# Properties

 Label 1728.2.a.k.1.1 Level $1728$ Weight $2$ Character 1728.1 Self dual yes Analytic conductor $13.798$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1728 = 2^{6} \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1728.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$13.7981494693$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 864) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1728.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{5} +3.00000 q^{7} +O(q^{10})$$ $$q-1.00000 q^{5} +3.00000 q^{7} -3.00000 q^{11} -4.00000 q^{17} -6.00000 q^{19} -6.00000 q^{23} -4.00000 q^{25} -2.00000 q^{29} +9.00000 q^{31} -3.00000 q^{35} +2.00000 q^{37} +10.0000 q^{41} -6.00000 q^{43} -6.00000 q^{47} +2.00000 q^{49} +13.0000 q^{53} +3.00000 q^{55} -12.0000 q^{59} -8.00000 q^{61} -6.00000 q^{67} -12.0000 q^{71} +9.00000 q^{73} -9.00000 q^{77} -3.00000 q^{83} +4.00000 q^{85} -14.0000 q^{89} +6.00000 q^{95} -9.00000 q^{97} +O(q^{100})$$

## 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
$$5$$ −1.00000 −0.447214 −0.223607 0.974679i $$-0.571783\pi$$
−0.223607 + 0.974679i $$0.571783\pi$$
$$6$$ 0 0
$$7$$ 3.00000 1.13389 0.566947 0.823754i $$-0.308125\pi$$
0.566947 + 0.823754i $$0.308125\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −3.00000 −0.904534 −0.452267 0.891883i $$-0.649385\pi$$
−0.452267 + 0.891883i $$0.649385\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −4.00000 −0.970143 −0.485071 0.874475i $$-0.661206\pi$$
−0.485071 + 0.874475i $$0.661206\pi$$
$$18$$ 0 0
$$19$$ −6.00000 −1.37649 −0.688247 0.725476i $$-0.741620\pi$$
−0.688247 + 0.725476i $$0.741620\pi$$
$$20$$ 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
$$25$$ −4.00000 −0.800000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −2.00000 −0.371391 −0.185695 0.982607i $$-0.559454\pi$$
−0.185695 + 0.982607i $$0.559454\pi$$
$$30$$ 0 0
$$31$$ 9.00000 1.61645 0.808224 0.588875i $$-0.200429\pi$$
0.808224 + 0.588875i $$0.200429\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −3.00000 −0.507093
$$36$$ 0 0
$$37$$ 2.00000 0.328798 0.164399 0.986394i $$-0.447432\pi$$
0.164399 + 0.986394i $$0.447432\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 10.0000 1.56174 0.780869 0.624695i $$-0.214777\pi$$
0.780869 + 0.624695i $$0.214777\pi$$
$$42$$ 0 0
$$43$$ −6.00000 −0.914991 −0.457496 0.889212i $$-0.651253\pi$$
−0.457496 + 0.889212i $$0.651253\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −6.00000 −0.875190 −0.437595 0.899172i $$-0.644170\pi$$
−0.437595 + 0.899172i $$0.644170\pi$$
$$48$$ 0 0
$$49$$ 2.00000 0.285714
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 13.0000 1.78569 0.892844 0.450367i $$-0.148707\pi$$
0.892844 + 0.450367i $$0.148707\pi$$
$$54$$ 0 0
$$55$$ 3.00000 0.404520
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −12.0000 −1.56227 −0.781133 0.624364i $$-0.785358\pi$$
−0.781133 + 0.624364i $$0.785358\pi$$
$$60$$ 0 0
$$61$$ −8.00000 −1.02430 −0.512148 0.858898i $$-0.671150\pi$$
−0.512148 + 0.858898i $$0.671150\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −6.00000 −0.733017 −0.366508 0.930415i $$-0.619447\pi$$
−0.366508 + 0.930415i $$0.619447\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −12.0000 −1.42414 −0.712069 0.702109i $$-0.752242\pi$$
−0.712069 + 0.702109i $$0.752242\pi$$
$$72$$ 0 0
$$73$$ 9.00000 1.05337 0.526685 0.850060i $$-0.323435\pi$$
0.526685 + 0.850060i $$0.323435\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −9.00000 −1.02565
$$78$$ 0 0
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −3.00000 −0.329293 −0.164646 0.986353i $$-0.552648\pi$$
−0.164646 + 0.986353i $$0.552648\pi$$
$$84$$ 0 0
$$85$$ 4.00000 0.433861
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −14.0000 −1.48400 −0.741999 0.670402i $$-0.766122\pi$$
−0.741999 + 0.670402i $$0.766122\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 6.00000 0.615587
$$96$$ 0 0
$$97$$ −9.00000 −0.913812 −0.456906 0.889515i $$-0.651042\pi$$
−0.456906 + 0.889515i $$0.651042\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −7.00000 −0.696526 −0.348263 0.937397i $$-0.613228\pi$$
−0.348263 + 0.937397i $$0.613228\pi$$
$$102$$ 0 0
$$103$$ −12.0000 −1.18240 −0.591198 0.806527i $$-0.701345\pi$$
−0.591198 + 0.806527i $$0.701345\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −15.0000 −1.45010 −0.725052 0.688694i $$-0.758184\pi$$
−0.725052 + 0.688694i $$0.758184\pi$$
$$108$$ 0 0
$$109$$ 18.0000 1.72409 0.862044 0.506834i $$-0.169184\pi$$
0.862044 + 0.506834i $$0.169184\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 10.0000 0.940721 0.470360 0.882474i $$-0.344124\pi$$
0.470360 + 0.882474i $$0.344124\pi$$
$$114$$ 0 0
$$115$$ 6.00000 0.559503
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −12.0000 −1.10004
$$120$$ 0 0
$$121$$ −2.00000 −0.181818
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 9.00000 0.804984
$$126$$ 0 0
$$127$$ −3.00000 −0.266207 −0.133103 0.991102i $$-0.542494\pi$$
−0.133103 + 0.991102i $$0.542494\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 9.00000 0.786334 0.393167 0.919467i $$-0.371379\pi$$
0.393167 + 0.919467i $$0.371379\pi$$
$$132$$ 0 0
$$133$$ −18.0000 −1.56080
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 2.00000 0.170872 0.0854358 0.996344i $$-0.472772\pi$$
0.0854358 + 0.996344i $$0.472772\pi$$
$$138$$ 0 0
$$139$$ 12.0000 1.01783 0.508913 0.860818i $$-0.330047\pi$$
0.508913 + 0.860818i $$0.330047\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 2.00000 0.166091
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −17.0000 −1.39269 −0.696347 0.717705i $$-0.745193\pi$$
−0.696347 + 0.717705i $$0.745193\pi$$
$$150$$ 0 0
$$151$$ −3.00000 −0.244137 −0.122068 0.992522i $$-0.538953\pi$$
−0.122068 + 0.992522i $$0.538953\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −9.00000 −0.722897
$$156$$ 0 0
$$157$$ −4.00000 −0.319235 −0.159617 0.987179i $$-0.551026\pi$$
−0.159617 + 0.987179i $$0.551026\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −18.0000 −1.41860
$$162$$ 0 0
$$163$$ 24.0000 1.87983 0.939913 0.341415i $$-0.110906\pi$$
0.939913 + 0.341415i $$0.110906\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −18.0000 −1.39288 −0.696441 0.717614i $$-0.745234\pi$$
−0.696441 + 0.717614i $$0.745234\pi$$
$$168$$ 0 0
$$169$$ −13.0000 −1.00000
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 11.0000 0.836315 0.418157 0.908375i $$-0.362676\pi$$
0.418157 + 0.908375i $$0.362676\pi$$
$$174$$ 0 0
$$175$$ −12.0000 −0.907115
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 15.0000 1.12115 0.560576 0.828103i $$-0.310580\pi$$
0.560576 + 0.828103i $$0.310580\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −2.00000 −0.147043
$$186$$ 0 0
$$187$$ 12.0000 0.877527
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 24.0000 1.73658 0.868290 0.496058i $$-0.165220\pi$$
0.868290 + 0.496058i $$0.165220\pi$$
$$192$$ 0 0
$$193$$ 13.0000 0.935760 0.467880 0.883792i $$-0.345018\pi$$
0.467880 + 0.883792i $$0.345018\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 5.00000 0.356235 0.178118 0.984009i $$-0.442999\pi$$
0.178118 + 0.984009i $$0.442999\pi$$
$$198$$ 0 0
$$199$$ −3.00000 −0.212664 −0.106332 0.994331i $$-0.533911\pi$$
−0.106332 + 0.994331i $$0.533911\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −6.00000 −0.421117
$$204$$ 0 0
$$205$$ −10.0000 −0.698430
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 18.0000 1.24509
$$210$$ 0 0
$$211$$ −6.00000 −0.413057 −0.206529 0.978441i $$-0.566217\pi$$
−0.206529 + 0.978441i $$0.566217\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 6.00000 0.409197
$$216$$ 0 0
$$217$$ 27.0000 1.83288
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −24.0000 −1.60716 −0.803579 0.595198i $$-0.797074\pi$$
−0.803579 + 0.595198i $$0.797074\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 12.0000 0.796468 0.398234 0.917284i $$-0.369623\pi$$
0.398234 + 0.917284i $$0.369623\pi$$
$$228$$ 0 0
$$229$$ 18.0000 1.18947 0.594737 0.803921i $$-0.297256\pi$$
0.594737 + 0.803921i $$0.297256\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 14.0000 0.917170 0.458585 0.888650i $$-0.348356\pi$$
0.458585 + 0.888650i $$0.348356\pi$$
$$234$$ 0 0
$$235$$ 6.00000 0.391397
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 6.00000 0.388108 0.194054 0.980991i $$-0.437836\pi$$
0.194054 + 0.980991i $$0.437836\pi$$
$$240$$ 0 0
$$241$$ −18.0000 −1.15948 −0.579741 0.814801i $$-0.696846\pi$$
−0.579741 + 0.814801i $$0.696846\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −2.00000 −0.127775
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 18.0000 1.13165
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 8.00000 0.499026 0.249513 0.968371i $$-0.419729\pi$$
0.249513 + 0.968371i $$0.419729\pi$$
$$258$$ 0 0
$$259$$ 6.00000 0.372822
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −6.00000 −0.369976 −0.184988 0.982741i $$-0.559225\pi$$
−0.184988 + 0.982741i $$0.559225\pi$$
$$264$$ 0 0
$$265$$ −13.0000 −0.798584
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 14.0000 0.853595 0.426798 0.904347i $$-0.359642\pi$$
0.426798 + 0.904347i $$0.359642\pi$$
$$270$$ 0 0
$$271$$ 3.00000 0.182237 0.0911185 0.995840i $$-0.470956\pi$$
0.0911185 + 0.995840i $$0.470956\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 12.0000 0.723627
$$276$$ 0 0
$$277$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −20.0000 −1.19310 −0.596550 0.802576i $$-0.703462\pi$$
−0.596550 + 0.802576i $$0.703462\pi$$
$$282$$ 0 0
$$283$$ 6.00000 0.356663 0.178331 0.983970i $$-0.442930\pi$$
0.178331 + 0.983970i $$0.442930\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 30.0000 1.77084
$$288$$ 0 0
$$289$$ −1.00000 −0.0588235
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 10.0000 0.584206 0.292103 0.956387i $$-0.405645\pi$$
0.292103 + 0.956387i $$0.405645\pi$$
$$294$$ 0 0
$$295$$ 12.0000 0.698667
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −18.0000 −1.03750
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 8.00000 0.458079
$$306$$ 0 0
$$307$$ −12.0000 −0.684876 −0.342438 0.939540i $$-0.611253\pi$$
−0.342438 + 0.939540i $$0.611253\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 18.0000 1.02069 0.510343 0.859971i $$-0.329518\pi$$
0.510343 + 0.859971i $$0.329518\pi$$
$$312$$ 0 0
$$313$$ −19.0000 −1.07394 −0.536972 0.843600i $$-0.680432\pi$$
−0.536972 + 0.843600i $$0.680432\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −7.00000 −0.393159 −0.196580 0.980488i $$-0.562983\pi$$
−0.196580 + 0.980488i $$0.562983\pi$$
$$318$$ 0 0
$$319$$ 6.00000 0.335936
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 24.0000 1.33540
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −18.0000 −0.992372
$$330$$ 0 0
$$331$$ −30.0000 −1.64895 −0.824475 0.565899i $$-0.808529\pi$$
−0.824475 + 0.565899i $$0.808529\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 6.00000 0.327815
$$336$$ 0 0
$$337$$ 18.0000 0.980522 0.490261 0.871576i $$-0.336901\pi$$
0.490261 + 0.871576i $$0.336901\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −27.0000 −1.46213
$$342$$ 0 0
$$343$$ −15.0000 −0.809924
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 3.00000 0.161048 0.0805242 0.996753i $$-0.474341\pi$$
0.0805242 + 0.996753i $$0.474341\pi$$
$$348$$ 0 0
$$349$$ −26.0000 −1.39175 −0.695874 0.718164i $$-0.744983\pi$$
−0.695874 + 0.718164i $$0.744983\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −2.00000 −0.106449 −0.0532246 0.998583i $$-0.516950\pi$$
−0.0532246 + 0.998583i $$0.516950\pi$$
$$354$$ 0 0
$$355$$ 12.0000 0.636894
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −18.0000 −0.950004 −0.475002 0.879985i $$-0.657553\pi$$
−0.475002 + 0.879985i $$0.657553\pi$$
$$360$$ 0 0
$$361$$ 17.0000 0.894737
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −9.00000 −0.471082
$$366$$ 0 0
$$367$$ 21.0000 1.09619 0.548096 0.836416i $$-0.315353\pi$$
0.548096 + 0.836416i $$0.315353\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 39.0000 2.02478
$$372$$ 0 0
$$373$$ 4.00000 0.207112 0.103556 0.994624i $$-0.466978\pi$$
0.103556 + 0.994624i $$0.466978\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −36.0000 −1.84920 −0.924598 0.380945i $$-0.875599\pi$$
−0.924598 + 0.380945i $$0.875599\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 36.0000 1.83951 0.919757 0.392488i $$-0.128386\pi$$
0.919757 + 0.392488i $$0.128386\pi$$
$$384$$ 0 0
$$385$$ 9.00000 0.458682
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 7.00000 0.354914 0.177457 0.984129i $$-0.443213\pi$$
0.177457 + 0.984129i $$0.443213\pi$$
$$390$$ 0 0
$$391$$ 24.0000 1.21373
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 16.0000 0.803017 0.401508 0.915855i $$-0.368486\pi$$
0.401508 + 0.915855i $$0.368486\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −28.0000 −1.39825 −0.699127 0.714998i $$-0.746428\pi$$
−0.699127 + 0.714998i $$0.746428\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −6.00000 −0.297409
$$408$$ 0 0
$$409$$ −9.00000 −0.445021 −0.222511 0.974930i $$-0.571425\pi$$
−0.222511 + 0.974930i $$0.571425\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −36.0000 −1.77144
$$414$$ 0 0
$$415$$ 3.00000 0.147264
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 12.0000 0.586238 0.293119 0.956076i $$-0.405307\pi$$
0.293119 + 0.956076i $$0.405307\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 16.0000 0.776114
$$426$$ 0 0
$$427$$ −24.0000 −1.16144
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 6.00000 0.289010 0.144505 0.989504i $$-0.453841\pi$$
0.144505 + 0.989504i $$0.453841\pi$$
$$432$$ 0 0
$$433$$ −11.0000 −0.528626 −0.264313 0.964437i $$-0.585145\pi$$
−0.264313 + 0.964437i $$0.585145\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 36.0000 1.72211
$$438$$ 0 0
$$439$$ 9.00000 0.429547 0.214773 0.976664i $$-0.431099\pi$$
0.214773 + 0.976664i $$0.431099\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −12.0000 −0.570137 −0.285069 0.958507i $$-0.592016\pi$$
−0.285069 + 0.958507i $$0.592016\pi$$
$$444$$ 0 0
$$445$$ 14.0000 0.663664
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 22.0000 1.03824 0.519122 0.854700i $$-0.326259\pi$$
0.519122 + 0.854700i $$0.326259\pi$$
$$450$$ 0 0
$$451$$ −30.0000 −1.41264
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −9.00000 −0.421002 −0.210501 0.977594i $$-0.567510\pi$$
−0.210501 + 0.977594i $$0.567510\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 7.00000 0.326023 0.163011 0.986624i $$-0.447879\pi$$
0.163011 + 0.986624i $$0.447879\pi$$
$$462$$ 0 0
$$463$$ 15.0000 0.697109 0.348555 0.937288i $$-0.386673\pi$$
0.348555 + 0.937288i $$0.386673\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −3.00000 −0.138823 −0.0694117 0.997588i $$-0.522112\pi$$
−0.0694117 + 0.997588i $$0.522112\pi$$
$$468$$ 0 0
$$469$$ −18.0000 −0.831163
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 18.0000 0.827641
$$474$$ 0 0
$$475$$ 24.0000 1.10120
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 42.0000 1.91903 0.959514 0.281659i $$-0.0908848\pi$$
0.959514 + 0.281659i $$0.0908848\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 9.00000 0.408669
$$486$$ 0 0
$$487$$ 24.0000 1.08754 0.543772 0.839233i $$-0.316996\pi$$
0.543772 + 0.839233i $$0.316996\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 15.0000 0.676941 0.338470 0.940977i $$-0.390091\pi$$
0.338470 + 0.940977i $$0.390091\pi$$
$$492$$ 0 0
$$493$$ 8.00000 0.360302
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −36.0000 −1.61482
$$498$$ 0 0
$$499$$ −6.00000 −0.268597 −0.134298 0.990941i $$-0.542878\pi$$
−0.134298 + 0.990941i $$0.542878\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 6.00000 0.267527 0.133763 0.991013i $$-0.457294\pi$$
0.133763 + 0.991013i $$0.457294\pi$$
$$504$$ 0 0
$$505$$ 7.00000 0.311496
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 37.0000 1.64000 0.819998 0.572366i $$-0.193974\pi$$
0.819998 + 0.572366i $$0.193974\pi$$
$$510$$ 0 0
$$511$$ 27.0000 1.19441
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 12.0000 0.528783
$$516$$ 0 0
$$517$$ 18.0000 0.791639
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 32.0000 1.40195 0.700973 0.713188i $$-0.252749\pi$$
0.700973 + 0.713188i $$0.252749\pi$$
$$522$$ 0 0
$$523$$ 36.0000 1.57417 0.787085 0.616844i $$-0.211589\pi$$
0.787085 + 0.616844i $$0.211589\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −36.0000 −1.56818
$$528$$ 0 0
$$529$$ 13.0000 0.565217
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 15.0000 0.648507
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −6.00000 −0.258438
$$540$$ 0 0
$$541$$ 36.0000 1.54776 0.773880 0.633332i $$-0.218313\pi$$
0.773880 + 0.633332i $$0.218313\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −18.0000 −0.771035
$$546$$ 0 0
$$547$$ −36.0000 −1.53925 −0.769624 0.638497i $$-0.779557\pi$$
−0.769624 + 0.638497i $$0.779557\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 12.0000 0.511217
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −41.0000 −1.73723 −0.868613 0.495491i $$-0.834988\pi$$
−0.868613 + 0.495491i $$0.834988\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 3.00000 0.126435 0.0632175 0.998000i $$-0.479864\pi$$
0.0632175 + 0.998000i $$0.479864\pi$$
$$564$$ 0 0
$$565$$ −10.0000 −0.420703
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 20.0000 0.838444 0.419222 0.907884i $$-0.362303\pi$$
0.419222 + 0.907884i $$0.362303\pi$$
$$570$$ 0 0
$$571$$ −24.0000 −1.00437 −0.502184 0.864761i $$-0.667470\pi$$
−0.502184 + 0.864761i $$0.667470\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 24.0000 1.00087
$$576$$ 0 0
$$577$$ −34.0000 −1.41544 −0.707719 0.706494i $$-0.750276\pi$$
−0.707719 + 0.706494i $$0.750276\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −9.00000 −0.373383
$$582$$ 0 0
$$583$$ −39.0000 −1.61521
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −27.0000 −1.11441 −0.557205 0.830375i $$-0.688126\pi$$
−0.557205 + 0.830375i $$0.688126\pi$$
$$588$$ 0 0
$$589$$ −54.0000 −2.22503
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 14.0000 0.574911 0.287456 0.957794i $$-0.407191\pi$$
0.287456 + 0.957794i $$0.407191\pi$$
$$594$$ 0 0
$$595$$ 12.0000 0.491952
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −6.00000 −0.245153 −0.122577 0.992459i $$-0.539116\pi$$
−0.122577 + 0.992459i $$0.539116\pi$$
$$600$$ 0 0
$$601$$ 19.0000 0.775026 0.387513 0.921864i $$-0.373334\pi$$
0.387513 + 0.921864i $$0.373334\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 2.00000 0.0813116
$$606$$ 0 0
$$607$$ −24.0000 −0.974130 −0.487065 0.873366i $$-0.661933\pi$$
−0.487065 + 0.873366i $$0.661933\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −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
$$617$$ −26.0000 −1.04672 −0.523360 0.852111i $$-0.675322\pi$$
−0.523360 + 0.852111i $$0.675322\pi$$
$$618$$ 0 0
$$619$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −42.0000 −1.68269
$$624$$ 0 0
$$625$$ 11.0000 0.440000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −8.00000 −0.318981
$$630$$ 0 0
$$631$$ 27.0000 1.07485 0.537427 0.843311i $$-0.319397\pi$$
0.537427 + 0.843311i $$0.319397\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 3.00000 0.119051
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 2.00000 0.0789953 0.0394976 0.999220i $$-0.487424\pi$$
0.0394976 + 0.999220i $$0.487424\pi$$
$$642$$ 0 0
$$643$$ 36.0000 1.41970 0.709851 0.704352i $$-0.248762\pi$$
0.709851 + 0.704352i $$0.248762\pi$$
$$644$$ 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
$$649$$ 36.0000 1.41312
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 35.0000 1.36966 0.684828 0.728705i $$-0.259877\pi$$
0.684828 + 0.728705i $$0.259877\pi$$
$$654$$ 0 0
$$655$$ −9.00000 −0.351659
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −21.0000 −0.818044 −0.409022 0.912525i $$-0.634130\pi$$
−0.409022 + 0.912525i $$0.634130\pi$$
$$660$$ 0 0
$$661$$ 14.0000 0.544537 0.272268 0.962221i $$-0.412226\pi$$
0.272268 + 0.962221i $$0.412226\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 18.0000 0.698010
$$666$$ 0 0
$$667$$ 12.0000 0.464642
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 24.0000 0.926510
$$672$$ 0 0
$$673$$ −19.0000 −0.732396 −0.366198 0.930537i $$-0.619341\pi$$
−0.366198 + 0.930537i $$0.619341\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 2.00000 0.0768662 0.0384331 0.999261i $$-0.487763\pi$$
0.0384331 + 0.999261i $$0.487763\pi$$
$$678$$ 0 0
$$679$$ −27.0000 −1.03616
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 12.0000 0.459167 0.229584 0.973289i $$-0.426264\pi$$
0.229584 + 0.973289i $$0.426264\pi$$
$$684$$ 0 0
$$685$$ −2.00000 −0.0764161
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −12.0000 −0.456502 −0.228251 0.973602i $$-0.573301\pi$$
−0.228251 + 0.973602i $$0.573301\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −12.0000 −0.455186
$$696$$ 0 0
$$697$$ −40.0000 −1.51511
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 13.0000 0.491003 0.245502 0.969396i $$-0.421047\pi$$
0.245502 + 0.969396i $$0.421047\pi$$
$$702$$ 0 0
$$703$$ −12.0000 −0.452589
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −21.0000 −0.789786
$$708$$ 0 0
$$709$$ 36.0000 1.35201 0.676004 0.736898i $$-0.263710\pi$$
0.676004 + 0.736898i $$0.263710\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −54.0000 −2.02232
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −36.0000 −1.34257 −0.671287 0.741198i $$-0.734258\pi$$
−0.671287 + 0.741198i $$0.734258\pi$$
$$720$$ 0 0
$$721$$ −36.0000 −1.34071
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 8.00000 0.297113
$$726$$ 0 0
$$727$$ −21.0000 −0.778847 −0.389423 0.921059i $$-0.627326\pi$$
−0.389423 + 0.921059i $$0.627326\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 24.0000 0.887672
$$732$$ 0 0
$$733$$ 18.0000 0.664845 0.332423 0.943131i $$-0.392134\pi$$
0.332423 + 0.943131i $$0.392134\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 18.0000 0.663039
$$738$$ 0 0
$$739$$ 12.0000 0.441427 0.220714 0.975339i $$-0.429161\pi$$
0.220714 + 0.975339i $$0.429161\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −24.0000 −0.880475 −0.440237 0.897881i $$-0.645106\pi$$
−0.440237 + 0.897881i $$0.645106\pi$$
$$744$$ 0 0
$$745$$ 17.0000 0.622832
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −45.0000 −1.64426
$$750$$ 0 0
$$751$$ −27.0000 −0.985244 −0.492622 0.870243i $$-0.663961\pi$$
−0.492622 + 0.870243i $$0.663961\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 3.00000 0.109181
$$756$$ 0 0
$$757$$ −18.0000 −0.654221 −0.327111 0.944986i $$-0.606075\pi$$
−0.327111 + 0.944986i $$0.606075\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −8.00000 −0.290000 −0.145000 0.989432i $$-0.546318\pi$$
−0.145000 + 0.989432i $$0.546318\pi$$
$$762$$ 0 0
$$763$$ 54.0000 1.95493
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 41.0000 1.47850 0.739249 0.673432i $$-0.235181\pi$$
0.739249 + 0.673432i $$0.235181\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −50.0000 −1.79838 −0.899188 0.437564i $$-0.855842\pi$$
−0.899188 + 0.437564i $$0.855842\pi$$
$$774$$ 0 0
$$775$$ −36.0000 −1.29316
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −60.0000 −2.14972
$$780$$ 0 0
$$781$$ 36.0000 1.28818
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 4.00000 0.142766
$$786$$ 0 0
$$787$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 30.0000 1.06668
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −37.0000 −1.31061 −0.655304 0.755366i $$-0.727459\pi$$
−0.655304 + 0.755366i $$0.727459\pi$$
$$798$$ 0 0
$$799$$ 24.0000 0.849059
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −27.0000 −0.952809
$$804$$ 0 0
$$805$$ 18.0000 0.634417
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −50.0000 −1.75791 −0.878953 0.476908i $$-0.841757\pi$$
−0.878953 + 0.476908i $$0.841757\pi$$
$$810$$ 0 0
$$811$$ 18.0000 0.632065 0.316033 0.948748i $$-0.397649\pi$$
0.316033 + 0.948748i $$0.397649\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −24.0000 −0.840683
$$816$$ 0 0
$$817$$ 36.0000 1.25948
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 38.0000 1.32621 0.663105 0.748527i $$-0.269238\pi$$
0.663105 + 0.748527i $$0.269238\pi$$
$$822$$ 0 0
$$823$$ −27.0000 −0.941161 −0.470580 0.882357i $$-0.655955\pi$$
−0.470580 + 0.882357i $$0.655955\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −48.0000 −1.66912 −0.834562 0.550914i $$-0.814279\pi$$
−0.834562 + 0.550914i $$0.814279\pi$$
$$828$$ 0 0
$$829$$ −18.0000 −0.625166 −0.312583 0.949890i $$-0.601194\pi$$
−0.312583 + 0.949890i $$0.601194\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −8.00000 −0.277184
$$834$$ 0 0
$$835$$ 18.0000 0.622916
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −36.0000 −1.24286 −0.621429 0.783470i $$-0.713448\pi$$
−0.621429 + 0.783470i $$0.713448\pi$$
$$840$$ 0 0
$$841$$ −25.0000 −0.862069
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 13.0000 0.447214
$$846$$ 0 0
$$847$$ −6.00000 −0.206162
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −12.0000 −0.411355
$$852$$ 0 0
$$853$$ 26.0000 0.890223 0.445112 0.895475i $$-0.353164\pi$$
0.445112 + 0.895475i $$0.353164\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 52.0000 1.77629 0.888143 0.459567i $$-0.151995\pi$$
0.888143 + 0.459567i $$0.151995\pi$$
$$858$$ 0 0
$$859$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −12.0000 −0.408485 −0.204242 0.978920i $$-0.565473\pi$$
−0.204242 + 0.978920i $$0.565473\pi$$
$$864$$ 0 0
$$865$$ −11.0000 −0.374011
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 27.0000 0.912767
$$876$$ 0 0
$$877$$ −50.0000 −1.68838 −0.844190 0.536044i $$-0.819918\pi$$
−0.844190 + 0.536044i $$0.819918\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 32.0000 1.07811 0.539054 0.842271i $$-0.318782\pi$$
0.539054 + 0.842271i $$0.318782\pi$$
$$882$$ 0 0
$$883$$ 18.0000 0.605748 0.302874 0.953031i $$-0.402054\pi$$
0.302874 + 0.953031i $$0.402054\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$888$$ 0 0
$$889$$ −9.00000 −0.301850
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 36.0000 1.20469
$$894$$ 0 0
$$895$$ −15.0000 −0.501395
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −18.0000 −0.600334
$$900$$ 0 0
$$901$$ −52.0000 −1.73237
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −6.00000 −0.199227 −0.0996134 0.995026i $$-0.531761\pi$$
−0.0996134 + 0.995026i $$0.531761\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −30.0000 −0.993944 −0.496972 0.867766i $$-0.665555\pi$$
−0.496972 + 0.867766i $$0.665555\pi$$
$$912$$ 0 0
$$913$$ 9.00000 0.297857
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 27.0000 0.891619
$$918$$ 0 0
$$919$$ −39.0000 −1.28649 −0.643246 0.765660i $$-0.722413\pi$$
−0.643246 + 0.765660i $$0.722413\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ −8.00000 −0.263038
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 20.0000 0.656179 0.328089 0.944647i $$-0.393595\pi$$
0.328089 + 0.944647i $$0.393595\pi$$
$$930$$ 0 0
$$931$$ −12.0000 −0.393284
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −12.0000 −0.392442
$$936$$ 0 0
$$937$$ −29.0000 −0.947389 −0.473694 0.880689i $$-0.657080\pi$$
−0.473694 + 0.880689i $$0.657080\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 19.0000 0.619382 0.309691 0.950837i $$-0.399774\pi$$
0.309691 + 0.950837i $$0.399774\pi$$
$$942$$ 0 0
$$943$$ −60.0000 −1.95387
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −45.0000 −1.46230 −0.731152 0.682215i $$-0.761017\pi$$
−0.731152 + 0.682215i $$0.761017\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −4.00000 −0.129573 −0.0647864 0.997899i $$-0.520637\pi$$
−0.0647864 + 0.997899i $$0.520637\pi$$
$$954$$ 0 0
$$955$$ −24.0000 −0.776622
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 6.00000 0.193750
$$960$$ 0 0
$$961$$ 50.0000 1.61290
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ −13.0000 −0.418485
$$966$$ 0 0
$$967$$ 51.0000 1.64005 0.820025 0.572328i $$-0.193960\pi$$
0.820025 + 0.572328i $$0.193960\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 21.0000 0.673922 0.336961 0.941519i $$-0.390601\pi$$
0.336961 + 0.941519i $$0.390601\pi$$
$$972$$ 0 0
$$973$$ 36.0000 1.15411
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 10.0000 0.319928 0.159964 0.987123i $$-0.448862\pi$$
0.159964 + 0.987123i $$0.448862\pi$$
$$978$$ 0 0
$$979$$ 42.0000 1.34233
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 42.0000 1.33959 0.669796 0.742545i $$-0.266382\pi$$
0.669796 + 0.742545i $$0.266382\pi$$
$$984$$ 0 0
$$985$$ −5.00000 −0.159313
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 36.0000 1.14473
$$990$$ 0 0
$$991$$ 51.0000 1.62007 0.810034 0.586383i $$-0.199448\pi$$
0.810034 + 0.586383i $$0.199448\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 3.00000 0.0951064
$$996$$ 0 0
$$997$$ −8.00000 −0.253363 −0.126681 0.991943i $$-0.540433\pi$$
−0.126681 + 0.991943i $$0.540433\pi$$
$$998$$ 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 1728.2.a.k.1.1 1
3.2 odd 2 1728.2.a.t.1.1 1
4.3 odd 2 1728.2.a.j.1.1 1
8.3 odd 2 864.2.a.g.1.1 yes 1
8.5 even 2 864.2.a.h.1.1 yes 1
12.11 even 2 1728.2.a.q.1.1 1
24.5 odd 2 864.2.a.f.1.1 yes 1
24.11 even 2 864.2.a.e.1.1 1
72.5 odd 6 2592.2.i.m.865.1 2
72.11 even 6 2592.2.i.p.1729.1 2
72.13 even 6 2592.2.i.i.865.1 2
72.29 odd 6 2592.2.i.m.1729.1 2
72.43 odd 6 2592.2.i.l.1729.1 2
72.59 even 6 2592.2.i.p.865.1 2
72.61 even 6 2592.2.i.i.1729.1 2
72.67 odd 6 2592.2.i.l.865.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
864.2.a.e.1.1 1 24.11 even 2
864.2.a.f.1.1 yes 1 24.5 odd 2
864.2.a.g.1.1 yes 1 8.3 odd 2
864.2.a.h.1.1 yes 1 8.5 even 2
1728.2.a.j.1.1 1 4.3 odd 2
1728.2.a.k.1.1 1 1.1 even 1 trivial
1728.2.a.q.1.1 1 12.11 even 2
1728.2.a.t.1.1 1 3.2 odd 2
2592.2.i.i.865.1 2 72.13 even 6
2592.2.i.i.1729.1 2 72.61 even 6
2592.2.i.l.865.1 2 72.67 odd 6
2592.2.i.l.1729.1 2 72.43 odd 6
2592.2.i.m.865.1 2 72.5 odd 6
2592.2.i.m.1729.1 2 72.29 odd 6
2592.2.i.p.865.1 2 72.59 even 6
2592.2.i.p.1729.1 2 72.11 even 6