# Properties

 Label 2160.4.a.k.1.1 Level $2160$ Weight $4$ Character 2160.1 Self dual yes Analytic conductor $127.444$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2160 = 2^{4} \cdot 3^{3} \cdot 5$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 2160.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$127.444125612$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 540) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 2160.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+5.00000 q^{5} -17.0000 q^{7} +O(q^{10})$$ $$q+5.00000 q^{5} -17.0000 q^{7} +30.0000 q^{11} -61.0000 q^{13} -120.000 q^{17} +43.0000 q^{19} -90.0000 q^{23} +25.0000 q^{25} -90.0000 q^{29} -8.00000 q^{31} -85.0000 q^{35} +317.000 q^{37} -30.0000 q^{41} +220.000 q^{43} +180.000 q^{47} -54.0000 q^{49} -630.000 q^{53} +150.000 q^{55} +840.000 q^{59} +599.000 q^{61} -305.000 q^{65} -107.000 q^{67} +210.000 q^{71} -421.000 q^{73} -510.000 q^{77} -353.000 q^{79} +1350.00 q^{83} -600.000 q^{85} +1020.00 q^{89} +1037.00 q^{91} +215.000 q^{95} -997.000 q^{97} +O(q^{100})$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ 5.00000 0.447214
$$6$$ 0 0
$$7$$ −17.0000 −0.917914 −0.458957 0.888459i $$-0.651777\pi$$
−0.458957 + 0.888459i $$0.651777\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 30.0000 0.822304 0.411152 0.911567i $$-0.365127\pi$$
0.411152 + 0.911567i $$0.365127\pi$$
$$12$$ 0 0
$$13$$ −61.0000 −1.30141 −0.650706 0.759330i $$-0.725527\pi$$
−0.650706 + 0.759330i $$0.725527\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −120.000 −1.71202 −0.856008 0.516962i $$-0.827063\pi$$
−0.856008 + 0.516962i $$0.827063\pi$$
$$18$$ 0 0
$$19$$ 43.0000 0.519204 0.259602 0.965716i $$-0.416409\pi$$
0.259602 + 0.965716i $$0.416409\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −90.0000 −0.815926 −0.407963 0.912998i $$-0.633761\pi$$
−0.407963 + 0.912998i $$0.633761\pi$$
$$24$$ 0 0
$$25$$ 25.0000 0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −90.0000 −0.576296 −0.288148 0.957586i $$-0.593039\pi$$
−0.288148 + 0.957586i $$0.593039\pi$$
$$30$$ 0 0
$$31$$ −8.00000 −0.0463498 −0.0231749 0.999731i $$-0.507377\pi$$
−0.0231749 + 0.999731i $$0.507377\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −85.0000 −0.410503
$$36$$ 0 0
$$37$$ 317.000 1.40850 0.704250 0.709952i $$-0.251284\pi$$
0.704250 + 0.709952i $$0.251284\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −30.0000 −0.114273 −0.0571367 0.998366i $$-0.518197\pi$$
−0.0571367 + 0.998366i $$0.518197\pi$$
$$42$$ 0 0
$$43$$ 220.000 0.780225 0.390113 0.920767i $$-0.372436\pi$$
0.390113 + 0.920767i $$0.372436\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 180.000 0.558632 0.279316 0.960199i $$-0.409892\pi$$
0.279316 + 0.960199i $$0.409892\pi$$
$$48$$ 0 0
$$49$$ −54.0000 −0.157434
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −630.000 −1.63278 −0.816388 0.577503i $$-0.804027\pi$$
−0.816388 + 0.577503i $$0.804027\pi$$
$$54$$ 0 0
$$55$$ 150.000 0.367745
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 840.000 1.85354 0.926769 0.375633i $$-0.122575\pi$$
0.926769 + 0.375633i $$0.122575\pi$$
$$60$$ 0 0
$$61$$ 599.000 1.25728 0.628640 0.777696i $$-0.283612\pi$$
0.628640 + 0.777696i $$0.283612\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −305.000 −0.582009
$$66$$ 0 0
$$67$$ −107.000 −0.195106 −0.0975532 0.995230i $$-0.531102\pi$$
−0.0975532 + 0.995230i $$0.531102\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 210.000 0.351020 0.175510 0.984478i $$-0.443843\pi$$
0.175510 + 0.984478i $$0.443843\pi$$
$$72$$ 0 0
$$73$$ −421.000 −0.674991 −0.337495 0.941327i $$-0.609580\pi$$
−0.337495 + 0.941327i $$0.609580\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −510.000 −0.754804
$$78$$ 0 0
$$79$$ −353.000 −0.502729 −0.251365 0.967892i $$-0.580879\pi$$
−0.251365 + 0.967892i $$0.580879\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 1350.00 1.78532 0.892661 0.450728i $$-0.148836\pi$$
0.892661 + 0.450728i $$0.148836\pi$$
$$84$$ 0 0
$$85$$ −600.000 −0.765637
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 1020.00 1.21483 0.607415 0.794385i $$-0.292207\pi$$
0.607415 + 0.794385i $$0.292207\pi$$
$$90$$ 0 0
$$91$$ 1037.00 1.19458
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 215.000 0.232195
$$96$$ 0 0
$$97$$ −997.000 −1.04361 −0.521804 0.853065i $$-0.674741\pi$$
−0.521804 + 0.853065i $$0.674741\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −960.000 −0.945778 −0.472889 0.881122i $$-0.656789\pi$$
−0.472889 + 0.881122i $$0.656789\pi$$
$$102$$ 0 0
$$103$$ −1181.00 −1.12978 −0.564890 0.825166i $$-0.691081\pi$$
−0.564890 + 0.825166i $$0.691081\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −330.000 −0.298152 −0.149076 0.988826i $$-0.547630\pi$$
−0.149076 + 0.988826i $$0.547630\pi$$
$$108$$ 0 0
$$109$$ 1454.00 1.27769 0.638844 0.769336i $$-0.279413\pi$$
0.638844 + 0.769336i $$0.279413\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 1230.00 1.02397 0.511985 0.858994i $$-0.328910\pi$$
0.511985 + 0.858994i $$0.328910\pi$$
$$114$$ 0 0
$$115$$ −450.000 −0.364893
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 2040.00 1.57148
$$120$$ 0 0
$$121$$ −431.000 −0.323817
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 125.000 0.0894427
$$126$$ 0 0
$$127$$ −1280.00 −0.894344 −0.447172 0.894448i $$-0.647569\pi$$
−0.447172 + 0.894448i $$0.647569\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 2220.00 1.48063 0.740314 0.672261i $$-0.234677\pi$$
0.740314 + 0.672261i $$0.234677\pi$$
$$132$$ 0 0
$$133$$ −731.000 −0.476585
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −1170.00 −0.729634 −0.364817 0.931079i $$-0.618868\pi$$
−0.364817 + 0.931079i $$0.618868\pi$$
$$138$$ 0 0
$$139$$ 1393.00 0.850020 0.425010 0.905189i $$-0.360271\pi$$
0.425010 + 0.905189i $$0.360271\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −1830.00 −1.07016
$$144$$ 0 0
$$145$$ −450.000 −0.257727
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 1380.00 0.758752 0.379376 0.925243i $$-0.376139\pi$$
0.379376 + 0.925243i $$0.376139\pi$$
$$150$$ 0 0
$$151$$ 2659.00 1.43302 0.716511 0.697576i $$-0.245738\pi$$
0.716511 + 0.697576i $$0.245738\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −40.0000 −0.0207282
$$156$$ 0 0
$$157$$ 1850.00 0.940421 0.470210 0.882554i $$-0.344178\pi$$
0.470210 + 0.882554i $$0.344178\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 1530.00 0.748950
$$162$$ 0 0
$$163$$ −1121.00 −0.538672 −0.269336 0.963046i $$-0.586804\pi$$
−0.269336 + 0.963046i $$0.586804\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −300.000 −0.139010 −0.0695051 0.997582i $$-0.522142\pi$$
−0.0695051 + 0.997582i $$0.522142\pi$$
$$168$$ 0 0
$$169$$ 1524.00 0.693673
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −1620.00 −0.711944 −0.355972 0.934497i $$-0.615850\pi$$
−0.355972 + 0.934497i $$0.615850\pi$$
$$174$$ 0 0
$$175$$ −425.000 −0.183583
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 630.000 0.263064 0.131532 0.991312i $$-0.458010\pi$$
0.131532 + 0.991312i $$0.458010\pi$$
$$180$$ 0 0
$$181$$ −2299.00 −0.944107 −0.472053 0.881570i $$-0.656487\pi$$
−0.472053 + 0.881570i $$0.656487\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 1585.00 0.629900
$$186$$ 0 0
$$187$$ −3600.00 −1.40780
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −900.000 −0.340951 −0.170476 0.985362i $$-0.554530\pi$$
−0.170476 + 0.985362i $$0.554530\pi$$
$$192$$ 0 0
$$193$$ 3461.00 1.29082 0.645410 0.763836i $$-0.276687\pi$$
0.645410 + 0.763836i $$0.276687\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 4560.00 1.64917 0.824585 0.565738i $$-0.191409\pi$$
0.824585 + 0.565738i $$0.191409\pi$$
$$198$$ 0 0
$$199$$ 2077.00 0.739872 0.369936 0.929057i $$-0.379380\pi$$
0.369936 + 0.929057i $$0.379380\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 1530.00 0.528990
$$204$$ 0 0
$$205$$ −150.000 −0.0511047
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 1290.00 0.426943
$$210$$ 0 0
$$211$$ 4021.00 1.31193 0.655965 0.754792i $$-0.272262\pi$$
0.655965 + 0.754792i $$0.272262\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 1100.00 0.348927
$$216$$ 0 0
$$217$$ 136.000 0.0425451
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 7320.00 2.22804
$$222$$ 0 0
$$223$$ −80.0000 −0.0240233 −0.0120117 0.999928i $$-0.503824\pi$$
−0.0120117 + 0.999928i $$0.503824\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 3750.00 1.09646 0.548230 0.836328i $$-0.315302\pi$$
0.548230 + 0.836328i $$0.315302\pi$$
$$228$$ 0 0
$$229$$ −1234.00 −0.356092 −0.178046 0.984022i $$-0.556978\pi$$
−0.178046 + 0.984022i $$0.556978\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 5880.00 1.65327 0.826634 0.562739i $$-0.190253\pi$$
0.826634 + 0.562739i $$0.190253\pi$$
$$234$$ 0 0
$$235$$ 900.000 0.249828
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −5130.00 −1.38842 −0.694209 0.719773i $$-0.744246\pi$$
−0.694209 + 0.719773i $$0.744246\pi$$
$$240$$ 0 0
$$241$$ −7231.00 −1.93274 −0.966369 0.257161i $$-0.917213\pi$$
−0.966369 + 0.257161i $$0.917213\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −270.000 −0.0704068
$$246$$ 0 0
$$247$$ −2623.00 −0.675698
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −7530.00 −1.89358 −0.946792 0.321847i $$-0.895696\pi$$
−0.946792 + 0.321847i $$0.895696\pi$$
$$252$$ 0 0
$$253$$ −2700.00 −0.670939
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 4560.00 1.10679 0.553395 0.832919i $$-0.313332\pi$$
0.553395 + 0.832919i $$0.313332\pi$$
$$258$$ 0 0
$$259$$ −5389.00 −1.29288
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 2100.00 0.492363 0.246182 0.969224i $$-0.420824\pi$$
0.246182 + 0.969224i $$0.420824\pi$$
$$264$$ 0 0
$$265$$ −3150.00 −0.730200
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 3120.00 0.707174 0.353587 0.935402i $$-0.384962\pi$$
0.353587 + 0.935402i $$0.384962\pi$$
$$270$$ 0 0
$$271$$ −3449.00 −0.773106 −0.386553 0.922267i $$-0.626334\pi$$
−0.386553 + 0.922267i $$0.626334\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 750.000 0.164461
$$276$$ 0 0
$$277$$ 3770.00 0.817752 0.408876 0.912590i $$-0.365921\pi$$
0.408876 + 0.912590i $$0.365921\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −6720.00 −1.42662 −0.713312 0.700846i $$-0.752806\pi$$
−0.713312 + 0.700846i $$0.752806\pi$$
$$282$$ 0 0
$$283$$ 100.000 0.0210049 0.0105024 0.999945i $$-0.496657\pi$$
0.0105024 + 0.999945i $$0.496657\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 510.000 0.104893
$$288$$ 0 0
$$289$$ 9487.00 1.93100
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 870.000 0.173467 0.0867337 0.996232i $$-0.472357\pi$$
0.0867337 + 0.996232i $$0.472357\pi$$
$$294$$ 0 0
$$295$$ 4200.00 0.828927
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 5490.00 1.06186
$$300$$ 0 0
$$301$$ −3740.00 −0.716179
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 2995.00 0.562273
$$306$$ 0 0
$$307$$ −3440.00 −0.639515 −0.319758 0.947499i $$-0.603601\pi$$
−0.319758 + 0.947499i $$0.603601\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 5880.00 1.07210 0.536052 0.844185i $$-0.319915\pi$$
0.536052 + 0.844185i $$0.319915\pi$$
$$312$$ 0 0
$$313$$ 1841.00 0.332458 0.166229 0.986087i $$-0.446841\pi$$
0.166229 + 0.986087i $$0.446841\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 3420.00 0.605951 0.302975 0.952998i $$-0.402020\pi$$
0.302975 + 0.952998i $$0.402020\pi$$
$$318$$ 0 0
$$319$$ −2700.00 −0.473890
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −5160.00 −0.888886
$$324$$ 0 0
$$325$$ −1525.00 −0.260282
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −3060.00 −0.512776
$$330$$ 0 0
$$331$$ 5641.00 0.936729 0.468365 0.883535i $$-0.344843\pi$$
0.468365 + 0.883535i $$0.344843\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −535.000 −0.0872542
$$336$$ 0 0
$$337$$ −1057.00 −0.170856 −0.0854280 0.996344i $$-0.527226\pi$$
−0.0854280 + 0.996344i $$0.527226\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −240.000 −0.0381136
$$342$$ 0 0
$$343$$ 6749.00 1.06242
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 1290.00 0.199570 0.0997851 0.995009i $$-0.468184\pi$$
0.0997851 + 0.995009i $$0.468184\pi$$
$$348$$ 0 0
$$349$$ 3467.00 0.531760 0.265880 0.964006i $$-0.414337\pi$$
0.265880 + 0.964006i $$0.414337\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 7740.00 1.16702 0.583511 0.812105i $$-0.301679\pi$$
0.583511 + 0.812105i $$0.301679\pi$$
$$354$$ 0 0
$$355$$ 1050.00 0.156981
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −8130.00 −1.19522 −0.597611 0.801786i $$-0.703883\pi$$
−0.597611 + 0.801786i $$0.703883\pi$$
$$360$$ 0 0
$$361$$ −5010.00 −0.730427
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −2105.00 −0.301865
$$366$$ 0 0
$$367$$ −12113.0 −1.72287 −0.861435 0.507867i $$-0.830434\pi$$
−0.861435 + 0.507867i $$0.830434\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 10710.0 1.49875
$$372$$ 0 0
$$373$$ 4349.00 0.603707 0.301853 0.953354i $$-0.402395\pi$$
0.301853 + 0.953354i $$0.402395\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 5490.00 0.749998
$$378$$ 0 0
$$379$$ 7663.00 1.03858 0.519290 0.854598i $$-0.326196\pi$$
0.519290 + 0.854598i $$0.326196\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 3960.00 0.528320 0.264160 0.964479i $$-0.414905\pi$$
0.264160 + 0.964479i $$0.414905\pi$$
$$384$$ 0 0
$$385$$ −2550.00 −0.337559
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 1320.00 0.172048 0.0860240 0.996293i $$-0.472584\pi$$
0.0860240 + 0.996293i $$0.472584\pi$$
$$390$$ 0 0
$$391$$ 10800.0 1.39688
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −1765.00 −0.224827
$$396$$ 0 0
$$397$$ 14390.0 1.81918 0.909589 0.415510i $$-0.136397\pi$$
0.909589 + 0.415510i $$0.136397\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 8610.00 1.07223 0.536113 0.844146i $$-0.319892\pi$$
0.536113 + 0.844146i $$0.319892\pi$$
$$402$$ 0 0
$$403$$ 488.000 0.0603201
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 9510.00 1.15821
$$408$$ 0 0
$$409$$ 7097.00 0.858005 0.429003 0.903303i $$-0.358865\pi$$
0.429003 + 0.903303i $$0.358865\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −14280.0 −1.70139
$$414$$ 0 0
$$415$$ 6750.00 0.798420
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 8880.00 1.03536 0.517681 0.855574i $$-0.326796\pi$$
0.517681 + 0.855574i $$0.326796\pi$$
$$420$$ 0 0
$$421$$ −5479.00 −0.634276 −0.317138 0.948379i $$-0.602722\pi$$
−0.317138 + 0.948379i $$0.602722\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −3000.00 −0.342403
$$426$$ 0 0
$$427$$ −10183.0 −1.15407
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 12510.0 1.39811 0.699055 0.715068i $$-0.253604\pi$$
0.699055 + 0.715068i $$0.253604\pi$$
$$432$$ 0 0
$$433$$ −6790.00 −0.753595 −0.376797 0.926296i $$-0.622975\pi$$
−0.376797 + 0.926296i $$0.622975\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −3870.00 −0.423632
$$438$$ 0 0
$$439$$ 11176.0 1.21504 0.607519 0.794305i $$-0.292165\pi$$
0.607519 + 0.794305i $$0.292165\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 13860.0 1.48648 0.743238 0.669028i $$-0.233289\pi$$
0.743238 + 0.669028i $$0.233289\pi$$
$$444$$ 0 0
$$445$$ 5100.00 0.543288
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −4740.00 −0.498206 −0.249103 0.968477i $$-0.580136\pi$$
−0.249103 + 0.968477i $$0.580136\pi$$
$$450$$ 0 0
$$451$$ −900.000 −0.0939675
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 5185.00 0.534234
$$456$$ 0 0
$$457$$ −1690.00 −0.172987 −0.0864933 0.996252i $$-0.527566\pi$$
−0.0864933 + 0.996252i $$0.527566\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 14700.0 1.48514 0.742568 0.669771i $$-0.233608\pi$$
0.742568 + 0.669771i $$0.233608\pi$$
$$462$$ 0 0
$$463$$ 331.000 0.0332244 0.0166122 0.999862i $$-0.494712\pi$$
0.0166122 + 0.999862i $$0.494712\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 8580.00 0.850182 0.425091 0.905151i $$-0.360242\pi$$
0.425091 + 0.905151i $$0.360242\pi$$
$$468$$ 0 0
$$469$$ 1819.00 0.179091
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 6600.00 0.641582
$$474$$ 0 0
$$475$$ 1075.00 0.103841
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 14790.0 1.41080 0.705399 0.708810i $$-0.250768\pi$$
0.705399 + 0.708810i $$0.250768\pi$$
$$480$$ 0 0
$$481$$ −19337.0 −1.83304
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −4985.00 −0.466716
$$486$$ 0 0
$$487$$ −13097.0 −1.21865 −0.609324 0.792921i $$-0.708559\pi$$
−0.609324 + 0.792921i $$0.708559\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −1590.00 −0.146142 −0.0730710 0.997327i $$-0.523280\pi$$
−0.0730710 + 0.997327i $$0.523280\pi$$
$$492$$ 0 0
$$493$$ 10800.0 0.986628
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −3570.00 −0.322206
$$498$$ 0 0
$$499$$ −17264.0 −1.54878 −0.774392 0.632707i $$-0.781944\pi$$
−0.774392 + 0.632707i $$0.781944\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 14730.0 1.30572 0.652861 0.757478i $$-0.273569\pi$$
0.652861 + 0.757478i $$0.273569\pi$$
$$504$$ 0 0
$$505$$ −4800.00 −0.422965
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 870.000 0.0757605 0.0378802 0.999282i $$-0.487939\pi$$
0.0378802 + 0.999282i $$0.487939\pi$$
$$510$$ 0 0
$$511$$ 7157.00 0.619583
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −5905.00 −0.505253
$$516$$ 0 0
$$517$$ 5400.00 0.459365
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −6990.00 −0.587788 −0.293894 0.955838i $$-0.594951\pi$$
−0.293894 + 0.955838i $$0.594951\pi$$
$$522$$ 0 0
$$523$$ −12119.0 −1.01324 −0.506622 0.862168i $$-0.669106\pi$$
−0.506622 + 0.862168i $$0.669106\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 960.000 0.0793515
$$528$$ 0 0
$$529$$ −4067.00 −0.334265
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 1830.00 0.148717
$$534$$ 0 0
$$535$$ −1650.00 −0.133338
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −1620.00 −0.129459
$$540$$ 0 0
$$541$$ −21511.0 −1.70948 −0.854741 0.519054i $$-0.826284\pi$$
−0.854741 + 0.519054i $$0.826284\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 7270.00 0.571399
$$546$$ 0 0
$$547$$ 10807.0 0.844742 0.422371 0.906423i $$-0.361198\pi$$
0.422371 + 0.906423i $$0.361198\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −3870.00 −0.299215
$$552$$ 0 0
$$553$$ 6001.00 0.461462
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −20460.0 −1.55641 −0.778203 0.628013i $$-0.783868\pi$$
−0.778203 + 0.628013i $$0.783868\pi$$
$$558$$ 0 0
$$559$$ −13420.0 −1.01539
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 4980.00 0.372792 0.186396 0.982475i $$-0.440319\pi$$
0.186396 + 0.982475i $$0.440319\pi$$
$$564$$ 0 0
$$565$$ 6150.00 0.457934
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 15840.0 1.16704 0.583521 0.812098i $$-0.301674\pi$$
0.583521 + 0.812098i $$0.301674\pi$$
$$570$$ 0 0
$$571$$ 24391.0 1.78762 0.893810 0.448445i $$-0.148022\pi$$
0.893810 + 0.448445i $$0.148022\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −2250.00 −0.163185
$$576$$ 0 0
$$577$$ 7673.00 0.553607 0.276803 0.960927i $$-0.410725\pi$$
0.276803 + 0.960927i $$0.410725\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −22950.0 −1.63877
$$582$$ 0 0
$$583$$ −18900.0 −1.34264
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −18930.0 −1.33105 −0.665524 0.746377i $$-0.731792\pi$$
−0.665524 + 0.746377i $$0.731792\pi$$
$$588$$ 0 0
$$589$$ −344.000 −0.0240650
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 14190.0 0.982653 0.491327 0.870975i $$-0.336512\pi$$
0.491327 + 0.870975i $$0.336512\pi$$
$$594$$ 0 0
$$595$$ 10200.0 0.702789
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 12870.0 0.877886 0.438943 0.898515i $$-0.355353\pi$$
0.438943 + 0.898515i $$0.355353\pi$$
$$600$$ 0 0
$$601$$ 19598.0 1.33015 0.665074 0.746777i $$-0.268400\pi$$
0.665074 + 0.746777i $$0.268400\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −2155.00 −0.144815
$$606$$ 0 0
$$607$$ 15163.0 1.01392 0.506958 0.861971i $$-0.330770\pi$$
0.506958 + 0.861971i $$0.330770\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −10980.0 −0.727010
$$612$$ 0 0
$$613$$ −29599.0 −1.95023 −0.975116 0.221695i $$-0.928841\pi$$
−0.975116 + 0.221695i $$0.928841\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −2490.00 −0.162469 −0.0812347 0.996695i $$-0.525886\pi$$
−0.0812347 + 0.996695i $$0.525886\pi$$
$$618$$ 0 0
$$619$$ −3713.00 −0.241095 −0.120548 0.992708i $$-0.538465\pi$$
−0.120548 + 0.992708i $$0.538465\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −17340.0 −1.11511
$$624$$ 0 0
$$625$$ 625.000 0.0400000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −38040.0 −2.41137
$$630$$ 0 0
$$631$$ −19409.0 −1.22450 −0.612250 0.790664i $$-0.709736\pi$$
−0.612250 + 0.790664i $$0.709736\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −6400.00 −0.399963
$$636$$ 0 0
$$637$$ 3294.00 0.204887
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 6480.00 0.399290 0.199645 0.979868i $$-0.436021\pi$$
0.199645 + 0.979868i $$0.436021\pi$$
$$642$$ 0 0
$$643$$ −30260.0 −1.85589 −0.927945 0.372716i $$-0.878427\pi$$
−0.927945 + 0.372716i $$0.878427\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −21510.0 −1.30703 −0.653513 0.756916i $$-0.726705\pi$$
−0.653513 + 0.756916i $$0.726705\pi$$
$$648$$ 0 0
$$649$$ 25200.0 1.52417
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −540.000 −0.0323612 −0.0161806 0.999869i $$-0.505151\pi$$
−0.0161806 + 0.999869i $$0.505151\pi$$
$$654$$ 0 0
$$655$$ 11100.0 0.662157
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −29280.0 −1.73078 −0.865392 0.501095i $$-0.832931\pi$$
−0.865392 + 0.501095i $$0.832931\pi$$
$$660$$ 0 0
$$661$$ −21769.0 −1.28096 −0.640481 0.767974i $$-0.721265\pi$$
−0.640481 + 0.767974i $$0.721265\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −3655.00 −0.213135
$$666$$ 0 0
$$667$$ 8100.00 0.470215
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 17970.0 1.03387
$$672$$ 0 0
$$673$$ −14551.0 −0.833432 −0.416716 0.909037i $$-0.636819\pi$$
−0.416716 + 0.909037i $$0.636819\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −1500.00 −0.0851546 −0.0425773 0.999093i $$-0.513557\pi$$
−0.0425773 + 0.999093i $$0.513557\pi$$
$$678$$ 0 0
$$679$$ 16949.0 0.957942
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −16530.0 −0.926066 −0.463033 0.886341i $$-0.653239\pi$$
−0.463033 + 0.886341i $$0.653239\pi$$
$$684$$ 0 0
$$685$$ −5850.00 −0.326302
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 38430.0 2.12491
$$690$$ 0 0
$$691$$ 25972.0 1.42984 0.714921 0.699205i $$-0.246462\pi$$
0.714921 + 0.699205i $$0.246462\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 6965.00 0.380140
$$696$$ 0 0
$$697$$ 3600.00 0.195638
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −10230.0 −0.551187 −0.275593 0.961274i $$-0.588874\pi$$
−0.275593 + 0.961274i $$0.588874\pi$$
$$702$$ 0 0
$$703$$ 13631.0 0.731299
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 16320.0 0.868143
$$708$$ 0 0
$$709$$ −14623.0 −0.774582 −0.387291 0.921958i $$-0.626589\pi$$
−0.387291 + 0.921958i $$0.626589\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 720.000 0.0378180
$$714$$ 0 0
$$715$$ −9150.00 −0.478588
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −6690.00 −0.347003 −0.173501 0.984834i $$-0.555508\pi$$
−0.173501 + 0.984834i $$0.555508\pi$$
$$720$$ 0 0
$$721$$ 20077.0 1.03704
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −2250.00 −0.115259
$$726$$ 0 0
$$727$$ −11720.0 −0.597896 −0.298948 0.954269i $$-0.596636\pi$$
−0.298948 + 0.954269i $$0.596636\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −26400.0 −1.33576
$$732$$ 0 0
$$733$$ −4750.00 −0.239352 −0.119676 0.992813i $$-0.538186\pi$$
−0.119676 + 0.992813i $$0.538186\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −3210.00 −0.160437
$$738$$ 0 0
$$739$$ 30724.0 1.52936 0.764682 0.644407i $$-0.222896\pi$$
0.764682 + 0.644407i $$0.222896\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −960.000 −0.0474011 −0.0237005 0.999719i $$-0.507545\pi$$
−0.0237005 + 0.999719i $$0.507545\pi$$
$$744$$ 0 0
$$745$$ 6900.00 0.339324
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 5610.00 0.273678
$$750$$ 0 0
$$751$$ −22781.0 −1.10691 −0.553456 0.832879i $$-0.686691\pi$$
−0.553456 + 0.832879i $$0.686691\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 13295.0 0.640867
$$756$$ 0 0
$$757$$ 32387.0 1.55499 0.777494 0.628891i $$-0.216491\pi$$
0.777494 + 0.628891i $$0.216491\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 25290.0 1.20468 0.602340 0.798239i $$-0.294235\pi$$
0.602340 + 0.798239i $$0.294235\pi$$
$$762$$ 0 0
$$763$$ −24718.0 −1.17281
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −51240.0 −2.41222
$$768$$ 0 0
$$769$$ 16283.0 0.763563 0.381782 0.924253i $$-0.375311\pi$$
0.381782 + 0.924253i $$0.375311\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −31050.0 −1.44475 −0.722374 0.691502i $$-0.756949\pi$$
−0.722374 + 0.691502i $$0.756949\pi$$
$$774$$ 0 0
$$775$$ −200.000 −0.00926995
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −1290.00 −0.0593313
$$780$$ 0 0
$$781$$ 6300.00 0.288645
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 9250.00 0.420569
$$786$$ 0 0
$$787$$ 5053.00 0.228869 0.114435 0.993431i $$-0.463494\pi$$
0.114435 + 0.993431i $$0.463494\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −20910.0 −0.939917
$$792$$ 0 0
$$793$$ −36539.0 −1.63624
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 43680.0 1.94131 0.970656 0.240474i $$-0.0773029\pi$$
0.970656 + 0.240474i $$0.0773029\pi$$
$$798$$ 0 0
$$799$$ −21600.0 −0.956387
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −12630.0 −0.555047
$$804$$ 0 0
$$805$$ 7650.00 0.334940
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 1920.00 0.0834408 0.0417204 0.999129i $$-0.486716\pi$$
0.0417204 + 0.999129i $$0.486716\pi$$
$$810$$ 0 0
$$811$$ −37268.0 −1.61363 −0.806817 0.590802i $$-0.798811\pi$$
−0.806817 + 0.590802i $$0.798811\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −5605.00 −0.240901
$$816$$ 0 0
$$817$$ 9460.00 0.405096
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 5280.00 0.224450 0.112225 0.993683i $$-0.464202\pi$$
0.112225 + 0.993683i $$0.464202\pi$$
$$822$$ 0 0
$$823$$ −4511.00 −0.191061 −0.0955307 0.995426i $$-0.530455\pi$$
−0.0955307 + 0.995426i $$0.530455\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 10140.0 0.426363 0.213182 0.977013i $$-0.431617\pi$$
0.213182 + 0.977013i $$0.431617\pi$$
$$828$$ 0 0
$$829$$ −11923.0 −0.499521 −0.249760 0.968308i $$-0.580352\pi$$
−0.249760 + 0.968308i $$0.580352\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 6480.00 0.269530
$$834$$ 0 0
$$835$$ −1500.00 −0.0621672
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −21300.0 −0.876469 −0.438235 0.898861i $$-0.644396\pi$$
−0.438235 + 0.898861i $$0.644396\pi$$
$$840$$ 0 0
$$841$$ −16289.0 −0.667883
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 7620.00 0.310220
$$846$$ 0 0
$$847$$ 7327.00 0.297236
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −28530.0 −1.14923
$$852$$ 0 0
$$853$$ −40771.0 −1.63654 −0.818272 0.574831i $$-0.805068\pi$$
−0.818272 + 0.574831i $$0.805068\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 25170.0 1.00326 0.501628 0.865083i $$-0.332735\pi$$
0.501628 + 0.865083i $$0.332735\pi$$
$$858$$ 0 0
$$859$$ 42757.0 1.69831 0.849156 0.528142i $$-0.177111\pi$$
0.849156 + 0.528142i $$0.177111\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −15300.0 −0.603497 −0.301749 0.953388i $$-0.597570\pi$$
−0.301749 + 0.953388i $$0.597570\pi$$
$$864$$ 0 0
$$865$$ −8100.00 −0.318391
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −10590.0 −0.413396
$$870$$ 0 0
$$871$$ 6527.00 0.253914
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ −2125.00 −0.0821007
$$876$$ 0 0
$$877$$ −23743.0 −0.914189 −0.457095 0.889418i $$-0.651110\pi$$
−0.457095 + 0.889418i $$0.651110\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −27810.0 −1.06350 −0.531750 0.846902i $$-0.678465\pi$$
−0.531750 + 0.846902i $$0.678465\pi$$
$$882$$ 0 0
$$883$$ 42991.0 1.63846 0.819231 0.573463i $$-0.194400\pi$$
0.819231 + 0.573463i $$0.194400\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 45600.0 1.72615 0.863077 0.505073i $$-0.168534\pi$$
0.863077 + 0.505073i $$0.168534\pi$$
$$888$$ 0 0
$$889$$ 21760.0 0.820930
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 7740.00 0.290044
$$894$$ 0 0
$$895$$ 3150.00 0.117646
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 720.000 0.0267112
$$900$$ 0 0
$$901$$ 75600.0 2.79534
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −11495.0 −0.422217
$$906$$ 0 0
$$907$$ 4993.00 0.182789 0.0913946 0.995815i $$-0.470868\pi$$
0.0913946 + 0.995815i $$0.470868\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 4920.00 0.178932 0.0894659 0.995990i $$-0.471484\pi$$
0.0894659 + 0.995990i $$0.471484\pi$$
$$912$$ 0 0
$$913$$ 40500.0 1.46808
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −37740.0 −1.35909
$$918$$ 0 0
$$919$$ −5456.00 −0.195840 −0.0979199 0.995194i $$-0.531219\pi$$
−0.0979199 + 0.995194i $$0.531219\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ −12810.0 −0.456822
$$924$$ 0 0
$$925$$ 7925.00 0.281700
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −14790.0 −0.522330 −0.261165 0.965294i $$-0.584107\pi$$
−0.261165 + 0.965294i $$0.584107\pi$$
$$930$$ 0 0
$$931$$ −2322.00 −0.0817406
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −18000.0 −0.629586
$$936$$ 0 0
$$937$$ −14023.0 −0.488913 −0.244456 0.969660i $$-0.578610\pi$$
−0.244456 + 0.969660i $$0.578610\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −35250.0 −1.22117 −0.610583 0.791952i $$-0.709065\pi$$
−0.610583 + 0.791952i $$0.709065\pi$$
$$942$$ 0 0
$$943$$ 2700.00 0.0932387
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 37920.0 1.30120 0.650599 0.759421i $$-0.274518\pi$$
0.650599 + 0.759421i $$0.274518\pi$$
$$948$$ 0 0
$$949$$ 25681.0 0.878441
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −49080.0 −1.66827 −0.834133 0.551564i $$-0.814031\pi$$
−0.834133 + 0.551564i $$0.814031\pi$$
$$954$$ 0 0
$$955$$ −4500.00 −0.152478
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 19890.0 0.669741
$$960$$ 0 0
$$961$$ −29727.0 −0.997852
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 17305.0 0.577272
$$966$$ 0 0
$$967$$ 33073.0 1.09985 0.549926 0.835214i $$-0.314656\pi$$
0.549926 + 0.835214i $$0.314656\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 6420.00 0.212181 0.106090 0.994356i $$-0.466167\pi$$
0.106090 + 0.994356i $$0.466167\pi$$
$$972$$ 0 0
$$973$$ −23681.0 −0.780245
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 25110.0 0.822252 0.411126 0.911579i $$-0.365136\pi$$
0.411126 + 0.911579i $$0.365136\pi$$
$$978$$ 0 0
$$979$$ 30600.0 0.998958
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −52410.0 −1.70053 −0.850264 0.526356i $$-0.823558\pi$$
−0.850264 + 0.526356i $$0.823558\pi$$
$$984$$ 0 0
$$985$$ 22800.0 0.737531
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −19800.0 −0.636606
$$990$$ 0 0
$$991$$ −52619.0 −1.68668 −0.843339 0.537382i $$-0.819413\pi$$
−0.843339 + 0.537382i $$0.819413\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 10385.0 0.330881
$$996$$ 0 0
$$997$$ −53890.0 −1.71185 −0.855924 0.517101i $$-0.827011\pi$$
−0.855924 + 0.517101i $$0.827011\pi$$
$$998$$ 0 0
$$999$$ 0 0
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 2160.4.a.k.1.1 1
3.2 odd 2 2160.4.a.a.1.1 1
4.3 odd 2 540.4.a.d.1.1 yes 1
12.11 even 2 540.4.a.b.1.1 1
36.7 odd 6 1620.4.i.b.1081.1 2
36.11 even 6 1620.4.i.h.1081.1 2
36.23 even 6 1620.4.i.h.541.1 2
36.31 odd 6 1620.4.i.b.541.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
540.4.a.b.1.1 1 12.11 even 2
540.4.a.d.1.1 yes 1 4.3 odd 2
1620.4.i.b.541.1 2 36.31 odd 6
1620.4.i.b.1081.1 2 36.7 odd 6
1620.4.i.h.541.1 2 36.23 even 6
1620.4.i.h.1081.1 2 36.11 even 6
2160.4.a.a.1.1 1 3.2 odd 2
2160.4.a.k.1.1 1 1.1 even 1 trivial