# Properties

 Label 648.1.bf.a.619.1 Level $648$ Weight $1$ Character 648.619 Analytic conductor $0.323$ Analytic rank $0$ Dimension $18$ Projective image $D_{27}$ CM discriminant -8 Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$648 = 2^{3} \cdot 3^{4}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 648.bf (of order $$54$$, degree $$18$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.323394128186$$ Analytic rank: $$0$$ Dimension: $$18$$ Coefficient field: $$\Q(\zeta_{54})$$ Defining polynomial: $$x^{18} - x^{9} + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{27}$$ Projective field: Galois closure of $$\mathbb{Q}[x]/(x^{27} + \cdots)$$

## Embedding invariants

 Embedding label 619.1 Root $$0.686242 - 0.727374i$$ of defining polynomial Character $$\chi$$ $$=$$ 648.619 Dual form 648.1.bf.a.67.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.835488 - 0.549509i) q^{2} +(0.973045 + 0.230616i) q^{3} +(0.396080 + 0.918216i) q^{4} +(-0.686242 - 0.727374i) q^{6} +(0.173648 - 0.984808i) q^{8} +(0.893633 + 0.448799i) q^{9} +O(q^{10})$$ $$q+(-0.835488 - 0.549509i) q^{2} +(0.973045 + 0.230616i) q^{3} +(0.396080 + 0.918216i) q^{4} +(-0.686242 - 0.727374i) q^{6} +(0.173648 - 0.984808i) q^{8} +(0.893633 + 0.448799i) q^{9} +(-0.227194 - 0.758881i) q^{11} +(0.173648 + 0.984808i) q^{12} +(-0.686242 + 0.727374i) q^{16} +(0.109277 + 0.0397734i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(0.539014 - 0.196185i) q^{19} +(-0.227194 + 0.758881i) q^{22} +(0.396080 - 0.918216i) q^{24} +(-0.0581448 + 0.998308i) q^{25} +(0.766044 + 0.642788i) q^{27} +(0.973045 - 0.230616i) q^{32} +(-0.0460600 - 0.790819i) q^{33} +(-0.0694434 - 0.0932786i) q^{34} +(-0.0581448 + 0.998308i) q^{36} +(-0.558145 - 0.132283i) q^{38} +(-1.62593 + 1.06939i) q^{41} +(-1.62593 - 0.385353i) q^{43} +(0.606829 - 0.509190i) q^{44} +(-0.835488 + 0.549509i) q^{48} +(0.973045 - 0.230616i) q^{49} +(0.597159 - 0.802123i) q^{50} +(0.0971586 + 0.0639022i) q^{51} +(-0.286803 - 0.957990i) q^{54} +(0.569728 - 0.0665916i) q^{57} +(0.393633 - 1.31482i) q^{59} +(-0.939693 - 0.342020i) q^{64} +(-0.396080 + 0.686030i) q^{66} +(-1.77518 - 0.891529i) q^{67} +(0.00676164 + 0.116093i) q^{68} +(0.597159 - 0.802123i) q^{72} +(0.310355 - 1.76011i) q^{73} +(-0.286803 + 0.957990i) q^{75} +(0.393633 + 0.417226i) q^{76} +(0.597159 + 0.802123i) q^{81} +1.94609 q^{82} +(-1.28004 - 0.841897i) q^{83} +(1.14669 + 1.21542i) q^{86} +(-0.786803 + 0.0919641i) q^{88} +(-0.326352 + 1.85083i) q^{89} +1.00000 q^{96} +(-0.819590 + 0.868715i) q^{97} +(-0.939693 - 0.342020i) q^{98} +(0.137557 - 0.780125i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$18q + O(q^{10})$$ $$18q - 9q^{18} - 9q^{38} - 9q^{51} - 9q^{59} + 18q^{68} - 9q^{76} - 9q^{88} - 9q^{89} + 18q^{96} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$$.

 $$n$$ $$325$$ $$487$$ $$569$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$e\left(\frac{5}{27}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.835488 0.549509i −0.835488 0.549509i
$$3$$ 0.973045 + 0.230616i 0.973045 + 0.230616i
$$4$$ 0.396080 + 0.918216i 0.396080 + 0.918216i
$$5$$ 0 0 −0.686242 0.727374i $$-0.740741\pi$$
0.686242 + 0.727374i $$0.259259\pi$$
$$6$$ −0.686242 0.727374i −0.686242 0.727374i
$$7$$ 0 0 0.993238 0.116093i $$-0.0370370\pi$$
−0.993238 + 0.116093i $$0.962963\pi$$
$$8$$ 0.173648 0.984808i 0.173648 0.984808i
$$9$$ 0.893633 + 0.448799i 0.893633 + 0.448799i
$$10$$ 0 0
$$11$$ −0.227194 0.758881i −0.227194 0.758881i −0.993238 0.116093i $$-0.962963\pi$$
0.766044 0.642788i $$-0.222222\pi$$
$$12$$ 0.173648 + 0.984808i 0.173648 + 0.984808i
$$13$$ 0 0 −0.0581448 0.998308i $$-0.518519\pi$$
0.0581448 + 0.998308i $$0.481481\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −0.686242 + 0.727374i −0.686242 + 0.727374i
$$17$$ 0.109277 + 0.0397734i 0.109277 + 0.0397734i 0.396080 0.918216i $$-0.370370\pi$$
−0.286803 + 0.957990i $$0.592593\pi$$
$$18$$ −0.500000 0.866025i −0.500000 0.866025i
$$19$$ 0.539014 0.196185i 0.539014 0.196185i −0.0581448 0.998308i $$-0.518519\pi$$
0.597159 + 0.802123i $$0.296296\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −0.227194 + 0.758881i −0.227194 + 0.758881i
$$23$$ 0 0 −0.993238 0.116093i $$-0.962963\pi$$
0.993238 + 0.116093i $$0.0370370\pi$$
$$24$$ 0.396080 0.918216i 0.396080 0.918216i
$$25$$ −0.0581448 + 0.998308i −0.0581448 + 0.998308i
$$26$$ 0 0
$$27$$ 0.766044 + 0.642788i 0.766044 + 0.642788i
$$28$$ 0 0
$$29$$ 0 0 0.893633 0.448799i $$-0.148148\pi$$
−0.893633 + 0.448799i $$0.851852\pi$$
$$30$$ 0 0
$$31$$ 0 0 0.597159 0.802123i $$-0.296296\pi$$
−0.597159 + 0.802123i $$0.703704\pi$$
$$32$$ 0.973045 0.230616i 0.973045 0.230616i
$$33$$ −0.0460600 0.790819i −0.0460600 0.790819i
$$34$$ −0.0694434 0.0932786i −0.0694434 0.0932786i
$$35$$ 0 0
$$36$$ −0.0581448 + 0.998308i −0.0581448 + 0.998308i
$$37$$ 0 0 0.766044 0.642788i $$-0.222222\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$38$$ −0.558145 0.132283i −0.558145 0.132283i
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −1.62593 + 1.06939i −1.62593 + 1.06939i −0.686242 + 0.727374i $$0.740741\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$42$$ 0 0
$$43$$ −1.62593 0.385353i −1.62593 0.385353i −0.686242 0.727374i $$-0.740741\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$44$$ 0.606829 0.509190i 0.606829 0.509190i
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 −0.597159 0.802123i $$-0.703704\pi$$
0.597159 + 0.802123i $$0.296296\pi$$
$$48$$ −0.835488 + 0.549509i −0.835488 + 0.549509i
$$49$$ 0.973045 0.230616i 0.973045 0.230616i
$$50$$ 0.597159 0.802123i 0.597159 0.802123i
$$51$$ 0.0971586 + 0.0639022i 0.0971586 + 0.0639022i
$$52$$ 0 0
$$53$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$54$$ −0.286803 0.957990i −0.286803 0.957990i
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0.569728 0.0665916i 0.569728 0.0665916i
$$58$$ 0 0
$$59$$ 0.393633 1.31482i 0.393633 1.31482i −0.500000 0.866025i $$-0.666667\pi$$
0.893633 0.448799i $$-0.148148\pi$$
$$60$$ 0 0
$$61$$ 0 0 0.396080 0.918216i $$-0.370370\pi$$
−0.396080 + 0.918216i $$0.629630\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ −0.939693 0.342020i −0.939693 0.342020i
$$65$$ 0 0
$$66$$ −0.396080 + 0.686030i −0.396080 + 0.686030i
$$67$$ −1.77518 0.891529i −1.77518 0.891529i −0.939693 0.342020i $$-0.888889\pi$$
−0.835488 0.549509i $$-0.814815\pi$$
$$68$$ 0.00676164 + 0.116093i 0.00676164 + 0.116093i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 −0.173648 0.984808i $$-0.555556\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$72$$ 0.597159 0.802123i 0.597159 0.802123i
$$73$$ 0.310355 1.76011i 0.310355 1.76011i −0.286803 0.957990i $$-0.592593\pi$$
0.597159 0.802123i $$-0.296296\pi$$
$$74$$ 0 0
$$75$$ −0.286803 + 0.957990i −0.286803 + 0.957990i
$$76$$ 0.393633 + 0.417226i 0.393633 + 0.417226i
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 −0.835488 0.549509i $$-0.814815\pi$$
0.835488 + 0.549509i $$0.185185\pi$$
$$80$$ 0 0
$$81$$ 0.597159 + 0.802123i 0.597159 + 0.802123i
$$82$$ 1.94609 1.94609
$$83$$ −1.28004 0.841897i −1.28004 0.841897i −0.286803 0.957990i $$-0.592593\pi$$
−0.993238 + 0.116093i $$0.962963\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 1.14669 + 1.21542i 1.14669 + 1.21542i
$$87$$ 0 0
$$88$$ −0.786803 + 0.0919641i −0.786803 + 0.0919641i
$$89$$ −0.326352 + 1.85083i −0.326352 + 1.85083i 0.173648 + 0.984808i $$0.444444\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 1.00000 1.00000
$$97$$ −0.819590 + 0.868715i −0.819590 + 0.868715i −0.993238 0.116093i $$-0.962963\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$98$$ −0.939693 0.342020i −0.939693 0.342020i
$$99$$ 0.137557 0.780125i 0.137557 0.780125i
$$100$$ −0.939693 + 0.342020i −0.939693 + 0.342020i
$$101$$ 0 0 0.396080 0.918216i $$-0.370370\pi$$
−0.396080 + 0.918216i $$0.629630\pi$$
$$102$$ −0.0460600 0.106779i −0.0460600 0.106779i
$$103$$ 0 0 0.286803 0.957990i $$-0.407407\pi$$
−0.286803 + 0.957990i $$0.592593\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −0.893633 + 1.54782i −0.893633 + 1.54782i −0.0581448 + 0.998308i $$0.518519\pi$$
−0.835488 + 0.549509i $$0.814815\pi$$
$$108$$ −0.286803 + 0.957990i −0.286803 + 0.957990i
$$109$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 0.337935 0.0800921i 0.337935 0.0800921i −0.0581448 0.998308i $$-0.518519\pi$$
0.396080 + 0.918216i $$0.370370\pi$$
$$114$$ −0.512593 0.257434i −0.512593 0.257434i
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ −1.05138 + 0.882215i −1.05138 + 0.882215i
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 0.311205 0.204683i 0.311205 0.204683i
$$122$$ 0 0
$$123$$ −1.82873 + 0.665602i −1.82873 + 0.665602i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 0 0 −0.766044 0.642788i $$-0.777778\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$128$$ 0.597159 + 0.802123i 0.597159 + 0.802123i
$$129$$ −1.49324 0.749932i −1.49324 0.749932i
$$130$$ 0 0
$$131$$ 0.207391 0.278574i 0.207391 0.278574i −0.686242 0.727374i $$-0.740741\pi$$
0.893633 + 0.448799i $$0.148148\pi$$
$$132$$ 0.707900 0.355521i 0.707900 0.355521i
$$133$$ 0 0
$$134$$ 0.993238 + 1.72034i 0.993238 + 1.72034i
$$135$$ 0 0
$$136$$ 0.0581448 0.100710i 0.0581448 0.100710i
$$137$$ −0.0694434 + 1.19230i −0.0694434 + 1.19230i 0.766044 + 0.642788i $$0.222222\pi$$
−0.835488 + 0.549509i $$0.814815\pi$$
$$138$$ 0 0
$$139$$ −1.18624 0.138652i −1.18624 0.138652i −0.500000 0.866025i $$-0.666667\pi$$
−0.686242 + 0.727374i $$0.740741\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ −0.939693 + 0.342020i −0.939693 + 0.342020i
$$145$$ 0 0
$$146$$ −1.22650 + 1.30001i −1.22650 + 1.30001i
$$147$$ 1.00000 1.00000
$$148$$ 0 0
$$149$$ 0 0 −0.0581448 0.998308i $$-0.518519\pi$$
0.0581448 + 0.998308i $$0.481481\pi$$
$$150$$ 0.766044 0.642788i 0.766044 0.642788i
$$151$$ 0 0 −0.286803 0.957990i $$-0.592593\pi$$
0.286803 + 0.957990i $$0.407407\pi$$
$$152$$ −0.0996057 0.564892i −0.0996057 0.564892i
$$153$$ 0.0798028 + 0.0845860i 0.0798028 + 0.0845860i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0 0 −0.686242 0.727374i $$-0.740741\pi$$
0.686242 + 0.727374i $$0.259259\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ −0.0581448 0.998308i −0.0581448 0.998308i
$$163$$ 0.347296 0.347296 0.173648 0.984808i $$-0.444444\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$164$$ −1.62593 1.06939i −1.62593 1.06939i
$$165$$ 0 0
$$166$$ 0.606829 + 1.40679i 0.606829 + 1.40679i
$$167$$ 0 0 −0.686242 0.727374i $$-0.740741\pi$$
0.686242 + 0.727374i $$0.259259\pi$$
$$168$$ 0 0
$$169$$ −0.993238 + 0.116093i −0.993238 + 0.116093i
$$170$$ 0 0
$$171$$ 0.569728 + 0.0665916i 0.569728 + 0.0665916i
$$172$$ −0.290162 1.64559i −0.290162 1.64559i
$$173$$ 0 0 −0.286803 0.957990i $$-0.592593\pi$$
0.286803 + 0.957990i $$0.407407\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0.707900 + 0.355521i 0.707900 + 0.355521i
$$177$$ 0.686242 1.18861i 0.686242 1.18861i
$$178$$ 1.28971 1.36702i 1.28971 1.36702i
$$179$$ 1.76604 + 0.642788i 1.76604 + 0.642788i 1.00000 $$0$$
0.766044 + 0.642788i $$0.222222\pi$$
$$180$$ 0 0
$$181$$ 0 0 0.939693 0.342020i $$-0.111111\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0.00535630 0.0919641i 0.00535630 0.0919641i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 0.893633 0.448799i $$-0.148148\pi$$
−0.893633 + 0.448799i $$0.851852\pi$$
$$192$$ −0.835488 0.549509i −0.835488 0.549509i
$$193$$ 1.16212 1.56100i 1.16212 1.56100i 0.396080 0.918216i $$-0.370370\pi$$
0.766044 0.642788i $$-0.222222\pi$$
$$194$$ 1.16212 0.275428i 1.16212 0.275428i
$$195$$ 0 0
$$196$$ 0.597159 + 0.802123i 0.597159 + 0.802123i
$$197$$ 0 0 −0.766044 0.642788i $$-0.777778\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$198$$ −0.543613 + 0.576196i −0.543613 + 0.576196i
$$199$$ 0 0 0.766044 0.642788i $$-0.222222\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$200$$ 0.973045 + 0.230616i 0.973045 + 0.230616i
$$201$$ −1.52173 1.27688i −1.52173 1.27688i
$$202$$ 0 0
$$203$$ 0 0
$$204$$ −0.0201935 + 0.114523i −0.0201935 + 0.114523i
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −0.271342 0.364475i −0.271342 0.364475i
$$210$$ 0 0
$$211$$ 1.49079 0.353324i 1.49079 0.353324i 0.597159 0.802123i $$-0.296296\pi$$
0.893633 + 0.448799i $$0.148148\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 1.59716 0.802123i 1.59716 0.802123i
$$215$$ 0 0
$$216$$ 0.766044 0.642788i 0.766044 0.642788i
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0.707900 1.64110i 0.707900 1.64110i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0 0 0.396080 0.918216i $$-0.370370\pi$$
−0.396080 + 0.918216i $$0.629630\pi$$
$$224$$ 0 0
$$225$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$226$$ −0.326352 0.118782i −0.326352 0.118782i
$$227$$ 1.14669 1.21542i 1.14669 1.21542i 0.173648 0.984808i $$-0.444444\pi$$
0.973045 0.230616i $$-0.0740741\pi$$
$$228$$ 0.286803 + 0.496758i 0.286803 + 0.496758i
$$229$$ 0 0 −0.893633 0.448799i $$-0.851852\pi$$
0.893633 + 0.448799i $$0.148148\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −0.238329 1.35163i −0.238329 1.35163i −0.835488 0.549509i $$-0.814815\pi$$
0.597159 0.802123i $$-0.296296\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 1.36320 0.159336i 1.36320 0.159336i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 −0.396080 0.918216i $$-0.629630\pi$$
0.396080 + 0.918216i $$0.370370\pi$$
$$240$$ 0 0
$$241$$ 1.65968 + 1.09159i 1.65968 + 1.09159i 0.893633 + 0.448799i $$0.148148\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$242$$ −0.372483 −0.372483
$$243$$ 0.396080 + 0.918216i 0.396080 + 0.918216i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 1.89363 + 0.448799i 1.89363 + 0.448799i
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −1.05138 1.11440i −1.05138 1.11440i
$$250$$ 0 0
$$251$$ −0.290162 + 1.64559i −0.290162 + 1.64559i 0.396080 + 0.918216i $$0.370370\pi$$
−0.686242 + 0.727374i $$0.740741\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ −0.0581448 0.998308i −0.0581448 0.998308i
$$257$$ −1.77518 0.891529i −1.77518 0.891529i −0.939693 0.342020i $$-0.888889\pi$$
−0.835488 0.549509i $$-0.814815\pi$$
$$258$$ 0.835488 + 1.44711i 0.835488 + 1.44711i
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −0.326352 + 0.118782i −0.326352 + 0.118782i
$$263$$ 0 0 0.396080 0.918216i $$-0.370370\pi$$
−0.396080 + 0.918216i $$0.629630\pi$$
$$264$$ −0.786803 0.0919641i −0.786803 0.0919641i
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −0.744386 + 1.72568i −0.744386 + 1.72568i
$$268$$ 0.115503 1.98312i 0.115503 1.98312i
$$269$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$270$$ 0 0
$$271$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$272$$ −0.103920 + 0.0521907i −0.103920 + 0.0521907i
$$273$$ 0 0
$$274$$ 0.713197 0.957990i 0.713197 0.957990i
$$275$$ 0.770807 0.182685i 0.770807 0.182685i
$$276$$ 0 0
$$277$$ 0 0 −0.597159 0.802123i $$-0.703704\pi$$
0.597159 + 0.802123i $$0.296296\pi$$
$$278$$ 0.914900 + 0.767692i 0.914900 + 0.767692i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 1.49079 + 0.353324i 1.49079 + 0.353324i 0.893633 0.448799i $$-0.148148\pi$$
0.597159 + 0.802123i $$0.296296\pi$$
$$282$$ 0 0
$$283$$ −1.28004 + 0.841897i −1.28004 + 0.841897i −0.993238 0.116093i $$-0.962963\pi$$
−0.286803 + 0.957990i $$0.592593\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0.973045 + 0.230616i 0.973045 + 0.230616i
$$289$$ −0.755685 0.634095i −0.755685 0.634095i
$$290$$ 0 0
$$291$$ −0.997837 + 0.656288i −0.997837 + 0.656288i
$$292$$ 1.73909 0.412172i 1.73909 0.412172i
$$293$$ 0 0 0.597159 0.802123i $$-0.296296\pi$$
−0.597159 + 0.802123i $$0.703704\pi$$
$$294$$ −0.835488 0.549509i −0.835488 0.549509i
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0.313758 0.727374i 0.313758 0.727374i
$$298$$ 0 0
$$299$$ 0 0
$$300$$ −0.993238 + 0.116093i −0.993238 + 0.116093i
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ −0.227194 + 0.526695i −0.227194 + 0.526695i
$$305$$ 0 0
$$306$$ −0.0201935 0.114523i −0.0201935 0.114523i
$$307$$ 1.28971 + 0.469417i 1.28971 + 0.469417i 0.893633 0.448799i $$-0.148148\pi$$
0.396080 + 0.918216i $$0.370370\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 −0.0581448 0.998308i $$-0.518519\pi$$
0.0581448 + 0.998308i $$0.481481\pi$$
$$312$$ 0 0
$$313$$ −0.558145 1.86433i −0.558145 1.86433i −0.500000 0.866025i $$-0.666667\pi$$
−0.0581448 0.998308i $$-0.518519\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 0 0 0.993238 0.116093i $$-0.0370370\pi$$
−0.993238 + 0.116093i $$0.962963\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ −1.22650 + 1.30001i −1.22650 + 1.30001i
$$322$$ 0 0
$$323$$ 0.0667045 0.0667045
$$324$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$325$$ 0 0
$$326$$ −0.290162 0.190842i −0.290162 0.190842i
$$327$$ 0 0
$$328$$ 0.770807 + 1.78693i 0.770807 + 1.78693i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 1.86668 0.218183i 1.86668 0.218183i 0.893633 0.448799i $$-0.148148\pi$$
0.973045 + 0.230616i $$0.0740741\pi$$
$$332$$ 0.266044 1.50881i 0.266044 1.50881i
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0.0971586 + 1.66815i 0.0971586 + 1.66815i 0.597159 + 0.802123i $$0.296296\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$338$$ 0.893633 + 0.448799i 0.893633 + 0.448799i
$$339$$ 0.347296 0.347296
$$340$$ 0 0
$$341$$ 0 0
$$342$$ −0.439408 0.368707i −0.439408 0.368707i
$$343$$ 0 0
$$344$$ −0.661840 + 1.53432i −0.661840 + 1.53432i
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0.569728 + 0.0665916i 0.569728 + 0.0665916i 0.396080 0.918216i $$-0.370370\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$348$$ 0 0
$$349$$ 0 0 0.0581448 0.998308i $$-0.481481\pi$$
−0.0581448 + 0.998308i $$0.518519\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −0.396080 0.686030i −0.396080 0.686030i
$$353$$ 1.59716 0.802123i 1.59716 0.802123i 0.597159 0.802123i $$-0.296296\pi$$
1.00000 $$0$$
$$354$$ −1.22650 + 0.615969i −1.22650 + 0.615969i
$$355$$ 0 0
$$356$$ −1.82873 + 0.433416i −1.82873 + 0.433416i
$$357$$ 0 0
$$358$$ −1.12229 1.50750i −1.12229 1.50750i
$$359$$ 0 0 −0.766044 0.642788i $$-0.777778\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$360$$ 0 0
$$361$$ −0.513997 + 0.431295i −0.513997 + 0.431295i
$$362$$ 0 0
$$363$$ 0.350020 0.127397i 0.350020 0.127397i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 −0.973045 0.230616i $$-0.925926\pi$$
0.973045 + 0.230616i $$0.0740741\pi$$
$$368$$ 0 0
$$369$$ −1.93293 + 0.225927i −1.93293 + 0.225927i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 0.973045 0.230616i $$-0.0740741\pi$$
−0.973045 + 0.230616i $$0.925926\pi$$
$$374$$ −0.0550102 + 0.0738916i −0.0550102 + 0.0738916i
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −0.973045 + 1.68536i −0.973045 + 1.68536i −0.286803 + 0.957990i $$0.592593\pi$$
−0.686242 + 0.727374i $$0.740741\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 0.286803 0.957990i $$-0.407407\pi$$
−0.286803 + 0.957990i $$0.592593\pi$$
$$384$$ 0.396080 + 0.918216i 0.396080 + 0.918216i
$$385$$ 0 0
$$386$$ −1.82873 + 0.665602i −1.82873 + 0.665602i
$$387$$ −1.28004 1.07408i −1.28004 1.07408i
$$388$$ −1.12229 0.408481i −1.12229 0.408481i
$$389$$ 0 0 0.686242 0.727374i $$-0.259259\pi$$
−0.686242 + 0.727374i $$0.740741\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ −0.0581448 0.998308i −0.0581448 0.998308i
$$393$$ 0.266044 0.223238i 0.266044 0.223238i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0.770807 0.182685i 0.770807 0.182685i
$$397$$ 0 0 0.173648 0.984808i $$-0.444444\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ −0.686242 0.727374i −0.686242 0.727374i
$$401$$ −0.227194 0.526695i −0.227194 0.526695i 0.766044 0.642788i $$-0.222222\pi$$
−0.993238 + 0.116093i $$0.962963\pi$$
$$402$$ 0.569728 + 1.90302i 0.569728 + 1.90302i
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0.0798028 0.0845860i 0.0798028 0.0845860i
$$409$$ −0.0460600 0.106779i −0.0460600 0.106779i 0.893633 0.448799i $$-0.148148\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$410$$ 0 0
$$411$$ −0.342534 + 1.14414i −0.342534 + 1.14414i
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −1.12229 0.408481i −1.12229 0.408481i
$$418$$ 0.0264203 + 0.453619i 0.0264203 + 0.453619i
$$419$$ 0.310355 + 0.155866i 0.310355 + 0.155866i 0.597159 0.802123i $$-0.296296\pi$$
−0.286803 + 0.957990i $$0.592593\pi$$
$$420$$ 0 0
$$421$$ 0 0 0.686242 0.727374i $$-0.259259\pi$$
−0.686242 + 0.727374i $$0.740741\pi$$
$$422$$ −1.43969 0.524005i −1.43969 0.524005i
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −0.0460600 + 0.106779i −0.0460600 + 0.106779i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −1.77518 0.207489i −1.77518 0.207489i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$432$$ −0.993238 + 0.116093i −0.993238 + 0.116093i
$$433$$ 0.0581448 + 0.100710i 0.0581448 + 0.100710i 0.893633 0.448799i $$-0.148148\pi$$
−0.835488 + 0.549509i $$0.814815\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ −1.49324 + 0.982118i −1.49324 + 0.982118i
$$439$$ 0 0 −0.597159 0.802123i $$-0.703704\pi$$
0.597159 + 0.802123i $$0.296296\pi$$
$$440$$ 0 0
$$441$$ 0.973045 + 0.230616i 0.973045 + 0.230616i
$$442$$ 0 0
$$443$$ 1.89363 + 0.448799i 1.89363 + 0.448799i 1.00000 $$0$$
0.893633 + 0.448799i $$0.148148\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 0.914900 0.767692i 0.914900 0.767692i −0.0581448 0.998308i $$-0.518519\pi$$
0.973045 + 0.230616i $$0.0740741\pi$$
$$450$$ 0.893633 0.448799i 0.893633 0.448799i
$$451$$ 1.18094 + 0.990930i 1.18094 + 0.990930i
$$452$$ 0.207391 + 0.278574i 0.207391 + 0.278574i
$$453$$ 0 0
$$454$$ −1.62593 + 0.385353i −1.62593 + 0.385353i
$$455$$ 0 0
$$456$$ 0.0333522 0.572636i 0.0333522 0.572636i
$$457$$ −1.22650 + 0.615969i −1.22650 + 0.615969i −0.939693 0.342020i $$-0.888889\pi$$
−0.286803 + 0.957990i $$0.592593\pi$$
$$458$$ 0 0
$$459$$ 0.0581448 + 0.100710i 0.0581448 + 0.100710i
$$460$$ 0 0
$$461$$ 0 0 0.0581448 0.998308i $$-0.481481\pi$$
−0.0581448 + 0.998308i $$0.518519\pi$$
$$462$$ 0 0
$$463$$ 0 0 −0.993238 0.116093i $$-0.962963\pi$$
0.993238 + 0.116093i $$0.0370370\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ −0.543613 + 1.26024i −0.543613 + 1.26024i
$$467$$ 0.539014 0.196185i 0.539014 0.196185i −0.0581448 0.998308i $$-0.518519\pi$$
0.597159 + 0.802123i $$0.296296\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ −1.22650 0.615969i −1.22650 0.615969i
$$473$$ 0.0769651 + 1.32144i 0.0769651 + 1.32144i
$$474$$ 0 0
$$475$$ 0.164512 + 0.549509i 0.164512 + 0.549509i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 0.993238 0.116093i $$-0.0370370\pi$$
−0.993238 + 0.116093i $$0.962963\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ −0.786803 1.82401i −0.786803 1.82401i
$$483$$ 0 0
$$484$$ 0.311205 + 0.204683i 0.311205 + 0.204683i
$$485$$ 0 0
$$486$$ 0.173648 0.984808i 0.173648 0.984808i
$$487$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$488$$ 0 0
$$489$$ 0.337935 + 0.0800921i 0.337935 + 0.0800921i
$$490$$ 0 0
$$491$$ −1.22650 1.30001i −1.22650 1.30001i −0.939693 0.342020i $$-0.888889\pi$$
−0.286803 0.957990i $$-0.592593\pi$$
$$492$$ −1.33549 1.41553i −1.33549 1.41553i
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0.266044 + 1.50881i 0.266044 + 1.50881i
$$499$$ 0.00676164 + 0.116093i 0.00676164 + 0.116093i 1.00000 $$0$$
−0.993238 + 0.116093i $$0.962963\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 1.14669 1.21542i 1.14669 1.21542i
$$503$$ 0 0 −0.939693 0.342020i $$-0.888889\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −0.993238 0.116093i −0.993238 0.116093i
$$508$$ 0 0
$$509$$ 0 0 −0.993238 0.116093i $$-0.962963\pi$$
0.993238 + 0.116093i $$0.0370370\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$513$$ 0.539014 + 0.196185i 0.539014 + 0.196185i
$$514$$ 0.993238 + 1.72034i 0.993238 + 1.72034i
$$515$$ 0 0
$$516$$ 0.0971586 1.66815i 0.0971586 1.66815i
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −1.28004 1.07408i −1.28004 1.07408i −0.993238 0.116093i $$-0.962963\pi$$
−0.286803 0.957990i $$-0.592593\pi$$
$$522$$ 0 0
$$523$$ 0.266044 0.223238i 0.266044 0.223238i −0.500000 0.866025i $$-0.666667\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$524$$ 0.337935 + 0.0800921i 0.337935 + 0.0800921i
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0.606829 + 0.509190i 0.606829 + 0.509190i
$$529$$ 0.973045 + 0.230616i 0.973045 + 0.230616i
$$530$$ 0 0
$$531$$ 0.941855 0.998308i 0.941855 0.998308i
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 1.57020 1.03274i 1.57020 1.03274i
$$535$$ 0 0
$$536$$ −1.18624 + 1.59340i −1.18624 + 1.59340i
$$537$$ 1.57020 + 1.03274i 1.57020 + 1.03274i
$$538$$ 0 0
$$539$$ −0.396080 0.686030i −0.396080 0.686030i
$$540$$ 0 0
$$541$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0.115503 + 0.0135004i 0.115503 + 0.0135004i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −0.0460600 + 0.106779i −0.0460600 + 0.106779i −0.939693 0.342020i $$-0.888889\pi$$
0.893633 + 0.448799i $$0.148148\pi$$
$$548$$ −1.12229 + 0.408481i −1.12229 + 0.408481i
$$549$$ 0 0
$$550$$ −0.744386 0.270935i −0.744386 0.270935i
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ −0.342534 1.14414i −0.342534 1.14414i
$$557$$ 0 0 −0.173648 0.984808i $$-0.555556\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0.0264203 0.0882500i 0.0264203 0.0882500i
$$562$$ −1.05138 1.11440i −1.05138 1.11440i
$$563$$ 0.473045 + 1.09664i 0.473045 + 1.09664i 0.973045 + 0.230616i $$0.0740741\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 1.53209 1.53209
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 1.14669 + 0.754192i 1.14669 + 0.754192i 0.973045 0.230616i $$-0.0740741\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$570$$ 0 0
$$571$$ 0.707900 + 1.64110i 0.707900 + 1.64110i 0.766044 + 0.642788i $$0.222222\pi$$
−0.0581448 + 0.998308i $$0.518519\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −0.686242 0.727374i −0.686242 0.727374i
$$577$$ 0.207391 + 1.17617i 0.207391 + 1.17617i 0.893633 + 0.448799i $$0.148148\pi$$
−0.686242 + 0.727374i $$0.740741\pi$$
$$578$$ 0.282925 + 0.945034i 0.282925 + 0.945034i
$$579$$ 1.49079 1.25092i 1.49079 1.25092i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 1.19432 1.19432
$$583$$ 0 0
$$584$$ −1.67948 0.611281i −1.67948 0.611281i
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −0.786803 + 1.82401i −0.786803 + 1.82401i −0.286803 + 0.957990i $$0.592593\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$588$$ 0.396080 + 0.918216i 0.396080 + 0.918216i
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 0.939693 1.62760i 0.939693 1.62760i 0.173648 0.984808i $$-0.444444\pi$$
0.766044 0.642788i $$-0.222222\pi$$
$$594$$ −0.661840 + 0.435299i −0.661840 + 0.435299i
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 0.973045 0.230616i $$-0.0740741\pi$$
−0.973045 + 0.230616i $$0.925926\pi$$
$$600$$ 0.893633 + 0.448799i 0.893633 + 0.448799i
$$601$$ 0.473045 + 0.635410i 0.473045 + 0.635410i 0.973045 0.230616i $$-0.0740741\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$602$$ 0 0
$$603$$ −1.18624 1.59340i −1.18624 1.59340i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 0 0 0.835488 0.549509i $$-0.185185\pi$$
−0.835488 + 0.549509i $$0.814815\pi$$
$$608$$ 0.479241 0.315202i 0.479241 0.315202i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ −0.0460600 + 0.106779i −0.0460600 + 0.106779i
$$613$$ 0 0 −0.766044 0.642788i $$-0.777778\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$614$$ −0.819590 1.10090i −0.819590 1.10090i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0.713197 0.957990i 0.713197 0.957990i −0.286803 0.957990i $$-0.592593\pi$$
1.00000 $$0$$
$$618$$ 0 0
$$619$$ 1.73909 0.873403i 1.73909 0.873403i 0.766044 0.642788i $$-0.222222\pi$$
0.973045 0.230616i $$-0.0740741\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −0.993238 0.116093i −0.993238 0.116093i
$$626$$ −0.558145 + 1.86433i −0.558145 + 1.86433i
$$627$$ −0.179974 0.417226i −0.179974 0.417226i
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 −0.939693 0.342020i $$-0.888889\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$632$$ 0 0
$$633$$ 1.53209 1.53209
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0.569728 0.0665916i 0.569728 0.0665916i 0.173648 0.984808i $$-0.444444\pi$$
0.396080 + 0.918216i $$0.370370\pi$$
$$642$$ 1.73909 0.412172i 1.73909 0.412172i
$$643$$ −0.543613 0.576196i −0.543613 0.576196i 0.396080 0.918216i $$-0.370370\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −0.0557308 0.0366547i −0.0557308 0.0366547i
$$647$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$648$$ 0.893633 0.448799i 0.893633 0.448799i
$$649$$ −1.08723 −1.08723
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0.137557 + 0.318893i 0.137557 + 0.318893i
$$653$$ 0 0 −0.686242 0.727374i $$-0.740741\pi$$
0.686242 + 0.727374i $$0.259259\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0.337935 1.91652i 0.337935 1.91652i
$$657$$ 1.06728 1.43361i 1.06728 1.43361i
$$658$$ 0 0
$$659$$ −0.439408 1.46773i −0.439408 1.46773i −0.835488 0.549509i $$-0.814815\pi$$
0.396080 0.918216i $$-0.370370\pi$$
$$660$$ 0 0
$$661$$ 0 0 −0.0581448 0.998308i $$-0.518519\pi$$
0.0581448 + 0.998308i $$0.481481\pi$$
$$662$$ −1.67948 0.843467i −1.67948 0.843467i
$$663$$ 0 0
$$664$$ −1.05138 + 1.11440i −1.05138 + 1.11440i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −0.0890830 + 1.52950i −0.0890830 + 1.52950i 0.597159 + 0.802123i $$0.296296\pi$$
−0.686242 + 0.727374i $$0.740741\pi$$
$$674$$ 0.835488 1.44711i 0.835488 1.44711i
$$675$$ −0.686242 + 0.727374i −0.686242 + 0.727374i
$$676$$ −0.500000 0.866025i −0.500000 0.866025i
$$677$$ 0 0 0.893633 0.448799i $$-0.148148\pi$$
−0.893633 + 0.448799i $$0.851852\pi$$
$$678$$ −0.290162 0.190842i −0.290162 0.190842i
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 1.39608 0.918216i 1.39608 0.918216i
$$682$$ 0 0
$$683$$ −1.52173 1.27688i −1.52173 1.27688i −0.835488 0.549509i $$-0.814815\pi$$
−0.686242 0.727374i $$-0.740741\pi$$
$$684$$ 0.164512 + 0.549509i 0.164512 + 0.549509i
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 1.39608 0.918216i 1.39608 0.918216i
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −1.82873 0.433416i −1.82873 0.433416i −0.835488 0.549509i $$-0.814815\pi$$
−0.993238 + 0.116093i $$0.962963\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ −0.439408 0.368707i −0.439408 0.368707i
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −0.220210 + 0.0521907i −0.220210 + 0.0521907i
$$698$$ 0 0
$$699$$ 0.0798028 1.37016i 0.0798028 1.37016i
$$700$$ 0 0
$$701$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ −0.0460600 + 0.790819i −0.0460600 + 0.790819i
$$705$$ 0 0
$$706$$ −1.77518 0.207489i −1.77518 0.207489i
$$707$$ 0 0
$$708$$ 1.36320 + 0.159336i 1.36320 + 0.159336i
$$709$$ 0 0 0.396080 0.918216i $$-0.370370\pi$$
−0.396080 + 0.918216i $$0.629630\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 1.76604 + 0.642788i 1.76604 + 0.642788i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0.109277 + 1.87621i 0.109277 + 1.87621i
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 −0.173648 0.984808i $$-0.555556\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0.666439 0.0778955i 0.666439 0.0778955i
$$723$$ 1.36320 + 1.44491i 1.36320 + 1.44491i
$$724$$ 0 0
$$725$$ 0 0
$$726$$ −0.362443 0.0859006i −0.362443 0.0859006i
$$727$$ 0 0 −0.835488 0.549509i $$-0.814815\pi$$
0.835488 + 0.549509i $$0.185185\pi$$
$$728$$ 0 0
$$729$$ 0.173648 + 0.984808i 0.173648 + 0.984808i
$$730$$ 0 0
$$731$$ −0.162350 0.106779i −0.162350 0.106779i
$$732$$ 0 0
$$733$$ 0 0 −0.396080 0.918216i $$-0.629630\pi$$
0.396080 + 0.918216i $$0.370370\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −0.273254 + 1.54970i −0.273254 + 1.54970i
$$738$$ 1.73909 + 0.873403i 1.73909 + 0.873403i
$$739$$ 0.137557 + 0.780125i 0.137557 + 0.780125i 0.973045 + 0.230616i $$0.0740741\pi$$
−0.835488 + 0.549509i $$0.814815\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 −0.893633 0.448799i $$-0.851852\pi$$
0.893633 + 0.448799i $$0.148148\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −0.766044 1.32683i −0.766044 1.32683i
$$748$$ 0.0865644 0.0315069i 0.0865644 0.0315069i
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 0.286803 0.957990i $$-0.407407\pi$$
−0.286803 + 0.957990i $$0.592593\pi$$
$$752$$ 0 0
$$753$$ −0.661840 + 1.53432i −0.661840 + 1.53432i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$758$$ 1.73909 0.873403i 1.73909 0.873403i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −0.973045 + 0.230616i −0.973045 + 0.230616i −0.686242 0.727374i $$-0.740741\pi$$
−0.286803 + 0.957990i $$0.592593\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0.173648 0.984808i 0.173648 0.984808i
$$769$$ −0.290162 + 0.190842i −0.290162 + 0.190842i −0.686242 0.727374i $$-0.740741\pi$$
0.396080 + 0.918216i $$0.370370\pi$$
$$770$$ 0 0
$$771$$ −1.52173 1.27688i −1.52173 1.27688i
$$772$$ 1.89363 + 0.448799i 1.89363 + 0.448799i
$$773$$ 0 0 0.766044 0.642788i $$-0.222222\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$774$$ 0.479241 + 1.60078i 0.479241 + 1.60078i
$$775$$ 0 0
$$776$$ 0.713197 + 0.957990i 0.713197 + 0.957990i
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −0.666602 + 0.895402i −0.666602 + 0.895402i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$785$$ 0 0
$$786$$ −0.344948 + 0.0403186i −0.344948 + 0.0403186i
$$787$$ −1.52173 0.177865i −1.52173 0.177865i −0.686242 0.727374i $$-0.740741\pi$$
−0.835488 + 0.549509i $$0.814815\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ −0.744386 0.270935i −0.744386 0.270935i
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 −0.0581448 0.998308i $$-0.518519\pi$$
0.0581448 + 0.998308i $$0.481481\pi$$
$$798$$ 0 0
$$799$$ 0 0