# Properties

 Label 869.1.j.a.236.1 Level $869$ Weight $1$ Character 869.236 Analytic conductor $0.434$ Analytic rank $0$ Dimension $20$ Projective image $D_{25}$ CM discriminant -79 Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$869 = 11 \cdot 79$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 869.j (of order $$10$$, degree $$4$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.433687495978$$ Analytic rank: $$0$$ Dimension: $$20$$ Relative dimension: $$5$$ over $$\Q(\zeta_{10})$$ Coefficient field: $$\Q(\zeta_{50})$$ Defining polynomial: $$x^{20} - x^{15} + x^{10} - x^{5} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{25}$$ Projective field: Galois closure of $$\mathbb{Q}[x]/(x^{25} - \cdots)$$

## Embedding invariants

 Embedding label 236.1 Root $$-0.876307 - 0.481754i$$ of defining polynomial Character $$\chi$$ $$=$$ 869.236 Dual form 869.1.j.a.394.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.613161 - 1.88711i) q^{2} +(-2.37622 + 1.72642i) q^{4} +(0.0388067 - 0.119435i) q^{5} +(3.10969 + 2.25932i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$$ $$q+(-0.613161 - 1.88711i) q^{2} +(-2.37622 + 1.72642i) q^{4} +(0.0388067 - 0.119435i) q^{5} +(3.10969 + 2.25932i) q^{8} +(0.309017 + 0.951057i) q^{9} -0.249182 q^{10} +(-0.992115 + 0.125333i) q^{11} +(0.541587 + 1.66683i) q^{13} +(1.44922 - 4.46025i) q^{16} +(1.60528 - 1.16630i) q^{18} +(1.03137 + 0.749337i) q^{19} +(0.113982 + 0.350799i) q^{20} +(0.844844 + 1.79538i) q^{22} -1.27485 q^{23} +(0.796258 + 0.578516i) q^{25} +(2.81343 - 2.04407i) q^{26} +(-0.263146 - 0.809880i) q^{31} -5.46182 q^{32} +(-2.37622 - 1.72642i) q^{36} +(0.781687 - 2.40578i) q^{38} +(0.390518 - 0.283728i) q^{40} +(2.14110 - 2.01063i) q^{44} +0.125581 q^{45} +(0.781687 + 2.40578i) q^{46} +(0.309017 - 0.951057i) q^{49} +(0.603491 - 1.85735i) q^{50} +(-4.16459 - 3.02575i) q^{52} +(-0.0235315 + 0.123357i) q^{55} +(-1.36699 + 0.993173i) q^{62} +(1.89975 + 5.84683i) q^{64} +0.220095 q^{65} +1.07165 q^{67} +(-1.18779 + 3.65565i) q^{72} +(-1.56720 + 1.13864i) q^{73} -3.74444 q^{76} +(0.309017 + 0.951057i) q^{79} +(-0.476468 - 0.346175i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(0.190983 - 0.587785i) q^{83} +(-3.36833 - 1.85176i) q^{88} +1.45794 q^{89} +(-0.0770013 - 0.236986i) q^{90} +(3.02932 - 2.20093i) q^{92} +(0.129521 - 0.0941025i) q^{95} +(-0.574633 - 1.76854i) q^{97} -1.98423 q^{98} +(-0.425779 - 0.904827i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$20q - 5q^{4} - 5q^{9} + O(q^{10})$$ $$20q - 5q^{4} - 5q^{9} - 5q^{16} + 15q^{20} - 5q^{22} - 5q^{25} + 15q^{26} - 10q^{32} - 5q^{36} - 10q^{40} - 5q^{49} - 10q^{50} - 10q^{62} - 5q^{64} - 10q^{76} - 5q^{79} - 10q^{80} - 5q^{81} + 15q^{83} - 5q^{88} + 15q^{92} + 15q^{95} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/869\mathbb{Z}\right)^\times$$.

 $$n$$ $$475$$ $$793$$ $$\chi(n)$$ $$e\left(\frac{2}{5}\right)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.613161 1.88711i −0.613161 1.88711i −0.425779 0.904827i $$-0.640000\pi$$
−0.187381 0.982287i $$-0.560000\pi$$
$$3$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$4$$ −2.37622 + 1.72642i −2.37622 + 1.72642i
$$5$$ 0.0388067 0.119435i 0.0388067 0.119435i −0.929776 0.368125i $$-0.880000\pi$$
0.968583 + 0.248690i $$0.0800000\pi$$
$$6$$ 0 0
$$7$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$8$$ 3.10969 + 2.25932i 3.10969 + 2.25932i
$$9$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$10$$ −0.249182 −0.249182
$$11$$ −0.992115 + 0.125333i −0.992115 + 0.125333i
$$12$$ 0 0
$$13$$ 0.541587 + 1.66683i 0.541587 + 1.66683i 0.728969 + 0.684547i $$0.240000\pi$$
−0.187381 + 0.982287i $$0.560000\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.44922 4.46025i 1.44922 4.46025i
$$17$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$18$$ 1.60528 1.16630i 1.60528 1.16630i
$$19$$ 1.03137 + 0.749337i 1.03137 + 0.749337i 0.968583 0.248690i $$-0.0800000\pi$$
0.0627905 + 0.998027i $$0.480000\pi$$
$$20$$ 0.113982 + 0.350799i 0.113982 + 0.350799i
$$21$$ 0 0
$$22$$ 0.844844 + 1.79538i 0.844844 + 1.79538i
$$23$$ −1.27485 −1.27485 −0.637424 0.770513i $$-0.720000\pi$$
−0.637424 + 0.770513i $$0.720000\pi$$
$$24$$ 0 0
$$25$$ 0.796258 + 0.578516i 0.796258 + 0.578516i
$$26$$ 2.81343 2.04407i 2.81343 2.04407i
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$30$$ 0 0
$$31$$ −0.263146 0.809880i −0.263146 0.809880i −0.992115 0.125333i $$-0.960000\pi$$
0.728969 0.684547i $$-0.240000\pi$$
$$32$$ −5.46182 −5.46182
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ −2.37622 1.72642i −2.37622 1.72642i
$$37$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$38$$ 0.781687 2.40578i 0.781687 2.40578i
$$39$$ 0 0
$$40$$ 0.390518 0.283728i 0.390518 0.283728i
$$41$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$44$$ 2.14110 2.01063i 2.14110 2.01063i
$$45$$ 0.125581 0.125581
$$46$$ 0.781687 + 2.40578i 0.781687 + 2.40578i
$$47$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$48$$ 0 0
$$49$$ 0.309017 0.951057i 0.309017 0.951057i
$$50$$ 0.603491 1.85735i 0.603491 1.85735i
$$51$$ 0 0
$$52$$ −4.16459 3.02575i −4.16459 3.02575i
$$53$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$54$$ 0 0
$$55$$ −0.0235315 + 0.123357i −0.0235315 + 0.123357i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$60$$ 0 0
$$61$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$62$$ −1.36699 + 0.993173i −1.36699 + 0.993173i
$$63$$ 0 0
$$64$$ 1.89975 + 5.84683i 1.89975 + 5.84683i
$$65$$ 0.220095 0.220095
$$66$$ 0 0
$$67$$ 1.07165 1.07165 0.535827 0.844328i $$-0.320000\pi$$
0.535827 + 0.844328i $$0.320000\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$72$$ −1.18779 + 3.65565i −1.18779 + 3.65565i
$$73$$ −1.56720 + 1.13864i −1.56720 + 1.13864i −0.637424 + 0.770513i $$0.720000\pi$$
−0.929776 + 0.368125i $$0.880000\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ −3.74444 −3.74444
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$80$$ −0.476468 0.346175i −0.476468 0.346175i
$$81$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$82$$ 0 0
$$83$$ 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i $$-0.800000\pi$$
1.00000 $$0$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ −3.36833 1.85176i −3.36833 1.85176i
$$89$$ 1.45794 1.45794 0.728969 0.684547i $$-0.240000\pi$$
0.728969 + 0.684547i $$0.240000\pi$$
$$90$$ −0.0770013 0.236986i −0.0770013 0.236986i
$$91$$ 0 0
$$92$$ 3.02932 2.20093i 3.02932 2.20093i
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0.129521 0.0941025i 0.129521 0.0941025i
$$96$$ 0 0
$$97$$ −0.574633 1.76854i −0.574633 1.76854i −0.637424 0.770513i $$-0.720000\pi$$
0.0627905 0.998027i $$-0.480000\pi$$
$$98$$ −1.98423 −1.98423
$$99$$ −0.425779 0.904827i −0.425779 0.904827i
$$100$$ −2.89085 −2.89085
$$101$$ 0.450527 + 1.38658i 0.450527 + 1.38658i 0.876307 + 0.481754i $$0.160000\pi$$
−0.425779 + 0.904827i $$0.640000\pi$$
$$102$$ 0 0
$$103$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$104$$ −2.08174 + 6.40695i −2.08174 + 6.40695i
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$108$$ 0 0
$$109$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$110$$ 0.247217 0.0312307i 0.247217 0.0312307i
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$114$$ 0 0
$$115$$ −0.0494726 + 0.152261i −0.0494726 + 0.152261i
$$116$$ 0 0
$$117$$ −1.41789 + 1.03016i −1.41789 + 1.03016i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 0.968583 0.248690i 0.968583 0.248690i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 2.02349 + 1.47015i 2.02349 + 1.47015i
$$125$$ 0.201592 0.146465i 0.201592 0.146465i
$$126$$ 0 0
$$127$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$128$$ 5.45008 3.95971i 5.45008 3.95971i
$$129$$ 0 0
$$130$$ −0.134954 0.415344i −0.134954 0.415344i
$$131$$ 1.93717 1.93717 0.968583 0.248690i $$-0.0800000\pi$$
0.968583 + 0.248690i $$0.0800000\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ −0.657096 2.02233i −0.657096 2.02233i
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$138$$ 0 0
$$139$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −0.746226 1.58581i −0.746226 1.58581i
$$144$$ 4.68978 4.68978
$$145$$ 0 0
$$146$$ 3.10969 + 2.25932i 3.10969 + 2.25932i
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$150$$ 0 0
$$151$$ −0.866986 0.629902i −0.866986 0.629902i 0.0627905 0.998027i $$-0.480000\pi$$
−0.929776 + 0.368125i $$0.880000\pi$$
$$152$$ 1.51426 + 4.66040i 1.51426 + 4.66040i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −0.106940 −0.106940
$$156$$ 0 0
$$157$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$158$$ 1.60528 1.16630i 1.60528 1.16630i
$$159$$ 0 0
$$160$$ −0.211955 + 0.652330i −0.211955 + 0.652330i
$$161$$ 0 0
$$162$$ 1.60528 + 1.16630i 1.60528 + 1.16630i
$$163$$ −0.115808 0.356420i −0.115808 0.356420i 0.876307 0.481754i $$-0.160000\pi$$
−0.992115 + 0.125333i $$0.960000\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ −1.22632 −1.22632
$$167$$ −0.263146 0.809880i −0.263146 0.809880i −0.992115 0.125333i $$-0.960000\pi$$
0.728969 0.684547i $$-0.240000\pi$$
$$168$$ 0 0
$$169$$ −1.67600 + 1.21769i −1.67600 + 1.21769i
$$170$$ 0 0
$$171$$ −0.393950 + 1.21245i −0.393950 + 1.21245i
$$172$$ 0 0
$$173$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −0.878777 + 4.60671i −0.878777 + 4.60671i
$$177$$ 0 0
$$178$$ −0.893950 2.75129i −0.893950 2.75129i
$$179$$ −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i $$-0.400000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$180$$ −0.298408 + 0.216806i −0.298408 + 0.216806i
$$181$$ 0.541587 1.66683i 0.541587 1.66683i −0.187381 0.982287i $$-0.560000\pi$$
0.728969 0.684547i $$-0.240000\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −3.96438 2.88029i −3.96438 2.88029i
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ −0.256999 0.186721i −0.256999 0.186721i
$$191$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$192$$ 0 0
$$193$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$194$$ −2.98509 + 2.16880i −2.98509 + 2.16880i
$$195$$ 0 0
$$196$$ 0.907634 + 2.79341i 0.907634 + 2.79341i
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ −1.44644 + 1.35830i −1.44644 + 1.35830i
$$199$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$200$$ 1.16906 + 3.59800i 1.16906 + 3.59800i
$$201$$ 0 0
$$202$$ 2.34039 1.70039i 2.34039 1.70039i
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −0.393950 1.21245i −0.393950 1.21245i
$$208$$ 8.21937 8.21937
$$209$$ −1.11716 0.614163i −1.11716 0.614163i
$$210$$ 0 0
$$211$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ −0.157050 0.333748i −0.157050 0.333748i
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i $$-0.400000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$224$$ 0 0
$$225$$ −0.304144 + 0.936058i −0.304144 + 0.936058i
$$226$$ 0 0
$$227$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$228$$ 0 0
$$229$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$230$$ 0.317669 0.317669
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$234$$ 2.81343 + 2.04407i 2.81343 + 2.04407i
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −0.101597 0.0738147i −0.101597 0.0738147i 0.535827 0.844328i $$-0.320000\pi$$
−0.637424 + 0.770513i $$0.720000\pi$$
$$240$$ 0 0
$$241$$ −0.374763 −0.374763 −0.187381 0.982287i $$-0.560000\pi$$
−0.187381 + 0.982287i $$0.560000\pi$$
$$242$$ −1.06320 1.67534i −1.06320 1.67534i
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −0.101597 0.0738147i −0.101597 0.0738147i
$$246$$ 0 0
$$247$$ −0.690441 + 2.12496i −0.690441 + 2.12496i
$$248$$ 1.01148 3.11300i 1.01148 3.11300i
$$249$$ 0 0
$$250$$ −0.400005 0.290621i −0.400005 0.290621i
$$251$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$252$$ 0 0
$$253$$ 1.26480 0.159781i 1.26480 0.159781i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ −5.84059 4.24344i −5.84059 4.24344i
$$257$$ −1.41789 + 1.03016i −1.41789 + 1.03016i −0.425779 + 0.904827i $$0.640000\pi$$
−0.992115 + 0.125333i $$0.960000\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ −0.522994 + 0.379977i −0.522994 + 0.379977i
$$261$$ 0 0
$$262$$ −1.18779 3.65565i −1.18779 3.65565i
$$263$$ −0.374763 −0.374763 −0.187381 0.982287i $$-0.560000\pi$$
−0.187381 + 0.982287i $$0.560000\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −2.54648 + 1.85013i −2.54648 + 1.85013i
$$269$$ 0.331159 1.01920i 0.331159 1.01920i −0.637424 0.770513i $$-0.720000\pi$$
0.968583 0.248690i $$-0.0800000\pi$$
$$270$$ 0 0
$$271$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −0.862487 0.474156i −0.862487 0.474156i
$$276$$ 0 0
$$277$$ 0.0388067 + 0.119435i 0.0388067 + 0.119435i 0.968583 0.248690i $$-0.0800000\pi$$
−0.929776 + 0.368125i $$0.880000\pi$$
$$278$$ 0 0
$$279$$ 0.688925 0.500534i 0.688925 0.500534i
$$280$$ 0 0
$$281$$ 0.0388067 0.119435i 0.0388067 0.119435i −0.929776 0.368125i $$-0.880000\pi$$
0.968583 + 0.248690i $$0.0800000\pi$$
$$282$$ 0 0
$$283$$ 0.688925 + 0.500534i 0.688925 + 0.500534i 0.876307 0.481754i $$-0.160000\pi$$
−0.187381 + 0.982287i $$0.560000\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ −2.53505 + 2.38057i −2.53505 + 2.38057i
$$287$$ 0 0
$$288$$ −1.68779 5.19450i −1.68779 5.19450i
$$289$$ −0.809017 0.587785i −0.809017 0.587785i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 1.75824 5.41130i 1.75824 5.41130i
$$293$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −0.690441 2.12496i −0.690441 2.12496i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −0.657096 + 2.02233i −0.657096 + 2.02233i
$$303$$ 0 0
$$304$$ 4.83692 3.51422i 4.83692 3.51422i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0.0655712 + 0.201807i 0.0655712 + 0.201807i
$$311$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$312$$ 0 0
$$313$$ −0.263146 + 0.809880i −0.263146 + 0.809880i 0.728969 + 0.684547i $$0.240000\pi$$
−0.992115 + 0.125333i $$0.960000\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ −2.37622 1.72642i −2.37622 1.72642i
$$317$$ −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i $$-0.800000\pi$$
0.309017 0.951057i $$-0.400000\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0.772037 0.772037
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0.907634 2.79341i 0.907634 2.79341i
$$325$$ −0.533046 + 1.64055i −0.533046 + 1.64055i
$$326$$ −0.601597 + 0.437086i −0.601597 + 0.437086i
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$332$$ 0.560949 + 1.72642i 0.560949 + 1.72642i
$$333$$ 0 0
$$334$$ −1.36699 + 0.993173i −1.36699 + 0.993173i
$$335$$ 0.0415873 0.127993i 0.0415873 0.127993i
$$336$$ 0 0
$$337$$ 1.50441 1.09302i 1.50441 1.09302i 0.535827 0.844328i $$-0.320000\pi$$
0.968583 0.248690i $$-0.0800000\pi$$
$$338$$ 3.32557 + 2.41617i 3.32557 + 2.41617i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0.362576 + 0.770513i 0.362576 + 0.770513i
$$342$$ 2.52959 2.52959
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0.331159 1.01920i 0.331159 1.01920i −0.637424 0.770513i $$-0.720000\pi$$
0.968583 0.248690i $$-0.0800000\pi$$
$$348$$ 0 0
$$349$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 5.41875 0.684547i 5.41875 0.684547i
$$353$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −3.46438 + 2.51702i −3.46438 + 2.51702i
$$357$$ 0 0
$$358$$ −0.378954 + 1.16630i −0.378954 + 1.16630i
$$359$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$360$$ 0.390518 + 0.283728i 0.390518 + 0.283728i
$$361$$ 0.193209 + 0.594636i 0.193209 + 0.594636i
$$362$$ −3.47759 −3.47759
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0.0751750 + 0.231365i 0.0751750 + 0.231365i
$$366$$ 0 0
$$367$$ −1.17950 + 0.856954i −1.17950 + 0.856954i −0.992115 0.125333i $$-0.960000\pi$$
−0.187381 + 0.982287i $$0.560000\pi$$
$$368$$ −1.84754 + 5.68613i −1.84754 + 5.68613i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$380$$ −0.145309 + 0.447216i −0.145309 + 0.447216i
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −0.613161 1.88711i −0.613161 1.88711i −0.425779 0.904827i $$-0.640000\pi$$
−0.187381 0.982287i $$-0.560000\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 4.41870 + 3.21038i 4.41870 + 3.21038i
$$389$$ 0.688925 0.500534i 0.688925 0.500534i −0.187381 0.982287i $$-0.560000\pi$$
0.876307 + 0.481754i $$0.160000\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 3.10969 2.25932i 3.10969 2.25932i
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0.125581 0.125581
$$396$$ 2.57386 + 1.41499i 2.57386 + 1.41499i
$$397$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 3.73428 2.71311i 3.73428 2.71311i
$$401$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$402$$ 0 0
$$403$$ 1.20742 0.877242i 1.20742 0.877242i
$$404$$ −3.46438 2.51702i −3.46438 2.51702i
$$405$$ 0.0388067 + 0.119435i 0.0388067 + 0.119435i
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ −2.04648 + 1.48686i −2.04648 + 1.48686i
$$415$$ −0.0627905 0.0456200i −0.0627905 0.0456200i
$$416$$ −2.95805 9.10394i −2.95805 9.10394i
$$417$$ 0 0
$$418$$ −0.473998 + 2.48478i −0.473998 + 2.48478i
$$419$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$420$$ 0 0
$$421$$ 1.50441 + 1.09302i 1.50441 + 1.09302i 0.968583 + 0.248690i $$0.0800000\pi$$
0.535827 + 0.844328i $$0.320000\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0.598617 + 1.84235i 0.598617 + 1.84235i 0.535827 + 0.844328i $$0.320000\pi$$
0.0627905 + 0.998027i $$0.480000\pi$$
$$432$$ 0 0
$$433$$ 1.03137 0.749337i 1.03137 0.749337i 0.0627905 0.998027i $$-0.480000\pi$$
0.968583 + 0.248690i $$0.0800000\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −1.31484 0.955291i −1.31484 0.955291i
$$438$$ 0 0
$$439$$ −1.85955 −1.85955 −0.929776 0.368125i $$-0.880000\pi$$
−0.929776 + 0.368125i $$0.880000\pi$$
$$440$$ −0.351878 + 0.330435i −0.351878 + 0.330435i
$$441$$ 1.00000 1.00000
$$442$$ 0 0
$$443$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$444$$ 0 0
$$445$$ 0.0565777 0.174128i 0.0565777 0.174128i
$$446$$ −0.378954 + 1.16630i −0.378954 + 1.16630i
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$450$$ 1.95294 1.95294
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0.450527 1.38658i 0.450527 1.38658i −0.425779 0.904827i $$-0.640000\pi$$
0.876307 0.481754i $$-0.160000\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ −0.145309 0.447216i −0.145309 0.447216i
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −0.613161 + 1.88711i −0.613161 + 1.88711i −0.187381 + 0.982287i $$0.560000\pi$$
−0.425779 + 0.904827i $$0.640000\pi$$
$$468$$ 1.59073 4.89577i 1.59073 4.89577i
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0.387737 + 1.19333i 0.387737 + 1.19333i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ −0.0770013 + 0.236986i −0.0770013 + 0.236986i
$$479$$ 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i $$-0.800000\pi$$
1.00000 $$0$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0.229790 + 0.707220i 0.229790 + 0.707220i
$$483$$ 0 0
$$484$$ −1.87222 + 2.26313i −1.87222 + 2.26313i
$$485$$ −0.233525 −0.233525
$$486$$ 0 0
$$487$$ −1.41789 1.03016i −1.41789 1.03016i −0.992115 0.125333i $$-0.960000\pi$$
−0.425779 0.904827i $$-0.640000\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ −0.0770013 + 0.236986i −0.0770013 + 0.236986i
$$491$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 4.43339 4.43339
$$495$$ −0.124591 + 0.0157395i −0.124591 + 0.0157395i
$$496$$ −3.99362 −3.99362
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 1.60528 1.16630i 1.60528 1.16630i 0.728969 0.684547i $$-0.240000\pi$$
0.876307 0.481754i $$-0.160000\pi$$
$$500$$ −0.226166 + 0.696067i −0.226166 + 0.696067i
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$504$$ 0 0
$$505$$ 0.183089 0.183089
$$506$$ −1.07705 2.28884i −1.07705 2.28884i
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −2.34489 + 7.21683i −2.34489 + 7.21683i
$$513$$ 0 0
$$514$$ 2.81343 + 2.04407i 2.81343 + 2.04407i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0.684426 + 0.497265i 0.684426 + 0.497265i
$$521$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$522$$ 0 0
$$523$$ 0.450527 1.38658i 0.450527 1.38658i −0.425779 0.904827i $$-0.640000\pi$$
0.876307 0.481754i $$-0.160000\pi$$
$$524$$ −4.60313 + 3.34437i −4.60313 + 3.34437i
$$525$$ 0 0
$$526$$ 0.229790 + 0.707220i 0.229790 + 0.707220i
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 0.625237 0.625237
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 3.33251 + 2.42121i 3.33251 + 2.42121i
$$537$$ 0 0
$$538$$ −2.12641 −2.12641
$$539$$ −0.187381 + 0.982287i −0.187381 + 0.982287i
$$540$$ 0 0
$$541$$ 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 $$0$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0.303189 + 0.220280i 0.303189 + 0.220280i 0.728969 0.684547i $$-0.240000\pi$$
−0.425779 + 0.904827i $$0.640000\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ −0.365944 + 1.91835i −0.365944 + 1.91835i
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0.201592 0.146465i 0.201592 0.146465i
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 1.03137 0.749337i 1.03137 0.749337i 0.0627905 0.998027i $$-0.480000\pi$$
0.968583 + 0.248690i $$0.0800000\pi$$
$$558$$ −1.36699 0.993173i −1.36699 0.993173i
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −0.249182 −0.249182
$$563$$ 0.618034 + 1.90211i 0.618034 + 1.90211i 0.309017 + 0.951057i $$0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0.522142 1.60699i 0.522142 1.60699i
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 1.50441 + 1.09302i 1.50441 + 1.09302i 0.968583 + 0.248690i $$0.0800000\pi$$
0.535827 + 0.844328i $$0.320000\pi$$
$$570$$ 0 0
$$571$$ −0.851559 −0.851559 −0.425779 0.904827i $$-0.640000\pi$$
−0.425779 + 0.904827i $$0.640000\pi$$
$$572$$ 4.51098 + 2.47993i 4.51098 + 2.47993i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −1.01511 0.737519i −1.01511 0.737519i
$$576$$ −4.97361 + 3.61354i −4.97361 + 3.61354i
$$577$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$578$$ −0.613161 + 1.88711i −0.613161 + 1.88711i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ −7.44605 −7.44605
$$585$$ 0.0680131 + 0.209323i 0.0680131 + 0.209323i
$$586$$ 0 0
$$587$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$588$$ 0 0
$$589$$ 0.335471 1.03247i 0.335471 1.03247i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 0.125581 0.125581 0.0627905 0.998027i $$-0.480000\pi$$
0.0627905 + 0.998027i $$0.480000\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ −3.58669 + 2.60588i −3.58669 + 2.60588i
$$599$$ 0.598617 1.84235i 0.598617 1.84235i 0.0627905 0.998027i $$-0.480000\pi$$
0.535827 0.844328i $$-0.320000\pi$$
$$600$$ 0 0
$$601$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$602$$ 0 0
$$603$$ 0.331159 + 1.01920i 0.331159 + 1.01920i
$$604$$ 3.14762 3.14762
$$605$$ 0.00788530 0.125333i 0.00788530 0.125333i
$$606$$ 0 0
$$607$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$608$$ −5.63317 4.09274i −5.63317 4.09274i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 1.75261 1.75261 0.876307 0.481754i $$-0.160000\pi$$
0.876307 + 0.481754i $$0.160000\pi$$
$$618$$ 0 0
$$619$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$620$$ 0.254112 0.184623i 0.254112 0.184623i
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0.294474 + 0.906297i 0.294474 + 0.906297i
$$626$$ 1.68969 1.68969
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$632$$ −1.18779 + 3.65565i −1.18779 + 3.65565i
$$633$$ 0 0
$$634$$ −2.59739 + 1.88711i −2.59739 + 1.88711i
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 1.75261 1.75261
$$638$$ 0 0
$$639$$ 0 0
$$640$$ −0.261428 0.804591i −0.261428 0.804591i
$$641$$ 1.03137 + 0.749337i 1.03137 + 0.749337i 0.968583 0.248690i $$-0.0800000\pi$$
0.0627905 + 0.998027i $$0.480000\pi$$
$$642$$ 0 0
$$643$$ 0.598617 1.84235i 0.598617 1.84235i 0.0627905 0.998027i $$-0.480000\pi$$
0.535827 0.844328i $$-0.320000\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$648$$ −3.84378 −3.84378
$$649$$ 0 0
$$650$$ 3.42274 3.42274
$$651$$ 0 0
$$652$$ 0.890518 + 0.646999i 0.890518 + 0.646999i
$$653$$ −1.17950 + 0.856954i −1.17950 + 0.856954i −0.992115 0.125333i $$-0.960000\pi$$
−0.187381 + 0.982287i $$0.560000\pi$$
$$654$$ 0 0
$$655$$ 0.0751750 0.231365i 0.0751750 0.231365i
$$656$$ 0 0
$$657$$ −1.56720 1.13864i −1.56720 1.13864i
$$658$$ 0 0
$$659$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$660$$ 0 0
$$661$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 1.92189 1.39634i 1.92189 1.39634i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 2.02349 + 1.47015i 2.02349 + 1.47015i
$$669$$ 0 0
$$670$$ −0.267036 −0.267036
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$674$$ −2.98509 2.16880i −2.98509 2.16880i
$$675$$ 0 0
$$676$$ 1.88030 5.78698i 1.88030 5.78698i
$$677$$ −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i $$0.400000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 1.23173 1.15667i 1.23173 1.15667i
$$683$$ 1.93717 1.93717 0.968583 0.248690i $$-0.0800000\pi$$
0.968583 + 0.248690i $$0.0800000\pi$$
$$684$$ −1.15710 3.56117i −1.15710 3.56117i
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ −2.12641 −2.12641
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ −2.61757 5.56262i −2.61757 5.56262i
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$710$$ 0 0
$$711$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$712$$ 4.53373 + 3.29394i 4.53373 + 3.29394i
$$713$$ 0.335471 + 1.03247i 0.335471 + 1.03247i
$$714$$ 0 0
$$715$$ −0.218359 + 0.0275852i −0.218359 + 0.0275852i
$$716$$ 1.81527 1.81527
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0.303189 0.220280i 0.303189 0.220280i −0.425779 0.904827i $$-0.640000\pi$$
0.728969 + 0.684547i $$0.240000\pi$$
$$720$$ 0.181995 0.560122i 0.181995 0.560122i
$$721$$ 0 0
$$722$$ 1.00368 0.729215i 1.00368 0.729215i
$$723$$ 0 0
$$724$$ 1.59073 + 4.89577i 1.59073 + 4.89577i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$728$$ 0 0
$$729$$ −0.809017 0.587785i −0.809017 0.587785i
$$730$$ 0.390518 0.283728i 0.390518 0.283728i
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −0.866986 + 0.629902i −0.866986 + 0.629902i −0.929776 0.368125i $$-0.880000\pi$$
0.0627905 + 0.998027i $$0.480000\pi$$
$$734$$ 2.34039 + 1.70039i 2.34039 + 1.70039i
$$735$$ 0 0
$$736$$ 6.96299 6.96299
$$737$$ −1.06320 + 0.134314i −1.06320 + 0.134314i
$$738$$ 0 0
$$739$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0.541587 1.66683i 0.541587 1.66683i −0.187381 0.982287i $$-0.560000\pi$$
0.728969 0.684547i $$-0.240000\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0.618034 0.618034
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 1.60528 + 1.16630i 1.60528 + 1.16630i 0.876307 + 0.481754i $$0.160000\pi$$
0.728969 + 0.684547i $$0.240000\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −0.108877 + 0.0791038i −0.108877 + 0.0791038i
$$756$$ 0 0
$$757$$ −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i $$-0.800000\pi$$
0.309017 0.951057i $$-0.400000\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0.615377 0.615377
$$761$$ −0.393950 1.21245i −0.393950 1.21245i −0.929776 0.368125i $$-0.880000\pi$$
0.535827 0.844328i $$-0.320000\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ −3.18523 + 2.31421i −3.18523 + 2.31421i
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −1.56720 1.13864i −1.56720 1.13864i −0.929776 0.368125i $$-0.880000\pi$$
−0.637424 0.770513i $$-0.720000\pi$$
$$774$$ 0 0
$$775$$ 0.258996 0.797108i 0.258996 0.797108i
$$776$$ 2.20877 6.79788i 2.20877 6.79788i
$$777$$ 0 0
$$778$$ −1.36699 0.993173i −1.36699 0.993173i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −3.79411 2.75658i −3.79411 2.75658i
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −0.574633 + 1.76854i −0.574633 + 1.76854i 0.0627905 + 0.998027i $$0.480000\pi$$
−0.637424 + 0.770513i $$0.720000\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ −0.0770013 0.236986i −0.0770013 0.236986i
$$791$$ 0 0
$$792$$ 0.720253 3.77570i 0.720253 3.77570i
$$793$$ 0 0
$$794$$ −0.378954 1.16630i −0.378954 1.16630i
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ −4.34902 3.15975i −4.34902 3.15975i
$$801$$ 0.450527 + 1.38658i 0.450527 + 1.38658i
$$802$$ 0 0
$$803$$