# Properties

 Label 2592.2.a.f.1.1 Level $2592$ Weight $2$ Character 2592.1 Self dual yes Analytic conductor $20.697$ 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] = [2592,2,Mod(1,2592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2592, 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("2592.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$2592 = 2^{5} \cdot 3^{4}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2592.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: $$20.6972242039$$ 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 $$\chi$$ $$=$$ 2592.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+1.00000 q^{5} +2.00000 q^{7} +O(q^{10})$$ $$q+1.00000 q^{5} +2.00000 q^{7} +2.00000 q^{11} +1.00000 q^{13} +3.00000 q^{17} +2.00000 q^{19} +6.00000 q^{23} -4.00000 q^{25} +1.00000 q^{29} -8.00000 q^{31} +2.00000 q^{35} +1.00000 q^{37} -2.00000 q^{41} +10.0000 q^{43} +4.00000 q^{47} -3.00000 q^{49} -10.0000 q^{53} +2.00000 q^{55} +4.00000 q^{59} +9.00000 q^{61} +1.00000 q^{65} -14.0000 q^{67} +10.0000 q^{71} -9.00000 q^{73} +4.00000 q^{77} +10.0000 q^{79} +12.0000 q^{83} +3.00000 q^{85} +11.0000 q^{89} +2.00000 q^{91} +2.00000 q^{95} -2.00000 q^{97} +O(q^{100})$$

## 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
$$5$$ 1.00000 0.447214 0.223607 0.974679i $$-0.428217\pi$$
0.223607 + 0.974679i $$0.428217\pi$$
$$6$$ 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
$$11$$ 2.00000 0.603023 0.301511 0.953463i $$-0.402509\pi$$
0.301511 + 0.953463i $$0.402509\pi$$
$$12$$ 0 0
$$13$$ 1.00000 0.277350 0.138675 0.990338i $$-0.455716\pi$$
0.138675 + 0.990338i $$0.455716\pi$$
$$14$$ 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
$$19$$ 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
$$23$$ 6.00000 1.25109 0.625543 0.780189i $$-0.284877\pi$$
0.625543 + 0.780189i $$0.284877\pi$$
$$24$$ 0 0
$$25$$ −4.00000 −0.800000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 1.00000 0.185695 0.0928477 0.995680i $$-0.470403\pi$$
0.0928477 + 0.995680i $$0.470403\pi$$
$$30$$ 0 0
$$31$$ −8.00000 −1.43684 −0.718421 0.695608i $$-0.755135\pi$$
−0.718421 + 0.695608i $$0.755135\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 2.00000 0.338062
$$36$$ 0 0
$$37$$ 1.00000 0.164399 0.0821995 0.996616i $$-0.473806\pi$$
0.0821995 + 0.996616i $$0.473806\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −2.00000 −0.312348 −0.156174 0.987730i $$-0.549916\pi$$
−0.156174 + 0.987730i $$0.549916\pi$$
$$42$$ 0 0
$$43$$ 10.0000 1.52499 0.762493 0.646997i $$-0.223975\pi$$
0.762493 + 0.646997i $$0.223975\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 4.00000 0.583460 0.291730 0.956501i $$-0.405769\pi$$
0.291730 + 0.956501i $$0.405769\pi$$
$$48$$ 0 0
$$49$$ −3.00000 −0.428571
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −10.0000 −1.37361 −0.686803 0.726844i $$-0.740986\pi$$
−0.686803 + 0.726844i $$0.740986\pi$$
$$54$$ 0 0
$$55$$ 2.00000 0.269680
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 4.00000 0.520756 0.260378 0.965507i $$-0.416153\pi$$
0.260378 + 0.965507i $$0.416153\pi$$
$$60$$ 0 0
$$61$$ 9.00000 1.15233 0.576166 0.817333i $$-0.304548\pi$$
0.576166 + 0.817333i $$0.304548\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 1.00000 0.124035
$$66$$ 0 0
$$67$$ −14.0000 −1.71037 −0.855186 0.518321i $$-0.826557\pi$$
−0.855186 + 0.518321i $$0.826557\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 10.0000 1.18678 0.593391 0.804914i $$-0.297789\pi$$
0.593391 + 0.804914i $$0.297789\pi$$
$$72$$ 0 0
$$73$$ −9.00000 −1.05337 −0.526685 0.850060i $$-0.676565\pi$$
−0.526685 + 0.850060i $$0.676565\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 4.00000 0.455842
$$78$$ 0 0
$$79$$ 10.0000 1.12509 0.562544 0.826767i $$-0.309823\pi$$
0.562544 + 0.826767i $$0.309823\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 12.0000 1.31717 0.658586 0.752506i $$-0.271155\pi$$
0.658586 + 0.752506i $$0.271155\pi$$
$$84$$ 0 0
$$85$$ 3.00000 0.325396
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 11.0000 1.16600 0.582999 0.812473i $$-0.301879\pi$$
0.582999 + 0.812473i $$0.301879\pi$$
$$90$$ 0 0
$$91$$ 2.00000 0.209657
$$92$$ 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 $$-0.532375\pi$$
−0.101535 + 0.994832i $$0.532375\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −6.00000 −0.597022 −0.298511 0.954406i $$-0.596490\pi$$
−0.298511 + 0.954406i $$0.596490\pi$$
$$102$$ 0 0
$$103$$ −12.0000 −1.18240 −0.591198 0.806527i $$-0.701345\pi$$
−0.591198 + 0.806527i $$0.701345\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 16.0000 1.54678 0.773389 0.633932i $$-0.218560\pi$$
0.773389 + 0.633932i $$0.218560\pi$$
$$108$$ 0 0
$$109$$ 5.00000 0.478913 0.239457 0.970907i $$-0.423031\pi$$
0.239457 + 0.970907i $$0.423031\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −17.0000 −1.59923 −0.799613 0.600516i $$-0.794962\pi$$
−0.799613 + 0.600516i $$0.794962\pi$$
$$114$$ 0 0
$$115$$ 6.00000 0.559503
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 6.00000 0.550019
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −9.00000 −0.804984
$$126$$ 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
$$131$$ 14.0000 1.22319 0.611593 0.791173i $$-0.290529\pi$$
0.611593 + 0.791173i $$0.290529\pi$$
$$132$$ 0 0
$$133$$ 4.00000 0.346844
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −9.00000 −0.768922 −0.384461 0.923141i $$-0.625613\pi$$
−0.384461 + 0.923141i $$0.625613\pi$$
$$138$$ 0 0
$$139$$ −20.0000 −1.69638 −0.848189 0.529694i $$-0.822307\pi$$
−0.848189 + 0.529694i $$0.822307\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 2.00000 0.167248
$$144$$ 0 0
$$145$$ 1.00000 0.0830455
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 21.0000 1.72039 0.860194 0.509968i $$-0.170343\pi$$
0.860194 + 0.509968i $$0.170343\pi$$
$$150$$ 0 0
$$151$$ 12.0000 0.976546 0.488273 0.872691i $$-0.337627\pi$$
0.488273 + 0.872691i $$0.337627\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −8.00000 −0.642575
$$156$$ 0 0
$$157$$ 17.0000 1.35675 0.678374 0.734717i $$-0.262685\pi$$
0.678374 + 0.734717i $$0.262685\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 12.0000 0.945732
$$162$$ 0 0
$$163$$ −4.00000 −0.313304 −0.156652 0.987654i $$-0.550070\pi$$
−0.156652 + 0.987654i $$0.550070\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −2.00000 −0.154765 −0.0773823 0.997001i $$-0.524656\pi$$
−0.0773823 + 0.997001i $$0.524656\pi$$
$$168$$ 0 0
$$169$$ −12.0000 −0.923077
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 21.0000 1.59660 0.798300 0.602260i $$-0.205733\pi$$
0.798300 + 0.602260i $$0.205733\pi$$
$$174$$ 0 0
$$175$$ −8.00000 −0.604743
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ 0 0
$$181$$ 14.0000 1.04061 0.520306 0.853980i $$-0.325818\pi$$
0.520306 + 0.853980i $$0.325818\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 1.00000 0.0735215
$$186$$ 0 0
$$187$$ 6.00000 0.438763
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 18.0000 1.30243 0.651217 0.758891i $$-0.274259\pi$$
0.651217 + 0.758891i $$0.274259\pi$$
$$192$$ 0 0
$$193$$ −9.00000 −0.647834 −0.323917 0.946085i $$-0.605000\pi$$
−0.323917 + 0.946085i $$0.605000\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −11.0000 −0.783718 −0.391859 0.920025i $$-0.628168\pi$$
−0.391859 + 0.920025i $$0.628168\pi$$
$$198$$ 0 0
$$199$$ 16.0000 1.13421 0.567105 0.823646i $$-0.308063\pi$$
0.567105 + 0.823646i $$0.308063\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 2.00000 0.140372
$$204$$ 0 0
$$205$$ −2.00000 −0.139686
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 4.00000 0.276686
$$210$$ 0 0
$$211$$ 2.00000 0.137686 0.0688428 0.997628i $$-0.478069\pi$$
0.0688428 + 0.997628i $$0.478069\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 10.0000 0.681994
$$216$$ 0 0
$$217$$ −16.0000 −1.08615
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 3.00000 0.201802
$$222$$ 0 0
$$223$$ 2.00000 0.133930 0.0669650 0.997755i $$-0.478668\pi$$
0.0669650 + 0.997755i $$0.478668\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 6.00000 0.398234 0.199117 0.979976i $$-0.436193\pi$$
0.199117 + 0.979976i $$0.436193\pi$$
$$228$$ 0 0
$$229$$ −7.00000 −0.462573 −0.231287 0.972886i $$-0.574293\pi$$
−0.231287 + 0.972886i $$0.574293\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 15.0000 0.982683 0.491341 0.870967i $$-0.336507\pi$$
0.491341 + 0.870967i $$0.336507\pi$$
$$234$$ 0 0
$$235$$ 4.00000 0.260931
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 12.0000 0.776215 0.388108 0.921614i $$-0.373129\pi$$
0.388108 + 0.921614i $$0.373129\pi$$
$$240$$ 0 0
$$241$$ −5.00000 −0.322078 −0.161039 0.986948i $$-0.551485\pi$$
−0.161039 + 0.986948i $$0.551485\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −3.00000 −0.191663
$$246$$ 0 0
$$247$$ 2.00000 0.127257
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −18.0000 −1.13615 −0.568075 0.822977i $$-0.692312\pi$$
−0.568075 + 0.822977i $$0.692312\pi$$
$$252$$ 0 0
$$253$$ 12.0000 0.754434
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −29.0000 −1.80897 −0.904485 0.426505i $$-0.859745\pi$$
−0.904485 + 0.426505i $$0.859745\pi$$
$$258$$ 0 0
$$259$$ 2.00000 0.124274
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −12.0000 −0.739952 −0.369976 0.929041i $$-0.620634\pi$$
−0.369976 + 0.929041i $$0.620634\pi$$
$$264$$ 0 0
$$265$$ −10.0000 −0.614295
$$266$$ 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
$$271$$ −6.00000 −0.364474 −0.182237 0.983255i $$-0.558334\pi$$
−0.182237 + 0.983255i $$0.558334\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −8.00000 −0.482418
$$276$$ 0 0
$$277$$ −2.00000 −0.120168 −0.0600842 0.998193i $$-0.519137\pi$$
−0.0600842 + 0.998193i $$0.519137\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −9.00000 −0.536895 −0.268447 0.963294i $$-0.586511\pi$$
−0.268447 + 0.963294i $$0.586511\pi$$
$$282$$ 0 0
$$283$$ 16.0000 0.951101 0.475551 0.879688i $$-0.342249\pi$$
0.475551 + 0.879688i $$0.342249\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −4.00000 −0.236113
$$288$$ 0 0
$$289$$ −8.00000 −0.470588
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 21.0000 1.22683 0.613417 0.789760i $$-0.289795\pi$$
0.613417 + 0.789760i $$0.289795\pi$$
$$294$$ 0 0
$$295$$ 4.00000 0.232889
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 6.00000 0.346989
$$300$$ 0 0
$$301$$ 20.0000 1.15278
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 9.00000 0.515339
$$306$$ 0 0
$$307$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$312$$ 0 0
$$313$$ 7.00000 0.395663 0.197832 0.980236i $$-0.436610\pi$$
0.197832 + 0.980236i $$0.436610\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −3.00000 −0.168497 −0.0842484 0.996445i $$-0.526849\pi$$
−0.0842484 + 0.996445i $$0.526849\pi$$
$$318$$ 0 0
$$319$$ 2.00000 0.111979
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 6.00000 0.333849
$$324$$ 0 0
$$325$$ −4.00000 −0.221880
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 8.00000 0.441054
$$330$$ 0 0
$$331$$ −14.0000 −0.769510 −0.384755 0.923019i $$-0.625714\pi$$
−0.384755 + 0.923019i $$0.625714\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −14.0000 −0.764902
$$336$$ 0 0
$$337$$ 14.0000 0.762629 0.381314 0.924445i $$-0.375472\pi$$
0.381314 + 0.924445i $$0.375472\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −16.0000 −0.866449
$$342$$ 0 0
$$343$$ −20.0000 −1.07990
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 10.0000 0.536828 0.268414 0.963304i $$-0.413500\pi$$
0.268414 + 0.963304i $$0.413500\pi$$
$$348$$ 0 0
$$349$$ 34.0000 1.81998 0.909989 0.414632i $$-0.136090\pi$$
0.909989 + 0.414632i $$0.136090\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 2.00000 0.106449 0.0532246 0.998583i $$-0.483050\pi$$
0.0532246 + 0.998583i $$0.483050\pi$$
$$354$$ 0 0
$$355$$ 10.0000 0.530745
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −34.0000 −1.79445 −0.897226 0.441572i $$-0.854421\pi$$
−0.897226 + 0.441572i $$0.854421\pi$$
$$360$$ 0 0
$$361$$ −15.0000 −0.789474
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −9.00000 −0.471082
$$366$$ 0 0
$$367$$ −24.0000 −1.25279 −0.626395 0.779506i $$-0.715470\pi$$
−0.626395 + 0.779506i $$0.715470\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −20.0000 −1.03835
$$372$$ 0 0
$$373$$ −10.0000 −0.517780 −0.258890 0.965907i $$-0.583357\pi$$
−0.258890 + 0.965907i $$0.583357\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 1.00000 0.0515026
$$378$$ 0 0
$$379$$ 8.00000 0.410932 0.205466 0.978664i $$-0.434129\pi$$
0.205466 + 0.978664i $$0.434129\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −14.0000 −0.715367 −0.357683 0.933843i $$-0.616433\pi$$
−0.357683 + 0.933843i $$0.616433\pi$$
$$384$$ 0 0
$$385$$ 4.00000 0.203859
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −18.0000 −0.912636 −0.456318 0.889817i $$-0.650832\pi$$
−0.456318 + 0.889817i $$0.650832\pi$$
$$390$$ 0 0
$$391$$ 18.0000 0.910299
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 10.0000 0.503155
$$396$$ 0 0
$$397$$ 13.0000 0.652451 0.326226 0.945292i $$-0.394223\pi$$
0.326226 + 0.945292i $$0.394223\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −25.0000 −1.24844 −0.624220 0.781248i $$-0.714583\pi$$
−0.624220 + 0.781248i $$0.714583\pi$$
$$402$$ 0 0
$$403$$ −8.00000 −0.398508
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 2.00000 0.0991363
$$408$$ 0 0
$$409$$ −29.0000 −1.43396 −0.716979 0.697095i $$-0.754476\pi$$
−0.716979 + 0.697095i $$0.754476\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 8.00000 0.393654
$$414$$ 0 0
$$415$$ 12.0000 0.589057
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −40.0000 −1.95413 −0.977064 0.212946i $$-0.931694\pi$$
−0.977064 + 0.212946i $$0.931694\pi$$
$$420$$ 0 0
$$421$$ −7.00000 −0.341159 −0.170580 0.985344i $$-0.554564\pi$$
−0.170580 + 0.985344i $$0.554564\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −12.0000 −0.582086
$$426$$ 0 0
$$427$$ 18.0000 0.871081
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 12.0000 0.578020 0.289010 0.957326i $$-0.406674\pi$$
0.289010 + 0.957326i $$0.406674\pi$$
$$432$$ 0 0
$$433$$ 19.0000 0.913082 0.456541 0.889702i $$-0.349088\pi$$
0.456541 + 0.889702i $$0.349088\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 12.0000 0.574038
$$438$$ 0 0
$$439$$ −28.0000 −1.33637 −0.668184 0.743996i $$-0.732928\pi$$
−0.668184 + 0.743996i $$0.732928\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 12.0000 0.570137 0.285069 0.958507i $$-0.407984\pi$$
0.285069 + 0.958507i $$0.407984\pi$$
$$444$$ 0 0
$$445$$ 11.0000 0.521450
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 14.0000 0.660701 0.330350 0.943858i $$-0.392833\pi$$
0.330350 + 0.943858i $$0.392833\pi$$
$$450$$ 0 0
$$451$$ −4.00000 −0.188353
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 2.00000 0.0937614
$$456$$ 0 0
$$457$$ −37.0000 −1.73079 −0.865393 0.501093i $$-0.832931\pi$$
−0.865393 + 0.501093i $$0.832931\pi$$
$$458$$ 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
$$463$$ 28.0000 1.30127 0.650635 0.759390i $$-0.274503\pi$$
0.650635 + 0.759390i $$0.274503\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −28.0000 −1.29569 −0.647843 0.761774i $$-0.724329\pi$$
−0.647843 + 0.761774i $$0.724329\pi$$
$$468$$ 0 0
$$469$$ −28.0000 −1.29292
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 20.0000 0.919601
$$474$$ 0 0
$$475$$ −8.00000 −0.367065
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −42.0000 −1.91903 −0.959514 0.281659i $$-0.909115\pi$$
−0.959514 + 0.281659i $$0.909115\pi$$
$$480$$ 0 0
$$481$$ 1.00000 0.0455961
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −2.00000 −0.0908153
$$486$$ 0 0
$$487$$ −16.0000 −0.725029 −0.362515 0.931978i $$-0.618082\pi$$
−0.362515 + 0.931978i $$0.618082\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −34.0000 −1.53440 −0.767199 0.641409i $$-0.778350\pi$$
−0.767199 + 0.641409i $$0.778350\pi$$
$$492$$ 0 0
$$493$$ 3.00000 0.135113
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 20.0000 0.897123
$$498$$ 0 0
$$499$$ 6.00000 0.268597 0.134298 0.990941i $$-0.457122\pi$$
0.134298 + 0.990941i $$0.457122\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ −6.00000 −0.266996
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −18.0000 −0.797836 −0.398918 0.916987i $$-0.630614\pi$$
−0.398918 + 0.916987i $$0.630614\pi$$
$$510$$ 0 0
$$511$$ −18.0000 −0.796273
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −12.0000 −0.528783
$$516$$ 0 0
$$517$$ 8.00000 0.351840
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −18.0000 −0.788594 −0.394297 0.918983i $$-0.629012\pi$$
−0.394297 + 0.918983i $$0.629012\pi$$
$$522$$ 0 0
$$523$$ −30.0000 −1.31181 −0.655904 0.754844i $$-0.727712\pi$$
−0.655904 + 0.754844i $$0.727712\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −24.0000 −1.04546
$$528$$ 0 0
$$529$$ 13.0000 0.565217
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −2.00000 −0.0866296
$$534$$ 0 0
$$535$$ 16.0000 0.691740
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −6.00000 −0.258438
$$540$$ 0 0
$$541$$ 13.0000 0.558914 0.279457 0.960158i $$-0.409846\pi$$
0.279457 + 0.960158i $$0.409846\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 5.00000 0.214176
$$546$$ 0 0
$$547$$ −12.0000 −0.513083 −0.256541 0.966533i $$-0.582583\pi$$
−0.256541 + 0.966533i $$0.582583\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 2.00000 0.0852029
$$552$$ 0 0
$$553$$ 20.0000 0.850487
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −11.0000 −0.466085 −0.233042 0.972467i $$-0.574868\pi$$
−0.233042 + 0.972467i $$0.574868\pi$$
$$558$$ 0 0
$$559$$ 10.0000 0.422955
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 36.0000 1.51722 0.758610 0.651546i $$-0.225879\pi$$
0.758610 + 0.651546i $$0.225879\pi$$
$$564$$ 0 0
$$565$$ −17.0000 −0.715195
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −5.00000 −0.209611 −0.104805 0.994493i $$-0.533422\pi$$
−0.104805 + 0.994493i $$0.533422\pi$$
$$570$$ 0 0
$$571$$ 20.0000 0.836974 0.418487 0.908223i $$-0.362561\pi$$
0.418487 + 0.908223i $$0.362561\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −24.0000 −1.00087
$$576$$ 0 0
$$577$$ 27.0000 1.12402 0.562012 0.827129i $$-0.310027\pi$$
0.562012 + 0.827129i $$0.310027\pi$$
$$578$$ 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
$$587$$ −30.0000 −1.23823 −0.619116 0.785299i $$-0.712509\pi$$
−0.619116 + 0.785299i $$0.712509\pi$$
$$588$$ 0 0
$$589$$ −16.0000 −0.659269
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 15.0000 0.615976 0.307988 0.951390i $$-0.400344\pi$$
0.307988 + 0.951390i $$0.400344\pi$$
$$594$$ 0 0
$$595$$ 6.00000 0.245976
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −32.0000 −1.30748 −0.653742 0.756717i $$-0.726802\pi$$
−0.653742 + 0.756717i $$0.726802\pi$$
$$600$$ 0 0
$$601$$ −17.0000 −0.693444 −0.346722 0.937968i $$-0.612705\pi$$
−0.346722 + 0.937968i $$0.612705\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −7.00000 −0.284590
$$606$$ 0 0
$$607$$ 22.0000 0.892952 0.446476 0.894795i $$-0.352679\pi$$
0.446476 + 0.894795i $$0.352679\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 4.00000 0.161823
$$612$$ 0 0
$$613$$ 6.00000 0.242338 0.121169 0.992632i $$-0.461336\pi$$
0.121169 + 0.992632i $$0.461336\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 15.0000 0.603877 0.301939 0.953327i $$-0.402366\pi$$
0.301939 + 0.953327i $$0.402366\pi$$
$$618$$ 0 0
$$619$$ −48.0000 −1.92928 −0.964641 0.263566i $$-0.915101\pi$$
−0.964641 + 0.263566i $$0.915101\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 22.0000 0.881411
$$624$$ 0 0
$$625$$ 11.0000 0.440000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 3.00000 0.119618
$$630$$ 0 0
$$631$$ −20.0000 −0.796187 −0.398094 0.917345i $$-0.630328\pi$$
−0.398094 + 0.917345i $$0.630328\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −2.00000 −0.0793676
$$636$$ 0 0
$$637$$ −3.00000 −0.118864
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 35.0000 1.38242 0.691208 0.722655i $$-0.257079\pi$$
0.691208 + 0.722655i $$0.257079\pi$$
$$642$$ 0 0
$$643$$ 36.0000 1.41970 0.709851 0.704352i $$-0.248762\pi$$
0.709851 + 0.704352i $$0.248762\pi$$
$$644$$ 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
$$649$$ 8.00000 0.314027
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −34.0000 −1.33052 −0.665261 0.746611i $$-0.731680\pi$$
−0.665261 + 0.746611i $$0.731680\pi$$
$$654$$ 0 0
$$655$$ 14.0000 0.547025
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −30.0000 −1.16863 −0.584317 0.811525i $$-0.698638\pi$$
−0.584317 + 0.811525i $$0.698638\pi$$
$$660$$ 0 0
$$661$$ −31.0000 −1.20576 −0.602880 0.797832i $$-0.705980\pi$$
−0.602880 + 0.797832i $$0.705980\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 4.00000 0.155113
$$666$$ 0 0
$$667$$ 6.00000 0.232321
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 18.0000 0.694882
$$672$$ 0 0
$$673$$ 23.0000 0.886585 0.443292 0.896377i $$-0.353810\pi$$
0.443292 + 0.896377i $$0.353810\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −34.0000 −1.30673 −0.653363 0.757045i $$-0.726642\pi$$
−0.653363 + 0.757045i $$0.726642\pi$$
$$678$$ 0 0
$$679$$ −4.00000 −0.153506
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −36.0000 −1.37750 −0.688751 0.724998i $$-0.741841\pi$$
−0.688751 + 0.724998i $$0.741841\pi$$
$$684$$ 0 0
$$685$$ −9.00000 −0.343872
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −10.0000 −0.380970
$$690$$ 0 0
$$691$$ −10.0000 −0.380418 −0.190209 0.981744i $$-0.560917\pi$$
−0.190209 + 0.981744i $$0.560917\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −20.0000 −0.758643
$$696$$ 0 0
$$697$$ −6.00000 −0.227266
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 45.0000 1.69963 0.849813 0.527084i $$-0.176715\pi$$
0.849813 + 0.527084i $$0.176715\pi$$
$$702$$ 0 0
$$703$$ 2.00000 0.0754314
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −12.0000 −0.451306
$$708$$ 0 0
$$709$$ 1.00000 0.0375558 0.0187779 0.999824i $$-0.494022\pi$$
0.0187779 + 0.999824i $$0.494022\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −48.0000 −1.79761
$$714$$ 0 0
$$715$$ 2.00000 0.0747958
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −14.0000 −0.522112 −0.261056 0.965324i $$-0.584071\pi$$
−0.261056 + 0.965324i $$0.584071\pi$$
$$720$$ 0 0
$$721$$ −24.0000 −0.893807
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −4.00000 −0.148556
$$726$$ 0 0
$$727$$ 6.00000 0.222528 0.111264 0.993791i $$-0.464510\pi$$
0.111264 + 0.993791i $$0.464510\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 30.0000 1.10959
$$732$$ 0 0
$$733$$ 14.0000 0.517102 0.258551 0.965998i $$-0.416755\pi$$
0.258551 + 0.965998i $$0.416755\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −28.0000 −1.03139
$$738$$ 0 0
$$739$$ 8.00000 0.294285 0.147142 0.989115i $$-0.452992\pi$$
0.147142 + 0.989115i $$0.452992\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −24.0000 −0.880475 −0.440237 0.897881i $$-0.645106\pi$$
−0.440237 + 0.897881i $$0.645106\pi$$
$$744$$ 0 0
$$745$$ 21.0000 0.769380
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 32.0000 1.16925
$$750$$ 0 0
$$751$$ 22.0000 0.802791 0.401396 0.915905i $$-0.368525\pi$$
0.401396 + 0.915905i $$0.368525\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 12.0000 0.436725
$$756$$ 0 0
$$757$$ −42.0000 −1.52652 −0.763258 0.646094i $$-0.776401\pi$$
−0.763258 + 0.646094i $$0.776401\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 39.0000 1.41375 0.706874 0.707339i $$-0.250105\pi$$
0.706874 + 0.707339i $$0.250105\pi$$
$$762$$ 0 0
$$763$$ 10.0000 0.362024
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 4.00000 0.144432
$$768$$ 0 0
$$769$$ 31.0000 1.11789 0.558944 0.829205i $$-0.311207\pi$$
0.558944 + 0.829205i $$0.311207\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 9.00000 0.323708 0.161854 0.986815i $$-0.448253\pi$$
0.161854 + 0.986815i $$0.448253\pi$$
$$774$$ 0 0
$$775$$ 32.0000 1.14947
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −4.00000 −0.143315
$$780$$ 0 0
$$781$$ 20.0000 0.715656
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 17.0000 0.606756
$$786$$ 0 0
$$787$$ 18.0000 0.641631 0.320815 0.947142i $$-0.396043\pi$$
0.320815 + 0.947142i $$0.396043\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −34.0000 −1.20890
$$792$$ 0 0
$$793$$ 9.00000 0.319599
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −39.0000 −1.38145 −0.690725 0.723117i $$-0.742709\pi$$
−0.690725 + 0.723117i $$0.742709\pi$$
$$798$$ 0 0
$$799$$ 12.0000 0.424529
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −18.0000 −0.635206
$$804$$ 0 0
$$805$$ 12.0000 0.422944
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −37.0000 −1.30085 −0.650425 0.759570i $$-0.725409\pi$$
−0.650425 + 0.759570i $$0.725409\pi$$
$$810$$ 0 0
$$811$$ −16.0000 −0.561836 −0.280918 0.959732i $$-0.590639\pi$$
−0.280918 + 0.959732i $$0.590639\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −4.00000 −0.140114
$$816$$ 0 0
$$817$$ 20.0000 0.699711
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −23.0000 −0.802706 −0.401353 0.915924i $$-0.631460\pi$$
−0.401353 + 0.915924i $$0.631460\pi$$
$$822$$ 0 0
$$823$$ 8.00000 0.278862 0.139431 0.990232i $$-0.455473\pi$$
0.139431 + 0.990232i $$0.455473\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −22.0000 −0.765015 −0.382507 0.923952i $$-0.624939\pi$$
−0.382507 + 0.923952i $$0.624939\pi$$
$$828$$ 0 0
$$829$$ 38.0000 1.31979 0.659897 0.751356i $$-0.270600\pi$$
0.659897 + 0.751356i $$0.270600\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −9.00000 −0.311832
$$834$$ 0 0
$$835$$ −2.00000 −0.0692129
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 22.0000 0.759524 0.379762 0.925084i $$-0.376006\pi$$
0.379762 + 0.925084i $$0.376006\pi$$
$$840$$ 0 0
$$841$$ −28.0000 −0.965517
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ −12.0000 −0.412813
$$846$$ 0 0
$$847$$ −14.0000 −0.481046
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 6.00000 0.205677
$$852$$ 0 0
$$853$$ −42.0000 −1.43805 −0.719026 0.694983i $$-0.755412\pi$$
−0.719026 + 0.694983i $$0.755412\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −13.0000 −0.444072 −0.222036 0.975039i $$-0.571270\pi$$
−0.222036 + 0.975039i $$0.571270\pi$$
$$858$$ 0 0
$$859$$ −44.0000 −1.50126 −0.750630 0.660722i $$-0.770250\pi$$
−0.750630 + 0.660722i $$0.770250\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 46.0000 1.56586 0.782929 0.622111i $$-0.213725\pi$$
0.782929 + 0.622111i $$0.213725\pi$$
$$864$$ 0 0
$$865$$ 21.0000 0.714021
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 20.0000 0.678454
$$870$$ 0 0
$$871$$ −14.0000 −0.474372
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ −18.0000 −0.608511
$$876$$ 0 0
$$877$$ −35.0000 −1.18187 −0.590933 0.806721i $$-0.701240\pi$$
−0.590933 + 0.806721i $$0.701240\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −42.0000 −1.41502 −0.707508 0.706705i $$-0.750181\pi$$
−0.707508 + 0.706705i $$0.750181\pi$$
$$882$$ 0 0
$$883$$ −20.0000 −0.673054 −0.336527 0.941674i $$-0.609252\pi$$
−0.336527 + 0.941674i $$0.609252\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 54.0000 1.81314 0.906571 0.422053i $$-0.138690\pi$$
0.906571 + 0.422053i $$0.138690\pi$$
$$888$$ 0 0
$$889$$ −4.00000 −0.134156
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 8.00000 0.267710
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −8.00000 −0.266815
$$900$$ 0 0
$$901$$ −30.0000 −0.999445
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 14.0000 0.465376
$$906$$ 0 0
$$907$$ 8.00000 0.265636 0.132818 0.991140i $$-0.457597\pi$$
0.132818 + 0.991140i $$0.457597\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −30.0000 −0.993944 −0.496972 0.867766i $$-0.665555\pi$$
−0.496972 + 0.867766i $$0.665555\pi$$
$$912$$ 0 0
$$913$$ 24.0000 0.794284
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 28.0000 0.924641
$$918$$ 0 0
$$919$$ 42.0000 1.38545 0.692726 0.721201i $$-0.256409\pi$$
0.692726 + 0.721201i $$0.256409\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 10.0000 0.329154
$$924$$ 0 0
$$925$$ −4.00000 −0.131519
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 27.0000 0.885841 0.442921 0.896561i $$-0.353942\pi$$
0.442921 + 0.896561i $$0.353942\pi$$
$$930$$ 0 0
$$931$$ −6.00000 −0.196642
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 6.00000 0.196221
$$936$$ 0 0
$$937$$ −25.0000 −0.816714 −0.408357 0.912822i $$-0.633898\pi$$
−0.408357 + 0.912822i $$0.633898\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −43.0000 −1.40176 −0.700880 0.713279i $$-0.747209\pi$$
−0.700880 + 0.713279i $$0.747209\pi$$
$$942$$ 0 0
$$943$$ −12.0000 −0.390774
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 54.0000 1.75476 0.877382 0.479792i $$-0.159288\pi$$
0.877382 + 0.479792i $$0.159288\pi$$
$$948$$ 0 0
$$949$$ −9.00000 −0.292152
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −21.0000 −0.680257 −0.340128 0.940379i $$-0.610471\pi$$
−0.340128 + 0.940379i $$0.610471\pi$$
$$954$$ 0 0
$$955$$ 18.0000 0.582466
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ −18.0000 −0.581250
$$960$$ 0 0
$$961$$ 33.0000 1.06452
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ −9.00000 −0.289720
$$966$$ 0 0
$$967$$ −18.0000 −0.578841 −0.289420 0.957202i $$-0.593463\pi$$
−0.289420 + 0.957202i $$0.593463\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 38.0000 1.21948 0.609739 0.792602i $$-0.291274\pi$$
0.609739 + 0.792602i $$0.291274\pi$$
$$972$$ 0 0
$$973$$ −40.0000 −1.28234
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −2.00000 −0.0639857 −0.0319928 0.999488i $$-0.510185\pi$$
−0.0319928 + 0.999488i $$0.510185\pi$$
$$978$$ 0 0
$$979$$ 22.0000 0.703123
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 24.0000 0.765481 0.382741 0.923856i $$-0.374980\pi$$
0.382741 + 0.923856i $$0.374980\pi$$
$$984$$ 0 0
$$985$$ −11.0000 −0.350489
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 60.0000 1.90789
$$990$$ 0 0
$$991$$ −38.0000 −1.20711 −0.603555 0.797321i $$-0.706250\pi$$
−0.603555 + 0.797321i $$0.706250\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 16.0000 0.507234
$$996$$ 0 0
$$997$$ −15.0000 −0.475055 −0.237527 0.971381i $$-0.576337\pi$$
−0.237527 + 0.971381i $$0.576337\pi$$
$$998$$ 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 2592.2.a.f.1.1 yes 1
3.2 odd 2 2592.2.a.d.1.1 yes 1
4.3 odd 2 2592.2.a.e.1.1 yes 1
8.3 odd 2 5184.2.a.j.1.1 1
8.5 even 2 5184.2.a.m.1.1 1
9.2 odd 6 2592.2.i.n.1729.1 2
9.4 even 3 2592.2.i.j.865.1 2
9.5 odd 6 2592.2.i.n.865.1 2
9.7 even 3 2592.2.i.j.1729.1 2
12.11 even 2 2592.2.a.c.1.1 1
24.5 odd 2 5184.2.a.w.1.1 1
24.11 even 2 5184.2.a.t.1.1 1
36.7 odd 6 2592.2.i.k.1729.1 2
36.11 even 6 2592.2.i.o.1729.1 2
36.23 even 6 2592.2.i.o.865.1 2
36.31 odd 6 2592.2.i.k.865.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
2592.2.a.c.1.1 1 12.11 even 2
2592.2.a.d.1.1 yes 1 3.2 odd 2
2592.2.a.e.1.1 yes 1 4.3 odd 2
2592.2.a.f.1.1 yes 1 1.1 even 1 trivial
2592.2.i.j.865.1 2 9.4 even 3
2592.2.i.j.1729.1 2 9.7 even 3
2592.2.i.k.865.1 2 36.31 odd 6
2592.2.i.k.1729.1 2 36.7 odd 6
2592.2.i.n.865.1 2 9.5 odd 6
2592.2.i.n.1729.1 2 9.2 odd 6
2592.2.i.o.865.1 2 36.23 even 6
2592.2.i.o.1729.1 2 36.11 even 6
5184.2.a.j.1.1 1 8.3 odd 2
5184.2.a.m.1.1 1 8.5 even 2
5184.2.a.t.1.1 1 24.11 even 2
5184.2.a.w.1.1 1 24.5 odd 2