# Properties

 Label 1280.2.d.j.641.1 Level $1280$ Weight $2$ Character 1280.641 Analytic conductor $10.221$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1280 = 2^{8} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1280.d (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$10.2208514587$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 40) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 641.1 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1280.641 Dual form 1280.2.d.j.641.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000i q^{5} +4.00000 q^{7} +3.00000 q^{9} +O(q^{10})$$ $$q-1.00000i q^{5} +4.00000 q^{7} +3.00000 q^{9} -4.00000i q^{11} -2.00000i q^{13} +2.00000 q^{17} +4.00000i q^{19} -4.00000 q^{23} -1.00000 q^{25} -2.00000i q^{29} -8.00000 q^{31} -4.00000i q^{35} -6.00000i q^{37} +6.00000 q^{41} +8.00000i q^{43} -3.00000i q^{45} +4.00000 q^{47} +9.00000 q^{49} -6.00000i q^{53} -4.00000 q^{55} +4.00000i q^{59} -2.00000i q^{61} +12.0000 q^{63} -2.00000 q^{65} +8.00000i q^{67} +6.00000 q^{73} -16.0000i q^{77} +9.00000 q^{81} -16.0000i q^{83} -2.00000i q^{85} +6.00000 q^{89} -8.00000i q^{91} +4.00000 q^{95} -14.0000 q^{97} -12.0000i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 8q^{7} + 6q^{9} + O(q^{10})$$ $$2q + 8q^{7} + 6q^{9} + 4q^{17} - 8q^{23} - 2q^{25} - 16q^{31} + 12q^{41} + 8q^{47} + 18q^{49} - 8q^{55} + 24q^{63} - 4q^{65} + 12q^{73} + 18q^{81} + 12q^{89} + 8q^{95} - 28q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times$$.

 $$n$$ $$257$$ $$261$$ $$511$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$

## 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$4$$ 0 0
$$5$$ − 1.00000i − 0.447214i
$$6$$ 0 0
$$7$$ 4.00000 1.51186 0.755929 0.654654i $$-0.227186\pi$$
0.755929 + 0.654654i $$0.227186\pi$$
$$8$$ 0 0
$$9$$ 3.00000 1.00000
$$10$$ 0 0
$$11$$ − 4.00000i − 1.20605i −0.797724 0.603023i $$-0.793963\pi$$
0.797724 0.603023i $$-0.206037\pi$$
$$12$$ 0 0
$$13$$ − 2.00000i − 0.554700i −0.960769 0.277350i $$-0.910544\pi$$
0.960769 0.277350i $$-0.0894562\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 2.00000 0.485071 0.242536 0.970143i $$-0.422021\pi$$
0.242536 + 0.970143i $$0.422021\pi$$
$$18$$ 0 0
$$19$$ 4.00000i 0.917663i 0.888523 + 0.458831i $$0.151732\pi$$
−0.888523 + 0.458831i $$0.848268\pi$$
$$20$$ 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
$$25$$ −1.00000 −0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ − 2.00000i − 0.371391i −0.982607 0.185695i $$-0.940546\pi$$
0.982607 0.185695i $$-0.0594537\pi$$
$$30$$ 0 0
$$31$$ −8.00000 −1.43684 −0.718421 0.695608i $$-0.755135\pi$$
−0.718421 + 0.695608i $$0.755135\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ − 4.00000i − 0.676123i
$$36$$ 0 0
$$37$$ − 6.00000i − 0.986394i −0.869918 0.493197i $$-0.835828\pi$$
0.869918 0.493197i $$-0.164172\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 6.00000 0.937043 0.468521 0.883452i $$-0.344787\pi$$
0.468521 + 0.883452i $$0.344787\pi$$
$$42$$ 0 0
$$43$$ 8.00000i 1.21999i 0.792406 + 0.609994i $$0.208828\pi$$
−0.792406 + 0.609994i $$0.791172\pi$$
$$44$$ 0 0
$$45$$ − 3.00000i − 0.447214i
$$46$$ 0 0
$$47$$ 4.00000 0.583460 0.291730 0.956501i $$-0.405769\pi$$
0.291730 + 0.956501i $$0.405769\pi$$
$$48$$ 0 0
$$49$$ 9.00000 1.28571
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ − 6.00000i − 0.824163i −0.911147 0.412082i $$-0.864802\pi$$
0.911147 0.412082i $$-0.135198\pi$$
$$54$$ 0 0
$$55$$ −4.00000 −0.539360
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 4.00000i 0.520756i 0.965507 + 0.260378i $$0.0838471\pi$$
−0.965507 + 0.260378i $$0.916153\pi$$
$$60$$ 0 0
$$61$$ − 2.00000i − 0.256074i −0.991769 0.128037i $$-0.959132\pi$$
0.991769 0.128037i $$-0.0408676\pi$$
$$62$$ 0 0
$$63$$ 12.0000 1.51186
$$64$$ 0 0
$$65$$ −2.00000 −0.248069
$$66$$ 0 0
$$67$$ 8.00000i 0.977356i 0.872464 + 0.488678i $$0.162521\pi$$
−0.872464 + 0.488678i $$0.837479\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ 6.00000 0.702247 0.351123 0.936329i $$-0.385800\pi$$
0.351123 + 0.936329i $$0.385800\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ − 16.0000i − 1.82337i
$$78$$ 0 0
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ 0 0
$$81$$ 9.00000 1.00000
$$82$$ 0 0
$$83$$ − 16.0000i − 1.75623i −0.478451 0.878114i $$-0.658802\pi$$
0.478451 0.878114i $$-0.341198\pi$$
$$84$$ 0 0
$$85$$ − 2.00000i − 0.216930i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 6.00000 0.635999 0.317999 0.948091i $$-0.396989\pi$$
0.317999 + 0.948091i $$0.396989\pi$$
$$90$$ 0 0
$$91$$ − 8.00000i − 0.838628i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 4.00000 0.410391
$$96$$ 0 0
$$97$$ −14.0000 −1.42148 −0.710742 0.703452i $$-0.751641\pi$$
−0.710742 + 0.703452i $$0.751641\pi$$
$$98$$ 0 0
$$99$$ − 12.0000i − 1.20605i
$$100$$ 0 0
$$101$$ − 6.00000i − 0.597022i −0.954406 0.298511i $$-0.903510\pi$$
0.954406 0.298511i $$-0.0964900\pi$$
$$102$$ 0 0
$$103$$ −4.00000 −0.394132 −0.197066 0.980390i $$-0.563141\pi$$
−0.197066 + 0.980390i $$0.563141\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$108$$ 0 0
$$109$$ 14.0000i 1.34096i 0.741929 + 0.670478i $$0.233911\pi$$
−0.741929 + 0.670478i $$0.766089\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 18.0000 1.69330 0.846649 0.532152i $$-0.178617\pi$$
0.846649 + 0.532152i $$0.178617\pi$$
$$114$$ 0 0
$$115$$ 4.00000i 0.373002i
$$116$$ 0 0
$$117$$ − 6.00000i − 0.554700i
$$118$$ 0 0
$$119$$ 8.00000 0.733359
$$120$$ 0 0
$$121$$ −5.00000 −0.454545
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 1.00000i 0.0894427i
$$126$$ 0 0
$$127$$ −12.0000 −1.06483 −0.532414 0.846484i $$-0.678715\pi$$
−0.532414 + 0.846484i $$0.678715\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 12.0000i 1.04844i 0.851581 + 0.524222i $$0.175644\pi$$
−0.851581 + 0.524222i $$0.824356\pi$$
$$132$$ 0 0
$$133$$ 16.0000i 1.38738i
$$134$$ 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
$$139$$ − 12.0000i − 1.01783i −0.860818 0.508913i $$-0.830047\pi$$
0.860818 0.508913i $$-0.169953\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −8.00000 −0.668994
$$144$$ 0 0
$$145$$ −2.00000 −0.166091
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 10.0000i 0.819232i 0.912258 + 0.409616i $$0.134337\pi$$
−0.912258 + 0.409616i $$0.865663\pi$$
$$150$$ 0 0
$$151$$ 16.0000 1.30206 0.651031 0.759051i $$-0.274337\pi$$
0.651031 + 0.759051i $$0.274337\pi$$
$$152$$ 0 0
$$153$$ 6.00000 0.485071
$$154$$ 0 0
$$155$$ 8.00000i 0.642575i
$$156$$ 0 0
$$157$$ − 2.00000i − 0.159617i −0.996810 0.0798087i $$-0.974569\pi$$
0.996810 0.0798087i $$-0.0254309\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −16.0000 −1.26098
$$162$$ 0 0
$$163$$ 16.0000i 1.25322i 0.779334 + 0.626608i $$0.215557\pi$$
−0.779334 + 0.626608i $$0.784443\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −12.0000 −0.928588 −0.464294 0.885681i $$-0.653692\pi$$
−0.464294 + 0.885681i $$0.653692\pi$$
$$168$$ 0 0
$$169$$ 9.00000 0.692308
$$170$$ 0 0
$$171$$ 12.0000i 0.917663i
$$172$$ 0 0
$$173$$ 14.0000i 1.06440i 0.846619 + 0.532200i $$0.178635\pi$$
−0.846619 + 0.532200i $$0.821365\pi$$
$$174$$ 0 0
$$175$$ −4.00000 −0.302372
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 20.0000i 1.49487i 0.664335 + 0.747435i $$0.268715\pi$$
−0.664335 + 0.747435i $$0.731285\pi$$
$$180$$ 0 0
$$181$$ 10.0000i 0.743294i 0.928374 + 0.371647i $$0.121207\pi$$
−0.928374 + 0.371647i $$0.878793\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −6.00000 −0.441129
$$186$$ 0 0
$$187$$ − 8.00000i − 0.585018i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 8.00000 0.578860 0.289430 0.957199i $$-0.406534\pi$$
0.289430 + 0.957199i $$0.406534\pi$$
$$192$$ 0 0
$$193$$ −14.0000 −1.00774 −0.503871 0.863779i $$-0.668091\pi$$
−0.503871 + 0.863779i $$0.668091\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ − 22.0000i − 1.56744i −0.621117 0.783718i $$-0.713321\pi$$
0.621117 0.783718i $$-0.286679\pi$$
$$198$$ 0 0
$$199$$ −8.00000 −0.567105 −0.283552 0.958957i $$-0.591513\pi$$
−0.283552 + 0.958957i $$0.591513\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ − 8.00000i − 0.561490i
$$204$$ 0 0
$$205$$ − 6.00000i − 0.419058i
$$206$$ 0 0
$$207$$ −12.0000 −0.834058
$$208$$ 0 0
$$209$$ 16.0000 1.10674
$$210$$ 0 0
$$211$$ − 4.00000i − 0.275371i −0.990476 0.137686i $$-0.956034\pi$$
0.990476 0.137686i $$-0.0439664\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 8.00000 0.545595
$$216$$ 0 0
$$217$$ −32.0000 −2.17230
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ − 4.00000i − 0.269069i
$$222$$ 0 0
$$223$$ −4.00000 −0.267860 −0.133930 0.990991i $$-0.542760\pi$$
−0.133930 + 0.990991i $$0.542760\pi$$
$$224$$ 0 0
$$225$$ −3.00000 −0.200000
$$226$$ 0 0
$$227$$ − 24.0000i − 1.59294i −0.604681 0.796468i $$-0.706699\pi$$
0.604681 0.796468i $$-0.293301\pi$$
$$228$$ 0 0
$$229$$ 26.0000i 1.71813i 0.511868 + 0.859064i $$0.328954\pi$$
−0.511868 + 0.859064i $$0.671046\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 6.00000 0.393073 0.196537 0.980497i $$-0.437031\pi$$
0.196537 + 0.980497i $$0.437031\pi$$
$$234$$ 0 0
$$235$$ − 4.00000i − 0.260931i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ 2.00000 0.128831 0.0644157 0.997923i $$-0.479482\pi$$
0.0644157 + 0.997923i $$0.479482\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ − 9.00000i − 0.574989i
$$246$$ 0 0
$$247$$ 8.00000 0.509028
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 12.0000i 0.757433i 0.925513 + 0.378717i $$0.123635\pi$$
−0.925513 + 0.378717i $$0.876365\pi$$
$$252$$ 0 0
$$253$$ 16.0000i 1.00591i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −30.0000 −1.87135 −0.935674 0.352865i $$-0.885208\pi$$
−0.935674 + 0.352865i $$0.885208\pi$$
$$258$$ 0 0
$$259$$ − 24.0000i − 1.49129i
$$260$$ 0 0
$$261$$ − 6.00000i − 0.371391i
$$262$$ 0 0
$$263$$ 12.0000 0.739952 0.369976 0.929041i $$-0.379366\pi$$
0.369976 + 0.929041i $$0.379366\pi$$
$$264$$ 0 0
$$265$$ −6.00000 −0.368577
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 14.0000i 0.853595i 0.904347 + 0.426798i $$0.140358\pi$$
−0.904347 + 0.426798i $$0.859642\pi$$
$$270$$ 0 0
$$271$$ 24.0000 1.45790 0.728948 0.684569i $$-0.240010\pi$$
0.728948 + 0.684569i $$0.240010\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 4.00000i 0.241209i
$$276$$ 0 0
$$277$$ 10.0000i 0.600842i 0.953807 + 0.300421i $$0.0971271\pi$$
−0.953807 + 0.300421i $$0.902873\pi$$
$$278$$ 0 0
$$279$$ −24.0000 −1.43684
$$280$$ 0 0
$$281$$ −10.0000 −0.596550 −0.298275 0.954480i $$-0.596411\pi$$
−0.298275 + 0.954480i $$0.596411\pi$$
$$282$$ 0 0
$$283$$ − 8.00000i − 0.475551i −0.971320 0.237775i $$-0.923582\pi$$
0.971320 0.237775i $$-0.0764182\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 24.0000 1.41668
$$288$$ 0 0
$$289$$ −13.0000 −0.764706
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 26.0000i 1.51894i 0.650545 + 0.759468i $$0.274541\pi$$
−0.650545 + 0.759468i $$0.725459\pi$$
$$294$$ 0 0
$$295$$ 4.00000 0.232889
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 8.00000i 0.462652i
$$300$$ 0 0
$$301$$ 32.0000i 1.84445i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −2.00000 −0.114520
$$306$$ 0 0
$$307$$ − 8.00000i − 0.456584i −0.973593 0.228292i $$-0.926686\pi$$
0.973593 0.228292i $$-0.0733141\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −32.0000 −1.81455 −0.907277 0.420534i $$-0.861843\pi$$
−0.907277 + 0.420534i $$0.861843\pi$$
$$312$$ 0 0
$$313$$ −26.0000 −1.46961 −0.734803 0.678280i $$-0.762726\pi$$
−0.734803 + 0.678280i $$0.762726\pi$$
$$314$$ 0 0
$$315$$ − 12.0000i − 0.676123i
$$316$$ 0 0
$$317$$ − 18.0000i − 1.01098i −0.862832 0.505490i $$-0.831312\pi$$
0.862832 0.505490i $$-0.168688\pi$$
$$318$$ 0 0
$$319$$ −8.00000 −0.447914
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 8.00000i 0.445132i
$$324$$ 0 0
$$325$$ 2.00000i 0.110940i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 16.0000 0.882109
$$330$$ 0 0
$$331$$ 12.0000i 0.659580i 0.944054 + 0.329790i $$0.106978\pi$$
−0.944054 + 0.329790i $$0.893022\pi$$
$$332$$ 0 0
$$333$$ − 18.0000i − 0.986394i
$$334$$ 0 0
$$335$$ 8.00000 0.437087
$$336$$ 0 0
$$337$$ −14.0000 −0.762629 −0.381314 0.924445i $$-0.624528\pi$$
−0.381314 + 0.924445i $$0.624528\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 32.0000i 1.73290i
$$342$$ 0 0
$$343$$ 8.00000 0.431959
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 16.0000i 0.858925i 0.903085 + 0.429463i $$0.141297\pi$$
−0.903085 + 0.429463i $$0.858703\pi$$
$$348$$ 0 0
$$349$$ 30.0000i 1.60586i 0.596071 + 0.802932i $$0.296728\pi$$
−0.596071 + 0.802932i $$0.703272\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 2.00000 0.106449 0.0532246 0.998583i $$-0.483050\pi$$
0.0532246 + 0.998583i $$0.483050\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 24.0000 1.26667 0.633336 0.773877i $$-0.281685\pi$$
0.633336 + 0.773877i $$0.281685\pi$$
$$360$$ 0 0
$$361$$ 3.00000 0.157895
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ − 6.00000i − 0.314054i
$$366$$ 0 0
$$367$$ 20.0000 1.04399 0.521996 0.852948i $$-0.325188\pi$$
0.521996 + 0.852948i $$0.325188\pi$$
$$368$$ 0 0
$$369$$ 18.0000 0.937043
$$370$$ 0 0
$$371$$ − 24.0000i − 1.24602i
$$372$$ 0 0
$$373$$ − 22.0000i − 1.13912i −0.821951 0.569558i $$-0.807114\pi$$
0.821951 0.569558i $$-0.192886\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −4.00000 −0.206010
$$378$$ 0 0
$$379$$ 20.0000i 1.02733i 0.857991 + 0.513665i $$0.171713\pi$$
−0.857991 + 0.513665i $$0.828287\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −36.0000 −1.83951 −0.919757 0.392488i $$-0.871614\pi$$
−0.919757 + 0.392488i $$0.871614\pi$$
$$384$$ 0 0
$$385$$ −16.0000 −0.815436
$$386$$ 0 0
$$387$$ 24.0000i 1.21999i
$$388$$ 0 0
$$389$$ − 6.00000i − 0.304212i −0.988364 0.152106i $$-0.951394\pi$$
0.988364 0.152106i $$-0.0486055\pi$$
$$390$$ 0 0
$$391$$ −8.00000 −0.404577
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ − 2.00000i − 0.100377i −0.998740 0.0501886i $$-0.984018\pi$$
0.998740 0.0501886i $$-0.0159822\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 18.0000 0.898877 0.449439 0.893311i $$-0.351624\pi$$
0.449439 + 0.893311i $$0.351624\pi$$
$$402$$ 0 0
$$403$$ 16.0000i 0.797017i
$$404$$ 0 0
$$405$$ − 9.00000i − 0.447214i
$$406$$ 0 0
$$407$$ −24.0000 −1.18964
$$408$$ 0 0
$$409$$ −10.0000 −0.494468 −0.247234 0.968956i $$-0.579522\pi$$
−0.247234 + 0.968956i $$0.579522\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 16.0000i 0.787309i
$$414$$ 0 0
$$415$$ −16.0000 −0.785409
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 36.0000i 1.75872i 0.476162 + 0.879358i $$0.342028\pi$$
−0.476162 + 0.879358i $$0.657972\pi$$
$$420$$ 0 0
$$421$$ − 6.00000i − 0.292422i −0.989253 0.146211i $$-0.953292\pi$$
0.989253 0.146211i $$-0.0467079\pi$$
$$422$$ 0 0
$$423$$ 12.0000 0.583460
$$424$$ 0 0
$$425$$ −2.00000 −0.0970143
$$426$$ 0 0
$$427$$ − 8.00000i − 0.387147i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −40.0000 −1.92673 −0.963366 0.268190i $$-0.913575\pi$$
−0.963366 + 0.268190i $$0.913575\pi$$
$$432$$ 0 0
$$433$$ 2.00000 0.0961139 0.0480569 0.998845i $$-0.484697\pi$$
0.0480569 + 0.998845i $$0.484697\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ − 16.0000i − 0.765384i
$$438$$ 0 0
$$439$$ 8.00000 0.381819 0.190910 0.981608i $$-0.438856\pi$$
0.190910 + 0.981608i $$0.438856\pi$$
$$440$$ 0 0
$$441$$ 27.0000 1.28571
$$442$$ 0 0
$$443$$ − 24.0000i − 1.14027i −0.821549 0.570137i $$-0.806890\pi$$
0.821549 0.570137i $$-0.193110\pi$$
$$444$$ 0 0
$$445$$ − 6.00000i − 0.284427i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 18.0000 0.849473 0.424736 0.905317i $$-0.360367\pi$$
0.424736 + 0.905317i $$0.360367\pi$$
$$450$$ 0 0
$$451$$ − 24.0000i − 1.13012i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −8.00000 −0.375046
$$456$$ 0 0
$$457$$ −10.0000 −0.467780 −0.233890 0.972263i $$-0.575146\pi$$
−0.233890 + 0.972263i $$0.575146\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ − 18.0000i − 0.838344i −0.907907 0.419172i $$-0.862320\pi$$
0.907907 0.419172i $$-0.137680\pi$$
$$462$$ 0 0
$$463$$ 12.0000 0.557687 0.278844 0.960337i $$-0.410049\pi$$
0.278844 + 0.960337i $$0.410049\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 8.00000i 0.370196i 0.982720 + 0.185098i $$0.0592602\pi$$
−0.982720 + 0.185098i $$0.940740\pi$$
$$468$$ 0 0
$$469$$ 32.0000i 1.47762i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 32.0000 1.47136
$$474$$ 0 0
$$475$$ − 4.00000i − 0.183533i
$$476$$ 0 0
$$477$$ − 18.0000i − 0.824163i
$$478$$ 0 0
$$479$$ 16.0000 0.731059 0.365529 0.930800i $$-0.380888\pi$$
0.365529 + 0.930800i $$0.380888\pi$$
$$480$$ 0 0
$$481$$ −12.0000 −0.547153
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 14.0000i 0.635707i
$$486$$ 0 0
$$487$$ 20.0000 0.906287 0.453143 0.891438i $$-0.350303\pi$$
0.453143 + 0.891438i $$0.350303\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ − 36.0000i − 1.62466i −0.583200 0.812329i $$-0.698200\pi$$
0.583200 0.812329i $$-0.301800\pi$$
$$492$$ 0 0
$$493$$ − 4.00000i − 0.180151i
$$494$$ 0 0
$$495$$ −12.0000 −0.539360
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ − 28.0000i − 1.25345i −0.779240 0.626726i $$-0.784395\pi$$
0.779240 0.626726i $$-0.215605\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 12.0000 0.535054 0.267527 0.963550i $$-0.413794\pi$$
0.267527 + 0.963550i $$0.413794\pi$$
$$504$$ 0 0
$$505$$ −6.00000 −0.266996
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ − 2.00000i − 0.0886484i −0.999017 0.0443242i $$-0.985887\pi$$
0.999017 0.0443242i $$-0.0141135\pi$$
$$510$$ 0 0
$$511$$ 24.0000 1.06170
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 4.00000i 0.176261i
$$516$$ 0 0
$$517$$ − 16.0000i − 0.703679i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −10.0000 −0.438108 −0.219054 0.975713i $$-0.570297\pi$$
−0.219054 + 0.975713i $$0.570297\pi$$
$$522$$ 0 0
$$523$$ 8.00000i 0.349816i 0.984585 + 0.174908i $$0.0559627\pi$$
−0.984585 + 0.174908i $$0.944037\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −16.0000 −0.696971
$$528$$ 0 0
$$529$$ −7.00000 −0.304348
$$530$$ 0 0
$$531$$ 12.0000i 0.520756i
$$532$$ 0 0
$$533$$ − 12.0000i − 0.519778i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ − 36.0000i − 1.55063i
$$540$$ 0 0
$$541$$ − 2.00000i − 0.0859867i −0.999075 0.0429934i $$-0.986311\pi$$
0.999075 0.0429934i $$-0.0136894\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 14.0000 0.599694
$$546$$ 0 0
$$547$$ 8.00000i 0.342055i 0.985266 + 0.171028i $$0.0547087\pi$$
−0.985266 + 0.171028i $$0.945291\pi$$
$$548$$ 0 0
$$549$$ − 6.00000i − 0.256074i
$$550$$ 0 0
$$551$$ 8.00000 0.340811
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 14.0000i 0.593199i 0.955002 + 0.296600i $$0.0958526\pi$$
−0.955002 + 0.296600i $$0.904147\pi$$
$$558$$ 0 0
$$559$$ 16.0000 0.676728
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 16.0000i 0.674320i 0.941447 + 0.337160i $$0.109466\pi$$
−0.941447 + 0.337160i $$0.890534\pi$$
$$564$$ 0 0
$$565$$ − 18.0000i − 0.757266i
$$566$$ 0 0
$$567$$ 36.0000 1.51186
$$568$$ 0 0
$$569$$ 22.0000 0.922288 0.461144 0.887325i $$-0.347439\pi$$
0.461144 + 0.887325i $$0.347439\pi$$
$$570$$ 0 0
$$571$$ − 4.00000i − 0.167395i −0.996491 0.0836974i $$-0.973327\pi$$
0.996491 0.0836974i $$-0.0266729\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 4.00000 0.166812
$$576$$ 0 0
$$577$$ 2.00000 0.0832611 0.0416305 0.999133i $$-0.486745\pi$$
0.0416305 + 0.999133i $$0.486745\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ − 64.0000i − 2.65517i
$$582$$ 0 0
$$583$$ −24.0000 −0.993978
$$584$$ 0 0
$$585$$ −6.00000 −0.248069
$$586$$ 0 0
$$587$$ 48.0000i 1.98117i 0.136892 + 0.990586i $$0.456289\pi$$
−0.136892 + 0.990586i $$0.543711\pi$$
$$588$$ 0 0
$$589$$ − 32.0000i − 1.31854i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 18.0000 0.739171 0.369586 0.929197i $$-0.379500\pi$$
0.369586 + 0.929197i $$0.379500\pi$$
$$594$$ 0 0
$$595$$ − 8.00000i − 0.327968i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 24.0000 0.980613 0.490307 0.871550i $$-0.336885\pi$$
0.490307 + 0.871550i $$0.336885\pi$$
$$600$$ 0 0
$$601$$ −10.0000 −0.407909 −0.203954 0.978980i $$-0.565379\pi$$
−0.203954 + 0.978980i $$0.565379\pi$$
$$602$$ 0 0
$$603$$ 24.0000i 0.977356i
$$604$$ 0 0
$$605$$ 5.00000i 0.203279i
$$606$$ 0 0
$$607$$ −12.0000 −0.487065 −0.243532 0.969893i $$-0.578306\pi$$
−0.243532 + 0.969893i $$0.578306\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ − 8.00000i − 0.323645i
$$612$$ 0 0
$$613$$ 42.0000i 1.69636i 0.529705 + 0.848182i $$0.322303\pi$$
−0.529705 + 0.848182i $$0.677697\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 6.00000 0.241551 0.120775 0.992680i $$-0.461462\pi$$
0.120775 + 0.992680i $$0.461462\pi$$
$$618$$ 0 0
$$619$$ 4.00000i 0.160774i 0.996764 + 0.0803868i $$0.0256155\pi$$
−0.996764 + 0.0803868i $$0.974384\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 24.0000 0.961540
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ − 12.0000i − 0.478471i
$$630$$ 0 0
$$631$$ −16.0000 −0.636950 −0.318475 0.947931i $$-0.603171\pi$$
−0.318475 + 0.947931i $$0.603171\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 12.0000i 0.476205i
$$636$$ 0 0
$$637$$ − 18.0000i − 0.713186i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 18.0000 0.710957 0.355479 0.934684i $$-0.384318\pi$$
0.355479 + 0.934684i $$0.384318\pi$$
$$642$$ 0 0
$$643$$ − 48.0000i − 1.89294i −0.322799 0.946468i $$-0.604624\pi$$
0.322799 0.946468i $$-0.395376\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −12.0000 −0.471769 −0.235884 0.971781i $$-0.575799\pi$$
−0.235884 + 0.971781i $$0.575799\pi$$
$$648$$ 0 0
$$649$$ 16.0000 0.628055
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ − 34.0000i − 1.33052i −0.746611 0.665261i $$-0.768320\pi$$
0.746611 0.665261i $$-0.231680\pi$$
$$654$$ 0 0
$$655$$ 12.0000 0.468879
$$656$$ 0 0
$$657$$ 18.0000 0.702247
$$658$$ 0 0
$$659$$ − 12.0000i − 0.467454i −0.972302 0.233727i $$-0.924908\pi$$
0.972302 0.233727i $$-0.0750921\pi$$
$$660$$ 0 0
$$661$$ 42.0000i 1.63361i 0.576913 + 0.816805i $$0.304257\pi$$
−0.576913 + 0.816805i $$0.695743\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 16.0000 0.620453
$$666$$ 0 0
$$667$$ 8.00000i 0.309761i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −8.00000 −0.308837
$$672$$ 0 0
$$673$$ 18.0000 0.693849 0.346925 0.937893i $$-0.387226\pi$$
0.346925 + 0.937893i $$0.387226\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ − 22.0000i − 0.845529i −0.906240 0.422764i $$-0.861060\pi$$
0.906240 0.422764i $$-0.138940\pi$$
$$678$$ 0 0
$$679$$ −56.0000 −2.14908
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ − 24.0000i − 0.918334i −0.888350 0.459167i $$-0.848148\pi$$
0.888350 0.459167i $$-0.151852\pi$$
$$684$$ 0 0
$$685$$ 10.0000i 0.382080i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −12.0000 −0.457164
$$690$$ 0 0
$$691$$ 44.0000i 1.67384i 0.547326 + 0.836919i $$0.315646\pi$$
−0.547326 + 0.836919i $$0.684354\pi$$
$$692$$ 0 0
$$693$$ − 48.0000i − 1.82337i
$$694$$ 0 0
$$695$$ −12.0000 −0.455186
$$696$$ 0 0
$$697$$ 12.0000 0.454532
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ − 34.0000i − 1.28416i −0.766637 0.642081i $$-0.778071\pi$$
0.766637 0.642081i $$-0.221929\pi$$
$$702$$ 0 0
$$703$$ 24.0000 0.905177
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ − 24.0000i − 0.902613i
$$708$$ 0 0
$$709$$ − 38.0000i − 1.42712i −0.700594 0.713560i $$-0.747082\pi$$
0.700594 0.713560i $$-0.252918\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 32.0000 1.19841
$$714$$ 0 0
$$715$$ 8.00000i 0.299183i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −32.0000 −1.19340 −0.596699 0.802465i $$-0.703521\pi$$
−0.596699 + 0.802465i $$0.703521\pi$$
$$720$$ 0 0
$$721$$ −16.0000 −0.595871
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 2.00000i 0.0742781i
$$726$$ 0 0
$$727$$ −44.0000 −1.63187 −0.815935 0.578144i $$-0.803777\pi$$
−0.815935 + 0.578144i $$0.803777\pi$$
$$728$$ 0 0
$$729$$ 27.0000 1.00000
$$730$$ 0 0
$$731$$ 16.0000i 0.591781i
$$732$$ 0 0
$$733$$ 30.0000i 1.10808i 0.832492 + 0.554038i $$0.186914\pi$$
−0.832492 + 0.554038i $$0.813086\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 32.0000 1.17874
$$738$$ 0 0
$$739$$ 36.0000i 1.32428i 0.749380 + 0.662141i $$0.230352\pi$$
−0.749380 + 0.662141i $$0.769648\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −36.0000 −1.32071 −0.660356 0.750953i $$-0.729595\pi$$
−0.660356 + 0.750953i $$0.729595\pi$$
$$744$$ 0 0
$$745$$ 10.0000 0.366372
$$746$$ 0 0
$$747$$ − 48.0000i − 1.75623i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −24.0000 −0.875772 −0.437886 0.899030i $$-0.644273\pi$$
−0.437886 + 0.899030i $$0.644273\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ − 16.0000i − 0.582300i
$$756$$ 0 0
$$757$$ 10.0000i 0.363456i 0.983349 + 0.181728i $$0.0581691\pi$$
−0.983349 + 0.181728i $$0.941831\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 6.00000 0.217500 0.108750 0.994069i $$-0.465315\pi$$
0.108750 + 0.994069i $$0.465315\pi$$
$$762$$ 0 0
$$763$$ 56.0000i 2.02734i
$$764$$ 0 0
$$765$$ − 6.00000i − 0.216930i
$$766$$ 0 0
$$767$$ 8.00000 0.288863
$$768$$ 0 0
$$769$$ 34.0000 1.22607 0.613036 0.790055i $$-0.289948\pi$$
0.613036 + 0.790055i $$0.289948\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 42.0000i 1.51064i 0.655359 + 0.755318i $$0.272517\pi$$
−0.655359 + 0.755318i $$0.727483\pi$$
$$774$$ 0 0
$$775$$ 8.00000 0.287368
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 24.0000i 0.859889i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −2.00000 −0.0713831
$$786$$ 0 0
$$787$$ 8.00000i 0.285169i 0.989783 + 0.142585i $$0.0455413\pi$$
−0.989783 + 0.142585i $$0.954459\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 72.0000 2.56003
$$792$$ 0 0
$$793$$ −4.00000 −0.142044
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ − 18.0000i − 0.637593i −0.947823 0.318796i $$-0.896721\pi$$
0.947823 0.318796i $$-0.103279\pi$$
$$798$$ 0 0
$$799$$ 8.00000 0.283020
$$800$$ 0 0
$$801$$ 18.0000 0.635999
$$802$$ 0 0
$$803$$ − 24.0000i − 0.846942i
$$804$$ 0 0
$$805$$ 16.0000i 0.563926i
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −42.0000 −1.47664 −0.738321 0.674450i $$-0.764381\pi$$
−0.738321 + 0.674450i $$0.764381\pi$$
$$810$$ 0 0
$$811$$ 28.0000i 0.983213i 0.870817 + 0.491606i $$0.163590\pi$$
−0.870817 + 0.491606i $$0.836410\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 16.0000 0.560456
$$816$$ 0 0
$$817$$ −32.0000 −1.11954
$$818$$ 0 0
$$819$$ − 24.0000i − 0.838628i
$$820$$ 0 0
$$821$$ − 22.0000i − 0.767805i −0.923374 0.383903i $$-0.874580\pi$$
0.923374 0.383903i $$-0.125420\pi$$
$$822$$ 0 0
$$823$$ −4.00000 −0.139431 −0.0697156 0.997567i $$-0.522209\pi$$
−0.0697156 + 0.997567i $$0.522209\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ − 48.0000i − 1.66912i −0.550914 0.834562i $$-0.685721\pi$$
0.550914 0.834562i $$-0.314279\pi$$
$$828$$ 0 0
$$829$$ − 2.00000i − 0.0694629i −0.999397 0.0347314i $$-0.988942\pi$$
0.999397 0.0347314i $$-0.0110576\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 18.0000 0.623663
$$834$$ 0 0
$$835$$ 12.0000i 0.415277i
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 40.0000 1.38095 0.690477 0.723355i $$-0.257401\pi$$
0.690477 + 0.723355i $$0.257401\pi$$
$$840$$ 0 0
$$841$$ 25.0000 0.862069
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ − 9.00000i − 0.309609i
$$846$$ 0 0
$$847$$ −20.0000 −0.687208
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 24.0000i 0.822709i
$$852$$ 0 0
$$853$$ − 38.0000i − 1.30110i −0.759465 0.650548i $$-0.774539\pi$$
0.759465 0.650548i $$-0.225461\pi$$
$$854$$ 0 0
$$855$$ 12.0000 0.410391
$$856$$ 0 0
$$857$$ 6.00000 0.204956 0.102478 0.994735i $$-0.467323\pi$$
0.102478 + 0.994735i $$0.467323\pi$$
$$858$$ 0 0
$$859$$ 4.00000i 0.136478i 0.997669 + 0.0682391i $$0.0217381\pi$$
−0.997669 + 0.0682391i $$0.978262\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 12.0000 0.408485 0.204242 0.978920i $$-0.434527\pi$$
0.204242 + 0.978920i $$0.434527\pi$$
$$864$$ 0 0
$$865$$ 14.0000 0.476014
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 16.0000 0.542139
$$872$$ 0 0
$$873$$ −42.0000 −1.42148
$$874$$ 0 0
$$875$$ 4.00000i 0.135225i
$$876$$ 0 0
$$877$$ 46.0000i 1.55331i 0.629926 + 0.776655i $$0.283085\pi$$
−0.629926 + 0.776655i $$0.716915\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −30.0000 −1.01073 −0.505363 0.862907i $$-0.668641\pi$$
−0.505363 + 0.862907i $$0.668641\pi$$
$$882$$ 0 0
$$883$$ − 16.0000i − 0.538443i −0.963078 0.269221i $$-0.913234\pi$$
0.963078 0.269221i $$-0.0867663\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 20.0000 0.671534 0.335767 0.941945i $$-0.391004\pi$$
0.335767 + 0.941945i $$0.391004\pi$$
$$888$$ 0 0
$$889$$ −48.0000 −1.60987
$$890$$ 0 0
$$891$$ − 36.0000i − 1.20605i
$$892$$ 0 0
$$893$$ 16.0000i 0.535420i
$$894$$ 0 0
$$895$$ 20.0000 0.668526
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 16.0000i 0.533630i
$$900$$ 0 0
$$901$$ − 12.0000i − 0.399778i
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 10.0000 0.332411
$$906$$ 0 0
$$907$$ − 48.0000i − 1.59381i −0.604102 0.796907i $$-0.706468\pi$$
0.604102 0.796907i $$-0.293532\pi$$
$$908$$ 0 0
$$909$$ − 18.0000i − 0.597022i
$$910$$ 0 0
$$911$$ 40.0000 1.32526 0.662630 0.748947i $$-0.269440\pi$$
0.662630 + 0.748947i $$0.269440\pi$$
$$912$$ 0 0
$$913$$ −64.0000 −2.11809
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 48.0000i 1.58510i
$$918$$ 0 0
$$919$$ −8.00000 −0.263896 −0.131948 0.991257i $$-0.542123\pi$$
−0.131948 + 0.991257i $$0.542123\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 6.00000i 0.197279i
$$926$$ 0 0
$$927$$ −12.0000 −0.394132
$$928$$ 0 0
$$929$$ −14.0000 −0.459325 −0.229663 0.973270i $$-0.573762\pi$$
−0.229663 + 0.973270i $$0.573762\pi$$
$$930$$ 0 0
$$931$$ 36.0000i 1.17985i
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −8.00000 −0.261628
$$936$$ 0 0
$$937$$ 38.0000 1.24141 0.620703 0.784046i $$-0.286847\pi$$
0.620703 + 0.784046i $$0.286847\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 46.0000i 1.49956i 0.661689 + 0.749779i $$0.269840\pi$$
−0.661689 + 0.749779i $$0.730160\pi$$
$$942$$ 0 0
$$943$$ −24.0000 −0.781548
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ − 8.00000i − 0.259965i −0.991516 0.129983i $$-0.958508\pi$$
0.991516 0.129983i $$-0.0414921\pi$$
$$948$$ 0 0
$$949$$ − 12.0000i − 0.389536i
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 6.00000 0.194359 0.0971795 0.995267i $$-0.469018\pi$$
0.0971795 + 0.995267i $$0.469018\pi$$
$$954$$ 0 0
$$955$$ − 8.00000i − 0.258874i
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ −40.0000 −1.29167
$$960$$ 0 0
$$961$$ 33.0000 1.06452
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 14.0000i 0.450676i
$$966$$ 0 0
$$967$$ 36.0000 1.15768 0.578841 0.815440i $$-0.303505\pi$$
0.578841 + 0.815440i $$0.303505\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ − 20.0000i − 0.641831i −0.947108 0.320915i $$-0.896010\pi$$
0.947108 0.320915i $$-0.103990\pi$$
$$972$$ 0 0
$$973$$ − 48.0000i − 1.53881i
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 2.00000 0.0639857 0.0319928 0.999488i $$-0.489815\pi$$
0.0319928 + 0.999488i $$0.489815\pi$$
$$978$$ 0 0
$$979$$ − 24.0000i − 0.767043i
$$980$$ 0 0
$$981$$ 42.0000i 1.34096i
$$982$$ 0 0
$$983$$ −36.0000 −1.14822 −0.574111 0.818778i $$-0.694652\pi$$
−0.574111 + 0.818778i $$0.694652\pi$$
$$984$$ 0 0
$$985$$ −22.0000 −0.700978
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ − 32.0000i − 1.01754i
$$990$$ 0 0
$$991$$ −40.0000 −1.27064 −0.635321 0.772248i $$-0.719132\pi$$
−0.635321 + 0.772248i $$0.719132\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 8.00000i 0.253617i
$$996$$ 0 0
$$997$$ 42.0000i 1.33015i 0.746775 + 0.665077i $$0.231601\pi$$
−0.746775 + 0.665077i $$0.768399\pi$$
$$998$$ 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 1280.2.d.j.641.1 2
4.3 odd 2 1280.2.d.a.641.1 2
8.3 odd 2 1280.2.d.a.641.2 2
8.5 even 2 inner 1280.2.d.j.641.2 2
16.3 odd 4 320.2.a.d.1.1 1
16.5 even 4 40.2.a.a.1.1 1
16.11 odd 4 80.2.a.a.1.1 1
16.13 even 4 320.2.a.c.1.1 1
48.5 odd 4 360.2.a.a.1.1 1
48.11 even 4 720.2.a.e.1.1 1
48.29 odd 4 2880.2.a.t.1.1 1
48.35 even 4 2880.2.a.bg.1.1 1
80.3 even 4 1600.2.c.m.449.1 2
80.13 odd 4 1600.2.c.k.449.2 2
80.19 odd 4 1600.2.a.k.1.1 1
80.27 even 4 400.2.c.d.49.2 2
80.29 even 4 1600.2.a.o.1.1 1
80.37 odd 4 200.2.c.b.49.1 2
80.43 even 4 400.2.c.d.49.1 2
80.53 odd 4 200.2.c.b.49.2 2
80.59 odd 4 400.2.a.e.1.1 1
80.67 even 4 1600.2.c.m.449.2 2
80.69 even 4 200.2.a.c.1.1 1
80.77 odd 4 1600.2.c.k.449.1 2
112.5 odd 12 1960.2.q.i.361.1 2
112.27 even 4 3920.2.a.s.1.1 1
112.37 even 12 1960.2.q.h.361.1 2
112.53 even 12 1960.2.q.h.961.1 2
112.69 odd 4 1960.2.a.g.1.1 1
112.101 odd 12 1960.2.q.i.961.1 2
144.5 odd 12 3240.2.q.x.2161.1 2
144.85 even 12 3240.2.q.k.2161.1 2
144.101 odd 12 3240.2.q.x.1081.1 2
144.133 even 12 3240.2.q.k.1081.1 2
176.21 odd 4 4840.2.a.f.1.1 1
176.43 even 4 9680.2.a.q.1.1 1
208.181 even 4 6760.2.a.i.1.1 1
240.53 even 4 1800.2.f.a.649.2 2
240.59 even 4 3600.2.a.h.1.1 1
240.107 odd 4 3600.2.f.t.2449.2 2
240.149 odd 4 1800.2.a.v.1.1 1
240.197 even 4 1800.2.f.a.649.1 2
240.203 odd 4 3600.2.f.t.2449.1 2
560.69 odd 4 9800.2.a.x.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
40.2.a.a.1.1 1 16.5 even 4
80.2.a.a.1.1 1 16.11 odd 4
200.2.a.c.1.1 1 80.69 even 4
200.2.c.b.49.1 2 80.37 odd 4
200.2.c.b.49.2 2 80.53 odd 4
320.2.a.c.1.1 1 16.13 even 4
320.2.a.d.1.1 1 16.3 odd 4
360.2.a.a.1.1 1 48.5 odd 4
400.2.a.e.1.1 1 80.59 odd 4
400.2.c.d.49.1 2 80.43 even 4
400.2.c.d.49.2 2 80.27 even 4
720.2.a.e.1.1 1 48.11 even 4
1280.2.d.a.641.1 2 4.3 odd 2
1280.2.d.a.641.2 2 8.3 odd 2
1280.2.d.j.641.1 2 1.1 even 1 trivial
1280.2.d.j.641.2 2 8.5 even 2 inner
1600.2.a.k.1.1 1 80.19 odd 4
1600.2.a.o.1.1 1 80.29 even 4
1600.2.c.k.449.1 2 80.77 odd 4
1600.2.c.k.449.2 2 80.13 odd 4
1600.2.c.m.449.1 2 80.3 even 4
1600.2.c.m.449.2 2 80.67 even 4
1800.2.a.v.1.1 1 240.149 odd 4
1800.2.f.a.649.1 2 240.197 even 4
1800.2.f.a.649.2 2 240.53 even 4
1960.2.a.g.1.1 1 112.69 odd 4
1960.2.q.h.361.1 2 112.37 even 12
1960.2.q.h.961.1 2 112.53 even 12
1960.2.q.i.361.1 2 112.5 odd 12
1960.2.q.i.961.1 2 112.101 odd 12
2880.2.a.t.1.1 1 48.29 odd 4
2880.2.a.bg.1.1 1 48.35 even 4
3240.2.q.k.1081.1 2 144.133 even 12
3240.2.q.k.2161.1 2 144.85 even 12
3240.2.q.x.1081.1 2 144.101 odd 12
3240.2.q.x.2161.1 2 144.5 odd 12
3600.2.a.h.1.1 1 240.59 even 4
3600.2.f.t.2449.1 2 240.203 odd 4
3600.2.f.t.2449.2 2 240.107 odd 4
3920.2.a.s.1.1 1 112.27 even 4
4840.2.a.f.1.1 1 176.21 odd 4
6760.2.a.i.1.1 1 208.181 even 4
9680.2.a.q.1.1 1 176.43 even 4
9800.2.a.x.1.1 1 560.69 odd 4