$
$$272$$ −176.000 −0.647059
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$278$$ 0 0
$$279$$ −477.000 −1.70968
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ 561.000 1.98233 0.991166 0.132627i $$-0.0423411\pi$$
0.991166 + 0.132627i $$0.0423411\pi$$
$$284$$ 108.000 0.380282
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −297.000 −1.03484
$$288$$ 0 0
$$289$$ −168.000 −0.581315
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 541.000 1.84642 0.923208 0.384300i $$-0.125557\pi$$
0.923208 + 0.384300i $$0.125557\pi$$
$$294$$ 0 0
$$295$$ −15.0000 −0.0508475
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 54.0000 0.179402
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 162.000 0.520900 0.260450 0.965487i $$-0.416129\pi$$
0.260450 + 0.965487i $$0.416129\pi$$
$$312$$ 0 0
$$313$$ 501.000 1.60064 0.800319 0.599574i $$-0.204663\pi$$
0.800319 + 0.599574i $$0.204663\pi$$
$$314$$ 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
$$320$$ −320.000 −1.00000
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 324.000 1.00000
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −373.000 −1.12689 −0.563444 0.826154i $$-0.690524\pi$$
−0.563444 + 0.826154i $$0.690524\pi$$
$$332$$ 164.000 0.493976
$$333$$ −459.000 −1.37838
$$334$$ 0 0
$$335$$ 555.000 1.65672
$$336$$ 0 0
$$337$$ −306.000 −0.908012 −0.454006 0.890999i $$-0.650006\pi$$
−0.454006 + 0.890999i $$0.650006\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 220.000 0.647059
$$341$$ 0 0
$$342$$ 0 0
$$343$$ −153.000 −0.446064
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$348$$ 0 0
$$349$$ −337.000 −0.965616 −0.482808 0.875726i $$-0.660383\pi$$
−0.482808 + 0.875726i $$0.660383\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$354$$ 0 0
$$355$$ −135.000 −0.380282
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$360$$ 0 0
$$361$$ 361.000 1.00000
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −711.000 −1.93733 −0.968665 0.248372i $$-0.920105\pi$$
−0.968665 + 0.248372i $$0.920105\pi$$
$$368$$ 368.000 1.00000
$$369$$ −297.000 −0.804878
$$370$$ 0 0
$$371$$ 909.000 2.45013
$$372$$ 0 0
$$373$$ 726.000 1.94638 0.973190 0.230001i $$-0.0738730\pi$$
0.973190 + 0.230001i $$0.0738730\pi$$
$$374$$ 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
$$383$$ 361.000 0.942559 0.471279 0.881984i $$-0.343792\pi$$
0.471279 + 0.881984i $$0.343792\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 54.0000 0.139535
$$388$$ 696.000 1.79381
$$389$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$390$$ 0 0
$$391$$ −253.000 −0.647059
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 400.000 1.00000
$$401$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 348.000 0.861386
$$405$$ −405.000 −1.00000
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 703.000 1.71883 0.859413 0.511282i $$-0.170829\pi$$
0.859413 + 0.511282i $$0.170829\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −456.000 −1.10680
$$413$$ 27.0000 0.0653753
$$414$$ 0 0
$$415$$ −205.000 −0.493976
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −275.000 −0.647059
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −764.000 −1.78505
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ 0 0
$$433$$ 261.000 0.602771 0.301386 0.953502i $$-0.402551\pi$$
0.301386 + 0.953502i $$0.402551\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 418.000 0.952164 0.476082 0.879401i $$-0.342057\pi$$
0.476082 + 0.879401i $$0.342057\pi$$
$$440$$ 0 0
$$441$$ 288.000 0.653061
$$442$$ 0 0
$$443$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 576.000 1.28571
$$449$$ 783.000 1.74388 0.871938 0.489617i $$-0.162863\pi$$
0.871938 + 0.489617i $$0.162863\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ −76.0000 −0.168142
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −891.000 −1.94967 −0.974836 0.222924i $$-0.928440\pi$$
−0.974836 + 0.222924i $$0.928440\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ −460.000 −1.00000
$$461$$ −918.000 −1.99132 −0.995662 0.0930482i $$-0.970339\pi$$
−0.995662 + 0.0930482i $$0.970339\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$464$$ −912.000 −1.96552
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 929.000 1.98929 0.994647 0.103334i $$-0.0329512\pi$$
0.994647 + 0.103334i $$0.0329512\pi$$
$$468$$ 0 0
$$469$$ −999.000 −2.13006
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ −396.000 −0.831933
$$477$$ 909.000 1.90566
$$478$$ 0 0
$$479$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 484.000 1.00000
$$485$$ −870.000 −1.79381
$$486$$ 0 0
$$487$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 867.000 1.76578 0.882892 0.469576i $$-0.155593\pi$$
0.882892 + 0.469576i $$0.155593\pi$$
$$492$$ 0 0
$$493$$ 627.000 1.27181
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −848.000 −1.70968
$$497$$ 243.000 0.488934
$$498$$ 0 0
$$499$$ −37.0000 −0.0741483 −0.0370741 0.999313i $$-0.511804\pi$$
−0.0370741 + 0.999313i $$0.511804\pi$$
$$500$$ −500.000 −1.00000
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −799.000 −1.58847 −0.794235 0.607611i $$-0.792128\pi$$
−0.794235 + 0.607611i $$0.792128\pi$$
$$504$$ 0 0
$$505$$ −435.000 −0.861386
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −822.000 −1.61493 −0.807466 0.589915i $$-0.799161\pi$$
−0.807466 + 0.589915i $$0.799161\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 570.000 1.10680
$$516$$ 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
$$523$$ −954.000 −1.82409 −0.912046 0.410088i $$-0.865498\pi$$
−0.912046 + 0.410088i $$0.865498\pi$$
$$524$$ −792.000 −1.51145
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 583.000 1.10626
$$528$$ 0 0
$$529$$ 529.000 1.00000
$$530$$ 0 0
$$531$$ 27.0000 0.0508475
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 955.000 1.78505
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −758.000 −1.40111 −0.700555 0.713599i $$-0.747064\pi$$
−0.700555 + 0.713599i $$0.747064\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$548$$ 376.000 0.686131
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 652.000 1.17266
$$557$$ −1091.00 −1.95871 −0.979354 0.202154i $$-0.935206\pi$$
−0.979354 + 0.202154i $$0.935206\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ −720.000 −1.28571
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 1.00000 0.00177620 0.000888099 1.00000i $$-0.499717\pi$$
0.000888099 1.00000i $$0.499717\pi$$
$$564$$ 0 0
$$565$$ 95.0000 0.168142
$$566$$ 0 0
$$567$$ 729.000 1.28571
$$568$$ 0 0
$$569$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$570$$ 0 0
$$571$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 575.000 1.00000
$$576$$ 576.000 1.00000
$$577$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 1140.00 1.96552
$$581$$ 369.000 0.635112
$$582$$ 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
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −816.000 −1.37838
$$593$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$594$$ 0 0
$$595$$ 495.000 0.831933
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 738.000 1.23205 0.616027 0.787725i $$-0.288741\pi$$
0.616027 + 0.787725i $$0.288741\pi$$
$$600$$ 0 0
$$601$$ 167.000 0.277870 0.138935 0.990301i $$-0.455632\pi$$
0.138935 + 0.990301i $$0.455632\pi$$
$$602$$ 0 0
$$603$$ −999.000 −1.65672
$$604$$ −632.000 −1.04636
$$605$$ −605.000 −1.00000
$$606$$ 0 0
$$607$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ −396.000 −0.647059
$$613$$ 246.000 0.401305 0.200653 0.979662i $$-0.435694\pi$$
0.200653 + 0.979662i $$0.435694\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 629.000 1.01945 0.509724 0.860338i $$-0.329747\pi$$
0.509724 + 0.860338i $$0.329747\pi$$
$$618$$ 0 0
$$619$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$620$$ 1060.00 1.70968
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 625.000 1.00000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ −1164.00 −1.85350
$$629$$ 561.000 0.891892
$$630$$ 0 0
$$631$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 243.000 0.380282
$$640$$ 0 0
$$641$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$642$$ 0 0
$$643$$ −159.000 −0.247278 −0.123639 0.992327i $$-0.539457\pi$$
−0.123639 + 0.992327i $$0.539457\pi$$
$$644$$ 828.000 1.28571
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$654$$ 0 0
$$655$$ 990.000 1.51145
$$656$$ −528.000 −0.804878
$$657$$ 0 0
$$658$$ 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
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −1311.00 −1.96552
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 676.000 1.00000
$$677$$ 509.000 0.751846 0.375923 0.926651i $$-0.377326\pi$$
0.375923 + 0.926651i $$0.377326\pi$$
$$678$$ 0 0
$$679$$ 1566.00 2.30633
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$684$$ 0 0
$$685$$ −470.000 −0.686131
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 96.0000 0.139535
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 922.000 1.33430 0.667149 0.744924i $$-0.267514\pi$$
0.667149 + 0.744924i $$0.267514\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −815.000 −1.17266
$$696$$ 0 0
$$697$$ 363.000 0.520803
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 900.000 1.28571
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 783.000 1.10750
$$708$$ 0 0
$$709$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −1219.00 −1.70968
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −408.000 −0.569832
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −1437.00 −1.99861 −0.999305 0.0372872i $$-0.988128\pi$$
−0.999305 + 0.0372872i $$0.988128\pi$$
$$720$$ −720.000 −1.00000
$$721$$ −1026.00 −1.42302
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −1425.00 −1.96552
$$726$$ 0 0
$$727$$ 1329.00 1.82806 0.914030 0.405646i $$-0.132953\pi$$
0.914030 + 0.405646i $$0.132953\pi$$
$$728$$ 0 0
$$729$$ 729.000 1.00000
$$730$$ 0 0
$$731$$ −66.0000 −0.0902873
$$732$$ 0 0
$$733$$ −339.000 −0.462483 −0.231241 0.972896i $$-0.574279\pi$$
−0.231241 + 0.972896i $$0.574279\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −1397.00 −1.89039 −0.945196 0.326503i $$-0.894130\pi$$
−0.945196 + 0.326503i $$0.894130\pi$$
$$740$$ 1020.00 1.37838
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −1394.00 −1.87618 −0.938089 0.346395i $$-0.887406\pi$$
−0.938089 + 0.346395i $$0.887406\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 369.000 0.493976
$$748$$ 0 0
$$749$$ −1719.00 −2.29506
$$750$$ 0 0
$$751$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 790.000 1.04636
$$756$$ 0 0
$$757$$ 1269.00 1.67635 0.838177 0.545398i $$-0.183622\pi$$
0.838177 + 0.545398i $$0.183622\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −1353.00 −1.77792 −0.888962 0.457981i $$-0.848573\pi$$
−0.888962 + 0.457981i $$0.848573\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 495.000 0.647059
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −74.0000 −0.0957309 −0.0478655 0.998854i $$-0.515242\pi$$
−0.0478655 + 0.998854i $$0.515242\pi$$
$$774$$ 0 0
$$775$$ −1325.00 −1.70968
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 512.000 0.653061
$$785$$ 1455.00 1.85350
$$786$$ 0 0
$$787$$ −1551.00 −1.97078 −0.985388 0.170327i $$-0.945518\pi$$
−0.985388 + 0.170327i $$0.945518\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −171.000 −0.216182
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 1189.00 1.49184 0.745922 0.666033i $$-0.232009\pi$$
0.745922 + 0.666033i $$0.232009\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ −1035.00 −1.28571
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −1257.00 −1.55377 −0.776885 0.629642i $$-0.783201\pi$$
−0.776885 + 0.629642i $$0.783201\pi$$
$$810$$ 0 0
$$811$$ 587.000 0.723798 0.361899 0.932217i $$-0.382129\pi$$
0.361899 + 0.932217i $$0.382129\pi$$
$$812$$ −2052.00 −2.52709
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 660.000 0.804878
$$821$$ −198.000 −0.241169 −0.120585 0.992703i $$-0.538477\pi$$
−0.120585 + 0.992703i $$0.538477\pi$$
$$822$$ 0 0
$$823$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 209.000 0.252721 0.126360 0.991984i $$-0.459670\pi$$
0.126360 + 0.991984i $$0.459670\pi$$
$$828$$ 828.000 1.00000
$$829$$ −1217.00 −1.46803 −0.734017 0.679131i $$-0.762357\pi$$
−0.734017 + 0.679131i $$0.762357\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −352.000 −0.422569
$$834$$ 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
$$841$$ 2408.00 2.86326
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 1228.00 1.45498
$$845$$ −845.000 −1.00000
$$846$$ 0 0
$$847$$ 1089.00 1.28571
$$848$$ 1616.00 1.90566
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −1173.00 −1.37838
$$852$$ 0 0
$$853$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$858$$ 0 0
$$859$$ 683.000 0.795111 0.397555 0.917578i $$-0.369859\pi$$
0.397555 + 0.917578i $$0.369859\pi$$
$$860$$ −120.000 −0.139535
$$861$$ 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
$$868$$ −1908.00 −2.19816
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 0 0
$$873$$ 1566.00 1.79381
$$874$$ 0 0
$$875$$ −1125.00 −1.28571
$$876$$ 0 0
$$877$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$882$$ 0 0
$$883$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$884$$ 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
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 510.000 0.569832
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 3021.00 3.36040
$$900$$ 900.000 1.00000
$$901$$ −1111.00 −1.23307
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 969.000 1.06836 0.534179 0.845372i $$-0.320621\pi$$
0.534179 + 0.845372i $$0.320621\pi$$
$$908$$ 1496.00 1.64758
$$909$$ 783.000 0.861386
$$910$$ 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
$$917$$ −1782.00 −1.94329
$$918$$ 0 0
$$919$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ −1275.00 −1.37838
$$926$$ 0 0
$$927$$ −1026.00 −1.10680
$$928$$ 0 0
$$929$$ −1017.00 −1.09473 −0.547363 0.836895i $$-0.684368\pi$$
−0.547363 + 0.836895i $$0.684368\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −1506.00 −1.60726 −0.803629 0.595131i $$-0.797100\pi$$
−0.803629 + 0.595131i $$0.797100\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$942$$ 0 0
$$943$$ −759.000 −0.804878
$$944$$ 48.0000 0.0508475
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 1406.00 1.47534 0.737671 0.675161i $$-0.235926\pi$$
0.737671 + 0.675161i $$0.235926\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 1452.00 1.51883
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 846.000 0.882169
$$960$$ 0 0
$$961$$ 1848.00 1.92300
$$962$$ 0 0
$$963$$ −1719.00 −1.78505
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$972$$ 0 0
$$973$$ 1467.00 1.50771
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 829.000 0.848516 0.424258 0.905541i $$-0.360535\pi$$
0.424258 + 0.905541i $$0.360535\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ −640.000 −0.653061
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 1921.00 1.95422 0.977111 0.212731i $$-0.0682357\pi$$
0.977111 + 0.212731i $$0.0682357\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 138.000 0.139535
$$990$$ 0 0
$$991$$ −893.000 −0.901110 −0.450555 0.892749i $$-0.648774\pi$$
−0.450555 + 0.892749i $$0.648774\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$998$$ 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 115.3.c.a.114.1 1
5.2 odd 4 575.3.d.a.551.2 2
5.3 odd 4 575.3.d.a.551.1 2
5.4 even 2 115.3.c.b.114.1 yes 1
23.22 odd 2 115.3.c.b.114.1 yes 1
115.22 even 4 575.3.d.a.551.1 2
115.68 even 4 575.3.d.a.551.2 2
115.114 odd 2 CM 115.3.c.a.114.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
115.3.c.a.114.1 1 1.1 even 1 trivial
115.3.c.a.114.1 1 115.114 odd 2 CM
115.3.c.b.114.1 yes 1 5.4 even 2
115.3.c.b.114.1 yes 1 23.22 odd 2
575.3.d.a.551.1 2 5.3 odd 4
575.3.d.a.551.1 2 115.22 even 4
575.3.d.a.551.2 2 5.2 odd 4
575.3.d.a.551.2 2 115.68 even 4