Properties

 Label 3200.2.f.s.449.3 Level $3200$ Weight $2$ Character 3200.449 Analytic conductor $25.552$ Analytic rank $0$ Dimension $8$ CM discriminant -8 Inner twists $8$

Related objects

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3200,2,Mod(449,3200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3200, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("3200.449");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$3200 = 2^{7} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3200.f (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: $$25.5521286468$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: $$\Q(\zeta_{24})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{8} - x^{4} + 1$$ x^8 - x^4 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{17}]$$ Coefficient ring index: $$2^{10}\cdot 5^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

 Embedding label 449.3 Root $$0.258819 + 0.965926i$$ of defining polynomial Character $$\chi$$ $$=$$ 3200.449 Dual form 3200.2.f.s.449.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-0.317837 q^{3} -2.89898 q^{9} +O(q^{10})$$ $$q-0.317837 q^{3} -2.89898 q^{9} -3.78194i q^{11} +1.89898i q^{17} +5.97469i q^{19} +1.87492 q^{27} +1.20204i q^{33} -6.79796 q^{41} +8.48528 q^{43} +7.00000 q^{49} -0.603566i q^{51} -1.89898i q^{57} +14.1421i q^{59} +16.3670 q^{67} -15.6969i q^{73} +8.10102 q^{81} +17.0027 q^{83} -4.10102 q^{89} -10.0000i q^{97} +10.9638i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q + 16 q^{9}+O(q^{10})$$ 8 * q + 16 * q^9 $$8 q + 16 q^{9} + 24 q^{41} + 56 q^{49} + 104 q^{81} - 72 q^{89}+O(q^{100})$$ 8 * q + 16 * q^9 + 24 * q^41 + 56 * q^49 + 104 * q^81 - 72 * q^89

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3200\mathbb{Z}\right)^\times$$.

 $$n$$ $$901$$ $$1151$$ $$2177$$ $$\chi(n)$$ $$-1$$ $$1$$ $$-1$$

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
$$3$$ −0.317837 −0.183503 −0.0917517 0.995782i $$-0.529247\pi$$
−0.0917517 + 0.995782i $$0.529247\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$8$$ 0 0
$$9$$ −2.89898 −0.966326
$$10$$ 0 0
$$11$$ − 3.78194i − 1.14030i −0.821541 0.570149i $$-0.806886\pi$$
0.821541 0.570149i $$-0.193114\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 1.89898i 0.460570i 0.973123 + 0.230285i $$0.0739659\pi$$
−0.973123 + 0.230285i $$0.926034\pi$$
$$18$$ 0 0
$$19$$ 5.97469i 1.37069i 0.728219 + 0.685344i $$0.240348\pi$$
−0.728219 + 0.685344i $$0.759652\pi$$
$$20$$ 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
$$27$$ 1.87492 0.360828
$$28$$ 0 0
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ 0 0
$$33$$ 1.20204i 0.209248i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −6.79796 −1.06166 −0.530831 0.847477i $$-0.678120\pi$$
−0.530831 + 0.847477i $$0.678120\pi$$
$$42$$ 0 0
$$43$$ 8.48528 1.29399 0.646997 0.762493i $$-0.276025\pi$$
0.646997 + 0.762493i $$0.276025\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$48$$ 0 0
$$49$$ 7.00000 1.00000
$$50$$ 0 0
$$51$$ − 0.603566i − 0.0845162i
$$52$$ 0 0
$$53$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ − 1.89898i − 0.251526i
$$58$$ 0 0
$$59$$ 14.1421i 1.84115i 0.390567 + 0.920575i $$0.372279\pi$$
−0.390567 + 0.920575i $$0.627721\pi$$
$$60$$ 0 0
$$61$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 16.3670 1.99955 0.999773 0.0212861i $$-0.00677610\pi$$
0.999773 + 0.0212861i $$0.00677610\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ − 15.6969i − 1.83719i −0.395203 0.918594i $$-0.629326\pi$$
0.395203 0.918594i $$-0.370674\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ 0 0
$$81$$ 8.10102 0.900113
$$82$$ 0 0
$$83$$ 17.0027 1.86629 0.933143 0.359506i $$-0.117055\pi$$
0.933143 + 0.359506i $$0.117055\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −4.10102 −0.434707 −0.217354 0.976093i $$-0.569742\pi$$
−0.217354 + 0.976093i $$0.569742\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ − 10.0000i − 1.01535i −0.861550 0.507673i $$-0.830506\pi$$
0.861550 0.507673i $$-0.169494\pi$$
$$98$$ 0 0
$$99$$ 10.9638i 1.10190i
$$100$$ 0 0
$$101$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 15.0956 1.45935 0.729676 0.683793i $$-0.239671\pi$$
0.729676 + 0.683793i $$0.239671\pi$$
$$108$$ 0 0
$$109$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 18.7980i 1.76836i 0.467143 + 0.884182i $$0.345283\pi$$
−0.467143 + 0.884182i $$0.654717\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −3.30306 −0.300278
$$122$$ 0 0
$$123$$ 2.16064 0.194819
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$128$$ 0 0
$$129$$ −2.69694 −0.237452
$$130$$ 0 0
$$131$$ − 14.1421i − 1.23560i −0.786334 0.617802i $$-0.788023\pi$$
0.786334 0.617802i $$-0.211977\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 22.5959i 1.93050i 0.261329 + 0.965250i $$0.415839\pi$$
−0.261329 + 0.965250i $$0.584161\pi$$
$$138$$ 0 0
$$139$$ 23.2952i 1.97587i 0.154859 + 0.987937i $$0.450508\pi$$
−0.154859 + 0.987937i $$0.549492\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −2.22486 −0.183503
$$148$$ 0 0
$$149$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$152$$ 0 0
$$153$$ − 5.50510i − 0.445061i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 14.4600 1.13259 0.566296 0.824202i $$-0.308376\pi$$
0.566296 + 0.824202i $$0.308376\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$168$$ 0 0
$$169$$ −13.0000 −1.00000
$$170$$ 0 0
$$171$$ − 17.3205i − 1.32453i
$$172$$ 0 0
$$173$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ − 4.49490i − 0.337857i
$$178$$ 0 0
$$179$$ 25.4880i 1.90506i 0.304446 + 0.952529i $$0.401529\pi$$
−0.304446 + 0.952529i $$0.598471\pi$$
$$180$$ 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
$$187$$ 7.18182 0.525187
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ 0 0
$$193$$ 25.6969i 1.84971i 0.380325 + 0.924853i $$0.375812\pi$$
−0.380325 + 0.924853i $$0.624188\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$200$$ 0 0
$$201$$ −5.20204 −0.366924
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 22.5959 1.56299
$$210$$ 0 0
$$211$$ 0.603566i 0.0415512i 0.999784 + 0.0207756i $$0.00661356\pi$$
−0.999784 + 0.0207756i $$0.993386\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 4.98907i 0.337130i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 2.82843 0.187729 0.0938647 0.995585i $$-0.470078\pi$$
0.0938647 + 0.995585i $$0.470078\pi$$
$$228$$ 0 0
$$229$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ − 30.0000i − 1.96537i −0.185296 0.982683i $$-0.559325\pi$$
0.185296 0.982683i $$-0.440675\pi$$
$$234$$ 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
$$241$$ 27.6969 1.78412 0.892058 0.451920i $$-0.149261\pi$$
0.892058 + 0.451920i $$0.149261\pi$$
$$242$$ 0 0
$$243$$ −8.19955 −0.526002
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −5.40408 −0.342470
$$250$$ 0 0
$$251$$ − 10.3602i − 0.653930i −0.945036 0.326965i $$-0.893974\pi$$
0.945036 0.326965i $$-0.106026\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ − 30.0000i − 1.87135i −0.352865 0.935674i $$-0.614792\pi$$
0.352865 0.935674i $$-0.385208\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 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
$$267$$ 1.30346 0.0797703
$$268$$ 0 0
$$269$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −18.0000 −1.07379 −0.536895 0.843649i $$-0.680403\pi$$
−0.536895 + 0.843649i $$0.680403\pi$$
$$282$$ 0 0
$$283$$ 31.7805 1.88915 0.944577 0.328291i $$-0.106473\pi$$
0.944577 + 0.328291i $$0.106473\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 13.3939 0.787875
$$290$$ 0 0
$$291$$ 3.17837i 0.186319i
$$292$$ 0 0
$$293$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ − 7.09082i − 0.411451i
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 33.6875 1.92265 0.961324 0.275421i $$-0.0888172\pi$$
0.961324 + 0.275421i $$0.0888172\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$312$$ 0 0
$$313$$ − 10.0000i − 0.565233i −0.959233 0.282617i $$-0.908798\pi$$
0.959233 0.282617i $$-0.0912024\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ −4.79796 −0.267796
$$322$$ 0 0
$$323$$ −11.3458 −0.631298
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 35.2446i 1.93722i 0.248590 + 0.968609i $$0.420033\pi$$
−0.248590 + 0.968609i $$0.579967\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 36.3939i 1.98250i 0.131995 + 0.991250i $$0.457862\pi$$
−0.131995 + 0.991250i $$0.542138\pi$$
$$338$$ 0 0
$$339$$ − 5.97469i − 0.324501i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −13.1886 −0.708002 −0.354001 0.935245i $$-0.615179\pi$$
−0.354001 + 0.935245i $$0.615179\pi$$
$$348$$ 0 0
$$349$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 30.0000i 1.59674i 0.602168 + 0.798369i $$0.294304\pi$$
−0.602168 + 0.798369i $$0.705696\pi$$
$$354$$ 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
$$361$$ −16.6969 −0.878786
$$362$$ 0 0
$$363$$ 1.04984 0.0551021
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$368$$ 0 0
$$369$$ 19.7071 1.02591
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ − 28.6663i − 1.47249i −0.676715 0.736245i $$-0.736597\pi$$
0.676715 0.736245i $$-0.263403\pi$$
$$380$$ 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
$$387$$ −24.5987 −1.25042
$$388$$ 0 0
$$389$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 4.49490i 0.226738i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 31.2929 1.56269 0.781345 0.624099i $$-0.214534\pi$$
0.781345 + 0.624099i $$0.214534\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −40.3939 −1.99735 −0.998674 0.0514740i $$-0.983608\pi$$
−0.998674 + 0.0514740i $$0.983608\pi$$
$$410$$ 0 0
$$411$$ − 7.18182i − 0.354253i
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ − 7.40408i − 0.362579i
$$418$$ 0 0
$$419$$ − 2.79632i − 0.136609i −0.997665 0.0683046i $$-0.978241\pi$$
0.997665 0.0683046i $$-0.0217590\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ 0 0
$$433$$ 4.30306i 0.206792i 0.994640 + 0.103396i $$0.0329709\pi$$
−0.994640 + 0.103396i $$0.967029\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$440$$ 0 0
$$441$$ −20.2929 −0.966326
$$442$$ 0 0
$$443$$ −34.9589 −1.66095 −0.830473 0.557059i $$-0.811930\pi$$
−0.830473 + 0.557059i $$0.811930\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −25.8990 −1.22225 −0.611124 0.791535i $$-0.709282\pi$$
−0.611124 + 0.791535i $$0.709282\pi$$
$$450$$ 0 0
$$451$$ 25.7095i 1.21061i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 16.3939i 0.766873i 0.923567 + 0.383437i $$0.125260\pi$$
−0.923567 + 0.383437i $$0.874740\pi$$
$$458$$ 0 0
$$459$$ 3.56043i 0.166186i
$$460$$ 0 0
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −31.1127 −1.43972 −0.719862 0.694117i $$-0.755795\pi$$
−0.719862 + 0.694117i $$0.755795\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ − 32.0908i − 1.47554i
$$474$$ 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
$$481$$ 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
$$489$$ −4.59592 −0.207835
$$490$$ 0 0
$$491$$ − 14.1421i − 0.638226i −0.947717 0.319113i $$-0.896615\pi$$
0.947717 0.319113i $$-0.103385\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ − 42.4264i − 1.89927i −0.313363 0.949633i $$-0.601456\pi$$
0.313363 0.949633i $$-0.398544\pi$$
$$500$$ 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
$$507$$ 4.13188 0.183503
$$508$$ 0 0
$$509$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 11.2020i 0.494582i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 42.1918 1.84846 0.924229 0.381839i $$-0.124709\pi$$
0.924229 + 0.381839i $$0.124709\pi$$
$$522$$ 0 0
$$523$$ −20.1810 −0.882455 −0.441228 0.897395i $$-0.645457\pi$$
−0.441228 + 0.897395i $$0.645457\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 23.0000 1.00000
$$530$$ 0 0
$$531$$ − 40.9978i − 1.77915i
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ − 8.10102i − 0.349585i
$$538$$ 0 0
$$539$$ − 26.4736i − 1.14030i
$$540$$ 0 0
$$541$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −35.5945 −1.52191 −0.760956 0.648803i $$-0.775270\pi$$
−0.760956 + 0.648803i $$0.775270\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ −2.28265 −0.0963736
$$562$$ 0 0
$$563$$ −36.7696 −1.54965 −0.774826 0.632175i $$-0.782163\pi$$
−0.774826 + 0.632175i $$0.782163\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 1.40408 0.0588622 0.0294311 0.999567i $$-0.490630\pi$$
0.0294311 + 0.999567i $$0.490630\pi$$
$$570$$ 0 0
$$571$$ 42.4264i 1.77549i 0.460336 + 0.887745i $$0.347729\pi$$
−0.460336 + 0.887745i $$0.652271\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ − 46.3939i − 1.93140i −0.259656 0.965701i $$-0.583609\pi$$
0.259656 0.965701i $$-0.416391\pi$$
$$578$$ 0 0
$$579$$ − 8.16744i − 0.339427i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −29.2378 −1.20677 −0.603386 0.797449i $$-0.706182\pi$$
−0.603386 + 0.797449i $$0.706182\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ − 30.1918i − 1.23983i −0.784669 0.619915i $$-0.787167\pi$$
0.784669 0.619915i $$-0.212833\pi$$
$$594$$ 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
$$601$$ −37.6969 −1.53769 −0.768845 0.639435i $$-0.779168\pi$$
−0.768845 + 0.639435i $$0.779168\pi$$
$$602$$ 0 0
$$603$$ −47.4476 −1.93222
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 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
$$613$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 30.0000i 1.20775i 0.797077 + 0.603877i $$0.206378\pi$$
−0.797077 + 0.603877i $$0.793622\pi$$
$$618$$ 0 0
$$619$$ − 42.4264i − 1.70526i −0.522514 0.852631i $$-0.675006\pi$$
0.522514 0.852631i $$-0.324994\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ −7.18182 −0.286814
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$632$$ 0 0
$$633$$ − 0.191836i − 0.00762479i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −42.0000 −1.65890 −0.829450 0.558581i $$-0.811346\pi$$
−0.829450 + 0.558581i $$0.811346\pi$$
$$642$$ 0 0
$$643$$ 8.48528 0.334627 0.167313 0.985904i $$-0.446491\pi$$
0.167313 + 0.985904i $$0.446491\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$648$$ 0 0
$$649$$ 53.4847 2.09946
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 45.5051i 1.77532i
$$658$$ 0 0
$$659$$ − 39.6301i − 1.54377i −0.635763 0.771885i $$-0.719314\pi$$
0.635763 0.771885i $$-0.280686\pi$$
$$660$$ 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
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 10.0000i 0.385472i 0.981251 + 0.192736i $$0.0617360\pi$$
−0.981251 + 0.192736i $$0.938264\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −0.898979 −0.0344490
$$682$$ 0 0
$$683$$ 20.8167 0.796530 0.398265 0.917270i $$-0.369613\pi$$
0.398265 + 0.917270i $$0.369613\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 52.5651i 1.99967i 0.0181572 + 0.999835i $$0.494220\pi$$
−0.0181572 + 0.999835i $$0.505780\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ − 12.9092i − 0.488970i
$$698$$ 0 0
$$699$$ 9.53512i 0.360651i
$$700$$ 0 0
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$710$$ 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
$$721$$ 0 0
$$722$$ 0 0
$$723$$ −8.80312 −0.327392
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$728$$ 0 0
$$729$$ −21.6969 −0.803590
$$730$$ 0 0
$$731$$ 16.1134i 0.595975i
$$732$$ 0 0
$$733$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ − 61.8990i − 2.28008i
$$738$$ 0 0
$$739$$ − 42.4264i − 1.56068i −0.625355 0.780340i $$-0.715046\pi$$
0.625355 0.780340i $$-0.284954\pi$$
$$740$$ 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
$$747$$ −49.2904 −1.80344
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$752$$ 0 0
$$753$$ 3.29286i 0.119998i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 36.7980 1.33392 0.666962 0.745091i $$-0.267594\pi$$
0.666962 + 0.745091i $$0.267594\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −33.0908 −1.19329 −0.596643 0.802507i $$-0.703499\pi$$
−0.596643 + 0.802507i $$0.703499\pi$$
$$770$$ 0 0
$$771$$ 9.53512i 0.343399i
$$772$$ 0 0
$$773$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ − 40.6157i − 1.45521i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 25.4558 0.907403 0.453701 0.891154i $$-0.350103\pi$$
0.453701 + 0.891154i $$0.350103\pi$$
$$788$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 11.8888 0.420069
$$802$$ 0 0
$$803$$ −59.3649 −2.09494
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 6.00000 0.210949 0.105474 0.994422i $$-0.466364\pi$$
0.105474 + 0.994422i $$0.466364\pi$$
$$810$$ 0 0
$$811$$ 42.4264i 1.48979i 0.667180 + 0.744896i $$0.267501\pi$$
−0.667180 + 0.744896i $$0.732499\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 50.6969i 1.77366i
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$822$$ 0 0
$$823$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −36.8659 −1.28195 −0.640976 0.767561i $$-0.721470\pi$$
−0.640976 + 0.767561i $$0.721470\pi$$
$$828$$ 0 0
$$829$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 13.2929i 0.460570i
$$834$$ 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
$$841$$ 29.0000 1.00000
$$842$$ 0 0
$$843$$ 5.72107 0.197044
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ −10.1010 −0.346666
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 7.40408i 0.252919i 0.991972 + 0.126459i $$0.0403613\pi$$
−0.991972 + 0.126459i $$0.959639\pi$$
$$858$$ 0 0
$$859$$ − 45.9868i − 1.56905i −0.620097 0.784525i $$-0.712907\pi$$
0.620097 0.784525i $$-0.287093\pi$$
$$860$$ 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
$$867$$ −4.25707 −0.144578
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 0 0
$$873$$ 28.9898i 0.981156i
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 18.0000 0.606435 0.303218 0.952921i $$-0.401939\pi$$
0.303218 + 0.952921i $$0.401939\pi$$
$$882$$ 0 0
$$883$$ 27.9664 0.941145 0.470573 0.882361i $$-0.344047\pi$$
0.470573 + 0.882361i $$0.344047\pi$$
$$884$$ 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
$$891$$ − 30.6376i − 1.02640i
$$892$$ 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
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 59.3970 1.97224 0.986122 0.166022i $$-0.0530924\pi$$
0.986122 + 0.166022i $$0.0530924\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$912$$ 0 0
$$913$$ − 64.3031i − 2.12812i
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$920$$ 0 0
$$921$$ −10.7071 −0.352812
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −54.0000 −1.77168 −0.885841 0.463988i $$-0.846418\pi$$
−0.885841 + 0.463988i $$0.846418\pi$$
$$930$$ 0 0
$$931$$ 41.8228i 1.37069i
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ − 27.0908i − 0.885018i −0.896764 0.442509i $$-0.854088\pi$$
0.896764 0.442509i $$-0.145912\pi$$
$$938$$ 0 0
$$939$$ 3.17837i 0.103722i
$$940$$ 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
$$947$$ −53.7401 −1.74632 −0.873160 0.487435i $$-0.837933\pi$$
−0.873160 + 0.487435i $$0.837933\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 60.1918i 1.94980i 0.222633 + 0.974902i $$0.428535\pi$$
−0.222633 + 0.974902i $$0.571465\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −31.0000 −1.00000
$$962$$ 0 0
$$963$$ −43.7620 −1.41021
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$968$$ 0 0
$$969$$ 3.60612 0.115845
$$970$$ 0 0
$$971$$ − 62.3217i − 2.00000i −0.000892350 1.00000i $$-0.500284\pi$$
0.000892350 1.00000i $$-0.499716\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 50.8888i 1.62808i 0.580812 + 0.814038i $$0.302735\pi$$
−0.580812 + 0.814038i $$0.697265\pi$$
$$978$$ 0 0
$$979$$ 15.5098i 0.495696i
$$980$$ 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
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$992$$ 0 0
$$993$$ − 11.2020i − 0.355486i
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$998$$ 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 3200.2.f.s.449.3 8
4.3 odd 2 inner 3200.2.f.s.449.6 8
5.2 odd 4 3200.2.d.q.1601.3 yes 4
5.3 odd 4 3200.2.d.n.1601.2 4
5.4 even 2 inner 3200.2.f.s.449.5 8
8.3 odd 2 CM 3200.2.f.s.449.3 8
8.5 even 2 inner 3200.2.f.s.449.6 8
20.3 even 4 3200.2.d.n.1601.3 yes 4
20.7 even 4 3200.2.d.q.1601.2 yes 4
20.19 odd 2 inner 3200.2.f.s.449.4 8
40.3 even 4 3200.2.d.n.1601.2 4
40.13 odd 4 3200.2.d.n.1601.3 yes 4
40.19 odd 2 inner 3200.2.f.s.449.5 8
40.27 even 4 3200.2.d.q.1601.3 yes 4
40.29 even 2 inner 3200.2.f.s.449.4 8
40.37 odd 4 3200.2.d.q.1601.2 yes 4
80.3 even 4 6400.2.a.cq.1.2 4
80.13 odd 4 6400.2.a.cq.1.3 4
80.27 even 4 6400.2.a.cr.1.2 4
80.37 odd 4 6400.2.a.cr.1.3 4
80.43 even 4 6400.2.a.cq.1.3 4
80.53 odd 4 6400.2.a.cq.1.2 4
80.67 even 4 6400.2.a.cr.1.3 4
80.77 odd 4 6400.2.a.cr.1.2 4

By twisted newform
Twist Min Dim Char Parity Ord Type
3200.2.d.n.1601.2 4 5.3 odd 4
3200.2.d.n.1601.2 4 40.3 even 4
3200.2.d.n.1601.3 yes 4 20.3 even 4
3200.2.d.n.1601.3 yes 4 40.13 odd 4
3200.2.d.q.1601.2 yes 4 20.7 even 4
3200.2.d.q.1601.2 yes 4 40.37 odd 4
3200.2.d.q.1601.3 yes 4 5.2 odd 4
3200.2.d.q.1601.3 yes 4 40.27 even 4
3200.2.f.s.449.3 8 1.1 even 1 trivial
3200.2.f.s.449.3 8 8.3 odd 2 CM
3200.2.f.s.449.4 8 20.19 odd 2 inner
3200.2.f.s.449.4 8 40.29 even 2 inner
3200.2.f.s.449.5 8 5.4 even 2 inner
3200.2.f.s.449.5 8 40.19 odd 2 inner
3200.2.f.s.449.6 8 4.3 odd 2 inner
3200.2.f.s.449.6 8 8.5 even 2 inner
6400.2.a.cq.1.2 4 80.3 even 4
6400.2.a.cq.1.2 4 80.53 odd 4
6400.2.a.cq.1.3 4 80.13 odd 4
6400.2.a.cq.1.3 4 80.43 even 4
6400.2.a.cr.1.2 4 80.27 even 4
6400.2.a.cr.1.2 4 80.77 odd 4
6400.2.a.cr.1.3 4 80.37 odd 4
6400.2.a.cr.1.3 4 80.67 even 4