# Properties

 Label 3675.2.a.o.1.1 Level $3675$ Weight $2$ Character 3675.1 Self dual yes Analytic conductor $29.345$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$3675 = 3 \cdot 5^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3675.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$29.3450227428$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 105) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 3675.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+2.00000 q^{2} -1.00000 q^{3} +2.00000 q^{4} -2.00000 q^{6} +1.00000 q^{9} +O(q^{10})$$ $$q+2.00000 q^{2} -1.00000 q^{3} +2.00000 q^{4} -2.00000 q^{6} +1.00000 q^{9} -6.00000 q^{11} -2.00000 q^{12} +3.00000 q^{13} -4.00000 q^{16} +4.00000 q^{17} +2.00000 q^{18} +1.00000 q^{19} -12.0000 q^{22} +4.00000 q^{23} +6.00000 q^{26} -1.00000 q^{27} -8.00000 q^{29} +1.00000 q^{31} -8.00000 q^{32} +6.00000 q^{33} +8.00000 q^{34} +2.00000 q^{36} -7.00000 q^{37} +2.00000 q^{38} -3.00000 q^{39} -6.00000 q^{41} -1.00000 q^{43} -12.0000 q^{44} +8.00000 q^{46} -2.00000 q^{47} +4.00000 q^{48} -4.00000 q^{51} +6.00000 q^{52} -4.00000 q^{53} -2.00000 q^{54} -1.00000 q^{57} -16.0000 q^{58} -8.00000 q^{59} -14.0000 q^{61} +2.00000 q^{62} -8.00000 q^{64} +12.0000 q^{66} -7.00000 q^{67} +8.00000 q^{68} -4.00000 q^{69} +6.00000 q^{71} -1.00000 q^{73} -14.0000 q^{74} +2.00000 q^{76} -6.00000 q^{78} -1.00000 q^{79} +1.00000 q^{81} -12.0000 q^{82} -2.00000 q^{83} -2.00000 q^{86} +8.00000 q^{87} -12.0000 q^{89} +8.00000 q^{92} -1.00000 q^{93} -4.00000 q^{94} +8.00000 q^{96} +6.00000 q^{97} -6.00000 q^{99} +O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 2.00000 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$3$$ −1.00000 −0.577350
$$4$$ 2.00000 1.00000
$$5$$ 0 0
$$6$$ −2.00000 −0.816497
$$7$$ 0 0
$$8$$ 0 0
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ −6.00000 −1.80907 −0.904534 0.426401i $$-0.859781\pi$$
−0.904534 + 0.426401i $$0.859781\pi$$
$$12$$ −2.00000 −0.577350
$$13$$ 3.00000 0.832050 0.416025 0.909353i $$-0.363423\pi$$
0.416025 + 0.909353i $$0.363423\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −4.00000 −1.00000
$$17$$ 4.00000 0.970143 0.485071 0.874475i $$-0.338794\pi$$
0.485071 + 0.874475i $$0.338794\pi$$
$$18$$ 2.00000 0.471405
$$19$$ 1.00000 0.229416 0.114708 0.993399i $$-0.463407\pi$$
0.114708 + 0.993399i $$0.463407\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −12.0000 −2.55841
$$23$$ 4.00000 0.834058 0.417029 0.908893i $$-0.363071\pi$$
0.417029 + 0.908893i $$0.363071\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 6.00000 1.17670
$$27$$ −1.00000 −0.192450
$$28$$ 0 0
$$29$$ −8.00000 −1.48556 −0.742781 0.669534i $$-0.766494\pi$$
−0.742781 + 0.669534i $$0.766494\pi$$
$$30$$ 0 0
$$31$$ 1.00000 0.179605 0.0898027 0.995960i $$-0.471376\pi$$
0.0898027 + 0.995960i $$0.471376\pi$$
$$32$$ −8.00000 −1.41421
$$33$$ 6.00000 1.04447
$$34$$ 8.00000 1.37199
$$35$$ 0 0
$$36$$ 2.00000 0.333333
$$37$$ −7.00000 −1.15079 −0.575396 0.817875i $$-0.695152\pi$$
−0.575396 + 0.817875i $$0.695152\pi$$
$$38$$ 2.00000 0.324443
$$39$$ −3.00000 −0.480384
$$40$$ 0 0
$$41$$ −6.00000 −0.937043 −0.468521 0.883452i $$-0.655213\pi$$
−0.468521 + 0.883452i $$0.655213\pi$$
$$42$$ 0 0
$$43$$ −1.00000 −0.152499 −0.0762493 0.997089i $$-0.524294\pi$$
−0.0762493 + 0.997089i $$0.524294\pi$$
$$44$$ −12.0000 −1.80907
$$45$$ 0 0
$$46$$ 8.00000 1.17954
$$47$$ −2.00000 −0.291730 −0.145865 0.989305i $$-0.546597\pi$$
−0.145865 + 0.989305i $$0.546597\pi$$
$$48$$ 4.00000 0.577350
$$49$$ 0 0
$$50$$ 0 0
$$51$$ −4.00000 −0.560112
$$52$$ 6.00000 0.832050
$$53$$ −4.00000 −0.549442 −0.274721 0.961524i $$-0.588586\pi$$
−0.274721 + 0.961524i $$0.588586\pi$$
$$54$$ −2.00000 −0.272166
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −1.00000 −0.132453
$$58$$ −16.0000 −2.10090
$$59$$ −8.00000 −1.04151 −0.520756 0.853706i $$-0.674350\pi$$
−0.520756 + 0.853706i $$0.674350\pi$$
$$60$$ 0 0
$$61$$ −14.0000 −1.79252 −0.896258 0.443533i $$-0.853725\pi$$
−0.896258 + 0.443533i $$0.853725\pi$$
$$62$$ 2.00000 0.254000
$$63$$ 0 0
$$64$$ −8.00000 −1.00000
$$65$$ 0 0
$$66$$ 12.0000 1.47710
$$67$$ −7.00000 −0.855186 −0.427593 0.903971i $$-0.640638\pi$$
−0.427593 + 0.903971i $$0.640638\pi$$
$$68$$ 8.00000 0.970143
$$69$$ −4.00000 −0.481543
$$70$$ 0 0
$$71$$ 6.00000 0.712069 0.356034 0.934473i $$-0.384129\pi$$
0.356034 + 0.934473i $$0.384129\pi$$
$$72$$ 0 0
$$73$$ −1.00000 −0.117041 −0.0585206 0.998286i $$-0.518638\pi$$
−0.0585206 + 0.998286i $$0.518638\pi$$
$$74$$ −14.0000 −1.62747
$$75$$ 0 0
$$76$$ 2.00000 0.229416
$$77$$ 0 0
$$78$$ −6.00000 −0.679366
$$79$$ −1.00000 −0.112509 −0.0562544 0.998416i $$-0.517916\pi$$
−0.0562544 + 0.998416i $$0.517916\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ −12.0000 −1.32518
$$83$$ −2.00000 −0.219529 −0.109764 0.993958i $$-0.535010\pi$$
−0.109764 + 0.993958i $$0.535010\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −2.00000 −0.215666
$$87$$ 8.00000 0.857690
$$88$$ 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
$$92$$ 8.00000 0.834058
$$93$$ −1.00000 −0.103695
$$94$$ −4.00000 −0.412568
$$95$$ 0 0
$$96$$ 8.00000 0.816497
$$97$$ 6.00000 0.609208 0.304604 0.952479i $$-0.401476\pi$$
0.304604 + 0.952479i $$0.401476\pi$$
$$98$$ 0 0
$$99$$ −6.00000 −0.603023
$$100$$ 0 0
$$101$$ −10.0000 −0.995037 −0.497519 0.867453i $$-0.665755\pi$$
−0.497519 + 0.867453i $$0.665755\pi$$
$$102$$ −8.00000 −0.792118
$$103$$ 19.0000 1.87213 0.936063 0.351833i $$-0.114441\pi$$
0.936063 + 0.351833i $$0.114441\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ −8.00000 −0.777029
$$107$$ −12.0000 −1.16008 −0.580042 0.814587i $$-0.696964\pi$$
−0.580042 + 0.814587i $$0.696964\pi$$
$$108$$ −2.00000 −0.192450
$$109$$ −15.0000 −1.43674 −0.718370 0.695662i $$-0.755111\pi$$
−0.718370 + 0.695662i $$0.755111\pi$$
$$110$$ 0 0
$$111$$ 7.00000 0.664411
$$112$$ 0 0
$$113$$ 6.00000 0.564433 0.282216 0.959351i $$-0.408930\pi$$
0.282216 + 0.959351i $$0.408930\pi$$
$$114$$ −2.00000 −0.187317
$$115$$ 0 0
$$116$$ −16.0000 −1.48556
$$117$$ 3.00000 0.277350
$$118$$ −16.0000 −1.47292
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 25.0000 2.27273
$$122$$ −28.0000 −2.53500
$$123$$ 6.00000 0.541002
$$124$$ 2.00000 0.179605
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −5.00000 −0.443678 −0.221839 0.975083i $$-0.571206\pi$$
−0.221839 + 0.975083i $$0.571206\pi$$
$$128$$ 0 0
$$129$$ 1.00000 0.0880451
$$130$$ 0 0
$$131$$ 2.00000 0.174741 0.0873704 0.996176i $$-0.472154\pi$$
0.0873704 + 0.996176i $$0.472154\pi$$
$$132$$ 12.0000 1.04447
$$133$$ 0 0
$$134$$ −14.0000 −1.20942
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −8.00000 −0.683486 −0.341743 0.939793i $$-0.611017\pi$$
−0.341743 + 0.939793i $$0.611017\pi$$
$$138$$ −8.00000 −0.681005
$$139$$ 21.0000 1.78120 0.890598 0.454791i $$-0.150286\pi$$
0.890598 + 0.454791i $$0.150286\pi$$
$$140$$ 0 0
$$141$$ 2.00000 0.168430
$$142$$ 12.0000 1.00702
$$143$$ −18.0000 −1.50524
$$144$$ −4.00000 −0.333333
$$145$$ 0 0
$$146$$ −2.00000 −0.165521
$$147$$ 0 0
$$148$$ −14.0000 −1.15079
$$149$$ −4.00000 −0.327693 −0.163846 0.986486i $$-0.552390\pi$$
−0.163846 + 0.986486i $$0.552390\pi$$
$$150$$ 0 0
$$151$$ 8.00000 0.651031 0.325515 0.945537i $$-0.394462\pi$$
0.325515 + 0.945537i $$0.394462\pi$$
$$152$$ 0 0
$$153$$ 4.00000 0.323381
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −6.00000 −0.480384
$$157$$ −10.0000 −0.798087 −0.399043 0.916932i $$-0.630658\pi$$
−0.399043 + 0.916932i $$0.630658\pi$$
$$158$$ −2.00000 −0.159111
$$159$$ 4.00000 0.317221
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 2.00000 0.157135
$$163$$ 12.0000 0.939913 0.469956 0.882690i $$-0.344270\pi$$
0.469956 + 0.882690i $$0.344270\pi$$
$$164$$ −12.0000 −0.937043
$$165$$ 0 0
$$166$$ −4.00000 −0.310460
$$167$$ 10.0000 0.773823 0.386912 0.922117i $$-0.373542\pi$$
0.386912 + 0.922117i $$0.373542\pi$$
$$168$$ 0 0
$$169$$ −4.00000 −0.307692
$$170$$ 0 0
$$171$$ 1.00000 0.0764719
$$172$$ −2.00000 −0.152499
$$173$$ −24.0000 −1.82469 −0.912343 0.409426i $$-0.865729\pi$$
−0.912343 + 0.409426i $$0.865729\pi$$
$$174$$ 16.0000 1.21296
$$175$$ 0 0
$$176$$ 24.0000 1.80907
$$177$$ 8.00000 0.601317
$$178$$ −24.0000 −1.79888
$$179$$ 18.0000 1.34538 0.672692 0.739923i $$-0.265138\pi$$
0.672692 + 0.739923i $$0.265138\pi$$
$$180$$ 0 0
$$181$$ 13.0000 0.966282 0.483141 0.875542i $$-0.339496\pi$$
0.483141 + 0.875542i $$0.339496\pi$$
$$182$$ 0 0
$$183$$ 14.0000 1.03491
$$184$$ 0 0
$$185$$ 0 0
$$186$$ −2.00000 −0.146647
$$187$$ −24.0000 −1.75505
$$188$$ −4.00000 −0.291730
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 10.0000 0.723575 0.361787 0.932261i $$-0.382167\pi$$
0.361787 + 0.932261i $$0.382167\pi$$
$$192$$ 8.00000 0.577350
$$193$$ 9.00000 0.647834 0.323917 0.946085i $$-0.395000\pi$$
0.323917 + 0.946085i $$0.395000\pi$$
$$194$$ 12.0000 0.861550
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −12.0000 −0.854965 −0.427482 0.904024i $$-0.640599\pi$$
−0.427482 + 0.904024i $$0.640599\pi$$
$$198$$ −12.0000 −0.852803
$$199$$ 8.00000 0.567105 0.283552 0.958957i $$-0.408487\pi$$
0.283552 + 0.958957i $$0.408487\pi$$
$$200$$ 0 0
$$201$$ 7.00000 0.493742
$$202$$ −20.0000 −1.40720
$$203$$ 0 0
$$204$$ −8.00000 −0.560112
$$205$$ 0 0
$$206$$ 38.0000 2.64759
$$207$$ 4.00000 0.278019
$$208$$ −12.0000 −0.832050
$$209$$ −6.00000 −0.415029
$$210$$ 0 0
$$211$$ −20.0000 −1.37686 −0.688428 0.725304i $$-0.741699\pi$$
−0.688428 + 0.725304i $$0.741699\pi$$
$$212$$ −8.00000 −0.549442
$$213$$ −6.00000 −0.411113
$$214$$ −24.0000 −1.64061
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ −30.0000 −2.03186
$$219$$ 1.00000 0.0675737
$$220$$ 0 0
$$221$$ 12.0000 0.807207
$$222$$ 14.0000 0.939618
$$223$$ 24.0000 1.60716 0.803579 0.595198i $$-0.202926\pi$$
0.803579 + 0.595198i $$0.202926\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 12.0000 0.798228
$$227$$ 10.0000 0.663723 0.331862 0.943328i $$-0.392323\pi$$
0.331862 + 0.943328i $$0.392323\pi$$
$$228$$ −2.00000 −0.132453
$$229$$ 13.0000 0.859064 0.429532 0.903052i $$-0.358679\pi$$
0.429532 + 0.903052i $$0.358679\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −6.00000 −0.393073 −0.196537 0.980497i $$-0.562969\pi$$
−0.196537 + 0.980497i $$0.562969\pi$$
$$234$$ 6.00000 0.392232
$$235$$ 0 0
$$236$$ −16.0000 −1.04151
$$237$$ 1.00000 0.0649570
$$238$$ 0 0
$$239$$ 14.0000 0.905585 0.452792 0.891616i $$-0.350428\pi$$
0.452792 + 0.891616i $$0.350428\pi$$
$$240$$ 0 0
$$241$$ −18.0000 −1.15948 −0.579741 0.814801i $$-0.696846\pi$$
−0.579741 + 0.814801i $$0.696846\pi$$
$$242$$ 50.0000 3.21412
$$243$$ −1.00000 −0.0641500
$$244$$ −28.0000 −1.79252
$$245$$ 0 0
$$246$$ 12.0000 0.765092
$$247$$ 3.00000 0.190885
$$248$$ 0 0
$$249$$ 2.00000 0.126745
$$250$$ 0 0
$$251$$ 12.0000 0.757433 0.378717 0.925513i $$-0.376365\pi$$
0.378717 + 0.925513i $$0.376365\pi$$
$$252$$ 0 0
$$253$$ −24.0000 −1.50887
$$254$$ −10.0000 −0.627456
$$255$$ 0 0
$$256$$ 16.0000 1.00000
$$257$$ 18.0000 1.12281 0.561405 0.827541i $$-0.310261\pi$$
0.561405 + 0.827541i $$0.310261\pi$$
$$258$$ 2.00000 0.124515
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −8.00000 −0.495188
$$262$$ 4.00000 0.247121
$$263$$ −4.00000 −0.246651 −0.123325 0.992366i $$-0.539356\pi$$
−0.123325 + 0.992366i $$0.539356\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 12.0000 0.734388
$$268$$ −14.0000 −0.855186
$$269$$ −10.0000 −0.609711 −0.304855 0.952399i $$-0.598608\pi$$
−0.304855 + 0.952399i $$0.598608\pi$$
$$270$$ 0 0
$$271$$ −24.0000 −1.45790 −0.728948 0.684569i $$-0.759990\pi$$
−0.728948 + 0.684569i $$0.759990\pi$$
$$272$$ −16.0000 −0.970143
$$273$$ 0 0
$$274$$ −16.0000 −0.966595
$$275$$ 0 0
$$276$$ −8.00000 −0.481543
$$277$$ 7.00000 0.420589 0.210295 0.977638i $$-0.432558\pi$$
0.210295 + 0.977638i $$0.432558\pi$$
$$278$$ 42.0000 2.51899
$$279$$ 1.00000 0.0598684
$$280$$ 0 0
$$281$$ −12.0000 −0.715860 −0.357930 0.933748i $$-0.616517\pi$$
−0.357930 + 0.933748i $$0.616517\pi$$
$$282$$ 4.00000 0.238197
$$283$$ 7.00000 0.416107 0.208053 0.978117i $$-0.433287\pi$$
0.208053 + 0.978117i $$0.433287\pi$$
$$284$$ 12.0000 0.712069
$$285$$ 0 0
$$286$$ −36.0000 −2.12872
$$287$$ 0 0
$$288$$ −8.00000 −0.471405
$$289$$ −1.00000 −0.0588235
$$290$$ 0 0
$$291$$ −6.00000 −0.351726
$$292$$ −2.00000 −0.117041
$$293$$ 16.0000 0.934730 0.467365 0.884064i $$-0.345203\pi$$
0.467365 + 0.884064i $$0.345203\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 6.00000 0.348155
$$298$$ −8.00000 −0.463428
$$299$$ 12.0000 0.693978
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 16.0000 0.920697
$$303$$ 10.0000 0.574485
$$304$$ −4.00000 −0.229416
$$305$$ 0 0
$$306$$ 8.00000 0.457330
$$307$$ −3.00000 −0.171219 −0.0856095 0.996329i $$-0.527284\pi$$
−0.0856095 + 0.996329i $$0.527284\pi$$
$$308$$ 0 0
$$309$$ −19.0000 −1.08087
$$310$$ 0 0
$$311$$ 6.00000 0.340229 0.170114 0.985424i $$-0.445586\pi$$
0.170114 + 0.985424i $$0.445586\pi$$
$$312$$ 0 0
$$313$$ −11.0000 −0.621757 −0.310878 0.950450i $$-0.600623\pi$$
−0.310878 + 0.950450i $$0.600623\pi$$
$$314$$ −20.0000 −1.12867
$$315$$ 0 0
$$316$$ −2.00000 −0.112509
$$317$$ −20.0000 −1.12331 −0.561656 0.827371i $$-0.689836\pi$$
−0.561656 + 0.827371i $$0.689836\pi$$
$$318$$ 8.00000 0.448618
$$319$$ 48.0000 2.68748
$$320$$ 0 0
$$321$$ 12.0000 0.669775
$$322$$ 0 0
$$323$$ 4.00000 0.222566
$$324$$ 2.00000 0.111111
$$325$$ 0 0
$$326$$ 24.0000 1.32924
$$327$$ 15.0000 0.829502
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −9.00000 −0.494685 −0.247342 0.968928i $$-0.579557\pi$$
−0.247342 + 0.968928i $$0.579557\pi$$
$$332$$ −4.00000 −0.219529
$$333$$ −7.00000 −0.383598
$$334$$ 20.0000 1.09435
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −25.0000 −1.36184 −0.680918 0.732359i $$-0.738419\pi$$
−0.680918 + 0.732359i $$0.738419\pi$$
$$338$$ −8.00000 −0.435143
$$339$$ −6.00000 −0.325875
$$340$$ 0 0
$$341$$ −6.00000 −0.324918
$$342$$ 2.00000 0.108148
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ −48.0000 −2.58050
$$347$$ −16.0000 −0.858925 −0.429463 0.903085i $$-0.641297\pi$$
−0.429463 + 0.903085i $$0.641297\pi$$
$$348$$ 16.0000 0.857690
$$349$$ 2.00000 0.107058 0.0535288 0.998566i $$-0.482953\pi$$
0.0535288 + 0.998566i $$0.482953\pi$$
$$350$$ 0 0
$$351$$ −3.00000 −0.160128
$$352$$ 48.0000 2.55841
$$353$$ 18.0000 0.958043 0.479022 0.877803i $$-0.340992\pi$$
0.479022 + 0.877803i $$0.340992\pi$$
$$354$$ 16.0000 0.850390
$$355$$ 0 0
$$356$$ −24.0000 −1.27200
$$357$$ 0 0
$$358$$ 36.0000 1.90266
$$359$$ −24.0000 −1.26667 −0.633336 0.773877i $$-0.718315\pi$$
−0.633336 + 0.773877i $$0.718315\pi$$
$$360$$ 0 0
$$361$$ −18.0000 −0.947368
$$362$$ 26.0000 1.36653
$$363$$ −25.0000 −1.31216
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 28.0000 1.46358
$$367$$ −19.0000 −0.991792 −0.495896 0.868382i $$-0.665160\pi$$
−0.495896 + 0.868382i $$0.665160\pi$$
$$368$$ −16.0000 −0.834058
$$369$$ −6.00000 −0.312348
$$370$$ 0 0
$$371$$ 0 0
$$372$$ −2.00000 −0.103695
$$373$$ −11.0000 −0.569558 −0.284779 0.958593i $$-0.591920\pi$$
−0.284779 + 0.958593i $$0.591920\pi$$
$$374$$ −48.0000 −2.48202
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −24.0000 −1.23606
$$378$$ 0 0
$$379$$ 11.0000 0.565032 0.282516 0.959263i $$-0.408831\pi$$
0.282516 + 0.959263i $$0.408831\pi$$
$$380$$ 0 0
$$381$$ 5.00000 0.256158
$$382$$ 20.0000 1.02329
$$383$$ −28.0000 −1.43073 −0.715367 0.698749i $$-0.753740\pi$$
−0.715367 + 0.698749i $$0.753740\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 18.0000 0.916176
$$387$$ −1.00000 −0.0508329
$$388$$ 12.0000 0.609208
$$389$$ 6.00000 0.304212 0.152106 0.988364i $$-0.451394\pi$$
0.152106 + 0.988364i $$0.451394\pi$$
$$390$$ 0 0
$$391$$ 16.0000 0.809155
$$392$$ 0 0
$$393$$ −2.00000 −0.100887
$$394$$ −24.0000 −1.20910
$$395$$ 0 0
$$396$$ −12.0000 −0.603023
$$397$$ 37.0000 1.85698 0.928488 0.371361i $$-0.121109\pi$$
0.928488 + 0.371361i $$0.121109\pi$$
$$398$$ 16.0000 0.802008
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −12.0000 −0.599251 −0.299626 0.954057i $$-0.596862\pi$$
−0.299626 + 0.954057i $$0.596862\pi$$
$$402$$ 14.0000 0.698257
$$403$$ 3.00000 0.149441
$$404$$ −20.0000 −0.995037
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 42.0000 2.08186
$$408$$ 0 0
$$409$$ 5.00000 0.247234 0.123617 0.992330i $$-0.460551\pi$$
0.123617 + 0.992330i $$0.460551\pi$$
$$410$$ 0 0
$$411$$ 8.00000 0.394611
$$412$$ 38.0000 1.87213
$$413$$ 0 0
$$414$$ 8.00000 0.393179
$$415$$ 0 0
$$416$$ −24.0000 −1.17670
$$417$$ −21.0000 −1.02837
$$418$$ −12.0000 −0.586939
$$419$$ 6.00000 0.293119 0.146560 0.989202i $$-0.453180\pi$$
0.146560 + 0.989202i $$0.453180\pi$$
$$420$$ 0 0
$$421$$ 1.00000 0.0487370 0.0243685 0.999703i $$-0.492242\pi$$
0.0243685 + 0.999703i $$0.492242\pi$$
$$422$$ −40.0000 −1.94717
$$423$$ −2.00000 −0.0972433
$$424$$ 0 0
$$425$$ 0 0
$$426$$ −12.0000 −0.581402
$$427$$ 0 0
$$428$$ −24.0000 −1.16008
$$429$$ 18.0000 0.869048
$$430$$ 0 0
$$431$$ −2.00000 −0.0963366 −0.0481683 0.998839i $$-0.515338\pi$$
−0.0481683 + 0.998839i $$0.515338\pi$$
$$432$$ 4.00000 0.192450
$$433$$ 5.00000 0.240285 0.120142 0.992757i $$-0.461665\pi$$
0.120142 + 0.992757i $$0.461665\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −30.0000 −1.43674
$$437$$ 4.00000 0.191346
$$438$$ 2.00000 0.0955637
$$439$$ 16.0000 0.763638 0.381819 0.924237i $$-0.375298\pi$$
0.381819 + 0.924237i $$0.375298\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 24.0000 1.14156
$$443$$ 36.0000 1.71041 0.855206 0.518289i $$-0.173431\pi$$
0.855206 + 0.518289i $$0.173431\pi$$
$$444$$ 14.0000 0.664411
$$445$$ 0 0
$$446$$ 48.0000 2.27287
$$447$$ 4.00000 0.189194
$$448$$ 0 0
$$449$$ 30.0000 1.41579 0.707894 0.706319i $$-0.249646\pi$$
0.707894 + 0.706319i $$0.249646\pi$$
$$450$$ 0 0
$$451$$ 36.0000 1.69517
$$452$$ 12.0000 0.564433
$$453$$ −8.00000 −0.375873
$$454$$ 20.0000 0.938647
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 15.0000 0.701670 0.350835 0.936437i $$-0.385898\pi$$
0.350835 + 0.936437i $$0.385898\pi$$
$$458$$ 26.0000 1.21490
$$459$$ −4.00000 −0.186704
$$460$$ 0 0
$$461$$ −8.00000 −0.372597 −0.186299 0.982493i $$-0.559649\pi$$
−0.186299 + 0.982493i $$0.559649\pi$$
$$462$$ 0 0
$$463$$ −3.00000 −0.139422 −0.0697109 0.997567i $$-0.522208\pi$$
−0.0697109 + 0.997567i $$0.522208\pi$$
$$464$$ 32.0000 1.48556
$$465$$ 0 0
$$466$$ −12.0000 −0.555889
$$467$$ −22.0000 −1.01804 −0.509019 0.860755i $$-0.669992\pi$$
−0.509019 + 0.860755i $$0.669992\pi$$
$$468$$ 6.00000 0.277350
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 10.0000 0.460776
$$472$$ 0 0
$$473$$ 6.00000 0.275880
$$474$$ 2.00000 0.0918630
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −4.00000 −0.183147
$$478$$ 28.0000 1.28069
$$479$$ −4.00000 −0.182765 −0.0913823 0.995816i $$-0.529129\pi$$
−0.0913823 + 0.995816i $$0.529129\pi$$
$$480$$ 0 0
$$481$$ −21.0000 −0.957518
$$482$$ −36.0000 −1.63976
$$483$$ 0 0
$$484$$ 50.0000 2.27273
$$485$$ 0 0
$$486$$ −2.00000 −0.0907218
$$487$$ 13.0000 0.589086 0.294543 0.955638i $$-0.404833\pi$$
0.294543 + 0.955638i $$0.404833\pi$$
$$488$$ 0 0
$$489$$ −12.0000 −0.542659
$$490$$ 0 0
$$491$$ −12.0000 −0.541552 −0.270776 0.962642i $$-0.587280\pi$$
−0.270776 + 0.962642i $$0.587280\pi$$
$$492$$ 12.0000 0.541002
$$493$$ −32.0000 −1.44121
$$494$$ 6.00000 0.269953
$$495$$ 0 0
$$496$$ −4.00000 −0.179605
$$497$$ 0 0
$$498$$ 4.00000 0.179244
$$499$$ 29.0000 1.29822 0.649109 0.760695i $$-0.275142\pi$$
0.649109 + 0.760695i $$0.275142\pi$$
$$500$$ 0 0
$$501$$ −10.0000 −0.446767
$$502$$ 24.0000 1.07117
$$503$$ 2.00000 0.0891756 0.0445878 0.999005i $$-0.485803\pi$$
0.0445878 + 0.999005i $$0.485803\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ −48.0000 −2.13386
$$507$$ 4.00000 0.177646
$$508$$ −10.0000 −0.443678
$$509$$ 10.0000 0.443242 0.221621 0.975133i $$-0.428865\pi$$
0.221621 + 0.975133i $$0.428865\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 32.0000 1.41421
$$513$$ −1.00000 −0.0441511
$$514$$ 36.0000 1.58789
$$515$$ 0 0
$$516$$ 2.00000 0.0880451
$$517$$ 12.0000 0.527759
$$518$$ 0 0
$$519$$ 24.0000 1.05348
$$520$$ 0 0
$$521$$ 4.00000 0.175243 0.0876216 0.996154i $$-0.472073\pi$$
0.0876216 + 0.996154i $$0.472073\pi$$
$$522$$ −16.0000 −0.700301
$$523$$ −11.0000 −0.480996 −0.240498 0.970650i $$-0.577311\pi$$
−0.240498 + 0.970650i $$0.577311\pi$$
$$524$$ 4.00000 0.174741
$$525$$ 0 0
$$526$$ −8.00000 −0.348817
$$527$$ 4.00000 0.174243
$$528$$ −24.0000 −1.04447
$$529$$ −7.00000 −0.304348
$$530$$ 0 0
$$531$$ −8.00000 −0.347170
$$532$$ 0 0
$$533$$ −18.0000 −0.779667
$$534$$ 24.0000 1.03858
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −18.0000 −0.776757
$$538$$ −20.0000 −0.862261
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −3.00000 −0.128980 −0.0644900 0.997918i $$-0.520542\pi$$
−0.0644900 + 0.997918i $$0.520542\pi$$
$$542$$ −48.0000 −2.06178
$$543$$ −13.0000 −0.557883
$$544$$ −32.0000 −1.37199
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −36.0000 −1.53925 −0.769624 0.638497i $$-0.779557\pi$$
−0.769624 + 0.638497i $$0.779557\pi$$
$$548$$ −16.0000 −0.683486
$$549$$ −14.0000 −0.597505
$$550$$ 0 0
$$551$$ −8.00000 −0.340811
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 14.0000 0.594803
$$555$$ 0 0
$$556$$ 42.0000 1.78120
$$557$$ 10.0000 0.423714 0.211857 0.977301i $$-0.432049\pi$$
0.211857 + 0.977301i $$0.432049\pi$$
$$558$$ 2.00000 0.0846668
$$559$$ −3.00000 −0.126886
$$560$$ 0 0
$$561$$ 24.0000 1.01328
$$562$$ −24.0000 −1.01238
$$563$$ 26.0000 1.09577 0.547885 0.836554i $$-0.315433\pi$$
0.547885 + 0.836554i $$0.315433\pi$$
$$564$$ 4.00000 0.168430
$$565$$ 0 0
$$566$$ 14.0000 0.588464
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 18.0000 0.754599 0.377300 0.926091i $$-0.376853\pi$$
0.377300 + 0.926091i $$0.376853\pi$$
$$570$$ 0 0
$$571$$ −3.00000 −0.125546 −0.0627730 0.998028i $$-0.519994\pi$$
−0.0627730 + 0.998028i $$0.519994\pi$$
$$572$$ −36.0000 −1.50524
$$573$$ −10.0000 −0.417756
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −8.00000 −0.333333
$$577$$ 29.0000 1.20729 0.603643 0.797255i $$-0.293715\pi$$
0.603643 + 0.797255i $$0.293715\pi$$
$$578$$ −2.00000 −0.0831890
$$579$$ −9.00000 −0.374027
$$580$$ 0 0
$$581$$ 0 0
$$582$$ −12.0000 −0.497416
$$583$$ 24.0000 0.993978
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 32.0000 1.32191
$$587$$ −12.0000 −0.495293 −0.247647 0.968850i $$-0.579657\pi$$
−0.247647 + 0.968850i $$0.579657\pi$$
$$588$$ 0 0
$$589$$ 1.00000 0.0412043
$$590$$ 0 0
$$591$$ 12.0000 0.493614
$$592$$ 28.0000 1.15079
$$593$$ 18.0000 0.739171 0.369586 0.929197i $$-0.379500\pi$$
0.369586 + 0.929197i $$0.379500\pi$$
$$594$$ 12.0000 0.492366
$$595$$ 0 0
$$596$$ −8.00000 −0.327693
$$597$$ −8.00000 −0.327418
$$598$$ 24.0000 0.981433
$$599$$ −4.00000 −0.163436 −0.0817178 0.996656i $$-0.526041\pi$$
−0.0817178 + 0.996656i $$0.526041\pi$$
$$600$$ 0 0
$$601$$ −33.0000 −1.34610 −0.673049 0.739598i $$-0.735016\pi$$
−0.673049 + 0.739598i $$0.735016\pi$$
$$602$$ 0 0
$$603$$ −7.00000 −0.285062
$$604$$ 16.0000 0.651031
$$605$$ 0 0
$$606$$ 20.0000 0.812444
$$607$$ −35.0000 −1.42061 −0.710303 0.703896i $$-0.751442\pi$$
−0.710303 + 0.703896i $$0.751442\pi$$
$$608$$ −8.00000 −0.324443
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −6.00000 −0.242734
$$612$$ 8.00000 0.323381
$$613$$ 30.0000 1.21169 0.605844 0.795583i $$-0.292835\pi$$
0.605844 + 0.795583i $$0.292835\pi$$
$$614$$ −6.00000 −0.242140
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −18.0000 −0.724653 −0.362326 0.932051i $$-0.618017\pi$$
−0.362326 + 0.932051i $$0.618017\pi$$
$$618$$ −38.0000 −1.52858
$$619$$ 3.00000 0.120580 0.0602901 0.998181i $$-0.480797\pi$$
0.0602901 + 0.998181i $$0.480797\pi$$
$$620$$ 0 0
$$621$$ −4.00000 −0.160514
$$622$$ 12.0000 0.481156
$$623$$ 0 0
$$624$$ 12.0000 0.480384
$$625$$ 0 0
$$626$$ −22.0000 −0.879297
$$627$$ 6.00000 0.239617
$$628$$ −20.0000 −0.798087
$$629$$ −28.0000 −1.11643
$$630$$ 0 0
$$631$$ 24.0000 0.955425 0.477712 0.878516i $$-0.341466\pi$$
0.477712 + 0.878516i $$0.341466\pi$$
$$632$$ 0 0
$$633$$ 20.0000 0.794929
$$634$$ −40.0000 −1.58860
$$635$$ 0 0
$$636$$ 8.00000 0.317221
$$637$$ 0 0
$$638$$ 96.0000 3.80068
$$639$$ 6.00000 0.237356
$$640$$ 0 0
$$641$$ 12.0000 0.473972 0.236986 0.971513i $$-0.423841\pi$$
0.236986 + 0.971513i $$0.423841\pi$$
$$642$$ 24.0000 0.947204
$$643$$ −1.00000 −0.0394362 −0.0197181 0.999806i $$-0.506277\pi$$
−0.0197181 + 0.999806i $$0.506277\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 8.00000 0.314756
$$647$$ −30.0000 −1.17942 −0.589711 0.807614i $$-0.700758\pi$$
−0.589711 + 0.807614i $$0.700758\pi$$
$$648$$ 0 0
$$649$$ 48.0000 1.88416
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 24.0000 0.939913
$$653$$ −14.0000 −0.547862 −0.273931 0.961749i $$-0.588324\pi$$
−0.273931 + 0.961749i $$0.588324\pi$$
$$654$$ 30.0000 1.17309
$$655$$ 0 0
$$656$$ 24.0000 0.937043
$$657$$ −1.00000 −0.0390137
$$658$$ 0 0
$$659$$ −12.0000 −0.467454 −0.233727 0.972302i $$-0.575092\pi$$
−0.233727 + 0.972302i $$0.575092\pi$$
$$660$$ 0 0
$$661$$ 23.0000 0.894596 0.447298 0.894385i $$-0.352386\pi$$
0.447298 + 0.894385i $$0.352386\pi$$
$$662$$ −18.0000 −0.699590
$$663$$ −12.0000 −0.466041
$$664$$ 0 0
$$665$$ 0 0
$$666$$ −14.0000 −0.542489
$$667$$ −32.0000 −1.23904
$$668$$ 20.0000 0.773823
$$669$$ −24.0000 −0.927894
$$670$$ 0 0
$$671$$ 84.0000 3.24278
$$672$$ 0 0
$$673$$ 37.0000 1.42625 0.713123 0.701039i $$-0.247280\pi$$
0.713123 + 0.701039i $$0.247280\pi$$
$$674$$ −50.0000 −1.92593
$$675$$ 0 0
$$676$$ −8.00000 −0.307692
$$677$$ −16.0000 −0.614930 −0.307465 0.951559i $$-0.599481\pi$$
−0.307465 + 0.951559i $$0.599481\pi$$
$$678$$ −12.0000 −0.460857
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −10.0000 −0.383201
$$682$$ −12.0000 −0.459504
$$683$$ 48.0000 1.83667 0.918334 0.395805i $$-0.129534\pi$$
0.918334 + 0.395805i $$0.129534\pi$$
$$684$$ 2.00000 0.0764719
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −13.0000 −0.495981
$$688$$ 4.00000 0.152499
$$689$$ −12.0000 −0.457164
$$690$$ 0 0
$$691$$ 27.0000 1.02713 0.513564 0.858051i $$-0.328325\pi$$
0.513564 + 0.858051i $$0.328325\pi$$
$$692$$ −48.0000 −1.82469
$$693$$ 0 0
$$694$$ −32.0000 −1.21470
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −24.0000 −0.909065
$$698$$ 4.00000 0.151402
$$699$$ 6.00000 0.226941
$$700$$ 0 0
$$701$$ −44.0000 −1.66186 −0.830929 0.556379i $$-0.812190\pi$$
−0.830929 + 0.556379i $$0.812190\pi$$
$$702$$ −6.00000 −0.226455
$$703$$ −7.00000 −0.264010
$$704$$ 48.0000 1.80907
$$705$$ 0 0
$$706$$ 36.0000 1.35488
$$707$$ 0 0
$$708$$ 16.0000 0.601317
$$709$$ −26.0000 −0.976450 −0.488225 0.872718i $$-0.662356\pi$$
−0.488225 + 0.872718i $$0.662356\pi$$
$$710$$ 0 0
$$711$$ −1.00000 −0.0375029
$$712$$ 0 0
$$713$$ 4.00000 0.149801
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 36.0000 1.34538
$$717$$ −14.0000 −0.522840
$$718$$ −48.0000 −1.79134
$$719$$ −34.0000 −1.26799 −0.633993 0.773339i $$-0.718585\pi$$
−0.633993 + 0.773339i $$0.718585\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −36.0000 −1.33978
$$723$$ 18.0000 0.669427
$$724$$ 26.0000 0.966282
$$725$$ 0 0
$$726$$ −50.0000 −1.85567
$$727$$ −7.00000 −0.259616 −0.129808 0.991539i $$-0.541436\pi$$
−0.129808 + 0.991539i $$0.541436\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ −4.00000 −0.147945
$$732$$ 28.0000 1.03491
$$733$$ 43.0000 1.58824 0.794121 0.607760i $$-0.207932\pi$$
0.794121 + 0.607760i $$0.207932\pi$$
$$734$$ −38.0000 −1.40261
$$735$$ 0 0
$$736$$ −32.0000 −1.17954
$$737$$ 42.0000 1.54709
$$738$$ −12.0000 −0.441726
$$739$$ 41.0000 1.50821 0.754105 0.656754i $$-0.228071\pi$$
0.754105 + 0.656754i $$0.228071\pi$$
$$740$$ 0 0
$$741$$ −3.00000 −0.110208
$$742$$ 0 0
$$743$$ −6.00000 −0.220119 −0.110059 0.993925i $$-0.535104\pi$$
−0.110059 + 0.993925i $$0.535104\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −22.0000 −0.805477
$$747$$ −2.00000 −0.0731762
$$748$$ −48.0000 −1.75505
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 29.0000 1.05823 0.529113 0.848552i $$-0.322525\pi$$
0.529113 + 0.848552i $$0.322525\pi$$
$$752$$ 8.00000 0.291730
$$753$$ −12.0000 −0.437304
$$754$$ −48.0000 −1.74806
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 22.0000 0.799604 0.399802 0.916602i $$-0.369079\pi$$
0.399802 + 0.916602i $$0.369079\pi$$
$$758$$ 22.0000 0.799076
$$759$$ 24.0000 0.871145
$$760$$ 0 0
$$761$$ −12.0000 −0.435000 −0.217500 0.976060i $$-0.569790\pi$$
−0.217500 + 0.976060i $$0.569790\pi$$
$$762$$ 10.0000 0.362262
$$763$$ 0 0
$$764$$ 20.0000 0.723575
$$765$$ 0 0
$$766$$ −56.0000 −2.02336
$$767$$ −24.0000 −0.866590
$$768$$ −16.0000 −0.577350
$$769$$ −49.0000 −1.76699 −0.883493 0.468445i $$-0.844814\pi$$
−0.883493 + 0.468445i $$0.844814\pi$$
$$770$$ 0 0
$$771$$ −18.0000 −0.648254
$$772$$ 18.0000 0.647834
$$773$$ −18.0000 −0.647415 −0.323708 0.946157i $$-0.604929\pi$$
−0.323708 + 0.946157i $$0.604929\pi$$
$$774$$ −2.00000 −0.0718885
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 12.0000 0.430221
$$779$$ −6.00000 −0.214972
$$780$$ 0 0
$$781$$ −36.0000 −1.28818
$$782$$ 32.0000 1.14432
$$783$$ 8.00000 0.285897
$$784$$ 0 0
$$785$$ 0 0
$$786$$ −4.00000 −0.142675
$$787$$ 32.0000 1.14068 0.570338 0.821410i $$-0.306812\pi$$
0.570338 + 0.821410i $$0.306812\pi$$
$$788$$ −24.0000 −0.854965
$$789$$ 4.00000 0.142404
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −42.0000 −1.49146
$$794$$ 74.0000 2.62616
$$795$$ 0 0
$$796$$ 16.0000 0.567105
$$797$$ 36.0000 1.27519 0.637593 0.770374i $$-0.279930\pi$$
0.637593 + 0.770374i $$0.279930\pi$$
$$798$$ 0 0
$$799$$ −8.00000 −0.283020
$$800$$ 0 0
$$801$$ −12.0000 −0.423999
$$802$$ −24.0000 −0.847469
$$803$$ 6.00000 0.211735
$$804$$ 14.0000 0.493742
$$805$$ 0 0
$$806$$ 6.00000 0.211341
$$807$$ 10.0000 0.352017
$$808$$ 0 0
$$809$$ −42.0000 −1.47664 −0.738321 0.674450i $$-0.764381\pi$$
−0.738321 + 0.674450i $$0.764381\pi$$
$$810$$ 0 0
$$811$$ −48.0000 −1.68551 −0.842754 0.538299i $$-0.819067\pi$$
−0.842754 + 0.538299i $$0.819067\pi$$
$$812$$ 0 0
$$813$$ 24.0000 0.841717
$$814$$ 84.0000 2.94420
$$815$$ 0 0
$$816$$ 16.0000 0.560112
$$817$$ −1.00000 −0.0349856
$$818$$ 10.0000 0.349642
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 54.0000 1.88461 0.942306 0.334751i $$-0.108652\pi$$
0.942306 + 0.334751i $$0.108652\pi$$
$$822$$ 16.0000 0.558064
$$823$$ −8.00000 −0.278862 −0.139431 0.990232i $$-0.544527\pi$$
−0.139431 + 0.990232i $$0.544527\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 30.0000 1.04320 0.521601 0.853189i $$-0.325335\pi$$
0.521601 + 0.853189i $$0.325335\pi$$
$$828$$ 8.00000 0.278019
$$829$$ 57.0000 1.97969 0.989846 0.142145i $$-0.0453998\pi$$
0.989846 + 0.142145i $$0.0453998\pi$$
$$830$$ 0 0
$$831$$ −7.00000 −0.242827
$$832$$ −24.0000 −0.832050
$$833$$ 0 0
$$834$$ −42.0000 −1.45434
$$835$$ 0 0
$$836$$ −12.0000 −0.415029
$$837$$ −1.00000 −0.0345651
$$838$$ 12.0000 0.414533
$$839$$ 24.0000 0.828572 0.414286 0.910147i $$-0.364031\pi$$
0.414286 + 0.910147i $$0.364031\pi$$
$$840$$ 0 0
$$841$$ 35.0000 1.20690
$$842$$ 2.00000 0.0689246
$$843$$ 12.0000 0.413302
$$844$$ −40.0000 −1.37686
$$845$$ 0 0
$$846$$ −4.00000 −0.137523
$$847$$ 0 0
$$848$$ 16.0000 0.549442
$$849$$ −7.00000 −0.240239
$$850$$ 0 0
$$851$$ −28.0000 −0.959828
$$852$$ −12.0000 −0.411113
$$853$$ 9.00000 0.308154 0.154077 0.988059i $$-0.450760\pi$$
0.154077 + 0.988059i $$0.450760\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 12.0000 0.409912 0.204956 0.978771i $$-0.434295\pi$$
0.204956 + 0.978771i $$0.434295\pi$$
$$858$$ 36.0000 1.22902
$$859$$ −40.0000 −1.36478 −0.682391 0.730987i $$-0.739060\pi$$
−0.682391 + 0.730987i $$0.739060\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ −4.00000 −0.136241
$$863$$ 6.00000 0.204242 0.102121 0.994772i $$-0.467437\pi$$
0.102121 + 0.994772i $$0.467437\pi$$
$$864$$ 8.00000 0.272166
$$865$$ 0 0
$$866$$ 10.0000 0.339814
$$867$$ 1.00000 0.0339618
$$868$$ 0 0
$$869$$ 6.00000 0.203536
$$870$$ 0 0
$$871$$ −21.0000 −0.711558
$$872$$ 0 0
$$873$$ 6.00000 0.203069
$$874$$ 8.00000 0.270604
$$875$$ 0 0
$$876$$ 2.00000 0.0675737
$$877$$ 22.0000 0.742887 0.371444 0.928456i $$-0.378863\pi$$
0.371444 + 0.928456i $$0.378863\pi$$
$$878$$ 32.0000 1.07995
$$879$$ −16.0000 −0.539667
$$880$$ 0 0
$$881$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$882$$ 0 0
$$883$$ −7.00000 −0.235569 −0.117784 0.993039i $$-0.537579\pi$$
−0.117784 + 0.993039i $$0.537579\pi$$
$$884$$ 24.0000 0.807207
$$885$$ 0 0
$$886$$ 72.0000 2.41889
$$887$$ −10.0000 −0.335767 −0.167884 0.985807i $$-0.553693\pi$$
−0.167884 + 0.985807i $$0.553693\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ −6.00000 −0.201008
$$892$$ 48.0000 1.60716
$$893$$ −2.00000 −0.0669274
$$894$$ 8.00000 0.267560
$$895$$ 0 0
$$896$$ 0 0
$$897$$ −12.0000 −0.400668
$$898$$ 60.0000 2.00223
$$899$$ −8.00000 −0.266815
$$900$$ 0 0
$$901$$ −16.0000 −0.533037
$$902$$ 72.0000 2.39734
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ −16.0000 −0.531564
$$907$$ −31.0000 −1.02934 −0.514669 0.857389i $$-0.672085\pi$$
−0.514669 + 0.857389i $$0.672085\pi$$
$$908$$ 20.0000 0.663723
$$909$$ −10.0000 −0.331679
$$910$$ 0 0
$$911$$ 12.0000 0.397578 0.198789 0.980042i $$-0.436299\pi$$
0.198789 + 0.980042i $$0.436299\pi$$
$$912$$ 4.00000 0.132453
$$913$$ 12.0000 0.397142
$$914$$ 30.0000 0.992312
$$915$$ 0 0
$$916$$ 26.0000 0.859064
$$917$$ 0 0
$$918$$ −8.00000 −0.264039
$$919$$ −9.00000 −0.296883 −0.148441 0.988921i $$-0.547426\pi$$
−0.148441 + 0.988921i $$0.547426\pi$$
$$920$$ 0 0
$$921$$ 3.00000 0.0988534
$$922$$ −16.0000 −0.526932
$$923$$ 18.0000 0.592477
$$924$$ 0 0
$$925$$ 0 0
$$926$$ −6.00000 −0.197172
$$927$$ 19.0000 0.624042
$$928$$ 64.0000 2.10090
$$929$$ −14.0000 −0.459325 −0.229663 0.973270i $$-0.573762\pi$$
−0.229663 + 0.973270i $$0.573762\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ −12.0000 −0.393073
$$933$$ −6.00000 −0.196431
$$934$$ −44.0000 −1.43972
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 29.0000 0.947389 0.473694 0.880689i $$-0.342920\pi$$
0.473694 + 0.880689i $$0.342920\pi$$
$$938$$ 0 0
$$939$$ 11.0000 0.358971
$$940$$ 0 0
$$941$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$942$$ 20.0000 0.651635
$$943$$ −24.0000 −0.781548
$$944$$ 32.0000 1.04151
$$945$$ 0 0
$$946$$ 12.0000 0.390154
$$947$$ −26.0000 −0.844886 −0.422443 0.906389i $$-0.638827\pi$$
−0.422443 + 0.906389i $$0.638827\pi$$
$$948$$ 2.00000 0.0649570
$$949$$ −3.00000 −0.0973841
$$950$$ 0 0
$$951$$ 20.0000 0.648544
$$952$$ 0 0
$$953$$ −4.00000 −0.129573 −0.0647864 0.997899i $$-0.520637\pi$$
−0.0647864 + 0.997899i $$0.520637\pi$$
$$954$$ −8.00000 −0.259010
$$955$$ 0 0
$$956$$ 28.0000 0.905585
$$957$$ −48.0000 −1.55162
$$958$$ −8.00000 −0.258468
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −30.0000 −0.967742
$$962$$ −42.0000 −1.35413
$$963$$ −12.0000 −0.386695
$$964$$ −36.0000 −1.15948
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −55.0000 −1.76868 −0.884340 0.466843i $$-0.845391\pi$$
−0.884340 + 0.466843i $$0.845391\pi$$
$$968$$ 0 0
$$969$$ −4.00000 −0.128499
$$970$$ 0 0
$$971$$ −52.0000 −1.66876 −0.834380 0.551190i $$-0.814174\pi$$
−0.834380 + 0.551190i $$0.814174\pi$$
$$972$$ −2.00000 −0.0641500
$$973$$ 0 0
$$974$$ 26.0000 0.833094
$$975$$ 0 0
$$976$$ 56.0000 1.79252
$$977$$ 22.0000 0.703842 0.351921 0.936030i $$-0.385529\pi$$
0.351921 + 0.936030i $$0.385529\pi$$
$$978$$ −24.0000 −0.767435
$$979$$ 72.0000 2.30113
$$980$$ 0 0
$$981$$ −15.0000 −0.478913
$$982$$ −24.0000 −0.765871
$$983$$ −32.0000 −1.02064 −0.510321 0.859984i $$-0.670473\pi$$
−0.510321 + 0.859984i $$0.670473\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ −64.0000 −2.03818
$$987$$ 0 0
$$988$$ 6.00000 0.190885
$$989$$ −4.00000 −0.127193
$$990$$ 0 0
$$991$$ −15.0000 −0.476491 −0.238245 0.971205i $$-0.576572\pi$$
−0.238245 + 0.971205i $$0.576572\pi$$
$$992$$ −8.00000 −0.254000
$$993$$ 9.00000 0.285606
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 4.00000 0.126745
$$997$$ 25.0000 0.791758 0.395879 0.918303i $$-0.370440\pi$$
0.395879 + 0.918303i $$0.370440\pi$$
$$998$$ 58.0000 1.83596
$$999$$ 7.00000 0.221470
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 3675.2.a.o.1.1 1
5.4 even 2 735.2.a.b.1.1 1
7.2 even 3 525.2.i.a.151.1 2
7.4 even 3 525.2.i.a.226.1 2
7.6 odd 2 3675.2.a.p.1.1 1
15.14 odd 2 2205.2.a.k.1.1 1
35.2 odd 12 525.2.r.d.424.2 4
35.4 even 6 105.2.i.b.16.1 2
35.9 even 6 105.2.i.b.46.1 yes 2
35.18 odd 12 525.2.r.d.499.2 4
35.19 odd 6 735.2.i.f.361.1 2
35.23 odd 12 525.2.r.d.424.1 4
35.24 odd 6 735.2.i.f.226.1 2
35.32 odd 12 525.2.r.d.499.1 4
35.34 odd 2 735.2.a.a.1.1 1
105.44 odd 6 315.2.j.a.46.1 2
105.74 odd 6 315.2.j.a.226.1 2
105.104 even 2 2205.2.a.m.1.1 1
140.39 odd 6 1680.2.bg.l.961.1 2
140.79 odd 6 1680.2.bg.l.1201.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.i.b.16.1 2 35.4 even 6
105.2.i.b.46.1 yes 2 35.9 even 6
315.2.j.a.46.1 2 105.44 odd 6
315.2.j.a.226.1 2 105.74 odd 6
525.2.i.a.151.1 2 7.2 even 3
525.2.i.a.226.1 2 7.4 even 3
525.2.r.d.424.1 4 35.23 odd 12
525.2.r.d.424.2 4 35.2 odd 12
525.2.r.d.499.1 4 35.32 odd 12
525.2.r.d.499.2 4 35.18 odd 12
735.2.a.a.1.1 1 35.34 odd 2
735.2.a.b.1.1 1 5.4 even 2
735.2.i.f.226.1 2 35.24 odd 6
735.2.i.f.361.1 2 35.19 odd 6
1680.2.bg.l.961.1 2 140.39 odd 6
1680.2.bg.l.1201.1 2 140.79 odd 6
2205.2.a.k.1.1 1 15.14 odd 2
2205.2.a.m.1.1 1 105.104 even 2
3675.2.a.o.1.1 1 1.1 even 1 trivial
3675.2.a.p.1.1 1 7.6 odd 2