# Properties

 Label 1620.2.a.c.1.1 Level $1620$ Weight $2$ Character 1620.1 Self dual yes Analytic conductor $12.936$ 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] = [1620,2,Mod(1,1620)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1620, 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("1620.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1620 = 2^{2} \cdot 3^{4} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1620.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: $$12.9357651274$$ 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 $$\chi$$ $$=$$ 1620.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-1.00000 q^{5} +2.00000 q^{7} +O(q^{10})$$ $$q-1.00000 q^{5} +2.00000 q^{7} +3.00000 q^{11} -4.00000 q^{13} +6.00000 q^{17} -7.00000 q^{19} +6.00000 q^{23} +1.00000 q^{25} +3.00000 q^{29} +5.00000 q^{31} -2.00000 q^{35} -4.00000 q^{37} +3.00000 q^{41} +8.00000 q^{43} -3.00000 q^{49} -6.00000 q^{53} -3.00000 q^{55} -3.00000 q^{59} +14.0000 q^{61} +4.00000 q^{65} +2.00000 q^{67} +15.0000 q^{71} -10.0000 q^{73} +6.00000 q^{77} +8.00000 q^{79} -6.00000 q^{85} +15.0000 q^{89} -8.00000 q^{91} +7.00000 q^{95} +8.00000 q^{97} +O(q^{100})$$

## 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
$$6$$ 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
$$11$$ 3.00000 0.904534 0.452267 0.891883i $$-0.350615\pi$$
0.452267 + 0.891883i $$0.350615\pi$$
$$12$$ 0 0
$$13$$ −4.00000 −1.10940 −0.554700 0.832050i $$-0.687167\pi$$
−0.554700 + 0.832050i $$0.687167\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 6.00000 1.45521 0.727607 0.685994i $$-0.240633\pi$$
0.727607 + 0.685994i $$0.240633\pi$$
$$18$$ 0 0
$$19$$ −7.00000 −1.60591 −0.802955 0.596040i $$-0.796740\pi$$
−0.802955 + 0.596040i $$0.796740\pi$$
$$20$$ 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
$$25$$ 1.00000 0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 3.00000 0.557086 0.278543 0.960424i $$-0.410149\pi$$
0.278543 + 0.960424i $$0.410149\pi$$
$$30$$ 0 0
$$31$$ 5.00000 0.898027 0.449013 0.893525i $$-0.351776\pi$$
0.449013 + 0.893525i $$0.351776\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −2.00000 −0.338062
$$36$$ 0 0
$$37$$ −4.00000 −0.657596 −0.328798 0.944400i $$-0.606644\pi$$
−0.328798 + 0.944400i $$0.606644\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 3.00000 0.468521 0.234261 0.972174i $$-0.424733\pi$$
0.234261 + 0.972174i $$0.424733\pi$$
$$42$$ 0 0
$$43$$ 8.00000 1.21999 0.609994 0.792406i $$-0.291172\pi$$
0.609994 + 0.792406i $$0.291172\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ −3.00000 −0.428571
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −6.00000 −0.824163 −0.412082 0.911147i $$-0.635198\pi$$
−0.412082 + 0.911147i $$0.635198\pi$$
$$54$$ 0 0
$$55$$ −3.00000 −0.404520
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −3.00000 −0.390567 −0.195283 0.980747i $$-0.562563\pi$$
−0.195283 + 0.980747i $$0.562563\pi$$
$$60$$ 0 0
$$61$$ 14.0000 1.79252 0.896258 0.443533i $$-0.146275\pi$$
0.896258 + 0.443533i $$0.146275\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 4.00000 0.496139
$$66$$ 0 0
$$67$$ 2.00000 0.244339 0.122169 0.992509i $$-0.461015\pi$$
0.122169 + 0.992509i $$0.461015\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 15.0000 1.78017 0.890086 0.455792i $$-0.150644\pi$$
0.890086 + 0.455792i $$0.150644\pi$$
$$72$$ 0 0
$$73$$ −10.0000 −1.17041 −0.585206 0.810885i $$-0.698986\pi$$
−0.585206 + 0.810885i $$0.698986\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 6.00000 0.683763
$$78$$ 0 0
$$79$$ 8.00000 0.900070 0.450035 0.893011i $$-0.351411\pi$$
0.450035 + 0.893011i $$0.351411\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ −6.00000 −0.650791
$$86$$ 0 0
$$87$$ 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
$$91$$ −8.00000 −0.838628
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 7.00000 0.718185
$$96$$ 0 0
$$97$$ 8.00000 0.812277 0.406138 0.913812i $$-0.366875\pi$$
0.406138 + 0.913812i $$0.366875\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −3.00000 −0.298511 −0.149256 0.988799i $$-0.547688\pi$$
−0.149256 + 0.988799i $$0.547688\pi$$
$$102$$ 0 0
$$103$$ 2.00000 0.197066 0.0985329 0.995134i $$-0.468585\pi$$
0.0985329 + 0.995134i $$0.468585\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −6.00000 −0.580042 −0.290021 0.957020i $$-0.593662\pi$$
−0.290021 + 0.957020i $$0.593662\pi$$
$$108$$ 0 0
$$109$$ 11.0000 1.05361 0.526804 0.849987i $$-0.323390\pi$$
0.526804 + 0.849987i $$0.323390\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 18.0000 1.69330 0.846649 0.532152i $$-0.178617\pi$$
0.846649 + 0.532152i $$0.178617\pi$$
$$114$$ 0 0
$$115$$ −6.00000 −0.559503
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 12.0000 1.10004
$$120$$ 0 0
$$121$$ −2.00000 −0.181818
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ 2.00000 0.177471 0.0887357 0.996055i $$-0.471717\pi$$
0.0887357 + 0.996055i $$0.471717\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −15.0000 −1.31056 −0.655278 0.755388i $$-0.727449\pi$$
−0.655278 + 0.755388i $$0.727449\pi$$
$$132$$ 0 0
$$133$$ −14.0000 −1.21395
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 12.0000 1.02523 0.512615 0.858619i $$-0.328677\pi$$
0.512615 + 0.858619i $$0.328677\pi$$
$$138$$ 0 0
$$139$$ −1.00000 −0.0848189 −0.0424094 0.999100i $$-0.513503\pi$$
−0.0424094 + 0.999100i $$0.513503\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −12.0000 −1.00349
$$144$$ 0 0
$$145$$ −3.00000 −0.249136
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 6.00000 0.491539 0.245770 0.969328i $$-0.420959\pi$$
0.245770 + 0.969328i $$0.420959\pi$$
$$150$$ 0 0
$$151$$ 5.00000 0.406894 0.203447 0.979086i $$-0.434786\pi$$
0.203447 + 0.979086i $$0.434786\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −5.00000 −0.401610
$$156$$ 0 0
$$157$$ −4.00000 −0.319235 −0.159617 0.987179i $$-0.551026\pi$$
−0.159617 + 0.987179i $$0.551026\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 12.0000 0.945732
$$162$$ 0 0
$$163$$ −22.0000 −1.72317 −0.861586 0.507611i $$-0.830529\pi$$
−0.861586 + 0.507611i $$0.830529\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −18.0000 −1.39288 −0.696441 0.717614i $$-0.745234\pi$$
−0.696441 + 0.717614i $$0.745234\pi$$
$$168$$ 0 0
$$169$$ 3.00000 0.230769
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 18.0000 1.36851 0.684257 0.729241i $$-0.260127\pi$$
0.684257 + 0.729241i $$0.260127\pi$$
$$174$$ 0 0
$$175$$ 2.00000 0.151186
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −15.0000 −1.12115 −0.560576 0.828103i $$-0.689420\pi$$
−0.560576 + 0.828103i $$0.689420\pi$$
$$180$$ 0 0
$$181$$ 23.0000 1.70958 0.854788 0.518977i $$-0.173687\pi$$
0.854788 + 0.518977i $$0.173687\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 4.00000 0.294086
$$186$$ 0 0
$$187$$ 18.0000 1.31629
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −21.0000 −1.51951 −0.759753 0.650211i $$-0.774680\pi$$
−0.759753 + 0.650211i $$0.774680\pi$$
$$192$$ 0 0
$$193$$ −16.0000 −1.15171 −0.575853 0.817554i $$-0.695330\pi$$
−0.575853 + 0.817554i $$0.695330\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 24.0000 1.70993 0.854965 0.518686i $$-0.173579\pi$$
0.854965 + 0.518686i $$0.173579\pi$$
$$198$$ 0 0
$$199$$ −16.0000 −1.13421 −0.567105 0.823646i $$-0.691937\pi$$
−0.567105 + 0.823646i $$0.691937\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 6.00000 0.421117
$$204$$ 0 0
$$205$$ −3.00000 −0.209529
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −21.0000 −1.45260
$$210$$ 0 0
$$211$$ 5.00000 0.344214 0.172107 0.985078i $$-0.444942\pi$$
0.172107 + 0.985078i $$0.444942\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −8.00000 −0.545595
$$216$$ 0 0
$$217$$ 10.0000 0.678844
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −24.0000 −1.61441
$$222$$ 0 0
$$223$$ −28.0000 −1.87502 −0.937509 0.347960i $$-0.886874\pi$$
−0.937509 + 0.347960i $$0.886874\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −18.0000 −1.19470 −0.597351 0.801980i $$-0.703780\pi$$
−0.597351 + 0.801980i $$0.703780\pi$$
$$228$$ 0 0
$$229$$ 14.0000 0.925146 0.462573 0.886581i $$-0.346926\pi$$
0.462573 + 0.886581i $$0.346926\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −24.0000 −1.57229 −0.786146 0.618041i $$-0.787927\pi$$
−0.786146 + 0.618041i $$0.787927\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ −7.00000 −0.450910 −0.225455 0.974254i $$-0.572387\pi$$
−0.225455 + 0.974254i $$0.572387\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 3.00000 0.191663
$$246$$ 0 0
$$247$$ 28.0000 1.78160
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 12.0000 0.757433 0.378717 0.925513i $$-0.376365\pi$$
0.378717 + 0.925513i $$0.376365\pi$$
$$252$$ 0 0
$$253$$ 18.0000 1.13165
$$254$$ 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
$$263$$ 6.00000 0.369976 0.184988 0.982741i $$-0.440775\pi$$
0.184988 + 0.982741i $$0.440775\pi$$
$$264$$ 0 0
$$265$$ 6.00000 0.368577
$$266$$ 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
$$271$$ 8.00000 0.485965 0.242983 0.970031i $$-0.421874\pi$$
0.242983 + 0.970031i $$0.421874\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 3.00000 0.180907
$$276$$ 0 0
$$277$$ −28.0000 −1.68236 −0.841178 0.540758i $$-0.818138\pi$$
−0.841178 + 0.540758i $$0.818138\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 30.0000 1.78965 0.894825 0.446417i $$-0.147300\pi$$
0.894825 + 0.446417i $$0.147300\pi$$
$$282$$ 0 0
$$283$$ −22.0000 −1.30776 −0.653882 0.756596i $$-0.726861\pi$$
−0.653882 + 0.756596i $$0.726861\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 6.00000 0.354169
$$288$$ 0 0
$$289$$ 19.0000 1.11765
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 24.0000 1.40209 0.701047 0.713115i $$-0.252716\pi$$
0.701047 + 0.713115i $$0.252716\pi$$
$$294$$ 0 0
$$295$$ 3.00000 0.174667
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −24.0000 −1.38796
$$300$$ 0 0
$$301$$ 16.0000 0.922225
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −14.0000 −0.801638
$$306$$ 0 0
$$307$$ 20.0000 1.14146 0.570730 0.821138i $$-0.306660\pi$$
0.570730 + 0.821138i $$0.306660\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −15.0000 −0.850572 −0.425286 0.905059i $$-0.639826\pi$$
−0.425286 + 0.905059i $$0.639826\pi$$
$$312$$ 0 0
$$313$$ −16.0000 −0.904373 −0.452187 0.891923i $$-0.649356\pi$$
−0.452187 + 0.891923i $$0.649356\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −12.0000 −0.673987 −0.336994 0.941507i $$-0.609410\pi$$
−0.336994 + 0.941507i $$0.609410\pi$$
$$318$$ 0 0
$$319$$ 9.00000 0.503903
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −42.0000 −2.33694
$$324$$ 0 0
$$325$$ −4.00000 −0.221880
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 17.0000 0.934405 0.467202 0.884150i $$-0.345262\pi$$
0.467202 + 0.884150i $$0.345262\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −2.00000 −0.109272
$$336$$ 0 0
$$337$$ −28.0000 −1.52526 −0.762629 0.646837i $$-0.776092\pi$$
−0.762629 + 0.646837i $$0.776092\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 15.0000 0.812296
$$342$$ 0 0
$$343$$ −20.0000 −1.07990
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 18.0000 0.966291 0.483145 0.875540i $$-0.339494\pi$$
0.483145 + 0.875540i $$0.339494\pi$$
$$348$$ 0 0
$$349$$ −7.00000 −0.374701 −0.187351 0.982293i $$-0.559990\pi$$
−0.187351 + 0.982293i $$0.559990\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −24.0000 −1.27739 −0.638696 0.769460i $$-0.720526\pi$$
−0.638696 + 0.769460i $$0.720526\pi$$
$$354$$ 0 0
$$355$$ −15.0000 −0.796117
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 27.0000 1.42501 0.712503 0.701669i $$-0.247562\pi$$
0.712503 + 0.701669i $$0.247562\pi$$
$$360$$ 0 0
$$361$$ 30.0000 1.57895
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 10.0000 0.523424
$$366$$ 0 0
$$367$$ −22.0000 −1.14839 −0.574195 0.818718i $$-0.694685\pi$$
−0.574195 + 0.818718i $$0.694685\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −12.0000 −0.623009
$$372$$ 0 0
$$373$$ −22.0000 −1.13912 −0.569558 0.821951i $$-0.692886\pi$$
−0.569558 + 0.821951i $$0.692886\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −12.0000 −0.618031
$$378$$ 0 0
$$379$$ 32.0000 1.64373 0.821865 0.569683i $$-0.192934\pi$$
0.821865 + 0.569683i $$0.192934\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −24.0000 −1.22634 −0.613171 0.789950i $$-0.710106\pi$$
−0.613171 + 0.789950i $$0.710106\pi$$
$$384$$ 0 0
$$385$$ −6.00000 −0.305788
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 6.00000 0.304212 0.152106 0.988364i $$-0.451394\pi$$
0.152106 + 0.988364i $$0.451394\pi$$
$$390$$ 0 0
$$391$$ 36.0000 1.82060
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −8.00000 −0.402524
$$396$$ 0 0
$$397$$ 2.00000 0.100377 0.0501886 0.998740i $$-0.484018\pi$$
0.0501886 + 0.998740i $$0.484018\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −6.00000 −0.299626 −0.149813 0.988714i $$-0.547867\pi$$
−0.149813 + 0.988714i $$0.547867\pi$$
$$402$$ 0 0
$$403$$ −20.0000 −0.996271
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −12.0000 −0.594818
$$408$$ 0 0
$$409$$ −10.0000 −0.494468 −0.247234 0.968956i $$-0.579522\pi$$
−0.247234 + 0.968956i $$0.579522\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −6.00000 −0.295241
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −36.0000 −1.75872 −0.879358 0.476162i $$-0.842028\pi$$
−0.879358 + 0.476162i $$0.842028\pi$$
$$420$$ 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
$$425$$ 6.00000 0.291043
$$426$$ 0 0
$$427$$ 28.0000 1.35501
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −3.00000 −0.144505 −0.0722525 0.997386i $$-0.523019\pi$$
−0.0722525 + 0.997386i $$0.523019\pi$$
$$432$$ 0 0
$$433$$ 2.00000 0.0961139 0.0480569 0.998845i $$-0.484697\pi$$
0.0480569 + 0.998845i $$0.484697\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −42.0000 −2.00913
$$438$$ 0 0
$$439$$ −19.0000 −0.906821 −0.453410 0.891302i $$-0.649793\pi$$
−0.453410 + 0.891302i $$0.649793\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$444$$ 0 0
$$445$$ −15.0000 −0.711068
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 9.00000 0.424736 0.212368 0.977190i $$-0.431882\pi$$
0.212368 + 0.977190i $$0.431882\pi$$
$$450$$ 0 0
$$451$$ 9.00000 0.423793
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 8.00000 0.375046
$$456$$ 0 0
$$457$$ 8.00000 0.374224 0.187112 0.982339i $$-0.440087\pi$$
0.187112 + 0.982339i $$0.440087\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −15.0000 −0.698620 −0.349310 0.937007i $$-0.613584\pi$$
−0.349310 + 0.937007i $$0.613584\pi$$
$$462$$ 0 0
$$463$$ 14.0000 0.650635 0.325318 0.945605i $$-0.394529\pi$$
0.325318 + 0.945605i $$0.394529\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −6.00000 −0.277647 −0.138823 0.990317i $$-0.544332\pi$$
−0.138823 + 0.990317i $$0.544332\pi$$
$$468$$ 0 0
$$469$$ 4.00000 0.184703
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 24.0000 1.10352
$$474$$ 0 0
$$475$$ −7.00000 −0.321182
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 27.0000 1.23366 0.616831 0.787096i $$-0.288416\pi$$
0.616831 + 0.787096i $$0.288416\pi$$
$$480$$ 0 0
$$481$$ 16.0000 0.729537
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −8.00000 −0.363261
$$486$$ 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
$$491$$ −39.0000 −1.76005 −0.880023 0.474932i $$-0.842473\pi$$
−0.880023 + 0.474932i $$0.842473\pi$$
$$492$$ 0 0
$$493$$ 18.0000 0.810679
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 30.0000 1.34568
$$498$$ 0 0
$$499$$ 5.00000 0.223831 0.111915 0.993718i $$-0.464301\pi$$
0.111915 + 0.993718i $$0.464301\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −36.0000 −1.60516 −0.802580 0.596544i $$-0.796540\pi$$
−0.802580 + 0.596544i $$0.796540\pi$$
$$504$$ 0 0
$$505$$ 3.00000 0.133498
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 30.0000 1.32973 0.664863 0.746965i $$-0.268490\pi$$
0.664863 + 0.746965i $$0.268490\pi$$
$$510$$ 0 0
$$511$$ −20.0000 −0.884748
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −2.00000 −0.0881305
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 42.0000 1.84005 0.920027 0.391856i $$-0.128167\pi$$
0.920027 + 0.391856i $$0.128167\pi$$
$$522$$ 0 0
$$523$$ −28.0000 −1.22435 −0.612177 0.790721i $$-0.709706\pi$$
−0.612177 + 0.790721i $$0.709706\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 30.0000 1.30682
$$528$$ 0 0
$$529$$ 13.0000 0.565217
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −12.0000 −0.519778
$$534$$ 0 0
$$535$$ 6.00000 0.259403
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −9.00000 −0.387657
$$540$$ 0 0
$$541$$ −13.0000 −0.558914 −0.279457 0.960158i $$-0.590154\pi$$
−0.279457 + 0.960158i $$0.590154\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −11.0000 −0.471188
$$546$$ 0 0
$$547$$ 32.0000 1.36822 0.684111 0.729378i $$-0.260191\pi$$
0.684111 + 0.729378i $$0.260191\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −21.0000 −0.894630
$$552$$ 0 0
$$553$$ 16.0000 0.680389
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 24.0000 1.01691 0.508456 0.861088i $$-0.330216\pi$$
0.508456 + 0.861088i $$0.330216\pi$$
$$558$$ 0 0
$$559$$ −32.0000 −1.35346
$$560$$ 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
$$565$$ −18.0000 −0.757266
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −3.00000 −0.125767 −0.0628833 0.998021i $$-0.520030\pi$$
−0.0628833 + 0.998021i $$0.520030\pi$$
$$570$$ 0 0
$$571$$ −37.0000 −1.54840 −0.774201 0.632940i $$-0.781848\pi$$
−0.774201 + 0.632940i $$0.781848\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 6.00000 0.250217
$$576$$ 0 0
$$577$$ 26.0000 1.08239 0.541197 0.840896i $$-0.317971\pi$$
0.541197 + 0.840896i $$0.317971\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −18.0000 −0.745484
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −12.0000 −0.495293 −0.247647 0.968850i $$-0.579657\pi$$
−0.247647 + 0.968850i $$0.579657\pi$$
$$588$$ 0 0
$$589$$ −35.0000 −1.44215
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −30.0000 −1.23195 −0.615976 0.787765i $$-0.711238\pi$$
−0.615976 + 0.787765i $$0.711238\pi$$
$$594$$ 0 0
$$595$$ −12.0000 −0.491952
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −39.0000 −1.59350 −0.796748 0.604311i $$-0.793448\pi$$
−0.796748 + 0.604311i $$0.793448\pi$$
$$600$$ 0 0
$$601$$ 17.0000 0.693444 0.346722 0.937968i $$-0.387295\pi$$
0.346722 + 0.937968i $$0.387295\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 2.00000 0.0813116
$$606$$ 0 0
$$607$$ 8.00000 0.324710 0.162355 0.986732i $$-0.448091\pi$$
0.162355 + 0.986732i $$0.448091\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 8.00000 0.323117 0.161558 0.986863i $$-0.448348\pi$$
0.161558 + 0.986863i $$0.448348\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −24.0000 −0.966204 −0.483102 0.875564i $$-0.660490\pi$$
−0.483102 + 0.875564i $$0.660490\pi$$
$$618$$ 0 0
$$619$$ −4.00000 −0.160774 −0.0803868 0.996764i $$-0.525616\pi$$
−0.0803868 + 0.996764i $$0.525616\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 30.0000 1.20192
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −24.0000 −0.956943
$$630$$ 0 0
$$631$$ 5.00000 0.199047 0.0995234 0.995035i $$-0.468268\pi$$
0.0995234 + 0.995035i $$0.468268\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −2.00000 −0.0793676
$$636$$ 0 0
$$637$$ 12.0000 0.475457
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −33.0000 −1.30342 −0.651711 0.758468i $$-0.725948\pi$$
−0.651711 + 0.758468i $$0.725948\pi$$
$$642$$ 0 0
$$643$$ −40.0000 −1.57745 −0.788723 0.614749i $$-0.789257\pi$$
−0.788723 + 0.614749i $$0.789257\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 18.0000 0.707653 0.353827 0.935311i $$-0.384880\pi$$
0.353827 + 0.935311i $$0.384880\pi$$
$$648$$ 0 0
$$649$$ −9.00000 −0.353281
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 24.0000 0.939193 0.469596 0.882881i $$-0.344399\pi$$
0.469596 + 0.882881i $$0.344399\pi$$
$$654$$ 0 0
$$655$$ 15.0000 0.586098
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 24.0000 0.934907 0.467454 0.884018i $$-0.345171\pi$$
0.467454 + 0.884018i $$0.345171\pi$$
$$660$$ 0 0
$$661$$ −7.00000 −0.272268 −0.136134 0.990690i $$-0.543468\pi$$
−0.136134 + 0.990690i $$0.543468\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 14.0000 0.542897
$$666$$ 0 0
$$667$$ 18.0000 0.696963
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 42.0000 1.62139
$$672$$ 0 0
$$673$$ −10.0000 −0.385472 −0.192736 0.981251i $$-0.561736\pi$$
−0.192736 + 0.981251i $$0.561736\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 6.00000 0.230599 0.115299 0.993331i $$-0.463217\pi$$
0.115299 + 0.993331i $$0.463217\pi$$
$$678$$ 0 0
$$679$$ 16.0000 0.614024
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 36.0000 1.37750 0.688751 0.724998i $$-0.258159\pi$$
0.688751 + 0.724998i $$0.258159\pi$$
$$684$$ 0 0
$$685$$ −12.0000 −0.458496
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 24.0000 0.914327
$$690$$ 0 0
$$691$$ 44.0000 1.67384 0.836919 0.547326i $$-0.184354\pi$$
0.836919 + 0.547326i $$0.184354\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 1.00000 0.0379322
$$696$$ 0 0
$$697$$ 18.0000 0.681799
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 3.00000 0.113308 0.0566542 0.998394i $$-0.481957\pi$$
0.0566542 + 0.998394i $$0.481957\pi$$
$$702$$ 0 0
$$703$$ 28.0000 1.05604
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −6.00000 −0.225653
$$708$$ 0 0
$$709$$ 26.0000 0.976450 0.488225 0.872718i $$-0.337644\pi$$
0.488225 + 0.872718i $$0.337644\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 30.0000 1.12351
$$714$$ 0 0
$$715$$ 12.0000 0.448775
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 9.00000 0.335643 0.167822 0.985817i $$-0.446327\pi$$
0.167822 + 0.985817i $$0.446327\pi$$
$$720$$ 0 0
$$721$$ 4.00000 0.148968
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 3.00000 0.111417
$$726$$ 0 0
$$727$$ 44.0000 1.63187 0.815935 0.578144i $$-0.196223\pi$$
0.815935 + 0.578144i $$0.196223\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 48.0000 1.77534
$$732$$ 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
$$737$$ 6.00000 0.221013
$$738$$ 0 0
$$739$$ −25.0000 −0.919640 −0.459820 0.888012i $$-0.652086\pi$$
−0.459820 + 0.888012i $$0.652086\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 54.0000 1.98107 0.990534 0.137268i $$-0.0438322\pi$$
0.990534 + 0.137268i $$0.0438322\pi$$
$$744$$ 0 0
$$745$$ −6.00000 −0.219823
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −12.0000 −0.438470
$$750$$ 0 0
$$751$$ 8.00000 0.291924 0.145962 0.989290i $$-0.453372\pi$$
0.145962 + 0.989290i $$0.453372\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −5.00000 −0.181969
$$756$$ 0 0
$$757$$ −28.0000 −1.01768 −0.508839 0.860862i $$-0.669925\pi$$
−0.508839 + 0.860862i $$0.669925\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 9.00000 0.326250 0.163125 0.986605i $$-0.447843\pi$$
0.163125 + 0.986605i $$0.447843\pi$$
$$762$$ 0 0
$$763$$ 22.0000 0.796453
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 12.0000 0.433295
$$768$$ 0 0
$$769$$ 41.0000 1.47850 0.739249 0.673432i $$-0.235181\pi$$
0.739249 + 0.673432i $$0.235181\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 36.0000 1.29483 0.647415 0.762138i $$-0.275850\pi$$
0.647415 + 0.762138i $$0.275850\pi$$
$$774$$ 0 0
$$775$$ 5.00000 0.179605
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −21.0000 −0.752403
$$780$$ 0 0
$$781$$ 45.0000 1.61023
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 4.00000 0.142766
$$786$$ 0 0
$$787$$ −34.0000 −1.21197 −0.605985 0.795476i $$-0.707221\pi$$
−0.605985 + 0.795476i $$0.707221\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 36.0000 1.28001
$$792$$ 0 0
$$793$$ −56.0000 −1.98862
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −30.0000 −1.05868
$$804$$ 0 0
$$805$$ −12.0000 −0.422944
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 15.0000 0.527372 0.263686 0.964609i $$-0.415062\pi$$
0.263686 + 0.964609i $$0.415062\pi$$
$$810$$ 0 0
$$811$$ −7.00000 −0.245803 −0.122902 0.992419i $$-0.539220\pi$$
−0.122902 + 0.992419i $$0.539220\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 22.0000 0.770626
$$816$$ 0 0
$$817$$ −56.0000 −1.95919
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 15.0000 0.523504 0.261752 0.965135i $$-0.415700\pi$$
0.261752 + 0.965135i $$0.415700\pi$$
$$822$$ 0 0
$$823$$ 14.0000 0.488009 0.244005 0.969774i $$-0.421539\pi$$
0.244005 + 0.969774i $$0.421539\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −12.0000 −0.417281 −0.208640 0.977992i $$-0.566904\pi$$
−0.208640 + 0.977992i $$0.566904\pi$$
$$828$$ 0 0
$$829$$ −25.0000 −0.868286 −0.434143 0.900844i $$-0.642949\pi$$
−0.434143 + 0.900844i $$0.642949\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −18.0000 −0.623663
$$834$$ 0 0
$$835$$ 18.0000 0.622916
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −9.00000 −0.310715 −0.155357 0.987858i $$-0.549653\pi$$
−0.155357 + 0.987858i $$0.549653\pi$$
$$840$$ 0 0
$$841$$ −20.0000 −0.689655
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ −3.00000 −0.103203
$$846$$ 0 0
$$847$$ −4.00000 −0.137442
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −24.0000 −0.822709
$$852$$ 0 0
$$853$$ 14.0000 0.479351 0.239675 0.970853i $$-0.422959\pi$$
0.239675 + 0.970853i $$0.422959\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$858$$ 0 0
$$859$$ −55.0000 −1.87658 −0.938288 0.345855i $$-0.887589\pi$$
−0.938288 + 0.345855i $$0.887589\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 6.00000 0.204242 0.102121 0.994772i $$-0.467437\pi$$
0.102121 + 0.994772i $$0.467437\pi$$
$$864$$ 0 0
$$865$$ −18.0000 −0.612018
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 24.0000 0.814144
$$870$$ 0 0
$$871$$ −8.00000 −0.271070
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ −2.00000 −0.0676123
$$876$$ 0 0
$$877$$ −28.0000 −0.945493 −0.472746 0.881199i $$-0.656737\pi$$
−0.472746 + 0.881199i $$0.656737\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −33.0000 −1.11180 −0.555899 0.831250i $$-0.687626\pi$$
−0.555899 + 0.831250i $$0.687626\pi$$
$$882$$ 0 0
$$883$$ 2.00000 0.0673054 0.0336527 0.999434i $$-0.489286\pi$$
0.0336527 + 0.999434i $$0.489286\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 48.0000 1.61168 0.805841 0.592132i $$-0.201714\pi$$
0.805841 + 0.592132i $$0.201714\pi$$
$$888$$ 0 0
$$889$$ 4.00000 0.134156
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 15.0000 0.501395
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 15.0000 0.500278
$$900$$ 0 0
$$901$$ −36.0000 −1.19933
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −23.0000 −0.764546
$$906$$ 0 0
$$907$$ 26.0000 0.863316 0.431658 0.902037i $$-0.357929\pi$$
0.431658 + 0.902037i $$0.357929\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 45.0000 1.49092 0.745458 0.666552i $$-0.232231\pi$$
0.745458 + 0.666552i $$0.232231\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −30.0000 −0.990687
$$918$$ 0 0
$$919$$ 11.0000 0.362857 0.181428 0.983404i $$-0.441928\pi$$
0.181428 + 0.983404i $$0.441928\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ −60.0000 −1.97492
$$924$$ 0 0
$$925$$ −4.00000 −0.131519
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 9.00000 0.295280 0.147640 0.989041i $$-0.452832\pi$$
0.147640 + 0.989041i $$0.452832\pi$$
$$930$$ 0 0
$$931$$ 21.0000 0.688247
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −18.0000 −0.588663
$$936$$ 0 0
$$937$$ −58.0000 −1.89478 −0.947389 0.320085i $$-0.896288\pi$$
−0.947389 + 0.320085i $$0.896288\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 6.00000 0.195594 0.0977972 0.995206i $$-0.468820\pi$$
0.0977972 + 0.995206i $$0.468820\pi$$
$$942$$ 0 0
$$943$$ 18.0000 0.586161
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −54.0000 −1.75476 −0.877382 0.479792i $$-0.840712\pi$$
−0.877382 + 0.479792i $$0.840712\pi$$
$$948$$ 0 0
$$949$$ 40.0000 1.29845
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$954$$ 0 0
$$955$$ 21.0000 0.679544
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 24.0000 0.775000
$$960$$ 0 0
$$961$$ −6.00000 −0.193548
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 16.0000 0.515058
$$966$$ 0 0
$$967$$ 2.00000 0.0643157 0.0321578 0.999483i $$-0.489762\pi$$
0.0321578 + 0.999483i $$0.489762\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −45.0000 −1.44412 −0.722059 0.691831i $$-0.756804\pi$$
−0.722059 + 0.691831i $$0.756804\pi$$
$$972$$ 0 0
$$973$$ −2.00000 −0.0641171
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 24.0000 0.767828 0.383914 0.923369i $$-0.374576\pi$$
0.383914 + 0.923369i $$0.374576\pi$$
$$978$$ 0 0
$$979$$ 45.0000 1.43821
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 42.0000 1.33959 0.669796 0.742545i $$-0.266382\pi$$
0.669796 + 0.742545i $$0.266382\pi$$
$$984$$ 0 0
$$985$$ −24.0000 −0.764704
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 48.0000 1.52631
$$990$$ 0 0
$$991$$ −19.0000 −0.603555 −0.301777 0.953378i $$-0.597580\pi$$
−0.301777 + 0.953378i $$0.597580\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 16.0000 0.507234
$$996$$ 0 0
$$997$$ 26.0000 0.823428 0.411714 0.911313i $$-0.364930\pi$$
0.411714 + 0.911313i $$0.364930\pi$$
$$998$$ 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 1620.2.a.c.1.1 1
3.2 odd 2 1620.2.a.f.1.1 yes 1
4.3 odd 2 6480.2.a.b.1.1 1
5.2 odd 4 8100.2.d.i.649.2 2
5.3 odd 4 8100.2.d.i.649.1 2
5.4 even 2 8100.2.a.e.1.1 1
9.2 odd 6 1620.2.i.c.1081.1 2
9.4 even 3 1620.2.i.g.541.1 2
9.5 odd 6 1620.2.i.c.541.1 2
9.7 even 3 1620.2.i.g.1081.1 2
12.11 even 2 6480.2.a.p.1.1 1
15.2 even 4 8100.2.d.d.649.2 2
15.8 even 4 8100.2.d.d.649.1 2
15.14 odd 2 8100.2.a.b.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
1620.2.a.c.1.1 1 1.1 even 1 trivial
1620.2.a.f.1.1 yes 1 3.2 odd 2
1620.2.i.c.541.1 2 9.5 odd 6
1620.2.i.c.1081.1 2 9.2 odd 6
1620.2.i.g.541.1 2 9.4 even 3
1620.2.i.g.1081.1 2 9.7 even 3
6480.2.a.b.1.1 1 4.3 odd 2
6480.2.a.p.1.1 1 12.11 even 2
8100.2.a.b.1.1 1 15.14 odd 2
8100.2.a.e.1.1 1 5.4 even 2
8100.2.d.d.649.1 2 15.8 even 4
8100.2.d.d.649.2 2 15.2 even 4
8100.2.d.i.649.1 2 5.3 odd 4
8100.2.d.i.649.2 2 5.2 odd 4