# Properties

 Label 1050.2.a.k.1.1 Level $1050$ Weight $2$ Character 1050.1 Self dual yes Analytic conductor $8.384$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1050.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$8.38429221223$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 210) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1050.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{12} -2.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} +6.00000 q^{17} +1.00000 q^{18} +8.00000 q^{19} +1.00000 q^{21} -1.00000 q^{24} -2.00000 q^{26} -1.00000 q^{27} -1.00000 q^{28} +6.00000 q^{29} -4.00000 q^{31} +1.00000 q^{32} +6.00000 q^{34} +1.00000 q^{36} +10.0000 q^{37} +8.00000 q^{38} +2.00000 q^{39} -6.00000 q^{41} +1.00000 q^{42} +4.00000 q^{43} -1.00000 q^{48} +1.00000 q^{49} -6.00000 q^{51} -2.00000 q^{52} +6.00000 q^{53} -1.00000 q^{54} -1.00000 q^{56} -8.00000 q^{57} +6.00000 q^{58} -12.0000 q^{59} -10.0000 q^{61} -4.00000 q^{62} -1.00000 q^{63} +1.00000 q^{64} +4.00000 q^{67} +6.00000 q^{68} +12.0000 q^{71} +1.00000 q^{72} +10.0000 q^{73} +10.0000 q^{74} +8.00000 q^{76} +2.00000 q^{78} +8.00000 q^{79} +1.00000 q^{81} -6.00000 q^{82} -12.0000 q^{83} +1.00000 q^{84} +4.00000 q^{86} -6.00000 q^{87} -6.00000 q^{89} +2.00000 q^{91} +4.00000 q^{93} -1.00000 q^{96} +10.0000 q^{97} +1.00000 q^{98} +O(q^{100})$$

## 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
$$3$$ −1.00000 −0.577350
$$4$$ 1.00000 0.500000
$$5$$ 0 0
$$6$$ −1.00000 −0.408248
$$7$$ −1.00000 −0.377964
$$8$$ 1.00000 0.353553
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ −1.00000 −0.288675
$$13$$ −2.00000 −0.554700 −0.277350 0.960769i $$-0.589456\pi$$
−0.277350 + 0.960769i $$0.589456\pi$$
$$14$$ −1.00000 −0.267261
$$15$$ 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
$$19$$ 8.00000 1.83533 0.917663 0.397360i $$-0.130073\pi$$
0.917663 + 0.397360i $$0.130073\pi$$
$$20$$ 0 0
$$21$$ 1.00000 0.218218
$$22$$ 0 0
$$23$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ −1.00000 −0.204124
$$25$$ 0 0
$$26$$ −2.00000 −0.392232
$$27$$ −1.00000 −0.192450
$$28$$ −1.00000 −0.188982
$$29$$ 6.00000 1.11417 0.557086 0.830455i $$-0.311919\pi$$
0.557086 + 0.830455i $$0.311919\pi$$
$$30$$ 0 0
$$31$$ −4.00000 −0.718421 −0.359211 0.933257i $$-0.616954\pi$$
−0.359211 + 0.933257i $$0.616954\pi$$
$$32$$ 1.00000 0.176777
$$33$$ 0 0
$$34$$ 6.00000 1.02899
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ 10.0000 1.64399 0.821995 0.569495i $$-0.192861\pi$$
0.821995 + 0.569495i $$0.192861\pi$$
$$38$$ 8.00000 1.29777
$$39$$ 2.00000 0.320256
$$40$$ 0 0
$$41$$ −6.00000 −0.937043 −0.468521 0.883452i $$-0.655213\pi$$
−0.468521 + 0.883452i $$0.655213\pi$$
$$42$$ 1.00000 0.154303
$$43$$ 4.00000 0.609994 0.304997 0.952353i $$-0.401344\pi$$
0.304997 + 0.952353i $$0.401344\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ −1.00000 −0.144338
$$49$$ 1.00000 0.142857
$$50$$ 0 0
$$51$$ −6.00000 −0.840168
$$52$$ −2.00000 −0.277350
$$53$$ 6.00000 0.824163 0.412082 0.911147i $$-0.364802\pi$$
0.412082 + 0.911147i $$0.364802\pi$$
$$54$$ −1.00000 −0.136083
$$55$$ 0 0
$$56$$ −1.00000 −0.133631
$$57$$ −8.00000 −1.05963
$$58$$ 6.00000 0.787839
$$59$$ −12.0000 −1.56227 −0.781133 0.624364i $$-0.785358\pi$$
−0.781133 + 0.624364i $$0.785358\pi$$
$$60$$ 0 0
$$61$$ −10.0000 −1.28037 −0.640184 0.768221i $$-0.721142\pi$$
−0.640184 + 0.768221i $$0.721142\pi$$
$$62$$ −4.00000 −0.508001
$$63$$ −1.00000 −0.125988
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 4.00000 0.488678 0.244339 0.969690i $$-0.421429\pi$$
0.244339 + 0.969690i $$0.421429\pi$$
$$68$$ 6.00000 0.727607
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 12.0000 1.42414 0.712069 0.702109i $$-0.247758\pi$$
0.712069 + 0.702109i $$0.247758\pi$$
$$72$$ 1.00000 0.117851
$$73$$ 10.0000 1.17041 0.585206 0.810885i $$-0.301014\pi$$
0.585206 + 0.810885i $$0.301014\pi$$
$$74$$ 10.0000 1.16248
$$75$$ 0 0
$$76$$ 8.00000 0.917663
$$77$$ 0 0
$$78$$ 2.00000 0.226455
$$79$$ 8.00000 0.900070 0.450035 0.893011i $$-0.351411\pi$$
0.450035 + 0.893011i $$0.351411\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ −6.00000 −0.662589
$$83$$ −12.0000 −1.31717 −0.658586 0.752506i $$-0.728845\pi$$
−0.658586 + 0.752506i $$0.728845\pi$$
$$84$$ 1.00000 0.109109
$$85$$ 0 0
$$86$$ 4.00000 0.431331
$$87$$ −6.00000 −0.643268
$$88$$ 0 0
$$89$$ −6.00000 −0.635999 −0.317999 0.948091i $$-0.603011\pi$$
−0.317999 + 0.948091i $$0.603011\pi$$
$$90$$ 0 0
$$91$$ 2.00000 0.209657
$$92$$ 0 0
$$93$$ 4.00000 0.414781
$$94$$ 0 0
$$95$$ 0 0
$$96$$ −1.00000 −0.102062
$$97$$ 10.0000 1.01535 0.507673 0.861550i $$-0.330506\pi$$
0.507673 + 0.861550i $$0.330506\pi$$
$$98$$ 1.00000 0.101015
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 6.00000 0.597022 0.298511 0.954406i $$-0.403510\pi$$
0.298511 + 0.954406i $$0.403510\pi$$
$$102$$ −6.00000 −0.594089
$$103$$ −8.00000 −0.788263 −0.394132 0.919054i $$-0.628955\pi$$
−0.394132 + 0.919054i $$0.628955\pi$$
$$104$$ −2.00000 −0.196116
$$105$$ 0 0
$$106$$ 6.00000 0.582772
$$107$$ −12.0000 −1.16008 −0.580042 0.814587i $$-0.696964\pi$$
−0.580042 + 0.814587i $$0.696964\pi$$
$$108$$ −1.00000 −0.0962250
$$109$$ 14.0000 1.34096 0.670478 0.741929i $$-0.266089\pi$$
0.670478 + 0.741929i $$0.266089\pi$$
$$110$$ 0 0
$$111$$ −10.0000 −0.949158
$$112$$ −1.00000 −0.0944911
$$113$$ −6.00000 −0.564433 −0.282216 0.959351i $$-0.591070\pi$$
−0.282216 + 0.959351i $$0.591070\pi$$
$$114$$ −8.00000 −0.749269
$$115$$ 0 0
$$116$$ 6.00000 0.557086
$$117$$ −2.00000 −0.184900
$$118$$ −12.0000 −1.10469
$$119$$ −6.00000 −0.550019
$$120$$ 0 0
$$121$$ −11.0000 −1.00000
$$122$$ −10.0000 −0.905357
$$123$$ 6.00000 0.541002
$$124$$ −4.00000 −0.359211
$$125$$ 0 0
$$126$$ −1.00000 −0.0890871
$$127$$ −8.00000 −0.709885 −0.354943 0.934888i $$-0.615500\pi$$
−0.354943 + 0.934888i $$0.615500\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ −4.00000 −0.352180
$$130$$ 0 0
$$131$$ −12.0000 −1.04844 −0.524222 0.851581i $$-0.675644\pi$$
−0.524222 + 0.851581i $$0.675644\pi$$
$$132$$ 0 0
$$133$$ −8.00000 −0.693688
$$134$$ 4.00000 0.345547
$$135$$ 0 0
$$136$$ 6.00000 0.514496
$$137$$ −6.00000 −0.512615 −0.256307 0.966595i $$-0.582506\pi$$
−0.256307 + 0.966595i $$0.582506\pi$$
$$138$$ 0 0
$$139$$ −16.0000 −1.35710 −0.678551 0.734553i $$-0.737392\pi$$
−0.678551 + 0.734553i $$0.737392\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 12.0000 1.00702
$$143$$ 0 0
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ 10.0000 0.827606
$$147$$ −1.00000 −0.0824786
$$148$$ 10.0000 0.821995
$$149$$ 6.00000 0.491539 0.245770 0.969328i $$-0.420959\pi$$
0.245770 + 0.969328i $$0.420959\pi$$
$$150$$ 0 0
$$151$$ 8.00000 0.651031 0.325515 0.945537i $$-0.394462\pi$$
0.325515 + 0.945537i $$0.394462\pi$$
$$152$$ 8.00000 0.648886
$$153$$ 6.00000 0.485071
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 2.00000 0.160128
$$157$$ 22.0000 1.75579 0.877896 0.478852i $$-0.158947\pi$$
0.877896 + 0.478852i $$0.158947\pi$$
$$158$$ 8.00000 0.636446
$$159$$ −6.00000 −0.475831
$$160$$ 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 $$0.786445\pi$$
$$164$$ −6.00000 −0.468521
$$165$$ 0 0
$$166$$ −12.0000 −0.931381
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 1.00000 0.0771517
$$169$$ −9.00000 −0.692308
$$170$$ 0 0
$$171$$ 8.00000 0.611775
$$172$$ 4.00000 0.304997
$$173$$ −6.00000 −0.456172 −0.228086 0.973641i $$-0.573247\pi$$
−0.228086 + 0.973641i $$0.573247\pi$$
$$174$$ −6.00000 −0.454859
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 12.0000 0.901975
$$178$$ −6.00000 −0.449719
$$179$$ −24.0000 −1.79384 −0.896922 0.442189i $$-0.854202\pi$$
−0.896922 + 0.442189i $$0.854202\pi$$
$$180$$ 0 0
$$181$$ −10.0000 −0.743294 −0.371647 0.928374i $$-0.621207\pi$$
−0.371647 + 0.928374i $$0.621207\pi$$
$$182$$ 2.00000 0.148250
$$183$$ 10.0000 0.739221
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 4.00000 0.293294
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 1.00000 0.0727393
$$190$$ 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
$$193$$ −2.00000 −0.143963 −0.0719816 0.997406i $$-0.522932\pi$$
−0.0719816 + 0.997406i $$0.522932\pi$$
$$194$$ 10.0000 0.717958
$$195$$ 0 0
$$196$$ 1.00000 0.0714286
$$197$$ −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 $$-0.249200\pi$$
0.708881 + 0.705328i $$0.249200\pi$$
$$200$$ 0 0
$$201$$ −4.00000 −0.282138
$$202$$ 6.00000 0.422159
$$203$$ −6.00000 −0.421117
$$204$$ −6.00000 −0.420084
$$205$$ 0 0
$$206$$ −8.00000 −0.557386
$$207$$ 0 0
$$208$$ −2.00000 −0.138675
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −4.00000 −0.275371 −0.137686 0.990476i $$-0.543966\pi$$
−0.137686 + 0.990476i $$0.543966\pi$$
$$212$$ 6.00000 0.412082
$$213$$ −12.0000 −0.822226
$$214$$ −12.0000 −0.820303
$$215$$ 0 0
$$216$$ −1.00000 −0.0680414
$$217$$ 4.00000 0.271538
$$218$$ 14.0000 0.948200
$$219$$ −10.0000 −0.675737
$$220$$ 0 0
$$221$$ −12.0000 −0.807207
$$222$$ −10.0000 −0.671156
$$223$$ −8.00000 −0.535720 −0.267860 0.963458i $$-0.586316\pi$$
−0.267860 + 0.963458i $$0.586316\pi$$
$$224$$ −1.00000 −0.0668153
$$225$$ 0 0
$$226$$ −6.00000 −0.399114
$$227$$ −12.0000 −0.796468 −0.398234 0.917284i $$-0.630377\pi$$
−0.398234 + 0.917284i $$0.630377\pi$$
$$228$$ −8.00000 −0.529813
$$229$$ 14.0000 0.925146 0.462573 0.886581i $$-0.346926\pi$$
0.462573 + 0.886581i $$0.346926\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 6.00000 0.393919
$$233$$ −30.0000 −1.96537 −0.982683 0.185296i $$-0.940675\pi$$
−0.982683 + 0.185296i $$0.940675\pi$$
$$234$$ −2.00000 −0.130744
$$235$$ 0 0
$$236$$ −12.0000 −0.781133
$$237$$ −8.00000 −0.519656
$$238$$ −6.00000 −0.388922
$$239$$ −12.0000 −0.776215 −0.388108 0.921614i $$-0.626871\pi$$
−0.388108 + 0.921614i $$0.626871\pi$$
$$240$$ 0 0
$$241$$ 26.0000 1.67481 0.837404 0.546585i $$-0.184072\pi$$
0.837404 + 0.546585i $$0.184072\pi$$
$$242$$ −11.0000 −0.707107
$$243$$ −1.00000 −0.0641500
$$244$$ −10.0000 −0.640184
$$245$$ 0 0
$$246$$ 6.00000 0.382546
$$247$$ −16.0000 −1.01806
$$248$$ −4.00000 −0.254000
$$249$$ 12.0000 0.760469
$$250$$ 0 0
$$251$$ −12.0000 −0.757433 −0.378717 0.925513i $$-0.623635\pi$$
−0.378717 + 0.925513i $$0.623635\pi$$
$$252$$ −1.00000 −0.0629941
$$253$$ 0 0
$$254$$ −8.00000 −0.501965
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 30.0000 1.87135 0.935674 0.352865i $$-0.114792\pi$$
0.935674 + 0.352865i $$0.114792\pi$$
$$258$$ −4.00000 −0.249029
$$259$$ −10.0000 −0.621370
$$260$$ 0 0
$$261$$ 6.00000 0.371391
$$262$$ −12.0000 −0.741362
$$263$$ 24.0000 1.47990 0.739952 0.672660i $$-0.234848\pi$$
0.739952 + 0.672660i $$0.234848\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ −8.00000 −0.490511
$$267$$ 6.00000 0.367194
$$268$$ 4.00000 0.244339
$$269$$ −18.0000 −1.09748 −0.548740 0.835993i $$-0.684892\pi$$
−0.548740 + 0.835993i $$0.684892\pi$$
$$270$$ 0 0
$$271$$ 20.0000 1.21491 0.607457 0.794353i $$-0.292190\pi$$
0.607457 + 0.794353i $$0.292190\pi$$
$$272$$ 6.00000 0.363803
$$273$$ −2.00000 −0.121046
$$274$$ −6.00000 −0.362473
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 10.0000 0.600842 0.300421 0.953807i $$-0.402873\pi$$
0.300421 + 0.953807i $$0.402873\pi$$
$$278$$ −16.0000 −0.959616
$$279$$ −4.00000 −0.239474
$$280$$ 0 0
$$281$$ 18.0000 1.07379 0.536895 0.843649i $$-0.319597\pi$$
0.536895 + 0.843649i $$0.319597\pi$$
$$282$$ 0 0
$$283$$ 4.00000 0.237775 0.118888 0.992908i $$-0.462067\pi$$
0.118888 + 0.992908i $$0.462067\pi$$
$$284$$ 12.0000 0.712069
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 6.00000 0.354169
$$288$$ 1.00000 0.0589256
$$289$$ 19.0000 1.11765
$$290$$ 0 0
$$291$$ −10.0000 −0.586210
$$292$$ 10.0000 0.585206
$$293$$ −30.0000 −1.75262 −0.876309 0.481749i $$-0.840002\pi$$
−0.876309 + 0.481749i $$0.840002\pi$$
$$294$$ −1.00000 −0.0583212
$$295$$ 0 0
$$296$$ 10.0000 0.581238
$$297$$ 0 0
$$298$$ 6.00000 0.347571
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −4.00000 −0.230556
$$302$$ 8.00000 0.460348
$$303$$ −6.00000 −0.344691
$$304$$ 8.00000 0.458831
$$305$$ 0 0
$$306$$ 6.00000 0.342997
$$307$$ 4.00000 0.228292 0.114146 0.993464i $$-0.463587\pi$$
0.114146 + 0.993464i $$0.463587\pi$$
$$308$$ 0 0
$$309$$ 8.00000 0.455104
$$310$$ 0 0
$$311$$ 24.0000 1.36092 0.680458 0.732787i $$-0.261781\pi$$
0.680458 + 0.732787i $$0.261781\pi$$
$$312$$ 2.00000 0.113228
$$313$$ −14.0000 −0.791327 −0.395663 0.918396i $$-0.629485\pi$$
−0.395663 + 0.918396i $$0.629485\pi$$
$$314$$ 22.0000 1.24153
$$315$$ 0 0
$$316$$ 8.00000 0.450035
$$317$$ −18.0000 −1.01098 −0.505490 0.862832i $$-0.668688\pi$$
−0.505490 + 0.862832i $$0.668688\pi$$
$$318$$ −6.00000 −0.336463
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 12.0000 0.669775
$$322$$ 0 0
$$323$$ 48.0000 2.67079
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ −20.0000 −1.10770
$$327$$ −14.0000 −0.774202
$$328$$ −6.00000 −0.331295
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −28.0000 −1.53902 −0.769510 0.638635i $$-0.779499\pi$$
−0.769510 + 0.638635i $$0.779499\pi$$
$$332$$ −12.0000 −0.658586
$$333$$ 10.0000 0.547997
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 1.00000 0.0545545
$$337$$ −2.00000 −0.108947 −0.0544735 0.998515i $$-0.517348\pi$$
−0.0544735 + 0.998515i $$0.517348\pi$$
$$338$$ −9.00000 −0.489535
$$339$$ 6.00000 0.325875
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 8.00000 0.432590
$$343$$ −1.00000 −0.0539949
$$344$$ 4.00000 0.215666
$$345$$ 0 0
$$346$$ −6.00000 −0.322562
$$347$$ 12.0000 0.644194 0.322097 0.946707i $$-0.395612\pi$$
0.322097 + 0.946707i $$0.395612\pi$$
$$348$$ −6.00000 −0.321634
$$349$$ −10.0000 −0.535288 −0.267644 0.963518i $$-0.586245\pi$$
−0.267644 + 0.963518i $$0.586245\pi$$
$$350$$ 0 0
$$351$$ 2.00000 0.106752
$$352$$ 0 0
$$353$$ 6.00000 0.319348 0.159674 0.987170i $$-0.448956\pi$$
0.159674 + 0.987170i $$0.448956\pi$$
$$354$$ 12.0000 0.637793
$$355$$ 0 0
$$356$$ −6.00000 −0.317999
$$357$$ 6.00000 0.317554
$$358$$ −24.0000 −1.26844
$$359$$ −12.0000 −0.633336 −0.316668 0.948536i $$-0.602564\pi$$
−0.316668 + 0.948536i $$0.602564\pi$$
$$360$$ 0 0
$$361$$ 45.0000 2.36842
$$362$$ −10.0000 −0.525588
$$363$$ 11.0000 0.577350
$$364$$ 2.00000 0.104828
$$365$$ 0 0
$$366$$ 10.0000 0.522708
$$367$$ −8.00000 −0.417597 −0.208798 0.977959i $$-0.566955\pi$$
−0.208798 + 0.977959i $$0.566955\pi$$
$$368$$ 0 0
$$369$$ −6.00000 −0.312348
$$370$$ 0 0
$$371$$ −6.00000 −0.311504
$$372$$ 4.00000 0.207390
$$373$$ 34.0000 1.76045 0.880227 0.474554i $$-0.157390\pi$$
0.880227 + 0.474554i $$0.157390\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −12.0000 −0.618031
$$378$$ 1.00000 0.0514344
$$379$$ −4.00000 −0.205466 −0.102733 0.994709i $$-0.532759\pi$$
−0.102733 + 0.994709i $$0.532759\pi$$
$$380$$ 0 0
$$381$$ 8.00000 0.409852
$$382$$ 12.0000 0.613973
$$383$$ −24.0000 −1.22634 −0.613171 0.789950i $$-0.710106\pi$$
−0.613171 + 0.789950i $$0.710106\pi$$
$$384$$ −1.00000 −0.0510310
$$385$$ 0 0
$$386$$ −2.00000 −0.101797
$$387$$ 4.00000 0.203331
$$388$$ 10.0000 0.507673
$$389$$ 6.00000 0.304212 0.152106 0.988364i $$-0.451394\pi$$
0.152106 + 0.988364i $$0.451394\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 1.00000 0.0505076
$$393$$ 12.0000 0.605320
$$394$$ −18.0000 −0.906827
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −2.00000 −0.100377 −0.0501886 0.998740i $$-0.515982\pi$$
−0.0501886 + 0.998740i $$0.515982\pi$$
$$398$$ 20.0000 1.00251
$$399$$ 8.00000 0.400501
$$400$$ 0 0
$$401$$ −30.0000 −1.49813 −0.749064 0.662497i $$-0.769497\pi$$
−0.749064 + 0.662497i $$0.769497\pi$$
$$402$$ −4.00000 −0.199502
$$403$$ 8.00000 0.398508
$$404$$ 6.00000 0.298511
$$405$$ 0 0
$$406$$ −6.00000 −0.297775
$$407$$ 0 0
$$408$$ −6.00000 −0.297044
$$409$$ 26.0000 1.28562 0.642809 0.766027i $$-0.277769\pi$$
0.642809 + 0.766027i $$0.277769\pi$$
$$410$$ 0 0
$$411$$ 6.00000 0.295958
$$412$$ −8.00000 −0.394132
$$413$$ 12.0000 0.590481
$$414$$ 0 0
$$415$$ 0 0
$$416$$ −2.00000 −0.0980581
$$417$$ 16.0000 0.783523
$$418$$ 0 0
$$419$$ −12.0000 −0.586238 −0.293119 0.956076i $$-0.594693\pi$$
−0.293119 + 0.956076i $$0.594693\pi$$
$$420$$ 0 0
$$421$$ 38.0000 1.85201 0.926003 0.377515i $$-0.123221\pi$$
0.926003 + 0.377515i $$0.123221\pi$$
$$422$$ −4.00000 −0.194717
$$423$$ 0 0
$$424$$ 6.00000 0.291386
$$425$$ 0 0
$$426$$ −12.0000 −0.581402
$$427$$ 10.0000 0.483934
$$428$$ −12.0000 −0.580042
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −12.0000 −0.578020 −0.289010 0.957326i $$-0.593326\pi$$
−0.289010 + 0.957326i $$0.593326\pi$$
$$432$$ −1.00000 −0.0481125
$$433$$ 10.0000 0.480569 0.240285 0.970702i $$-0.422759\pi$$
0.240285 + 0.970702i $$0.422759\pi$$
$$434$$ 4.00000 0.192006
$$435$$ 0 0
$$436$$ 14.0000 0.670478
$$437$$ 0 0
$$438$$ −10.0000 −0.477818
$$439$$ −28.0000 −1.33637 −0.668184 0.743996i $$-0.732928\pi$$
−0.668184 + 0.743996i $$0.732928\pi$$
$$440$$ 0 0
$$441$$ 1.00000 0.0476190
$$442$$ −12.0000 −0.570782
$$443$$ 12.0000 0.570137 0.285069 0.958507i $$-0.407984\pi$$
0.285069 + 0.958507i $$0.407984\pi$$
$$444$$ −10.0000 −0.474579
$$445$$ 0 0
$$446$$ −8.00000 −0.378811
$$447$$ −6.00000 −0.283790
$$448$$ −1.00000 −0.0472456
$$449$$ 18.0000 0.849473 0.424736 0.905317i $$-0.360367\pi$$
0.424736 + 0.905317i $$0.360367\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ −6.00000 −0.282216
$$453$$ −8.00000 −0.375873
$$454$$ −12.0000 −0.563188
$$455$$ 0 0
$$456$$ −8.00000 −0.374634
$$457$$ −2.00000 −0.0935561 −0.0467780 0.998905i $$-0.514895\pi$$
−0.0467780 + 0.998905i $$0.514895\pi$$
$$458$$ 14.0000 0.654177
$$459$$ −6.00000 −0.280056
$$460$$ 0 0
$$461$$ −18.0000 −0.838344 −0.419172 0.907907i $$-0.637680\pi$$
−0.419172 + 0.907907i $$0.637680\pi$$
$$462$$ 0 0
$$463$$ 40.0000 1.85896 0.929479 0.368875i $$-0.120257\pi$$
0.929479 + 0.368875i $$0.120257\pi$$
$$464$$ 6.00000 0.278543
$$465$$ 0 0
$$466$$ −30.0000 −1.38972
$$467$$ 36.0000 1.66588 0.832941 0.553362i $$-0.186655\pi$$
0.832941 + 0.553362i $$0.186655\pi$$
$$468$$ −2.00000 −0.0924500
$$469$$ −4.00000 −0.184703
$$470$$ 0 0
$$471$$ −22.0000 −1.01371
$$472$$ −12.0000 −0.552345
$$473$$ 0 0
$$474$$ −8.00000 −0.367452
$$475$$ 0 0
$$476$$ −6.00000 −0.275010
$$477$$ 6.00000 0.274721
$$478$$ −12.0000 −0.548867
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ −20.0000 −0.911922
$$482$$ 26.0000 1.18427
$$483$$ 0 0
$$484$$ −11.0000 −0.500000
$$485$$ 0 0
$$486$$ −1.00000 −0.0453609
$$487$$ −32.0000 −1.45006 −0.725029 0.688718i $$-0.758174\pi$$
−0.725029 + 0.688718i $$0.758174\pi$$
$$488$$ −10.0000 −0.452679
$$489$$ 20.0000 0.904431
$$490$$ 0 0
$$491$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$492$$ 6.00000 0.270501
$$493$$ 36.0000 1.62136
$$494$$ −16.0000 −0.719874
$$495$$ 0 0
$$496$$ −4.00000 −0.179605
$$497$$ −12.0000 −0.538274
$$498$$ 12.0000 0.537733
$$499$$ 20.0000 0.895323 0.447661 0.894203i $$-0.352257\pi$$
0.447661 + 0.894203i $$0.352257\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ −12.0000 −0.535586
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ −1.00000 −0.0445435
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 9.00000 0.399704
$$508$$ −8.00000 −0.354943
$$509$$ 30.0000 1.32973 0.664863 0.746965i $$-0.268490\pi$$
0.664863 + 0.746965i $$0.268490\pi$$
$$510$$ 0 0
$$511$$ −10.0000 −0.442374
$$512$$ 1.00000 0.0441942
$$513$$ −8.00000 −0.353209
$$514$$ 30.0000 1.32324
$$515$$ 0 0
$$516$$ −4.00000 −0.176090
$$517$$ 0 0
$$518$$ −10.0000 −0.439375
$$519$$ 6.00000 0.263371
$$520$$ 0 0
$$521$$ −6.00000 −0.262865 −0.131432 0.991325i $$-0.541958\pi$$
−0.131432 + 0.991325i $$0.541958\pi$$
$$522$$ 6.00000 0.262613
$$523$$ 28.0000 1.22435 0.612177 0.790721i $$-0.290294\pi$$
0.612177 + 0.790721i $$0.290294\pi$$
$$524$$ −12.0000 −0.524222
$$525$$ 0 0
$$526$$ 24.0000 1.04645
$$527$$ −24.0000 −1.04546
$$528$$ 0 0
$$529$$ −23.0000 −1.00000
$$530$$ 0 0
$$531$$ −12.0000 −0.520756
$$532$$ −8.00000 −0.346844
$$533$$ 12.0000 0.519778
$$534$$ 6.00000 0.259645
$$535$$ 0 0
$$536$$ 4.00000 0.172774
$$537$$ 24.0000 1.03568
$$538$$ −18.0000 −0.776035
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −34.0000 −1.46177 −0.730887 0.682498i $$-0.760893\pi$$
−0.730887 + 0.682498i $$0.760893\pi$$
$$542$$ 20.0000 0.859074
$$543$$ 10.0000 0.429141
$$544$$ 6.00000 0.257248
$$545$$ 0 0
$$546$$ −2.00000 −0.0855921
$$547$$ −44.0000 −1.88130 −0.940652 0.339372i $$-0.889785\pi$$
−0.940652 + 0.339372i $$0.889785\pi$$
$$548$$ −6.00000 −0.256307
$$549$$ −10.0000 −0.426790
$$550$$ 0 0
$$551$$ 48.0000 2.04487
$$552$$ 0 0
$$553$$ −8.00000 −0.340195
$$554$$ 10.0000 0.424859
$$555$$ 0 0
$$556$$ −16.0000 −0.678551
$$557$$ −18.0000 −0.762684 −0.381342 0.924434i $$-0.624538\pi$$
−0.381342 + 0.924434i $$0.624538\pi$$
$$558$$ −4.00000 −0.169334
$$559$$ −8.00000 −0.338364
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 18.0000 0.759284
$$563$$ −36.0000 −1.51722 −0.758610 0.651546i $$-0.774121\pi$$
−0.758610 + 0.651546i $$0.774121\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 4.00000 0.168133
$$567$$ −1.00000 −0.0419961
$$568$$ 12.0000 0.503509
$$569$$ −6.00000 −0.251533 −0.125767 0.992060i $$-0.540139\pi$$
−0.125767 + 0.992060i $$0.540139\pi$$
$$570$$ 0 0
$$571$$ −4.00000 −0.167395 −0.0836974 0.996491i $$-0.526673\pi$$
−0.0836974 + 0.996491i $$0.526673\pi$$
$$572$$ 0 0
$$573$$ −12.0000 −0.501307
$$574$$ 6.00000 0.250435
$$575$$ 0 0
$$576$$ 1.00000 0.0416667
$$577$$ 10.0000 0.416305 0.208153 0.978096i $$-0.433255\pi$$
0.208153 + 0.978096i $$0.433255\pi$$
$$578$$ 19.0000 0.790296
$$579$$ 2.00000 0.0831172
$$580$$ 0 0
$$581$$ 12.0000 0.497844
$$582$$ −10.0000 −0.414513
$$583$$ 0 0
$$584$$ 10.0000 0.413803
$$585$$ 0 0
$$586$$ −30.0000 −1.23929
$$587$$ −12.0000 −0.495293 −0.247647 0.968850i $$-0.579657\pi$$
−0.247647 + 0.968850i $$0.579657\pi$$
$$588$$ −1.00000 −0.0412393
$$589$$ −32.0000 −1.31854
$$590$$ 0 0
$$591$$ 18.0000 0.740421
$$592$$ 10.0000 0.410997
$$593$$ 6.00000 0.246390 0.123195 0.992382i $$-0.460686\pi$$
0.123195 + 0.992382i $$0.460686\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 6.00000 0.245770
$$597$$ −20.0000 −0.818546
$$598$$ 0 0
$$599$$ 36.0000 1.47092 0.735460 0.677568i $$-0.236966\pi$$
0.735460 + 0.677568i $$0.236966\pi$$
$$600$$ 0 0
$$601$$ 2.00000 0.0815817 0.0407909 0.999168i $$-0.487012\pi$$
0.0407909 + 0.999168i $$0.487012\pi$$
$$602$$ −4.00000 −0.163028
$$603$$ 4.00000 0.162893
$$604$$ 8.00000 0.325515
$$605$$ 0 0
$$606$$ −6.00000 −0.243733
$$607$$ −8.00000 −0.324710 −0.162355 0.986732i $$-0.551909\pi$$
−0.162355 + 0.986732i $$0.551909\pi$$
$$608$$ 8.00000 0.324443
$$609$$ 6.00000 0.243132
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 6.00000 0.242536
$$613$$ −38.0000 −1.53481 −0.767403 0.641165i $$-0.778451\pi$$
−0.767403 + 0.641165i $$0.778451\pi$$
$$614$$ 4.00000 0.161427
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 18.0000 0.724653 0.362326 0.932051i $$-0.381983\pi$$
0.362326 + 0.932051i $$0.381983\pi$$
$$618$$ 8.00000 0.321807
$$619$$ 32.0000 1.28619 0.643094 0.765787i $$-0.277650\pi$$
0.643094 + 0.765787i $$0.277650\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 24.0000 0.962312
$$623$$ 6.00000 0.240385
$$624$$ 2.00000 0.0800641
$$625$$ 0 0
$$626$$ −14.0000 −0.559553
$$627$$ 0 0
$$628$$ 22.0000 0.877896
$$629$$ 60.0000 2.39236
$$630$$ 0 0
$$631$$ −16.0000 −0.636950 −0.318475 0.947931i $$-0.603171\pi$$
−0.318475 + 0.947931i $$0.603171\pi$$
$$632$$ 8.00000 0.318223
$$633$$ 4.00000 0.158986
$$634$$ −18.0000 −0.714871
$$635$$ 0 0
$$636$$ −6.00000 −0.237915
$$637$$ −2.00000 −0.0792429
$$638$$ 0 0
$$639$$ 12.0000 0.474713
$$640$$ 0 0
$$641$$ 42.0000 1.65890 0.829450 0.558581i $$-0.188654\pi$$
0.829450 + 0.558581i $$0.188654\pi$$
$$642$$ 12.0000 0.473602
$$643$$ 4.00000 0.157745 0.0788723 0.996885i $$-0.474868\pi$$
0.0788723 + 0.996885i $$0.474868\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 48.0000 1.88853
$$647$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$648$$ 1.00000 0.0392837
$$649$$ 0 0
$$650$$ 0 0
$$651$$ −4.00000 −0.156772
$$652$$ −20.0000 −0.783260
$$653$$ 6.00000 0.234798 0.117399 0.993085i $$-0.462544\pi$$
0.117399 + 0.993085i $$0.462544\pi$$
$$654$$ −14.0000 −0.547443
$$655$$ 0 0
$$656$$ −6.00000 −0.234261
$$657$$ 10.0000 0.390137
$$658$$ 0 0
$$659$$ 48.0000 1.86981 0.934907 0.354892i $$-0.115482\pi$$
0.934907 + 0.354892i $$0.115482\pi$$
$$660$$ 0 0
$$661$$ −34.0000 −1.32245 −0.661223 0.750189i $$-0.729962\pi$$
−0.661223 + 0.750189i $$0.729962\pi$$
$$662$$ −28.0000 −1.08825
$$663$$ 12.0000 0.466041
$$664$$ −12.0000 −0.465690
$$665$$ 0 0
$$666$$ 10.0000 0.387492
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 8.00000 0.309298
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 1.00000 0.0385758
$$673$$ −26.0000 −1.00223 −0.501113 0.865382i $$-0.667076\pi$$
−0.501113 + 0.865382i $$0.667076\pi$$
$$674$$ −2.00000 −0.0770371
$$675$$ 0 0
$$676$$ −9.00000 −0.346154
$$677$$ 18.0000 0.691796 0.345898 0.938272i $$-0.387574\pi$$
0.345898 + 0.938272i $$0.387574\pi$$
$$678$$ 6.00000 0.230429
$$679$$ −10.0000 −0.383765
$$680$$ 0 0
$$681$$ 12.0000 0.459841
$$682$$ 0 0
$$683$$ −36.0000 −1.37750 −0.688751 0.724998i $$-0.741841\pi$$
−0.688751 + 0.724998i $$0.741841\pi$$
$$684$$ 8.00000 0.305888
$$685$$ 0 0
$$686$$ −1.00000 −0.0381802
$$687$$ −14.0000 −0.534133
$$688$$ 4.00000 0.152499
$$689$$ −12.0000 −0.457164
$$690$$ 0 0
$$691$$ −16.0000 −0.608669 −0.304334 0.952565i $$-0.598434\pi$$
−0.304334 + 0.952565i $$0.598434\pi$$
$$692$$ −6.00000 −0.228086
$$693$$ 0 0
$$694$$ 12.0000 0.455514
$$695$$ 0 0
$$696$$ −6.00000 −0.227429
$$697$$ −36.0000 −1.36360
$$698$$ −10.0000 −0.378506
$$699$$ 30.0000 1.13470
$$700$$ 0 0
$$701$$ 6.00000 0.226617 0.113308 0.993560i $$-0.463855\pi$$
0.113308 + 0.993560i $$0.463855\pi$$
$$702$$ 2.00000 0.0754851
$$703$$ 80.0000 3.01726
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 6.00000 0.225813
$$707$$ −6.00000 −0.225653
$$708$$ 12.0000 0.450988
$$709$$ −10.0000 −0.375558 −0.187779 0.982211i $$-0.560129\pi$$
−0.187779 + 0.982211i $$0.560129\pi$$
$$710$$ 0 0
$$711$$ 8.00000 0.300023
$$712$$ −6.00000 −0.224860
$$713$$ 0 0
$$714$$ 6.00000 0.224544
$$715$$ 0 0
$$716$$ −24.0000 −0.896922
$$717$$ 12.0000 0.448148
$$718$$ −12.0000 −0.447836
$$719$$ −24.0000 −0.895049 −0.447524 0.894272i $$-0.647694\pi$$
−0.447524 + 0.894272i $$0.647694\pi$$
$$720$$ 0 0
$$721$$ 8.00000 0.297936
$$722$$ 45.0000 1.67473
$$723$$ −26.0000 −0.966950
$$724$$ −10.0000 −0.371647
$$725$$ 0 0
$$726$$ 11.0000 0.408248
$$727$$ −32.0000 −1.18681 −0.593407 0.804902i $$-0.702218\pi$$
−0.593407 + 0.804902i $$0.702218\pi$$
$$728$$ 2.00000 0.0741249
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 24.0000 0.887672
$$732$$ 10.0000 0.369611
$$733$$ −2.00000 −0.0738717 −0.0369358 0.999318i $$-0.511760\pi$$
−0.0369358 + 0.999318i $$0.511760\pi$$
$$734$$ −8.00000 −0.295285
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ −6.00000 −0.220863
$$739$$ −28.0000 −1.03000 −0.514998 0.857191i $$-0.672207\pi$$
−0.514998 + 0.857191i $$0.672207\pi$$
$$740$$ 0 0
$$741$$ 16.0000 0.587775
$$742$$ −6.00000 −0.220267
$$743$$ 24.0000 0.880475 0.440237 0.897881i $$-0.354894\pi$$
0.440237 + 0.897881i $$0.354894\pi$$
$$744$$ 4.00000 0.146647
$$745$$ 0 0
$$746$$ 34.0000 1.24483
$$747$$ −12.0000 −0.439057
$$748$$ 0 0
$$749$$ 12.0000 0.438470
$$750$$ 0 0
$$751$$ 8.00000 0.291924 0.145962 0.989290i $$-0.453372\pi$$
0.145962 + 0.989290i $$0.453372\pi$$
$$752$$ 0 0
$$753$$ 12.0000 0.437304
$$754$$ −12.0000 −0.437014
$$755$$ 0 0
$$756$$ 1.00000 0.0363696
$$757$$ 34.0000 1.23575 0.617876 0.786276i $$-0.287994\pi$$
0.617876 + 0.786276i $$0.287994\pi$$
$$758$$ −4.00000 −0.145287
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −6.00000 −0.217500 −0.108750 0.994069i $$-0.534685\pi$$
−0.108750 + 0.994069i $$0.534685\pi$$
$$762$$ 8.00000 0.289809
$$763$$ −14.0000 −0.506834
$$764$$ 12.0000 0.434145
$$765$$ 0 0
$$766$$ −24.0000 −0.867155
$$767$$ 24.0000 0.866590
$$768$$ −1.00000 −0.0360844
$$769$$ 26.0000 0.937584 0.468792 0.883309i $$-0.344689\pi$$
0.468792 + 0.883309i $$0.344689\pi$$
$$770$$ 0 0
$$771$$ −30.0000 −1.08042
$$772$$ −2.00000 −0.0719816
$$773$$ 18.0000 0.647415 0.323708 0.946157i $$-0.395071\pi$$
0.323708 + 0.946157i $$0.395071\pi$$
$$774$$ 4.00000 0.143777
$$775$$ 0 0
$$776$$ 10.0000 0.358979
$$777$$ 10.0000 0.358748
$$778$$ 6.00000 0.215110
$$779$$ −48.0000 −1.71978
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ −6.00000 −0.214423
$$784$$ 1.00000 0.0357143
$$785$$ 0 0
$$786$$ 12.0000 0.428026
$$787$$ 4.00000 0.142585 0.0712923 0.997455i $$-0.477288\pi$$
0.0712923 + 0.997455i $$0.477288\pi$$
$$788$$ −18.0000 −0.641223
$$789$$ −24.0000 −0.854423
$$790$$ 0 0
$$791$$ 6.00000 0.213335
$$792$$ 0 0
$$793$$ 20.0000 0.710221
$$794$$ −2.00000 −0.0709773
$$795$$ 0 0
$$796$$ 20.0000 0.708881
$$797$$ 42.0000 1.48772 0.743858 0.668338i $$-0.232994\pi$$
0.743858 + 0.668338i $$0.232994\pi$$
$$798$$ 8.00000 0.283197
$$799$$ 0 0
$$800$$ 0 0
$$801$$ −6.00000 −0.212000
$$802$$ −30.0000 −1.05934
$$803$$ 0 0
$$804$$ −4.00000 −0.141069
$$805$$ 0 0
$$806$$ 8.00000 0.281788
$$807$$ 18.0000 0.633630
$$808$$ 6.00000 0.211079
$$809$$ −30.0000 −1.05474 −0.527372 0.849635i $$-0.676823\pi$$
−0.527372 + 0.849635i $$0.676823\pi$$
$$810$$ 0 0
$$811$$ −16.0000 −0.561836 −0.280918 0.959732i $$-0.590639\pi$$
−0.280918 + 0.959732i $$0.590639\pi$$
$$812$$ −6.00000 −0.210559
$$813$$ −20.0000 −0.701431
$$814$$ 0 0
$$815$$ 0 0
$$816$$ −6.00000 −0.210042
$$817$$ 32.0000 1.11954
$$818$$ 26.0000 0.909069
$$819$$ 2.00000 0.0698857
$$820$$ 0 0
$$821$$ −18.0000 −0.628204 −0.314102 0.949389i $$-0.601703\pi$$
−0.314102 + 0.949389i $$0.601703\pi$$
$$822$$ 6.00000 0.209274
$$823$$ −32.0000 −1.11545 −0.557725 0.830026i $$-0.688326\pi$$
−0.557725 + 0.830026i $$0.688326\pi$$
$$824$$ −8.00000 −0.278693
$$825$$ 0 0
$$826$$ 12.0000 0.417533
$$827$$ 36.0000 1.25184 0.625921 0.779886i $$-0.284723\pi$$
0.625921 + 0.779886i $$0.284723\pi$$
$$828$$ 0 0
$$829$$ −34.0000 −1.18087 −0.590434 0.807086i $$-0.701044\pi$$
−0.590434 + 0.807086i $$0.701044\pi$$
$$830$$ 0 0
$$831$$ −10.0000 −0.346896
$$832$$ −2.00000 −0.0693375
$$833$$ 6.00000 0.207888
$$834$$ 16.0000 0.554035
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 4.00000 0.138260
$$838$$ −12.0000 −0.414533
$$839$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$840$$ 0 0
$$841$$ 7.00000 0.241379
$$842$$ 38.0000 1.30957
$$843$$ −18.0000 −0.619953
$$844$$ −4.00000 −0.137686
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 11.0000 0.377964
$$848$$ 6.00000 0.206041
$$849$$ −4.00000 −0.137280
$$850$$ 0 0
$$851$$ 0 0
$$852$$ −12.0000 −0.411113
$$853$$ −26.0000 −0.890223 −0.445112 0.895475i $$-0.646836\pi$$
−0.445112 + 0.895475i $$0.646836\pi$$
$$854$$ 10.0000 0.342193
$$855$$ 0 0
$$856$$ −12.0000 −0.410152
$$857$$ 6.00000 0.204956 0.102478 0.994735i $$-0.467323\pi$$
0.102478 + 0.994735i $$0.467323\pi$$
$$858$$ 0 0
$$859$$ −40.0000 −1.36478 −0.682391 0.730987i $$-0.739060\pi$$
−0.682391 + 0.730987i $$0.739060\pi$$
$$860$$ 0 0
$$861$$ −6.00000 −0.204479
$$862$$ −12.0000 −0.408722
$$863$$ 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
$$866$$ 10.0000 0.339814
$$867$$ −19.0000 −0.645274
$$868$$ 4.00000 0.135769
$$869$$ 0 0
$$870$$ 0 0
$$871$$ −8.00000 −0.271070
$$872$$ 14.0000 0.474100
$$873$$ 10.0000 0.338449
$$874$$ 0 0
$$875$$ 0 0
$$876$$ −10.0000 −0.337869
$$877$$ −14.0000 −0.472746 −0.236373 0.971662i $$-0.575959\pi$$
−0.236373 + 0.971662i $$0.575959\pi$$
$$878$$ −28.0000 −0.944954
$$879$$ 30.0000 1.01187
$$880$$ 0 0
$$881$$ −30.0000 −1.01073 −0.505363 0.862907i $$-0.668641\pi$$
−0.505363 + 0.862907i $$0.668641\pi$$
$$882$$ 1.00000 0.0336718
$$883$$ −44.0000 −1.48072 −0.740359 0.672212i $$-0.765344\pi$$
−0.740359 + 0.672212i $$0.765344\pi$$
$$884$$ −12.0000 −0.403604
$$885$$ 0 0
$$886$$ 12.0000 0.403148
$$887$$ −24.0000 −0.805841 −0.402921 0.915235i $$-0.632005\pi$$
−0.402921 + 0.915235i $$0.632005\pi$$
$$888$$ −10.0000 −0.335578
$$889$$ 8.00000 0.268311
$$890$$ 0 0
$$891$$ 0 0
$$892$$ −8.00000 −0.267860
$$893$$ 0 0
$$894$$ −6.00000 −0.200670
$$895$$ 0 0
$$896$$ −1.00000 −0.0334077
$$897$$ 0 0
$$898$$ 18.0000 0.600668
$$899$$ −24.0000 −0.800445
$$900$$ 0 0
$$901$$ 36.0000 1.19933
$$902$$ 0 0
$$903$$ 4.00000 0.133112
$$904$$ −6.00000 −0.199557
$$905$$ 0 0
$$906$$ −8.00000 −0.265782
$$907$$ 28.0000 0.929725 0.464862 0.885383i $$-0.346104\pi$$
0.464862 + 0.885383i $$0.346104\pi$$
$$908$$ −12.0000 −0.398234
$$909$$ 6.00000 0.199007
$$910$$ 0 0
$$911$$ 12.0000 0.397578 0.198789 0.980042i $$-0.436299\pi$$
0.198789 + 0.980042i $$0.436299\pi$$
$$912$$ −8.00000 −0.264906
$$913$$ 0 0
$$914$$ −2.00000 −0.0661541
$$915$$ 0 0
$$916$$ 14.0000 0.462573
$$917$$ 12.0000 0.396275
$$918$$ −6.00000 −0.198030
$$919$$ 32.0000 1.05558 0.527791 0.849374i $$-0.323020\pi$$
0.527791 + 0.849374i $$0.323020\pi$$
$$920$$ 0 0
$$921$$ −4.00000 −0.131804
$$922$$ −18.0000 −0.592798
$$923$$ −24.0000 −0.789970
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 40.0000 1.31448
$$927$$ −8.00000 −0.262754
$$928$$ 6.00000 0.196960
$$929$$ −30.0000 −0.984268 −0.492134 0.870519i $$-0.663783\pi$$
−0.492134 + 0.870519i $$0.663783\pi$$
$$930$$ 0 0
$$931$$ 8.00000 0.262189
$$932$$ −30.0000 −0.982683
$$933$$ −24.0000 −0.785725
$$934$$ 36.0000 1.17796
$$935$$ 0 0
$$936$$ −2.00000 −0.0653720
$$937$$ −38.0000 −1.24141 −0.620703 0.784046i $$-0.713153\pi$$
−0.620703 + 0.784046i $$0.713153\pi$$
$$938$$ −4.00000 −0.130605
$$939$$ 14.0000 0.456873
$$940$$ 0 0
$$941$$ −18.0000 −0.586783 −0.293392 0.955992i $$-0.594784\pi$$
−0.293392 + 0.955992i $$0.594784\pi$$
$$942$$ −22.0000 −0.716799
$$943$$ 0 0
$$944$$ −12.0000 −0.390567
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 36.0000 1.16984 0.584921 0.811090i $$-0.301125\pi$$
0.584921 + 0.811090i $$0.301125\pi$$
$$948$$ −8.00000 −0.259828
$$949$$ −20.0000 −0.649227
$$950$$ 0 0
$$951$$ 18.0000 0.583690
$$952$$ −6.00000 −0.194461
$$953$$ −30.0000 −0.971795 −0.485898 0.874016i $$-0.661507\pi$$
−0.485898 + 0.874016i $$0.661507\pi$$
$$954$$ 6.00000 0.194257
$$955$$ 0 0
$$956$$ −12.0000 −0.388108
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 6.00000 0.193750
$$960$$ 0 0
$$961$$ −15.0000 −0.483871
$$962$$ −20.0000 −0.644826
$$963$$ −12.0000 −0.386695
$$964$$ 26.0000 0.837404
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −8.00000 −0.257263 −0.128631 0.991692i $$-0.541058\pi$$
−0.128631 + 0.991692i $$0.541058\pi$$
$$968$$ −11.0000 −0.353553
$$969$$ −48.0000 −1.54198
$$970$$ 0 0
$$971$$ 36.0000 1.15529 0.577647 0.816286i $$-0.303971\pi$$
0.577647 + 0.816286i $$0.303971\pi$$
$$972$$ −1.00000 −0.0320750
$$973$$ 16.0000 0.512936
$$974$$ −32.0000 −1.02535
$$975$$ 0 0
$$976$$ −10.0000 −0.320092
$$977$$ −6.00000 −0.191957 −0.0959785 0.995383i $$-0.530598\pi$$
−0.0959785 + 0.995383i $$0.530598\pi$$
$$978$$ 20.0000 0.639529
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 14.0000 0.446986
$$982$$ 0 0
$$983$$ −24.0000 −0.765481 −0.382741 0.923856i $$-0.625020\pi$$
−0.382741 + 0.923856i $$0.625020\pi$$
$$984$$ 6.00000 0.191273
$$985$$ 0 0
$$986$$ 36.0000 1.14647
$$987$$ 0 0
$$988$$ −16.0000 −0.509028
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 8.00000 0.254128 0.127064 0.991894i $$-0.459445\pi$$
0.127064 + 0.991894i $$0.459445\pi$$
$$992$$ −4.00000 −0.127000
$$993$$ 28.0000 0.888553
$$994$$ −12.0000 −0.380617
$$995$$ 0 0
$$996$$ 12.0000 0.380235
$$997$$ −26.0000 −0.823428 −0.411714 0.911313i $$-0.635070\pi$$
−0.411714 + 0.911313i $$0.635070\pi$$
$$998$$ 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 1050.2.a.k.1.1 1
3.2 odd 2 3150.2.a.f.1.1 1
4.3 odd 2 8400.2.a.cm.1.1 1
5.2 odd 4 1050.2.g.c.799.2 2
5.3 odd 4 1050.2.g.c.799.1 2
5.4 even 2 210.2.a.b.1.1 1
7.6 odd 2 7350.2.a.cs.1.1 1
15.2 even 4 3150.2.g.i.2899.1 2
15.8 even 4 3150.2.g.i.2899.2 2
15.14 odd 2 630.2.a.h.1.1 1
20.19 odd 2 1680.2.a.g.1.1 1
35.4 even 6 1470.2.i.l.961.1 2
35.9 even 6 1470.2.i.l.361.1 2
35.19 odd 6 1470.2.i.s.361.1 2
35.24 odd 6 1470.2.i.s.961.1 2
35.34 odd 2 1470.2.a.b.1.1 1
40.19 odd 2 6720.2.a.bi.1.1 1
40.29 even 2 6720.2.a.n.1.1 1
60.59 even 2 5040.2.a.g.1.1 1
105.104 even 2 4410.2.a.bi.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.a.b.1.1 1 5.4 even 2
630.2.a.h.1.1 1 15.14 odd 2
1050.2.a.k.1.1 1 1.1 even 1 trivial
1050.2.g.c.799.1 2 5.3 odd 4
1050.2.g.c.799.2 2 5.2 odd 4
1470.2.a.b.1.1 1 35.34 odd 2
1470.2.i.l.361.1 2 35.9 even 6
1470.2.i.l.961.1 2 35.4 even 6
1470.2.i.s.361.1 2 35.19 odd 6
1470.2.i.s.961.1 2 35.24 odd 6
1680.2.a.g.1.1 1 20.19 odd 2
3150.2.a.f.1.1 1 3.2 odd 2
3150.2.g.i.2899.1 2 15.2 even 4
3150.2.g.i.2899.2 2 15.8 even 4
4410.2.a.bi.1.1 1 105.104 even 2
5040.2.a.g.1.1 1 60.59 even 2
6720.2.a.n.1.1 1 40.29 even 2
6720.2.a.bi.1.1 1 40.19 odd 2
7350.2.a.cs.1.1 1 7.6 odd 2
8400.2.a.cm.1.1 1 4.3 odd 2