# Properties

 Label 2850.2.a.j.1.1 Level $2850$ Weight $2$ Character 2850.1 Self dual yes Analytic conductor $22.757$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2850.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$22.7573645761$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 114) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 2850.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -4.00000 q^{11} +1.00000 q^{12} -2.00000 q^{13} +1.00000 q^{16} +6.00000 q^{17} -1.00000 q^{18} -1.00000 q^{19} +4.00000 q^{22} +4.00000 q^{23} -1.00000 q^{24} +2.00000 q^{26} +1.00000 q^{27} -2.00000 q^{29} +4.00000 q^{31} -1.00000 q^{32} -4.00000 q^{33} -6.00000 q^{34} +1.00000 q^{36} -10.0000 q^{37} +1.00000 q^{38} -2.00000 q^{39} +10.0000 q^{41} -4.00000 q^{43} -4.00000 q^{44} -4.00000 q^{46} +4.00000 q^{47} +1.00000 q^{48} -7.00000 q^{49} +6.00000 q^{51} -2.00000 q^{52} +10.0000 q^{53} -1.00000 q^{54} -1.00000 q^{57} +2.00000 q^{58} +12.0000 q^{59} +14.0000 q^{61} -4.00000 q^{62} +1.00000 q^{64} +4.00000 q^{66} +12.0000 q^{67} +6.00000 q^{68} +4.00000 q^{69} +8.00000 q^{71} -1.00000 q^{72} +6.00000 q^{73} +10.0000 q^{74} -1.00000 q^{76} +2.00000 q^{78} -4.00000 q^{79} +1.00000 q^{81} -10.0000 q^{82} -12.0000 q^{83} +4.00000 q^{86} -2.00000 q^{87} +4.00000 q^{88} -6.00000 q^{89} +4.00000 q^{92} +4.00000 q^{93} -4.00000 q^{94} -1.00000 q^{96} -10.0000 q^{97} +7.00000 q^{98} -4.00000 q^{99} +O(q^{100})$$

## 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
$$6$$ −1.00000 −0.408248
$$7$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ −4.00000 −1.20605 −0.603023 0.797724i $$-0.706037\pi$$
−0.603023 + 0.797724i $$0.706037\pi$$
$$12$$ 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
$$17$$ 6.00000 1.45521 0.727607 0.685994i $$-0.240633\pi$$
0.727607 + 0.685994i $$0.240633\pi$$
$$18$$ −1.00000 −0.235702
$$19$$ −1.00000 −0.229416
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 4.00000 0.852803
$$23$$ 4.00000 0.834058 0.417029 0.908893i $$-0.363071\pi$$
0.417029 + 0.908893i $$0.363071\pi$$
$$24$$ −1.00000 −0.204124
$$25$$ 0 0
$$26$$ 2.00000 0.392232
$$27$$ 1.00000 0.192450
$$28$$ 0 0
$$29$$ −2.00000 −0.371391 −0.185695 0.982607i $$-0.559454\pi$$
−0.185695 + 0.982607i $$0.559454\pi$$
$$30$$ 0 0
$$31$$ 4.00000 0.718421 0.359211 0.933257i $$-0.383046\pi$$
0.359211 + 0.933257i $$0.383046\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ −4.00000 −0.696311
$$34$$ −6.00000 −1.02899
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ −10.0000 −1.64399 −0.821995 0.569495i $$-0.807139\pi$$
−0.821995 + 0.569495i $$0.807139\pi$$
$$38$$ 1.00000 0.162221
$$39$$ −2.00000 −0.320256
$$40$$ 0 0
$$41$$ 10.0000 1.56174 0.780869 0.624695i $$-0.214777\pi$$
0.780869 + 0.624695i $$0.214777\pi$$
$$42$$ 0 0
$$43$$ −4.00000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ −4.00000 −0.603023
$$45$$ 0 0
$$46$$ −4.00000 −0.589768
$$47$$ 4.00000 0.583460 0.291730 0.956501i $$-0.405769\pi$$
0.291730 + 0.956501i $$0.405769\pi$$
$$48$$ 1.00000 0.144338
$$49$$ −7.00000 −1.00000
$$50$$ 0 0
$$51$$ 6.00000 0.840168
$$52$$ −2.00000 −0.277350
$$53$$ 10.0000 1.37361 0.686803 0.726844i $$-0.259014\pi$$
0.686803 + 0.726844i $$0.259014\pi$$
$$54$$ −1.00000 −0.136083
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −1.00000 −0.132453
$$58$$ 2.00000 0.262613
$$59$$ 12.0000 1.56227 0.781133 0.624364i $$-0.214642\pi$$
0.781133 + 0.624364i $$0.214642\pi$$
$$60$$ 0 0
$$61$$ 14.0000 1.79252 0.896258 0.443533i $$-0.146275\pi$$
0.896258 + 0.443533i $$0.146275\pi$$
$$62$$ −4.00000 −0.508001
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 4.00000 0.492366
$$67$$ 12.0000 1.46603 0.733017 0.680211i $$-0.238112\pi$$
0.733017 + 0.680211i $$0.238112\pi$$
$$68$$ 6.00000 0.727607
$$69$$ 4.00000 0.481543
$$70$$ 0 0
$$71$$ 8.00000 0.949425 0.474713 0.880141i $$-0.342552\pi$$
0.474713 + 0.880141i $$0.342552\pi$$
$$72$$ −1.00000 −0.117851
$$73$$ 6.00000 0.702247 0.351123 0.936329i $$-0.385800\pi$$
0.351123 + 0.936329i $$0.385800\pi$$
$$74$$ 10.0000 1.16248
$$75$$ 0 0
$$76$$ −1.00000 −0.114708
$$77$$ 0 0
$$78$$ 2.00000 0.226455
$$79$$ −4.00000 −0.450035 −0.225018 0.974355i $$-0.572244\pi$$
−0.225018 + 0.974355i $$0.572244\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ −10.0000 −1.10432
$$83$$ −12.0000 −1.31717 −0.658586 0.752506i $$-0.728845\pi$$
−0.658586 + 0.752506i $$0.728845\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 4.00000 0.431331
$$87$$ −2.00000 −0.214423
$$88$$ 4.00000 0.426401
$$89$$ −6.00000 −0.635999 −0.317999 0.948091i $$-0.603011\pi$$
−0.317999 + 0.948091i $$0.603011\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 4.00000 0.417029
$$93$$ 4.00000 0.414781
$$94$$ −4.00000 −0.412568
$$95$$ 0 0
$$96$$ −1.00000 −0.102062
$$97$$ −10.0000 −1.01535 −0.507673 0.861550i $$-0.669494\pi$$
−0.507673 + 0.861550i $$0.669494\pi$$
$$98$$ 7.00000 0.707107
$$99$$ −4.00000 −0.402015
$$100$$ 0 0
$$101$$ 2.00000 0.199007 0.0995037 0.995037i $$-0.468274\pi$$
0.0995037 + 0.995037i $$0.468274\pi$$
$$102$$ −6.00000 −0.594089
$$103$$ 12.0000 1.18240 0.591198 0.806527i $$-0.298655\pi$$
0.591198 + 0.806527i $$0.298655\pi$$
$$104$$ 2.00000 0.196116
$$105$$ 0 0
$$106$$ −10.0000 −0.971286
$$107$$ 4.00000 0.386695 0.193347 0.981130i $$-0.438066\pi$$
0.193347 + 0.981130i $$0.438066\pi$$
$$108$$ 1.00000 0.0962250
$$109$$ −6.00000 −0.574696 −0.287348 0.957826i $$-0.592774\pi$$
−0.287348 + 0.957826i $$0.592774\pi$$
$$110$$ 0 0
$$111$$ −10.0000 −0.949158
$$112$$ 0 0
$$113$$ −2.00000 −0.188144 −0.0940721 0.995565i $$-0.529988\pi$$
−0.0940721 + 0.995565i $$0.529988\pi$$
$$114$$ 1.00000 0.0936586
$$115$$ 0 0
$$116$$ −2.00000 −0.185695
$$117$$ −2.00000 −0.184900
$$118$$ −12.0000 −1.10469
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 5.00000 0.454545
$$122$$ −14.0000 −1.26750
$$123$$ 10.0000 0.901670
$$124$$ 4.00000 0.359211
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 12.0000 1.06483 0.532414 0.846484i $$-0.321285\pi$$
0.532414 + 0.846484i $$0.321285\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ −4.00000 −0.352180
$$130$$ 0 0
$$131$$ 12.0000 1.04844 0.524222 0.851581i $$-0.324356\pi$$
0.524222 + 0.851581i $$0.324356\pi$$
$$132$$ −4.00000 −0.348155
$$133$$ 0 0
$$134$$ −12.0000 −1.03664
$$135$$ 0 0
$$136$$ −6.00000 −0.514496
$$137$$ 14.0000 1.19610 0.598050 0.801459i $$-0.295942\pi$$
0.598050 + 0.801459i $$0.295942\pi$$
$$138$$ −4.00000 −0.340503
$$139$$ 12.0000 1.01783 0.508913 0.860818i $$-0.330047\pi$$
0.508913 + 0.860818i $$0.330047\pi$$
$$140$$ 0 0
$$141$$ 4.00000 0.336861
$$142$$ −8.00000 −0.671345
$$143$$ 8.00000 0.668994
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ −6.00000 −0.496564
$$147$$ −7.00000 −0.577350
$$148$$ −10.0000 −0.821995
$$149$$ −6.00000 −0.491539 −0.245770 0.969328i $$-0.579041\pi$$
−0.245770 + 0.969328i $$0.579041\pi$$
$$150$$ 0 0
$$151$$ 20.0000 1.62758 0.813788 0.581161i $$-0.197401\pi$$
0.813788 + 0.581161i $$0.197401\pi$$
$$152$$ 1.00000 0.0811107
$$153$$ 6.00000 0.485071
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −2.00000 −0.160128
$$157$$ −22.0000 −1.75579 −0.877896 0.478852i $$-0.841053\pi$$
−0.877896 + 0.478852i $$0.841053\pi$$
$$158$$ 4.00000 0.318223
$$159$$ 10.0000 0.793052
$$160$$ 0 0
$$161$$ 0 0
$$162$$ −1.00000 −0.0785674
$$163$$ −20.0000 −1.56652 −0.783260 0.621694i $$-0.786445\pi$$
−0.783260 + 0.621694i $$0.786445\pi$$
$$164$$ 10.0000 0.780869
$$165$$ 0 0
$$166$$ 12.0000 0.931381
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ 0 0
$$171$$ −1.00000 −0.0764719
$$172$$ −4.00000 −0.304997
$$173$$ −6.00000 −0.456172 −0.228086 0.973641i $$-0.573247\pi$$
−0.228086 + 0.973641i $$0.573247\pi$$
$$174$$ 2.00000 0.151620
$$175$$ 0 0
$$176$$ −4.00000 −0.301511
$$177$$ 12.0000 0.901975
$$178$$ 6.00000 0.449719
$$179$$ 12.0000 0.896922 0.448461 0.893802i $$-0.351972\pi$$
0.448461 + 0.893802i $$0.351972\pi$$
$$180$$ 0 0
$$181$$ −14.0000 −1.04061 −0.520306 0.853980i $$-0.674182\pi$$
−0.520306 + 0.853980i $$0.674182\pi$$
$$182$$ 0 0
$$183$$ 14.0000 1.03491
$$184$$ −4.00000 −0.294884
$$185$$ 0 0
$$186$$ −4.00000 −0.293294
$$187$$ −24.0000 −1.75505
$$188$$ 4.00000 0.291730
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 4.00000 0.289430 0.144715 0.989473i $$-0.453773\pi$$
0.144715 + 0.989473i $$0.453773\pi$$
$$192$$ 1.00000 0.0721688
$$193$$ 6.00000 0.431889 0.215945 0.976406i $$-0.430717\pi$$
0.215945 + 0.976406i $$0.430717\pi$$
$$194$$ 10.0000 0.717958
$$195$$ 0 0
$$196$$ −7.00000 −0.500000
$$197$$ 22.0000 1.56744 0.783718 0.621117i $$-0.213321\pi$$
0.783718 + 0.621117i $$0.213321\pi$$
$$198$$ 4.00000 0.284268
$$199$$ −16.0000 −1.13421 −0.567105 0.823646i $$-0.691937\pi$$
−0.567105 + 0.823646i $$0.691937\pi$$
$$200$$ 0 0
$$201$$ 12.0000 0.846415
$$202$$ −2.00000 −0.140720
$$203$$ 0 0
$$204$$ 6.00000 0.420084
$$205$$ 0 0
$$206$$ −12.0000 −0.836080
$$207$$ 4.00000 0.278019
$$208$$ −2.00000 −0.138675
$$209$$ 4.00000 0.276686
$$210$$ 0 0
$$211$$ 12.0000 0.826114 0.413057 0.910705i $$-0.364461\pi$$
0.413057 + 0.910705i $$0.364461\pi$$
$$212$$ 10.0000 0.686803
$$213$$ 8.00000 0.548151
$$214$$ −4.00000 −0.273434
$$215$$ 0 0
$$216$$ −1.00000 −0.0680414
$$217$$ 0 0
$$218$$ 6.00000 0.406371
$$219$$ 6.00000 0.405442
$$220$$ 0 0
$$221$$ −12.0000 −0.807207
$$222$$ 10.0000 0.671156
$$223$$ 28.0000 1.87502 0.937509 0.347960i $$-0.113126\pi$$
0.937509 + 0.347960i $$0.113126\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 2.00000 0.133038
$$227$$ −28.0000 −1.85843 −0.929213 0.369546i $$-0.879513\pi$$
−0.929213 + 0.369546i $$0.879513\pi$$
$$228$$ −1.00000 −0.0662266
$$229$$ −10.0000 −0.660819 −0.330409 0.943838i $$-0.607187\pi$$
−0.330409 + 0.943838i $$0.607187\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 2.00000 0.131306
$$233$$ 6.00000 0.393073 0.196537 0.980497i $$-0.437031\pi$$
0.196537 + 0.980497i $$0.437031\pi$$
$$234$$ 2.00000 0.130744
$$235$$ 0 0
$$236$$ 12.0000 0.781133
$$237$$ −4.00000 −0.259828
$$238$$ 0 0
$$239$$ 12.0000 0.776215 0.388108 0.921614i $$-0.373129\pi$$
0.388108 + 0.921614i $$0.373129\pi$$
$$240$$ 0 0
$$241$$ 10.0000 0.644157 0.322078 0.946713i $$-0.395619\pi$$
0.322078 + 0.946713i $$0.395619\pi$$
$$242$$ −5.00000 −0.321412
$$243$$ 1.00000 0.0641500
$$244$$ 14.0000 0.896258
$$245$$ 0 0
$$246$$ −10.0000 −0.637577
$$247$$ 2.00000 0.127257
$$248$$ −4.00000 −0.254000
$$249$$ −12.0000 −0.760469
$$250$$ 0 0
$$251$$ −28.0000 −1.76734 −0.883672 0.468106i $$-0.844936\pi$$
−0.883672 + 0.468106i $$0.844936\pi$$
$$252$$ 0 0
$$253$$ −16.0000 −1.00591
$$254$$ −12.0000 −0.752947
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −2.00000 −0.124757 −0.0623783 0.998053i $$-0.519869\pi$$
−0.0623783 + 0.998053i $$0.519869\pi$$
$$258$$ 4.00000 0.249029
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −2.00000 −0.123797
$$262$$ −12.0000 −0.741362
$$263$$ 12.0000 0.739952 0.369976 0.929041i $$-0.379366\pi$$
0.369976 + 0.929041i $$0.379366\pi$$
$$264$$ 4.00000 0.246183
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −6.00000 −0.367194
$$268$$ 12.0000 0.733017
$$269$$ 6.00000 0.365826 0.182913 0.983129i $$-0.441447\pi$$
0.182913 + 0.983129i $$0.441447\pi$$
$$270$$ 0 0
$$271$$ −8.00000 −0.485965 −0.242983 0.970031i $$-0.578126\pi$$
−0.242983 + 0.970031i $$0.578126\pi$$
$$272$$ 6.00000 0.363803
$$273$$ 0 0
$$274$$ −14.0000 −0.845771
$$275$$ 0 0
$$276$$ 4.00000 0.240772
$$277$$ 26.0000 1.56219 0.781094 0.624413i $$-0.214662\pi$$
0.781094 + 0.624413i $$0.214662\pi$$
$$278$$ −12.0000 −0.719712
$$279$$ 4.00000 0.239474
$$280$$ 0 0
$$281$$ 10.0000 0.596550 0.298275 0.954480i $$-0.403589\pi$$
0.298275 + 0.954480i $$0.403589\pi$$
$$282$$ −4.00000 −0.238197
$$283$$ −12.0000 −0.713326 −0.356663 0.934233i $$-0.616086\pi$$
−0.356663 + 0.934233i $$0.616086\pi$$
$$284$$ 8.00000 0.474713
$$285$$ 0 0
$$286$$ −8.00000 −0.473050
$$287$$ 0 0
$$288$$ −1.00000 −0.0589256
$$289$$ 19.0000 1.11765
$$290$$ 0 0
$$291$$ −10.0000 −0.586210
$$292$$ 6.00000 0.351123
$$293$$ 18.0000 1.05157 0.525786 0.850617i $$-0.323771\pi$$
0.525786 + 0.850617i $$0.323771\pi$$
$$294$$ 7.00000 0.408248
$$295$$ 0 0
$$296$$ 10.0000 0.581238
$$297$$ −4.00000 −0.232104
$$298$$ 6.00000 0.347571
$$299$$ −8.00000 −0.462652
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −20.0000 −1.15087
$$303$$ 2.00000 0.114897
$$304$$ −1.00000 −0.0573539
$$305$$ 0 0
$$306$$ −6.00000 −0.342997
$$307$$ 12.0000 0.684876 0.342438 0.939540i $$-0.388747\pi$$
0.342438 + 0.939540i $$0.388747\pi$$
$$308$$ 0 0
$$309$$ 12.0000 0.682656
$$310$$ 0 0
$$311$$ 4.00000 0.226819 0.113410 0.993548i $$-0.463823\pi$$
0.113410 + 0.993548i $$0.463823\pi$$
$$312$$ 2.00000 0.113228
$$313$$ 22.0000 1.24351 0.621757 0.783210i $$-0.286419\pi$$
0.621757 + 0.783210i $$0.286419\pi$$
$$314$$ 22.0000 1.24153
$$315$$ 0 0
$$316$$ −4.00000 −0.225018
$$317$$ −6.00000 −0.336994 −0.168497 0.985702i $$-0.553891\pi$$
−0.168497 + 0.985702i $$0.553891\pi$$
$$318$$ −10.0000 −0.560772
$$319$$ 8.00000 0.447914
$$320$$ 0 0
$$321$$ 4.00000 0.223258
$$322$$ 0 0
$$323$$ −6.00000 −0.333849
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ 20.0000 1.10770
$$327$$ −6.00000 −0.331801
$$328$$ −10.0000 −0.552158
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −4.00000 −0.219860 −0.109930 0.993939i $$-0.535063\pi$$
−0.109930 + 0.993939i $$0.535063\pi$$
$$332$$ −12.0000 −0.658586
$$333$$ −10.0000 −0.547997
$$334$$ 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
$$339$$ −2.00000 −0.108625
$$340$$ 0 0
$$341$$ −16.0000 −0.866449
$$342$$ 1.00000 0.0540738
$$343$$ 0 0
$$344$$ 4.00000 0.215666
$$345$$ 0 0
$$346$$ 6.00000 0.322562
$$347$$ 20.0000 1.07366 0.536828 0.843692i $$-0.319622\pi$$
0.536828 + 0.843692i $$0.319622\pi$$
$$348$$ −2.00000 −0.107211
$$349$$ −26.0000 −1.39175 −0.695874 0.718164i $$-0.744983\pi$$
−0.695874 + 0.718164i $$0.744983\pi$$
$$350$$ 0 0
$$351$$ −2.00000 −0.106752
$$352$$ 4.00000 0.213201
$$353$$ −18.0000 −0.958043 −0.479022 0.877803i $$-0.659008\pi$$
−0.479022 + 0.877803i $$0.659008\pi$$
$$354$$ −12.0000 −0.637793
$$355$$ 0 0
$$356$$ −6.00000 −0.317999
$$357$$ 0 0
$$358$$ −12.0000 −0.634220
$$359$$ 12.0000 0.633336 0.316668 0.948536i $$-0.397436\pi$$
0.316668 + 0.948536i $$0.397436\pi$$
$$360$$ 0 0
$$361$$ 1.00000 0.0526316
$$362$$ 14.0000 0.735824
$$363$$ 5.00000 0.262432
$$364$$ 0 0
$$365$$ 0 0
$$366$$ −14.0000 −0.731792
$$367$$ 8.00000 0.417597 0.208798 0.977959i $$-0.433045\pi$$
0.208798 + 0.977959i $$0.433045\pi$$
$$368$$ 4.00000 0.208514
$$369$$ 10.0000 0.520579
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 4.00000 0.207390
$$373$$ −26.0000 −1.34623 −0.673114 0.739538i $$-0.735044\pi$$
−0.673114 + 0.739538i $$0.735044\pi$$
$$374$$ 24.0000 1.24101
$$375$$ 0 0
$$376$$ −4.00000 −0.206284
$$377$$ 4.00000 0.206010
$$378$$ 0 0
$$379$$ −36.0000 −1.84920 −0.924598 0.380945i $$-0.875599\pi$$
−0.924598 + 0.380945i $$0.875599\pi$$
$$380$$ 0 0
$$381$$ 12.0000 0.614779
$$382$$ −4.00000 −0.204658
$$383$$ −16.0000 −0.817562 −0.408781 0.912633i $$-0.634046\pi$$
−0.408781 + 0.912633i $$0.634046\pi$$
$$384$$ −1.00000 −0.0510310
$$385$$ 0 0
$$386$$ −6.00000 −0.305392
$$387$$ −4.00000 −0.203331
$$388$$ −10.0000 −0.507673
$$389$$ 18.0000 0.912636 0.456318 0.889817i $$-0.349168\pi$$
0.456318 + 0.889817i $$0.349168\pi$$
$$390$$ 0 0
$$391$$ 24.0000 1.21373
$$392$$ 7.00000 0.353553
$$393$$ 12.0000 0.605320
$$394$$ −22.0000 −1.10834
$$395$$ 0 0
$$396$$ −4.00000 −0.201008
$$397$$ 10.0000 0.501886 0.250943 0.968002i $$-0.419259\pi$$
0.250943 + 0.968002i $$0.419259\pi$$
$$398$$ 16.0000 0.802008
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −14.0000 −0.699127 −0.349563 0.936913i $$-0.613670\pi$$
−0.349563 + 0.936913i $$0.613670\pi$$
$$402$$ −12.0000 −0.598506
$$403$$ −8.00000 −0.398508
$$404$$ 2.00000 0.0995037
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 40.0000 1.98273
$$408$$ −6.00000 −0.297044
$$409$$ −14.0000 −0.692255 −0.346128 0.938187i $$-0.612504\pi$$
−0.346128 + 0.938187i $$0.612504\pi$$
$$410$$ 0 0
$$411$$ 14.0000 0.690569
$$412$$ 12.0000 0.591198
$$413$$ 0 0
$$414$$ −4.00000 −0.196589
$$415$$ 0 0
$$416$$ 2.00000 0.0980581
$$417$$ 12.0000 0.587643
$$418$$ −4.00000 −0.195646
$$419$$ −12.0000 −0.586238 −0.293119 0.956076i $$-0.594693\pi$$
−0.293119 + 0.956076i $$0.594693\pi$$
$$420$$ 0 0
$$421$$ 26.0000 1.26716 0.633581 0.773676i $$-0.281584\pi$$
0.633581 + 0.773676i $$0.281584\pi$$
$$422$$ −12.0000 −0.584151
$$423$$ 4.00000 0.194487
$$424$$ −10.0000 −0.485643
$$425$$ 0 0
$$426$$ −8.00000 −0.387601
$$427$$ 0 0
$$428$$ 4.00000 0.193347
$$429$$ 8.00000 0.386244
$$430$$ 0 0
$$431$$ −24.0000 −1.15604 −0.578020 0.816023i $$-0.696174\pi$$
−0.578020 + 0.816023i $$0.696174\pi$$
$$432$$ 1.00000 0.0481125
$$433$$ −26.0000 −1.24948 −0.624740 0.780833i $$-0.714795\pi$$
−0.624740 + 0.780833i $$0.714795\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −6.00000 −0.287348
$$437$$ −4.00000 −0.191346
$$438$$ −6.00000 −0.286691
$$439$$ −4.00000 −0.190910 −0.0954548 0.995434i $$-0.530431\pi$$
−0.0954548 + 0.995434i $$0.530431\pi$$
$$440$$ 0 0
$$441$$ −7.00000 −0.333333
$$442$$ 12.0000 0.570782
$$443$$ 20.0000 0.950229 0.475114 0.879924i $$-0.342407\pi$$
0.475114 + 0.879924i $$0.342407\pi$$
$$444$$ −10.0000 −0.474579
$$445$$ 0 0
$$446$$ −28.0000 −1.32584
$$447$$ −6.00000 −0.283790
$$448$$ 0 0
$$449$$ 34.0000 1.60456 0.802280 0.596948i $$-0.203620\pi$$
0.802280 + 0.596948i $$0.203620\pi$$
$$450$$ 0 0
$$451$$ −40.0000 −1.88353
$$452$$ −2.00000 −0.0940721
$$453$$ 20.0000 0.939682
$$454$$ 28.0000 1.31411
$$455$$ 0 0
$$456$$ 1.00000 0.0468293
$$457$$ −26.0000 −1.21623 −0.608114 0.793849i $$-0.708074\pi$$
−0.608114 + 0.793849i $$0.708074\pi$$
$$458$$ 10.0000 0.467269
$$459$$ 6.00000 0.280056
$$460$$ 0 0
$$461$$ 2.00000 0.0931493 0.0465746 0.998915i $$-0.485169\pi$$
0.0465746 + 0.998915i $$0.485169\pi$$
$$462$$ 0 0
$$463$$ 8.00000 0.371792 0.185896 0.982569i $$-0.440481\pi$$
0.185896 + 0.982569i $$0.440481\pi$$
$$464$$ −2.00000 −0.0928477
$$465$$ 0 0
$$466$$ −6.00000 −0.277945
$$467$$ 20.0000 0.925490 0.462745 0.886492i $$-0.346865\pi$$
0.462745 + 0.886492i $$0.346865\pi$$
$$468$$ −2.00000 −0.0924500
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −22.0000 −1.01371
$$472$$ −12.0000 −0.552345
$$473$$ 16.0000 0.735681
$$474$$ 4.00000 0.183726
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 10.0000 0.457869
$$478$$ −12.0000 −0.548867
$$479$$ 4.00000 0.182765 0.0913823 0.995816i $$-0.470871\pi$$
0.0913823 + 0.995816i $$0.470871\pi$$
$$480$$ 0 0
$$481$$ 20.0000 0.911922
$$482$$ −10.0000 −0.455488
$$483$$ 0 0
$$484$$ 5.00000 0.227273
$$485$$ 0 0
$$486$$ −1.00000 −0.0453609
$$487$$ −4.00000 −0.181257 −0.0906287 0.995885i $$-0.528888\pi$$
−0.0906287 + 0.995885i $$0.528888\pi$$
$$488$$ −14.0000 −0.633750
$$489$$ −20.0000 −0.904431
$$490$$ 0 0
$$491$$ 20.0000 0.902587 0.451294 0.892375i $$-0.350963\pi$$
0.451294 + 0.892375i $$0.350963\pi$$
$$492$$ 10.0000 0.450835
$$493$$ −12.0000 −0.540453
$$494$$ −2.00000 −0.0899843
$$495$$ 0 0
$$496$$ 4.00000 0.179605
$$497$$ 0 0
$$498$$ 12.0000 0.537733
$$499$$ −20.0000 −0.895323 −0.447661 0.894203i $$-0.647743\pi$$
−0.447661 + 0.894203i $$0.647743\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 28.0000 1.24970
$$503$$ −36.0000 −1.60516 −0.802580 0.596544i $$-0.796540\pi$$
−0.802580 + 0.596544i $$0.796540\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 16.0000 0.711287
$$507$$ −9.00000 −0.399704
$$508$$ 12.0000 0.532414
$$509$$ 6.00000 0.265945 0.132973 0.991120i $$-0.457548\pi$$
0.132973 + 0.991120i $$0.457548\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −1.00000 −0.0441942
$$513$$ −1.00000 −0.0441511
$$514$$ 2.00000 0.0882162
$$515$$ 0 0
$$516$$ −4.00000 −0.176090
$$517$$ −16.0000 −0.703679
$$518$$ 0 0
$$519$$ −6.00000 −0.263371
$$520$$ 0 0
$$521$$ 26.0000 1.13908 0.569540 0.821963i $$-0.307121\pi$$
0.569540 + 0.821963i $$0.307121\pi$$
$$522$$ 2.00000 0.0875376
$$523$$ 4.00000 0.174908 0.0874539 0.996169i $$-0.472127\pi$$
0.0874539 + 0.996169i $$0.472127\pi$$
$$524$$ 12.0000 0.524222
$$525$$ 0 0
$$526$$ −12.0000 −0.523225
$$527$$ 24.0000 1.04546
$$528$$ −4.00000 −0.174078
$$529$$ −7.00000 −0.304348
$$530$$ 0 0
$$531$$ 12.0000 0.520756
$$532$$ 0 0
$$533$$ −20.0000 −0.866296
$$534$$ 6.00000 0.259645
$$535$$ 0 0
$$536$$ −12.0000 −0.518321
$$537$$ 12.0000 0.517838
$$538$$ −6.00000 −0.258678
$$539$$ 28.0000 1.20605
$$540$$ 0 0
$$541$$ 38.0000 1.63375 0.816874 0.576816i $$-0.195705\pi$$
0.816874 + 0.576816i $$0.195705\pi$$
$$542$$ 8.00000 0.343629
$$543$$ −14.0000 −0.600798
$$544$$ −6.00000 −0.257248
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −4.00000 −0.171028 −0.0855138 0.996337i $$-0.527253\pi$$
−0.0855138 + 0.996337i $$0.527253\pi$$
$$548$$ 14.0000 0.598050
$$549$$ 14.0000 0.597505
$$550$$ 0 0
$$551$$ 2.00000 0.0852029
$$552$$ −4.00000 −0.170251
$$553$$ 0 0
$$554$$ −26.0000 −1.10463
$$555$$ 0 0
$$556$$ 12.0000 0.508913
$$557$$ −34.0000 −1.44063 −0.720313 0.693649i $$-0.756002\pi$$
−0.720313 + 0.693649i $$0.756002\pi$$
$$558$$ −4.00000 −0.169334
$$559$$ 8.00000 0.338364
$$560$$ 0 0
$$561$$ −24.0000 −1.01328
$$562$$ −10.0000 −0.421825
$$563$$ 12.0000 0.505740 0.252870 0.967500i $$-0.418626\pi$$
0.252870 + 0.967500i $$0.418626\pi$$
$$564$$ 4.00000 0.168430
$$565$$ 0 0
$$566$$ 12.0000 0.504398
$$567$$ 0 0
$$568$$ −8.00000 −0.335673
$$569$$ −38.0000 −1.59304 −0.796521 0.604610i $$-0.793329\pi$$
−0.796521 + 0.604610i $$0.793329\pi$$
$$570$$ 0 0
$$571$$ 20.0000 0.836974 0.418487 0.908223i $$-0.362561\pi$$
0.418487 + 0.908223i $$0.362561\pi$$
$$572$$ 8.00000 0.334497
$$573$$ 4.00000 0.167102
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 1.00000 0.0416667
$$577$$ −2.00000 −0.0832611 −0.0416305 0.999133i $$-0.513255\pi$$
−0.0416305 + 0.999133i $$0.513255\pi$$
$$578$$ −19.0000 −0.790296
$$579$$ 6.00000 0.249351
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 10.0000 0.414513
$$583$$ −40.0000 −1.65663
$$584$$ −6.00000 −0.248282
$$585$$ 0 0
$$586$$ −18.0000 −0.743573
$$587$$ −12.0000 −0.495293 −0.247647 0.968850i $$-0.579657\pi$$
−0.247647 + 0.968850i $$0.579657\pi$$
$$588$$ −7.00000 −0.288675
$$589$$ −4.00000 −0.164817
$$590$$ 0 0
$$591$$ 22.0000 0.904959
$$592$$ −10.0000 −0.410997
$$593$$ −34.0000 −1.39621 −0.698106 0.715994i $$-0.745974\pi$$
−0.698106 + 0.715994i $$0.745974\pi$$
$$594$$ 4.00000 0.164122
$$595$$ 0 0
$$596$$ −6.00000 −0.245770
$$597$$ −16.0000 −0.654836
$$598$$ 8.00000 0.327144
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 0 0
$$601$$ 10.0000 0.407909 0.203954 0.978980i $$-0.434621\pi$$
0.203954 + 0.978980i $$0.434621\pi$$
$$602$$ 0 0
$$603$$ 12.0000 0.488678
$$604$$ 20.0000 0.813788
$$605$$ 0 0
$$606$$ −2.00000 −0.0812444
$$607$$ 4.00000 0.162355 0.0811775 0.996700i $$-0.474132\pi$$
0.0811775 + 0.996700i $$0.474132\pi$$
$$608$$ 1.00000 0.0405554
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −8.00000 −0.323645
$$612$$ 6.00000 0.242536
$$613$$ 2.00000 0.0807792 0.0403896 0.999184i $$-0.487140\pi$$
0.0403896 + 0.999184i $$0.487140\pi$$
$$614$$ −12.0000 −0.484281
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −42.0000 −1.69086 −0.845428 0.534089i $$-0.820655\pi$$
−0.845428 + 0.534089i $$0.820655\pi$$
$$618$$ −12.0000 −0.482711
$$619$$ 4.00000 0.160774 0.0803868 0.996764i $$-0.474384\pi$$
0.0803868 + 0.996764i $$0.474384\pi$$
$$620$$ 0 0
$$621$$ 4.00000 0.160514
$$622$$ −4.00000 −0.160385
$$623$$ 0 0
$$624$$ −2.00000 −0.0800641
$$625$$ 0 0
$$626$$ −22.0000 −0.879297
$$627$$ 4.00000 0.159745
$$628$$ −22.0000 −0.877896
$$629$$ −60.0000 −2.39236
$$630$$ 0 0
$$631$$ −40.0000 −1.59237 −0.796187 0.605050i $$-0.793153\pi$$
−0.796187 + 0.605050i $$0.793153\pi$$
$$632$$ 4.00000 0.159111
$$633$$ 12.0000 0.476957
$$634$$ 6.00000 0.238290
$$635$$ 0 0
$$636$$ 10.0000 0.396526
$$637$$ 14.0000 0.554700
$$638$$ −8.00000 −0.316723
$$639$$ 8.00000 0.316475
$$640$$ 0 0
$$641$$ 18.0000 0.710957 0.355479 0.934684i $$-0.384318\pi$$
0.355479 + 0.934684i $$0.384318\pi$$
$$642$$ −4.00000 −0.157867
$$643$$ −4.00000 −0.157745 −0.0788723 0.996885i $$-0.525132\pi$$
−0.0788723 + 0.996885i $$0.525132\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 6.00000 0.236067
$$647$$ 4.00000 0.157256 0.0786281 0.996904i $$-0.474946\pi$$
0.0786281 + 0.996904i $$0.474946\pi$$
$$648$$ −1.00000 −0.0392837
$$649$$ −48.0000 −1.88416
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −20.0000 −0.783260
$$653$$ −18.0000 −0.704394 −0.352197 0.935926i $$-0.614565\pi$$
−0.352197 + 0.935926i $$0.614565\pi$$
$$654$$ 6.00000 0.234619
$$655$$ 0 0
$$656$$ 10.0000 0.390434
$$657$$ 6.00000 0.234082
$$658$$ 0 0
$$659$$ −4.00000 −0.155818 −0.0779089 0.996960i $$-0.524824\pi$$
−0.0779089 + 0.996960i $$0.524824\pi$$
$$660$$ 0 0
$$661$$ −38.0000 −1.47803 −0.739014 0.673690i $$-0.764708\pi$$
−0.739014 + 0.673690i $$0.764708\pi$$
$$662$$ 4.00000 0.155464
$$663$$ −12.0000 −0.466041
$$664$$ 12.0000 0.465690
$$665$$ 0 0
$$666$$ 10.0000 0.387492
$$667$$ −8.00000 −0.309761
$$668$$ 0 0
$$669$$ 28.0000 1.08254
$$670$$ 0 0
$$671$$ −56.0000 −2.16186
$$672$$ 0 0
$$673$$ −26.0000 −1.00223 −0.501113 0.865382i $$-0.667076\pi$$
−0.501113 + 0.865382i $$0.667076\pi$$
$$674$$ −14.0000 −0.539260
$$675$$ 0 0
$$676$$ −9.00000 −0.346154
$$677$$ 26.0000 0.999261 0.499631 0.866239i $$-0.333469\pi$$
0.499631 + 0.866239i $$0.333469\pi$$
$$678$$ 2.00000 0.0768095
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −28.0000 −1.07296
$$682$$ 16.0000 0.612672
$$683$$ −4.00000 −0.153056 −0.0765279 0.997067i $$-0.524383\pi$$
−0.0765279 + 0.997067i $$0.524383\pi$$
$$684$$ −1.00000 −0.0382360
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −10.0000 −0.381524
$$688$$ −4.00000 −0.152499
$$689$$ −20.0000 −0.761939
$$690$$ 0 0
$$691$$ −36.0000 −1.36950 −0.684752 0.728776i $$-0.740090\pi$$
−0.684752 + 0.728776i $$0.740090\pi$$
$$692$$ −6.00000 −0.228086
$$693$$ 0 0
$$694$$ −20.0000 −0.759190
$$695$$ 0 0
$$696$$ 2.00000 0.0758098
$$697$$ 60.0000 2.27266
$$698$$ 26.0000 0.984115
$$699$$ 6.00000 0.226941
$$700$$ 0 0
$$701$$ −22.0000 −0.830929 −0.415464 0.909610i $$-0.636381\pi$$
−0.415464 + 0.909610i $$0.636381\pi$$
$$702$$ 2.00000 0.0754851
$$703$$ 10.0000 0.377157
$$704$$ −4.00000 −0.150756
$$705$$ 0 0
$$706$$ 18.0000 0.677439
$$707$$ 0 0
$$708$$ 12.0000 0.450988
$$709$$ −42.0000 −1.57734 −0.788672 0.614815i $$-0.789231\pi$$
−0.788672 + 0.614815i $$0.789231\pi$$
$$710$$ 0 0
$$711$$ −4.00000 −0.150012
$$712$$ 6.00000 0.224860
$$713$$ 16.0000 0.599205
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 12.0000 0.448461
$$717$$ 12.0000 0.448148
$$718$$ −12.0000 −0.447836
$$719$$ 28.0000 1.04422 0.522112 0.852877i $$-0.325144\pi$$
0.522112 + 0.852877i $$0.325144\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −1.00000 −0.0372161
$$723$$ 10.0000 0.371904
$$724$$ −14.0000 −0.520306
$$725$$ 0 0
$$726$$ −5.00000 −0.185567
$$727$$ 8.00000 0.296704 0.148352 0.988935i $$-0.452603\pi$$
0.148352 + 0.988935i $$0.452603\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ −24.0000 −0.887672
$$732$$ 14.0000 0.517455
$$733$$ −6.00000 −0.221615 −0.110808 0.993842i $$-0.535344\pi$$
−0.110808 + 0.993842i $$0.535344\pi$$
$$734$$ −8.00000 −0.295285
$$735$$ 0 0
$$736$$ −4.00000 −0.147442
$$737$$ −48.0000 −1.76810
$$738$$ −10.0000 −0.368105
$$739$$ 20.0000 0.735712 0.367856 0.929883i $$-0.380092\pi$$
0.367856 + 0.929883i $$0.380092\pi$$
$$740$$ 0 0
$$741$$ 2.00000 0.0734718
$$742$$ 0 0
$$743$$ −32.0000 −1.17397 −0.586983 0.809599i $$-0.699684\pi$$
−0.586983 + 0.809599i $$0.699684\pi$$
$$744$$ −4.00000 −0.146647
$$745$$ 0 0
$$746$$ 26.0000 0.951928
$$747$$ −12.0000 −0.439057
$$748$$ −24.0000 −0.877527
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 44.0000 1.60558 0.802791 0.596260i $$-0.203347\pi$$
0.802791 + 0.596260i $$0.203347\pi$$
$$752$$ 4.00000 0.145865
$$753$$ −28.0000 −1.02038
$$754$$ −4.00000 −0.145671
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 2.00000 0.0726912 0.0363456 0.999339i $$-0.488428\pi$$
0.0363456 + 0.999339i $$0.488428\pi$$
$$758$$ 36.0000 1.30758
$$759$$ −16.0000 −0.580763
$$760$$ 0 0
$$761$$ −30.0000 −1.08750 −0.543750 0.839248i $$-0.682996\pi$$
−0.543750 + 0.839248i $$0.682996\pi$$
$$762$$ −12.0000 −0.434714
$$763$$ 0 0
$$764$$ 4.00000 0.144715
$$765$$ 0 0
$$766$$ 16.0000 0.578103
$$767$$ −24.0000 −0.866590
$$768$$ 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
$$771$$ −2.00000 −0.0720282
$$772$$ 6.00000 0.215945
$$773$$ −30.0000 −1.07903 −0.539513 0.841978i $$-0.681391\pi$$
−0.539513 + 0.841978i $$0.681391\pi$$
$$774$$ 4.00000 0.143777
$$775$$ 0 0
$$776$$ 10.0000 0.358979
$$777$$ 0 0
$$778$$ −18.0000 −0.645331
$$779$$ −10.0000 −0.358287
$$780$$ 0 0
$$781$$ −32.0000 −1.14505
$$782$$ −24.0000 −0.858238
$$783$$ −2.00000 −0.0714742
$$784$$ −7.00000 −0.250000
$$785$$ 0 0
$$786$$ −12.0000 −0.428026
$$787$$ 20.0000 0.712923 0.356462 0.934310i $$-0.383983\pi$$
0.356462 + 0.934310i $$0.383983\pi$$
$$788$$ 22.0000 0.783718
$$789$$ 12.0000 0.427211
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 4.00000 0.142134
$$793$$ −28.0000 −0.994309
$$794$$ −10.0000 −0.354887
$$795$$ 0 0
$$796$$ −16.0000 −0.567105
$$797$$ −6.00000 −0.212531 −0.106265 0.994338i $$-0.533889\pi$$
−0.106265 + 0.994338i $$0.533889\pi$$
$$798$$ 0 0
$$799$$ 24.0000 0.849059
$$800$$ 0 0
$$801$$ −6.00000 −0.212000
$$802$$ 14.0000 0.494357
$$803$$ −24.0000 −0.846942
$$804$$ 12.0000 0.423207
$$805$$ 0 0
$$806$$ 8.00000 0.281788
$$807$$ 6.00000 0.211210
$$808$$ −2.00000 −0.0703598
$$809$$ −30.0000 −1.05474 −0.527372 0.849635i $$-0.676823\pi$$
−0.527372 + 0.849635i $$0.676823\pi$$
$$810$$ 0 0
$$811$$ 12.0000 0.421377 0.210688 0.977553i $$-0.432429\pi$$
0.210688 + 0.977553i $$0.432429\pi$$
$$812$$ 0 0
$$813$$ −8.00000 −0.280572
$$814$$ −40.0000 −1.40200
$$815$$ 0 0
$$816$$ 6.00000 0.210042
$$817$$ 4.00000 0.139942
$$818$$ 14.0000 0.489499
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −30.0000 −1.04701 −0.523504 0.852023i $$-0.675375\pi$$
−0.523504 + 0.852023i $$0.675375\pi$$
$$822$$ −14.0000 −0.488306
$$823$$ −8.00000 −0.278862 −0.139431 0.990232i $$-0.544527\pi$$
−0.139431 + 0.990232i $$0.544527\pi$$
$$824$$ −12.0000 −0.418040
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 28.0000 0.973655 0.486828 0.873498i $$-0.338154\pi$$
0.486828 + 0.873498i $$0.338154\pi$$
$$828$$ 4.00000 0.139010
$$829$$ 42.0000 1.45872 0.729360 0.684130i $$-0.239818\pi$$
0.729360 + 0.684130i $$0.239818\pi$$
$$830$$ 0 0
$$831$$ 26.0000 0.901930
$$832$$ −2.00000 −0.0693375
$$833$$ −42.0000 −1.45521
$$834$$ −12.0000 −0.415526
$$835$$ 0 0
$$836$$ 4.00000 0.138343
$$837$$ 4.00000 0.138260
$$838$$ 12.0000 0.414533
$$839$$ −16.0000 −0.552381 −0.276191 0.961103i $$-0.589072\pi$$
−0.276191 + 0.961103i $$0.589072\pi$$
$$840$$ 0 0
$$841$$ −25.0000 −0.862069
$$842$$ −26.0000 −0.896019
$$843$$ 10.0000 0.344418
$$844$$ 12.0000 0.413057
$$845$$ 0 0
$$846$$ −4.00000 −0.137523
$$847$$ 0 0
$$848$$ 10.0000 0.343401
$$849$$ −12.0000 −0.411839
$$850$$ 0 0
$$851$$ −40.0000 −1.37118
$$852$$ 8.00000 0.274075
$$853$$ −6.00000 −0.205436 −0.102718 0.994711i $$-0.532754\pi$$
−0.102718 + 0.994711i $$0.532754\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ −4.00000 −0.136717
$$857$$ −42.0000 −1.43469 −0.717346 0.696717i $$-0.754643\pi$$
−0.717346 + 0.696717i $$0.754643\pi$$
$$858$$ −8.00000 −0.273115
$$859$$ 52.0000 1.77422 0.887109 0.461561i $$-0.152710\pi$$
0.887109 + 0.461561i $$0.152710\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 24.0000 0.817443
$$863$$ 24.0000 0.816970 0.408485 0.912765i $$-0.366057\pi$$
0.408485 + 0.912765i $$0.366057\pi$$
$$864$$ −1.00000 −0.0340207
$$865$$ 0 0
$$866$$ 26.0000 0.883516
$$867$$ 19.0000 0.645274
$$868$$ 0 0
$$869$$ 16.0000 0.542763
$$870$$ 0 0
$$871$$ −24.0000 −0.813209
$$872$$ 6.00000 0.203186
$$873$$ −10.0000 −0.338449
$$874$$ 4.00000 0.135302
$$875$$ 0 0
$$876$$ 6.00000 0.202721
$$877$$ −34.0000 −1.14810 −0.574049 0.818821i $$-0.694628\pi$$
−0.574049 + 0.818821i $$0.694628\pi$$
$$878$$ 4.00000 0.134993
$$879$$ 18.0000 0.607125
$$880$$ 0 0
$$881$$ 18.0000 0.606435 0.303218 0.952921i $$-0.401939\pi$$
0.303218 + 0.952921i $$0.401939\pi$$
$$882$$ 7.00000 0.235702
$$883$$ 20.0000 0.673054 0.336527 0.941674i $$-0.390748\pi$$
0.336527 + 0.941674i $$0.390748\pi$$
$$884$$ −12.0000 −0.403604
$$885$$ 0 0
$$886$$ −20.0000 −0.671913
$$887$$ 32.0000 1.07445 0.537227 0.843437i $$-0.319472\pi$$
0.537227 + 0.843437i $$0.319472\pi$$
$$888$$ 10.0000 0.335578
$$889$$ 0 0
$$890$$ 0 0
$$891$$ −4.00000 −0.134005
$$892$$ 28.0000 0.937509
$$893$$ −4.00000 −0.133855
$$894$$ 6.00000 0.200670
$$895$$ 0 0
$$896$$ 0 0
$$897$$ −8.00000 −0.267112
$$898$$ −34.0000 −1.13459
$$899$$ −8.00000 −0.266815
$$900$$ 0 0
$$901$$ 60.0000 1.99889
$$902$$ 40.0000 1.33185
$$903$$ 0 0
$$904$$ 2.00000 0.0665190
$$905$$ 0 0
$$906$$ −20.0000 −0.664455
$$907$$ −44.0000 −1.46100 −0.730498 0.682915i $$-0.760712\pi$$
−0.730498 + 0.682915i $$0.760712\pi$$
$$908$$ −28.0000 −0.929213
$$909$$ 2.00000 0.0663358
$$910$$ 0 0
$$911$$ 24.0000 0.795155 0.397578 0.917568i $$-0.369851\pi$$
0.397578 + 0.917568i $$0.369851\pi$$
$$912$$ −1.00000 −0.0331133
$$913$$ 48.0000 1.58857
$$914$$ 26.0000 0.860004
$$915$$ 0 0
$$916$$ −10.0000 −0.330409
$$917$$ 0 0
$$918$$ −6.00000 −0.198030
$$919$$ 8.00000 0.263896 0.131948 0.991257i $$-0.457877\pi$$
0.131948 + 0.991257i $$0.457877\pi$$
$$920$$ 0 0
$$921$$ 12.0000 0.395413
$$922$$ −2.00000 −0.0658665
$$923$$ −16.0000 −0.526646
$$924$$ 0 0
$$925$$ 0 0
$$926$$ −8.00000 −0.262896
$$927$$ 12.0000 0.394132
$$928$$ 2.00000 0.0656532
$$929$$ −22.0000 −0.721797 −0.360898 0.932605i $$-0.617530\pi$$
−0.360898 + 0.932605i $$0.617530\pi$$
$$930$$ 0 0
$$931$$ 7.00000 0.229416
$$932$$ 6.00000 0.196537
$$933$$ 4.00000 0.130954
$$934$$ −20.0000 −0.654420
$$935$$ 0 0
$$936$$ 2.00000 0.0653720
$$937$$ −26.0000 −0.849383 −0.424691 0.905338i $$-0.639617\pi$$
−0.424691 + 0.905338i $$0.639617\pi$$
$$938$$ 0 0
$$939$$ 22.0000 0.717943
$$940$$ 0 0
$$941$$ 22.0000 0.717180 0.358590 0.933495i $$-0.383258\pi$$
0.358590 + 0.933495i $$0.383258\pi$$
$$942$$ 22.0000 0.716799
$$943$$ 40.0000 1.30258
$$944$$ 12.0000 0.390567
$$945$$ 0 0
$$946$$ −16.0000 −0.520205
$$947$$ −12.0000 −0.389948 −0.194974 0.980808i $$-0.562462\pi$$
−0.194974 + 0.980808i $$0.562462\pi$$
$$948$$ −4.00000 −0.129914
$$949$$ −12.0000 −0.389536
$$950$$ 0 0
$$951$$ −6.00000 −0.194563
$$952$$ 0 0
$$953$$ 22.0000 0.712650 0.356325 0.934362i $$-0.384030\pi$$
0.356325 + 0.934362i $$0.384030\pi$$
$$954$$ −10.0000 −0.323762
$$955$$ 0 0
$$956$$ 12.0000 0.388108
$$957$$ 8.00000 0.258603
$$958$$ −4.00000 −0.129234
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −15.0000 −0.483871
$$962$$ −20.0000 −0.644826
$$963$$ 4.00000 0.128898
$$964$$ 10.0000 0.322078
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −48.0000 −1.54358 −0.771788 0.635880i $$-0.780637\pi$$
−0.771788 + 0.635880i $$0.780637\pi$$
$$968$$ −5.00000 −0.160706
$$969$$ −6.00000 −0.192748
$$970$$ 0 0
$$971$$ −28.0000 −0.898563 −0.449281 0.893390i $$-0.648320\pi$$
−0.449281 + 0.893390i $$0.648320\pi$$
$$972$$ 1.00000 0.0320750
$$973$$ 0 0
$$974$$ 4.00000 0.128168
$$975$$ 0 0
$$976$$ 14.0000 0.448129
$$977$$ 46.0000 1.47167 0.735835 0.677161i $$-0.236790\pi$$
0.735835 + 0.677161i $$0.236790\pi$$
$$978$$ 20.0000 0.639529
$$979$$ 24.0000 0.767043
$$980$$ 0 0
$$981$$ −6.00000 −0.191565
$$982$$ −20.0000 −0.638226
$$983$$ 24.0000 0.765481 0.382741 0.923856i $$-0.374980\pi$$
0.382741 + 0.923856i $$0.374980\pi$$
$$984$$ −10.0000 −0.318788
$$985$$ 0 0
$$986$$ 12.0000 0.382158
$$987$$ 0 0
$$988$$ 2.00000 0.0636285
$$989$$ −16.0000 −0.508770
$$990$$ 0 0
$$991$$ 4.00000 0.127064 0.0635321 0.997980i $$-0.479763\pi$$
0.0635321 + 0.997980i $$0.479763\pi$$
$$992$$ −4.00000 −0.127000
$$993$$ −4.00000 −0.126936
$$994$$ 0 0
$$995$$ 0 0
$$996$$ −12.0000 −0.380235
$$997$$ 2.00000 0.0633406 0.0316703 0.999498i $$-0.489917\pi$$
0.0316703 + 0.999498i $$0.489917\pi$$
$$998$$ 20.0000 0.633089
$$999$$ −10.0000 −0.316386
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 2850.2.a.j.1.1 1
3.2 odd 2 8550.2.a.ba.1.1 1
5.2 odd 4 2850.2.d.b.799.1 2
5.3 odd 4 2850.2.d.b.799.2 2
5.4 even 2 114.2.a.b.1.1 1
15.14 odd 2 342.2.a.b.1.1 1
20.19 odd 2 912.2.a.k.1.1 1
35.34 odd 2 5586.2.a.y.1.1 1
40.19 odd 2 3648.2.a.c.1.1 1
40.29 even 2 3648.2.a.x.1.1 1
60.59 even 2 2736.2.a.d.1.1 1
95.94 odd 2 2166.2.a.d.1.1 1
285.284 even 2 6498.2.a.p.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
114.2.a.b.1.1 1 5.4 even 2
342.2.a.b.1.1 1 15.14 odd 2
912.2.a.k.1.1 1 20.19 odd 2
2166.2.a.d.1.1 1 95.94 odd 2
2736.2.a.d.1.1 1 60.59 even 2
2850.2.a.j.1.1 1 1.1 even 1 trivial
2850.2.d.b.799.1 2 5.2 odd 4
2850.2.d.b.799.2 2 5.3 odd 4
3648.2.a.c.1.1 1 40.19 odd 2
3648.2.a.x.1.1 1 40.29 even 2
5586.2.a.y.1.1 1 35.34 odd 2
6498.2.a.p.1.1 1 285.284 even 2
8550.2.a.ba.1.1 1 3.2 odd 2