# Properties

 Label 1344.2.k.d.1217.4 Level $1344$ Weight $2$ Character 1344.1217 Analytic conductor $10.732$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1344 = 2^{6} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1344.k (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$10.7318940317$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(i, \sqrt{6})$$ Defining polynomial: $$x^{4} + 9$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$3$$ Twist minimal: no (minimal twist has level 42) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 1217.4 Root $$1.22474 + 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 1344.1217 Dual form 1344.2.k.d.1217.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.22474 + 1.22474i) q^{3} +2.44949 q^{5} +(1.00000 + 2.44949i) q^{7} +3.00000i q^{9} +O(q^{10})$$ $$q+(1.22474 + 1.22474i) q^{3} +2.44949 q^{5} +(1.00000 + 2.44949i) q^{7} +3.00000i q^{9} -2.44949i q^{13} +(3.00000 + 3.00000i) q^{15} +4.89898 q^{17} -2.44949i q^{19} +(-1.77526 + 4.22474i) q^{21} +6.00000i q^{23} +1.00000 q^{25} +(-3.67423 + 3.67423i) q^{27} -6.00000i q^{29} +(2.44949 + 6.00000i) q^{35} +2.00000 q^{37} +(3.00000 - 3.00000i) q^{39} -4.89898 q^{41} +4.00000 q^{43} +7.34847i q^{45} -4.89898 q^{47} +(-5.00000 + 4.89898i) q^{49} +(6.00000 + 6.00000i) q^{51} +6.00000i q^{53} +(3.00000 - 3.00000i) q^{57} -12.2474 q^{59} -12.2474i q^{61} +(-7.34847 + 3.00000i) q^{63} -6.00000i q^{65} +8.00000 q^{67} +(-7.34847 + 7.34847i) q^{69} -9.79796i q^{73} +(1.22474 + 1.22474i) q^{75} +10.0000 q^{79} -9.00000 q^{81} +2.44949 q^{83} +12.0000 q^{85} +(7.34847 - 7.34847i) q^{87} +(6.00000 - 2.44949i) q^{91} -6.00000i q^{95} -4.89898i q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 4q^{7} + O(q^{10})$$ $$4q + 4q^{7} + 12q^{15} - 12q^{21} + 4q^{25} + 8q^{37} + 12q^{39} + 16q^{43} - 20q^{49} + 24q^{51} + 12q^{57} + 32q^{67} + 40q^{79} - 36q^{81} + 48q^{85} + 24q^{91} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$449$$ $$577$$ $$1093$$ $$\chi(n)$$ $$1$$ $$-1$$ $$-1$$ $$1$$

## 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
$$3$$ 1.22474 + 1.22474i 0.707107 + 0.707107i
$$4$$ 0 0
$$5$$ 2.44949 1.09545 0.547723 0.836660i $$-0.315495\pi$$
0.547723 + 0.836660i $$0.315495\pi$$
$$6$$ 0 0
$$7$$ 1.00000 + 2.44949i 0.377964 + 0.925820i
$$8$$ 0 0
$$9$$ 3.00000i 1.00000i
$$10$$ 0 0
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 0 0
$$13$$ 2.44949i 0.679366i −0.940540 0.339683i $$-0.889680\pi$$
0.940540 0.339683i $$-0.110320\pi$$
$$14$$ 0 0
$$15$$ 3.00000 + 3.00000i 0.774597 + 0.774597i
$$16$$ 0 0
$$17$$ 4.89898 1.18818 0.594089 0.804400i $$-0.297513\pi$$
0.594089 + 0.804400i $$0.297513\pi$$
$$18$$ 0 0
$$19$$ 2.44949i 0.561951i −0.959715 0.280976i $$-0.909342\pi$$
0.959715 0.280976i $$-0.0906580\pi$$
$$20$$ 0 0
$$21$$ −1.77526 + 4.22474i −0.387392 + 0.921915i
$$22$$ 0 0
$$23$$ 6.00000i 1.25109i 0.780189 + 0.625543i $$0.215123\pi$$
−0.780189 + 0.625543i $$0.784877\pi$$
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ 0 0
$$27$$ −3.67423 + 3.67423i −0.707107 + 0.707107i
$$28$$ 0 0
$$29$$ 6.00000i 1.11417i −0.830455 0.557086i $$-0.811919\pi$$
0.830455 0.557086i $$-0.188081\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 2.44949 + 6.00000i 0.414039 + 1.01419i
$$36$$ 0 0
$$37$$ 2.00000 0.328798 0.164399 0.986394i $$-0.447432\pi$$
0.164399 + 0.986394i $$0.447432\pi$$
$$38$$ 0 0
$$39$$ 3.00000 3.00000i 0.480384 0.480384i
$$40$$ 0 0
$$41$$ −4.89898 −0.765092 −0.382546 0.923936i $$-0.624953\pi$$
−0.382546 + 0.923936i $$0.624953\pi$$
$$42$$ 0 0
$$43$$ 4.00000 0.609994 0.304997 0.952353i $$-0.401344\pi$$
0.304997 + 0.952353i $$0.401344\pi$$
$$44$$ 0 0
$$45$$ 7.34847i 1.09545i
$$46$$ 0 0
$$47$$ −4.89898 −0.714590 −0.357295 0.933992i $$-0.616301\pi$$
−0.357295 + 0.933992i $$0.616301\pi$$
$$48$$ 0 0
$$49$$ −5.00000 + 4.89898i −0.714286 + 0.699854i
$$50$$ 0 0
$$51$$ 6.00000 + 6.00000i 0.840168 + 0.840168i
$$52$$ 0 0
$$53$$ 6.00000i 0.824163i 0.911147 + 0.412082i $$0.135198\pi$$
−0.911147 + 0.412082i $$0.864802\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 3.00000 3.00000i 0.397360 0.397360i
$$58$$ 0 0
$$59$$ −12.2474 −1.59448 −0.797241 0.603661i $$-0.793708\pi$$
−0.797241 + 0.603661i $$0.793708\pi$$
$$60$$ 0 0
$$61$$ 12.2474i 1.56813i −0.620682 0.784063i $$-0.713144\pi$$
0.620682 0.784063i $$-0.286856\pi$$
$$62$$ 0 0
$$63$$ −7.34847 + 3.00000i −0.925820 + 0.377964i
$$64$$ 0 0
$$65$$ 6.00000i 0.744208i
$$66$$ 0 0
$$67$$ 8.00000 0.977356 0.488678 0.872464i $$-0.337479\pi$$
0.488678 + 0.872464i $$0.337479\pi$$
$$68$$ 0 0
$$69$$ −7.34847 + 7.34847i −0.884652 + 0.884652i
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0 0
$$73$$ 9.79796i 1.14676i −0.819288 0.573382i $$-0.805631\pi$$
0.819288 0.573382i $$-0.194369\pi$$
$$74$$ 0 0
$$75$$ 1.22474 + 1.22474i 0.141421 + 0.141421i
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 10.0000 1.12509 0.562544 0.826767i $$-0.309823\pi$$
0.562544 + 0.826767i $$0.309823\pi$$
$$80$$ 0 0
$$81$$ −9.00000 −1.00000
$$82$$ 0 0
$$83$$ 2.44949 0.268866 0.134433 0.990923i $$-0.457079\pi$$
0.134433 + 0.990923i $$0.457079\pi$$
$$84$$ 0 0
$$85$$ 12.0000 1.30158
$$86$$ 0 0
$$87$$ 7.34847 7.34847i 0.787839 0.787839i
$$88$$ 0 0
$$89$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$90$$ 0 0
$$91$$ 6.00000 2.44949i 0.628971 0.256776i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 6.00000i 0.615587i
$$96$$ 0 0
$$97$$ 4.89898i 0.497416i −0.968579 0.248708i $$-0.919994\pi$$
0.968579 0.248708i $$-0.0800060\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −7.34847 −0.731200 −0.365600 0.930772i $$-0.619136\pi$$
−0.365600 + 0.930772i $$0.619136\pi$$
$$102$$ 0 0
$$103$$ 9.79796i 0.965422i 0.875780 + 0.482711i $$0.160348\pi$$
−0.875780 + 0.482711i $$0.839652\pi$$
$$104$$ 0 0
$$105$$ −4.34847 + 10.3485i −0.424367 + 1.00991i
$$106$$ 0 0
$$107$$ 12.0000i 1.16008i 0.814587 + 0.580042i $$0.196964\pi$$
−0.814587 + 0.580042i $$0.803036\pi$$
$$108$$ 0 0
$$109$$ −10.0000 −0.957826 −0.478913 0.877862i $$-0.658969\pi$$
−0.478913 + 0.877862i $$0.658969\pi$$
$$110$$ 0 0
$$111$$ 2.44949 + 2.44949i 0.232495 + 0.232495i
$$112$$ 0 0
$$113$$ 6.00000i 0.564433i −0.959351 0.282216i $$-0.908930\pi$$
0.959351 0.282216i $$-0.0910696\pi$$
$$114$$ 0 0
$$115$$ 14.6969i 1.37050i
$$116$$ 0 0
$$117$$ 7.34847 0.679366
$$118$$ 0 0
$$119$$ 4.89898 + 12.0000i 0.449089 + 1.10004i
$$120$$ 0 0
$$121$$ 11.0000 1.00000
$$122$$ 0 0
$$123$$ −6.00000 6.00000i −0.541002 0.541002i
$$124$$ 0 0
$$125$$ −9.79796 −0.876356
$$126$$ 0 0
$$127$$ −8.00000 −0.709885 −0.354943 0.934888i $$-0.615500\pi$$
−0.354943 + 0.934888i $$0.615500\pi$$
$$128$$ 0 0
$$129$$ 4.89898 + 4.89898i 0.431331 + 0.431331i
$$130$$ 0 0
$$131$$ 7.34847 0.642039 0.321019 0.947073i $$-0.395975\pi$$
0.321019 + 0.947073i $$0.395975\pi$$
$$132$$ 0 0
$$133$$ 6.00000 2.44949i 0.520266 0.212398i
$$134$$ 0 0
$$135$$ −9.00000 + 9.00000i −0.774597 + 0.774597i
$$136$$ 0 0
$$137$$ 12.0000i 1.02523i 0.858619 + 0.512615i $$0.171323\pi$$
−0.858619 + 0.512615i $$0.828677\pi$$
$$138$$ 0 0
$$139$$ 2.44949i 0.207763i −0.994590 0.103882i $$-0.966874\pi$$
0.994590 0.103882i $$-0.0331263\pi$$
$$140$$ 0 0
$$141$$ −6.00000 6.00000i −0.505291 0.505291i
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 14.6969i 1.22051i
$$146$$ 0 0
$$147$$ −12.1237 0.123724i −0.999948 0.0102046i
$$148$$ 0 0
$$149$$ 6.00000i 0.491539i −0.969328 0.245770i $$-0.920959\pi$$
0.969328 0.245770i $$-0.0790407\pi$$
$$150$$ 0 0
$$151$$ 8.00000 0.651031 0.325515 0.945537i $$-0.394462\pi$$
0.325515 + 0.945537i $$0.394462\pi$$
$$152$$ 0 0
$$153$$ 14.6969i 1.18818i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 7.34847i 0.586472i −0.956040 0.293236i $$-0.905268\pi$$
0.956040 0.293236i $$-0.0947321\pi$$
$$158$$ 0 0
$$159$$ −7.34847 + 7.34847i −0.582772 + 0.582772i
$$160$$ 0 0
$$161$$ −14.6969 + 6.00000i −1.15828 + 0.472866i
$$162$$ 0 0
$$163$$ −16.0000 −1.25322 −0.626608 0.779334i $$-0.715557\pi$$
−0.626608 + 0.779334i $$0.715557\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −4.89898 −0.379094 −0.189547 0.981872i $$-0.560702\pi$$
−0.189547 + 0.981872i $$0.560702\pi$$
$$168$$ 0 0
$$169$$ 7.00000 0.538462
$$170$$ 0 0
$$171$$ 7.34847 0.561951
$$172$$ 0 0
$$173$$ 22.0454 1.67608 0.838041 0.545608i $$-0.183701\pi$$
0.838041 + 0.545608i $$0.183701\pi$$
$$174$$ 0 0
$$175$$ 1.00000 + 2.44949i 0.0755929 + 0.185164i
$$176$$ 0 0
$$177$$ −15.0000 15.0000i −1.12747 1.12747i
$$178$$ 0 0
$$179$$ 24.0000i 1.79384i −0.442189 0.896922i $$-0.645798\pi$$
0.442189 0.896922i $$-0.354202\pi$$
$$180$$ 0 0
$$181$$ 12.2474i 0.910346i 0.890403 + 0.455173i $$0.150423\pi$$
−0.890403 + 0.455173i $$0.849577\pi$$
$$182$$ 0 0
$$183$$ 15.0000 15.0000i 1.10883 1.10883i
$$184$$ 0 0
$$185$$ 4.89898 0.360180
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ −12.6742 5.32577i −0.921915 0.387392i
$$190$$ 0 0
$$191$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$192$$ 0 0
$$193$$ 4.00000 0.287926 0.143963 0.989583i $$-0.454015\pi$$
0.143963 + 0.989583i $$0.454015\pi$$
$$194$$ 0 0
$$195$$ 7.34847 7.34847i 0.526235 0.526235i
$$196$$ 0 0
$$197$$ 18.0000i 1.28245i 0.767354 + 0.641223i $$0.221573\pi$$
−0.767354 + 0.641223i $$0.778427\pi$$
$$198$$ 0 0
$$199$$ 9.79796i 0.694559i −0.937762 0.347279i $$-0.887106\pi$$
0.937762 0.347279i $$-0.112894\pi$$
$$200$$ 0 0
$$201$$ 9.79796 + 9.79796i 0.691095 + 0.691095i
$$202$$ 0 0
$$203$$ 14.6969 6.00000i 1.03152 0.421117i
$$204$$ 0 0
$$205$$ −12.0000 −0.838116
$$206$$ 0 0
$$207$$ −18.0000 −1.25109
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −8.00000 −0.550743 −0.275371 0.961338i $$-0.588801\pi$$
−0.275371 + 0.961338i $$0.588801\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 9.79796 0.668215
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 12.0000 12.0000i 0.810885 0.810885i
$$220$$ 0 0
$$221$$ 12.0000i 0.807207i
$$222$$ 0 0
$$223$$ 14.6969i 0.984180i −0.870544 0.492090i $$-0.836233\pi$$
0.870544 0.492090i $$-0.163767\pi$$
$$224$$ 0 0
$$225$$ 3.00000i 0.200000i
$$226$$ 0 0
$$227$$ −7.34847 −0.487735 −0.243868 0.969809i $$-0.578416\pi$$
−0.243868 + 0.969809i $$0.578416\pi$$
$$228$$ 0 0
$$229$$ 22.0454i 1.45680i −0.685151 0.728401i $$-0.740264\pi$$
0.685151 0.728401i $$-0.259736\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 24.0000i 1.57229i 0.618041 + 0.786146i $$0.287927\pi$$
−0.618041 + 0.786146i $$0.712073\pi$$
$$234$$ 0 0
$$235$$ −12.0000 −0.782794
$$236$$ 0 0
$$237$$ 12.2474 + 12.2474i 0.795557 + 0.795557i
$$238$$ 0 0
$$239$$ 6.00000i 0.388108i −0.980991 0.194054i $$-0.937836\pi$$
0.980991 0.194054i $$-0.0621637\pi$$
$$240$$ 0 0
$$241$$ 24.4949i 1.57786i −0.614486 0.788928i $$-0.710637\pi$$
0.614486 0.788928i $$-0.289363\pi$$
$$242$$ 0 0
$$243$$ −11.0227 11.0227i −0.707107 0.707107i
$$244$$ 0 0
$$245$$ −12.2474 + 12.0000i −0.782461 + 0.766652i
$$246$$ 0 0
$$247$$ −6.00000 −0.381771
$$248$$ 0 0
$$249$$ 3.00000 + 3.00000i 0.190117 + 0.190117i
$$250$$ 0 0
$$251$$ −17.1464 −1.08227 −0.541136 0.840935i $$-0.682006\pi$$
−0.541136 + 0.840935i $$0.682006\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 14.6969 + 14.6969i 0.920358 + 0.920358i
$$256$$ 0 0
$$257$$ 29.3939 1.83354 0.916770 0.399416i $$-0.130787\pi$$
0.916770 + 0.399416i $$0.130787\pi$$
$$258$$ 0 0
$$259$$ 2.00000 + 4.89898i 0.124274 + 0.304408i
$$260$$ 0 0
$$261$$ 18.0000 1.11417
$$262$$ 0 0
$$263$$ 24.0000i 1.47990i −0.672660 0.739952i $$-0.734848\pi$$
0.672660 0.739952i $$-0.265152\pi$$
$$264$$ 0 0
$$265$$ 14.6969i 0.902826i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 12.2474 0.746740 0.373370 0.927682i $$-0.378202\pi$$
0.373370 + 0.927682i $$0.378202\pi$$
$$270$$ 0 0
$$271$$ 24.4949i 1.48796i −0.668202 0.743980i $$-0.732936\pi$$
0.668202 0.743980i $$-0.267064\pi$$
$$272$$ 0 0
$$273$$ 10.3485 + 4.34847i 0.626318 + 0.263181i
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 22.0000 1.32185 0.660926 0.750451i $$-0.270164\pi$$
0.660926 + 0.750451i $$0.270164\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ 22.0454i 1.31046i −0.755428 0.655232i $$-0.772571\pi$$
0.755428 0.655232i $$-0.227429\pi$$
$$284$$ 0 0
$$285$$ 7.34847 7.34847i 0.435286 0.435286i
$$286$$ 0 0
$$287$$ −4.89898 12.0000i −0.289178 0.708338i
$$288$$ 0 0
$$289$$ 7.00000 0.411765
$$290$$ 0 0
$$291$$ 6.00000 6.00000i 0.351726 0.351726i
$$292$$ 0 0
$$293$$ −2.44949 −0.143101 −0.0715504 0.997437i $$-0.522795\pi$$
−0.0715504 + 0.997437i $$0.522795\pi$$
$$294$$ 0 0
$$295$$ −30.0000 −1.74667
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 14.6969 0.849946
$$300$$ 0 0
$$301$$ 4.00000 + 9.79796i 0.230556 + 0.564745i
$$302$$ 0 0
$$303$$ −9.00000 9.00000i −0.517036 0.517036i
$$304$$ 0 0
$$305$$ 30.0000i 1.71780i
$$306$$ 0 0
$$307$$ 7.34847i 0.419399i 0.977766 + 0.209700i $$0.0672486\pi$$
−0.977766 + 0.209700i $$0.932751\pi$$
$$308$$ 0 0
$$309$$ −12.0000 + 12.0000i −0.682656 + 0.682656i
$$310$$ 0 0
$$311$$ −19.5959 −1.11118 −0.555591 0.831456i $$-0.687508\pi$$
−0.555591 + 0.831456i $$0.687508\pi$$
$$312$$ 0 0
$$313$$ 34.2929i 1.93835i −0.246380 0.969173i $$-0.579241\pi$$
0.246380 0.969173i $$-0.420759\pi$$
$$314$$ 0 0
$$315$$ −18.0000 + 7.34847i −1.01419 + 0.414039i
$$316$$ 0 0
$$317$$ 18.0000i 1.01098i 0.862832 + 0.505490i $$0.168688\pi$$
−0.862832 + 0.505490i $$0.831312\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ −14.6969 + 14.6969i −0.820303 + 0.820303i
$$322$$ 0 0
$$323$$ 12.0000i 0.667698i
$$324$$ 0 0
$$325$$ 2.44949i 0.135873i
$$326$$ 0 0
$$327$$ −12.2474 12.2474i −0.677285 0.677285i
$$328$$ 0 0
$$329$$ −4.89898 12.0000i −0.270089 0.661581i
$$330$$ 0 0
$$331$$ −8.00000 −0.439720 −0.219860 0.975531i $$-0.570560\pi$$
−0.219860 + 0.975531i $$0.570560\pi$$
$$332$$ 0 0
$$333$$ 6.00000i 0.328798i
$$334$$ 0 0
$$335$$ 19.5959 1.07064
$$336$$ 0 0
$$337$$ −32.0000 −1.74315 −0.871576 0.490261i $$-0.836901\pi$$
−0.871576 + 0.490261i $$0.836901\pi$$
$$338$$ 0 0
$$339$$ 7.34847 7.34847i 0.399114 0.399114i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ −17.0000 7.34847i −0.917914 0.396780i
$$344$$ 0 0
$$345$$ −18.0000 + 18.0000i −0.969087 + 0.969087i
$$346$$ 0 0
$$347$$ 12.0000i 0.644194i 0.946707 + 0.322097i $$0.104388\pi$$
−0.946707 + 0.322097i $$0.895612\pi$$
$$348$$ 0 0
$$349$$ 2.44949i 0.131118i 0.997849 + 0.0655591i $$0.0208831\pi$$
−0.997849 + 0.0655591i $$0.979117\pi$$
$$350$$ 0 0
$$351$$ 9.00000 + 9.00000i 0.480384 + 0.480384i
$$352$$ 0 0
$$353$$ −9.79796 −0.521493 −0.260746 0.965407i $$-0.583969\pi$$
−0.260746 + 0.965407i $$0.583969\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ −8.69694 + 20.6969i −0.460291 + 1.09540i
$$358$$ 0 0
$$359$$ 6.00000i 0.316668i −0.987386 0.158334i $$-0.949388\pi$$
0.987386 0.158334i $$-0.0506123\pi$$
$$360$$ 0 0
$$361$$ 13.0000 0.684211
$$362$$ 0 0
$$363$$ 13.4722 + 13.4722i 0.707107 + 0.707107i
$$364$$ 0 0
$$365$$ 24.0000i 1.25622i
$$366$$ 0 0
$$367$$ 4.89898i 0.255725i 0.991792 + 0.127862i $$0.0408116\pi$$
−0.991792 + 0.127862i $$0.959188\pi$$
$$368$$ 0 0
$$369$$ 14.6969i 0.765092i
$$370$$ 0 0
$$371$$ −14.6969 + 6.00000i −0.763027 + 0.311504i
$$372$$ 0 0
$$373$$ −14.0000 −0.724893 −0.362446 0.932005i $$-0.618058\pi$$
−0.362446 + 0.932005i $$0.618058\pi$$
$$374$$ 0 0
$$375$$ −12.0000 12.0000i −0.619677 0.619677i
$$376$$ 0 0
$$377$$ −14.6969 −0.756931
$$378$$ 0 0
$$379$$ −20.0000 −1.02733 −0.513665 0.857991i $$-0.671713\pi$$
−0.513665 + 0.857991i $$0.671713\pi$$
$$380$$ 0 0
$$381$$ −9.79796 9.79796i −0.501965 0.501965i
$$382$$ 0 0
$$383$$ 34.2929 1.75228 0.876142 0.482054i $$-0.160109\pi$$
0.876142 + 0.482054i $$0.160109\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 12.0000i 0.609994i
$$388$$ 0 0
$$389$$ 6.00000i 0.304212i −0.988364 0.152106i $$-0.951394\pi$$
0.988364 0.152106i $$-0.0486055\pi$$
$$390$$ 0 0
$$391$$ 29.3939i 1.48651i
$$392$$ 0 0
$$393$$ 9.00000 + 9.00000i 0.453990 + 0.453990i
$$394$$ 0 0
$$395$$ 24.4949 1.23247
$$396$$ 0 0
$$397$$ 7.34847i 0.368809i −0.982850 0.184405i $$-0.940964\pi$$
0.982850 0.184405i $$-0.0590357\pi$$
$$398$$ 0 0
$$399$$ 10.3485 + 4.34847i 0.518071 + 0.217696i
$$400$$ 0 0
$$401$$ 30.0000i 1.49813i −0.662497 0.749064i $$-0.730503\pi$$
0.662497 0.749064i $$-0.269497\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ −22.0454 −1.09545
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 34.2929i 1.69567i 0.530258 + 0.847836i $$0.322095\pi$$
−0.530258 + 0.847836i $$0.677905\pi$$
$$410$$ 0 0
$$411$$ −14.6969 + 14.6969i −0.724947 + 0.724947i
$$412$$ 0 0
$$413$$ −12.2474 30.0000i −0.602658 1.47620i
$$414$$ 0 0
$$415$$ 6.00000 0.294528
$$416$$ 0 0
$$417$$ 3.00000 3.00000i 0.146911 0.146911i
$$418$$ 0 0
$$419$$ 12.2474 0.598327 0.299164 0.954202i $$-0.403292\pi$$
0.299164 + 0.954202i $$0.403292\pi$$
$$420$$ 0 0
$$421$$ −2.00000 −0.0974740 −0.0487370 0.998812i $$-0.515520\pi$$
−0.0487370 + 0.998812i $$0.515520\pi$$
$$422$$ 0 0
$$423$$ 14.6969i 0.714590i
$$424$$ 0 0
$$425$$ 4.89898 0.237635
$$426$$ 0 0
$$427$$ 30.0000 12.2474i 1.45180 0.592696i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 30.0000i 1.44505i 0.691345 + 0.722525i $$0.257018\pi$$
−0.691345 + 0.722525i $$0.742982\pi$$
$$432$$ 0 0
$$433$$ 14.6969i 0.706290i 0.935569 + 0.353145i $$0.114888\pi$$
−0.935569 + 0.353145i $$0.885112\pi$$
$$434$$ 0 0
$$435$$ 18.0000 18.0000i 0.863034 0.863034i
$$436$$ 0 0
$$437$$ 14.6969 0.703050
$$438$$ 0 0
$$439$$ 14.6969i 0.701447i 0.936479 + 0.350723i $$0.114064\pi$$
−0.936479 + 0.350723i $$0.885936\pi$$
$$440$$ 0 0
$$441$$ −14.6969 15.0000i −0.699854 0.714286i
$$442$$ 0 0
$$443$$ 36.0000i 1.71041i −0.518289 0.855206i $$-0.673431\pi$$
0.518289 0.855206i $$-0.326569\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 7.34847 7.34847i 0.347571 0.347571i
$$448$$ 0 0
$$449$$ 36.0000i 1.69895i 0.527633 + 0.849473i $$0.323080\pi$$
−0.527633 + 0.849473i $$0.676920\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 9.79796 + 9.79796i 0.460348 + 0.460348i
$$454$$ 0 0
$$455$$ 14.6969 6.00000i 0.689003 0.281284i
$$456$$ 0 0
$$457$$ 28.0000 1.30978 0.654892 0.755722i $$-0.272714\pi$$
0.654892 + 0.755722i $$0.272714\pi$$
$$458$$ 0 0
$$459$$ −18.0000 + 18.0000i −0.840168 + 0.840168i
$$460$$ 0 0
$$461$$ −31.8434 −1.48309 −0.741547 0.670901i $$-0.765907\pi$$
−0.741547 + 0.670901i $$0.765907\pi$$
$$462$$ 0 0
$$463$$ −14.0000 −0.650635 −0.325318 0.945605i $$-0.605471\pi$$
−0.325318 + 0.945605i $$0.605471\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −7.34847 −0.340047 −0.170023 0.985440i $$-0.554384\pi$$
−0.170023 + 0.985440i $$0.554384\pi$$
$$468$$ 0 0
$$469$$ 8.00000 + 19.5959i 0.369406 + 0.904855i
$$470$$ 0 0
$$471$$ 9.00000 9.00000i 0.414698 0.414698i
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 2.44949i 0.112390i
$$476$$ 0 0
$$477$$ −18.0000 −0.824163
$$478$$ 0 0
$$479$$ −24.4949 −1.11920 −0.559600 0.828763i $$-0.689045\pi$$
−0.559600 + 0.828763i $$0.689045\pi$$
$$480$$ 0 0
$$481$$ 4.89898i 0.223374i
$$482$$ 0 0
$$483$$ −25.3485 10.6515i −1.15340 0.484661i
$$484$$ 0 0
$$485$$ 12.0000i 0.544892i
$$486$$ 0 0
$$487$$ 32.0000 1.45006 0.725029 0.688718i $$-0.241826\pi$$
0.725029 + 0.688718i $$0.241826\pi$$
$$488$$ 0 0
$$489$$ −19.5959 19.5959i −0.886158 0.886158i
$$490$$ 0 0
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ 29.3939i 1.32383i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −20.0000 −0.895323 −0.447661 0.894203i $$-0.647743\pi$$
−0.447661 + 0.894203i $$0.647743\pi$$
$$500$$ 0 0
$$501$$ −6.00000 6.00000i −0.268060 0.268060i
$$502$$ 0 0
$$503$$ −39.1918 −1.74748 −0.873739 0.486395i $$-0.838311\pi$$
−0.873739 + 0.486395i $$0.838311\pi$$
$$504$$ 0 0
$$505$$ −18.0000 −0.800989
$$506$$ 0 0
$$507$$ 8.57321 + 8.57321i 0.380750 + 0.380750i
$$508$$ 0 0
$$509$$ 12.2474 0.542859 0.271429 0.962458i $$-0.412504\pi$$
0.271429 + 0.962458i $$0.412504\pi$$
$$510$$ 0 0
$$511$$ 24.0000 9.79796i 1.06170 0.433436i
$$512$$ 0 0
$$513$$ 9.00000 + 9.00000i 0.397360 + 0.397360i
$$514$$ 0 0
$$515$$ 24.0000i 1.05757i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 27.0000 + 27.0000i 1.18517 + 1.18517i
$$520$$ 0 0
$$521$$ −4.89898 −0.214628 −0.107314 0.994225i $$-0.534225\pi$$
−0.107314 + 0.994225i $$0.534225\pi$$
$$522$$ 0 0
$$523$$ 2.44949i 0.107109i 0.998565 + 0.0535544i $$0.0170550\pi$$
−0.998565 + 0.0535544i $$0.982945\pi$$
$$524$$ 0 0
$$525$$ −1.77526 + 4.22474i −0.0774785 + 0.184383i
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −13.0000 −0.565217
$$530$$ 0 0
$$531$$ 36.7423i 1.59448i
$$532$$ 0 0
$$533$$ 12.0000i 0.519778i
$$534$$ 0 0
$$535$$ 29.3939i 1.27081i
$$536$$ 0 0
$$537$$ 29.3939 29.3939i 1.26844 1.26844i
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −2.00000 −0.0859867 −0.0429934 0.999075i $$-0.513689\pi$$
−0.0429934 + 0.999075i $$0.513689\pi$$
$$542$$ 0 0
$$543$$ −15.0000 + 15.0000i −0.643712 + 0.643712i
$$544$$ 0 0
$$545$$ −24.4949 −1.04925
$$546$$ 0 0
$$547$$ 8.00000 0.342055 0.171028 0.985266i $$-0.445291\pi$$
0.171028 + 0.985266i $$0.445291\pi$$
$$548$$ 0 0
$$549$$ 36.7423 1.56813
$$550$$ 0 0
$$551$$ −14.6969 −0.626111
$$552$$ 0 0
$$553$$ 10.0000 + 24.4949i 0.425243 + 1.04163i
$$554$$ 0 0
$$555$$ 6.00000 + 6.00000i 0.254686 + 0.254686i
$$556$$ 0 0
$$557$$ 18.0000i 0.762684i 0.924434 + 0.381342i $$0.124538\pi$$
−0.924434 + 0.381342i $$0.875462\pi$$
$$558$$ 0 0
$$559$$ 9.79796i 0.414410i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −22.0454 −0.929103 −0.464552 0.885546i $$-0.653784\pi$$
−0.464552 + 0.885546i $$0.653784\pi$$
$$564$$ 0 0
$$565$$ 14.6969i 0.618305i
$$566$$ 0 0
$$567$$ −9.00000 22.0454i −0.377964 0.925820i
$$568$$ 0 0
$$569$$ 6.00000i 0.251533i 0.992060 + 0.125767i $$0.0401390\pi$$
−0.992060 + 0.125767i $$0.959861\pi$$
$$570$$ 0 0
$$571$$ 32.0000 1.33916 0.669579 0.742741i $$-0.266474\pi$$
0.669579 + 0.742741i $$0.266474\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 6.00000i 0.250217i
$$576$$ 0 0
$$577$$ 19.5959i 0.815789i 0.913029 + 0.407894i $$0.133737\pi$$
−0.913029 + 0.407894i $$0.866263\pi$$
$$578$$ 0 0
$$579$$ 4.89898 + 4.89898i 0.203595 + 0.203595i
$$580$$ 0 0
$$581$$ 2.44949 + 6.00000i 0.101622 + 0.248922i
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 18.0000 0.744208
$$586$$ 0 0
$$587$$ −7.34847 −0.303304 −0.151652 0.988434i $$-0.548459\pi$$
−0.151652 + 0.988434i $$0.548459\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ −22.0454 + 22.0454i −0.906827 + 0.906827i
$$592$$ 0 0
$$593$$ 39.1918 1.60942 0.804708 0.593671i $$-0.202322\pi$$
0.804708 + 0.593671i $$0.202322\pi$$
$$594$$ 0 0
$$595$$ 12.0000 + 29.3939i 0.491952 + 1.20503i
$$596$$ 0 0
$$597$$ 12.0000 12.0000i 0.491127 0.491127i
$$598$$ 0 0
$$599$$ 24.0000i 0.980613i 0.871550 + 0.490307i $$0.163115\pi$$
−0.871550 + 0.490307i $$0.836885\pi$$
$$600$$ 0 0
$$601$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$602$$ 0 0
$$603$$ 24.0000i 0.977356i
$$604$$ 0 0
$$605$$ 26.9444 1.09545
$$606$$ 0 0
$$607$$ 4.89898i 0.198843i 0.995045 + 0.0994217i $$0.0316993\pi$$
−0.995045 + 0.0994217i $$0.968301\pi$$
$$608$$ 0 0
$$609$$ 25.3485 + 10.6515i 1.02717 + 0.431622i
$$610$$ 0 0
$$611$$ 12.0000i 0.485468i
$$612$$ 0 0
$$613$$ −14.0000 −0.565455 −0.282727 0.959200i $$-0.591239\pi$$
−0.282727 + 0.959200i $$0.591239\pi$$
$$614$$ 0 0
$$615$$ −14.6969 14.6969i −0.592638 0.592638i
$$616$$ 0 0
$$617$$ 18.0000i 0.724653i −0.932051 0.362326i $$-0.881983\pi$$
0.932051 0.362326i $$-0.118017\pi$$
$$618$$ 0 0
$$619$$ 26.9444i 1.08299i −0.840705 0.541493i $$-0.817859\pi$$
0.840705 0.541493i $$-0.182141\pi$$
$$620$$ 0 0
$$621$$ −22.0454 22.0454i −0.884652 0.884652i
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −29.0000 −1.16000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 9.79796 0.390670
$$630$$ 0 0
$$631$$ −2.00000 −0.0796187 −0.0398094 0.999207i $$-0.512675\pi$$
−0.0398094 + 0.999207i $$0.512675\pi$$
$$632$$ 0 0
$$633$$ −9.79796 9.79796i −0.389434 0.389434i
$$634$$ 0 0
$$635$$ −19.5959 −0.777640
$$636$$ 0 0
$$637$$ 12.0000 + 12.2474i 0.475457 + 0.485262i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 30.0000i 1.18493i 0.805597 + 0.592464i $$0.201845\pi$$
−0.805597 + 0.592464i $$0.798155\pi$$
$$642$$ 0 0
$$643$$ 22.0454i 0.869386i −0.900579 0.434693i $$-0.856857\pi$$
0.900579 0.434693i $$-0.143143\pi$$
$$644$$ 0 0
$$645$$ 12.0000 + 12.0000i 0.472500 + 0.472500i
$$646$$ 0 0
$$647$$ 44.0908 1.73339 0.866694 0.498839i $$-0.166240\pi$$
0.866694 + 0.498839i $$0.166240\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 6.00000i 0.234798i 0.993085 + 0.117399i $$0.0374557\pi$$
−0.993085 + 0.117399i $$0.962544\pi$$
$$654$$ 0 0
$$655$$ 18.0000 0.703318
$$656$$ 0 0
$$657$$ 29.3939 1.14676
$$658$$ 0 0
$$659$$ 36.0000i 1.40236i 0.712984 + 0.701180i $$0.247343\pi$$
−0.712984 + 0.701180i $$0.752657\pi$$
$$660$$ 0 0
$$661$$ 12.2474i 0.476371i 0.971220 + 0.238185i $$0.0765525\pi$$
−0.971220 + 0.238185i $$0.923447\pi$$
$$662$$ 0 0
$$663$$ 14.6969 14.6969i 0.570782 0.570782i
$$664$$ 0 0
$$665$$ 14.6969 6.00000i 0.569923 0.232670i
$$666$$ 0 0
$$667$$ 36.0000 1.39393
$$668$$ 0 0
$$669$$ 18.0000 18.0000i 0.695920 0.695920i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 34.0000 1.31060 0.655302 0.755367i $$-0.272541\pi$$
0.655302 + 0.755367i $$0.272541\pi$$
$$674$$ 0 0
$$675$$ −3.67423 + 3.67423i −0.141421 + 0.141421i
$$676$$ 0 0
$$677$$ 7.34847 0.282425 0.141212 0.989979i $$-0.454900\pi$$
0.141212 + 0.989979i $$0.454900\pi$$
$$678$$ 0 0
$$679$$ 12.0000 4.89898i 0.460518 0.188006i
$$680$$ 0 0
$$681$$ −9.00000 9.00000i −0.344881 0.344881i
$$682$$ 0 0
$$683$$ 24.0000i 0.918334i 0.888350 + 0.459167i $$0.151852\pi$$
−0.888350 + 0.459167i $$0.848148\pi$$
$$684$$ 0 0
$$685$$ 29.3939i 1.12308i
$$686$$ 0 0
$$687$$ 27.0000 27.0000i 1.03011 1.03011i
$$688$$ 0 0
$$689$$ 14.6969 0.559909
$$690$$ 0 0
$$691$$ 36.7423i 1.39774i 0.715246 + 0.698872i $$0.246314\pi$$
−0.715246 + 0.698872i $$0.753686\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 6.00000i 0.227593i
$$696$$ 0 0
$$697$$ −24.0000 −0.909065
$$698$$ 0 0
$$699$$ −29.3939 + 29.3939i −1.11178 + 1.11178i
$$700$$ 0 0
$$701$$ 30.0000i 1.13308i 0.824033 + 0.566542i $$0.191719\pi$$
−0.824033 + 0.566542i $$0.808281\pi$$
$$702$$ 0 0
$$703$$ 4.89898i 0.184769i
$$704$$ 0 0
$$705$$ −14.6969 14.6969i −0.553519 0.553519i
$$706$$ 0 0
$$707$$ −7.34847 18.0000i −0.276368 0.676960i
$$708$$ 0 0
$$709$$ −10.0000 −0.375558 −0.187779 0.982211i $$-0.560129\pi$$
−0.187779 + 0.982211i $$0.560129\pi$$
$$710$$ 0 0
$$711$$ 30.0000i 1.12509i
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 7.34847 7.34847i 0.274434 0.274434i
$$718$$ 0 0
$$719$$ −24.4949 −0.913506 −0.456753 0.889594i $$-0.650988\pi$$
−0.456753 + 0.889594i $$0.650988\pi$$
$$720$$ 0 0
$$721$$ −24.0000 + 9.79796i −0.893807 + 0.364895i
$$722$$ 0 0
$$723$$ 30.0000 30.0000i 1.11571 1.11571i
$$724$$ 0 0
$$725$$ 6.00000i 0.222834i
$$726$$ 0 0
$$727$$ 29.3939i 1.09016i 0.838385 + 0.545079i $$0.183500\pi$$
−0.838385 + 0.545079i $$0.816500\pi$$
$$728$$ 0 0
$$729$$ 27.0000i 1.00000i
$$730$$ 0 0
$$731$$ 19.5959 0.724781
$$732$$ 0 0
$$733$$ 22.0454i 0.814266i 0.913369 + 0.407133i $$0.133471\pi$$
−0.913369 + 0.407133i $$0.866529\pi$$
$$734$$ 0 0
$$735$$ −29.6969 0.303062i −1.09539 0.0111786i
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 20.0000 0.735712 0.367856 0.929883i $$-0.380092\pi$$
0.367856 + 0.929883i $$0.380092\pi$$
$$740$$ 0 0
$$741$$ −7.34847 7.34847i −0.269953 0.269953i
$$742$$ 0 0
$$743$$ 6.00000i 0.220119i 0.993925 + 0.110059i $$0.0351041\pi$$
−0.993925 + 0.110059i $$0.964896\pi$$
$$744$$ 0 0
$$745$$ 14.6969i 0.538454i
$$746$$ 0 0
$$747$$ 7.34847i 0.268866i
$$748$$ 0 0
$$749$$ −29.3939 + 12.0000i −1.07403 + 0.438470i
$$750$$ 0 0
$$751$$ 8.00000 0.291924 0.145962 0.989290i $$-0.453372\pi$$
0.145962 + 0.989290i $$0.453372\pi$$
$$752$$ 0 0
$$753$$ −21.0000 21.0000i −0.765283 0.765283i
$$754$$ 0 0
$$755$$ 19.5959 0.713168
$$756$$ 0 0
$$757$$ 2.00000 0.0726912 0.0363456 0.999339i $$-0.488428\pi$$
0.0363456 + 0.999339i $$0.488428\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −4.89898 −0.177588 −0.0887939 0.996050i $$-0.528301\pi$$
−0.0887939 + 0.996050i $$0.528301\pi$$
$$762$$ 0 0
$$763$$ −10.0000 24.4949i −0.362024 0.886775i
$$764$$ 0 0
$$765$$ 36.0000i 1.30158i
$$766$$ 0 0
$$767$$ 30.0000i 1.08324i
$$768$$ 0 0
$$769$$ 34.2929i 1.23663i 0.785930 + 0.618316i $$0.212185\pi$$
−0.785930 + 0.618316i $$0.787815\pi$$
$$770$$ 0 0
$$771$$ 36.0000 + 36.0000i 1.29651 + 1.29651i
$$772$$ 0 0
$$773$$ −26.9444 −0.969122 −0.484561 0.874757i $$-0.661021\pi$$
−0.484561 + 0.874757i $$0.661021\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ −3.55051 + 8.44949i −0.127374 + 0.303124i
$$778$$ 0 0
$$779$$ 12.0000i 0.429945i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 22.0454 + 22.0454i 0.787839 + 0.787839i
$$784$$ 0 0
$$785$$ 18.0000i 0.642448i
$$786$$ 0 0
$$787$$ 31.8434i 1.13509i 0.823341 + 0.567547i $$0.192107\pi$$
−0.823341 + 0.567547i $$0.807893\pi$$
$$788$$ 0 0
$$789$$ 29.3939 29.3939i 1.04645 1.04645i
$$790$$ 0 0
$$791$$ 14.6969 6.00000i 0.522563 0.213335i
$$792$$ 0 0
$$793$$ −30.0000 −1.06533
$$794$$ 0 0
$$795$$ −18.0000 + 18.0000i −0.638394 + 0.638394i
$$796$$ 0 0
$$797$$ 7.34847 0.260296 0.130148 0.991495i $$-0.458455\pi$$
0.130148 + 0.991495i $$0.458455\pi$$
$$798$$ 0 0
$$799$$ −24.0000 −0.849059
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0