# Properties

 Label 6762.2.a.e.1.1 Level $6762$ Weight $2$ Character 6762.1 Self dual yes Analytic conductor $53.995$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 6762.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$53.9948418468$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 966) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 6762.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -3.00000 q^{11} -1.00000 q^{12} -2.00000 q^{13} +1.00000 q^{16} +3.00000 q^{17} -1.00000 q^{18} -2.00000 q^{19} +3.00000 q^{22} -1.00000 q^{23} +1.00000 q^{24} -5.00000 q^{25} +2.00000 q^{26} -1.00000 q^{27} +3.00000 q^{29} -2.00000 q^{31} -1.00000 q^{32} +3.00000 q^{33} -3.00000 q^{34} +1.00000 q^{36} +2.00000 q^{37} +2.00000 q^{38} +2.00000 q^{39} -6.00000 q^{41} +2.00000 q^{43} -3.00000 q^{44} +1.00000 q^{46} +3.00000 q^{47} -1.00000 q^{48} +5.00000 q^{50} -3.00000 q^{51} -2.00000 q^{52} -6.00000 q^{53} +1.00000 q^{54} +2.00000 q^{57} -3.00000 q^{58} -2.00000 q^{61} +2.00000 q^{62} +1.00000 q^{64} -3.00000 q^{66} +2.00000 q^{67} +3.00000 q^{68} +1.00000 q^{69} +3.00000 q^{71} -1.00000 q^{72} -11.0000 q^{73} -2.00000 q^{74} +5.00000 q^{75} -2.00000 q^{76} -2.00000 q^{78} +11.0000 q^{79} +1.00000 q^{81} +6.00000 q^{82} -2.00000 q^{86} -3.00000 q^{87} +3.00000 q^{88} +6.00000 q^{89} -1.00000 q^{92} +2.00000 q^{93} -3.00000 q^{94} +1.00000 q^{96} -8.00000 q^{97} -3.00000 q^{99} +O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 −0.707107
$$3$$ −1.00000 −0.577350
$$4$$ 1.00000 0.500000
$$5$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$6$$ 1.00000 0.408248
$$7$$ 0 0
$$8$$ −1.00000 −0.353553
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ −3.00000 −0.904534 −0.452267 0.891883i $$-0.649385\pi$$
−0.452267 + 0.891883i $$0.649385\pi$$
$$12$$ −1.00000 −0.288675
$$13$$ −2.00000 −0.554700 −0.277350 0.960769i $$-0.589456\pi$$
−0.277350 + 0.960769i $$0.589456\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 3.00000 0.727607 0.363803 0.931476i $$-0.381478\pi$$
0.363803 + 0.931476i $$0.381478\pi$$
$$18$$ −1.00000 −0.235702
$$19$$ −2.00000 −0.458831 −0.229416 0.973329i $$-0.573682\pi$$
−0.229416 + 0.973329i $$0.573682\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 3.00000 0.639602
$$23$$ −1.00000 −0.208514
$$24$$ 1.00000 0.204124
$$25$$ −5.00000 −1.00000
$$26$$ 2.00000 0.392232
$$27$$ −1.00000 −0.192450
$$28$$ 0 0
$$29$$ 3.00000 0.557086 0.278543 0.960424i $$-0.410149\pi$$
0.278543 + 0.960424i $$0.410149\pi$$
$$30$$ 0 0
$$31$$ −2.00000 −0.359211 −0.179605 0.983739i $$-0.557482\pi$$
−0.179605 + 0.983739i $$0.557482\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 3.00000 0.522233
$$34$$ −3.00000 −0.514496
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ 2.00000 0.328798 0.164399 0.986394i $$-0.447432\pi$$
0.164399 + 0.986394i $$0.447432\pi$$
$$38$$ 2.00000 0.324443
$$39$$ 2.00000 0.320256
$$40$$ 0 0
$$41$$ −6.00000 −0.937043 −0.468521 0.883452i $$-0.655213\pi$$
−0.468521 + 0.883452i $$0.655213\pi$$
$$42$$ 0 0
$$43$$ 2.00000 0.304997 0.152499 0.988304i $$-0.451268\pi$$
0.152499 + 0.988304i $$0.451268\pi$$
$$44$$ −3.00000 −0.452267
$$45$$ 0 0
$$46$$ 1.00000 0.147442
$$47$$ 3.00000 0.437595 0.218797 0.975770i $$-0.429787\pi$$
0.218797 + 0.975770i $$0.429787\pi$$
$$48$$ −1.00000 −0.144338
$$49$$ 0 0
$$50$$ 5.00000 0.707107
$$51$$ −3.00000 −0.420084
$$52$$ −2.00000 −0.277350
$$53$$ −6.00000 −0.824163 −0.412082 0.911147i $$-0.635198\pi$$
−0.412082 + 0.911147i $$0.635198\pi$$
$$54$$ 1.00000 0.136083
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 2.00000 0.264906
$$58$$ −3.00000 −0.393919
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ −2.00000 −0.256074 −0.128037 0.991769i $$-0.540868\pi$$
−0.128037 + 0.991769i $$0.540868\pi$$
$$62$$ 2.00000 0.254000
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ −3.00000 −0.369274
$$67$$ 2.00000 0.244339 0.122169 0.992509i $$-0.461015\pi$$
0.122169 + 0.992509i $$0.461015\pi$$
$$68$$ 3.00000 0.363803
$$69$$ 1.00000 0.120386
$$70$$ 0 0
$$71$$ 3.00000 0.356034 0.178017 0.984027i $$-0.443032\pi$$
0.178017 + 0.984027i $$0.443032\pi$$
$$72$$ −1.00000 −0.117851
$$73$$ −11.0000 −1.28745 −0.643726 0.765256i $$-0.722612\pi$$
−0.643726 + 0.765256i $$0.722612\pi$$
$$74$$ −2.00000 −0.232495
$$75$$ 5.00000 0.577350
$$76$$ −2.00000 −0.229416
$$77$$ 0 0
$$78$$ −2.00000 −0.226455
$$79$$ 11.0000 1.23760 0.618798 0.785550i $$-0.287620\pi$$
0.618798 + 0.785550i $$0.287620\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 6.00000 0.662589
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −2.00000 −0.215666
$$87$$ −3.00000 −0.321634
$$88$$ 3.00000 0.319801
$$89$$ 6.00000 0.635999 0.317999 0.948091i $$-0.396989\pi$$
0.317999 + 0.948091i $$0.396989\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −1.00000 −0.104257
$$93$$ 2.00000 0.207390
$$94$$ −3.00000 −0.309426
$$95$$ 0 0
$$96$$ 1.00000 0.102062
$$97$$ −8.00000 −0.812277 −0.406138 0.913812i $$-0.633125\pi$$
−0.406138 + 0.913812i $$0.633125\pi$$
$$98$$ 0 0
$$99$$ −3.00000 −0.301511
$$100$$ −5.00000 −0.500000
$$101$$ 3.00000 0.298511 0.149256 0.988799i $$-0.452312\pi$$
0.149256 + 0.988799i $$0.452312\pi$$
$$102$$ 3.00000 0.297044
$$103$$ −5.00000 −0.492665 −0.246332 0.969185i $$-0.579225\pi$$
−0.246332 + 0.969185i $$0.579225\pi$$
$$104$$ 2.00000 0.196116
$$105$$ 0 0
$$106$$ 6.00000 0.582772
$$107$$ 12.0000 1.16008 0.580042 0.814587i $$-0.303036\pi$$
0.580042 + 0.814587i $$0.303036\pi$$
$$108$$ −1.00000 −0.0962250
$$109$$ −1.00000 −0.0957826 −0.0478913 0.998853i $$-0.515250\pi$$
−0.0478913 + 0.998853i $$0.515250\pi$$
$$110$$ 0 0
$$111$$ −2.00000 −0.189832
$$112$$ 0 0
$$113$$ 18.0000 1.69330 0.846649 0.532152i $$-0.178617\pi$$
0.846649 + 0.532152i $$0.178617\pi$$
$$114$$ −2.00000 −0.187317
$$115$$ 0 0
$$116$$ 3.00000 0.278543
$$117$$ −2.00000 −0.184900
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −2.00000 −0.181818
$$122$$ 2.00000 0.181071
$$123$$ 6.00000 0.541002
$$124$$ −2.00000 −0.179605
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 2.00000 0.177471 0.0887357 0.996055i $$-0.471717\pi$$
0.0887357 + 0.996055i $$0.471717\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ −2.00000 −0.176090
$$130$$ 0 0
$$131$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ 3.00000 0.261116
$$133$$ 0 0
$$134$$ −2.00000 −0.172774
$$135$$ 0 0
$$136$$ −3.00000 −0.257248
$$137$$ −21.0000 −1.79415 −0.897076 0.441877i $$-0.854313\pi$$
−0.897076 + 0.441877i $$0.854313\pi$$
$$138$$ −1.00000 −0.0851257
$$139$$ 13.0000 1.10265 0.551323 0.834292i $$-0.314123\pi$$
0.551323 + 0.834292i $$0.314123\pi$$
$$140$$ 0 0
$$141$$ −3.00000 −0.252646
$$142$$ −3.00000 −0.251754
$$143$$ 6.00000 0.501745
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ 11.0000 0.910366
$$147$$ 0 0
$$148$$ 2.00000 0.164399
$$149$$ 12.0000 0.983078 0.491539 0.870855i $$-0.336434\pi$$
0.491539 + 0.870855i $$0.336434\pi$$
$$150$$ −5.00000 −0.408248
$$151$$ −4.00000 −0.325515 −0.162758 0.986666i $$-0.552039\pi$$
−0.162758 + 0.986666i $$0.552039\pi$$
$$152$$ 2.00000 0.162221
$$153$$ 3.00000 0.242536
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 2.00000 0.160128
$$157$$ −23.0000 −1.83560 −0.917800 0.397043i $$-0.870036\pi$$
−0.917800 + 0.397043i $$0.870036\pi$$
$$158$$ −11.0000 −0.875113
$$159$$ 6.00000 0.475831
$$160$$ 0 0
$$161$$ 0 0
$$162$$ −1.00000 −0.0785674
$$163$$ 23.0000 1.80150 0.900750 0.434339i $$-0.143018\pi$$
0.900750 + 0.434339i $$0.143018\pi$$
$$164$$ −6.00000 −0.468521
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ 0 0
$$171$$ −2.00000 −0.152944
$$172$$ 2.00000 0.152499
$$173$$ 15.0000 1.14043 0.570214 0.821496i $$-0.306860\pi$$
0.570214 + 0.821496i $$0.306860\pi$$
$$174$$ 3.00000 0.227429
$$175$$ 0 0
$$176$$ −3.00000 −0.226134
$$177$$ 0 0
$$178$$ −6.00000 −0.449719
$$179$$ 6.00000 0.448461 0.224231 0.974536i $$-0.428013\pi$$
0.224231 + 0.974536i $$0.428013\pi$$
$$180$$ 0 0
$$181$$ −11.0000 −0.817624 −0.408812 0.912619i $$-0.634057\pi$$
−0.408812 + 0.912619i $$0.634057\pi$$
$$182$$ 0 0
$$183$$ 2.00000 0.147844
$$184$$ 1.00000 0.0737210
$$185$$ 0 0
$$186$$ −2.00000 −0.146647
$$187$$ −9.00000 −0.658145
$$188$$ 3.00000 0.218797
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 12.0000 0.868290 0.434145 0.900843i $$-0.357051\pi$$
0.434145 + 0.900843i $$0.357051\pi$$
$$192$$ −1.00000 −0.0721688
$$193$$ 14.0000 1.00774 0.503871 0.863779i $$-0.331909\pi$$
0.503871 + 0.863779i $$0.331909\pi$$
$$194$$ 8.00000 0.574367
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 15.0000 1.06871 0.534353 0.845262i $$-0.320555\pi$$
0.534353 + 0.845262i $$0.320555\pi$$
$$198$$ 3.00000 0.213201
$$199$$ −17.0000 −1.20510 −0.602549 0.798082i $$-0.705848\pi$$
−0.602549 + 0.798082i $$0.705848\pi$$
$$200$$ 5.00000 0.353553
$$201$$ −2.00000 −0.141069
$$202$$ −3.00000 −0.211079
$$203$$ 0 0
$$204$$ −3.00000 −0.210042
$$205$$ 0 0
$$206$$ 5.00000 0.348367
$$207$$ −1.00000 −0.0695048
$$208$$ −2.00000 −0.138675
$$209$$ 6.00000 0.415029
$$210$$ 0 0
$$211$$ −19.0000 −1.30801 −0.654007 0.756489i $$-0.726913\pi$$
−0.654007 + 0.756489i $$0.726913\pi$$
$$212$$ −6.00000 −0.412082
$$213$$ −3.00000 −0.205557
$$214$$ −12.0000 −0.820303
$$215$$ 0 0
$$216$$ 1.00000 0.0680414
$$217$$ 0 0
$$218$$ 1.00000 0.0677285
$$219$$ 11.0000 0.743311
$$220$$ 0 0
$$221$$ −6.00000 −0.403604
$$222$$ 2.00000 0.134231
$$223$$ 10.0000 0.669650 0.334825 0.942280i $$-0.391323\pi$$
0.334825 + 0.942280i $$0.391323\pi$$
$$224$$ 0 0
$$225$$ −5.00000 −0.333333
$$226$$ −18.0000 −1.19734
$$227$$ 3.00000 0.199117 0.0995585 0.995032i $$-0.468257\pi$$
0.0995585 + 0.995032i $$0.468257\pi$$
$$228$$ 2.00000 0.132453
$$229$$ 1.00000 0.0660819 0.0330409 0.999454i $$-0.489481\pi$$
0.0330409 + 0.999454i $$0.489481\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −3.00000 −0.196960
$$233$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$234$$ 2.00000 0.130744
$$235$$ 0 0
$$236$$ 0 0
$$237$$ −11.0000 −0.714527
$$238$$ 0 0
$$239$$ 15.0000 0.970269 0.485135 0.874439i $$-0.338771\pi$$
0.485135 + 0.874439i $$0.338771\pi$$
$$240$$ 0 0
$$241$$ −2.00000 −0.128831 −0.0644157 0.997923i $$-0.520518\pi$$
−0.0644157 + 0.997923i $$0.520518\pi$$
$$242$$ 2.00000 0.128565
$$243$$ −1.00000 −0.0641500
$$244$$ −2.00000 −0.128037
$$245$$ 0 0
$$246$$ −6.00000 −0.382546
$$247$$ 4.00000 0.254514
$$248$$ 2.00000 0.127000
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −3.00000 −0.189358 −0.0946792 0.995508i $$-0.530183\pi$$
−0.0946792 + 0.995508i $$0.530183\pi$$
$$252$$ 0 0
$$253$$ 3.00000 0.188608
$$254$$ −2.00000 −0.125491
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −6.00000 −0.374270 −0.187135 0.982334i $$-0.559920\pi$$
−0.187135 + 0.982334i $$0.559920\pi$$
$$258$$ 2.00000 0.124515
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 3.00000 0.185695
$$262$$ 0 0
$$263$$ 24.0000 1.47990 0.739952 0.672660i $$-0.234848\pi$$
0.739952 + 0.672660i $$0.234848\pi$$
$$264$$ −3.00000 −0.184637
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −6.00000 −0.367194
$$268$$ 2.00000 0.122169
$$269$$ −15.0000 −0.914566 −0.457283 0.889321i $$-0.651177\pi$$
−0.457283 + 0.889321i $$0.651177\pi$$
$$270$$ 0 0
$$271$$ 22.0000 1.33640 0.668202 0.743980i $$-0.267064\pi$$
0.668202 + 0.743980i $$0.267064\pi$$
$$272$$ 3.00000 0.181902
$$273$$ 0 0
$$274$$ 21.0000 1.26866
$$275$$ 15.0000 0.904534
$$276$$ 1.00000 0.0601929
$$277$$ 8.00000 0.480673 0.240337 0.970690i $$-0.422742\pi$$
0.240337 + 0.970690i $$0.422742\pi$$
$$278$$ −13.0000 −0.779688
$$279$$ −2.00000 −0.119737
$$280$$ 0 0
$$281$$ −3.00000 −0.178965 −0.0894825 0.995988i $$-0.528521\pi$$
−0.0894825 + 0.995988i $$0.528521\pi$$
$$282$$ 3.00000 0.178647
$$283$$ −8.00000 −0.475551 −0.237775 0.971320i $$-0.576418\pi$$
−0.237775 + 0.971320i $$0.576418\pi$$
$$284$$ 3.00000 0.178017
$$285$$ 0 0
$$286$$ −6.00000 −0.354787
$$287$$ 0 0
$$288$$ −1.00000 −0.0589256
$$289$$ −8.00000 −0.470588
$$290$$ 0 0
$$291$$ 8.00000 0.468968
$$292$$ −11.0000 −0.643726
$$293$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ −2.00000 −0.116248
$$297$$ 3.00000 0.174078
$$298$$ −12.0000 −0.695141
$$299$$ 2.00000 0.115663
$$300$$ 5.00000 0.288675
$$301$$ 0 0
$$302$$ 4.00000 0.230174
$$303$$ −3.00000 −0.172345
$$304$$ −2.00000 −0.114708
$$305$$ 0 0
$$306$$ −3.00000 −0.171499
$$307$$ −11.0000 −0.627803 −0.313902 0.949456i $$-0.601636\pi$$
−0.313902 + 0.949456i $$0.601636\pi$$
$$308$$ 0 0
$$309$$ 5.00000 0.284440
$$310$$ 0 0
$$311$$ 3.00000 0.170114 0.0850572 0.996376i $$-0.472893\pi$$
0.0850572 + 0.996376i $$0.472893\pi$$
$$312$$ −2.00000 −0.113228
$$313$$ −8.00000 −0.452187 −0.226093 0.974106i $$-0.572595\pi$$
−0.226093 + 0.974106i $$0.572595\pi$$
$$314$$ 23.0000 1.29797
$$315$$ 0 0
$$316$$ 11.0000 0.618798
$$317$$ −18.0000 −1.01098 −0.505490 0.862832i $$-0.668688\pi$$
−0.505490 + 0.862832i $$0.668688\pi$$
$$318$$ −6.00000 −0.336463
$$319$$ −9.00000 −0.503903
$$320$$ 0 0
$$321$$ −12.0000 −0.669775
$$322$$ 0 0
$$323$$ −6.00000 −0.333849
$$324$$ 1.00000 0.0555556
$$325$$ 10.0000 0.554700
$$326$$ −23.0000 −1.27385
$$327$$ 1.00000 0.0553001
$$328$$ 6.00000 0.331295
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 8.00000 0.439720 0.219860 0.975531i $$-0.429440\pi$$
0.219860 + 0.975531i $$0.429440\pi$$
$$332$$ 0 0
$$333$$ 2.00000 0.109599
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 14.0000 0.762629 0.381314 0.924445i $$-0.375472\pi$$
0.381314 + 0.924445i $$0.375472\pi$$
$$338$$ 9.00000 0.489535
$$339$$ −18.0000 −0.977626
$$340$$ 0 0
$$341$$ 6.00000 0.324918
$$342$$ 2.00000 0.108148
$$343$$ 0 0
$$344$$ −2.00000 −0.107833
$$345$$ 0 0
$$346$$ −15.0000 −0.806405
$$347$$ 6.00000 0.322097 0.161048 0.986947i $$-0.448512\pi$$
0.161048 + 0.986947i $$0.448512\pi$$
$$348$$ −3.00000 −0.160817
$$349$$ 22.0000 1.17763 0.588817 0.808267i $$-0.299594\pi$$
0.588817 + 0.808267i $$0.299594\pi$$
$$350$$ 0 0
$$351$$ 2.00000 0.106752
$$352$$ 3.00000 0.159901
$$353$$ 18.0000 0.958043 0.479022 0.877803i $$-0.340992\pi$$
0.479022 + 0.877803i $$0.340992\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 6.00000 0.317999
$$357$$ 0 0
$$358$$ −6.00000 −0.317110
$$359$$ −12.0000 −0.633336 −0.316668 0.948536i $$-0.602564\pi$$
−0.316668 + 0.948536i $$0.602564\pi$$
$$360$$ 0 0
$$361$$ −15.0000 −0.789474
$$362$$ 11.0000 0.578147
$$363$$ 2.00000 0.104973
$$364$$ 0 0
$$365$$ 0 0
$$366$$ −2.00000 −0.104542
$$367$$ −8.00000 −0.417597 −0.208798 0.977959i $$-0.566955\pi$$
−0.208798 + 0.977959i $$0.566955\pi$$
$$368$$ −1.00000 −0.0521286
$$369$$ −6.00000 −0.312348
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 2.00000 0.103695
$$373$$ −13.0000 −0.673114 −0.336557 0.941663i $$-0.609263\pi$$
−0.336557 + 0.941663i $$0.609263\pi$$
$$374$$ 9.00000 0.465379
$$375$$ 0 0
$$376$$ −3.00000 −0.154713
$$377$$ −6.00000 −0.309016
$$378$$ 0 0
$$379$$ 20.0000 1.02733 0.513665 0.857991i $$-0.328287\pi$$
0.513665 + 0.857991i $$0.328287\pi$$
$$380$$ 0 0
$$381$$ −2.00000 −0.102463
$$382$$ −12.0000 −0.613973
$$383$$ 6.00000 0.306586 0.153293 0.988181i $$-0.451012\pi$$
0.153293 + 0.988181i $$0.451012\pi$$
$$384$$ 1.00000 0.0510310
$$385$$ 0 0
$$386$$ −14.0000 −0.712581
$$387$$ 2.00000 0.101666
$$388$$ −8.00000 −0.406138
$$389$$ 24.0000 1.21685 0.608424 0.793612i $$-0.291802\pi$$
0.608424 + 0.793612i $$0.291802\pi$$
$$390$$ 0 0
$$391$$ −3.00000 −0.151717
$$392$$ 0 0
$$393$$ 0 0
$$394$$ −15.0000 −0.755689
$$395$$ 0 0
$$396$$ −3.00000 −0.150756
$$397$$ 34.0000 1.70641 0.853206 0.521575i $$-0.174655\pi$$
0.853206 + 0.521575i $$0.174655\pi$$
$$398$$ 17.0000 0.852133
$$399$$ 0 0
$$400$$ −5.00000 −0.250000
$$401$$ −15.0000 −0.749064 −0.374532 0.927214i $$-0.622197\pi$$
−0.374532 + 0.927214i $$0.622197\pi$$
$$402$$ 2.00000 0.0997509
$$403$$ 4.00000 0.199254
$$404$$ 3.00000 0.149256
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −6.00000 −0.297409
$$408$$ 3.00000 0.148522
$$409$$ −29.0000 −1.43396 −0.716979 0.697095i $$-0.754476\pi$$
−0.716979 + 0.697095i $$0.754476\pi$$
$$410$$ 0 0
$$411$$ 21.0000 1.03585
$$412$$ −5.00000 −0.246332
$$413$$ 0 0
$$414$$ 1.00000 0.0491473
$$415$$ 0 0
$$416$$ 2.00000 0.0980581
$$417$$ −13.0000 −0.636613
$$418$$ −6.00000 −0.293470
$$419$$ 21.0000 1.02592 0.512959 0.858413i $$-0.328549\pi$$
0.512959 + 0.858413i $$0.328549\pi$$
$$420$$ 0 0
$$421$$ 17.0000 0.828529 0.414265 0.910156i $$-0.364039\pi$$
0.414265 + 0.910156i $$0.364039\pi$$
$$422$$ 19.0000 0.924906
$$423$$ 3.00000 0.145865
$$424$$ 6.00000 0.291386
$$425$$ −15.0000 −0.727607
$$426$$ 3.00000 0.145350
$$427$$ 0 0
$$428$$ 12.0000 0.580042
$$429$$ −6.00000 −0.289683
$$430$$ 0 0
$$431$$ 30.0000 1.44505 0.722525 0.691345i $$-0.242982\pi$$
0.722525 + 0.691345i $$0.242982\pi$$
$$432$$ −1.00000 −0.0481125
$$433$$ −2.00000 −0.0961139 −0.0480569 0.998845i $$-0.515303\pi$$
−0.0480569 + 0.998845i $$0.515303\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −1.00000 −0.0478913
$$437$$ 2.00000 0.0956730
$$438$$ −11.0000 −0.525600
$$439$$ −8.00000 −0.381819 −0.190910 0.981608i $$-0.561144\pi$$
−0.190910 + 0.981608i $$0.561144\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 6.00000 0.285391
$$443$$ −24.0000 −1.14027 −0.570137 0.821549i $$-0.693110\pi$$
−0.570137 + 0.821549i $$0.693110\pi$$
$$444$$ −2.00000 −0.0949158
$$445$$ 0 0
$$446$$ −10.0000 −0.473514
$$447$$ −12.0000 −0.567581
$$448$$ 0 0
$$449$$ 12.0000 0.566315 0.283158 0.959073i $$-0.408618\pi$$
0.283158 + 0.959073i $$0.408618\pi$$
$$450$$ 5.00000 0.235702
$$451$$ 18.0000 0.847587
$$452$$ 18.0000 0.846649
$$453$$ 4.00000 0.187936
$$454$$ −3.00000 −0.140797
$$455$$ 0 0
$$456$$ −2.00000 −0.0936586
$$457$$ 20.0000 0.935561 0.467780 0.883845i $$-0.345054\pi$$
0.467780 + 0.883845i $$0.345054\pi$$
$$458$$ −1.00000 −0.0467269
$$459$$ −3.00000 −0.140028
$$460$$ 0 0
$$461$$ 30.0000 1.39724 0.698620 0.715493i $$-0.253798\pi$$
0.698620 + 0.715493i $$0.253798\pi$$
$$462$$ 0 0
$$463$$ 32.0000 1.48717 0.743583 0.668644i $$-0.233125\pi$$
0.743583 + 0.668644i $$0.233125\pi$$
$$464$$ 3.00000 0.139272
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 21.0000 0.971764 0.485882 0.874024i $$-0.338498\pi$$
0.485882 + 0.874024i $$0.338498\pi$$
$$468$$ −2.00000 −0.0924500
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 23.0000 1.05978
$$472$$ 0 0
$$473$$ −6.00000 −0.275880
$$474$$ 11.0000 0.505247
$$475$$ 10.0000 0.458831
$$476$$ 0 0
$$477$$ −6.00000 −0.274721
$$478$$ −15.0000 −0.686084
$$479$$ −30.0000 −1.37073 −0.685367 0.728197i $$-0.740358\pi$$
−0.685367 + 0.728197i $$0.740358\pi$$
$$480$$ 0 0
$$481$$ −4.00000 −0.182384
$$482$$ 2.00000 0.0910975
$$483$$ 0 0
$$484$$ −2.00000 −0.0909091
$$485$$ 0 0
$$486$$ 1.00000 0.0453609
$$487$$ 2.00000 0.0906287 0.0453143 0.998973i $$-0.485571\pi$$
0.0453143 + 0.998973i $$0.485571\pi$$
$$488$$ 2.00000 0.0905357
$$489$$ −23.0000 −1.04010
$$490$$ 0 0
$$491$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$492$$ 6.00000 0.270501
$$493$$ 9.00000 0.405340
$$494$$ −4.00000 −0.179969
$$495$$ 0 0
$$496$$ −2.00000 −0.0898027
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 35.0000 1.56682 0.783408 0.621508i $$-0.213480\pi$$
0.783408 + 0.621508i $$0.213480\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 3.00000 0.133897
$$503$$ −30.0000 −1.33763 −0.668817 0.743427i $$-0.733199\pi$$
−0.668817 + 0.743427i $$0.733199\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ −3.00000 −0.133366
$$507$$ 9.00000 0.399704
$$508$$ 2.00000 0.0887357
$$509$$ 21.0000 0.930809 0.465404 0.885098i $$-0.345909\pi$$
0.465404 + 0.885098i $$0.345909\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −1.00000 −0.0441942
$$513$$ 2.00000 0.0883022
$$514$$ 6.00000 0.264649
$$515$$ 0 0
$$516$$ −2.00000 −0.0880451
$$517$$ −9.00000 −0.395820
$$518$$ 0 0
$$519$$ −15.0000 −0.658427
$$520$$ 0 0
$$521$$ 42.0000 1.84005 0.920027 0.391856i $$-0.128167\pi$$
0.920027 + 0.391856i $$0.128167\pi$$
$$522$$ −3.00000 −0.131306
$$523$$ 22.0000 0.961993 0.480996 0.876723i $$-0.340275\pi$$
0.480996 + 0.876723i $$0.340275\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ −24.0000 −1.04645
$$527$$ −6.00000 −0.261364
$$528$$ 3.00000 0.130558
$$529$$ 1.00000 0.0434783
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 12.0000 0.519778
$$534$$ 6.00000 0.259645
$$535$$ 0 0
$$536$$ −2.00000 −0.0863868
$$537$$ −6.00000 −0.258919
$$538$$ 15.0000 0.646696
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 20.0000 0.859867 0.429934 0.902861i $$-0.358537\pi$$
0.429934 + 0.902861i $$0.358537\pi$$
$$542$$ −22.0000 −0.944981
$$543$$ 11.0000 0.472055
$$544$$ −3.00000 −0.128624
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 17.0000 0.726868 0.363434 0.931620i $$-0.381604\pi$$
0.363434 + 0.931620i $$0.381604\pi$$
$$548$$ −21.0000 −0.897076
$$549$$ −2.00000 −0.0853579
$$550$$ −15.0000 −0.639602
$$551$$ −6.00000 −0.255609
$$552$$ −1.00000 −0.0425628
$$553$$ 0 0
$$554$$ −8.00000 −0.339887
$$555$$ 0 0
$$556$$ 13.0000 0.551323
$$557$$ 30.0000 1.27114 0.635570 0.772043i $$-0.280765\pi$$
0.635570 + 0.772043i $$0.280765\pi$$
$$558$$ 2.00000 0.0846668
$$559$$ −4.00000 −0.169182
$$560$$ 0 0
$$561$$ 9.00000 0.379980
$$562$$ 3.00000 0.126547
$$563$$ 9.00000 0.379305 0.189652 0.981851i $$-0.439264\pi$$
0.189652 + 0.981851i $$0.439264\pi$$
$$564$$ −3.00000 −0.126323
$$565$$ 0 0
$$566$$ 8.00000 0.336265
$$567$$ 0 0
$$568$$ −3.00000 −0.125877
$$569$$ −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 $$0.526673\pi$$
$$572$$ 6.00000 0.250873
$$573$$ −12.0000 −0.501307
$$574$$ 0 0
$$575$$ 5.00000 0.208514
$$576$$ 1.00000 0.0416667
$$577$$ 31.0000 1.29055 0.645273 0.763952i $$-0.276743\pi$$
0.645273 + 0.763952i $$0.276743\pi$$
$$578$$ 8.00000 0.332756
$$579$$ −14.0000 −0.581820
$$580$$ 0 0
$$581$$ 0 0
$$582$$ −8.00000 −0.331611
$$583$$ 18.0000 0.745484
$$584$$ 11.0000 0.455183
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 12.0000 0.495293 0.247647 0.968850i $$-0.420343\pi$$
0.247647 + 0.968850i $$0.420343\pi$$
$$588$$ 0 0
$$589$$ 4.00000 0.164817
$$590$$ 0 0
$$591$$ −15.0000 −0.617018
$$592$$ 2.00000 0.0821995
$$593$$ 42.0000 1.72473 0.862367 0.506284i $$-0.168981\pi$$
0.862367 + 0.506284i $$0.168981\pi$$
$$594$$ −3.00000 −0.123091
$$595$$ 0 0
$$596$$ 12.0000 0.491539
$$597$$ 17.0000 0.695764
$$598$$ −2.00000 −0.0817861
$$599$$ 15.0000 0.612883 0.306442 0.951889i $$-0.400862\pi$$
0.306442 + 0.951889i $$0.400862\pi$$
$$600$$ −5.00000 −0.204124
$$601$$ −26.0000 −1.06056 −0.530281 0.847822i $$-0.677914\pi$$
−0.530281 + 0.847822i $$0.677914\pi$$
$$602$$ 0 0
$$603$$ 2.00000 0.0814463
$$604$$ −4.00000 −0.162758
$$605$$ 0 0
$$606$$ 3.00000 0.121867
$$607$$ −14.0000 −0.568242 −0.284121 0.958788i $$-0.591702\pi$$
−0.284121 + 0.958788i $$0.591702\pi$$
$$608$$ 2.00000 0.0811107
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −6.00000 −0.242734
$$612$$ 3.00000 0.121268
$$613$$ 5.00000 0.201948 0.100974 0.994889i $$-0.467804\pi$$
0.100974 + 0.994889i $$0.467804\pi$$
$$614$$ 11.0000 0.443924
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 33.0000 1.32853 0.664265 0.747497i $$-0.268745\pi$$
0.664265 + 0.747497i $$0.268745\pi$$
$$618$$ −5.00000 −0.201129
$$619$$ −32.0000 −1.28619 −0.643094 0.765787i $$-0.722350\pi$$
−0.643094 + 0.765787i $$0.722350\pi$$
$$620$$ 0 0
$$621$$ 1.00000 0.0401286
$$622$$ −3.00000 −0.120289
$$623$$ 0 0
$$624$$ 2.00000 0.0800641
$$625$$ 25.0000 1.00000
$$626$$ 8.00000 0.319744
$$627$$ −6.00000 −0.239617
$$628$$ −23.0000 −0.917800
$$629$$ 6.00000 0.239236
$$630$$ 0 0
$$631$$ 17.0000 0.676759 0.338380 0.941010i $$-0.390121\pi$$
0.338380 + 0.941010i $$0.390121\pi$$
$$632$$ −11.0000 −0.437557
$$633$$ 19.0000 0.755182
$$634$$ 18.0000 0.714871
$$635$$ 0 0
$$636$$ 6.00000 0.237915
$$637$$ 0 0
$$638$$ 9.00000 0.356313
$$639$$ 3.00000 0.118678
$$640$$ 0 0
$$641$$ −3.00000 −0.118493 −0.0592464 0.998243i $$-0.518870\pi$$
−0.0592464 + 0.998243i $$0.518870\pi$$
$$642$$ 12.0000 0.473602
$$643$$ 28.0000 1.10421 0.552106 0.833774i $$-0.313824\pi$$
0.552106 + 0.833774i $$0.313824\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 6.00000 0.236067
$$647$$ 15.0000 0.589711 0.294855 0.955542i $$-0.404729\pi$$
0.294855 + 0.955542i $$0.404729\pi$$
$$648$$ −1.00000 −0.0392837
$$649$$ 0 0
$$650$$ −10.0000 −0.392232
$$651$$ 0 0
$$652$$ 23.0000 0.900750
$$653$$ 3.00000 0.117399 0.0586995 0.998276i $$-0.481305\pi$$
0.0586995 + 0.998276i $$0.481305\pi$$
$$654$$ −1.00000 −0.0391031
$$655$$ 0 0
$$656$$ −6.00000 −0.234261
$$657$$ −11.0000 −0.429151
$$658$$ 0 0
$$659$$ 3.00000 0.116863 0.0584317 0.998291i $$-0.481390\pi$$
0.0584317 + 0.998291i $$0.481390\pi$$
$$660$$ 0 0
$$661$$ −5.00000 −0.194477 −0.0972387 0.995261i $$-0.531001\pi$$
−0.0972387 + 0.995261i $$0.531001\pi$$
$$662$$ −8.00000 −0.310929
$$663$$ 6.00000 0.233021
$$664$$ 0 0
$$665$$ 0 0
$$666$$ −2.00000 −0.0774984
$$667$$ −3.00000 −0.116160
$$668$$ 0 0
$$669$$ −10.0000 −0.386622
$$670$$ 0 0
$$671$$ 6.00000 0.231627
$$672$$ 0 0
$$673$$ −19.0000 −0.732396 −0.366198 0.930537i $$-0.619341\pi$$
−0.366198 + 0.930537i $$0.619341\pi$$
$$674$$ −14.0000 −0.539260
$$675$$ 5.00000 0.192450
$$676$$ −9.00000 −0.346154
$$677$$ 18.0000 0.691796 0.345898 0.938272i $$-0.387574\pi$$
0.345898 + 0.938272i $$0.387574\pi$$
$$678$$ 18.0000 0.691286
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −3.00000 −0.114960
$$682$$ −6.00000 −0.229752
$$683$$ 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
$$687$$ −1.00000 −0.0381524
$$688$$ 2.00000 0.0762493
$$689$$ 12.0000 0.457164
$$690$$ 0 0
$$691$$ −17.0000 −0.646710 −0.323355 0.946278i $$-0.604811\pi$$
−0.323355 + 0.946278i $$0.604811\pi$$
$$692$$ 15.0000 0.570214
$$693$$ 0 0
$$694$$ −6.00000 −0.227757
$$695$$ 0 0
$$696$$ 3.00000 0.113715
$$697$$ −18.0000 −0.681799
$$698$$ −22.0000 −0.832712
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −42.0000 −1.58632 −0.793159 0.609015i $$-0.791565\pi$$
−0.793159 + 0.609015i $$0.791565\pi$$
$$702$$ −2.00000 −0.0754851
$$703$$ −4.00000 −0.150863
$$704$$ −3.00000 −0.113067
$$705$$ 0 0
$$706$$ −18.0000 −0.677439
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −31.0000 −1.16423 −0.582115 0.813107i $$-0.697775\pi$$
−0.582115 + 0.813107i $$0.697775\pi$$
$$710$$ 0 0
$$711$$ 11.0000 0.412532
$$712$$ −6.00000 −0.224860
$$713$$ 2.00000 0.0749006
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 6.00000 0.224231
$$717$$ −15.0000 −0.560185
$$718$$ 12.0000 0.447836
$$719$$ 48.0000 1.79010 0.895049 0.445968i $$-0.147140\pi$$
0.895049 + 0.445968i $$0.147140\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 15.0000 0.558242
$$723$$ 2.00000 0.0743808
$$724$$ −11.0000 −0.408812
$$725$$ −15.0000 −0.557086
$$726$$ −2.00000 −0.0742270
$$727$$ −23.0000 −0.853023 −0.426511 0.904482i $$-0.640258\pi$$
−0.426511 + 0.904482i $$0.640258\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 6.00000 0.221918
$$732$$ 2.00000 0.0739221
$$733$$ −41.0000 −1.51437 −0.757185 0.653201i $$-0.773426\pi$$
−0.757185 + 0.653201i $$0.773426\pi$$
$$734$$ 8.00000 0.295285
$$735$$ 0 0
$$736$$ 1.00000 0.0368605
$$737$$ −6.00000 −0.221013
$$738$$ 6.00000 0.220863
$$739$$ −25.0000 −0.919640 −0.459820 0.888012i $$-0.652086\pi$$
−0.459820 + 0.888012i $$0.652086\pi$$
$$740$$ 0 0
$$741$$ −4.00000 −0.146944
$$742$$ 0 0
$$743$$ −12.0000 −0.440237 −0.220119 0.975473i $$-0.570644\pi$$
−0.220119 + 0.975473i $$0.570644\pi$$
$$744$$ −2.00000 −0.0733236
$$745$$ 0 0
$$746$$ 13.0000 0.475964
$$747$$ 0 0
$$748$$ −9.00000 −0.329073
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 32.0000 1.16770 0.583848 0.811863i $$-0.301546\pi$$
0.583848 + 0.811863i $$0.301546\pi$$
$$752$$ 3.00000 0.109399
$$753$$ 3.00000 0.109326
$$754$$ 6.00000 0.218507
$$755$$ 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
$$759$$ −3.00000 −0.108893
$$760$$ 0 0
$$761$$ −48.0000 −1.74000 −0.869999 0.493053i $$-0.835881\pi$$
−0.869999 + 0.493053i $$0.835881\pi$$
$$762$$ 2.00000 0.0724524
$$763$$ 0 0
$$764$$ 12.0000 0.434145
$$765$$ 0 0
$$766$$ −6.00000 −0.216789
$$767$$ 0 0
$$768$$ −1.00000 −0.0360844
$$769$$ −14.0000 −0.504853 −0.252426 0.967616i $$-0.581229\pi$$
−0.252426 + 0.967616i $$0.581229\pi$$
$$770$$ 0 0
$$771$$ 6.00000 0.216085
$$772$$ 14.0000 0.503871
$$773$$ 36.0000 1.29483 0.647415 0.762138i $$-0.275850\pi$$
0.647415 + 0.762138i $$0.275850\pi$$
$$774$$ −2.00000 −0.0718885
$$775$$ 10.0000 0.359211
$$776$$ 8.00000 0.287183
$$777$$ 0 0
$$778$$ −24.0000 −0.860442
$$779$$ 12.0000 0.429945
$$780$$ 0 0
$$781$$ −9.00000 −0.322045
$$782$$ 3.00000 0.107280
$$783$$ −3.00000 −0.107211
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 40.0000 1.42585 0.712923 0.701242i $$-0.247371\pi$$
0.712923 + 0.701242i $$0.247371\pi$$
$$788$$ 15.0000 0.534353
$$789$$ −24.0000 −0.854423
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 3.00000 0.106600
$$793$$ 4.00000 0.142044
$$794$$ −34.0000 −1.20661
$$795$$ 0 0
$$796$$ −17.0000 −0.602549
$$797$$ −30.0000 −1.06265 −0.531327 0.847167i $$-0.678307\pi$$
−0.531327 + 0.847167i $$0.678307\pi$$
$$798$$ 0 0
$$799$$ 9.00000 0.318397
$$800$$ 5.00000 0.176777
$$801$$ 6.00000 0.212000
$$802$$ 15.0000 0.529668
$$803$$ 33.0000 1.16454
$$804$$ −2.00000 −0.0705346
$$805$$ 0 0
$$806$$ −4.00000 −0.140894
$$807$$ 15.0000 0.528025
$$808$$ −3.00000 −0.105540
$$809$$ 30.0000 1.05474 0.527372 0.849635i $$-0.323177\pi$$
0.527372 + 0.849635i $$0.323177\pi$$
$$810$$ 0 0
$$811$$ 7.00000 0.245803 0.122902 0.992419i $$-0.460780\pi$$
0.122902 + 0.992419i $$0.460780\pi$$
$$812$$ 0 0
$$813$$ −22.0000 −0.771574
$$814$$ 6.00000 0.210300
$$815$$ 0 0
$$816$$ −3.00000 −0.105021
$$817$$ −4.00000 −0.139942
$$818$$ 29.0000 1.01396
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 33.0000 1.15171 0.575854 0.817553i $$-0.304670\pi$$
0.575854 + 0.817553i $$0.304670\pi$$
$$822$$ −21.0000 −0.732459
$$823$$ −22.0000 −0.766872 −0.383436 0.923567i $$-0.625259\pi$$
−0.383436 + 0.923567i $$0.625259\pi$$
$$824$$ 5.00000 0.174183
$$825$$ −15.0000 −0.522233
$$826$$ 0 0
$$827$$ −21.0000 −0.730242 −0.365121 0.930960i $$-0.618972\pi$$
−0.365121 + 0.930960i $$0.618972\pi$$
$$828$$ −1.00000 −0.0347524
$$829$$ −38.0000 −1.31979 −0.659897 0.751356i $$-0.729400\pi$$
−0.659897 + 0.751356i $$0.729400\pi$$
$$830$$ 0 0
$$831$$ −8.00000 −0.277517
$$832$$ −2.00000 −0.0693375
$$833$$ 0 0
$$834$$ 13.0000 0.450153
$$835$$ 0 0
$$836$$ 6.00000 0.207514
$$837$$ 2.00000 0.0691301
$$838$$ −21.0000 −0.725433
$$839$$ 36.0000 1.24286 0.621429 0.783470i $$-0.286552\pi$$
0.621429 + 0.783470i $$0.286552\pi$$
$$840$$ 0 0
$$841$$ −20.0000 −0.689655
$$842$$ −17.0000 −0.585859
$$843$$ 3.00000 0.103325
$$844$$ −19.0000 −0.654007
$$845$$ 0 0
$$846$$ −3.00000 −0.103142
$$847$$ 0 0
$$848$$ −6.00000 −0.206041
$$849$$ 8.00000 0.274559
$$850$$ 15.0000 0.514496
$$851$$ −2.00000 −0.0685591
$$852$$ −3.00000 −0.102778
$$853$$ 46.0000 1.57501 0.787505 0.616308i $$-0.211372\pi$$
0.787505 + 0.616308i $$0.211372\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ −12.0000 −0.410152
$$857$$ 18.0000 0.614868 0.307434 0.951569i $$-0.400530\pi$$
0.307434 + 0.951569i $$0.400530\pi$$
$$858$$ 6.00000 0.204837
$$859$$ −11.0000 −0.375315 −0.187658 0.982235i $$-0.560090\pi$$
−0.187658 + 0.982235i $$0.560090\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ −30.0000 −1.02180
$$863$$ 3.00000 0.102121 0.0510606 0.998696i $$-0.483740\pi$$
0.0510606 + 0.998696i $$0.483740\pi$$
$$864$$ 1.00000 0.0340207
$$865$$ 0 0
$$866$$ 2.00000 0.0679628
$$867$$ 8.00000 0.271694
$$868$$ 0 0
$$869$$ −33.0000 −1.11945
$$870$$ 0 0
$$871$$ −4.00000 −0.135535
$$872$$ 1.00000 0.0338643
$$873$$ −8.00000 −0.270759
$$874$$ −2.00000 −0.0676510
$$875$$ 0 0
$$876$$ 11.0000 0.371656
$$877$$ −4.00000 −0.135070 −0.0675352 0.997717i $$-0.521513\pi$$
−0.0675352 + 0.997717i $$0.521513\pi$$
$$878$$ 8.00000 0.269987
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 15.0000 0.505363 0.252681 0.967550i $$-0.418688\pi$$
0.252681 + 0.967550i $$0.418688\pi$$
$$882$$ 0 0
$$883$$ 20.0000 0.673054 0.336527 0.941674i $$-0.390748\pi$$
0.336527 + 0.941674i $$0.390748\pi$$
$$884$$ −6.00000 −0.201802
$$885$$ 0 0
$$886$$ 24.0000 0.806296
$$887$$ −27.0000 −0.906571 −0.453286 0.891365i $$-0.649748\pi$$
−0.453286 + 0.891365i $$0.649748\pi$$
$$888$$ 2.00000 0.0671156
$$889$$ 0 0
$$890$$ 0 0
$$891$$ −3.00000 −0.100504
$$892$$ 10.0000 0.334825
$$893$$ −6.00000 −0.200782
$$894$$ 12.0000 0.401340
$$895$$ 0 0
$$896$$ 0 0
$$897$$ −2.00000 −0.0667781
$$898$$ −12.0000 −0.400445
$$899$$ −6.00000 −0.200111
$$900$$ −5.00000 −0.166667
$$901$$ −18.0000 −0.599667
$$902$$ −18.0000 −0.599334
$$903$$ 0 0
$$904$$ −18.0000 −0.598671
$$905$$ 0 0
$$906$$ −4.00000 −0.132891
$$907$$ 44.0000 1.46100 0.730498 0.682915i $$-0.239288\pi$$
0.730498 + 0.682915i $$0.239288\pi$$
$$908$$ 3.00000 0.0995585
$$909$$ 3.00000 0.0995037
$$910$$ 0 0
$$911$$ −24.0000 −0.795155 −0.397578 0.917568i $$-0.630149\pi$$
−0.397578 + 0.917568i $$0.630149\pi$$
$$912$$ 2.00000 0.0662266
$$913$$ 0 0
$$914$$ −20.0000 −0.661541
$$915$$ 0 0
$$916$$ 1.00000 0.0330409
$$917$$ 0 0
$$918$$ 3.00000 0.0990148
$$919$$ 29.0000 0.956622 0.478311 0.878191i $$-0.341249\pi$$
0.478311 + 0.878191i $$0.341249\pi$$
$$920$$ 0 0
$$921$$ 11.0000 0.362462
$$922$$ −30.0000 −0.987997
$$923$$ −6.00000 −0.197492
$$924$$ 0 0
$$925$$ −10.0000 −0.328798
$$926$$ −32.0000 −1.05159
$$927$$ −5.00000 −0.164222
$$928$$ −3.00000 −0.0984798
$$929$$ −42.0000 −1.37798 −0.688988 0.724773i $$-0.741945\pi$$
−0.688988 + 0.724773i $$0.741945\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ −3.00000 −0.0982156
$$934$$ −21.0000 −0.687141
$$935$$ 0 0
$$936$$ 2.00000 0.0653720
$$937$$ −38.0000 −1.24141 −0.620703 0.784046i $$-0.713153\pi$$
−0.620703 + 0.784046i $$0.713153\pi$$
$$938$$ 0 0
$$939$$ 8.00000 0.261070
$$940$$ 0 0
$$941$$ −54.0000 −1.76035 −0.880175 0.474650i $$-0.842575\pi$$
−0.880175 + 0.474650i $$0.842575\pi$$
$$942$$ −23.0000 −0.749380
$$943$$ 6.00000 0.195387
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 6.00000 0.195077
$$947$$ −6.00000 −0.194974 −0.0974869 0.995237i $$-0.531080\pi$$
−0.0974869 + 0.995237i $$0.531080\pi$$
$$948$$ −11.0000 −0.357263
$$949$$ 22.0000 0.714150
$$950$$ −10.0000 −0.324443
$$951$$ 18.0000 0.583690
$$952$$ 0 0
$$953$$ 33.0000 1.06897 0.534487 0.845176i $$-0.320505\pi$$
0.534487 + 0.845176i $$0.320505\pi$$
$$954$$ 6.00000 0.194257
$$955$$ 0 0
$$956$$ 15.0000 0.485135
$$957$$ 9.00000 0.290929
$$958$$ 30.0000 0.969256
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −27.0000 −0.870968
$$962$$ 4.00000 0.128965
$$963$$ 12.0000 0.386695
$$964$$ −2.00000 −0.0644157
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 14.0000 0.450210 0.225105 0.974335i $$-0.427728\pi$$
0.225105 + 0.974335i $$0.427728\pi$$
$$968$$ 2.00000 0.0642824
$$969$$ 6.00000 0.192748
$$970$$ 0 0
$$971$$ −45.0000 −1.44412 −0.722059 0.691831i $$-0.756804\pi$$
−0.722059 + 0.691831i $$0.756804\pi$$
$$972$$ −1.00000 −0.0320750
$$973$$ 0 0
$$974$$ −2.00000 −0.0640841
$$975$$ −10.0000 −0.320256
$$976$$ −2.00000 −0.0640184
$$977$$ 18.0000 0.575871 0.287936 0.957650i $$-0.407031\pi$$
0.287936 + 0.957650i $$0.407031\pi$$
$$978$$ 23.0000 0.735459
$$979$$ −18.0000 −0.575282
$$980$$ 0 0
$$981$$ −1.00000 −0.0319275
$$982$$ 0 0
$$983$$ 18.0000 0.574111 0.287055 0.957914i $$-0.407324\pi$$
0.287055 + 0.957914i $$0.407324\pi$$
$$984$$ −6.00000 −0.191273
$$985$$ 0 0
$$986$$ −9.00000 −0.286618
$$987$$ 0 0
$$988$$ 4.00000 0.127257
$$989$$ −2.00000 −0.0635963
$$990$$ 0 0
$$991$$ −40.0000 −1.27064 −0.635321 0.772248i $$-0.719132\pi$$
−0.635321 + 0.772248i $$0.719132\pi$$
$$992$$ 2.00000 0.0635001
$$993$$ −8.00000 −0.253872
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 52.0000 1.64686 0.823428 0.567420i $$-0.192059\pi$$
0.823428 + 0.567420i $$0.192059\pi$$
$$998$$ −35.0000 −1.10791
$$999$$ −2.00000 −0.0632772
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 6762.2.a.e.1.1 1
7.3 odd 6 966.2.i.f.415.1 yes 2
7.5 odd 6 966.2.i.f.277.1 2
7.6 odd 2 6762.2.a.o.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
966.2.i.f.277.1 2 7.5 odd 6
966.2.i.f.415.1 yes 2 7.3 odd 6
6762.2.a.e.1.1 1 1.1 even 1 trivial
6762.2.a.o.1.1 1 7.6 odd 2