# Properties

 Label 7280.2.a.a.1.1 Level $7280$ Weight $2$ Character 7280.1 Self dual yes Analytic conductor $58.131$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$7280 = 2^{4} \cdot 5 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 7280.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$58.1310926715$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 3640) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 7280.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-2.00000 q^{3} -1.00000 q^{5} -1.00000 q^{7} +1.00000 q^{9} +O(q^{10})$$ $$q-2.00000 q^{3} -1.00000 q^{5} -1.00000 q^{7} +1.00000 q^{9} -6.00000 q^{11} -1.00000 q^{13} +2.00000 q^{15} -2.00000 q^{17} -2.00000 q^{19} +2.00000 q^{21} +2.00000 q^{23} +1.00000 q^{25} +4.00000 q^{27} +10.0000 q^{29} +6.00000 q^{31} +12.0000 q^{33} +1.00000 q^{35} +6.00000 q^{37} +2.00000 q^{39} -2.00000 q^{41} -10.0000 q^{43} -1.00000 q^{45} +1.00000 q^{49} +4.00000 q^{51} +14.0000 q^{53} +6.00000 q^{55} +4.00000 q^{57} +2.00000 q^{59} +2.00000 q^{61} -1.00000 q^{63} +1.00000 q^{65} -8.00000 q^{67} -4.00000 q^{69} +10.0000 q^{71} +2.00000 q^{73} -2.00000 q^{75} +6.00000 q^{77} -4.00000 q^{79} -11.0000 q^{81} +4.00000 q^{83} +2.00000 q^{85} -20.0000 q^{87} -2.00000 q^{89} +1.00000 q^{91} -12.0000 q^{93} +2.00000 q^{95} +14.0000 q^{97} -6.00000 q^{99} +O(q^{100})$$

## 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
$$3$$ −2.00000 −1.15470 −0.577350 0.816497i $$-0.695913\pi$$
−0.577350 + 0.816497i $$0.695913\pi$$
$$4$$ 0 0
$$5$$ −1.00000 −0.447214
$$6$$ 0 0
$$7$$ −1.00000 −0.377964
$$8$$ 0 0
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ −6.00000 −1.80907 −0.904534 0.426401i $$-0.859781\pi$$
−0.904534 + 0.426401i $$0.859781\pi$$
$$12$$ 0 0
$$13$$ −1.00000 −0.277350
$$14$$ 0 0
$$15$$ 2.00000 0.516398
$$16$$ 0 0
$$17$$ −2.00000 −0.485071 −0.242536 0.970143i $$-0.577979\pi$$
−0.242536 + 0.970143i $$0.577979\pi$$
$$18$$ 0 0
$$19$$ −2.00000 −0.458831 −0.229416 0.973329i $$-0.573682\pi$$
−0.229416 + 0.973329i $$0.573682\pi$$
$$20$$ 0 0
$$21$$ 2.00000 0.436436
$$22$$ 0 0
$$23$$ 2.00000 0.417029 0.208514 0.978019i $$-0.433137\pi$$
0.208514 + 0.978019i $$0.433137\pi$$
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ 0 0
$$27$$ 4.00000 0.769800
$$28$$ 0 0
$$29$$ 10.0000 1.85695 0.928477 0.371391i $$-0.121119\pi$$
0.928477 + 0.371391i $$0.121119\pi$$
$$30$$ 0 0
$$31$$ 6.00000 1.07763 0.538816 0.842424i $$-0.318872\pi$$
0.538816 + 0.842424i $$0.318872\pi$$
$$32$$ 0 0
$$33$$ 12.0000 2.08893
$$34$$ 0 0
$$35$$ 1.00000 0.169031
$$36$$ 0 0
$$37$$ 6.00000 0.986394 0.493197 0.869918i $$-0.335828\pi$$
0.493197 + 0.869918i $$0.335828\pi$$
$$38$$ 0 0
$$39$$ 2.00000 0.320256
$$40$$ 0 0
$$41$$ −2.00000 −0.312348 −0.156174 0.987730i $$-0.549916\pi$$
−0.156174 + 0.987730i $$0.549916\pi$$
$$42$$ 0 0
$$43$$ −10.0000 −1.52499 −0.762493 0.646997i $$-0.776025\pi$$
−0.762493 + 0.646997i $$0.776025\pi$$
$$44$$ 0 0
$$45$$ −1.00000 −0.149071
$$46$$ 0 0
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ 1.00000 0.142857
$$50$$ 0 0
$$51$$ 4.00000 0.560112
$$52$$ 0 0
$$53$$ 14.0000 1.92305 0.961524 0.274721i $$-0.0885855\pi$$
0.961524 + 0.274721i $$0.0885855\pi$$
$$54$$ 0 0
$$55$$ 6.00000 0.809040
$$56$$ 0 0
$$57$$ 4.00000 0.529813
$$58$$ 0 0
$$59$$ 2.00000 0.260378 0.130189 0.991489i $$-0.458442\pi$$
0.130189 + 0.991489i $$0.458442\pi$$
$$60$$ 0 0
$$61$$ 2.00000 0.256074 0.128037 0.991769i $$-0.459132\pi$$
0.128037 + 0.991769i $$0.459132\pi$$
$$62$$ 0 0
$$63$$ −1.00000 −0.125988
$$64$$ 0 0
$$65$$ 1.00000 0.124035
$$66$$ 0 0
$$67$$ −8.00000 −0.977356 −0.488678 0.872464i $$-0.662521\pi$$
−0.488678 + 0.872464i $$0.662521\pi$$
$$68$$ 0 0
$$69$$ −4.00000 −0.481543
$$70$$ 0 0
$$71$$ 10.0000 1.18678 0.593391 0.804914i $$-0.297789\pi$$
0.593391 + 0.804914i $$0.297789\pi$$
$$72$$ 0 0
$$73$$ 2.00000 0.234082 0.117041 0.993127i $$-0.462659\pi$$
0.117041 + 0.993127i $$0.462659\pi$$
$$74$$ 0 0
$$75$$ −2.00000 −0.230940
$$76$$ 0 0
$$77$$ 6.00000 0.683763
$$78$$ 0 0
$$79$$ −4.00000 −0.450035 −0.225018 0.974355i $$-0.572244\pi$$
−0.225018 + 0.974355i $$0.572244\pi$$
$$80$$ 0 0
$$81$$ −11.0000 −1.22222
$$82$$ 0 0
$$83$$ 4.00000 0.439057 0.219529 0.975606i $$-0.429548\pi$$
0.219529 + 0.975606i $$0.429548\pi$$
$$84$$ 0 0
$$85$$ 2.00000 0.216930
$$86$$ 0 0
$$87$$ −20.0000 −2.14423
$$88$$ 0 0
$$89$$ −2.00000 −0.212000 −0.106000 0.994366i $$-0.533804\pi$$
−0.106000 + 0.994366i $$0.533804\pi$$
$$90$$ 0 0
$$91$$ 1.00000 0.104828
$$92$$ 0 0
$$93$$ −12.0000 −1.24434
$$94$$ 0 0
$$95$$ 2.00000 0.205196
$$96$$ 0 0
$$97$$ 14.0000 1.42148 0.710742 0.703452i $$-0.248359\pi$$
0.710742 + 0.703452i $$0.248359\pi$$
$$98$$ 0 0
$$99$$ −6.00000 −0.603023
$$100$$ 0 0
$$101$$ −18.0000 −1.79107 −0.895533 0.444994i $$-0.853206\pi$$
−0.895533 + 0.444994i $$0.853206\pi$$
$$102$$ 0 0
$$103$$ 14.0000 1.37946 0.689730 0.724066i $$-0.257729\pi$$
0.689730 + 0.724066i $$0.257729\pi$$
$$104$$ 0 0
$$105$$ −2.00000 −0.195180
$$106$$ 0 0
$$107$$ −18.0000 −1.74013 −0.870063 0.492941i $$-0.835922\pi$$
−0.870063 + 0.492941i $$0.835922\pi$$
$$108$$ 0 0
$$109$$ −10.0000 −0.957826 −0.478913 0.877862i $$-0.658969\pi$$
−0.478913 + 0.877862i $$0.658969\pi$$
$$110$$ 0 0
$$111$$ −12.0000 −1.13899
$$112$$ 0 0
$$113$$ −6.00000 −0.564433 −0.282216 0.959351i $$-0.591070\pi$$
−0.282216 + 0.959351i $$0.591070\pi$$
$$114$$ 0 0
$$115$$ −2.00000 −0.186501
$$116$$ 0 0
$$117$$ −1.00000 −0.0924500
$$118$$ 0 0
$$119$$ 2.00000 0.183340
$$120$$ 0 0
$$121$$ 25.0000 2.27273
$$122$$ 0 0
$$123$$ 4.00000 0.360668
$$124$$ 0 0
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ 22.0000 1.95218 0.976092 0.217357i $$-0.0697436\pi$$
0.976092 + 0.217357i $$0.0697436\pi$$
$$128$$ 0 0
$$129$$ 20.0000 1.76090
$$130$$ 0 0
$$131$$ −12.0000 −1.04844 −0.524222 0.851581i $$-0.675644\pi$$
−0.524222 + 0.851581i $$0.675644\pi$$
$$132$$ 0 0
$$133$$ 2.00000 0.173422
$$134$$ 0 0
$$135$$ −4.00000 −0.344265
$$136$$ 0 0
$$137$$ −10.0000 −0.854358 −0.427179 0.904167i $$-0.640493\pi$$
−0.427179 + 0.904167i $$0.640493\pi$$
$$138$$ 0 0
$$139$$ −16.0000 −1.35710 −0.678551 0.734553i $$-0.737392\pi$$
−0.678551 + 0.734553i $$0.737392\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 6.00000 0.501745
$$144$$ 0 0
$$145$$ −10.0000 −0.830455
$$146$$ 0 0
$$147$$ −2.00000 −0.164957
$$148$$ 0 0
$$149$$ 14.0000 1.14692 0.573462 0.819232i $$-0.305600\pi$$
0.573462 + 0.819232i $$0.305600\pi$$
$$150$$ 0 0
$$151$$ −2.00000 −0.162758 −0.0813788 0.996683i $$-0.525932\pi$$
−0.0813788 + 0.996683i $$0.525932\pi$$
$$152$$ 0 0
$$153$$ −2.00000 −0.161690
$$154$$ 0 0
$$155$$ −6.00000 −0.481932
$$156$$ 0 0
$$157$$ −22.0000 −1.75579 −0.877896 0.478852i $$-0.841053\pi$$
−0.877896 + 0.478852i $$0.841053\pi$$
$$158$$ 0 0
$$159$$ −28.0000 −2.22054
$$160$$ 0 0
$$161$$ −2.00000 −0.157622
$$162$$ 0 0
$$163$$ −24.0000 −1.87983 −0.939913 0.341415i $$-0.889094\pi$$
−0.939913 + 0.341415i $$0.889094\pi$$
$$164$$ 0 0
$$165$$ −12.0000 −0.934199
$$166$$ 0 0
$$167$$ −16.0000 −1.23812 −0.619059 0.785345i $$-0.712486\pi$$
−0.619059 + 0.785345i $$0.712486\pi$$
$$168$$ 0 0
$$169$$ 1.00000 0.0769231
$$170$$ 0 0
$$171$$ −2.00000 −0.152944
$$172$$ 0 0
$$173$$ 18.0000 1.36851 0.684257 0.729241i $$-0.260127\pi$$
0.684257 + 0.729241i $$0.260127\pi$$
$$174$$ 0 0
$$175$$ −1.00000 −0.0755929
$$176$$ 0 0
$$177$$ −4.00000 −0.300658
$$178$$ 0 0
$$179$$ 4.00000 0.298974 0.149487 0.988764i $$-0.452238\pi$$
0.149487 + 0.988764i $$0.452238\pi$$
$$180$$ 0 0
$$181$$ −22.0000 −1.63525 −0.817624 0.575753i $$-0.804709\pi$$
−0.817624 + 0.575753i $$0.804709\pi$$
$$182$$ 0 0
$$183$$ −4.00000 −0.295689
$$184$$ 0 0
$$185$$ −6.00000 −0.441129
$$186$$ 0 0
$$187$$ 12.0000 0.877527
$$188$$ 0 0
$$189$$ −4.00000 −0.290957
$$190$$ 0 0
$$191$$ 8.00000 0.578860 0.289430 0.957199i $$-0.406534\pi$$
0.289430 + 0.957199i $$0.406534\pi$$
$$192$$ 0 0
$$193$$ 22.0000 1.58359 0.791797 0.610784i $$-0.209146\pi$$
0.791797 + 0.610784i $$0.209146\pi$$
$$194$$ 0 0
$$195$$ −2.00000 −0.143223
$$196$$ 0 0
$$197$$ 18.0000 1.28245 0.641223 0.767354i $$-0.278427\pi$$
0.641223 + 0.767354i $$0.278427\pi$$
$$198$$ 0 0
$$199$$ −16.0000 −1.13421 −0.567105 0.823646i $$-0.691937\pi$$
−0.567105 + 0.823646i $$0.691937\pi$$
$$200$$ 0 0
$$201$$ 16.0000 1.12855
$$202$$ 0 0
$$203$$ −10.0000 −0.701862
$$204$$ 0 0
$$205$$ 2.00000 0.139686
$$206$$ 0 0
$$207$$ 2.00000 0.139010
$$208$$ 0 0
$$209$$ 12.0000 0.830057
$$210$$ 0 0
$$211$$ 12.0000 0.826114 0.413057 0.910705i $$-0.364461\pi$$
0.413057 + 0.910705i $$0.364461\pi$$
$$212$$ 0 0
$$213$$ −20.0000 −1.37038
$$214$$ 0 0
$$215$$ 10.0000 0.681994
$$216$$ 0 0
$$217$$ −6.00000 −0.407307
$$218$$ 0 0
$$219$$ −4.00000 −0.270295
$$220$$ 0 0
$$221$$ 2.00000 0.134535
$$222$$ 0 0
$$223$$ 8.00000 0.535720 0.267860 0.963458i $$-0.413684\pi$$
0.267860 + 0.963458i $$0.413684\pi$$
$$224$$ 0 0
$$225$$ 1.00000 0.0666667
$$226$$ 0 0
$$227$$ 24.0000 1.59294 0.796468 0.604681i $$-0.206699\pi$$
0.796468 + 0.604681i $$0.206699\pi$$
$$228$$ 0 0
$$229$$ 26.0000 1.71813 0.859064 0.511868i $$-0.171046\pi$$
0.859064 + 0.511868i $$0.171046\pi$$
$$230$$ 0 0
$$231$$ −12.0000 −0.789542
$$232$$ 0 0
$$233$$ 18.0000 1.17922 0.589610 0.807688i $$-0.299282\pi$$
0.589610 + 0.807688i $$0.299282\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 8.00000 0.519656
$$238$$ 0 0
$$239$$ 6.00000 0.388108 0.194054 0.980991i $$-0.437836\pi$$
0.194054 + 0.980991i $$0.437836\pi$$
$$240$$ 0 0
$$241$$ −10.0000 −0.644157 −0.322078 0.946713i $$-0.604381\pi$$
−0.322078 + 0.946713i $$0.604381\pi$$
$$242$$ 0 0
$$243$$ 10.0000 0.641500
$$244$$ 0 0
$$245$$ −1.00000 −0.0638877
$$246$$ 0 0
$$247$$ 2.00000 0.127257
$$248$$ 0 0
$$249$$ −8.00000 −0.506979
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ −12.0000 −0.754434
$$254$$ 0 0
$$255$$ −4.00000 −0.250490
$$256$$ 0 0
$$257$$ 6.00000 0.374270 0.187135 0.982334i $$-0.440080\pi$$
0.187135 + 0.982334i $$0.440080\pi$$
$$258$$ 0 0
$$259$$ −6.00000 −0.372822
$$260$$ 0 0
$$261$$ 10.0000 0.618984
$$262$$ 0 0
$$263$$ 6.00000 0.369976 0.184988 0.982741i $$-0.440775\pi$$
0.184988 + 0.982741i $$0.440775\pi$$
$$264$$ 0 0
$$265$$ −14.0000 −0.860013
$$266$$ 0 0
$$267$$ 4.00000 0.244796
$$268$$ 0 0
$$269$$ −10.0000 −0.609711 −0.304855 0.952399i $$-0.598608\pi$$
−0.304855 + 0.952399i $$0.598608\pi$$
$$270$$ 0 0
$$271$$ 18.0000 1.09342 0.546711 0.837321i $$-0.315880\pi$$
0.546711 + 0.837321i $$0.315880\pi$$
$$272$$ 0 0
$$273$$ −2.00000 −0.121046
$$274$$ 0 0
$$275$$ −6.00000 −0.361814
$$276$$ 0 0
$$277$$ −26.0000 −1.56219 −0.781094 0.624413i $$-0.785338\pi$$
−0.781094 + 0.624413i $$0.785338\pi$$
$$278$$ 0 0
$$279$$ 6.00000 0.359211
$$280$$ 0 0
$$281$$ 10.0000 0.596550 0.298275 0.954480i $$-0.403589\pi$$
0.298275 + 0.954480i $$0.403589\pi$$
$$282$$ 0 0
$$283$$ −14.0000 −0.832214 −0.416107 0.909316i $$-0.636606\pi$$
−0.416107 + 0.909316i $$0.636606\pi$$
$$284$$ 0 0
$$285$$ −4.00000 −0.236940
$$286$$ 0 0
$$287$$ 2.00000 0.118056
$$288$$ 0 0
$$289$$ −13.0000 −0.764706
$$290$$ 0 0
$$291$$ −28.0000 −1.64139
$$292$$ 0 0
$$293$$ 14.0000 0.817889 0.408944 0.912559i $$-0.365897\pi$$
0.408944 + 0.912559i $$0.365897\pi$$
$$294$$ 0 0
$$295$$ −2.00000 −0.116445
$$296$$ 0 0
$$297$$ −24.0000 −1.39262
$$298$$ 0 0
$$299$$ −2.00000 −0.115663
$$300$$ 0 0
$$301$$ 10.0000 0.576390
$$302$$ 0 0
$$303$$ 36.0000 2.06815
$$304$$ 0 0
$$305$$ −2.00000 −0.114520
$$306$$ 0 0
$$307$$ −12.0000 −0.684876 −0.342438 0.939540i $$-0.611253\pi$$
−0.342438 + 0.939540i $$0.611253\pi$$
$$308$$ 0 0
$$309$$ −28.0000 −1.59286
$$310$$ 0 0
$$311$$ −12.0000 −0.680458 −0.340229 0.940343i $$-0.610505\pi$$
−0.340229 + 0.940343i $$0.610505\pi$$
$$312$$ 0 0
$$313$$ −26.0000 −1.46961 −0.734803 0.678280i $$-0.762726\pi$$
−0.734803 + 0.678280i $$0.762726\pi$$
$$314$$ 0 0
$$315$$ 1.00000 0.0563436
$$316$$ 0 0
$$317$$ 14.0000 0.786318 0.393159 0.919470i $$-0.371382\pi$$
0.393159 + 0.919470i $$0.371382\pi$$
$$318$$ 0 0
$$319$$ −60.0000 −3.35936
$$320$$ 0 0
$$321$$ 36.0000 2.00932
$$322$$ 0 0
$$323$$ 4.00000 0.222566
$$324$$ 0 0
$$325$$ −1.00000 −0.0554700
$$326$$ 0 0
$$327$$ 20.0000 1.10600
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 6.00000 0.329790 0.164895 0.986311i $$-0.447272\pi$$
0.164895 + 0.986311i $$0.447272\pi$$
$$332$$ 0 0
$$333$$ 6.00000 0.328798
$$334$$ 0 0
$$335$$ 8.00000 0.437087
$$336$$ 0 0
$$337$$ −6.00000 −0.326841 −0.163420 0.986557i $$-0.552253\pi$$
−0.163420 + 0.986557i $$0.552253\pi$$
$$338$$ 0 0
$$339$$ 12.0000 0.651751
$$340$$ 0 0
$$341$$ −36.0000 −1.94951
$$342$$ 0 0
$$343$$ −1.00000 −0.0539949
$$344$$ 0 0
$$345$$ 4.00000 0.215353
$$346$$ 0 0
$$347$$ 22.0000 1.18102 0.590511 0.807030i $$-0.298926\pi$$
0.590511 + 0.807030i $$0.298926\pi$$
$$348$$ 0 0
$$349$$ −14.0000 −0.749403 −0.374701 0.927146i $$-0.622255\pi$$
−0.374701 + 0.927146i $$0.622255\pi$$
$$350$$ 0 0
$$351$$ −4.00000 −0.213504
$$352$$ 0 0
$$353$$ 2.00000 0.106449 0.0532246 0.998583i $$-0.483050\pi$$
0.0532246 + 0.998583i $$0.483050\pi$$
$$354$$ 0 0
$$355$$ −10.0000 −0.530745
$$356$$ 0 0
$$357$$ −4.00000 −0.211702
$$358$$ 0 0
$$359$$ 34.0000 1.79445 0.897226 0.441572i $$-0.145579\pi$$
0.897226 + 0.441572i $$0.145579\pi$$
$$360$$ 0 0
$$361$$ −15.0000 −0.789474
$$362$$ 0 0
$$363$$ −50.0000 −2.62432
$$364$$ 0 0
$$365$$ −2.00000 −0.104685
$$366$$ 0 0
$$367$$ 30.0000 1.56599 0.782994 0.622030i $$-0.213692\pi$$
0.782994 + 0.622030i $$0.213692\pi$$
$$368$$ 0 0
$$369$$ −2.00000 −0.104116
$$370$$ 0 0
$$371$$ −14.0000 −0.726844
$$372$$ 0 0
$$373$$ −26.0000 −1.34623 −0.673114 0.739538i $$-0.735044\pi$$
−0.673114 + 0.739538i $$0.735044\pi$$
$$374$$ 0 0
$$375$$ 2.00000 0.103280
$$376$$ 0 0
$$377$$ −10.0000 −0.515026
$$378$$ 0 0
$$379$$ 2.00000 0.102733 0.0513665 0.998680i $$-0.483642\pi$$
0.0513665 + 0.998680i $$0.483642\pi$$
$$380$$ 0 0
$$381$$ −44.0000 −2.25419
$$382$$ 0 0
$$383$$ −32.0000 −1.63512 −0.817562 0.575841i $$-0.804675\pi$$
−0.817562 + 0.575841i $$0.804675\pi$$
$$384$$ 0 0
$$385$$ −6.00000 −0.305788
$$386$$ 0 0
$$387$$ −10.0000 −0.508329
$$388$$ 0 0
$$389$$ −26.0000 −1.31825 −0.659126 0.752032i $$-0.729074\pi$$
−0.659126 + 0.752032i $$0.729074\pi$$
$$390$$ 0 0
$$391$$ −4.00000 −0.202289
$$392$$ 0 0
$$393$$ 24.0000 1.21064
$$394$$ 0 0
$$395$$ 4.00000 0.201262
$$396$$ 0 0
$$397$$ −2.00000 −0.100377 −0.0501886 0.998740i $$-0.515982\pi$$
−0.0501886 + 0.998740i $$0.515982\pi$$
$$398$$ 0 0
$$399$$ −4.00000 −0.200250
$$400$$ 0 0
$$401$$ −6.00000 −0.299626 −0.149813 0.988714i $$-0.547867\pi$$
−0.149813 + 0.988714i $$0.547867\pi$$
$$402$$ 0 0
$$403$$ −6.00000 −0.298881
$$404$$ 0 0
$$405$$ 11.0000 0.546594
$$406$$ 0 0
$$407$$ −36.0000 −1.78445
$$408$$ 0 0
$$409$$ −26.0000 −1.28562 −0.642809 0.766027i $$-0.722231\pi$$
−0.642809 + 0.766027i $$0.722231\pi$$
$$410$$ 0 0
$$411$$ 20.0000 0.986527
$$412$$ 0 0
$$413$$ −2.00000 −0.0984136
$$414$$ 0 0
$$415$$ −4.00000 −0.196352
$$416$$ 0 0
$$417$$ 32.0000 1.56705
$$418$$ 0 0
$$419$$ −24.0000 −1.17248 −0.586238 0.810139i $$-0.699392\pi$$
−0.586238 + 0.810139i $$0.699392\pi$$
$$420$$ 0 0
$$421$$ −26.0000 −1.26716 −0.633581 0.773676i $$-0.718416\pi$$
−0.633581 + 0.773676i $$0.718416\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −2.00000 −0.0970143
$$426$$ 0 0
$$427$$ −2.00000 −0.0967868
$$428$$ 0 0
$$429$$ −12.0000 −0.579365
$$430$$ 0 0
$$431$$ 10.0000 0.481683 0.240842 0.970564i $$-0.422577\pi$$
0.240842 + 0.970564i $$0.422577\pi$$
$$432$$ 0 0
$$433$$ −2.00000 −0.0961139 −0.0480569 0.998845i $$-0.515303\pi$$
−0.0480569 + 0.998845i $$0.515303\pi$$
$$434$$ 0 0
$$435$$ 20.0000 0.958927
$$436$$ 0 0
$$437$$ −4.00000 −0.191346
$$438$$ 0 0
$$439$$ −32.0000 −1.52728 −0.763638 0.645644i $$-0.776589\pi$$
−0.763638 + 0.645644i $$0.776589\pi$$
$$440$$ 0 0
$$441$$ 1.00000 0.0476190
$$442$$ 0 0
$$443$$ 10.0000 0.475114 0.237557 0.971374i $$-0.423653\pi$$
0.237557 + 0.971374i $$0.423653\pi$$
$$444$$ 0 0
$$445$$ 2.00000 0.0948091
$$446$$ 0 0
$$447$$ −28.0000 −1.32435
$$448$$ 0 0
$$449$$ −22.0000 −1.03824 −0.519122 0.854700i $$-0.673741\pi$$
−0.519122 + 0.854700i $$0.673741\pi$$
$$450$$ 0 0
$$451$$ 12.0000 0.565058
$$452$$ 0 0
$$453$$ 4.00000 0.187936
$$454$$ 0 0
$$455$$ −1.00000 −0.0468807
$$456$$ 0 0
$$457$$ −18.0000 −0.842004 −0.421002 0.907060i $$-0.638322\pi$$
−0.421002 + 0.907060i $$0.638322\pi$$
$$458$$ 0 0
$$459$$ −8.00000 −0.373408
$$460$$ 0 0
$$461$$ −6.00000 −0.279448 −0.139724 0.990190i $$-0.544622\pi$$
−0.139724 + 0.990190i $$0.544622\pi$$
$$462$$ 0 0
$$463$$ 36.0000 1.67306 0.836531 0.547920i $$-0.184580\pi$$
0.836531 + 0.547920i $$0.184580\pi$$
$$464$$ 0 0
$$465$$ 12.0000 0.556487
$$466$$ 0 0
$$467$$ 14.0000 0.647843 0.323921 0.946084i $$-0.394999\pi$$
0.323921 + 0.946084i $$0.394999\pi$$
$$468$$ 0 0
$$469$$ 8.00000 0.369406
$$470$$ 0 0
$$471$$ 44.0000 2.02741
$$472$$ 0 0
$$473$$ 60.0000 2.75880
$$474$$ 0 0
$$475$$ −2.00000 −0.0917663
$$476$$ 0 0
$$477$$ 14.0000 0.641016
$$478$$ 0 0
$$479$$ −34.0000 −1.55350 −0.776750 0.629809i $$-0.783133\pi$$
−0.776750 + 0.629809i $$0.783133\pi$$
$$480$$ 0 0
$$481$$ −6.00000 −0.273576
$$482$$ 0 0
$$483$$ 4.00000 0.182006
$$484$$ 0 0
$$485$$ −14.0000 −0.635707
$$486$$ 0 0
$$487$$ −20.0000 −0.906287 −0.453143 0.891438i $$-0.649697\pi$$
−0.453143 + 0.891438i $$0.649697\pi$$
$$488$$ 0 0
$$489$$ 48.0000 2.17064
$$490$$ 0 0
$$491$$ 8.00000 0.361035 0.180517 0.983572i $$-0.442223\pi$$
0.180517 + 0.983572i $$0.442223\pi$$
$$492$$ 0 0
$$493$$ −20.0000 −0.900755
$$494$$ 0 0
$$495$$ 6.00000 0.269680
$$496$$ 0 0
$$497$$ −10.0000 −0.448561
$$498$$ 0 0
$$499$$ 10.0000 0.447661 0.223831 0.974628i $$-0.428144\pi$$
0.223831 + 0.974628i $$0.428144\pi$$
$$500$$ 0 0
$$501$$ 32.0000 1.42965
$$502$$ 0 0
$$503$$ −6.00000 −0.267527 −0.133763 0.991013i $$-0.542706\pi$$
−0.133763 + 0.991013i $$0.542706\pi$$
$$504$$ 0 0
$$505$$ 18.0000 0.800989
$$506$$ 0 0
$$507$$ −2.00000 −0.0888231
$$508$$ 0 0
$$509$$ 26.0000 1.15243 0.576215 0.817298i $$-0.304529\pi$$
0.576215 + 0.817298i $$0.304529\pi$$
$$510$$ 0 0
$$511$$ −2.00000 −0.0884748
$$512$$ 0 0
$$513$$ −8.00000 −0.353209
$$514$$ 0 0
$$515$$ −14.0000 −0.616914
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ −36.0000 −1.58022
$$520$$ 0 0
$$521$$ −10.0000 −0.438108 −0.219054 0.975713i $$-0.570297\pi$$
−0.219054 + 0.975713i $$0.570297\pi$$
$$522$$ 0 0
$$523$$ 6.00000 0.262362 0.131181 0.991358i $$-0.458123\pi$$
0.131181 + 0.991358i $$0.458123\pi$$
$$524$$ 0 0
$$525$$ 2.00000 0.0872872
$$526$$ 0 0
$$527$$ −12.0000 −0.522728
$$528$$ 0 0
$$529$$ −19.0000 −0.826087
$$530$$ 0 0
$$531$$ 2.00000 0.0867926
$$532$$ 0 0
$$533$$ 2.00000 0.0866296
$$534$$ 0 0
$$535$$ 18.0000 0.778208
$$536$$ 0 0
$$537$$ −8.00000 −0.345225
$$538$$ 0 0
$$539$$ −6.00000 −0.258438
$$540$$ 0 0
$$541$$ 30.0000 1.28980 0.644900 0.764267i $$-0.276899\pi$$
0.644900 + 0.764267i $$0.276899\pi$$
$$542$$ 0 0
$$543$$ 44.0000 1.88822
$$544$$ 0 0
$$545$$ 10.0000 0.428353
$$546$$ 0 0
$$547$$ 22.0000 0.940652 0.470326 0.882493i $$-0.344136\pi$$
0.470326 + 0.882493i $$0.344136\pi$$
$$548$$ 0 0
$$549$$ 2.00000 0.0853579
$$550$$ 0 0
$$551$$ −20.0000 −0.852029
$$552$$ 0 0
$$553$$ 4.00000 0.170097
$$554$$ 0 0
$$555$$ 12.0000 0.509372
$$556$$ 0 0
$$557$$ 14.0000 0.593199 0.296600 0.955002i $$-0.404147\pi$$
0.296600 + 0.955002i $$0.404147\pi$$
$$558$$ 0 0
$$559$$ 10.0000 0.422955
$$560$$ 0 0
$$561$$ −24.0000 −1.01328
$$562$$ 0 0
$$563$$ −22.0000 −0.927189 −0.463595 0.886047i $$-0.653441\pi$$
−0.463595 + 0.886047i $$0.653441\pi$$
$$564$$ 0 0
$$565$$ 6.00000 0.252422
$$566$$ 0 0
$$567$$ 11.0000 0.461957
$$568$$ 0 0
$$569$$ −42.0000 −1.76073 −0.880366 0.474295i $$-0.842703\pi$$
−0.880366 + 0.474295i $$0.842703\pi$$
$$570$$ 0 0
$$571$$ 8.00000 0.334790 0.167395 0.985890i $$-0.446465\pi$$
0.167395 + 0.985890i $$0.446465\pi$$
$$572$$ 0 0
$$573$$ −16.0000 −0.668410
$$574$$ 0 0
$$575$$ 2.00000 0.0834058
$$576$$ 0 0
$$577$$ 42.0000 1.74848 0.874241 0.485491i $$-0.161359\pi$$
0.874241 + 0.485491i $$0.161359\pi$$
$$578$$ 0 0
$$579$$ −44.0000 −1.82858
$$580$$ 0 0
$$581$$ −4.00000 −0.165948
$$582$$ 0 0
$$583$$ −84.0000 −3.47892
$$584$$ 0 0
$$585$$ 1.00000 0.0413449
$$586$$ 0 0
$$587$$ −24.0000 −0.990586 −0.495293 0.868726i $$-0.664939\pi$$
−0.495293 + 0.868726i $$0.664939\pi$$
$$588$$ 0 0
$$589$$ −12.0000 −0.494451
$$590$$ 0 0
$$591$$ −36.0000 −1.48084
$$592$$ 0 0
$$593$$ −18.0000 −0.739171 −0.369586 0.929197i $$-0.620500\pi$$
−0.369586 + 0.929197i $$0.620500\pi$$
$$594$$ 0 0
$$595$$ −2.00000 −0.0819920
$$596$$ 0 0
$$597$$ 32.0000 1.30967
$$598$$ 0 0
$$599$$ 4.00000 0.163436 0.0817178 0.996656i $$-0.473959\pi$$
0.0817178 + 0.996656i $$0.473959\pi$$
$$600$$ 0 0
$$601$$ −22.0000 −0.897399 −0.448699 0.893683i $$-0.648113\pi$$
−0.448699 + 0.893683i $$0.648113\pi$$
$$602$$ 0 0
$$603$$ −8.00000 −0.325785
$$604$$ 0 0
$$605$$ −25.0000 −1.01639
$$606$$ 0 0
$$607$$ −10.0000 −0.405887 −0.202944 0.979190i $$-0.565051\pi$$
−0.202944 + 0.979190i $$0.565051\pi$$
$$608$$ 0 0
$$609$$ 20.0000 0.810441
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −22.0000 −0.888572 −0.444286 0.895885i $$-0.646543\pi$$
−0.444286 + 0.895885i $$0.646543\pi$$
$$614$$ 0 0
$$615$$ −4.00000 −0.161296
$$616$$ 0 0
$$617$$ 30.0000 1.20775 0.603877 0.797077i $$-0.293622\pi$$
0.603877 + 0.797077i $$0.293622\pi$$
$$618$$ 0 0
$$619$$ 34.0000 1.36658 0.683288 0.730149i $$-0.260549\pi$$
0.683288 + 0.730149i $$0.260549\pi$$
$$620$$ 0 0
$$621$$ 8.00000 0.321029
$$622$$ 0 0
$$623$$ 2.00000 0.0801283
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 0 0
$$627$$ −24.0000 −0.958468
$$628$$ 0 0
$$629$$ −12.0000 −0.478471
$$630$$ 0 0
$$631$$ 38.0000 1.51276 0.756378 0.654135i $$-0.226967\pi$$
0.756378 + 0.654135i $$0.226967\pi$$
$$632$$ 0 0
$$633$$ −24.0000 −0.953914
$$634$$ 0 0
$$635$$ −22.0000 −0.873043
$$636$$ 0 0
$$637$$ −1.00000 −0.0396214
$$638$$ 0 0
$$639$$ 10.0000 0.395594
$$640$$ 0 0
$$641$$ −30.0000 −1.18493 −0.592464 0.805597i $$-0.701845\pi$$
−0.592464 + 0.805597i $$0.701845\pi$$
$$642$$ 0 0
$$643$$ 20.0000 0.788723 0.394362 0.918955i $$-0.370966\pi$$
0.394362 + 0.918955i $$0.370966\pi$$
$$644$$ 0 0
$$645$$ −20.0000 −0.787499
$$646$$ 0 0
$$647$$ 50.0000 1.96570 0.982851 0.184399i $$-0.0590339\pi$$
0.982851 + 0.184399i $$0.0590339\pi$$
$$648$$ 0 0
$$649$$ −12.0000 −0.471041
$$650$$ 0 0
$$651$$ 12.0000 0.470317
$$652$$ 0 0
$$653$$ 22.0000 0.860927 0.430463 0.902608i $$-0.358350\pi$$
0.430463 + 0.902608i $$0.358350\pi$$
$$654$$ 0 0
$$655$$ 12.0000 0.468879
$$656$$ 0 0
$$657$$ 2.00000 0.0780274
$$658$$ 0 0
$$659$$ −40.0000 −1.55818 −0.779089 0.626913i $$-0.784318\pi$$
−0.779089 + 0.626913i $$0.784318\pi$$
$$660$$ 0 0
$$661$$ −14.0000 −0.544537 −0.272268 0.962221i $$-0.587774\pi$$
−0.272268 + 0.962221i $$0.587774\pi$$
$$662$$ 0 0
$$663$$ −4.00000 −0.155347
$$664$$ 0 0
$$665$$ −2.00000 −0.0775567
$$666$$ 0 0
$$667$$ 20.0000 0.774403
$$668$$ 0 0
$$669$$ −16.0000 −0.618596
$$670$$ 0 0
$$671$$ −12.0000 −0.463255
$$672$$ 0 0
$$673$$ −6.00000 −0.231283 −0.115642 0.993291i $$-0.536892\pi$$
−0.115642 + 0.993291i $$0.536892\pi$$
$$674$$ 0 0
$$675$$ 4.00000 0.153960
$$676$$ 0 0
$$677$$ −46.0000 −1.76792 −0.883962 0.467559i $$-0.845134\pi$$
−0.883962 + 0.467559i $$0.845134\pi$$
$$678$$ 0 0
$$679$$ −14.0000 −0.537271
$$680$$ 0 0
$$681$$ −48.0000 −1.83936
$$682$$ 0 0
$$683$$ −16.0000 −0.612223 −0.306111 0.951996i $$-0.599028\pi$$
−0.306111 + 0.951996i $$0.599028\pi$$
$$684$$ 0 0
$$685$$ 10.0000 0.382080
$$686$$ 0 0
$$687$$ −52.0000 −1.98392
$$688$$ 0 0
$$689$$ −14.0000 −0.533358
$$690$$ 0 0
$$691$$ 10.0000 0.380418 0.190209 0.981744i $$-0.439083\pi$$
0.190209 + 0.981744i $$0.439083\pi$$
$$692$$ 0 0
$$693$$ 6.00000 0.227921
$$694$$ 0 0
$$695$$ 16.0000 0.606915
$$696$$ 0 0
$$697$$ 4.00000 0.151511
$$698$$ 0 0
$$699$$ −36.0000 −1.36165
$$700$$ 0 0
$$701$$ −2.00000 −0.0755390 −0.0377695 0.999286i $$-0.512025\pi$$
−0.0377695 + 0.999286i $$0.512025\pi$$
$$702$$ 0 0
$$703$$ −12.0000 −0.452589
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 18.0000 0.676960
$$708$$ 0 0
$$709$$ −18.0000 −0.676004 −0.338002 0.941145i $$-0.609751\pi$$
−0.338002 + 0.941145i $$0.609751\pi$$
$$710$$ 0 0
$$711$$ −4.00000 −0.150012
$$712$$ 0 0
$$713$$ 12.0000 0.449404
$$714$$ 0 0
$$715$$ −6.00000 −0.224387
$$716$$ 0 0
$$717$$ −12.0000 −0.448148
$$718$$ 0 0
$$719$$ −32.0000 −1.19340 −0.596699 0.802465i $$-0.703521\pi$$
−0.596699 + 0.802465i $$0.703521\pi$$
$$720$$ 0 0
$$721$$ −14.0000 −0.521387
$$722$$ 0 0
$$723$$ 20.0000 0.743808
$$724$$ 0 0
$$725$$ 10.0000 0.371391
$$726$$ 0 0
$$727$$ 42.0000 1.55769 0.778847 0.627214i $$-0.215805\pi$$
0.778847 + 0.627214i $$0.215805\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ 20.0000 0.739727
$$732$$ 0 0
$$733$$ −30.0000 −1.10808 −0.554038 0.832492i $$-0.686914\pi$$
−0.554038 + 0.832492i $$0.686914\pi$$
$$734$$ 0 0
$$735$$ 2.00000 0.0737711
$$736$$ 0 0
$$737$$ 48.0000 1.76810
$$738$$ 0 0
$$739$$ −26.0000 −0.956425 −0.478213 0.878244i $$-0.658715\pi$$
−0.478213 + 0.878244i $$0.658715\pi$$
$$740$$ 0 0
$$741$$ −4.00000 −0.146944
$$742$$ 0 0
$$743$$ 24.0000 0.880475 0.440237 0.897881i $$-0.354894\pi$$
0.440237 + 0.897881i $$0.354894\pi$$
$$744$$ 0 0
$$745$$ −14.0000 −0.512920
$$746$$ 0 0
$$747$$ 4.00000 0.146352
$$748$$ 0 0
$$749$$ 18.0000 0.657706
$$750$$ 0 0
$$751$$ 20.0000 0.729810 0.364905 0.931045i $$-0.381101\pi$$
0.364905 + 0.931045i $$0.381101\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 2.00000 0.0727875
$$756$$ 0 0
$$757$$ −10.0000 −0.363456 −0.181728 0.983349i $$-0.558169\pi$$
−0.181728 + 0.983349i $$0.558169\pi$$
$$758$$ 0 0
$$759$$ 24.0000 0.871145
$$760$$ 0 0
$$761$$ −10.0000 −0.362500 −0.181250 0.983437i $$-0.558014\pi$$
−0.181250 + 0.983437i $$0.558014\pi$$
$$762$$ 0 0
$$763$$ 10.0000 0.362024
$$764$$ 0 0
$$765$$ 2.00000 0.0723102
$$766$$ 0 0
$$767$$ −2.00000 −0.0722158
$$768$$ 0 0
$$769$$ −10.0000 −0.360609 −0.180305 0.983611i $$-0.557708\pi$$
−0.180305 + 0.983611i $$0.557708\pi$$
$$770$$ 0 0
$$771$$ −12.0000 −0.432169
$$772$$ 0 0
$$773$$ 6.00000 0.215805 0.107903 0.994161i $$-0.465587\pi$$
0.107903 + 0.994161i $$0.465587\pi$$
$$774$$ 0 0
$$775$$ 6.00000 0.215526
$$776$$ 0 0
$$777$$ 12.0000 0.430498
$$778$$ 0 0
$$779$$ 4.00000 0.143315
$$780$$ 0 0
$$781$$ −60.0000 −2.14697
$$782$$ 0 0
$$783$$ 40.0000 1.42948
$$784$$ 0 0
$$785$$ 22.0000 0.785214
$$786$$ 0 0
$$787$$ −28.0000 −0.998092 −0.499046 0.866575i $$-0.666316\pi$$
−0.499046 + 0.866575i $$0.666316\pi$$
$$788$$ 0 0
$$789$$ −12.0000 −0.427211
$$790$$ 0 0
$$791$$ 6.00000 0.213335
$$792$$ 0 0
$$793$$ −2.00000 −0.0710221
$$794$$ 0 0
$$795$$ 28.0000 0.993058
$$796$$ 0 0
$$797$$ 42.0000 1.48772 0.743858 0.668338i $$-0.232994\pi$$
0.743858 + 0.668338i $$0.232994\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ −2.00000 −0.0706665
$$802$$ 0 0
$$803$$ −12.0000 −0.423471
$$804$$ 0 0
$$805$$ 2.00000 0.0704907
$$806$$ 0 0
$$807$$ 20.0000 0.704033
$$808$$ 0 0
$$809$$ −34.0000 −1.19538 −0.597688 0.801729i $$-0.703914\pi$$
−0.597688 + 0.801729i $$0.703914\pi$$
$$810$$ 0 0
$$811$$ −14.0000 −0.491606 −0.245803 0.969320i $$-0.579052\pi$$
−0.245803 + 0.969320i $$0.579052\pi$$
$$812$$ 0 0
$$813$$ −36.0000 −1.26258
$$814$$ 0 0
$$815$$ 24.0000 0.840683
$$816$$ 0 0
$$817$$ 20.0000 0.699711
$$818$$ 0 0
$$819$$ 1.00000 0.0349428
$$820$$ 0 0
$$821$$ 30.0000 1.04701 0.523504 0.852023i $$-0.324625\pi$$
0.523504 + 0.852023i $$0.324625\pi$$
$$822$$ 0 0
$$823$$ −38.0000 −1.32460 −0.662298 0.749240i $$-0.730419\pi$$
−0.662298 + 0.749240i $$0.730419\pi$$
$$824$$ 0 0
$$825$$ 12.0000 0.417786
$$826$$ 0 0
$$827$$ 12.0000 0.417281 0.208640 0.977992i $$-0.433096\pi$$
0.208640 + 0.977992i $$0.433096\pi$$
$$828$$ 0 0
$$829$$ −30.0000 −1.04194 −0.520972 0.853574i $$-0.674430\pi$$
−0.520972 + 0.853574i $$0.674430\pi$$
$$830$$ 0 0
$$831$$ 52.0000 1.80386
$$832$$ 0 0
$$833$$ −2.00000 −0.0692959
$$834$$ 0 0
$$835$$ 16.0000 0.553703
$$836$$ 0 0
$$837$$ 24.0000 0.829561
$$838$$ 0 0
$$839$$ −18.0000 −0.621429 −0.310715 0.950503i $$-0.600568\pi$$
−0.310715 + 0.950503i $$0.600568\pi$$
$$840$$ 0 0
$$841$$ 71.0000 2.44828
$$842$$ 0 0
$$843$$ −20.0000 −0.688837
$$844$$ 0 0
$$845$$ −1.00000 −0.0344010
$$846$$ 0 0
$$847$$ −25.0000 −0.859010
$$848$$ 0 0
$$849$$ 28.0000 0.960958
$$850$$ 0 0
$$851$$ 12.0000 0.411355
$$852$$ 0 0
$$853$$ 14.0000 0.479351 0.239675 0.970853i $$-0.422959\pi$$
0.239675 + 0.970853i $$0.422959\pi$$
$$854$$ 0 0
$$855$$ 2.00000 0.0683986
$$856$$ 0 0
$$857$$ 38.0000 1.29806 0.649028 0.760765i $$-0.275176\pi$$
0.649028 + 0.760765i $$0.275176\pi$$
$$858$$ 0 0
$$859$$ −24.0000 −0.818869 −0.409435 0.912339i $$-0.634274\pi$$
−0.409435 + 0.912339i $$0.634274\pi$$
$$860$$ 0 0
$$861$$ −4.00000 −0.136320
$$862$$ 0 0
$$863$$ 48.0000 1.63394 0.816970 0.576681i $$-0.195652\pi$$
0.816970 + 0.576681i $$0.195652\pi$$
$$864$$ 0 0
$$865$$ −18.0000 −0.612018
$$866$$ 0 0
$$867$$ 26.0000 0.883006
$$868$$ 0 0
$$869$$ 24.0000 0.814144
$$870$$ 0 0
$$871$$ 8.00000 0.271070
$$872$$ 0 0
$$873$$ 14.0000 0.473828
$$874$$ 0 0
$$875$$ 1.00000 0.0338062
$$876$$ 0 0
$$877$$ 10.0000 0.337676 0.168838 0.985644i $$-0.445999\pi$$
0.168838 + 0.985644i $$0.445999\pi$$
$$878$$ 0 0
$$879$$ −28.0000 −0.944417
$$880$$ 0 0
$$881$$ −18.0000 −0.606435 −0.303218 0.952921i $$-0.598061\pi$$
−0.303218 + 0.952921i $$0.598061\pi$$
$$882$$ 0 0
$$883$$ −18.0000 −0.605748 −0.302874 0.953031i $$-0.597946\pi$$
−0.302874 + 0.953031i $$0.597946\pi$$
$$884$$ 0 0
$$885$$ 4.00000 0.134459
$$886$$ 0 0
$$887$$ 22.0000 0.738688 0.369344 0.929293i $$-0.379582\pi$$
0.369344 + 0.929293i $$0.379582\pi$$
$$888$$ 0 0
$$889$$ −22.0000 −0.737856
$$890$$ 0 0
$$891$$ 66.0000 2.21108
$$892$$ 0 0
$$893$$ 0 0
$$894$$ 0 0
$$895$$ −4.00000 −0.133705
$$896$$ 0 0
$$897$$ 4.00000 0.133556
$$898$$ 0 0
$$899$$ 60.0000 2.00111
$$900$$ 0 0
$$901$$ −28.0000 −0.932815
$$902$$ 0 0
$$903$$ −20.0000 −0.665558
$$904$$ 0 0
$$905$$ 22.0000 0.731305
$$906$$ 0 0
$$907$$ 26.0000 0.863316 0.431658 0.902037i $$-0.357929\pi$$
0.431658 + 0.902037i $$0.357929\pi$$
$$908$$ 0 0
$$909$$ −18.0000 −0.597022
$$910$$ 0 0
$$911$$ 8.00000 0.265052 0.132526 0.991180i $$-0.457691\pi$$
0.132526 + 0.991180i $$0.457691\pi$$
$$912$$ 0 0
$$913$$ −24.0000 −0.794284
$$914$$ 0 0
$$915$$ 4.00000 0.132236
$$916$$ 0 0
$$917$$ 12.0000 0.396275
$$918$$ 0 0
$$919$$ 4.00000 0.131948 0.0659739 0.997821i $$-0.478985\pi$$
0.0659739 + 0.997821i $$0.478985\pi$$
$$920$$ 0 0
$$921$$ 24.0000 0.790827
$$922$$ 0 0
$$923$$ −10.0000 −0.329154
$$924$$ 0 0
$$925$$ 6.00000 0.197279
$$926$$ 0 0
$$927$$ 14.0000 0.459820
$$928$$ 0 0
$$929$$ 6.00000 0.196854 0.0984268 0.995144i $$-0.468619\pi$$
0.0984268 + 0.995144i $$0.468619\pi$$
$$930$$ 0 0
$$931$$ −2.00000 −0.0655474
$$932$$ 0 0
$$933$$ 24.0000 0.785725
$$934$$ 0 0
$$935$$ −12.0000 −0.392442
$$936$$ 0 0
$$937$$ 30.0000 0.980057 0.490029 0.871706i $$-0.336986\pi$$
0.490029 + 0.871706i $$0.336986\pi$$
$$938$$ 0 0
$$939$$ 52.0000 1.69696
$$940$$ 0 0
$$941$$ 42.0000 1.36916 0.684580 0.728937i $$-0.259985\pi$$
0.684580 + 0.728937i $$0.259985\pi$$
$$942$$ 0 0
$$943$$ −4.00000 −0.130258
$$944$$ 0 0
$$945$$ 4.00000 0.130120
$$946$$ 0 0
$$947$$ 4.00000 0.129983 0.0649913 0.997886i $$-0.479298\pi$$
0.0649913 + 0.997886i $$0.479298\pi$$
$$948$$ 0 0
$$949$$ −2.00000 −0.0649227
$$950$$ 0 0
$$951$$ −28.0000 −0.907962
$$952$$ 0 0
$$953$$ −38.0000 −1.23094 −0.615470 0.788160i $$-0.711034\pi$$
−0.615470 + 0.788160i $$0.711034\pi$$
$$954$$ 0 0
$$955$$ −8.00000 −0.258874
$$956$$ 0 0
$$957$$ 120.000 3.87905
$$958$$ 0 0
$$959$$ 10.0000 0.322917
$$960$$ 0 0
$$961$$ 5.00000 0.161290
$$962$$ 0 0
$$963$$ −18.0000 −0.580042
$$964$$ 0 0
$$965$$ −22.0000 −0.708205
$$966$$ 0 0
$$967$$ −4.00000 −0.128631 −0.0643157 0.997930i $$-0.520486\pi$$
−0.0643157 + 0.997930i $$0.520486\pi$$
$$968$$ 0 0
$$969$$ −8.00000 −0.256997
$$970$$ 0 0
$$971$$ −12.0000 −0.385098 −0.192549 0.981287i $$-0.561675\pi$$
−0.192549 + 0.981287i $$0.561675\pi$$
$$972$$ 0 0
$$973$$ 16.0000 0.512936
$$974$$ 0 0
$$975$$ 2.00000 0.0640513
$$976$$ 0 0
$$977$$ 2.00000 0.0639857 0.0319928 0.999488i $$-0.489815\pi$$
0.0319928 + 0.999488i $$0.489815\pi$$
$$978$$ 0 0
$$979$$ 12.0000 0.383522
$$980$$ 0 0
$$981$$ −10.0000 −0.319275
$$982$$ 0 0
$$983$$ 12.0000 0.382741 0.191370 0.981518i $$-0.438707\pi$$
0.191370 + 0.981518i $$0.438707\pi$$
$$984$$ 0 0
$$985$$ −18.0000 −0.573528
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −20.0000 −0.635963
$$990$$ 0 0
$$991$$ 24.0000 0.762385 0.381193 0.924496i $$-0.375513\pi$$
0.381193 + 0.924496i $$0.375513\pi$$
$$992$$ 0 0
$$993$$ −12.0000 −0.380808
$$994$$ 0 0
$$995$$ 16.0000 0.507234
$$996$$ 0 0
$$997$$ −38.0000 −1.20347 −0.601736 0.798695i $$-0.705524\pi$$
−0.601736 + 0.798695i $$0.705524\pi$$
$$998$$ 0 0
$$999$$ 24.0000 0.759326
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 7280.2.a.a.1.1 1
4.3 odd 2 3640.2.a.h.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
3640.2.a.h.1.1 1 4.3 odd 2
7280.2.a.a.1.1 1 1.1 even 1 trivial