# Properties

 Label 1680.2.t.e.1009.2 Level $1680$ Weight $2$ Character 1680.1009 Analytic conductor $13.415$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1680.t (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$13.4148675396$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 210) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 1009.2 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1680.1009 Dual form 1680.2.t.e.1009.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000i q^{3} +(1.00000 - 2.00000i) q^{5} +1.00000i q^{7} -1.00000 q^{9} +O(q^{10})$$ $$q+1.00000i q^{3} +(1.00000 - 2.00000i) q^{5} +1.00000i q^{7} -1.00000 q^{9} -2.00000 q^{11} -6.00000i q^{13} +(2.00000 + 1.00000i) q^{15} +4.00000i q^{17} -6.00000 q^{19} -1.00000 q^{21} -8.00000i q^{23} +(-3.00000 - 4.00000i) q^{25} -1.00000i q^{27} -6.00000 q^{29} +2.00000 q^{31} -2.00000i q^{33} +(2.00000 + 1.00000i) q^{35} +4.00000i q^{37} +6.00000 q^{39} +2.00000 q^{41} +4.00000i q^{43} +(-1.00000 + 2.00000i) q^{45} -8.00000i q^{47} -1.00000 q^{49} -4.00000 q^{51} -6.00000i q^{53} +(-2.00000 + 4.00000i) q^{55} -6.00000i q^{57} -8.00000 q^{59} -10.0000 q^{61} -1.00000i q^{63} +(-12.0000 - 6.00000i) q^{65} -8.00000i q^{67} +8.00000 q^{69} +6.00000 q^{71} +14.0000i q^{73} +(4.00000 - 3.00000i) q^{75} -2.00000i q^{77} -12.0000 q^{79} +1.00000 q^{81} -8.00000i q^{83} +(8.00000 + 4.00000i) q^{85} -6.00000i q^{87} +10.0000 q^{89} +6.00000 q^{91} +2.00000i q^{93} +(-6.00000 + 12.0000i) q^{95} -10.0000i q^{97} +2.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 2q^{5} - 2q^{9} + O(q^{10})$$ $$2q + 2q^{5} - 2q^{9} - 4q^{11} + 4q^{15} - 12q^{19} - 2q^{21} - 6q^{25} - 12q^{29} + 4q^{31} + 4q^{35} + 12q^{39} + 4q^{41} - 2q^{45} - 2q^{49} - 8q^{51} - 4q^{55} - 16q^{59} - 20q^{61} - 24q^{65} + 16q^{69} + 12q^{71} + 8q^{75} - 24q^{79} + 2q^{81} + 16q^{85} + 20q^{89} + 12q^{91} - 12q^{95} + 4q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$$.

 $$n$$ $$241$$ $$337$$ $$421$$ $$1121$$ $$1471$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 1.00000i 0.577350i
$$4$$ 0 0
$$5$$ 1.00000 2.00000i 0.447214 0.894427i
$$6$$ 0 0
$$7$$ 1.00000i 0.377964i
$$8$$ 0 0
$$9$$ −1.00000 −0.333333
$$10$$ 0 0
$$11$$ −2.00000 −0.603023 −0.301511 0.953463i $$-0.597491\pi$$
−0.301511 + 0.953463i $$0.597491\pi$$
$$12$$ 0 0
$$13$$ 6.00000i 1.66410i −0.554700 0.832050i $$-0.687167\pi$$
0.554700 0.832050i $$-0.312833\pi$$
$$14$$ 0 0
$$15$$ 2.00000 + 1.00000i 0.516398 + 0.258199i
$$16$$ 0 0
$$17$$ 4.00000i 0.970143i 0.874475 + 0.485071i $$0.161206\pi$$
−0.874475 + 0.485071i $$0.838794\pi$$
$$18$$ 0 0
$$19$$ −6.00000 −1.37649 −0.688247 0.725476i $$-0.741620\pi$$
−0.688247 + 0.725476i $$0.741620\pi$$
$$20$$ 0 0
$$21$$ −1.00000 −0.218218
$$22$$ 0 0
$$23$$ 8.00000i 1.66812i −0.551677 0.834058i $$-0.686012\pi$$
0.551677 0.834058i $$-0.313988\pi$$
$$24$$ 0 0
$$25$$ −3.00000 4.00000i −0.600000 0.800000i
$$26$$ 0 0
$$27$$ 1.00000i 0.192450i
$$28$$ 0 0
$$29$$ −6.00000 −1.11417 −0.557086 0.830455i $$-0.688081\pi$$
−0.557086 + 0.830455i $$0.688081\pi$$
$$30$$ 0 0
$$31$$ 2.00000 0.359211 0.179605 0.983739i $$-0.442518\pi$$
0.179605 + 0.983739i $$0.442518\pi$$
$$32$$ 0 0
$$33$$ 2.00000i 0.348155i
$$34$$ 0 0
$$35$$ 2.00000 + 1.00000i 0.338062 + 0.169031i
$$36$$ 0 0
$$37$$ 4.00000i 0.657596i 0.944400 + 0.328798i $$0.106644\pi$$
−0.944400 + 0.328798i $$0.893356\pi$$
$$38$$ 0 0
$$39$$ 6.00000 0.960769
$$40$$ 0 0
$$41$$ 2.00000 0.312348 0.156174 0.987730i $$-0.450084\pi$$
0.156174 + 0.987730i $$0.450084\pi$$
$$42$$ 0 0
$$43$$ 4.00000i 0.609994i 0.952353 + 0.304997i $$0.0986555\pi$$
−0.952353 + 0.304997i $$0.901344\pi$$
$$44$$ 0 0
$$45$$ −1.00000 + 2.00000i −0.149071 + 0.298142i
$$46$$ 0 0
$$47$$ 8.00000i 1.16692i −0.812142 0.583460i $$-0.801699\pi$$
0.812142 0.583460i $$-0.198301\pi$$
$$48$$ 0 0
$$49$$ −1.00000 −0.142857
$$50$$ 0 0
$$51$$ −4.00000 −0.560112
$$52$$ 0 0
$$53$$ 6.00000i 0.824163i −0.911147 0.412082i $$-0.864802\pi$$
0.911147 0.412082i $$-0.135198\pi$$
$$54$$ 0 0
$$55$$ −2.00000 + 4.00000i −0.269680 + 0.539360i
$$56$$ 0 0
$$57$$ 6.00000i 0.794719i
$$58$$ 0 0
$$59$$ −8.00000 −1.04151 −0.520756 0.853706i $$-0.674350\pi$$
−0.520756 + 0.853706i $$0.674350\pi$$
$$60$$ 0 0
$$61$$ −10.0000 −1.28037 −0.640184 0.768221i $$-0.721142\pi$$
−0.640184 + 0.768221i $$0.721142\pi$$
$$62$$ 0 0
$$63$$ 1.00000i 0.125988i
$$64$$ 0 0
$$65$$ −12.0000 6.00000i −1.48842 0.744208i
$$66$$ 0 0
$$67$$ 8.00000i 0.977356i −0.872464 0.488678i $$-0.837479\pi$$
0.872464 0.488678i $$-0.162521\pi$$
$$68$$ 0 0
$$69$$ 8.00000 0.963087
$$70$$ 0 0
$$71$$ 6.00000 0.712069 0.356034 0.934473i $$-0.384129\pi$$
0.356034 + 0.934473i $$0.384129\pi$$
$$72$$ 0 0
$$73$$ 14.0000i 1.63858i 0.573382 + 0.819288i $$0.305631\pi$$
−0.573382 + 0.819288i $$0.694369\pi$$
$$74$$ 0 0
$$75$$ 4.00000 3.00000i 0.461880 0.346410i
$$76$$ 0 0
$$77$$ 2.00000i 0.227921i
$$78$$ 0 0
$$79$$ −12.0000 −1.35011 −0.675053 0.737769i $$-0.735879\pi$$
−0.675053 + 0.737769i $$0.735879\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ 8.00000i 0.878114i −0.898459 0.439057i $$-0.855313\pi$$
0.898459 0.439057i $$-0.144687\pi$$
$$84$$ 0 0
$$85$$ 8.00000 + 4.00000i 0.867722 + 0.433861i
$$86$$ 0 0
$$87$$ 6.00000i 0.643268i
$$88$$ 0 0
$$89$$ 10.0000 1.06000 0.529999 0.847998i $$-0.322192\pi$$
0.529999 + 0.847998i $$0.322192\pi$$
$$90$$ 0 0
$$91$$ 6.00000 0.628971
$$92$$ 0 0
$$93$$ 2.00000i 0.207390i
$$94$$ 0 0
$$95$$ −6.00000 + 12.0000i −0.615587 + 1.23117i
$$96$$ 0 0
$$97$$ 10.0000i 1.01535i −0.861550 0.507673i $$-0.830506\pi$$
0.861550 0.507673i $$-0.169494\pi$$
$$98$$ 0 0
$$99$$ 2.00000 0.201008
$$100$$ 0 0
$$101$$ 10.0000 0.995037 0.497519 0.867453i $$-0.334245\pi$$
0.497519 + 0.867453i $$0.334245\pi$$
$$102$$ 0 0
$$103$$ 8.00000i 0.788263i 0.919054 + 0.394132i $$0.128955\pi$$
−0.919054 + 0.394132i $$0.871045\pi$$
$$104$$ 0 0
$$105$$ −1.00000 + 2.00000i −0.0975900 + 0.195180i
$$106$$ 0 0
$$107$$ 12.0000i 1.16008i −0.814587 0.580042i $$-0.803036\pi$$
0.814587 0.580042i $$-0.196964\pi$$
$$108$$ 0 0
$$109$$ 14.0000 1.34096 0.670478 0.741929i $$-0.266089\pi$$
0.670478 + 0.741929i $$0.266089\pi$$
$$110$$ 0 0
$$111$$ −4.00000 −0.379663
$$112$$ 0 0
$$113$$ 6.00000i 0.564433i −0.959351 0.282216i $$-0.908930\pi$$
0.959351 0.282216i $$-0.0910696\pi$$
$$114$$ 0 0
$$115$$ −16.0000 8.00000i −1.49201 0.746004i
$$116$$ 0 0
$$117$$ 6.00000i 0.554700i
$$118$$ 0 0
$$119$$ −4.00000 −0.366679
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ 0 0
$$123$$ 2.00000i 0.180334i
$$124$$ 0 0
$$125$$ −11.0000 + 2.00000i −0.983870 + 0.178885i
$$126$$ 0 0
$$127$$ 4.00000i 0.354943i −0.984126 0.177471i $$-0.943208\pi$$
0.984126 0.177471i $$-0.0567917\pi$$
$$128$$ 0 0
$$129$$ −4.00000 −0.352180
$$130$$ 0 0
$$131$$ 12.0000 1.04844 0.524222 0.851581i $$-0.324356\pi$$
0.524222 + 0.851581i $$0.324356\pi$$
$$132$$ 0 0
$$133$$ 6.00000i 0.520266i
$$134$$ 0 0
$$135$$ −2.00000 1.00000i −0.172133 0.0860663i
$$136$$ 0 0
$$137$$ 6.00000i 0.512615i −0.966595 0.256307i $$-0.917494\pi$$
0.966595 0.256307i $$-0.0825059\pi$$
$$138$$ 0 0
$$139$$ −14.0000 −1.18746 −0.593732 0.804663i $$-0.702346\pi$$
−0.593732 + 0.804663i $$0.702346\pi$$
$$140$$ 0 0
$$141$$ 8.00000 0.673722
$$142$$ 0 0
$$143$$ 12.0000i 1.00349i
$$144$$ 0 0
$$145$$ −6.00000 + 12.0000i −0.498273 + 0.996546i
$$146$$ 0 0
$$147$$ 1.00000i 0.0824786i
$$148$$ 0 0
$$149$$ −10.0000 −0.819232 −0.409616 0.912258i $$-0.634337\pi$$
−0.409616 + 0.912258i $$0.634337\pi$$
$$150$$ 0 0
$$151$$ 8.00000 0.651031 0.325515 0.945537i $$-0.394462\pi$$
0.325515 + 0.945537i $$0.394462\pi$$
$$152$$ 0 0
$$153$$ 4.00000i 0.323381i
$$154$$ 0 0
$$155$$ 2.00000 4.00000i 0.160644 0.321288i
$$156$$ 0 0
$$157$$ 22.0000i 1.75579i −0.478852 0.877896i $$-0.658947\pi$$
0.478852 0.877896i $$-0.341053\pi$$
$$158$$ 0 0
$$159$$ 6.00000 0.475831
$$160$$ 0 0
$$161$$ 8.00000 0.630488
$$162$$ 0 0
$$163$$ 4.00000i 0.313304i −0.987654 0.156652i $$-0.949930\pi$$
0.987654 0.156652i $$-0.0500701\pi$$
$$164$$ 0 0
$$165$$ −4.00000 2.00000i −0.311400 0.155700i
$$166$$ 0 0
$$167$$ 12.0000i 0.928588i 0.885681 + 0.464294i $$0.153692\pi$$
−0.885681 + 0.464294i $$0.846308\pi$$
$$168$$ 0 0
$$169$$ −23.0000 −1.76923
$$170$$ 0 0
$$171$$ 6.00000 0.458831
$$172$$ 0 0
$$173$$ 8.00000i 0.608229i −0.952636 0.304114i $$-0.901639\pi$$
0.952636 0.304114i $$-0.0983605\pi$$
$$174$$ 0 0
$$175$$ 4.00000 3.00000i 0.302372 0.226779i
$$176$$ 0 0
$$177$$ 8.00000i 0.601317i
$$178$$ 0 0
$$179$$ 10.0000 0.747435 0.373718 0.927543i $$-0.378083\pi$$
0.373718 + 0.927543i $$0.378083\pi$$
$$180$$ 0 0
$$181$$ 2.00000 0.148659 0.0743294 0.997234i $$-0.476318\pi$$
0.0743294 + 0.997234i $$0.476318\pi$$
$$182$$ 0 0
$$183$$ 10.0000i 0.739221i
$$184$$ 0 0
$$185$$ 8.00000 + 4.00000i 0.588172 + 0.294086i
$$186$$ 0 0
$$187$$ 8.00000i 0.585018i
$$188$$ 0 0
$$189$$ 1.00000 0.0727393
$$190$$ 0 0
$$191$$ 18.0000 1.30243 0.651217 0.758891i $$-0.274259\pi$$
0.651217 + 0.758891i $$0.274259\pi$$
$$192$$ 0 0
$$193$$ 8.00000i 0.575853i 0.957653 + 0.287926i $$0.0929658\pi$$
−0.957653 + 0.287926i $$0.907034\pi$$
$$194$$ 0 0
$$195$$ 6.00000 12.0000i 0.429669 0.859338i
$$196$$ 0 0
$$197$$ 2.00000i 0.142494i 0.997459 + 0.0712470i $$0.0226979\pi$$
−0.997459 + 0.0712470i $$0.977302\pi$$
$$198$$ 0 0
$$199$$ 6.00000 0.425329 0.212664 0.977125i $$-0.431786\pi$$
0.212664 + 0.977125i $$0.431786\pi$$
$$200$$ 0 0
$$201$$ 8.00000 0.564276
$$202$$ 0 0
$$203$$ 6.00000i 0.421117i
$$204$$ 0 0
$$205$$ 2.00000 4.00000i 0.139686 0.279372i
$$206$$ 0 0
$$207$$ 8.00000i 0.556038i
$$208$$ 0 0
$$209$$ 12.0000 0.830057
$$210$$ 0 0
$$211$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$212$$ 0 0
$$213$$ 6.00000i 0.411113i
$$214$$ 0 0
$$215$$ 8.00000 + 4.00000i 0.545595 + 0.272798i
$$216$$ 0 0
$$217$$ 2.00000i 0.135769i
$$218$$ 0 0
$$219$$ −14.0000 −0.946032
$$220$$ 0 0
$$221$$ 24.0000 1.61441
$$222$$ 0 0
$$223$$ 8.00000i 0.535720i −0.963458 0.267860i $$-0.913684\pi$$
0.963458 0.267860i $$-0.0863164\pi$$
$$224$$ 0 0
$$225$$ 3.00000 + 4.00000i 0.200000 + 0.266667i
$$226$$ 0 0
$$227$$ 8.00000i 0.530979i 0.964114 + 0.265489i $$0.0855335\pi$$
−0.964114 + 0.265489i $$0.914466\pi$$
$$228$$ 0 0
$$229$$ −14.0000 −0.925146 −0.462573 0.886581i $$-0.653074\pi$$
−0.462573 + 0.886581i $$0.653074\pi$$
$$230$$ 0 0
$$231$$ 2.00000 0.131590
$$232$$ 0 0
$$233$$ 10.0000i 0.655122i 0.944830 + 0.327561i $$0.106227\pi$$
−0.944830 + 0.327561i $$0.893773\pi$$
$$234$$ 0 0
$$235$$ −16.0000 8.00000i −1.04372 0.521862i
$$236$$ 0 0
$$237$$ 12.0000i 0.779484i
$$238$$ 0 0
$$239$$ 26.0000 1.68180 0.840900 0.541190i $$-0.182026\pi$$
0.840900 + 0.541190i $$0.182026\pi$$
$$240$$ 0 0
$$241$$ −26.0000 −1.67481 −0.837404 0.546585i $$-0.815928\pi$$
−0.837404 + 0.546585i $$0.815928\pi$$
$$242$$ 0 0
$$243$$ 1.00000i 0.0641500i
$$244$$ 0 0
$$245$$ −1.00000 + 2.00000i −0.0638877 + 0.127775i
$$246$$ 0 0
$$247$$ 36.0000i 2.29063i
$$248$$ 0 0
$$249$$ 8.00000 0.506979
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 16.0000i 1.00591i
$$254$$ 0 0
$$255$$ −4.00000 + 8.00000i −0.250490 + 0.500979i
$$256$$ 0 0
$$257$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$258$$ 0 0
$$259$$ −4.00000 −0.248548
$$260$$ 0 0
$$261$$ 6.00000 0.371391
$$262$$ 0 0
$$263$$ 16.0000i 0.986602i 0.869859 + 0.493301i $$0.164210\pi$$
−0.869859 + 0.493301i $$0.835790\pi$$
$$264$$ 0 0
$$265$$ −12.0000 6.00000i −0.737154 0.368577i
$$266$$ 0 0
$$267$$ 10.0000i 0.611990i
$$268$$ 0 0
$$269$$ −18.0000 −1.09748 −0.548740 0.835993i $$-0.684892\pi$$
−0.548740 + 0.835993i $$0.684892\pi$$
$$270$$ 0 0
$$271$$ −10.0000 −0.607457 −0.303728 0.952759i $$-0.598232\pi$$
−0.303728 + 0.952759i $$0.598232\pi$$
$$272$$ 0 0
$$273$$ 6.00000i 0.363137i
$$274$$ 0 0
$$275$$ 6.00000 + 8.00000i 0.361814 + 0.482418i
$$276$$ 0 0
$$277$$ 28.0000i 1.68236i 0.540758 + 0.841178i $$0.318138\pi$$
−0.540758 + 0.841178i $$0.681862\pi$$
$$278$$ 0 0
$$279$$ −2.00000 −0.119737
$$280$$ 0 0
$$281$$ 30.0000 1.78965 0.894825 0.446417i $$-0.147300\pi$$
0.894825 + 0.446417i $$0.147300\pi$$
$$282$$ 0 0
$$283$$ 20.0000i 1.18888i 0.804141 + 0.594438i $$0.202626\pi$$
−0.804141 + 0.594438i $$0.797374\pi$$
$$284$$ 0 0
$$285$$ −12.0000 6.00000i −0.710819 0.355409i
$$286$$ 0 0
$$287$$ 2.00000i 0.118056i
$$288$$ 0 0
$$289$$ 1.00000 0.0588235
$$290$$ 0 0
$$291$$ 10.0000 0.586210
$$292$$ 0 0
$$293$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$294$$ 0 0
$$295$$ −8.00000 + 16.0000i −0.465778 + 0.931556i
$$296$$ 0 0
$$297$$ 2.00000i 0.116052i
$$298$$ 0 0
$$299$$ −48.0000 −2.77591
$$300$$ 0 0
$$301$$ −4.00000 −0.230556
$$302$$ 0 0
$$303$$ 10.0000i 0.574485i
$$304$$ 0 0
$$305$$ −10.0000 + 20.0000i −0.572598 + 1.14520i
$$306$$ 0 0
$$307$$ 12.0000i 0.684876i 0.939540 + 0.342438i $$0.111253\pi$$
−0.939540 + 0.342438i $$0.888747\pi$$
$$308$$ 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 $$0.738219\pi$$
$$312$$ 0 0
$$313$$ 2.00000i 0.113047i 0.998401 + 0.0565233i $$0.0180015\pi$$
−0.998401 + 0.0565233i $$0.981998\pi$$
$$314$$ 0 0
$$315$$ −2.00000 1.00000i −0.112687 0.0563436i
$$316$$ 0 0
$$317$$ 2.00000i 0.112331i −0.998421 0.0561656i $$-0.982113\pi$$
0.998421 0.0561656i $$-0.0178875\pi$$
$$318$$ 0 0
$$319$$ 12.0000 0.671871
$$320$$ 0 0
$$321$$ 12.0000 0.669775
$$322$$ 0 0
$$323$$ 24.0000i 1.33540i
$$324$$ 0 0
$$325$$ −24.0000 + 18.0000i −1.33128 + 0.998460i
$$326$$ 0 0
$$327$$ 14.0000i 0.774202i
$$328$$ 0 0
$$329$$ 8.00000 0.441054
$$330$$ 0 0
$$331$$ 8.00000 0.439720 0.219860 0.975531i $$-0.429440\pi$$
0.219860 + 0.975531i $$0.429440\pi$$
$$332$$ 0 0
$$333$$ 4.00000i 0.219199i
$$334$$ 0 0
$$335$$ −16.0000 8.00000i −0.874173 0.437087i
$$336$$ 0 0
$$337$$ 8.00000i 0.435788i −0.975972 0.217894i $$-0.930081\pi$$
0.975972 0.217894i $$-0.0699187\pi$$
$$338$$ 0 0
$$339$$ 6.00000 0.325875
$$340$$ 0 0
$$341$$ −4.00000 −0.216612
$$342$$ 0 0
$$343$$ 1.00000i 0.0539949i
$$344$$ 0 0
$$345$$ 8.00000 16.0000i 0.430706 0.861411i
$$346$$ 0 0
$$347$$ 36.0000i 1.93258i −0.257454 0.966291i $$-0.582883\pi$$
0.257454 0.966291i $$-0.417117\pi$$
$$348$$ 0 0
$$349$$ 26.0000 1.39175 0.695874 0.718164i $$-0.255017\pi$$
0.695874 + 0.718164i $$0.255017\pi$$
$$350$$ 0 0
$$351$$ −6.00000 −0.320256
$$352$$ 0 0
$$353$$ 20.0000i 1.06449i −0.846590 0.532246i $$-0.821348\pi$$
0.846590 0.532246i $$-0.178652\pi$$
$$354$$ 0 0
$$355$$ 6.00000 12.0000i 0.318447 0.636894i
$$356$$ 0 0
$$357$$ 4.00000i 0.211702i
$$358$$ 0 0
$$359$$ 6.00000 0.316668 0.158334 0.987386i $$-0.449388\pi$$
0.158334 + 0.987386i $$0.449388\pi$$
$$360$$ 0 0
$$361$$ 17.0000 0.894737
$$362$$ 0 0
$$363$$ 7.00000i 0.367405i
$$364$$ 0 0
$$365$$ 28.0000 + 14.0000i 1.46559 + 0.732793i
$$366$$ 0 0
$$367$$ 32.0000i 1.67039i 0.549957 + 0.835193i $$0.314644\pi$$
−0.549957 + 0.835193i $$0.685356\pi$$
$$368$$ 0 0
$$369$$ −2.00000 −0.104116
$$370$$ 0 0
$$371$$ 6.00000 0.311504
$$372$$ 0 0
$$373$$ 24.0000i 1.24267i 0.783544 + 0.621336i $$0.213410\pi$$
−0.783544 + 0.621336i $$0.786590\pi$$
$$374$$ 0 0
$$375$$ −2.00000 11.0000i −0.103280 0.568038i
$$376$$ 0 0
$$377$$ 36.0000i 1.85409i
$$378$$ 0 0
$$379$$ 20.0000 1.02733 0.513665 0.857991i $$-0.328287\pi$$
0.513665 + 0.857991i $$0.328287\pi$$
$$380$$ 0 0
$$381$$ 4.00000 0.204926
$$382$$ 0 0
$$383$$ 20.0000i 1.02195i 0.859595 + 0.510976i $$0.170716\pi$$
−0.859595 + 0.510976i $$0.829284\pi$$
$$384$$ 0 0
$$385$$ −4.00000 2.00000i −0.203859 0.101929i
$$386$$ 0 0
$$387$$ 4.00000i 0.203331i
$$388$$ 0 0
$$389$$ −2.00000 −0.101404 −0.0507020 0.998714i $$-0.516146\pi$$
−0.0507020 + 0.998714i $$0.516146\pi$$
$$390$$ 0 0
$$391$$ 32.0000 1.61831
$$392$$ 0 0
$$393$$ 12.0000i 0.605320i
$$394$$ 0 0
$$395$$ −12.0000 + 24.0000i −0.603786 + 1.20757i
$$396$$ 0 0
$$397$$ 2.00000i 0.100377i −0.998740 0.0501886i $$-0.984018\pi$$
0.998740 0.0501886i $$-0.0159822\pi$$
$$398$$ 0 0
$$399$$ 6.00000 0.300376
$$400$$ 0 0
$$401$$ −14.0000 −0.699127 −0.349563 0.936913i $$-0.613670\pi$$
−0.349563 + 0.936913i $$0.613670\pi$$
$$402$$ 0 0
$$403$$ 12.0000i 0.597763i
$$404$$ 0 0
$$405$$ 1.00000 2.00000i 0.0496904 0.0993808i
$$406$$ 0 0
$$407$$ 8.00000i 0.396545i
$$408$$ 0 0
$$409$$ −26.0000 −1.28562 −0.642809 0.766027i $$-0.722231\pi$$
−0.642809 + 0.766027i $$0.722231\pi$$
$$410$$ 0 0
$$411$$ 6.00000 0.295958
$$412$$ 0 0
$$413$$ 8.00000i 0.393654i
$$414$$ 0 0
$$415$$ −16.0000 8.00000i −0.785409 0.392705i
$$416$$ 0 0
$$417$$ 14.0000i 0.685583i
$$418$$ 0 0
$$419$$ 20.0000 0.977064 0.488532 0.872546i $$-0.337533\pi$$
0.488532 + 0.872546i $$0.337533\pi$$
$$420$$ 0 0
$$421$$ 34.0000 1.65706 0.828529 0.559946i $$-0.189178\pi$$
0.828529 + 0.559946i $$0.189178\pi$$
$$422$$ 0 0
$$423$$ 8.00000i 0.388973i
$$424$$ 0 0
$$425$$ 16.0000 12.0000i 0.776114 0.582086i
$$426$$ 0 0
$$427$$ 10.0000i 0.483934i
$$428$$ 0 0
$$429$$ −12.0000 −0.579365
$$430$$ 0 0
$$431$$ −2.00000 −0.0963366 −0.0481683 0.998839i $$-0.515338\pi$$
−0.0481683 + 0.998839i $$0.515338\pi$$
$$432$$ 0 0
$$433$$ 26.0000i 1.24948i 0.780833 + 0.624740i $$0.214795\pi$$
−0.780833 + 0.624740i $$0.785205\pi$$
$$434$$ 0 0
$$435$$ −12.0000 6.00000i −0.575356 0.287678i
$$436$$ 0 0
$$437$$ 48.0000i 2.29615i
$$438$$ 0 0
$$439$$ −18.0000 −0.859093 −0.429547 0.903045i $$-0.641327\pi$$
−0.429547 + 0.903045i $$0.641327\pi$$
$$440$$ 0 0
$$441$$ 1.00000 0.0476190
$$442$$ 0 0
$$443$$ 12.0000i 0.570137i −0.958507 0.285069i $$-0.907984\pi$$
0.958507 0.285069i $$-0.0920164\pi$$
$$444$$ 0 0
$$445$$ 10.0000 20.0000i 0.474045 0.948091i
$$446$$ 0 0
$$447$$ 10.0000i 0.472984i
$$448$$ 0 0
$$449$$ 6.00000 0.283158 0.141579 0.989927i $$-0.454782\pi$$
0.141579 + 0.989927i $$0.454782\pi$$
$$450$$ 0 0
$$451$$ −4.00000 −0.188353
$$452$$ 0 0
$$453$$ 8.00000i 0.375873i
$$454$$ 0 0
$$455$$ 6.00000 12.0000i 0.281284 0.562569i
$$456$$ 0 0
$$457$$ 28.0000i 1.30978i 0.755722 + 0.654892i $$0.227286\pi$$
−0.755722 + 0.654892i $$0.772714\pi$$
$$458$$ 0 0
$$459$$ 4.00000 0.186704
$$460$$ 0 0
$$461$$ −18.0000 −0.838344 −0.419172 0.907907i $$-0.637680\pi$$
−0.419172 + 0.907907i $$0.637680\pi$$
$$462$$ 0 0
$$463$$ 36.0000i 1.67306i 0.547920 + 0.836531i $$0.315420\pi$$
−0.547920 + 0.836531i $$0.684580\pi$$
$$464$$ 0 0
$$465$$ 4.00000 + 2.00000i 0.185496 + 0.0927478i
$$466$$ 0 0
$$467$$ 24.0000i 1.11059i 0.831654 + 0.555294i $$0.187394\pi$$
−0.831654 + 0.555294i $$0.812606\pi$$
$$468$$ 0 0
$$469$$ 8.00000 0.369406
$$470$$ 0 0
$$471$$ 22.0000 1.01371
$$472$$ 0 0
$$473$$ 8.00000i 0.367840i
$$474$$ 0 0
$$475$$ 18.0000 + 24.0000i 0.825897 + 1.10120i
$$476$$ 0 0
$$477$$ 6.00000i 0.274721i
$$478$$ 0 0
$$479$$ 8.00000 0.365529 0.182765 0.983157i $$-0.441495\pi$$
0.182765 + 0.983157i $$0.441495\pi$$
$$480$$ 0 0
$$481$$ 24.0000 1.09431
$$482$$ 0 0
$$483$$ 8.00000i 0.364013i
$$484$$ 0 0
$$485$$ −20.0000 10.0000i −0.908153 0.454077i
$$486$$ 0 0
$$487$$ 12.0000i 0.543772i −0.962329 0.271886i $$-0.912353\pi$$
0.962329 0.271886i $$-0.0876473\pi$$
$$488$$ 0 0
$$489$$ 4.00000 0.180886
$$490$$ 0 0
$$491$$ 30.0000 1.35388 0.676941 0.736038i $$-0.263305\pi$$
0.676941 + 0.736038i $$0.263305\pi$$
$$492$$ 0 0
$$493$$ 24.0000i 1.08091i
$$494$$ 0 0
$$495$$ 2.00000 4.00000i 0.0898933 0.179787i
$$496$$ 0 0
$$497$$ 6.00000i 0.269137i
$$498$$ 0 0
$$499$$ −12.0000 −0.537194 −0.268597 0.963253i $$-0.586560\pi$$
−0.268597 + 0.963253i $$0.586560\pi$$
$$500$$ 0 0
$$501$$ −12.0000 −0.536120
$$502$$ 0 0
$$503$$ 12.0000i 0.535054i −0.963550 0.267527i $$-0.913794\pi$$
0.963550 0.267527i $$-0.0862064\pi$$
$$504$$ 0 0
$$505$$ 10.0000 20.0000i 0.444994 0.889988i
$$506$$ 0 0
$$507$$ 23.0000i 1.02147i
$$508$$ 0 0
$$509$$ −30.0000 −1.32973 −0.664863 0.746965i $$-0.731510\pi$$
−0.664863 + 0.746965i $$0.731510\pi$$
$$510$$ 0 0
$$511$$ −14.0000 −0.619324
$$512$$ 0 0
$$513$$ 6.00000i 0.264906i
$$514$$ 0 0
$$515$$ 16.0000 + 8.00000i 0.705044 + 0.352522i
$$516$$ 0 0
$$517$$ 16.0000i 0.703679i
$$518$$ 0 0
$$519$$ 8.00000 0.351161
$$520$$ 0 0
$$521$$ −26.0000 −1.13908 −0.569540 0.821963i $$-0.692879\pi$$
−0.569540 + 0.821963i $$0.692879\pi$$
$$522$$ 0 0
$$523$$ 28.0000i 1.22435i −0.790721 0.612177i $$-0.790294\pi$$
0.790721 0.612177i $$-0.209706\pi$$
$$524$$ 0 0
$$525$$ 3.00000 + 4.00000i 0.130931 + 0.174574i
$$526$$ 0 0
$$527$$ 8.00000i 0.348485i
$$528$$ 0 0
$$529$$ −41.0000 −1.78261
$$530$$ 0 0
$$531$$ 8.00000 0.347170
$$532$$ 0 0
$$533$$ 12.0000i 0.519778i
$$534$$ 0 0
$$535$$ −24.0000 12.0000i −1.03761 0.518805i
$$536$$ 0 0
$$537$$ 10.0000i 0.431532i
$$538$$ 0 0
$$539$$ 2.00000 0.0861461
$$540$$ 0 0
$$541$$ 22.0000 0.945854 0.472927 0.881102i $$-0.343197\pi$$
0.472927 + 0.881102i $$0.343197\pi$$
$$542$$ 0 0
$$543$$ 2.00000i 0.0858282i
$$544$$ 0 0
$$545$$ 14.0000 28.0000i 0.599694 1.19939i
$$546$$ 0 0
$$547$$ 40.0000i 1.71028i −0.518400 0.855138i $$-0.673472\pi$$
0.518400 0.855138i $$-0.326528\pi$$
$$548$$ 0 0
$$549$$ 10.0000 0.426790
$$550$$ 0 0
$$551$$ 36.0000 1.53365
$$552$$ 0 0
$$553$$ 12.0000i 0.510292i
$$554$$ 0 0
$$555$$ −4.00000 + 8.00000i −0.169791 + 0.339581i
$$556$$ 0 0
$$557$$ 42.0000i 1.77960i −0.456354 0.889799i $$-0.650845\pi$$
0.456354 0.889799i $$-0.349155\pi$$
$$558$$ 0 0
$$559$$ 24.0000 1.01509
$$560$$ 0 0
$$561$$ 8.00000 0.337760
$$562$$ 0 0
$$563$$ 4.00000i 0.168580i −0.996441 0.0842900i $$-0.973138\pi$$
0.996441 0.0842900i $$-0.0268622\pi$$
$$564$$ 0 0
$$565$$ −12.0000 6.00000i −0.504844 0.252422i
$$566$$ 0 0
$$567$$ 1.00000i 0.0419961i
$$568$$ 0 0
$$569$$ 46.0000 1.92842 0.964210 0.265139i $$-0.0854179\pi$$
0.964210 + 0.265139i $$0.0854179\pi$$
$$570$$ 0 0
$$571$$ −4.00000 −0.167395 −0.0836974 0.996491i $$-0.526673\pi$$
−0.0836974 + 0.996491i $$0.526673\pi$$
$$572$$ 0 0
$$573$$ 18.0000i 0.751961i
$$574$$ 0 0
$$575$$ −32.0000 + 24.0000i −1.33449 + 1.00087i
$$576$$ 0 0
$$577$$ 26.0000i 1.08239i −0.840896 0.541197i $$-0.817971\pi$$
0.840896 0.541197i $$-0.182029\pi$$
$$578$$ 0 0
$$579$$ −8.00000 −0.332469
$$580$$ 0 0
$$581$$ 8.00000 0.331896
$$582$$ 0 0
$$583$$ 12.0000i 0.496989i
$$584$$ 0 0
$$585$$ 12.0000 + 6.00000i 0.496139 + 0.248069i
$$586$$ 0 0
$$587$$ 12.0000i 0.495293i 0.968850 + 0.247647i $$0.0796572\pi$$
−0.968850 + 0.247647i $$0.920343\pi$$
$$588$$ 0 0
$$589$$ −12.0000 −0.494451
$$590$$ 0 0
$$591$$ −2.00000 −0.0822690
$$592$$ 0 0
$$593$$ 12.0000i 0.492781i −0.969171 0.246390i $$-0.920755\pi$$
0.969171 0.246390i $$-0.0792446\pi$$
$$594$$ 0 0
$$595$$ −4.00000 + 8.00000i −0.163984 + 0.327968i
$$596$$ 0 0
$$597$$ 6.00000i 0.245564i
$$598$$ 0 0
$$599$$ 30.0000 1.22577 0.612883 0.790173i $$-0.290010\pi$$
0.612883 + 0.790173i $$0.290010\pi$$
$$600$$ 0 0
$$601$$ 38.0000 1.55005 0.775026 0.631929i $$-0.217737\pi$$
0.775026 + 0.631929i $$0.217737\pi$$
$$602$$ 0 0
$$603$$ 8.00000i 0.325785i
$$604$$ 0 0
$$605$$ −7.00000 + 14.0000i −0.284590 + 0.569181i
$$606$$ 0 0
$$607$$ 8.00000i 0.324710i −0.986732 0.162355i $$-0.948091\pi$$
0.986732 0.162355i $$-0.0519090\pi$$
$$608$$ 0 0
$$609$$ 6.00000 0.243132
$$610$$ 0 0
$$611$$ −48.0000 −1.94187
$$612$$ 0 0
$$613$$ 28.0000i 1.13091i −0.824779 0.565455i $$-0.808701\pi$$
0.824779 0.565455i $$-0.191299\pi$$
$$614$$ 0 0
$$615$$ 4.00000 + 2.00000i 0.161296 + 0.0806478i
$$616$$ 0 0
$$617$$ 26.0000i 1.04672i −0.852111 0.523360i $$-0.824678\pi$$
0.852111 0.523360i $$-0.175322\pi$$
$$618$$ 0 0
$$619$$ −22.0000 −0.884255 −0.442127 0.896952i $$-0.645776\pi$$
−0.442127 + 0.896952i $$0.645776\pi$$
$$620$$ 0 0
$$621$$ −8.00000 −0.321029
$$622$$ 0 0
$$623$$ 10.0000i 0.400642i
$$624$$ 0 0
$$625$$ −7.00000 + 24.0000i −0.280000 + 0.960000i
$$626$$ 0 0
$$627$$ 12.0000i 0.479234i
$$628$$ 0 0
$$629$$ −16.0000 −0.637962
$$630$$ 0 0
$$631$$ 4.00000 0.159237 0.0796187 0.996825i $$-0.474630\pi$$
0.0796187 + 0.996825i $$0.474630\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −8.00000 4.00000i −0.317470 0.158735i
$$636$$ 0 0
$$637$$ 6.00000i 0.237729i
$$638$$ 0 0
$$639$$ −6.00000 −0.237356
$$640$$ 0 0
$$641$$ 14.0000 0.552967 0.276483 0.961019i $$-0.410831\pi$$
0.276483 + 0.961019i $$0.410831\pi$$
$$642$$ 0 0
$$643$$ 12.0000i 0.473234i 0.971603 + 0.236617i $$0.0760386\pi$$
−0.971603 + 0.236617i $$0.923961\pi$$
$$644$$ 0 0
$$645$$ −4.00000 + 8.00000i −0.157500 + 0.315000i
$$646$$ 0 0
$$647$$ 36.0000i 1.41531i −0.706560 0.707653i $$-0.749754\pi$$
0.706560 0.707653i $$-0.250246\pi$$
$$648$$ 0 0
$$649$$ 16.0000 0.628055
$$650$$ 0 0
$$651$$ −2.00000 −0.0783862
$$652$$ 0 0
$$653$$ 34.0000i 1.33052i −0.746611 0.665261i $$-0.768320\pi$$
0.746611 0.665261i $$-0.231680\pi$$
$$654$$ 0 0
$$655$$ 12.0000 24.0000i 0.468879 0.937758i
$$656$$ 0 0
$$657$$ 14.0000i 0.546192i
$$658$$ 0 0
$$659$$ −26.0000 −1.01282 −0.506408 0.862294i $$-0.669027\pi$$
−0.506408 + 0.862294i $$0.669027\pi$$
$$660$$ 0 0
$$661$$ 38.0000 1.47803 0.739014 0.673690i $$-0.235292\pi$$
0.739014 + 0.673690i $$0.235292\pi$$
$$662$$ 0 0
$$663$$ 24.0000i 0.932083i
$$664$$ 0 0
$$665$$ −12.0000 6.00000i −0.465340 0.232670i
$$666$$ 0 0
$$667$$ 48.0000i 1.85857i
$$668$$ 0 0
$$669$$ 8.00000 0.309298
$$670$$ 0 0
$$671$$ 20.0000 0.772091
$$672$$ 0 0
$$673$$ 12.0000i 0.462566i −0.972887 0.231283i $$-0.925708\pi$$
0.972887 0.231283i $$-0.0742923\pi$$
$$674$$ 0 0
$$675$$ −4.00000 + 3.00000i −0.153960 + 0.115470i
$$676$$ 0 0
$$677$$ 40.0000i 1.53732i 0.639655 + 0.768662i $$0.279077\pi$$
−0.639655 + 0.768662i $$0.720923\pi$$
$$678$$ 0 0
$$679$$ 10.0000 0.383765
$$680$$ 0 0
$$681$$ −8.00000 −0.306561
$$682$$ 0 0
$$683$$ 4.00000i 0.153056i 0.997067 + 0.0765279i $$0.0243834\pi$$
−0.997067 + 0.0765279i $$0.975617\pi$$
$$684$$ 0 0
$$685$$ −12.0000 6.00000i −0.458496 0.229248i
$$686$$ 0 0
$$687$$ 14.0000i 0.534133i
$$688$$ 0 0
$$689$$ −36.0000 −1.37149
$$690$$ 0 0
$$691$$ 2.00000 0.0760836 0.0380418 0.999276i $$-0.487888\pi$$
0.0380418 + 0.999276i $$0.487888\pi$$
$$692$$ 0 0
$$693$$ 2.00000i 0.0759737i
$$694$$ 0 0
$$695$$ −14.0000 + 28.0000i −0.531050 + 1.06210i
$$696$$ 0 0
$$697$$ 8.00000i 0.303022i
$$698$$ 0 0
$$699$$ −10.0000 −0.378235
$$700$$ 0 0
$$701$$ −34.0000 −1.28416 −0.642081 0.766637i $$-0.721929\pi$$
−0.642081 + 0.766637i $$0.721929\pi$$
$$702$$ 0 0
$$703$$ 24.0000i 0.905177i
$$704$$ 0 0
$$705$$ 8.00000 16.0000i 0.301297 0.602595i
$$706$$ 0 0
$$707$$ 10.0000i 0.376089i
$$708$$ 0 0
$$709$$ 6.00000 0.225335 0.112667 0.993633i $$-0.464061\pi$$
0.112667 + 0.993633i $$0.464061\pi$$
$$710$$ 0 0
$$711$$ 12.0000 0.450035
$$712$$ 0 0
$$713$$ 16.0000i 0.599205i
$$714$$ 0 0
$$715$$ 24.0000 + 12.0000i 0.897549 + 0.448775i
$$716$$ 0 0
$$717$$ 26.0000i 0.970988i
$$718$$ 0 0
$$719$$ −4.00000 −0.149175 −0.0745874 0.997214i $$-0.523764\pi$$
−0.0745874 + 0.997214i $$0.523764\pi$$
$$720$$ 0 0
$$721$$ −8.00000 −0.297936
$$722$$ 0 0
$$723$$ 26.0000i 0.966950i
$$724$$ 0 0
$$725$$ 18.0000 + 24.0000i 0.668503 + 0.891338i
$$726$$ 0 0
$$727$$ 24.0000i 0.890111i −0.895503 0.445055i $$-0.853184\pi$$
0.895503 0.445055i $$-0.146816\pi$$
$$728$$ 0 0
$$729$$ −1.00000 −0.0370370
$$730$$ 0 0
$$731$$ −16.0000 −0.591781
$$732$$ 0 0
$$733$$ 14.0000i 0.517102i −0.965998 0.258551i $$-0.916755\pi$$
0.965998 0.258551i $$-0.0832450\pi$$
$$734$$ 0 0
$$735$$ −2.00000 1.00000i −0.0737711 0.0368856i
$$736$$ 0 0
$$737$$ 16.0000i 0.589368i
$$738$$ 0 0
$$739$$ −44.0000 −1.61857 −0.809283 0.587419i $$-0.800144\pi$$
−0.809283 + 0.587419i $$0.800144\pi$$
$$740$$ 0 0
$$741$$ −36.0000 −1.32249
$$742$$ 0 0
$$743$$ 48.0000i 1.76095i −0.474093 0.880475i $$-0.657224\pi$$
0.474093 0.880475i $$-0.342776\pi$$
$$744$$ 0 0
$$745$$ −10.0000 + 20.0000i −0.366372 + 0.732743i
$$746$$ 0 0
$$747$$ 8.00000i 0.292705i
$$748$$ 0 0
$$749$$ 12.0000 0.438470
$$750$$ 0 0
$$751$$ −20.0000 −0.729810 −0.364905 0.931045i $$-0.618899\pi$$
−0.364905 + 0.931045i $$0.618899\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 8.00000 16.0000i 0.291150 0.582300i
$$756$$ 0 0
$$757$$ 32.0000i 1.16306i −0.813525 0.581530i $$-0.802454\pi$$
0.813525 0.581530i $$-0.197546\pi$$
$$758$$ 0 0
$$759$$ −16.0000 −0.580763
$$760$$ 0 0
$$761$$ −6.00000 −0.217500 −0.108750 0.994069i $$-0.534685\pi$$
−0.108750 + 0.994069i $$0.534685\pi$$
$$762$$ 0 0
$$763$$ 14.0000i 0.506834i
$$764$$ 0 0
$$765$$ −8.00000 4.00000i −0.289241 0.144620i
$$766$$ 0 0
$$767$$ 48.0000i 1.73318i
$$768$$ 0 0
$$769$$ −30.0000 −1.08183 −0.540914 0.841078i $$-0.681921\pi$$
−0.540914 + 0.841078i $$0.681921\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$774$$ 0 0
$$775$$ −6.00000 8.00000i −0.215526 0.287368i
$$776$$ 0 0
$$777$$ 4.00000i 0.143499i
$$778$$ 0 0
$$779$$ −12.0000 −0.429945
$$780$$ 0 0
$$781$$ −12.0000 −0.429394
$$782$$ 0 0
$$783$$ 6.00000i 0.214423i
$$784$$ 0 0
$$785$$ −44.0000 22.0000i −1.57043 0.785214i
$$786$$ 0 0
$$787$$ 28.0000i 0.998092i −0.866575 0.499046i $$-0.833684\pi$$
0.866575 0.499046i $$-0.166316\pi$$
$$788$$ 0 0
$$789$$ −16.0000 −0.569615
$$790$$ 0 0
$$791$$ 6.00000 0.213335
$$792$$ 0 0
$$793$$ 60.0000i 2.13066i
$$794$$ 0 0
$$795$$ 6.00000 12.0000i 0.212798 0.425596i
$$796$$ 0 0
$$797$$ 8.00000i 0.283375i −0.989911 0.141687i $$-0.954747\pi$$
0.989911 0.141687i $$-0.0452527\pi$$
$$798$$ 0 0
$$799$$ 32.0000 1.13208
$$800$$ 0 0
$$801$$ −10.0000 −0.353333
$$802$$ 0 0