# Properties

 Label 980.2.a.c.1.1 Level $980$ Weight $2$ Character 980.1 Self dual yes Analytic conductor $7.825$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$980 = 2^{2} \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 980.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$7.82533939809$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 140) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 980.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{3} -1.00000 q^{5} -2.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{3} -1.00000 q^{5} -2.00000 q^{9} +3.00000 q^{11} +1.00000 q^{13} +1.00000 q^{15} +3.00000 q^{17} -2.00000 q^{19} -6.00000 q^{23} +1.00000 q^{25} +5.00000 q^{27} -9.00000 q^{29} -8.00000 q^{31} -3.00000 q^{33} -10.0000 q^{37} -1.00000 q^{39} +2.00000 q^{43} +2.00000 q^{45} +3.00000 q^{47} -3.00000 q^{51} -3.00000 q^{55} +2.00000 q^{57} -12.0000 q^{59} -8.00000 q^{61} -1.00000 q^{65} +8.00000 q^{67} +6.00000 q^{69} -14.0000 q^{73} -1.00000 q^{75} +5.00000 q^{79} +1.00000 q^{81} +12.0000 q^{83} -3.00000 q^{85} +9.00000 q^{87} -12.0000 q^{89} +8.00000 q^{93} +2.00000 q^{95} -17.0000 q^{97} -6.00000 q^{99} +O(q^{100})$$

## 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 −0.288675 0.957427i $$-0.593215\pi$$
−0.288675 + 0.957427i $$0.593215\pi$$
$$4$$ 0 0
$$5$$ −1.00000 −0.447214
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ −2.00000 −0.666667
$$10$$ 0 0
$$11$$ 3.00000 0.904534 0.452267 0.891883i $$-0.350615\pi$$
0.452267 + 0.891883i $$0.350615\pi$$
$$12$$ 0 0
$$13$$ 1.00000 0.277350 0.138675 0.990338i $$-0.455716\pi$$
0.138675 + 0.990338i $$0.455716\pi$$
$$14$$ 0 0
$$15$$ 1.00000 0.258199
$$16$$ 0 0
$$17$$ 3.00000 0.727607 0.363803 0.931476i $$-0.381478\pi$$
0.363803 + 0.931476i $$0.381478\pi$$
$$18$$ 0 0
$$19$$ −2.00000 −0.458831 −0.229416 0.973329i $$-0.573682\pi$$
−0.229416 + 0.973329i $$0.573682\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −6.00000 −1.25109 −0.625543 0.780189i $$-0.715123\pi$$
−0.625543 + 0.780189i $$0.715123\pi$$
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ 0 0
$$27$$ 5.00000 0.962250
$$28$$ 0 0
$$29$$ −9.00000 −1.67126 −0.835629 0.549294i $$-0.814897\pi$$
−0.835629 + 0.549294i $$0.814897\pi$$
$$30$$ 0 0
$$31$$ −8.00000 −1.43684 −0.718421 0.695608i $$-0.755135\pi$$
−0.718421 + 0.695608i $$0.755135\pi$$
$$32$$ 0 0
$$33$$ −3.00000 −0.522233
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −10.0000 −1.64399 −0.821995 0.569495i $$-0.807139\pi$$
−0.821995 + 0.569495i $$0.807139\pi$$
$$38$$ 0 0
$$39$$ −1.00000 −0.160128
$$40$$ 0 0
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ 2.00000 0.304997 0.152499 0.988304i $$-0.451268\pi$$
0.152499 + 0.988304i $$0.451268\pi$$
$$44$$ 0 0
$$45$$ 2.00000 0.298142
$$46$$ 0 0
$$47$$ 3.00000 0.437595 0.218797 0.975770i $$-0.429787\pi$$
0.218797 + 0.975770i $$0.429787\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ −3.00000 −0.420084
$$52$$ 0 0
$$53$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$54$$ 0 0
$$55$$ −3.00000 −0.404520
$$56$$ 0 0
$$57$$ 2.00000 0.264906
$$58$$ 0 0
$$59$$ −12.0000 −1.56227 −0.781133 0.624364i $$-0.785358\pi$$
−0.781133 + 0.624364i $$0.785358\pi$$
$$60$$ 0 0
$$61$$ −8.00000 −1.02430 −0.512148 0.858898i $$-0.671150\pi$$
−0.512148 + 0.858898i $$0.671150\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −1.00000 −0.124035
$$66$$ 0 0
$$67$$ 8.00000 0.977356 0.488678 0.872464i $$-0.337479\pi$$
0.488678 + 0.872464i $$0.337479\pi$$
$$68$$ 0 0
$$69$$ 6.00000 0.722315
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ −14.0000 −1.63858 −0.819288 0.573382i $$-0.805631\pi$$
−0.819288 + 0.573382i $$0.805631\pi$$
$$74$$ 0 0
$$75$$ −1.00000 −0.115470
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 5.00000 0.562544 0.281272 0.959628i $$-0.409244\pi$$
0.281272 + 0.959628i $$0.409244\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ 12.0000 1.31717 0.658586 0.752506i $$-0.271155\pi$$
0.658586 + 0.752506i $$0.271155\pi$$
$$84$$ 0 0
$$85$$ −3.00000 −0.325396
$$86$$ 0 0
$$87$$ 9.00000 0.964901
$$88$$ 0 0
$$89$$ −12.0000 −1.27200 −0.635999 0.771690i $$-0.719412\pi$$
−0.635999 + 0.771690i $$0.719412\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 8.00000 0.829561
$$94$$ 0 0
$$95$$ 2.00000 0.205196
$$96$$ 0 0
$$97$$ −17.0000 −1.72609 −0.863044 0.505128i $$-0.831445\pi$$
−0.863044 + 0.505128i $$0.831445\pi$$
$$98$$ 0 0
$$99$$ −6.00000 −0.603023
$$100$$ 0 0
$$101$$ 6.00000 0.597022 0.298511 0.954406i $$-0.403510\pi$$
0.298511 + 0.954406i $$0.403510\pi$$
$$102$$ 0 0
$$103$$ 7.00000 0.689730 0.344865 0.938652i $$-0.387925\pi$$
0.344865 + 0.938652i $$0.387925\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −6.00000 −0.580042 −0.290021 0.957020i $$-0.593662\pi$$
−0.290021 + 0.957020i $$0.593662\pi$$
$$108$$ 0 0
$$109$$ −19.0000 −1.81987 −0.909935 0.414751i $$-0.863869\pi$$
−0.909935 + 0.414751i $$0.863869\pi$$
$$110$$ 0 0
$$111$$ 10.0000 0.949158
$$112$$ 0 0
$$113$$ −6.00000 −0.564433 −0.282216 0.959351i $$-0.591070\pi$$
−0.282216 + 0.959351i $$0.591070\pi$$
$$114$$ 0 0
$$115$$ 6.00000 0.559503
$$116$$ 0 0
$$117$$ −2.00000 −0.184900
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −2.00000 −0.181818
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ 20.0000 1.77471 0.887357 0.461084i $$-0.152539\pi$$
0.887357 + 0.461084i $$0.152539\pi$$
$$128$$ 0 0
$$129$$ −2.00000 −0.176090
$$130$$ 0 0
$$131$$ 18.0000 1.57267 0.786334 0.617802i $$-0.211977\pi$$
0.786334 + 0.617802i $$0.211977\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ −5.00000 −0.430331
$$136$$ 0 0
$$137$$ 12.0000 1.02523 0.512615 0.858619i $$-0.328677\pi$$
0.512615 + 0.858619i $$0.328677\pi$$
$$138$$ 0 0
$$139$$ −2.00000 −0.169638 −0.0848189 0.996396i $$-0.527031\pi$$
−0.0848189 + 0.996396i $$0.527031\pi$$
$$140$$ 0 0
$$141$$ −3.00000 −0.252646
$$142$$ 0 0
$$143$$ 3.00000 0.250873
$$144$$ 0 0
$$145$$ 9.00000 0.747409
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 18.0000 1.47462 0.737309 0.675556i $$-0.236096\pi$$
0.737309 + 0.675556i $$0.236096\pi$$
$$150$$ 0 0
$$151$$ −19.0000 −1.54620 −0.773099 0.634285i $$-0.781294\pi$$
−0.773099 + 0.634285i $$0.781294\pi$$
$$152$$ 0 0
$$153$$ −6.00000 −0.485071
$$154$$ 0 0
$$155$$ 8.00000 0.642575
$$156$$ 0 0
$$157$$ 22.0000 1.75579 0.877896 0.478852i $$-0.158947\pi$$
0.877896 + 0.478852i $$0.158947\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 2.00000 0.156652 0.0783260 0.996928i $$-0.475042\pi$$
0.0783260 + 0.996928i $$0.475042\pi$$
$$164$$ 0 0
$$165$$ 3.00000 0.233550
$$166$$ 0 0
$$167$$ −9.00000 −0.696441 −0.348220 0.937413i $$-0.613214\pi$$
−0.348220 + 0.937413i $$0.613214\pi$$
$$168$$ 0 0
$$169$$ −12.0000 −0.923077
$$170$$ 0 0
$$171$$ 4.00000 0.305888
$$172$$ 0 0
$$173$$ 3.00000 0.228086 0.114043 0.993476i $$-0.463620\pi$$
0.114043 + 0.993476i $$0.463620\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 12.0000 0.901975
$$178$$ 0 0
$$179$$ 12.0000 0.896922 0.448461 0.893802i $$-0.351972\pi$$
0.448461 + 0.893802i $$0.351972\pi$$
$$180$$ 0 0
$$181$$ −8.00000 −0.594635 −0.297318 0.954779i $$-0.596092\pi$$
−0.297318 + 0.954779i $$0.596092\pi$$
$$182$$ 0 0
$$183$$ 8.00000 0.591377
$$184$$ 0 0
$$185$$ 10.0000 0.735215
$$186$$ 0 0
$$187$$ 9.00000 0.658145
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 3.00000 0.217072 0.108536 0.994092i $$-0.465384\pi$$
0.108536 + 0.994092i $$0.465384\pi$$
$$192$$ 0 0
$$193$$ −4.00000 −0.287926 −0.143963 0.989583i $$-0.545985\pi$$
−0.143963 + 0.989583i $$0.545985\pi$$
$$194$$ 0 0
$$195$$ 1.00000 0.0716115
$$196$$ 0 0
$$197$$ 12.0000 0.854965 0.427482 0.904024i $$-0.359401\pi$$
0.427482 + 0.904024i $$0.359401\pi$$
$$198$$ 0 0
$$199$$ −20.0000 −1.41776 −0.708881 0.705328i $$-0.750800\pi$$
−0.708881 + 0.705328i $$0.750800\pi$$
$$200$$ 0 0
$$201$$ −8.00000 −0.564276
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 12.0000 0.834058
$$208$$ 0 0
$$209$$ −6.00000 −0.415029
$$210$$ 0 0
$$211$$ 5.00000 0.344214 0.172107 0.985078i $$-0.444942\pi$$
0.172107 + 0.985078i $$0.444942\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −2.00000 −0.136399
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 14.0000 0.946032
$$220$$ 0 0
$$221$$ 3.00000 0.201802
$$222$$ 0 0
$$223$$ −17.0000 −1.13840 −0.569202 0.822198i $$-0.692748\pi$$
−0.569202 + 0.822198i $$0.692748\pi$$
$$224$$ 0 0
$$225$$ −2.00000 −0.133333
$$226$$ 0 0
$$227$$ 27.0000 1.79205 0.896026 0.444001i $$-0.146441\pi$$
0.896026 + 0.444001i $$0.146441\pi$$
$$228$$ 0 0
$$229$$ 16.0000 1.05731 0.528655 0.848837i $$-0.322697\pi$$
0.528655 + 0.848837i $$0.322697\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 24.0000 1.57229 0.786146 0.618041i $$-0.212073\pi$$
0.786146 + 0.618041i $$0.212073\pi$$
$$234$$ 0 0
$$235$$ −3.00000 −0.195698
$$236$$ 0 0
$$237$$ −5.00000 −0.324785
$$238$$ 0 0
$$239$$ 9.00000 0.582162 0.291081 0.956698i $$-0.405985\pi$$
0.291081 + 0.956698i $$0.405985\pi$$
$$240$$ 0 0
$$241$$ 10.0000 0.644157 0.322078 0.946713i $$-0.395619\pi$$
0.322078 + 0.946713i $$0.395619\pi$$
$$242$$ 0 0
$$243$$ −16.0000 −1.02640
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −2.00000 −0.127257
$$248$$ 0 0
$$249$$ −12.0000 −0.760469
$$250$$ 0 0
$$251$$ −6.00000 −0.378717 −0.189358 0.981908i $$-0.560641\pi$$
−0.189358 + 0.981908i $$0.560641\pi$$
$$252$$ 0 0
$$253$$ −18.0000 −1.13165
$$254$$ 0 0
$$255$$ 3.00000 0.187867
$$256$$ 0 0
$$257$$ 6.00000 0.374270 0.187135 0.982334i $$-0.440080\pi$$
0.187135 + 0.982334i $$0.440080\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 18.0000 1.11417
$$262$$ 0 0
$$263$$ −30.0000 −1.84988 −0.924940 0.380114i $$-0.875885\pi$$
−0.924940 + 0.380114i $$0.875885\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 12.0000 0.734388
$$268$$ 0 0
$$269$$ −18.0000 −1.09748 −0.548740 0.835993i $$-0.684892\pi$$
−0.548740 + 0.835993i $$0.684892\pi$$
$$270$$ 0 0
$$271$$ 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
$$275$$ 3.00000 0.180907
$$276$$ 0 0
$$277$$ −22.0000 −1.32185 −0.660926 0.750451i $$-0.729836\pi$$
−0.660926 + 0.750451i $$0.729836\pi$$
$$278$$ 0 0
$$279$$ 16.0000 0.957895
$$280$$ 0 0
$$281$$ −21.0000 −1.25275 −0.626377 0.779520i $$-0.715463\pi$$
−0.626377 + 0.779520i $$0.715463\pi$$
$$282$$ 0 0
$$283$$ −11.0000 −0.653882 −0.326941 0.945045i $$-0.606018\pi$$
−0.326941 + 0.945045i $$0.606018\pi$$
$$284$$ 0 0
$$285$$ −2.00000 −0.118470
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −8.00000 −0.470588
$$290$$ 0 0
$$291$$ 17.0000 0.996558
$$292$$ 0 0
$$293$$ 15.0000 0.876309 0.438155 0.898900i $$-0.355632\pi$$
0.438155 + 0.898900i $$0.355632\pi$$
$$294$$ 0 0
$$295$$ 12.0000 0.698667
$$296$$ 0 0
$$297$$ 15.0000 0.870388
$$298$$ 0 0
$$299$$ −6.00000 −0.346989
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ −6.00000 −0.344691
$$304$$ 0 0
$$305$$ 8.00000 0.458079
$$306$$ 0 0
$$307$$ 13.0000 0.741949 0.370975 0.928643i $$-0.379024\pi$$
0.370975 + 0.928643i $$0.379024\pi$$
$$308$$ 0 0
$$309$$ −7.00000 −0.398216
$$310$$ 0 0
$$311$$ −18.0000 −1.02069 −0.510343 0.859971i $$-0.670482\pi$$
−0.510343 + 0.859971i $$0.670482\pi$$
$$312$$ 0 0
$$313$$ 13.0000 0.734803 0.367402 0.930062i $$-0.380247\pi$$
0.367402 + 0.930062i $$0.380247\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −18.0000 −1.01098 −0.505490 0.862832i $$-0.668688\pi$$
−0.505490 + 0.862832i $$0.668688\pi$$
$$318$$ 0 0
$$319$$ −27.0000 −1.51171
$$320$$ 0 0
$$321$$ 6.00000 0.334887
$$322$$ 0 0
$$323$$ −6.00000 −0.333849
$$324$$ 0 0
$$325$$ 1.00000 0.0554700
$$326$$ 0 0
$$327$$ 19.0000 1.05070
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 20.0000 1.09930 0.549650 0.835395i $$-0.314761\pi$$
0.549650 + 0.835395i $$0.314761\pi$$
$$332$$ 0 0
$$333$$ 20.0000 1.09599
$$334$$ 0 0
$$335$$ −8.00000 −0.437087
$$336$$ 0 0
$$337$$ 2.00000 0.108947 0.0544735 0.998515i $$-0.482652\pi$$
0.0544735 + 0.998515i $$0.482652\pi$$
$$338$$ 0 0
$$339$$ 6.00000 0.325875
$$340$$ 0 0
$$341$$ −24.0000 −1.29967
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ −6.00000 −0.323029
$$346$$ 0 0
$$347$$ 30.0000 1.61048 0.805242 0.592946i $$-0.202035\pi$$
0.805242 + 0.592946i $$0.202035\pi$$
$$348$$ 0 0
$$349$$ 10.0000 0.535288 0.267644 0.963518i $$-0.413755\pi$$
0.267644 + 0.963518i $$0.413755\pi$$
$$350$$ 0 0
$$351$$ 5.00000 0.266880
$$352$$ 0 0
$$353$$ 15.0000 0.798369 0.399185 0.916871i $$-0.369293\pi$$
0.399185 + 0.916871i $$0.369293\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 0 0
$$361$$ −15.0000 −0.789474
$$362$$ 0 0
$$363$$ 2.00000 0.104973
$$364$$ 0 0
$$365$$ 14.0000 0.732793
$$366$$ 0 0
$$367$$ −5.00000 −0.260998 −0.130499 0.991448i $$-0.541658\pi$$
−0.130499 + 0.991448i $$0.541658\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −4.00000 −0.207112 −0.103556 0.994624i $$-0.533022\pi$$
−0.103556 + 0.994624i $$0.533022\pi$$
$$374$$ 0 0
$$375$$ 1.00000 0.0516398
$$376$$ 0 0
$$377$$ −9.00000 −0.463524
$$378$$ 0 0
$$379$$ −4.00000 −0.205466 −0.102733 0.994709i $$-0.532759\pi$$
−0.102733 + 0.994709i $$0.532759\pi$$
$$380$$ 0 0
$$381$$ −20.0000 −1.02463
$$382$$ 0 0
$$383$$ −36.0000 −1.83951 −0.919757 0.392488i $$-0.871614\pi$$
−0.919757 + 0.392488i $$0.871614\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −4.00000 −0.203331
$$388$$ 0 0
$$389$$ 9.00000 0.456318 0.228159 0.973624i $$-0.426729\pi$$
0.228159 + 0.973624i $$0.426729\pi$$
$$390$$ 0 0
$$391$$ −18.0000 −0.910299
$$392$$ 0 0
$$393$$ −18.0000 −0.907980
$$394$$ 0 0
$$395$$ −5.00000 −0.251577
$$396$$ 0 0
$$397$$ −5.00000 −0.250943 −0.125471 0.992097i $$-0.540044\pi$$
−0.125471 + 0.992097i $$0.540044\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −15.0000 −0.749064 −0.374532 0.927214i $$-0.622197\pi$$
−0.374532 + 0.927214i $$0.622197\pi$$
$$402$$ 0 0
$$403$$ −8.00000 −0.398508
$$404$$ 0 0
$$405$$ −1.00000 −0.0496904
$$406$$ 0 0
$$407$$ −30.0000 −1.48704
$$408$$ 0 0
$$409$$ −26.0000 −1.28562 −0.642809 0.766027i $$-0.722231\pi$$
−0.642809 + 0.766027i $$0.722231\pi$$
$$410$$ 0 0
$$411$$ −12.0000 −0.591916
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −12.0000 −0.589057
$$416$$ 0 0
$$417$$ 2.00000 0.0979404
$$418$$ 0 0
$$419$$ 24.0000 1.17248 0.586238 0.810139i $$-0.300608\pi$$
0.586238 + 0.810139i $$0.300608\pi$$
$$420$$ 0 0
$$421$$ 29.0000 1.41337 0.706687 0.707527i $$-0.250189\pi$$
0.706687 + 0.707527i $$0.250189\pi$$
$$422$$ 0 0
$$423$$ −6.00000 −0.291730
$$424$$ 0 0
$$425$$ 3.00000 0.145521
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ −3.00000 −0.144841
$$430$$ 0 0
$$431$$ 15.0000 0.722525 0.361262 0.932464i $$-0.382346\pi$$
0.361262 + 0.932464i $$0.382346\pi$$
$$432$$ 0 0
$$433$$ −14.0000 −0.672797 −0.336399 0.941720i $$-0.609209\pi$$
−0.336399 + 0.941720i $$0.609209\pi$$
$$434$$ 0 0
$$435$$ −9.00000 −0.431517
$$436$$ 0 0
$$437$$ 12.0000 0.574038
$$438$$ 0 0
$$439$$ 10.0000 0.477274 0.238637 0.971109i $$-0.423299\pi$$
0.238637 + 0.971109i $$0.423299\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −6.00000 −0.285069 −0.142534 0.989790i $$-0.545525\pi$$
−0.142534 + 0.989790i $$0.545525\pi$$
$$444$$ 0 0
$$445$$ 12.0000 0.568855
$$446$$ 0 0
$$447$$ −18.0000 −0.851371
$$448$$ 0 0
$$449$$ 15.0000 0.707894 0.353947 0.935266i $$-0.384839\pi$$
0.353947 + 0.935266i $$0.384839\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 19.0000 0.892698
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −28.0000 −1.30978 −0.654892 0.755722i $$-0.727286\pi$$
−0.654892 + 0.755722i $$0.727286\pi$$
$$458$$ 0 0
$$459$$ 15.0000 0.700140
$$460$$ 0 0
$$461$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$462$$ 0 0
$$463$$ 8.00000 0.371792 0.185896 0.982569i $$-0.440481\pi$$
0.185896 + 0.982569i $$0.440481\pi$$
$$464$$ 0 0
$$465$$ −8.00000 −0.370991
$$466$$ 0 0
$$467$$ −15.0000 −0.694117 −0.347059 0.937843i $$-0.612820\pi$$
−0.347059 + 0.937843i $$0.612820\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −22.0000 −1.01371
$$472$$ 0 0
$$473$$ 6.00000 0.275880
$$474$$ 0 0
$$475$$ −2.00000 −0.0917663
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −6.00000 −0.274147 −0.137073 0.990561i $$-0.543770\pi$$
−0.137073 + 0.990561i $$0.543770\pi$$
$$480$$ 0 0
$$481$$ −10.0000 −0.455961
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 17.0000 0.771930
$$486$$ 0 0
$$487$$ −10.0000 −0.453143 −0.226572 0.973995i $$-0.572752\pi$$
−0.226572 + 0.973995i $$0.572752\pi$$
$$488$$ 0 0
$$489$$ −2.00000 −0.0904431
$$490$$ 0 0
$$491$$ −15.0000 −0.676941 −0.338470 0.940977i $$-0.609909\pi$$
−0.338470 + 0.940977i $$0.609909\pi$$
$$492$$ 0 0
$$493$$ −27.0000 −1.21602
$$494$$ 0 0
$$495$$ 6.00000 0.269680
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −25.0000 −1.11915 −0.559577 0.828778i $$-0.689036\pi$$
−0.559577 + 0.828778i $$0.689036\pi$$
$$500$$ 0 0
$$501$$ 9.00000 0.402090
$$502$$ 0 0
$$503$$ 33.0000 1.47140 0.735699 0.677309i $$-0.236854\pi$$
0.735699 + 0.677309i $$0.236854\pi$$
$$504$$ 0 0
$$505$$ −6.00000 −0.266996
$$506$$ 0 0
$$507$$ 12.0000 0.532939
$$508$$ 0 0
$$509$$ −18.0000 −0.797836 −0.398918 0.916987i $$-0.630614\pi$$
−0.398918 + 0.916987i $$0.630614\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ −10.0000 −0.441511
$$514$$ 0 0
$$515$$ −7.00000 −0.308457
$$516$$ 0 0
$$517$$ 9.00000 0.395820
$$518$$ 0 0
$$519$$ −3.00000 −0.131685
$$520$$ 0 0
$$521$$ 30.0000 1.31432 0.657162 0.753749i $$-0.271757\pi$$
0.657162 + 0.753749i $$0.271757\pi$$
$$522$$ 0 0
$$523$$ −20.0000 −0.874539 −0.437269 0.899331i $$-0.644054\pi$$
−0.437269 + 0.899331i $$0.644054\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −24.0000 −1.04546
$$528$$ 0 0
$$529$$ 13.0000 0.565217
$$530$$ 0 0
$$531$$ 24.0000 1.04151
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 6.00000 0.259403
$$536$$ 0 0
$$537$$ −12.0000 −0.517838
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −25.0000 −1.07483 −0.537417 0.843317i $$-0.680600\pi$$
−0.537417 + 0.843317i $$0.680600\pi$$
$$542$$ 0 0
$$543$$ 8.00000 0.343313
$$544$$ 0 0
$$545$$ 19.0000 0.813871
$$546$$ 0 0
$$547$$ 8.00000 0.342055 0.171028 0.985266i $$-0.445291\pi$$
0.171028 + 0.985266i $$0.445291\pi$$
$$548$$ 0 0
$$549$$ 16.0000 0.682863
$$550$$ 0 0
$$551$$ 18.0000 0.766826
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ −10.0000 −0.424476
$$556$$ 0 0
$$557$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$558$$ 0 0
$$559$$ 2.00000 0.0845910
$$560$$ 0 0
$$561$$ −9.00000 −0.379980
$$562$$ 0 0
$$563$$ 12.0000 0.505740 0.252870 0.967500i $$-0.418626\pi$$
0.252870 + 0.967500i $$0.418626\pi$$
$$564$$ 0 0
$$565$$ 6.00000 0.252422
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −6.00000 −0.251533 −0.125767 0.992060i $$-0.540139\pi$$
−0.125767 + 0.992060i $$0.540139\pi$$
$$570$$ 0 0
$$571$$ −4.00000 −0.167395 −0.0836974 0.996491i $$-0.526673\pi$$
−0.0836974 + 0.996491i $$0.526673\pi$$
$$572$$ 0 0
$$573$$ −3.00000 −0.125327
$$574$$ 0 0
$$575$$ −6.00000 −0.250217
$$576$$ 0 0
$$577$$ −47.0000 −1.95664 −0.978318 0.207109i $$-0.933594\pi$$
−0.978318 + 0.207109i $$0.933594\pi$$
$$578$$ 0 0
$$579$$ 4.00000 0.166234
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 2.00000 0.0826898
$$586$$ 0 0
$$587$$ 24.0000 0.990586 0.495293 0.868726i $$-0.335061\pi$$
0.495293 + 0.868726i $$0.335061\pi$$
$$588$$ 0 0
$$589$$ 16.0000 0.659269
$$590$$ 0 0
$$591$$ −12.0000 −0.493614
$$592$$ 0 0
$$593$$ 33.0000 1.35515 0.677574 0.735455i $$-0.263031\pi$$
0.677574 + 0.735455i $$0.263031\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 20.0000 0.818546
$$598$$ 0 0
$$599$$ −9.00000 −0.367730 −0.183865 0.982952i $$-0.558861\pi$$
−0.183865 + 0.982952i $$0.558861\pi$$
$$600$$ 0 0
$$601$$ 22.0000 0.897399 0.448699 0.893683i $$-0.351887\pi$$
0.448699 + 0.893683i $$0.351887\pi$$
$$602$$ 0 0
$$603$$ −16.0000 −0.651570
$$604$$ 0 0
$$605$$ 2.00000 0.0813116
$$606$$ 0 0
$$607$$ 1.00000 0.0405887 0.0202944 0.999794i $$-0.493540\pi$$
0.0202944 + 0.999794i $$0.493540\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 3.00000 0.121367
$$612$$ 0 0
$$613$$ 2.00000 0.0807792 0.0403896 0.999184i $$-0.487140\pi$$
0.0403896 + 0.999184i $$0.487140\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 30.0000 1.20775 0.603877 0.797077i $$-0.293622\pi$$
0.603877 + 0.797077i $$0.293622\pi$$
$$618$$ 0 0
$$619$$ 10.0000 0.401934 0.200967 0.979598i $$-0.435592\pi$$
0.200967 + 0.979598i $$0.435592\pi$$
$$620$$ 0 0
$$621$$ −30.0000 −1.20386
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 0 0
$$627$$ 6.00000 0.239617
$$628$$ 0 0
$$629$$ −30.0000 −1.19618
$$630$$ 0 0
$$631$$ −25.0000 −0.995234 −0.497617 0.867397i $$-0.665792\pi$$
−0.497617 + 0.867397i $$0.665792\pi$$
$$632$$ 0 0
$$633$$ −5.00000 −0.198732
$$634$$ 0 0
$$635$$ −20.0000 −0.793676
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −30.0000 −1.18493 −0.592464 0.805597i $$-0.701845\pi$$
−0.592464 + 0.805597i $$0.701845\pi$$
$$642$$ 0 0
$$643$$ −41.0000 −1.61688 −0.808441 0.588577i $$-0.799688\pi$$
−0.808441 + 0.588577i $$0.799688\pi$$
$$644$$ 0 0
$$645$$ 2.00000 0.0787499
$$646$$ 0 0
$$647$$ −48.0000 −1.88707 −0.943537 0.331266i $$-0.892524\pi$$
−0.943537 + 0.331266i $$0.892524\pi$$
$$648$$ 0 0
$$649$$ −36.0000 −1.41312
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −6.00000 −0.234798 −0.117399 0.993085i $$-0.537456\pi$$
−0.117399 + 0.993085i $$0.537456\pi$$
$$654$$ 0 0
$$655$$ −18.0000 −0.703318
$$656$$ 0 0
$$657$$ 28.0000 1.09238
$$658$$ 0 0
$$659$$ −33.0000 −1.28550 −0.642749 0.766077i $$-0.722206\pi$$
−0.642749 + 0.766077i $$0.722206\pi$$
$$660$$ 0 0
$$661$$ −8.00000 −0.311164 −0.155582 0.987823i $$-0.549725\pi$$
−0.155582 + 0.987823i $$0.549725\pi$$
$$662$$ 0 0
$$663$$ −3.00000 −0.116510
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 54.0000 2.09089
$$668$$ 0 0
$$669$$ 17.0000 0.657258
$$670$$ 0 0
$$671$$ −24.0000 −0.926510
$$672$$ 0 0
$$673$$ 20.0000 0.770943 0.385472 0.922720i $$-0.374039\pi$$
0.385472 + 0.922720i $$0.374039\pi$$
$$674$$ 0 0
$$675$$ 5.00000 0.192450
$$676$$ 0 0
$$677$$ −15.0000 −0.576497 −0.288248 0.957556i $$-0.593073\pi$$
−0.288248 + 0.957556i $$0.593073\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −27.0000 −1.03464
$$682$$ 0 0
$$683$$ 24.0000 0.918334 0.459167 0.888350i $$-0.348148\pi$$
0.459167 + 0.888350i $$0.348148\pi$$
$$684$$ 0 0
$$685$$ −12.0000 −0.458496
$$686$$ 0 0
$$687$$ −16.0000 −0.610438
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 28.0000 1.06517 0.532585 0.846376i $$-0.321221\pi$$
0.532585 + 0.846376i $$0.321221\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 2.00000 0.0758643
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ −24.0000 −0.907763
$$700$$ 0 0
$$701$$ 3.00000 0.113308 0.0566542 0.998394i $$-0.481957\pi$$
0.0566542 + 0.998394i $$0.481957\pi$$
$$702$$ 0 0
$$703$$ 20.0000 0.754314
$$704$$ 0 0
$$705$$ 3.00000 0.112987
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −1.00000 −0.0375558 −0.0187779 0.999824i $$-0.505978\pi$$
−0.0187779 + 0.999824i $$0.505978\pi$$
$$710$$ 0 0
$$711$$ −10.0000 −0.375029
$$712$$ 0 0
$$713$$ 48.0000 1.79761
$$714$$ 0 0
$$715$$ −3.00000 −0.112194
$$716$$ 0 0
$$717$$ −9.00000 −0.336111
$$718$$ 0 0
$$719$$ 18.0000 0.671287 0.335643 0.941989i $$-0.391046\pi$$
0.335643 + 0.941989i $$0.391046\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ −10.0000 −0.371904
$$724$$ 0 0
$$725$$ −9.00000 −0.334252
$$726$$ 0 0
$$727$$ −32.0000 −1.18681 −0.593407 0.804902i $$-0.702218\pi$$
−0.593407 + 0.804902i $$0.702218\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ 6.00000 0.221918
$$732$$ 0 0
$$733$$ 13.0000 0.480166 0.240083 0.970752i $$-0.422825\pi$$
0.240083 + 0.970752i $$0.422825\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 24.0000 0.884051
$$738$$ 0 0
$$739$$ 11.0000 0.404642 0.202321 0.979319i $$-0.435152\pi$$
0.202321 + 0.979319i $$0.435152\pi$$
$$740$$ 0 0
$$741$$ 2.00000 0.0734718
$$742$$ 0 0
$$743$$ 48.0000 1.76095 0.880475 0.474093i $$-0.157224\pi$$
0.880475 + 0.474093i $$0.157224\pi$$
$$744$$ 0 0
$$745$$ −18.0000 −0.659469
$$746$$ 0 0
$$747$$ −24.0000 −0.878114
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 53.0000 1.93400 0.966999 0.254781i $$-0.0820034\pi$$
0.966999 + 0.254781i $$0.0820034\pi$$
$$752$$ 0 0
$$753$$ 6.00000 0.218652
$$754$$ 0 0
$$755$$ 19.0000 0.691481
$$756$$ 0 0
$$757$$ −16.0000 −0.581530 −0.290765 0.956795i $$-0.593910\pi$$
−0.290765 + 0.956795i $$0.593910\pi$$
$$758$$ 0 0
$$759$$ 18.0000 0.653359
$$760$$ 0 0
$$761$$ 42.0000 1.52250 0.761249 0.648459i $$-0.224586\pi$$
0.761249 + 0.648459i $$0.224586\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 6.00000 0.216930
$$766$$ 0 0
$$767$$ −12.0000 −0.433295
$$768$$ 0 0
$$769$$ −2.00000 −0.0721218 −0.0360609 0.999350i $$-0.511481\pi$$
−0.0360609 + 0.999350i $$0.511481\pi$$
$$770$$ 0 0
$$771$$ −6.00000 −0.216085
$$772$$ 0 0
$$773$$ −15.0000 −0.539513 −0.269756 0.962929i $$-0.586943\pi$$
−0.269756 + 0.962929i $$0.586943\pi$$
$$774$$ 0 0
$$775$$ −8.00000 −0.287368
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ −45.0000 −1.60817
$$784$$ 0 0
$$785$$ −22.0000 −0.785214
$$786$$ 0 0
$$787$$ −5.00000 −0.178231 −0.0891154 0.996021i $$-0.528404\pi$$
−0.0891154 + 0.996021i $$0.528404\pi$$
$$788$$ 0 0
$$789$$ 30.0000 1.06803
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −8.00000 −0.284088
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 3.00000 0.106265 0.0531327 0.998587i $$-0.483079\pi$$
0.0531327 + 0.998587i $$0.483079\pi$$
$$798$$ 0 0
$$799$$ 9.00000 0.318397
$$800$$ 0 0
$$801$$ 24.0000 0.847998
$$802$$ 0 0
$$803$$ −42.0000 −1.48215
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 18.0000 0.633630
$$808$$ 0 0
$$809$$ 9.00000 0.316423 0.158212 0.987405i $$-0.449427\pi$$
0.158212 + 0.987405i $$0.449427\pi$$
$$810$$ 0 0
$$811$$ 34.0000 1.19390 0.596951 0.802278i $$-0.296379\pi$$
0.596951 + 0.802278i $$0.296379\pi$$
$$812$$ 0 0
$$813$$ −16.0000 −0.561144
$$814$$ 0 0
$$815$$ −2.00000 −0.0700569
$$816$$ 0 0
$$817$$ −4.00000 −0.139942
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −15.0000 −0.523504 −0.261752 0.965135i $$-0.584300\pi$$
−0.261752 + 0.965135i $$0.584300\pi$$
$$822$$ 0 0
$$823$$ −40.0000 −1.39431 −0.697156 0.716919i $$-0.745552\pi$$
−0.697156 + 0.716919i $$0.745552\pi$$
$$824$$ 0 0
$$825$$ −3.00000 −0.104447
$$826$$ 0 0
$$827$$ −42.0000 −1.46048 −0.730242 0.683189i $$-0.760592\pi$$
−0.730242 + 0.683189i $$0.760592\pi$$
$$828$$ 0 0
$$829$$ 40.0000 1.38926 0.694629 0.719368i $$-0.255569\pi$$
0.694629 + 0.719368i $$0.255569\pi$$
$$830$$ 0 0
$$831$$ 22.0000 0.763172
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 9.00000 0.311458
$$836$$ 0 0
$$837$$ −40.0000 −1.38260
$$838$$ 0 0
$$839$$ −18.0000 −0.621429 −0.310715 0.950503i $$-0.600568\pi$$
−0.310715 + 0.950503i $$0.600568\pi$$
$$840$$ 0 0
$$841$$ 52.0000 1.79310
$$842$$ 0 0
$$843$$ 21.0000 0.723278
$$844$$ 0 0
$$845$$ 12.0000 0.412813
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ 11.0000 0.377519
$$850$$ 0 0
$$851$$ 60.0000 2.05677
$$852$$ 0 0
$$853$$ 22.0000 0.753266 0.376633 0.926363i $$-0.377082\pi$$
0.376633 + 0.926363i $$0.377082\pi$$
$$854$$ 0 0
$$855$$ −4.00000 −0.136797
$$856$$ 0 0
$$857$$ −6.00000 −0.204956 −0.102478 0.994735i $$-0.532677\pi$$
−0.102478 + 0.994735i $$0.532677\pi$$
$$858$$ 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
$$862$$ 0 0
$$863$$ 12.0000 0.408485 0.204242 0.978920i $$-0.434527\pi$$
0.204242 + 0.978920i $$0.434527\pi$$
$$864$$ 0 0
$$865$$ −3.00000 −0.102003
$$866$$ 0 0
$$867$$ 8.00000 0.271694
$$868$$ 0 0
$$869$$ 15.0000 0.508840
$$870$$ 0 0
$$871$$ 8.00000 0.271070
$$872$$ 0 0
$$873$$ 34.0000 1.15073
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −22.0000 −0.742887 −0.371444 0.928456i $$-0.621137\pi$$
−0.371444 + 0.928456i $$0.621137\pi$$
$$878$$ 0 0
$$879$$ −15.0000 −0.505937
$$880$$ 0 0
$$881$$ −48.0000 −1.61716 −0.808581 0.588386i $$-0.799764\pi$$
−0.808581 + 0.588386i $$0.799764\pi$$
$$882$$ 0 0
$$883$$ 20.0000 0.673054 0.336527 0.941674i $$-0.390748\pi$$
0.336527 + 0.941674i $$0.390748\pi$$
$$884$$ 0 0
$$885$$ −12.0000 −0.403376
$$886$$ 0 0
$$887$$ 48.0000 1.61168 0.805841 0.592132i $$-0.201714\pi$$
0.805841 + 0.592132i $$0.201714\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 3.00000 0.100504
$$892$$ 0 0
$$893$$ −6.00000 −0.200782
$$894$$ 0 0
$$895$$ −12.0000 −0.401116
$$896$$ 0 0
$$897$$ 6.00000 0.200334
$$898$$ 0 0
$$899$$ 72.0000 2.40133
$$900$$ 0 0
$$901$$ 0 0
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 8.00000 0.265929
$$906$$ 0 0
$$907$$ −22.0000 −0.730498 −0.365249 0.930910i $$-0.619016\pi$$
−0.365249 + 0.930910i $$0.619016\pi$$
$$908$$ 0 0
$$909$$ −12.0000 −0.398015
$$910$$ 0 0
$$911$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$912$$ 0 0
$$913$$ 36.0000 1.19143
$$914$$ 0 0
$$915$$ −8.00000 −0.264472
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 41.0000 1.35247 0.676233 0.736688i $$-0.263611\pi$$
0.676233 + 0.736688i $$0.263611\pi$$
$$920$$ 0 0
$$921$$ −13.0000 −0.428365
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ −10.0000 −0.328798
$$926$$ 0 0
$$927$$ −14.0000 −0.459820
$$928$$ 0 0
$$929$$ 24.0000 0.787414 0.393707 0.919236i $$-0.371192\pi$$
0.393707 + 0.919236i $$0.371192\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ 18.0000 0.589294
$$934$$ 0 0
$$935$$ −9.00000 −0.294331
$$936$$ 0 0
$$937$$ 7.00000 0.228680 0.114340 0.993442i $$-0.463525\pi$$
0.114340 + 0.993442i $$0.463525\pi$$
$$938$$ 0 0
$$939$$ −13.0000 −0.424239
$$940$$ 0 0
$$941$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 36.0000 1.16984 0.584921 0.811090i $$-0.301125\pi$$
0.584921 + 0.811090i $$0.301125\pi$$
$$948$$ 0 0
$$949$$ −14.0000 −0.454459
$$950$$ 0 0
$$951$$ 18.0000 0.583690
$$952$$ 0 0
$$953$$ 36.0000 1.16615 0.583077 0.812417i $$-0.301849\pi$$
0.583077 + 0.812417i $$0.301849\pi$$
$$954$$ 0 0
$$955$$ −3.00000 −0.0970777
$$956$$ 0 0
$$957$$ 27.0000 0.872786
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 33.0000 1.06452
$$962$$ 0 0
$$963$$ 12.0000 0.386695
$$964$$ 0 0
$$965$$ 4.00000 0.128765
$$966$$ 0 0
$$967$$ −34.0000 −1.09337 −0.546683 0.837340i $$-0.684110\pi$$
−0.546683 + 0.837340i $$0.684110\pi$$
$$968$$ 0 0
$$969$$ 6.00000 0.192748
$$970$$ 0 0
$$971$$ −36.0000 −1.15529 −0.577647 0.816286i $$-0.696029\pi$$
−0.577647 + 0.816286i $$0.696029\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ −1.00000 −0.0320256
$$976$$ 0 0
$$977$$ −18.0000 −0.575871 −0.287936 0.957650i $$-0.592969\pi$$
−0.287936 + 0.957650i $$0.592969\pi$$
$$978$$ 0 0
$$979$$ −36.0000 −1.15056
$$980$$ 0 0
$$981$$ 38.0000 1.21325
$$982$$ 0 0
$$983$$ 33.0000 1.05254 0.526268 0.850319i $$-0.323591\pi$$
0.526268 + 0.850319i $$0.323591\pi$$
$$984$$ 0 0
$$985$$ −12.0000 −0.382352
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −12.0000 −0.381578
$$990$$ 0 0
$$991$$ −16.0000 −0.508257 −0.254128 0.967170i $$-0.581789\pi$$
−0.254128 + 0.967170i $$0.581789\pi$$
$$992$$ 0 0
$$993$$ −20.0000 −0.634681
$$994$$ 0 0
$$995$$ 20.0000 0.634043
$$996$$ 0 0
$$997$$ −17.0000 −0.538395 −0.269198 0.963085i $$-0.586759\pi$$
−0.269198 + 0.963085i $$0.586759\pi$$
$$998$$ 0 0
$$999$$ −50.0000 −1.58193
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 980.2.a.c.1.1 1
3.2 odd 2 8820.2.a.r.1.1 1
4.3 odd 2 3920.2.a.u.1.1 1
5.2 odd 4 4900.2.e.l.2549.2 2
5.3 odd 4 4900.2.e.l.2549.1 2
5.4 even 2 4900.2.a.p.1.1 1
7.2 even 3 980.2.i.h.361.1 2
7.3 odd 6 980.2.i.d.961.1 2
7.4 even 3 980.2.i.h.961.1 2
7.5 odd 6 980.2.i.d.361.1 2
7.6 odd 2 140.2.a.a.1.1 1
21.20 even 2 1260.2.a.c.1.1 1
28.27 even 2 560.2.a.c.1.1 1
35.13 even 4 700.2.e.c.449.2 2
35.27 even 4 700.2.e.c.449.1 2
35.34 odd 2 700.2.a.d.1.1 1
56.13 odd 2 2240.2.a.g.1.1 1
56.27 even 2 2240.2.a.r.1.1 1
84.83 odd 2 5040.2.a.h.1.1 1
105.62 odd 4 6300.2.k.c.6049.2 2
105.83 odd 4 6300.2.k.c.6049.1 2
105.104 even 2 6300.2.a.d.1.1 1
140.27 odd 4 2800.2.g.j.449.2 2
140.83 odd 4 2800.2.g.j.449.1 2
140.139 even 2 2800.2.a.y.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.a.a.1.1 1 7.6 odd 2
560.2.a.c.1.1 1 28.27 even 2
700.2.a.d.1.1 1 35.34 odd 2
700.2.e.c.449.1 2 35.27 even 4
700.2.e.c.449.2 2 35.13 even 4
980.2.a.c.1.1 1 1.1 even 1 trivial
980.2.i.d.361.1 2 7.5 odd 6
980.2.i.d.961.1 2 7.3 odd 6
980.2.i.h.361.1 2 7.2 even 3
980.2.i.h.961.1 2 7.4 even 3
1260.2.a.c.1.1 1 21.20 even 2
2240.2.a.g.1.1 1 56.13 odd 2
2240.2.a.r.1.1 1 56.27 even 2
2800.2.a.y.1.1 1 140.139 even 2
2800.2.g.j.449.1 2 140.83 odd 4
2800.2.g.j.449.2 2 140.27 odd 4
3920.2.a.u.1.1 1 4.3 odd 2
4900.2.a.p.1.1 1 5.4 even 2
4900.2.e.l.2549.1 2 5.3 odd 4
4900.2.e.l.2549.2 2 5.2 odd 4
5040.2.a.h.1.1 1 84.83 odd 2
6300.2.a.d.1.1 1 105.104 even 2
6300.2.k.c.6049.1 2 105.83 odd 4
6300.2.k.c.6049.2 2 105.62 odd 4
8820.2.a.r.1.1 1 3.2 odd 2