# Properties

 Label 9792.2.a.b.1.1 Level $9792$ Weight $2$ Character 9792.1 Self dual yes Analytic conductor $78.190$ 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] = [9792,2,Mod(1,9792)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9792, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("9792.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$9792 = 2^{6} \cdot 3^{2} \cdot 17$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 9792.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: $$78.1895136592$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 102) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 9792.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-4.00000 q^{5} +2.00000 q^{7} +O(q^{10})$$ $$q-4.00000 q^{5} +2.00000 q^{7} +6.00000 q^{13} +1.00000 q^{17} +4.00000 q^{19} +6.00000 q^{23} +11.0000 q^{25} -4.00000 q^{29} +6.00000 q^{31} -8.00000 q^{35} +4.00000 q^{37} +10.0000 q^{41} -4.00000 q^{43} +4.00000 q^{47} -3.00000 q^{49} -2.00000 q^{53} -12.0000 q^{59} +4.00000 q^{61} -24.0000 q^{65} -12.0000 q^{67} -6.00000 q^{71} +2.00000 q^{73} -10.0000 q^{79} +12.0000 q^{83} -4.00000 q^{85} +2.00000 q^{89} +12.0000 q^{91} -16.0000 q^{95} +6.00000 q^{97} +O(q^{100})$$

## 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
$$5$$ −4.00000 −1.78885 −0.894427 0.447214i $$-0.852416\pi$$
−0.894427 + 0.447214i $$0.852416\pi$$
$$6$$ 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
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ 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
$$17$$ 1.00000 0.242536
$$18$$ 0 0
$$19$$ 4.00000 0.917663 0.458831 0.888523i $$-0.348268\pi$$
0.458831 + 0.888523i $$0.348268\pi$$
$$20$$ 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
$$25$$ 11.0000 2.20000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −4.00000 −0.742781 −0.371391 0.928477i $$-0.621119\pi$$
−0.371391 + 0.928477i $$0.621119\pi$$
$$30$$ 0 0
$$31$$ 6.00000 1.07763 0.538816 0.842424i $$-0.318872\pi$$
0.538816 + 0.842424i $$0.318872\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −8.00000 −1.35225
$$36$$ 0 0
$$37$$ 4.00000 0.657596 0.328798 0.944400i $$-0.393356\pi$$
0.328798 + 0.944400i $$0.393356\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 10.0000 1.56174 0.780869 0.624695i $$-0.214777\pi$$
0.780869 + 0.624695i $$0.214777\pi$$
$$42$$ 0 0
$$43$$ −4.00000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ 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
$$53$$ −2.00000 −0.274721 −0.137361 0.990521i $$-0.543862\pi$$
−0.137361 + 0.990521i $$0.543862\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −12.0000 −1.56227 −0.781133 0.624364i $$-0.785358\pi$$
−0.781133 + 0.624364i $$0.785358\pi$$
$$60$$ 0 0
$$61$$ 4.00000 0.512148 0.256074 0.966657i $$-0.417571\pi$$
0.256074 + 0.966657i $$0.417571\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −24.0000 −2.97683
$$66$$ 0 0
$$67$$ −12.0000 −1.46603 −0.733017 0.680211i $$-0.761888\pi$$
−0.733017 + 0.680211i $$0.761888\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −6.00000 −0.712069 −0.356034 0.934473i $$-0.615871\pi$$
−0.356034 + 0.934473i $$0.615871\pi$$
$$72$$ 0 0
$$73$$ 2.00000 0.234082 0.117041 0.993127i $$-0.462659\pi$$
0.117041 + 0.993127i $$0.462659\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −10.0000 −1.12509 −0.562544 0.826767i $$-0.690177\pi$$
−0.562544 + 0.826767i $$0.690177\pi$$
$$80$$ 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
$$85$$ −4.00000 −0.433861
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 2.00000 0.212000 0.106000 0.994366i $$-0.466196\pi$$
0.106000 + 0.994366i $$0.466196\pi$$
$$90$$ 0 0
$$91$$ 12.0000 1.25794
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −16.0000 −1.64157
$$96$$ 0 0
$$97$$ 6.00000 0.609208 0.304604 0.952479i $$-0.401476\pi$$
0.304604 + 0.952479i $$0.401476\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 14.0000 1.39305 0.696526 0.717532i $$-0.254728\pi$$
0.696526 + 0.717532i $$0.254728\pi$$
$$102$$ 0 0
$$103$$ −4.00000 −0.394132 −0.197066 0.980390i $$-0.563141\pi$$
−0.197066 + 0.980390i $$0.563141\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$108$$ 0 0
$$109$$ −16.0000 −1.53252 −0.766261 0.642529i $$-0.777885\pi$$
−0.766261 + 0.642529i $$0.777885\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −2.00000 −0.188144 −0.0940721 0.995565i $$-0.529988\pi$$
−0.0940721 + 0.995565i $$0.529988\pi$$
$$114$$ 0 0
$$115$$ −24.0000 −2.23801
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 2.00000 0.183340
$$120$$ 0 0
$$121$$ −11.0000 −1.00000
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −24.0000 −2.14663
$$126$$ 0 0
$$127$$ −8.00000 −0.709885 −0.354943 0.934888i $$-0.615500\pi$$
−0.354943 + 0.934888i $$0.615500\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 16.0000 1.39793 0.698963 0.715158i $$-0.253645\pi$$
0.698963 + 0.715158i $$0.253645\pi$$
$$132$$ 0 0
$$133$$ 8.00000 0.693688
$$134$$ 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
$$139$$ 8.00000 0.678551 0.339276 0.940687i $$-0.389818\pi$$
0.339276 + 0.940687i $$0.389818\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 16.0000 1.32873
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −6.00000 −0.491539 −0.245770 0.969328i $$-0.579041\pi$$
−0.245770 + 0.969328i $$0.579041\pi$$
$$150$$ 0 0
$$151$$ 24.0000 1.95309 0.976546 0.215308i $$-0.0690756\pi$$
0.976546 + 0.215308i $$0.0690756\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −24.0000 −1.92773
$$156$$ 0 0
$$157$$ −6.00000 −0.478852 −0.239426 0.970915i $$-0.576959\pi$$
−0.239426 + 0.970915i $$0.576959\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 12.0000 0.945732
$$162$$ 0 0
$$163$$ 12.0000 0.939913 0.469956 0.882690i $$-0.344270\pi$$
0.469956 + 0.882690i $$0.344270\pi$$
$$164$$ 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
$$169$$ 23.0000 1.76923
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −4.00000 −0.304114 −0.152057 0.988372i $$-0.548590\pi$$
−0.152057 + 0.988372i $$0.548590\pi$$
$$174$$ 0 0
$$175$$ 22.0000 1.66304
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 12.0000 0.896922 0.448461 0.893802i $$-0.351972\pi$$
0.448461 + 0.893802i $$0.351972\pi$$
$$180$$ 0 0
$$181$$ 20.0000 1.48659 0.743294 0.668965i $$-0.233262\pi$$
0.743294 + 0.668965i $$0.233262\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −16.0000 −1.17634
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −4.00000 −0.289430 −0.144715 0.989473i $$-0.546227\pi$$
−0.144715 + 0.989473i $$0.546227\pi$$
$$192$$ 0 0
$$193$$ 6.00000 0.431889 0.215945 0.976406i $$-0.430717\pi$$
0.215945 + 0.976406i $$0.430717\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 8.00000 0.569976 0.284988 0.958531i $$-0.408010\pi$$
0.284988 + 0.958531i $$0.408010\pi$$
$$198$$ 0 0
$$199$$ −14.0000 −0.992434 −0.496217 0.868199i $$-0.665278\pi$$
−0.496217 + 0.868199i $$0.665278\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −8.00000 −0.561490
$$204$$ 0 0
$$205$$ −40.0000 −2.79372
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 8.00000 0.550743 0.275371 0.961338i $$-0.411199\pi$$
0.275371 + 0.961338i $$0.411199\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 16.0000 1.09119
$$216$$ 0 0
$$217$$ 12.0000 0.814613
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 6.00000 0.403604
$$222$$ 0 0
$$223$$ 4.00000 0.267860 0.133930 0.990991i $$-0.457240\pi$$
0.133930 + 0.990991i $$0.457240\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −4.00000 −0.265489 −0.132745 0.991150i $$-0.542379\pi$$
−0.132745 + 0.991150i $$0.542379\pi$$
$$228$$ 0 0
$$229$$ 2.00000 0.132164 0.0660819 0.997814i $$-0.478950\pi$$
0.0660819 + 0.997814i $$0.478950\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 6.00000 0.393073 0.196537 0.980497i $$-0.437031\pi$$
0.196537 + 0.980497i $$0.437031\pi$$
$$234$$ 0 0
$$235$$ −16.0000 −1.04372
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −20.0000 −1.29369 −0.646846 0.762620i $$-0.723912\pi$$
−0.646846 + 0.762620i $$0.723912\pi$$
$$240$$ 0 0
$$241$$ −18.0000 −1.15948 −0.579741 0.814801i $$-0.696846\pi$$
−0.579741 + 0.814801i $$0.696846\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 12.0000 0.766652
$$246$$ 0 0
$$247$$ 24.0000 1.52708
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −12.0000 −0.757433 −0.378717 0.925513i $$-0.623635\pi$$
−0.378717 + 0.925513i $$0.623635\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −18.0000 −1.12281 −0.561405 0.827541i $$-0.689739\pi$$
−0.561405 + 0.827541i $$0.689739\pi$$
$$258$$ 0 0
$$259$$ 8.00000 0.497096
$$260$$ 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
$$265$$ 8.00000 0.491436
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −12.0000 −0.731653 −0.365826 0.930683i $$-0.619214\pi$$
−0.365826 + 0.930683i $$0.619214\pi$$
$$270$$ 0 0
$$271$$ 16.0000 0.971931 0.485965 0.873978i $$-0.338468\pi$$
0.485965 + 0.873978i $$0.338468\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 8.00000 0.480673 0.240337 0.970690i $$-0.422742\pi$$
0.240337 + 0.970690i $$0.422742\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 18.0000 1.07379 0.536895 0.843649i $$-0.319597\pi$$
0.536895 + 0.843649i $$0.319597\pi$$
$$282$$ 0 0
$$283$$ 32.0000 1.90220 0.951101 0.308879i $$-0.0999539\pi$$
0.951101 + 0.308879i $$0.0999539\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 20.0000 1.18056
$$288$$ 0 0
$$289$$ 1.00000 0.0588235
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 2.00000 0.116841 0.0584206 0.998292i $$-0.481394\pi$$
0.0584206 + 0.998292i $$0.481394\pi$$
$$294$$ 0 0
$$295$$ 48.0000 2.79467
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 36.0000 2.08193
$$300$$ 0 0
$$301$$ −8.00000 −0.461112
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −16.0000 −0.916157
$$306$$ 0 0
$$307$$ −12.0000 −0.684876 −0.342438 0.939540i $$-0.611253\pi$$
−0.342438 + 0.939540i $$0.611253\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 30.0000 1.70114 0.850572 0.525859i $$-0.176256\pi$$
0.850572 + 0.525859i $$0.176256\pi$$
$$312$$ 0 0
$$313$$ −26.0000 −1.46961 −0.734803 0.678280i $$-0.762726\pi$$
−0.734803 + 0.678280i $$0.762726\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −16.0000 −0.898650 −0.449325 0.893368i $$-0.648335\pi$$
−0.449325 + 0.893368i $$0.648335\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 4.00000 0.222566
$$324$$ 0 0
$$325$$ 66.0000 3.66102
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 8.00000 0.441054
$$330$$ 0 0
$$331$$ 20.0000 1.09930 0.549650 0.835395i $$-0.314761\pi$$
0.549650 + 0.835395i $$0.314761\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 48.0000 2.62252
$$336$$ 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
$$341$$ 0 0
$$342$$ 0 0
$$343$$ −20.0000 −1.07990
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 4.00000 0.214731 0.107366 0.994220i $$-0.465758\pi$$
0.107366 + 0.994220i $$0.465758\pi$$
$$348$$ 0 0
$$349$$ 30.0000 1.60586 0.802932 0.596071i $$-0.203272\pi$$
0.802932 + 0.596071i $$0.203272\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −14.0000 −0.745145 −0.372572 0.928003i $$-0.621524\pi$$
−0.372572 + 0.928003i $$0.621524\pi$$
$$354$$ 0 0
$$355$$ 24.0000 1.27379
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 0 0
$$361$$ −3.00000 −0.157895
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −8.00000 −0.418739
$$366$$ 0 0
$$367$$ −10.0000 −0.521996 −0.260998 0.965339i $$-0.584052\pi$$
−0.260998 + 0.965339i $$0.584052\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −4.00000 −0.207670
$$372$$ 0 0
$$373$$ 14.0000 0.724893 0.362446 0.932005i $$-0.381942\pi$$
0.362446 + 0.932005i $$0.381942\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −24.0000 −1.23606
$$378$$ 0 0
$$379$$ −4.00000 −0.205466 −0.102733 0.994709i $$-0.532759\pi$$
−0.102733 + 0.994709i $$0.532759\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 28.0000 1.43073 0.715367 0.698749i $$-0.246260\pi$$
0.715367 + 0.698749i $$0.246260\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −14.0000 −0.709828 −0.354914 0.934899i $$-0.615490\pi$$
−0.354914 + 0.934899i $$0.615490\pi$$
$$390$$ 0 0
$$391$$ 6.00000 0.303433
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 40.0000 2.01262
$$396$$ 0 0
$$397$$ −20.0000 −1.00377 −0.501886 0.864934i $$-0.667360\pi$$
−0.501886 + 0.864934i $$0.667360\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −30.0000 −1.49813 −0.749064 0.662497i $$-0.769497\pi$$
−0.749064 + 0.662497i $$0.769497\pi$$
$$402$$ 0 0
$$403$$ 36.0000 1.79329
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −26.0000 −1.28562 −0.642809 0.766027i $$-0.722231\pi$$
−0.642809 + 0.766027i $$0.722231\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −24.0000 −1.18096
$$414$$ 0 0
$$415$$ −48.0000 −2.35623
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 12.0000 0.586238 0.293119 0.956076i $$-0.405307\pi$$
0.293119 + 0.956076i $$0.405307\pi$$
$$420$$ 0 0
$$421$$ −34.0000 −1.65706 −0.828529 0.559946i $$-0.810822\pi$$
−0.828529 + 0.559946i $$0.810822\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 11.0000 0.533578
$$426$$ 0 0
$$427$$ 8.00000 0.387147
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 14.0000 0.674356 0.337178 0.941441i $$-0.390528\pi$$
0.337178 + 0.941441i $$0.390528\pi$$
$$432$$ 0 0
$$433$$ −18.0000 −0.865025 −0.432512 0.901628i $$-0.642373\pi$$
−0.432512 + 0.901628i $$0.642373\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 24.0000 1.14808
$$438$$ 0 0
$$439$$ 10.0000 0.477274 0.238637 0.971109i $$-0.423299\pi$$
0.238637 + 0.971109i $$0.423299\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −12.0000 −0.570137 −0.285069 0.958507i $$-0.592016\pi$$
−0.285069 + 0.958507i $$0.592016\pi$$
$$444$$ 0 0
$$445$$ −8.00000 −0.379236
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 26.0000 1.22702 0.613508 0.789689i $$-0.289758\pi$$
0.613508 + 0.789689i $$0.289758\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −48.0000 −2.25027
$$456$$ 0 0
$$457$$ 22.0000 1.02912 0.514558 0.857455i $$-0.327956\pi$$
0.514558 + 0.857455i $$0.327956\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −10.0000 −0.465746 −0.232873 0.972507i $$-0.574813\pi$$
−0.232873 + 0.972507i $$0.574813\pi$$
$$462$$ 0 0
$$463$$ 4.00000 0.185896 0.0929479 0.995671i $$-0.470371\pi$$
0.0929479 + 0.995671i $$0.470371\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 36.0000 1.66588 0.832941 0.553362i $$-0.186655\pi$$
0.832941 + 0.553362i $$0.186655\pi$$
$$468$$ 0 0
$$469$$ −24.0000 −1.10822
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 44.0000 2.01886
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 10.0000 0.456912 0.228456 0.973554i $$-0.426632\pi$$
0.228456 + 0.973554i $$0.426632\pi$$
$$480$$ 0 0
$$481$$ 24.0000 1.09431
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −24.0000 −1.08978
$$486$$ 0 0
$$487$$ 38.0000 1.72194 0.860972 0.508652i $$-0.169856\pi$$
0.860972 + 0.508652i $$0.169856\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 20.0000 0.902587 0.451294 0.892375i $$-0.350963\pi$$
0.451294 + 0.892375i $$0.350963\pi$$
$$492$$ 0 0
$$493$$ −4.00000 −0.180151
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −12.0000 −0.538274
$$498$$ 0 0
$$499$$ 32.0000 1.43252 0.716258 0.697835i $$-0.245853\pi$$
0.716258 + 0.697835i $$0.245853\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −26.0000 −1.15928 −0.579641 0.814872i $$-0.696807\pi$$
−0.579641 + 0.814872i $$0.696807\pi$$
$$504$$ 0 0
$$505$$ −56.0000 −2.49197
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 26.0000 1.15243 0.576215 0.817298i $$-0.304529\pi$$
0.576215 + 0.817298i $$0.304529\pi$$
$$510$$ 0 0
$$511$$ 4.00000 0.176950
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 16.0000 0.705044
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 10.0000 0.438108 0.219054 0.975713i $$-0.429703\pi$$
0.219054 + 0.975713i $$0.429703\pi$$
$$522$$ 0 0
$$523$$ −20.0000 −0.874539 −0.437269 0.899331i $$-0.644054\pi$$
−0.437269 + 0.899331i $$0.644054\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 6.00000 0.261364
$$528$$ 0 0
$$529$$ 13.0000 0.565217
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 60.0000 2.59889
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 12.0000 0.515920 0.257960 0.966156i $$-0.416950\pi$$
0.257960 + 0.966156i $$0.416950\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 64.0000 2.74146
$$546$$ 0 0
$$547$$ −8.00000 −0.342055 −0.171028 0.985266i $$-0.554709\pi$$
−0.171028 + 0.985266i $$0.554709\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −16.0000 −0.681623
$$552$$ 0 0
$$553$$ −20.0000 −0.850487
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 14.0000 0.593199 0.296600 0.955002i $$-0.404147\pi$$
0.296600 + 0.955002i $$0.404147\pi$$
$$558$$ 0 0
$$559$$ −24.0000 −1.01509
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 4.00000 0.168580 0.0842900 0.996441i $$-0.473138\pi$$
0.0842900 + 0.996441i $$0.473138\pi$$
$$564$$ 0 0
$$565$$ 8.00000 0.336563
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 6.00000 0.251533 0.125767 0.992060i $$-0.459861\pi$$
0.125767 + 0.992060i $$0.459861\pi$$
$$570$$ 0 0
$$571$$ 44.0000 1.84134 0.920671 0.390339i $$-0.127642\pi$$
0.920671 + 0.390339i $$0.127642\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 66.0000 2.75239
$$576$$ 0 0
$$577$$ −30.0000 −1.24892 −0.624458 0.781058i $$-0.714680\pi$$
−0.624458 + 0.781058i $$0.714680\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 24.0000 0.995688
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −36.0000 −1.48588 −0.742940 0.669359i $$-0.766569\pi$$
−0.742940 + 0.669359i $$0.766569\pi$$
$$588$$ 0 0
$$589$$ 24.0000 0.988903
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 30.0000 1.23195 0.615976 0.787765i $$-0.288762\pi$$
0.615976 + 0.787765i $$0.288762\pi$$
$$594$$ 0 0
$$595$$ −8.00000 −0.327968
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −16.0000 −0.653742 −0.326871 0.945069i $$-0.605994\pi$$
−0.326871 + 0.945069i $$0.605994\pi$$
$$600$$ 0 0
$$601$$ −38.0000 −1.55005 −0.775026 0.631929i $$-0.782263\pi$$
−0.775026 + 0.631929i $$0.782263\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 44.0000 1.78885
$$606$$ 0 0
$$607$$ 38.0000 1.54237 0.771186 0.636610i $$-0.219664\pi$$
0.771186 + 0.636610i $$0.219664\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 24.0000 0.970936
$$612$$ 0 0
$$613$$ −30.0000 −1.21169 −0.605844 0.795583i $$-0.707165\pi$$
−0.605844 + 0.795583i $$0.707165\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 6.00000 0.241551 0.120775 0.992680i $$-0.461462\pi$$
0.120775 + 0.992680i $$0.461462\pi$$
$$618$$ 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
$$623$$ 4.00000 0.160257
$$624$$ 0 0
$$625$$ 41.0000 1.64000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 4.00000 0.159490
$$630$$ 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
$$635$$ 32.0000 1.26988
$$636$$ 0 0
$$637$$ −18.0000 −0.713186
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 2.00000 0.0789953 0.0394976 0.999220i $$-0.487424\pi$$
0.0394976 + 0.999220i $$0.487424\pi$$
$$642$$ 0 0
$$643$$ 4.00000 0.157745 0.0788723 0.996885i $$-0.474868\pi$$
0.0788723 + 0.996885i $$0.474868\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 28.0000 1.10079 0.550397 0.834903i $$-0.314476\pi$$
0.550397 + 0.834903i $$0.314476\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 20.0000 0.782660 0.391330 0.920250i $$-0.372015\pi$$
0.391330 + 0.920250i $$0.372015\pi$$
$$654$$ 0 0
$$655$$ −64.0000 −2.50069
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −12.0000 −0.467454 −0.233727 0.972302i $$-0.575092\pi$$
−0.233727 + 0.972302i $$0.575092\pi$$
$$660$$ 0 0
$$661$$ 14.0000 0.544537 0.272268 0.962221i $$-0.412226\pi$$
0.272268 + 0.962221i $$0.412226\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −32.0000 −1.24091
$$666$$ 0 0
$$667$$ −24.0000 −0.929284
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −26.0000 −1.00223 −0.501113 0.865382i $$-0.667076\pi$$
−0.501113 + 0.865382i $$0.667076\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 8.00000 0.307465 0.153732 0.988113i $$-0.450871\pi$$
0.153732 + 0.988113i $$0.450871\pi$$
$$678$$ 0 0
$$679$$ 12.0000 0.460518
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −12.0000 −0.459167 −0.229584 0.973289i $$-0.573736\pi$$
−0.229584 + 0.973289i $$0.573736\pi$$
$$684$$ 0 0
$$685$$ −24.0000 −0.916993
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −12.0000 −0.457164
$$690$$ 0 0
$$691$$ 16.0000 0.608669 0.304334 0.952565i $$-0.401566\pi$$
0.304334 + 0.952565i $$0.401566\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −32.0000 −1.21383
$$696$$ 0 0
$$697$$ 10.0000 0.378777
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −18.0000 −0.679851 −0.339925 0.940452i $$-0.610402\pi$$
−0.339925 + 0.940452i $$0.610402\pi$$
$$702$$ 0 0
$$703$$ 16.0000 0.603451
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 28.0000 1.05305
$$708$$ 0 0
$$709$$ 16.0000 0.600893 0.300446 0.953799i $$-0.402864\pi$$
0.300446 + 0.953799i $$0.402864\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 36.0000 1.34821
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 42.0000 1.56634 0.783168 0.621810i $$-0.213603\pi$$
0.783168 + 0.621810i $$0.213603\pi$$
$$720$$ 0 0
$$721$$ −8.00000 −0.297936
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −44.0000 −1.63412
$$726$$ 0 0
$$727$$ 8.00000 0.296704 0.148352 0.988935i $$-0.452603\pi$$
0.148352 + 0.988935i $$0.452603\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −4.00000 −0.147945
$$732$$ 0 0
$$733$$ −18.0000 −0.664845 −0.332423 0.943131i $$-0.607866\pi$$
−0.332423 + 0.943131i $$0.607866\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −12.0000 −0.441427 −0.220714 0.975339i $$-0.570839\pi$$
−0.220714 + 0.975339i $$0.570839\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 38.0000 1.39408 0.697042 0.717030i $$-0.254499\pi$$
0.697042 + 0.717030i $$0.254499\pi$$
$$744$$ 0 0
$$745$$ 24.0000 0.879292
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 34.0000 1.24068 0.620339 0.784334i $$-0.286995\pi$$
0.620339 + 0.784334i $$0.286995\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −96.0000 −3.49380
$$756$$ 0 0
$$757$$ −14.0000 −0.508839 −0.254419 0.967094i $$-0.581884\pi$$
−0.254419 + 0.967094i $$0.581884\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −10.0000 −0.362500 −0.181250 0.983437i $$-0.558014\pi$$
−0.181250 + 0.983437i $$0.558014\pi$$
$$762$$ 0 0
$$763$$ −32.0000 −1.15848
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −72.0000 −2.59977
$$768$$ 0 0
$$769$$ 26.0000 0.937584 0.468792 0.883309i $$-0.344689\pi$$
0.468792 + 0.883309i $$0.344689\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 42.0000 1.51064 0.755318 0.655359i $$-0.227483\pi$$
0.755318 + 0.655359i $$0.227483\pi$$
$$774$$ 0 0
$$775$$ 66.0000 2.37079
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 40.0000 1.43315
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 24.0000 0.856597
$$786$$ 0 0
$$787$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −4.00000 −0.142224
$$792$$ 0 0
$$793$$ 24.0000 0.852265
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 46.0000 1.62940 0.814702 0.579880i $$-0.196901\pi$$
0.814702 + 0.579880i $$0.196901\pi$$
$$798$$ 0 0
$$799$$ 4.00000 0.141510
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ −48.0000 −1.69178
$$806$$ 0 0
$$807$$ 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
$$811$$ −12.0000 −0.421377 −0.210688 0.977553i $$-0.567571\pi$$
−0.210688 + 0.977553i $$0.567571\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −48.0000 −1.68137
$$816$$ 0 0
$$817$$ −16.0000 −0.559769
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$822$$ 0 0
$$823$$ −18.0000 −0.627441 −0.313720 0.949515i $$-0.601575\pi$$
−0.313720 + 0.949515i $$0.601575\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −16.0000 −0.556375 −0.278187 0.960527i $$-0.589734\pi$$
−0.278187 + 0.960527i $$0.589734\pi$$
$$828$$ 0 0
$$829$$ −6.00000 −0.208389 −0.104194 0.994557i $$-0.533226\pi$$
−0.104194 + 0.994557i $$0.533226\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −3.00000 −0.103944
$$834$$ 0 0
$$835$$ 8.00000 0.276851
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −30.0000 −1.03572 −0.517858 0.855467i $$-0.673270\pi$$
−0.517858 + 0.855467i $$0.673270\pi$$
$$840$$ 0 0
$$841$$ −13.0000 −0.448276
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ −92.0000 −3.16490
$$846$$ 0 0
$$847$$ −22.0000 −0.755929
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 24.0000 0.822709
$$852$$ 0 0
$$853$$ 16.0000 0.547830 0.273915 0.961754i $$-0.411681\pi$$
0.273915 + 0.961754i $$0.411681\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 10.0000 0.341593 0.170797 0.985306i $$-0.445366\pi$$
0.170797 + 0.985306i $$0.445366\pi$$
$$858$$ 0 0
$$859$$ 20.0000 0.682391 0.341196 0.939992i $$-0.389168\pi$$
0.341196 + 0.939992i $$0.389168\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −48.0000 −1.63394 −0.816970 0.576681i $$-0.804348\pi$$
−0.816970 + 0.576681i $$0.804348\pi$$
$$864$$ 0 0
$$865$$ 16.0000 0.544016
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ −72.0000 −2.43963
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ −48.0000 −1.62270
$$876$$ 0 0
$$877$$ 24.0000 0.810422 0.405211 0.914223i $$-0.367198\pi$$
0.405211 + 0.914223i $$0.367198\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −50.0000 −1.68454 −0.842271 0.539054i $$-0.818782\pi$$
−0.842271 + 0.539054i $$0.818782\pi$$
$$882$$ 0 0
$$883$$ −52.0000 −1.74994 −0.874970 0.484178i $$-0.839119\pi$$
−0.874970 + 0.484178i $$0.839119\pi$$
$$884$$ 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
$$889$$ −16.0000 −0.536623
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 16.0000 0.535420
$$894$$ 0 0
$$895$$ −48.0000 −1.60446
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −24.0000 −0.800445
$$900$$ 0 0
$$901$$ −2.00000 −0.0666297
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −80.0000 −2.65929
$$906$$ 0 0
$$907$$ 24.0000 0.796907 0.398453 0.917189i $$-0.369547\pi$$
0.398453 + 0.917189i $$0.369547\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 26.0000 0.861418 0.430709 0.902491i $$-0.358263\pi$$
0.430709 + 0.902491i $$0.358263\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 32.0000 1.05673
$$918$$ 0 0
$$919$$ −16.0000 −0.527791 −0.263896 0.964551i $$-0.585007\pi$$
−0.263896 + 0.964551i $$0.585007\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ −36.0000 −1.18495
$$924$$ 0 0
$$925$$ 44.0000 1.44671
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 34.0000 1.11550 0.557752 0.830008i $$-0.311664\pi$$
0.557752 + 0.830008i $$0.311664\pi$$
$$930$$ 0 0
$$931$$ −12.0000 −0.393284
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 22.0000 0.718709 0.359354 0.933201i $$-0.382997\pi$$
0.359354 + 0.933201i $$0.382997\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 48.0000 1.56476 0.782378 0.622804i $$-0.214007\pi$$
0.782378 + 0.622804i $$0.214007\pi$$
$$942$$ 0 0
$$943$$ 60.0000 1.95387
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 24.0000 0.779895 0.389948 0.920837i $$-0.372493\pi$$
0.389948 + 0.920837i $$0.372493\pi$$
$$948$$ 0 0
$$949$$ 12.0000 0.389536
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −22.0000 −0.712650 −0.356325 0.934362i $$-0.615970\pi$$
−0.356325 + 0.934362i $$0.615970\pi$$
$$954$$ 0 0
$$955$$ 16.0000 0.517748
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 12.0000 0.387500
$$960$$ 0 0
$$961$$ 5.00000 0.161290
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ −24.0000 −0.772587
$$966$$ 0 0
$$967$$ 44.0000 1.41494 0.707472 0.706741i $$-0.249835\pi$$
0.707472 + 0.706741i $$0.249835\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −20.0000 −0.641831 −0.320915 0.947108i $$-0.603990\pi$$
−0.320915 + 0.947108i $$0.603990\pi$$
$$972$$ 0 0
$$973$$ 16.0000 0.512936
$$974$$ 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
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −38.0000 −1.21201 −0.606006 0.795460i $$-0.707229\pi$$
−0.606006 + 0.795460i $$0.707229\pi$$
$$984$$ 0 0
$$985$$ −32.0000 −1.01960
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −24.0000 −0.763156
$$990$$ 0 0
$$991$$ 34.0000 1.08005 0.540023 0.841650i $$-0.318416\pi$$
0.540023 + 0.841650i $$0.318416\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 56.0000 1.77532
$$996$$ 0 0
$$997$$ 20.0000 0.633406 0.316703 0.948525i $$-0.397424\pi$$
0.316703 + 0.948525i $$0.397424\pi$$
$$998$$ 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 9792.2.a.b.1.1 1
3.2 odd 2 3264.2.a.p.1.1 1
4.3 odd 2 9792.2.a.a.1.1 1
8.3 odd 2 306.2.a.d.1.1 1
8.5 even 2 2448.2.a.t.1.1 1
12.11 even 2 3264.2.a.bf.1.1 1
24.5 odd 2 816.2.a.h.1.1 1
24.11 even 2 102.2.a.a.1.1 1
40.19 odd 2 7650.2.a.z.1.1 1
120.59 even 2 2550.2.a.be.1.1 1
120.83 odd 4 2550.2.d.q.2449.2 2
120.107 odd 4 2550.2.d.q.2449.1 2
136.67 odd 2 5202.2.a.g.1.1 1
168.83 odd 2 4998.2.a.x.1.1 1
408.59 even 8 1734.2.f.g.829.2 4
408.83 even 8 1734.2.f.g.1483.2 4
408.155 even 8 1734.2.f.g.1483.1 4
408.179 even 8 1734.2.f.g.829.1 4
408.203 even 2 1734.2.a.h.1.1 1
408.251 even 4 1734.2.b.d.577.1 2
408.395 even 4 1734.2.b.d.577.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
102.2.a.a.1.1 1 24.11 even 2
306.2.a.d.1.1 1 8.3 odd 2
816.2.a.h.1.1 1 24.5 odd 2
1734.2.a.h.1.1 1 408.203 even 2
1734.2.b.d.577.1 2 408.251 even 4
1734.2.b.d.577.2 2 408.395 even 4
1734.2.f.g.829.1 4 408.179 even 8
1734.2.f.g.829.2 4 408.59 even 8
1734.2.f.g.1483.1 4 408.155 even 8
1734.2.f.g.1483.2 4 408.83 even 8
2448.2.a.t.1.1 1 8.5 even 2
2550.2.a.be.1.1 1 120.59 even 2
2550.2.d.q.2449.1 2 120.107 odd 4
2550.2.d.q.2449.2 2 120.83 odd 4
3264.2.a.p.1.1 1 3.2 odd 2
3264.2.a.bf.1.1 1 12.11 even 2
4998.2.a.x.1.1 1 168.83 odd 2
5202.2.a.g.1.1 1 136.67 odd 2
7650.2.a.z.1.1 1 40.19 odd 2
9792.2.a.a.1.1 1 4.3 odd 2
9792.2.a.b.1.1 1 1.1 even 1 trivial