# Properties

 Label 1134.2.a.p.1.1 Level $1134$ Weight $2$ Character 1134.1 Self dual yes Analytic conductor $9.055$ Analytic rank $0$ Dimension $2$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1134 = 2 \cdot 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1134.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$9.05503558921$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{6})$$ Defining polynomial: $$x^{2} - 6$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 126) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Root $$-2.44949$$ of defining polynomial Character $$\chi$$ $$=$$ 1134.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +1.00000 q^{4} -1.44949 q^{5} -1.00000 q^{7} +1.00000 q^{8} +O(q^{10})$$ $$q+1.00000 q^{2} +1.00000 q^{4} -1.44949 q^{5} -1.00000 q^{7} +1.00000 q^{8} -1.44949 q^{10} +2.00000 q^{11} +4.89898 q^{13} -1.00000 q^{14} +1.00000 q^{16} +2.00000 q^{17} +2.55051 q^{19} -1.44949 q^{20} +2.00000 q^{22} -1.00000 q^{23} -2.89898 q^{25} +4.89898 q^{26} -1.00000 q^{28} -6.89898 q^{29} +6.00000 q^{31} +1.00000 q^{32} +2.00000 q^{34} +1.44949 q^{35} +11.7980 q^{37} +2.55051 q^{38} -1.44949 q^{40} +9.79796 q^{41} +6.89898 q^{43} +2.00000 q^{44} -1.00000 q^{46} +9.79796 q^{47} +1.00000 q^{49} -2.89898 q^{50} +4.89898 q^{52} -10.8990 q^{53} -2.89898 q^{55} -1.00000 q^{56} -6.89898 q^{58} -2.00000 q^{59} +6.55051 q^{61} +6.00000 q^{62} +1.00000 q^{64} -7.10102 q^{65} -12.8990 q^{67} +2.00000 q^{68} +1.44949 q^{70} +0.101021 q^{71} -6.89898 q^{73} +11.7980 q^{74} +2.55051 q^{76} -2.00000 q^{77} -1.89898 q^{79} -1.44949 q^{80} +9.79796 q^{82} +2.00000 q^{83} -2.89898 q^{85} +6.89898 q^{86} +2.00000 q^{88} -16.8990 q^{89} -4.89898 q^{91} -1.00000 q^{92} +9.79796 q^{94} -3.69694 q^{95} +2.89898 q^{97} +1.00000 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 2q^{2} + 2q^{4} + 2q^{5} - 2q^{7} + 2q^{8} + O(q^{10})$$ $$2q + 2q^{2} + 2q^{4} + 2q^{5} - 2q^{7} + 2q^{8} + 2q^{10} + 4q^{11} - 2q^{14} + 2q^{16} + 4q^{17} + 10q^{19} + 2q^{20} + 4q^{22} - 2q^{23} + 4q^{25} - 2q^{28} - 4q^{29} + 12q^{31} + 2q^{32} + 4q^{34} - 2q^{35} + 4q^{37} + 10q^{38} + 2q^{40} + 4q^{43} + 4q^{44} - 2q^{46} + 2q^{49} + 4q^{50} - 12q^{53} + 4q^{55} - 2q^{56} - 4q^{58} - 4q^{59} + 18q^{61} + 12q^{62} + 2q^{64} - 24q^{65} - 16q^{67} + 4q^{68} - 2q^{70} + 10q^{71} - 4q^{73} + 4q^{74} + 10q^{76} - 4q^{77} + 6q^{79} + 2q^{80} + 4q^{83} + 4q^{85} + 4q^{86} + 4q^{88} - 24q^{89} - 2q^{92} + 22q^{95} - 4q^{97} + 2q^{98} + O(q^{100})$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 0.707107
$$3$$ 0 0
$$4$$ 1.00000 0.500000
$$5$$ −1.44949 −0.648232 −0.324116 0.946017i $$-0.605067\pi$$
−0.324116 + 0.946017i $$0.605067\pi$$
$$6$$ 0 0
$$7$$ −1.00000 −0.377964
$$8$$ 1.00000 0.353553
$$9$$ 0 0
$$10$$ −1.44949 −0.458369
$$11$$ 2.00000 0.603023 0.301511 0.953463i $$-0.402509\pi$$
0.301511 + 0.953463i $$0.402509\pi$$
$$12$$ 0 0
$$13$$ 4.89898 1.35873 0.679366 0.733799i $$-0.262255\pi$$
0.679366 + 0.733799i $$0.262255\pi$$
$$14$$ −1.00000 −0.267261
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 2.00000 0.485071 0.242536 0.970143i $$-0.422021\pi$$
0.242536 + 0.970143i $$0.422021\pi$$
$$18$$ 0 0
$$19$$ 2.55051 0.585127 0.292564 0.956246i $$-0.405492\pi$$
0.292564 + 0.956246i $$0.405492\pi$$
$$20$$ −1.44949 −0.324116
$$21$$ 0 0
$$22$$ 2.00000 0.426401
$$23$$ −1.00000 −0.208514 −0.104257 0.994550i $$-0.533247\pi$$
−0.104257 + 0.994550i $$0.533247\pi$$
$$24$$ 0 0
$$25$$ −2.89898 −0.579796
$$26$$ 4.89898 0.960769
$$27$$ 0 0
$$28$$ −1.00000 −0.188982
$$29$$ −6.89898 −1.28111 −0.640554 0.767913i $$-0.721295\pi$$
−0.640554 + 0.767913i $$0.721295\pi$$
$$30$$ 0 0
$$31$$ 6.00000 1.07763 0.538816 0.842424i $$-0.318872\pi$$
0.538816 + 0.842424i $$0.318872\pi$$
$$32$$ 1.00000 0.176777
$$33$$ 0 0
$$34$$ 2.00000 0.342997
$$35$$ 1.44949 0.245008
$$36$$ 0 0
$$37$$ 11.7980 1.93957 0.969786 0.243956i $$-0.0784453\pi$$
0.969786 + 0.243956i $$0.0784453\pi$$
$$38$$ 2.55051 0.413747
$$39$$ 0 0
$$40$$ −1.44949 −0.229184
$$41$$ 9.79796 1.53018 0.765092 0.643921i $$-0.222693\pi$$
0.765092 + 0.643921i $$0.222693\pi$$
$$42$$ 0 0
$$43$$ 6.89898 1.05208 0.526042 0.850458i $$-0.323675\pi$$
0.526042 + 0.850458i $$0.323675\pi$$
$$44$$ 2.00000 0.301511
$$45$$ 0 0
$$46$$ −1.00000 −0.147442
$$47$$ 9.79796 1.42918 0.714590 0.699544i $$-0.246613\pi$$
0.714590 + 0.699544i $$0.246613\pi$$
$$48$$ 0 0
$$49$$ 1.00000 0.142857
$$50$$ −2.89898 −0.409978
$$51$$ 0 0
$$52$$ 4.89898 0.679366
$$53$$ −10.8990 −1.49709 −0.748545 0.663084i $$-0.769247\pi$$
−0.748545 + 0.663084i $$0.769247\pi$$
$$54$$ 0 0
$$55$$ −2.89898 −0.390898
$$56$$ −1.00000 −0.133631
$$57$$ 0 0
$$58$$ −6.89898 −0.905880
$$59$$ −2.00000 −0.260378 −0.130189 0.991489i $$-0.541558\pi$$
−0.130189 + 0.991489i $$0.541558\pi$$
$$60$$ 0 0
$$61$$ 6.55051 0.838707 0.419353 0.907823i $$-0.362257\pi$$
0.419353 + 0.907823i $$0.362257\pi$$
$$62$$ 6.00000 0.762001
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ −7.10102 −0.880773
$$66$$ 0 0
$$67$$ −12.8990 −1.57586 −0.787931 0.615764i $$-0.788847\pi$$
−0.787931 + 0.615764i $$0.788847\pi$$
$$68$$ 2.00000 0.242536
$$69$$ 0 0
$$70$$ 1.44949 0.173247
$$71$$ 0.101021 0.0119889 0.00599446 0.999982i $$-0.498092\pi$$
0.00599446 + 0.999982i $$0.498092\pi$$
$$72$$ 0 0
$$73$$ −6.89898 −0.807464 −0.403732 0.914877i $$-0.632287\pi$$
−0.403732 + 0.914877i $$0.632287\pi$$
$$74$$ 11.7980 1.37148
$$75$$ 0 0
$$76$$ 2.55051 0.292564
$$77$$ −2.00000 −0.227921
$$78$$ 0 0
$$79$$ −1.89898 −0.213652 −0.106826 0.994278i $$-0.534069\pi$$
−0.106826 + 0.994278i $$0.534069\pi$$
$$80$$ −1.44949 −0.162058
$$81$$ 0 0
$$82$$ 9.79796 1.08200
$$83$$ 2.00000 0.219529 0.109764 0.993958i $$-0.464990\pi$$
0.109764 + 0.993958i $$0.464990\pi$$
$$84$$ 0 0
$$85$$ −2.89898 −0.314438
$$86$$ 6.89898 0.743936
$$87$$ 0 0
$$88$$ 2.00000 0.213201
$$89$$ −16.8990 −1.79129 −0.895644 0.444771i $$-0.853285\pi$$
−0.895644 + 0.444771i $$0.853285\pi$$
$$90$$ 0 0
$$91$$ −4.89898 −0.513553
$$92$$ −1.00000 −0.104257
$$93$$ 0 0
$$94$$ 9.79796 1.01058
$$95$$ −3.69694 −0.379298
$$96$$ 0 0
$$97$$ 2.89898 0.294347 0.147173 0.989111i $$-0.452982\pi$$
0.147173 + 0.989111i $$0.452982\pi$$
$$98$$ 1.00000 0.101015
$$99$$ 0 0
$$100$$ −2.89898 −0.289898
$$101$$ −17.2474 −1.71619 −0.858093 0.513495i $$-0.828351\pi$$
−0.858093 + 0.513495i $$0.828351\pi$$
$$102$$ 0 0
$$103$$ 14.0000 1.37946 0.689730 0.724066i $$-0.257729\pi$$
0.689730 + 0.724066i $$0.257729\pi$$
$$104$$ 4.89898 0.480384
$$105$$ 0 0
$$106$$ −10.8990 −1.05860
$$107$$ −12.0000 −1.16008 −0.580042 0.814587i $$-0.696964\pi$$
−0.580042 + 0.814587i $$0.696964\pi$$
$$108$$ 0 0
$$109$$ 12.6969 1.21615 0.608073 0.793881i $$-0.291943\pi$$
0.608073 + 0.793881i $$0.291943\pi$$
$$110$$ −2.89898 −0.276407
$$111$$ 0 0
$$112$$ −1.00000 −0.0944911
$$113$$ −6.10102 −0.573936 −0.286968 0.957940i $$-0.592647\pi$$
−0.286968 + 0.957940i $$0.592647\pi$$
$$114$$ 0 0
$$115$$ 1.44949 0.135166
$$116$$ −6.89898 −0.640554
$$117$$ 0 0
$$118$$ −2.00000 −0.184115
$$119$$ −2.00000 −0.183340
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ 6.55051 0.593055
$$123$$ 0 0
$$124$$ 6.00000 0.538816
$$125$$ 11.4495 1.02407
$$126$$ 0 0
$$127$$ −3.00000 −0.266207 −0.133103 0.991102i $$-0.542494\pi$$
−0.133103 + 0.991102i $$0.542494\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ 0 0
$$130$$ −7.10102 −0.622801
$$131$$ −8.55051 −0.747062 −0.373531 0.927618i $$-0.621853\pi$$
−0.373531 + 0.927618i $$0.621853\pi$$
$$132$$ 0 0
$$133$$ −2.55051 −0.221157
$$134$$ −12.8990 −1.11430
$$135$$ 0 0
$$136$$ 2.00000 0.171499
$$137$$ 7.79796 0.666225 0.333112 0.942887i $$-0.391901\pi$$
0.333112 + 0.942887i $$0.391901\pi$$
$$138$$ 0 0
$$139$$ 4.55051 0.385969 0.192985 0.981202i $$-0.438183\pi$$
0.192985 + 0.981202i $$0.438183\pi$$
$$140$$ 1.44949 0.122504
$$141$$ 0 0
$$142$$ 0.101021 0.00847745
$$143$$ 9.79796 0.819346
$$144$$ 0 0
$$145$$ 10.0000 0.830455
$$146$$ −6.89898 −0.570964
$$147$$ 0 0
$$148$$ 11.7980 0.969786
$$149$$ −6.00000 −0.491539 −0.245770 0.969328i $$-0.579041\pi$$
−0.245770 + 0.969328i $$0.579041\pi$$
$$150$$ 0 0
$$151$$ −5.00000 −0.406894 −0.203447 0.979086i $$-0.565214\pi$$
−0.203447 + 0.979086i $$0.565214\pi$$
$$152$$ 2.55051 0.206874
$$153$$ 0 0
$$154$$ −2.00000 −0.161165
$$155$$ −8.69694 −0.698555
$$156$$ 0 0
$$157$$ −8.34847 −0.666280 −0.333140 0.942877i $$-0.608108\pi$$
−0.333140 + 0.942877i $$0.608108\pi$$
$$158$$ −1.89898 −0.151075
$$159$$ 0 0
$$160$$ −1.44949 −0.114592
$$161$$ 1.00000 0.0788110
$$162$$ 0 0
$$163$$ −19.7980 −1.55070 −0.775348 0.631534i $$-0.782425\pi$$
−0.775348 + 0.631534i $$0.782425\pi$$
$$164$$ 9.79796 0.765092
$$165$$ 0 0
$$166$$ 2.00000 0.155230
$$167$$ −10.6969 −0.827754 −0.413877 0.910333i $$-0.635826\pi$$
−0.413877 + 0.910333i $$0.635826\pi$$
$$168$$ 0 0
$$169$$ 11.0000 0.846154
$$170$$ −2.89898 −0.222342
$$171$$ 0 0
$$172$$ 6.89898 0.526042
$$173$$ −3.10102 −0.235766 −0.117883 0.993027i $$-0.537611\pi$$
−0.117883 + 0.993027i $$0.537611\pi$$
$$174$$ 0 0
$$175$$ 2.89898 0.219142
$$176$$ 2.00000 0.150756
$$177$$ 0 0
$$178$$ −16.8990 −1.26663
$$179$$ 20.6969 1.54696 0.773481 0.633820i $$-0.218514\pi$$
0.773481 + 0.633820i $$0.218514\pi$$
$$180$$ 0 0
$$181$$ −10.3485 −0.769196 −0.384598 0.923084i $$-0.625660\pi$$
−0.384598 + 0.923084i $$0.625660\pi$$
$$182$$ −4.89898 −0.363137
$$183$$ 0 0
$$184$$ −1.00000 −0.0737210
$$185$$ −17.1010 −1.25729
$$186$$ 0 0
$$187$$ 4.00000 0.292509
$$188$$ 9.79796 0.714590
$$189$$ 0 0
$$190$$ −3.69694 −0.268204
$$191$$ 4.10102 0.296739 0.148370 0.988932i $$-0.452597\pi$$
0.148370 + 0.988932i $$0.452597\pi$$
$$192$$ 0 0
$$193$$ −17.8990 −1.28840 −0.644198 0.764858i $$-0.722809\pi$$
−0.644198 + 0.764858i $$0.722809\pi$$
$$194$$ 2.89898 0.208135
$$195$$ 0 0
$$196$$ 1.00000 0.0714286
$$197$$ 16.6969 1.18961 0.594804 0.803871i $$-0.297230\pi$$
0.594804 + 0.803871i $$0.297230\pi$$
$$198$$ 0 0
$$199$$ −2.89898 −0.205503 −0.102752 0.994707i $$-0.532765\pi$$
−0.102752 + 0.994707i $$0.532765\pi$$
$$200$$ −2.89898 −0.204989
$$201$$ 0 0
$$202$$ −17.2474 −1.21353
$$203$$ 6.89898 0.484213
$$204$$ 0 0
$$205$$ −14.2020 −0.991914
$$206$$ 14.0000 0.975426
$$207$$ 0 0
$$208$$ 4.89898 0.339683
$$209$$ 5.10102 0.352845
$$210$$ 0 0
$$211$$ 12.8990 0.888002 0.444001 0.896026i $$-0.353559\pi$$
0.444001 + 0.896026i $$0.353559\pi$$
$$212$$ −10.8990 −0.748545
$$213$$ 0 0
$$214$$ −12.0000 −0.820303
$$215$$ −10.0000 −0.681994
$$216$$ 0 0
$$217$$ −6.00000 −0.407307
$$218$$ 12.6969 0.859945
$$219$$ 0 0
$$220$$ −2.89898 −0.195449
$$221$$ 9.79796 0.659082
$$222$$ 0 0
$$223$$ −11.1010 −0.743379 −0.371690 0.928357i $$-0.621221\pi$$
−0.371690 + 0.928357i $$0.621221\pi$$
$$224$$ −1.00000 −0.0668153
$$225$$ 0 0
$$226$$ −6.10102 −0.405834
$$227$$ −5.44949 −0.361695 −0.180848 0.983511i $$-0.557884\pi$$
−0.180848 + 0.983511i $$0.557884\pi$$
$$228$$ 0 0
$$229$$ 1.24745 0.0824337 0.0412169 0.999150i $$-0.486877\pi$$
0.0412169 + 0.999150i $$0.486877\pi$$
$$230$$ 1.44949 0.0955765
$$231$$ 0 0
$$232$$ −6.89898 −0.452940
$$233$$ −7.00000 −0.458585 −0.229293 0.973358i $$-0.573641\pi$$
−0.229293 + 0.973358i $$0.573641\pi$$
$$234$$ 0 0
$$235$$ −14.2020 −0.926439
$$236$$ −2.00000 −0.130189
$$237$$ 0 0
$$238$$ −2.00000 −0.129641
$$239$$ 6.79796 0.439723 0.219862 0.975531i $$-0.429439\pi$$
0.219862 + 0.975531i $$0.429439\pi$$
$$240$$ 0 0
$$241$$ 0.898979 0.0579084 0.0289542 0.999581i $$-0.490782\pi$$
0.0289542 + 0.999581i $$0.490782\pi$$
$$242$$ −7.00000 −0.449977
$$243$$ 0 0
$$244$$ 6.55051 0.419353
$$245$$ −1.44949 −0.0926045
$$246$$ 0 0
$$247$$ 12.4949 0.795031
$$248$$ 6.00000 0.381000
$$249$$ 0 0
$$250$$ 11.4495 0.724129
$$251$$ 17.4495 1.10140 0.550701 0.834703i $$-0.314360\pi$$
0.550701 + 0.834703i $$0.314360\pi$$
$$252$$ 0 0
$$253$$ −2.00000 −0.125739
$$254$$ −3.00000 −0.188237
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 8.20204 0.511629 0.255815 0.966726i $$-0.417656\pi$$
0.255815 + 0.966726i $$0.417656\pi$$
$$258$$ 0 0
$$259$$ −11.7980 −0.733090
$$260$$ −7.10102 −0.440387
$$261$$ 0 0
$$262$$ −8.55051 −0.528252
$$263$$ 25.8990 1.59700 0.798500 0.601995i $$-0.205627\pi$$
0.798500 + 0.601995i $$0.205627\pi$$
$$264$$ 0 0
$$265$$ 15.7980 0.970461
$$266$$ −2.55051 −0.156382
$$267$$ 0 0
$$268$$ −12.8990 −0.787931
$$269$$ −18.3485 −1.11873 −0.559363 0.828923i $$-0.688954\pi$$
−0.559363 + 0.828923i $$0.688954\pi$$
$$270$$ 0 0
$$271$$ 7.10102 0.431356 0.215678 0.976465i $$-0.430804\pi$$
0.215678 + 0.976465i $$0.430804\pi$$
$$272$$ 2.00000 0.121268
$$273$$ 0 0
$$274$$ 7.79796 0.471092
$$275$$ −5.79796 −0.349630
$$276$$ 0 0
$$277$$ −18.6969 −1.12339 −0.561695 0.827344i $$-0.689851\pi$$
−0.561695 + 0.827344i $$0.689851\pi$$
$$278$$ 4.55051 0.272921
$$279$$ 0 0
$$280$$ 1.44949 0.0866236
$$281$$ −19.0000 −1.13344 −0.566722 0.823909i $$-0.691789\pi$$
−0.566722 + 0.823909i $$0.691789\pi$$
$$282$$ 0 0
$$283$$ −25.4495 −1.51282 −0.756408 0.654101i $$-0.773047\pi$$
−0.756408 + 0.654101i $$0.773047\pi$$
$$284$$ 0.101021 0.00599446
$$285$$ 0 0
$$286$$ 9.79796 0.579365
$$287$$ −9.79796 −0.578355
$$288$$ 0 0
$$289$$ −13.0000 −0.764706
$$290$$ 10.0000 0.587220
$$291$$ 0 0
$$292$$ −6.89898 −0.403732
$$293$$ 2.75255 0.160806 0.0804029 0.996762i $$-0.474379\pi$$
0.0804029 + 0.996762i $$0.474379\pi$$
$$294$$ 0 0
$$295$$ 2.89898 0.168785
$$296$$ 11.7980 0.685742
$$297$$ 0 0
$$298$$ −6.00000 −0.347571
$$299$$ −4.89898 −0.283315
$$300$$ 0 0
$$301$$ −6.89898 −0.397651
$$302$$ −5.00000 −0.287718
$$303$$ 0 0
$$304$$ 2.55051 0.146282
$$305$$ −9.49490 −0.543676
$$306$$ 0 0
$$307$$ 25.2474 1.44095 0.720474 0.693482i $$-0.243924\pi$$
0.720474 + 0.693482i $$0.243924\pi$$
$$308$$ −2.00000 −0.113961
$$309$$ 0 0
$$310$$ −8.69694 −0.493953
$$311$$ 30.6969 1.74066 0.870332 0.492466i $$-0.163904\pi$$
0.870332 + 0.492466i $$0.163904\pi$$
$$312$$ 0 0
$$313$$ −4.69694 −0.265487 −0.132743 0.991150i $$-0.542379\pi$$
−0.132743 + 0.991150i $$0.542379\pi$$
$$314$$ −8.34847 −0.471131
$$315$$ 0 0
$$316$$ −1.89898 −0.106826
$$317$$ 20.6969 1.16246 0.581228 0.813741i $$-0.302572\pi$$
0.581228 + 0.813741i $$0.302572\pi$$
$$318$$ 0 0
$$319$$ −13.7980 −0.772537
$$320$$ −1.44949 −0.0810289
$$321$$ 0 0
$$322$$ 1.00000 0.0557278
$$323$$ 5.10102 0.283828
$$324$$ 0 0
$$325$$ −14.2020 −0.787787
$$326$$ −19.7980 −1.09651
$$327$$ 0 0
$$328$$ 9.79796 0.541002
$$329$$ −9.79796 −0.540179
$$330$$ 0 0
$$331$$ 4.69694 0.258167 0.129084 0.991634i $$-0.458796\pi$$
0.129084 + 0.991634i $$0.458796\pi$$
$$332$$ 2.00000 0.109764
$$333$$ 0 0
$$334$$ −10.6969 −0.585310
$$335$$ 18.6969 1.02152
$$336$$ 0 0
$$337$$ −23.3939 −1.27435 −0.637173 0.770721i $$-0.719896\pi$$
−0.637173 + 0.770721i $$0.719896\pi$$
$$338$$ 11.0000 0.598321
$$339$$ 0 0
$$340$$ −2.89898 −0.157219
$$341$$ 12.0000 0.649836
$$342$$ 0 0
$$343$$ −1.00000 −0.0539949
$$344$$ 6.89898 0.371968
$$345$$ 0 0
$$346$$ −3.10102 −0.166712
$$347$$ 19.5959 1.05196 0.525982 0.850496i $$-0.323698\pi$$
0.525982 + 0.850496i $$0.323698\pi$$
$$348$$ 0 0
$$349$$ 11.1010 0.594224 0.297112 0.954843i $$-0.403977\pi$$
0.297112 + 0.954843i $$0.403977\pi$$
$$350$$ 2.89898 0.154957
$$351$$ 0 0
$$352$$ 2.00000 0.106600
$$353$$ −6.00000 −0.319348 −0.159674 0.987170i $$-0.551044\pi$$
−0.159674 + 0.987170i $$0.551044\pi$$
$$354$$ 0 0
$$355$$ −0.146428 −0.00777160
$$356$$ −16.8990 −0.895644
$$357$$ 0 0
$$358$$ 20.6969 1.09387
$$359$$ −8.79796 −0.464339 −0.232169 0.972675i $$-0.574582\pi$$
−0.232169 + 0.972675i $$0.574582\pi$$
$$360$$ 0 0
$$361$$ −12.4949 −0.657626
$$362$$ −10.3485 −0.543903
$$363$$ 0 0
$$364$$ −4.89898 −0.256776
$$365$$ 10.0000 0.523424
$$366$$ 0 0
$$367$$ −13.7980 −0.720248 −0.360124 0.932905i $$-0.617266\pi$$
−0.360124 + 0.932905i $$0.617266\pi$$
$$368$$ −1.00000 −0.0521286
$$369$$ 0 0
$$370$$ −17.1010 −0.889040
$$371$$ 10.8990 0.565847
$$372$$ 0 0
$$373$$ −6.89898 −0.357216 −0.178608 0.983920i $$-0.557159\pi$$
−0.178608 + 0.983920i $$0.557159\pi$$
$$374$$ 4.00000 0.206835
$$375$$ 0 0
$$376$$ 9.79796 0.505291
$$377$$ −33.7980 −1.74068
$$378$$ 0 0
$$379$$ 22.4949 1.15549 0.577743 0.816219i $$-0.303934\pi$$
0.577743 + 0.816219i $$0.303934\pi$$
$$380$$ −3.69694 −0.189649
$$381$$ 0 0
$$382$$ 4.10102 0.209826
$$383$$ −2.89898 −0.148131 −0.0740655 0.997253i $$-0.523597\pi$$
−0.0740655 + 0.997253i $$0.523597\pi$$
$$384$$ 0 0
$$385$$ 2.89898 0.147746
$$386$$ −17.8990 −0.911034
$$387$$ 0 0
$$388$$ 2.89898 0.147173
$$389$$ −24.8990 −1.26243 −0.631214 0.775609i $$-0.717443\pi$$
−0.631214 + 0.775609i $$0.717443\pi$$
$$390$$ 0 0
$$391$$ −2.00000 −0.101144
$$392$$ 1.00000 0.0505076
$$393$$ 0 0
$$394$$ 16.6969 0.841180
$$395$$ 2.75255 0.138496
$$396$$ 0 0
$$397$$ 38.6969 1.94214 0.971072 0.238788i $$-0.0767500\pi$$
0.971072 + 0.238788i $$0.0767500\pi$$
$$398$$ −2.89898 −0.145313
$$399$$ 0 0
$$400$$ −2.89898 −0.144949
$$401$$ −19.8990 −0.993708 −0.496854 0.867834i $$-0.665511\pi$$
−0.496854 + 0.867834i $$0.665511\pi$$
$$402$$ 0 0
$$403$$ 29.3939 1.46421
$$404$$ −17.2474 −0.858093
$$405$$ 0 0
$$406$$ 6.89898 0.342391
$$407$$ 23.5959 1.16961
$$408$$ 0 0
$$409$$ −13.7980 −0.682265 −0.341133 0.940015i $$-0.610811\pi$$
−0.341133 + 0.940015i $$0.610811\pi$$
$$410$$ −14.2020 −0.701389
$$411$$ 0 0
$$412$$ 14.0000 0.689730
$$413$$ 2.00000 0.0984136
$$414$$ 0 0
$$415$$ −2.89898 −0.142305
$$416$$ 4.89898 0.240192
$$417$$ 0 0
$$418$$ 5.10102 0.249499
$$419$$ 29.4495 1.43870 0.719351 0.694647i $$-0.244439\pi$$
0.719351 + 0.694647i $$0.244439\pi$$
$$420$$ 0 0
$$421$$ 22.8990 1.11603 0.558014 0.829832i $$-0.311564\pi$$
0.558014 + 0.829832i $$0.311564\pi$$
$$422$$ 12.8990 0.627912
$$423$$ 0 0
$$424$$ −10.8990 −0.529301
$$425$$ −5.79796 −0.281242
$$426$$ 0 0
$$427$$ −6.55051 −0.317001
$$428$$ −12.0000 −0.580042
$$429$$ 0 0
$$430$$ −10.0000 −0.482243
$$431$$ 31.5959 1.52192 0.760961 0.648798i $$-0.224728\pi$$
0.760961 + 0.648798i $$0.224728\pi$$
$$432$$ 0 0
$$433$$ −7.79796 −0.374746 −0.187373 0.982289i $$-0.559997\pi$$
−0.187373 + 0.982289i $$0.559997\pi$$
$$434$$ −6.00000 −0.288009
$$435$$ 0 0
$$436$$ 12.6969 0.608073
$$437$$ −2.55051 −0.122007
$$438$$ 0 0
$$439$$ 2.20204 0.105098 0.0525488 0.998618i $$-0.483265\pi$$
0.0525488 + 0.998618i $$0.483265\pi$$
$$440$$ −2.89898 −0.138203
$$441$$ 0 0
$$442$$ 9.79796 0.466041
$$443$$ −14.8990 −0.707872 −0.353936 0.935270i $$-0.615157\pi$$
−0.353936 + 0.935270i $$0.615157\pi$$
$$444$$ 0 0
$$445$$ 24.4949 1.16117
$$446$$ −11.1010 −0.525649
$$447$$ 0 0
$$448$$ −1.00000 −0.0472456
$$449$$ 20.5959 0.971981 0.485991 0.873964i $$-0.338459\pi$$
0.485991 + 0.873964i $$0.338459\pi$$
$$450$$ 0 0
$$451$$ 19.5959 0.922736
$$452$$ −6.10102 −0.286968
$$453$$ 0 0
$$454$$ −5.44949 −0.255757
$$455$$ 7.10102 0.332901
$$456$$ 0 0
$$457$$ −17.4949 −0.818377 −0.409188 0.912450i $$-0.634188\pi$$
−0.409188 + 0.912450i $$0.634188\pi$$
$$458$$ 1.24745 0.0582895
$$459$$ 0 0
$$460$$ 1.44949 0.0675828
$$461$$ 5.65153 0.263218 0.131609 0.991302i $$-0.457986\pi$$
0.131609 + 0.991302i $$0.457986\pi$$
$$462$$ 0 0
$$463$$ 3.69694 0.171811 0.0859057 0.996303i $$-0.472622\pi$$
0.0859057 + 0.996303i $$0.472622\pi$$
$$464$$ −6.89898 −0.320277
$$465$$ 0 0
$$466$$ −7.00000 −0.324269
$$467$$ 10.0000 0.462745 0.231372 0.972865i $$-0.425678\pi$$
0.231372 + 0.972865i $$0.425678\pi$$
$$468$$ 0 0
$$469$$ 12.8990 0.595620
$$470$$ −14.2020 −0.655091
$$471$$ 0 0
$$472$$ −2.00000 −0.0920575
$$473$$ 13.7980 0.634431
$$474$$ 0 0
$$475$$ −7.39388 −0.339254
$$476$$ −2.00000 −0.0916698
$$477$$ 0 0
$$478$$ 6.79796 0.310931
$$479$$ 9.59592 0.438449 0.219224 0.975674i $$-0.429647\pi$$
0.219224 + 0.975674i $$0.429647\pi$$
$$480$$ 0 0
$$481$$ 57.7980 2.63536
$$482$$ 0.898979 0.0409474
$$483$$ 0 0
$$484$$ −7.00000 −0.318182
$$485$$ −4.20204 −0.190805
$$486$$ 0 0
$$487$$ −36.3939 −1.64916 −0.824582 0.565742i $$-0.808590\pi$$
−0.824582 + 0.565742i $$0.808590\pi$$
$$488$$ 6.55051 0.296528
$$489$$ 0 0
$$490$$ −1.44949 −0.0654813
$$491$$ 15.7980 0.712952 0.356476 0.934304i $$-0.383978\pi$$
0.356476 + 0.934304i $$0.383978\pi$$
$$492$$ 0 0
$$493$$ −13.7980 −0.621429
$$494$$ 12.4949 0.562172
$$495$$ 0 0
$$496$$ 6.00000 0.269408
$$497$$ −0.101021 −0.00453139
$$498$$ 0 0
$$499$$ −25.3939 −1.13679 −0.568393 0.822757i $$-0.692435\pi$$
−0.568393 + 0.822757i $$0.692435\pi$$
$$500$$ 11.4495 0.512037
$$501$$ 0 0
$$502$$ 17.4495 0.778809
$$503$$ −24.4949 −1.09217 −0.546087 0.837729i $$-0.683883\pi$$
−0.546087 + 0.837729i $$0.683883\pi$$
$$504$$ 0 0
$$505$$ 25.0000 1.11249
$$506$$ −2.00000 −0.0889108
$$507$$ 0 0
$$508$$ −3.00000 −0.133103
$$509$$ −7.10102 −0.314747 −0.157374 0.987539i $$-0.550303\pi$$
−0.157374 + 0.987539i $$0.550303\pi$$
$$510$$ 0 0
$$511$$ 6.89898 0.305193
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ 8.20204 0.361777
$$515$$ −20.2929 −0.894210
$$516$$ 0 0
$$517$$ 19.5959 0.861827
$$518$$ −11.7980 −0.518373
$$519$$ 0 0
$$520$$ −7.10102 −0.311400
$$521$$ −9.30306 −0.407575 −0.203787 0.979015i $$-0.565325\pi$$
−0.203787 + 0.979015i $$0.565325\pi$$
$$522$$ 0 0
$$523$$ −14.3485 −0.627415 −0.313707 0.949520i $$-0.601571\pi$$
−0.313707 + 0.949520i $$0.601571\pi$$
$$524$$ −8.55051 −0.373531
$$525$$ 0 0
$$526$$ 25.8990 1.12925
$$527$$ 12.0000 0.522728
$$528$$ 0 0
$$529$$ −22.0000 −0.956522
$$530$$ 15.7980 0.686219
$$531$$ 0 0
$$532$$ −2.55051 −0.110579
$$533$$ 48.0000 2.07911
$$534$$ 0 0
$$535$$ 17.3939 0.752003
$$536$$ −12.8990 −0.557151
$$537$$ 0 0
$$538$$ −18.3485 −0.791059
$$539$$ 2.00000 0.0861461
$$540$$ 0 0
$$541$$ −18.4949 −0.795158 −0.397579 0.917568i $$-0.630149\pi$$
−0.397579 + 0.917568i $$0.630149\pi$$
$$542$$ 7.10102 0.305015
$$543$$ 0 0
$$544$$ 2.00000 0.0857493
$$545$$ −18.4041 −0.788344
$$546$$ 0 0
$$547$$ −7.59592 −0.324778 −0.162389 0.986727i $$-0.551920\pi$$
−0.162389 + 0.986727i $$0.551920\pi$$
$$548$$ 7.79796 0.333112
$$549$$ 0 0
$$550$$ −5.79796 −0.247226
$$551$$ −17.5959 −0.749611
$$552$$ 0 0
$$553$$ 1.89898 0.0807528
$$554$$ −18.6969 −0.794357
$$555$$ 0 0
$$556$$ 4.55051 0.192985
$$557$$ −12.8990 −0.546547 −0.273274 0.961936i $$-0.588106\pi$$
−0.273274 + 0.961936i $$0.588106\pi$$
$$558$$ 0 0
$$559$$ 33.7980 1.42950
$$560$$ 1.44949 0.0612521
$$561$$ 0 0
$$562$$ −19.0000 −0.801467
$$563$$ −39.9444 −1.68346 −0.841728 0.539902i $$-0.818461\pi$$
−0.841728 + 0.539902i $$0.818461\pi$$
$$564$$ 0 0
$$565$$ 8.84337 0.372043
$$566$$ −25.4495 −1.06972
$$567$$ 0 0
$$568$$ 0.101021 0.00423873
$$569$$ −30.0000 −1.25767 −0.628833 0.777541i $$-0.716467\pi$$
−0.628833 + 0.777541i $$0.716467\pi$$
$$570$$ 0 0
$$571$$ 33.7980 1.41440 0.707200 0.707013i $$-0.249958\pi$$
0.707200 + 0.707013i $$0.249958\pi$$
$$572$$ 9.79796 0.409673
$$573$$ 0 0
$$574$$ −9.79796 −0.408959
$$575$$ 2.89898 0.120896
$$576$$ 0 0
$$577$$ −15.5959 −0.649267 −0.324633 0.945840i $$-0.605241\pi$$
−0.324633 + 0.945840i $$0.605241\pi$$
$$578$$ −13.0000 −0.540729
$$579$$ 0 0
$$580$$ 10.0000 0.415227
$$581$$ −2.00000 −0.0829740
$$582$$ 0 0
$$583$$ −21.7980 −0.902779
$$584$$ −6.89898 −0.285482
$$585$$ 0 0
$$586$$ 2.75255 0.113707
$$587$$ 16.1464 0.666434 0.333217 0.942850i $$-0.391866\pi$$
0.333217 + 0.942850i $$0.391866\pi$$
$$588$$ 0 0
$$589$$ 15.3031 0.630552
$$590$$ 2.89898 0.119349
$$591$$ 0 0
$$592$$ 11.7980 0.484893
$$593$$ 14.6969 0.603531 0.301765 0.953382i $$-0.402424\pi$$
0.301765 + 0.953382i $$0.402424\pi$$
$$594$$ 0 0
$$595$$ 2.89898 0.118847
$$596$$ −6.00000 −0.245770
$$597$$ 0 0
$$598$$ −4.89898 −0.200334
$$599$$ −33.7980 −1.38095 −0.690474 0.723358i $$-0.742598\pi$$
−0.690474 + 0.723358i $$0.742598\pi$$
$$600$$ 0 0
$$601$$ 16.6969 0.681082 0.340541 0.940230i $$-0.389390\pi$$
0.340541 + 0.940230i $$0.389390\pi$$
$$602$$ −6.89898 −0.281181
$$603$$ 0 0
$$604$$ −5.00000 −0.203447
$$605$$ 10.1464 0.412511
$$606$$ 0 0
$$607$$ 20.6969 0.840063 0.420031 0.907510i $$-0.362019\pi$$
0.420031 + 0.907510i $$0.362019\pi$$
$$608$$ 2.55051 0.103437
$$609$$ 0 0
$$610$$ −9.49490 −0.384437
$$611$$ 48.0000 1.94187
$$612$$ 0 0
$$613$$ −14.6969 −0.593604 −0.296802 0.954939i $$-0.595920\pi$$
−0.296802 + 0.954939i $$0.595920\pi$$
$$614$$ 25.2474 1.01890
$$615$$ 0 0
$$616$$ −2.00000 −0.0805823
$$617$$ −15.3939 −0.619734 −0.309867 0.950780i $$-0.600285\pi$$
−0.309867 + 0.950780i $$0.600285\pi$$
$$618$$ 0 0
$$619$$ 30.1464 1.21169 0.605844 0.795584i $$-0.292836\pi$$
0.605844 + 0.795584i $$0.292836\pi$$
$$620$$ −8.69694 −0.349277
$$621$$ 0 0
$$622$$ 30.6969 1.23084
$$623$$ 16.8990 0.677043
$$624$$ 0 0
$$625$$ −2.10102 −0.0840408
$$626$$ −4.69694 −0.187727
$$627$$ 0 0
$$628$$ −8.34847 −0.333140
$$629$$ 23.5959 0.940831
$$630$$ 0 0
$$631$$ 27.8990 1.11064 0.555320 0.831636i $$-0.312596\pi$$
0.555320 + 0.831636i $$0.312596\pi$$
$$632$$ −1.89898 −0.0755373
$$633$$ 0 0
$$634$$ 20.6969 0.821980
$$635$$ 4.34847 0.172564
$$636$$ 0 0
$$637$$ 4.89898 0.194105
$$638$$ −13.7980 −0.546266
$$639$$ 0 0
$$640$$ −1.44949 −0.0572961
$$641$$ −7.49490 −0.296031 −0.148015 0.988985i $$-0.547288\pi$$
−0.148015 + 0.988985i $$0.547288\pi$$
$$642$$ 0 0
$$643$$ −39.3939 −1.55354 −0.776771 0.629783i $$-0.783144\pi$$
−0.776771 + 0.629783i $$0.783144\pi$$
$$644$$ 1.00000 0.0394055
$$645$$ 0 0
$$646$$ 5.10102 0.200697
$$647$$ −50.6969 −1.99310 −0.996551 0.0829807i $$-0.973556\pi$$
−0.996551 + 0.0829807i $$0.973556\pi$$
$$648$$ 0 0
$$649$$ −4.00000 −0.157014
$$650$$ −14.2020 −0.557050
$$651$$ 0 0
$$652$$ −19.7980 −0.775348
$$653$$ 9.79796 0.383424 0.191712 0.981451i $$-0.438596\pi$$
0.191712 + 0.981451i $$0.438596\pi$$
$$654$$ 0 0
$$655$$ 12.3939 0.484269
$$656$$ 9.79796 0.382546
$$657$$ 0 0
$$658$$ −9.79796 −0.381964
$$659$$ −24.6969 −0.962056 −0.481028 0.876705i $$-0.659736\pi$$
−0.481028 + 0.876705i $$0.659736\pi$$
$$660$$ 0 0
$$661$$ 4.55051 0.176994 0.0884972 0.996076i $$-0.471794\pi$$
0.0884972 + 0.996076i $$0.471794\pi$$
$$662$$ 4.69694 0.182552
$$663$$ 0 0
$$664$$ 2.00000 0.0776151
$$665$$ 3.69694 0.143361
$$666$$ 0 0
$$667$$ 6.89898 0.267130
$$668$$ −10.6969 −0.413877
$$669$$ 0 0
$$670$$ 18.6969 0.722326
$$671$$ 13.1010 0.505759
$$672$$ 0 0
$$673$$ −8.59592 −0.331348 −0.165674 0.986181i $$-0.552980\pi$$
−0.165674 + 0.986181i $$0.552980\pi$$
$$674$$ −23.3939 −0.901098
$$675$$ 0 0
$$676$$ 11.0000 0.423077
$$677$$ 14.6969 0.564849 0.282425 0.959289i $$-0.408861\pi$$
0.282425 + 0.959289i $$0.408861\pi$$
$$678$$ 0 0
$$679$$ −2.89898 −0.111253
$$680$$ −2.89898 −0.111171
$$681$$ 0 0
$$682$$ 12.0000 0.459504
$$683$$ 51.7980 1.98199 0.990997 0.133885i $$-0.0427452\pi$$
0.990997 + 0.133885i $$0.0427452\pi$$
$$684$$ 0 0
$$685$$ −11.3031 −0.431868
$$686$$ −1.00000 −0.0381802
$$687$$ 0 0
$$688$$ 6.89898 0.263021
$$689$$ −53.3939 −2.03414
$$690$$ 0 0
$$691$$ 51.0454 1.94186 0.970929 0.239366i $$-0.0769396\pi$$
0.970929 + 0.239366i $$0.0769396\pi$$
$$692$$ −3.10102 −0.117883
$$693$$ 0 0
$$694$$ 19.5959 0.743851
$$695$$ −6.59592 −0.250197
$$696$$ 0 0
$$697$$ 19.5959 0.742248
$$698$$ 11.1010 0.420180
$$699$$ 0 0
$$700$$ 2.89898 0.109571
$$701$$ −7.39388 −0.279263 −0.139631 0.990204i $$-0.544592\pi$$
−0.139631 + 0.990204i $$0.544592\pi$$
$$702$$ 0 0
$$703$$ 30.0908 1.13490
$$704$$ 2.00000 0.0753778
$$705$$ 0 0
$$706$$ −6.00000 −0.225813
$$707$$ 17.2474 0.648657
$$708$$ 0 0
$$709$$ 27.5959 1.03639 0.518193 0.855264i $$-0.326605\pi$$
0.518193 + 0.855264i $$0.326605\pi$$
$$710$$ −0.146428 −0.00549535
$$711$$ 0 0
$$712$$ −16.8990 −0.633316
$$713$$ −6.00000 −0.224702
$$714$$ 0 0
$$715$$ −14.2020 −0.531126
$$716$$ 20.6969 0.773481
$$717$$ 0 0
$$718$$ −8.79796 −0.328337
$$719$$ 9.79796 0.365402 0.182701 0.983169i $$-0.441516\pi$$
0.182701 + 0.983169i $$0.441516\pi$$
$$720$$ 0 0
$$721$$ −14.0000 −0.521387
$$722$$ −12.4949 −0.465012
$$723$$ 0 0
$$724$$ −10.3485 −0.384598
$$725$$ 20.0000 0.742781
$$726$$ 0 0
$$727$$ −8.49490 −0.315058 −0.157529 0.987514i $$-0.550353\pi$$
−0.157529 + 0.987514i $$0.550353\pi$$
$$728$$ −4.89898 −0.181568
$$729$$ 0 0
$$730$$ 10.0000 0.370117
$$731$$ 13.7980 0.510336
$$732$$ 0 0
$$733$$ −17.4495 −0.644512 −0.322256 0.946653i $$-0.604441\pi$$
−0.322256 + 0.946653i $$0.604441\pi$$
$$734$$ −13.7980 −0.509292
$$735$$ 0 0
$$736$$ −1.00000 −0.0368605
$$737$$ −25.7980 −0.950280
$$738$$ 0 0
$$739$$ 13.5959 0.500134 0.250067 0.968229i $$-0.419547\pi$$
0.250067 + 0.968229i $$0.419547\pi$$
$$740$$ −17.1010 −0.628646
$$741$$ 0 0
$$742$$ 10.8990 0.400114
$$743$$ 36.0000 1.32071 0.660356 0.750953i $$-0.270405\pi$$
0.660356 + 0.750953i $$0.270405\pi$$
$$744$$ 0 0
$$745$$ 8.69694 0.318631
$$746$$ −6.89898 −0.252590
$$747$$ 0 0
$$748$$ 4.00000 0.146254
$$749$$ 12.0000 0.438470
$$750$$ 0 0
$$751$$ 1.40408 0.0512357 0.0256178 0.999672i $$-0.491845\pi$$
0.0256178 + 0.999672i $$0.491845\pi$$
$$752$$ 9.79796 0.357295
$$753$$ 0 0
$$754$$ −33.7980 −1.23085
$$755$$ 7.24745 0.263762
$$756$$ 0 0
$$757$$ −35.3939 −1.28641 −0.643206 0.765693i $$-0.722396\pi$$
−0.643206 + 0.765693i $$0.722396\pi$$
$$758$$ 22.4949 0.817051
$$759$$ 0 0
$$760$$ −3.69694 −0.134102
$$761$$ 2.00000 0.0724999 0.0362500 0.999343i $$-0.488459\pi$$
0.0362500 + 0.999343i $$0.488459\pi$$
$$762$$ 0 0
$$763$$ −12.6969 −0.459660
$$764$$ 4.10102 0.148370
$$765$$ 0 0
$$766$$ −2.89898 −0.104744
$$767$$ −9.79796 −0.353784
$$768$$ 0 0
$$769$$ −34.0908 −1.22935 −0.614673 0.788782i $$-0.710712\pi$$
−0.614673 + 0.788782i $$0.710712\pi$$
$$770$$ 2.89898 0.104472
$$771$$ 0 0
$$772$$ −17.8990 −0.644198
$$773$$ 33.9444 1.22089 0.610447 0.792057i $$-0.290990\pi$$
0.610447 + 0.792057i $$0.290990\pi$$
$$774$$ 0 0
$$775$$ −17.3939 −0.624807
$$776$$ 2.89898 0.104067
$$777$$ 0 0
$$778$$ −24.8990 −0.892672
$$779$$ 24.9898 0.895352
$$780$$ 0 0
$$781$$ 0.202041 0.00722960
$$782$$ −2.00000 −0.0715199
$$783$$ 0 0
$$784$$ 1.00000 0.0357143
$$785$$ 12.1010 0.431904
$$786$$ 0 0
$$787$$ −11.3939 −0.406148 −0.203074 0.979163i $$-0.565093\pi$$
−0.203074 + 0.979163i $$0.565093\pi$$
$$788$$ 16.6969 0.594804
$$789$$ 0 0
$$790$$ 2.75255 0.0979314
$$791$$ 6.10102 0.216927
$$792$$ 0 0
$$793$$ 32.0908 1.13958
$$794$$ 38.6969 1.37330
$$795$$ 0 0
$$796$$ −2.89898 −0.102752
$$797$$ −17.9444 −0.635623 −0.317811 0.948154i $$-0.602948\pi$$
−0.317811 + 0.948154i $$0.602948\pi$$
$$798$$ 0 0
$$799$$ 19.5959 0.693254
$$800$$ −2.89898 −0.102494
$$801$$ 0 0
$$802$$ −19.8990 −0.702657
$$803$$ −13.7980 −0.486919
$$804$$ 0 0
$$805$$ −1.44949 −0.0510878
$$806$$ 29.3939 1.03536
$$807$$ 0 0
$$808$$ −17.2474 −0.606763
$$809$$ −16.2020 −0.569633 −0.284817 0.958582i $$-0.591933\pi$$
−0.284817 + 0.958582i $$0.591933\pi$$
$$810$$ 0 0
$$811$$ −2.00000 −0.0702295 −0.0351147 0.999383i $$-0.511180\pi$$
−0.0351147 + 0.999383i $$0.511180\pi$$
$$812$$ 6.89898 0.242107
$$813$$ 0 0
$$814$$ 23.5959 0.827036
$$815$$ 28.6969 1.00521
$$816$$ 0 0
$$817$$ 17.5959 0.615603
$$818$$ −13.7980 −0.482434
$$819$$ 0 0
$$820$$ −14.2020 −0.495957
$$821$$ 0.404082 0.0141026 0.00705128 0.999975i $$-0.497755\pi$$
0.00705128 + 0.999975i $$0.497755\pi$$
$$822$$ 0 0
$$823$$ −13.3939 −0.466881 −0.233441 0.972371i $$-0.574998\pi$$
−0.233441 + 0.972371i $$0.574998\pi$$
$$824$$ 14.0000 0.487713
$$825$$ 0 0
$$826$$ 2.00000 0.0695889
$$827$$ −36.4949 −1.26905 −0.634526 0.772902i $$-0.718805\pi$$
−0.634526 + 0.772902i $$0.718805\pi$$
$$828$$ 0 0
$$829$$ 1.30306 0.0452572 0.0226286 0.999744i $$-0.492796\pi$$
0.0226286 + 0.999744i $$0.492796\pi$$
$$830$$ −2.89898 −0.100625
$$831$$ 0 0
$$832$$ 4.89898 0.169842
$$833$$ 2.00000 0.0692959
$$834$$ 0 0
$$835$$ 15.5051 0.536576
$$836$$ 5.10102 0.176422
$$837$$ 0 0
$$838$$ 29.4495 1.01732
$$839$$ −35.1010 −1.21182 −0.605911 0.795533i $$-0.707191\pi$$
−0.605911 + 0.795533i $$0.707191\pi$$
$$840$$ 0 0
$$841$$ 18.5959 0.641239
$$842$$ 22.8990 0.789151
$$843$$ 0 0
$$844$$ 12.8990 0.444001
$$845$$ −15.9444 −0.548504
$$846$$ 0 0
$$847$$ 7.00000 0.240523
$$848$$ −10.8990 −0.374272
$$849$$ 0 0
$$850$$ −5.79796 −0.198868
$$851$$ −11.7980 −0.404429
$$852$$ 0 0
$$853$$ 24.8434 0.850621 0.425310 0.905048i $$-0.360165\pi$$
0.425310 + 0.905048i $$0.360165\pi$$
$$854$$ −6.55051 −0.224154
$$855$$ 0 0
$$856$$ −12.0000 −0.410152
$$857$$ −34.8990 −1.19213 −0.596063 0.802938i $$-0.703269\pi$$
−0.596063 + 0.802938i $$0.703269\pi$$
$$858$$ 0 0
$$859$$ −10.0000 −0.341196 −0.170598 0.985341i $$-0.554570\pi$$
−0.170598 + 0.985341i $$0.554570\pi$$
$$860$$ −10.0000 −0.340997
$$861$$ 0 0
$$862$$ 31.5959 1.07616
$$863$$ 11.8990 0.405046 0.202523 0.979278i $$-0.435086\pi$$
0.202523 + 0.979278i $$0.435086\pi$$
$$864$$ 0 0
$$865$$ 4.49490 0.152831
$$866$$ −7.79796 −0.264985
$$867$$ 0 0
$$868$$ −6.00000 −0.203653
$$869$$ −3.79796 −0.128837
$$870$$ 0 0
$$871$$ −63.1918 −2.14117
$$872$$ 12.6969 0.429973
$$873$$ 0 0
$$874$$ −2.55051 −0.0862723
$$875$$ −11.4495 −0.387063
$$876$$ 0 0
$$877$$ 22.4949 0.759599 0.379799 0.925069i $$-0.375993\pi$$
0.379799 + 0.925069i $$0.375993\pi$$
$$878$$ 2.20204 0.0743153
$$879$$ 0 0
$$880$$ −2.89898 −0.0977246
$$881$$ 19.5959 0.660203 0.330102 0.943945i $$-0.392917\pi$$
0.330102 + 0.943945i $$0.392917\pi$$
$$882$$ 0 0
$$883$$ −19.7980 −0.666254 −0.333127 0.942882i $$-0.608104\pi$$
−0.333127 + 0.942882i $$0.608104\pi$$
$$884$$ 9.79796 0.329541
$$885$$ 0 0
$$886$$ −14.8990 −0.500541
$$887$$ −14.2020 −0.476858 −0.238429 0.971160i $$-0.576632\pi$$
−0.238429 + 0.971160i $$0.576632\pi$$
$$888$$ 0 0
$$889$$ 3.00000 0.100617
$$890$$ 24.4949 0.821071
$$891$$ 0 0
$$892$$ −11.1010 −0.371690
$$893$$ 24.9898 0.836252
$$894$$ 0 0
$$895$$ −30.0000 −1.00279
$$896$$ −1.00000 −0.0334077
$$897$$ 0 0
$$898$$ 20.5959 0.687295
$$899$$ −41.3939 −1.38056
$$900$$ 0 0
$$901$$ −21.7980 −0.726195
$$902$$ 19.5959 0.652473
$$903$$ 0 0
$$904$$ −6.10102 −0.202917
$$905$$ 15.0000 0.498617
$$906$$ 0 0
$$907$$ 2.69694 0.0895504 0.0447752 0.998997i $$-0.485743\pi$$
0.0447752 + 0.998997i $$0.485743\pi$$
$$908$$ −5.44949 −0.180848
$$909$$ 0 0
$$910$$ 7.10102 0.235397
$$911$$ 51.9898 1.72250 0.861249 0.508183i $$-0.169682\pi$$
0.861249 + 0.508183i $$0.169682\pi$$
$$912$$ 0 0
$$913$$ 4.00000 0.132381
$$914$$ −17.4949 −0.578680
$$915$$ 0 0
$$916$$ 1.24745 0.0412169
$$917$$ 8.55051 0.282363
$$918$$ 0 0
$$919$$ −25.6969 −0.847664 −0.423832 0.905741i $$-0.639315\pi$$
−0.423832 + 0.905741i $$0.639315\pi$$
$$920$$ 1.44949 0.0477883
$$921$$ 0 0
$$922$$ 5.65153 0.186123
$$923$$ 0.494897 0.0162897
$$924$$ 0 0
$$925$$ −34.2020 −1.12456
$$926$$ 3.69694 0.121489
$$927$$ 0 0
$$928$$ −6.89898 −0.226470
$$929$$ 34.2929 1.12511 0.562556 0.826759i $$-0.309818\pi$$
0.562556 + 0.826759i $$0.309818\pi$$
$$930$$ 0 0
$$931$$ 2.55051 0.0835896
$$932$$ −7.00000 −0.229293
$$933$$ 0 0
$$934$$ 10.0000 0.327210
$$935$$ −5.79796 −0.189614
$$936$$ 0 0
$$937$$ 45.5959 1.48955 0.744777 0.667314i $$-0.232556\pi$$
0.744777 + 0.667314i $$0.232556\pi$$
$$938$$ 12.8990 0.421167
$$939$$ 0 0
$$940$$ −14.2020 −0.463220
$$941$$ −1.44949 −0.0472520 −0.0236260 0.999721i $$-0.507521\pi$$
−0.0236260 + 0.999721i $$0.507521\pi$$
$$942$$ 0 0
$$943$$ −9.79796 −0.319065
$$944$$ −2.00000 −0.0650945
$$945$$ 0 0
$$946$$ 13.7980 0.448610
$$947$$ 52.4949 1.70585 0.852927 0.522029i $$-0.174825\pi$$
0.852927 + 0.522029i $$0.174825\pi$$
$$948$$ 0 0
$$949$$ −33.7980 −1.09713
$$950$$ −7.39388 −0.239889
$$951$$ 0 0
$$952$$ −2.00000 −0.0648204
$$953$$ −3.39388 −0.109938 −0.0549692 0.998488i $$-0.517506\pi$$
−0.0549692 + 0.998488i $$0.517506\pi$$
$$954$$ 0 0
$$955$$ −5.94439 −0.192356
$$956$$ 6.79796 0.219862
$$957$$ 0 0
$$958$$ 9.59592 0.310030
$$959$$ −7.79796 −0.251809
$$960$$ 0 0
$$961$$ 5.00000 0.161290
$$962$$ 57.7980 1.86348
$$963$$ 0 0
$$964$$ 0.898979 0.0289542
$$965$$ 25.9444 0.835179
$$966$$ 0 0
$$967$$ 24.5959 0.790951 0.395476 0.918476i $$-0.370580\pi$$
0.395476 + 0.918476i $$0.370580\pi$$
$$968$$ −7.00000 −0.224989
$$969$$ 0 0
$$970$$ −4.20204 −0.134919
$$971$$ −0.0556128 −0.00178470 −0.000892350 1.00000i $$-0.500284\pi$$
−0.000892350 1.00000i $$0.500284\pi$$
$$972$$ 0 0
$$973$$ −4.55051 −0.145883
$$974$$ −36.3939 −1.16614
$$975$$ 0 0
$$976$$ 6.55051 0.209677
$$977$$ −37.5959 −1.20280 −0.601400 0.798948i $$-0.705390\pi$$
−0.601400 + 0.798948i $$0.705390\pi$$
$$978$$ 0 0
$$979$$ −33.7980 −1.08019
$$980$$ −1.44949 −0.0463023
$$981$$ 0 0
$$982$$ 15.7980 0.504133
$$983$$ −33.1918 −1.05866 −0.529328 0.848418i $$-0.677556\pi$$
−0.529328 + 0.848418i $$0.677556\pi$$
$$984$$ 0 0
$$985$$ −24.2020 −0.771141
$$986$$ −13.7980 −0.439417
$$987$$ 0 0
$$988$$ 12.4949 0.397516
$$989$$ −6.89898 −0.219375
$$990$$ 0 0
$$991$$ −1.79796 −0.0571140 −0.0285570 0.999592i $$-0.509091\pi$$
−0.0285570 + 0.999592i $$0.509091\pi$$
$$992$$ 6.00000 0.190500
$$993$$ 0 0
$$994$$ −0.101021 −0.00320418
$$995$$ 4.20204 0.133214
$$996$$ 0 0
$$997$$ 52.1464 1.65149 0.825747 0.564041i $$-0.190754\pi$$
0.825747 + 0.564041i $$0.190754\pi$$
$$998$$ −25.3939 −0.803829
$$999$$ 0 0
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1134.2.a.p.1.1 2
3.2 odd 2 1134.2.a.i.1.2 2
4.3 odd 2 9072.2.a.bk.1.1 2
7.6 odd 2 7938.2.a.bn.1.2 2
9.2 odd 6 378.2.f.d.253.1 4
9.4 even 3 126.2.f.c.43.2 4
9.5 odd 6 378.2.f.d.127.1 4
9.7 even 3 126.2.f.c.85.1 yes 4
12.11 even 2 9072.2.a.bd.1.2 2
21.20 even 2 7938.2.a.bm.1.1 2
36.7 odd 6 1008.2.r.e.337.2 4
36.11 even 6 3024.2.r.e.1009.1 4
36.23 even 6 3024.2.r.e.2017.1 4
36.31 odd 6 1008.2.r.e.673.1 4
63.2 odd 6 2646.2.h.m.361.2 4
63.4 even 3 882.2.h.k.79.2 4
63.5 even 6 2646.2.e.k.2125.2 4
63.11 odd 6 2646.2.e.l.1549.1 4
63.13 odd 6 882.2.f.j.295.1 4
63.16 even 3 882.2.h.k.67.2 4
63.20 even 6 2646.2.f.k.1765.2 4
63.23 odd 6 2646.2.e.l.2125.1 4
63.25 even 3 882.2.e.m.373.1 4
63.31 odd 6 882.2.h.l.79.1 4
63.32 odd 6 2646.2.h.m.667.2 4
63.34 odd 6 882.2.f.j.589.2 4
63.38 even 6 2646.2.e.k.1549.2 4
63.40 odd 6 882.2.e.n.655.2 4
63.41 even 6 2646.2.f.k.883.2 4
63.47 even 6 2646.2.h.n.361.1 4
63.52 odd 6 882.2.e.n.373.2 4
63.58 even 3 882.2.e.m.655.1 4
63.59 even 6 2646.2.h.n.667.1 4
63.61 odd 6 882.2.h.l.67.1 4

By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.f.c.43.2 4 9.4 even 3
126.2.f.c.85.1 yes 4 9.7 even 3
378.2.f.d.127.1 4 9.5 odd 6
378.2.f.d.253.1 4 9.2 odd 6
882.2.e.m.373.1 4 63.25 even 3
882.2.e.m.655.1 4 63.58 even 3
882.2.e.n.373.2 4 63.52 odd 6
882.2.e.n.655.2 4 63.40 odd 6
882.2.f.j.295.1 4 63.13 odd 6
882.2.f.j.589.2 4 63.34 odd 6
882.2.h.k.67.2 4 63.16 even 3
882.2.h.k.79.2 4 63.4 even 3
882.2.h.l.67.1 4 63.61 odd 6
882.2.h.l.79.1 4 63.31 odd 6
1008.2.r.e.337.2 4 36.7 odd 6
1008.2.r.e.673.1 4 36.31 odd 6
1134.2.a.i.1.2 2 3.2 odd 2
1134.2.a.p.1.1 2 1.1 even 1 trivial
2646.2.e.k.1549.2 4 63.38 even 6
2646.2.e.k.2125.2 4 63.5 even 6
2646.2.e.l.1549.1 4 63.11 odd 6
2646.2.e.l.2125.1 4 63.23 odd 6
2646.2.f.k.883.2 4 63.41 even 6
2646.2.f.k.1765.2 4 63.20 even 6
2646.2.h.m.361.2 4 63.2 odd 6
2646.2.h.m.667.2 4 63.32 odd 6
2646.2.h.n.361.1 4 63.47 even 6
2646.2.h.n.667.1 4 63.59 even 6
3024.2.r.e.1009.1 4 36.11 even 6
3024.2.r.e.2017.1 4 36.23 even 6
7938.2.a.bm.1.1 2 21.20 even 2
7938.2.a.bn.1.2 2 7.6 odd 2
9072.2.a.bd.1.2 2 12.11 even 2
9072.2.a.bk.1.1 2 4.3 odd 2