# Properties

 Label 3675.2.a.f.1.1 Level $3675$ Weight $2$ Character 3675.1 Self dual yes Analytic conductor $29.345$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$3675 = 3 \cdot 5^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3675.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$29.3450227428$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 105) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 3675.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +1.00000 q^{3} -1.00000 q^{4} -1.00000 q^{6} +3.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} +1.00000 q^{3} -1.00000 q^{4} -1.00000 q^{6} +3.00000 q^{8} +1.00000 q^{9} -1.00000 q^{12} -6.00000 q^{13} -1.00000 q^{16} +2.00000 q^{17} -1.00000 q^{18} +8.00000 q^{19} -8.00000 q^{23} +3.00000 q^{24} +6.00000 q^{26} +1.00000 q^{27} -2.00000 q^{29} -4.00000 q^{31} -5.00000 q^{32} -2.00000 q^{34} -1.00000 q^{36} +2.00000 q^{37} -8.00000 q^{38} -6.00000 q^{39} +6.00000 q^{41} -4.00000 q^{43} +8.00000 q^{46} +8.00000 q^{47} -1.00000 q^{48} +2.00000 q^{51} +6.00000 q^{52} -10.0000 q^{53} -1.00000 q^{54} +8.00000 q^{57} +2.00000 q^{58} -4.00000 q^{59} +2.00000 q^{61} +4.00000 q^{62} +7.00000 q^{64} -4.00000 q^{67} -2.00000 q^{68} -8.00000 q^{69} -12.0000 q^{71} +3.00000 q^{72} -2.00000 q^{73} -2.00000 q^{74} -8.00000 q^{76} +6.00000 q^{78} +8.00000 q^{79} +1.00000 q^{81} -6.00000 q^{82} -4.00000 q^{83} +4.00000 q^{86} -2.00000 q^{87} +6.00000 q^{89} +8.00000 q^{92} -4.00000 q^{93} -8.00000 q^{94} -5.00000 q^{96} -18.0000 q^{97} +O(q^{100})$$

## 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 −0.353553 0.935414i $$-0.615027\pi$$
−0.353553 + 0.935414i $$0.615027\pi$$
$$3$$ 1.00000 0.577350
$$4$$ −1.00000 −0.500000
$$5$$ 0 0
$$6$$ −1.00000 −0.408248
$$7$$ 0 0
$$8$$ 3.00000 1.06066
$$9$$ 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
$$13$$ −6.00000 −1.66410 −0.832050 0.554700i $$-0.812833\pi$$
−0.832050 + 0.554700i $$0.812833\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −1.00000 −0.250000
$$17$$ 2.00000 0.485071 0.242536 0.970143i $$-0.422021\pi$$
0.242536 + 0.970143i $$0.422021\pi$$
$$18$$ −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
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −8.00000 −1.66812 −0.834058 0.551677i $$-0.813988\pi$$
−0.834058 + 0.551677i $$0.813988\pi$$
$$24$$ 3.00000 0.612372
$$25$$ 0 0
$$26$$ 6.00000 1.17670
$$27$$ 1.00000 0.192450
$$28$$ 0 0
$$29$$ −2.00000 −0.371391 −0.185695 0.982607i $$-0.559454\pi$$
−0.185695 + 0.982607i $$0.559454\pi$$
$$30$$ 0 0
$$31$$ −4.00000 −0.718421 −0.359211 0.933257i $$-0.616954\pi$$
−0.359211 + 0.933257i $$0.616954\pi$$
$$32$$ −5.00000 −0.883883
$$33$$ 0 0
$$34$$ −2.00000 −0.342997
$$35$$ 0 0
$$36$$ −1.00000 −0.166667
$$37$$ 2.00000 0.328798 0.164399 0.986394i $$-0.447432\pi$$
0.164399 + 0.986394i $$0.447432\pi$$
$$38$$ −8.00000 −1.29777
$$39$$ −6.00000 −0.960769
$$40$$ 0 0
$$41$$ 6.00000 0.937043 0.468521 0.883452i $$-0.344787\pi$$
0.468521 + 0.883452i $$0.344787\pi$$
$$42$$ 0 0
$$43$$ −4.00000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 8.00000 1.17954
$$47$$ 8.00000 1.16692 0.583460 0.812142i $$-0.301699\pi$$
0.583460 + 0.812142i $$0.301699\pi$$
$$48$$ −1.00000 −0.144338
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 2.00000 0.280056
$$52$$ 6.00000 0.832050
$$53$$ −10.0000 −1.37361 −0.686803 0.726844i $$-0.740986\pi$$
−0.686803 + 0.726844i $$0.740986\pi$$
$$54$$ −1.00000 −0.136083
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 8.00000 1.05963
$$58$$ 2.00000 0.262613
$$59$$ −4.00000 −0.520756 −0.260378 0.965507i $$-0.583847\pi$$
−0.260378 + 0.965507i $$0.583847\pi$$
$$60$$ 0 0
$$61$$ 2.00000 0.256074 0.128037 0.991769i $$-0.459132\pi$$
0.128037 + 0.991769i $$0.459132\pi$$
$$62$$ 4.00000 0.508001
$$63$$ 0 0
$$64$$ 7.00000 0.875000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −4.00000 −0.488678 −0.244339 0.969690i $$-0.578571\pi$$
−0.244339 + 0.969690i $$0.578571\pi$$
$$68$$ −2.00000 −0.242536
$$69$$ −8.00000 −0.963087
$$70$$ 0 0
$$71$$ −12.0000 −1.42414 −0.712069 0.702109i $$-0.752242\pi$$
−0.712069 + 0.702109i $$0.752242\pi$$
$$72$$ 3.00000 0.353553
$$73$$ −2.00000 −0.234082 −0.117041 0.993127i $$-0.537341\pi$$
−0.117041 + 0.993127i $$0.537341\pi$$
$$74$$ −2.00000 −0.232495
$$75$$ 0 0
$$76$$ −8.00000 −0.917663
$$77$$ 0 0
$$78$$ 6.00000 0.679366
$$79$$ 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
$$83$$ −4.00000 −0.439057 −0.219529 0.975606i $$-0.570452\pi$$
−0.219529 + 0.975606i $$0.570452\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 4.00000 0.431331
$$87$$ −2.00000 −0.214423
$$88$$ 0 0
$$89$$ 6.00000 0.635999 0.317999 0.948091i $$-0.396989\pi$$
0.317999 + 0.948091i $$0.396989\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 8.00000 0.834058
$$93$$ −4.00000 −0.414781
$$94$$ −8.00000 −0.825137
$$95$$ 0 0
$$96$$ −5.00000 −0.510310
$$97$$ −18.0000 −1.82762 −0.913812 0.406138i $$-0.866875\pi$$
−0.913812 + 0.406138i $$0.866875\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 10.0000 0.995037 0.497519 0.867453i $$-0.334245\pi$$
0.497519 + 0.867453i $$0.334245\pi$$
$$102$$ −2.00000 −0.198030
$$103$$ 8.00000 0.788263 0.394132 0.919054i $$-0.371045\pi$$
0.394132 + 0.919054i $$0.371045\pi$$
$$104$$ −18.0000 −1.76505
$$105$$ 0 0
$$106$$ 10.0000 0.971286
$$107$$ 12.0000 1.16008 0.580042 0.814587i $$-0.303036\pi$$
0.580042 + 0.814587i $$0.303036\pi$$
$$108$$ −1.00000 −0.0962250
$$109$$ −18.0000 −1.72409 −0.862044 0.506834i $$-0.830816\pi$$
−0.862044 + 0.506834i $$0.830816\pi$$
$$110$$ 0 0
$$111$$ 2.00000 0.189832
$$112$$ 0 0
$$113$$ −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
$$116$$ 2.00000 0.185695
$$117$$ −6.00000 −0.554700
$$118$$ 4.00000 0.368230
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −11.0000 −1.00000
$$122$$ −2.00000 −0.181071
$$123$$ 6.00000 0.541002
$$124$$ 4.00000 0.359211
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −8.00000 −0.709885 −0.354943 0.934888i $$-0.615500\pi$$
−0.354943 + 0.934888i $$0.615500\pi$$
$$128$$ 3.00000 0.265165
$$129$$ −4.00000 −0.352180
$$130$$ 0 0
$$131$$ −20.0000 −1.74741 −0.873704 0.486458i $$-0.838289\pi$$
−0.873704 + 0.486458i $$0.838289\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 4.00000 0.345547
$$135$$ 0 0
$$136$$ 6.00000 0.514496
$$137$$ 10.0000 0.854358 0.427179 0.904167i $$-0.359507\pi$$
0.427179 + 0.904167i $$0.359507\pi$$
$$138$$ 8.00000 0.681005
$$139$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$140$$ 0 0
$$141$$ 8.00000 0.673722
$$142$$ 12.0000 1.00702
$$143$$ 0 0
$$144$$ −1.00000 −0.0833333
$$145$$ 0 0
$$146$$ 2.00000 0.165521
$$147$$ 0 0
$$148$$ −2.00000 −0.164399
$$149$$ 14.0000 1.14692 0.573462 0.819232i $$-0.305600\pi$$
0.573462 + 0.819232i $$0.305600\pi$$
$$150$$ 0 0
$$151$$ 8.00000 0.651031 0.325515 0.945537i $$-0.394462\pi$$
0.325515 + 0.945537i $$0.394462\pi$$
$$152$$ 24.0000 1.94666
$$153$$ 2.00000 0.161690
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 6.00000 0.480384
$$157$$ −14.0000 −1.11732 −0.558661 0.829396i $$-0.688685\pi$$
−0.558661 + 0.829396i $$0.688685\pi$$
$$158$$ −8.00000 −0.636446
$$159$$ −10.0000 −0.793052
$$160$$ 0 0
$$161$$ 0 0
$$162$$ −1.00000 −0.0785674
$$163$$ −12.0000 −0.939913 −0.469956 0.882690i $$-0.655730\pi$$
−0.469956 + 0.882690i $$0.655730\pi$$
$$164$$ −6.00000 −0.468521
$$165$$ 0 0
$$166$$ 4.00000 0.310460
$$167$$ 8.00000 0.619059 0.309529 0.950890i $$-0.399829\pi$$
0.309529 + 0.950890i $$0.399829\pi$$
$$168$$ 0 0
$$169$$ 23.0000 1.76923
$$170$$ 0 0
$$171$$ 8.00000 0.611775
$$172$$ 4.00000 0.304997
$$173$$ 6.00000 0.456172 0.228086 0.973641i $$-0.426753\pi$$
0.228086 + 0.973641i $$0.426753\pi$$
$$174$$ 2.00000 0.151620
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −4.00000 −0.300658
$$178$$ −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
$$181$$ 2.00000 0.148659 0.0743294 0.997234i $$-0.476318\pi$$
0.0743294 + 0.997234i $$0.476318\pi$$
$$182$$ 0 0
$$183$$ 2.00000 0.147844
$$184$$ −24.0000 −1.76930
$$185$$ 0 0
$$186$$ 4.00000 0.293294
$$187$$ 0 0
$$188$$ −8.00000 −0.583460
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 4.00000 0.289430 0.144715 0.989473i $$-0.453773\pi$$
0.144715 + 0.989473i $$0.453773\pi$$
$$192$$ 7.00000 0.505181
$$193$$ −18.0000 −1.29567 −0.647834 0.761781i $$-0.724325\pi$$
−0.647834 + 0.761781i $$0.724325\pi$$
$$194$$ 18.0000 1.29232
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −18.0000 −1.28245 −0.641223 0.767354i $$-0.721573\pi$$
−0.641223 + 0.767354i $$0.721573\pi$$
$$198$$ 0 0
$$199$$ 4.00000 0.283552 0.141776 0.989899i $$-0.454719\pi$$
0.141776 + 0.989899i $$0.454719\pi$$
$$200$$ 0 0
$$201$$ −4.00000 −0.282138
$$202$$ −10.0000 −0.703598
$$203$$ 0 0
$$204$$ −2.00000 −0.140028
$$205$$ 0 0
$$206$$ −8.00000 −0.557386
$$207$$ −8.00000 −0.556038
$$208$$ 6.00000 0.416025
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −20.0000 −1.37686 −0.688428 0.725304i $$-0.741699\pi$$
−0.688428 + 0.725304i $$0.741699\pi$$
$$212$$ 10.0000 0.686803
$$213$$ −12.0000 −0.822226
$$214$$ −12.0000 −0.820303
$$215$$ 0 0
$$216$$ 3.00000 0.204124
$$217$$ 0 0
$$218$$ 18.0000 1.21911
$$219$$ −2.00000 −0.135147
$$220$$ 0 0
$$221$$ −12.0000 −0.807207
$$222$$ −2.00000 −0.134231
$$223$$ −24.0000 −1.60716 −0.803579 0.595198i $$-0.797074\pi$$
−0.803579 + 0.595198i $$0.797074\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 6.00000 0.399114
$$227$$ −4.00000 −0.265489 −0.132745 0.991150i $$-0.542379\pi$$
−0.132745 + 0.991150i $$0.542379\pi$$
$$228$$ −8.00000 −0.529813
$$229$$ −22.0000 −1.45380 −0.726900 0.686743i $$-0.759040\pi$$
−0.726900 + 0.686743i $$0.759040\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −6.00000 −0.393919
$$233$$ 18.0000 1.17922 0.589610 0.807688i $$-0.299282\pi$$
0.589610 + 0.807688i $$0.299282\pi$$
$$234$$ 6.00000 0.392232
$$235$$ 0 0
$$236$$ 4.00000 0.260378
$$237$$ 8.00000 0.519656
$$238$$ 0 0
$$239$$ −4.00000 −0.258738 −0.129369 0.991596i $$-0.541295\pi$$
−0.129369 + 0.991596i $$0.541295\pi$$
$$240$$ 0 0
$$241$$ 6.00000 0.386494 0.193247 0.981150i $$-0.438098\pi$$
0.193247 + 0.981150i $$0.438098\pi$$
$$242$$ 11.0000 0.707107
$$243$$ 1.00000 0.0641500
$$244$$ −2.00000 −0.128037
$$245$$ 0 0
$$246$$ −6.00000 −0.382546
$$247$$ −48.0000 −3.05417
$$248$$ −12.0000 −0.762001
$$249$$ −4.00000 −0.253490
$$250$$ 0 0
$$251$$ 12.0000 0.757433 0.378717 0.925513i $$-0.376365\pi$$
0.378717 + 0.925513i $$0.376365\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 8.00000 0.501965
$$255$$ 0 0
$$256$$ −17.0000 −1.06250
$$257$$ −6.00000 −0.374270 −0.187135 0.982334i $$-0.559920\pi$$
−0.187135 + 0.982334i $$0.559920\pi$$
$$258$$ 4.00000 0.249029
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −2.00000 −0.123797
$$262$$ 20.0000 1.23560
$$263$$ −16.0000 −0.986602 −0.493301 0.869859i $$-0.664210\pi$$
−0.493301 + 0.869859i $$0.664210\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 6.00000 0.367194
$$268$$ 4.00000 0.244339
$$269$$ −14.0000 −0.853595 −0.426798 0.904347i $$-0.640358\pi$$
−0.426798 + 0.904347i $$0.640358\pi$$
$$270$$ 0 0
$$271$$ −12.0000 −0.728948 −0.364474 0.931214i $$-0.618751\pi$$
−0.364474 + 0.931214i $$0.618751\pi$$
$$272$$ −2.00000 −0.121268
$$273$$ 0 0
$$274$$ −10.0000 −0.604122
$$275$$ 0 0
$$276$$ 8.00000 0.481543
$$277$$ −14.0000 −0.841178 −0.420589 0.907251i $$-0.638177\pi$$
−0.420589 + 0.907251i $$0.638177\pi$$
$$278$$ 0 0
$$279$$ −4.00000 −0.239474
$$280$$ 0 0
$$281$$ 18.0000 1.07379 0.536895 0.843649i $$-0.319597\pi$$
0.536895 + 0.843649i $$0.319597\pi$$
$$282$$ −8.00000 −0.476393
$$283$$ −4.00000 −0.237775 −0.118888 0.992908i $$-0.537933\pi$$
−0.118888 + 0.992908i $$0.537933\pi$$
$$284$$ 12.0000 0.712069
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ −5.00000 −0.294628
$$289$$ −13.0000 −0.764706
$$290$$ 0 0
$$291$$ −18.0000 −1.05518
$$292$$ 2.00000 0.117041
$$293$$ 14.0000 0.817889 0.408944 0.912559i $$-0.365897\pi$$
0.408944 + 0.912559i $$0.365897\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 6.00000 0.348743
$$297$$ 0 0
$$298$$ −14.0000 −0.810998
$$299$$ 48.0000 2.77591
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −8.00000 −0.460348
$$303$$ 10.0000 0.574485
$$304$$ −8.00000 −0.458831
$$305$$ 0 0
$$306$$ −2.00000 −0.114332
$$307$$ 12.0000 0.684876 0.342438 0.939540i $$-0.388747\pi$$
0.342438 + 0.939540i $$0.388747\pi$$
$$308$$ 0 0
$$309$$ 8.00000 0.455104
$$310$$ 0 0
$$311$$ −24.0000 −1.36092 −0.680458 0.732787i $$-0.738219\pi$$
−0.680458 + 0.732787i $$0.738219\pi$$
$$312$$ −18.0000 −1.01905
$$313$$ −10.0000 −0.565233 −0.282617 0.959233i $$-0.591202\pi$$
−0.282617 + 0.959233i $$0.591202\pi$$
$$314$$ 14.0000 0.790066
$$315$$ 0 0
$$316$$ −8.00000 −0.450035
$$317$$ −2.00000 −0.112331 −0.0561656 0.998421i $$-0.517887\pi$$
−0.0561656 + 0.998421i $$0.517887\pi$$
$$318$$ 10.0000 0.560772
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 12.0000 0.669775
$$322$$ 0 0
$$323$$ 16.0000 0.890264
$$324$$ −1.00000 −0.0555556
$$325$$ 0 0
$$326$$ 12.0000 0.664619
$$327$$ −18.0000 −0.995402
$$328$$ 18.0000 0.993884
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −12.0000 −0.659580 −0.329790 0.944054i $$-0.606978\pi$$
−0.329790 + 0.944054i $$0.606978\pi$$
$$332$$ 4.00000 0.219529
$$333$$ 2.00000 0.109599
$$334$$ −8.00000 −0.437741
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 14.0000 0.762629 0.381314 0.924445i $$-0.375472\pi$$
0.381314 + 0.924445i $$0.375472\pi$$
$$338$$ −23.0000 −1.25104
$$339$$ −6.00000 −0.325875
$$340$$ 0 0
$$341$$ 0 0
$$342$$ −8.00000 −0.432590
$$343$$ 0 0
$$344$$ −12.0000 −0.646997
$$345$$ 0 0
$$346$$ −6.00000 −0.322562
$$347$$ 20.0000 1.07366 0.536828 0.843692i $$-0.319622\pi$$
0.536828 + 0.843692i $$0.319622\pi$$
$$348$$ 2.00000 0.107211
$$349$$ −14.0000 −0.749403 −0.374701 0.927146i $$-0.622255\pi$$
−0.374701 + 0.927146i $$0.622255\pi$$
$$350$$ 0 0
$$351$$ −6.00000 −0.320256
$$352$$ 0 0
$$353$$ 18.0000 0.958043 0.479022 0.877803i $$-0.340992\pi$$
0.479022 + 0.877803i $$0.340992\pi$$
$$354$$ 4.00000 0.212598
$$355$$ 0 0
$$356$$ −6.00000 −0.317999
$$357$$ 0 0
$$358$$ 24.0000 1.26844
$$359$$ −36.0000 −1.90001 −0.950004 0.312239i $$-0.898921\pi$$
−0.950004 + 0.312239i $$0.898921\pi$$
$$360$$ 0 0
$$361$$ 45.0000 2.36842
$$362$$ −2.00000 −0.105118
$$363$$ −11.0000 −0.577350
$$364$$ 0 0
$$365$$ 0 0
$$366$$ −2.00000 −0.104542
$$367$$ −8.00000 −0.417597 −0.208798 0.977959i $$-0.566955\pi$$
−0.208798 + 0.977959i $$0.566955\pi$$
$$368$$ 8.00000 0.417029
$$369$$ 6.00000 0.312348
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 4.00000 0.207390
$$373$$ 10.0000 0.517780 0.258890 0.965907i $$-0.416643\pi$$
0.258890 + 0.965907i $$0.416643\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 24.0000 1.23771
$$377$$ 12.0000 0.618031
$$378$$ 0 0
$$379$$ −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
$$382$$ −4.00000 −0.204658
$$383$$ −32.0000 −1.63512 −0.817562 0.575841i $$-0.804675\pi$$
−0.817562 + 0.575841i $$0.804675\pi$$
$$384$$ 3.00000 0.153093
$$385$$ 0 0
$$386$$ 18.0000 0.916176
$$387$$ −4.00000 −0.203331
$$388$$ 18.0000 0.913812
$$389$$ 30.0000 1.52106 0.760530 0.649303i $$-0.224939\pi$$
0.760530 + 0.649303i $$0.224939\pi$$
$$390$$ 0 0
$$391$$ −16.0000 −0.809155
$$392$$ 0 0
$$393$$ −20.0000 −1.00887
$$394$$ 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 $$0.686163\pi$$
$$398$$ −4.00000 −0.200502
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 18.0000 0.898877 0.449439 0.893311i $$-0.351624\pi$$
0.449439 + 0.893311i $$0.351624\pi$$
$$402$$ 4.00000 0.199502
$$403$$ 24.0000 1.19553
$$404$$ −10.0000 −0.497519
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 6.00000 0.297044
$$409$$ 22.0000 1.08783 0.543915 0.839140i $$-0.316941\pi$$
0.543915 + 0.839140i $$0.316941\pi$$
$$410$$ 0 0
$$411$$ 10.0000 0.493264
$$412$$ −8.00000 −0.394132
$$413$$ 0 0
$$414$$ 8.00000 0.393179
$$415$$ 0 0
$$416$$ 30.0000 1.47087
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 12.0000 0.586238 0.293119 0.956076i $$-0.405307\pi$$
0.293119 + 0.956076i $$0.405307\pi$$
$$420$$ 0 0
$$421$$ −26.0000 −1.26716 −0.633581 0.773676i $$-0.718416\pi$$
−0.633581 + 0.773676i $$0.718416\pi$$
$$422$$ 20.0000 0.973585
$$423$$ 8.00000 0.388973
$$424$$ −30.0000 −1.45693
$$425$$ 0 0
$$426$$ 12.0000 0.581402
$$427$$ 0 0
$$428$$ −12.0000 −0.580042
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 28.0000 1.34871 0.674356 0.738406i $$-0.264421\pi$$
0.674356 + 0.738406i $$0.264421\pi$$
$$432$$ −1.00000 −0.0481125
$$433$$ −2.00000 −0.0961139 −0.0480569 0.998845i $$-0.515303\pi$$
−0.0480569 + 0.998845i $$0.515303\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 18.0000 0.862044
$$437$$ −64.0000 −3.06154
$$438$$ 2.00000 0.0955637
$$439$$ −28.0000 −1.33637 −0.668184 0.743996i $$-0.732928\pi$$
−0.668184 + 0.743996i $$0.732928\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 12.0000 0.570782
$$443$$ −12.0000 −0.570137 −0.285069 0.958507i $$-0.592016\pi$$
−0.285069 + 0.958507i $$0.592016\pi$$
$$444$$ −2.00000 −0.0949158
$$445$$ 0 0
$$446$$ 24.0000 1.13643
$$447$$ 14.0000 0.662177
$$448$$ 0 0
$$449$$ −30.0000 −1.41579 −0.707894 0.706319i $$-0.750354\pi$$
−0.707894 + 0.706319i $$0.750354\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 6.00000 0.282216
$$453$$ 8.00000 0.375873
$$454$$ 4.00000 0.187729
$$455$$ 0 0
$$456$$ 24.0000 1.12390
$$457$$ −18.0000 −0.842004 −0.421002 0.907060i $$-0.638322\pi$$
−0.421002 + 0.907060i $$0.638322\pi$$
$$458$$ 22.0000 1.02799
$$459$$ 2.00000 0.0933520
$$460$$ 0 0
$$461$$ 2.00000 0.0931493 0.0465746 0.998915i $$-0.485169\pi$$
0.0465746 + 0.998915i $$0.485169\pi$$
$$462$$ 0 0
$$463$$ 24.0000 1.11537 0.557687 0.830051i $$-0.311689\pi$$
0.557687 + 0.830051i $$0.311689\pi$$
$$464$$ 2.00000 0.0928477
$$465$$ 0 0
$$466$$ −18.0000 −0.833834
$$467$$ 28.0000 1.29569 0.647843 0.761774i $$-0.275671\pi$$
0.647843 + 0.761774i $$0.275671\pi$$
$$468$$ 6.00000 0.277350
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −14.0000 −0.645086
$$472$$ −12.0000 −0.552345
$$473$$ 0 0
$$474$$ −8.00000 −0.367452
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −10.0000 −0.457869
$$478$$ 4.00000 0.182956
$$479$$ −32.0000 −1.46212 −0.731059 0.682315i $$-0.760973\pi$$
−0.731059 + 0.682315i $$0.760973\pi$$
$$480$$ 0 0
$$481$$ −12.0000 −0.547153
$$482$$ −6.00000 −0.273293
$$483$$ 0 0
$$484$$ 11.0000 0.500000
$$485$$ 0 0
$$486$$ −1.00000 −0.0453609
$$487$$ 16.0000 0.725029 0.362515 0.931978i $$-0.381918\pi$$
0.362515 + 0.931978i $$0.381918\pi$$
$$488$$ 6.00000 0.271607
$$489$$ −12.0000 −0.542659
$$490$$ 0 0
$$491$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$492$$ −6.00000 −0.270501
$$493$$ −4.00000 −0.180151
$$494$$ 48.0000 2.15962
$$495$$ 0 0
$$496$$ 4.00000 0.179605
$$497$$ 0 0
$$498$$ 4.00000 0.179244
$$499$$ 20.0000 0.895323 0.447661 0.894203i $$-0.352257\pi$$
0.447661 + 0.894203i $$0.352257\pi$$
$$500$$ 0 0
$$501$$ 8.00000 0.357414
$$502$$ −12.0000 −0.535586
$$503$$ −8.00000 −0.356702 −0.178351 0.983967i $$-0.557076\pi$$
−0.178351 + 0.983967i $$0.557076\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 23.0000 1.02147
$$508$$ 8.00000 0.354943
$$509$$ 2.00000 0.0886484 0.0443242 0.999017i $$-0.485887\pi$$
0.0443242 + 0.999017i $$0.485887\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 11.0000 0.486136
$$513$$ 8.00000 0.353209
$$514$$ 6.00000 0.264649
$$515$$ 0 0
$$516$$ 4.00000 0.176090
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 6.00000 0.263371
$$520$$ 0 0
$$521$$ −10.0000 −0.438108 −0.219054 0.975713i $$-0.570297\pi$$
−0.219054 + 0.975713i $$0.570297\pi$$
$$522$$ 2.00000 0.0875376
$$523$$ 20.0000 0.874539 0.437269 0.899331i $$-0.355946\pi$$
0.437269 + 0.899331i $$0.355946\pi$$
$$524$$ 20.0000 0.873704
$$525$$ 0 0
$$526$$ 16.0000 0.697633
$$527$$ −8.00000 −0.348485
$$528$$ 0 0
$$529$$ 41.0000 1.78261
$$530$$ 0 0
$$531$$ −4.00000 −0.173585
$$532$$ 0 0
$$533$$ −36.0000 −1.55933
$$534$$ −6.00000 −0.259645
$$535$$ 0 0
$$536$$ −12.0000 −0.518321
$$537$$ −24.0000 −1.03568
$$538$$ 14.0000 0.603583
$$539$$ 0 0
$$540$$ 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
$$543$$ 2.00000 0.0858282
$$544$$ −10.0000 −0.428746
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 12.0000 0.513083 0.256541 0.966533i $$-0.417417\pi$$
0.256541 + 0.966533i $$0.417417\pi$$
$$548$$ −10.0000 −0.427179
$$549$$ 2.00000 0.0853579
$$550$$ 0 0
$$551$$ −16.0000 −0.681623
$$552$$ −24.0000 −1.02151
$$553$$ 0 0
$$554$$ 14.0000 0.594803
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −2.00000 −0.0847427 −0.0423714 0.999102i $$-0.513491\pi$$
−0.0423714 + 0.999102i $$0.513491\pi$$
$$558$$ 4.00000 0.169334
$$559$$ 24.0000 1.01509
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −18.0000 −0.759284
$$563$$ 4.00000 0.168580 0.0842900 0.996441i $$-0.473138\pi$$
0.0842900 + 0.996441i $$0.473138\pi$$
$$564$$ −8.00000 −0.336861
$$565$$ 0 0
$$566$$ 4.00000 0.168133
$$567$$ 0 0
$$568$$ −36.0000 −1.51053
$$569$$ 42.0000 1.76073 0.880366 0.474295i $$-0.157297\pi$$
0.880366 + 0.474295i $$0.157297\pi$$
$$570$$ 0 0
$$571$$ −36.0000 −1.50655 −0.753277 0.657704i $$-0.771528\pi$$
−0.753277 + 0.657704i $$0.771528\pi$$
$$572$$ 0 0
$$573$$ 4.00000 0.167102
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 7.00000 0.291667
$$577$$ −2.00000 −0.0832611 −0.0416305 0.999133i $$-0.513255\pi$$
−0.0416305 + 0.999133i $$0.513255\pi$$
$$578$$ 13.0000 0.540729
$$579$$ −18.0000 −0.748054
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 18.0000 0.746124
$$583$$ 0 0
$$584$$ −6.00000 −0.248282
$$585$$ 0 0
$$586$$ −14.0000 −0.578335
$$587$$ 12.0000 0.495293 0.247647 0.968850i $$-0.420343\pi$$
0.247647 + 0.968850i $$0.420343\pi$$
$$588$$ 0 0
$$589$$ −32.0000 −1.31854
$$590$$ 0 0
$$591$$ −18.0000 −0.740421
$$592$$ −2.00000 −0.0821995
$$593$$ −30.0000 −1.23195 −0.615976 0.787765i $$-0.711238\pi$$
−0.615976 + 0.787765i $$0.711238\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −14.0000 −0.573462
$$597$$ 4.00000 0.163709
$$598$$ −48.0000 −1.96287
$$599$$ −4.00000 −0.163436 −0.0817178 0.996656i $$-0.526041\pi$$
−0.0817178 + 0.996656i $$0.526041\pi$$
$$600$$ 0 0
$$601$$ −18.0000 −0.734235 −0.367118 0.930175i $$-0.619655\pi$$
−0.367118 + 0.930175i $$0.619655\pi$$
$$602$$ 0 0
$$603$$ −4.00000 −0.162893
$$604$$ −8.00000 −0.325515
$$605$$ 0 0
$$606$$ −10.0000 −0.406222
$$607$$ 8.00000 0.324710 0.162355 0.986732i $$-0.448091\pi$$
0.162355 + 0.986732i $$0.448091\pi$$
$$608$$ −40.0000 −1.62221
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −48.0000 −1.94187
$$612$$ −2.00000 −0.0808452
$$613$$ 18.0000 0.727013 0.363507 0.931592i $$-0.381579\pi$$
0.363507 + 0.931592i $$0.381579\pi$$
$$614$$ −12.0000 −0.484281
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −30.0000 −1.20775 −0.603877 0.797077i $$-0.706378\pi$$
−0.603877 + 0.797077i $$0.706378\pi$$
$$618$$ −8.00000 −0.321807
$$619$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$620$$ 0 0
$$621$$ −8.00000 −0.321029
$$622$$ 24.0000 0.962312
$$623$$ 0 0
$$624$$ 6.00000 0.240192
$$625$$ 0 0
$$626$$ 10.0000 0.399680
$$627$$ 0 0
$$628$$ 14.0000 0.558661
$$629$$ 4.00000 0.159490
$$630$$ 0 0
$$631$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$632$$ 24.0000 0.954669
$$633$$ −20.0000 −0.794929
$$634$$ 2.00000 0.0794301
$$635$$ 0 0
$$636$$ 10.0000 0.396526
$$637$$ 0 0
$$638$$ 0 0
$$639$$ −12.0000 −0.474713
$$640$$ 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
$$643$$ 28.0000 1.10421 0.552106 0.833774i $$-0.313824\pi$$
0.552106 + 0.833774i $$0.313824\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −16.0000 −0.629512
$$647$$ 24.0000 0.943537 0.471769 0.881722i $$-0.343616\pi$$
0.471769 + 0.881722i $$0.343616\pi$$
$$648$$ 3.00000 0.117851
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 12.0000 0.469956
$$653$$ 22.0000 0.860927 0.430463 0.902608i $$-0.358350\pi$$
0.430463 + 0.902608i $$0.358350\pi$$
$$654$$ 18.0000 0.703856
$$655$$ 0 0
$$656$$ −6.00000 −0.234261
$$657$$ −2.00000 −0.0780274
$$658$$ 0 0
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ 0 0
$$661$$ −38.0000 −1.47803 −0.739014 0.673690i $$-0.764708\pi$$
−0.739014 + 0.673690i $$0.764708\pi$$
$$662$$ 12.0000 0.466393
$$663$$ −12.0000 −0.466041
$$664$$ −12.0000 −0.465690
$$665$$ 0 0
$$666$$ −2.00000 −0.0774984
$$667$$ 16.0000 0.619522
$$668$$ −8.00000 −0.309529
$$669$$ −24.0000 −0.927894
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −26.0000 −1.00223 −0.501113 0.865382i $$-0.667076\pi$$
−0.501113 + 0.865382i $$0.667076\pi$$
$$674$$ −14.0000 −0.539260
$$675$$ 0 0
$$676$$ −23.0000 −0.884615
$$677$$ 46.0000 1.76792 0.883962 0.467559i $$-0.154866\pi$$
0.883962 + 0.467559i $$0.154866\pi$$
$$678$$ 6.00000 0.230429
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −4.00000 −0.153280
$$682$$ 0 0
$$683$$ −12.0000 −0.459167 −0.229584 0.973289i $$-0.573736\pi$$
−0.229584 + 0.973289i $$0.573736\pi$$
$$684$$ −8.00000 −0.305888
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −22.0000 −0.839352
$$688$$ 4.00000 0.152499
$$689$$ 60.0000 2.28582
$$690$$ 0 0
$$691$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$692$$ −6.00000 −0.228086
$$693$$ 0 0
$$694$$ −20.0000 −0.759190
$$695$$ 0 0
$$696$$ −6.00000 −0.227429
$$697$$ 12.0000 0.454532
$$698$$ 14.0000 0.529908
$$699$$ 18.0000 0.680823
$$700$$ 0 0
$$701$$ −2.00000 −0.0755390 −0.0377695 0.999286i $$-0.512025\pi$$
−0.0377695 + 0.999286i $$0.512025\pi$$
$$702$$ 6.00000 0.226455
$$703$$ 16.0000 0.603451
$$704$$ 0 0
$$705$$ 0 0
$$706$$ −18.0000 −0.677439
$$707$$ 0 0
$$708$$ 4.00000 0.150329
$$709$$ −26.0000 −0.976450 −0.488225 0.872718i $$-0.662356\pi$$
−0.488225 + 0.872718i $$0.662356\pi$$
$$710$$ 0 0
$$711$$ 8.00000 0.300023
$$712$$ 18.0000 0.674579
$$713$$ 32.0000 1.19841
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 24.0000 0.896922
$$717$$ −4.00000 −0.149383
$$718$$ 36.0000 1.34351
$$719$$ −8.00000 −0.298350 −0.149175 0.988811i $$-0.547662\pi$$
−0.149175 + 0.988811i $$0.547662\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −45.0000 −1.67473
$$723$$ 6.00000 0.223142
$$724$$ −2.00000 −0.0743294
$$725$$ 0 0
$$726$$ 11.0000 0.408248
$$727$$ 16.0000 0.593407 0.296704 0.954970i $$-0.404113\pi$$
0.296704 + 0.954970i $$0.404113\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ −8.00000 −0.295891
$$732$$ −2.00000 −0.0739221
$$733$$ 26.0000 0.960332 0.480166 0.877178i $$-0.340576\pi$$
0.480166 + 0.877178i $$0.340576\pi$$
$$734$$ 8.00000 0.295285
$$735$$ 0 0
$$736$$ 40.0000 1.47442
$$737$$ 0 0
$$738$$ −6.00000 −0.220863
$$739$$ 20.0000 0.735712 0.367856 0.929883i $$-0.380092\pi$$
0.367856 + 0.929883i $$0.380092\pi$$
$$740$$ 0 0
$$741$$ −48.0000 −1.76332
$$742$$ 0 0
$$743$$ 48.0000 1.76095 0.880475 0.474093i $$-0.157224\pi$$
0.880475 + 0.474093i $$0.157224\pi$$
$$744$$ −12.0000 −0.439941
$$745$$ 0 0
$$746$$ −10.0000 −0.366126
$$747$$ −4.00000 −0.146352
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 8.00000 0.291924 0.145962 0.989290i $$-0.453372\pi$$
0.145962 + 0.989290i $$0.453372\pi$$
$$752$$ −8.00000 −0.291730
$$753$$ 12.0000 0.437304
$$754$$ −12.0000 −0.437014
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 10.0000 0.363456 0.181728 0.983349i $$-0.441831\pi$$
0.181728 + 0.983349i $$0.441831\pi$$
$$758$$ 4.00000 0.145287
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 54.0000 1.95750 0.978749 0.205061i $$-0.0657392\pi$$
0.978749 + 0.205061i $$0.0657392\pi$$
$$762$$ 8.00000 0.289809
$$763$$ 0 0
$$764$$ −4.00000 −0.144715
$$765$$ 0 0
$$766$$ 32.0000 1.15621
$$767$$ 24.0000 0.866590
$$768$$ −17.0000 −0.613435
$$769$$ −26.0000 −0.937584 −0.468792 0.883309i $$-0.655311\pi$$
−0.468792 + 0.883309i $$0.655311\pi$$
$$770$$ 0 0
$$771$$ −6.00000 −0.216085
$$772$$ 18.0000 0.647834
$$773$$ 30.0000 1.07903 0.539513 0.841978i $$-0.318609\pi$$
0.539513 + 0.841978i $$0.318609\pi$$
$$774$$ 4.00000 0.143777
$$775$$ 0 0
$$776$$ −54.0000 −1.93849
$$777$$ 0 0
$$778$$ −30.0000 −1.07555
$$779$$ 48.0000 1.71978
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 16.0000 0.572159
$$783$$ −2.00000 −0.0714742
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 20.0000 0.713376
$$787$$ 28.0000 0.998092 0.499046 0.866575i $$-0.333684\pi$$
0.499046 + 0.866575i $$0.333684\pi$$
$$788$$ 18.0000 0.641223
$$789$$ −16.0000 −0.569615
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −12.0000 −0.426132
$$794$$ 22.0000 0.780751
$$795$$ 0 0
$$796$$ −4.00000 −0.141776
$$797$$ 54.0000 1.91278 0.956389 0.292096i $$-0.0943526\pi$$
0.956389 + 0.292096i $$0.0943526\pi$$
$$798$$ 0 0
$$799$$ 16.0000 0.566039
$$800$$ 0 0
$$801$$ 6.00000 0.212000
$$802$$ −18.0000 −0.635602
$$803$$ 0 0
$$804$$ 4.00000 0.141069
$$805$$ 0 0
$$806$$ −24.0000 −0.845364
$$807$$ −14.0000 −0.492823
$$808$$ 30.0000 1.05540
$$809$$ 18.0000 0.632846 0.316423 0.948618i $$-0.397518\pi$$
0.316423 + 0.948618i $$0.397518\pi$$
$$810$$ 0 0
$$811$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$812$$ 0 0
$$813$$ −12.0000 −0.420858
$$814$$ 0 0
$$815$$ 0 0
$$816$$ −2.00000 −0.0700140
$$817$$ −32.0000 −1.11954
$$818$$ −22.0000 −0.769212
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −42.0000 −1.46581 −0.732905 0.680331i $$-0.761836\pi$$
−0.732905 + 0.680331i $$0.761836\pi$$
$$822$$ −10.0000 −0.348790
$$823$$ 16.0000 0.557725 0.278862 0.960331i $$-0.410043\pi$$
0.278862 + 0.960331i $$0.410043\pi$$
$$824$$ 24.0000 0.836080
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 12.0000 0.417281 0.208640 0.977992i $$-0.433096\pi$$
0.208640 + 0.977992i $$0.433096\pi$$
$$828$$ 8.00000 0.278019
$$829$$ 42.0000 1.45872 0.729360 0.684130i $$-0.239818\pi$$
0.729360 + 0.684130i $$0.239818\pi$$
$$830$$ 0 0
$$831$$ −14.0000 −0.485655
$$832$$ −42.0000 −1.45609
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 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
$$841$$ −25.0000 −0.862069
$$842$$ 26.0000 0.896019
$$843$$ 18.0000 0.619953
$$844$$ 20.0000 0.688428
$$845$$ 0 0
$$846$$ −8.00000 −0.275046
$$847$$ 0 0
$$848$$ 10.0000 0.343401
$$849$$ −4.00000 −0.137280
$$850$$ 0 0
$$851$$ −16.0000 −0.548473
$$852$$ 12.0000 0.411113
$$853$$ −30.0000 −1.02718 −0.513590 0.858036i $$-0.671685\pi$$
−0.513590 + 0.858036i $$0.671685\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 36.0000 1.23045
$$857$$ 18.0000 0.614868 0.307434 0.951569i $$-0.400530\pi$$
0.307434 + 0.951569i $$0.400530\pi$$
$$858$$ 0 0
$$859$$ 40.0000 1.36478 0.682391 0.730987i $$-0.260940\pi$$
0.682391 + 0.730987i $$0.260940\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ −28.0000 −0.953684
$$863$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$864$$ −5.00000 −0.170103
$$865$$ 0 0
$$866$$ 2.00000 0.0679628
$$867$$ −13.0000 −0.441503
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 24.0000 0.813209
$$872$$ −54.0000 −1.82867
$$873$$ −18.0000 −0.609208
$$874$$ 64.0000 2.16483
$$875$$ 0 0
$$876$$ 2.00000 0.0675737
$$877$$ 58.0000 1.95852 0.979260 0.202606i $$-0.0649409\pi$$
0.979260 + 0.202606i $$0.0649409\pi$$
$$878$$ 28.0000 0.944954
$$879$$ 14.0000 0.472208
$$880$$ 0 0
$$881$$ 30.0000 1.01073 0.505363 0.862907i $$-0.331359\pi$$
0.505363 + 0.862907i $$0.331359\pi$$
$$882$$ 0 0
$$883$$ −4.00000 −0.134611 −0.0673054 0.997732i $$-0.521440\pi$$
−0.0673054 + 0.997732i $$0.521440\pi$$
$$884$$ 12.0000 0.403604
$$885$$ 0 0
$$886$$ 12.0000 0.403148
$$887$$ 16.0000 0.537227 0.268614 0.963248i $$-0.413434\pi$$
0.268614 + 0.963248i $$0.413434\pi$$
$$888$$ 6.00000 0.201347
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 24.0000 0.803579
$$893$$ 64.0000 2.14168
$$894$$ −14.0000 −0.468230
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 48.0000 1.60267
$$898$$ 30.0000 1.00111
$$899$$ 8.00000 0.266815
$$900$$ 0 0
$$901$$ −20.0000 −0.666297
$$902$$ 0 0
$$903$$ 0 0
$$904$$ −18.0000 −0.598671
$$905$$ 0 0
$$906$$ −8.00000 −0.265782
$$907$$ −28.0000 −0.929725 −0.464862 0.885383i $$-0.653896\pi$$
−0.464862 + 0.885383i $$0.653896\pi$$
$$908$$ 4.00000 0.132745
$$909$$ 10.0000 0.331679
$$910$$ 0 0
$$911$$ 36.0000 1.19273 0.596367 0.802712i $$-0.296610\pi$$
0.596367 + 0.802712i $$0.296610\pi$$
$$912$$ −8.00000 −0.264906
$$913$$ 0 0
$$914$$ 18.0000 0.595387
$$915$$ 0 0
$$916$$ 22.0000 0.726900
$$917$$ 0 0
$$918$$ −2.00000 −0.0660098
$$919$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$920$$ 0 0
$$921$$ 12.0000 0.395413
$$922$$ −2.00000 −0.0658665
$$923$$ 72.0000 2.36991
$$924$$ 0 0
$$925$$ 0 0
$$926$$ −24.0000 −0.788689
$$927$$ 8.00000 0.262754
$$928$$ 10.0000 0.328266
$$929$$ 14.0000 0.459325 0.229663 0.973270i $$-0.426238\pi$$
0.229663 + 0.973270i $$0.426238\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ −18.0000 −0.589610
$$933$$ −24.0000 −0.785725
$$934$$ −28.0000 −0.916188
$$935$$ 0 0
$$936$$ −18.0000 −0.588348
$$937$$ −2.00000 −0.0653372 −0.0326686 0.999466i $$-0.510401\pi$$
−0.0326686 + 0.999466i $$0.510401\pi$$
$$938$$ 0 0
$$939$$ −10.0000 −0.326338
$$940$$ 0 0
$$941$$ 18.0000 0.586783 0.293392 0.955992i $$-0.405216\pi$$
0.293392 + 0.955992i $$0.405216\pi$$
$$942$$ 14.0000 0.456145
$$943$$ −48.0000 −1.56310
$$944$$ 4.00000 0.130189
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −20.0000 −0.649913 −0.324956 0.945729i $$-0.605350\pi$$
−0.324956 + 0.945729i $$0.605350\pi$$
$$948$$ −8.00000 −0.259828
$$949$$ 12.0000 0.389536
$$950$$ 0 0
$$951$$ −2.00000 −0.0648544
$$952$$ 0 0
$$953$$ 2.00000 0.0647864 0.0323932 0.999475i $$-0.489687\pi$$
0.0323932 + 0.999475i $$0.489687\pi$$
$$954$$ 10.0000 0.323762
$$955$$ 0 0
$$956$$ 4.00000 0.129369
$$957$$ 0 0
$$958$$ 32.0000 1.03387
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −15.0000 −0.483871
$$962$$ 12.0000 0.386896
$$963$$ 12.0000 0.386695
$$964$$ −6.00000 −0.193247
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 8.00000 0.257263 0.128631 0.991692i $$-0.458942\pi$$
0.128631 + 0.991692i $$0.458942\pi$$
$$968$$ −33.0000 −1.06066
$$969$$ 16.0000 0.513994
$$970$$ 0 0
$$971$$ −20.0000 −0.641831 −0.320915 0.947108i $$-0.603990\pi$$
−0.320915 + 0.947108i $$0.603990\pi$$
$$972$$ −1.00000 −0.0320750
$$973$$ 0 0
$$974$$ −16.0000 −0.512673
$$975$$ 0 0
$$976$$ −2.00000 −0.0640184
$$977$$ 10.0000 0.319928 0.159964 0.987123i $$-0.448862\pi$$
0.159964 + 0.987123i $$0.448862\pi$$
$$978$$ 12.0000 0.383718
$$979$$ 0 0
$$980$$ 0 0
$$981$$ −18.0000 −0.574696
$$982$$ 0 0
$$983$$ −16.0000 −0.510321 −0.255160 0.966899i $$-0.582128\pi$$
−0.255160 + 0.966899i $$0.582128\pi$$
$$984$$ 18.0000 0.573819
$$985$$ 0 0
$$986$$ 4.00000 0.127386
$$987$$ 0 0
$$988$$ 48.0000 1.52708
$$989$$ 32.0000 1.01754
$$990$$ 0 0
$$991$$ −24.0000 −0.762385 −0.381193 0.924496i $$-0.624487\pi$$
−0.381193 + 0.924496i $$0.624487\pi$$
$$992$$ 20.0000 0.635001
$$993$$ −12.0000 −0.380808
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 4.00000 0.126745
$$997$$ 2.00000 0.0633406 0.0316703 0.999498i $$-0.489917\pi$$
0.0316703 + 0.999498i $$0.489917\pi$$
$$998$$ −20.0000 −0.633089
$$999$$ 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 3675.2.a.f.1.1 1
5.4 even 2 735.2.a.f.1.1 1
7.6 odd 2 525.2.a.a.1.1 1
15.14 odd 2 2205.2.a.b.1.1 1
21.20 even 2 1575.2.a.h.1.1 1
28.27 even 2 8400.2.a.co.1.1 1
35.4 even 6 735.2.i.b.226.1 2
35.9 even 6 735.2.i.b.361.1 2
35.13 even 4 525.2.d.b.274.2 2
35.19 odd 6 735.2.i.a.361.1 2
35.24 odd 6 735.2.i.a.226.1 2
35.27 even 4 525.2.d.b.274.1 2
35.34 odd 2 105.2.a.a.1.1 1
105.62 odd 4 1575.2.d.b.1324.2 2
105.83 odd 4 1575.2.d.b.1324.1 2
105.104 even 2 315.2.a.a.1.1 1
140.139 even 2 1680.2.a.f.1.1 1
280.69 odd 2 6720.2.a.p.1.1 1
280.139 even 2 6720.2.a.bk.1.1 1
420.419 odd 2 5040.2.a.d.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.a.a.1.1 1 35.34 odd 2
315.2.a.a.1.1 1 105.104 even 2
525.2.a.a.1.1 1 7.6 odd 2
525.2.d.b.274.1 2 35.27 even 4
525.2.d.b.274.2 2 35.13 even 4
735.2.a.f.1.1 1 5.4 even 2
735.2.i.a.226.1 2 35.24 odd 6
735.2.i.a.361.1 2 35.19 odd 6
735.2.i.b.226.1 2 35.4 even 6
735.2.i.b.361.1 2 35.9 even 6
1575.2.a.h.1.1 1 21.20 even 2
1575.2.d.b.1324.1 2 105.83 odd 4
1575.2.d.b.1324.2 2 105.62 odd 4
1680.2.a.f.1.1 1 140.139 even 2
2205.2.a.b.1.1 1 15.14 odd 2
3675.2.a.f.1.1 1 1.1 even 1 trivial
5040.2.a.d.1.1 1 420.419 odd 2
6720.2.a.p.1.1 1 280.69 odd 2
6720.2.a.bk.1.1 1 280.139 even 2
8400.2.a.co.1.1 1 28.27 even 2