# Properties

 Label 4704.2.a.bk.1.1 Level $4704$ Weight $2$ Character 4704.1 Self dual yes Analytic conductor $37.562$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$4704 = 2^{5} \cdot 3 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 4704.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$37.5616291108$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{8})^+$$ Defining polynomial: $$x^{2} - 2$$ Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Root $$-1.41421$$ of defining polynomial Character $$\chi$$ $$=$$ 4704.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{3} +1.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{3} +1.00000 q^{9} -5.65685 q^{11} -5.65685 q^{13} -5.65685 q^{17} +4.00000 q^{19} -5.65685 q^{23} -5.00000 q^{25} -1.00000 q^{27} -6.00000 q^{29} +8.00000 q^{31} +5.65685 q^{33} +2.00000 q^{37} +5.65685 q^{39} +5.65685 q^{41} +8.00000 q^{47} +5.65685 q^{51} -2.00000 q^{53} -4.00000 q^{57} +4.00000 q^{59} -5.65685 q^{61} +11.3137 q^{67} +5.65685 q^{69} +5.65685 q^{71} +11.3137 q^{73} +5.00000 q^{75} +11.3137 q^{79} +1.00000 q^{81} -12.0000 q^{83} +6.00000 q^{87} -5.65685 q^{89} -8.00000 q^{93} -5.65685 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 2q^{3} + 2q^{9} + O(q^{10})$$ $$2q - 2q^{3} + 2q^{9} + 8q^{19} - 10q^{25} - 2q^{27} - 12q^{29} + 16q^{31} + 4q^{37} + 16q^{47} - 4q^{53} - 8q^{57} + 8q^{59} + 10q^{75} + 2q^{81} - 24q^{83} + 12q^{87} - 16q^{93} + O(q^{100})$$

## 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
$$3$$ −1.00000 −0.577350
$$4$$ 0 0
$$5$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ −5.65685 −1.70561 −0.852803 0.522233i $$-0.825099\pi$$
−0.852803 + 0.522233i $$0.825099\pi$$
$$12$$ 0 0
$$13$$ −5.65685 −1.56893 −0.784465 0.620174i $$-0.787062\pi$$
−0.784465 + 0.620174i $$0.787062\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −5.65685 −1.37199 −0.685994 0.727607i $$-0.740633\pi$$
−0.685994 + 0.727607i $$0.740633\pi$$
$$18$$ 0 0
$$19$$ 4.00000 0.917663 0.458831 0.888523i $$-0.348268\pi$$
0.458831 + 0.888523i $$0.348268\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −5.65685 −1.17954 −0.589768 0.807573i $$-0.700781\pi$$
−0.589768 + 0.807573i $$0.700781\pi$$
$$24$$ 0 0
$$25$$ −5.00000 −1.00000
$$26$$ 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
$$31$$ 8.00000 1.43684 0.718421 0.695608i $$-0.244865\pi$$
0.718421 + 0.695608i $$0.244865\pi$$
$$32$$ 0 0
$$33$$ 5.65685 0.984732
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 2.00000 0.328798 0.164399 0.986394i $$-0.447432\pi$$
0.164399 + 0.986394i $$0.447432\pi$$
$$38$$ 0 0
$$39$$ 5.65685 0.905822
$$40$$ 0 0
$$41$$ 5.65685 0.883452 0.441726 0.897150i $$-0.354366\pi$$
0.441726 + 0.897150i $$0.354366\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 8.00000 1.16692 0.583460 0.812142i $$-0.301699\pi$$
0.583460 + 0.812142i $$0.301699\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 5.65685 0.792118
$$52$$ 0 0
$$53$$ −2.00000 −0.274721 −0.137361 0.990521i $$-0.543862\pi$$
−0.137361 + 0.990521i $$0.543862\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −4.00000 −0.529813
$$58$$ 0 0
$$59$$ 4.00000 0.520756 0.260378 0.965507i $$-0.416153\pi$$
0.260378 + 0.965507i $$0.416153\pi$$
$$60$$ 0 0
$$61$$ −5.65685 −0.724286 −0.362143 0.932123i $$-0.617955\pi$$
−0.362143 + 0.932123i $$0.617955\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 11.3137 1.38219 0.691095 0.722764i $$-0.257129\pi$$
0.691095 + 0.722764i $$0.257129\pi$$
$$68$$ 0 0
$$69$$ 5.65685 0.681005
$$70$$ 0 0
$$71$$ 5.65685 0.671345 0.335673 0.941979i $$-0.391036\pi$$
0.335673 + 0.941979i $$0.391036\pi$$
$$72$$ 0 0
$$73$$ 11.3137 1.32417 0.662085 0.749429i $$-0.269672\pi$$
0.662085 + 0.749429i $$0.269672\pi$$
$$74$$ 0 0
$$75$$ 5.00000 0.577350
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 11.3137 1.27289 0.636446 0.771321i $$-0.280404\pi$$
0.636446 + 0.771321i $$0.280404\pi$$
$$80$$ 0 0
$$81$$ 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
$$89$$ −5.65685 −0.599625 −0.299813 0.953998i $$-0.596924\pi$$
−0.299813 + 0.953998i $$0.596924\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ −8.00000 −0.829561
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$98$$ 0 0
$$99$$ −5.65685 −0.568535
$$100$$ 0 0
$$101$$ 11.3137 1.12576 0.562878 0.826540i $$-0.309694\pi$$
0.562878 + 0.826540i $$0.309694\pi$$
$$102$$ 0 0
$$103$$ 8.00000 0.788263 0.394132 0.919054i $$-0.371045\pi$$
0.394132 + 0.919054i $$0.371045\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −5.65685 −0.546869 −0.273434 0.961891i $$-0.588160\pi$$
−0.273434 + 0.961891i $$0.588160\pi$$
$$108$$ 0 0
$$109$$ −6.00000 −0.574696 −0.287348 0.957826i $$-0.592774\pi$$
−0.287348 + 0.957826i $$0.592774\pi$$
$$110$$ 0 0
$$111$$ −2.00000 −0.189832
$$112$$ 0 0
$$113$$ 2.00000 0.188144 0.0940721 0.995565i $$-0.470012\pi$$
0.0940721 + 0.995565i $$0.470012\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −5.65685 −0.522976
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 21.0000 1.90909
$$122$$ 0 0
$$123$$ −5.65685 −0.510061
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −11.3137 −1.00393 −0.501965 0.864888i $$-0.667389\pi$$
−0.501965 + 0.864888i $$0.667389\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 20.0000 1.74741 0.873704 0.486458i $$-0.161711\pi$$
0.873704 + 0.486458i $$0.161711\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −10.0000 −0.854358 −0.427179 0.904167i $$-0.640493\pi$$
−0.427179 + 0.904167i $$0.640493\pi$$
$$138$$ 0 0
$$139$$ −20.0000 −1.69638 −0.848189 0.529694i $$-0.822307\pi$$
−0.848189 + 0.529694i $$0.822307\pi$$
$$140$$ 0 0
$$141$$ −8.00000 −0.673722
$$142$$ 0 0
$$143$$ 32.0000 2.67597
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −2.00000 −0.163846 −0.0819232 0.996639i $$-0.526106\pi$$
−0.0819232 + 0.996639i $$0.526106\pi$$
$$150$$ 0 0
$$151$$ −22.6274 −1.84139 −0.920697 0.390279i $$-0.872378\pi$$
−0.920697 + 0.390279i $$0.872378\pi$$
$$152$$ 0 0
$$153$$ −5.65685 −0.457330
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −16.9706 −1.35440 −0.677199 0.735800i $$-0.736806\pi$$
−0.677199 + 0.735800i $$0.736806\pi$$
$$158$$ 0 0
$$159$$ 2.00000 0.158610
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −11.3137 −0.886158 −0.443079 0.896483i $$-0.646114\pi$$
−0.443079 + 0.896483i $$0.646114\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 8.00000 0.619059 0.309529 0.950890i $$-0.399829\pi$$
0.309529 + 0.950890i $$0.399829\pi$$
$$168$$ 0 0
$$169$$ 19.0000 1.46154
$$170$$ 0 0
$$171$$ 4.00000 0.305888
$$172$$ 0 0
$$173$$ 22.6274 1.72033 0.860165 0.510015i $$-0.170360\pi$$
0.860165 + 0.510015i $$0.170360\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −4.00000 −0.300658
$$178$$ 0 0
$$179$$ 5.65685 0.422813 0.211407 0.977398i $$-0.432196\pi$$
0.211407 + 0.977398i $$0.432196\pi$$
$$180$$ 0 0
$$181$$ 16.9706 1.26141 0.630706 0.776022i $$-0.282765\pi$$
0.630706 + 0.776022i $$0.282765\pi$$
$$182$$ 0 0
$$183$$ 5.65685 0.418167
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 32.0000 2.34007
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 5.65685 0.409316 0.204658 0.978834i $$-0.434392\pi$$
0.204658 + 0.978834i $$0.434392\pi$$
$$192$$ 0 0
$$193$$ 2.00000 0.143963 0.0719816 0.997406i $$-0.477068\pi$$
0.0719816 + 0.997406i $$0.477068\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −18.0000 −1.28245 −0.641223 0.767354i $$-0.721573\pi$$
−0.641223 + 0.767354i $$0.721573\pi$$
$$198$$ 0 0
$$199$$ 24.0000 1.70131 0.850657 0.525720i $$-0.176204\pi$$
0.850657 + 0.525720i $$0.176204\pi$$
$$200$$ 0 0
$$201$$ −11.3137 −0.798007
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −5.65685 −0.393179
$$208$$ 0 0
$$209$$ −22.6274 −1.56517
$$210$$ 0 0
$$211$$ 22.6274 1.55774 0.778868 0.627188i $$-0.215794\pi$$
0.778868 + 0.627188i $$0.215794\pi$$
$$212$$ 0 0
$$213$$ −5.65685 −0.387601
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ −11.3137 −0.764510
$$220$$ 0 0
$$221$$ 32.0000 2.15255
$$222$$ 0 0
$$223$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$224$$ 0 0
$$225$$ −5.00000 −0.333333
$$226$$ 0 0
$$227$$ −12.0000 −0.796468 −0.398234 0.917284i $$-0.630377\pi$$
−0.398234 + 0.917284i $$0.630377\pi$$
$$228$$ 0 0
$$229$$ 16.9706 1.12145 0.560723 0.828003i $$-0.310523\pi$$
0.560723 + 0.828003i $$0.310523\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −26.0000 −1.70332 −0.851658 0.524097i $$-0.824403\pi$$
−0.851658 + 0.524097i $$0.824403\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ −11.3137 −0.734904
$$238$$ 0 0
$$239$$ −5.65685 −0.365911 −0.182956 0.983121i $$-0.558567\pi$$
−0.182956 + 0.983121i $$0.558567\pi$$
$$240$$ 0 0
$$241$$ −22.6274 −1.45756 −0.728780 0.684748i $$-0.759912\pi$$
−0.728780 + 0.684748i $$0.759912\pi$$
$$242$$ 0 0
$$243$$ −1.00000 −0.0641500
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −22.6274 −1.43975
$$248$$ 0 0
$$249$$ 12.0000 0.760469
$$250$$ 0 0
$$251$$ −20.0000 −1.26239 −0.631194 0.775625i $$-0.717435\pi$$
−0.631194 + 0.775625i $$0.717435\pi$$
$$252$$ 0 0
$$253$$ 32.0000 2.01182
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −5.65685 −0.352865 −0.176432 0.984313i $$-0.556456\pi$$
−0.176432 + 0.984313i $$0.556456\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −6.00000 −0.371391
$$262$$ 0 0
$$263$$ 16.9706 1.04645 0.523225 0.852195i $$-0.324729\pi$$
0.523225 + 0.852195i $$0.324729\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 5.65685 0.346194
$$268$$ 0 0
$$269$$ −11.3137 −0.689809 −0.344904 0.938638i $$-0.612089\pi$$
−0.344904 + 0.938638i $$0.612089\pi$$
$$270$$ 0 0
$$271$$ 16.0000 0.971931 0.485965 0.873978i $$-0.338468\pi$$
0.485965 + 0.873978i $$0.338468\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 28.2843 1.70561
$$276$$ 0 0
$$277$$ −18.0000 −1.08152 −0.540758 0.841178i $$-0.681862\pi$$
−0.540758 + 0.841178i $$0.681862\pi$$
$$278$$ 0 0
$$279$$ 8.00000 0.478947
$$280$$ 0 0
$$281$$ −10.0000 −0.596550 −0.298275 0.954480i $$-0.596411\pi$$
−0.298275 + 0.954480i $$0.596411\pi$$
$$282$$ 0 0
$$283$$ 4.00000 0.237775 0.118888 0.992908i $$-0.462067\pi$$
0.118888 + 0.992908i $$0.462067\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 15.0000 0.882353
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −11.3137 −0.660954 −0.330477 0.943814i $$-0.607210\pi$$
−0.330477 + 0.943814i $$0.607210\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 5.65685 0.328244
$$298$$ 0 0
$$299$$ 32.0000 1.85061
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ −11.3137 −0.649956
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −12.0000 −0.684876 −0.342438 0.939540i $$-0.611253\pi$$
−0.342438 + 0.939540i $$0.611253\pi$$
$$308$$ 0 0
$$309$$ −8.00000 −0.455104
$$310$$ 0 0
$$311$$ 16.0000 0.907277 0.453638 0.891186i $$-0.350126\pi$$
0.453638 + 0.891186i $$0.350126\pi$$
$$312$$ 0 0
$$313$$ 11.3137 0.639489 0.319744 0.947504i $$-0.396403\pi$$
0.319744 + 0.947504i $$0.396403\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 6.00000 0.336994 0.168497 0.985702i $$-0.446109\pi$$
0.168497 + 0.985702i $$0.446109\pi$$
$$318$$ 0 0
$$319$$ 33.9411 1.90034
$$320$$ 0 0
$$321$$ 5.65685 0.315735
$$322$$ 0 0
$$323$$ −22.6274 −1.25902
$$324$$ 0 0
$$325$$ 28.2843 1.56893
$$326$$ 0 0
$$327$$ 6.00000 0.331801
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 22.6274 1.24372 0.621858 0.783130i $$-0.286378\pi$$
0.621858 + 0.783130i $$0.286378\pi$$
$$332$$ 0 0
$$333$$ 2.00000 0.109599
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 30.0000 1.63420 0.817102 0.576493i $$-0.195579\pi$$
0.817102 + 0.576493i $$0.195579\pi$$
$$338$$ 0 0
$$339$$ −2.00000 −0.108625
$$340$$ 0 0
$$341$$ −45.2548 −2.45069
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 5.65685 0.303676 0.151838 0.988405i $$-0.451481\pi$$
0.151838 + 0.988405i $$0.451481\pi$$
$$348$$ 0 0
$$349$$ 5.65685 0.302804 0.151402 0.988472i $$-0.451621\pi$$
0.151402 + 0.988472i $$0.451621\pi$$
$$350$$ 0 0
$$351$$ 5.65685 0.301941
$$352$$ 0 0
$$353$$ 28.2843 1.50542 0.752710 0.658352i $$-0.228746\pi$$
0.752710 + 0.658352i $$0.228746\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 28.2843 1.49279 0.746393 0.665505i $$-0.231784\pi$$
0.746393 + 0.665505i $$0.231784\pi$$
$$360$$ 0 0
$$361$$ −3.00000 −0.157895
$$362$$ 0 0
$$363$$ −21.0000 −1.10221
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 32.0000 1.67039 0.835193 0.549957i $$-0.185356\pi$$
0.835193 + 0.549957i $$0.185356\pi$$
$$368$$ 0 0
$$369$$ 5.65685 0.294484
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 14.0000 0.724893 0.362446 0.932005i $$-0.381942\pi$$
0.362446 + 0.932005i $$0.381942\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 33.9411 1.74806
$$378$$ 0 0
$$379$$ −22.6274 −1.16229 −0.581146 0.813799i $$-0.697396\pi$$
−0.581146 + 0.813799i $$0.697396\pi$$
$$380$$ 0 0
$$381$$ 11.3137 0.579619
$$382$$ 0 0
$$383$$ 8.00000 0.408781 0.204390 0.978889i $$-0.434479\pi$$
0.204390 + 0.978889i $$0.434479\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 18.0000 0.912636 0.456318 0.889817i $$-0.349168\pi$$
0.456318 + 0.889817i $$0.349168\pi$$
$$390$$ 0 0
$$391$$ 32.0000 1.61831
$$392$$ 0 0
$$393$$ −20.0000 −1.00887
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −16.9706 −0.851728 −0.425864 0.904787i $$-0.640030\pi$$
−0.425864 + 0.904787i $$0.640030\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −18.0000 −0.898877 −0.449439 0.893311i $$-0.648376\pi$$
−0.449439 + 0.893311i $$0.648376\pi$$
$$402$$ 0 0
$$403$$ −45.2548 −2.25430
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −11.3137 −0.560800
$$408$$ 0 0
$$409$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$410$$ 0 0
$$411$$ 10.0000 0.493264
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 20.0000 0.979404
$$418$$ 0 0
$$419$$ −4.00000 −0.195413 −0.0977064 0.995215i $$-0.531151\pi$$
−0.0977064 + 0.995215i $$0.531151\pi$$
$$420$$ 0 0
$$421$$ 30.0000 1.46211 0.731055 0.682318i $$-0.239028\pi$$
0.731055 + 0.682318i $$0.239028\pi$$
$$422$$ 0 0
$$423$$ 8.00000 0.388973
$$424$$ 0 0
$$425$$ 28.2843 1.37199
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ −32.0000 −1.54497
$$430$$ 0 0
$$431$$ −16.9706 −0.817443 −0.408722 0.912659i $$-0.634025\pi$$
−0.408722 + 0.912659i $$0.634025\pi$$
$$432$$ 0 0
$$433$$ 11.3137 0.543702 0.271851 0.962339i $$-0.412364\pi$$
0.271851 + 0.962339i $$0.412364\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −22.6274 −1.08242
$$438$$ 0 0
$$439$$ −32.0000 −1.52728 −0.763638 0.645644i $$-0.776589\pi$$
−0.763638 + 0.645644i $$0.776589\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −16.9706 −0.806296 −0.403148 0.915135i $$-0.632084\pi$$
−0.403148 + 0.915135i $$0.632084\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 2.00000 0.0945968
$$448$$ 0 0
$$449$$ 18.0000 0.849473 0.424736 0.905317i $$-0.360367\pi$$
0.424736 + 0.905317i $$0.360367\pi$$
$$450$$ 0 0
$$451$$ −32.0000 −1.50682
$$452$$ 0 0
$$453$$ 22.6274 1.06313
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 26.0000 1.21623 0.608114 0.793849i $$-0.291926\pi$$
0.608114 + 0.793849i $$0.291926\pi$$
$$458$$ 0 0
$$459$$ 5.65685 0.264039
$$460$$ 0 0
$$461$$ 22.6274 1.05386 0.526932 0.849907i $$-0.323342\pi$$
0.526932 + 0.849907i $$0.323342\pi$$
$$462$$ 0 0
$$463$$ 33.9411 1.57738 0.788689 0.614792i $$-0.210760\pi$$
0.788689 + 0.614792i $$0.210760\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −12.0000 −0.555294 −0.277647 0.960683i $$-0.589555\pi$$
−0.277647 + 0.960683i $$0.589555\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 16.9706 0.781962
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ −20.0000 −0.917663
$$476$$ 0 0
$$477$$ −2.00000 −0.0915737
$$478$$ 0 0
$$479$$ 24.0000 1.09659 0.548294 0.836286i $$-0.315277\pi$$
0.548294 + 0.836286i $$0.315277\pi$$
$$480$$ 0 0
$$481$$ −11.3137 −0.515861
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$488$$ 0 0
$$489$$ 11.3137 0.511624
$$490$$ 0 0
$$491$$ 28.2843 1.27645 0.638226 0.769849i $$-0.279669\pi$$
0.638226 + 0.769849i $$0.279669\pi$$
$$492$$ 0 0
$$493$$ 33.9411 1.52863
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −22.6274 −1.01294 −0.506471 0.862257i $$-0.669050\pi$$
−0.506471 + 0.862257i $$0.669050\pi$$
$$500$$ 0 0
$$501$$ −8.00000 −0.357414
$$502$$ 0 0
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −19.0000 −0.843820
$$508$$ 0 0
$$509$$ −11.3137 −0.501471 −0.250736 0.968056i $$-0.580672\pi$$
−0.250736 + 0.968056i $$0.580672\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ −4.00000 −0.176604
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −45.2548 −1.99031
$$518$$ 0 0
$$519$$ −22.6274 −0.993233
$$520$$ 0 0
$$521$$ −28.2843 −1.23916 −0.619578 0.784935i $$-0.712696\pi$$
−0.619578 + 0.784935i $$0.712696\pi$$
$$522$$ 0 0
$$523$$ 4.00000 0.174908 0.0874539 0.996169i $$-0.472127\pi$$
0.0874539 + 0.996169i $$0.472127\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −45.2548 −1.97133
$$528$$ 0 0
$$529$$ 9.00000 0.391304
$$530$$ 0 0
$$531$$ 4.00000 0.173585
$$532$$ 0 0
$$533$$ −32.0000 −1.38607
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −5.65685 −0.244111
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 22.0000 0.945854 0.472927 0.881102i $$-0.343197\pi$$
0.472927 + 0.881102i $$0.343197\pi$$
$$542$$ 0 0
$$543$$ −16.9706 −0.728277
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −33.9411 −1.45122 −0.725609 0.688107i $$-0.758442\pi$$
−0.725609 + 0.688107i $$0.758442\pi$$
$$548$$ 0 0
$$549$$ −5.65685 −0.241429
$$550$$ 0 0
$$551$$ −24.0000 −1.02243
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −10.0000 −0.423714 −0.211857 0.977301i $$-0.567951\pi$$
−0.211857 + 0.977301i $$0.567951\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ −32.0000 −1.35104
$$562$$ 0 0
$$563$$ −36.0000 −1.51722 −0.758610 0.651546i $$-0.774121\pi$$
−0.758610 + 0.651546i $$0.774121\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −42.0000 −1.76073 −0.880366 0.474295i $$-0.842703\pi$$
−0.880366 + 0.474295i $$0.842703\pi$$
$$570$$ 0 0
$$571$$ 33.9411 1.42039 0.710196 0.704004i $$-0.248606\pi$$
0.710196 + 0.704004i $$0.248606\pi$$
$$572$$ 0 0
$$573$$ −5.65685 −0.236318
$$574$$ 0 0
$$575$$ 28.2843 1.17954
$$576$$ 0 0
$$577$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$578$$ 0 0
$$579$$ −2.00000 −0.0831172
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 11.3137 0.468566
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −4.00000 −0.165098 −0.0825488 0.996587i $$-0.526306\pi$$
−0.0825488 + 0.996587i $$0.526306\pi$$
$$588$$ 0 0
$$589$$ 32.0000 1.31854
$$590$$ 0 0
$$591$$ 18.0000 0.740421
$$592$$ 0 0
$$593$$ 5.65685 0.232299 0.116150 0.993232i $$-0.462945\pi$$
0.116150 + 0.993232i $$0.462945\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −24.0000 −0.982255
$$598$$ 0 0
$$599$$ −16.9706 −0.693398 −0.346699 0.937976i $$-0.612698\pi$$
−0.346699 + 0.937976i $$0.612698\pi$$
$$600$$ 0 0
$$601$$ −45.2548 −1.84598 −0.922992 0.384820i $$-0.874263\pi$$
−0.922992 + 0.384820i $$0.874263\pi$$
$$602$$ 0 0
$$603$$ 11.3137 0.460730
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 16.0000 0.649420 0.324710 0.945814i $$-0.394733\pi$$
0.324710 + 0.945814i $$0.394733\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −45.2548 −1.83081
$$612$$ 0 0
$$613$$ −30.0000 −1.21169 −0.605844 0.795583i $$-0.707165\pi$$
−0.605844 + 0.795583i $$0.707165\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −42.0000 −1.69086 −0.845428 0.534089i $$-0.820655\pi$$
−0.845428 + 0.534089i $$0.820655\pi$$
$$618$$ 0 0
$$619$$ −12.0000 −0.482321 −0.241160 0.970485i $$-0.577528\pi$$
−0.241160 + 0.970485i $$0.577528\pi$$
$$620$$ 0 0
$$621$$ 5.65685 0.227002
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 25.0000 1.00000
$$626$$ 0 0
$$627$$ 22.6274 0.903652
$$628$$ 0 0
$$629$$ −11.3137 −0.451107
$$630$$ 0 0
$$631$$ 11.3137 0.450392 0.225196 0.974314i $$-0.427698\pi$$
0.225196 + 0.974314i $$0.427698\pi$$
$$632$$ 0 0
$$633$$ −22.6274 −0.899359
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 5.65685 0.223782
$$640$$ 0 0
$$641$$ −2.00000 −0.0789953 −0.0394976 0.999220i $$-0.512576\pi$$
−0.0394976 + 0.999220i $$0.512576\pi$$
$$642$$ 0 0
$$643$$ −4.00000 −0.157745 −0.0788723 0.996885i $$-0.525132\pi$$
−0.0788723 + 0.996885i $$0.525132\pi$$
$$644$$ 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
$$649$$ −22.6274 −0.888204
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 42.0000 1.64359 0.821794 0.569785i $$-0.192974\pi$$
0.821794 + 0.569785i $$0.192974\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 11.3137 0.441390
$$658$$ 0 0
$$659$$ 39.5980 1.54252 0.771259 0.636521i $$-0.219627\pi$$
0.771259 + 0.636521i $$0.219627\pi$$
$$660$$ 0 0
$$661$$ −50.9117 −1.98024 −0.990118 0.140240i $$-0.955213\pi$$
−0.990118 + 0.140240i $$0.955213\pi$$
$$662$$ 0 0
$$663$$ −32.0000 −1.24278
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 33.9411 1.31421
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 32.0000 1.23535
$$672$$ 0 0
$$673$$ 14.0000 0.539660 0.269830 0.962908i $$-0.413032\pi$$
0.269830 + 0.962908i $$0.413032\pi$$
$$674$$ 0 0
$$675$$ 5.00000 0.192450
$$676$$ 0 0
$$677$$ 45.2548 1.73928 0.869642 0.493682i $$-0.164349\pi$$
0.869642 + 0.493682i $$0.164349\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 12.0000 0.459841
$$682$$ 0 0
$$683$$ 5.65685 0.216454 0.108227 0.994126i $$-0.465483\pi$$
0.108227 + 0.994126i $$0.465483\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −16.9706 −0.647467
$$688$$ 0 0
$$689$$ 11.3137 0.431018
$$690$$ 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
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −32.0000 −1.21209
$$698$$ 0 0
$$699$$ 26.0000 0.983410
$$700$$ 0 0
$$701$$ −6.00000 −0.226617 −0.113308 0.993560i $$-0.536145\pi$$
−0.113308 + 0.993560i $$0.536145\pi$$
$$702$$ 0 0
$$703$$ 8.00000 0.301726
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 34.0000 1.27690 0.638448 0.769665i $$-0.279577\pi$$
0.638448 + 0.769665i $$0.279577\pi$$
$$710$$ 0 0
$$711$$ 11.3137 0.424297
$$712$$ 0 0
$$713$$ −45.2548 −1.69481
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 5.65685 0.211259
$$718$$ 0 0
$$719$$ −8.00000 −0.298350 −0.149175 0.988811i $$-0.547662\pi$$
−0.149175 + 0.988811i $$0.547662\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 22.6274 0.841523
$$724$$ 0 0
$$725$$ 30.0000 1.11417
$$726$$ 0 0
$$727$$ 8.00000 0.296704 0.148352 0.988935i $$-0.452603\pi$$
0.148352 + 0.988935i $$0.452603\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 5.65685 0.208941 0.104470 0.994528i $$-0.466685\pi$$
0.104470 + 0.994528i $$0.466685\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −64.0000 −2.35747
$$738$$ 0 0
$$739$$ −11.3137 −0.416181 −0.208091 0.978110i $$-0.566725\pi$$
−0.208091 + 0.978110i $$0.566725\pi$$
$$740$$ 0 0
$$741$$ 22.6274 0.831239
$$742$$ 0 0
$$743$$ −39.5980 −1.45271 −0.726354 0.687320i $$-0.758787\pi$$
−0.726354 + 0.687320i $$0.758787\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −12.0000 −0.439057
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 22.6274 0.825686 0.412843 0.910802i $$-0.364536\pi$$
0.412843 + 0.910802i $$0.364536\pi$$
$$752$$ 0 0
$$753$$ 20.0000 0.728841
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 50.0000 1.81728 0.908640 0.417579i $$-0.137121\pi$$
0.908640 + 0.417579i $$0.137121\pi$$
$$758$$ 0 0
$$759$$ −32.0000 −1.16153
$$760$$ 0 0
$$761$$ 5.65685 0.205061 0.102530 0.994730i $$-0.467306\pi$$
0.102530 + 0.994730i $$0.467306\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −22.6274 −0.817029
$$768$$ 0 0
$$769$$ 33.9411 1.22395 0.611974 0.790878i $$-0.290376\pi$$
0.611974 + 0.790878i $$0.290376\pi$$
$$770$$ 0 0
$$771$$ 5.65685 0.203727
$$772$$ 0 0
$$773$$ 11.3137 0.406926 0.203463 0.979083i $$-0.434780\pi$$
0.203463 + 0.979083i $$0.434780\pi$$
$$774$$ 0 0
$$775$$ −40.0000 −1.43684
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 22.6274 0.810711
$$780$$ 0 0
$$781$$ −32.0000 −1.14505
$$782$$ 0 0
$$783$$ 6.00000 0.214423
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −44.0000 −1.56843 −0.784215 0.620489i $$-0.786934\pi$$
−0.784215 + 0.620489i $$0.786934\pi$$
$$788$$ 0 0
$$789$$ −16.9706 −0.604168
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 32.0000 1.13635
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 22.6274 0.801504 0.400752 0.916187i $$-0.368749\pi$$
0.400752 + 0.916187i $$0.368749\pi$$
$$798$$ 0 0
$$799$$ −45.2548 −1.60100
$$800$$ 0 0
$$801$$ −5.65685 −0.199875
$$802$$ 0 0
$$803$$ −64.0000 −2.25851
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 11.3137 0.398261
$$808$$ 0 0
$$809$$ −38.0000 −1.33601 −0.668004 0.744157i $$-0.732851\pi$$
−0.668004 + 0.744157i $$0.732851\pi$$
$$810$$ 0 0
$$811$$ 20.0000 0.702295 0.351147 0.936320i $$-0.385792\pi$$
0.351147 + 0.936320i $$0.385792\pi$$
$$812$$ 0 0
$$813$$ −16.0000 −0.561144
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 30.0000 1.04701 0.523504 0.852023i $$-0.324625\pi$$
0.523504 + 0.852023i $$0.324625\pi$$
$$822$$ 0 0
$$823$$ 33.9411 1.18311 0.591557 0.806263i $$-0.298514\pi$$
0.591557 + 0.806263i $$0.298514\pi$$
$$824$$ 0 0
$$825$$ −28.2843 −0.984732
$$826$$ 0 0
$$827$$ −28.2843 −0.983540 −0.491770 0.870725i $$-0.663650\pi$$
−0.491770 + 0.870725i $$0.663650\pi$$
$$828$$ 0 0
$$829$$ −16.9706 −0.589412 −0.294706 0.955588i $$-0.595222\pi$$
−0.294706 + 0.955588i $$0.595222\pi$$
$$830$$ 0 0
$$831$$ 18.0000 0.624413
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ −8.00000 −0.276520
$$838$$ 0 0
$$839$$ 56.0000 1.93333 0.966667 0.256036i $$-0.0824164\pi$$
0.966667 + 0.256036i $$0.0824164\pi$$
$$840$$ 0 0
$$841$$ 7.00000 0.241379
$$842$$ 0 0
$$843$$ 10.0000 0.344418
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ −4.00000 −0.137280
$$850$$ 0 0
$$851$$ −11.3137 −0.387829
$$852$$ 0 0
$$853$$ 50.9117 1.74318 0.871592 0.490233i $$-0.163088\pi$$
0.871592 + 0.490233i $$0.163088\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 28.2843 0.966172 0.483086 0.875573i $$-0.339516\pi$$
0.483086 + 0.875573i $$0.339516\pi$$
$$858$$ 0 0
$$859$$ −4.00000 −0.136478 −0.0682391 0.997669i $$-0.521738\pi$$
−0.0682391 + 0.997669i $$0.521738\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 16.9706 0.577685 0.288842 0.957377i $$-0.406730\pi$$
0.288842 + 0.957377i $$0.406730\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ −15.0000 −0.509427
$$868$$ 0 0
$$869$$ −64.0000 −2.17105
$$870$$ 0 0
$$871$$ −64.0000 −2.16856
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −38.0000 −1.28317 −0.641584 0.767052i $$-0.721723\pi$$
−0.641584 + 0.767052i $$0.721723\pi$$
$$878$$ 0 0
$$879$$ 11.3137 0.381602
$$880$$ 0 0
$$881$$ 5.65685 0.190584 0.0952921 0.995449i $$-0.469621\pi$$
0.0952921 + 0.995449i $$0.469621\pi$$
$$882$$ 0 0
$$883$$ 22.6274 0.761473 0.380737 0.924684i $$-0.375670\pi$$
0.380737 + 0.924684i $$0.375670\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −40.0000 −1.34307 −0.671534 0.740973i $$-0.734364\pi$$
−0.671534 + 0.740973i $$0.734364\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ −5.65685 −0.189512
$$892$$ 0 0
$$893$$ 32.0000 1.07084
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ −32.0000 −1.06845
$$898$$ 0 0
$$899$$ −48.0000 −1.60089
$$900$$ 0 0
$$901$$ 11.3137 0.376914
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$908$$ 0 0
$$909$$ 11.3137 0.375252
$$910$$ 0 0
$$911$$ −16.9706 −0.562260 −0.281130 0.959670i $$-0.590709\pi$$
−0.281130 + 0.959670i $$0.590709\pi$$
$$912$$ 0 0
$$913$$ 67.8823 2.24657
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ −22.6274 −0.746410 −0.373205 0.927749i $$-0.621741\pi$$
−0.373205 + 0.927749i $$0.621741\pi$$
$$920$$ 0 0
$$921$$ 12.0000 0.395413
$$922$$ 0 0
$$923$$ −32.0000 −1.05329
$$924$$ 0 0
$$925$$ −10.0000 −0.328798
$$926$$ 0 0
$$927$$ 8.00000 0.262754
$$928$$ 0 0
$$929$$ −39.5980 −1.29917 −0.649584 0.760290i $$-0.725057\pi$$
−0.649584 + 0.760290i $$0.725057\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ −16.0000 −0.523816
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 22.6274 0.739205 0.369603 0.929190i $$-0.379494\pi$$
0.369603 + 0.929190i $$0.379494\pi$$
$$938$$ 0 0
$$939$$ −11.3137 −0.369209
$$940$$ 0 0
$$941$$ 45.2548 1.47527 0.737633 0.675202i $$-0.235944\pi$$
0.737633 + 0.675202i $$0.235944\pi$$
$$942$$ 0 0
$$943$$ −32.0000 −1.04206
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 16.9706 0.551469 0.275735 0.961234i $$-0.411079\pi$$
0.275735 + 0.961234i $$0.411079\pi$$
$$948$$ 0 0
$$949$$ −64.0000 −2.07753
$$950$$ 0 0
$$951$$ −6.00000 −0.194563
$$952$$ 0 0
$$953$$ −6.00000 −0.194359 −0.0971795 0.995267i $$-0.530982\pi$$
−0.0971795 + 0.995267i $$0.530982\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ −33.9411 −1.09716
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 33.0000 1.06452
$$962$$ 0 0
$$963$$ −5.65685 −0.182290
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 33.9411 1.09147 0.545737 0.837957i $$-0.316250\pi$$
0.545737 + 0.837957i $$0.316250\pi$$
$$968$$ 0 0
$$969$$ 22.6274 0.726897
$$970$$ 0 0
$$971$$ 36.0000 1.15529 0.577647 0.816286i $$-0.303971\pi$$
0.577647 + 0.816286i $$0.303971\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ −28.2843 −0.905822
$$976$$ 0 0
$$977$$ −34.0000 −1.08776 −0.543878 0.839164i $$-0.683045\pi$$
−0.543878 + 0.839164i $$0.683045\pi$$
$$978$$ 0 0
$$979$$ 32.0000 1.02272
$$980$$ 0 0
$$981$$ −6.00000 −0.191565
$$982$$ 0 0
$$983$$ −8.00000 −0.255160 −0.127580 0.991828i $$-0.540721\pi$$
−0.127580 + 0.991828i $$0.540721\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ −22.6274 −0.718784 −0.359392 0.933187i $$-0.617016\pi$$
−0.359392 + 0.933187i $$0.617016\pi$$
$$992$$ 0 0
$$993$$ −22.6274 −0.718059
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ −5.65685 −0.179154 −0.0895772 0.995980i $$-0.528552\pi$$
−0.0895772 + 0.995980i $$0.528552\pi$$
$$998$$ 0 0
$$999$$ −2.00000 −0.0632772
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 4704.2.a.bk.1.1 2
4.3 odd 2 4704.2.a.bp.1.2 yes 2
7.6 odd 2 4704.2.a.bp.1.1 yes 2
8.3 odd 2 9408.2.a.dm.1.1 2
8.5 even 2 9408.2.a.dz.1.2 2
28.27 even 2 inner 4704.2.a.bk.1.2 yes 2
56.13 odd 2 9408.2.a.dm.1.2 2
56.27 even 2 9408.2.a.dz.1.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
4704.2.a.bk.1.1 2 1.1 even 1 trivial
4704.2.a.bk.1.2 yes 2 28.27 even 2 inner
4704.2.a.bp.1.1 yes 2 7.6 odd 2
4704.2.a.bp.1.2 yes 2 4.3 odd 2
9408.2.a.dm.1.1 2 8.3 odd 2
9408.2.a.dm.1.2 2 56.13 odd 2
9408.2.a.dz.1.1 2 56.27 even 2
9408.2.a.dz.1.2 2 8.5 even 2