# Properties

 Label 2070.2.a.s.1.1 Level $2070$ Weight $2$ Character 2070.1 Self dual yes Analytic conductor $16.529$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2070.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$16.5290332184$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 690) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 2070.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} +4.00000 q^{7} +1.00000 q^{8} +O(q^{10})$$ $$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} +4.00000 q^{7} +1.00000 q^{8} +1.00000 q^{10} +2.00000 q^{11} +4.00000 q^{14} +1.00000 q^{16} -2.00000 q^{17} +1.00000 q^{20} +2.00000 q^{22} -1.00000 q^{23} +1.00000 q^{25} +4.00000 q^{28} +4.00000 q^{29} +1.00000 q^{32} -2.00000 q^{34} +4.00000 q^{35} +10.0000 q^{37} +1.00000 q^{40} -6.00000 q^{41} +2.00000 q^{43} +2.00000 q^{44} -1.00000 q^{46} -12.0000 q^{47} +9.00000 q^{49} +1.00000 q^{50} -6.00000 q^{53} +2.00000 q^{55} +4.00000 q^{56} +4.00000 q^{58} -12.0000 q^{59} -14.0000 q^{61} +1.00000 q^{64} +2.00000 q^{67} -2.00000 q^{68} +4.00000 q^{70} +2.00000 q^{71} +6.00000 q^{73} +10.0000 q^{74} +8.00000 q^{77} +8.00000 q^{79} +1.00000 q^{80} -6.00000 q^{82} -8.00000 q^{83} -2.00000 q^{85} +2.00000 q^{86} +2.00000 q^{88} +8.00000 q^{89} -1.00000 q^{92} -12.0000 q^{94} +9.00000 q^{98} +O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 0.707107
$$3$$ 0 0
$$4$$ 1.00000 0.500000
$$5$$ 1.00000 0.447214
$$6$$ 0 0
$$7$$ 4.00000 1.51186 0.755929 0.654654i $$-0.227186\pi$$
0.755929 + 0.654654i $$0.227186\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 0 0
$$10$$ 1.00000 0.316228
$$11$$ 2.00000 0.603023 0.301511 0.953463i $$-0.402509\pi$$
0.301511 + 0.953463i $$0.402509\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 4.00000 1.06904
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ −2.00000 −0.485071 −0.242536 0.970143i $$-0.577979\pi$$
−0.242536 + 0.970143i $$0.577979\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ 1.00000 0.223607
$$21$$ 0 0
$$22$$ 2.00000 0.426401
$$23$$ −1.00000 −0.208514
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 4.00000 0.755929
$$29$$ 4.00000 0.742781 0.371391 0.928477i $$-0.378881\pi$$
0.371391 + 0.928477i $$0.378881\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ 1.00000 0.176777
$$33$$ 0 0
$$34$$ −2.00000 −0.342997
$$35$$ 4.00000 0.676123
$$36$$ 0 0
$$37$$ 10.0000 1.64399 0.821995 0.569495i $$-0.192861\pi$$
0.821995 + 0.569495i $$0.192861\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 1.00000 0.158114
$$41$$ −6.00000 −0.937043 −0.468521 0.883452i $$-0.655213\pi$$
−0.468521 + 0.883452i $$0.655213\pi$$
$$42$$ 0 0
$$43$$ 2.00000 0.304997 0.152499 0.988304i $$-0.451268\pi$$
0.152499 + 0.988304i $$0.451268\pi$$
$$44$$ 2.00000 0.301511
$$45$$ 0 0
$$46$$ −1.00000 −0.147442
$$47$$ −12.0000 −1.75038 −0.875190 0.483779i $$-0.839264\pi$$
−0.875190 + 0.483779i $$0.839264\pi$$
$$48$$ 0 0
$$49$$ 9.00000 1.28571
$$50$$ 1.00000 0.141421
$$51$$ 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
$$55$$ 2.00000 0.269680
$$56$$ 4.00000 0.534522
$$57$$ 0 0
$$58$$ 4.00000 0.525226
$$59$$ −12.0000 −1.56227 −0.781133 0.624364i $$-0.785358\pi$$
−0.781133 + 0.624364i $$0.785358\pi$$
$$60$$ 0 0
$$61$$ −14.0000 −1.79252 −0.896258 0.443533i $$-0.853725\pi$$
−0.896258 + 0.443533i $$0.853725\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 2.00000 0.244339 0.122169 0.992509i $$-0.461015\pi$$
0.122169 + 0.992509i $$0.461015\pi$$
$$68$$ −2.00000 −0.242536
$$69$$ 0 0
$$70$$ 4.00000 0.478091
$$71$$ 2.00000 0.237356 0.118678 0.992933i $$-0.462134\pi$$
0.118678 + 0.992933i $$0.462134\pi$$
$$72$$ 0 0
$$73$$ 6.00000 0.702247 0.351123 0.936329i $$-0.385800\pi$$
0.351123 + 0.936329i $$0.385800\pi$$
$$74$$ 10.0000 1.16248
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 8.00000 0.911685
$$78$$ 0 0
$$79$$ 8.00000 0.900070 0.450035 0.893011i $$-0.351411\pi$$
0.450035 + 0.893011i $$0.351411\pi$$
$$80$$ 1.00000 0.111803
$$81$$ 0 0
$$82$$ −6.00000 −0.662589
$$83$$ −8.00000 −0.878114 −0.439057 0.898459i $$-0.644687\pi$$
−0.439057 + 0.898459i $$0.644687\pi$$
$$84$$ 0 0
$$85$$ −2.00000 −0.216930
$$86$$ 2.00000 0.215666
$$87$$ 0 0
$$88$$ 2.00000 0.213201
$$89$$ 8.00000 0.847998 0.423999 0.905663i $$-0.360626\pi$$
0.423999 + 0.905663i $$0.360626\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −1.00000 −0.104257
$$93$$ 0 0
$$94$$ −12.0000 −1.23771
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$98$$ 9.00000 0.909137
$$99$$ 0 0
$$100$$ 1.00000 0.100000
$$101$$ 12.0000 1.19404 0.597022 0.802225i $$-0.296350\pi$$
0.597022 + 0.802225i $$0.296350\pi$$
$$102$$ 0 0
$$103$$ 4.00000 0.394132 0.197066 0.980390i $$-0.436859\pi$$
0.197066 + 0.980390i $$0.436859\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ −6.00000 −0.582772
$$107$$ 12.0000 1.16008 0.580042 0.814587i $$-0.303036\pi$$
0.580042 + 0.814587i $$0.303036\pi$$
$$108$$ 0 0
$$109$$ 14.0000 1.34096 0.670478 0.741929i $$-0.266089\pi$$
0.670478 + 0.741929i $$0.266089\pi$$
$$110$$ 2.00000 0.190693
$$111$$ 0 0
$$112$$ 4.00000 0.377964
$$113$$ −6.00000 −0.564433 −0.282216 0.959351i $$-0.591070\pi$$
−0.282216 + 0.959351i $$0.591070\pi$$
$$114$$ 0 0
$$115$$ −1.00000 −0.0932505
$$116$$ 4.00000 0.371391
$$117$$ 0 0
$$118$$ −12.0000 −1.10469
$$119$$ −8.00000 −0.733359
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ −14.0000 −1.26750
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 1.00000 0.0894427
$$126$$ 0 0
$$127$$ 6.00000 0.532414 0.266207 0.963916i $$-0.414230\pi$$
0.266207 + 0.963916i $$0.414230\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 2.00000 0.172774
$$135$$ 0 0
$$136$$ −2.00000 −0.171499
$$137$$ 2.00000 0.170872 0.0854358 0.996344i $$-0.472772\pi$$
0.0854358 + 0.996344i $$0.472772\pi$$
$$138$$ 0 0
$$139$$ 20.0000 1.69638 0.848189 0.529694i $$-0.177693\pi$$
0.848189 + 0.529694i $$0.177693\pi$$
$$140$$ 4.00000 0.338062
$$141$$ 0 0
$$142$$ 2.00000 0.167836
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 4.00000 0.332182
$$146$$ 6.00000 0.496564
$$147$$ 0 0
$$148$$ 10.0000 0.821995
$$149$$ 14.0000 1.14692 0.573462 0.819232i $$-0.305600\pi$$
0.573462 + 0.819232i $$0.305600\pi$$
$$150$$ 0 0
$$151$$ −12.0000 −0.976546 −0.488273 0.872691i $$-0.662373\pi$$
−0.488273 + 0.872691i $$0.662373\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 8.00000 0.644658
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −22.0000 −1.75579 −0.877896 0.478852i $$-0.841053\pi$$
−0.877896 + 0.478852i $$0.841053\pi$$
$$158$$ 8.00000 0.636446
$$159$$ 0 0
$$160$$ 1.00000 0.0790569
$$161$$ −4.00000 −0.315244
$$162$$ 0 0
$$163$$ −16.0000 −1.25322 −0.626608 0.779334i $$-0.715557\pi$$
−0.626608 + 0.779334i $$0.715557\pi$$
$$164$$ −6.00000 −0.468521
$$165$$ 0 0
$$166$$ −8.00000 −0.620920
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ −13.0000 −1.00000
$$170$$ −2.00000 −0.153393
$$171$$ 0 0
$$172$$ 2.00000 0.152499
$$173$$ 6.00000 0.456172 0.228086 0.973641i $$-0.426753\pi$$
0.228086 + 0.973641i $$0.426753\pi$$
$$174$$ 0 0
$$175$$ 4.00000 0.302372
$$176$$ 2.00000 0.150756
$$177$$ 0 0
$$178$$ 8.00000 0.599625
$$179$$ −4.00000 −0.298974 −0.149487 0.988764i $$-0.547762\pi$$
−0.149487 + 0.988764i $$0.547762\pi$$
$$180$$ 0 0
$$181$$ −6.00000 −0.445976 −0.222988 0.974821i $$-0.571581\pi$$
−0.222988 + 0.974821i $$0.571581\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −1.00000 −0.0737210
$$185$$ 10.0000 0.735215
$$186$$ 0 0
$$187$$ −4.00000 −0.292509
$$188$$ −12.0000 −0.875190
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ 0 0
$$193$$ −14.0000 −1.00774 −0.503871 0.863779i $$-0.668091\pi$$
−0.503871 + 0.863779i $$0.668091\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 9.00000 0.642857
$$197$$ 6.00000 0.427482 0.213741 0.976890i $$-0.431435\pi$$
0.213741 + 0.976890i $$0.431435\pi$$
$$198$$ 0 0
$$199$$ 16.0000 1.13421 0.567105 0.823646i $$-0.308063\pi$$
0.567105 + 0.823646i $$0.308063\pi$$
$$200$$ 1.00000 0.0707107
$$201$$ 0 0
$$202$$ 12.0000 0.844317
$$203$$ 16.0000 1.12298
$$204$$ 0 0
$$205$$ −6.00000 −0.419058
$$206$$ 4.00000 0.278693
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 4.00000 0.275371 0.137686 0.990476i $$-0.456034\pi$$
0.137686 + 0.990476i $$0.456034\pi$$
$$212$$ −6.00000 −0.412082
$$213$$ 0 0
$$214$$ 12.0000 0.820303
$$215$$ 2.00000 0.136399
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 14.0000 0.948200
$$219$$ 0 0
$$220$$ 2.00000 0.134840
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 2.00000 0.133930 0.0669650 0.997755i $$-0.478668\pi$$
0.0669650 + 0.997755i $$0.478668\pi$$
$$224$$ 4.00000 0.267261
$$225$$ 0 0
$$226$$ −6.00000 −0.399114
$$227$$ −12.0000 −0.796468 −0.398234 0.917284i $$-0.630377\pi$$
−0.398234 + 0.917284i $$0.630377\pi$$
$$228$$ 0 0
$$229$$ −26.0000 −1.71813 −0.859064 0.511868i $$-0.828954\pi$$
−0.859064 + 0.511868i $$0.828954\pi$$
$$230$$ −1.00000 −0.0659380
$$231$$ 0 0
$$232$$ 4.00000 0.262613
$$233$$ −10.0000 −0.655122 −0.327561 0.944830i $$-0.606227\pi$$
−0.327561 + 0.944830i $$0.606227\pi$$
$$234$$ 0 0
$$235$$ −12.0000 −0.782794
$$236$$ −12.0000 −0.781133
$$237$$ 0 0
$$238$$ −8.00000 −0.518563
$$239$$ −22.0000 −1.42306 −0.711531 0.702655i $$-0.751998\pi$$
−0.711531 + 0.702655i $$0.751998\pi$$
$$240$$ 0 0
$$241$$ −14.0000 −0.901819 −0.450910 0.892570i $$-0.648900\pi$$
−0.450910 + 0.892570i $$0.648900\pi$$
$$242$$ −7.00000 −0.449977
$$243$$ 0 0
$$244$$ −14.0000 −0.896258
$$245$$ 9.00000 0.574989
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 1.00000 0.0632456
$$251$$ −18.0000 −1.13615 −0.568075 0.822977i $$-0.692312\pi$$
−0.568075 + 0.822977i $$0.692312\pi$$
$$252$$ 0 0
$$253$$ −2.00000 −0.125739
$$254$$ 6.00000 0.376473
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −2.00000 −0.124757 −0.0623783 0.998053i $$-0.519869\pi$$
−0.0623783 + 0.998053i $$0.519869\pi$$
$$258$$ 0 0
$$259$$ 40.0000 2.48548
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 32.0000 1.97320 0.986602 0.163144i $$-0.0521635\pi$$
0.986602 + 0.163144i $$0.0521635\pi$$
$$264$$ 0 0
$$265$$ −6.00000 −0.368577
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 2.00000 0.122169
$$269$$ −24.0000 −1.46331 −0.731653 0.681677i $$-0.761251\pi$$
−0.731653 + 0.681677i $$0.761251\pi$$
$$270$$ 0 0
$$271$$ 8.00000 0.485965 0.242983 0.970031i $$-0.421874\pi$$
0.242983 + 0.970031i $$0.421874\pi$$
$$272$$ −2.00000 −0.121268
$$273$$ 0 0
$$274$$ 2.00000 0.120824
$$275$$ 2.00000 0.120605
$$276$$ 0 0
$$277$$ 8.00000 0.480673 0.240337 0.970690i $$-0.422742\pi$$
0.240337 + 0.970690i $$0.422742\pi$$
$$278$$ 20.0000 1.19952
$$279$$ 0 0
$$280$$ 4.00000 0.239046
$$281$$ −32.0000 −1.90896 −0.954480 0.298275i $$-0.903589\pi$$
−0.954480 + 0.298275i $$0.903589\pi$$
$$282$$ 0 0
$$283$$ −10.0000 −0.594438 −0.297219 0.954809i $$-0.596059\pi$$
−0.297219 + 0.954809i $$0.596059\pi$$
$$284$$ 2.00000 0.118678
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −24.0000 −1.41668
$$288$$ 0 0
$$289$$ −13.0000 −0.764706
$$290$$ 4.00000 0.234888
$$291$$ 0 0
$$292$$ 6.00000 0.351123
$$293$$ −14.0000 −0.817889 −0.408944 0.912559i $$-0.634103\pi$$
−0.408944 + 0.912559i $$0.634103\pi$$
$$294$$ 0 0
$$295$$ −12.0000 −0.698667
$$296$$ 10.0000 0.581238
$$297$$ 0 0
$$298$$ 14.0000 0.810998
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 8.00000 0.461112
$$302$$ −12.0000 −0.690522
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −14.0000 −0.801638
$$306$$ 0 0
$$307$$ 4.00000 0.228292 0.114146 0.993464i $$-0.463587\pi$$
0.114146 + 0.993464i $$0.463587\pi$$
$$308$$ 8.00000 0.455842
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 2.00000 0.113410 0.0567048 0.998391i $$-0.481941\pi$$
0.0567048 + 0.998391i $$0.481941\pi$$
$$312$$ 0 0
$$313$$ 20.0000 1.13047 0.565233 0.824931i $$-0.308786\pi$$
0.565233 + 0.824931i $$0.308786\pi$$
$$314$$ −22.0000 −1.24153
$$315$$ 0 0
$$316$$ 8.00000 0.450035
$$317$$ 10.0000 0.561656 0.280828 0.959758i $$-0.409391\pi$$
0.280828 + 0.959758i $$0.409391\pi$$
$$318$$ 0 0
$$319$$ 8.00000 0.447914
$$320$$ 1.00000 0.0559017
$$321$$ 0 0
$$322$$ −4.00000 −0.222911
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 0 0
$$326$$ −16.0000 −0.886158
$$327$$ 0 0
$$328$$ −6.00000 −0.331295
$$329$$ −48.0000 −2.64633
$$330$$ 0 0
$$331$$ −28.0000 −1.53902 −0.769510 0.638635i $$-0.779499\pi$$
−0.769510 + 0.638635i $$0.779499\pi$$
$$332$$ −8.00000 −0.439057
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 2.00000 0.109272
$$336$$ 0 0
$$337$$ −4.00000 −0.217894 −0.108947 0.994048i $$-0.534748\pi$$
−0.108947 + 0.994048i $$0.534748\pi$$
$$338$$ −13.0000 −0.707107
$$339$$ 0 0
$$340$$ −2.00000 −0.108465
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 8.00000 0.431959
$$344$$ 2.00000 0.107833
$$345$$ 0 0
$$346$$ 6.00000 0.322562
$$347$$ −4.00000 −0.214731 −0.107366 0.994220i $$-0.534242\pi$$
−0.107366 + 0.994220i $$0.534242\pi$$
$$348$$ 0 0
$$349$$ −30.0000 −1.60586 −0.802932 0.596071i $$-0.796728\pi$$
−0.802932 + 0.596071i $$0.796728\pi$$
$$350$$ 4.00000 0.213809
$$351$$ 0 0
$$352$$ 2.00000 0.106600
$$353$$ 34.0000 1.80964 0.904819 0.425797i $$-0.140006\pi$$
0.904819 + 0.425797i $$0.140006\pi$$
$$354$$ 0 0
$$355$$ 2.00000 0.106149
$$356$$ 8.00000 0.423999
$$357$$ 0 0
$$358$$ −4.00000 −0.211407
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 0 0
$$361$$ −19.0000 −1.00000
$$362$$ −6.00000 −0.315353
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 6.00000 0.314054
$$366$$ 0 0
$$367$$ 4.00000 0.208798 0.104399 0.994535i $$-0.466708\pi$$
0.104399 + 0.994535i $$0.466708\pi$$
$$368$$ −1.00000 −0.0521286
$$369$$ 0 0
$$370$$ 10.0000 0.519875
$$371$$ −24.0000 −1.24602
$$372$$ 0 0
$$373$$ −22.0000 −1.13912 −0.569558 0.821951i $$-0.692886\pi$$
−0.569558 + 0.821951i $$0.692886\pi$$
$$374$$ −4.00000 −0.206835
$$375$$ 0 0
$$376$$ −12.0000 −0.618853
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 4.00000 0.205466 0.102733 0.994709i $$-0.467241\pi$$
0.102733 + 0.994709i $$0.467241\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 24.0000 1.22634 0.613171 0.789950i $$-0.289894\pi$$
0.613171 + 0.789950i $$0.289894\pi$$
$$384$$ 0 0
$$385$$ 8.00000 0.407718
$$386$$ −14.0000 −0.712581
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −22.0000 −1.11544 −0.557722 0.830028i $$-0.688325\pi$$
−0.557722 + 0.830028i $$0.688325\pi$$
$$390$$ 0 0
$$391$$ 2.00000 0.101144
$$392$$ 9.00000 0.454569
$$393$$ 0 0
$$394$$ 6.00000 0.302276
$$395$$ 8.00000 0.402524
$$396$$ 0 0
$$397$$ 32.0000 1.60603 0.803017 0.595956i $$-0.203227\pi$$
0.803017 + 0.595956i $$0.203227\pi$$
$$398$$ 16.0000 0.802008
$$399$$ 0 0
$$400$$ 1.00000 0.0500000
$$401$$ 12.0000 0.599251 0.299626 0.954057i $$-0.403138\pi$$
0.299626 + 0.954057i $$0.403138\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 12.0000 0.597022
$$405$$ 0 0
$$406$$ 16.0000 0.794067
$$407$$ 20.0000 0.991363
$$408$$ 0 0
$$409$$ −10.0000 −0.494468 −0.247234 0.968956i $$-0.579522\pi$$
−0.247234 + 0.968956i $$0.579522\pi$$
$$410$$ −6.00000 −0.296319
$$411$$ 0 0
$$412$$ 4.00000 0.197066
$$413$$ −48.0000 −2.36193
$$414$$ 0 0
$$415$$ −8.00000 −0.392705
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 26.0000 1.27018 0.635092 0.772437i $$-0.280962\pi$$
0.635092 + 0.772437i $$0.280962\pi$$
$$420$$ 0 0
$$421$$ −6.00000 −0.292422 −0.146211 0.989253i $$-0.546708\pi$$
−0.146211 + 0.989253i $$0.546708\pi$$
$$422$$ 4.00000 0.194717
$$423$$ 0 0
$$424$$ −6.00000 −0.291386
$$425$$ −2.00000 −0.0970143
$$426$$ 0 0
$$427$$ −56.0000 −2.71003
$$428$$ 12.0000 0.580042
$$429$$ 0 0
$$430$$ 2.00000 0.0964486
$$431$$ −24.0000 −1.15604 −0.578020 0.816023i $$-0.696174\pi$$
−0.578020 + 0.816023i $$0.696174\pi$$
$$432$$ 0 0
$$433$$ 24.0000 1.15337 0.576683 0.816968i $$-0.304347\pi$$
0.576683 + 0.816968i $$0.304347\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 14.0000 0.670478
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 20.0000 0.954548 0.477274 0.878755i $$-0.341625\pi$$
0.477274 + 0.878755i $$0.341625\pi$$
$$440$$ 2.00000 0.0953463
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 20.0000 0.950229 0.475114 0.879924i $$-0.342407\pi$$
0.475114 + 0.879924i $$0.342407\pi$$
$$444$$ 0 0
$$445$$ 8.00000 0.379236
$$446$$ 2.00000 0.0947027
$$447$$ 0 0
$$448$$ 4.00000 0.188982
$$449$$ 34.0000 1.60456 0.802280 0.596948i $$-0.203620\pi$$
0.802280 + 0.596948i $$0.203620\pi$$
$$450$$ 0 0
$$451$$ −12.0000 −0.565058
$$452$$ −6.00000 −0.282216
$$453$$ 0 0
$$454$$ −12.0000 −0.563188
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −24.0000 −1.12267 −0.561336 0.827588i $$-0.689713\pi$$
−0.561336 + 0.827588i $$0.689713\pi$$
$$458$$ −26.0000 −1.21490
$$459$$ 0 0
$$460$$ −1.00000 −0.0466252
$$461$$ −20.0000 −0.931493 −0.465746 0.884918i $$-0.654214\pi$$
−0.465746 + 0.884918i $$0.654214\pi$$
$$462$$ 0 0
$$463$$ 18.0000 0.836531 0.418265 0.908325i $$-0.362638\pi$$
0.418265 + 0.908325i $$0.362638\pi$$
$$464$$ 4.00000 0.185695
$$465$$ 0 0
$$466$$ −10.0000 −0.463241
$$467$$ −24.0000 −1.11059 −0.555294 0.831654i $$-0.687394\pi$$
−0.555294 + 0.831654i $$0.687394\pi$$
$$468$$ 0 0
$$469$$ 8.00000 0.369406
$$470$$ −12.0000 −0.553519
$$471$$ 0 0
$$472$$ −12.0000 −0.552345
$$473$$ 4.00000 0.183920
$$474$$ 0 0
$$475$$ 0 0
$$476$$ −8.00000 −0.366679
$$477$$ 0 0
$$478$$ −22.0000 −1.00626
$$479$$ 40.0000 1.82765 0.913823 0.406112i $$-0.133116\pi$$
0.913823 + 0.406112i $$0.133116\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ −14.0000 −0.637683
$$483$$ 0 0
$$484$$ −7.00000 −0.318182
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 18.0000 0.815658 0.407829 0.913058i $$-0.366286\pi$$
0.407829 + 0.913058i $$0.366286\pi$$
$$488$$ −14.0000 −0.633750
$$489$$ 0 0
$$490$$ 9.00000 0.406579
$$491$$ 24.0000 1.08310 0.541552 0.840667i $$-0.317837\pi$$
0.541552 + 0.840667i $$0.317837\pi$$
$$492$$ 0 0
$$493$$ −8.00000 −0.360302
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 8.00000 0.358849
$$498$$ 0 0
$$499$$ −28.0000 −1.25345 −0.626726 0.779240i $$-0.715605\pi$$
−0.626726 + 0.779240i $$0.715605\pi$$
$$500$$ 1.00000 0.0447214
$$501$$ 0 0
$$502$$ −18.0000 −0.803379
$$503$$ 8.00000 0.356702 0.178351 0.983967i $$-0.442924\pi$$
0.178351 + 0.983967i $$0.442924\pi$$
$$504$$ 0 0
$$505$$ 12.0000 0.533993
$$506$$ −2.00000 −0.0889108
$$507$$ 0 0
$$508$$ 6.00000 0.266207
$$509$$ −28.0000 −1.24108 −0.620539 0.784176i $$-0.713086\pi$$
−0.620539 + 0.784176i $$0.713086\pi$$
$$510$$ 0 0
$$511$$ 24.0000 1.06170
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ −2.00000 −0.0882162
$$515$$ 4.00000 0.176261
$$516$$ 0 0
$$517$$ −24.0000 −1.05552
$$518$$ 40.0000 1.75750
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −32.0000 −1.40195 −0.700973 0.713188i $$-0.747251\pi$$
−0.700973 + 0.713188i $$0.747251\pi$$
$$522$$ 0 0
$$523$$ 22.0000 0.961993 0.480996 0.876723i $$-0.340275\pi$$
0.480996 + 0.876723i $$0.340275\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 32.0000 1.39527
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 1.00000 0.0434783
$$530$$ −6.00000 −0.260623
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 12.0000 0.518805
$$536$$ 2.00000 0.0863868
$$537$$ 0 0
$$538$$ −24.0000 −1.03471
$$539$$ 18.0000 0.775315
$$540$$ 0 0
$$541$$ −22.0000 −0.945854 −0.472927 0.881102i $$-0.656803\pi$$
−0.472927 + 0.881102i $$0.656803\pi$$
$$542$$ 8.00000 0.343629
$$543$$ 0 0
$$544$$ −2.00000 −0.0857493
$$545$$ 14.0000 0.599694
$$546$$ 0 0
$$547$$ 12.0000 0.513083 0.256541 0.966533i $$-0.417417\pi$$
0.256541 + 0.966533i $$0.417417\pi$$
$$548$$ 2.00000 0.0854358
$$549$$ 0 0
$$550$$ 2.00000 0.0852803
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 32.0000 1.36078
$$554$$ 8.00000 0.339887
$$555$$ 0 0
$$556$$ 20.0000 0.848189
$$557$$ −26.0000 −1.10166 −0.550828 0.834619i $$-0.685688\pi$$
−0.550828 + 0.834619i $$0.685688\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 4.00000 0.169031
$$561$$ 0 0
$$562$$ −32.0000 −1.34984
$$563$$ −8.00000 −0.337160 −0.168580 0.985688i $$-0.553918\pi$$
−0.168580 + 0.985688i $$0.553918\pi$$
$$564$$ 0 0
$$565$$ −6.00000 −0.252422
$$566$$ −10.0000 −0.420331
$$567$$ 0 0
$$568$$ 2.00000 0.0839181
$$569$$ 12.0000 0.503066 0.251533 0.967849i $$-0.419065\pi$$
0.251533 + 0.967849i $$0.419065\pi$$
$$570$$ 0 0
$$571$$ −36.0000 −1.50655 −0.753277 0.657704i $$-0.771528\pi$$
−0.753277 + 0.657704i $$0.771528\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ −24.0000 −1.00174
$$575$$ −1.00000 −0.0417029
$$576$$ 0 0
$$577$$ −10.0000 −0.416305 −0.208153 0.978096i $$-0.566745\pi$$
−0.208153 + 0.978096i $$0.566745\pi$$
$$578$$ −13.0000 −0.540729
$$579$$ 0 0
$$580$$ 4.00000 0.166091
$$581$$ −32.0000 −1.32758
$$582$$ 0 0
$$583$$ −12.0000 −0.496989
$$584$$ 6.00000 0.248282
$$585$$ 0 0
$$586$$ −14.0000 −0.578335
$$587$$ 4.00000 0.165098 0.0825488 0.996587i $$-0.473694\pi$$
0.0825488 + 0.996587i $$0.473694\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ −12.0000 −0.494032
$$591$$ 0 0
$$592$$ 10.0000 0.410997
$$593$$ 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
$$596$$ 14.0000 0.573462
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 30.0000 1.22577 0.612883 0.790173i $$-0.290010\pi$$
0.612883 + 0.790173i $$0.290010\pi$$
$$600$$ 0 0
$$601$$ −10.0000 −0.407909 −0.203954 0.978980i $$-0.565379\pi$$
−0.203954 + 0.978980i $$0.565379\pi$$
$$602$$ 8.00000 0.326056
$$603$$ 0 0
$$604$$ −12.0000 −0.488273
$$605$$ −7.00000 −0.284590
$$606$$ 0 0
$$607$$ −14.0000 −0.568242 −0.284121 0.958788i $$-0.591702\pi$$
−0.284121 + 0.958788i $$0.591702\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ −14.0000 −0.566843
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 14.0000 0.565455 0.282727 0.959200i $$-0.408761\pi$$
0.282727 + 0.959200i $$0.408761\pi$$
$$614$$ 4.00000 0.161427
$$615$$ 0 0
$$616$$ 8.00000 0.322329
$$617$$ 14.0000 0.563619 0.281809 0.959470i $$-0.409065\pi$$
0.281809 + 0.959470i $$0.409065\pi$$
$$618$$ 0 0
$$619$$ −24.0000 −0.964641 −0.482321 0.875995i $$-0.660206\pi$$
−0.482321 + 0.875995i $$0.660206\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 2.00000 0.0801927
$$623$$ 32.0000 1.28205
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 20.0000 0.799361
$$627$$ 0 0
$$628$$ −22.0000 −0.877896
$$629$$ −20.0000 −0.797452
$$630$$ 0 0
$$631$$ −16.0000 −0.636950 −0.318475 0.947931i $$-0.603171\pi$$
−0.318475 + 0.947931i $$0.603171\pi$$
$$632$$ 8.00000 0.318223
$$633$$ 0 0
$$634$$ 10.0000 0.397151
$$635$$ 6.00000 0.238103
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 8.00000 0.316723
$$639$$ 0 0
$$640$$ 1.00000 0.0395285
$$641$$ 8.00000 0.315981 0.157991 0.987441i $$-0.449498\pi$$
0.157991 + 0.987441i $$0.449498\pi$$
$$642$$ 0 0
$$643$$ 14.0000 0.552106 0.276053 0.961142i $$-0.410973\pi$$
0.276053 + 0.961142i $$0.410973\pi$$
$$644$$ −4.00000 −0.157622
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −12.0000 −0.471769 −0.235884 0.971781i $$-0.575799\pi$$
−0.235884 + 0.971781i $$0.575799\pi$$
$$648$$ 0 0
$$649$$ −24.0000 −0.942082
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −16.0000 −0.626608
$$653$$ 26.0000 1.01746 0.508729 0.860927i $$-0.330115\pi$$
0.508729 + 0.860927i $$0.330115\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −6.00000 −0.234261
$$657$$ 0 0
$$658$$ −48.0000 −1.87123
$$659$$ 18.0000 0.701180 0.350590 0.936529i $$-0.385981\pi$$
0.350590 + 0.936529i $$0.385981\pi$$
$$660$$ 0 0
$$661$$ 6.00000 0.233373 0.116686 0.993169i $$-0.462773\pi$$
0.116686 + 0.993169i $$0.462773\pi$$
$$662$$ −28.0000 −1.08825
$$663$$ 0 0
$$664$$ −8.00000 −0.310460
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −4.00000 −0.154881
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 2.00000 0.0772667
$$671$$ −28.0000 −1.08093
$$672$$ 0 0
$$673$$ −18.0000 −0.693849 −0.346925 0.937893i $$-0.612774\pi$$
−0.346925 + 0.937893i $$0.612774\pi$$
$$674$$ −4.00000 −0.154074
$$675$$ 0 0
$$676$$ −13.0000 −0.500000
$$677$$ 22.0000 0.845529 0.422764 0.906240i $$-0.361060\pi$$
0.422764 + 0.906240i $$0.361060\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ −2.00000 −0.0766965
$$681$$ 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
$$685$$ 2.00000 0.0764161
$$686$$ 8.00000 0.305441
$$687$$ 0 0
$$688$$ 2.00000 0.0762493
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −20.0000 −0.760836 −0.380418 0.924815i $$-0.624220\pi$$
−0.380418 + 0.924815i $$0.624220\pi$$
$$692$$ 6.00000 0.228086
$$693$$ 0 0
$$694$$ −4.00000 −0.151838
$$695$$ 20.0000 0.758643
$$696$$ 0 0
$$697$$ 12.0000 0.454532
$$698$$ −30.0000 −1.13552
$$699$$ 0 0
$$700$$ 4.00000 0.151186
$$701$$ −6.00000 −0.226617 −0.113308 0.993560i $$-0.536145\pi$$
−0.113308 + 0.993560i $$0.536145\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 2.00000 0.0753778
$$705$$ 0 0
$$706$$ 34.0000 1.27961
$$707$$ 48.0000 1.80523
$$708$$ 0 0
$$709$$ 22.0000 0.826227 0.413114 0.910679i $$-0.364441\pi$$
0.413114 + 0.910679i $$0.364441\pi$$
$$710$$ 2.00000 0.0750587
$$711$$ 0 0
$$712$$ 8.00000 0.299813
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −4.00000 −0.149487
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −18.0000 −0.671287 −0.335643 0.941989i $$-0.608954\pi$$
−0.335643 + 0.941989i $$0.608954\pi$$
$$720$$ 0 0
$$721$$ 16.0000 0.595871
$$722$$ −19.0000 −0.707107
$$723$$ 0 0
$$724$$ −6.00000 −0.222988
$$725$$ 4.00000 0.148556
$$726$$ 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
$$730$$ 6.00000 0.222070
$$731$$ −4.00000 −0.147945
$$732$$ 0 0
$$733$$ −30.0000 −1.10808 −0.554038 0.832492i $$-0.686914\pi$$
−0.554038 + 0.832492i $$0.686914\pi$$
$$734$$ 4.00000 0.147643
$$735$$ 0 0
$$736$$ −1.00000 −0.0368605
$$737$$ 4.00000 0.147342
$$738$$ 0 0
$$739$$ 36.0000 1.32428 0.662141 0.749380i $$-0.269648\pi$$
0.662141 + 0.749380i $$0.269648\pi$$
$$740$$ 10.0000 0.367607
$$741$$ 0 0
$$742$$ −24.0000 −0.881068
$$743$$ −16.0000 −0.586983 −0.293492 0.955962i $$-0.594817\pi$$
−0.293492 + 0.955962i $$0.594817\pi$$
$$744$$ 0 0
$$745$$ 14.0000 0.512920
$$746$$ −22.0000 −0.805477
$$747$$ 0 0
$$748$$ −4.00000 −0.146254
$$749$$ 48.0000 1.75388
$$750$$ 0 0
$$751$$ 40.0000 1.45962 0.729810 0.683650i $$-0.239608\pi$$
0.729810 + 0.683650i $$0.239608\pi$$
$$752$$ −12.0000 −0.437595
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −12.0000 −0.436725
$$756$$ 0 0
$$757$$ 22.0000 0.799604 0.399802 0.916602i $$-0.369079\pi$$
0.399802 + 0.916602i $$0.369079\pi$$
$$758$$ 4.00000 0.145287
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −2.00000 −0.0724999 −0.0362500 0.999343i $$-0.511541\pi$$
−0.0362500 + 0.999343i $$0.511541\pi$$
$$762$$ 0 0
$$763$$ 56.0000 2.02734
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 24.0000 0.867155
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 6.00000 0.216366 0.108183 0.994131i $$-0.465497\pi$$
0.108183 + 0.994131i $$0.465497\pi$$
$$770$$ 8.00000 0.288300
$$771$$ 0 0
$$772$$ −14.0000 −0.503871
$$773$$ −6.00000 −0.215805 −0.107903 0.994161i $$-0.534413\pi$$
−0.107903 + 0.994161i $$0.534413\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ −22.0000 −0.788738
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 4.00000 0.143131
$$782$$ 2.00000 0.0715199
$$783$$ 0 0
$$784$$ 9.00000 0.321429
$$785$$ −22.0000 −0.785214
$$786$$ 0 0
$$787$$ −34.0000 −1.21197 −0.605985 0.795476i $$-0.707221\pi$$
−0.605985 + 0.795476i $$0.707221\pi$$
$$788$$ 6.00000 0.213741
$$789$$ 0 0
$$790$$ 8.00000 0.284627
$$791$$ −24.0000 −0.853342
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 32.0000 1.13564
$$795$$ 0 0
$$796$$ 16.0000 0.567105
$$797$$ −50.0000 −1.77109 −0.885545 0.464553i $$-0.846215\pi$$
−0.885545 + 0.464553i $$0.846215\pi$$
$$798$$ 0 0
$$799$$ 24.0000 0.849059
$$800$$ 1.00000 0.0353553
$$801$$ 0 0
$$802$$ 12.0000 0.423735
$$803$$ 12.0000 0.423471
$$804$$ 0 0
$$805$$ −4.00000 −0.140981
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 12.0000 0.422159
$$809$$ 30.0000 1.05474 0.527372 0.849635i $$-0.323177\pi$$
0.527372 + 0.849635i $$0.323177\pi$$
$$810$$ 0 0
$$811$$ 52.0000 1.82597 0.912983 0.407997i $$-0.133772\pi$$
0.912983 + 0.407997i $$0.133772\pi$$
$$812$$ 16.0000 0.561490
$$813$$ 0 0
$$814$$ 20.0000 0.701000
$$815$$ −16.0000 −0.560456
$$816$$ 0 0
$$817$$ 0 0
$$818$$ −10.0000 −0.349642
$$819$$ 0 0
$$820$$ −6.00000 −0.209529
$$821$$ 16.0000 0.558404 0.279202 0.960232i $$-0.409930\pi$$
0.279202 + 0.960232i $$0.409930\pi$$
$$822$$ 0 0
$$823$$ −10.0000 −0.348578 −0.174289 0.984695i $$-0.555763\pi$$
−0.174289 + 0.984695i $$0.555763\pi$$
$$824$$ 4.00000 0.139347
$$825$$ 0 0
$$826$$ −48.0000 −1.67013
$$827$$ −44.0000 −1.53003 −0.765015 0.644013i $$-0.777268\pi$$
−0.765015 + 0.644013i $$0.777268\pi$$
$$828$$ 0 0
$$829$$ 10.0000 0.347314 0.173657 0.984806i $$-0.444442\pi$$
0.173657 + 0.984806i $$0.444442\pi$$
$$830$$ −8.00000 −0.277684
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −18.0000 −0.623663
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 26.0000 0.898155
$$839$$ 20.0000 0.690477 0.345238 0.938515i $$-0.387798\pi$$
0.345238 + 0.938515i $$0.387798\pi$$
$$840$$ 0 0
$$841$$ −13.0000 −0.448276
$$842$$ −6.00000 −0.206774
$$843$$ 0 0
$$844$$ 4.00000 0.137686
$$845$$ −13.0000 −0.447214
$$846$$ 0 0
$$847$$ −28.0000 −0.962091
$$848$$ −6.00000 −0.206041
$$849$$ 0 0
$$850$$ −2.00000 −0.0685994
$$851$$ −10.0000 −0.342796
$$852$$ 0 0
$$853$$ 56.0000 1.91740 0.958702 0.284413i $$-0.0917988\pi$$
0.958702 + 0.284413i $$0.0917988\pi$$
$$854$$ −56.0000 −1.91628
$$855$$ 0 0
$$856$$ 12.0000 0.410152
$$857$$ 42.0000 1.43469 0.717346 0.696717i $$-0.245357\pi$$
0.717346 + 0.696717i $$0.245357\pi$$
$$858$$ 0 0
$$859$$ 36.0000 1.22830 0.614152 0.789188i $$-0.289498\pi$$
0.614152 + 0.789188i $$0.289498\pi$$
$$860$$ 2.00000 0.0681994
$$861$$ 0 0
$$862$$ −24.0000 −0.817443
$$863$$ −36.0000 −1.22545 −0.612727 0.790295i $$-0.709928\pi$$
−0.612727 + 0.790295i $$0.709928\pi$$
$$864$$ 0 0
$$865$$ 6.00000 0.204006
$$866$$ 24.0000 0.815553
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 16.0000 0.542763
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 14.0000 0.474100
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 4.00000 0.135225
$$876$$ 0 0
$$877$$ −56.0000 −1.89099 −0.945493 0.325643i $$-0.894419\pi$$
−0.945493 + 0.325643i $$0.894419\pi$$
$$878$$ 20.0000 0.674967
$$879$$ 0 0
$$880$$ 2.00000 0.0674200
$$881$$ −40.0000 −1.34763 −0.673817 0.738898i $$-0.735346\pi$$
−0.673817 + 0.738898i $$0.735346\pi$$
$$882$$ 0 0
$$883$$ −48.0000 −1.61533 −0.807664 0.589643i $$-0.799269\pi$$
−0.807664 + 0.589643i $$0.799269\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 20.0000 0.671913
$$887$$ 36.0000 1.20876 0.604381 0.796696i $$-0.293421\pi$$
0.604381 + 0.796696i $$0.293421\pi$$
$$888$$ 0 0
$$889$$ 24.0000 0.804934
$$890$$ 8.00000 0.268161
$$891$$ 0 0
$$892$$ 2.00000 0.0669650
$$893$$ 0 0
$$894$$ 0 0
$$895$$ −4.00000 −0.133705
$$896$$ 4.00000 0.133631
$$897$$ 0 0
$$898$$ 34.0000 1.13459
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 12.0000 0.399778
$$902$$ −12.0000 −0.399556
$$903$$ 0 0
$$904$$ −6.00000 −0.199557
$$905$$ −6.00000 −0.199447
$$906$$ 0 0
$$907$$ 42.0000 1.39459 0.697294 0.716786i $$-0.254387\pi$$
0.697294 + 0.716786i $$0.254387\pi$$
$$908$$ −12.0000 −0.398234
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 12.0000 0.397578 0.198789 0.980042i $$-0.436299\pi$$
0.198789 + 0.980042i $$0.436299\pi$$
$$912$$ 0 0
$$913$$ −16.0000 −0.529523
$$914$$ −24.0000 −0.793849
$$915$$ 0 0
$$916$$ −26.0000 −0.859064
$$917$$ 0 0
$$918$$ 0 0
$$919$$ −32.0000 −1.05558 −0.527791 0.849374i $$-0.676980\pi$$
−0.527791 + 0.849374i $$0.676980\pi$$
$$920$$ −1.00000 −0.0329690
$$921$$ 0 0
$$922$$ −20.0000 −0.658665
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 10.0000 0.328798
$$926$$ 18.0000 0.591517
$$927$$ 0 0
$$928$$ 4.00000 0.131306
$$929$$ −30.0000 −0.984268 −0.492134 0.870519i $$-0.663783\pi$$
−0.492134 + 0.870519i $$0.663783\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ −10.0000 −0.327561
$$933$$ 0 0
$$934$$ −24.0000 −0.785304
$$935$$ −4.00000 −0.130814
$$936$$ 0 0
$$937$$ 48.0000 1.56809 0.784046 0.620703i $$-0.213153\pi$$
0.784046 + 0.620703i $$0.213153\pi$$
$$938$$ 8.00000 0.261209
$$939$$ 0 0
$$940$$ −12.0000 −0.391397
$$941$$ −26.0000 −0.847576 −0.423788 0.905761i $$-0.639300\pi$$
−0.423788 + 0.905761i $$0.639300\pi$$
$$942$$ 0 0
$$943$$ 6.00000 0.195387
$$944$$ −12.0000 −0.390567
$$945$$ 0 0
$$946$$ 4.00000 0.130051
$$947$$ 52.0000 1.68977 0.844886 0.534946i $$-0.179668\pi$$
0.844886 + 0.534946i $$0.179668\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0 0
$$951$$ 0 0
$$952$$ −8.00000 −0.259281
$$953$$ −14.0000 −0.453504 −0.226752 0.973952i $$-0.572811\pi$$
−0.226752 + 0.973952i $$0.572811\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ −22.0000 −0.711531
$$957$$ 0 0
$$958$$ 40.0000 1.29234
$$959$$ 8.00000 0.258333
$$960$$ 0 0
$$961$$ −31.0000 −1.00000
$$962$$ 0 0
$$963$$ 0 0
$$964$$ −14.0000 −0.450910
$$965$$ −14.0000 −0.450676
$$966$$ 0 0
$$967$$ 58.0000 1.86515 0.932577 0.360971i $$-0.117555\pi$$
0.932577 + 0.360971i $$0.117555\pi$$
$$968$$ −7.00000 −0.224989
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −50.0000 −1.60458 −0.802288 0.596937i $$-0.796384\pi$$
−0.802288 + 0.596937i $$0.796384\pi$$
$$972$$ 0 0
$$973$$ 80.0000 2.56468
$$974$$ 18.0000 0.576757
$$975$$ 0 0
$$976$$ −14.0000 −0.448129
$$977$$ −18.0000 −0.575871 −0.287936 0.957650i $$-0.592969\pi$$
−0.287936 + 0.957650i $$0.592969\pi$$
$$978$$ 0 0
$$979$$ 16.0000 0.511362
$$980$$ 9.00000 0.287494
$$981$$ 0 0
$$982$$ 24.0000 0.765871
$$983$$ −24.0000 −0.765481 −0.382741 0.923856i $$-0.625020\pi$$
−0.382741 + 0.923856i $$0.625020\pi$$
$$984$$ 0 0
$$985$$ 6.00000 0.191176
$$986$$ −8.00000 −0.254772
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −2.00000 −0.0635963
$$990$$ 0 0
$$991$$ 52.0000 1.65183 0.825917 0.563791i $$-0.190658\pi$$
0.825917 + 0.563791i $$0.190658\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 8.00000 0.253745
$$995$$ 16.0000 0.507234
$$996$$ 0 0
$$997$$ 40.0000 1.26681 0.633406 0.773819i $$-0.281656\pi$$
0.633406 + 0.773819i $$0.281656\pi$$
$$998$$ −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 2070.2.a.s.1.1 1
3.2 odd 2 690.2.a.b.1.1 1
12.11 even 2 5520.2.a.r.1.1 1
15.2 even 4 3450.2.d.n.2899.1 2
15.8 even 4 3450.2.d.n.2899.2 2
15.14 odd 2 3450.2.a.t.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
690.2.a.b.1.1 1 3.2 odd 2
2070.2.a.s.1.1 1 1.1 even 1 trivial
3450.2.a.t.1.1 1 15.14 odd 2
3450.2.d.n.2899.1 2 15.2 even 4
3450.2.d.n.2899.2 2 15.8 even 4
5520.2.a.r.1.1 1 12.11 even 2