# Properties

 Label 1950.2.a.o.1.1 Level $1950$ Weight $2$ Character 1950.1 Self dual yes Analytic conductor $15.571$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1950.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$15.5708283941$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 390) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1950.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{12} -1.00000 q^{13} -2.00000 q^{14} +1.00000 q^{16} +1.00000 q^{18} +2.00000 q^{19} +2.00000 q^{21} +6.00000 q^{23} -1.00000 q^{24} -1.00000 q^{26} -1.00000 q^{27} -2.00000 q^{28} +8.00000 q^{31} +1.00000 q^{32} +1.00000 q^{36} -2.00000 q^{37} +2.00000 q^{38} +1.00000 q^{39} +6.00000 q^{41} +2.00000 q^{42} +4.00000 q^{43} +6.00000 q^{46} -1.00000 q^{48} -3.00000 q^{49} -1.00000 q^{52} +6.00000 q^{53} -1.00000 q^{54} -2.00000 q^{56} -2.00000 q^{57} +14.0000 q^{61} +8.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} +4.00000 q^{67} -6.00000 q^{69} +1.00000 q^{72} +4.00000 q^{73} -2.00000 q^{74} +2.00000 q^{76} +1.00000 q^{78} -16.0000 q^{79} +1.00000 q^{81} +6.00000 q^{82} +12.0000 q^{83} +2.00000 q^{84} +4.00000 q^{86} -6.00000 q^{89} +2.00000 q^{91} +6.00000 q^{92} -8.00000 q^{93} -1.00000 q^{96} +4.00000 q^{97} -3.00000 q^{98} +O(q^{100})$$

## 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
$$3$$ −1.00000 −0.577350
$$4$$ 1.00000 0.500000
$$5$$ 0 0
$$6$$ −1.00000 −0.408248
$$7$$ −2.00000 −0.755929 −0.377964 0.925820i $$-0.623376\pi$$
−0.377964 + 0.925820i $$0.623376\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 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
$$13$$ −1.00000 −0.277350
$$14$$ −2.00000 −0.534522
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ 1.00000 0.235702
$$19$$ 2.00000 0.458831 0.229416 0.973329i $$-0.426318\pi$$
0.229416 + 0.973329i $$0.426318\pi$$
$$20$$ 0 0
$$21$$ 2.00000 0.436436
$$22$$ 0 0
$$23$$ 6.00000 1.25109 0.625543 0.780189i $$-0.284877\pi$$
0.625543 + 0.780189i $$0.284877\pi$$
$$24$$ −1.00000 −0.204124
$$25$$ 0 0
$$26$$ −1.00000 −0.196116
$$27$$ −1.00000 −0.192450
$$28$$ −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 $$-0.244865\pi$$
0.718421 + 0.695608i $$0.244865\pi$$
$$32$$ 1.00000 0.176777
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ −2.00000 −0.328798 −0.164399 0.986394i $$-0.552568\pi$$
−0.164399 + 0.986394i $$0.552568\pi$$
$$38$$ 2.00000 0.324443
$$39$$ 1.00000 0.160128
$$40$$ 0 0
$$41$$ 6.00000 0.937043 0.468521 0.883452i $$-0.344787\pi$$
0.468521 + 0.883452i $$0.344787\pi$$
$$42$$ 2.00000 0.308607
$$43$$ 4.00000 0.609994 0.304997 0.952353i $$-0.401344\pi$$
0.304997 + 0.952353i $$0.401344\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 6.00000 0.884652
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ −1.00000 −0.144338
$$49$$ −3.00000 −0.428571
$$50$$ 0 0
$$51$$ 0 0
$$52$$ −1.00000 −0.138675
$$53$$ 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
$$56$$ −2.00000 −0.267261
$$57$$ −2.00000 −0.264906
$$58$$ 0 0
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ 14.0000 1.79252 0.896258 0.443533i $$-0.146275\pi$$
0.896258 + 0.443533i $$0.146275\pi$$
$$62$$ 8.00000 1.01600
$$63$$ −2.00000 −0.251976
$$64$$ 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 $$0.421429\pi$$
$$68$$ 0 0
$$69$$ −6.00000 −0.722315
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 1.00000 0.117851
$$73$$ 4.00000 0.468165 0.234082 0.972217i $$-0.424791\pi$$
0.234082 + 0.972217i $$0.424791\pi$$
$$74$$ −2.00000 −0.232495
$$75$$ 0 0
$$76$$ 2.00000 0.229416
$$77$$ 0 0
$$78$$ 1.00000 0.113228
$$79$$ −16.0000 −1.80014 −0.900070 0.435745i $$-0.856485\pi$$
−0.900070 + 0.435745i $$0.856485\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 6.00000 0.662589
$$83$$ 12.0000 1.31717 0.658586 0.752506i $$-0.271155\pi$$
0.658586 + 0.752506i $$0.271155\pi$$
$$84$$ 2.00000 0.218218
$$85$$ 0 0
$$86$$ 4.00000 0.431331
$$87$$ 0 0
$$88$$ 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
$$92$$ 6.00000 0.625543
$$93$$ −8.00000 −0.829561
$$94$$ 0 0
$$95$$ 0 0
$$96$$ −1.00000 −0.102062
$$97$$ 4.00000 0.406138 0.203069 0.979164i $$-0.434908\pi$$
0.203069 + 0.979164i $$0.434908\pi$$
$$98$$ −3.00000 −0.303046
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −12.0000 −1.19404 −0.597022 0.802225i $$-0.703650\pi$$
−0.597022 + 0.802225i $$0.703650\pi$$
$$102$$ 0 0
$$103$$ 16.0000 1.57653 0.788263 0.615338i $$-0.210980\pi$$
0.788263 + 0.615338i $$0.210980\pi$$
$$104$$ −1.00000 −0.0980581
$$105$$ 0 0
$$106$$ 6.00000 0.582772
$$107$$ 12.0000 1.16008 0.580042 0.814587i $$-0.303036\pi$$
0.580042 + 0.814587i $$0.303036\pi$$
$$108$$ −1.00000 −0.0962250
$$109$$ −4.00000 −0.383131 −0.191565 0.981480i $$-0.561356\pi$$
−0.191565 + 0.981480i $$0.561356\pi$$
$$110$$ 0 0
$$111$$ 2.00000 0.189832
$$112$$ −2.00000 −0.188982
$$113$$ −12.0000 −1.12887 −0.564433 0.825479i $$-0.690905\pi$$
−0.564433 + 0.825479i $$0.690905\pi$$
$$114$$ −2.00000 −0.187317
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −1.00000 −0.0924500
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −11.0000 −1.00000
$$122$$ 14.0000 1.26750
$$123$$ −6.00000 −0.541002
$$124$$ 8.00000 0.718421
$$125$$ 0 0
$$126$$ −2.00000 −0.178174
$$127$$ 16.0000 1.41977 0.709885 0.704317i $$-0.248747\pi$$
0.709885 + 0.704317i $$0.248747\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ −4.00000 −0.352180
$$130$$ 0 0
$$131$$ 6.00000 0.524222 0.262111 0.965038i $$-0.415581\pi$$
0.262111 + 0.965038i $$0.415581\pi$$
$$132$$ 0 0
$$133$$ −4.00000 −0.346844
$$134$$ 4.00000 0.345547
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −6.00000 −0.512615 −0.256307 0.966595i $$-0.582506\pi$$
−0.256307 + 0.966595i $$0.582506\pi$$
$$138$$ −6.00000 −0.510754
$$139$$ 8.00000 0.678551 0.339276 0.940687i $$-0.389818\pi$$
0.339276 + 0.940687i $$0.389818\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ 4.00000 0.331042
$$147$$ 3.00000 0.247436
$$148$$ −2.00000 −0.164399
$$149$$ 18.0000 1.47462 0.737309 0.675556i $$-0.236096\pi$$
0.737309 + 0.675556i $$0.236096\pi$$
$$150$$ 0 0
$$151$$ 8.00000 0.651031 0.325515 0.945537i $$-0.394462\pi$$
0.325515 + 0.945537i $$0.394462\pi$$
$$152$$ 2.00000 0.162221
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 1.00000 0.0800641
$$157$$ −2.00000 −0.159617 −0.0798087 0.996810i $$-0.525431\pi$$
−0.0798087 + 0.996810i $$0.525431\pi$$
$$158$$ −16.0000 −1.27289
$$159$$ −6.00000 −0.475831
$$160$$ 0 0
$$161$$ −12.0000 −0.945732
$$162$$ 1.00000 0.0785674
$$163$$ 16.0000 1.25322 0.626608 0.779334i $$-0.284443\pi$$
0.626608 + 0.779334i $$0.284443\pi$$
$$164$$ 6.00000 0.468521
$$165$$ 0 0
$$166$$ 12.0000 0.931381
$$167$$ −12.0000 −0.928588 −0.464294 0.885681i $$-0.653692\pi$$
−0.464294 + 0.885681i $$0.653692\pi$$
$$168$$ 2.00000 0.154303
$$169$$ 1.00000 0.0769231
$$170$$ 0 0
$$171$$ 2.00000 0.152944
$$172$$ 4.00000 0.304997
$$173$$ −18.0000 −1.36851 −0.684257 0.729241i $$-0.739873\pi$$
−0.684257 + 0.729241i $$0.739873\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ −6.00000 −0.449719
$$179$$ −6.00000 −0.448461 −0.224231 0.974536i $$-0.571987\pi$$
−0.224231 + 0.974536i $$0.571987\pi$$
$$180$$ 0 0
$$181$$ 2.00000 0.148659 0.0743294 0.997234i $$-0.476318\pi$$
0.0743294 + 0.997234i $$0.476318\pi$$
$$182$$ 2.00000 0.148250
$$183$$ −14.0000 −1.03491
$$184$$ 6.00000 0.442326
$$185$$ 0 0
$$186$$ −8.00000 −0.586588
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 2.00000 0.145479
$$190$$ 0 0
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ −1.00000 −0.0721688
$$193$$ −8.00000 −0.575853 −0.287926 0.957653i $$-0.592966\pi$$
−0.287926 + 0.957653i $$0.592966\pi$$
$$194$$ 4.00000 0.287183
$$195$$ 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
$$199$$ −16.0000 −1.13421 −0.567105 0.823646i $$-0.691937\pi$$
−0.567105 + 0.823646i $$0.691937\pi$$
$$200$$ 0 0
$$201$$ −4.00000 −0.282138
$$202$$ −12.0000 −0.844317
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 16.0000 1.11477
$$207$$ 6.00000 0.417029
$$208$$ −1.00000 −0.0693375
$$209$$ 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
$$213$$ 0 0
$$214$$ 12.0000 0.820303
$$215$$ 0 0
$$216$$ −1.00000 −0.0680414
$$217$$ −16.0000 −1.08615
$$218$$ −4.00000 −0.270914
$$219$$ −4.00000 −0.270295
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 2.00000 0.134231
$$223$$ 10.0000 0.669650 0.334825 0.942280i $$-0.391323\pi$$
0.334825 + 0.942280i $$0.391323\pi$$
$$224$$ −2.00000 −0.133631
$$225$$ 0 0
$$226$$ −12.0000 −0.798228
$$227$$ −12.0000 −0.796468 −0.398234 0.917284i $$-0.630377\pi$$
−0.398234 + 0.917284i $$0.630377\pi$$
$$228$$ −2.00000 −0.132453
$$229$$ −4.00000 −0.264327 −0.132164 0.991228i $$-0.542192\pi$$
−0.132164 + 0.991228i $$0.542192\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$234$$ −1.00000 −0.0653720
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 16.0000 1.03931
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 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
$$244$$ 14.0000 0.896258
$$245$$ 0 0
$$246$$ −6.00000 −0.382546
$$247$$ −2.00000 −0.127257
$$248$$ 8.00000 0.508001
$$249$$ −12.0000 −0.760469
$$250$$ 0 0
$$251$$ −30.0000 −1.89358 −0.946792 0.321847i $$-0.895696\pi$$
−0.946792 + 0.321847i $$0.895696\pi$$
$$252$$ −2.00000 −0.125988
$$253$$ 0 0
$$254$$ 16.0000 1.00393
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 12.0000 0.748539 0.374270 0.927320i $$-0.377893\pi$$
0.374270 + 0.927320i $$0.377893\pi$$
$$258$$ −4.00000 −0.249029
$$259$$ 4.00000 0.248548
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 6.00000 0.370681
$$263$$ −30.0000 −1.84988 −0.924940 0.380114i $$-0.875885\pi$$
−0.924940 + 0.380114i $$0.875885\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ −4.00000 −0.245256
$$267$$ 6.00000 0.367194
$$268$$ 4.00000 0.244339
$$269$$ 12.0000 0.731653 0.365826 0.930683i $$-0.380786\pi$$
0.365826 + 0.930683i $$0.380786\pi$$
$$270$$ 0 0
$$271$$ 8.00000 0.485965 0.242983 0.970031i $$-0.421874\pi$$
0.242983 + 0.970031i $$0.421874\pi$$
$$272$$ 0 0
$$273$$ −2.00000 −0.121046
$$274$$ −6.00000 −0.362473
$$275$$ 0 0
$$276$$ −6.00000 −0.361158
$$277$$ −26.0000 −1.56219 −0.781094 0.624413i $$-0.785338\pi$$
−0.781094 + 0.624413i $$0.785338\pi$$
$$278$$ 8.00000 0.479808
$$279$$ 8.00000 0.478947
$$280$$ 0 0
$$281$$ −30.0000 −1.78965 −0.894825 0.446417i $$-0.852700\pi$$
−0.894825 + 0.446417i $$0.852700\pi$$
$$282$$ 0 0
$$283$$ 28.0000 1.66443 0.832214 0.554455i $$-0.187073\pi$$
0.832214 + 0.554455i $$0.187073\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −12.0000 −0.708338
$$288$$ 1.00000 0.0589256
$$289$$ −17.0000 −1.00000
$$290$$ 0 0
$$291$$ −4.00000 −0.234484
$$292$$ 4.00000 0.234082
$$293$$ 6.00000 0.350524 0.175262 0.984522i $$-0.443923\pi$$
0.175262 + 0.984522i $$0.443923\pi$$
$$294$$ 3.00000 0.174964
$$295$$ 0 0
$$296$$ −2.00000 −0.116248
$$297$$ 0 0
$$298$$ 18.0000 1.04271
$$299$$ −6.00000 −0.346989
$$300$$ 0 0
$$301$$ −8.00000 −0.461112
$$302$$ 8.00000 0.460348
$$303$$ 12.0000 0.689382
$$304$$ 2.00000 0.114708
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 4.00000 0.228292 0.114146 0.993464i $$-0.463587\pi$$
0.114146 + 0.993464i $$0.463587\pi$$
$$308$$ 0 0
$$309$$ −16.0000 −0.910208
$$310$$ 0 0
$$311$$ 24.0000 1.36092 0.680458 0.732787i $$-0.261781\pi$$
0.680458 + 0.732787i $$0.261781\pi$$
$$312$$ 1.00000 0.0566139
$$313$$ 10.0000 0.565233 0.282617 0.959233i $$-0.408798\pi$$
0.282617 + 0.959233i $$0.408798\pi$$
$$314$$ −2.00000 −0.112867
$$315$$ 0 0
$$316$$ −16.0000 −0.900070
$$317$$ 18.0000 1.01098 0.505490 0.862832i $$-0.331312\pi$$
0.505490 + 0.862832i $$0.331312\pi$$
$$318$$ −6.00000 −0.336463
$$319$$ 0 0
$$320$$ 0 0
$$321$$ −12.0000 −0.669775
$$322$$ −12.0000 −0.668734
$$323$$ 0 0
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ 16.0000 0.886158
$$327$$ 4.00000 0.221201
$$328$$ 6.00000 0.331295
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 2.00000 0.109930 0.0549650 0.998488i $$-0.482495\pi$$
0.0549650 + 0.998488i $$0.482495\pi$$
$$332$$ 12.0000 0.658586
$$333$$ −2.00000 −0.109599
$$334$$ −12.0000 −0.656611
$$335$$ 0 0
$$336$$ 2.00000 0.109109
$$337$$ −14.0000 −0.762629 −0.381314 0.924445i $$-0.624528\pi$$
−0.381314 + 0.924445i $$0.624528\pi$$
$$338$$ 1.00000 0.0543928
$$339$$ 12.0000 0.651751
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 2.00000 0.108148
$$343$$ 20.0000 1.07990
$$344$$ 4.00000 0.215666
$$345$$ 0 0
$$346$$ −18.0000 −0.967686
$$347$$ −24.0000 −1.28839 −0.644194 0.764862i $$-0.722807\pi$$
−0.644194 + 0.764862i $$0.722807\pi$$
$$348$$ 0 0
$$349$$ 20.0000 1.07058 0.535288 0.844670i $$-0.320203\pi$$
0.535288 + 0.844670i $$0.320203\pi$$
$$350$$ 0 0
$$351$$ 1.00000 0.0533761
$$352$$ 0 0
$$353$$ −6.00000 −0.319348 −0.159674 0.987170i $$-0.551044\pi$$
−0.159674 + 0.987170i $$0.551044\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −6.00000 −0.317999
$$357$$ 0 0
$$358$$ −6.00000 −0.317110
$$359$$ −24.0000 −1.26667 −0.633336 0.773877i $$-0.718315\pi$$
−0.633336 + 0.773877i $$0.718315\pi$$
$$360$$ 0 0
$$361$$ −15.0000 −0.789474
$$362$$ 2.00000 0.105118
$$363$$ 11.0000 0.577350
$$364$$ 2.00000 0.104828
$$365$$ 0 0
$$366$$ −14.0000 −0.731792
$$367$$ −8.00000 −0.417597 −0.208798 0.977959i $$-0.566955\pi$$
−0.208798 + 0.977959i $$0.566955\pi$$
$$368$$ 6.00000 0.312772
$$369$$ 6.00000 0.312348
$$370$$ 0 0
$$371$$ −12.0000 −0.623009
$$372$$ −8.00000 −0.414781
$$373$$ −26.0000 −1.34623 −0.673114 0.739538i $$-0.735044\pi$$
−0.673114 + 0.739538i $$0.735044\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 2.00000 0.102869
$$379$$ −34.0000 −1.74646 −0.873231 0.487306i $$-0.837980\pi$$
−0.873231 + 0.487306i $$0.837980\pi$$
$$380$$ 0 0
$$381$$ −16.0000 −0.819705
$$382$$ 0 0
$$383$$ −12.0000 −0.613171 −0.306586 0.951843i $$-0.599187\pi$$
−0.306586 + 0.951843i $$0.599187\pi$$
$$384$$ −1.00000 −0.0510310
$$385$$ 0 0
$$386$$ −8.00000 −0.407189
$$387$$ 4.00000 0.203331
$$388$$ 4.00000 0.203069
$$389$$ 36.0000 1.82527 0.912636 0.408773i $$-0.134043\pi$$
0.912636 + 0.408773i $$0.134043\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ −3.00000 −0.151523
$$393$$ −6.00000 −0.302660
$$394$$ −18.0000 −0.906827
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −26.0000 −1.30490 −0.652451 0.757831i $$-0.726259\pi$$
−0.652451 + 0.757831i $$0.726259\pi$$
$$398$$ −16.0000 −0.802008
$$399$$ 4.00000 0.200250
$$400$$ 0 0
$$401$$ −18.0000 −0.898877 −0.449439 0.893311i $$-0.648376\pi$$
−0.449439 + 0.893311i $$0.648376\pi$$
$$402$$ −4.00000 −0.199502
$$403$$ −8.00000 −0.398508
$$404$$ −12.0000 −0.597022
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 14.0000 0.692255 0.346128 0.938187i $$-0.387496\pi$$
0.346128 + 0.938187i $$0.387496\pi$$
$$410$$ 0 0
$$411$$ 6.00000 0.295958
$$412$$ 16.0000 0.788263
$$413$$ 0 0
$$414$$ 6.00000 0.294884
$$415$$ 0 0
$$416$$ −1.00000 −0.0490290
$$417$$ −8.00000 −0.391762
$$418$$ 0 0
$$419$$ 6.00000 0.293119 0.146560 0.989202i $$-0.453180\pi$$
0.146560 + 0.989202i $$0.453180\pi$$
$$420$$ 0 0
$$421$$ 32.0000 1.55958 0.779792 0.626038i $$-0.215325\pi$$
0.779792 + 0.626038i $$0.215325\pi$$
$$422$$ −4.00000 −0.194717
$$423$$ 0 0
$$424$$ 6.00000 0.291386
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −28.0000 −1.35501
$$428$$ 12.0000 0.580042
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 24.0000 1.15604 0.578020 0.816023i $$-0.303826\pi$$
0.578020 + 0.816023i $$0.303826\pi$$
$$432$$ −1.00000 −0.0481125
$$433$$ −14.0000 −0.672797 −0.336399 0.941720i $$-0.609209\pi$$
−0.336399 + 0.941720i $$0.609209\pi$$
$$434$$ −16.0000 −0.768025
$$435$$ 0 0
$$436$$ −4.00000 −0.191565
$$437$$ 12.0000 0.574038
$$438$$ −4.00000 −0.191127
$$439$$ 32.0000 1.52728 0.763638 0.645644i $$-0.223411\pi$$
0.763638 + 0.645644i $$0.223411\pi$$
$$440$$ 0 0
$$441$$ −3.00000 −0.142857
$$442$$ 0 0
$$443$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$444$$ 2.00000 0.0949158
$$445$$ 0 0
$$446$$ 10.0000 0.473514
$$447$$ −18.0000 −0.851371
$$448$$ −2.00000 −0.0944911
$$449$$ −30.0000 −1.41579 −0.707894 0.706319i $$-0.750354\pi$$
−0.707894 + 0.706319i $$0.750354\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ −12.0000 −0.564433
$$453$$ −8.00000 −0.375873
$$454$$ −12.0000 −0.563188
$$455$$ 0 0
$$456$$ −2.00000 −0.0936586
$$457$$ 28.0000 1.30978 0.654892 0.755722i $$-0.272714\pi$$
0.654892 + 0.755722i $$0.272714\pi$$
$$458$$ −4.00000 −0.186908
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −42.0000 −1.95614 −0.978068 0.208288i $$-0.933211\pi$$
−0.978068 + 0.208288i $$0.933211\pi$$
$$462$$ 0 0
$$463$$ 10.0000 0.464739 0.232370 0.972628i $$-0.425352\pi$$
0.232370 + 0.972628i $$0.425352\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −36.0000 −1.66588 −0.832941 0.553362i $$-0.813345\pi$$
−0.832941 + 0.553362i $$0.813345\pi$$
$$468$$ −1.00000 −0.0462250
$$469$$ −8.00000 −0.369406
$$470$$ 0 0
$$471$$ 2.00000 0.0921551
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 16.0000 0.734904
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 6.00000 0.274721
$$478$$ 0 0
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ 2.00000 0.0911922
$$482$$ 26.0000 1.18427
$$483$$ 12.0000 0.546019
$$484$$ −11.0000 −0.500000
$$485$$ 0 0
$$486$$ −1.00000 −0.0453609
$$487$$ −2.00000 −0.0906287 −0.0453143 0.998973i $$-0.514429\pi$$
−0.0453143 + 0.998973i $$0.514429\pi$$
$$488$$ 14.0000 0.633750
$$489$$ −16.0000 −0.723545
$$490$$ 0 0
$$491$$ 6.00000 0.270776 0.135388 0.990793i $$-0.456772\pi$$
0.135388 + 0.990793i $$0.456772\pi$$
$$492$$ −6.00000 −0.270501
$$493$$ 0 0
$$494$$ −2.00000 −0.0899843
$$495$$ 0 0
$$496$$ 8.00000 0.359211
$$497$$ 0 0
$$498$$ −12.0000 −0.537733
$$499$$ 14.0000 0.626726 0.313363 0.949633i $$-0.398544\pi$$
0.313363 + 0.949633i $$0.398544\pi$$
$$500$$ 0 0
$$501$$ 12.0000 0.536120
$$502$$ −30.0000 −1.33897
$$503$$ 18.0000 0.802580 0.401290 0.915951i $$-0.368562\pi$$
0.401290 + 0.915951i $$0.368562\pi$$
$$504$$ −2.00000 −0.0890871
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −1.00000 −0.0444116
$$508$$ 16.0000 0.709885
$$509$$ 6.00000 0.265945 0.132973 0.991120i $$-0.457548\pi$$
0.132973 + 0.991120i $$0.457548\pi$$
$$510$$ 0 0
$$511$$ −8.00000 −0.353899
$$512$$ 1.00000 0.0441942
$$513$$ −2.00000 −0.0883022
$$514$$ 12.0000 0.529297
$$515$$ 0 0
$$516$$ −4.00000 −0.176090
$$517$$ 0 0
$$518$$ 4.00000 0.175750
$$519$$ 18.0000 0.790112
$$520$$ 0 0
$$521$$ −42.0000 −1.84005 −0.920027 0.391856i $$-0.871833\pi$$
−0.920027 + 0.391856i $$0.871833\pi$$
$$522$$ 0 0
$$523$$ −20.0000 −0.874539 −0.437269 0.899331i $$-0.644054\pi$$
−0.437269 + 0.899331i $$0.644054\pi$$
$$524$$ 6.00000 0.262111
$$525$$ 0 0
$$526$$ −30.0000 −1.30806
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 13.0000 0.565217
$$530$$ 0 0
$$531$$ 0 0
$$532$$ −4.00000 −0.173422
$$533$$ −6.00000 −0.259889
$$534$$ 6.00000 0.259645
$$535$$ 0 0
$$536$$ 4.00000 0.172774
$$537$$ 6.00000 0.258919
$$538$$ 12.0000 0.517357
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 8.00000 0.343947 0.171973 0.985102i $$-0.444986\pi$$
0.171973 + 0.985102i $$0.444986\pi$$
$$542$$ 8.00000 0.343629
$$543$$ −2.00000 −0.0858282
$$544$$ 0 0
$$545$$ 0 0
$$546$$ −2.00000 −0.0855921
$$547$$ −20.0000 −0.855138 −0.427569 0.903983i $$-0.640630\pi$$
−0.427569 + 0.903983i $$0.640630\pi$$
$$548$$ −6.00000 −0.256307
$$549$$ 14.0000 0.597505
$$550$$ 0 0
$$551$$ 0 0
$$552$$ −6.00000 −0.255377
$$553$$ 32.0000 1.36078
$$554$$ −26.0000 −1.10463
$$555$$ 0 0
$$556$$ 8.00000 0.339276
$$557$$ −30.0000 −1.27114 −0.635570 0.772043i $$-0.719235\pi$$
−0.635570 + 0.772043i $$0.719235\pi$$
$$558$$ 8.00000 0.338667
$$559$$ −4.00000 −0.169182
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −30.0000 −1.26547
$$563$$ −24.0000 −1.01148 −0.505740 0.862686i $$-0.668780\pi$$
−0.505740 + 0.862686i $$0.668780\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 28.0000 1.17693
$$567$$ −2.00000 −0.0839921
$$568$$ 0 0
$$569$$ 6.00000 0.251533 0.125767 0.992060i $$-0.459861\pi$$
0.125767 + 0.992060i $$0.459861\pi$$
$$570$$ 0 0
$$571$$ 32.0000 1.33916 0.669579 0.742741i $$-0.266474\pi$$
0.669579 + 0.742741i $$0.266474\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ −12.0000 −0.500870
$$575$$ 0 0
$$576$$ 1.00000 0.0416667
$$577$$ 16.0000 0.666089 0.333044 0.942911i $$-0.391924\pi$$
0.333044 + 0.942911i $$0.391924\pi$$
$$578$$ −17.0000 −0.707107
$$579$$ 8.00000 0.332469
$$580$$ 0 0
$$581$$ −24.0000 −0.995688
$$582$$ −4.00000 −0.165805
$$583$$ 0 0
$$584$$ 4.00000 0.165521
$$585$$ 0 0
$$586$$ 6.00000 0.247858
$$587$$ −12.0000 −0.495293 −0.247647 0.968850i $$-0.579657\pi$$
−0.247647 + 0.968850i $$0.579657\pi$$
$$588$$ 3.00000 0.123718
$$589$$ 16.0000 0.659269
$$590$$ 0 0
$$591$$ 18.0000 0.740421
$$592$$ −2.00000 −0.0821995
$$593$$ 6.00000 0.246390 0.123195 0.992382i $$-0.460686\pi$$
0.123195 + 0.992382i $$0.460686\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 18.0000 0.737309
$$597$$ 16.0000 0.654836
$$598$$ −6.00000 −0.245358
$$599$$ 24.0000 0.980613 0.490307 0.871550i $$-0.336885\pi$$
0.490307 + 0.871550i $$0.336885\pi$$
$$600$$ 0 0
$$601$$ −10.0000 −0.407909 −0.203954 0.978980i $$-0.565379\pi$$
−0.203954 + 0.978980i $$0.565379\pi$$
$$602$$ −8.00000 −0.326056
$$603$$ 4.00000 0.162893
$$604$$ 8.00000 0.325515
$$605$$ 0 0
$$606$$ 12.0000 0.487467
$$607$$ 40.0000 1.62355 0.811775 0.583970i $$-0.198502\pi$$
0.811775 + 0.583970i $$0.198502\pi$$
$$608$$ 2.00000 0.0811107
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 22.0000 0.888572 0.444286 0.895885i $$-0.353457\pi$$
0.444286 + 0.895885i $$0.353457\pi$$
$$614$$ 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 $$0.381983\pi$$
$$618$$ −16.0000 −0.643614
$$619$$ 38.0000 1.52735 0.763674 0.645601i $$-0.223393\pi$$
0.763674 + 0.645601i $$0.223393\pi$$
$$620$$ 0 0
$$621$$ −6.00000 −0.240772
$$622$$ 24.0000 0.962312
$$623$$ 12.0000 0.480770
$$624$$ 1.00000 0.0400320
$$625$$ 0 0
$$626$$ 10.0000 0.399680
$$627$$ 0 0
$$628$$ −2.00000 −0.0798087
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 20.0000 0.796187 0.398094 0.917345i $$-0.369672\pi$$
0.398094 + 0.917345i $$0.369672\pi$$
$$632$$ −16.0000 −0.636446
$$633$$ 4.00000 0.158986
$$634$$ 18.0000 0.714871
$$635$$ 0 0
$$636$$ −6.00000 −0.237915
$$637$$ 3.00000 0.118864
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −6.00000 −0.236986 −0.118493 0.992955i $$-0.537806\pi$$
−0.118493 + 0.992955i $$0.537806\pi$$
$$642$$ −12.0000 −0.473602
$$643$$ 4.00000 0.157745 0.0788723 0.996885i $$-0.474868\pi$$
0.0788723 + 0.996885i $$0.474868\pi$$
$$644$$ −12.0000 −0.472866
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −6.00000 −0.235884 −0.117942 0.993020i $$-0.537630\pi$$
−0.117942 + 0.993020i $$0.537630\pi$$
$$648$$ 1.00000 0.0392837
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 16.0000 0.627089
$$652$$ 16.0000 0.626608
$$653$$ −30.0000 −1.17399 −0.586995 0.809590i $$-0.699689\pi$$
−0.586995 + 0.809590i $$0.699689\pi$$
$$654$$ 4.00000 0.156412
$$655$$ 0 0
$$656$$ 6.00000 0.234261
$$657$$ 4.00000 0.156055
$$658$$ 0 0
$$659$$ −18.0000 −0.701180 −0.350590 0.936529i $$-0.614019\pi$$
−0.350590 + 0.936529i $$0.614019\pi$$
$$660$$ 0 0
$$661$$ −16.0000 −0.622328 −0.311164 0.950356i $$-0.600719\pi$$
−0.311164 + 0.950356i $$0.600719\pi$$
$$662$$ 2.00000 0.0777322
$$663$$ 0 0
$$664$$ 12.0000 0.465690
$$665$$ 0 0
$$666$$ −2.00000 −0.0774984
$$667$$ 0 0
$$668$$ −12.0000 −0.464294
$$669$$ −10.0000 −0.386622
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 2.00000 0.0771517
$$673$$ −2.00000 −0.0770943 −0.0385472 0.999257i $$-0.512273\pi$$
−0.0385472 + 0.999257i $$0.512273\pi$$
$$674$$ −14.0000 −0.539260
$$675$$ 0 0
$$676$$ 1.00000 0.0384615
$$677$$ 42.0000 1.61419 0.807096 0.590421i $$-0.201038\pi$$
0.807096 + 0.590421i $$0.201038\pi$$
$$678$$ 12.0000 0.460857
$$679$$ −8.00000 −0.307012
$$680$$ 0 0
$$681$$ 12.0000 0.459841
$$682$$ 0 0
$$683$$ 36.0000 1.37750 0.688751 0.724998i $$-0.258159\pi$$
0.688751 + 0.724998i $$0.258159\pi$$
$$684$$ 2.00000 0.0764719
$$685$$ 0 0
$$686$$ 20.0000 0.763604
$$687$$ 4.00000 0.152610
$$688$$ 4.00000 0.152499
$$689$$ −6.00000 −0.228582
$$690$$ 0 0
$$691$$ 26.0000 0.989087 0.494543 0.869153i $$-0.335335\pi$$
0.494543 + 0.869153i $$0.335335\pi$$
$$692$$ −18.0000 −0.684257
$$693$$ 0 0
$$694$$ −24.0000 −0.911028
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 20.0000 0.757011
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 36.0000 1.35970 0.679851 0.733351i $$-0.262045\pi$$
0.679851 + 0.733351i $$0.262045\pi$$
$$702$$ 1.00000 0.0377426
$$703$$ −4.00000 −0.150863
$$704$$ 0 0
$$705$$ 0 0
$$706$$ −6.00000 −0.225813
$$707$$ 24.0000 0.902613
$$708$$ 0 0
$$709$$ 20.0000 0.751116 0.375558 0.926799i $$-0.377451\pi$$
0.375558 + 0.926799i $$0.377451\pi$$
$$710$$ 0 0
$$711$$ −16.0000 −0.600047
$$712$$ −6.00000 −0.224860
$$713$$ 48.0000 1.79761
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −6.00000 −0.224231
$$717$$ 0 0
$$718$$ −24.0000 −0.895672
$$719$$ 12.0000 0.447524 0.223762 0.974644i $$-0.428166\pi$$
0.223762 + 0.974644i $$0.428166\pi$$
$$720$$ 0 0
$$721$$ −32.0000 −1.19174
$$722$$ −15.0000 −0.558242
$$723$$ −26.0000 −0.966950
$$724$$ 2.00000 0.0743294
$$725$$ 0 0
$$726$$ 11.0000 0.408248
$$727$$ 4.00000 0.148352 0.0741759 0.997245i $$-0.476367\pi$$
0.0741759 + 0.997245i $$0.476367\pi$$
$$728$$ 2.00000 0.0741249
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 0 0
$$732$$ −14.0000 −0.517455
$$733$$ −50.0000 −1.84679 −0.923396 0.383849i $$-0.874598\pi$$
−0.923396 + 0.383849i $$0.874598\pi$$
$$734$$ −8.00000 −0.295285
$$735$$ 0 0
$$736$$ 6.00000 0.221163
$$737$$ 0 0
$$738$$ 6.00000 0.220863
$$739$$ 38.0000 1.39785 0.698926 0.715194i $$-0.253662\pi$$
0.698926 + 0.715194i $$0.253662\pi$$
$$740$$ 0 0
$$741$$ 2.00000 0.0734718
$$742$$ −12.0000 −0.440534
$$743$$ −36.0000 −1.32071 −0.660356 0.750953i $$-0.729595\pi$$
−0.660356 + 0.750953i $$0.729595\pi$$
$$744$$ −8.00000 −0.293294
$$745$$ 0 0
$$746$$ −26.0000 −0.951928
$$747$$ 12.0000 0.439057
$$748$$ 0 0
$$749$$ −24.0000 −0.876941
$$750$$ 0 0
$$751$$ −40.0000 −1.45962 −0.729810 0.683650i $$-0.760392\pi$$
−0.729810 + 0.683650i $$0.760392\pi$$
$$752$$ 0 0
$$753$$ 30.0000 1.09326
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 2.00000 0.0727393
$$757$$ 34.0000 1.23575 0.617876 0.786276i $$-0.287994\pi$$
0.617876 + 0.786276i $$0.287994\pi$$
$$758$$ −34.0000 −1.23494
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 6.00000 0.217500 0.108750 0.994069i $$-0.465315\pi$$
0.108750 + 0.994069i $$0.465315\pi$$
$$762$$ −16.0000 −0.579619
$$763$$ 8.00000 0.289619
$$764$$ 0 0
$$765$$ 0 0
$$766$$ −12.0000 −0.433578
$$767$$ 0 0
$$768$$ −1.00000 −0.0360844
$$769$$ −22.0000 −0.793340 −0.396670 0.917961i $$-0.629834\pi$$
−0.396670 + 0.917961i $$0.629834\pi$$
$$770$$ 0 0
$$771$$ −12.0000 −0.432169
$$772$$ −8.00000 −0.287926
$$773$$ 6.00000 0.215805 0.107903 0.994161i $$-0.465587\pi$$
0.107903 + 0.994161i $$0.465587\pi$$
$$774$$ 4.00000 0.143777
$$775$$ 0 0
$$776$$ 4.00000 0.143592
$$777$$ −4.00000 −0.143499
$$778$$ 36.0000 1.29066
$$779$$ 12.0000 0.429945
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −3.00000 −0.107143
$$785$$ 0 0
$$786$$ −6.00000 −0.214013
$$787$$ 16.0000 0.570338 0.285169 0.958477i $$-0.407950\pi$$
0.285169 + 0.958477i $$0.407950\pi$$
$$788$$ −18.0000 −0.641223
$$789$$ 30.0000 1.06803
$$790$$ 0 0
$$791$$ 24.0000 0.853342
$$792$$ 0 0
$$793$$ −14.0000 −0.497155
$$794$$ −26.0000 −0.922705
$$795$$ 0 0
$$796$$ −16.0000 −0.567105
$$797$$ 30.0000 1.06265 0.531327 0.847167i $$-0.321693\pi$$
0.531327 + 0.847167i $$0.321693\pi$$
$$798$$ 4.00000 0.141598
$$799$$ 0 0
$$800$$ 0 0
$$801$$ −6.00000 −0.212000
$$802$$ −18.0000 −0.635602
$$803$$ 0 0
$$804$$ −4.00000 −0.141069
$$805$$ 0 0
$$806$$ −8.00000 −0.281788
$$807$$ −12.0000 −0.422420
$$808$$ −12.0000 −0.422159
$$809$$ −6.00000 −0.210949 −0.105474 0.994422i $$-0.533636\pi$$
−0.105474 + 0.994422i $$0.533636\pi$$
$$810$$ 0 0
$$811$$ 26.0000 0.912983 0.456492 0.889728i $$-0.349106\pi$$
0.456492 + 0.889728i $$0.349106\pi$$
$$812$$ 0 0
$$813$$ −8.00000 −0.280572
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 8.00000 0.279885
$$818$$ 14.0000 0.489499
$$819$$ 2.00000 0.0698857
$$820$$ 0 0
$$821$$ −6.00000 −0.209401 −0.104701 0.994504i $$-0.533388\pi$$
−0.104701 + 0.994504i $$0.533388\pi$$
$$822$$ 6.00000 0.209274
$$823$$ −32.0000 −1.11545 −0.557725 0.830026i $$-0.688326\pi$$
−0.557725 + 0.830026i $$0.688326\pi$$
$$824$$ 16.0000 0.557386
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 12.0000 0.417281 0.208640 0.977992i $$-0.433096\pi$$
0.208640 + 0.977992i $$0.433096\pi$$
$$828$$ 6.00000 0.208514
$$829$$ 14.0000 0.486240 0.243120 0.969996i $$-0.421829\pi$$
0.243120 + 0.969996i $$0.421829\pi$$
$$830$$ 0 0
$$831$$ 26.0000 0.901930
$$832$$ −1.00000 −0.0346688
$$833$$ 0 0
$$834$$ −8.00000 −0.277017
$$835$$ 0 0
$$836$$ 0 0
$$837$$ −8.00000 −0.276520
$$838$$ 6.00000 0.207267
$$839$$ −48.0000 −1.65714 −0.828572 0.559883i $$-0.810846\pi$$
−0.828572 + 0.559883i $$0.810846\pi$$
$$840$$ 0 0
$$841$$ −29.0000 −1.00000
$$842$$ 32.0000 1.10279
$$843$$ 30.0000 1.03325
$$844$$ −4.00000 −0.137686
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 22.0000 0.755929
$$848$$ 6.00000 0.206041
$$849$$ −28.0000 −0.960958
$$850$$ 0 0
$$851$$ −12.0000 −0.411355
$$852$$ 0 0
$$853$$ −26.0000 −0.890223 −0.445112 0.895475i $$-0.646836\pi$$
−0.445112 + 0.895475i $$0.646836\pi$$
$$854$$ −28.0000 −0.958140
$$855$$ 0 0
$$856$$ 12.0000 0.410152
$$857$$ 12.0000 0.409912 0.204956 0.978771i $$-0.434295\pi$$
0.204956 + 0.978771i $$0.434295\pi$$
$$858$$ 0 0
$$859$$ 20.0000 0.682391 0.341196 0.939992i $$-0.389168\pi$$
0.341196 + 0.939992i $$0.389168\pi$$
$$860$$ 0 0
$$861$$ 12.0000 0.408959
$$862$$ 24.0000 0.817443
$$863$$ 12.0000 0.408485 0.204242 0.978920i $$-0.434527\pi$$
0.204242 + 0.978920i $$0.434527\pi$$
$$864$$ −1.00000 −0.0340207
$$865$$ 0 0
$$866$$ −14.0000 −0.475739
$$867$$ 17.0000 0.577350
$$868$$ −16.0000 −0.543075
$$869$$ 0 0
$$870$$ 0 0
$$871$$ −4.00000 −0.135535
$$872$$ −4.00000 −0.135457
$$873$$ 4.00000 0.135379
$$874$$ 12.0000 0.405906
$$875$$ 0 0
$$876$$ −4.00000 −0.135147
$$877$$ 58.0000 1.95852 0.979260 0.202606i $$-0.0649409\pi$$
0.979260 + 0.202606i $$0.0649409\pi$$
$$878$$ 32.0000 1.07995
$$879$$ −6.00000 −0.202375
$$880$$ 0 0
$$881$$ 6.00000 0.202145 0.101073 0.994879i $$-0.467773\pi$$
0.101073 + 0.994879i $$0.467773\pi$$
$$882$$ −3.00000 −0.101015
$$883$$ 28.0000 0.942275 0.471138 0.882060i $$-0.343844\pi$$
0.471138 + 0.882060i $$0.343844\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 30.0000 1.00730 0.503651 0.863907i $$-0.331990\pi$$
0.503651 + 0.863907i $$0.331990\pi$$
$$888$$ 2.00000 0.0671156
$$889$$ −32.0000 −1.07325
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 10.0000 0.334825
$$893$$ 0 0
$$894$$ −18.0000 −0.602010
$$895$$ 0 0
$$896$$ −2.00000 −0.0668153
$$897$$ 6.00000 0.200334
$$898$$ −30.0000 −1.00111
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 0 0
$$902$$ 0 0
$$903$$ 8.00000 0.266223
$$904$$ −12.0000 −0.399114
$$905$$ 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
$$909$$ −12.0000 −0.398015
$$910$$ 0 0
$$911$$ −12.0000 −0.397578 −0.198789 0.980042i $$-0.563701\pi$$
−0.198789 + 0.980042i $$0.563701\pi$$
$$912$$ −2.00000 −0.0662266
$$913$$ 0 0
$$914$$ 28.0000 0.926158
$$915$$ 0 0
$$916$$ −4.00000 −0.132164
$$917$$ −12.0000 −0.396275
$$918$$ 0 0
$$919$$ −16.0000 −0.527791 −0.263896 0.964551i $$-0.585007\pi$$
−0.263896 + 0.964551i $$0.585007\pi$$
$$920$$ 0 0
$$921$$ −4.00000 −0.131804
$$922$$ −42.0000 −1.38320
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 10.0000 0.328620
$$927$$ 16.0000 0.525509
$$928$$ 0 0
$$929$$ −54.0000 −1.77168 −0.885841 0.463988i $$-0.846418\pi$$
−0.885841 + 0.463988i $$0.846418\pi$$
$$930$$ 0 0
$$931$$ −6.00000 −0.196642
$$932$$ 0 0
$$933$$ −24.0000 −0.785725
$$934$$ −36.0000 −1.17796
$$935$$ 0 0
$$936$$ −1.00000 −0.0326860
$$937$$ −2.00000 −0.0653372 −0.0326686 0.999466i $$-0.510401\pi$$
−0.0326686 + 0.999466i $$0.510401\pi$$
$$938$$ −8.00000 −0.261209
$$939$$ −10.0000 −0.326338
$$940$$ 0 0
$$941$$ 42.0000 1.36916 0.684580 0.728937i $$-0.259985\pi$$
0.684580 + 0.728937i $$0.259985\pi$$
$$942$$ 2.00000 0.0651635
$$943$$ 36.0000 1.17232
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −36.0000 −1.16984 −0.584921 0.811090i $$-0.698875\pi$$
−0.584921 + 0.811090i $$0.698875\pi$$
$$948$$ 16.0000 0.519656
$$949$$ −4.00000 −0.129845
$$950$$ 0 0
$$951$$ −18.0000 −0.583690
$$952$$ 0 0
$$953$$ −24.0000 −0.777436 −0.388718 0.921357i $$-0.627082\pi$$
−0.388718 + 0.921357i $$0.627082\pi$$
$$954$$ 6.00000 0.194257
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 12.0000 0.387500
$$960$$ 0 0
$$961$$ 33.0000 1.06452
$$962$$ 2.00000 0.0644826
$$963$$ 12.0000 0.386695
$$964$$ 26.0000 0.837404
$$965$$ 0 0
$$966$$ 12.0000 0.386094
$$967$$ −50.0000 −1.60789 −0.803946 0.594703i $$-0.797270\pi$$
−0.803946 + 0.594703i $$0.797270\pi$$
$$968$$ −11.0000 −0.353553
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −30.0000 −0.962746 −0.481373 0.876516i $$-0.659862\pi$$
−0.481373 + 0.876516i $$0.659862\pi$$
$$972$$ −1.00000 −0.0320750
$$973$$ −16.0000 −0.512936
$$974$$ −2.00000 −0.0640841
$$975$$ 0 0
$$976$$ 14.0000 0.448129
$$977$$ −42.0000 −1.34370 −0.671850 0.740688i $$-0.734500\pi$$
−0.671850 + 0.740688i $$0.734500\pi$$
$$978$$ −16.0000 −0.511624
$$979$$ 0 0
$$980$$ 0 0
$$981$$ −4.00000 −0.127710
$$982$$ 6.00000 0.191468
$$983$$ −36.0000 −1.14822 −0.574111 0.818778i $$-0.694652\pi$$
−0.574111 + 0.818778i $$0.694652\pi$$
$$984$$ −6.00000 −0.191273
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ −2.00000 −0.0636285
$$989$$ 24.0000 0.763156
$$990$$ 0 0
$$991$$ −16.0000 −0.508257 −0.254128 0.967170i $$-0.581789\pi$$
−0.254128 + 0.967170i $$0.581789\pi$$
$$992$$ 8.00000 0.254000
$$993$$ −2.00000 −0.0634681
$$994$$ 0 0
$$995$$ 0 0
$$996$$ −12.0000 −0.380235
$$997$$ 46.0000 1.45683 0.728417 0.685134i $$-0.240256\pi$$
0.728417 + 0.685134i $$0.240256\pi$$
$$998$$ 14.0000 0.443162
$$999$$ 2.00000 0.0632772
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1950.2.a.o.1.1 1
3.2 odd 2 5850.2.a.g.1.1 1
5.2 odd 4 1950.2.e.d.1249.2 2
5.3 odd 4 1950.2.e.d.1249.1 2
5.4 even 2 390.2.a.d.1.1 1
15.2 even 4 5850.2.e.o.5149.1 2
15.8 even 4 5850.2.e.o.5149.2 2
15.14 odd 2 1170.2.a.k.1.1 1
20.19 odd 2 3120.2.a.j.1.1 1
60.59 even 2 9360.2.a.g.1.1 1
65.34 odd 4 5070.2.b.m.1351.1 2
65.44 odd 4 5070.2.b.m.1351.2 2
65.64 even 2 5070.2.a.t.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
390.2.a.d.1.1 1 5.4 even 2
1170.2.a.k.1.1 1 15.14 odd 2
1950.2.a.o.1.1 1 1.1 even 1 trivial
1950.2.e.d.1249.1 2 5.3 odd 4
1950.2.e.d.1249.2 2 5.2 odd 4
3120.2.a.j.1.1 1 20.19 odd 2
5070.2.a.t.1.1 1 65.64 even 2
5070.2.b.m.1351.1 2 65.34 odd 4
5070.2.b.m.1351.2 2 65.44 odd 4
5850.2.a.g.1.1 1 3.2 odd 2
5850.2.e.o.5149.1 2 15.2 even 4
5850.2.e.o.5149.2 2 15.8 even 4
9360.2.a.g.1.1 1 60.59 even 2