# Properties

 Label 585.2.a.b.1.1 Level $585$ Weight $2$ Character 585.1 Self dual yes Analytic conductor $4.671$ 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] = [585,2,Mod(1,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, 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("585.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$585 = 3^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 585.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: $$4.67124851824$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 195) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 585.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-2.00000 q^{2} +2.00000 q^{4} -1.00000 q^{5} +3.00000 q^{7} +O(q^{10})$$ $$q-2.00000 q^{2} +2.00000 q^{4} -1.00000 q^{5} +3.00000 q^{7} +2.00000 q^{10} +1.00000 q^{11} -1.00000 q^{13} -6.00000 q^{14} -4.00000 q^{16} +1.00000 q^{17} -2.00000 q^{19} -2.00000 q^{20} -2.00000 q^{22} +3.00000 q^{23} +1.00000 q^{25} +2.00000 q^{26} +6.00000 q^{28} +2.00000 q^{29} -6.00000 q^{31} +8.00000 q^{32} -2.00000 q^{34} -3.00000 q^{35} +11.0000 q^{37} +4.00000 q^{38} +5.00000 q^{41} +4.00000 q^{43} +2.00000 q^{44} -6.00000 q^{46} +10.0000 q^{47} +2.00000 q^{49} -2.00000 q^{50} -2.00000 q^{52} -11.0000 q^{53} -1.00000 q^{55} -4.00000 q^{58} -8.00000 q^{59} +13.0000 q^{61} +12.0000 q^{62} -8.00000 q^{64} +1.00000 q^{65} +12.0000 q^{67} +2.00000 q^{68} +6.00000 q^{70} +5.00000 q^{71} +10.0000 q^{73} -22.0000 q^{74} -4.00000 q^{76} +3.00000 q^{77} -3.00000 q^{79} +4.00000 q^{80} -10.0000 q^{82} +12.0000 q^{83} -1.00000 q^{85} -8.00000 q^{86} +15.0000 q^{89} -3.00000 q^{91} +6.00000 q^{92} -20.0000 q^{94} +2.00000 q^{95} +17.0000 q^{97} -4.00000 q^{98} +O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −2.00000 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$3$$ 0 0
$$4$$ 2.00000 1.00000
$$5$$ −1.00000 −0.447214
$$6$$ 0 0
$$7$$ 3.00000 1.13389 0.566947 0.823754i $$-0.308125\pi$$
0.566947 + 0.823754i $$0.308125\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 2.00000 0.632456
$$11$$ 1.00000 0.301511 0.150756 0.988571i $$-0.451829\pi$$
0.150756 + 0.988571i $$0.451829\pi$$
$$12$$ 0 0
$$13$$ −1.00000 −0.277350
$$14$$ −6.00000 −1.60357
$$15$$ 0 0
$$16$$ −4.00000 −1.00000
$$17$$ 1.00000 0.242536 0.121268 0.992620i $$-0.461304\pi$$
0.121268 + 0.992620i $$0.461304\pi$$
$$18$$ 0 0
$$19$$ −2.00000 −0.458831 −0.229416 0.973329i $$-0.573682\pi$$
−0.229416 + 0.973329i $$0.573682\pi$$
$$20$$ −2.00000 −0.447214
$$21$$ 0 0
$$22$$ −2.00000 −0.426401
$$23$$ 3.00000 0.625543 0.312772 0.949828i $$-0.398743\pi$$
0.312772 + 0.949828i $$0.398743\pi$$
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ 2.00000 0.392232
$$27$$ 0 0
$$28$$ 6.00000 1.13389
$$29$$ 2.00000 0.371391 0.185695 0.982607i $$-0.440546\pi$$
0.185695 + 0.982607i $$0.440546\pi$$
$$30$$ 0 0
$$31$$ −6.00000 −1.07763 −0.538816 0.842424i $$-0.681128\pi$$
−0.538816 + 0.842424i $$0.681128\pi$$
$$32$$ 8.00000 1.41421
$$33$$ 0 0
$$34$$ −2.00000 −0.342997
$$35$$ −3.00000 −0.507093
$$36$$ 0 0
$$37$$ 11.0000 1.80839 0.904194 0.427121i $$-0.140472\pi$$
0.904194 + 0.427121i $$0.140472\pi$$
$$38$$ 4.00000 0.648886
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 5.00000 0.780869 0.390434 0.920631i $$-0.372325\pi$$
0.390434 + 0.920631i $$0.372325\pi$$
$$42$$ 0 0
$$43$$ 4.00000 0.609994 0.304997 0.952353i $$-0.401344\pi$$
0.304997 + 0.952353i $$0.401344\pi$$
$$44$$ 2.00000 0.301511
$$45$$ 0 0
$$46$$ −6.00000 −0.884652
$$47$$ 10.0000 1.45865 0.729325 0.684167i $$-0.239834\pi$$
0.729325 + 0.684167i $$0.239834\pi$$
$$48$$ 0 0
$$49$$ 2.00000 0.285714
$$50$$ −2.00000 −0.282843
$$51$$ 0 0
$$52$$ −2.00000 −0.277350
$$53$$ −11.0000 −1.51097 −0.755483 0.655168i $$-0.772598\pi$$
−0.755483 + 0.655168i $$0.772598\pi$$
$$54$$ 0 0
$$55$$ −1.00000 −0.134840
$$56$$ 0 0
$$57$$ 0 0
$$58$$ −4.00000 −0.525226
$$59$$ −8.00000 −1.04151 −0.520756 0.853706i $$-0.674350\pi$$
−0.520756 + 0.853706i $$0.674350\pi$$
$$60$$ 0 0
$$61$$ 13.0000 1.66448 0.832240 0.554416i $$-0.187058\pi$$
0.832240 + 0.554416i $$0.187058\pi$$
$$62$$ 12.0000 1.52400
$$63$$ 0 0
$$64$$ −8.00000 −1.00000
$$65$$ 1.00000 0.124035
$$66$$ 0 0
$$67$$ 12.0000 1.46603 0.733017 0.680211i $$-0.238112\pi$$
0.733017 + 0.680211i $$0.238112\pi$$
$$68$$ 2.00000 0.242536
$$69$$ 0 0
$$70$$ 6.00000 0.717137
$$71$$ 5.00000 0.593391 0.296695 0.954972i $$-0.404115\pi$$
0.296695 + 0.954972i $$0.404115\pi$$
$$72$$ 0 0
$$73$$ 10.0000 1.17041 0.585206 0.810885i $$-0.301014\pi$$
0.585206 + 0.810885i $$0.301014\pi$$
$$74$$ −22.0000 −2.55745
$$75$$ 0 0
$$76$$ −4.00000 −0.458831
$$77$$ 3.00000 0.341882
$$78$$ 0 0
$$79$$ −3.00000 −0.337526 −0.168763 0.985657i $$-0.553977\pi$$
−0.168763 + 0.985657i $$0.553977\pi$$
$$80$$ 4.00000 0.447214
$$81$$ 0 0
$$82$$ −10.0000 −1.10432
$$83$$ 12.0000 1.31717 0.658586 0.752506i $$-0.271155\pi$$
0.658586 + 0.752506i $$0.271155\pi$$
$$84$$ 0 0
$$85$$ −1.00000 −0.108465
$$86$$ −8.00000 −0.862662
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 15.0000 1.59000 0.794998 0.606612i $$-0.207472\pi$$
0.794998 + 0.606612i $$0.207472\pi$$
$$90$$ 0 0
$$91$$ −3.00000 −0.314485
$$92$$ 6.00000 0.625543
$$93$$ 0 0
$$94$$ −20.0000 −2.06284
$$95$$ 2.00000 0.205196
$$96$$ 0 0
$$97$$ 17.0000 1.72609 0.863044 0.505128i $$-0.168555\pi$$
0.863044 + 0.505128i $$0.168555\pi$$
$$98$$ −4.00000 −0.404061
$$99$$ 0 0
$$100$$ 2.00000 0.200000
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ 0 0
$$103$$ −16.0000 −1.57653 −0.788263 0.615338i $$-0.789020\pi$$
−0.788263 + 0.615338i $$0.789020\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 22.0000 2.13683
$$107$$ −9.00000 −0.870063 −0.435031 0.900415i $$-0.643263\pi$$
−0.435031 + 0.900415i $$0.643263\pi$$
$$108$$ 0 0
$$109$$ −16.0000 −1.53252 −0.766261 0.642529i $$-0.777885\pi$$
−0.766261 + 0.642529i $$0.777885\pi$$
$$110$$ 2.00000 0.190693
$$111$$ 0 0
$$112$$ −12.0000 −1.13389
$$113$$ −14.0000 −1.31701 −0.658505 0.752577i $$-0.728811\pi$$
−0.658505 + 0.752577i $$0.728811\pi$$
$$114$$ 0 0
$$115$$ −3.00000 −0.279751
$$116$$ 4.00000 0.371391
$$117$$ 0 0
$$118$$ 16.0000 1.47292
$$119$$ 3.00000 0.275010
$$120$$ 0 0
$$121$$ −10.0000 −0.909091
$$122$$ −26.0000 −2.35393
$$123$$ 0 0
$$124$$ −12.0000 −1.07763
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ 10.0000 0.887357 0.443678 0.896186i $$-0.353673\pi$$
0.443678 + 0.896186i $$0.353673\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ −2.00000 −0.175412
$$131$$ 6.00000 0.524222 0.262111 0.965038i $$-0.415581\pi$$
0.262111 + 0.965038i $$0.415581\pi$$
$$132$$ 0 0
$$133$$ −6.00000 −0.520266
$$134$$ −24.0000 −2.07328
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −18.0000 −1.53784 −0.768922 0.639343i $$-0.779207\pi$$
−0.768922 + 0.639343i $$0.779207\pi$$
$$138$$ 0 0
$$139$$ −1.00000 −0.0848189 −0.0424094 0.999100i $$-0.513503\pi$$
−0.0424094 + 0.999100i $$0.513503\pi$$
$$140$$ −6.00000 −0.507093
$$141$$ 0 0
$$142$$ −10.0000 −0.839181
$$143$$ −1.00000 −0.0836242
$$144$$ 0 0
$$145$$ −2.00000 −0.166091
$$146$$ −20.0000 −1.65521
$$147$$ 0 0
$$148$$ 22.0000 1.80839
$$149$$ −13.0000 −1.06500 −0.532501 0.846430i $$-0.678748\pi$$
−0.532501 + 0.846430i $$0.678748\pi$$
$$150$$ 0 0
$$151$$ 16.0000 1.30206 0.651031 0.759051i $$-0.274337\pi$$
0.651031 + 0.759051i $$0.274337\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ −6.00000 −0.483494
$$155$$ 6.00000 0.481932
$$156$$ 0 0
$$157$$ −10.0000 −0.798087 −0.399043 0.916932i $$-0.630658\pi$$
−0.399043 + 0.916932i $$0.630658\pi$$
$$158$$ 6.00000 0.477334
$$159$$ 0 0
$$160$$ −8.00000 −0.632456
$$161$$ 9.00000 0.709299
$$162$$ 0 0
$$163$$ −13.0000 −1.01824 −0.509119 0.860696i $$-0.670029\pi$$
−0.509119 + 0.860696i $$0.670029\pi$$
$$164$$ 10.0000 0.780869
$$165$$ 0 0
$$166$$ −24.0000 −1.86276
$$167$$ 12.0000 0.928588 0.464294 0.885681i $$-0.346308\pi$$
0.464294 + 0.885681i $$0.346308\pi$$
$$168$$ 0 0
$$169$$ 1.00000 0.0769231
$$170$$ 2.00000 0.153393
$$171$$ 0 0
$$172$$ 8.00000 0.609994
$$173$$ 6.00000 0.456172 0.228086 0.973641i $$-0.426753\pi$$
0.228086 + 0.973641i $$0.426753\pi$$
$$174$$ 0 0
$$175$$ 3.00000 0.226779
$$176$$ −4.00000 −0.301511
$$177$$ 0 0
$$178$$ −30.0000 −2.24860
$$179$$ −2.00000 −0.149487 −0.0747435 0.997203i $$-0.523814\pi$$
−0.0747435 + 0.997203i $$0.523814\pi$$
$$180$$ 0 0
$$181$$ −7.00000 −0.520306 −0.260153 0.965567i $$-0.583773\pi$$
−0.260153 + 0.965567i $$0.583773\pi$$
$$182$$ 6.00000 0.444750
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −11.0000 −0.808736
$$186$$ 0 0
$$187$$ 1.00000 0.0731272
$$188$$ 20.0000 1.45865
$$189$$ 0 0
$$190$$ −4.00000 −0.290191
$$191$$ 8.00000 0.578860 0.289430 0.957199i $$-0.406534\pi$$
0.289430 + 0.957199i $$0.406534\pi$$
$$192$$ 0 0
$$193$$ −13.0000 −0.935760 −0.467880 0.883792i $$-0.654982\pi$$
−0.467880 + 0.883792i $$0.654982\pi$$
$$194$$ −34.0000 −2.44106
$$195$$ 0 0
$$196$$ 4.00000 0.285714
$$197$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$198$$ 0 0
$$199$$ 4.00000 0.283552 0.141776 0.989899i $$-0.454719\pi$$
0.141776 + 0.989899i $$0.454719\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 6.00000 0.421117
$$204$$ 0 0
$$205$$ −5.00000 −0.349215
$$206$$ 32.0000 2.22955
$$207$$ 0 0
$$208$$ 4.00000 0.277350
$$209$$ −2.00000 −0.138343
$$210$$ 0 0
$$211$$ −4.00000 −0.275371 −0.137686 0.990476i $$-0.543966\pi$$
−0.137686 + 0.990476i $$0.543966\pi$$
$$212$$ −22.0000 −1.51097
$$213$$ 0 0
$$214$$ 18.0000 1.23045
$$215$$ −4.00000 −0.272798
$$216$$ 0 0
$$217$$ −18.0000 −1.22192
$$218$$ 32.0000 2.16731
$$219$$ 0 0
$$220$$ −2.00000 −0.134840
$$221$$ −1.00000 −0.0672673
$$222$$ 0 0
$$223$$ 8.00000 0.535720 0.267860 0.963458i $$-0.413684\pi$$
0.267860 + 0.963458i $$0.413684\pi$$
$$224$$ 24.0000 1.60357
$$225$$ 0 0
$$226$$ 28.0000 1.86253
$$227$$ −22.0000 −1.46019 −0.730096 0.683345i $$-0.760525\pi$$
−0.730096 + 0.683345i $$0.760525\pi$$
$$228$$ 0 0
$$229$$ 18.0000 1.18947 0.594737 0.803921i $$-0.297256\pi$$
0.594737 + 0.803921i $$0.297256\pi$$
$$230$$ 6.00000 0.395628
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 27.0000 1.76883 0.884414 0.466702i $$-0.154558\pi$$
0.884414 + 0.466702i $$0.154558\pi$$
$$234$$ 0 0
$$235$$ −10.0000 −0.652328
$$236$$ −16.0000 −1.04151
$$237$$ 0 0
$$238$$ −6.00000 −0.388922
$$239$$ 13.0000 0.840900 0.420450 0.907316i $$-0.361872\pi$$
0.420450 + 0.907316i $$0.361872\pi$$
$$240$$ 0 0
$$241$$ −2.00000 −0.128831 −0.0644157 0.997923i $$-0.520518\pi$$
−0.0644157 + 0.997923i $$0.520518\pi$$
$$242$$ 20.0000 1.28565
$$243$$ 0 0
$$244$$ 26.0000 1.66448
$$245$$ −2.00000 −0.127775
$$246$$ 0 0
$$247$$ 2.00000 0.127257
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 2.00000 0.126491
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 3.00000 0.188608
$$254$$ −20.0000 −1.25491
$$255$$ 0 0
$$256$$ 16.0000 1.00000
$$257$$ 18.0000 1.12281 0.561405 0.827541i $$-0.310261\pi$$
0.561405 + 0.827541i $$0.310261\pi$$
$$258$$ 0 0
$$259$$ 33.0000 2.05052
$$260$$ 2.00000 0.124035
$$261$$ 0 0
$$262$$ −12.0000 −0.741362
$$263$$ 8.00000 0.493301 0.246651 0.969104i $$-0.420670\pi$$
0.246651 + 0.969104i $$0.420670\pi$$
$$264$$ 0 0
$$265$$ 11.0000 0.675725
$$266$$ 12.0000 0.735767
$$267$$ 0 0
$$268$$ 24.0000 1.46603
$$269$$ 4.00000 0.243884 0.121942 0.992537i $$-0.461088\pi$$
0.121942 + 0.992537i $$0.461088\pi$$
$$270$$ 0 0
$$271$$ 22.0000 1.33640 0.668202 0.743980i $$-0.267064\pi$$
0.668202 + 0.743980i $$0.267064\pi$$
$$272$$ −4.00000 −0.242536
$$273$$ 0 0
$$274$$ 36.0000 2.17484
$$275$$ 1.00000 0.0603023
$$276$$ 0 0
$$277$$ −18.0000 −1.08152 −0.540758 0.841178i $$-0.681862\pi$$
−0.540758 + 0.841178i $$0.681862\pi$$
$$278$$ 2.00000 0.119952
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −30.0000 −1.78965 −0.894825 0.446417i $$-0.852700\pi$$
−0.894825 + 0.446417i $$0.852700\pi$$
$$282$$ 0 0
$$283$$ −12.0000 −0.713326 −0.356663 0.934233i $$-0.616086\pi$$
−0.356663 + 0.934233i $$0.616086\pi$$
$$284$$ 10.0000 0.593391
$$285$$ 0 0
$$286$$ 2.00000 0.118262
$$287$$ 15.0000 0.885422
$$288$$ 0 0
$$289$$ −16.0000 −0.941176
$$290$$ 4.00000 0.234888
$$291$$ 0 0
$$292$$ 20.0000 1.17041
$$293$$ −24.0000 −1.40209 −0.701047 0.713115i $$-0.747284\pi$$
−0.701047 + 0.713115i $$0.747284\pi$$
$$294$$ 0 0
$$295$$ 8.00000 0.465778
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 26.0000 1.50614
$$299$$ −3.00000 −0.173494
$$300$$ 0 0
$$301$$ 12.0000 0.691669
$$302$$ −32.0000 −1.84139
$$303$$ 0 0
$$304$$ 8.00000 0.458831
$$305$$ −13.0000 −0.744378
$$306$$ 0 0
$$307$$ −5.00000 −0.285365 −0.142683 0.989769i $$-0.545573\pi$$
−0.142683 + 0.989769i $$0.545573\pi$$
$$308$$ 6.00000 0.341882
$$309$$ 0 0
$$310$$ −12.0000 −0.681554
$$311$$ −24.0000 −1.36092 −0.680458 0.732787i $$-0.738219\pi$$
−0.680458 + 0.732787i $$0.738219\pi$$
$$312$$ 0 0
$$313$$ −10.0000 −0.565233 −0.282617 0.959233i $$-0.591202\pi$$
−0.282617 + 0.959233i $$0.591202\pi$$
$$314$$ 20.0000 1.12867
$$315$$ 0 0
$$316$$ −6.00000 −0.337526
$$317$$ −28.0000 −1.57264 −0.786318 0.617822i $$-0.788015\pi$$
−0.786318 + 0.617822i $$0.788015\pi$$
$$318$$ 0 0
$$319$$ 2.00000 0.111979
$$320$$ 8.00000 0.447214
$$321$$ 0 0
$$322$$ −18.0000 −1.00310
$$323$$ −2.00000 −0.111283
$$324$$ 0 0
$$325$$ −1.00000 −0.0554700
$$326$$ 26.0000 1.44001
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 30.0000 1.65395
$$330$$ 0 0
$$331$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$332$$ 24.0000 1.31717
$$333$$ 0 0
$$334$$ −24.0000 −1.31322
$$335$$ −12.0000 −0.655630
$$336$$ 0 0
$$337$$ 4.00000 0.217894 0.108947 0.994048i $$-0.465252\pi$$
0.108947 + 0.994048i $$0.465252\pi$$
$$338$$ −2.00000 −0.108786
$$339$$ 0 0
$$340$$ −2.00000 −0.108465
$$341$$ −6.00000 −0.324918
$$342$$ 0 0
$$343$$ −15.0000 −0.809924
$$344$$ 0 0
$$345$$ 0 0
$$346$$ −12.0000 −0.645124
$$347$$ 19.0000 1.01997 0.509987 0.860182i $$-0.329650\pi$$
0.509987 + 0.860182i $$0.329650\pi$$
$$348$$ 0 0
$$349$$ −8.00000 −0.428230 −0.214115 0.976808i $$-0.568687\pi$$
−0.214115 + 0.976808i $$0.568687\pi$$
$$350$$ −6.00000 −0.320713
$$351$$ 0 0
$$352$$ 8.00000 0.426401
$$353$$ −6.00000 −0.319348 −0.159674 0.987170i $$-0.551044\pi$$
−0.159674 + 0.987170i $$0.551044\pi$$
$$354$$ 0 0
$$355$$ −5.00000 −0.265372
$$356$$ 30.0000 1.59000
$$357$$ 0 0
$$358$$ 4.00000 0.211407
$$359$$ −24.0000 −1.26667 −0.633336 0.773877i $$-0.718315\pi$$
−0.633336 + 0.773877i $$0.718315\pi$$
$$360$$ 0 0
$$361$$ −15.0000 −0.789474
$$362$$ 14.0000 0.735824
$$363$$ 0 0
$$364$$ −6.00000 −0.314485
$$365$$ −10.0000 −0.523424
$$366$$ 0 0
$$367$$ 36.0000 1.87918 0.939592 0.342296i $$-0.111204\pi$$
0.939592 + 0.342296i $$0.111204\pi$$
$$368$$ −12.0000 −0.625543
$$369$$ 0 0
$$370$$ 22.0000 1.14373
$$371$$ −33.0000 −1.71327
$$372$$ 0 0
$$373$$ 4.00000 0.207112 0.103556 0.994624i $$-0.466978\pi$$
0.103556 + 0.994624i $$0.466978\pi$$
$$374$$ −2.00000 −0.103418
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −2.00000 −0.103005
$$378$$ 0 0
$$379$$ −14.0000 −0.719132 −0.359566 0.933120i $$-0.617075\pi$$
−0.359566 + 0.933120i $$0.617075\pi$$
$$380$$ 4.00000 0.205196
$$381$$ 0 0
$$382$$ −16.0000 −0.818631
$$383$$ 30.0000 1.53293 0.766464 0.642287i $$-0.222014\pi$$
0.766464 + 0.642287i $$0.222014\pi$$
$$384$$ 0 0
$$385$$ −3.00000 −0.152894
$$386$$ 26.0000 1.32337
$$387$$ 0 0
$$388$$ 34.0000 1.72609
$$389$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$390$$ 0 0
$$391$$ 3.00000 0.151717
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 3.00000 0.150946
$$396$$ 0 0
$$397$$ −29.0000 −1.45547 −0.727734 0.685859i $$-0.759427\pi$$
−0.727734 + 0.685859i $$0.759427\pi$$
$$398$$ −8.00000 −0.401004
$$399$$ 0 0
$$400$$ −4.00000 −0.200000
$$401$$ −30.0000 −1.49813 −0.749064 0.662497i $$-0.769497\pi$$
−0.749064 + 0.662497i $$0.769497\pi$$
$$402$$ 0 0
$$403$$ 6.00000 0.298881
$$404$$ 0 0
$$405$$ 0 0
$$406$$ −12.0000 −0.595550
$$407$$ 11.0000 0.545250
$$408$$ 0 0
$$409$$ 2.00000 0.0988936 0.0494468 0.998777i $$-0.484254\pi$$
0.0494468 + 0.998777i $$0.484254\pi$$
$$410$$ 10.0000 0.493865
$$411$$ 0 0
$$412$$ −32.0000 −1.57653
$$413$$ −24.0000 −1.18096
$$414$$ 0 0
$$415$$ −12.0000 −0.589057
$$416$$ −8.00000 −0.392232
$$417$$ 0 0
$$418$$ 4.00000 0.195646
$$419$$ 26.0000 1.27018 0.635092 0.772437i $$-0.280962\pi$$
0.635092 + 0.772437i $$0.280962\pi$$
$$420$$ 0 0
$$421$$ 4.00000 0.194948 0.0974740 0.995238i $$-0.468924\pi$$
0.0974740 + 0.995238i $$0.468924\pi$$
$$422$$ 8.00000 0.389434
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 1.00000 0.0485071
$$426$$ 0 0
$$427$$ 39.0000 1.88734
$$428$$ −18.0000 −0.870063
$$429$$ 0 0
$$430$$ 8.00000 0.385794
$$431$$ 24.0000 1.15604 0.578020 0.816023i $$-0.303826\pi$$
0.578020 + 0.816023i $$0.303826\pi$$
$$432$$ 0 0
$$433$$ 4.00000 0.192228 0.0961139 0.995370i $$-0.469359\pi$$
0.0961139 + 0.995370i $$0.469359\pi$$
$$434$$ 36.0000 1.72806
$$435$$ 0 0
$$436$$ −32.0000 −1.53252
$$437$$ −6.00000 −0.287019
$$438$$ 0 0
$$439$$ −17.0000 −0.811366 −0.405683 0.914014i $$-0.632966\pi$$
−0.405683 + 0.914014i $$0.632966\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 2.00000 0.0951303
$$443$$ −9.00000 −0.427603 −0.213801 0.976877i $$-0.568585\pi$$
−0.213801 + 0.976877i $$0.568585\pi$$
$$444$$ 0 0
$$445$$ −15.0000 −0.711068
$$446$$ −16.0000 −0.757622
$$447$$ 0 0
$$448$$ −24.0000 −1.13389
$$449$$ 13.0000 0.613508 0.306754 0.951789i $$-0.400757\pi$$
0.306754 + 0.951789i $$0.400757\pi$$
$$450$$ 0 0
$$451$$ 5.00000 0.235441
$$452$$ −28.0000 −1.31701
$$453$$ 0 0
$$454$$ 44.0000 2.06502
$$455$$ 3.00000 0.140642
$$456$$ 0 0
$$457$$ −11.0000 −0.514558 −0.257279 0.966337i $$-0.582826\pi$$
−0.257279 + 0.966337i $$0.582826\pi$$
$$458$$ −36.0000 −1.68217
$$459$$ 0 0
$$460$$ −6.00000 −0.279751
$$461$$ −15.0000 −0.698620 −0.349310 0.937007i $$-0.613584\pi$$
−0.349310 + 0.937007i $$0.613584\pi$$
$$462$$ 0 0
$$463$$ 27.0000 1.25480 0.627398 0.778699i $$-0.284120\pi$$
0.627398 + 0.778699i $$0.284120\pi$$
$$464$$ −8.00000 −0.371391
$$465$$ 0 0
$$466$$ −54.0000 −2.50150
$$467$$ 23.0000 1.06431 0.532157 0.846646i $$-0.321382\pi$$
0.532157 + 0.846646i $$0.321382\pi$$
$$468$$ 0 0
$$469$$ 36.0000 1.66233
$$470$$ 20.0000 0.922531
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 4.00000 0.183920
$$474$$ 0 0
$$475$$ −2.00000 −0.0917663
$$476$$ 6.00000 0.275010
$$477$$ 0 0
$$478$$ −26.0000 −1.18921
$$479$$ −9.00000 −0.411220 −0.205610 0.978634i $$-0.565918\pi$$
−0.205610 + 0.978634i $$0.565918\pi$$
$$480$$ 0 0
$$481$$ −11.0000 −0.501557
$$482$$ 4.00000 0.182195
$$483$$ 0 0
$$484$$ −20.0000 −0.909091
$$485$$ −17.0000 −0.771930
$$486$$ 0 0
$$487$$ −7.00000 −0.317200 −0.158600 0.987343i $$-0.550698\pi$$
−0.158600 + 0.987343i $$0.550698\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 4.00000 0.180702
$$491$$ −28.0000 −1.26362 −0.631811 0.775122i $$-0.717688\pi$$
−0.631811 + 0.775122i $$0.717688\pi$$
$$492$$ 0 0
$$493$$ 2.00000 0.0900755
$$494$$ −4.00000 −0.179969
$$495$$ 0 0
$$496$$ 24.0000 1.07763
$$497$$ 15.0000 0.672842
$$498$$ 0 0
$$499$$ −14.0000 −0.626726 −0.313363 0.949633i $$-0.601456\pi$$
−0.313363 + 0.949633i $$0.601456\pi$$
$$500$$ −2.00000 −0.0894427
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −28.0000 −1.24846 −0.624229 0.781241i $$-0.714587\pi$$
−0.624229 + 0.781241i $$0.714587\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ −6.00000 −0.266733
$$507$$ 0 0
$$508$$ 20.0000 0.887357
$$509$$ 7.00000 0.310270 0.155135 0.987893i $$-0.450419\pi$$
0.155135 + 0.987893i $$0.450419\pi$$
$$510$$ 0 0
$$511$$ 30.0000 1.32712
$$512$$ −32.0000 −1.41421
$$513$$ 0 0
$$514$$ −36.0000 −1.58789
$$515$$ 16.0000 0.705044
$$516$$ 0 0
$$517$$ 10.0000 0.439799
$$518$$ −66.0000 −2.89987
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 14.0000 0.613351 0.306676 0.951814i $$-0.400783\pi$$
0.306676 + 0.951814i $$0.400783\pi$$
$$522$$ 0 0
$$523$$ 16.0000 0.699631 0.349816 0.936819i $$-0.386244\pi$$
0.349816 + 0.936819i $$0.386244\pi$$
$$524$$ 12.0000 0.524222
$$525$$ 0 0
$$526$$ −16.0000 −0.697633
$$527$$ −6.00000 −0.261364
$$528$$ 0 0
$$529$$ −14.0000 −0.608696
$$530$$ −22.0000 −0.955619
$$531$$ 0 0
$$532$$ −12.0000 −0.520266
$$533$$ −5.00000 −0.216574
$$534$$ 0 0
$$535$$ 9.00000 0.389104
$$536$$ 0 0
$$537$$ 0 0
$$538$$ −8.00000 −0.344904
$$539$$ 2.00000 0.0861461
$$540$$ 0 0
$$541$$ −30.0000 −1.28980 −0.644900 0.764267i $$-0.723101\pi$$
−0.644900 + 0.764267i $$0.723101\pi$$
$$542$$ −44.0000 −1.88996
$$543$$ 0 0
$$544$$ 8.00000 0.342997
$$545$$ 16.0000 0.685365
$$546$$ 0 0
$$547$$ −32.0000 −1.36822 −0.684111 0.729378i $$-0.739809\pi$$
−0.684111 + 0.729378i $$0.739809\pi$$
$$548$$ −36.0000 −1.53784
$$549$$ 0 0
$$550$$ −2.00000 −0.0852803
$$551$$ −4.00000 −0.170406
$$552$$ 0 0
$$553$$ −9.00000 −0.382719
$$554$$ 36.0000 1.52949
$$555$$ 0 0
$$556$$ −2.00000 −0.0848189
$$557$$ 30.0000 1.27114 0.635570 0.772043i $$-0.280765\pi$$
0.635570 + 0.772043i $$0.280765\pi$$
$$558$$ 0 0
$$559$$ −4.00000 −0.169182
$$560$$ 12.0000 0.507093
$$561$$ 0 0
$$562$$ 60.0000 2.53095
$$563$$ −21.0000 −0.885044 −0.442522 0.896758i $$-0.645916\pi$$
−0.442522 + 0.896758i $$0.645916\pi$$
$$564$$ 0 0
$$565$$ 14.0000 0.588984
$$566$$ 24.0000 1.00880
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$570$$ 0 0
$$571$$ −31.0000 −1.29731 −0.648655 0.761083i $$-0.724668\pi$$
−0.648655 + 0.761083i $$0.724668\pi$$
$$572$$ −2.00000 −0.0836242
$$573$$ 0 0
$$574$$ −30.0000 −1.25218
$$575$$ 3.00000 0.125109
$$576$$ 0 0
$$577$$ −19.0000 −0.790980 −0.395490 0.918470i $$-0.629425\pi$$
−0.395490 + 0.918470i $$0.629425\pi$$
$$578$$ 32.0000 1.33102
$$579$$ 0 0
$$580$$ −4.00000 −0.166091
$$581$$ 36.0000 1.49353
$$582$$ 0 0
$$583$$ −11.0000 −0.455573
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 48.0000 1.98286
$$587$$ 18.0000 0.742940 0.371470 0.928445i $$-0.378854\pi$$
0.371470 + 0.928445i $$0.378854\pi$$
$$588$$ 0 0
$$589$$ 12.0000 0.494451
$$590$$ −16.0000 −0.658710
$$591$$ 0 0
$$592$$ −44.0000 −1.80839
$$593$$ −4.00000 −0.164260 −0.0821302 0.996622i $$-0.526172\pi$$
−0.0821302 + 0.996622i $$0.526172\pi$$
$$594$$ 0 0
$$595$$ −3.00000 −0.122988
$$596$$ −26.0000 −1.06500
$$597$$ 0 0
$$598$$ 6.00000 0.245358
$$599$$ −16.0000 −0.653742 −0.326871 0.945069i $$-0.605994\pi$$
−0.326871 + 0.945069i $$0.605994\pi$$
$$600$$ 0 0
$$601$$ −37.0000 −1.50926 −0.754631 0.656150i $$-0.772184\pi$$
−0.754631 + 0.656150i $$0.772184\pi$$
$$602$$ −24.0000 −0.978167
$$603$$ 0 0
$$604$$ 32.0000 1.30206
$$605$$ 10.0000 0.406558
$$606$$ 0 0
$$607$$ −32.0000 −1.29884 −0.649420 0.760430i $$-0.724988\pi$$
−0.649420 + 0.760430i $$0.724988\pi$$
$$608$$ −16.0000 −0.648886
$$609$$ 0 0
$$610$$ 26.0000 1.05271
$$611$$ −10.0000 −0.404557
$$612$$ 0 0
$$613$$ 13.0000 0.525065 0.262533 0.964923i $$-0.415442\pi$$
0.262533 + 0.964923i $$0.415442\pi$$
$$614$$ 10.0000 0.403567
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 42.0000 1.69086 0.845428 0.534089i $$-0.179345\pi$$
0.845428 + 0.534089i $$0.179345\pi$$
$$618$$ 0 0
$$619$$ −34.0000 −1.36658 −0.683288 0.730149i $$-0.739451\pi$$
−0.683288 + 0.730149i $$0.739451\pi$$
$$620$$ 12.0000 0.481932
$$621$$ 0 0
$$622$$ 48.0000 1.92462
$$623$$ 45.0000 1.80289
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 20.0000 0.799361
$$627$$ 0 0
$$628$$ −20.0000 −0.798087
$$629$$ 11.0000 0.438599
$$630$$ 0 0
$$631$$ 40.0000 1.59237 0.796187 0.605050i $$-0.206847\pi$$
0.796187 + 0.605050i $$0.206847\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 56.0000 2.22404
$$635$$ −10.0000 −0.396838
$$636$$ 0 0
$$637$$ −2.00000 −0.0792429
$$638$$ −4.00000 −0.158362
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 12.0000 0.473972 0.236986 0.971513i $$-0.423841\pi$$
0.236986 + 0.971513i $$0.423841\pi$$
$$642$$ 0 0
$$643$$ 15.0000 0.591542 0.295771 0.955259i $$-0.404423\pi$$
0.295771 + 0.955259i $$0.404423\pi$$
$$644$$ 18.0000 0.709299
$$645$$ 0 0
$$646$$ 4.00000 0.157378
$$647$$ −47.0000 −1.84776 −0.923880 0.382682i $$-0.875001\pi$$
−0.923880 + 0.382682i $$0.875001\pi$$
$$648$$ 0 0
$$649$$ −8.00000 −0.314027
$$650$$ 2.00000 0.0784465
$$651$$ 0 0
$$652$$ −26.0000 −1.01824
$$653$$ −22.0000 −0.860927 −0.430463 0.902608i $$-0.641650\pi$$
−0.430463 + 0.902608i $$0.641650\pi$$
$$654$$ 0 0
$$655$$ −6.00000 −0.234439
$$656$$ −20.0000 −0.780869
$$657$$ 0 0
$$658$$ −60.0000 −2.33904
$$659$$ −20.0000 −0.779089 −0.389545 0.921008i $$-0.627368\pi$$
−0.389545 + 0.921008i $$0.627368\pi$$
$$660$$ 0 0
$$661$$ 4.00000 0.155582 0.0777910 0.996970i $$-0.475213\pi$$
0.0777910 + 0.996970i $$0.475213\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 6.00000 0.232670
$$666$$ 0 0
$$667$$ 6.00000 0.232321
$$668$$ 24.0000 0.928588
$$669$$ 0 0
$$670$$ 24.0000 0.927201
$$671$$ 13.0000 0.501859
$$672$$ 0 0
$$673$$ −6.00000 −0.231283 −0.115642 0.993291i $$-0.536892\pi$$
−0.115642 + 0.993291i $$0.536892\pi$$
$$674$$ −8.00000 −0.308148
$$675$$ 0 0
$$676$$ 2.00000 0.0769231
$$677$$ −3.00000 −0.115299 −0.0576497 0.998337i $$-0.518361\pi$$
−0.0576497 + 0.998337i $$0.518361\pi$$
$$678$$ 0 0
$$679$$ 51.0000 1.95720
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 12.0000 0.459504
$$683$$ 24.0000 0.918334 0.459167 0.888350i $$-0.348148\pi$$
0.459167 + 0.888350i $$0.348148\pi$$
$$684$$ 0 0
$$685$$ 18.0000 0.687745
$$686$$ 30.0000 1.14541
$$687$$ 0 0
$$688$$ −16.0000 −0.609994
$$689$$ 11.0000 0.419067
$$690$$ 0 0
$$691$$ 22.0000 0.836919 0.418460 0.908235i $$-0.362570\pi$$
0.418460 + 0.908235i $$0.362570\pi$$
$$692$$ 12.0000 0.456172
$$693$$ 0 0
$$694$$ −38.0000 −1.44246
$$695$$ 1.00000 0.0379322
$$696$$ 0 0
$$697$$ 5.00000 0.189389
$$698$$ 16.0000 0.605609
$$699$$ 0 0
$$700$$ 6.00000 0.226779
$$701$$ 20.0000 0.755390 0.377695 0.925930i $$-0.376717\pi$$
0.377695 + 0.925930i $$0.376717\pi$$
$$702$$ 0 0
$$703$$ −22.0000 −0.829746
$$704$$ −8.00000 −0.301511
$$705$$ 0 0
$$706$$ 12.0000 0.451626
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 4.00000 0.150223 0.0751116 0.997175i $$-0.476069\pi$$
0.0751116 + 0.997175i $$0.476069\pi$$
$$710$$ 10.0000 0.375293
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −18.0000 −0.674105
$$714$$ 0 0
$$715$$ 1.00000 0.0373979
$$716$$ −4.00000 −0.149487
$$717$$ 0 0
$$718$$ 48.0000 1.79134
$$719$$ 24.0000 0.895049 0.447524 0.894272i $$-0.352306\pi$$
0.447524 + 0.894272i $$0.352306\pi$$
$$720$$ 0 0
$$721$$ −48.0000 −1.78761
$$722$$ 30.0000 1.11648
$$723$$ 0 0
$$724$$ −14.0000 −0.520306
$$725$$ 2.00000 0.0742781
$$726$$ 0 0
$$727$$ 38.0000 1.40934 0.704671 0.709534i $$-0.251095\pi$$
0.704671 + 0.709534i $$0.251095\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 20.0000 0.740233
$$731$$ 4.00000 0.147945
$$732$$ 0 0
$$733$$ −49.0000 −1.80986 −0.904928 0.425564i $$-0.860076\pi$$
−0.904928 + 0.425564i $$0.860076\pi$$
$$734$$ −72.0000 −2.65757
$$735$$ 0 0
$$736$$ 24.0000 0.884652
$$737$$ 12.0000 0.442026
$$738$$ 0 0
$$739$$ 10.0000 0.367856 0.183928 0.982940i $$-0.441119\pi$$
0.183928 + 0.982940i $$0.441119\pi$$
$$740$$ −22.0000 −0.808736
$$741$$ 0 0
$$742$$ 66.0000 2.42294
$$743$$ 34.0000 1.24734 0.623670 0.781688i $$-0.285641\pi$$
0.623670 + 0.781688i $$0.285641\pi$$
$$744$$ 0 0
$$745$$ 13.0000 0.476283
$$746$$ −8.00000 −0.292901
$$747$$ 0 0
$$748$$ 2.00000 0.0731272
$$749$$ −27.0000 −0.986559
$$750$$ 0 0
$$751$$ −5.00000 −0.182453 −0.0912263 0.995830i $$-0.529079\pi$$
−0.0912263 + 0.995830i $$0.529079\pi$$
$$752$$ −40.0000 −1.45865
$$753$$ 0 0
$$754$$ 4.00000 0.145671
$$755$$ −16.0000 −0.582300
$$756$$ 0 0
$$757$$ −8.00000 −0.290765 −0.145382 0.989376i $$-0.546441\pi$$
−0.145382 + 0.989376i $$0.546441\pi$$
$$758$$ 28.0000 1.01701
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 6.00000 0.217500 0.108750 0.994069i $$-0.465315\pi$$
0.108750 + 0.994069i $$0.465315\pi$$
$$762$$ 0 0
$$763$$ −48.0000 −1.73772
$$764$$ 16.0000 0.578860
$$765$$ 0 0
$$766$$ −60.0000 −2.16789
$$767$$ 8.00000 0.288863
$$768$$ 0 0
$$769$$ −40.0000 −1.44244 −0.721218 0.692708i $$-0.756418\pi$$
−0.721218 + 0.692708i $$0.756418\pi$$
$$770$$ 6.00000 0.216225
$$771$$ 0 0
$$772$$ −26.0000 −0.935760
$$773$$ −36.0000 −1.29483 −0.647415 0.762138i $$-0.724150\pi$$
−0.647415 + 0.762138i $$0.724150\pi$$
$$774$$ 0 0
$$775$$ −6.00000 −0.215526
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −10.0000 −0.358287
$$780$$ 0 0
$$781$$ 5.00000 0.178914
$$782$$ −6.00000 −0.214560
$$783$$ 0 0
$$784$$ −8.00000 −0.285714
$$785$$ 10.0000 0.356915
$$786$$ 0 0
$$787$$ 52.0000 1.85360 0.926800 0.375555i $$-0.122548\pi$$
0.926800 + 0.375555i $$0.122548\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ −6.00000 −0.213470
$$791$$ −42.0000 −1.49335
$$792$$ 0 0
$$793$$ −13.0000 −0.461644
$$794$$ 58.0000 2.05834
$$795$$ 0 0
$$796$$ 8.00000 0.283552
$$797$$ 47.0000 1.66483 0.832413 0.554156i $$-0.186959\pi$$
0.832413 + 0.554156i $$0.186959\pi$$
$$798$$ 0 0
$$799$$ 10.0000 0.353775
$$800$$ 8.00000 0.282843
$$801$$ 0 0
$$802$$ 60.0000 2.11867
$$803$$ 10.0000 0.352892
$$804$$ 0 0
$$805$$ −9.00000 −0.317208
$$806$$ −12.0000 −0.422682
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 26.0000 0.914111 0.457056 0.889438i $$-0.348904\pi$$
0.457056 + 0.889438i $$0.348904\pi$$
$$810$$ 0 0
$$811$$ 36.0000 1.26413 0.632065 0.774915i $$-0.282207\pi$$
0.632065 + 0.774915i $$0.282207\pi$$
$$812$$ 12.0000 0.421117
$$813$$ 0 0
$$814$$ −22.0000 −0.771100
$$815$$ 13.0000 0.455370
$$816$$ 0 0
$$817$$ −8.00000 −0.279885
$$818$$ −4.00000 −0.139857
$$819$$ 0 0
$$820$$ −10.0000 −0.349215
$$821$$ −27.0000 −0.942306 −0.471153 0.882051i $$-0.656162\pi$$
−0.471153 + 0.882051i $$0.656162\pi$$
$$822$$ 0 0
$$823$$ 20.0000 0.697156 0.348578 0.937280i $$-0.386665\pi$$
0.348578 + 0.937280i $$0.386665\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 48.0000 1.67013
$$827$$ −26.0000 −0.904109 −0.452054 0.891990i $$-0.649309\pi$$
−0.452054 + 0.891990i $$0.649309\pi$$
$$828$$ 0 0
$$829$$ 30.0000 1.04194 0.520972 0.853574i $$-0.325570\pi$$
0.520972 + 0.853574i $$0.325570\pi$$
$$830$$ 24.0000 0.833052
$$831$$ 0 0
$$832$$ 8.00000 0.277350
$$833$$ 2.00000 0.0692959
$$834$$ 0 0
$$835$$ −12.0000 −0.415277
$$836$$ −4.00000 −0.138343
$$837$$ 0 0
$$838$$ −52.0000 −1.79631
$$839$$ 5.00000 0.172619 0.0863096 0.996268i $$-0.472493\pi$$
0.0863096 + 0.996268i $$0.472493\pi$$
$$840$$ 0 0
$$841$$ −25.0000 −0.862069
$$842$$ −8.00000 −0.275698
$$843$$ 0 0
$$844$$ −8.00000 −0.275371
$$845$$ −1.00000 −0.0344010
$$846$$ 0 0
$$847$$ −30.0000 −1.03081
$$848$$ 44.0000 1.51097
$$849$$ 0 0
$$850$$ −2.00000 −0.0685994
$$851$$ 33.0000 1.13123
$$852$$ 0 0
$$853$$ 45.0000 1.54077 0.770385 0.637579i $$-0.220064\pi$$
0.770385 + 0.637579i $$0.220064\pi$$
$$854$$ −78.0000 −2.66911
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −29.0000 −0.990621 −0.495311 0.868716i $$-0.664946\pi$$
−0.495311 + 0.868716i $$0.664946\pi$$
$$858$$ 0 0
$$859$$ −29.0000 −0.989467 −0.494734 0.869045i $$-0.664734\pi$$
−0.494734 + 0.869045i $$0.664734\pi$$
$$860$$ −8.00000 −0.272798
$$861$$ 0 0
$$862$$ −48.0000 −1.63489
$$863$$ −34.0000 −1.15737 −0.578687 0.815550i $$-0.696435\pi$$
−0.578687 + 0.815550i $$0.696435\pi$$
$$864$$ 0 0
$$865$$ −6.00000 −0.204006
$$866$$ −8.00000 −0.271851
$$867$$ 0 0
$$868$$ −36.0000 −1.22192
$$869$$ −3.00000 −0.101768
$$870$$ 0 0
$$871$$ −12.0000 −0.406604
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 12.0000 0.405906
$$875$$ −3.00000 −0.101419
$$876$$ 0 0
$$877$$ 18.0000 0.607817 0.303908 0.952701i $$-0.401708\pi$$
0.303908 + 0.952701i $$0.401708\pi$$
$$878$$ 34.0000 1.14744
$$879$$ 0 0
$$880$$ 4.00000 0.134840
$$881$$ −2.00000 −0.0673817 −0.0336909 0.999432i $$-0.510726\pi$$
−0.0336909 + 0.999432i $$0.510726\pi$$
$$882$$ 0 0
$$883$$ −16.0000 −0.538443 −0.269221 0.963078i $$-0.586766\pi$$
−0.269221 + 0.963078i $$0.586766\pi$$
$$884$$ −2.00000 −0.0672673
$$885$$ 0 0
$$886$$ 18.0000 0.604722
$$887$$ 21.0000 0.705111 0.352555 0.935791i $$-0.385313\pi$$
0.352555 + 0.935791i $$0.385313\pi$$
$$888$$ 0 0
$$889$$ 30.0000 1.00617
$$890$$ 30.0000 1.00560
$$891$$ 0 0
$$892$$ 16.0000 0.535720
$$893$$ −20.0000 −0.669274
$$894$$ 0 0
$$895$$ 2.00000 0.0668526
$$896$$ 0 0
$$897$$ 0 0
$$898$$ −26.0000 −0.867631
$$899$$ −12.0000 −0.400222
$$900$$ 0 0
$$901$$ −11.0000 −0.366463
$$902$$ −10.0000 −0.332964
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 7.00000 0.232688
$$906$$ 0 0
$$907$$ 6.00000 0.199227 0.0996134 0.995026i $$-0.468239\pi$$
0.0996134 + 0.995026i $$0.468239\pi$$
$$908$$ −44.0000 −1.46019
$$909$$ 0 0
$$910$$ −6.00000 −0.198898
$$911$$ −44.0000 −1.45779 −0.728893 0.684628i $$-0.759965\pi$$
−0.728893 + 0.684628i $$0.759965\pi$$
$$912$$ 0 0
$$913$$ 12.0000 0.397142
$$914$$ 22.0000 0.727695
$$915$$ 0 0
$$916$$ 36.0000 1.18947
$$917$$ 18.0000 0.594412
$$918$$ 0 0
$$919$$ 37.0000 1.22052 0.610259 0.792202i $$-0.291065\pi$$
0.610259 + 0.792202i $$0.291065\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 30.0000 0.987997
$$923$$ −5.00000 −0.164577
$$924$$ 0 0
$$925$$ 11.0000 0.361678
$$926$$ −54.0000 −1.77455
$$927$$ 0 0
$$928$$ 16.0000 0.525226
$$929$$ −1.00000 −0.0328089 −0.0164045 0.999865i $$-0.505222\pi$$
−0.0164045 + 0.999865i $$0.505222\pi$$
$$930$$ 0 0
$$931$$ −4.00000 −0.131095
$$932$$ 54.0000 1.76883
$$933$$ 0 0
$$934$$ −46.0000 −1.50517
$$935$$ −1.00000 −0.0327035
$$936$$ 0 0
$$937$$ 30.0000 0.980057 0.490029 0.871706i $$-0.336986\pi$$
0.490029 + 0.871706i $$0.336986\pi$$
$$938$$ −72.0000 −2.35088
$$939$$ 0 0
$$940$$ −20.0000 −0.652328
$$941$$ −37.0000 −1.20617 −0.603083 0.797679i $$-0.706061\pi$$
−0.603083 + 0.797679i $$0.706061\pi$$
$$942$$ 0 0
$$943$$ 15.0000 0.488467
$$944$$ 32.0000 1.04151
$$945$$ 0 0
$$946$$ −8.00000 −0.260102
$$947$$ 24.0000 0.779895 0.389948 0.920837i $$-0.372493\pi$$
0.389948 + 0.920837i $$0.372493\pi$$
$$948$$ 0 0
$$949$$ −10.0000 −0.324614
$$950$$ 4.00000 0.129777
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 1.00000 0.0323932 0.0161966 0.999869i $$-0.494844\pi$$
0.0161966 + 0.999869i $$0.494844\pi$$
$$954$$ 0 0
$$955$$ −8.00000 −0.258874
$$956$$ 26.0000 0.840900
$$957$$ 0 0
$$958$$ 18.0000 0.581554
$$959$$ −54.0000 −1.74375
$$960$$ 0 0
$$961$$ 5.00000 0.161290
$$962$$ 22.0000 0.709308
$$963$$ 0 0
$$964$$ −4.00000 −0.128831
$$965$$ 13.0000 0.418485
$$966$$ 0 0
$$967$$ −16.0000 −0.514525 −0.257263 0.966342i $$-0.582821\pi$$
−0.257263 + 0.966342i $$0.582821\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 34.0000 1.09167
$$971$$ −12.0000 −0.385098 −0.192549 0.981287i $$-0.561675\pi$$
−0.192549 + 0.981287i $$0.561675\pi$$
$$972$$ 0 0
$$973$$ −3.00000 −0.0961756
$$974$$ 14.0000 0.448589
$$975$$ 0 0
$$976$$ −52.0000 −1.66448
$$977$$ −32.0000 −1.02377 −0.511885 0.859054i $$-0.671053\pi$$
−0.511885 + 0.859054i $$0.671053\pi$$
$$978$$ 0 0
$$979$$ 15.0000 0.479402
$$980$$ −4.00000 −0.127775
$$981$$ 0 0
$$982$$ 56.0000 1.78703
$$983$$ 12.0000 0.382741 0.191370 0.981518i $$-0.438707\pi$$
0.191370 + 0.981518i $$0.438707\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ −4.00000 −0.127386
$$987$$ 0 0
$$988$$ 4.00000 0.127257
$$989$$ 12.0000 0.381578
$$990$$ 0 0
$$991$$ −25.0000 −0.794151 −0.397076 0.917786i $$-0.629975\pi$$
−0.397076 + 0.917786i $$0.629975\pi$$
$$992$$ −48.0000 −1.52400
$$993$$ 0 0
$$994$$ −30.0000 −0.951542
$$995$$ −4.00000 −0.126809
$$996$$ 0 0
$$997$$ −36.0000 −1.14013 −0.570066 0.821599i $$-0.693082\pi$$
−0.570066 + 0.821599i $$0.693082\pi$$
$$998$$ 28.0000 0.886325
$$999$$ 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 585.2.a.b.1.1 1
3.2 odd 2 195.2.a.b.1.1 1
4.3 odd 2 9360.2.a.d.1.1 1
5.2 odd 4 2925.2.c.c.2224.1 2
5.3 odd 4 2925.2.c.c.2224.2 2
5.4 even 2 2925.2.a.q.1.1 1
12.11 even 2 3120.2.a.u.1.1 1
13.12 even 2 7605.2.a.u.1.1 1
15.2 even 4 975.2.c.a.274.2 2
15.8 even 4 975.2.c.a.274.1 2
15.14 odd 2 975.2.a.c.1.1 1
21.20 even 2 9555.2.a.v.1.1 1
39.38 odd 2 2535.2.a.a.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
195.2.a.b.1.1 1 3.2 odd 2
585.2.a.b.1.1 1 1.1 even 1 trivial
975.2.a.c.1.1 1 15.14 odd 2
975.2.c.a.274.1 2 15.8 even 4
975.2.c.a.274.2 2 15.2 even 4
2535.2.a.a.1.1 1 39.38 odd 2
2925.2.a.q.1.1 1 5.4 even 2
2925.2.c.c.2224.1 2 5.2 odd 4
2925.2.c.c.2224.2 2 5.3 odd 4
3120.2.a.u.1.1 1 12.11 even 2
7605.2.a.u.1.1 1 13.12 even 2
9360.2.a.d.1.1 1 4.3 odd 2
9555.2.a.v.1.1 1 21.20 even 2