# Properties

 Label 460.2.a.b.1.1 Level $460$ Weight $2$ Character 460.1 Self dual yes Analytic conductor $3.673$ 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] = [460,2,Mod(1,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, 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("460.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$460 = 2^{2} \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 460.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: $$3.67311849298$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: yes Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 460.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-1.00000 q^{5} -1.00000 q^{7} -3.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{5} -1.00000 q^{7} -3.00000 q^{9} +6.00000 q^{11} +6.00000 q^{13} +7.00000 q^{17} +2.00000 q^{19} -1.00000 q^{23} +1.00000 q^{25} -5.00000 q^{29} +1.00000 q^{31} +1.00000 q^{35} -5.00000 q^{37} -7.00000 q^{41} +8.00000 q^{43} +3.00000 q^{45} +8.00000 q^{47} -6.00000 q^{49} +3.00000 q^{53} -6.00000 q^{55} +13.0000 q^{59} -8.00000 q^{61} +3.00000 q^{63} -6.00000 q^{65} -9.00000 q^{67} +7.00000 q^{71} -2.00000 q^{73} -6.00000 q^{77} -12.0000 q^{79} +9.00000 q^{81} -5.00000 q^{83} -7.00000 q^{85} -12.0000 q^{89} -6.00000 q^{91} -2.00000 q^{95} +2.00000 q^{97} -18.0000 q^{99} +O(q^{100})$$

## 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$4$$ 0 0
$$5$$ −1.00000 −0.447214
$$6$$ 0 0
$$7$$ −1.00000 −0.377964 −0.188982 0.981981i $$-0.560519\pi$$
−0.188982 + 0.981981i $$0.560519\pi$$
$$8$$ 0 0
$$9$$ −3.00000 −1.00000
$$10$$ 0 0
$$11$$ 6.00000 1.80907 0.904534 0.426401i $$-0.140219\pi$$
0.904534 + 0.426401i $$0.140219\pi$$
$$12$$ 0 0
$$13$$ 6.00000 1.66410 0.832050 0.554700i $$-0.187167\pi$$
0.832050 + 0.554700i $$0.187167\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 7.00000 1.69775 0.848875 0.528594i $$-0.177281\pi$$
0.848875 + 0.528594i $$0.177281\pi$$
$$18$$ 0 0
$$19$$ 2.00000 0.458831 0.229416 0.973329i $$-0.426318\pi$$
0.229416 + 0.973329i $$0.426318\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −1.00000 −0.208514
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −5.00000 −0.928477 −0.464238 0.885710i $$-0.653672\pi$$
−0.464238 + 0.885710i $$0.653672\pi$$
$$30$$ 0 0
$$31$$ 1.00000 0.179605 0.0898027 0.995960i $$-0.471376\pi$$
0.0898027 + 0.995960i $$0.471376\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 1.00000 0.169031
$$36$$ 0 0
$$37$$ −5.00000 −0.821995 −0.410997 0.911636i $$-0.634819\pi$$
−0.410997 + 0.911636i $$0.634819\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −7.00000 −1.09322 −0.546608 0.837389i $$-0.684081\pi$$
−0.546608 + 0.837389i $$0.684081\pi$$
$$42$$ 0 0
$$43$$ 8.00000 1.21999 0.609994 0.792406i $$-0.291172\pi$$
0.609994 + 0.792406i $$0.291172\pi$$
$$44$$ 0 0
$$45$$ 3.00000 0.447214
$$46$$ 0 0
$$47$$ 8.00000 1.16692 0.583460 0.812142i $$-0.301699\pi$$
0.583460 + 0.812142i $$0.301699\pi$$
$$48$$ 0 0
$$49$$ −6.00000 −0.857143
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 3.00000 0.412082 0.206041 0.978543i $$-0.433942\pi$$
0.206041 + 0.978543i $$0.433942\pi$$
$$54$$ 0 0
$$55$$ −6.00000 −0.809040
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 13.0000 1.69246 0.846228 0.532821i $$-0.178868\pi$$
0.846228 + 0.532821i $$0.178868\pi$$
$$60$$ 0 0
$$61$$ −8.00000 −1.02430 −0.512148 0.858898i $$-0.671150\pi$$
−0.512148 + 0.858898i $$0.671150\pi$$
$$62$$ 0 0
$$63$$ 3.00000 0.377964
$$64$$ 0 0
$$65$$ −6.00000 −0.744208
$$66$$ 0 0
$$67$$ −9.00000 −1.09952 −0.549762 0.835321i $$-0.685282\pi$$
−0.549762 + 0.835321i $$0.685282\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 7.00000 0.830747 0.415374 0.909651i $$-0.363651\pi$$
0.415374 + 0.909651i $$0.363651\pi$$
$$72$$ 0 0
$$73$$ −2.00000 −0.234082 −0.117041 0.993127i $$-0.537341\pi$$
−0.117041 + 0.993127i $$0.537341\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −6.00000 −0.683763
$$78$$ 0 0
$$79$$ −12.0000 −1.35011 −0.675053 0.737769i $$-0.735879\pi$$
−0.675053 + 0.737769i $$0.735879\pi$$
$$80$$ 0 0
$$81$$ 9.00000 1.00000
$$82$$ 0 0
$$83$$ −5.00000 −0.548821 −0.274411 0.961613i $$-0.588483\pi$$
−0.274411 + 0.961613i $$0.588483\pi$$
$$84$$ 0 0
$$85$$ −7.00000 −0.759257
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −12.0000 −1.27200 −0.635999 0.771690i $$-0.719412\pi$$
−0.635999 + 0.771690i $$0.719412\pi$$
$$90$$ 0 0
$$91$$ −6.00000 −0.628971
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −2.00000 −0.205196
$$96$$ 0 0
$$97$$ 2.00000 0.203069 0.101535 0.994832i $$-0.467625\pi$$
0.101535 + 0.994832i $$0.467625\pi$$
$$98$$ 0 0
$$99$$ −18.0000 −1.80907
$$100$$ 0 0
$$101$$ 7.00000 0.696526 0.348263 0.937397i $$-0.386772\pi$$
0.348263 + 0.937397i $$0.386772\pi$$
$$102$$ 0 0
$$103$$ 8.00000 0.788263 0.394132 0.919054i $$-0.371045\pi$$
0.394132 + 0.919054i $$0.371045\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 19.0000 1.83680 0.918400 0.395654i $$-0.129482\pi$$
0.918400 + 0.395654i $$0.129482\pi$$
$$108$$ 0 0
$$109$$ −10.0000 −0.957826 −0.478913 0.877862i $$-0.658969\pi$$
−0.478913 + 0.877862i $$0.658969\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 3.00000 0.282216 0.141108 0.989994i $$-0.454933\pi$$
0.141108 + 0.989994i $$0.454933\pi$$
$$114$$ 0 0
$$115$$ 1.00000 0.0932505
$$116$$ 0 0
$$117$$ −18.0000 −1.66410
$$118$$ 0 0
$$119$$ −7.00000 −0.641689
$$120$$ 0 0
$$121$$ 25.0000 2.27273
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ −4.00000 −0.354943 −0.177471 0.984126i $$-0.556792\pi$$
−0.177471 + 0.984126i $$0.556792\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −12.0000 −1.04844 −0.524222 0.851581i $$-0.675644\pi$$
−0.524222 + 0.851581i $$0.675644\pi$$
$$132$$ 0 0
$$133$$ −2.00000 −0.173422
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 6.00000 0.512615 0.256307 0.966595i $$-0.417494\pi$$
0.256307 + 0.966595i $$0.417494\pi$$
$$138$$ 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
$$143$$ 36.0000 3.01047
$$144$$ 0 0
$$145$$ 5.00000 0.415227
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −24.0000 −1.96616 −0.983078 0.183186i $$-0.941359\pi$$
−0.983078 + 0.183186i $$0.941359\pi$$
$$150$$ 0 0
$$151$$ −4.00000 −0.325515 −0.162758 0.986666i $$-0.552039\pi$$
−0.162758 + 0.986666i $$0.552039\pi$$
$$152$$ 0 0
$$153$$ −21.0000 −1.69775
$$154$$ 0 0
$$155$$ −1.00000 −0.0803219
$$156$$ 0 0
$$157$$ −23.0000 −1.83560 −0.917800 0.397043i $$-0.870036\pi$$
−0.917800 + 0.397043i $$0.870036\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 1.00000 0.0788110
$$162$$ 0 0
$$163$$ −14.0000 −1.09656 −0.548282 0.836293i $$-0.684718\pi$$
−0.548282 + 0.836293i $$0.684718\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 8.00000 0.619059 0.309529 0.950890i $$-0.399829\pi$$
0.309529 + 0.950890i $$0.399829\pi$$
$$168$$ 0 0
$$169$$ 23.0000 1.76923
$$170$$ 0 0
$$171$$ −6.00000 −0.458831
$$172$$ 0 0
$$173$$ 8.00000 0.608229 0.304114 0.952636i $$-0.401639\pi$$
0.304114 + 0.952636i $$0.401639\pi$$
$$174$$ 0 0
$$175$$ −1.00000 −0.0755929
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 24.0000 1.79384 0.896922 0.442189i $$-0.145798\pi$$
0.896922 + 0.442189i $$0.145798\pi$$
$$180$$ 0 0
$$181$$ −16.0000 −1.18927 −0.594635 0.803996i $$-0.702704\pi$$
−0.594635 + 0.803996i $$0.702704\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 5.00000 0.367607
$$186$$ 0 0
$$187$$ 42.0000 3.07134
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ 0 0
$$193$$ 24.0000 1.72756 0.863779 0.503871i $$-0.168091\pi$$
0.863779 + 0.503871i $$0.168091\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −10.0000 −0.712470 −0.356235 0.934396i $$-0.615940\pi$$
−0.356235 + 0.934396i $$0.615940\pi$$
$$198$$ 0 0
$$199$$ 6.00000 0.425329 0.212664 0.977125i $$-0.431786\pi$$
0.212664 + 0.977125i $$0.431786\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 5.00000 0.350931
$$204$$ 0 0
$$205$$ 7.00000 0.488901
$$206$$ 0 0
$$207$$ 3.00000 0.208514
$$208$$ 0 0
$$209$$ 12.0000 0.830057
$$210$$ 0 0
$$211$$ −7.00000 −0.481900 −0.240950 0.970538i $$-0.577459\pi$$
−0.240950 + 0.970538i $$0.577459\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −8.00000 −0.545595
$$216$$ 0 0
$$217$$ −1.00000 −0.0678844
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 42.0000 2.82523
$$222$$ 0 0
$$223$$ −6.00000 −0.401790 −0.200895 0.979613i $$-0.564385\pi$$
−0.200895 + 0.979613i $$0.564385\pi$$
$$224$$ 0 0
$$225$$ −3.00000 −0.200000
$$226$$ 0 0
$$227$$ −28.0000 −1.85843 −0.929213 0.369546i $$-0.879513\pi$$
−0.929213 + 0.369546i $$0.879513\pi$$
$$228$$ 0 0
$$229$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −4.00000 −0.262049 −0.131024 0.991379i $$-0.541827\pi$$
−0.131024 + 0.991379i $$0.541827\pi$$
$$234$$ 0 0
$$235$$ −8.00000 −0.521862
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 9.00000 0.582162 0.291081 0.956698i $$-0.405985\pi$$
0.291081 + 0.956698i $$0.405985\pi$$
$$240$$ 0 0
$$241$$ −10.0000 −0.644157 −0.322078 0.946713i $$-0.604381\pi$$
−0.322078 + 0.946713i $$0.604381\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 6.00000 0.383326
$$246$$ 0 0
$$247$$ 12.0000 0.763542
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 2.00000 0.126239 0.0631194 0.998006i $$-0.479895\pi$$
0.0631194 + 0.998006i $$0.479895\pi$$
$$252$$ 0 0
$$253$$ −6.00000 −0.377217
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 16.0000 0.998053 0.499026 0.866587i $$-0.333691\pi$$
0.499026 + 0.866587i $$0.333691\pi$$
$$258$$ 0 0
$$259$$ 5.00000 0.310685
$$260$$ 0 0
$$261$$ 15.0000 0.928477
$$262$$ 0 0
$$263$$ −11.0000 −0.678289 −0.339145 0.940734i $$-0.610138\pi$$
−0.339145 + 0.940734i $$0.610138\pi$$
$$264$$ 0 0
$$265$$ −3.00000 −0.184289
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −15.0000 −0.914566 −0.457283 0.889321i $$-0.651177\pi$$
−0.457283 + 0.889321i $$0.651177\pi$$
$$270$$ 0 0
$$271$$ −17.0000 −1.03268 −0.516338 0.856385i $$-0.672705\pi$$
−0.516338 + 0.856385i $$0.672705\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 6.00000 0.361814
$$276$$ 0 0
$$277$$ 22.0000 1.32185 0.660926 0.750451i $$-0.270164\pi$$
0.660926 + 0.750451i $$0.270164\pi$$
$$278$$ 0 0
$$279$$ −3.00000 −0.179605
$$280$$ 0 0
$$281$$ 18.0000 1.07379 0.536895 0.843649i $$-0.319597\pi$$
0.536895 + 0.843649i $$0.319597\pi$$
$$282$$ 0 0
$$283$$ −15.0000 −0.891657 −0.445829 0.895118i $$-0.647091\pi$$
−0.445829 + 0.895118i $$0.647091\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 7.00000 0.413197
$$288$$ 0 0
$$289$$ 32.0000 1.88235
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 9.00000 0.525786 0.262893 0.964825i $$-0.415323\pi$$
0.262893 + 0.964825i $$0.415323\pi$$
$$294$$ 0 0
$$295$$ −13.0000 −0.756889
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −6.00000 −0.346989
$$300$$ 0 0
$$301$$ −8.00000 −0.461112
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 8.00000 0.458079
$$306$$ 0 0
$$307$$ 18.0000 1.02731 0.513657 0.857996i $$-0.328290\pi$$
0.513657 + 0.857996i $$0.328290\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −16.0000 −0.907277 −0.453638 0.891186i $$-0.649874\pi$$
−0.453638 + 0.891186i $$0.649874\pi$$
$$312$$ 0 0
$$313$$ 1.00000 0.0565233 0.0282617 0.999601i $$-0.491003\pi$$
0.0282617 + 0.999601i $$0.491003\pi$$
$$314$$ 0 0
$$315$$ −3.00000 −0.169031
$$316$$ 0 0
$$317$$ −12.0000 −0.673987 −0.336994 0.941507i $$-0.609410\pi$$
−0.336994 + 0.941507i $$0.609410\pi$$
$$318$$ 0 0
$$319$$ −30.0000 −1.67968
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 14.0000 0.778981
$$324$$ 0 0
$$325$$ 6.00000 0.332820
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −8.00000 −0.441054
$$330$$ 0 0
$$331$$ 13.0000 0.714545 0.357272 0.934000i $$-0.383707\pi$$
0.357272 + 0.934000i $$0.383707\pi$$
$$332$$ 0 0
$$333$$ 15.0000 0.821995
$$334$$ 0 0
$$335$$ 9.00000 0.491723
$$336$$ 0 0
$$337$$ −6.00000 −0.326841 −0.163420 0.986557i $$-0.552253\pi$$
−0.163420 + 0.986557i $$0.552253\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 6.00000 0.324918
$$342$$ 0 0
$$343$$ 13.0000 0.701934
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −28.0000 −1.50312 −0.751559 0.659665i $$-0.770698\pi$$
−0.751559 + 0.659665i $$0.770698\pi$$
$$348$$ 0 0
$$349$$ −25.0000 −1.33822 −0.669110 0.743164i $$-0.733324\pi$$
−0.669110 + 0.743164i $$0.733324\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −24.0000 −1.27739 −0.638696 0.769460i $$-0.720526\pi$$
−0.638696 + 0.769460i $$0.720526\pi$$
$$354$$ 0 0
$$355$$ −7.00000 −0.371521
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 28.0000 1.47778 0.738892 0.673824i $$-0.235349\pi$$
0.738892 + 0.673824i $$0.235349\pi$$
$$360$$ 0 0
$$361$$ −15.0000 −0.789474
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 2.00000 0.104685
$$366$$ 0 0
$$367$$ −11.0000 −0.574195 −0.287098 0.957901i $$-0.592690\pi$$
−0.287098 + 0.957901i $$0.592690\pi$$
$$368$$ 0 0
$$369$$ 21.0000 1.09322
$$370$$ 0 0
$$371$$ −3.00000 −0.155752
$$372$$ 0 0
$$373$$ −18.0000 −0.932005 −0.466002 0.884783i $$-0.654306\pi$$
−0.466002 + 0.884783i $$0.654306\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −30.0000 −1.54508
$$378$$ 0 0
$$379$$ 20.0000 1.02733 0.513665 0.857991i $$-0.328287\pi$$
0.513665 + 0.857991i $$0.328287\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −3.00000 −0.153293 −0.0766464 0.997058i $$-0.524421\pi$$
−0.0766464 + 0.997058i $$0.524421\pi$$
$$384$$ 0 0
$$385$$ 6.00000 0.305788
$$386$$ 0 0
$$387$$ −24.0000 −1.21999
$$388$$ 0 0
$$389$$ 18.0000 0.912636 0.456318 0.889817i $$-0.349168\pi$$
0.456318 + 0.889817i $$0.349168\pi$$
$$390$$ 0 0
$$391$$ −7.00000 −0.354005
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 12.0000 0.603786
$$396$$ 0 0
$$397$$ 12.0000 0.602263 0.301131 0.953583i $$-0.402636\pi$$
0.301131 + 0.953583i $$0.402636\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −14.0000 −0.699127 −0.349563 0.936913i $$-0.613670\pi$$
−0.349563 + 0.936913i $$0.613670\pi$$
$$402$$ 0 0
$$403$$ 6.00000 0.298881
$$404$$ 0 0
$$405$$ −9.00000 −0.447214
$$406$$ 0 0
$$407$$ −30.0000 −1.48704
$$408$$ 0 0
$$409$$ −3.00000 −0.148340 −0.0741702 0.997246i $$-0.523631\pi$$
−0.0741702 + 0.997246i $$0.523631\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −13.0000 −0.639688
$$414$$ 0 0
$$415$$ 5.00000 0.245440
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 18.0000 0.879358 0.439679 0.898155i $$-0.355092\pi$$
0.439679 + 0.898155i $$0.355092\pi$$
$$420$$ 0 0
$$421$$ −26.0000 −1.26716 −0.633581 0.773676i $$-0.718416\pi$$
−0.633581 + 0.773676i $$0.718416\pi$$
$$422$$ 0 0
$$423$$ −24.0000 −1.16692
$$424$$ 0 0
$$425$$ 7.00000 0.339550
$$426$$ 0 0
$$427$$ 8.00000 0.387147
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −4.00000 −0.192673 −0.0963366 0.995349i $$-0.530713\pi$$
−0.0963366 + 0.995349i $$0.530713\pi$$
$$432$$ 0 0
$$433$$ −29.0000 −1.39365 −0.696826 0.717241i $$-0.745405\pi$$
−0.696826 + 0.717241i $$0.745405\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −2.00000 −0.0956730
$$438$$ 0 0
$$439$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$440$$ 0 0
$$441$$ 18.0000 0.857143
$$442$$ 0 0
$$443$$ −24.0000 −1.14027 −0.570137 0.821549i $$-0.693110\pi$$
−0.570137 + 0.821549i $$0.693110\pi$$
$$444$$ 0 0
$$445$$ 12.0000 0.568855
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 11.0000 0.519122 0.259561 0.965727i $$-0.416422\pi$$
0.259561 + 0.965727i $$0.416422\pi$$
$$450$$ 0 0
$$451$$ −42.0000 −1.97770
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 6.00000 0.281284
$$456$$ 0 0
$$457$$ 13.0000 0.608114 0.304057 0.952654i $$-0.401659\pi$$
0.304057 + 0.952654i $$0.401659\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 30.0000 1.39724 0.698620 0.715493i $$-0.253798\pi$$
0.698620 + 0.715493i $$0.253798\pi$$
$$462$$ 0 0
$$463$$ −38.0000 −1.76601 −0.883005 0.469364i $$-0.844483\pi$$
−0.883005 + 0.469364i $$0.844483\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 11.0000 0.509019 0.254510 0.967070i $$-0.418086\pi$$
0.254510 + 0.967070i $$0.418086\pi$$
$$468$$ 0 0
$$469$$ 9.00000 0.415581
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 48.0000 2.20704
$$474$$ 0 0
$$475$$ 2.00000 0.0917663
$$476$$ 0 0
$$477$$ −9.00000 −0.412082
$$478$$ 0 0
$$479$$ 20.0000 0.913823 0.456912 0.889512i $$-0.348956\pi$$
0.456912 + 0.889512i $$0.348956\pi$$
$$480$$ 0 0
$$481$$ −30.0000 −1.36788
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −2.00000 −0.0908153
$$486$$ 0 0
$$487$$ −12.0000 −0.543772 −0.271886 0.962329i $$-0.587647\pi$$
−0.271886 + 0.962329i $$0.587647\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −9.00000 −0.406164 −0.203082 0.979162i $$-0.565096\pi$$
−0.203082 + 0.979162i $$0.565096\pi$$
$$492$$ 0 0
$$493$$ −35.0000 −1.57632
$$494$$ 0 0
$$495$$ 18.0000 0.809040
$$496$$ 0 0
$$497$$ −7.00000 −0.313993
$$498$$ 0 0
$$499$$ 15.0000 0.671492 0.335746 0.941953i $$-0.391012\pi$$
0.335746 + 0.941953i $$0.391012\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −39.0000 −1.73892 −0.869462 0.494000i $$-0.835534\pi$$
−0.869462 + 0.494000i $$0.835534\pi$$
$$504$$ 0 0
$$505$$ −7.00000 −0.311496
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −30.0000 −1.32973 −0.664863 0.746965i $$-0.731510\pi$$
−0.664863 + 0.746965i $$0.731510\pi$$
$$510$$ 0 0
$$511$$ 2.00000 0.0884748
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −8.00000 −0.352522
$$516$$ 0 0
$$517$$ 48.0000 2.11104
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 22.0000 0.963837 0.481919 0.876216i $$-0.339940\pi$$
0.481919 + 0.876216i $$0.339940\pi$$
$$522$$ 0 0
$$523$$ −4.00000 −0.174908 −0.0874539 0.996169i $$-0.527873\pi$$
−0.0874539 + 0.996169i $$0.527873\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 7.00000 0.304925
$$528$$ 0 0
$$529$$ 1.00000 0.0434783
$$530$$ 0 0
$$531$$ −39.0000 −1.69246
$$532$$ 0 0
$$533$$ −42.0000 −1.81922
$$534$$ 0 0
$$535$$ −19.0000 −0.821442
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −36.0000 −1.55063
$$540$$ 0 0
$$541$$ 22.0000 0.945854 0.472927 0.881102i $$-0.343197\pi$$
0.472927 + 0.881102i $$0.343197\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 10.0000 0.428353
$$546$$ 0 0
$$547$$ 8.00000 0.342055 0.171028 0.985266i $$-0.445291\pi$$
0.171028 + 0.985266i $$0.445291\pi$$
$$548$$ 0 0
$$549$$ 24.0000 1.02430
$$550$$ 0 0
$$551$$ −10.0000 −0.426014
$$552$$ 0 0
$$553$$ 12.0000 0.510292
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 3.00000 0.127114 0.0635570 0.997978i $$-0.479756\pi$$
0.0635570 + 0.997978i $$0.479756\pi$$
$$558$$ 0 0
$$559$$ 48.0000 2.03018
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −11.0000 −0.463595 −0.231797 0.972764i $$-0.574461\pi$$
−0.231797 + 0.972764i $$0.574461\pi$$
$$564$$ 0 0
$$565$$ −3.00000 −0.126211
$$566$$ 0 0
$$567$$ −9.00000 −0.377964
$$568$$ 0 0
$$569$$ 18.0000 0.754599 0.377300 0.926091i $$-0.376853\pi$$
0.377300 + 0.926091i $$0.376853\pi$$
$$570$$ 0 0
$$571$$ −32.0000 −1.33916 −0.669579 0.742741i $$-0.733526\pi$$
−0.669579 + 0.742741i $$0.733526\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −1.00000 −0.0417029
$$576$$ 0 0
$$577$$ 4.00000 0.166522 0.0832611 0.996528i $$-0.473466\pi$$
0.0832611 + 0.996528i $$0.473466\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 5.00000 0.207435
$$582$$ 0 0
$$583$$ 18.0000 0.745484
$$584$$ 0 0
$$585$$ 18.0000 0.744208
$$586$$ 0 0
$$587$$ 46.0000 1.89862 0.949312 0.314337i $$-0.101782\pi$$
0.949312 + 0.314337i $$0.101782\pi$$
$$588$$ 0 0
$$589$$ 2.00000 0.0824086
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −4.00000 −0.164260 −0.0821302 0.996622i $$-0.526172\pi$$
−0.0821302 + 0.996622i $$0.526172\pi$$
$$594$$ 0 0
$$595$$ 7.00000 0.286972
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 16.0000 0.653742 0.326871 0.945069i $$-0.394006\pi$$
0.326871 + 0.945069i $$0.394006\pi$$
$$600$$ 0 0
$$601$$ 43.0000 1.75401 0.877003 0.480484i $$-0.159539\pi$$
0.877003 + 0.480484i $$0.159539\pi$$
$$602$$ 0 0
$$603$$ 27.0000 1.09952
$$604$$ 0 0
$$605$$ −25.0000 −1.01639
$$606$$ 0 0
$$607$$ 32.0000 1.29884 0.649420 0.760430i $$-0.275012\pi$$
0.649420 + 0.760430i $$0.275012\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 48.0000 1.94187
$$612$$ 0 0
$$613$$ 38.0000 1.53481 0.767403 0.641165i $$-0.221549\pi$$
0.767403 + 0.641165i $$0.221549\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −15.0000 −0.603877 −0.301939 0.953327i $$-0.597634\pi$$
−0.301939 + 0.953327i $$0.597634\pi$$
$$618$$ 0 0
$$619$$ −20.0000 −0.803868 −0.401934 0.915669i $$-0.631662\pi$$
−0.401934 + 0.915669i $$0.631662\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 12.0000 0.480770
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −35.0000 −1.39554
$$630$$ 0 0
$$631$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 4.00000 0.158735
$$636$$ 0 0
$$637$$ −36.0000 −1.42637
$$638$$ 0 0
$$639$$ −21.0000 −0.830747
$$640$$ 0 0
$$641$$ 6.00000 0.236986 0.118493 0.992955i $$-0.462194\pi$$
0.118493 + 0.992955i $$0.462194\pi$$
$$642$$ 0 0
$$643$$ 19.0000 0.749287 0.374643 0.927169i $$-0.377765\pi$$
0.374643 + 0.927169i $$0.377765\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −22.0000 −0.864909 −0.432455 0.901656i $$-0.642352\pi$$
−0.432455 + 0.901656i $$0.642352\pi$$
$$648$$ 0 0
$$649$$ 78.0000 3.06177
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −14.0000 −0.547862 −0.273931 0.961749i $$-0.588324\pi$$
−0.273931 + 0.961749i $$0.588324\pi$$
$$654$$ 0 0
$$655$$ 12.0000 0.468879
$$656$$ 0 0
$$657$$ 6.00000 0.234082
$$658$$ 0 0
$$659$$ −10.0000 −0.389545 −0.194772 0.980848i $$-0.562397\pi$$
−0.194772 + 0.980848i $$0.562397\pi$$
$$660$$ 0 0
$$661$$ −30.0000 −1.16686 −0.583432 0.812162i $$-0.698291\pi$$
−0.583432 + 0.812162i $$0.698291\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 2.00000 0.0775567
$$666$$ 0 0
$$667$$ 5.00000 0.193601
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −48.0000 −1.85302
$$672$$ 0 0
$$673$$ 44.0000 1.69608 0.848038 0.529936i $$-0.177784\pi$$
0.848038 + 0.529936i $$0.177784\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −27.0000 −1.03769 −0.518847 0.854867i $$-0.673639\pi$$
−0.518847 + 0.854867i $$0.673639\pi$$
$$678$$ 0 0
$$679$$ −2.00000 −0.0767530
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −20.0000 −0.765279 −0.382639 0.923898i $$-0.624985\pi$$
−0.382639 + 0.923898i $$0.624985\pi$$
$$684$$ 0 0
$$685$$ −6.00000 −0.229248
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 18.0000 0.685745
$$690$$ 0 0
$$691$$ −4.00000 −0.152167 −0.0760836 0.997101i $$-0.524242\pi$$
−0.0760836 + 0.997101i $$0.524242\pi$$
$$692$$ 0 0
$$693$$ 18.0000 0.683763
$$694$$ 0 0
$$695$$ 13.0000 0.493118
$$696$$ 0 0
$$697$$ −49.0000 −1.85601
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −32.0000 −1.20862 −0.604312 0.796748i $$-0.706552\pi$$
−0.604312 + 0.796748i $$0.706552\pi$$
$$702$$ 0 0
$$703$$ −10.0000 −0.377157
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −7.00000 −0.263262
$$708$$ 0 0
$$709$$ 4.00000 0.150223 0.0751116 0.997175i $$-0.476069\pi$$
0.0751116 + 0.997175i $$0.476069\pi$$
$$710$$ 0 0
$$711$$ 36.0000 1.35011
$$712$$ 0 0
$$713$$ −1.00000 −0.0374503
$$714$$ 0 0
$$715$$ −36.0000 −1.34632
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 41.0000 1.52904 0.764521 0.644599i $$-0.222976\pi$$
0.764521 + 0.644599i $$0.222976\pi$$
$$720$$ 0 0
$$721$$ −8.00000 −0.297936
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −5.00000 −0.185695
$$726$$ 0 0
$$727$$ 37.0000 1.37225 0.686127 0.727482i $$-0.259309\pi$$
0.686127 + 0.727482i $$0.259309\pi$$
$$728$$ 0 0
$$729$$ −27.0000 −1.00000
$$730$$ 0 0
$$731$$ 56.0000 2.07123
$$732$$ 0 0
$$733$$ 19.0000 0.701781 0.350891 0.936416i $$-0.385879\pi$$
0.350891 + 0.936416i $$0.385879\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −54.0000 −1.98912
$$738$$ 0 0
$$739$$ 41.0000 1.50821 0.754105 0.656754i $$-0.228071\pi$$
0.754105 + 0.656754i $$0.228071\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 16.0000 0.586983 0.293492 0.955962i $$-0.405183\pi$$
0.293492 + 0.955962i $$0.405183\pi$$
$$744$$ 0 0
$$745$$ 24.0000 0.879292
$$746$$ 0 0
$$747$$ 15.0000 0.548821
$$748$$ 0 0
$$749$$ −19.0000 −0.694245
$$750$$ 0 0
$$751$$ 6.00000 0.218943 0.109472 0.993990i $$-0.465084\pi$$
0.109472 + 0.993990i $$0.465084\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 4.00000 0.145575
$$756$$ 0 0
$$757$$ 29.0000 1.05402 0.527011 0.849858i $$-0.323312\pi$$
0.527011 + 0.849858i $$0.323312\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −3.00000 −0.108750 −0.0543750 0.998521i $$-0.517317\pi$$
−0.0543750 + 0.998521i $$0.517317\pi$$
$$762$$ 0 0
$$763$$ 10.0000 0.362024
$$764$$ 0 0
$$765$$ 21.0000 0.759257
$$766$$ 0 0
$$767$$ 78.0000 2.81642
$$768$$ 0 0
$$769$$ −24.0000 −0.865462 −0.432731 0.901523i $$-0.642450\pi$$
−0.432731 + 0.901523i $$0.642450\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −10.0000 −0.359675 −0.179838 0.983696i $$-0.557557\pi$$
−0.179838 + 0.983696i $$0.557557\pi$$
$$774$$ 0 0
$$775$$ 1.00000 0.0359211
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −14.0000 −0.501602
$$780$$ 0 0
$$781$$ 42.0000 1.50288
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 23.0000 0.820905
$$786$$ 0 0
$$787$$ −29.0000 −1.03374 −0.516869 0.856064i $$-0.672903\pi$$
−0.516869 + 0.856064i $$0.672903\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −3.00000 −0.106668
$$792$$ 0 0
$$793$$ −48.0000 −1.70453
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −27.0000 −0.956389 −0.478195 0.878254i $$-0.658709\pi$$
−0.478195 + 0.878254i $$0.658709\pi$$
$$798$$ 0 0
$$799$$ 56.0000 1.98114
$$800$$ 0 0
$$801$$ 36.0000 1.27200
$$802$$ 0 0
$$803$$ −12.0000 −0.423471
$$804$$ 0 0
$$805$$ −1.00000 −0.0352454
$$806$$ 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
$$811$$ −23.0000 −0.807639 −0.403820 0.914839i $$-0.632318\pi$$
−0.403820 + 0.914839i $$0.632318\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 14.0000 0.490399
$$816$$ 0 0
$$817$$ 16.0000 0.559769
$$818$$ 0 0
$$819$$ 18.0000 0.628971
$$820$$ 0 0
$$821$$ 10.0000 0.349002 0.174501 0.984657i $$-0.444169\pi$$
0.174501 + 0.984657i $$0.444169\pi$$
$$822$$ 0 0
$$823$$ −16.0000 −0.557725 −0.278862 0.960331i $$-0.589957\pi$$
−0.278862 + 0.960331i $$0.589957\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −7.00000 −0.243414 −0.121707 0.992566i $$-0.538837\pi$$
−0.121707 + 0.992566i $$0.538837\pi$$
$$828$$ 0 0
$$829$$ 33.0000 1.14614 0.573069 0.819507i $$-0.305753\pi$$
0.573069 + 0.819507i $$0.305753\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −42.0000 −1.45521
$$834$$ 0 0
$$835$$ −8.00000 −0.276851
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −22.0000 −0.759524 −0.379762 0.925084i $$-0.623994\pi$$
−0.379762 + 0.925084i $$0.623994\pi$$
$$840$$ 0 0
$$841$$ −4.00000 −0.137931
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ −23.0000 −0.791224
$$846$$ 0 0
$$847$$ −25.0000 −0.859010
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 5.00000 0.171398
$$852$$ 0 0
$$853$$ 18.0000 0.616308 0.308154 0.951336i $$-0.400289\pi$$
0.308154 + 0.951336i $$0.400289\pi$$
$$854$$ 0 0
$$855$$ 6.00000 0.205196
$$856$$ 0 0
$$857$$ 6.00000 0.204956 0.102478 0.994735i $$-0.467323\pi$$
0.102478 + 0.994735i $$0.467323\pi$$
$$858$$ 0 0
$$859$$ −35.0000 −1.19418 −0.597092 0.802173i $$-0.703677\pi$$
−0.597092 + 0.802173i $$0.703677\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −30.0000 −1.02121 −0.510606 0.859815i $$-0.670579\pi$$
−0.510606 + 0.859815i $$0.670579\pi$$
$$864$$ 0 0
$$865$$ −8.00000 −0.272008
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −72.0000 −2.44243
$$870$$ 0 0
$$871$$ −54.0000 −1.82972
$$872$$ 0 0
$$873$$ −6.00000 −0.203069
$$874$$ 0 0
$$875$$ 1.00000 0.0338062
$$876$$ 0 0
$$877$$ 22.0000 0.742887 0.371444 0.928456i $$-0.378863\pi$$
0.371444 + 0.928456i $$0.378863\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −48.0000 −1.61716 −0.808581 0.588386i $$-0.799764\pi$$
−0.808581 + 0.588386i $$0.799764\pi$$
$$882$$ 0 0
$$883$$ 16.0000 0.538443 0.269221 0.963078i $$-0.413234\pi$$
0.269221 + 0.963078i $$0.413234\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 18.0000 0.604381 0.302190 0.953248i $$-0.402282\pi$$
0.302190 + 0.953248i $$0.402282\pi$$
$$888$$ 0 0
$$889$$ 4.00000 0.134156
$$890$$ 0 0
$$891$$ 54.0000 1.80907
$$892$$ 0 0
$$893$$ 16.0000 0.535420
$$894$$ 0 0
$$895$$ −24.0000 −0.802232
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −5.00000 −0.166759
$$900$$ 0 0
$$901$$ 21.0000 0.699611
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 16.0000 0.531858
$$906$$ 0 0
$$907$$ 55.0000 1.82625 0.913123 0.407685i $$-0.133664\pi$$
0.913123 + 0.407685i $$0.133664\pi$$
$$908$$ 0 0
$$909$$ −21.0000 −0.696526
$$910$$ 0 0
$$911$$ −16.0000 −0.530104 −0.265052 0.964234i $$-0.585389\pi$$
−0.265052 + 0.964234i $$0.585389\pi$$
$$912$$ 0 0
$$913$$ −30.0000 −0.992855
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 12.0000 0.396275
$$918$$ 0 0
$$919$$ −20.0000 −0.659739 −0.329870 0.944027i $$-0.607005\pi$$
−0.329870 + 0.944027i $$0.607005\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 42.0000 1.38245
$$924$$ 0 0
$$925$$ −5.00000 −0.164399
$$926$$ 0 0
$$927$$ −24.0000 −0.788263
$$928$$ 0 0
$$929$$ 35.0000 1.14831 0.574156 0.818746i $$-0.305330\pi$$
0.574156 + 0.818746i $$0.305330\pi$$
$$930$$ 0 0
$$931$$ −12.0000 −0.393284
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −42.0000 −1.37355
$$936$$ 0 0
$$937$$ −54.0000 −1.76410 −0.882052 0.471153i $$-0.843838\pi$$
−0.882052 + 0.471153i $$0.843838\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −8.00000 −0.260793 −0.130396 0.991462i $$-0.541625\pi$$
−0.130396 + 0.991462i $$0.541625\pi$$
$$942$$ 0 0
$$943$$ 7.00000 0.227951
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 12.0000 0.389948 0.194974 0.980808i $$-0.437538\pi$$
0.194974 + 0.980808i $$0.437538\pi$$
$$948$$ 0 0
$$949$$ −12.0000 −0.389536
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −6.00000 −0.194359 −0.0971795 0.995267i $$-0.530982\pi$$
−0.0971795 + 0.995267i $$0.530982\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ −6.00000 −0.193750
$$960$$ 0 0
$$961$$ −30.0000 −0.967742
$$962$$ 0 0
$$963$$ −57.0000 −1.83680
$$964$$ 0 0
$$965$$ −24.0000 −0.772587
$$966$$ 0 0
$$967$$ −20.0000 −0.643157 −0.321578 0.946883i $$-0.604213\pi$$
−0.321578 + 0.946883i $$0.604213\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 12.0000 0.385098 0.192549 0.981287i $$-0.438325\pi$$
0.192549 + 0.981287i $$0.438325\pi$$
$$972$$ 0 0
$$973$$ 13.0000 0.416761
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 13.0000 0.415907 0.207953 0.978139i $$-0.433320\pi$$
0.207953 + 0.978139i $$0.433320\pi$$
$$978$$ 0 0
$$979$$ −72.0000 −2.30113
$$980$$ 0 0
$$981$$ 30.0000 0.957826
$$982$$ 0 0
$$983$$ 15.0000 0.478426 0.239213 0.970967i $$-0.423111\pi$$
0.239213 + 0.970967i $$0.423111\pi$$
$$984$$ 0 0
$$985$$ 10.0000 0.318626
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −8.00000 −0.254385
$$990$$ 0 0
$$991$$ 53.0000 1.68360 0.841800 0.539789i $$-0.181496\pi$$
0.841800 + 0.539789i $$0.181496\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ −6.00000 −0.190213
$$996$$ 0 0
$$997$$ 56.0000 1.77354 0.886769 0.462213i $$-0.152944\pi$$
0.886769 + 0.462213i $$0.152944\pi$$
$$998$$ 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 460.2.a.b.1.1 1
3.2 odd 2 4140.2.a.h.1.1 1
4.3 odd 2 1840.2.a.e.1.1 1
5.2 odd 4 2300.2.c.g.1749.1 2
5.3 odd 4 2300.2.c.g.1749.2 2
5.4 even 2 2300.2.a.e.1.1 1
8.3 odd 2 7360.2.a.r.1.1 1
8.5 even 2 7360.2.a.m.1.1 1
20.19 odd 2 9200.2.a.q.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
460.2.a.b.1.1 1 1.1 even 1 trivial
1840.2.a.e.1.1 1 4.3 odd 2
2300.2.a.e.1.1 1 5.4 even 2
2300.2.c.g.1749.1 2 5.2 odd 4
2300.2.c.g.1749.2 2 5.3 odd 4
4140.2.a.h.1.1 1 3.2 odd 2
7360.2.a.m.1.1 1 8.5 even 2
7360.2.a.r.1.1 1 8.3 odd 2
9200.2.a.q.1.1 1 20.19 odd 2