# Properties

 Label 5184.2.a.bf.1.1 Level $5184$ Weight $2$ Character 5184.1 Self dual yes Analytic conductor $41.394$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5184,2,Mod(1,5184)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5184, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5184.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$5184 = 2^{6} \cdot 3^{4}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5184.a (trivial)

## 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: $$41.3944484078$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 288) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 5184.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+4.00000 q^{5} +2.00000 q^{7} +O(q^{10})$$ $$q+4.00000 q^{5} +2.00000 q^{7} +5.00000 q^{11} +2.00000 q^{13} +3.00000 q^{17} +1.00000 q^{19} -6.00000 q^{23} +11.0000 q^{25} -2.00000 q^{29} +4.00000 q^{31} +8.00000 q^{35} +8.00000 q^{37} -1.00000 q^{41} -7.00000 q^{43} +2.00000 q^{47} -3.00000 q^{49} -4.00000 q^{53} +20.0000 q^{55} -5.00000 q^{59} +8.00000 q^{65} -13.0000 q^{67} +8.00000 q^{71} +3.00000 q^{73} +10.0000 q^{77} -8.00000 q^{79} -12.0000 q^{83} +12.0000 q^{85} +10.0000 q^{89} +4.00000 q^{91} +4.00000 q^{95} -11.0000 q^{97} +O(q^{100})$$

## 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
$$4$$ 0 0
$$5$$ 4.00000 1.78885 0.894427 0.447214i $$-0.147584\pi$$
0.894427 + 0.447214i $$0.147584\pi$$
$$6$$ 0 0
$$7$$ 2.00000 0.755929 0.377964 0.925820i $$-0.376624\pi$$
0.377964 + 0.925820i $$0.376624\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 5.00000 1.50756 0.753778 0.657129i $$-0.228229\pi$$
0.753778 + 0.657129i $$0.228229\pi$$
$$12$$ 0 0
$$13$$ 2.00000 0.554700 0.277350 0.960769i $$-0.410544\pi$$
0.277350 + 0.960769i $$0.410544\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 3.00000 0.727607 0.363803 0.931476i $$-0.381478\pi$$
0.363803 + 0.931476i $$0.381478\pi$$
$$18$$ 0 0
$$19$$ 1.00000 0.229416 0.114708 0.993399i $$-0.463407\pi$$
0.114708 + 0.993399i $$0.463407\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −6.00000 −1.25109 −0.625543 0.780189i $$-0.715123\pi$$
−0.625543 + 0.780189i $$0.715123\pi$$
$$24$$ 0 0
$$25$$ 11.0000 2.20000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −2.00000 −0.371391 −0.185695 0.982607i $$-0.559454\pi$$
−0.185695 + 0.982607i $$0.559454\pi$$
$$30$$ 0 0
$$31$$ 4.00000 0.718421 0.359211 0.933257i $$-0.383046\pi$$
0.359211 + 0.933257i $$0.383046\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 8.00000 1.35225
$$36$$ 0 0
$$37$$ 8.00000 1.31519 0.657596 0.753371i $$-0.271573\pi$$
0.657596 + 0.753371i $$0.271573\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −1.00000 −0.156174 −0.0780869 0.996947i $$-0.524881\pi$$
−0.0780869 + 0.996947i $$0.524881\pi$$
$$42$$ 0 0
$$43$$ −7.00000 −1.06749 −0.533745 0.845645i $$-0.679216\pi$$
−0.533745 + 0.845645i $$0.679216\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 2.00000 0.291730 0.145865 0.989305i $$-0.453403\pi$$
0.145865 + 0.989305i $$0.453403\pi$$
$$48$$ 0 0
$$49$$ −3.00000 −0.428571
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −4.00000 −0.549442 −0.274721 0.961524i $$-0.588586\pi$$
−0.274721 + 0.961524i $$0.588586\pi$$
$$54$$ 0 0
$$55$$ 20.0000 2.69680
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −5.00000 −0.650945 −0.325472 0.945552i $$-0.605523\pi$$
−0.325472 + 0.945552i $$0.605523\pi$$
$$60$$ 0 0
$$61$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 8.00000 0.992278
$$66$$ 0 0
$$67$$ −13.0000 −1.58820 −0.794101 0.607785i $$-0.792058\pi$$
−0.794101 + 0.607785i $$0.792058\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 8.00000 0.949425 0.474713 0.880141i $$-0.342552\pi$$
0.474713 + 0.880141i $$0.342552\pi$$
$$72$$ 0 0
$$73$$ 3.00000 0.351123 0.175562 0.984468i $$-0.443826\pi$$
0.175562 + 0.984468i $$0.443826\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 10.0000 1.13961
$$78$$ 0 0
$$79$$ −8.00000 −0.900070 −0.450035 0.893011i $$-0.648589\pi$$
−0.450035 + 0.893011i $$0.648589\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −12.0000 −1.31717 −0.658586 0.752506i $$-0.728845\pi$$
−0.658586 + 0.752506i $$0.728845\pi$$
$$84$$ 0 0
$$85$$ 12.0000 1.30158
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 10.0000 1.06000 0.529999 0.847998i $$-0.322192\pi$$
0.529999 + 0.847998i $$0.322192\pi$$
$$90$$ 0 0
$$91$$ 4.00000 0.419314
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 4.00000 0.410391
$$96$$ 0 0
$$97$$ −11.0000 −1.11688 −0.558440 0.829545i $$-0.688600\pi$$
−0.558440 + 0.829545i $$0.688600\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 12.0000 1.19404 0.597022 0.802225i $$-0.296350\pi$$
0.597022 + 0.802225i $$0.296350\pi$$
$$102$$ 0 0
$$103$$ −6.00000 −0.591198 −0.295599 0.955312i $$-0.595519\pi$$
−0.295599 + 0.955312i $$0.595519\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −5.00000 −0.483368 −0.241684 0.970355i $$-0.577700\pi$$
−0.241684 + 0.970355i $$0.577700\pi$$
$$108$$ 0 0
$$109$$ −8.00000 −0.766261 −0.383131 0.923694i $$-0.625154\pi$$
−0.383131 + 0.923694i $$0.625154\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 2.00000 0.188144 0.0940721 0.995565i $$-0.470012\pi$$
0.0940721 + 0.995565i $$0.470012\pi$$
$$114$$ 0 0
$$115$$ −24.0000 −2.23801
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 6.00000 0.550019
$$120$$ 0 0
$$121$$ 14.0000 1.27273
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 24.0000 2.14663
$$126$$ 0 0
$$127$$ −2.00000 −0.177471 −0.0887357 0.996055i $$-0.528283\pi$$
−0.0887357 + 0.996055i $$0.528283\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −16.0000 −1.39793 −0.698963 0.715158i $$-0.746355\pi$$
−0.698963 + 0.715158i $$0.746355\pi$$
$$132$$ 0 0
$$133$$ 2.00000 0.173422
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 3.00000 0.256307 0.128154 0.991754i $$-0.459095\pi$$
0.128154 + 0.991754i $$0.459095\pi$$
$$138$$ 0 0
$$139$$ −13.0000 −1.10265 −0.551323 0.834292i $$-0.685877\pi$$
−0.551323 + 0.834292i $$0.685877\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 10.0000 0.836242
$$144$$ 0 0
$$145$$ −8.00000 −0.664364
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −18.0000 −1.47462 −0.737309 0.675556i $$-0.763904\pi$$
−0.737309 + 0.675556i $$0.763904\pi$$
$$150$$ 0 0
$$151$$ 18.0000 1.46482 0.732410 0.680864i $$-0.238396\pi$$
0.732410 + 0.680864i $$0.238396\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 16.0000 1.28515
$$156$$ 0 0
$$157$$ −20.0000 −1.59617 −0.798087 0.602542i $$-0.794154\pi$$
−0.798087 + 0.602542i $$0.794154\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −12.0000 −0.945732
$$162$$ 0 0
$$163$$ −20.0000 −1.56652 −0.783260 0.621694i $$-0.786445\pi$$
−0.783260 + 0.621694i $$0.786445\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −16.0000 −1.23812 −0.619059 0.785345i $$-0.712486\pi$$
−0.619059 + 0.785345i $$0.712486\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 18.0000 1.36851 0.684257 0.729241i $$-0.260127\pi$$
0.684257 + 0.729241i $$0.260127\pi$$
$$174$$ 0 0
$$175$$ 22.0000 1.66304
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −12.0000 −0.896922 −0.448461 0.893802i $$-0.648028\pi$$
−0.448461 + 0.893802i $$0.648028\pi$$
$$180$$ 0 0
$$181$$ −2.00000 −0.148659 −0.0743294 0.997234i $$-0.523682\pi$$
−0.0743294 + 0.997234i $$0.523682\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 32.0000 2.35269
$$186$$ 0 0
$$187$$ 15.0000 1.09691
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −6.00000 −0.434145 −0.217072 0.976156i $$-0.569651\pi$$
−0.217072 + 0.976156i $$0.569651\pi$$
$$192$$ 0 0
$$193$$ −3.00000 −0.215945 −0.107972 0.994154i $$-0.534436\pi$$
−0.107972 + 0.994154i $$0.534436\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 4.00000 0.284988 0.142494 0.989796i $$-0.454488\pi$$
0.142494 + 0.989796i $$0.454488\pi$$
$$198$$ 0 0
$$199$$ −2.00000 −0.141776 −0.0708881 0.997484i $$-0.522583\pi$$
−0.0708881 + 0.997484i $$0.522583\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −4.00000 −0.280745
$$204$$ 0 0
$$205$$ −4.00000 −0.279372
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 5.00000 0.345857
$$210$$ 0 0
$$211$$ 28.0000 1.92760 0.963800 0.266627i $$-0.0859092\pi$$
0.963800 + 0.266627i $$0.0859092\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −28.0000 −1.90958
$$216$$ 0 0
$$217$$ 8.00000 0.543075
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 6.00000 0.403604
$$222$$ 0 0
$$223$$ 14.0000 0.937509 0.468755 0.883328i $$-0.344703\pi$$
0.468755 + 0.883328i $$0.344703\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −3.00000 −0.199117 −0.0995585 0.995032i $$-0.531743\pi$$
−0.0995585 + 0.995032i $$0.531743\pi$$
$$228$$ 0 0
$$229$$ −14.0000 −0.925146 −0.462573 0.886581i $$-0.653074\pi$$
−0.462573 + 0.886581i $$0.653074\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 21.0000 1.37576 0.687878 0.725826i $$-0.258542\pi$$
0.687878 + 0.725826i $$0.258542\pi$$
$$234$$ 0 0
$$235$$ 8.00000 0.521862
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 6.00000 0.388108 0.194054 0.980991i $$-0.437836\pi$$
0.194054 + 0.980991i $$0.437836\pi$$
$$240$$ 0 0
$$241$$ −23.0000 −1.48156 −0.740780 0.671748i $$-0.765544\pi$$
−0.740780 + 0.671748i $$0.765544\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −12.0000 −0.766652
$$246$$ 0 0
$$247$$ 2.00000 0.127257
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 21.0000 1.32551 0.662754 0.748837i $$-0.269387\pi$$
0.662754 + 0.748837i $$0.269387\pi$$
$$252$$ 0 0
$$253$$ −30.0000 −1.88608
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 5.00000 0.311891 0.155946 0.987766i $$-0.450158\pi$$
0.155946 + 0.987766i $$0.450158\pi$$
$$258$$ 0 0
$$259$$ 16.0000 0.994192
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 6.00000 0.369976 0.184988 0.982741i $$-0.440775\pi$$
0.184988 + 0.982741i $$0.440775\pi$$
$$264$$ 0 0
$$265$$ −16.0000 −0.982872
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$270$$ 0 0
$$271$$ 12.0000 0.728948 0.364474 0.931214i $$-0.381249\pi$$
0.364474 + 0.931214i $$0.381249\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 55.0000 3.31662
$$276$$ 0 0
$$277$$ 14.0000 0.841178 0.420589 0.907251i $$-0.361823\pi$$
0.420589 + 0.907251i $$0.361823\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 18.0000 1.07379 0.536895 0.843649i $$-0.319597\pi$$
0.536895 + 0.843649i $$0.319597\pi$$
$$282$$ 0 0
$$283$$ −28.0000 −1.66443 −0.832214 0.554455i $$-0.812927\pi$$
−0.832214 + 0.554455i $$0.812927\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −2.00000 −0.118056
$$288$$ 0 0
$$289$$ −8.00000 −0.470588
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 30.0000 1.75262 0.876309 0.481749i $$-0.159998\pi$$
0.876309 + 0.481749i $$0.159998\pi$$
$$294$$ 0 0
$$295$$ −20.0000 −1.16445
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −12.0000 −0.693978
$$300$$ 0 0
$$301$$ −14.0000 −0.806947
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −9.00000 −0.513657 −0.256829 0.966457i $$-0.582678\pi$$
−0.256829 + 0.966457i $$0.582678\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 18.0000 1.02069 0.510343 0.859971i $$-0.329518\pi$$
0.510343 + 0.859971i $$0.329518\pi$$
$$312$$ 0 0
$$313$$ 13.0000 0.734803 0.367402 0.930062i $$-0.380247\pi$$
0.367402 + 0.930062i $$0.380247\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 18.0000 1.01098 0.505490 0.862832i $$-0.331312\pi$$
0.505490 + 0.862832i $$0.331312\pi$$
$$318$$ 0 0
$$319$$ −10.0000 −0.559893
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 3.00000 0.166924
$$324$$ 0 0
$$325$$ 22.0000 1.22034
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 4.00000 0.220527
$$330$$ 0 0
$$331$$ −4.00000 −0.219860 −0.109930 0.993939i $$-0.535063\pi$$
−0.109930 + 0.993939i $$0.535063\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −52.0000 −2.84106
$$336$$ 0 0
$$337$$ −25.0000 −1.36184 −0.680918 0.732359i $$-0.738419\pi$$
−0.680918 + 0.732359i $$0.738419\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 20.0000 1.08306
$$342$$ 0 0
$$343$$ −20.0000 −1.07990
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 1.00000 0.0536828 0.0268414 0.999640i $$-0.491455\pi$$
0.0268414 + 0.999640i $$0.491455\pi$$
$$348$$ 0 0
$$349$$ −16.0000 −0.856460 −0.428230 0.903670i $$-0.640863\pi$$
−0.428230 + 0.903670i $$0.640863\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −35.0000 −1.86286 −0.931431 0.363918i $$-0.881439\pi$$
−0.931431 + 0.363918i $$0.881439\pi$$
$$354$$ 0 0
$$355$$ 32.0000 1.69838
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −14.0000 −0.738892 −0.369446 0.929252i $$-0.620452\pi$$
−0.369446 + 0.929252i $$0.620452\pi$$
$$360$$ 0 0
$$361$$ −18.0000 −0.947368
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 12.0000 0.628109
$$366$$ 0 0
$$367$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −8.00000 −0.415339
$$372$$ 0 0
$$373$$ 22.0000 1.13912 0.569558 0.821951i $$-0.307114\pi$$
0.569558 + 0.821951i $$0.307114\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −4.00000 −0.206010
$$378$$ 0 0
$$379$$ 1.00000 0.0513665 0.0256833 0.999670i $$-0.491824\pi$$
0.0256833 + 0.999670i $$0.491824\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 20.0000 1.02195 0.510976 0.859595i $$-0.329284\pi$$
0.510976 + 0.859595i $$0.329284\pi$$
$$384$$ 0 0
$$385$$ 40.0000 2.03859
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −6.00000 −0.304212 −0.152106 0.988364i $$-0.548606\pi$$
−0.152106 + 0.988364i $$0.548606\pi$$
$$390$$ 0 0
$$391$$ −18.0000 −0.910299
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −32.0000 −1.61009
$$396$$ 0 0
$$397$$ 32.0000 1.60603 0.803017 0.595956i $$-0.203227\pi$$
0.803017 + 0.595956i $$0.203227\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −5.00000 −0.249688 −0.124844 0.992176i $$-0.539843\pi$$
−0.124844 + 0.992176i $$0.539843\pi$$
$$402$$ 0 0
$$403$$ 8.00000 0.398508
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 40.0000 1.98273
$$408$$ 0 0
$$409$$ 25.0000 1.23617 0.618085 0.786111i $$-0.287909\pi$$
0.618085 + 0.786111i $$0.287909\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −10.0000 −0.492068
$$414$$ 0 0
$$415$$ −48.0000 −2.35623
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −4.00000 −0.195413 −0.0977064 0.995215i $$-0.531151\pi$$
−0.0977064 + 0.995215i $$0.531151\pi$$
$$420$$ 0 0
$$421$$ −8.00000 −0.389896 −0.194948 0.980814i $$-0.562454\pi$$
−0.194948 + 0.980814i $$0.562454\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 33.0000 1.60074
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 30.0000 1.44505 0.722525 0.691345i $$-0.242982\pi$$
0.722525 + 0.691345i $$0.242982\pi$$
$$432$$ 0 0
$$433$$ 1.00000 0.0480569 0.0240285 0.999711i $$-0.492351\pi$$
0.0240285 + 0.999711i $$0.492351\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −6.00000 −0.287019
$$438$$ 0 0
$$439$$ 8.00000 0.381819 0.190910 0.981608i $$-0.438856\pi$$
0.190910 + 0.981608i $$0.438856\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 27.0000 1.28281 0.641404 0.767203i $$-0.278352\pi$$
0.641404 + 0.767203i $$0.278352\pi$$
$$444$$ 0 0
$$445$$ 40.0000 1.89618
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 31.0000 1.46298 0.731490 0.681852i $$-0.238825\pi$$
0.731490 + 0.681852i $$0.238825\pi$$
$$450$$ 0 0
$$451$$ −5.00000 −0.235441
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 16.0000 0.750092
$$456$$ 0 0
$$457$$ −7.00000 −0.327446 −0.163723 0.986506i $$-0.552350\pi$$
−0.163723 + 0.986506i $$0.552350\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −18.0000 −0.838344 −0.419172 0.907907i $$-0.637680\pi$$
−0.419172 + 0.907907i $$0.637680\pi$$
$$462$$ 0 0
$$463$$ 16.0000 0.743583 0.371792 0.928316i $$-0.378744\pi$$
0.371792 + 0.928316i $$0.378744\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −7.00000 −0.323921 −0.161961 0.986797i $$-0.551782\pi$$
−0.161961 + 0.986797i $$0.551782\pi$$
$$468$$ 0 0
$$469$$ −26.0000 −1.20057
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −35.0000 −1.60930
$$474$$ 0 0
$$475$$ 11.0000 0.504715
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 18.0000 0.822441 0.411220 0.911536i $$-0.365103\pi$$
0.411220 + 0.911536i $$0.365103\pi$$
$$480$$ 0 0
$$481$$ 16.0000 0.729537
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −44.0000 −1.99794
$$486$$ 0 0
$$487$$ −22.0000 −0.996915 −0.498458 0.866914i $$-0.666100\pi$$
−0.498458 + 0.866914i $$0.666100\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −7.00000 −0.315906 −0.157953 0.987447i $$-0.550489\pi$$
−0.157953 + 0.987447i $$0.550489\pi$$
$$492$$ 0 0
$$493$$ −6.00000 −0.270226
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 16.0000 0.717698
$$498$$ 0 0
$$499$$ 21.0000 0.940089 0.470045 0.882643i $$-0.344238\pi$$
0.470045 + 0.882643i $$0.344238\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 24.0000 1.07011 0.535054 0.844818i $$-0.320291\pi$$
0.535054 + 0.844818i $$0.320291\pi$$
$$504$$ 0 0
$$505$$ 48.0000 2.13597
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 24.0000 1.06378 0.531891 0.846813i $$-0.321482\pi$$
0.531891 + 0.846813i $$0.321482\pi$$
$$510$$ 0 0
$$511$$ 6.00000 0.265424
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −24.0000 −1.05757
$$516$$ 0 0
$$517$$ 10.0000 0.439799
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 3.00000 0.131432 0.0657162 0.997838i $$-0.479067\pi$$
0.0657162 + 0.997838i $$0.479067\pi$$
$$522$$ 0 0
$$523$$ −12.0000 −0.524723 −0.262362 0.964970i $$-0.584501\pi$$
−0.262362 + 0.964970i $$0.584501\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 12.0000 0.522728
$$528$$ 0 0
$$529$$ 13.0000 0.565217
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −2.00000 −0.0866296
$$534$$ 0 0
$$535$$ −20.0000 −0.864675
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −15.0000 −0.646096
$$540$$ 0 0
$$541$$ 32.0000 1.37579 0.687894 0.725811i $$-0.258536\pi$$
0.687894 + 0.725811i $$0.258536\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −32.0000 −1.37073
$$546$$ 0 0
$$547$$ 33.0000 1.41098 0.705489 0.708721i $$-0.250727\pi$$
0.705489 + 0.708721i $$0.250727\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −2.00000 −0.0852029
$$552$$ 0 0
$$553$$ −16.0000 −0.680389
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 10.0000 0.423714 0.211857 0.977301i $$-0.432049\pi$$
0.211857 + 0.977301i $$0.432049\pi$$
$$558$$ 0 0
$$559$$ −14.0000 −0.592137
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −15.0000 −0.632175 −0.316087 0.948730i $$-0.602369\pi$$
−0.316087 + 0.948730i $$0.602369\pi$$
$$564$$ 0 0
$$565$$ 8.00000 0.336563
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 11.0000 0.461144 0.230572 0.973055i $$-0.425940\pi$$
0.230572 + 0.973055i $$0.425940\pi$$
$$570$$ 0 0
$$571$$ 13.0000 0.544033 0.272017 0.962293i $$-0.412309\pi$$
0.272017 + 0.962293i $$0.412309\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −66.0000 −2.75239
$$576$$ 0 0
$$577$$ 3.00000 0.124892 0.0624458 0.998048i $$-0.480110\pi$$
0.0624458 + 0.998048i $$0.480110\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −24.0000 −0.995688
$$582$$ 0 0
$$583$$ −20.0000 −0.828315
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −9.00000 −0.371470 −0.185735 0.982600i $$-0.559467\pi$$
−0.185735 + 0.982600i $$0.559467\pi$$
$$588$$ 0 0
$$589$$ 4.00000 0.164817
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −6.00000 −0.246390 −0.123195 0.992382i $$-0.539314\pi$$
−0.123195 + 0.992382i $$0.539314\pi$$
$$594$$ 0 0
$$595$$ 24.0000 0.983904
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −40.0000 −1.63436 −0.817178 0.576386i $$-0.804463\pi$$
−0.817178 + 0.576386i $$0.804463\pi$$
$$600$$ 0 0
$$601$$ 19.0000 0.775026 0.387513 0.921864i $$-0.373334\pi$$
0.387513 + 0.921864i $$0.373334\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 56.0000 2.27672
$$606$$ 0 0
$$607$$ −20.0000 −0.811775 −0.405887 0.913923i $$-0.633038\pi$$
−0.405887 + 0.913923i $$0.633038\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 4.00000 0.161823
$$612$$ 0 0
$$613$$ −12.0000 −0.484675 −0.242338 0.970192i $$-0.577914\pi$$
−0.242338 + 0.970192i $$0.577914\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 45.0000 1.81163 0.905816 0.423672i $$-0.139259\pi$$
0.905816 + 0.423672i $$0.139259\pi$$
$$618$$ 0 0
$$619$$ 21.0000 0.844061 0.422031 0.906582i $$-0.361317\pi$$
0.422031 + 0.906582i $$0.361317\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 20.0000 0.801283
$$624$$ 0 0
$$625$$ 41.0000 1.64000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 24.0000 0.956943
$$630$$ 0 0
$$631$$ 28.0000 1.11466 0.557331 0.830290i $$-0.311825\pi$$
0.557331 + 0.830290i $$0.311825\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −8.00000 −0.317470
$$636$$ 0 0
$$637$$ −6.00000 −0.237729
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −5.00000 −0.197488 −0.0987441 0.995113i $$-0.531483\pi$$
−0.0987441 + 0.995113i $$0.531483\pi$$
$$642$$ 0 0
$$643$$ −15.0000 −0.591542 −0.295771 0.955259i $$-0.595577\pi$$
−0.295771 + 0.955259i $$0.595577\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 6.00000 0.235884 0.117942 0.993020i $$-0.462370\pi$$
0.117942 + 0.993020i $$0.462370\pi$$
$$648$$ 0 0
$$649$$ −25.0000 −0.981336
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −22.0000 −0.860927 −0.430463 0.902608i $$-0.641650\pi$$
−0.430463 + 0.902608i $$0.641650\pi$$
$$654$$ 0 0
$$655$$ −64.0000 −2.50069
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 12.0000 0.467454 0.233727 0.972302i $$-0.424908\pi$$
0.233727 + 0.972302i $$0.424908\pi$$
$$660$$ 0 0
$$661$$ −32.0000 −1.24466 −0.622328 0.782757i $$-0.713813\pi$$
−0.622328 + 0.782757i $$0.713813\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 8.00000 0.310227
$$666$$ 0 0
$$667$$ 12.0000 0.464642
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 2.00000 0.0770943 0.0385472 0.999257i $$-0.487727\pi$$
0.0385472 + 0.999257i $$0.487727\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −28.0000 −1.07613 −0.538064 0.842904i $$-0.680844\pi$$
−0.538064 + 0.842904i $$0.680844\pi$$
$$678$$ 0 0
$$679$$ −22.0000 −0.844283
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 15.0000 0.573959 0.286980 0.957937i $$-0.407349\pi$$
0.286980 + 0.957937i $$0.407349\pi$$
$$684$$ 0 0
$$685$$ 12.0000 0.458496
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −8.00000 −0.304776
$$690$$ 0 0
$$691$$ −8.00000 −0.304334 −0.152167 0.988355i $$-0.548625\pi$$
−0.152167 + 0.988355i $$0.548625\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −52.0000 −1.97247
$$696$$ 0 0
$$697$$ −3.00000 −0.113633
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 42.0000 1.58632 0.793159 0.609015i $$-0.208435\pi$$
0.793159 + 0.609015i $$0.208435\pi$$
$$702$$ 0 0
$$703$$ 8.00000 0.301726
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 24.0000 0.902613
$$708$$ 0 0
$$709$$ 20.0000 0.751116 0.375558 0.926799i $$-0.377451\pi$$
0.375558 + 0.926799i $$0.377451\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −24.0000 −0.898807
$$714$$ 0 0
$$715$$ 40.0000 1.49592
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 32.0000 1.19340 0.596699 0.802465i $$-0.296479\pi$$
0.596699 + 0.802465i $$0.296479\pi$$
$$720$$ 0 0
$$721$$ −12.0000 −0.446903
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −22.0000 −0.817059
$$726$$ 0 0
$$727$$ 30.0000 1.11264 0.556319 0.830969i $$-0.312213\pi$$
0.556319 + 0.830969i $$0.312213\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −21.0000 −0.776713
$$732$$ 0 0
$$733$$ 34.0000 1.25582 0.627909 0.778287i $$-0.283911\pi$$
0.627909 + 0.778287i $$0.283911\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −65.0000 −2.39431
$$738$$ 0 0
$$739$$ 49.0000 1.80249 0.901247 0.433306i $$-0.142653\pi$$
0.901247 + 0.433306i $$0.142653\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −6.00000 −0.220119 −0.110059 0.993925i $$-0.535104\pi$$
−0.110059 + 0.993925i $$0.535104\pi$$
$$744$$ 0 0
$$745$$ −72.0000 −2.63788
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −10.0000 −0.365392
$$750$$ 0 0
$$751$$ 52.0000 1.89751 0.948753 0.316017i $$-0.102346\pi$$
0.948753 + 0.316017i $$0.102346\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 72.0000 2.62035
$$756$$ 0 0
$$757$$ −18.0000 −0.654221 −0.327111 0.944986i $$-0.606075\pi$$
−0.327111 + 0.944986i $$0.606075\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 30.0000 1.08750 0.543750 0.839248i $$-0.317004\pi$$
0.543750 + 0.839248i $$0.317004\pi$$
$$762$$ 0 0
$$763$$ −16.0000 −0.579239
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −10.0000 −0.361079
$$768$$ 0 0
$$769$$ 10.0000 0.360609 0.180305 0.983611i $$-0.442292\pi$$
0.180305 + 0.983611i $$0.442292\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −42.0000 −1.51064 −0.755318 0.655359i $$-0.772517\pi$$
−0.755318 + 0.655359i $$0.772517\pi$$
$$774$$ 0 0
$$775$$ 44.0000 1.58053
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −1.00000 −0.0358287
$$780$$ 0 0
$$781$$ 40.0000 1.43131
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −80.0000 −2.85532
$$786$$ 0 0
$$787$$ −36.0000 −1.28326 −0.641631 0.767014i $$-0.721742\pi$$
−0.641631 + 0.767014i $$0.721742\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 4.00000 0.142224
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 24.0000 0.850124 0.425062 0.905164i $$-0.360252\pi$$
0.425062 + 0.905164i $$0.360252\pi$$
$$798$$ 0 0
$$799$$ 6.00000 0.212265
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 15.0000 0.529339
$$804$$ 0 0
$$805$$ −48.0000 −1.69178
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −17.0000 −0.597688 −0.298844 0.954302i $$-0.596601\pi$$
−0.298844 + 0.954302i $$0.596601\pi$$
$$810$$ 0 0
$$811$$ 55.0000 1.93131 0.965656 0.259825i $$-0.0836650\pi$$
0.965656 + 0.259825i $$0.0836650\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −80.0000 −2.80228
$$816$$ 0 0
$$817$$ −7.00000 −0.244899
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −50.0000 −1.74501 −0.872506 0.488603i $$-0.837507\pi$$
−0.872506 + 0.488603i $$0.837507\pi$$
$$822$$ 0 0
$$823$$ −28.0000 −0.976019 −0.488009 0.872838i $$-0.662277\pi$$
−0.488009 + 0.872838i $$0.662277\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −28.0000 −0.973655 −0.486828 0.873498i $$-0.661846\pi$$
−0.486828 + 0.873498i $$0.661846\pi$$
$$828$$ 0 0
$$829$$ −14.0000 −0.486240 −0.243120 0.969996i $$-0.578171\pi$$
−0.243120 + 0.969996i $$0.578171\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −9.00000 −0.311832
$$834$$ 0 0
$$835$$ −64.0000 −2.21481
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −4.00000 −0.138095 −0.0690477 0.997613i $$-0.521996\pi$$
−0.0690477 + 0.997613i $$0.521996\pi$$
$$840$$ 0 0
$$841$$ −25.0000 −0.862069
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ −36.0000 −1.23844
$$846$$ 0 0
$$847$$ 28.0000 0.962091
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −48.0000 −1.64542
$$852$$ 0 0
$$853$$ −30.0000 −1.02718 −0.513590 0.858036i $$-0.671685\pi$$
−0.513590 + 0.858036i $$0.671685\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 10.0000 0.341593 0.170797 0.985306i $$-0.445366\pi$$
0.170797 + 0.985306i $$0.445366\pi$$
$$858$$ 0 0
$$859$$ 5.00000 0.170598 0.0852989 0.996355i $$-0.472815\pi$$
0.0852989 + 0.996355i $$0.472815\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −28.0000 −0.953131 −0.476566 0.879139i $$-0.658119\pi$$
−0.476566 + 0.879139i $$0.658119\pi$$
$$864$$ 0 0
$$865$$ 72.0000 2.44807
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −40.0000 −1.35691
$$870$$ 0 0
$$871$$ −26.0000 −0.880976
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 48.0000 1.62270
$$876$$ 0 0
$$877$$ −40.0000 −1.35070 −0.675352 0.737496i $$-0.736008\pi$$
−0.675352 + 0.737496i $$0.736008\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −30.0000 −1.01073 −0.505363 0.862907i $$-0.668641\pi$$
−0.505363 + 0.862907i $$0.668641\pi$$
$$882$$ 0 0
$$883$$ −13.0000 −0.437485 −0.218742 0.975783i $$-0.570195\pi$$
−0.218742 + 0.975783i $$0.570195\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 36.0000 1.20876 0.604381 0.796696i $$-0.293421\pi$$
0.604381 + 0.796696i $$0.293421\pi$$
$$888$$ 0 0
$$889$$ −4.00000 −0.134156
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 2.00000 0.0669274
$$894$$ 0 0
$$895$$ −48.0000 −1.60446
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −8.00000 −0.266815
$$900$$ 0 0
$$901$$ −12.0000 −0.399778
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −8.00000 −0.265929
$$906$$ 0 0
$$907$$ 7.00000 0.232431 0.116216 0.993224i $$-0.462924\pi$$
0.116216 + 0.993224i $$0.462924\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −24.0000 −0.795155 −0.397578 0.917568i $$-0.630149\pi$$
−0.397578 + 0.917568i $$0.630149\pi$$
$$912$$ 0 0
$$913$$ −60.0000 −1.98571
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −32.0000 −1.05673
$$918$$ 0 0
$$919$$ −54.0000 −1.78130 −0.890648 0.454694i $$-0.849749\pi$$
−0.890648 + 0.454694i $$0.849749\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 16.0000 0.526646
$$924$$ 0 0
$$925$$ 88.0000 2.89342
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 6.00000 0.196854 0.0984268 0.995144i $$-0.468619\pi$$
0.0984268 + 0.995144i $$0.468619\pi$$
$$930$$ 0 0
$$931$$ −3.00000 −0.0983210
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 60.0000 1.96221
$$936$$ 0 0
$$937$$ −58.0000 −1.89478 −0.947389 0.320085i $$-0.896288\pi$$
−0.947389 + 0.320085i $$0.896288\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −28.0000 −0.912774 −0.456387 0.889781i $$-0.650857\pi$$
−0.456387 + 0.889781i $$0.650857\pi$$
$$942$$ 0 0
$$943$$ 6.00000 0.195387
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 27.0000 0.877382 0.438691 0.898638i $$-0.355442\pi$$
0.438691 + 0.898638i $$0.355442\pi$$
$$948$$ 0 0
$$949$$ 6.00000 0.194768
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 39.0000 1.26333 0.631667 0.775240i $$-0.282371\pi$$
0.631667 + 0.775240i $$0.282371\pi$$
$$954$$ 0 0
$$955$$ −24.0000 −0.776622
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 6.00000 0.193750
$$960$$ 0 0
$$961$$ −15.0000 −0.483871
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ −12.0000 −0.386294
$$966$$ 0 0
$$967$$ 42.0000 1.35063 0.675314 0.737530i $$-0.264008\pi$$
0.675314 + 0.737530i $$0.264008\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 20.0000 0.641831 0.320915 0.947108i $$-0.396010\pi$$
0.320915 + 0.947108i $$0.396010\pi$$
$$972$$ 0 0
$$973$$ −26.0000 −0.833522
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 11.0000 0.351921 0.175961 0.984397i $$-0.443697\pi$$
0.175961 + 0.984397i $$0.443697\pi$$
$$978$$ 0 0
$$979$$ 50.0000 1.59801
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 36.0000 1.14822 0.574111 0.818778i $$-0.305348\pi$$
0.574111 + 0.818778i $$0.305348\pi$$
$$984$$ 0 0
$$985$$ 16.0000 0.509802
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 42.0000 1.33552
$$990$$ 0 0
$$991$$ 16.0000 0.508257 0.254128 0.967170i $$-0.418211\pi$$
0.254128 + 0.967170i $$0.418211\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ −8.00000 −0.253617
$$996$$ 0 0
$$997$$ −60.0000 −1.90022 −0.950110 0.311916i $$-0.899029\pi$$
−0.950110 + 0.311916i $$0.899029\pi$$
$$998$$ 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 5184.2.a.bf.1.1 1
3.2 odd 2 5184.2.a.b.1.1 1
4.3 odd 2 5184.2.a.be.1.1 1
8.3 odd 2 2592.2.a.a.1.1 1
8.5 even 2 2592.2.a.b.1.1 1
9.2 odd 6 576.2.i.h.193.1 2
9.4 even 3 1728.2.i.a.1153.1 2
9.5 odd 6 576.2.i.h.385.1 2
9.7 even 3 1728.2.i.a.577.1 2
12.11 even 2 5184.2.a.a.1.1 1
24.5 odd 2 2592.2.a.h.1.1 1
24.11 even 2 2592.2.a.g.1.1 1
36.7 odd 6 1728.2.i.b.577.1 2
36.11 even 6 576.2.i.b.193.1 2
36.23 even 6 576.2.i.b.385.1 2
36.31 odd 6 1728.2.i.b.1153.1 2
72.5 odd 6 288.2.i.a.97.1 2
72.11 even 6 288.2.i.b.193.1 yes 2
72.13 even 6 864.2.i.a.289.1 2
72.29 odd 6 288.2.i.a.193.1 yes 2
72.43 odd 6 864.2.i.b.577.1 2
72.59 even 6 288.2.i.b.97.1 yes 2
72.61 even 6 864.2.i.a.577.1 2
72.67 odd 6 864.2.i.b.289.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
288.2.i.a.97.1 2 72.5 odd 6
288.2.i.a.193.1 yes 2 72.29 odd 6
288.2.i.b.97.1 yes 2 72.59 even 6
288.2.i.b.193.1 yes 2 72.11 even 6
576.2.i.b.193.1 2 36.11 even 6
576.2.i.b.385.1 2 36.23 even 6
576.2.i.h.193.1 2 9.2 odd 6
576.2.i.h.385.1 2 9.5 odd 6
864.2.i.a.289.1 2 72.13 even 6
864.2.i.a.577.1 2 72.61 even 6
864.2.i.b.289.1 2 72.67 odd 6
864.2.i.b.577.1 2 72.43 odd 6
1728.2.i.a.577.1 2 9.7 even 3
1728.2.i.a.1153.1 2 9.4 even 3
1728.2.i.b.577.1 2 36.7 odd 6
1728.2.i.b.1153.1 2 36.31 odd 6
2592.2.a.a.1.1 1 8.3 odd 2
2592.2.a.b.1.1 1 8.5 even 2
2592.2.a.g.1.1 1 24.11 even 2
2592.2.a.h.1.1 1 24.5 odd 2
5184.2.a.a.1.1 1 12.11 even 2
5184.2.a.b.1.1 1 3.2 odd 2
5184.2.a.be.1.1 1 4.3 odd 2
5184.2.a.bf.1.1 1 1.1 even 1 trivial