# Properties

 Label 3675.2.a.i.1.1 Level $3675$ Weight $2$ Character 3675.1 Self dual yes Analytic conductor $29.345$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$3675 = 3 \cdot 5^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3675.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$29.3450227428$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 105) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 3675.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{3} -2.00000 q^{4} +1.00000 q^{9} +O(q^{10})$$ $$q+1.00000 q^{3} -2.00000 q^{4} +1.00000 q^{9} -2.00000 q^{12} -1.00000 q^{13} +4.00000 q^{16} +6.00000 q^{17} -5.00000 q^{19} -6.00000 q^{23} +1.00000 q^{27} -6.00000 q^{29} -5.00000 q^{31} -2.00000 q^{36} +7.00000 q^{37} -1.00000 q^{39} -12.0000 q^{41} +1.00000 q^{43} +6.00000 q^{47} +4.00000 q^{48} +6.00000 q^{51} +2.00000 q^{52} -5.00000 q^{57} +6.00000 q^{59} -2.00000 q^{61} -8.00000 q^{64} +7.00000 q^{67} -12.0000 q^{68} -6.00000 q^{69} +12.0000 q^{71} +11.0000 q^{73} +10.0000 q^{76} -13.0000 q^{79} +1.00000 q^{81} -12.0000 q^{83} -6.00000 q^{87} -6.00000 q^{89} +12.0000 q^{92} -5.00000 q^{93} -10.0000 q^{97} +O(q^{100})$$

## 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$3$$ 1.00000 0.577350
$$4$$ −2.00000 −1.00000
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ −2.00000 −0.577350
$$13$$ −1.00000 −0.277350 −0.138675 0.990338i $$-0.544284\pi$$
−0.138675 + 0.990338i $$0.544284\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 4.00000 1.00000
$$17$$ 6.00000 1.45521 0.727607 0.685994i $$-0.240633\pi$$
0.727607 + 0.685994i $$0.240633\pi$$
$$18$$ 0 0
$$19$$ −5.00000 −1.14708 −0.573539 0.819178i $$-0.694430\pi$$
−0.573539 + 0.819178i $$0.694430\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −6.00000 −1.25109 −0.625543 0.780189i $$-0.715123\pi$$
−0.625543 + 0.780189i $$0.715123\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 1.00000 0.192450
$$28$$ 0 0
$$29$$ −6.00000 −1.11417 −0.557086 0.830455i $$-0.688081\pi$$
−0.557086 + 0.830455i $$0.688081\pi$$
$$30$$ 0 0
$$31$$ −5.00000 −0.898027 −0.449013 0.893525i $$-0.648224\pi$$
−0.449013 + 0.893525i $$0.648224\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ −2.00000 −0.333333
$$37$$ 7.00000 1.15079 0.575396 0.817875i $$-0.304848\pi$$
0.575396 + 0.817875i $$0.304848\pi$$
$$38$$ 0 0
$$39$$ −1.00000 −0.160128
$$40$$ 0 0
$$41$$ −12.0000 −1.87409 −0.937043 0.349215i $$-0.886448\pi$$
−0.937043 + 0.349215i $$0.886448\pi$$
$$42$$ 0 0
$$43$$ 1.00000 0.152499 0.0762493 0.997089i $$-0.475706\pi$$
0.0762493 + 0.997089i $$0.475706\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 6.00000 0.875190 0.437595 0.899172i $$-0.355830\pi$$
0.437595 + 0.899172i $$0.355830\pi$$
$$48$$ 4.00000 0.577350
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 6.00000 0.840168
$$52$$ 2.00000 0.277350
$$53$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −5.00000 −0.662266
$$58$$ 0 0
$$59$$ 6.00000 0.781133 0.390567 0.920575i $$-0.372279\pi$$
0.390567 + 0.920575i $$0.372279\pi$$
$$60$$ 0 0
$$61$$ −2.00000 −0.256074 −0.128037 0.991769i $$-0.540868\pi$$
−0.128037 + 0.991769i $$0.540868\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ −8.00000 −1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 7.00000 0.855186 0.427593 0.903971i $$-0.359362\pi$$
0.427593 + 0.903971i $$0.359362\pi$$
$$68$$ −12.0000 −1.45521
$$69$$ −6.00000 −0.722315
$$70$$ 0 0
$$71$$ 12.0000 1.42414 0.712069 0.702109i $$-0.247758\pi$$
0.712069 + 0.702109i $$0.247758\pi$$
$$72$$ 0 0
$$73$$ 11.0000 1.28745 0.643726 0.765256i $$-0.277388\pi$$
0.643726 + 0.765256i $$0.277388\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 10.0000 1.14708
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −13.0000 −1.46261 −0.731307 0.682048i $$-0.761089\pi$$
−0.731307 + 0.682048i $$0.761089\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ −12.0000 −1.31717 −0.658586 0.752506i $$-0.728845\pi$$
−0.658586 + 0.752506i $$0.728845\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −6.00000 −0.643268
$$88$$ 0 0
$$89$$ −6.00000 −0.635999 −0.317999 0.948091i $$-0.603011\pi$$
−0.317999 + 0.948091i $$0.603011\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 12.0000 1.25109
$$93$$ −5.00000 −0.518476
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −10.0000 −1.01535 −0.507673 0.861550i $$-0.669494\pi$$
−0.507673 + 0.861550i $$0.669494\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ 0 0
$$103$$ −1.00000 −0.0985329 −0.0492665 0.998786i $$-0.515688\pi$$
−0.0492665 + 0.998786i $$0.515688\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −18.0000 −1.74013 −0.870063 0.492941i $$-0.835922\pi$$
−0.870063 + 0.492941i $$0.835922\pi$$
$$108$$ −2.00000 −0.192450
$$109$$ −7.00000 −0.670478 −0.335239 0.942133i $$-0.608817\pi$$
−0.335239 + 0.942133i $$0.608817\pi$$
$$110$$ 0 0
$$111$$ 7.00000 0.664411
$$112$$ 0 0
$$113$$ −18.0000 −1.69330 −0.846649 0.532152i $$-0.821383\pi$$
−0.846649 + 0.532152i $$0.821383\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 12.0000 1.11417
$$117$$ −1.00000 −0.0924500
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −11.0000 −1.00000
$$122$$ 0 0
$$123$$ −12.0000 −1.08200
$$124$$ 10.0000 0.898027
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −11.0000 −0.976092 −0.488046 0.872818i $$-0.662290\pi$$
−0.488046 + 0.872818i $$0.662290\pi$$
$$128$$ 0 0
$$129$$ 1.00000 0.0880451
$$130$$ 0 0
$$131$$ 6.00000 0.524222 0.262111 0.965038i $$-0.415581\pi$$
0.262111 + 0.965038i $$0.415581\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −6.00000 −0.512615 −0.256307 0.966595i $$-0.582506\pi$$
−0.256307 + 0.966595i $$0.582506\pi$$
$$138$$ 0 0
$$139$$ −5.00000 −0.424094 −0.212047 0.977259i $$-0.568013\pi$$
−0.212047 + 0.977259i $$0.568013\pi$$
$$140$$ 0 0
$$141$$ 6.00000 0.505291
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 4.00000 0.333333
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ −14.0000 −1.15079
$$149$$ −24.0000 −1.96616 −0.983078 0.183186i $$-0.941359\pi$$
−0.983078 + 0.183186i $$0.941359\pi$$
$$150$$ 0 0
$$151$$ −16.0000 −1.30206 −0.651031 0.759051i $$-0.725663\pi$$
−0.651031 + 0.759051i $$0.725663\pi$$
$$152$$ 0 0
$$153$$ 6.00000 0.485071
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 2.00000 0.160128
$$157$$ −10.0000 −0.798087 −0.399043 0.916932i $$-0.630658\pi$$
−0.399043 + 0.916932i $$0.630658\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 4.00000 0.313304 0.156652 0.987654i $$-0.449930\pi$$
0.156652 + 0.987654i $$0.449930\pi$$
$$164$$ 24.0000 1.87409
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 12.0000 0.928588 0.464294 0.885681i $$-0.346308\pi$$
0.464294 + 0.885681i $$0.346308\pi$$
$$168$$ 0 0
$$169$$ −12.0000 −0.923077
$$170$$ 0 0
$$171$$ −5.00000 −0.382360
$$172$$ −2.00000 −0.152499
$$173$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 6.00000 0.450988
$$178$$ 0 0
$$179$$ 18.0000 1.34538 0.672692 0.739923i $$-0.265138\pi$$
0.672692 + 0.739923i $$0.265138\pi$$
$$180$$ 0 0
$$181$$ 7.00000 0.520306 0.260153 0.965567i $$-0.416227\pi$$
0.260153 + 0.965567i $$0.416227\pi$$
$$182$$ 0 0
$$183$$ −2.00000 −0.147844
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ −12.0000 −0.875190
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −6.00000 −0.434145 −0.217072 0.976156i $$-0.569651\pi$$
−0.217072 + 0.976156i $$0.569651\pi$$
$$192$$ −8.00000 −0.577350
$$193$$ −5.00000 −0.359908 −0.179954 0.983675i $$-0.557595\pi$$
−0.179954 + 0.983675i $$0.557595\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −6.00000 −0.427482 −0.213741 0.976890i $$-0.568565\pi$$
−0.213741 + 0.976890i $$0.568565\pi$$
$$198$$ 0 0
$$199$$ 16.0000 1.13421 0.567105 0.823646i $$-0.308063\pi$$
0.567105 + 0.823646i $$0.308063\pi$$
$$200$$ 0 0
$$201$$ 7.00000 0.493742
$$202$$ 0 0
$$203$$ 0 0
$$204$$ −12.0000 −0.840168
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −6.00000 −0.417029
$$208$$ −4.00000 −0.277350
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −4.00000 −0.275371 −0.137686 0.990476i $$-0.543966\pi$$
−0.137686 + 0.990476i $$0.543966\pi$$
$$212$$ 0 0
$$213$$ 12.0000 0.822226
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 11.0000 0.743311
$$220$$ 0 0
$$221$$ −6.00000 −0.403604
$$222$$ 0 0
$$223$$ −4.00000 −0.267860 −0.133930 0.990991i $$-0.542760\pi$$
−0.133930 + 0.990991i $$0.542760\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 12.0000 0.796468 0.398234 0.917284i $$-0.369623\pi$$
0.398234 + 0.917284i $$0.369623\pi$$
$$228$$ 10.0000 0.662266
$$229$$ −29.0000 −1.91637 −0.958187 0.286143i $$-0.907627\pi$$
−0.958187 + 0.286143i $$0.907627\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −6.00000 −0.393073 −0.196537 0.980497i $$-0.562969\pi$$
−0.196537 + 0.980497i $$0.562969\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −12.0000 −0.781133
$$237$$ −13.0000 −0.844441
$$238$$ 0 0
$$239$$ −6.00000 −0.388108 −0.194054 0.980991i $$-0.562164\pi$$
−0.194054 + 0.980991i $$0.562164\pi$$
$$240$$ 0 0
$$241$$ −2.00000 −0.128831 −0.0644157 0.997923i $$-0.520518\pi$$
−0.0644157 + 0.997923i $$0.520518\pi$$
$$242$$ 0 0
$$243$$ 1.00000 0.0641500
$$244$$ 4.00000 0.256074
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 5.00000 0.318142
$$248$$ 0 0
$$249$$ −12.0000 −0.760469
$$250$$ 0 0
$$251$$ 18.0000 1.13615 0.568075 0.822977i $$-0.307688\pi$$
0.568075 + 0.822977i $$0.307688\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 16.0000 1.00000
$$257$$ −12.0000 −0.748539 −0.374270 0.927320i $$-0.622107\pi$$
−0.374270 + 0.927320i $$0.622107\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −6.00000 −0.371391
$$262$$ 0 0
$$263$$ 12.0000 0.739952 0.369976 0.929041i $$-0.379366\pi$$
0.369976 + 0.929041i $$0.379366\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −6.00000 −0.367194
$$268$$ −14.0000 −0.855186
$$269$$ 18.0000 1.09748 0.548740 0.835993i $$-0.315108\pi$$
0.548740 + 0.835993i $$0.315108\pi$$
$$270$$ 0 0
$$271$$ 16.0000 0.971931 0.485965 0.873978i $$-0.338468\pi$$
0.485965 + 0.873978i $$0.338468\pi$$
$$272$$ 24.0000 1.45521
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 12.0000 0.722315
$$277$$ −23.0000 −1.38194 −0.690968 0.722885i $$-0.742815\pi$$
−0.690968 + 0.722885i $$0.742815\pi$$
$$278$$ 0 0
$$279$$ −5.00000 −0.299342
$$280$$ 0 0
$$281$$ −24.0000 −1.43172 −0.715860 0.698244i $$-0.753965\pi$$
−0.715860 + 0.698244i $$0.753965\pi$$
$$282$$ 0 0
$$283$$ 11.0000 0.653882 0.326941 0.945045i $$-0.393982\pi$$
0.326941 + 0.945045i $$0.393982\pi$$
$$284$$ −24.0000 −1.42414
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 19.0000 1.11765
$$290$$ 0 0
$$291$$ −10.0000 −0.586210
$$292$$ −22.0000 −1.28745
$$293$$ 12.0000 0.701047 0.350524 0.936554i $$-0.386004\pi$$
0.350524 + 0.936554i $$0.386004\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 6.00000 0.346989
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ −20.0000 −1.14708
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −7.00000 −0.399511 −0.199756 0.979846i $$-0.564015\pi$$
−0.199756 + 0.979846i $$0.564015\pi$$
$$308$$ 0 0
$$309$$ −1.00000 −0.0568880
$$310$$ 0 0
$$311$$ −12.0000 −0.680458 −0.340229 0.940343i $$-0.610505\pi$$
−0.340229 + 0.940343i $$0.610505\pi$$
$$312$$ 0 0
$$313$$ 17.0000 0.960897 0.480448 0.877023i $$-0.340474\pi$$
0.480448 + 0.877023i $$0.340474\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 26.0000 1.46261
$$317$$ −6.00000 −0.336994 −0.168497 0.985702i $$-0.553891\pi$$
−0.168497 + 0.985702i $$0.553891\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ −18.0000 −1.00466
$$322$$ 0 0
$$323$$ −30.0000 −1.66924
$$324$$ −2.00000 −0.111111
$$325$$ 0 0
$$326$$ 0 0
$$327$$ −7.00000 −0.387101
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 23.0000 1.26419 0.632097 0.774889i $$-0.282194\pi$$
0.632097 + 0.774889i $$0.282194\pi$$
$$332$$ 24.0000 1.31717
$$333$$ 7.00000 0.383598
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 13.0000 0.708155 0.354078 0.935216i $$-0.384795\pi$$
0.354078 + 0.935216i $$0.384795\pi$$
$$338$$ 0 0
$$339$$ −18.0000 −0.977626
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 24.0000 1.28839 0.644194 0.764862i $$-0.277193\pi$$
0.644194 + 0.764862i $$0.277193\pi$$
$$348$$ 12.0000 0.643268
$$349$$ −26.0000 −1.39175 −0.695874 0.718164i $$-0.744983\pi$$
−0.695874 + 0.718164i $$0.744983\pi$$
$$350$$ 0 0
$$351$$ −1.00000 −0.0533761
$$352$$ 0 0
$$353$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 12.0000 0.635999
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −6.00000 −0.316668 −0.158334 0.987386i $$-0.550612\pi$$
−0.158334 + 0.987386i $$0.550612\pi$$
$$360$$ 0 0
$$361$$ 6.00000 0.315789
$$362$$ 0 0
$$363$$ −11.0000 −0.577350
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −19.0000 −0.991792 −0.495896 0.868382i $$-0.665160\pi$$
−0.495896 + 0.868382i $$0.665160\pi$$
$$368$$ −24.0000 −1.25109
$$369$$ −12.0000 −0.624695
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 10.0000 0.518476
$$373$$ −17.0000 −0.880227 −0.440113 0.897942i $$-0.645062\pi$$
−0.440113 + 0.897942i $$0.645062\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 6.00000 0.309016
$$378$$ 0 0
$$379$$ −25.0000 −1.28416 −0.642082 0.766636i $$-0.721929\pi$$
−0.642082 + 0.766636i $$0.721929\pi$$
$$380$$ 0 0
$$381$$ −11.0000 −0.563547
$$382$$ 0 0
$$383$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 1.00000 0.0508329
$$388$$ 20.0000 1.01535
$$389$$ 12.0000 0.608424 0.304212 0.952604i $$-0.401607\pi$$
0.304212 + 0.952604i $$0.401607\pi$$
$$390$$ 0 0
$$391$$ −36.0000 −1.82060
$$392$$ 0 0
$$393$$ 6.00000 0.302660
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 29.0000 1.45547 0.727734 0.685859i $$-0.240573\pi$$
0.727734 + 0.685859i $$0.240573\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 24.0000 1.19850 0.599251 0.800561i $$-0.295465\pi$$
0.599251 + 0.800561i $$0.295465\pi$$
$$402$$ 0 0
$$403$$ 5.00000 0.249068
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −5.00000 −0.247234 −0.123617 0.992330i $$-0.539449\pi$$
−0.123617 + 0.992330i $$0.539449\pi$$
$$410$$ 0 0
$$411$$ −6.00000 −0.295958
$$412$$ 2.00000 0.0985329
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −5.00000 −0.244851
$$418$$ 0 0
$$419$$ 30.0000 1.46560 0.732798 0.680446i $$-0.238214\pi$$
0.732798 + 0.680446i $$0.238214\pi$$
$$420$$ 0 0
$$421$$ −7.00000 −0.341159 −0.170580 0.985344i $$-0.554564\pi$$
−0.170580 + 0.985344i $$0.554564\pi$$
$$422$$ 0 0
$$423$$ 6.00000 0.291730
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 36.0000 1.74013
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 6.00000 0.289010 0.144505 0.989504i $$-0.453841\pi$$
0.144505 + 0.989504i $$0.453841\pi$$
$$432$$ 4.00000 0.192450
$$433$$ 29.0000 1.39365 0.696826 0.717241i $$-0.254595\pi$$
0.696826 + 0.717241i $$0.254595\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 14.0000 0.670478
$$437$$ 30.0000 1.43509
$$438$$ 0 0
$$439$$ 28.0000 1.33637 0.668184 0.743996i $$-0.267072\pi$$
0.668184 + 0.743996i $$0.267072\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 36.0000 1.71041 0.855206 0.518289i $$-0.173431\pi$$
0.855206 + 0.518289i $$0.173431\pi$$
$$444$$ −14.0000 −0.664411
$$445$$ 0 0
$$446$$ 0 0
$$447$$ −24.0000 −1.13516
$$448$$ 0 0
$$449$$ 30.0000 1.41579 0.707894 0.706319i $$-0.249646\pi$$
0.707894 + 0.706319i $$0.249646\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 36.0000 1.69330
$$453$$ −16.0000 −0.751746
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −11.0000 −0.514558 −0.257279 0.966337i $$-0.582826\pi$$
−0.257279 + 0.966337i $$0.582826\pi$$
$$458$$ 0 0
$$459$$ 6.00000 0.280056
$$460$$ 0 0
$$461$$ 6.00000 0.279448 0.139724 0.990190i $$-0.455378\pi$$
0.139724 + 0.990190i $$0.455378\pi$$
$$462$$ 0 0
$$463$$ 7.00000 0.325318 0.162659 0.986682i $$-0.447993\pi$$
0.162659 + 0.986682i $$0.447993\pi$$
$$464$$ −24.0000 −1.11417
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 30.0000 1.38823 0.694117 0.719862i $$-0.255795\pi$$
0.694117 + 0.719862i $$0.255795\pi$$
$$468$$ 2.00000 0.0924500
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −10.0000 −0.460776
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ −7.00000 −0.319173
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 22.0000 1.00000
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 7.00000 0.317200 0.158600 0.987343i $$-0.449302\pi$$
0.158600 + 0.987343i $$0.449302\pi$$
$$488$$ 0 0
$$489$$ 4.00000 0.180886
$$490$$ 0 0
$$491$$ −12.0000 −0.541552 −0.270776 0.962642i $$-0.587280\pi$$
−0.270776 + 0.962642i $$0.587280\pi$$
$$492$$ 24.0000 1.08200
$$493$$ −36.0000 −1.62136
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −20.0000 −0.898027
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 17.0000 0.761025 0.380512 0.924776i $$-0.375748\pi$$
0.380512 + 0.924776i $$0.375748\pi$$
$$500$$ 0 0
$$501$$ 12.0000 0.536120
$$502$$ 0 0
$$503$$ −6.00000 −0.267527 −0.133763 0.991013i $$-0.542706\pi$$
−0.133763 + 0.991013i $$0.542706\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −12.0000 −0.532939
$$508$$ 22.0000 0.976092
$$509$$ 18.0000 0.797836 0.398918 0.916987i $$-0.369386\pi$$
0.398918 + 0.916987i $$0.369386\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ −5.00000 −0.220755
$$514$$ 0 0
$$515$$ 0 0
$$516$$ −2.00000 −0.0880451
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 24.0000 1.05146 0.525730 0.850652i $$-0.323792\pi$$
0.525730 + 0.850652i $$0.323792\pi$$
$$522$$ 0 0
$$523$$ −43.0000 −1.88026 −0.940129 0.340818i $$-0.889296\pi$$
−0.940129 + 0.340818i $$0.889296\pi$$
$$524$$ −12.0000 −0.524222
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −30.0000 −1.30682
$$528$$ 0 0
$$529$$ 13.0000 0.565217
$$530$$ 0 0
$$531$$ 6.00000 0.260378
$$532$$ 0 0
$$533$$ 12.0000 0.519778
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 18.0000 0.776757
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −19.0000 −0.816874 −0.408437 0.912787i $$-0.633926\pi$$
−0.408437 + 0.912787i $$0.633926\pi$$
$$542$$ 0 0
$$543$$ 7.00000 0.300399
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −8.00000 −0.342055 −0.171028 0.985266i $$-0.554709\pi$$
−0.171028 + 0.985266i $$0.554709\pi$$
$$548$$ 12.0000 0.512615
$$549$$ −2.00000 −0.0853579
$$550$$ 0 0
$$551$$ 30.0000 1.27804
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 10.0000 0.424094
$$557$$ −18.0000 −0.762684 −0.381342 0.924434i $$-0.624538\pi$$
−0.381342 + 0.924434i $$0.624538\pi$$
$$558$$ 0 0
$$559$$ −1.00000 −0.0422955
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −18.0000 −0.758610 −0.379305 0.925272i $$-0.623837\pi$$
−0.379305 + 0.925272i $$0.623837\pi$$
$$564$$ −12.0000 −0.505291
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −24.0000 −1.00613 −0.503066 0.864248i $$-0.667795\pi$$
−0.503066 + 0.864248i $$0.667795\pi$$
$$570$$ 0 0
$$571$$ −7.00000 −0.292941 −0.146470 0.989215i $$-0.546791\pi$$
−0.146470 + 0.989215i $$0.546791\pi$$
$$572$$ 0 0
$$573$$ −6.00000 −0.250654
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −8.00000 −0.333333
$$577$$ −7.00000 −0.291414 −0.145707 0.989328i $$-0.546546\pi$$
−0.145707 + 0.989328i $$0.546546\pi$$
$$578$$ 0 0
$$579$$ −5.00000 −0.207793
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −18.0000 −0.742940 −0.371470 0.928445i $$-0.621146\pi$$
−0.371470 + 0.928445i $$0.621146\pi$$
$$588$$ 0 0
$$589$$ 25.0000 1.03011
$$590$$ 0 0
$$591$$ −6.00000 −0.246807
$$592$$ 28.0000 1.15079
$$593$$ 36.0000 1.47834 0.739171 0.673517i $$-0.235217\pi$$
0.739171 + 0.673517i $$0.235217\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 48.0000 1.96616
$$597$$ 16.0000 0.654836
$$598$$ 0 0
$$599$$ 12.0000 0.490307 0.245153 0.969484i $$-0.421162\pi$$
0.245153 + 0.969484i $$0.421162\pi$$
$$600$$ 0 0
$$601$$ 1.00000 0.0407909 0.0203954 0.999792i $$-0.493507\pi$$
0.0203954 + 0.999792i $$0.493507\pi$$
$$602$$ 0 0
$$603$$ 7.00000 0.285062
$$604$$ 32.0000 1.30206
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −19.0000 −0.771186 −0.385593 0.922669i $$-0.626003\pi$$
−0.385593 + 0.922669i $$0.626003\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −6.00000 −0.242734
$$612$$ −12.0000 −0.485071
$$613$$ −38.0000 −1.53481 −0.767403 0.641165i $$-0.778451\pi$$
−0.767403 + 0.641165i $$0.778451\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 42.0000 1.69086 0.845428 0.534089i $$-0.179345\pi$$
0.845428 + 0.534089i $$0.179345\pi$$
$$618$$ 0 0
$$619$$ −35.0000 −1.40677 −0.703384 0.710810i $$-0.748329\pi$$
−0.703384 + 0.710810i $$0.748329\pi$$
$$620$$ 0 0
$$621$$ −6.00000 −0.240772
$$622$$ 0 0
$$623$$ 0 0
$$624$$ −4.00000 −0.160128
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 20.0000 0.798087
$$629$$ 42.0000 1.67465
$$630$$ 0 0
$$631$$ −40.0000 −1.59237 −0.796187 0.605050i $$-0.793153\pi$$
−0.796187 + 0.605050i $$0.793153\pi$$
$$632$$ 0 0
$$633$$ −4.00000 −0.158986
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 12.0000 0.474713
$$640$$ 0 0
$$641$$ −30.0000 −1.18493 −0.592464 0.805597i $$-0.701845\pi$$
−0.592464 + 0.805597i $$0.701845\pi$$
$$642$$ 0 0
$$643$$ −25.0000 −0.985904 −0.492952 0.870057i $$-0.664082\pi$$
−0.492952 + 0.870057i $$0.664082\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −24.0000 −0.943537 −0.471769 0.881722i $$-0.656384\pi$$
−0.471769 + 0.881722i $$0.656384\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −8.00000 −0.313304
$$653$$ 24.0000 0.939193 0.469596 0.882881i $$-0.344399\pi$$
0.469596 + 0.882881i $$0.344399\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −48.0000 −1.87409
$$657$$ 11.0000 0.429151
$$658$$ 0 0
$$659$$ 36.0000 1.40236 0.701180 0.712984i $$-0.252657\pi$$
0.701180 + 0.712984i $$0.252657\pi$$
$$660$$ 0 0
$$661$$ 13.0000 0.505641 0.252821 0.967513i $$-0.418642\pi$$
0.252821 + 0.967513i $$0.418642\pi$$
$$662$$ 0 0
$$663$$ −6.00000 −0.233021
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 36.0000 1.39393
$$668$$ −24.0000 −0.928588
$$669$$ −4.00000 −0.154649
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 31.0000 1.19496 0.597481 0.801883i $$-0.296168\pi$$
0.597481 + 0.801883i $$0.296168\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 24.0000 0.923077
$$677$$ −18.0000 −0.691796 −0.345898 0.938272i $$-0.612426\pi$$
−0.345898 + 0.938272i $$0.612426\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 12.0000 0.459841
$$682$$ 0 0
$$683$$ −18.0000 −0.688751 −0.344375 0.938832i $$-0.611909\pi$$
−0.344375 + 0.938832i $$0.611909\pi$$
$$684$$ 10.0000 0.382360
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −29.0000 −1.10642
$$688$$ 4.00000 0.152499
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −11.0000 −0.418460 −0.209230 0.977866i $$-0.567096\pi$$
−0.209230 + 0.977866i $$0.567096\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −72.0000 −2.72719
$$698$$ 0 0
$$699$$ −6.00000 −0.226941
$$700$$ 0 0
$$701$$ 6.00000 0.226617 0.113308 0.993560i $$-0.463855\pi$$
0.113308 + 0.993560i $$0.463855\pi$$
$$702$$ 0 0
$$703$$ −35.0000 −1.32005
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ −12.0000 −0.450988
$$709$$ −10.0000 −0.375558 −0.187779 0.982211i $$-0.560129\pi$$
−0.187779 + 0.982211i $$0.560129\pi$$
$$710$$ 0 0
$$711$$ −13.0000 −0.487538
$$712$$ 0 0
$$713$$ 30.0000 1.12351
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −36.0000 −1.34538
$$717$$ −6.00000 −0.224074
$$718$$ 0 0
$$719$$ −6.00000 −0.223762 −0.111881 0.993722i $$-0.535688\pi$$
−0.111881 + 0.993722i $$0.535688\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ −2.00000 −0.0743808
$$724$$ −14.0000 −0.520306
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −7.00000 −0.259616 −0.129808 0.991539i $$-0.541436\pi$$
−0.129808 + 0.991539i $$0.541436\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 6.00000 0.221918
$$732$$ 4.00000 0.147844
$$733$$ −13.0000 −0.480166 −0.240083 0.970752i $$-0.577175\pi$$
−0.240083 + 0.970752i $$0.577175\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −7.00000 −0.257499 −0.128750 0.991677i $$-0.541096\pi$$
−0.128750 + 0.991677i $$0.541096\pi$$
$$740$$ 0 0
$$741$$ 5.00000 0.183680
$$742$$ 0 0
$$743$$ 24.0000 0.880475 0.440237 0.897881i $$-0.354894\pi$$
0.440237 + 0.897881i $$0.354894\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −12.0000 −0.439057
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −19.0000 −0.693320 −0.346660 0.937991i $$-0.612684\pi$$
−0.346660 + 0.937991i $$0.612684\pi$$
$$752$$ 24.0000 0.875190
$$753$$ 18.0000 0.655956
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −50.0000 −1.81728 −0.908640 0.417579i $$-0.862879\pi$$
−0.908640 + 0.417579i $$0.862879\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 42.0000 1.52250 0.761249 0.648459i $$-0.224586\pi$$
0.761249 + 0.648459i $$0.224586\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 12.0000 0.434145
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −6.00000 −0.216647
$$768$$ 16.0000 0.577350
$$769$$ 13.0000 0.468792 0.234396 0.972141i $$-0.424689\pi$$
0.234396 + 0.972141i $$0.424689\pi$$
$$770$$ 0 0
$$771$$ −12.0000 −0.432169
$$772$$ 10.0000 0.359908
$$773$$ −24.0000 −0.863220 −0.431610 0.902060i $$-0.642054\pi$$
−0.431610 + 0.902060i $$0.642054\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 60.0000 2.14972
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ −6.00000 −0.214423
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −28.0000 −0.998092 −0.499046 0.866575i $$-0.666316\pi$$
−0.499046 + 0.866575i $$0.666316\pi$$
$$788$$ 12.0000 0.427482
$$789$$ 12.0000 0.427211
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 2.00000 0.0710221
$$794$$ 0 0
$$795$$ 0 0
$$796$$ −32.0000 −1.13421
$$797$$ 18.0000 0.637593 0.318796 0.947823i $$-0.396721\pi$$
0.318796 + 0.947823i $$0.396721\pi$$
$$798$$ 0 0
$$799$$ 36.0000 1.27359
$$800$$ 0 0
$$801$$ −6.00000 −0.212000
$$802$$ 0 0
$$803$$ 0 0
$$804$$ −14.0000 −0.493742
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 18.0000 0.633630
$$808$$ 0 0
$$809$$ 18.0000 0.632846 0.316423 0.948618i $$-0.397518\pi$$
0.316423 + 0.948618i $$0.397518\pi$$
$$810$$ 0 0
$$811$$ 28.0000 0.983213 0.491606 0.870817i $$-0.336410\pi$$
0.491606 + 0.870817i $$0.336410\pi$$
$$812$$ 0 0
$$813$$ 16.0000 0.561144
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 24.0000 0.840168
$$817$$ −5.00000 −0.174928
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −24.0000 −0.837606 −0.418803 0.908077i $$-0.637550\pi$$
−0.418803 + 0.908077i $$0.637550\pi$$
$$822$$ 0 0
$$823$$ 40.0000 1.39431 0.697156 0.716919i $$-0.254448\pi$$
0.697156 + 0.716919i $$0.254448\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 6.00000 0.208640 0.104320 0.994544i $$-0.466733\pi$$
0.104320 + 0.994544i $$0.466733\pi$$
$$828$$ 12.0000 0.417029
$$829$$ 19.0000 0.659897 0.329949 0.943999i $$-0.392969\pi$$
0.329949 + 0.943999i $$0.392969\pi$$
$$830$$ 0 0
$$831$$ −23.0000 −0.797861
$$832$$ 8.00000 0.277350
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ −5.00000 −0.172825
$$838$$ 0 0
$$839$$ 30.0000 1.03572 0.517858 0.855467i $$-0.326730\pi$$
0.517858 + 0.855467i $$0.326730\pi$$
$$840$$ 0 0
$$841$$ 7.00000 0.241379
$$842$$ 0 0
$$843$$ −24.0000 −0.826604
$$844$$ 8.00000 0.275371
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ 11.0000 0.377519
$$850$$ 0 0
$$851$$ −42.0000 −1.43974
$$852$$ −24.0000 −0.822226
$$853$$ 17.0000 0.582069 0.291034 0.956713i $$-0.406001\pi$$
0.291034 + 0.956713i $$0.406001\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 42.0000 1.43469 0.717346 0.696717i $$-0.245357\pi$$
0.717346 + 0.696717i $$0.245357\pi$$
$$858$$ 0 0
$$859$$ 4.00000 0.136478 0.0682391 0.997669i $$-0.478262\pi$$
0.0682391 + 0.997669i $$0.478262\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 6.00000 0.204242 0.102121 0.994772i $$-0.467437\pi$$
0.102121 + 0.994772i $$0.467437\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 19.0000 0.645274
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ −7.00000 −0.237186
$$872$$ 0 0
$$873$$ −10.0000 −0.338449
$$874$$ 0 0
$$875$$ 0 0
$$876$$ −22.0000 −0.743311
$$877$$ −2.00000 −0.0675352 −0.0337676 0.999430i $$-0.510751\pi$$
−0.0337676 + 0.999430i $$0.510751\pi$$
$$878$$ 0 0
$$879$$ 12.0000 0.404750
$$880$$ 0 0
$$881$$ −12.0000 −0.404290 −0.202145 0.979356i $$-0.564791\pi$$
−0.202145 + 0.979356i $$0.564791\pi$$
$$882$$ 0 0
$$883$$ 31.0000 1.04323 0.521617 0.853180i $$-0.325329\pi$$
0.521617 + 0.853180i $$0.325329\pi$$
$$884$$ 12.0000 0.403604
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 12.0000 0.402921 0.201460 0.979497i $$-0.435431\pi$$
0.201460 + 0.979497i $$0.435431\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 8.00000 0.267860
$$893$$ −30.0000 −1.00391
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 6.00000 0.200334
$$898$$ 0 0
$$899$$ 30.0000 1.00056
$$900$$ 0 0
$$901$$ 0 0
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 31.0000 1.02934 0.514669 0.857389i $$-0.327915\pi$$
0.514669 + 0.857389i $$0.327915\pi$$
$$908$$ −24.0000 −0.796468
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −18.0000 −0.596367 −0.298183 0.954509i $$-0.596381\pi$$
−0.298183 + 0.954509i $$0.596381\pi$$
$$912$$ −20.0000 −0.662266
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 58.0000 1.91637
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 47.0000 1.55039 0.775193 0.631724i $$-0.217652\pi$$
0.775193 + 0.631724i $$0.217652\pi$$
$$920$$ 0 0
$$921$$ −7.00000 −0.230658
$$922$$ 0 0
$$923$$ −12.0000 −0.394985
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ −1.00000 −0.0328443
$$928$$ 0 0
$$929$$ 12.0000 0.393707 0.196854 0.980433i $$-0.436928\pi$$
0.196854 + 0.980433i $$0.436928\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 12.0000 0.393073
$$933$$ −12.0000 −0.392862
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 29.0000 0.947389 0.473694 0.880689i $$-0.342920\pi$$
0.473694 + 0.880689i $$0.342920\pi$$
$$938$$ 0 0
$$939$$ 17.0000 0.554774
$$940$$ 0 0
$$941$$ 30.0000 0.977972 0.488986 0.872292i $$-0.337367\pi$$
0.488986 + 0.872292i $$0.337367\pi$$
$$942$$ 0 0
$$943$$ 72.0000 2.34464
$$944$$ 24.0000 0.781133
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −48.0000 −1.55979 −0.779895 0.625910i $$-0.784728\pi$$
−0.779895 + 0.625910i $$0.784728\pi$$
$$948$$ 26.0000 0.844441
$$949$$ −11.0000 −0.357075
$$950$$ 0 0
$$951$$ −6.00000 −0.194563
$$952$$ 0 0
$$953$$ 24.0000 0.777436 0.388718 0.921357i $$-0.372918\pi$$
0.388718 + 0.921357i $$0.372918\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 12.0000 0.388108
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −6.00000 −0.193548
$$962$$ 0 0
$$963$$ −18.0000 −0.580042
$$964$$ 4.00000 0.128831
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 55.0000 1.76868 0.884340 0.466843i $$-0.154609\pi$$
0.884340 + 0.466843i $$0.154609\pi$$
$$968$$ 0 0
$$969$$ −30.0000 −0.963739
$$970$$ 0 0
$$971$$ 24.0000 0.770197 0.385098 0.922876i $$-0.374168\pi$$
0.385098 + 0.922876i $$0.374168\pi$$
$$972$$ −2.00000 −0.0641500
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ −8.00000 −0.256074
$$977$$ 12.0000 0.383914 0.191957 0.981403i $$-0.438517\pi$$
0.191957 + 0.981403i $$0.438517\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ −7.00000 −0.223493
$$982$$ 0 0
$$983$$ 18.0000 0.574111 0.287055 0.957914i $$-0.407324\pi$$
0.287055 + 0.957914i $$0.407324\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ −10.0000 −0.318142
$$989$$ −6.00000 −0.190789
$$990$$ 0 0
$$991$$ −43.0000 −1.36594 −0.682970 0.730446i $$-0.739312\pi$$
−0.682970 + 0.730446i $$0.739312\pi$$
$$992$$ 0 0
$$993$$ 23.0000 0.729883
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 24.0000 0.760469
$$997$$ −31.0000 −0.981780 −0.490890 0.871222i $$-0.663328\pi$$
−0.490890 + 0.871222i $$0.663328\pi$$
$$998$$ 0 0
$$999$$ 7.00000 0.221470
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 3675.2.a.i.1.1 1
5.4 even 2 735.2.a.d.1.1 1
7.3 odd 6 525.2.i.c.226.1 2
7.5 odd 6 525.2.i.c.151.1 2
7.6 odd 2 3675.2.a.h.1.1 1
15.14 odd 2 2205.2.a.d.1.1 1
35.3 even 12 525.2.r.b.499.1 4
35.4 even 6 735.2.i.c.226.1 2
35.9 even 6 735.2.i.c.361.1 2
35.12 even 12 525.2.r.b.424.1 4
35.17 even 12 525.2.r.b.499.2 4
35.19 odd 6 105.2.i.a.46.1 yes 2
35.24 odd 6 105.2.i.a.16.1 2
35.33 even 12 525.2.r.b.424.2 4
35.34 odd 2 735.2.a.e.1.1 1
105.59 even 6 315.2.j.b.226.1 2
105.89 even 6 315.2.j.b.46.1 2
105.104 even 2 2205.2.a.f.1.1 1
140.19 even 6 1680.2.bg.m.1201.1 2
140.59 even 6 1680.2.bg.m.961.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.i.a.16.1 2 35.24 odd 6
105.2.i.a.46.1 yes 2 35.19 odd 6
315.2.j.b.46.1 2 105.89 even 6
315.2.j.b.226.1 2 105.59 even 6
525.2.i.c.151.1 2 7.5 odd 6
525.2.i.c.226.1 2 7.3 odd 6
525.2.r.b.424.1 4 35.12 even 12
525.2.r.b.424.2 4 35.33 even 12
525.2.r.b.499.1 4 35.3 even 12
525.2.r.b.499.2 4 35.17 even 12
735.2.a.d.1.1 1 5.4 even 2
735.2.a.e.1.1 1 35.34 odd 2
735.2.i.c.226.1 2 35.4 even 6
735.2.i.c.361.1 2 35.9 even 6
1680.2.bg.m.961.1 2 140.59 even 6
1680.2.bg.m.1201.1 2 140.19 even 6
2205.2.a.d.1.1 1 15.14 odd 2
2205.2.a.f.1.1 1 105.104 even 2
3675.2.a.h.1.1 1 7.6 odd 2
3675.2.a.i.1.1 1 1.1 even 1 trivial