# Properties

 Label 4928.2.a.bf.1.1 Level $4928$ Weight $2$ Character 4928.1 Self dual yes Analytic conductor $39.350$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$4928 = 2^{6} \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 4928.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$39.3502781161$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 154) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 4928.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+2.00000 q^{3} -2.00000 q^{5} +1.00000 q^{7} +1.00000 q^{9} +O(q^{10})$$ $$q+2.00000 q^{3} -2.00000 q^{5} +1.00000 q^{7} +1.00000 q^{9} +1.00000 q^{11} +4.00000 q^{13} -4.00000 q^{15} +4.00000 q^{19} +2.00000 q^{21} -4.00000 q^{23} -1.00000 q^{25} -4.00000 q^{27} -2.00000 q^{29} +10.0000 q^{31} +2.00000 q^{33} -2.00000 q^{35} +6.00000 q^{37} +8.00000 q^{39} -4.00000 q^{43} -2.00000 q^{45} -10.0000 q^{47} +1.00000 q^{49} +14.0000 q^{53} -2.00000 q^{55} +8.00000 q^{57} +10.0000 q^{59} +8.00000 q^{61} +1.00000 q^{63} -8.00000 q^{65} +8.00000 q^{67} -8.00000 q^{69} +4.00000 q^{71} +4.00000 q^{73} -2.00000 q^{75} +1.00000 q^{77} -16.0000 q^{79} -11.0000 q^{81} +4.00000 q^{83} -4.00000 q^{87} +10.0000 q^{89} +4.00000 q^{91} +20.0000 q^{93} -8.00000 q^{95} +6.00000 q^{97} +1.00000 q^{99} +O(q^{100})$$

## 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 $$-0.304087\pi$$
0.577350 + 0.816497i $$0.304087\pi$$
$$4$$ 0 0
$$5$$ −2.00000 −0.894427 −0.447214 0.894427i $$-0.647584\pi$$
−0.447214 + 0.894427i $$0.647584\pi$$
$$6$$ 0 0
$$7$$ 1.00000 0.377964
$$8$$ 0 0
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ 1.00000 0.301511
$$12$$ 0 0
$$13$$ 4.00000 1.10940 0.554700 0.832050i $$-0.312833\pi$$
0.554700 + 0.832050i $$0.312833\pi$$
$$14$$ 0 0
$$15$$ −4.00000 −1.03280
$$16$$ 0 0
$$17$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ 0 0
$$19$$ 4.00000 0.917663 0.458831 0.888523i $$-0.348268\pi$$
0.458831 + 0.888523i $$0.348268\pi$$
$$20$$ 0 0
$$21$$ 2.00000 0.436436
$$22$$ 0 0
$$23$$ −4.00000 −0.834058 −0.417029 0.908893i $$-0.636929\pi$$
−0.417029 + 0.908893i $$0.636929\pi$$
$$24$$ 0 0
$$25$$ −1.00000 −0.200000
$$26$$ 0 0
$$27$$ −4.00000 −0.769800
$$28$$ 0 0
$$29$$ −2.00000 −0.371391 −0.185695 0.982607i $$-0.559454\pi$$
−0.185695 + 0.982607i $$0.559454\pi$$
$$30$$ 0 0
$$31$$ 10.0000 1.79605 0.898027 0.439941i $$-0.145001\pi$$
0.898027 + 0.439941i $$0.145001\pi$$
$$32$$ 0 0
$$33$$ 2.00000 0.348155
$$34$$ 0 0
$$35$$ −2.00000 −0.338062
$$36$$ 0 0
$$37$$ 6.00000 0.986394 0.493197 0.869918i $$-0.335828\pi$$
0.493197 + 0.869918i $$0.335828\pi$$
$$38$$ 0 0
$$39$$ 8.00000 1.28103
$$40$$ 0 0
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ −4.00000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ 0 0
$$45$$ −2.00000 −0.298142
$$46$$ 0 0
$$47$$ −10.0000 −1.45865 −0.729325 0.684167i $$-0.760166\pi$$
−0.729325 + 0.684167i $$0.760166\pi$$
$$48$$ 0 0
$$49$$ 1.00000 0.142857
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 14.0000 1.92305 0.961524 0.274721i $$-0.0885855\pi$$
0.961524 + 0.274721i $$0.0885855\pi$$
$$54$$ 0 0
$$55$$ −2.00000 −0.269680
$$56$$ 0 0
$$57$$ 8.00000 1.05963
$$58$$ 0 0
$$59$$ 10.0000 1.30189 0.650945 0.759125i $$-0.274373\pi$$
0.650945 + 0.759125i $$0.274373\pi$$
$$60$$ 0 0
$$61$$ 8.00000 1.02430 0.512148 0.858898i $$-0.328850\pi$$
0.512148 + 0.858898i $$0.328850\pi$$
$$62$$ 0 0
$$63$$ 1.00000 0.125988
$$64$$ 0 0
$$65$$ −8.00000 −0.992278
$$66$$ 0 0
$$67$$ 8.00000 0.977356 0.488678 0.872464i $$-0.337479\pi$$
0.488678 + 0.872464i $$0.337479\pi$$
$$68$$ 0 0
$$69$$ −8.00000 −0.963087
$$70$$ 0 0
$$71$$ 4.00000 0.474713 0.237356 0.971423i $$-0.423719\pi$$
0.237356 + 0.971423i $$0.423719\pi$$
$$72$$ 0 0
$$73$$ 4.00000 0.468165 0.234082 0.972217i $$-0.424791\pi$$
0.234082 + 0.972217i $$0.424791\pi$$
$$74$$ 0 0
$$75$$ −2.00000 −0.230940
$$76$$ 0 0
$$77$$ 1.00000 0.113961
$$78$$ 0 0
$$79$$ −16.0000 −1.80014 −0.900070 0.435745i $$-0.856485\pi$$
−0.900070 + 0.435745i $$0.856485\pi$$
$$80$$ 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
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −4.00000 −0.428845
$$88$$ 0 0
$$89$$ 10.0000 1.06000 0.529999 0.847998i $$-0.322192\pi$$
0.529999 + 0.847998i $$0.322192\pi$$
$$90$$ 0 0
$$91$$ 4.00000 0.419314
$$92$$ 0 0
$$93$$ 20.0000 2.07390
$$94$$ 0 0
$$95$$ −8.00000 −0.820783
$$96$$ 0 0
$$97$$ 6.00000 0.609208 0.304604 0.952479i $$-0.401476\pi$$
0.304604 + 0.952479i $$0.401476\pi$$
$$98$$ 0 0
$$99$$ 1.00000 0.100504
$$100$$ 0 0
$$101$$ −12.0000 −1.19404 −0.597022 0.802225i $$-0.703650\pi$$
−0.597022 + 0.802225i $$0.703650\pi$$
$$102$$ 0 0
$$103$$ −2.00000 −0.197066 −0.0985329 0.995134i $$-0.531415\pi$$
−0.0985329 + 0.995134i $$0.531415\pi$$
$$104$$ 0 0
$$105$$ −4.00000 −0.390360
$$106$$ 0 0
$$107$$ −12.0000 −1.16008 −0.580042 0.814587i $$-0.696964\pi$$
−0.580042 + 0.814587i $$0.696964\pi$$
$$108$$ 0 0
$$109$$ 14.0000 1.34096 0.670478 0.741929i $$-0.266089\pi$$
0.670478 + 0.741929i $$0.266089\pi$$
$$110$$ 0 0
$$111$$ 12.0000 1.13899
$$112$$ 0 0
$$113$$ −14.0000 −1.31701 −0.658505 0.752577i $$-0.728811\pi$$
−0.658505 + 0.752577i $$0.728811\pi$$
$$114$$ 0 0
$$115$$ 8.00000 0.746004
$$116$$ 0 0
$$117$$ 4.00000 0.369800
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 1.00000 0.0909091
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 12.0000 1.07331
$$126$$ 0 0
$$127$$ 16.0000 1.41977 0.709885 0.704317i $$-0.248747\pi$$
0.709885 + 0.704317i $$0.248747\pi$$
$$128$$ 0 0
$$129$$ −8.00000 −0.704361
$$130$$ 0 0
$$131$$ 8.00000 0.698963 0.349482 0.936943i $$-0.386358\pi$$
0.349482 + 0.936943i $$0.386358\pi$$
$$132$$ 0 0
$$133$$ 4.00000 0.346844
$$134$$ 0 0
$$135$$ 8.00000 0.688530
$$136$$ 0 0
$$137$$ 6.00000 0.512615 0.256307 0.966595i $$-0.417494\pi$$
0.256307 + 0.966595i $$0.417494\pi$$
$$138$$ 0 0
$$139$$ 20.0000 1.69638 0.848189 0.529694i $$-0.177693\pi$$
0.848189 + 0.529694i $$0.177693\pi$$
$$140$$ 0 0
$$141$$ −20.0000 −1.68430
$$142$$ 0 0
$$143$$ 4.00000 0.334497
$$144$$ 0 0
$$145$$ 4.00000 0.332182
$$146$$ 0 0
$$147$$ 2.00000 0.164957
$$148$$ 0 0
$$149$$ −22.0000 −1.80231 −0.901155 0.433497i $$-0.857280\pi$$
−0.901155 + 0.433497i $$0.857280\pi$$
$$150$$ 0 0
$$151$$ −16.0000 −1.30206 −0.651031 0.759051i $$-0.725663\pi$$
−0.651031 + 0.759051i $$0.725663\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −20.0000 −1.60644
$$156$$ 0 0
$$157$$ −10.0000 −0.798087 −0.399043 0.916932i $$-0.630658\pi$$
−0.399043 + 0.916932i $$0.630658\pi$$
$$158$$ 0 0
$$159$$ 28.0000 2.22054
$$160$$ 0 0
$$161$$ −4.00000 −0.315244
$$162$$ 0 0
$$163$$ 24.0000 1.87983 0.939913 0.341415i $$-0.110906\pi$$
0.939913 + 0.341415i $$0.110906\pi$$
$$164$$ 0 0
$$165$$ −4.00000 −0.311400
$$166$$ 0 0
$$167$$ 8.00000 0.619059 0.309529 0.950890i $$-0.399829\pi$$
0.309529 + 0.950890i $$0.399829\pi$$
$$168$$ 0 0
$$169$$ 3.00000 0.230769
$$170$$ 0 0
$$171$$ 4.00000 0.305888
$$172$$ 0 0
$$173$$ −4.00000 −0.304114 −0.152057 0.988372i $$-0.548590\pi$$
−0.152057 + 0.988372i $$0.548590\pi$$
$$174$$ 0 0
$$175$$ −1.00000 −0.0755929
$$176$$ 0 0
$$177$$ 20.0000 1.50329
$$178$$ 0 0
$$179$$ 12.0000 0.896922 0.448461 0.893802i $$-0.351972\pi$$
0.448461 + 0.893802i $$0.351972\pi$$
$$180$$ 0 0
$$181$$ −14.0000 −1.04061 −0.520306 0.853980i $$-0.674182\pi$$
−0.520306 + 0.853980i $$0.674182\pi$$
$$182$$ 0 0
$$183$$ 16.0000 1.18275
$$184$$ 0 0
$$185$$ −12.0000 −0.882258
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ −4.00000 −0.290957
$$190$$ 0 0
$$191$$ −8.00000 −0.578860 −0.289430 0.957199i $$-0.593466\pi$$
−0.289430 + 0.957199i $$0.593466\pi$$
$$192$$ 0 0
$$193$$ −6.00000 −0.431889 −0.215945 0.976406i $$-0.569283\pi$$
−0.215945 + 0.976406i $$0.569283\pi$$
$$194$$ 0 0
$$195$$ −16.0000 −1.14578
$$196$$ 0 0
$$197$$ 18.0000 1.28245 0.641223 0.767354i $$-0.278427\pi$$
0.641223 + 0.767354i $$0.278427\pi$$
$$198$$ 0 0
$$199$$ 14.0000 0.992434 0.496217 0.868199i $$-0.334722\pi$$
0.496217 + 0.868199i $$0.334722\pi$$
$$200$$ 0 0
$$201$$ 16.0000 1.12855
$$202$$ 0 0
$$203$$ −2.00000 −0.140372
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −4.00000 −0.278019
$$208$$ 0 0
$$209$$ 4.00000 0.276686
$$210$$ 0 0
$$211$$ −4.00000 −0.275371 −0.137686 0.990476i $$-0.543966\pi$$
−0.137686 + 0.990476i $$0.543966\pi$$
$$212$$ 0 0
$$213$$ 8.00000 0.548151
$$214$$ 0 0
$$215$$ 8.00000 0.545595
$$216$$ 0 0
$$217$$ 10.0000 0.678844
$$218$$ 0 0
$$219$$ 8.00000 0.540590
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 14.0000 0.937509 0.468755 0.883328i $$-0.344703\pi$$
0.468755 + 0.883328i $$0.344703\pi$$
$$224$$ 0 0
$$225$$ −1.00000 −0.0666667
$$226$$ 0 0
$$227$$ 8.00000 0.530979 0.265489 0.964114i $$-0.414466\pi$$
0.265489 + 0.964114i $$0.414466\pi$$
$$228$$ 0 0
$$229$$ 10.0000 0.660819 0.330409 0.943838i $$-0.392813\pi$$
0.330409 + 0.943838i $$0.392813\pi$$
$$230$$ 0 0
$$231$$ 2.00000 0.131590
$$232$$ 0 0
$$233$$ 6.00000 0.393073 0.196537 0.980497i $$-0.437031\pi$$
0.196537 + 0.980497i $$0.437031\pi$$
$$234$$ 0 0
$$235$$ 20.0000 1.30466
$$236$$ 0 0
$$237$$ −32.0000 −2.07862
$$238$$ 0 0
$$239$$ 8.00000 0.517477 0.258738 0.965947i $$-0.416693\pi$$
0.258738 + 0.965947i $$0.416693\pi$$
$$240$$ 0 0
$$241$$ 8.00000 0.515325 0.257663 0.966235i $$-0.417048\pi$$
0.257663 + 0.966235i $$0.417048\pi$$
$$242$$ 0 0
$$243$$ −10.0000 −0.641500
$$244$$ 0 0
$$245$$ −2.00000 −0.127775
$$246$$ 0 0
$$247$$ 16.0000 1.01806
$$248$$ 0 0
$$249$$ 8.00000 0.506979
$$250$$ 0 0
$$251$$ −26.0000 −1.64111 −0.820553 0.571571i $$-0.806334\pi$$
−0.820553 + 0.571571i $$0.806334\pi$$
$$252$$ 0 0
$$253$$ −4.00000 −0.251478
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 2.00000 0.124757 0.0623783 0.998053i $$-0.480131\pi$$
0.0623783 + 0.998053i $$0.480131\pi$$
$$258$$ 0 0
$$259$$ 6.00000 0.372822
$$260$$ 0 0
$$261$$ −2.00000 −0.123797
$$262$$ 0 0
$$263$$ 24.0000 1.47990 0.739952 0.672660i $$-0.234848\pi$$
0.739952 + 0.672660i $$0.234848\pi$$
$$264$$ 0 0
$$265$$ −28.0000 −1.72003
$$266$$ 0 0
$$267$$ 20.0000 1.22398
$$268$$ 0 0
$$269$$ −14.0000 −0.853595 −0.426798 0.904347i $$-0.640358\pi$$
−0.426798 + 0.904347i $$0.640358\pi$$
$$270$$ 0 0
$$271$$ 28.0000 1.70088 0.850439 0.526073i $$-0.176336\pi$$
0.850439 + 0.526073i $$0.176336\pi$$
$$272$$ 0 0
$$273$$ 8.00000 0.484182
$$274$$ 0 0
$$275$$ −1.00000 −0.0603023
$$276$$ 0 0
$$277$$ −6.00000 −0.360505 −0.180253 0.983620i $$-0.557691\pi$$
−0.180253 + 0.983620i $$0.557691\pi$$
$$278$$ 0 0
$$279$$ 10.0000 0.598684
$$280$$ 0 0
$$281$$ 30.0000 1.78965 0.894825 0.446417i $$-0.147300\pi$$
0.894825 + 0.446417i $$0.147300\pi$$
$$282$$ 0 0
$$283$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$284$$ 0 0
$$285$$ −16.0000 −0.947758
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −17.0000 −1.00000
$$290$$ 0 0
$$291$$ 12.0000 0.703452
$$292$$ 0 0
$$293$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$294$$ 0 0
$$295$$ −20.0000 −1.16445
$$296$$ 0 0
$$297$$ −4.00000 −0.232104
$$298$$ 0 0
$$299$$ −16.0000 −0.925304
$$300$$ 0 0
$$301$$ −4.00000 −0.230556
$$302$$ 0 0
$$303$$ −24.0000 −1.37876
$$304$$ 0 0
$$305$$ −16.0000 −0.916157
$$306$$ 0 0
$$307$$ 16.0000 0.913168 0.456584 0.889680i $$-0.349073\pi$$
0.456584 + 0.889680i $$0.349073\pi$$
$$308$$ 0 0
$$309$$ −4.00000 −0.227552
$$310$$ 0 0
$$311$$ 6.00000 0.340229 0.170114 0.985424i $$-0.445586\pi$$
0.170114 + 0.985424i $$0.445586\pi$$
$$312$$ 0 0
$$313$$ −6.00000 −0.339140 −0.169570 0.985518i $$-0.554238\pi$$
−0.169570 + 0.985518i $$0.554238\pi$$
$$314$$ 0 0
$$315$$ −2.00000 −0.112687
$$316$$ 0 0
$$317$$ 18.0000 1.01098 0.505490 0.862832i $$-0.331312\pi$$
0.505490 + 0.862832i $$0.331312\pi$$
$$318$$ 0 0
$$319$$ −2.00000 −0.111979
$$320$$ 0 0
$$321$$ −24.0000 −1.33955
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ −4.00000 −0.221880
$$326$$ 0 0
$$327$$ 28.0000 1.54840
$$328$$ 0 0
$$329$$ −10.0000 −0.551318
$$330$$ 0 0
$$331$$ −20.0000 −1.09930 −0.549650 0.835395i $$-0.685239\pi$$
−0.549650 + 0.835395i $$0.685239\pi$$
$$332$$ 0 0
$$333$$ 6.00000 0.328798
$$334$$ 0 0
$$335$$ −16.0000 −0.874173
$$336$$ 0 0
$$337$$ −34.0000 −1.85210 −0.926049 0.377403i $$-0.876817\pi$$
−0.926049 + 0.377403i $$0.876817\pi$$
$$338$$ 0 0
$$339$$ −28.0000 −1.52075
$$340$$ 0 0
$$341$$ 10.0000 0.541530
$$342$$ 0 0
$$343$$ 1.00000 0.0539949
$$344$$ 0 0
$$345$$ 16.0000 0.861411
$$346$$ 0 0
$$347$$ −12.0000 −0.644194 −0.322097 0.946707i $$-0.604388\pi$$
−0.322097 + 0.946707i $$0.604388\pi$$
$$348$$ 0 0
$$349$$ −32.0000 −1.71292 −0.856460 0.516213i $$-0.827341\pi$$
−0.856460 + 0.516213i $$0.827341\pi$$
$$350$$ 0 0
$$351$$ −16.0000 −0.854017
$$352$$ 0 0
$$353$$ 2.00000 0.106449 0.0532246 0.998583i $$-0.483050\pi$$
0.0532246 + 0.998583i $$0.483050\pi$$
$$354$$ 0 0
$$355$$ −8.00000 −0.424596
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 0 0
$$361$$ −3.00000 −0.157895
$$362$$ 0 0
$$363$$ 2.00000 0.104973
$$364$$ 0 0
$$365$$ −8.00000 −0.418739
$$366$$ 0 0
$$367$$ −18.0000 −0.939592 −0.469796 0.882775i $$-0.655673\pi$$
−0.469796 + 0.882775i $$0.655673\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 14.0000 0.726844
$$372$$ 0 0
$$373$$ 34.0000 1.76045 0.880227 0.474554i $$-0.157390\pi$$
0.880227 + 0.474554i $$0.157390\pi$$
$$374$$ 0 0
$$375$$ 24.0000 1.23935
$$376$$ 0 0
$$377$$ −8.00000 −0.412021
$$378$$ 0 0
$$379$$ 8.00000 0.410932 0.205466 0.978664i $$-0.434129\pi$$
0.205466 + 0.978664i $$0.434129\pi$$
$$380$$ 0 0
$$381$$ 32.0000 1.63941
$$382$$ 0 0
$$383$$ −14.0000 −0.715367 −0.357683 0.933843i $$-0.616433\pi$$
−0.357683 + 0.933843i $$0.616433\pi$$
$$384$$ 0 0
$$385$$ −2.00000 −0.101929
$$386$$ 0 0
$$387$$ −4.00000 −0.203331
$$388$$ 0 0
$$389$$ 18.0000 0.912636 0.456318 0.889817i $$-0.349168\pi$$
0.456318 + 0.889817i $$0.349168\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 16.0000 0.807093
$$394$$ 0 0
$$395$$ 32.0000 1.61009
$$396$$ 0 0
$$397$$ −18.0000 −0.903394 −0.451697 0.892171i $$-0.649181\pi$$
−0.451697 + 0.892171i $$0.649181\pi$$
$$398$$ 0 0
$$399$$ 8.00000 0.400501
$$400$$ 0 0
$$401$$ 10.0000 0.499376 0.249688 0.968326i $$-0.419672\pi$$
0.249688 + 0.968326i $$0.419672\pi$$
$$402$$ 0 0
$$403$$ 40.0000 1.99254
$$404$$ 0 0
$$405$$ 22.0000 1.09319
$$406$$ 0 0
$$407$$ 6.00000 0.297409
$$408$$ 0 0
$$409$$ −4.00000 −0.197787 −0.0988936 0.995098i $$-0.531530\pi$$
−0.0988936 + 0.995098i $$0.531530\pi$$
$$410$$ 0 0
$$411$$ 12.0000 0.591916
$$412$$ 0 0
$$413$$ 10.0000 0.492068
$$414$$ 0 0
$$415$$ −8.00000 −0.392705
$$416$$ 0 0
$$417$$ 40.0000 1.95881
$$418$$ 0 0
$$419$$ −30.0000 −1.46560 −0.732798 0.680446i $$-0.761786\pi$$
−0.732798 + 0.680446i $$0.761786\pi$$
$$420$$ 0 0
$$421$$ −10.0000 −0.487370 −0.243685 0.969854i $$-0.578356\pi$$
−0.243685 + 0.969854i $$0.578356\pi$$
$$422$$ 0 0
$$423$$ −10.0000 −0.486217
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 8.00000 0.387147
$$428$$ 0 0
$$429$$ 8.00000 0.386244
$$430$$ 0 0
$$431$$ 16.0000 0.770693 0.385346 0.922772i $$-0.374082\pi$$
0.385346 + 0.922772i $$0.374082\pi$$
$$432$$ 0 0
$$433$$ −10.0000 −0.480569 −0.240285 0.970702i $$-0.577241\pi$$
−0.240285 + 0.970702i $$0.577241\pi$$
$$434$$ 0 0
$$435$$ 8.00000 0.383571
$$436$$ 0 0
$$437$$ −16.0000 −0.765384
$$438$$ 0 0
$$439$$ 28.0000 1.33637 0.668184 0.743996i $$-0.267072\pi$$
0.668184 + 0.743996i $$0.267072\pi$$
$$440$$ 0 0
$$441$$ 1.00000 0.0476190
$$442$$ 0 0
$$443$$ 4.00000 0.190046 0.0950229 0.995475i $$-0.469708\pi$$
0.0950229 + 0.995475i $$0.469708\pi$$
$$444$$ 0 0
$$445$$ −20.0000 −0.948091
$$446$$ 0 0
$$447$$ −44.0000 −2.08113
$$448$$ 0 0
$$449$$ 6.00000 0.283158 0.141579 0.989927i $$-0.454782\pi$$
0.141579 + 0.989927i $$0.454782\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ −32.0000 −1.50349
$$454$$ 0 0
$$455$$ −8.00000 −0.375046
$$456$$ 0 0
$$457$$ −38.0000 −1.77757 −0.888783 0.458329i $$-0.848448\pi$$
−0.888783 + 0.458329i $$0.848448\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −32.0000 −1.49039 −0.745194 0.666847i $$-0.767643\pi$$
−0.745194 + 0.666847i $$0.767643\pi$$
$$462$$ 0 0
$$463$$ −12.0000 −0.557687 −0.278844 0.960337i $$-0.589951\pi$$
−0.278844 + 0.960337i $$0.589951\pi$$
$$464$$ 0 0
$$465$$ −40.0000 −1.85496
$$466$$ 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
$$471$$ −20.0000 −0.921551
$$472$$ 0 0
$$473$$ −4.00000 −0.183920
$$474$$ 0 0
$$475$$ −4.00000 −0.183533
$$476$$ 0 0
$$477$$ 14.0000 0.641016
$$478$$ 0 0
$$479$$ −12.0000 −0.548294 −0.274147 0.961688i $$-0.588395\pi$$
−0.274147 + 0.961688i $$0.588395\pi$$
$$480$$ 0 0
$$481$$ 24.0000 1.09431
$$482$$ 0 0
$$483$$ −8.00000 −0.364013
$$484$$ 0 0
$$485$$ −12.0000 −0.544892
$$486$$ 0 0
$$487$$ −12.0000 −0.543772 −0.271886 0.962329i $$-0.587647\pi$$
−0.271886 + 0.962329i $$0.587647\pi$$
$$488$$ 0 0
$$489$$ 48.0000 2.17064
$$490$$ 0 0
$$491$$ −28.0000 −1.26362 −0.631811 0.775122i $$-0.717688\pi$$
−0.631811 + 0.775122i $$0.717688\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ −2.00000 −0.0898933
$$496$$ 0 0
$$497$$ 4.00000 0.179425
$$498$$ 0 0
$$499$$ −16.0000 −0.716258 −0.358129 0.933672i $$-0.616585\pi$$
−0.358129 + 0.933672i $$0.616585\pi$$
$$500$$ 0 0
$$501$$ 16.0000 0.714827
$$502$$ 0 0
$$503$$ −12.0000 −0.535054 −0.267527 0.963550i $$-0.586206\pi$$
−0.267527 + 0.963550i $$0.586206\pi$$
$$504$$ 0 0
$$505$$ 24.0000 1.06799
$$506$$ 0 0
$$507$$ 6.00000 0.266469
$$508$$ 0 0
$$509$$ −38.0000 −1.68432 −0.842160 0.539227i $$-0.818716\pi$$
−0.842160 + 0.539227i $$0.818716\pi$$
$$510$$ 0 0
$$511$$ 4.00000 0.176950
$$512$$ 0 0
$$513$$ −16.0000 −0.706417
$$514$$ 0 0
$$515$$ 4.00000 0.176261
$$516$$ 0 0
$$517$$ −10.0000 −0.439799
$$518$$ 0 0
$$519$$ −8.00000 −0.351161
$$520$$ 0 0
$$521$$ −42.0000 −1.84005 −0.920027 0.391856i $$-0.871833\pi$$
−0.920027 + 0.391856i $$0.871833\pi$$
$$522$$ 0 0
$$523$$ 16.0000 0.699631 0.349816 0.936819i $$-0.386244\pi$$
0.349816 + 0.936819i $$0.386244\pi$$
$$524$$ 0 0
$$525$$ −2.00000 −0.0872872
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −7.00000 −0.304348
$$530$$ 0 0
$$531$$ 10.0000 0.433963
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 24.0000 1.03761
$$536$$ 0 0
$$537$$ 24.0000 1.03568
$$538$$ 0 0
$$539$$ 1.00000 0.0430730
$$540$$ 0 0
$$541$$ 2.00000 0.0859867 0.0429934 0.999075i $$-0.486311\pi$$
0.0429934 + 0.999075i $$0.486311\pi$$
$$542$$ 0 0
$$543$$ −28.0000 −1.20160
$$544$$ 0 0
$$545$$ −28.0000 −1.19939
$$546$$ 0 0
$$547$$ 4.00000 0.171028 0.0855138 0.996337i $$-0.472747\pi$$
0.0855138 + 0.996337i $$0.472747\pi$$
$$548$$ 0 0
$$549$$ 8.00000 0.341432
$$550$$ 0 0
$$551$$ −8.00000 −0.340811
$$552$$ 0 0
$$553$$ −16.0000 −0.680389
$$554$$ 0 0
$$555$$ −24.0000 −1.01874
$$556$$ 0 0
$$557$$ −30.0000 −1.27114 −0.635570 0.772043i $$-0.719235\pi$$
−0.635570 + 0.772043i $$0.719235\pi$$
$$558$$ 0 0
$$559$$ −16.0000 −0.676728
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 12.0000 0.505740 0.252870 0.967500i $$-0.418626\pi$$
0.252870 + 0.967500i $$0.418626\pi$$
$$564$$ 0 0
$$565$$ 28.0000 1.17797
$$566$$ 0 0
$$567$$ −11.0000 −0.461957
$$568$$ 0 0
$$569$$ 14.0000 0.586911 0.293455 0.955973i $$-0.405195\pi$$
0.293455 + 0.955973i $$0.405195\pi$$
$$570$$ 0 0
$$571$$ −28.0000 −1.17176 −0.585882 0.810397i $$-0.699252\pi$$
−0.585882 + 0.810397i $$0.699252\pi$$
$$572$$ 0 0
$$573$$ −16.0000 −0.668410
$$574$$ 0 0
$$575$$ 4.00000 0.166812
$$576$$ 0 0
$$577$$ −42.0000 −1.74848 −0.874241 0.485491i $$-0.838641\pi$$
−0.874241 + 0.485491i $$0.838641\pi$$
$$578$$ 0 0
$$579$$ −12.0000 −0.498703
$$580$$ 0 0
$$581$$ 4.00000 0.165948
$$582$$ 0 0
$$583$$ 14.0000 0.579821
$$584$$ 0 0
$$585$$ −8.00000 −0.330759
$$586$$ 0 0
$$587$$ −42.0000 −1.73353 −0.866763 0.498721i $$-0.833803\pi$$
−0.866763 + 0.498721i $$0.833803\pi$$
$$588$$ 0 0
$$589$$ 40.0000 1.64817
$$590$$ 0 0
$$591$$ 36.0000 1.48084
$$592$$ 0 0
$$593$$ 12.0000 0.492781 0.246390 0.969171i $$-0.420755\pi$$
0.246390 + 0.969171i $$0.420755\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 28.0000 1.14596
$$598$$ 0 0
$$599$$ 12.0000 0.490307 0.245153 0.969484i $$-0.421162\pi$$
0.245153 + 0.969484i $$0.421162\pi$$
$$600$$ 0 0
$$601$$ −24.0000 −0.978980 −0.489490 0.872009i $$-0.662817\pi$$
−0.489490 + 0.872009i $$0.662817\pi$$
$$602$$ 0 0
$$603$$ 8.00000 0.325785
$$604$$ 0 0
$$605$$ −2.00000 −0.0813116
$$606$$ 0 0
$$607$$ 24.0000 0.974130 0.487065 0.873366i $$-0.338067\pi$$
0.487065 + 0.873366i $$0.338067\pi$$
$$608$$ 0 0
$$609$$ −4.00000 −0.162088
$$610$$ 0 0
$$611$$ −40.0000 −1.61823
$$612$$ 0 0
$$613$$ −2.00000 −0.0807792 −0.0403896 0.999184i $$-0.512860\pi$$
−0.0403896 + 0.999184i $$0.512860\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 38.0000 1.52982 0.764911 0.644136i $$-0.222783\pi$$
0.764911 + 0.644136i $$0.222783\pi$$
$$618$$ 0 0
$$619$$ −2.00000 −0.0803868 −0.0401934 0.999192i $$-0.512797\pi$$
−0.0401934 + 0.999192i $$0.512797\pi$$
$$620$$ 0 0
$$621$$ 16.0000 0.642058
$$622$$ 0 0
$$623$$ 10.0000 0.400642
$$624$$ 0 0
$$625$$ −19.0000 −0.760000
$$626$$ 0 0
$$627$$ 8.00000 0.319489
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −8.00000 −0.318475 −0.159237 0.987240i $$-0.550904\pi$$
−0.159237 + 0.987240i $$0.550904\pi$$
$$632$$ 0 0
$$633$$ −8.00000 −0.317971
$$634$$ 0 0
$$635$$ −32.0000 −1.26988
$$636$$ 0 0
$$637$$ 4.00000 0.158486
$$638$$ 0 0
$$639$$ 4.00000 0.158238
$$640$$ 0 0
$$641$$ −18.0000 −0.710957 −0.355479 0.934684i $$-0.615682\pi$$
−0.355479 + 0.934684i $$0.615682\pi$$
$$642$$ 0 0
$$643$$ 22.0000 0.867595 0.433798 0.901010i $$-0.357173\pi$$
0.433798 + 0.901010i $$0.357173\pi$$
$$644$$ 0 0
$$645$$ 16.0000 0.629999
$$646$$ 0 0
$$647$$ −6.00000 −0.235884 −0.117942 0.993020i $$-0.537630\pi$$
−0.117942 + 0.993020i $$0.537630\pi$$
$$648$$ 0 0
$$649$$ 10.0000 0.392534
$$650$$ 0 0
$$651$$ 20.0000 0.783862
$$652$$ 0 0
$$653$$ −46.0000 −1.80012 −0.900060 0.435767i $$-0.856477\pi$$
−0.900060 + 0.435767i $$0.856477\pi$$
$$654$$ 0 0
$$655$$ −16.0000 −0.625172
$$656$$ 0 0
$$657$$ 4.00000 0.156055
$$658$$ 0 0
$$659$$ 20.0000 0.779089 0.389545 0.921008i $$-0.372632\pi$$
0.389545 + 0.921008i $$0.372632\pi$$
$$660$$ 0 0
$$661$$ 38.0000 1.47803 0.739014 0.673690i $$-0.235292\pi$$
0.739014 + 0.673690i $$0.235292\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −8.00000 −0.310227
$$666$$ 0 0
$$667$$ 8.00000 0.309761
$$668$$ 0 0
$$669$$ 28.0000 1.08254
$$670$$ 0 0
$$671$$ 8.00000 0.308837
$$672$$ 0 0
$$673$$ −10.0000 −0.385472 −0.192736 0.981251i $$-0.561736\pi$$
−0.192736 + 0.981251i $$0.561736\pi$$
$$674$$ 0 0
$$675$$ 4.00000 0.153960
$$676$$ 0 0
$$677$$ −12.0000 −0.461197 −0.230599 0.973049i $$-0.574068\pi$$
−0.230599 + 0.973049i $$0.574068\pi$$
$$678$$ 0 0
$$679$$ 6.00000 0.230259
$$680$$ 0 0
$$681$$ 16.0000 0.613121
$$682$$ 0 0
$$683$$ 12.0000 0.459167 0.229584 0.973289i $$-0.426264\pi$$
0.229584 + 0.973289i $$0.426264\pi$$
$$684$$ 0 0
$$685$$ −12.0000 −0.458496
$$686$$ 0 0
$$687$$ 20.0000 0.763048
$$688$$ 0 0
$$689$$ 56.0000 2.13343
$$690$$ 0 0
$$691$$ 42.0000 1.59776 0.798878 0.601494i $$-0.205427\pi$$
0.798878 + 0.601494i $$0.205427\pi$$
$$692$$ 0 0
$$693$$ 1.00000 0.0379869
$$694$$ 0 0
$$695$$ −40.0000 −1.51729
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 12.0000 0.453882
$$700$$ 0 0
$$701$$ 6.00000 0.226617 0.113308 0.993560i $$-0.463855\pi$$
0.113308 + 0.993560i $$0.463855\pi$$
$$702$$ 0 0
$$703$$ 24.0000 0.905177
$$704$$ 0 0
$$705$$ 40.0000 1.50649
$$706$$ 0 0
$$707$$ −12.0000 −0.451306
$$708$$ 0 0
$$709$$ 10.0000 0.375558 0.187779 0.982211i $$-0.439871\pi$$
0.187779 + 0.982211i $$0.439871\pi$$
$$710$$ 0 0
$$711$$ −16.0000 −0.600047
$$712$$ 0 0
$$713$$ −40.0000 −1.49801
$$714$$ 0 0
$$715$$ −8.00000 −0.299183
$$716$$ 0 0
$$717$$ 16.0000 0.597531
$$718$$ 0 0
$$719$$ −6.00000 −0.223762 −0.111881 0.993722i $$-0.535688\pi$$
−0.111881 + 0.993722i $$0.535688\pi$$
$$720$$ 0 0
$$721$$ −2.00000 −0.0744839
$$722$$ 0 0
$$723$$ 16.0000 0.595046
$$724$$ 0 0
$$725$$ 2.00000 0.0742781
$$726$$ 0 0
$$727$$ −46.0000 −1.70605 −0.853023 0.521874i $$-0.825233\pi$$
−0.853023 + 0.521874i $$0.825233\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 8.00000 0.295487 0.147743 0.989026i $$-0.452799\pi$$
0.147743 + 0.989026i $$0.452799\pi$$
$$734$$ 0 0
$$735$$ −4.00000 −0.147542
$$736$$ 0 0
$$737$$ 8.00000 0.294684
$$738$$ 0 0
$$739$$ −52.0000 −1.91285 −0.956425 0.291977i $$-0.905687\pi$$
−0.956425 + 0.291977i $$0.905687\pi$$
$$740$$ 0 0
$$741$$ 32.0000 1.17555
$$742$$ 0 0
$$743$$ −16.0000 −0.586983 −0.293492 0.955962i $$-0.594817\pi$$
−0.293492 + 0.955962i $$0.594817\pi$$
$$744$$ 0 0
$$745$$ 44.0000 1.61204
$$746$$ 0 0
$$747$$ 4.00000 0.146352
$$748$$ 0 0
$$749$$ −12.0000 −0.438470
$$750$$ 0 0
$$751$$ −20.0000 −0.729810 −0.364905 0.931045i $$-0.618899\pi$$
−0.364905 + 0.931045i $$0.618899\pi$$
$$752$$ 0 0
$$753$$ −52.0000 −1.89499
$$754$$ 0 0
$$755$$ 32.0000 1.16460
$$756$$ 0 0
$$757$$ −30.0000 −1.09037 −0.545184 0.838316i $$-0.683540\pi$$
−0.545184 + 0.838316i $$0.683540\pi$$
$$758$$ 0 0
$$759$$ −8.00000 −0.290382
$$760$$ 0 0
$$761$$ −12.0000 −0.435000 −0.217500 0.976060i $$-0.569790\pi$$
−0.217500 + 0.976060i $$0.569790\pi$$
$$762$$ 0 0
$$763$$ 14.0000 0.506834
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 40.0000 1.44432
$$768$$ 0 0
$$769$$ 4.00000 0.144244 0.0721218 0.997396i $$-0.477023\pi$$
0.0721218 + 0.997396i $$0.477023\pi$$
$$770$$ 0 0
$$771$$ 4.00000 0.144056
$$772$$ 0 0
$$773$$ 34.0000 1.22290 0.611448 0.791285i $$-0.290588\pi$$
0.611448 + 0.791285i $$0.290588\pi$$
$$774$$ 0 0
$$775$$ −10.0000 −0.359211
$$776$$ 0 0
$$777$$ 12.0000 0.430498
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 4.00000 0.143131
$$782$$ 0 0
$$783$$ 8.00000 0.285897
$$784$$ 0 0
$$785$$ 20.0000 0.713831
$$786$$ 0 0
$$787$$ 20.0000 0.712923 0.356462 0.934310i $$-0.383983\pi$$
0.356462 + 0.934310i $$0.383983\pi$$
$$788$$ 0 0
$$789$$ 48.0000 1.70885
$$790$$ 0 0
$$791$$ −14.0000 −0.497783
$$792$$ 0 0
$$793$$ 32.0000 1.13635
$$794$$ 0 0
$$795$$ −56.0000 −1.98612
$$796$$ 0 0
$$797$$ −26.0000 −0.920967 −0.460484 0.887668i $$-0.652324\pi$$
−0.460484 + 0.887668i $$0.652324\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 10.0000 0.353333
$$802$$ 0 0
$$803$$ 4.00000 0.141157
$$804$$ 0 0
$$805$$ 8.00000 0.281963
$$806$$ 0 0
$$807$$ −28.0000 −0.985647
$$808$$ 0 0
$$809$$ 26.0000 0.914111 0.457056 0.889438i $$-0.348904\pi$$
0.457056 + 0.889438i $$0.348904\pi$$
$$810$$ 0 0
$$811$$ −40.0000 −1.40459 −0.702295 0.711886i $$-0.747841\pi$$
−0.702295 + 0.711886i $$0.747841\pi$$
$$812$$ 0 0
$$813$$ 56.0000 1.96401
$$814$$ 0 0
$$815$$ −48.0000 −1.68137
$$816$$ 0 0
$$817$$ −16.0000 −0.559769
$$818$$ 0 0
$$819$$ 4.00000 0.139771
$$820$$ 0 0
$$821$$ 50.0000 1.74501 0.872506 0.488603i $$-0.162493\pi$$
0.872506 + 0.488603i $$0.162493\pi$$
$$822$$ 0 0
$$823$$ −8.00000 −0.278862 −0.139431 0.990232i $$-0.544527\pi$$
−0.139431 + 0.990232i $$0.544527\pi$$
$$824$$ 0 0
$$825$$ −2.00000 −0.0696311
$$826$$ 0 0
$$827$$ −20.0000 −0.695468 −0.347734 0.937593i $$-0.613049\pi$$
−0.347734 + 0.937593i $$0.613049\pi$$
$$828$$ 0 0
$$829$$ 14.0000 0.486240 0.243120 0.969996i $$-0.421829\pi$$
0.243120 + 0.969996i $$0.421829\pi$$
$$830$$ 0 0
$$831$$ −12.0000 −0.416275
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ −16.0000 −0.553703
$$836$$ 0 0
$$837$$ −40.0000 −1.38260
$$838$$ 0 0
$$839$$ −30.0000 −1.03572 −0.517858 0.855467i $$-0.673270\pi$$
−0.517858 + 0.855467i $$0.673270\pi$$
$$840$$ 0 0
$$841$$ −25.0000 −0.862069
$$842$$ 0 0
$$843$$ 60.0000 2.06651
$$844$$ 0 0
$$845$$ −6.00000 −0.206406
$$846$$ 0 0
$$847$$ 1.00000 0.0343604
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −24.0000 −0.822709
$$852$$ 0 0
$$853$$ −4.00000 −0.136957 −0.0684787 0.997653i $$-0.521815\pi$$
−0.0684787 + 0.997653i $$0.521815\pi$$
$$854$$ 0 0
$$855$$ −8.00000 −0.273594
$$856$$ 0 0
$$857$$ 12.0000 0.409912 0.204956 0.978771i $$-0.434295\pi$$
0.204956 + 0.978771i $$0.434295\pi$$
$$858$$ 0 0
$$859$$ 14.0000 0.477674 0.238837 0.971060i $$-0.423234\pi$$
0.238837 + 0.971060i $$0.423234\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −40.0000 −1.36162 −0.680808 0.732462i $$-0.738371\pi$$
−0.680808 + 0.732462i $$0.738371\pi$$
$$864$$ 0 0
$$865$$ 8.00000 0.272008
$$866$$ 0 0
$$867$$ −34.0000 −1.15470
$$868$$ 0 0
$$869$$ −16.0000 −0.542763
$$870$$ 0 0
$$871$$ 32.0000 1.08428
$$872$$ 0 0
$$873$$ 6.00000 0.203069
$$874$$ 0 0
$$875$$ 12.0000 0.405674
$$876$$ 0 0
$$877$$ 22.0000 0.742887 0.371444 0.928456i $$-0.378863\pi$$
0.371444 + 0.928456i $$0.378863\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −42.0000 −1.41502 −0.707508 0.706705i $$-0.750181\pi$$
−0.707508 + 0.706705i $$0.750181\pi$$
$$882$$ 0 0
$$883$$ −4.00000 −0.134611 −0.0673054 0.997732i $$-0.521440\pi$$
−0.0673054 + 0.997732i $$0.521440\pi$$
$$884$$ 0 0
$$885$$ −40.0000 −1.34459
$$886$$ 0 0
$$887$$ 28.0000 0.940148 0.470074 0.882627i $$-0.344227\pi$$
0.470074 + 0.882627i $$0.344227\pi$$
$$888$$ 0 0
$$889$$ 16.0000 0.536623
$$890$$ 0 0
$$891$$ −11.0000 −0.368514
$$892$$ 0 0
$$893$$ −40.0000 −1.33855
$$894$$ 0 0
$$895$$ −24.0000 −0.802232
$$896$$ 0 0
$$897$$ −32.0000 −1.06845
$$898$$ 0 0
$$899$$ −20.0000 −0.667037
$$900$$ 0 0
$$901$$ 0 0
$$902$$ 0 0
$$903$$ −8.00000 −0.266223
$$904$$ 0 0
$$905$$ 28.0000 0.930751
$$906$$ 0 0
$$907$$ 48.0000 1.59381 0.796907 0.604102i $$-0.206468\pi$$
0.796907 + 0.604102i $$0.206468\pi$$
$$908$$ 0 0
$$909$$ −12.0000 −0.398015
$$910$$ 0 0
$$911$$ 4.00000 0.132526 0.0662630 0.997802i $$-0.478892\pi$$
0.0662630 + 0.997802i $$0.478892\pi$$
$$912$$ 0 0
$$913$$ 4.00000 0.132381
$$914$$ 0 0
$$915$$ −32.0000 −1.05789
$$916$$ 0 0
$$917$$ 8.00000 0.264183
$$918$$ 0 0
$$919$$ 56.0000 1.84727 0.923635 0.383274i $$-0.125203\pi$$
0.923635 + 0.383274i $$0.125203\pi$$
$$920$$ 0 0
$$921$$ 32.0000 1.05444
$$922$$ 0 0
$$923$$ 16.0000 0.526646
$$924$$ 0 0
$$925$$ −6.00000 −0.197279
$$926$$ 0 0
$$927$$ −2.00000 −0.0656886
$$928$$ 0 0
$$929$$ −10.0000 −0.328089 −0.164045 0.986453i $$-0.552454\pi$$
−0.164045 + 0.986453i $$0.552454\pi$$
$$930$$ 0 0
$$931$$ 4.00000 0.131095
$$932$$ 0 0
$$933$$ 12.0000 0.392862
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −52.0000 −1.69877 −0.849383 0.527777i $$-0.823026\pi$$
−0.849383 + 0.527777i $$0.823026\pi$$
$$938$$ 0 0
$$939$$ −12.0000 −0.391605
$$940$$ 0 0
$$941$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 0 0
$$945$$ 8.00000 0.260240
$$946$$ 0 0
$$947$$ 12.0000 0.389948 0.194974 0.980808i $$-0.437538\pi$$
0.194974 + 0.980808i $$0.437538\pi$$
$$948$$ 0 0
$$949$$ 16.0000 0.519382
$$950$$ 0 0
$$951$$ 36.0000 1.16738
$$952$$ 0 0
$$953$$ 34.0000 1.10137 0.550684 0.834714i $$-0.314367\pi$$
0.550684 + 0.834714i $$0.314367\pi$$
$$954$$ 0 0
$$955$$ 16.0000 0.517748
$$956$$ 0 0
$$957$$ −4.00000 −0.129302
$$958$$ 0 0
$$959$$ 6.00000 0.193750
$$960$$ 0 0
$$961$$ 69.0000 2.22581
$$962$$ 0 0
$$963$$ −12.0000 −0.386695
$$964$$ 0 0
$$965$$ 12.0000 0.386294
$$966$$ 0 0
$$967$$ 24.0000 0.771788 0.385894 0.922543i $$-0.373893\pi$$
0.385894 + 0.922543i $$0.373893\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 30.0000 0.962746 0.481373 0.876516i $$-0.340138\pi$$
0.481373 + 0.876516i $$0.340138\pi$$
$$972$$ 0 0
$$973$$ 20.0000 0.641171
$$974$$ 0 0
$$975$$ −8.00000 −0.256205
$$976$$ 0 0
$$977$$ −22.0000 −0.703842 −0.351921 0.936030i $$-0.614471\pi$$
−0.351921 + 0.936030i $$0.614471\pi$$
$$978$$ 0 0
$$979$$ 10.0000 0.319601
$$980$$ 0 0
$$981$$ 14.0000 0.446986
$$982$$ 0 0
$$983$$ −26.0000 −0.829271 −0.414636 0.909988i $$-0.636091\pi$$
−0.414636 + 0.909988i $$0.636091\pi$$
$$984$$ 0 0
$$985$$ −36.0000 −1.14706
$$986$$ 0 0
$$987$$ −20.0000 −0.636607
$$988$$ 0 0
$$989$$ 16.0000 0.508770
$$990$$ 0 0
$$991$$ 4.00000 0.127064 0.0635321 0.997980i $$-0.479763\pi$$
0.0635321 + 0.997980i $$0.479763\pi$$
$$992$$ 0 0
$$993$$ −40.0000 −1.26936
$$994$$ 0 0
$$995$$ −28.0000 −0.887660
$$996$$ 0 0
$$997$$ −36.0000 −1.14013 −0.570066 0.821599i $$-0.693082\pi$$
−0.570066 + 0.821599i $$0.693082\pi$$
$$998$$ 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 4928.2.a.bf.1.1 1
4.3 odd 2 4928.2.a.d.1.1 1
8.3 odd 2 154.2.a.b.1.1 1
8.5 even 2 1232.2.a.c.1.1 1
24.11 even 2 1386.2.a.f.1.1 1
40.3 even 4 3850.2.c.d.1849.2 2
40.19 odd 2 3850.2.a.o.1.1 1
40.27 even 4 3850.2.c.d.1849.1 2
56.3 even 6 1078.2.e.l.177.1 2
56.11 odd 6 1078.2.e.h.177.1 2
56.13 odd 2 8624.2.a.z.1.1 1
56.19 even 6 1078.2.e.l.67.1 2
56.27 even 2 1078.2.a.b.1.1 1
56.51 odd 6 1078.2.e.h.67.1 2
88.43 even 2 1694.2.a.i.1.1 1
168.83 odd 2 9702.2.a.bz.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
154.2.a.b.1.1 1 8.3 odd 2
1078.2.a.b.1.1 1 56.27 even 2
1078.2.e.h.67.1 2 56.51 odd 6
1078.2.e.h.177.1 2 56.11 odd 6
1078.2.e.l.67.1 2 56.19 even 6
1078.2.e.l.177.1 2 56.3 even 6
1232.2.a.c.1.1 1 8.5 even 2
1386.2.a.f.1.1 1 24.11 even 2
1694.2.a.i.1.1 1 88.43 even 2
3850.2.a.o.1.1 1 40.19 odd 2
3850.2.c.d.1849.1 2 40.27 even 4
3850.2.c.d.1849.2 2 40.3 even 4
4928.2.a.d.1.1 1 4.3 odd 2
4928.2.a.bf.1.1 1 1.1 even 1 trivial
8624.2.a.z.1.1 1 56.13 odd 2
9702.2.a.bz.1.1 1 168.83 odd 2