# Properties

 Label 1710.2.a.b.1.1 Level $1710$ Weight $2$ Character 1710.1 Self dual yes Analytic conductor $13.654$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1710.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$13.6544187456$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 570) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1710.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} -2.00000 q^{7} -1.00000 q^{8} +O(q^{10})$$ $$q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{10} -2.00000 q^{11} +4.00000 q^{13} +2.00000 q^{14} +1.00000 q^{16} +2.00000 q^{17} -1.00000 q^{19} -1.00000 q^{20} +2.00000 q^{22} -4.00000 q^{23} +1.00000 q^{25} -4.00000 q^{26} -2.00000 q^{28} -8.00000 q^{31} -1.00000 q^{32} -2.00000 q^{34} +2.00000 q^{35} +8.00000 q^{37} +1.00000 q^{38} +1.00000 q^{40} +8.00000 q^{41} -6.00000 q^{43} -2.00000 q^{44} +4.00000 q^{46} +12.0000 q^{47} -3.00000 q^{49} -1.00000 q^{50} +4.00000 q^{52} +6.00000 q^{53} +2.00000 q^{55} +2.00000 q^{56} +2.00000 q^{61} +8.00000 q^{62} +1.00000 q^{64} -4.00000 q^{65} +8.00000 q^{67} +2.00000 q^{68} -2.00000 q^{70} +8.00000 q^{71} +14.0000 q^{73} -8.00000 q^{74} -1.00000 q^{76} +4.00000 q^{77} -1.00000 q^{80} -8.00000 q^{82} -4.00000 q^{83} -2.00000 q^{85} +6.00000 q^{86} +2.00000 q^{88} -8.00000 q^{91} -4.00000 q^{92} -12.0000 q^{94} +1.00000 q^{95} -12.0000 q^{97} +3.00000 q^{98} +O(q^{100})$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 −0.707107
$$3$$ 0 0
$$4$$ 1.00000 0.500000
$$5$$ −1.00000 −0.447214
$$6$$ 0 0
$$7$$ −2.00000 −0.755929 −0.377964 0.925820i $$-0.623376\pi$$
−0.377964 + 0.925820i $$0.623376\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ 0 0
$$10$$ 1.00000 0.316228
$$11$$ −2.00000 −0.603023 −0.301511 0.953463i $$-0.597491\pi$$
−0.301511 + 0.953463i $$0.597491\pi$$
$$12$$ 0 0
$$13$$ 4.00000 1.10940 0.554700 0.832050i $$-0.312833\pi$$
0.554700 + 0.832050i $$0.312833\pi$$
$$14$$ 2.00000 0.534522
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 2.00000 0.485071 0.242536 0.970143i $$-0.422021\pi$$
0.242536 + 0.970143i $$0.422021\pi$$
$$18$$ 0 0
$$19$$ −1.00000 −0.229416
$$20$$ −1.00000 −0.223607
$$21$$ 0 0
$$22$$ 2.00000 0.426401
$$23$$ −4.00000 −0.834058 −0.417029 0.908893i $$-0.636929\pi$$
−0.417029 + 0.908893i $$0.636929\pi$$
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ −4.00000 −0.784465
$$27$$ 0 0
$$28$$ −2.00000 −0.377964
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0 0
$$31$$ −8.00000 −1.43684 −0.718421 0.695608i $$-0.755135\pi$$
−0.718421 + 0.695608i $$0.755135\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 0 0
$$34$$ −2.00000 −0.342997
$$35$$ 2.00000 0.338062
$$36$$ 0 0
$$37$$ 8.00000 1.31519 0.657596 0.753371i $$-0.271573\pi$$
0.657596 + 0.753371i $$0.271573\pi$$
$$38$$ 1.00000 0.162221
$$39$$ 0 0
$$40$$ 1.00000 0.158114
$$41$$ 8.00000 1.24939 0.624695 0.780869i $$-0.285223\pi$$
0.624695 + 0.780869i $$0.285223\pi$$
$$42$$ 0 0
$$43$$ −6.00000 −0.914991 −0.457496 0.889212i $$-0.651253\pi$$
−0.457496 + 0.889212i $$0.651253\pi$$
$$44$$ −2.00000 −0.301511
$$45$$ 0 0
$$46$$ 4.00000 0.589768
$$47$$ 12.0000 1.75038 0.875190 0.483779i $$-0.160736\pi$$
0.875190 + 0.483779i $$0.160736\pi$$
$$48$$ 0 0
$$49$$ −3.00000 −0.428571
$$50$$ −1.00000 −0.141421
$$51$$ 0 0
$$52$$ 4.00000 0.554700
$$53$$ 6.00000 0.824163 0.412082 0.911147i $$-0.364802\pi$$
0.412082 + 0.911147i $$0.364802\pi$$
$$54$$ 0 0
$$55$$ 2.00000 0.269680
$$56$$ 2.00000 0.267261
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ 2.00000 0.256074 0.128037 0.991769i $$-0.459132\pi$$
0.128037 + 0.991769i $$0.459132\pi$$
$$62$$ 8.00000 1.01600
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ −4.00000 −0.496139
$$66$$ 0 0
$$67$$ 8.00000 0.977356 0.488678 0.872464i $$-0.337479\pi$$
0.488678 + 0.872464i $$0.337479\pi$$
$$68$$ 2.00000 0.242536
$$69$$ 0 0
$$70$$ −2.00000 −0.239046
$$71$$ 8.00000 0.949425 0.474713 0.880141i $$-0.342552\pi$$
0.474713 + 0.880141i $$0.342552\pi$$
$$72$$ 0 0
$$73$$ 14.0000 1.63858 0.819288 0.573382i $$-0.194369\pi$$
0.819288 + 0.573382i $$0.194369\pi$$
$$74$$ −8.00000 −0.929981
$$75$$ 0 0
$$76$$ −1.00000 −0.114708
$$77$$ 4.00000 0.455842
$$78$$ 0 0
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ −1.00000 −0.111803
$$81$$ 0 0
$$82$$ −8.00000 −0.883452
$$83$$ −4.00000 −0.439057 −0.219529 0.975606i $$-0.570452\pi$$
−0.219529 + 0.975606i $$0.570452\pi$$
$$84$$ 0 0
$$85$$ −2.00000 −0.216930
$$86$$ 6.00000 0.646997
$$87$$ 0 0
$$88$$ 2.00000 0.213201
$$89$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$90$$ 0 0
$$91$$ −8.00000 −0.838628
$$92$$ −4.00000 −0.417029
$$93$$ 0 0
$$94$$ −12.0000 −1.23771
$$95$$ 1.00000 0.102598
$$96$$ 0 0
$$97$$ −12.0000 −1.21842 −0.609208 0.793011i $$-0.708512\pi$$
−0.609208 + 0.793011i $$0.708512\pi$$
$$98$$ 3.00000 0.303046
$$99$$ 0 0
$$100$$ 1.00000 0.100000
$$101$$ −2.00000 −0.199007 −0.0995037 0.995037i $$-0.531726\pi$$
−0.0995037 + 0.995037i $$0.531726\pi$$
$$102$$ 0 0
$$103$$ 4.00000 0.394132 0.197066 0.980390i $$-0.436859\pi$$
0.197066 + 0.980390i $$0.436859\pi$$
$$104$$ −4.00000 −0.392232
$$105$$ 0 0
$$106$$ −6.00000 −0.582772
$$107$$ 12.0000 1.16008 0.580042 0.814587i $$-0.303036\pi$$
0.580042 + 0.814587i $$0.303036\pi$$
$$108$$ 0 0
$$109$$ 10.0000 0.957826 0.478913 0.877862i $$-0.341031\pi$$
0.478913 + 0.877862i $$0.341031\pi$$
$$110$$ −2.00000 −0.190693
$$111$$ 0 0
$$112$$ −2.00000 −0.188982
$$113$$ 6.00000 0.564433 0.282216 0.959351i $$-0.408930\pi$$
0.282216 + 0.959351i $$0.408930\pi$$
$$114$$ 0 0
$$115$$ 4.00000 0.373002
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −4.00000 −0.366679
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ −2.00000 −0.181071
$$123$$ 0 0
$$124$$ −8.00000 −0.718421
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ 8.00000 0.709885 0.354943 0.934888i $$-0.384500\pi$$
0.354943 + 0.934888i $$0.384500\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ 0 0
$$130$$ 4.00000 0.350823
$$131$$ 18.0000 1.57267 0.786334 0.617802i $$-0.211977\pi$$
0.786334 + 0.617802i $$0.211977\pi$$
$$132$$ 0 0
$$133$$ 2.00000 0.173422
$$134$$ −8.00000 −0.691095
$$135$$ 0 0
$$136$$ −2.00000 −0.171499
$$137$$ 22.0000 1.87959 0.939793 0.341743i $$-0.111017\pi$$
0.939793 + 0.341743i $$0.111017\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$140$$ 2.00000 0.169031
$$141$$ 0 0
$$142$$ −8.00000 −0.671345
$$143$$ −8.00000 −0.668994
$$144$$ 0 0
$$145$$ 0 0
$$146$$ −14.0000 −1.15865
$$147$$ 0 0
$$148$$ 8.00000 0.657596
$$149$$ −10.0000 −0.819232 −0.409616 0.912258i $$-0.634337\pi$$
−0.409616 + 0.912258i $$0.634337\pi$$
$$150$$ 0 0
$$151$$ −8.00000 −0.651031 −0.325515 0.945537i $$-0.605538\pi$$
−0.325515 + 0.945537i $$0.605538\pi$$
$$152$$ 1.00000 0.0811107
$$153$$ 0 0
$$154$$ −4.00000 −0.322329
$$155$$ 8.00000 0.642575
$$156$$ 0 0
$$157$$ 18.0000 1.43656 0.718278 0.695756i $$-0.244931\pi$$
0.718278 + 0.695756i $$0.244931\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 1.00000 0.0790569
$$161$$ 8.00000 0.630488
$$162$$ 0 0
$$163$$ 14.0000 1.09656 0.548282 0.836293i $$-0.315282\pi$$
0.548282 + 0.836293i $$0.315282\pi$$
$$164$$ 8.00000 0.624695
$$165$$ 0 0
$$166$$ 4.00000 0.310460
$$167$$ −8.00000 −0.619059 −0.309529 0.950890i $$-0.600171\pi$$
−0.309529 + 0.950890i $$0.600171\pi$$
$$168$$ 0 0
$$169$$ 3.00000 0.230769
$$170$$ 2.00000 0.153393
$$171$$ 0 0
$$172$$ −6.00000 −0.457496
$$173$$ −14.0000 −1.06440 −0.532200 0.846619i $$-0.678635\pi$$
−0.532200 + 0.846619i $$0.678635\pi$$
$$174$$ 0 0
$$175$$ −2.00000 −0.151186
$$176$$ −2.00000 −0.150756
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ 0 0
$$181$$ 2.00000 0.148659 0.0743294 0.997234i $$-0.476318\pi$$
0.0743294 + 0.997234i $$0.476318\pi$$
$$182$$ 8.00000 0.592999
$$183$$ 0 0
$$184$$ 4.00000 0.294884
$$185$$ −8.00000 −0.588172
$$186$$ 0 0
$$187$$ −4.00000 −0.292509
$$188$$ 12.0000 0.875190
$$189$$ 0 0
$$190$$ −1.00000 −0.0725476
$$191$$ 18.0000 1.30243 0.651217 0.758891i $$-0.274259\pi$$
0.651217 + 0.758891i $$0.274259\pi$$
$$192$$ 0 0
$$193$$ 24.0000 1.72756 0.863779 0.503871i $$-0.168091\pi$$
0.863779 + 0.503871i $$0.168091\pi$$
$$194$$ 12.0000 0.861550
$$195$$ 0 0
$$196$$ −3.00000 −0.214286
$$197$$ −18.0000 −1.28245 −0.641223 0.767354i $$-0.721573\pi$$
−0.641223 + 0.767354i $$0.721573\pi$$
$$198$$ 0 0
$$199$$ −20.0000 −1.41776 −0.708881 0.705328i $$-0.750800\pi$$
−0.708881 + 0.705328i $$0.750800\pi$$
$$200$$ −1.00000 −0.0707107
$$201$$ 0 0
$$202$$ 2.00000 0.140720
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −8.00000 −0.558744
$$206$$ −4.00000 −0.278693
$$207$$ 0 0
$$208$$ 4.00000 0.277350
$$209$$ 2.00000 0.138343
$$210$$ 0 0
$$211$$ 12.0000 0.826114 0.413057 0.910705i $$-0.364461\pi$$
0.413057 + 0.910705i $$0.364461\pi$$
$$212$$ 6.00000 0.412082
$$213$$ 0 0
$$214$$ −12.0000 −0.820303
$$215$$ 6.00000 0.409197
$$216$$ 0 0
$$217$$ 16.0000 1.08615
$$218$$ −10.0000 −0.677285
$$219$$ 0 0
$$220$$ 2.00000 0.134840
$$221$$ 8.00000 0.538138
$$222$$ 0 0
$$223$$ 4.00000 0.267860 0.133930 0.990991i $$-0.457240\pi$$
0.133930 + 0.990991i $$0.457240\pi$$
$$224$$ 2.00000 0.133631
$$225$$ 0 0
$$226$$ −6.00000 −0.399114
$$227$$ 12.0000 0.796468 0.398234 0.917284i $$-0.369623\pi$$
0.398234 + 0.917284i $$0.369623\pi$$
$$228$$ 0 0
$$229$$ 10.0000 0.660819 0.330409 0.943838i $$-0.392813\pi$$
0.330409 + 0.943838i $$0.392813\pi$$
$$230$$ −4.00000 −0.263752
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 6.00000 0.393073 0.196537 0.980497i $$-0.437031\pi$$
0.196537 + 0.980497i $$0.437031\pi$$
$$234$$ 0 0
$$235$$ −12.0000 −0.782794
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 4.00000 0.259281
$$239$$ −10.0000 −0.646846 −0.323423 0.946254i $$-0.604834\pi$$
−0.323423 + 0.946254i $$0.604834\pi$$
$$240$$ 0 0
$$241$$ 2.00000 0.128831 0.0644157 0.997923i $$-0.479482\pi$$
0.0644157 + 0.997923i $$0.479482\pi$$
$$242$$ 7.00000 0.449977
$$243$$ 0 0
$$244$$ 2.00000 0.128037
$$245$$ 3.00000 0.191663
$$246$$ 0 0
$$247$$ −4.00000 −0.254514
$$248$$ 8.00000 0.508001
$$249$$ 0 0
$$250$$ 1.00000 0.0632456
$$251$$ −2.00000 −0.126239 −0.0631194 0.998006i $$-0.520105\pi$$
−0.0631194 + 0.998006i $$0.520105\pi$$
$$252$$ 0 0
$$253$$ 8.00000 0.502956
$$254$$ −8.00000 −0.501965
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −18.0000 −1.12281 −0.561405 0.827541i $$-0.689739\pi$$
−0.561405 + 0.827541i $$0.689739\pi$$
$$258$$ 0 0
$$259$$ −16.0000 −0.994192
$$260$$ −4.00000 −0.248069
$$261$$ 0 0
$$262$$ −18.0000 −1.11204
$$263$$ −24.0000 −1.47990 −0.739952 0.672660i $$-0.765152\pi$$
−0.739952 + 0.672660i $$0.765152\pi$$
$$264$$ 0 0
$$265$$ −6.00000 −0.368577
$$266$$ −2.00000 −0.122628
$$267$$ 0 0
$$268$$ 8.00000 0.488678
$$269$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$270$$ 0 0
$$271$$ 12.0000 0.728948 0.364474 0.931214i $$-0.381249\pi$$
0.364474 + 0.931214i $$0.381249\pi$$
$$272$$ 2.00000 0.121268
$$273$$ 0 0
$$274$$ −22.0000 −1.32907
$$275$$ −2.00000 −0.120605
$$276$$ 0 0
$$277$$ 18.0000 1.08152 0.540758 0.841178i $$-0.318138\pi$$
0.540758 + 0.841178i $$0.318138\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ −2.00000 −0.119523
$$281$$ −12.0000 −0.715860 −0.357930 0.933748i $$-0.616517\pi$$
−0.357930 + 0.933748i $$0.616517\pi$$
$$282$$ 0 0
$$283$$ 14.0000 0.832214 0.416107 0.909316i $$-0.363394\pi$$
0.416107 + 0.909316i $$0.363394\pi$$
$$284$$ 8.00000 0.474713
$$285$$ 0 0
$$286$$ 8.00000 0.473050
$$287$$ −16.0000 −0.944450
$$288$$ 0 0
$$289$$ −13.0000 −0.764706
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 14.0000 0.819288
$$293$$ −14.0000 −0.817889 −0.408944 0.912559i $$-0.634103\pi$$
−0.408944 + 0.912559i $$0.634103\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ −8.00000 −0.464991
$$297$$ 0 0
$$298$$ 10.0000 0.579284
$$299$$ −16.0000 −0.925304
$$300$$ 0 0
$$301$$ 12.0000 0.691669
$$302$$ 8.00000 0.460348
$$303$$ 0 0
$$304$$ −1.00000 −0.0573539
$$305$$ −2.00000 −0.114520
$$306$$ 0 0
$$307$$ −32.0000 −1.82634 −0.913168 0.407583i $$-0.866372\pi$$
−0.913168 + 0.407583i $$0.866372\pi$$
$$308$$ 4.00000 0.227921
$$309$$ 0 0
$$310$$ −8.00000 −0.454369
$$311$$ 18.0000 1.02069 0.510343 0.859971i $$-0.329518\pi$$
0.510343 + 0.859971i $$0.329518\pi$$
$$312$$ 0 0
$$313$$ −6.00000 −0.339140 −0.169570 0.985518i $$-0.554238\pi$$
−0.169570 + 0.985518i $$0.554238\pi$$
$$314$$ −18.0000 −1.01580
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −18.0000 −1.01098 −0.505490 0.862832i $$-0.668688\pi$$
−0.505490 + 0.862832i $$0.668688\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ −1.00000 −0.0559017
$$321$$ 0 0
$$322$$ −8.00000 −0.445823
$$323$$ −2.00000 −0.111283
$$324$$ 0 0
$$325$$ 4.00000 0.221880
$$326$$ −14.0000 −0.775388
$$327$$ 0 0
$$328$$ −8.00000 −0.441726
$$329$$ −24.0000 −1.32316
$$330$$ 0 0
$$331$$ 12.0000 0.659580 0.329790 0.944054i $$-0.393022\pi$$
0.329790 + 0.944054i $$0.393022\pi$$
$$332$$ −4.00000 −0.219529
$$333$$ 0 0
$$334$$ 8.00000 0.437741
$$335$$ −8.00000 −0.437087
$$336$$ 0 0
$$337$$ 28.0000 1.52526 0.762629 0.646837i $$-0.223908\pi$$
0.762629 + 0.646837i $$0.223908\pi$$
$$338$$ −3.00000 −0.163178
$$339$$ 0 0
$$340$$ −2.00000 −0.108465
$$341$$ 16.0000 0.866449
$$342$$ 0 0
$$343$$ 20.0000 1.07990
$$344$$ 6.00000 0.323498
$$345$$ 0 0
$$346$$ 14.0000 0.752645
$$347$$ 12.0000 0.644194 0.322097 0.946707i $$-0.395612\pi$$
0.322097 + 0.946707i $$0.395612\pi$$
$$348$$ 0 0
$$349$$ −10.0000 −0.535288 −0.267644 0.963518i $$-0.586245\pi$$
−0.267644 + 0.963518i $$0.586245\pi$$
$$350$$ 2.00000 0.106904
$$351$$ 0 0
$$352$$ 2.00000 0.106600
$$353$$ 6.00000 0.319348 0.159674 0.987170i $$-0.448956\pi$$
0.159674 + 0.987170i $$0.448956\pi$$
$$354$$ 0 0
$$355$$ −8.00000 −0.424596
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 10.0000 0.527780 0.263890 0.964553i $$-0.414994\pi$$
0.263890 + 0.964553i $$0.414994\pi$$
$$360$$ 0 0
$$361$$ 1.00000 0.0526316
$$362$$ −2.00000 −0.105118
$$363$$ 0 0
$$364$$ −8.00000 −0.419314
$$365$$ −14.0000 −0.732793
$$366$$ 0 0
$$367$$ 18.0000 0.939592 0.469796 0.882775i $$-0.344327\pi$$
0.469796 + 0.882775i $$0.344327\pi$$
$$368$$ −4.00000 −0.208514
$$369$$ 0 0
$$370$$ 8.00000 0.415900
$$371$$ −12.0000 −0.623009
$$372$$ 0 0
$$373$$ −36.0000 −1.86401 −0.932005 0.362446i $$-0.881942\pi$$
−0.932005 + 0.362446i $$0.881942\pi$$
$$374$$ 4.00000 0.206835
$$375$$ 0 0
$$376$$ −12.0000 −0.618853
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −20.0000 −1.02733 −0.513665 0.857991i $$-0.671713\pi$$
−0.513665 + 0.857991i $$0.671713\pi$$
$$380$$ 1.00000 0.0512989
$$381$$ 0 0
$$382$$ −18.0000 −0.920960
$$383$$ −24.0000 −1.22634 −0.613171 0.789950i $$-0.710106\pi$$
−0.613171 + 0.789950i $$0.710106\pi$$
$$384$$ 0 0
$$385$$ −4.00000 −0.203859
$$386$$ −24.0000 −1.22157
$$387$$ 0 0
$$388$$ −12.0000 −0.609208
$$389$$ −30.0000 −1.52106 −0.760530 0.649303i $$-0.775061\pi$$
−0.760530 + 0.649303i $$0.775061\pi$$
$$390$$ 0 0
$$391$$ −8.00000 −0.404577
$$392$$ 3.00000 0.151523
$$393$$ 0 0
$$394$$ 18.0000 0.906827
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −22.0000 −1.10415 −0.552074 0.833795i $$-0.686163\pi$$
−0.552074 + 0.833795i $$0.686163\pi$$
$$398$$ 20.0000 1.00251
$$399$$ 0 0
$$400$$ 1.00000 0.0500000
$$401$$ −12.0000 −0.599251 −0.299626 0.954057i $$-0.596862\pi$$
−0.299626 + 0.954057i $$0.596862\pi$$
$$402$$ 0 0
$$403$$ −32.0000 −1.59403
$$404$$ −2.00000 −0.0995037
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −16.0000 −0.793091
$$408$$ 0 0
$$409$$ 30.0000 1.48340 0.741702 0.670729i $$-0.234019\pi$$
0.741702 + 0.670729i $$0.234019\pi$$
$$410$$ 8.00000 0.395092
$$411$$ 0 0
$$412$$ 4.00000 0.197066
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 4.00000 0.196352
$$416$$ −4.00000 −0.196116
$$417$$ 0 0
$$418$$ −2.00000 −0.0978232
$$419$$ 30.0000 1.46560 0.732798 0.680446i $$-0.238214\pi$$
0.732798 + 0.680446i $$0.238214\pi$$
$$420$$ 0 0
$$421$$ 22.0000 1.07221 0.536107 0.844150i $$-0.319894\pi$$
0.536107 + 0.844150i $$0.319894\pi$$
$$422$$ −12.0000 −0.584151
$$423$$ 0 0
$$424$$ −6.00000 −0.291386
$$425$$ 2.00000 0.0970143
$$426$$ 0 0
$$427$$ −4.00000 −0.193574
$$428$$ 12.0000 0.580042
$$429$$ 0 0
$$430$$ −6.00000 −0.289346
$$431$$ −12.0000 −0.578020 −0.289010 0.957326i $$-0.593326\pi$$
−0.289010 + 0.957326i $$0.593326\pi$$
$$432$$ 0 0
$$433$$ −16.0000 −0.768911 −0.384455 0.923144i $$-0.625611\pi$$
−0.384455 + 0.923144i $$0.625611\pi$$
$$434$$ −16.0000 −0.768025
$$435$$ 0 0
$$436$$ 10.0000 0.478913
$$437$$ 4.00000 0.191346
$$438$$ 0 0
$$439$$ −40.0000 −1.90910 −0.954548 0.298057i $$-0.903661\pi$$
−0.954548 + 0.298057i $$0.903661\pi$$
$$440$$ −2.00000 −0.0953463
$$441$$ 0 0
$$442$$ −8.00000 −0.380521
$$443$$ −24.0000 −1.14027 −0.570137 0.821549i $$-0.693110\pi$$
−0.570137 + 0.821549i $$0.693110\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −4.00000 −0.189405
$$447$$ 0 0
$$448$$ −2.00000 −0.0944911
$$449$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$450$$ 0 0
$$451$$ −16.0000 −0.753411
$$452$$ 6.00000 0.282216
$$453$$ 0 0
$$454$$ −12.0000 −0.563188
$$455$$ 8.00000 0.375046
$$456$$ 0 0
$$457$$ 18.0000 0.842004 0.421002 0.907060i $$-0.361678\pi$$
0.421002 + 0.907060i $$0.361678\pi$$
$$458$$ −10.0000 −0.467269
$$459$$ 0 0
$$460$$ 4.00000 0.186501
$$461$$ −2.00000 −0.0931493 −0.0465746 0.998915i $$-0.514831\pi$$
−0.0465746 + 0.998915i $$0.514831\pi$$
$$462$$ 0 0
$$463$$ −6.00000 −0.278844 −0.139422 0.990233i $$-0.544524\pi$$
−0.139422 + 0.990233i $$0.544524\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ −6.00000 −0.277945
$$467$$ −8.00000 −0.370196 −0.185098 0.982720i $$-0.559260\pi$$
−0.185098 + 0.982720i $$0.559260\pi$$
$$468$$ 0 0
$$469$$ −16.0000 −0.738811
$$470$$ 12.0000 0.553519
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 12.0000 0.551761
$$474$$ 0 0
$$475$$ −1.00000 −0.0458831
$$476$$ −4.00000 −0.183340
$$477$$ 0 0
$$478$$ 10.0000 0.457389
$$479$$ 10.0000 0.456912 0.228456 0.973554i $$-0.426632\pi$$
0.228456 + 0.973554i $$0.426632\pi$$
$$480$$ 0 0
$$481$$ 32.0000 1.45907
$$482$$ −2.00000 −0.0910975
$$483$$ 0 0
$$484$$ −7.00000 −0.318182
$$485$$ 12.0000 0.544892
$$486$$ 0 0
$$487$$ 28.0000 1.26880 0.634401 0.773004i $$-0.281247\pi$$
0.634401 + 0.773004i $$0.281247\pi$$
$$488$$ −2.00000 −0.0905357
$$489$$ 0 0
$$490$$ −3.00000 −0.135526
$$491$$ −22.0000 −0.992846 −0.496423 0.868081i $$-0.665354\pi$$
−0.496423 + 0.868081i $$0.665354\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 4.00000 0.179969
$$495$$ 0 0
$$496$$ −8.00000 −0.359211
$$497$$ −16.0000 −0.717698
$$498$$ 0 0
$$499$$ −40.0000 −1.79065 −0.895323 0.445418i $$-0.853055\pi$$
−0.895323 + 0.445418i $$0.853055\pi$$
$$500$$ −1.00000 −0.0447214
$$501$$ 0 0
$$502$$ 2.00000 0.0892644
$$503$$ 16.0000 0.713405 0.356702 0.934218i $$-0.383901\pi$$
0.356702 + 0.934218i $$0.383901\pi$$
$$504$$ 0 0
$$505$$ 2.00000 0.0889988
$$506$$ −8.00000 −0.355643
$$507$$ 0 0
$$508$$ 8.00000 0.354943
$$509$$ −20.0000 −0.886484 −0.443242 0.896402i $$-0.646172\pi$$
−0.443242 + 0.896402i $$0.646172\pi$$
$$510$$ 0 0
$$511$$ −28.0000 −1.23865
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ 18.0000 0.793946
$$515$$ −4.00000 −0.176261
$$516$$ 0 0
$$517$$ −24.0000 −1.05552
$$518$$ 16.0000 0.703000
$$519$$ 0 0
$$520$$ 4.00000 0.175412
$$521$$ 28.0000 1.22670 0.613351 0.789810i $$-0.289821\pi$$
0.613351 + 0.789810i $$0.289821\pi$$
$$522$$ 0 0
$$523$$ 4.00000 0.174908 0.0874539 0.996169i $$-0.472127\pi$$
0.0874539 + 0.996169i $$0.472127\pi$$
$$524$$ 18.0000 0.786334
$$525$$ 0 0
$$526$$ 24.0000 1.04645
$$527$$ −16.0000 −0.696971
$$528$$ 0 0
$$529$$ −7.00000 −0.304348
$$530$$ 6.00000 0.260623
$$531$$ 0 0
$$532$$ 2.00000 0.0867110
$$533$$ 32.0000 1.38607
$$534$$ 0 0
$$535$$ −12.0000 −0.518805
$$536$$ −8.00000 −0.345547
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 6.00000 0.258438
$$540$$ 0 0
$$541$$ −18.0000 −0.773880 −0.386940 0.922105i $$-0.626468\pi$$
−0.386940 + 0.922105i $$0.626468\pi$$
$$542$$ −12.0000 −0.515444
$$543$$ 0 0
$$544$$ −2.00000 −0.0857493
$$545$$ −10.0000 −0.428353
$$546$$ 0 0
$$547$$ −32.0000 −1.36822 −0.684111 0.729378i $$-0.739809\pi$$
−0.684111 + 0.729378i $$0.739809\pi$$
$$548$$ 22.0000 0.939793
$$549$$ 0 0
$$550$$ 2.00000 0.0852803
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −18.0000 −0.764747
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 42.0000 1.77960 0.889799 0.456354i $$-0.150845\pi$$
0.889799 + 0.456354i $$0.150845\pi$$
$$558$$ 0 0
$$559$$ −24.0000 −1.01509
$$560$$ 2.00000 0.0845154
$$561$$ 0 0
$$562$$ 12.0000 0.506189
$$563$$ −4.00000 −0.168580 −0.0842900 0.996441i $$-0.526862\pi$$
−0.0842900 + 0.996441i $$0.526862\pi$$
$$564$$ 0 0
$$565$$ −6.00000 −0.252422
$$566$$ −14.0000 −0.588464
$$567$$ 0 0
$$568$$ −8.00000 −0.335673
$$569$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$570$$ 0 0
$$571$$ 32.0000 1.33916 0.669579 0.742741i $$-0.266474\pi$$
0.669579 + 0.742741i $$0.266474\pi$$
$$572$$ −8.00000 −0.334497
$$573$$ 0 0
$$574$$ 16.0000 0.667827
$$575$$ −4.00000 −0.166812
$$576$$ 0 0
$$577$$ −22.0000 −0.915872 −0.457936 0.888985i $$-0.651411\pi$$
−0.457936 + 0.888985i $$0.651411\pi$$
$$578$$ 13.0000 0.540729
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 8.00000 0.331896
$$582$$ 0 0
$$583$$ −12.0000 −0.496989
$$584$$ −14.0000 −0.579324
$$585$$ 0 0
$$586$$ 14.0000 0.578335
$$587$$ −8.00000 −0.330195 −0.165098 0.986277i $$-0.552794\pi$$
−0.165098 + 0.986277i $$0.552794\pi$$
$$588$$ 0 0
$$589$$ 8.00000 0.329634
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 8.00000 0.328798
$$593$$ 46.0000 1.88899 0.944497 0.328521i $$-0.106550\pi$$
0.944497 + 0.328521i $$0.106550\pi$$
$$594$$ 0 0
$$595$$ 4.00000 0.163984
$$596$$ −10.0000 −0.409616
$$597$$ 0 0
$$598$$ 16.0000 0.654289
$$599$$ −20.0000 −0.817178 −0.408589 0.912719i $$-0.633979\pi$$
−0.408589 + 0.912719i $$0.633979\pi$$
$$600$$ 0 0
$$601$$ −18.0000 −0.734235 −0.367118 0.930175i $$-0.619655\pi$$
−0.367118 + 0.930175i $$0.619655\pi$$
$$602$$ −12.0000 −0.489083
$$603$$ 0 0
$$604$$ −8.00000 −0.325515
$$605$$ 7.00000 0.284590
$$606$$ 0 0
$$607$$ −12.0000 −0.487065 −0.243532 0.969893i $$-0.578306\pi$$
−0.243532 + 0.969893i $$0.578306\pi$$
$$608$$ 1.00000 0.0405554
$$609$$ 0 0
$$610$$ 2.00000 0.0809776
$$611$$ 48.0000 1.94187
$$612$$ 0 0
$$613$$ −6.00000 −0.242338 −0.121169 0.992632i $$-0.538664\pi$$
−0.121169 + 0.992632i $$0.538664\pi$$
$$614$$ 32.0000 1.29141
$$615$$ 0 0
$$616$$ −4.00000 −0.161165
$$617$$ 42.0000 1.69086 0.845428 0.534089i $$-0.179345\pi$$
0.845428 + 0.534089i $$0.179345\pi$$
$$618$$ 0 0
$$619$$ −40.0000 −1.60774 −0.803868 0.594808i $$-0.797228\pi$$
−0.803868 + 0.594808i $$0.797228\pi$$
$$620$$ 8.00000 0.321288
$$621$$ 0 0
$$622$$ −18.0000 −0.721734
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 6.00000 0.239808
$$627$$ 0 0
$$628$$ 18.0000 0.718278
$$629$$ 16.0000 0.637962
$$630$$ 0 0
$$631$$ 32.0000 1.27390 0.636950 0.770905i $$-0.280196\pi$$
0.636950 + 0.770905i $$0.280196\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 18.0000 0.714871
$$635$$ −8.00000 −0.317470
$$636$$ 0 0
$$637$$ −12.0000 −0.475457
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 1.00000 0.0395285
$$641$$ −32.0000 −1.26392 −0.631962 0.774999i $$-0.717750\pi$$
−0.631962 + 0.774999i $$0.717750\pi$$
$$642$$ 0 0
$$643$$ 14.0000 0.552106 0.276053 0.961142i $$-0.410973\pi$$
0.276053 + 0.961142i $$0.410973\pi$$
$$644$$ 8.00000 0.315244
$$645$$ 0 0
$$646$$ 2.00000 0.0786889
$$647$$ 32.0000 1.25805 0.629025 0.777385i $$-0.283454\pi$$
0.629025 + 0.777385i $$0.283454\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ −4.00000 −0.156893
$$651$$ 0 0
$$652$$ 14.0000 0.548282
$$653$$ 46.0000 1.80012 0.900060 0.435767i $$-0.143523\pi$$
0.900060 + 0.435767i $$0.143523\pi$$
$$654$$ 0 0
$$655$$ −18.0000 −0.703318
$$656$$ 8.00000 0.312348
$$657$$ 0 0
$$658$$ 24.0000 0.935617
$$659$$ −20.0000 −0.779089 −0.389545 0.921008i $$-0.627368\pi$$
−0.389545 + 0.921008i $$0.627368\pi$$
$$660$$ 0 0
$$661$$ 42.0000 1.63361 0.816805 0.576913i $$-0.195743\pi$$
0.816805 + 0.576913i $$0.195743\pi$$
$$662$$ −12.0000 −0.466393
$$663$$ 0 0
$$664$$ 4.00000 0.155230
$$665$$ −2.00000 −0.0775567
$$666$$ 0 0
$$667$$ 0 0
$$668$$ −8.00000 −0.309529
$$669$$ 0 0
$$670$$ 8.00000 0.309067
$$671$$ −4.00000 −0.154418
$$672$$ 0 0
$$673$$ 4.00000 0.154189 0.0770943 0.997024i $$-0.475436\pi$$
0.0770943 + 0.997024i $$0.475436\pi$$
$$674$$ −28.0000 −1.07852
$$675$$ 0 0
$$676$$ 3.00000 0.115385
$$677$$ −18.0000 −0.691796 −0.345898 0.938272i $$-0.612426\pi$$
−0.345898 + 0.938272i $$0.612426\pi$$
$$678$$ 0 0
$$679$$ 24.0000 0.921035
$$680$$ 2.00000 0.0766965
$$681$$ 0 0
$$682$$ −16.0000 −0.612672
$$683$$ 36.0000 1.37750 0.688751 0.724998i $$-0.258159\pi$$
0.688751 + 0.724998i $$0.258159\pi$$
$$684$$ 0 0
$$685$$ −22.0000 −0.840577
$$686$$ −20.0000 −0.763604
$$687$$ 0 0
$$688$$ −6.00000 −0.228748
$$689$$ 24.0000 0.914327
$$690$$ 0 0
$$691$$ −8.00000 −0.304334 −0.152167 0.988355i $$-0.548625\pi$$
−0.152167 + 0.988355i $$0.548625\pi$$
$$692$$ −14.0000 −0.532200
$$693$$ 0 0
$$694$$ −12.0000 −0.455514
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 16.0000 0.606043
$$698$$ 10.0000 0.378506
$$699$$ 0 0
$$700$$ −2.00000 −0.0755929
$$701$$ −2.00000 −0.0755390 −0.0377695 0.999286i $$-0.512025\pi$$
−0.0377695 + 0.999286i $$0.512025\pi$$
$$702$$ 0 0
$$703$$ −8.00000 −0.301726
$$704$$ −2.00000 −0.0753778
$$705$$ 0 0
$$706$$ −6.00000 −0.225813
$$707$$ 4.00000 0.150435
$$708$$ 0 0
$$709$$ 10.0000 0.375558 0.187779 0.982211i $$-0.439871\pi$$
0.187779 + 0.982211i $$0.439871\pi$$
$$710$$ 8.00000 0.300235
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 32.0000 1.19841
$$714$$ 0 0
$$715$$ 8.00000 0.299183
$$716$$ 0 0
$$717$$ 0 0
$$718$$ −10.0000 −0.373197
$$719$$ −50.0000 −1.86469 −0.932343 0.361576i $$-0.882239\pi$$
−0.932343 + 0.361576i $$0.882239\pi$$
$$720$$ 0 0
$$721$$ −8.00000 −0.297936
$$722$$ −1.00000 −0.0372161
$$723$$ 0 0
$$724$$ 2.00000 0.0743294
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 18.0000 0.667583 0.333792 0.942647i $$-0.391672\pi$$
0.333792 + 0.942647i $$0.391672\pi$$
$$728$$ 8.00000 0.296500
$$729$$ 0 0
$$730$$ 14.0000 0.518163
$$731$$ −12.0000 −0.443836
$$732$$ 0 0
$$733$$ −26.0000 −0.960332 −0.480166 0.877178i $$-0.659424\pi$$
−0.480166 + 0.877178i $$0.659424\pi$$
$$734$$ −18.0000 −0.664392
$$735$$ 0 0
$$736$$ 4.00000 0.147442
$$737$$ −16.0000 −0.589368
$$738$$ 0 0
$$739$$ 20.0000 0.735712 0.367856 0.929883i $$-0.380092\pi$$
0.367856 + 0.929883i $$0.380092\pi$$
$$740$$ −8.00000 −0.294086
$$741$$ 0 0
$$742$$ 12.0000 0.440534
$$743$$ −24.0000 −0.880475 −0.440237 0.897881i $$-0.645106\pi$$
−0.440237 + 0.897881i $$0.645106\pi$$
$$744$$ 0 0
$$745$$ 10.0000 0.366372
$$746$$ 36.0000 1.31805
$$747$$ 0 0
$$748$$ −4.00000 −0.146254
$$749$$ −24.0000 −0.876941
$$750$$ 0 0
$$751$$ −8.00000 −0.291924 −0.145962 0.989290i $$-0.546628\pi$$
−0.145962 + 0.989290i $$0.546628\pi$$
$$752$$ 12.0000 0.437595
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 8.00000 0.291150
$$756$$ 0 0
$$757$$ −2.00000 −0.0726912 −0.0363456 0.999339i $$-0.511572\pi$$
−0.0363456 + 0.999339i $$0.511572\pi$$
$$758$$ 20.0000 0.726433
$$759$$ 0 0
$$760$$ −1.00000 −0.0362738
$$761$$ 18.0000 0.652499 0.326250 0.945284i $$-0.394215\pi$$
0.326250 + 0.945284i $$0.394215\pi$$
$$762$$ 0 0
$$763$$ −20.0000 −0.724049
$$764$$ 18.0000 0.651217
$$765$$ 0 0
$$766$$ 24.0000 0.867155
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 50.0000 1.80305 0.901523 0.432731i $$-0.142450\pi$$
0.901523 + 0.432731i $$0.142450\pi$$
$$770$$ 4.00000 0.144150
$$771$$ 0 0
$$772$$ 24.0000 0.863779
$$773$$ −34.0000 −1.22290 −0.611448 0.791285i $$-0.709412\pi$$
−0.611448 + 0.791285i $$0.709412\pi$$
$$774$$ 0 0
$$775$$ −8.00000 −0.287368
$$776$$ 12.0000 0.430775
$$777$$ 0 0
$$778$$ 30.0000 1.07555
$$779$$ −8.00000 −0.286630
$$780$$ 0 0
$$781$$ −16.0000 −0.572525
$$782$$ 8.00000 0.286079
$$783$$ 0 0
$$784$$ −3.00000 −0.107143
$$785$$ −18.0000 −0.642448
$$786$$ 0 0
$$787$$ 28.0000 0.998092 0.499046 0.866575i $$-0.333684\pi$$
0.499046 + 0.866575i $$0.333684\pi$$
$$788$$ −18.0000 −0.641223
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −12.0000 −0.426671
$$792$$ 0 0
$$793$$ 8.00000 0.284088
$$794$$ 22.0000 0.780751
$$795$$ 0 0
$$796$$ −20.0000 −0.708881
$$797$$ 2.00000 0.0708436 0.0354218 0.999372i $$-0.488723\pi$$
0.0354218 + 0.999372i $$0.488723\pi$$
$$798$$ 0 0
$$799$$ 24.0000 0.849059
$$800$$ −1.00000 −0.0353553
$$801$$ 0 0
$$802$$ 12.0000 0.423735
$$803$$ −28.0000 −0.988099
$$804$$ 0 0
$$805$$ −8.00000 −0.281963
$$806$$ 32.0000 1.12715
$$807$$ 0 0
$$808$$ 2.00000 0.0703598
$$809$$ 30.0000 1.05474 0.527372 0.849635i $$-0.323177\pi$$
0.527372 + 0.849635i $$0.323177\pi$$
$$810$$ 0 0
$$811$$ 12.0000 0.421377 0.210688 0.977553i $$-0.432429\pi$$
0.210688 + 0.977553i $$0.432429\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 16.0000 0.560800
$$815$$ −14.0000 −0.490399
$$816$$ 0 0
$$817$$ 6.00000 0.209913
$$818$$ −30.0000 −1.04893
$$819$$ 0 0
$$820$$ −8.00000 −0.279372
$$821$$ 38.0000 1.32621 0.663105 0.748527i $$-0.269238\pi$$
0.663105 + 0.748527i $$0.269238\pi$$
$$822$$ 0 0
$$823$$ 34.0000 1.18517 0.592583 0.805510i $$-0.298108\pi$$
0.592583 + 0.805510i $$0.298108\pi$$
$$824$$ −4.00000 −0.139347
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −28.0000 −0.973655 −0.486828 0.873498i $$-0.661846\pi$$
−0.486828 + 0.873498i $$0.661846\pi$$
$$828$$ 0 0
$$829$$ 10.0000 0.347314 0.173657 0.984806i $$-0.444442\pi$$
0.173657 + 0.984806i $$0.444442\pi$$
$$830$$ −4.00000 −0.138842
$$831$$ 0 0
$$832$$ 4.00000 0.138675
$$833$$ −6.00000 −0.207888
$$834$$ 0 0
$$835$$ 8.00000 0.276851
$$836$$ 2.00000 0.0691714
$$837$$ 0 0
$$838$$ −30.0000 −1.03633
$$839$$ 40.0000 1.38095 0.690477 0.723355i $$-0.257401\pi$$
0.690477 + 0.723355i $$0.257401\pi$$
$$840$$ 0 0
$$841$$ −29.0000 −1.00000
$$842$$ −22.0000 −0.758170
$$843$$ 0 0
$$844$$ 12.0000 0.413057
$$845$$ −3.00000 −0.103203
$$846$$ 0 0
$$847$$ 14.0000 0.481046
$$848$$ 6.00000 0.206041
$$849$$ 0 0
$$850$$ −2.00000 −0.0685994
$$851$$ −32.0000 −1.09695
$$852$$ 0 0
$$853$$ 14.0000 0.479351 0.239675 0.970853i $$-0.422959\pi$$
0.239675 + 0.970853i $$0.422959\pi$$
$$854$$ 4.00000 0.136877
$$855$$ 0 0
$$856$$ −12.0000 −0.410152
$$857$$ 42.0000 1.43469 0.717346 0.696717i $$-0.245357\pi$$
0.717346 + 0.696717i $$0.245357\pi$$
$$858$$ 0 0
$$859$$ 20.0000 0.682391 0.341196 0.939992i $$-0.389168\pi$$
0.341196 + 0.939992i $$0.389168\pi$$
$$860$$ 6.00000 0.204598
$$861$$ 0 0
$$862$$ 12.0000 0.408722
$$863$$ 16.0000 0.544646 0.272323 0.962206i $$-0.412208\pi$$
0.272323 + 0.962206i $$0.412208\pi$$
$$864$$ 0 0
$$865$$ 14.0000 0.476014
$$866$$ 16.0000 0.543702
$$867$$ 0 0
$$868$$ 16.0000 0.543075
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 32.0000 1.08428
$$872$$ −10.0000 −0.338643
$$873$$ 0 0
$$874$$ −4.00000 −0.135302
$$875$$ 2.00000 0.0676123
$$876$$ 0 0
$$877$$ −12.0000 −0.405211 −0.202606 0.979260i $$-0.564941\pi$$
−0.202606 + 0.979260i $$0.564941\pi$$
$$878$$ 40.0000 1.34993
$$879$$ 0 0
$$880$$ 2.00000 0.0674200
$$881$$ 18.0000 0.606435 0.303218 0.952921i $$-0.401939\pi$$
0.303218 + 0.952921i $$0.401939\pi$$
$$882$$ 0 0
$$883$$ −26.0000 −0.874970 −0.437485 0.899226i $$-0.644131\pi$$
−0.437485 + 0.899226i $$0.644131\pi$$
$$884$$ 8.00000 0.269069
$$885$$ 0 0
$$886$$ 24.0000 0.806296
$$887$$ −48.0000 −1.61168 −0.805841 0.592132i $$-0.798286\pi$$
−0.805841 + 0.592132i $$0.798286\pi$$
$$888$$ 0 0
$$889$$ −16.0000 −0.536623
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 4.00000 0.133930
$$893$$ −12.0000 −0.401565
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 2.00000 0.0668153
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 12.0000 0.399778
$$902$$ 16.0000 0.532742
$$903$$ 0 0
$$904$$ −6.00000 −0.199557
$$905$$ −2.00000 −0.0664822
$$906$$ 0 0
$$907$$ 28.0000 0.929725 0.464862 0.885383i $$-0.346104\pi$$
0.464862 + 0.885383i $$0.346104\pi$$
$$908$$ 12.0000 0.398234
$$909$$ 0 0
$$910$$ −8.00000 −0.265197
$$911$$ −32.0000 −1.06021 −0.530104 0.847933i $$-0.677847\pi$$
−0.530104 + 0.847933i $$0.677847\pi$$
$$912$$ 0 0
$$913$$ 8.00000 0.264761
$$914$$ −18.0000 −0.595387
$$915$$ 0 0
$$916$$ 10.0000 0.330409
$$917$$ −36.0000 −1.18882
$$918$$ 0 0
$$919$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$920$$ −4.00000 −0.131876
$$921$$ 0 0
$$922$$ 2.00000 0.0658665
$$923$$ 32.0000 1.05329
$$924$$ 0 0
$$925$$ 8.00000 0.263038
$$926$$ 6.00000 0.197172
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 30.0000 0.984268 0.492134 0.870519i $$-0.336217\pi$$
0.492134 + 0.870519i $$0.336217\pi$$
$$930$$ 0 0
$$931$$ 3.00000 0.0983210
$$932$$ 6.00000 0.196537
$$933$$ 0 0
$$934$$ 8.00000 0.261768
$$935$$ 4.00000 0.130814
$$936$$ 0 0
$$937$$ −2.00000 −0.0653372 −0.0326686 0.999466i $$-0.510401\pi$$
−0.0326686 + 0.999466i $$0.510401\pi$$
$$938$$ 16.0000 0.522419
$$939$$ 0 0
$$940$$ −12.0000 −0.391397
$$941$$ 8.00000 0.260793 0.130396 0.991462i $$-0.458375\pi$$
0.130396 + 0.991462i $$0.458375\pi$$
$$942$$ 0 0
$$943$$ −32.0000 −1.04206
$$944$$ 0 0
$$945$$ 0 0
$$946$$ −12.0000 −0.390154
$$947$$ 52.0000 1.68977 0.844886 0.534946i $$-0.179668\pi$$
0.844886 + 0.534946i $$0.179668\pi$$
$$948$$ 0 0
$$949$$ 56.0000 1.81784
$$950$$ 1.00000 0.0324443
$$951$$ 0 0
$$952$$ 4.00000 0.129641
$$953$$ −34.0000 −1.10137 −0.550684 0.834714i $$-0.685633\pi$$
−0.550684 + 0.834714i $$0.685633\pi$$
$$954$$ 0 0
$$955$$ −18.0000 −0.582466
$$956$$ −10.0000 −0.323423
$$957$$ 0 0
$$958$$ −10.0000 −0.323085
$$959$$ −44.0000 −1.42083
$$960$$ 0 0
$$961$$ 33.0000 1.06452
$$962$$ −32.0000 −1.03172
$$963$$ 0 0
$$964$$ 2.00000 0.0644157
$$965$$ −24.0000 −0.772587
$$966$$ 0 0
$$967$$ 58.0000 1.86515 0.932577 0.360971i $$-0.117555\pi$$
0.932577 + 0.360971i $$0.117555\pi$$
$$968$$ 7.00000 0.224989
$$969$$ 0 0
$$970$$ −12.0000 −0.385297
$$971$$ −12.0000 −0.385098 −0.192549 0.981287i $$-0.561675\pi$$
−0.192549 + 0.981287i $$0.561675\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ −28.0000 −0.897178
$$975$$ 0 0
$$976$$ 2.00000 0.0640184
$$977$$ −38.0000 −1.21573 −0.607864 0.794041i $$-0.707973\pi$$
−0.607864 + 0.794041i $$0.707973\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 3.00000 0.0958315
$$981$$ 0 0
$$982$$ 22.0000 0.702048
$$983$$ −24.0000 −0.765481 −0.382741 0.923856i $$-0.625020\pi$$
−0.382741 + 0.923856i $$0.625020\pi$$
$$984$$ 0 0
$$985$$ 18.0000 0.573528
$$986$$ 0 0
$$987$$ 0 0
$$988$$ −4.00000 −0.127257
$$989$$ 24.0000 0.763156
$$990$$ 0 0
$$991$$ −8.00000 −0.254128 −0.127064 0.991894i $$-0.540555\pi$$
−0.127064 + 0.991894i $$0.540555\pi$$
$$992$$ 8.00000 0.254000
$$993$$ 0 0
$$994$$ 16.0000 0.507489
$$995$$ 20.0000 0.634043
$$996$$ 0 0
$$997$$ −62.0000 −1.96356 −0.981780 0.190022i $$-0.939144\pi$$
−0.981780 + 0.190022i $$0.939144\pi$$
$$998$$ 40.0000 1.26618
$$999$$ 0 0
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1710.2.a.b.1.1 1
3.2 odd 2 570.2.a.l.1.1 1
5.4 even 2 8550.2.a.bf.1.1 1
12.11 even 2 4560.2.a.o.1.1 1
15.2 even 4 2850.2.d.q.799.2 2
15.8 even 4 2850.2.d.q.799.1 2
15.14 odd 2 2850.2.a.e.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
570.2.a.l.1.1 1 3.2 odd 2
1710.2.a.b.1.1 1 1.1 even 1 trivial
2850.2.a.e.1.1 1 15.14 odd 2
2850.2.d.q.799.1 2 15.8 even 4
2850.2.d.q.799.2 2 15.2 even 4
4560.2.a.o.1.1 1 12.11 even 2
8550.2.a.bf.1.1 1 5.4 even 2