# Properties

 Label 1375.1.ch.a.1341.1 Level $1375$ Weight $1$ Character 1375.1341 Analytic conductor $0.686$ Analytic rank $0$ Dimension $20$ Projective image $D_{25}$ CM discriminant -11 Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1375 = 5^{3} \cdot 11$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1375.ch (of order $$50$$, degree $$20$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.686214392370$$ Analytic rank: $$0$$ Dimension: $$20$$ Coefficient field: $$\Q(\zeta_{50})$$ Defining polynomial: $$x^{20} - x^{15} + x^{10} - x^{5} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{4}]$$ 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 1341.1 Root $$0.929776 - 0.368125i$$ of defining polynomial Character $$\chi$$ $$=$$ 1375.1341 Dual form 1375.1.ch.a.1011.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.939097 - 1.47978i) q^{3} +(0.0627905 + 0.998027i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-0.882067 - 1.87449i) q^{9} +O(q^{10})$$ $$q+(0.939097 - 1.47978i) q^{3} +(0.0627905 + 0.998027i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-0.882067 - 1.87449i) q^{9} +(0.728969 + 0.684547i) q^{11} +(1.53583 + 0.844328i) q^{12} +(1.69755 + 0.435857i) q^{15} +(-0.992115 + 0.125333i) q^{16} +(-0.929776 + 0.368125i) q^{20} +(-0.200808 - 1.05267i) q^{23} +(-0.809017 + 0.587785i) q^{25} +(-1.86338 - 0.235400i) q^{27} +(-0.0235315 + 0.374023i) q^{31} +(1.69755 - 0.435857i) q^{33} +(1.81540 - 0.998027i) q^{36} +(1.60528 - 0.202793i) q^{37} +(-0.637424 + 0.770513i) q^{44} +(1.51017 - 1.41814i) q^{45} +(-0.393950 - 0.476203i) q^{47} +(-0.746226 + 1.58581i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(1.41213 + 0.362574i) q^{53} +(-0.425779 + 0.904827i) q^{55} +(-1.73879 - 0.955910i) q^{59} +(-0.328407 + 1.72157i) q^{60} +(-0.187381 - 0.982287i) q^{64} +(-1.80113 - 0.713118i) q^{67} +(-1.74630 - 0.691409i) q^{69} +(-1.11716 - 1.35041i) q^{71} +(0.110048 + 1.74915i) q^{75} +(-0.425779 - 0.904827i) q^{80} +(-0.777718 + 0.940099i) q^{81} +(-1.11716 + 0.614163i) q^{89} +(1.03799 - 0.266509i) q^{92} +(0.531374 + 0.386066i) q^{93} +(1.84489 - 0.730444i) q^{97} +(0.640176 - 1.97026i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$20q - 5q^{5} + O(q^{10})$$ $$20q - 5q^{5} + 20q^{12} - 5q^{25} - 5q^{27} - 5q^{48} - 5q^{49} - 5q^{59} - 5q^{60} - 5q^{67} - 5q^{69} - 5q^{81} - 5q^{92} - 10q^{93} - 5q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1375\mathbb{Z}\right)^\times$$.

 $$n$$ $$376$$ $$1002$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{6}{25}\right)$$

## 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 −0.728969 0.684547i $$-0.760000\pi$$
0.728969 + 0.684547i $$0.240000\pi$$
$$3$$ 0.939097 1.47978i 0.939097 1.47978i 0.0627905 0.998027i $$-0.480000\pi$$
0.876307 0.481754i $$-0.160000\pi$$
$$4$$ 0.0627905 + 0.998027i 0.0627905 + 0.998027i
$$5$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$6$$ 0 0
$$7$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$8$$ 0 0
$$9$$ −0.882067 1.87449i −0.882067 1.87449i
$$10$$ 0 0
$$11$$ 0.728969 + 0.684547i 0.728969 + 0.684547i
$$12$$ 1.53583 + 0.844328i 1.53583 + 0.844328i
$$13$$ 0 0 −0.425779 0.904827i $$-0.640000\pi$$
0.425779 + 0.904827i $$0.360000\pi$$
$$14$$ 0 0
$$15$$ 1.69755 + 0.435857i 1.69755 + 0.435857i
$$16$$ −0.992115 + 0.125333i −0.992115 + 0.125333i
$$17$$ 0 0 0.0627905 0.998027i $$-0.480000\pi$$
−0.0627905 + 0.998027i $$0.520000\pi$$
$$18$$ 0 0
$$19$$ 0 0 −0.535827 0.844328i $$-0.680000\pi$$
0.535827 + 0.844328i $$0.320000\pi$$
$$20$$ −0.929776 + 0.368125i −0.929776 + 0.368125i
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −0.200808 1.05267i −0.200808 1.05267i −0.929776 0.368125i $$-0.880000\pi$$
0.728969 0.684547i $$-0.240000\pi$$
$$24$$ 0 0
$$25$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$26$$ 0 0
$$27$$ −1.86338 0.235400i −1.86338 0.235400i
$$28$$ 0 0
$$29$$ 0 0 0.929776 0.368125i $$-0.120000\pi$$
−0.929776 + 0.368125i $$0.880000\pi$$
$$30$$ 0 0
$$31$$ −0.0235315 + 0.374023i −0.0235315 + 0.374023i 0.968583 + 0.248690i $$0.0800000\pi$$
−0.992115 + 0.125333i $$0.960000\pi$$
$$32$$ 0 0
$$33$$ 1.69755 0.435857i 1.69755 0.435857i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 1.81540 0.998027i 1.81540 0.998027i
$$37$$ 1.60528 0.202793i 1.60528 0.202793i 0.728969 0.684547i $$-0.240000\pi$$
0.876307 + 0.481754i $$0.160000\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0 0 0.187381 0.982287i $$-0.440000\pi$$
−0.187381 + 0.982287i $$0.560000\pi$$
$$42$$ 0 0
$$43$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$44$$ −0.637424 + 0.770513i −0.637424 + 0.770513i
$$45$$ 1.51017 1.41814i 1.51017 1.41814i
$$46$$ 0 0
$$47$$ −0.393950 0.476203i −0.393950 0.476203i 0.535827 0.844328i $$-0.320000\pi$$
−0.929776 + 0.368125i $$0.880000\pi$$
$$48$$ −0.746226 + 1.58581i −0.746226 + 1.58581i
$$49$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 1.41213 + 0.362574i 1.41213 + 0.362574i 0.876307 0.481754i $$-0.160000\pi$$
0.535827 + 0.844328i $$0.320000\pi$$
$$54$$ 0 0
$$55$$ −0.425779 + 0.904827i −0.425779 + 0.904827i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −1.73879 0.955910i −1.73879 0.955910i −0.929776 0.368125i $$-0.880000\pi$$
−0.809017 0.587785i $$-0.800000\pi$$
$$60$$ −0.328407 + 1.72157i −0.328407 + 1.72157i
$$61$$ 0 0 −0.187381 0.982287i $$-0.560000\pi$$
0.187381 + 0.982287i $$0.440000\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ −0.187381 0.982287i −0.187381 0.982287i
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −1.80113 0.713118i −1.80113 0.713118i −0.992115 0.125333i $$-0.960000\pi$$
−0.809017 0.587785i $$-0.800000\pi$$
$$68$$ 0 0
$$69$$ −1.74630 0.691409i −1.74630 0.691409i
$$70$$ 0 0
$$71$$ −1.11716 1.35041i −1.11716 1.35041i −0.929776 0.368125i $$-0.880000\pi$$
−0.187381 0.982287i $$-0.560000\pi$$
$$72$$ 0 0
$$73$$ 0 0 0.876307 0.481754i $$-0.160000\pi$$
−0.876307 + 0.481754i $$0.840000\pi$$
$$74$$ 0 0
$$75$$ 0.110048 + 1.74915i 0.110048 + 1.74915i
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 0.535827 0.844328i $$-0.320000\pi$$
−0.535827 + 0.844328i $$0.680000\pi$$
$$80$$ −0.425779 0.904827i −0.425779 0.904827i
$$81$$ −0.777718 + 0.940099i −0.777718 + 0.940099i
$$82$$ 0 0
$$83$$ 0 0 −0.535827 0.844328i $$-0.680000\pi$$
0.535827 + 0.844328i $$0.320000\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −1.11716 + 0.614163i −1.11716 + 0.614163i −0.929776 0.368125i $$-0.880000\pi$$
−0.187381 + 0.982287i $$0.560000\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 1.03799 0.266509i 1.03799 0.266509i
$$93$$ 0.531374 + 0.386066i 0.531374 + 0.386066i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 1.84489 0.730444i 1.84489 0.730444i 0.876307 0.481754i $$-0.160000\pi$$
0.968583 0.248690i $$-0.0800000\pi$$
$$98$$ 0 0
$$99$$ 0.640176 1.97026i 0.640176 1.97026i
$$100$$ −0.637424 0.770513i −0.637424 0.770513i
$$101$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$102$$ 0 0
$$103$$ 0.121636 + 1.93334i 0.121636 + 1.93334i 0.309017 + 0.951057i $$0.400000\pi$$
−0.187381 + 0.982287i $$0.560000\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$108$$ 0.117933 1.87449i 0.117933 1.87449i
$$109$$ 0 0 0.992115 0.125333i $$-0.0400000\pi$$
−0.992115 + 0.125333i $$0.960000\pi$$
$$110$$ 0 0
$$111$$ 1.20742 2.56590i 1.20742 2.56590i
$$112$$ 0 0
$$113$$ −1.11716 0.614163i −1.11716 0.614163i −0.187381 0.982287i $$-0.560000\pi$$
−0.929776 + 0.368125i $$0.880000\pi$$
$$114$$ 0 0
$$115$$ 0.939097 0.516273i 0.939097 0.516273i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 0.0627905 + 0.998027i 0.0627905 + 0.998027i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ −0.374763 −0.374763
$$125$$ −0.809017 0.587785i −0.809017 0.587785i
$$126$$ 0 0
$$127$$ 0 0 −0.728969 0.684547i $$-0.760000\pi$$
0.728969 + 0.684547i $$0.240000\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 0.968583 0.248690i $$-0.0800000\pi$$
−0.968583 + 0.248690i $$0.920000\pi$$
$$132$$ 0.541587 + 1.66683i 0.541587 + 1.66683i
$$133$$ 0 0
$$134$$ 0 0
$$135$$ −0.351939 1.84493i −0.351939 1.84493i
$$136$$ 0 0
$$137$$ −1.62954 0.895846i −1.62954 0.895846i −0.992115 0.125333i $$-0.960000\pi$$
−0.637424 0.770513i $$-0.720000\pi$$
$$138$$ 0 0
$$139$$ 0 0 0.425779 0.904827i $$-0.360000\pi$$
−0.425779 + 0.904827i $$0.640000\pi$$
$$140$$ 0 0
$$141$$ −1.07463 + 0.135758i −1.07463 + 0.135758i
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 1.11005 + 1.74915i 1.11005 + 1.74915i
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0.110048 + 1.74915i 0.110048 + 1.74915i
$$148$$ 0.303189 + 1.58937i 0.303189 + 1.58937i
$$149$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$150$$ 0 0
$$151$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −0.362989 + 0.0931997i −0.362989 + 0.0931997i
$$156$$ 0 0
$$157$$ −0.101597 0.0738147i −0.101597 0.0738147i 0.535827 0.844328i $$-0.320000\pi$$
−0.637424 + 0.770513i $$0.720000\pi$$
$$158$$ 0 0
$$159$$ 1.86266 1.74915i 1.86266 1.74915i
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 0.0702235 0.368125i 0.0702235 0.368125i −0.929776 0.368125i $$-0.880000\pi$$
1.00000 $$0$$
$$164$$ 0 0
$$165$$ 0.939097 + 1.47978i 0.939097 + 1.47978i
$$166$$ 0 0
$$167$$ 0 0 −0.535827 0.844328i $$-0.680000\pi$$
0.535827 + 0.844328i $$0.320000\pi$$
$$168$$ 0 0
$$169$$ −0.637424 + 0.770513i −0.637424 + 0.770513i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 0 0 0.425779 0.904827i $$-0.360000\pi$$
−0.425779 + 0.904827i $$0.640000\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −0.809017 0.587785i −0.809017 0.587785i
$$177$$ −3.04743 + 1.67534i −3.04743 + 1.67534i
$$178$$ 0 0
$$179$$ 1.18532 + 1.43281i 1.18532 + 1.43281i 0.876307 + 0.481754i $$0.160000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$180$$ 1.51017 + 1.41814i 1.51017 + 1.41814i
$$181$$ 1.50441 + 0.595638i 1.50441 + 0.595638i 0.968583 0.248690i $$-0.0800000\pi$$
0.535827 + 0.844328i $$0.320000\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0.688925 + 1.46404i 0.688925 + 1.46404i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0.450527 0.423073i 0.450527 0.423073i
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −1.11716 0.614163i −1.11716 0.614163i −0.187381 0.982287i $$-0.560000\pi$$
−0.929776 + 0.368125i $$0.880000\pi$$
$$192$$ −1.62954 0.645180i −1.62954 0.645180i
$$193$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ −0.637424 0.770513i −0.637424 0.770513i
$$197$$ 0 0 −0.968583 0.248690i $$-0.920000\pi$$
0.968583 + 0.248690i $$0.0800000\pi$$
$$198$$ 0 0
$$199$$ 1.50441 + 1.09302i 1.50441 + 1.09302i 0.968583 + 0.248690i $$0.0800000\pi$$
0.535827 + 0.844328i $$0.320000\pi$$
$$200$$ 0 0
$$201$$ −2.74670 + 1.99559i −2.74670 + 1.99559i
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −1.79609 + 1.30494i −1.79609 + 1.30494i
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 −0.992115 0.125333i $$-0.960000\pi$$
0.992115 + 0.125333i $$0.0400000\pi$$
$$212$$ −0.273190 + 1.43211i −0.273190 + 1.43211i
$$213$$ −3.04743 + 0.384980i −3.04743 + 0.384980i
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ −0.929776 0.368125i −0.929776 0.368125i
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0.844844 + 0.106729i 0.844844 + 0.106729i 0.535827 0.844328i $$-0.320000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$224$$ 0 0
$$225$$ 1.81540 + 0.998027i 1.81540 + 0.998027i
$$226$$ 0 0
$$227$$ 0 0 −0.187381 0.982287i $$-0.560000\pi$$
0.187381 + 0.982287i $$0.440000\pi$$
$$228$$ 0 0
$$229$$ 0.121636 + 0.0312307i 0.121636 + 0.0312307i 0.309017 0.951057i $$-0.400000\pi$$
−0.187381 + 0.982287i $$0.560000\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 0.0627905 0.998027i $$-0.480000\pi$$
−0.0627905 + 0.998027i $$0.520000\pi$$
$$234$$ 0 0
$$235$$ 0.331159 0.521823i 0.331159 0.521823i
$$236$$ 0.844844 1.79538i 0.844844 1.79538i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 −0.728969 0.684547i $$-0.760000\pi$$
0.728969 + 0.684547i $$0.240000\pi$$
$$240$$ −1.73879 0.219661i −1.73879 0.219661i
$$241$$ 0 0 −0.425779 0.904827i $$-0.640000\pi$$
0.425779 + 0.904827i $$0.360000\pi$$
$$242$$ 0 0
$$243$$ 0.0803940 + 0.247427i 0.0803940 + 0.247427i
$$244$$ 0 0
$$245$$ −0.809017 0.587785i −0.809017 0.587785i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 1.45794 1.45794 0.728969 0.684547i $$-0.240000\pi$$
0.728969 + 0.684547i $$0.240000\pi$$
$$252$$ 0 0
$$253$$ 0.574221 0.904827i 0.574221 0.904827i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0.968583 0.248690i 0.968583 0.248690i
$$257$$ 0.331159 + 1.01920i 0.331159 + 1.01920i 0.968583 + 0.248690i $$0.0800000\pi$$
−0.637424 + 0.770513i $$0.720000\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 0 0 −0.425779 0.904827i $$-0.640000\pi$$
0.425779 + 0.904827i $$0.360000\pi$$
$$264$$ 0 0
$$265$$ 0.0915446 + 1.45506i 0.0915446 + 1.45506i
$$266$$ 0 0
$$267$$ −0.140294 + 2.22991i −0.140294 + 2.22991i
$$268$$ 0.598617 1.84235i 0.598617 1.84235i
$$269$$ 0.0672897 + 0.106032i 0.0672897 + 0.106032i 0.876307 0.481754i $$-0.160000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$270$$ 0 0
$$271$$ 0 0 −0.968583 0.248690i $$-0.920000\pi$$
0.968583 + 0.248690i $$0.0800000\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −0.992115 0.125333i −0.992115 0.125333i
$$276$$ 0.580394 1.78627i 0.580394 1.78627i
$$277$$ 0 0 −0.992115 0.125333i $$-0.960000\pi$$
0.992115 + 0.125333i $$0.0400000\pi$$
$$278$$ 0 0
$$279$$ 0.721858 0.285804i 0.721858 0.285804i
$$280$$ 0 0
$$281$$ 0 0 0.0627905 0.998027i $$-0.480000\pi$$
−0.0627905 + 0.998027i $$0.520000\pi$$
$$282$$ 0 0
$$283$$ 0 0 0.968583 0.248690i $$-0.0800000\pi$$
−0.968583 + 0.248690i $$0.920000\pi$$
$$284$$ 1.27760 1.19975i 1.27760 1.19975i
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −0.992115 0.125333i −0.992115 0.125333i
$$290$$ 0 0
$$291$$ 0.651635 3.41599i 0.651635 3.41599i
$$292$$ 0 0
$$293$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$294$$ 0 0
$$295$$ 0.371808 1.94908i 0.371808 1.94908i
$$296$$ 0 0
$$297$$ −1.19721 1.44717i −1.19721 1.44717i
$$298$$ 0 0
$$299$$ 0 0
$$300$$ −1.73879 + 0.219661i −1.73879 + 0.219661i
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$308$$ 0 0
$$309$$ 2.97515 + 1.63560i 2.97515 + 1.63560i
$$310$$ 0 0
$$311$$ −0.362989 1.90285i −0.362989 1.90285i −0.425779 0.904827i $$-0.640000\pi$$
0.0627905 0.998027i $$-0.480000\pi$$
$$312$$ 0 0
$$313$$ −1.35556 + 1.27295i −1.35556 + 1.27295i −0.425779 + 0.904827i $$0.640000\pi$$
−0.929776 + 0.368125i $$0.880000\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 0.791759 + 0.313480i 0.791759 + 0.313480i 0.728969 0.684547i $$-0.240000\pi$$
0.0627905 + 0.998027i $$0.480000\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0.876307 0.481754i 0.876307 0.481754i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ −0.987078 0.717154i −0.987078 0.717154i
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −1.23480 + 1.49261i −1.23480 + 1.49261i −0.425779 + 0.904827i $$0.640000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$332$$ 0 0
$$333$$ −1.79609 2.83019i −1.79609 2.83019i
$$334$$ 0 0
$$335$$ 0.121636 1.93334i 0.121636 1.93334i
$$336$$ 0 0
$$337$$ 0 0 0.187381 0.982287i $$-0.440000\pi$$
−0.187381 + 0.982287i $$0.560000\pi$$
$$338$$ 0 0
$$339$$ −1.95795 + 1.07639i −1.95795 + 1.07639i
$$340$$ 0 0
$$341$$ −0.273190 + 0.256543i −0.273190 + 0.256543i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0.117933 1.87449i 0.117933 1.87449i
$$346$$ 0 0
$$347$$ 0 0 0.929776 0.368125i $$-0.120000\pi$$
−0.929776 + 0.368125i $$0.880000\pi$$
$$348$$ 0 0
$$349$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 0.125581 + 1.99605i 0.125581 + 1.99605i 0.0627905 + 0.998027i $$0.480000\pi$$
0.0627905 + 0.998027i $$0.480000\pi$$
$$354$$ 0 0
$$355$$ 0.939097 1.47978i 0.939097 1.47978i
$$356$$ −0.683098 1.07639i −0.683098 1.07639i
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 0.992115 0.125333i $$-0.0400000\pi$$
−0.992115 + 0.125333i $$0.960000\pi$$
$$360$$ 0 0
$$361$$ −0.425779 + 0.904827i −0.425779 + 0.904827i
$$362$$ 0 0
$$363$$ 1.53583 + 0.844328i 1.53583 + 0.844328i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 1.18532 1.43281i 1.18532 1.43281i 0.309017 0.951057i $$-0.400000\pi$$
0.876307 0.481754i $$-0.160000\pi$$
$$368$$ 0.331159 + 1.01920i 0.331159 + 1.01920i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ −0.351939 + 0.554566i −0.351939 + 0.554566i
$$373$$ 0 0 −0.728969 0.684547i $$-0.760000\pi$$
0.728969 + 0.684547i $$0.240000\pi$$
$$374$$ 0 0
$$375$$ −1.62954 + 0.645180i −1.62954 + 0.645180i
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 0.0388067 + 0.616814i 0.0388067 + 0.616814i 0.968583 + 0.248690i $$0.0800000\pi$$
−0.929776 + 0.368125i $$0.880000\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0.238883 0.288760i 0.238883 0.288760i −0.637424 0.770513i $$-0.720000\pi$$
0.876307 + 0.481754i $$0.160000\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0.844844 + 1.79538i 0.844844 + 1.79538i
$$389$$ 0.362576 0.770513i 0.362576 0.770513i −0.637424 0.770513i $$-0.720000\pi$$
1.00000 $$0$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 2.00657 + 0.515199i 2.00657 + 0.515199i
$$397$$ −0.0800484 1.27233i −0.0800484 1.27233i −0.809017 0.587785i $$-0.800000\pi$$
0.728969 0.684547i $$-0.240000\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0.728969 0.684547i 0.728969 0.684547i
$$401$$ 0.450527 1.38658i 0.450527 1.38658i −0.425779 0.904827i $$-0.640000\pi$$
0.876307 0.481754i $$-0.160000\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ −1.13442 0.449147i −1.13442 0.449147i
$$406$$ 0 0
$$407$$ 1.30902 + 0.951057i 1.30902 + 0.951057i
$$408$$ 0 0
$$409$$ 0 0 0.728969 0.684547i $$-0.240000\pi$$
−0.728969 + 0.684547i $$0.760000\pi$$
$$410$$ 0 0
$$411$$ −2.85595 + 1.57007i −2.85595 + 1.57007i
$$412$$ −1.92189 + 0.242791i −1.92189 + 0.242791i
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 1.26480 1.52888i 1.26480 1.52888i 0.535827 0.844328i $$-0.320000\pi$$
0.728969 0.684547i $$-0.240000\pi$$
$$420$$ 0 0
$$421$$ −0.683098 + 1.07639i −0.683098 + 1.07639i 0.309017 + 0.951057i $$0.400000\pi$$
−0.992115 + 0.125333i $$0.960000\pi$$
$$422$$ 0 0
$$423$$ −0.545148 + 1.15850i −0.545148 + 1.15850i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 −0.929776 0.368125i $$-0.880000\pi$$
0.929776 + 0.368125i $$0.120000\pi$$
$$432$$ 1.87819 1.87819
$$433$$ 1.50441 + 0.595638i 1.50441 + 0.595638i 0.968583 0.248690i $$-0.0800000\pi$$
0.535827 + 0.844328i $$0.320000\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 −0.187381 0.982287i $$-0.560000\pi$$
0.187381 + 0.982287i $$0.440000\pi$$
$$440$$ 0 0
$$441$$ 1.81540 + 0.998027i 1.81540 + 0.998027i
$$442$$ 0 0
$$443$$ −1.98423 −1.98423 −0.992115 0.125333i $$-0.960000\pi$$
−0.992115 + 0.125333i $$0.960000\pi$$
$$444$$ 2.63665 + 1.04392i 2.63665 + 1.04392i
$$445$$ −0.929324 0.872693i −0.929324 0.872693i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −0.866986 0.629902i −0.866986 0.629902i 0.0627905 0.998027i $$-0.480000\pi$$
−0.929776 + 0.368125i $$0.880000\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0.542804 1.15352i 0.542804 1.15352i
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0.574221 + 0.904827i 0.574221 + 0.904827i
$$461$$ 0 0 −0.992115 0.125333i $$-0.960000\pi$$
0.992115 + 0.125333i $$0.0400000\pi$$
$$462$$ 0 0
$$463$$ 1.26480 0.159781i 1.26480 0.159781i 0.535827 0.844328i $$-0.320000\pi$$
0.728969 + 0.684547i $$0.240000\pi$$
$$464$$ 0 0
$$465$$ −0.202967 + 0.624667i −0.202967 + 0.624667i
$$466$$ 0 0
$$467$$ 0.598617 0.153699i 0.598617 0.153699i 0.0627905 0.998027i $$-0.480000\pi$$
0.535827 + 0.844328i $$0.320000\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −0.204639 + 0.0810224i −0.204639 + 0.0810224i
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −0.565955 2.96684i −0.565955 2.96684i
$$478$$ 0 0
$$479$$ 0 0 −0.968583 0.248690i $$-0.920000\pi$$
0.968583 + 0.248690i $$0.0800000\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ −0.992115 + 0.125333i −0.992115 + 0.125333i
$$485$$ 1.26480 + 1.52888i 1.26480 + 1.52888i
$$486$$ 0 0
$$487$$ −0.851559 1.80965i −0.851559 1.80965i −0.425779 0.904827i $$-0.640000\pi$$
−0.425779 0.904827i $$-0.640000\pi$$
$$488$$ 0 0
$$489$$ −0.478797 0.449620i −0.478797 0.449620i
$$490$$ 0 0
$$491$$ 0 0 −0.425779 0.904827i $$-0.640000\pi$$
0.425779 + 0.904827i $$0.360000\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 2.07165 2.07165
$$496$$ −0.0235315 0.374023i −0.0235315 0.374023i
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 1.45794 1.45794 0.728969 0.684547i $$-0.240000\pi$$
0.728969 + 0.684547i $$0.240000\pi$$
$$500$$ 0.535827 0.844328i 0.535827 0.844328i
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 0.535827 0.844328i $$-0.320000\pi$$
−0.535827 + 0.844328i $$0.680000\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0.541587 + 1.66683i 0.541587 + 1.66683i
$$508$$ 0 0
$$509$$ 0.791759 + 1.68257i 0.791759 + 1.68257i 0.728969 + 0.684547i $$0.240000\pi$$
0.0627905 + 0.998027i $$0.480000\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −1.80113 + 0.713118i −1.80113 + 0.713118i
$$516$$ 0 0
$$517$$ 0.0388067 0.616814i 0.0388067 0.616814i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 1.87631 + 0.481754i 1.87631 + 0.481754i 1.00000 $$0$$
0.876307 + 0.481754i $$0.160000\pi$$
$$522$$ 0 0
$$523$$ 0 0 −0.187381 0.982287i $$-0.560000\pi$$
0.187381 + 0.982287i $$0.440000\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ −1.62954 + 0.645180i −1.62954 + 0.645180i
$$529$$ −0.138017 + 0.0546449i −0.138017 + 0.0546449i
$$530$$ 0 0
$$531$$ −0.258109 + 4.10252i −0.258109 + 4.10252i
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 3.23338 0.408471i 3.23338 0.408471i
$$538$$ 0 0
$$539$$ −0.992115 0.125333i −0.992115 0.125333i
$$540$$ 1.81919 0.467088i 1.81919 0.467088i
$$541$$ 0 0 0.187381 0.982287i $$-0.440000\pi$$
−0.187381 + 0.982287i $$0.560000\pi$$
$$542$$ 0 0
$$543$$ 2.29420 1.66683i 2.29420 1.66683i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0 0 −0.637424 0.770513i $$-0.720000\pi$$
0.637424 + 0.770513i $$0.280000\pi$$
$$548$$ 0.791759 1.68257i 0.791759 1.68257i
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 2.81343 + 0.355418i 2.81343 + 0.355418i
$$556$$ 0 0
$$557$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 0.728969 0.684547i $$-0.240000\pi$$
−0.728969 + 0.684547i $$0.760000\pi$$
$$564$$ −0.202967 1.06399i −0.202967 1.06399i
$$565$$ 0.238883 1.25227i 0.238883 1.25227i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 0 0 −0.929776 0.368125i $$-0.880000\pi$$
0.929776 + 0.368125i $$0.120000\pi$$
$$570$$ 0 0
$$571$$ 0 0 −0.637424 0.770513i $$-0.720000\pi$$
0.637424 + 0.770513i $$0.280000\pi$$
$$572$$ 0 0
$$573$$ −1.95795 + 1.07639i −1.95795 + 1.07639i
$$574$$ 0 0
$$575$$ 0.781202 + 0.733597i 0.781202 + 0.733597i
$$576$$ −1.67600 + 1.21769i −1.67600 + 1.21769i
$$577$$ 0.362576 0.770513i 0.362576 0.770513i −0.637424 0.770513i $$-0.720000\pi$$
1.00000 $$0$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0.781202 + 1.23098i 0.781202 + 1.23098i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0.371808 1.94908i 0.371808 1.94908i 0.0627905 0.998027i $$-0.480000\pi$$
0.309017 0.951057i $$-0.400000\pi$$
$$588$$ −1.73879 + 0.219661i −1.73879 + 0.219661i
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −1.56720 + 0.402389i −1.56720 + 0.402389i
$$593$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 3.03021 1.19975i 3.03021 1.19975i
$$598$$ 0 0
$$599$$ −0.263146 + 0.809880i −0.263146 + 0.809880i 0.728969 + 0.684547i $$0.240000\pi$$
−0.992115 + 0.125333i $$0.960000\pi$$
$$600$$ 0 0
$$601$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$602$$ 0 0
$$603$$ 0.251987 + 4.00522i 0.251987 + 4.00522i
$$604$$ 0 0
$$605$$ −0.929776 + 0.368125i −0.929776 + 0.368125i
$$606$$ 0 0
$$607$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 −0.876307 0.481754i $$-0.840000\pi$$
0.876307 + 0.481754i $$0.160000\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0.542804 0.656137i 0.542804 0.656137i −0.425779 0.904827i $$-0.640000\pi$$
0.968583 + 0.248690i $$0.0800000\pi$$
$$618$$ 0 0
$$619$$ −0.362989 + 0.0931997i −0.362989 + 0.0931997i −0.425779 0.904827i $$-0.640000\pi$$
0.0627905 + 0.998027i $$0.480000\pi$$
$$620$$ −0.115808 0.356420i −0.115808 0.356420i
$$621$$ 0.126383 + 2.00880i 0.126383 + 2.00880i
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0.309017 0.951057i 0.309017 0.951057i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0.0672897 0.106032i 0.0672897 0.106032i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 1.87631 0.481754i 1.87631 0.481754i 0.876307 0.481754i $$-0.160000\pi$$
1.00000 $$0$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 1.86266 + 1.74915i 1.86266 + 1.74915i
$$637$$ 0 0
$$638$$ 0 0
$$639$$ −1.54592 + 3.28525i −1.54592 + 3.28525i
$$640$$ 0 0
$$641$$ −1.73879 + 0.219661i −1.73879 + 0.219661i −0.929776 0.368125i $$-0.880000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$642$$ 0 0
$$643$$ −0.115808 + 0.356420i −0.115808 + 0.356420i −0.992115 0.125333i $$-0.960000\pi$$
0.876307 + 0.481754i $$0.160000\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0.121636 + 1.93334i 0.121636 + 1.93334i 0.309017 + 0.951057i $$0.400000\pi$$
−0.187381 + 0.982287i $$0.560000\pi$$
$$648$$ 0 0
$$649$$ −0.613161 1.88711i −0.613161 1.88711i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0.371808 + 0.0469702i 0.371808 + 0.0469702i
$$653$$ 0.348445 0.137959i 0.348445 0.137959i −0.187381 0.982287i $$-0.560000\pi$$
0.535827 + 0.844328i $$0.320000\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 0.728969 0.684547i $$-0.240000\pi$$
−0.728969 + 0.684547i $$0.760000\pi$$
$$660$$ −1.41789 + 1.03016i −1.41789 + 1.03016i
$$661$$ −1.62954 + 0.895846i −1.62954 + 0.895846i −0.637424 + 0.770513i $$0.720000\pi$$
−0.992115 + 0.125333i $$0.960000\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0.951325 1.14995i 0.951325 1.14995i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 0.425779 0.904827i $$-0.360000\pi$$
−0.425779 + 0.904827i $$0.640000\pi$$
$$674$$ 0 0
$$675$$ 1.64587 0.904827i 1.64587 0.904827i
$$676$$ −0.809017 0.587785i −0.809017 0.587785i
$$677$$ 0 0 0.876307 0.481754i $$-0.160000\pi$$
−0.876307 + 0.481754i $$0.840000\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −0.116762 0.0462295i −0.116762 0.0462295i 0.309017 0.951057i $$-0.400000\pi$$
−0.425779 + 0.904827i $$0.640000\pi$$
$$684$$ 0 0
$$685$$ 0.348445 1.82662i 0.348445 1.82662i
$$686$$ 0 0
$$687$$ 0.160442 0.150665i 0.160442 0.150665i
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0.939097 + 0.516273i 0.939097 + 0.516273i 0.876307 0.481754i $$-0.160000\pi$$
0.0627905 + 0.998027i $$0.480000\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0.535827 0.844328i 0.535827 0.844328i
$$705$$ −0.461193 0.980086i −0.461193 0.980086i
$$706$$ 0 0
$$707$$ 0 0
$$708$$ −1.86338 2.93622i −1.86338 2.93622i
$$709$$ −0.273190 + 1.43211i −0.273190 + 1.43211i 0.535827 + 0.844328i $$0.320000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0.398449 0.0503358i 0.398449 0.0503358i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −1.35556 + 1.27295i −1.35556 + 1.27295i
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0.00788530 0.125333i 0.00788530 0.125333i −0.992115 0.125333i $$-0.960000\pi$$
1.00000 $$0$$
$$720$$ −1.32052 + 1.59624i −1.32052 + 1.59624i
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 0 0
$$724$$ −0.500000 + 1.53884i −0.500000 + 1.53884i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 0.371808 + 1.94908i 0.371808 + 1.94908i 0.309017 + 0.951057i $$0.400000\pi$$
0.0627905 + 0.998027i $$0.480000\pi$$
$$728$$ 0 0
$$729$$ −0.740128 0.190032i −0.740128 0.190032i
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 0 0 0.0627905 0.998027i $$-0.480000\pi$$
−0.0627905 + 0.998027i $$0.520000\pi$$
$$734$$ 0 0
$$735$$ −1.62954 + 0.645180i −1.62954 + 0.645180i
$$736$$ 0 0
$$737$$ −0.824805 1.75280i −0.824805 1.75280i
$$738$$ 0 0
$$739$$ 0 0 −0.728969 0.684547i $$-0.760000\pi$$
0.728969 + 0.684547i $$0.240000\pi$$
$$740$$ −1.41789 + 0.779494i −1.41789 + 0.779494i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −1.27485 −1.27485 −0.637424 0.770513i $$-0.720000\pi$$
−0.637424 + 0.770513i $$0.720000\pi$$
$$752$$ 0.450527 + 0.423073i 0.450527 + 0.423073i
$$753$$ 1.36914 2.15743i 1.36914 2.15743i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −0.613161 1.88711i −0.613161 1.88711i −0.425779 0.904827i $$-0.640000\pi$$
−0.187381 0.982287i $$-0.560000\pi$$
$$758$$ 0 0
$$759$$ −0.799696 1.69944i −0.799696 1.69944i
$$760$$ 0 0
$$761$$ 0 0 −0.728969 0.684547i $$-0.760000\pi$$
0.728969 + 0.684547i $$0.240000\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0.542804 1.15352i 0.542804 1.15352i
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0.541587 1.66683i 0.541587 1.66683i
$$769$$ 0 0 −0.535827 0.844328i $$-0.680000\pi$$
0.535827 + 0.844328i $$0.320000\pi$$
$$770$$ 0 0
$$771$$ 1.81919 + 0.467088i 1.81919 + 0.467088i
$$772$$ 0 0
$$773$$ −0.273190 1.43211i −0.273190 1.43211i −0.809017 0.587785i $$-0.800000\pi$$
0.535827 0.844328i $$-0.320000\pi$$
$$774$$ 0 0
$$775$$ −0.200808 0.316423i −0.200808 0.316423i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0.110048 1.74915i 0.110048 1.74915i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0.728969 0.684547i 0.728969 0.684547i
$$785$$ 0.0388067 0.119435i 0.0388067 0.119435i
$$786$$ 0 0
$$787$$ 0 0 0.992115 0.125333i $$-0.0400000\pi$$
−0.992115 + 0.125333i $$0.960000\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 2.23914 + 1.23098i 2.23914 + 1.23098i
$$796$$ −0.996398 + 1.57007i −0.996398 + 1.57007i
$$797$$ 0.812619 + 0.982287i 0.812619 + 0.982287i 1.00000 $$0$$
−0.187381 + 0.982287i $$0.560000\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 2.13665 + 1.55237i 2.13665 + 1.55237i
$$802$$ 0 0