# Properties

 Label 3549.2.a.a.1.1 Level $3549$ Weight $2$ Character 3549.1 Self dual yes Analytic conductor $28.339$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$3549 = 3 \cdot 7 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3549.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$28.3389076774$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 273) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 3549.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-2.00000 q^{2} +1.00000 q^{3} +2.00000 q^{4} -3.00000 q^{5} -2.00000 q^{6} -1.00000 q^{7} +1.00000 q^{9} +O(q^{10})$$ $$q-2.00000 q^{2} +1.00000 q^{3} +2.00000 q^{4} -3.00000 q^{5} -2.00000 q^{6} -1.00000 q^{7} +1.00000 q^{9} +6.00000 q^{10} +2.00000 q^{12} +2.00000 q^{14} -3.00000 q^{15} -4.00000 q^{16} +2.00000 q^{17} -2.00000 q^{18} -1.00000 q^{19} -6.00000 q^{20} -1.00000 q^{21} +1.00000 q^{23} +4.00000 q^{25} +1.00000 q^{27} -2.00000 q^{28} +5.00000 q^{29} +6.00000 q^{30} -5.00000 q^{31} +8.00000 q^{32} -4.00000 q^{34} +3.00000 q^{35} +2.00000 q^{36} -8.00000 q^{37} +2.00000 q^{38} +10.0000 q^{41} +2.00000 q^{42} -9.00000 q^{43} -3.00000 q^{45} -2.00000 q^{46} +7.00000 q^{47} -4.00000 q^{48} +1.00000 q^{49} -8.00000 q^{50} +2.00000 q^{51} +9.00000 q^{53} -2.00000 q^{54} -1.00000 q^{57} -10.0000 q^{58} -4.00000 q^{59} -6.00000 q^{60} -8.00000 q^{61} +10.0000 q^{62} -1.00000 q^{63} -8.00000 q^{64} -2.00000 q^{67} +4.00000 q^{68} +1.00000 q^{69} -6.00000 q^{70} +9.00000 q^{73} +16.0000 q^{74} +4.00000 q^{75} -2.00000 q^{76} +15.0000 q^{79} +12.0000 q^{80} +1.00000 q^{81} -20.0000 q^{82} -9.00000 q^{83} -2.00000 q^{84} -6.00000 q^{85} +18.0000 q^{86} +5.00000 q^{87} -9.00000 q^{89} +6.00000 q^{90} +2.00000 q^{92} -5.00000 q^{93} -14.0000 q^{94} +3.00000 q^{95} +8.00000 q^{96} +13.0000 q^{97} -2.00000 q^{98} +O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −2.00000 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$3$$ 1.00000 0.577350
$$4$$ 2.00000 1.00000
$$5$$ −3.00000 −1.34164 −0.670820 0.741620i $$-0.734058\pi$$
−0.670820 + 0.741620i $$0.734058\pi$$
$$6$$ −2.00000 −0.816497
$$7$$ −1.00000 −0.377964
$$8$$ 0 0
$$9$$ 1.00000 0.333333
$$10$$ 6.00000 1.89737
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ 2.00000 0.577350
$$13$$ 0 0
$$14$$ 2.00000 0.534522
$$15$$ −3.00000 −0.774597
$$16$$ −4.00000 −1.00000
$$17$$ 2.00000 0.485071 0.242536 0.970143i $$-0.422021\pi$$
0.242536 + 0.970143i $$0.422021\pi$$
$$18$$ −2.00000 −0.471405
$$19$$ −1.00000 −0.229416 −0.114708 0.993399i $$-0.536593\pi$$
−0.114708 + 0.993399i $$0.536593\pi$$
$$20$$ −6.00000 −1.34164
$$21$$ −1.00000 −0.218218
$$22$$ 0 0
$$23$$ 1.00000 0.208514 0.104257 0.994550i $$-0.466753\pi$$
0.104257 + 0.994550i $$0.466753\pi$$
$$24$$ 0 0
$$25$$ 4.00000 0.800000
$$26$$ 0 0
$$27$$ 1.00000 0.192450
$$28$$ −2.00000 −0.377964
$$29$$ 5.00000 0.928477 0.464238 0.885710i $$-0.346328\pi$$
0.464238 + 0.885710i $$0.346328\pi$$
$$30$$ 6.00000 1.09545
$$31$$ −5.00000 −0.898027 −0.449013 0.893525i $$-0.648224\pi$$
−0.449013 + 0.893525i $$0.648224\pi$$
$$32$$ 8.00000 1.41421
$$33$$ 0 0
$$34$$ −4.00000 −0.685994
$$35$$ 3.00000 0.507093
$$36$$ 2.00000 0.333333
$$37$$ −8.00000 −1.31519 −0.657596 0.753371i $$-0.728427\pi$$
−0.657596 + 0.753371i $$0.728427\pi$$
$$38$$ 2.00000 0.324443
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 10.0000 1.56174 0.780869 0.624695i $$-0.214777\pi$$
0.780869 + 0.624695i $$0.214777\pi$$
$$42$$ 2.00000 0.308607
$$43$$ −9.00000 −1.37249 −0.686244 0.727372i $$-0.740742\pi$$
−0.686244 + 0.727372i $$0.740742\pi$$
$$44$$ 0 0
$$45$$ −3.00000 −0.447214
$$46$$ −2.00000 −0.294884
$$47$$ 7.00000 1.02105 0.510527 0.859861i $$-0.329450\pi$$
0.510527 + 0.859861i $$0.329450\pi$$
$$48$$ −4.00000 −0.577350
$$49$$ 1.00000 0.142857
$$50$$ −8.00000 −1.13137
$$51$$ 2.00000 0.280056
$$52$$ 0 0
$$53$$ 9.00000 1.23625 0.618123 0.786082i $$-0.287894\pi$$
0.618123 + 0.786082i $$0.287894\pi$$
$$54$$ −2.00000 −0.272166
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −1.00000 −0.132453
$$58$$ −10.0000 −1.31306
$$59$$ −4.00000 −0.520756 −0.260378 0.965507i $$-0.583847\pi$$
−0.260378 + 0.965507i $$0.583847\pi$$
$$60$$ −6.00000 −0.774597
$$61$$ −8.00000 −1.02430 −0.512148 0.858898i $$-0.671150\pi$$
−0.512148 + 0.858898i $$0.671150\pi$$
$$62$$ 10.0000 1.27000
$$63$$ −1.00000 −0.125988
$$64$$ −8.00000 −1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −2.00000 −0.244339 −0.122169 0.992509i $$-0.538985\pi$$
−0.122169 + 0.992509i $$0.538985\pi$$
$$68$$ 4.00000 0.485071
$$69$$ 1.00000 0.120386
$$70$$ −6.00000 −0.717137
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ 9.00000 1.05337 0.526685 0.850060i $$-0.323435\pi$$
0.526685 + 0.850060i $$0.323435\pi$$
$$74$$ 16.0000 1.85996
$$75$$ 4.00000 0.461880
$$76$$ −2.00000 −0.229416
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 15.0000 1.68763 0.843816 0.536633i $$-0.180304\pi$$
0.843816 + 0.536633i $$0.180304\pi$$
$$80$$ 12.0000 1.34164
$$81$$ 1.00000 0.111111
$$82$$ −20.0000 −2.20863
$$83$$ −9.00000 −0.987878 −0.493939 0.869496i $$-0.664443\pi$$
−0.493939 + 0.869496i $$0.664443\pi$$
$$84$$ −2.00000 −0.218218
$$85$$ −6.00000 −0.650791
$$86$$ 18.0000 1.94099
$$87$$ 5.00000 0.536056
$$88$$ 0 0
$$89$$ −9.00000 −0.953998 −0.476999 0.878904i $$-0.658275\pi$$
−0.476999 + 0.878904i $$0.658275\pi$$
$$90$$ 6.00000 0.632456
$$91$$ 0 0
$$92$$ 2.00000 0.208514
$$93$$ −5.00000 −0.518476
$$94$$ −14.0000 −1.44399
$$95$$ 3.00000 0.307794
$$96$$ 8.00000 0.816497
$$97$$ 13.0000 1.31995 0.659975 0.751288i $$-0.270567\pi$$
0.659975 + 0.751288i $$0.270567\pi$$
$$98$$ −2.00000 −0.202031
$$99$$ 0 0
$$100$$ 8.00000 0.800000
$$101$$ 8.00000 0.796030 0.398015 0.917379i $$-0.369699\pi$$
0.398015 + 0.917379i $$0.369699\pi$$
$$102$$ −4.00000 −0.396059
$$103$$ 16.0000 1.57653 0.788263 0.615338i $$-0.210980\pi$$
0.788263 + 0.615338i $$0.210980\pi$$
$$104$$ 0 0
$$105$$ 3.00000 0.292770
$$106$$ −18.0000 −1.74831
$$107$$ −12.0000 −1.16008 −0.580042 0.814587i $$-0.696964\pi$$
−0.580042 + 0.814587i $$0.696964\pi$$
$$108$$ 2.00000 0.192450
$$109$$ 14.0000 1.34096 0.670478 0.741929i $$-0.266089\pi$$
0.670478 + 0.741929i $$0.266089\pi$$
$$110$$ 0 0
$$111$$ −8.00000 −0.759326
$$112$$ 4.00000 0.377964
$$113$$ −21.0000 −1.97551 −0.987757 0.156001i $$-0.950140\pi$$
−0.987757 + 0.156001i $$0.950140\pi$$
$$114$$ 2.00000 0.187317
$$115$$ −3.00000 −0.279751
$$116$$ 10.0000 0.928477
$$117$$ 0 0
$$118$$ 8.00000 0.736460
$$119$$ −2.00000 −0.183340
$$120$$ 0 0
$$121$$ −11.0000 −1.00000
$$122$$ 16.0000 1.44857
$$123$$ 10.0000 0.901670
$$124$$ −10.0000 −0.898027
$$125$$ 3.00000 0.268328
$$126$$ 2.00000 0.178174
$$127$$ −8.00000 −0.709885 −0.354943 0.934888i $$-0.615500\pi$$
−0.354943 + 0.934888i $$0.615500\pi$$
$$128$$ 0 0
$$129$$ −9.00000 −0.792406
$$130$$ 0 0
$$131$$ −18.0000 −1.57267 −0.786334 0.617802i $$-0.788023\pi$$
−0.786334 + 0.617802i $$0.788023\pi$$
$$132$$ 0 0
$$133$$ 1.00000 0.0867110
$$134$$ 4.00000 0.345547
$$135$$ −3.00000 −0.258199
$$136$$ 0 0
$$137$$ 12.0000 1.02523 0.512615 0.858619i $$-0.328677\pi$$
0.512615 + 0.858619i $$0.328677\pi$$
$$138$$ −2.00000 −0.170251
$$139$$ −20.0000 −1.69638 −0.848189 0.529694i $$-0.822307\pi$$
−0.848189 + 0.529694i $$0.822307\pi$$
$$140$$ 6.00000 0.507093
$$141$$ 7.00000 0.589506
$$142$$ 0 0
$$143$$ 0 0
$$144$$ −4.00000 −0.333333
$$145$$ −15.0000 −1.24568
$$146$$ −18.0000 −1.48969
$$147$$ 1.00000 0.0824786
$$148$$ −16.0000 −1.31519
$$149$$ 4.00000 0.327693 0.163846 0.986486i $$-0.447610\pi$$
0.163846 + 0.986486i $$0.447610\pi$$
$$150$$ −8.00000 −0.653197
$$151$$ −20.0000 −1.62758 −0.813788 0.581161i $$-0.802599\pi$$
−0.813788 + 0.581161i $$0.802599\pi$$
$$152$$ 0 0
$$153$$ 2.00000 0.161690
$$154$$ 0 0
$$155$$ 15.0000 1.20483
$$156$$ 0 0
$$157$$ −2.00000 −0.159617 −0.0798087 0.996810i $$-0.525431\pi$$
−0.0798087 + 0.996810i $$0.525431\pi$$
$$158$$ −30.0000 −2.38667
$$159$$ 9.00000 0.713746
$$160$$ −24.0000 −1.89737
$$161$$ −1.00000 −0.0788110
$$162$$ −2.00000 −0.157135
$$163$$ −6.00000 −0.469956 −0.234978 0.972001i $$-0.575502\pi$$
−0.234978 + 0.972001i $$0.575502\pi$$
$$164$$ 20.0000 1.56174
$$165$$ 0 0
$$166$$ 18.0000 1.39707
$$167$$ −3.00000 −0.232147 −0.116073 0.993241i $$-0.537031\pi$$
−0.116073 + 0.993241i $$0.537031\pi$$
$$168$$ 0 0
$$169$$ 0 0
$$170$$ 12.0000 0.920358
$$171$$ −1.00000 −0.0764719
$$172$$ −18.0000 −1.37249
$$173$$ −24.0000 −1.82469 −0.912343 0.409426i $$-0.865729\pi$$
−0.912343 + 0.409426i $$0.865729\pi$$
$$174$$ −10.0000 −0.758098
$$175$$ −4.00000 −0.302372
$$176$$ 0 0
$$177$$ −4.00000 −0.300658
$$178$$ 18.0000 1.34916
$$179$$ 5.00000 0.373718 0.186859 0.982387i $$-0.440169\pi$$
0.186859 + 0.982387i $$0.440169\pi$$
$$180$$ −6.00000 −0.447214
$$181$$ 8.00000 0.594635 0.297318 0.954779i $$-0.403908\pi$$
0.297318 + 0.954779i $$0.403908\pi$$
$$182$$ 0 0
$$183$$ −8.00000 −0.591377
$$184$$ 0 0
$$185$$ 24.0000 1.76452
$$186$$ 10.0000 0.733236
$$187$$ 0 0
$$188$$ 14.0000 1.02105
$$189$$ −1.00000 −0.0727393
$$190$$ −6.00000 −0.435286
$$191$$ −8.00000 −0.578860 −0.289430 0.957199i $$-0.593466\pi$$
−0.289430 + 0.957199i $$0.593466\pi$$
$$192$$ −8.00000 −0.577350
$$193$$ 14.0000 1.00774 0.503871 0.863779i $$-0.331909\pi$$
0.503871 + 0.863779i $$0.331909\pi$$
$$194$$ −26.0000 −1.86669
$$195$$ 0 0
$$196$$ 2.00000 0.142857
$$197$$ −12.0000 −0.854965 −0.427482 0.904024i $$-0.640599\pi$$
−0.427482 + 0.904024i $$0.640599\pi$$
$$198$$ 0 0
$$199$$ −10.0000 −0.708881 −0.354441 0.935079i $$-0.615329\pi$$
−0.354441 + 0.935079i $$0.615329\pi$$
$$200$$ 0 0
$$201$$ −2.00000 −0.141069
$$202$$ −16.0000 −1.12576
$$203$$ −5.00000 −0.350931
$$204$$ 4.00000 0.280056
$$205$$ −30.0000 −2.09529
$$206$$ −32.0000 −2.22955
$$207$$ 1.00000 0.0695048
$$208$$ 0 0
$$209$$ 0 0
$$210$$ −6.00000 −0.414039
$$211$$ −13.0000 −0.894957 −0.447478 0.894295i $$-0.647678\pi$$
−0.447478 + 0.894295i $$0.647678\pi$$
$$212$$ 18.0000 1.23625
$$213$$ 0 0
$$214$$ 24.0000 1.64061
$$215$$ 27.0000 1.84138
$$216$$ 0 0
$$217$$ 5.00000 0.339422
$$218$$ −28.0000 −1.89640
$$219$$ 9.00000 0.608164
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 16.0000 1.07385
$$223$$ −19.0000 −1.27233 −0.636167 0.771551i $$-0.719481\pi$$
−0.636167 + 0.771551i $$0.719481\pi$$
$$224$$ −8.00000 −0.534522
$$225$$ 4.00000 0.266667
$$226$$ 42.0000 2.79380
$$227$$ −12.0000 −0.796468 −0.398234 0.917284i $$-0.630377\pi$$
−0.398234 + 0.917284i $$0.630377\pi$$
$$228$$ −2.00000 −0.132453
$$229$$ −14.0000 −0.925146 −0.462573 0.886581i $$-0.653074\pi$$
−0.462573 + 0.886581i $$0.653074\pi$$
$$230$$ 6.00000 0.395628
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 1.00000 0.0655122 0.0327561 0.999463i $$-0.489572\pi$$
0.0327561 + 0.999463i $$0.489572\pi$$
$$234$$ 0 0
$$235$$ −21.0000 −1.36989
$$236$$ −8.00000 −0.520756
$$237$$ 15.0000 0.974355
$$238$$ 4.00000 0.259281
$$239$$ −6.00000 −0.388108 −0.194054 0.980991i $$-0.562164\pi$$
−0.194054 + 0.980991i $$0.562164\pi$$
$$240$$ 12.0000 0.774597
$$241$$ −15.0000 −0.966235 −0.483117 0.875556i $$-0.660496\pi$$
−0.483117 + 0.875556i $$0.660496\pi$$
$$242$$ 22.0000 1.41421
$$243$$ 1.00000 0.0641500
$$244$$ −16.0000 −1.02430
$$245$$ −3.00000 −0.191663
$$246$$ −20.0000 −1.27515
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −9.00000 −0.570352
$$250$$ −6.00000 −0.379473
$$251$$ 28.0000 1.76734 0.883672 0.468106i $$-0.155064\pi$$
0.883672 + 0.468106i $$0.155064\pi$$
$$252$$ −2.00000 −0.125988
$$253$$ 0 0
$$254$$ 16.0000 1.00393
$$255$$ −6.00000 −0.375735
$$256$$ 16.0000 1.00000
$$257$$ 12.0000 0.748539 0.374270 0.927320i $$-0.377893\pi$$
0.374270 + 0.927320i $$0.377893\pi$$
$$258$$ 18.0000 1.12063
$$259$$ 8.00000 0.497096
$$260$$ 0 0
$$261$$ 5.00000 0.309492
$$262$$ 36.0000 2.22409
$$263$$ 19.0000 1.17159 0.585795 0.810459i $$-0.300782\pi$$
0.585795 + 0.810459i $$0.300782\pi$$
$$264$$ 0 0
$$265$$ −27.0000 −1.65860
$$266$$ −2.00000 −0.122628
$$267$$ −9.00000 −0.550791
$$268$$ −4.00000 −0.244339
$$269$$ 10.0000 0.609711 0.304855 0.952399i $$-0.401392\pi$$
0.304855 + 0.952399i $$0.401392\pi$$
$$270$$ 6.00000 0.365148
$$271$$ 20.0000 1.21491 0.607457 0.794353i $$-0.292190\pi$$
0.607457 + 0.794353i $$0.292190\pi$$
$$272$$ −8.00000 −0.485071
$$273$$ 0 0
$$274$$ −24.0000 −1.44989
$$275$$ 0 0
$$276$$ 2.00000 0.120386
$$277$$ −3.00000 −0.180253 −0.0901263 0.995930i $$-0.528727\pi$$
−0.0901263 + 0.995930i $$0.528727\pi$$
$$278$$ 40.0000 2.39904
$$279$$ −5.00000 −0.299342
$$280$$ 0 0
$$281$$ 10.0000 0.596550 0.298275 0.954480i $$-0.403589\pi$$
0.298275 + 0.954480i $$0.403589\pi$$
$$282$$ −14.0000 −0.833688
$$283$$ −24.0000 −1.42665 −0.713326 0.700832i $$-0.752812\pi$$
−0.713326 + 0.700832i $$0.752812\pi$$
$$284$$ 0 0
$$285$$ 3.00000 0.177705
$$286$$ 0 0
$$287$$ −10.0000 −0.590281
$$288$$ 8.00000 0.471405
$$289$$ −13.0000 −0.764706
$$290$$ 30.0000 1.76166
$$291$$ 13.0000 0.762073
$$292$$ 18.0000 1.05337
$$293$$ −31.0000 −1.81104 −0.905520 0.424304i $$-0.860519\pi$$
−0.905520 + 0.424304i $$0.860519\pi$$
$$294$$ −2.00000 −0.116642
$$295$$ 12.0000 0.698667
$$296$$ 0 0
$$297$$ 0 0
$$298$$ −8.00000 −0.463428
$$299$$ 0 0
$$300$$ 8.00000 0.461880
$$301$$ 9.00000 0.518751
$$302$$ 40.0000 2.30174
$$303$$ 8.00000 0.459588
$$304$$ 4.00000 0.229416
$$305$$ 24.0000 1.37424
$$306$$ −4.00000 −0.228665
$$307$$ 17.0000 0.970241 0.485121 0.874447i $$-0.338776\pi$$
0.485121 + 0.874447i $$0.338776\pi$$
$$308$$ 0 0
$$309$$ 16.0000 0.910208
$$310$$ −30.0000 −1.70389
$$311$$ −2.00000 −0.113410 −0.0567048 0.998391i $$-0.518059\pi$$
−0.0567048 + 0.998391i $$0.518059\pi$$
$$312$$ 0 0
$$313$$ 4.00000 0.226093 0.113047 0.993590i $$-0.463939\pi$$
0.113047 + 0.993590i $$0.463939\pi$$
$$314$$ 4.00000 0.225733
$$315$$ 3.00000 0.169031
$$316$$ 30.0000 1.68763
$$317$$ −2.00000 −0.112331 −0.0561656 0.998421i $$-0.517887\pi$$
−0.0561656 + 0.998421i $$0.517887\pi$$
$$318$$ −18.0000 −1.00939
$$319$$ 0 0
$$320$$ 24.0000 1.34164
$$321$$ −12.0000 −0.669775
$$322$$ 2.00000 0.111456
$$323$$ −2.00000 −0.111283
$$324$$ 2.00000 0.111111
$$325$$ 0 0
$$326$$ 12.0000 0.664619
$$327$$ 14.0000 0.774202
$$328$$ 0 0
$$329$$ −7.00000 −0.385922
$$330$$ 0 0
$$331$$ −20.0000 −1.09930 −0.549650 0.835395i $$-0.685239\pi$$
−0.549650 + 0.835395i $$0.685239\pi$$
$$332$$ −18.0000 −0.987878
$$333$$ −8.00000 −0.438397
$$334$$ 6.00000 0.328305
$$335$$ 6.00000 0.327815
$$336$$ 4.00000 0.218218
$$337$$ −23.0000 −1.25289 −0.626445 0.779466i $$-0.715491\pi$$
−0.626445 + 0.779466i $$0.715491\pi$$
$$338$$ 0 0
$$339$$ −21.0000 −1.14056
$$340$$ −12.0000 −0.650791
$$341$$ 0 0
$$342$$ 2.00000 0.108148
$$343$$ −1.00000 −0.0539949
$$344$$ 0 0
$$345$$ −3.00000 −0.161515
$$346$$ 48.0000 2.58050
$$347$$ −12.0000 −0.644194 −0.322097 0.946707i $$-0.604388\pi$$
−0.322097 + 0.946707i $$0.604388\pi$$
$$348$$ 10.0000 0.536056
$$349$$ 1.00000 0.0535288 0.0267644 0.999642i $$-0.491480\pi$$
0.0267644 + 0.999642i $$0.491480\pi$$
$$350$$ 8.00000 0.427618
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 6.00000 0.319348 0.159674 0.987170i $$-0.448956\pi$$
0.159674 + 0.987170i $$0.448956\pi$$
$$354$$ 8.00000 0.425195
$$355$$ 0 0
$$356$$ −18.0000 −0.953998
$$357$$ −2.00000 −0.105851
$$358$$ −10.0000 −0.528516
$$359$$ −14.0000 −0.738892 −0.369446 0.929252i $$-0.620452\pi$$
−0.369446 + 0.929252i $$0.620452\pi$$
$$360$$ 0 0
$$361$$ −18.0000 −0.947368
$$362$$ −16.0000 −0.840941
$$363$$ −11.0000 −0.577350
$$364$$ 0 0
$$365$$ −27.0000 −1.41324
$$366$$ 16.0000 0.836333
$$367$$ 18.0000 0.939592 0.469796 0.882775i $$-0.344327\pi$$
0.469796 + 0.882775i $$0.344327\pi$$
$$368$$ −4.00000 −0.208514
$$369$$ 10.0000 0.520579
$$370$$ −48.0000 −2.49540
$$371$$ −9.00000 −0.467257
$$372$$ −10.0000 −0.518476
$$373$$ −26.0000 −1.34623 −0.673114 0.739538i $$-0.735044\pi$$
−0.673114 + 0.739538i $$0.735044\pi$$
$$374$$ 0 0
$$375$$ 3.00000 0.154919
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 2.00000 0.102869
$$379$$ 4.00000 0.205466 0.102733 0.994709i $$-0.467241\pi$$
0.102733 + 0.994709i $$0.467241\pi$$
$$380$$ 6.00000 0.307794
$$381$$ −8.00000 −0.409852
$$382$$ 16.0000 0.818631
$$383$$ 16.0000 0.817562 0.408781 0.912633i $$-0.365954\pi$$
0.408781 + 0.912633i $$0.365954\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −28.0000 −1.42516
$$387$$ −9.00000 −0.457496
$$388$$ 26.0000 1.31995
$$389$$ −30.0000 −1.52106 −0.760530 0.649303i $$-0.775061\pi$$
−0.760530 + 0.649303i $$0.775061\pi$$
$$390$$ 0 0
$$391$$ 2.00000 0.101144
$$392$$ 0 0
$$393$$ −18.0000 −0.907980
$$394$$ 24.0000 1.20910
$$395$$ −45.0000 −2.26420
$$396$$ 0 0
$$397$$ 17.0000 0.853206 0.426603 0.904439i $$-0.359710\pi$$
0.426603 + 0.904439i $$0.359710\pi$$
$$398$$ 20.0000 1.00251
$$399$$ 1.00000 0.0500626
$$400$$ −16.0000 −0.800000
$$401$$ −10.0000 −0.499376 −0.249688 0.968326i $$-0.580328\pi$$
−0.249688 + 0.968326i $$0.580328\pi$$
$$402$$ 4.00000 0.199502
$$403$$ 0 0
$$404$$ 16.0000 0.796030
$$405$$ −3.00000 −0.149071
$$406$$ 10.0000 0.496292
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −31.0000 −1.53285 −0.766426 0.642333i $$-0.777967\pi$$
−0.766426 + 0.642333i $$0.777967\pi$$
$$410$$ 60.0000 2.96319
$$411$$ 12.0000 0.591916
$$412$$ 32.0000 1.57653
$$413$$ 4.00000 0.196827
$$414$$ −2.00000 −0.0982946
$$415$$ 27.0000 1.32538
$$416$$ 0 0
$$417$$ −20.0000 −0.979404
$$418$$ 0 0
$$419$$ −20.0000 −0.977064 −0.488532 0.872546i $$-0.662467\pi$$
−0.488532 + 0.872546i $$0.662467\pi$$
$$420$$ 6.00000 0.292770
$$421$$ −10.0000 −0.487370 −0.243685 0.969854i $$-0.578356\pi$$
−0.243685 + 0.969854i $$0.578356\pi$$
$$422$$ 26.0000 1.26566
$$423$$ 7.00000 0.340352
$$424$$ 0 0
$$425$$ 8.00000 0.388057
$$426$$ 0 0
$$427$$ 8.00000 0.387147
$$428$$ −24.0000 −1.16008
$$429$$ 0 0
$$430$$ −54.0000 −2.60411
$$431$$ −20.0000 −0.963366 −0.481683 0.876346i $$-0.659974\pi$$
−0.481683 + 0.876346i $$0.659974\pi$$
$$432$$ −4.00000 −0.192450
$$433$$ 6.00000 0.288342 0.144171 0.989553i $$-0.453949\pi$$
0.144171 + 0.989553i $$0.453949\pi$$
$$434$$ −10.0000 −0.480015
$$435$$ −15.0000 −0.719195
$$436$$ 28.0000 1.34096
$$437$$ −1.00000 −0.0478365
$$438$$ −18.0000 −0.860073
$$439$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$440$$ 0 0
$$441$$ 1.00000 0.0476190
$$442$$ 0 0
$$443$$ −31.0000 −1.47285 −0.736427 0.676517i $$-0.763489\pi$$
−0.736427 + 0.676517i $$0.763489\pi$$
$$444$$ −16.0000 −0.759326
$$445$$ 27.0000 1.27992
$$446$$ 38.0000 1.79935
$$447$$ 4.00000 0.189194
$$448$$ 8.00000 0.377964
$$449$$ −34.0000 −1.60456 −0.802280 0.596948i $$-0.796380\pi$$
−0.802280 + 0.596948i $$0.796380\pi$$
$$450$$ −8.00000 −0.377124
$$451$$ 0 0
$$452$$ −42.0000 −1.97551
$$453$$ −20.0000 −0.939682
$$454$$ 24.0000 1.12638
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −42.0000 −1.96468 −0.982339 0.187112i $$-0.940087\pi$$
−0.982339 + 0.187112i $$0.940087\pi$$
$$458$$ 28.0000 1.30835
$$459$$ 2.00000 0.0933520
$$460$$ −6.00000 −0.279751
$$461$$ 10.0000 0.465746 0.232873 0.972507i $$-0.425187\pi$$
0.232873 + 0.972507i $$0.425187\pi$$
$$462$$ 0 0
$$463$$ −26.0000 −1.20832 −0.604161 0.796862i $$-0.706492\pi$$
−0.604161 + 0.796862i $$0.706492\pi$$
$$464$$ −20.0000 −0.928477
$$465$$ 15.0000 0.695608
$$466$$ −2.00000 −0.0926482
$$467$$ −18.0000 −0.832941 −0.416470 0.909149i $$-0.636733\pi$$
−0.416470 + 0.909149i $$0.636733\pi$$
$$468$$ 0 0
$$469$$ 2.00000 0.0923514
$$470$$ 42.0000 1.93732
$$471$$ −2.00000 −0.0921551
$$472$$ 0 0
$$473$$ 0 0
$$474$$ −30.0000 −1.37795
$$475$$ −4.00000 −0.183533
$$476$$ −4.00000 −0.183340
$$477$$ 9.00000 0.412082
$$478$$ 12.0000 0.548867
$$479$$ 21.0000 0.959514 0.479757 0.877401i $$-0.340725\pi$$
0.479757 + 0.877401i $$0.340725\pi$$
$$480$$ −24.0000 −1.09545
$$481$$ 0 0
$$482$$ 30.0000 1.36646
$$483$$ −1.00000 −0.0455016
$$484$$ −22.0000 −1.00000
$$485$$ −39.0000 −1.77090
$$486$$ −2.00000 −0.0907218
$$487$$ 8.00000 0.362515 0.181257 0.983436i $$-0.441983\pi$$
0.181257 + 0.983436i $$0.441983\pi$$
$$488$$ 0 0
$$489$$ −6.00000 −0.271329
$$490$$ 6.00000 0.271052
$$491$$ −32.0000 −1.44414 −0.722070 0.691820i $$-0.756809\pi$$
−0.722070 + 0.691820i $$0.756809\pi$$
$$492$$ 20.0000 0.901670
$$493$$ 10.0000 0.450377
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 20.0000 0.898027
$$497$$ 0 0
$$498$$ 18.0000 0.806599
$$499$$ 14.0000 0.626726 0.313363 0.949633i $$-0.398544\pi$$
0.313363 + 0.949633i $$0.398544\pi$$
$$500$$ 6.00000 0.268328
$$501$$ −3.00000 −0.134030
$$502$$ −56.0000 −2.49940
$$503$$ 24.0000 1.07011 0.535054 0.844818i $$-0.320291\pi$$
0.535054 + 0.844818i $$0.320291\pi$$
$$504$$ 0 0
$$505$$ −24.0000 −1.06799
$$506$$ 0 0
$$507$$ 0 0
$$508$$ −16.0000 −0.709885
$$509$$ 9.00000 0.398918 0.199459 0.979906i $$-0.436082\pi$$
0.199459 + 0.979906i $$0.436082\pi$$
$$510$$ 12.0000 0.531369
$$511$$ −9.00000 −0.398137
$$512$$ −32.0000 −1.41421
$$513$$ −1.00000 −0.0441511
$$514$$ −24.0000 −1.05859
$$515$$ −48.0000 −2.11513
$$516$$ −18.0000 −0.792406
$$517$$ 0 0
$$518$$ −16.0000 −0.703000
$$519$$ −24.0000 −1.05348
$$520$$ 0 0
$$521$$ 12.0000 0.525730 0.262865 0.964833i $$-0.415333\pi$$
0.262865 + 0.964833i $$0.415333\pi$$
$$522$$ −10.0000 −0.437688
$$523$$ 4.00000 0.174908 0.0874539 0.996169i $$-0.472127\pi$$
0.0874539 + 0.996169i $$0.472127\pi$$
$$524$$ −36.0000 −1.57267
$$525$$ −4.00000 −0.174574
$$526$$ −38.0000 −1.65688
$$527$$ −10.0000 −0.435607
$$528$$ 0 0
$$529$$ −22.0000 −0.956522
$$530$$ 54.0000 2.34561
$$531$$ −4.00000 −0.173585
$$532$$ 2.00000 0.0867110
$$533$$ 0 0
$$534$$ 18.0000 0.778936
$$535$$ 36.0000 1.55642
$$536$$ 0 0
$$537$$ 5.00000 0.215766
$$538$$ −20.0000 −0.862261
$$539$$ 0 0
$$540$$ −6.00000 −0.258199
$$541$$ 20.0000 0.859867 0.429934 0.902861i $$-0.358537\pi$$
0.429934 + 0.902861i $$0.358537\pi$$
$$542$$ −40.0000 −1.71815
$$543$$ 8.00000 0.343313
$$544$$ 16.0000 0.685994
$$545$$ −42.0000 −1.79908
$$546$$ 0 0
$$547$$ 13.0000 0.555840 0.277920 0.960604i $$-0.410355\pi$$
0.277920 + 0.960604i $$0.410355\pi$$
$$548$$ 24.0000 1.02523
$$549$$ −8.00000 −0.341432
$$550$$ 0 0
$$551$$ −5.00000 −0.213007
$$552$$ 0 0
$$553$$ −15.0000 −0.637865
$$554$$ 6.00000 0.254916
$$555$$ 24.0000 1.01874
$$556$$ −40.0000 −1.69638
$$557$$ 32.0000 1.35588 0.677942 0.735116i $$-0.262872\pi$$
0.677942 + 0.735116i $$0.262872\pi$$
$$558$$ 10.0000 0.423334
$$559$$ 0 0
$$560$$ −12.0000 −0.507093
$$561$$ 0 0
$$562$$ −20.0000 −0.843649
$$563$$ 26.0000 1.09577 0.547885 0.836554i $$-0.315433\pi$$
0.547885 + 0.836554i $$0.315433\pi$$
$$564$$ 14.0000 0.589506
$$565$$ 63.0000 2.65043
$$566$$ 48.0000 2.01759
$$567$$ −1.00000 −0.0419961
$$568$$ 0 0
$$569$$ 5.00000 0.209611 0.104805 0.994493i $$-0.466578\pi$$
0.104805 + 0.994493i $$0.466578\pi$$
$$570$$ −6.00000 −0.251312
$$571$$ 23.0000 0.962520 0.481260 0.876578i $$-0.340179\pi$$
0.481260 + 0.876578i $$0.340179\pi$$
$$572$$ 0 0
$$573$$ −8.00000 −0.334205
$$574$$ 20.0000 0.834784
$$575$$ 4.00000 0.166812
$$576$$ −8.00000 −0.333333
$$577$$ −22.0000 −0.915872 −0.457936 0.888985i $$-0.651411\pi$$
−0.457936 + 0.888985i $$0.651411\pi$$
$$578$$ 26.0000 1.08146
$$579$$ 14.0000 0.581820
$$580$$ −30.0000 −1.24568
$$581$$ 9.00000 0.373383
$$582$$ −26.0000 −1.07773
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 62.0000 2.56120
$$587$$ 3.00000 0.123823 0.0619116 0.998082i $$-0.480280\pi$$
0.0619116 + 0.998082i $$0.480280\pi$$
$$588$$ 2.00000 0.0824786
$$589$$ 5.00000 0.206021
$$590$$ −24.0000 −0.988064
$$591$$ −12.0000 −0.493614
$$592$$ 32.0000 1.31519
$$593$$ 9.00000 0.369586 0.184793 0.982777i $$-0.440839\pi$$
0.184793 + 0.982777i $$0.440839\pi$$
$$594$$ 0 0
$$595$$ 6.00000 0.245976
$$596$$ 8.00000 0.327693
$$597$$ −10.0000 −0.409273
$$598$$ 0 0
$$599$$ −35.0000 −1.43006 −0.715031 0.699093i $$-0.753587\pi$$
−0.715031 + 0.699093i $$0.753587\pi$$
$$600$$ 0 0
$$601$$ 2.00000 0.0815817 0.0407909 0.999168i $$-0.487012\pi$$
0.0407909 + 0.999168i $$0.487012\pi$$
$$602$$ −18.0000 −0.733625
$$603$$ −2.00000 −0.0814463
$$604$$ −40.0000 −1.62758
$$605$$ 33.0000 1.34164
$$606$$ −16.0000 −0.649956
$$607$$ 28.0000 1.13648 0.568242 0.822861i $$-0.307624\pi$$
0.568242 + 0.822861i $$0.307624\pi$$
$$608$$ −8.00000 −0.324443
$$609$$ −5.00000 −0.202610
$$610$$ −48.0000 −1.94346
$$611$$ 0 0
$$612$$ 4.00000 0.161690
$$613$$ 26.0000 1.05013 0.525065 0.851062i $$-0.324041\pi$$
0.525065 + 0.851062i $$0.324041\pi$$
$$614$$ −34.0000 −1.37213
$$615$$ −30.0000 −1.20972
$$616$$ 0 0
$$617$$ 48.0000 1.93241 0.966204 0.257780i $$-0.0829910\pi$$
0.966204 + 0.257780i $$0.0829910\pi$$
$$618$$ −32.0000 −1.28723
$$619$$ −44.0000 −1.76851 −0.884255 0.467005i $$-0.845333\pi$$
−0.884255 + 0.467005i $$0.845333\pi$$
$$620$$ 30.0000 1.20483
$$621$$ 1.00000 0.0401286
$$622$$ 4.00000 0.160385
$$623$$ 9.00000 0.360577
$$624$$ 0 0
$$625$$ −29.0000 −1.16000
$$626$$ −8.00000 −0.319744
$$627$$ 0 0
$$628$$ −4.00000 −0.159617
$$629$$ −16.0000 −0.637962
$$630$$ −6.00000 −0.239046
$$631$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$632$$ 0 0
$$633$$ −13.0000 −0.516704
$$634$$ 4.00000 0.158860
$$635$$ 24.0000 0.952411
$$636$$ 18.0000 0.713746
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −17.0000 −0.671460 −0.335730 0.941958i $$-0.608983\pi$$
−0.335730 + 0.941958i $$0.608983\pi$$
$$642$$ 24.0000 0.947204
$$643$$ −44.0000 −1.73519 −0.867595 0.497271i $$-0.834335\pi$$
−0.867595 + 0.497271i $$0.834335\pi$$
$$644$$ −2.00000 −0.0788110
$$645$$ 27.0000 1.06312
$$646$$ 4.00000 0.157378
$$647$$ 2.00000 0.0786281 0.0393141 0.999227i $$-0.487483\pi$$
0.0393141 + 0.999227i $$0.487483\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 5.00000 0.195965
$$652$$ −12.0000 −0.469956
$$653$$ 14.0000 0.547862 0.273931 0.961749i $$-0.411676\pi$$
0.273931 + 0.961749i $$0.411676\pi$$
$$654$$ −28.0000 −1.09489
$$655$$ 54.0000 2.10995
$$656$$ −40.0000 −1.56174
$$657$$ 9.00000 0.351123
$$658$$ 14.0000 0.545777
$$659$$ 15.0000 0.584317 0.292159 0.956370i $$-0.405627\pi$$
0.292159 + 0.956370i $$0.405627\pi$$
$$660$$ 0 0
$$661$$ −15.0000 −0.583432 −0.291716 0.956505i $$-0.594226\pi$$
−0.291716 + 0.956505i $$0.594226\pi$$
$$662$$ 40.0000 1.55464
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −3.00000 −0.116335
$$666$$ 16.0000 0.619987
$$667$$ 5.00000 0.193601
$$668$$ −6.00000 −0.232147
$$669$$ −19.0000 −0.734582
$$670$$ −12.0000 −0.463600
$$671$$ 0 0
$$672$$ −8.00000 −0.308607
$$673$$ −19.0000 −0.732396 −0.366198 0.930537i $$-0.619341\pi$$
−0.366198 + 0.930537i $$0.619341\pi$$
$$674$$ 46.0000 1.77185
$$675$$ 4.00000 0.153960
$$676$$ 0 0
$$677$$ 18.0000 0.691796 0.345898 0.938272i $$-0.387574\pi$$
0.345898 + 0.938272i $$0.387574\pi$$
$$678$$ 42.0000 1.61300
$$679$$ −13.0000 −0.498894
$$680$$ 0 0
$$681$$ −12.0000 −0.459841
$$682$$ 0 0
$$683$$ 24.0000 0.918334 0.459167 0.888350i $$-0.348148\pi$$
0.459167 + 0.888350i $$0.348148\pi$$
$$684$$ −2.00000 −0.0764719
$$685$$ −36.0000 −1.37549
$$686$$ 2.00000 0.0763604
$$687$$ −14.0000 −0.534133
$$688$$ 36.0000 1.37249
$$689$$ 0 0
$$690$$ 6.00000 0.228416
$$691$$ −35.0000 −1.33146 −0.665731 0.746191i $$-0.731880\pi$$
−0.665731 + 0.746191i $$0.731880\pi$$
$$692$$ −48.0000 −1.82469
$$693$$ 0 0
$$694$$ 24.0000 0.911028
$$695$$ 60.0000 2.27593
$$696$$ 0 0
$$697$$ 20.0000 0.757554
$$698$$ −2.00000 −0.0757011
$$699$$ 1.00000 0.0378235
$$700$$ −8.00000 −0.302372
$$701$$ 23.0000 0.868698 0.434349 0.900745i $$-0.356978\pi$$
0.434349 + 0.900745i $$0.356978\pi$$
$$702$$ 0 0
$$703$$ 8.00000 0.301726
$$704$$ 0 0
$$705$$ −21.0000 −0.790906
$$706$$ −12.0000 −0.451626
$$707$$ −8.00000 −0.300871
$$708$$ −8.00000 −0.300658
$$709$$ 16.0000 0.600893 0.300446 0.953799i $$-0.402864\pi$$
0.300446 + 0.953799i $$0.402864\pi$$
$$710$$ 0 0
$$711$$ 15.0000 0.562544
$$712$$ 0 0
$$713$$ −5.00000 −0.187251
$$714$$ 4.00000 0.149696
$$715$$ 0 0
$$716$$ 10.0000 0.373718
$$717$$ −6.00000 −0.224074
$$718$$ 28.0000 1.04495
$$719$$ −50.0000 −1.86469 −0.932343 0.361576i $$-0.882239\pi$$
−0.932343 + 0.361576i $$0.882239\pi$$
$$720$$ 12.0000 0.447214
$$721$$ −16.0000 −0.595871
$$722$$ 36.0000 1.33978
$$723$$ −15.0000 −0.557856
$$724$$ 16.0000 0.594635
$$725$$ 20.0000 0.742781
$$726$$ 22.0000 0.816497
$$727$$ 2.00000 0.0741759 0.0370879 0.999312i $$-0.488192\pi$$
0.0370879 + 0.999312i $$0.488192\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 54.0000 1.99863
$$731$$ −18.0000 −0.665754
$$732$$ −16.0000 −0.591377
$$733$$ −19.0000 −0.701781 −0.350891 0.936416i $$-0.614121\pi$$
−0.350891 + 0.936416i $$0.614121\pi$$
$$734$$ −36.0000 −1.32878
$$735$$ −3.00000 −0.110657
$$736$$ 8.00000 0.294884
$$737$$ 0 0
$$738$$ −20.0000 −0.736210
$$739$$ −4.00000 −0.147142 −0.0735712 0.997290i $$-0.523440\pi$$
−0.0735712 + 0.997290i $$0.523440\pi$$
$$740$$ 48.0000 1.76452
$$741$$ 0 0
$$742$$ 18.0000 0.660801
$$743$$ 26.0000 0.953847 0.476924 0.878945i $$-0.341752\pi$$
0.476924 + 0.878945i $$0.341752\pi$$
$$744$$ 0 0
$$745$$ −12.0000 −0.439646
$$746$$ 52.0000 1.90386
$$747$$ −9.00000 −0.329293
$$748$$ 0 0
$$749$$ 12.0000 0.438470
$$750$$ −6.00000 −0.219089
$$751$$ 23.0000 0.839282 0.419641 0.907690i $$-0.362156\pi$$
0.419641 + 0.907690i $$0.362156\pi$$
$$752$$ −28.0000 −1.02105
$$753$$ 28.0000 1.02038
$$754$$ 0 0
$$755$$ 60.0000 2.18362
$$756$$ −2.00000 −0.0727393
$$757$$ 13.0000 0.472493 0.236247 0.971693i $$-0.424083\pi$$
0.236247 + 0.971693i $$0.424083\pi$$
$$758$$ −8.00000 −0.290573
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 45.0000 1.63125 0.815624 0.578582i $$-0.196394\pi$$
0.815624 + 0.578582i $$0.196394\pi$$
$$762$$ 16.0000 0.579619
$$763$$ −14.0000 −0.506834
$$764$$ −16.0000 −0.578860
$$765$$ −6.00000 −0.216930
$$766$$ −32.0000 −1.15621
$$767$$ 0 0
$$768$$ 16.0000 0.577350
$$769$$ −1.00000 −0.0360609 −0.0180305 0.999837i $$-0.505740\pi$$
−0.0180305 + 0.999837i $$0.505740\pi$$
$$770$$ 0 0
$$771$$ 12.0000 0.432169
$$772$$ 28.0000 1.00774
$$773$$ 6.00000 0.215805 0.107903 0.994161i $$-0.465587\pi$$
0.107903 + 0.994161i $$0.465587\pi$$
$$774$$ 18.0000 0.646997
$$775$$ −20.0000 −0.718421
$$776$$ 0 0
$$777$$ 8.00000 0.286998
$$778$$ 60.0000 2.15110
$$779$$ −10.0000 −0.358287
$$780$$ 0 0
$$781$$ 0 0
$$782$$ −4.00000 −0.143040
$$783$$ 5.00000 0.178685
$$784$$ −4.00000 −0.142857
$$785$$ 6.00000 0.214149
$$786$$ 36.0000 1.28408
$$787$$ 7.00000 0.249523 0.124762 0.992187i $$-0.460183\pi$$
0.124762 + 0.992187i $$0.460183\pi$$
$$788$$ −24.0000 −0.854965
$$789$$ 19.0000 0.676418
$$790$$ 90.0000 3.20206
$$791$$ 21.0000 0.746674
$$792$$ 0 0
$$793$$ 0 0
$$794$$ −34.0000 −1.20661
$$795$$ −27.0000 −0.957591
$$796$$ −20.0000 −0.708881
$$797$$ 42.0000 1.48772 0.743858 0.668338i $$-0.232994\pi$$
0.743858 + 0.668338i $$0.232994\pi$$
$$798$$ −2.00000 −0.0707992
$$799$$ 14.0000 0.495284
$$800$$ 32.0000 1.13137
$$801$$ −9.00000 −0.317999
$$802$$ 20.0000 0.706225
$$803$$ 0 0
$$804$$ −4.00000 −0.141069
$$805$$ 3.00000 0.105736
$$806$$ 0 0
$$807$$ 10.0000 0.352017
$$808$$ 0 0
$$809$$ −45.0000 −1.58212 −0.791058 0.611741i $$-0.790469\pi$$
−0.791058 + 0.611741i $$0.790469\pi$$
$$810$$ 6.00000 0.210819
$$811$$ 20.0000 0.702295 0.351147 0.936320i $$-0.385792\pi$$
0.351147 + 0.936320i $$0.385792\pi$$
$$812$$ −10.0000 −0.350931
$$813$$ 20.0000 0.701431
$$814$$ 0 0
$$815$$ 18.0000 0.630512
$$816$$ −8.00000 −0.280056
$$817$$ 9.00000 0.314870
$$818$$ 62.0000 2.16778
$$819$$ 0 0
$$820$$ −60.0000 −2.09529
$$821$$ −30.0000 −1.04701 −0.523504 0.852023i $$-0.675375\pi$$
−0.523504 + 0.852023i $$0.675375\pi$$
$$822$$ −24.0000 −0.837096
$$823$$ 16.0000 0.557725 0.278862 0.960331i $$-0.410043\pi$$
0.278862 + 0.960331i $$0.410043\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ −8.00000 −0.278356
$$827$$ 42.0000 1.46048 0.730242 0.683189i $$-0.239408\pi$$
0.730242 + 0.683189i $$0.239408\pi$$
$$828$$ 2.00000 0.0695048
$$829$$ 10.0000 0.347314 0.173657 0.984806i $$-0.444442\pi$$
0.173657 + 0.984806i $$0.444442\pi$$
$$830$$ −54.0000 −1.87437
$$831$$ −3.00000 −0.104069
$$832$$ 0 0
$$833$$ 2.00000 0.0692959
$$834$$ 40.0000 1.38509
$$835$$ 9.00000 0.311458
$$836$$ 0 0
$$837$$ −5.00000 −0.172825
$$838$$ 40.0000 1.38178
$$839$$ −24.0000 −0.828572 −0.414286 0.910147i $$-0.635969\pi$$
−0.414286 + 0.910147i $$0.635969\pi$$
$$840$$ 0 0
$$841$$ −4.00000 −0.137931
$$842$$ 20.0000 0.689246
$$843$$ 10.0000 0.344418
$$844$$ −26.0000 −0.894957
$$845$$ 0 0
$$846$$ −14.0000 −0.481330
$$847$$ 11.0000 0.377964
$$848$$ −36.0000 −1.23625
$$849$$ −24.0000 −0.823678
$$850$$ −16.0000 −0.548795
$$851$$ −8.00000 −0.274236
$$852$$ 0 0
$$853$$ −1.00000 −0.0342393 −0.0171197 0.999853i $$-0.505450\pi$$
−0.0171197 + 0.999853i $$0.505450\pi$$
$$854$$ −16.0000 −0.547509
$$855$$ 3.00000 0.102598
$$856$$ 0 0
$$857$$ −8.00000 −0.273275 −0.136637 0.990621i $$-0.543630\pi$$
−0.136637 + 0.990621i $$0.543630\pi$$
$$858$$ 0 0
$$859$$ 30.0000 1.02359 0.511793 0.859109i $$-0.328981\pi$$
0.511793 + 0.859109i $$0.328981\pi$$
$$860$$ 54.0000 1.84138
$$861$$ −10.0000 −0.340799
$$862$$ 40.0000 1.36241
$$863$$ −4.00000 −0.136162 −0.0680808 0.997680i $$-0.521688\pi$$
−0.0680808 + 0.997680i $$0.521688\pi$$
$$864$$ 8.00000 0.272166
$$865$$ 72.0000 2.44807
$$866$$ −12.0000 −0.407777
$$867$$ −13.0000 −0.441503
$$868$$ 10.0000 0.339422
$$869$$ 0 0
$$870$$ 30.0000 1.01710
$$871$$ 0 0
$$872$$ 0 0
$$873$$ 13.0000 0.439983
$$874$$ 2.00000 0.0676510
$$875$$ −3.00000 −0.101419
$$876$$ 18.0000 0.608164
$$877$$ −22.0000 −0.742887 −0.371444 0.928456i $$-0.621137\pi$$
−0.371444 + 0.928456i $$0.621137\pi$$
$$878$$ 0 0
$$879$$ −31.0000 −1.04560
$$880$$ 0 0
$$881$$ 18.0000 0.606435 0.303218 0.952921i $$-0.401939\pi$$
0.303218 + 0.952921i $$0.401939\pi$$
$$882$$ −2.00000 −0.0673435
$$883$$ 16.0000 0.538443 0.269221 0.963078i $$-0.413234\pi$$
0.269221 + 0.963078i $$0.413234\pi$$
$$884$$ 0 0
$$885$$ 12.0000 0.403376
$$886$$ 62.0000 2.08293
$$887$$ 18.0000 0.604381 0.302190 0.953248i $$-0.402282\pi$$
0.302190 + 0.953248i $$0.402282\pi$$
$$888$$ 0 0
$$889$$ 8.00000 0.268311
$$890$$ −54.0000 −1.81008
$$891$$ 0 0
$$892$$ −38.0000 −1.27233
$$893$$ −7.00000 −0.234246
$$894$$ −8.00000 −0.267560
$$895$$ −15.0000 −0.501395
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 68.0000 2.26919
$$899$$ −25.0000 −0.833797
$$900$$ 8.00000 0.266667
$$901$$ 18.0000 0.599667
$$902$$ 0 0
$$903$$ 9.00000 0.299501
$$904$$ 0 0
$$905$$ −24.0000 −0.797787
$$906$$ 40.0000 1.32891
$$907$$ 27.0000 0.896520 0.448260 0.893903i $$-0.352044\pi$$
0.448260 + 0.893903i $$0.352044\pi$$
$$908$$ −24.0000 −0.796468
$$909$$ 8.00000 0.265343
$$910$$ 0 0
$$911$$ −33.0000 −1.09334 −0.546669 0.837349i $$-0.684105\pi$$
−0.546669 + 0.837349i $$0.684105\pi$$
$$912$$ 4.00000 0.132453
$$913$$ 0 0
$$914$$ 84.0000 2.77847
$$915$$ 24.0000 0.793416
$$916$$ −28.0000 −0.925146
$$917$$ 18.0000 0.594412
$$918$$ −4.00000 −0.132020
$$919$$ 40.0000 1.31948 0.659739 0.751495i $$-0.270667\pi$$
0.659739 + 0.751495i $$0.270667\pi$$
$$920$$ 0 0
$$921$$ 17.0000 0.560169
$$922$$ −20.0000 −0.658665
$$923$$ 0 0
$$924$$ 0 0
$$925$$ −32.0000 −1.05215
$$926$$ 52.0000 1.70883
$$927$$ 16.0000 0.525509
$$928$$ 40.0000 1.31306
$$929$$ 29.0000 0.951459 0.475730 0.879592i $$-0.342184\pi$$
0.475730 + 0.879592i $$0.342184\pi$$
$$930$$ −30.0000 −0.983739
$$931$$ −1.00000 −0.0327737
$$932$$ 2.00000 0.0655122
$$933$$ −2.00000 −0.0654771
$$934$$ 36.0000 1.17796
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 28.0000 0.914720 0.457360 0.889282i $$-0.348795\pi$$
0.457360 + 0.889282i $$0.348795\pi$$
$$938$$ −4.00000 −0.130605
$$939$$ 4.00000 0.130535
$$940$$ −42.0000 −1.36989
$$941$$ −5.00000 −0.162995 −0.0814977 0.996674i $$-0.525970\pi$$
−0.0814977 + 0.996674i $$0.525970\pi$$
$$942$$ 4.00000 0.130327
$$943$$ 10.0000 0.325645
$$944$$ 16.0000 0.520756
$$945$$ 3.00000 0.0975900
$$946$$ 0 0
$$947$$ 2.00000 0.0649913 0.0324956 0.999472i $$-0.489654\pi$$
0.0324956 + 0.999472i $$0.489654\pi$$
$$948$$ 30.0000 0.974355
$$949$$ 0 0
$$950$$ 8.00000 0.259554
$$951$$ −2.00000 −0.0648544
$$952$$ 0 0
$$953$$ −29.0000 −0.939402 −0.469701 0.882826i $$-0.655638\pi$$
−0.469701 + 0.882826i $$0.655638\pi$$
$$954$$ −18.0000 −0.582772
$$955$$ 24.0000 0.776622
$$956$$ −12.0000 −0.388108
$$957$$ 0 0
$$958$$ −42.0000 −1.35696
$$959$$ −12.0000 −0.387500
$$960$$ 24.0000 0.774597
$$961$$ −6.00000 −0.193548
$$962$$ 0 0
$$963$$ −12.0000 −0.386695
$$964$$ −30.0000 −0.966235
$$965$$ −42.0000 −1.35203
$$966$$ 2.00000 0.0643489
$$967$$ −52.0000 −1.67221 −0.836104 0.548572i $$-0.815172\pi$$
−0.836104 + 0.548572i $$0.815172\pi$$
$$968$$ 0 0
$$969$$ −2.00000 −0.0642493
$$970$$ 78.0000 2.50443
$$971$$ −28.0000 −0.898563 −0.449281 0.893390i $$-0.648320\pi$$
−0.449281 + 0.893390i $$0.648320\pi$$
$$972$$ 2.00000 0.0641500
$$973$$ 20.0000 0.641171
$$974$$ −16.0000 −0.512673
$$975$$ 0 0
$$976$$ 32.0000 1.02430
$$977$$ −52.0000 −1.66363 −0.831814 0.555055i $$-0.812697\pi$$
−0.831814 + 0.555055i $$0.812697\pi$$
$$978$$ 12.0000 0.383718
$$979$$ 0 0
$$980$$ −6.00000 −0.191663
$$981$$ 14.0000 0.446986
$$982$$ 64.0000 2.04232
$$983$$ −31.0000 −0.988746 −0.494373 0.869250i $$-0.664602\pi$$
−0.494373 + 0.869250i $$0.664602\pi$$
$$984$$ 0 0
$$985$$ 36.0000 1.14706
$$986$$ −20.0000 −0.636930
$$987$$ −7.00000 −0.222812
$$988$$ 0 0
$$989$$ −9.00000 −0.286183
$$990$$ 0 0
$$991$$ 32.0000 1.01651 0.508257 0.861206i $$-0.330290\pi$$
0.508257 + 0.861206i $$0.330290\pi$$
$$992$$ −40.0000 −1.27000
$$993$$ −20.0000 −0.634681
$$994$$ 0 0
$$995$$ 30.0000 0.951064
$$996$$ −18.0000 −0.570352
$$997$$ −32.0000 −1.01345 −0.506725 0.862108i $$-0.669144\pi$$
−0.506725 + 0.862108i $$0.669144\pi$$
$$998$$ −28.0000 −0.886325
$$999$$ −8.00000 −0.253109
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 3549.2.a.a.1.1 1
13.5 odd 4 273.2.c.a.64.2 yes 2
13.8 odd 4 273.2.c.a.64.1 2
13.12 even 2 3549.2.a.e.1.1 1
39.5 even 4 819.2.c.a.64.1 2
39.8 even 4 819.2.c.a.64.2 2
52.31 even 4 4368.2.h.e.337.2 2
52.47 even 4 4368.2.h.e.337.1 2
91.34 even 4 1911.2.c.a.883.1 2
91.83 even 4 1911.2.c.a.883.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.c.a.64.1 2 13.8 odd 4
273.2.c.a.64.2 yes 2 13.5 odd 4
819.2.c.a.64.1 2 39.5 even 4
819.2.c.a.64.2 2 39.8 even 4
1911.2.c.a.883.1 2 91.34 even 4
1911.2.c.a.883.2 2 91.83 even 4
3549.2.a.a.1.1 1 1.1 even 1 trivial
3549.2.a.e.1.1 1 13.12 even 2
4368.2.h.e.337.1 2 52.47 even 4
4368.2.h.e.337.2 2 52.31 even 4