# Properties

 Label 2601.2.a.i.1.1 Level $2601$ Weight $2$ Character 2601.1 Self dual yes Analytic conductor $20.769$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2601 = 3^{2} \cdot 17^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2601.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$20.7690895657$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 51) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 2601.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} -1.00000 q^{4} -4.00000 q^{7} -3.00000 q^{8} +O(q^{10})$$ $$q+1.00000 q^{2} -1.00000 q^{4} -4.00000 q^{7} -3.00000 q^{8} -4.00000 q^{11} +2.00000 q^{13} -4.00000 q^{14} -1.00000 q^{16} +4.00000 q^{19} -4.00000 q^{22} +4.00000 q^{23} -5.00000 q^{25} +2.00000 q^{26} +4.00000 q^{28} +4.00000 q^{31} +5.00000 q^{32} -8.00000 q^{37} +4.00000 q^{38} +8.00000 q^{41} +4.00000 q^{43} +4.00000 q^{44} +4.00000 q^{46} +8.00000 q^{47} +9.00000 q^{49} -5.00000 q^{50} -2.00000 q^{52} +6.00000 q^{53} +12.0000 q^{56} -12.0000 q^{59} -8.00000 q^{61} +4.00000 q^{62} +7.00000 q^{64} +12.0000 q^{67} +12.0000 q^{71} -8.00000 q^{74} -4.00000 q^{76} +16.0000 q^{77} -4.00000 q^{79} +8.00000 q^{82} +12.0000 q^{83} +4.00000 q^{86} +12.0000 q^{88} +10.0000 q^{89} -8.00000 q^{91} -4.00000 q^{92} +8.00000 q^{94} -16.0000 q^{97} +9.00000 q^{98} +O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 0.707107 0.353553 0.935414i $$-0.384973\pi$$
0.353553 + 0.935414i $$0.384973\pi$$
$$3$$ 0 0
$$4$$ −1.00000 −0.500000
$$5$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$6$$ 0 0
$$7$$ −4.00000 −1.51186 −0.755929 0.654654i $$-0.772814\pi$$
−0.755929 + 0.654654i $$0.772814\pi$$
$$8$$ −3.00000 −1.06066
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −4.00000 −1.20605 −0.603023 0.797724i $$-0.706037\pi$$
−0.603023 + 0.797724i $$0.706037\pi$$
$$12$$ 0 0
$$13$$ 2.00000 0.554700 0.277350 0.960769i $$-0.410544\pi$$
0.277350 + 0.960769i $$0.410544\pi$$
$$14$$ −4.00000 −1.06904
$$15$$ 0 0
$$16$$ −1.00000 −0.250000
$$17$$ 0 0
$$18$$ 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
$$22$$ −4.00000 −0.852803
$$23$$ 4.00000 0.834058 0.417029 0.908893i $$-0.363071\pi$$
0.417029 + 0.908893i $$0.363071\pi$$
$$24$$ 0 0
$$25$$ −5.00000 −1.00000
$$26$$ 2.00000 0.392232
$$27$$ 0 0
$$28$$ 4.00000 0.755929
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0 0
$$31$$ 4.00000 0.718421 0.359211 0.933257i $$-0.383046\pi$$
0.359211 + 0.933257i $$0.383046\pi$$
$$32$$ 5.00000 0.883883
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −8.00000 −1.31519 −0.657596 0.753371i $$-0.728427\pi$$
−0.657596 + 0.753371i $$0.728427\pi$$
$$38$$ 4.00000 0.648886
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 8.00000 1.24939 0.624695 0.780869i $$-0.285223\pi$$
0.624695 + 0.780869i $$0.285223\pi$$
$$42$$ 0 0
$$43$$ 4.00000 0.609994 0.304997 0.952353i $$-0.401344\pi$$
0.304997 + 0.952353i $$0.401344\pi$$
$$44$$ 4.00000 0.603023
$$45$$ 0 0
$$46$$ 4.00000 0.589768
$$47$$ 8.00000 1.16692 0.583460 0.812142i $$-0.301699\pi$$
0.583460 + 0.812142i $$0.301699\pi$$
$$48$$ 0 0
$$49$$ 9.00000 1.28571
$$50$$ −5.00000 −0.707107
$$51$$ 0 0
$$52$$ −2.00000 −0.277350
$$53$$ 6.00000 0.824163 0.412082 0.911147i $$-0.364802\pi$$
0.412082 + 0.911147i $$0.364802\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 12.0000 1.60357
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −12.0000 −1.56227 −0.781133 0.624364i $$-0.785358\pi$$
−0.781133 + 0.624364i $$0.785358\pi$$
$$60$$ 0 0
$$61$$ −8.00000 −1.02430 −0.512148 0.858898i $$-0.671150\pi$$
−0.512148 + 0.858898i $$0.671150\pi$$
$$62$$ 4.00000 0.508001
$$63$$ 0 0
$$64$$ 7.00000 0.875000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 12.0000 1.46603 0.733017 0.680211i $$-0.238112\pi$$
0.733017 + 0.680211i $$0.238112\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 12.0000 1.42414 0.712069 0.702109i $$-0.247758\pi$$
0.712069 + 0.702109i $$0.247758\pi$$
$$72$$ 0 0
$$73$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$74$$ −8.00000 −0.929981
$$75$$ 0 0
$$76$$ −4.00000 −0.458831
$$77$$ 16.0000 1.82337
$$78$$ 0 0
$$79$$ −4.00000 −0.450035 −0.225018 0.974355i $$-0.572244\pi$$
−0.225018 + 0.974355i $$0.572244\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 8.00000 0.883452
$$83$$ 12.0000 1.31717 0.658586 0.752506i $$-0.271155\pi$$
0.658586 + 0.752506i $$0.271155\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 4.00000 0.431331
$$87$$ 0 0
$$88$$ 12.0000 1.27920
$$89$$ 10.0000 1.06000 0.529999 0.847998i $$-0.322192\pi$$
0.529999 + 0.847998i $$0.322192\pi$$
$$90$$ 0 0
$$91$$ −8.00000 −0.838628
$$92$$ −4.00000 −0.417029
$$93$$ 0 0
$$94$$ 8.00000 0.825137
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −16.0000 −1.62455 −0.812277 0.583272i $$-0.801772\pi$$
−0.812277 + 0.583272i $$0.801772\pi$$
$$98$$ 9.00000 0.909137
$$99$$ 0 0
$$100$$ 5.00000 0.500000
$$101$$ 6.00000 0.597022 0.298511 0.954406i $$-0.403510\pi$$
0.298511 + 0.954406i $$0.403510\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$104$$ −6.00000 −0.588348
$$105$$ 0 0
$$106$$ 6.00000 0.582772
$$107$$ −12.0000 −1.16008 −0.580042 0.814587i $$-0.696964\pi$$
−0.580042 + 0.814587i $$0.696964\pi$$
$$108$$ 0 0
$$109$$ 8.00000 0.766261 0.383131 0.923694i $$-0.374846\pi$$
0.383131 + 0.923694i $$0.374846\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 4.00000 0.377964
$$113$$ 8.00000 0.752577 0.376288 0.926503i $$-0.377200\pi$$
0.376288 + 0.926503i $$0.377200\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ −12.0000 −1.10469
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 5.00000 0.454545
$$122$$ −8.00000 −0.724286
$$123$$ 0 0
$$124$$ −4.00000 −0.359211
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −8.00000 −0.709885 −0.354943 0.934888i $$-0.615500\pi$$
−0.354943 + 0.934888i $$0.615500\pi$$
$$128$$ −3.00000 −0.265165
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 4.00000 0.349482 0.174741 0.984614i $$-0.444091\pi$$
0.174741 + 0.984614i $$0.444091\pi$$
$$132$$ 0 0
$$133$$ −16.0000 −1.38738
$$134$$ 12.0000 1.03664
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 10.0000 0.854358 0.427179 0.904167i $$-0.359507\pi$$
0.427179 + 0.904167i $$0.359507\pi$$
$$138$$ 0 0
$$139$$ −4.00000 −0.339276 −0.169638 0.985506i $$-0.554260\pi$$
−0.169638 + 0.985506i $$0.554260\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 12.0000 1.00702
$$143$$ −8.00000 −0.668994
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 8.00000 0.657596
$$149$$ −6.00000 −0.491539 −0.245770 0.969328i $$-0.579041\pi$$
−0.245770 + 0.969328i $$0.579041\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$152$$ −12.0000 −0.973329
$$153$$ 0 0
$$154$$ 16.0000 1.28932
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −2.00000 −0.159617 −0.0798087 0.996810i $$-0.525431\pi$$
−0.0798087 + 0.996810i $$0.525431\pi$$
$$158$$ −4.00000 −0.318223
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −16.0000 −1.26098
$$162$$ 0 0
$$163$$ 20.0000 1.56652 0.783260 0.621694i $$-0.213555\pi$$
0.783260 + 0.621694i $$0.213555\pi$$
$$164$$ −8.00000 −0.624695
$$165$$ 0 0
$$166$$ 12.0000 0.931381
$$167$$ 12.0000 0.928588 0.464294 0.885681i $$-0.346308\pi$$
0.464294 + 0.885681i $$0.346308\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ 0 0
$$171$$ 0 0
$$172$$ −4.00000 −0.304997
$$173$$ −16.0000 −1.21646 −0.608229 0.793762i $$-0.708120\pi$$
−0.608229 + 0.793762i $$0.708120\pi$$
$$174$$ 0 0
$$175$$ 20.0000 1.51186
$$176$$ 4.00000 0.301511
$$177$$ 0 0
$$178$$ 10.0000 0.749532
$$179$$ 4.00000 0.298974 0.149487 0.988764i $$-0.452238\pi$$
0.149487 + 0.988764i $$0.452238\pi$$
$$180$$ 0 0
$$181$$ −8.00000 −0.594635 −0.297318 0.954779i $$-0.596092\pi$$
−0.297318 + 0.954779i $$0.596092\pi$$
$$182$$ −8.00000 −0.592999
$$183$$ 0 0
$$184$$ −12.0000 −0.884652
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ −8.00000 −0.583460
$$189$$ 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
$$193$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$194$$ −16.0000 −1.14873
$$195$$ 0 0
$$196$$ −9.00000 −0.642857
$$197$$ −16.0000 −1.13995 −0.569976 0.821661i $$-0.693048\pi$$
−0.569976 + 0.821661i $$0.693048\pi$$
$$198$$ 0 0
$$199$$ 20.0000 1.41776 0.708881 0.705328i $$-0.249200\pi$$
0.708881 + 0.705328i $$0.249200\pi$$
$$200$$ 15.0000 1.06066
$$201$$ 0 0
$$202$$ 6.00000 0.422159
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ −2.00000 −0.138675
$$209$$ −16.0000 −1.10674
$$210$$ 0 0
$$211$$ 4.00000 0.275371 0.137686 0.990476i $$-0.456034\pi$$
0.137686 + 0.990476i $$0.456034\pi$$
$$212$$ −6.00000 −0.412082
$$213$$ 0 0
$$214$$ −12.0000 −0.820303
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −16.0000 −1.08615
$$218$$ 8.00000 0.541828
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −16.0000 −1.07144 −0.535720 0.844396i $$-0.679960\pi$$
−0.535720 + 0.844396i $$0.679960\pi$$
$$224$$ −20.0000 −1.33631
$$225$$ 0 0
$$226$$ 8.00000 0.532152
$$227$$ 12.0000 0.796468 0.398234 0.917284i $$-0.369623\pi$$
0.398234 + 0.917284i $$0.369623\pi$$
$$228$$ 0 0
$$229$$ −10.0000 −0.660819 −0.330409 0.943838i $$-0.607187\pi$$
−0.330409 + 0.943838i $$0.607187\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 8.00000 0.524097 0.262049 0.965055i $$-0.415602\pi$$
0.262049 + 0.965055i $$0.415602\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 12.0000 0.781133
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 8.00000 0.517477 0.258738 0.965947i $$-0.416693\pi$$
0.258738 + 0.965947i $$0.416693\pi$$
$$240$$ 0 0
$$241$$ 16.0000 1.03065 0.515325 0.856995i $$-0.327671\pi$$
0.515325 + 0.856995i $$0.327671\pi$$
$$242$$ 5.00000 0.321412
$$243$$ 0 0
$$244$$ 8.00000 0.512148
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 8.00000 0.509028
$$248$$ −12.0000 −0.762001
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −12.0000 −0.757433 −0.378717 0.925513i $$-0.623635\pi$$
−0.378717 + 0.925513i $$0.623635\pi$$
$$252$$ 0 0
$$253$$ −16.0000 −1.00591
$$254$$ −8.00000 −0.501965
$$255$$ 0 0
$$256$$ −17.0000 −1.06250
$$257$$ −2.00000 −0.124757 −0.0623783 0.998053i $$-0.519869\pi$$
−0.0623783 + 0.998053i $$0.519869\pi$$
$$258$$ 0 0
$$259$$ 32.0000 1.98838
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 4.00000 0.247121
$$263$$ 24.0000 1.47990 0.739952 0.672660i $$-0.234848\pi$$
0.739952 + 0.672660i $$0.234848\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ −16.0000 −0.981023
$$267$$ 0 0
$$268$$ −12.0000 −0.733017
$$269$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 10.0000 0.604122
$$275$$ 20.0000 1.20605
$$276$$ 0 0
$$277$$ 8.00000 0.480673 0.240337 0.970690i $$-0.422742\pi$$
0.240337 + 0.970690i $$0.422742\pi$$
$$278$$ −4.00000 −0.239904
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 10.0000 0.596550 0.298275 0.954480i $$-0.403589\pi$$
0.298275 + 0.954480i $$0.403589\pi$$
$$282$$ 0 0
$$283$$ 4.00000 0.237775 0.118888 0.992908i $$-0.462067\pi$$
0.118888 + 0.992908i $$0.462067\pi$$
$$284$$ −12.0000 −0.712069
$$285$$ 0 0
$$286$$ −8.00000 −0.473050
$$287$$ −32.0000 −1.88890
$$288$$ 0 0
$$289$$ 0 0
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 10.0000 0.584206 0.292103 0.956387i $$-0.405645\pi$$
0.292103 + 0.956387i $$0.405645\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 24.0000 1.39497
$$297$$ 0 0
$$298$$ −6.00000 −0.347571
$$299$$ 8.00000 0.462652
$$300$$ 0 0
$$301$$ −16.0000 −0.922225
$$302$$ 0 0
$$303$$ 0 0
$$304$$ −4.00000 −0.229416
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −12.0000 −0.684876 −0.342438 0.939540i $$-0.611253\pi$$
−0.342438 + 0.939540i $$0.611253\pi$$
$$308$$ −16.0000 −0.911685
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 12.0000 0.680458 0.340229 0.940343i $$-0.389495\pi$$
0.340229 + 0.940343i $$0.389495\pi$$
$$312$$ 0 0
$$313$$ −16.0000 −0.904373 −0.452187 0.891923i $$-0.649356\pi$$
−0.452187 + 0.891923i $$0.649356\pi$$
$$314$$ −2.00000 −0.112867
$$315$$ 0 0
$$316$$ 4.00000 0.225018
$$317$$ 32.0000 1.79730 0.898650 0.438667i $$-0.144549\pi$$
0.898650 + 0.438667i $$0.144549\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ −16.0000 −0.891645
$$323$$ 0 0
$$324$$ 0 0
$$325$$ −10.0000 −0.554700
$$326$$ 20.0000 1.10770
$$327$$ 0 0
$$328$$ −24.0000 −1.32518
$$329$$ −32.0000 −1.76422
$$330$$ 0 0
$$331$$ 20.0000 1.09930 0.549650 0.835395i $$-0.314761\pi$$
0.549650 + 0.835395i $$0.314761\pi$$
$$332$$ −12.0000 −0.658586
$$333$$ 0 0
$$334$$ 12.0000 0.656611
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 16.0000 0.871576 0.435788 0.900049i $$-0.356470\pi$$
0.435788 + 0.900049i $$0.356470\pi$$
$$338$$ −9.00000 −0.489535
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −16.0000 −0.866449
$$342$$ 0 0
$$343$$ −8.00000 −0.431959
$$344$$ −12.0000 −0.646997
$$345$$ 0 0
$$346$$ −16.0000 −0.860165
$$347$$ −4.00000 −0.214731 −0.107366 0.994220i $$-0.534242\pi$$
−0.107366 + 0.994220i $$0.534242\pi$$
$$348$$ 0 0
$$349$$ 2.00000 0.107058 0.0535288 0.998566i $$-0.482953\pi$$
0.0535288 + 0.998566i $$0.482953\pi$$
$$350$$ 20.0000 1.06904
$$351$$ 0 0
$$352$$ −20.0000 −1.06600
$$353$$ −18.0000 −0.958043 −0.479022 0.877803i $$-0.659008\pi$$
−0.479022 + 0.877803i $$0.659008\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −10.0000 −0.529999
$$357$$ 0 0
$$358$$ 4.00000 0.211407
$$359$$ 32.0000 1.68890 0.844448 0.535638i $$-0.179929\pi$$
0.844448 + 0.535638i $$0.179929\pi$$
$$360$$ 0 0
$$361$$ −3.00000 −0.157895
$$362$$ −8.00000 −0.420471
$$363$$ 0 0
$$364$$ 8.00000 0.419314
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 12.0000 0.626395 0.313197 0.949688i $$-0.398600\pi$$
0.313197 + 0.949688i $$0.398600\pi$$
$$368$$ −4.00000 −0.208514
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −24.0000 −1.24602
$$372$$ 0 0
$$373$$ 26.0000 1.34623 0.673114 0.739538i $$-0.264956\pi$$
0.673114 + 0.739538i $$0.264956\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ −24.0000 −1.23771
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −20.0000 −1.02733 −0.513665 0.857991i $$-0.671713\pi$$
−0.513665 + 0.857991i $$0.671713\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 8.00000 0.409316
$$383$$ −16.0000 −0.817562 −0.408781 0.912633i $$-0.634046\pi$$
−0.408781 + 0.912633i $$0.634046\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 16.0000 0.812277
$$389$$ −6.00000 −0.304212 −0.152106 0.988364i $$-0.548606\pi$$
−0.152106 + 0.988364i $$0.548606\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ −27.0000 −1.36371
$$393$$ 0 0
$$394$$ −16.0000 −0.806068
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −8.00000 −0.401508 −0.200754 0.979642i $$-0.564339\pi$$
−0.200754 + 0.979642i $$0.564339\pi$$
$$398$$ 20.0000 1.00251
$$399$$ 0 0
$$400$$ 5.00000 0.250000
$$401$$ 24.0000 1.19850 0.599251 0.800561i $$-0.295465\pi$$
0.599251 + 0.800561i $$0.295465\pi$$
$$402$$ 0 0
$$403$$ 8.00000 0.398508
$$404$$ −6.00000 −0.298511
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 32.0000 1.58618
$$408$$ 0 0
$$409$$ 10.0000 0.494468 0.247234 0.968956i $$-0.420478\pi$$
0.247234 + 0.968956i $$0.420478\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 48.0000 2.36193
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 10.0000 0.490290
$$417$$ 0 0
$$418$$ −16.0000 −0.782586
$$419$$ −4.00000 −0.195413 −0.0977064 0.995215i $$-0.531151\pi$$
−0.0977064 + 0.995215i $$0.531151\pi$$
$$420$$ 0 0
$$421$$ −22.0000 −1.07221 −0.536107 0.844150i $$-0.680106\pi$$
−0.536107 + 0.844150i $$0.680106\pi$$
$$422$$ 4.00000 0.194717
$$423$$ 0 0
$$424$$ −18.0000 −0.874157
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 32.0000 1.54859
$$428$$ 12.0000 0.580042
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 20.0000 0.963366 0.481683 0.876346i $$-0.340026\pi$$
0.481683 + 0.876346i $$0.340026\pi$$
$$432$$ 0 0
$$433$$ 2.00000 0.0961139 0.0480569 0.998845i $$-0.484697\pi$$
0.0480569 + 0.998845i $$0.484697\pi$$
$$434$$ −16.0000 −0.768025
$$435$$ 0 0
$$436$$ −8.00000 −0.383131
$$437$$ 16.0000 0.765384
$$438$$ 0 0
$$439$$ 36.0000 1.71819 0.859093 0.511819i $$-0.171028\pi$$
0.859093 + 0.511819i $$0.171028\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 20.0000 0.950229 0.475114 0.879924i $$-0.342407\pi$$
0.475114 + 0.879924i $$0.342407\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −16.0000 −0.757622
$$447$$ 0 0
$$448$$ −28.0000 −1.32288
$$449$$ −8.00000 −0.377543 −0.188772 0.982021i $$-0.560451\pi$$
−0.188772 + 0.982021i $$0.560451\pi$$
$$450$$ 0 0
$$451$$ −32.0000 −1.50682
$$452$$ −8.00000 −0.376288
$$453$$ 0 0
$$454$$ 12.0000 0.563188
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −38.0000 −1.77757 −0.888783 0.458329i $$-0.848448\pi$$
−0.888783 + 0.458329i $$0.848448\pi$$
$$458$$ −10.0000 −0.467269
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −34.0000 −1.58354 −0.791769 0.610821i $$-0.790840\pi$$
−0.791769 + 0.610821i $$0.790840\pi$$
$$462$$ 0 0
$$463$$ −40.0000 −1.85896 −0.929479 0.368875i $$-0.879743\pi$$
−0.929479 + 0.368875i $$0.879743\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 8.00000 0.370593
$$467$$ 4.00000 0.185098 0.0925490 0.995708i $$-0.470499\pi$$
0.0925490 + 0.995708i $$0.470499\pi$$
$$468$$ 0 0
$$469$$ −48.0000 −2.21643
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 36.0000 1.65703
$$473$$ −16.0000 −0.735681
$$474$$ 0 0
$$475$$ −20.0000 −0.917663
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 8.00000 0.365911
$$479$$ 12.0000 0.548294 0.274147 0.961688i $$-0.411605\pi$$
0.274147 + 0.961688i $$0.411605\pi$$
$$480$$ 0 0
$$481$$ −16.0000 −0.729537
$$482$$ 16.0000 0.728780
$$483$$ 0 0
$$484$$ −5.00000 −0.227273
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −4.00000 −0.181257 −0.0906287 0.995885i $$-0.528888\pi$$
−0.0906287 + 0.995885i $$0.528888\pi$$
$$488$$ 24.0000 1.08643
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −20.0000 −0.902587 −0.451294 0.892375i $$-0.649037\pi$$
−0.451294 + 0.892375i $$0.649037\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 8.00000 0.359937
$$495$$ 0 0
$$496$$ −4.00000 −0.179605
$$497$$ −48.0000 −2.15309
$$498$$ 0 0
$$499$$ 36.0000 1.61158 0.805791 0.592200i $$-0.201741\pi$$
0.805791 + 0.592200i $$0.201741\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ −12.0000 −0.535586
$$503$$ −12.0000 −0.535054 −0.267527 0.963550i $$-0.586206\pi$$
−0.267527 + 0.963550i $$0.586206\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ −16.0000 −0.711287
$$507$$ 0 0
$$508$$ 8.00000 0.354943
$$509$$ 18.0000 0.797836 0.398918 0.916987i $$-0.369386\pi$$
0.398918 + 0.916987i $$0.369386\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −11.0000 −0.486136
$$513$$ 0 0
$$514$$ −2.00000 −0.0882162
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −32.0000 −1.40736
$$518$$ 32.0000 1.40600
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −24.0000 −1.05146 −0.525730 0.850652i $$-0.676208\pi$$
−0.525730 + 0.850652i $$0.676208\pi$$
$$522$$ 0 0
$$523$$ −12.0000 −0.524723 −0.262362 0.964970i $$-0.584501\pi$$
−0.262362 + 0.964970i $$0.584501\pi$$
$$524$$ −4.00000 −0.174741
$$525$$ 0 0
$$526$$ 24.0000 1.04645
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −7.00000 −0.304348
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 16.0000 0.693688
$$533$$ 16.0000 0.693037
$$534$$ 0 0
$$535$$ 0 0
$$536$$ −36.0000 −1.55496
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −36.0000 −1.55063
$$540$$ 0 0
$$541$$ −40.0000 −1.71973 −0.859867 0.510518i $$-0.829454\pi$$
−0.859867 + 0.510518i $$0.829454\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −36.0000 −1.53925 −0.769624 0.638497i $$-0.779557\pi$$
−0.769624 + 0.638497i $$0.779557\pi$$
$$548$$ −10.0000 −0.427179
$$549$$ 0 0
$$550$$ 20.0000 0.852803
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 16.0000 0.680389
$$554$$ 8.00000 0.339887
$$555$$ 0 0
$$556$$ 4.00000 0.169638
$$557$$ −18.0000 −0.762684 −0.381342 0.924434i $$-0.624538\pi$$
−0.381342 + 0.924434i $$0.624538\pi$$
$$558$$ 0 0
$$559$$ 8.00000 0.338364
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 10.0000 0.421825
$$563$$ 44.0000 1.85438 0.927189 0.374593i $$-0.122217\pi$$
0.927189 + 0.374593i $$0.122217\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 4.00000 0.168133
$$567$$ 0 0
$$568$$ −36.0000 −1.51053
$$569$$ 26.0000 1.08998 0.544988 0.838444i $$-0.316534\pi$$
0.544988 + 0.838444i $$0.316534\pi$$
$$570$$ 0 0
$$571$$ 20.0000 0.836974 0.418487 0.908223i $$-0.362561\pi$$
0.418487 + 0.908223i $$0.362561\pi$$
$$572$$ 8.00000 0.334497
$$573$$ 0 0
$$574$$ −32.0000 −1.33565
$$575$$ −20.0000 −0.834058
$$576$$ 0 0
$$577$$ 30.0000 1.24892 0.624458 0.781058i $$-0.285320\pi$$
0.624458 + 0.781058i $$0.285320\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −48.0000 −1.99138
$$582$$ 0 0
$$583$$ −24.0000 −0.993978
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 10.0000 0.413096
$$587$$ 12.0000 0.495293 0.247647 0.968850i $$-0.420343\pi$$
0.247647 + 0.968850i $$0.420343\pi$$
$$588$$ 0 0
$$589$$ 16.0000 0.659269
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 8.00000 0.328798
$$593$$ −46.0000 −1.88899 −0.944497 0.328521i $$-0.893450\pi$$
−0.944497 + 0.328521i $$0.893450\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 6.00000 0.245770
$$597$$ 0 0
$$598$$ 8.00000 0.327144
$$599$$ 8.00000 0.326871 0.163436 0.986554i $$-0.447742\pi$$
0.163436 + 0.986554i $$0.447742\pi$$
$$600$$ 0 0
$$601$$ 16.0000 0.652654 0.326327 0.945257i $$-0.394189\pi$$
0.326327 + 0.945257i $$0.394189\pi$$
$$602$$ −16.0000 −0.652111
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 4.00000 0.162355 0.0811775 0.996700i $$-0.474132\pi$$
0.0811775 + 0.996700i $$0.474132\pi$$
$$608$$ 20.0000 0.811107
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 16.0000 0.647291
$$612$$ 0 0
$$613$$ 6.00000 0.242338 0.121169 0.992632i $$-0.461336\pi$$
0.121169 + 0.992632i $$0.461336\pi$$
$$614$$ −12.0000 −0.484281
$$615$$ 0 0
$$616$$ −48.0000 −1.93398
$$617$$ −24.0000 −0.966204 −0.483102 0.875564i $$-0.660490\pi$$
−0.483102 + 0.875564i $$0.660490\pi$$
$$618$$ 0 0
$$619$$ 36.0000 1.44696 0.723481 0.690344i $$-0.242541\pi$$
0.723481 + 0.690344i $$0.242541\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 12.0000 0.481156
$$623$$ −40.0000 −1.60257
$$624$$ 0 0
$$625$$ 25.0000 1.00000
$$626$$ −16.0000 −0.639489
$$627$$ 0 0
$$628$$ 2.00000 0.0798087
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 8.00000 0.318475 0.159237 0.987240i $$-0.449096\pi$$
0.159237 + 0.987240i $$0.449096\pi$$
$$632$$ 12.0000 0.477334
$$633$$ 0 0
$$634$$ 32.0000 1.27088
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 18.0000 0.713186
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 8.00000 0.315981 0.157991 0.987441i $$-0.449498\pi$$
0.157991 + 0.987441i $$0.449498\pi$$
$$642$$ 0 0
$$643$$ −4.00000 −0.157745 −0.0788723 0.996885i $$-0.525132\pi$$
−0.0788723 + 0.996885i $$0.525132\pi$$
$$644$$ 16.0000 0.630488
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −32.0000 −1.25805 −0.629025 0.777385i $$-0.716546\pi$$
−0.629025 + 0.777385i $$0.716546\pi$$
$$648$$ 0 0
$$649$$ 48.0000 1.88416
$$650$$ −10.0000 −0.392232
$$651$$ 0 0
$$652$$ −20.0000 −0.783260
$$653$$ 32.0000 1.25226 0.626128 0.779720i $$-0.284639\pi$$
0.626128 + 0.779720i $$0.284639\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −8.00000 −0.312348
$$657$$ 0 0
$$658$$ −32.0000 −1.24749
$$659$$ 4.00000 0.155818 0.0779089 0.996960i $$-0.475176\pi$$
0.0779089 + 0.996960i $$0.475176\pi$$
$$660$$ 0 0
$$661$$ 42.0000 1.63361 0.816805 0.576913i $$-0.195743\pi$$
0.816805 + 0.576913i $$0.195743\pi$$
$$662$$ 20.0000 0.777322
$$663$$ 0 0
$$664$$ −36.0000 −1.39707
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ −12.0000 −0.464294
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 32.0000 1.23535
$$672$$ 0 0
$$673$$ 32.0000 1.23351 0.616755 0.787155i $$-0.288447\pi$$
0.616755 + 0.787155i $$0.288447\pi$$
$$674$$ 16.0000 0.616297
$$675$$ 0 0
$$676$$ 9.00000 0.346154
$$677$$ 48.0000 1.84479 0.922395 0.386248i $$-0.126229\pi$$
0.922395 + 0.386248i $$0.126229\pi$$
$$678$$ 0 0
$$679$$ 64.0000 2.45609
$$680$$ 0 0
$$681$$ 0 0
$$682$$ −16.0000 −0.612672
$$683$$ −12.0000 −0.459167 −0.229584 0.973289i $$-0.573736\pi$$
−0.229584 + 0.973289i $$0.573736\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −8.00000 −0.305441
$$687$$ 0 0
$$688$$ −4.00000 −0.152499
$$689$$ 12.0000 0.457164
$$690$$ 0 0
$$691$$ 20.0000 0.760836 0.380418 0.924815i $$-0.375780\pi$$
0.380418 + 0.924815i $$0.375780\pi$$
$$692$$ 16.0000 0.608229
$$693$$ 0 0
$$694$$ −4.00000 −0.151838
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 2.00000 0.0757011
$$699$$ 0 0
$$700$$ −20.0000 −0.755929
$$701$$ −34.0000 −1.28416 −0.642081 0.766637i $$-0.721929\pi$$
−0.642081 + 0.766637i $$0.721929\pi$$
$$702$$ 0 0
$$703$$ −32.0000 −1.20690
$$704$$ −28.0000 −1.05529
$$705$$ 0 0
$$706$$ −18.0000 −0.677439
$$707$$ −24.0000 −0.902613
$$708$$ 0 0
$$709$$ 40.0000 1.50223 0.751116 0.660171i $$-0.229516\pi$$
0.751116 + 0.660171i $$0.229516\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −30.0000 −1.12430
$$713$$ 16.0000 0.599205
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −4.00000 −0.149487
$$717$$ 0 0
$$718$$ 32.0000 1.19423
$$719$$ −36.0000 −1.34257 −0.671287 0.741198i $$-0.734258\pi$$
−0.671287 + 0.741198i $$0.734258\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −3.00000 −0.111648
$$723$$ 0 0
$$724$$ 8.00000 0.297318
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 8.00000 0.296704 0.148352 0.988935i $$-0.452603\pi$$
0.148352 + 0.988935i $$0.452603\pi$$
$$728$$ 24.0000 0.889499
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 34.0000 1.25582 0.627909 0.778287i $$-0.283911\pi$$
0.627909 + 0.778287i $$0.283911\pi$$
$$734$$ 12.0000 0.442928
$$735$$ 0 0
$$736$$ 20.0000 0.737210
$$737$$ −48.0000 −1.76810
$$738$$ 0 0
$$739$$ 4.00000 0.147142 0.0735712 0.997290i $$-0.476560\pi$$
0.0735712 + 0.997290i $$0.476560\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ −24.0000 −0.881068
$$743$$ −36.0000 −1.32071 −0.660356 0.750953i $$-0.729595\pi$$
−0.660356 + 0.750953i $$0.729595\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 26.0000 0.951928
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 48.0000 1.75388
$$750$$ 0 0
$$751$$ 20.0000 0.729810 0.364905 0.931045i $$-0.381101\pi$$
0.364905 + 0.931045i $$0.381101\pi$$
$$752$$ −8.00000 −0.291730
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 38.0000 1.38113 0.690567 0.723269i $$-0.257361\pi$$
0.690567 + 0.723269i $$0.257361\pi$$
$$758$$ −20.0000 −0.726433
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −6.00000 −0.217500 −0.108750 0.994069i $$-0.534685\pi$$
−0.108750 + 0.994069i $$0.534685\pi$$
$$762$$ 0 0
$$763$$ −32.0000 −1.15848
$$764$$ −8.00000 −0.289430
$$765$$ 0 0
$$766$$ −16.0000 −0.578103
$$767$$ −24.0000 −0.866590
$$768$$ 0 0
$$769$$ −34.0000 −1.22607 −0.613036 0.790055i $$-0.710052\pi$$
−0.613036 + 0.790055i $$0.710052\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −6.00000 −0.215805 −0.107903 0.994161i $$-0.534413\pi$$
−0.107903 + 0.994161i $$0.534413\pi$$
$$774$$ 0 0
$$775$$ −20.0000 −0.718421
$$776$$ 48.0000 1.72310
$$777$$ 0 0
$$778$$ −6.00000 −0.215110
$$779$$ 32.0000 1.14652
$$780$$ 0 0
$$781$$ −48.0000 −1.71758
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −9.00000 −0.321429
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 12.0000 0.427754 0.213877 0.976861i $$-0.431391\pi$$
0.213877 + 0.976861i $$0.431391\pi$$
$$788$$ 16.0000 0.569976
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −32.0000 −1.13779
$$792$$ 0 0
$$793$$ −16.0000 −0.568177
$$794$$ −8.00000 −0.283909
$$795$$ 0 0
$$796$$ −20.0000 −0.708881
$$797$$ −18.0000 −0.637593 −0.318796 0.947823i $$-0.603279\pi$$
−0.318796 + 0.947823i $$0.603279\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ −25.0000 −0.883883
$$801$$ 0 0
$$802$$ 24.0000 0.847469
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 8.00000 0.281788
$$807$$ 0 0
$$808$$ −18.0000 −0.633238
$$809$$ 40.0000 1.40633 0.703163 0.711029i $$-0.251771\pi$$
0.703163 + 0.711029i $$0.251771\pi$$
$$810$$ 0 0
$$811$$ −4.00000 −0.140459 −0.0702295 0.997531i $$-0.522373\pi$$
−0.0702295 + 0.997531i $$0.522373\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 32.0000 1.12160
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 16.0000 0.559769
$$818$$ 10.0000 0.349642
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 32.0000 1.11681 0.558404 0.829569i $$-0.311414\pi$$
0.558404 + 0.829569i $$0.311414\pi$$
$$822$$ 0 0
$$823$$ 44.0000 1.53374 0.766872 0.641800i $$-0.221812\pi$$
0.766872 + 0.641800i $$0.221812\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 48.0000 1.67013
$$827$$ 12.0000 0.417281 0.208640 0.977992i $$-0.433096\pi$$
0.208640 + 0.977992i $$0.433096\pi$$
$$828$$ 0 0
$$829$$ −2.00000 −0.0694629 −0.0347314 0.999397i $$-0.511058\pi$$
−0.0347314 + 0.999397i $$0.511058\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 14.0000 0.485363
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 16.0000 0.553372
$$837$$ 0 0
$$838$$ −4.00000 −0.138178
$$839$$ −44.0000 −1.51905 −0.759524 0.650479i $$-0.774568\pi$$
−0.759524 + 0.650479i $$0.774568\pi$$
$$840$$ 0 0
$$841$$ −29.0000 −1.00000
$$842$$ −22.0000 −0.758170
$$843$$ 0 0
$$844$$ −4.00000 −0.137686
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −20.0000 −0.687208
$$848$$ −6.00000 −0.206041
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −32.0000 −1.09695
$$852$$ 0 0
$$853$$ 24.0000 0.821744 0.410872 0.911693i $$-0.365224\pi$$
0.410872 + 0.911693i $$0.365224\pi$$
$$854$$ 32.0000 1.09502
$$855$$ 0 0
$$856$$ 36.0000 1.23045
$$857$$ −8.00000 −0.273275 −0.136637 0.990621i $$-0.543630\pi$$
−0.136637 + 0.990621i $$0.543630\pi$$
$$858$$ 0 0
$$859$$ 4.00000 0.136478 0.0682391 0.997669i $$-0.478262\pi$$
0.0682391 + 0.997669i $$0.478262\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 20.0000 0.681203
$$863$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 2.00000 0.0679628
$$867$$ 0 0
$$868$$ 16.0000 0.543075
$$869$$ 16.0000 0.542763
$$870$$ 0 0
$$871$$ 24.0000 0.813209
$$872$$ −24.0000 −0.812743
$$873$$ 0 0
$$874$$ 16.0000 0.541208
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −40.0000 −1.35070 −0.675352 0.737496i $$-0.736008\pi$$
−0.675352 + 0.737496i $$0.736008\pi$$
$$878$$ 36.0000 1.21494
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 24.0000 0.808581 0.404290 0.914631i $$-0.367519\pi$$
0.404290 + 0.914631i $$0.367519\pi$$
$$882$$ 0 0
$$883$$ −20.0000 −0.673054 −0.336527 0.941674i $$-0.609252\pi$$
−0.336527 + 0.941674i $$0.609252\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 20.0000 0.671913
$$887$$ −4.00000 −0.134307 −0.0671534 0.997743i $$-0.521392\pi$$
−0.0671534 + 0.997743i $$0.521392\pi$$
$$888$$ 0 0
$$889$$ 32.0000 1.07325
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 16.0000 0.535720
$$893$$ 32.0000 1.07084
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 12.0000 0.400892
$$897$$ 0 0
$$898$$ −8.00000 −0.266963
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 0 0
$$902$$ −32.0000 −1.06548
$$903$$ 0 0
$$904$$ −24.0000 −0.798228
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −28.0000 −0.929725 −0.464862 0.885383i $$-0.653896\pi$$
−0.464862 + 0.885383i $$0.653896\pi$$
$$908$$ −12.0000 −0.398234
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −28.0000 −0.927681 −0.463841 0.885919i $$-0.653529\pi$$
−0.463841 + 0.885919i $$0.653529\pi$$
$$912$$ 0 0
$$913$$ −48.0000 −1.58857
$$914$$ −38.0000 −1.25693
$$915$$ 0 0
$$916$$ 10.0000 0.330409
$$917$$ −16.0000 −0.528367
$$918$$ 0 0
$$919$$ 24.0000 0.791687 0.395843 0.918318i $$-0.370452\pi$$
0.395843 + 0.918318i $$0.370452\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ −34.0000 −1.11973
$$923$$ 24.0000 0.789970
$$924$$ 0 0
$$925$$ 40.0000 1.31519
$$926$$ −40.0000 −1.31448
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −24.0000 −0.787414 −0.393707 0.919236i $$-0.628808\pi$$
−0.393707 + 0.919236i $$0.628808\pi$$
$$930$$ 0 0
$$931$$ 36.0000 1.17985
$$932$$ −8.00000 −0.262049
$$933$$ 0 0
$$934$$ 4.00000 0.130884
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −26.0000 −0.849383 −0.424691 0.905338i $$-0.639617\pi$$
−0.424691 + 0.905338i $$0.639617\pi$$
$$938$$ −48.0000 −1.56726
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 48.0000 1.56476 0.782378 0.622804i $$-0.214007\pi$$
0.782378 + 0.622804i $$0.214007\pi$$
$$942$$ 0 0
$$943$$ 32.0000 1.04206
$$944$$ 12.0000 0.390567
$$945$$ 0 0
$$946$$ −16.0000 −0.520205
$$947$$ −12.0000 −0.389948 −0.194974 0.980808i $$-0.562462\pi$$
−0.194974 + 0.980808i $$0.562462\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ −20.0000 −0.648886
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 42.0000 1.36051 0.680257 0.732974i $$-0.261868\pi$$
0.680257 + 0.732974i $$0.261868\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ −8.00000 −0.258738
$$957$$ 0 0
$$958$$ 12.0000 0.387702
$$959$$ −40.0000 −1.29167
$$960$$ 0 0
$$961$$ −15.0000 −0.483871
$$962$$ −16.0000 −0.515861
$$963$$ 0 0
$$964$$ −16.0000 −0.515325
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −24.0000 −0.771788 −0.385894 0.922543i $$-0.626107\pi$$
−0.385894 + 0.922543i $$0.626107\pi$$
$$968$$ −15.0000 −0.482118
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 36.0000 1.15529 0.577647 0.816286i $$-0.303971\pi$$
0.577647 + 0.816286i $$0.303971\pi$$
$$972$$ 0 0
$$973$$ 16.0000 0.512936
$$974$$ −4.00000 −0.128168
$$975$$ 0 0
$$976$$ 8.00000 0.256074
$$977$$ −46.0000 −1.47167 −0.735835 0.677161i $$-0.763210\pi$$
−0.735835 + 0.677161i $$0.763210\pi$$
$$978$$ 0 0
$$979$$ −40.0000 −1.27841
$$980$$ 0 0
$$981$$ 0 0
$$982$$ −20.0000 −0.638226
$$983$$ −20.0000 −0.637901 −0.318950 0.947771i $$-0.603330\pi$$
−0.318950 + 0.947771i $$0.603330\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ −8.00000 −0.254514
$$989$$ 16.0000 0.508770
$$990$$ 0 0
$$991$$ −12.0000 −0.381193 −0.190596 0.981669i $$-0.561042\pi$$
−0.190596 + 0.981669i $$0.561042\pi$$
$$992$$ 20.0000 0.635001
$$993$$ 0 0
$$994$$ −48.0000 −1.52247
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 8.00000 0.253363 0.126681 0.991943i $$-0.459567\pi$$
0.126681 + 0.991943i $$0.459567\pi$$
$$998$$ 36.0000 1.13956
$$999$$ 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 2601.2.a.i.1.1 1
3.2 odd 2 867.2.a.a.1.1 1
17.4 even 4 153.2.d.a.118.1 2
17.13 even 4 153.2.d.a.118.2 2
17.16 even 2 2601.2.a.j.1.1 1
51.2 odd 8 867.2.e.d.616.1 4
51.5 even 16 867.2.h.d.688.2 8
51.8 odd 8 867.2.e.d.829.2 4
51.11 even 16 867.2.h.d.733.2 8
51.14 even 16 867.2.h.d.757.2 8
51.20 even 16 867.2.h.d.757.1 8
51.23 even 16 867.2.h.d.733.1 8
51.26 odd 8 867.2.e.d.829.1 4
51.29 even 16 867.2.h.d.688.1 8
51.32 odd 8 867.2.e.d.616.2 4
51.38 odd 4 51.2.d.b.16.2 yes 2
51.41 even 16 867.2.h.d.712.2 8
51.44 even 16 867.2.h.d.712.1 8
51.47 odd 4 51.2.d.b.16.1 2
51.50 odd 2 867.2.a.b.1.1 1
68.47 odd 4 2448.2.c.j.577.1 2
68.55 odd 4 2448.2.c.j.577.2 2
204.47 even 4 816.2.c.c.577.2 2
204.191 even 4 816.2.c.c.577.1 2
255.38 even 4 1275.2.d.b.424.1 2
255.47 even 4 1275.2.d.b.424.2 2
255.89 odd 4 1275.2.g.a.526.1 2
255.98 even 4 1275.2.d.d.424.1 2
255.149 odd 4 1275.2.g.a.526.2 2
255.242 even 4 1275.2.d.d.424.2 2
408.149 odd 4 3264.2.c.e.577.2 2
408.251 even 4 3264.2.c.d.577.1 2
408.293 odd 4 3264.2.c.e.577.1 2
408.395 even 4 3264.2.c.d.577.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
51.2.d.b.16.1 2 51.47 odd 4
51.2.d.b.16.2 yes 2 51.38 odd 4
153.2.d.a.118.1 2 17.4 even 4
153.2.d.a.118.2 2 17.13 even 4
816.2.c.c.577.1 2 204.191 even 4
816.2.c.c.577.2 2 204.47 even 4
867.2.a.a.1.1 1 3.2 odd 2
867.2.a.b.1.1 1 51.50 odd 2
867.2.e.d.616.1 4 51.2 odd 8
867.2.e.d.616.2 4 51.32 odd 8
867.2.e.d.829.1 4 51.26 odd 8
867.2.e.d.829.2 4 51.8 odd 8
867.2.h.d.688.1 8 51.29 even 16
867.2.h.d.688.2 8 51.5 even 16
867.2.h.d.712.1 8 51.44 even 16
867.2.h.d.712.2 8 51.41 even 16
867.2.h.d.733.1 8 51.23 even 16
867.2.h.d.733.2 8 51.11 even 16
867.2.h.d.757.1 8 51.20 even 16
867.2.h.d.757.2 8 51.14 even 16
1275.2.d.b.424.1 2 255.38 even 4
1275.2.d.b.424.2 2 255.47 even 4
1275.2.d.d.424.1 2 255.98 even 4
1275.2.d.d.424.2 2 255.242 even 4
1275.2.g.a.526.1 2 255.89 odd 4
1275.2.g.a.526.2 2 255.149 odd 4
2448.2.c.j.577.1 2 68.47 odd 4
2448.2.c.j.577.2 2 68.55 odd 4
2601.2.a.i.1.1 1 1.1 even 1 trivial
2601.2.a.j.1.1 1 17.16 even 2
3264.2.c.d.577.1 2 408.251 even 4
3264.2.c.d.577.2 2 408.395 even 4
3264.2.c.e.577.1 2 408.293 odd 4
3264.2.c.e.577.2 2 408.149 odd 4