# Properties

 Label 1872.2.a.w.1.2 Level $1872$ Weight $2$ Character 1872.1 Self dual yes Analytic conductor $14.948$ Analytic rank $1$ Dimension $2$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1872 = 2^{4} \cdot 3^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1872.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$14.9479952584$$ Analytic rank: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{8})^+$$ Defining polynomial: $$x^{2} - 2$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2$$ Twist minimal: no (minimal twist has level 39) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.2 Root $$1.41421$$ of defining polynomial Character $$\chi$$ $$=$$ 1872.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+2.82843 q^{5} -2.82843 q^{7} +O(q^{10})$$ $$q+2.82843 q^{5} -2.82843 q^{7} -2.00000 q^{11} -1.00000 q^{13} -7.65685 q^{17} +2.82843 q^{19} -4.00000 q^{23} +3.00000 q^{25} -2.00000 q^{29} +1.17157 q^{31} -8.00000 q^{35} -7.65685 q^{37} -5.17157 q^{41} +1.65685 q^{43} -11.6569 q^{47} +1.00000 q^{49} +2.00000 q^{53} -5.65685 q^{55} +7.65685 q^{59} +13.3137 q^{61} -2.82843 q^{65} -6.82843 q^{67} +2.00000 q^{71} +0.343146 q^{73} +5.65685 q^{77} +11.3137 q^{79} +3.65685 q^{83} -21.6569 q^{85} -14.8284 q^{89} +2.82843 q^{91} +8.00000 q^{95} +3.65685 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + O(q^{10})$$ $$2q - 4q^{11} - 2q^{13} - 4q^{17} - 8q^{23} + 6q^{25} - 4q^{29} + 8q^{31} - 16q^{35} - 4q^{37} - 16q^{41} - 8q^{43} - 12q^{47} + 2q^{49} + 4q^{53} + 4q^{59} + 4q^{61} - 8q^{67} + 4q^{71} + 12q^{73} - 4q^{83} - 32q^{85} - 24q^{89} + 16q^{95} - 4q^{97} + O(q^{100})$$

## 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
$$5$$ 2.82843 1.26491 0.632456 0.774597i $$-0.282047\pi$$
0.632456 + 0.774597i $$0.282047\pi$$
$$6$$ 0 0
$$7$$ −2.82843 −1.06904 −0.534522 0.845154i $$-0.679509\pi$$
−0.534522 + 0.845154i $$0.679509\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −2.00000 −0.603023 −0.301511 0.953463i $$-0.597491\pi$$
−0.301511 + 0.953463i $$0.597491\pi$$
$$12$$ 0 0
$$13$$ −1.00000 −0.277350
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −7.65685 −1.85706 −0.928530 0.371257i $$-0.878927\pi$$
−0.928530 + 0.371257i $$0.878927\pi$$
$$18$$ 0 0
$$19$$ 2.82843 0.648886 0.324443 0.945905i $$-0.394823\pi$$
0.324443 + 0.945905i $$0.394823\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −4.00000 −0.834058 −0.417029 0.908893i $$-0.636929\pi$$
−0.417029 + 0.908893i $$0.636929\pi$$
$$24$$ 0 0
$$25$$ 3.00000 0.600000
$$26$$ 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
$$31$$ 1.17157 0.210421 0.105210 0.994450i $$-0.466448\pi$$
0.105210 + 0.994450i $$0.466448\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −8.00000 −1.35225
$$36$$ 0 0
$$37$$ −7.65685 −1.25878 −0.629390 0.777090i $$-0.716695\pi$$
−0.629390 + 0.777090i $$0.716695\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −5.17157 −0.807664 −0.403832 0.914833i $$-0.632322\pi$$
−0.403832 + 0.914833i $$0.632322\pi$$
$$42$$ 0 0
$$43$$ 1.65685 0.252668 0.126334 0.991988i $$-0.459679\pi$$
0.126334 + 0.991988i $$0.459679\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −11.6569 −1.70033 −0.850163 0.526519i $$-0.823497\pi$$
−0.850163 + 0.526519i $$0.823497\pi$$
$$48$$ 0 0
$$49$$ 1.00000 0.142857
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 2.00000 0.274721 0.137361 0.990521i $$-0.456138\pi$$
0.137361 + 0.990521i $$0.456138\pi$$
$$54$$ 0 0
$$55$$ −5.65685 −0.762770
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 7.65685 0.996838 0.498419 0.866936i $$-0.333914\pi$$
0.498419 + 0.866936i $$0.333914\pi$$
$$60$$ 0 0
$$61$$ 13.3137 1.70465 0.852323 0.523016i $$-0.175193\pi$$
0.852323 + 0.523016i $$0.175193\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −2.82843 −0.350823
$$66$$ 0 0
$$67$$ −6.82843 −0.834225 −0.417113 0.908855i $$-0.636958\pi$$
−0.417113 + 0.908855i $$0.636958\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 2.00000 0.237356 0.118678 0.992933i $$-0.462134\pi$$
0.118678 + 0.992933i $$0.462134\pi$$
$$72$$ 0 0
$$73$$ 0.343146 0.0401622 0.0200811 0.999798i $$-0.493608\pi$$
0.0200811 + 0.999798i $$0.493608\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 5.65685 0.644658
$$78$$ 0 0
$$79$$ 11.3137 1.27289 0.636446 0.771321i $$-0.280404\pi$$
0.636446 + 0.771321i $$0.280404\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 3.65685 0.401392 0.200696 0.979654i $$-0.435680\pi$$
0.200696 + 0.979654i $$0.435680\pi$$
$$84$$ 0 0
$$85$$ −21.6569 −2.34902
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −14.8284 −1.57181 −0.785905 0.618347i $$-0.787803\pi$$
−0.785905 + 0.618347i $$0.787803\pi$$
$$90$$ 0 0
$$91$$ 2.82843 0.296500
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 8.00000 0.820783
$$96$$ 0 0
$$97$$ 3.65685 0.371297 0.185649 0.982616i $$-0.440561\pi$$
0.185649 + 0.982616i $$0.440561\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −7.65685 −0.761885 −0.380943 0.924599i $$-0.624401\pi$$
−0.380943 + 0.924599i $$0.624401\pi$$
$$102$$ 0 0
$$103$$ −2.34315 −0.230877 −0.115439 0.993315i $$-0.536827\pi$$
−0.115439 + 0.993315i $$0.536827\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −11.3137 −1.09374 −0.546869 0.837218i $$-0.684180\pi$$
−0.546869 + 0.837218i $$0.684180\pi$$
$$108$$ 0 0
$$109$$ 5.31371 0.508961 0.254480 0.967078i $$-0.418096\pi$$
0.254480 + 0.967078i $$0.418096\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 5.31371 0.499872 0.249936 0.968262i $$-0.419590\pi$$
0.249936 + 0.968262i $$0.419590\pi$$
$$114$$ 0 0
$$115$$ −11.3137 −1.05501
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 21.6569 1.98528
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −5.65685 −0.505964
$$126$$ 0 0
$$127$$ −5.65685 −0.501965 −0.250982 0.967992i $$-0.580754\pi$$
−0.250982 + 0.967992i $$0.580754\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −8.00000 −0.698963 −0.349482 0.936943i $$-0.613642\pi$$
−0.349482 + 0.936943i $$0.613642\pi$$
$$132$$ 0 0
$$133$$ −8.00000 −0.693688
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 10.8284 0.925135 0.462567 0.886584i $$-0.346928\pi$$
0.462567 + 0.886584i $$0.346928\pi$$
$$138$$ 0 0
$$139$$ 7.31371 0.620341 0.310170 0.950681i $$-0.399614\pi$$
0.310170 + 0.950681i $$0.399614\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 2.00000 0.167248
$$144$$ 0 0
$$145$$ −5.65685 −0.469776
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 9.17157 0.751365 0.375682 0.926749i $$-0.377408\pi$$
0.375682 + 0.926749i $$0.377408\pi$$
$$150$$ 0 0
$$151$$ 3.51472 0.286024 0.143012 0.989721i $$-0.454321\pi$$
0.143012 + 0.989721i $$0.454321\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 3.31371 0.266163
$$156$$ 0 0
$$157$$ −10.0000 −0.798087 −0.399043 0.916932i $$-0.630658\pi$$
−0.399043 + 0.916932i $$0.630658\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 11.3137 0.891645
$$162$$ 0 0
$$163$$ −18.8284 −1.47476 −0.737378 0.675480i $$-0.763936\pi$$
−0.737378 + 0.675480i $$0.763936\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −3.65685 −0.282976 −0.141488 0.989940i $$-0.545189\pi$$
−0.141488 + 0.989940i $$0.545189\pi$$
$$168$$ 0 0
$$169$$ 1.00000 0.0769231
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 11.6569 0.886254 0.443127 0.896459i $$-0.353869\pi$$
0.443127 + 0.896459i $$0.353869\pi$$
$$174$$ 0 0
$$175$$ −8.48528 −0.641427
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −23.3137 −1.74255 −0.871274 0.490797i $$-0.836706\pi$$
−0.871274 + 0.490797i $$0.836706\pi$$
$$180$$ 0 0
$$181$$ 14.0000 1.04061 0.520306 0.853980i $$-0.325818\pi$$
0.520306 + 0.853980i $$0.325818\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −21.6569 −1.59224
$$186$$ 0 0
$$187$$ 15.3137 1.11985
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 3.31371 0.239772 0.119886 0.992788i $$-0.461747\pi$$
0.119886 + 0.992788i $$0.461747\pi$$
$$192$$ 0 0
$$193$$ 5.31371 0.382489 0.191245 0.981542i $$-0.438748\pi$$
0.191245 + 0.981542i $$0.438748\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −0.485281 −0.0345749 −0.0172874 0.999851i $$-0.505503\pi$$
−0.0172874 + 0.999851i $$0.505503\pi$$
$$198$$ 0 0
$$199$$ −21.6569 −1.53521 −0.767607 0.640921i $$-0.778553\pi$$
−0.767607 + 0.640921i $$0.778553\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 5.65685 0.397033
$$204$$ 0 0
$$205$$ −14.6274 −1.02162
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −5.65685 −0.391293
$$210$$ 0 0
$$211$$ 12.0000 0.826114 0.413057 0.910705i $$-0.364461\pi$$
0.413057 + 0.910705i $$0.364461\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 4.68629 0.319602
$$216$$ 0 0
$$217$$ −3.31371 −0.224949
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 7.65685 0.515056
$$222$$ 0 0
$$223$$ 12.4853 0.836076 0.418038 0.908429i $$-0.362718\pi$$
0.418038 + 0.908429i $$0.362718\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −17.3137 −1.14915 −0.574576 0.818452i $$-0.694833\pi$$
−0.574576 + 0.818452i $$0.694833\pi$$
$$228$$ 0 0
$$229$$ −1.31371 −0.0868123 −0.0434062 0.999058i $$-0.513821\pi$$
−0.0434062 + 0.999058i $$0.513821\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −6.97056 −0.456657 −0.228328 0.973584i $$-0.573326\pi$$
−0.228328 + 0.973584i $$0.573326\pi$$
$$234$$ 0 0
$$235$$ −32.9706 −2.15076
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 2.00000 0.129369 0.0646846 0.997906i $$-0.479396\pi$$
0.0646846 + 0.997906i $$0.479396\pi$$
$$240$$ 0 0
$$241$$ 0.343146 0.0221040 0.0110520 0.999939i $$-0.496482\pi$$
0.0110520 + 0.999939i $$0.496482\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 2.82843 0.180702
$$246$$ 0 0
$$247$$ −2.82843 −0.179969
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 8.00000 0.502956
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 4.34315 0.270918 0.135459 0.990783i $$-0.456749\pi$$
0.135459 + 0.990783i $$0.456749\pi$$
$$258$$ 0 0
$$259$$ 21.6569 1.34569
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 12.0000 0.739952 0.369976 0.929041i $$-0.379366\pi$$
0.369976 + 0.929041i $$0.379366\pi$$
$$264$$ 0 0
$$265$$ 5.65685 0.347498
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −18.0000 −1.09748 −0.548740 0.835993i $$-0.684892\pi$$
−0.548740 + 0.835993i $$0.684892\pi$$
$$270$$ 0 0
$$271$$ 27.7990 1.68867 0.844334 0.535817i $$-0.179996\pi$$
0.844334 + 0.535817i $$0.179996\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −6.00000 −0.361814
$$276$$ 0 0
$$277$$ −2.00000 −0.120168 −0.0600842 0.998193i $$-0.519137\pi$$
−0.0600842 + 0.998193i $$0.519137\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −21.1716 −1.26299 −0.631495 0.775380i $$-0.717558\pi$$
−0.631495 + 0.775380i $$0.717558\pi$$
$$282$$ 0 0
$$283$$ −28.9706 −1.72212 −0.861061 0.508502i $$-0.830199\pi$$
−0.861061 + 0.508502i $$0.830199\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 14.6274 0.863429
$$288$$ 0 0
$$289$$ 41.6274 2.44867
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −2.14214 −0.125145 −0.0625724 0.998040i $$-0.519930\pi$$
−0.0625724 + 0.998040i $$0.519930\pi$$
$$294$$ 0 0
$$295$$ 21.6569 1.26091
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 4.00000 0.231326
$$300$$ 0 0
$$301$$ −4.68629 −0.270113
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 37.6569 2.15623
$$306$$ 0 0
$$307$$ 22.8284 1.30289 0.651444 0.758697i $$-0.274164\pi$$
0.651444 + 0.758697i $$0.274164\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −10.6274 −0.602626 −0.301313 0.953525i $$-0.597425\pi$$
−0.301313 + 0.953525i $$0.597425\pi$$
$$312$$ 0 0
$$313$$ 6.00000 0.339140 0.169570 0.985518i $$-0.445762\pi$$
0.169570 + 0.985518i $$0.445762\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −8.48528 −0.476581 −0.238290 0.971194i $$-0.576587\pi$$
−0.238290 + 0.971194i $$0.576587\pi$$
$$318$$ 0 0
$$319$$ 4.00000 0.223957
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −21.6569 −1.20502
$$324$$ 0 0
$$325$$ −3.00000 −0.166410
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 32.9706 1.81773
$$330$$ 0 0
$$331$$ −26.1421 −1.43690 −0.718451 0.695578i $$-0.755148\pi$$
−0.718451 + 0.695578i $$0.755148\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −19.3137 −1.05522
$$336$$ 0 0
$$337$$ 9.31371 0.507350 0.253675 0.967290i $$-0.418361\pi$$
0.253675 + 0.967290i $$0.418361\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −2.34315 −0.126888
$$342$$ 0 0
$$343$$ 16.9706 0.916324
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −8.68629 −0.466305 −0.233152 0.972440i $$-0.574904\pi$$
−0.233152 + 0.972440i $$0.574904\pi$$
$$348$$ 0 0
$$349$$ 3.65685 0.195747 0.0978735 0.995199i $$-0.468796\pi$$
0.0978735 + 0.995199i $$0.468796\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 33.4558 1.78067 0.890337 0.455301i $$-0.150468\pi$$
0.890337 + 0.455301i $$0.150468\pi$$
$$354$$ 0 0
$$355$$ 5.65685 0.300235
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 34.9706 1.84568 0.922838 0.385189i $$-0.125864\pi$$
0.922838 + 0.385189i $$0.125864\pi$$
$$360$$ 0 0
$$361$$ −11.0000 −0.578947
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0.970563 0.0508016
$$366$$ 0 0
$$367$$ 24.0000 1.25279 0.626395 0.779506i $$-0.284530\pi$$
0.626395 + 0.779506i $$0.284530\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −5.65685 −0.293689
$$372$$ 0 0
$$373$$ 10.0000 0.517780 0.258890 0.965907i $$-0.416643\pi$$
0.258890 + 0.965907i $$0.416643\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 2.00000 0.103005
$$378$$ 0 0
$$379$$ −0.485281 −0.0249272 −0.0124636 0.999922i $$-0.503967\pi$$
−0.0124636 + 0.999922i $$0.503967\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 30.9706 1.58252 0.791261 0.611479i $$-0.209425\pi$$
0.791261 + 0.611479i $$0.209425\pi$$
$$384$$ 0 0
$$385$$ 16.0000 0.815436
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 26.9706 1.36746 0.683731 0.729734i $$-0.260356\pi$$
0.683731 + 0.729734i $$0.260356\pi$$
$$390$$ 0 0
$$391$$ 30.6274 1.54890
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 32.0000 1.61009
$$396$$ 0 0
$$397$$ 30.9706 1.55437 0.777184 0.629273i $$-0.216647\pi$$
0.777184 + 0.629273i $$0.216647\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −26.1421 −1.30548 −0.652738 0.757584i $$-0.726380\pi$$
−0.652738 + 0.757584i $$0.726380\pi$$
$$402$$ 0 0
$$403$$ −1.17157 −0.0583602
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 15.3137 0.759072
$$408$$ 0 0
$$409$$ −34.9706 −1.72918 −0.864592 0.502475i $$-0.832423\pi$$
−0.864592 + 0.502475i $$0.832423\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −21.6569 −1.06566
$$414$$ 0 0
$$415$$ 10.3431 0.507725
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 14.6274 0.714596 0.357298 0.933990i $$-0.383698\pi$$
0.357298 + 0.933990i $$0.383698\pi$$
$$420$$ 0 0
$$421$$ 37.3137 1.81856 0.909279 0.416186i $$-0.136634\pi$$
0.909279 + 0.416186i $$0.136634\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −22.9706 −1.11424
$$426$$ 0 0
$$427$$ −37.6569 −1.82234
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 8.34315 0.401875 0.200938 0.979604i $$-0.435601\pi$$
0.200938 + 0.979604i $$0.435601\pi$$
$$432$$ 0 0
$$433$$ −21.3137 −1.02427 −0.512136 0.858905i $$-0.671146\pi$$
−0.512136 + 0.858905i $$0.671146\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −11.3137 −0.541208
$$438$$ 0 0
$$439$$ −16.9706 −0.809961 −0.404980 0.914325i $$-0.632722\pi$$
−0.404980 + 0.914325i $$0.632722\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −25.9411 −1.23250 −0.616250 0.787551i $$-0.711349\pi$$
−0.616250 + 0.787551i $$0.711349\pi$$
$$444$$ 0 0
$$445$$ −41.9411 −1.98820
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 31.7990 1.50069 0.750344 0.661048i $$-0.229888\pi$$
0.750344 + 0.661048i $$0.229888\pi$$
$$450$$ 0 0
$$451$$ 10.3431 0.487040
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 8.00000 0.375046
$$456$$ 0 0
$$457$$ −7.65685 −0.358173 −0.179086 0.983833i $$-0.557314\pi$$
−0.179086 + 0.983833i $$0.557314\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −5.17157 −0.240864 −0.120432 0.992722i $$-0.538428\pi$$
−0.120432 + 0.992722i $$0.538428\pi$$
$$462$$ 0 0
$$463$$ 24.4853 1.13793 0.568964 0.822363i $$-0.307344\pi$$
0.568964 + 0.822363i $$0.307344\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −8.00000 −0.370196 −0.185098 0.982720i $$-0.559260\pi$$
−0.185098 + 0.982720i $$0.559260\pi$$
$$468$$ 0 0
$$469$$ 19.3137 0.891824
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −3.31371 −0.152364
$$474$$ 0 0
$$475$$ 8.48528 0.389331
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 25.3137 1.15661 0.578306 0.815820i $$-0.303714\pi$$
0.578306 + 0.815820i $$0.303714\pi$$
$$480$$ 0 0
$$481$$ 7.65685 0.349123
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 10.3431 0.469658
$$486$$ 0 0
$$487$$ 7.79899 0.353406 0.176703 0.984264i $$-0.443457\pi$$
0.176703 + 0.984264i $$0.443457\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 30.6274 1.38220 0.691098 0.722761i $$-0.257127\pi$$
0.691098 + 0.722761i $$0.257127\pi$$
$$492$$ 0 0
$$493$$ 15.3137 0.689695
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −5.65685 −0.253745
$$498$$ 0 0
$$499$$ −26.1421 −1.17028 −0.585141 0.810931i $$-0.698961\pi$$
−0.585141 + 0.810931i $$0.698961\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −7.31371 −0.326102 −0.163051 0.986618i $$-0.552134\pi$$
−0.163051 + 0.986618i $$0.552134\pi$$
$$504$$ 0 0
$$505$$ −21.6569 −0.963717
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −11.7990 −0.522981 −0.261491 0.965206i $$-0.584214\pi$$
−0.261491 + 0.965206i $$0.584214\pi$$
$$510$$ 0 0
$$511$$ −0.970563 −0.0429352
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −6.62742 −0.292039
$$516$$ 0 0
$$517$$ 23.3137 1.02534
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −25.3137 −1.10901 −0.554507 0.832179i $$-0.687093\pi$$
−0.554507 + 0.832179i $$0.687093\pi$$
$$522$$ 0 0
$$523$$ 15.3137 0.669622 0.334811 0.942285i $$-0.391328\pi$$
0.334811 + 0.942285i $$0.391328\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −8.97056 −0.390764
$$528$$ 0 0
$$529$$ −7.00000 −0.304348
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 5.17157 0.224006
$$534$$ 0 0
$$535$$ −32.0000 −1.38348
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −2.00000 −0.0861461
$$540$$ 0 0
$$541$$ 10.0000 0.429934 0.214967 0.976621i $$-0.431036\pi$$
0.214967 + 0.976621i $$0.431036\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 15.0294 0.643790
$$546$$ 0 0
$$547$$ −23.3137 −0.996822 −0.498411 0.866941i $$-0.666083\pi$$
−0.498411 + 0.866941i $$0.666083\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −5.65685 −0.240990
$$552$$ 0 0
$$553$$ −32.0000 −1.36078
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 7.79899 0.330454 0.165227 0.986256i $$-0.447164\pi$$
0.165227 + 0.986256i $$0.447164\pi$$
$$558$$ 0 0
$$559$$ −1.65685 −0.0700775
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 4.00000 0.168580 0.0842900 0.996441i $$-0.473138\pi$$
0.0842900 + 0.996441i $$0.473138\pi$$
$$564$$ 0 0
$$565$$ 15.0294 0.632293
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 42.9706 1.80142 0.900710 0.434421i $$-0.143047\pi$$
0.900710 + 0.434421i $$0.143047\pi$$
$$570$$ 0 0
$$571$$ 12.9706 0.542801 0.271401 0.962466i $$-0.412513\pi$$
0.271401 + 0.962466i $$0.412513\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −12.0000 −0.500435
$$576$$ 0 0
$$577$$ −31.9411 −1.32973 −0.664863 0.746965i $$-0.731510\pi$$
−0.664863 + 0.746965i $$0.731510\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −10.3431 −0.429106
$$582$$ 0 0
$$583$$ −4.00000 −0.165663
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −10.9706 −0.452804 −0.226402 0.974034i $$-0.572696\pi$$
−0.226402 + 0.974034i $$0.572696\pi$$
$$588$$ 0 0
$$589$$ 3.31371 0.136539
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 20.4853 0.841230 0.420615 0.907239i $$-0.361814\pi$$
0.420615 + 0.907239i $$0.361814\pi$$
$$594$$ 0 0
$$595$$ 61.2548 2.51120
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −23.3137 −0.952572 −0.476286 0.879290i $$-0.658017\pi$$
−0.476286 + 0.879290i $$0.658017\pi$$
$$600$$ 0 0
$$601$$ −0.627417 −0.0255929 −0.0127964 0.999918i $$-0.504073\pi$$
−0.0127964 + 0.999918i $$0.504073\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −19.7990 −0.804943
$$606$$ 0 0
$$607$$ −41.9411 −1.70234 −0.851169 0.524892i $$-0.824106\pi$$
−0.851169 + 0.524892i $$0.824106\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 11.6569 0.471586
$$612$$ 0 0
$$613$$ −47.6569 −1.92484 −0.962421 0.271561i $$-0.912460\pi$$
−0.962421 + 0.271561i $$0.912460\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 34.8284 1.40214 0.701070 0.713093i $$-0.252706\pi$$
0.701070 + 0.713093i $$0.252706\pi$$
$$618$$ 0 0
$$619$$ −23.7990 −0.956562 −0.478281 0.878207i $$-0.658740\pi$$
−0.478281 + 0.878207i $$0.658740\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 41.9411 1.68034
$$624$$ 0 0
$$625$$ −31.0000 −1.24000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 58.6274 2.33763
$$630$$ 0 0
$$631$$ −43.1127 −1.71629 −0.858145 0.513408i $$-0.828383\pi$$
−0.858145 + 0.513408i $$0.828383\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −16.0000 −0.634941
$$636$$ 0 0
$$637$$ −1.00000 −0.0396214
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −30.2843 −1.19616 −0.598078 0.801438i $$-0.704069\pi$$
−0.598078 + 0.801438i $$0.704069\pi$$
$$642$$ 0 0
$$643$$ −22.8284 −0.900265 −0.450133 0.892962i $$-0.648623\pi$$
−0.450133 + 0.892962i $$0.648623\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 11.3137 0.444788 0.222394 0.974957i $$-0.428613\pi$$
0.222394 + 0.974957i $$0.428613\pi$$
$$648$$ 0 0
$$649$$ −15.3137 −0.601116
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 25.3137 0.990602 0.495301 0.868721i $$-0.335058\pi$$
0.495301 + 0.868721i $$0.335058\pi$$
$$654$$ 0 0
$$655$$ −22.6274 −0.884126
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −47.3137 −1.84308 −0.921540 0.388283i $$-0.873068\pi$$
−0.921540 + 0.388283i $$0.873068\pi$$
$$660$$ 0 0
$$661$$ −34.9706 −1.36020 −0.680099 0.733121i $$-0.738063\pi$$
−0.680099 + 0.733121i $$0.738063\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −22.6274 −0.877454
$$666$$ 0 0
$$667$$ 8.00000 0.309761
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −26.6274 −1.02794
$$672$$ 0 0
$$673$$ 16.6274 0.640940 0.320470 0.947259i $$-0.396159\pi$$
0.320470 + 0.947259i $$0.396159\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −26.6863 −1.02564 −0.512819 0.858497i $$-0.671399\pi$$
−0.512819 + 0.858497i $$0.671399\pi$$
$$678$$ 0 0
$$679$$ −10.3431 −0.396934
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 47.9411 1.83442 0.917208 0.398408i $$-0.130437\pi$$
0.917208 + 0.398408i $$0.130437\pi$$
$$684$$ 0 0
$$685$$ 30.6274 1.17021
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −2.00000 −0.0761939
$$690$$ 0 0
$$691$$ 5.85786 0.222844 0.111422 0.993773i $$-0.464460\pi$$
0.111422 + 0.993773i $$0.464460\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 20.6863 0.784676
$$696$$ 0 0
$$697$$ 39.5980 1.49988
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −5.02944 −0.189959 −0.0949796 0.995479i $$-0.530279\pi$$
−0.0949796 + 0.995479i $$0.530279\pi$$
$$702$$ 0 0
$$703$$ −21.6569 −0.816804
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 21.6569 0.814490
$$708$$ 0 0
$$709$$ −4.62742 −0.173786 −0.0868931 0.996218i $$-0.527694\pi$$
−0.0868931 + 0.996218i $$0.527694\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −4.68629 −0.175503
$$714$$ 0 0
$$715$$ 5.65685 0.211554
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −29.9411 −1.11662 −0.558308 0.829634i $$-0.688549\pi$$
−0.558308 + 0.829634i $$0.688549\pi$$
$$720$$ 0 0
$$721$$ 6.62742 0.246818
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −6.00000 −0.222834
$$726$$ 0 0
$$727$$ 10.3431 0.383606 0.191803 0.981433i $$-0.438567\pi$$
0.191803 + 0.981433i $$0.438567\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −12.6863 −0.469219
$$732$$ 0 0
$$733$$ −36.6274 −1.35286 −0.676432 0.736505i $$-0.736475\pi$$
−0.676432 + 0.736505i $$0.736475\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 13.6569 0.503057
$$738$$ 0 0
$$739$$ 18.1421 0.667369 0.333685 0.942685i $$-0.391708\pi$$
0.333685 + 0.942685i $$0.391708\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 2.00000 0.0733729 0.0366864 0.999327i $$-0.488320\pi$$
0.0366864 + 0.999327i $$0.488320\pi$$
$$744$$ 0 0
$$745$$ 25.9411 0.950409
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 32.0000 1.16925
$$750$$ 0 0
$$751$$ 0.970563 0.0354163 0.0177082 0.999843i $$-0.494363\pi$$
0.0177082 + 0.999843i $$0.494363\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 9.94113 0.361795
$$756$$ 0 0
$$757$$ 51.9411 1.88783 0.943916 0.330185i $$-0.107111\pi$$
0.943916 + 0.330185i $$0.107111\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −32.4853 −1.17759 −0.588795 0.808282i $$-0.700398\pi$$
−0.588795 + 0.808282i $$0.700398\pi$$
$$762$$ 0 0
$$763$$ −15.0294 −0.544102
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −7.65685 −0.276473
$$768$$ 0 0
$$769$$ 42.0000 1.51456 0.757279 0.653091i $$-0.226528\pi$$
0.757279 + 0.653091i $$0.226528\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −34.1421 −1.22801 −0.614004 0.789303i $$-0.710442\pi$$
−0.614004 + 0.789303i $$0.710442\pi$$
$$774$$ 0 0
$$775$$ 3.51472 0.126252
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −14.6274 −0.524082
$$780$$ 0 0
$$781$$ −4.00000 −0.143131
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −28.2843 −1.00951
$$786$$ 0 0
$$787$$ 40.7696 1.45328 0.726639 0.687020i $$-0.241081\pi$$
0.726639 + 0.687020i $$0.241081\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −15.0294 −0.534385
$$792$$ 0 0
$$793$$ −13.3137 −0.472784
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −24.3431 −0.862278 −0.431139 0.902285i $$-0.641888\pi$$
−0.431139 + 0.902285i $$0.641888\pi$$
$$798$$ 0 0
$$799$$ 89.2548 3.15761
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −0.686292 −0.0242187
$$804$$ 0 0
$$805$$ 32.0000 1.12785
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −18.6863 −0.656975 −0.328488 0.944508i $$-0.606539\pi$$
−0.328488 + 0.944508i $$0.606539\pi$$
$$810$$ 0 0
$$811$$ 30.1421 1.05843 0.529217 0.848487i $$-0.322486\pi$$
0.529217 + 0.848487i $$0.322486\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −53.2548 −1.86544
$$816$$ 0 0
$$817$$ 4.68629 0.163953
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 23.7990 0.830590 0.415295 0.909687i $$-0.363678\pi$$
0.415295 + 0.909687i $$0.363678\pi$$
$$822$$ 0 0
$$823$$ −15.0294 −0.523893 −0.261947 0.965082i $$-0.584364\pi$$
−0.261947 + 0.965082i $$0.584364\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −26.0000 −0.904109 −0.452054 0.891990i $$-0.649309\pi$$
−0.452054 + 0.891990i $$0.649309\pi$$
$$828$$ 0 0
$$829$$ −17.3137 −0.601330 −0.300665 0.953730i $$-0.597209\pi$$
−0.300665 + 0.953730i $$0.597209\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −7.65685 −0.265294
$$834$$ 0 0
$$835$$ −10.3431 −0.357939
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 43.2548 1.49332 0.746661 0.665204i $$-0.231656\pi$$
0.746661 + 0.665204i $$0.231656\pi$$
$$840$$ 0 0
$$841$$ −25.0000 −0.862069
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 2.82843 0.0973009
$$846$$ 0 0
$$847$$ 19.7990 0.680301
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 30.6274 1.04989
$$852$$ 0 0
$$853$$ 3.65685 0.125208 0.0626042 0.998038i $$-0.480059\pi$$
0.0626042 + 0.998038i $$0.480059\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 49.5980 1.69423 0.847117 0.531406i $$-0.178336\pi$$
0.847117 + 0.531406i $$0.178336\pi$$
$$858$$ 0 0
$$859$$ 0.686292 0.0234160 0.0117080 0.999931i $$-0.496273\pi$$
0.0117080 + 0.999931i $$0.496273\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −28.3431 −0.964812 −0.482406 0.875948i $$-0.660237\pi$$
−0.482406 + 0.875948i $$0.660237\pi$$
$$864$$ 0 0
$$865$$ 32.9706 1.12103
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −22.6274 −0.767583
$$870$$ 0 0
$$871$$ 6.82843 0.231372
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 16.0000 0.540899
$$876$$ 0 0
$$877$$ 42.2843 1.42784 0.713919 0.700228i $$-0.246918\pi$$
0.713919 + 0.700228i $$0.246918\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 25.5980 0.862418 0.431209 0.902252i $$-0.358087\pi$$
0.431209 + 0.902252i $$0.358087\pi$$
$$882$$ 0 0
$$883$$ −27.5980 −0.928746 −0.464373 0.885640i $$-0.653720\pi$$
−0.464373 + 0.885640i $$0.653720\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −8.00000 −0.268614 −0.134307 0.990940i $$-0.542881\pi$$
−0.134307 + 0.990940i $$0.542881\pi$$
$$888$$ 0 0
$$889$$ 16.0000 0.536623
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −32.9706 −1.10332
$$894$$ 0 0
$$895$$ −65.9411 −2.20417
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −2.34315 −0.0781483
$$900$$ 0 0
$$901$$ −15.3137 −0.510174
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 39.5980 1.31628
$$906$$ 0 0
$$907$$ 12.9706 0.430680 0.215340 0.976539i $$-0.430914\pi$$
0.215340 + 0.976539i $$0.430914\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −40.0000 −1.32526 −0.662630 0.748947i $$-0.730560\pi$$
−0.662630 + 0.748947i $$0.730560\pi$$
$$912$$ 0 0
$$913$$ −7.31371 −0.242048
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 22.6274 0.747223
$$918$$ 0 0
$$919$$ −3.31371 −0.109309 −0.0546546 0.998505i $$-0.517406\pi$$
−0.0546546 + 0.998505i $$0.517406\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ −2.00000 −0.0658308
$$924$$ 0 0
$$925$$ −22.9706 −0.755267
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −11.7990 −0.387112 −0.193556 0.981089i $$-0.562002\pi$$
−0.193556 + 0.981089i $$0.562002\pi$$
$$930$$ 0 0
$$931$$ 2.82843 0.0926980
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 43.3137 1.41651
$$936$$ 0 0
$$937$$ −21.3137 −0.696289 −0.348144 0.937441i $$-0.613188\pi$$
−0.348144 + 0.937441i $$0.613188\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −34.1421 −1.11300 −0.556501 0.830847i $$-0.687856\pi$$
−0.556501 + 0.830847i $$0.687856\pi$$
$$942$$ 0 0
$$943$$ 20.6863 0.673638
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −21.0294 −0.683365 −0.341682 0.939815i $$-0.610997\pi$$
−0.341682 + 0.939815i $$0.610997\pi$$
$$948$$ 0 0
$$949$$ −0.343146 −0.0111390
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −40.3431 −1.30684 −0.653421 0.756994i $$-0.726667\pi$$
−0.653421 + 0.756994i $$0.726667\pi$$
$$954$$ 0 0
$$955$$ 9.37258 0.303290
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ −30.6274 −0.989011
$$960$$ 0 0
$$961$$ −29.6274 −0.955723
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 15.0294 0.483815
$$966$$ 0 0
$$967$$ −18.1421 −0.583412 −0.291706 0.956508i $$-0.594223\pi$$
−0.291706 + 0.956508i $$0.594223\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −15.3137 −0.491440 −0.245720 0.969341i $$-0.579024\pi$$
−0.245720 + 0.969341i $$0.579024\pi$$
$$972$$ 0 0
$$973$$ −20.6863 −0.663172
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −42.1421 −1.34825 −0.674123 0.738619i $$-0.735478\pi$$
−0.674123 + 0.738619i $$0.735478\pi$$
$$978$$ 0 0
$$979$$ 29.6569 0.947837
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 25.3137 0.807382 0.403691 0.914895i $$-0.367727\pi$$
0.403691 + 0.914895i $$0.367727\pi$$
$$984$$ 0 0
$$985$$ −1.37258 −0.0437341
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −6.62742 −0.210740
$$990$$ 0 0
$$991$$ −4.68629 −0.148865 −0.0744325 0.997226i $$-0.523715\pi$$
−0.0744325 + 0.997226i $$0.523715\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ −61.2548 −1.94191
$$996$$ 0 0
$$997$$ −39.2548 −1.24321 −0.621607 0.783330i $$-0.713520\pi$$
−0.621607 + 0.783330i $$0.713520\pi$$
$$998$$ 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 1872.2.a.w.1.2 2
3.2 odd 2 624.2.a.k.1.1 2
4.3 odd 2 117.2.a.c.1.1 2
8.3 odd 2 7488.2.a.cl.1.1 2
8.5 even 2 7488.2.a.co.1.1 2
12.11 even 2 39.2.a.b.1.2 2
20.3 even 4 2925.2.c.u.2224.3 4
20.7 even 4 2925.2.c.u.2224.2 4
20.19 odd 2 2925.2.a.v.1.2 2
24.5 odd 2 2496.2.a.bi.1.2 2
24.11 even 2 2496.2.a.bf.1.2 2
28.27 even 2 5733.2.a.u.1.1 2
36.7 odd 6 1053.2.e.e.352.2 4
36.11 even 6 1053.2.e.m.352.1 4
36.23 even 6 1053.2.e.m.703.1 4
36.31 odd 6 1053.2.e.e.703.2 4
39.38 odd 2 8112.2.a.bm.1.2 2
52.31 even 4 1521.2.b.j.1351.3 4
52.47 even 4 1521.2.b.j.1351.2 4
52.51 odd 2 1521.2.a.f.1.2 2
60.23 odd 4 975.2.c.h.274.2 4
60.47 odd 4 975.2.c.h.274.3 4
60.59 even 2 975.2.a.l.1.1 2
84.83 odd 2 1911.2.a.h.1.2 2
132.131 odd 2 4719.2.a.p.1.1 2
156.11 odd 12 507.2.j.f.316.2 8
156.23 even 6 507.2.e.d.22.2 4
156.35 even 6 507.2.e.h.484.1 4
156.47 odd 4 507.2.b.e.337.3 4
156.59 odd 12 507.2.j.f.361.3 8
156.71 odd 12 507.2.j.f.361.2 8
156.83 odd 4 507.2.b.e.337.2 4
156.95 even 6 507.2.e.d.484.2 4
156.107 even 6 507.2.e.h.22.1 4
156.119 odd 12 507.2.j.f.316.3 8
156.155 even 2 507.2.a.h.1.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
39.2.a.b.1.2 2 12.11 even 2
117.2.a.c.1.1 2 4.3 odd 2
507.2.a.h.1.1 2 156.155 even 2
507.2.b.e.337.2 4 156.83 odd 4
507.2.b.e.337.3 4 156.47 odd 4
507.2.e.d.22.2 4 156.23 even 6
507.2.e.d.484.2 4 156.95 even 6
507.2.e.h.22.1 4 156.107 even 6
507.2.e.h.484.1 4 156.35 even 6
507.2.j.f.316.2 8 156.11 odd 12
507.2.j.f.316.3 8 156.119 odd 12
507.2.j.f.361.2 8 156.71 odd 12
507.2.j.f.361.3 8 156.59 odd 12
624.2.a.k.1.1 2 3.2 odd 2
975.2.a.l.1.1 2 60.59 even 2
975.2.c.h.274.2 4 60.23 odd 4
975.2.c.h.274.3 4 60.47 odd 4
1053.2.e.e.352.2 4 36.7 odd 6
1053.2.e.e.703.2 4 36.31 odd 6
1053.2.e.m.352.1 4 36.11 even 6
1053.2.e.m.703.1 4 36.23 even 6
1521.2.a.f.1.2 2 52.51 odd 2
1521.2.b.j.1351.2 4 52.47 even 4
1521.2.b.j.1351.3 4 52.31 even 4
1872.2.a.w.1.2 2 1.1 even 1 trivial
1911.2.a.h.1.2 2 84.83 odd 2
2496.2.a.bf.1.2 2 24.11 even 2
2496.2.a.bi.1.2 2 24.5 odd 2
2925.2.a.v.1.2 2 20.19 odd 2
2925.2.c.u.2224.2 4 20.7 even 4
2925.2.c.u.2224.3 4 20.3 even 4
4719.2.a.p.1.1 2 132.131 odd 2
5733.2.a.u.1.1 2 28.27 even 2
7488.2.a.cl.1.1 2 8.3 odd 2
7488.2.a.co.1.1 2 8.5 even 2
8112.2.a.bm.1.2 2 39.38 odd 2