# Properties

 Label 960.1.cl.a.869.1 Level $960$ Weight $1$ Character 960.869 Analytic conductor $0.479$ Analytic rank $0$ Dimension $16$ Projective image $D_{16}$ CM discriminant -15 Inner twists $8$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$960 = 2^{6} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 960.cl (of order $$16$$, degree $$8$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.479102412128$$ Analytic rank: $$0$$ Dimension: $$16$$ Relative dimension: $$2$$ over $$\Q(\zeta_{16})$$ Coefficient field: $$\Q(\zeta_{32})$$ Defining polynomial: $$x^{16} + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{16}$$ Projective field: Galois closure of $$\mathbb{Q}[x]/(x^{16} - \cdots)$$

## Embedding invariants

 Embedding label 869.1 Root $$0.555570 - 0.831470i$$ of defining polynomial Character $$\chi$$ $$=$$ 960.869 Dual form 960.1.cl.a.749.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.980785 + 0.195090i) q^{2} +(0.555570 - 0.831470i) q^{3} +(0.923880 - 0.382683i) q^{4} +(-0.195090 + 0.980785i) q^{5} +(-0.382683 + 0.923880i) q^{6} +(-0.831470 + 0.555570i) q^{8} +(-0.382683 - 0.923880i) q^{9} +O(q^{10})$$ $$q+(-0.980785 + 0.195090i) q^{2} +(0.555570 - 0.831470i) q^{3} +(0.923880 - 0.382683i) q^{4} +(-0.195090 + 0.980785i) q^{5} +(-0.382683 + 0.923880i) q^{6} +(-0.831470 + 0.555570i) q^{8} +(-0.382683 - 0.923880i) q^{9} -1.00000i q^{10} +(0.195090 - 0.980785i) q^{12} +(0.707107 + 0.707107i) q^{15} +(0.707107 - 0.707107i) q^{16} +(0.275899 - 0.275899i) q^{17} +(0.555570 + 0.831470i) q^{18} +(1.63099 - 0.324423i) q^{19} +(0.195090 + 0.980785i) q^{20} +(1.81225 - 0.750661i) q^{23} +1.00000i q^{24} +(-0.923880 - 0.382683i) q^{25} +(-0.980785 - 0.195090i) q^{27} +(-0.831470 - 0.555570i) q^{30} +1.84776i q^{31} +(-0.555570 + 0.831470i) q^{32} +(-0.216773 + 0.324423i) q^{34} +(-0.707107 - 0.707107i) q^{36} +(-1.53636 + 0.636379i) q^{38} +(-0.382683 - 0.923880i) q^{40} +(0.980785 - 0.195090i) q^{45} +(-1.63099 + 1.08979i) q^{46} +(0.785695 - 0.785695i) q^{47} +(-0.195090 - 0.980785i) q^{48} +(-0.707107 - 0.707107i) q^{49} +(0.980785 + 0.195090i) q^{50} +(-0.0761205 - 0.382683i) q^{51} +(-0.636379 + 0.425215i) q^{53} +1.00000 q^{54} +(0.636379 - 1.53636i) q^{57} +(0.923880 + 0.382683i) q^{60} +(-0.923880 + 1.38268i) q^{61} +(-0.360480 - 1.81225i) q^{62} +(0.382683 - 0.923880i) q^{64} +(0.149316 - 0.360480i) q^{68} +(0.382683 - 1.92388i) q^{69} +(0.831470 + 0.555570i) q^{72} +(-0.831470 + 0.555570i) q^{75} +(1.38268 - 0.923880i) q^{76} +(-1.00000 - 1.00000i) q^{79} +(0.555570 + 0.831470i) q^{80} +(-0.707107 + 0.707107i) q^{81} +(-0.750661 + 0.149316i) q^{83} +(0.216773 + 0.324423i) q^{85} +(-0.923880 + 0.382683i) q^{90} +(1.38704 - 1.38704i) q^{92} +(1.53636 + 1.02656i) q^{93} +(-0.617317 + 0.923880i) q^{94} +1.66294i q^{95} +(0.382683 + 0.923880i) q^{96} +(0.831470 + 0.555570i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16 q + O(q^{10})$$ $$16 q - 16 q^{51} + 16 q^{54} + 16 q^{76} - 16 q^{79} - 16 q^{94} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$$.

 $$n$$ $$511$$ $$577$$ $$641$$ $$901$$ $$\chi(n)$$ $$1$$ $$-1$$ $$-1$$ $$e\left(\frac{9}{16}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.980785 + 0.195090i −0.980785 + 0.195090i
$$3$$ 0.555570 0.831470i 0.555570 0.831470i
$$4$$ 0.923880 0.382683i 0.923880 0.382683i
$$5$$ −0.195090 + 0.980785i −0.195090 + 0.980785i
$$6$$ −0.382683 + 0.923880i −0.382683 + 0.923880i
$$7$$ 0 0 0.382683 0.923880i $$-0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$8$$ −0.831470 + 0.555570i −0.831470 + 0.555570i
$$9$$ −0.382683 0.923880i −0.382683 0.923880i
$$10$$ 1.00000i 1.00000i
$$11$$ 0 0 0.831470 0.555570i $$-0.187500\pi$$
−0.831470 + 0.555570i $$0.812500\pi$$
$$12$$ 0.195090 0.980785i 0.195090 0.980785i
$$13$$ 0 0 −0.195090 0.980785i $$-0.562500\pi$$
0.195090 + 0.980785i $$0.437500\pi$$
$$14$$ 0 0
$$15$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$16$$ 0.707107 0.707107i 0.707107 0.707107i
$$17$$ 0.275899 0.275899i 0.275899 0.275899i −0.555570 0.831470i $$-0.687500\pi$$
0.831470 + 0.555570i $$0.187500\pi$$
$$18$$ 0.555570 + 0.831470i 0.555570 + 0.831470i
$$19$$ 1.63099 0.324423i 1.63099 0.324423i 0.707107 0.707107i $$-0.250000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$20$$ 0.195090 + 0.980785i 0.195090 + 0.980785i
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 1.81225 0.750661i 1.81225 0.750661i 0.831470 0.555570i $$-0.187500\pi$$
0.980785 0.195090i $$-0.0625000\pi$$
$$24$$ 1.00000i 1.00000i
$$25$$ −0.923880 0.382683i −0.923880 0.382683i
$$26$$ 0 0
$$27$$ −0.980785 0.195090i −0.980785 0.195090i
$$28$$ 0 0
$$29$$ 0 0 −0.831470 0.555570i $$-0.812500\pi$$
0.831470 + 0.555570i $$0.187500\pi$$
$$30$$ −0.831470 0.555570i −0.831470 0.555570i
$$31$$ 1.84776i 1.84776i 0.382683 + 0.923880i $$0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$32$$ −0.555570 + 0.831470i −0.555570 + 0.831470i
$$33$$ 0 0
$$34$$ −0.216773 + 0.324423i −0.216773 + 0.324423i
$$35$$ 0 0
$$36$$ −0.707107 0.707107i −0.707107 0.707107i
$$37$$ 0 0 −0.980785 0.195090i $$-0.937500\pi$$
0.980785 + 0.195090i $$0.0625000\pi$$
$$38$$ −1.53636 + 0.636379i −1.53636 + 0.636379i
$$39$$ 0 0
$$40$$ −0.382683 0.923880i −0.382683 0.923880i
$$41$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$42$$ 0 0
$$43$$ 0 0 −0.555570 0.831470i $$-0.687500\pi$$
0.555570 + 0.831470i $$0.312500\pi$$
$$44$$ 0 0
$$45$$ 0.980785 0.195090i 0.980785 0.195090i
$$46$$ −1.63099 + 1.08979i −1.63099 + 1.08979i
$$47$$ 0.785695 0.785695i 0.785695 0.785695i −0.195090 0.980785i $$-0.562500\pi$$
0.980785 + 0.195090i $$0.0625000\pi$$
$$48$$ −0.195090 0.980785i −0.195090 0.980785i
$$49$$ −0.707107 0.707107i −0.707107 0.707107i
$$50$$ 0.980785 + 0.195090i 0.980785 + 0.195090i
$$51$$ −0.0761205 0.382683i −0.0761205 0.382683i
$$52$$ 0 0
$$53$$ −0.636379 + 0.425215i −0.636379 + 0.425215i −0.831470 0.555570i $$-0.812500\pi$$
0.195090 + 0.980785i $$0.437500\pi$$
$$54$$ 1.00000 1.00000
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0.636379 1.53636i 0.636379 1.53636i
$$58$$ 0 0
$$59$$ 0 0 0.195090 0.980785i $$-0.437500\pi$$
−0.195090 + 0.980785i $$0.562500\pi$$
$$60$$ 0.923880 + 0.382683i 0.923880 + 0.382683i
$$61$$ −0.923880 + 1.38268i −0.923880 + 1.38268i 1.00000i $$0.5\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$62$$ −0.360480 1.81225i −0.360480 1.81225i
$$63$$ 0 0
$$64$$ 0.382683 0.923880i 0.382683 0.923880i
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0 0 0.555570 0.831470i $$-0.312500\pi$$
−0.555570 + 0.831470i $$0.687500\pi$$
$$68$$ 0.149316 0.360480i 0.149316 0.360480i
$$69$$ 0.382683 1.92388i 0.382683 1.92388i
$$70$$ 0 0
$$71$$ 0 0 0.382683 0.923880i $$-0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$72$$ 0.831470 + 0.555570i 0.831470 + 0.555570i
$$73$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$74$$ 0 0
$$75$$ −0.831470 + 0.555570i −0.831470 + 0.555570i
$$76$$ 1.38268 0.923880i 1.38268 0.923880i
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$80$$ 0.555570 + 0.831470i 0.555570 + 0.831470i
$$81$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$82$$ 0 0
$$83$$ −0.750661 + 0.149316i −0.750661 + 0.149316i −0.555570 0.831470i $$-0.687500\pi$$
−0.195090 + 0.980785i $$0.562500\pi$$
$$84$$ 0 0
$$85$$ 0.216773 + 0.324423i 0.216773 + 0.324423i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$90$$ −0.923880 + 0.382683i −0.923880 + 0.382683i
$$91$$ 0 0
$$92$$ 1.38704 1.38704i 1.38704 1.38704i
$$93$$ 1.53636 + 1.02656i 1.53636 + 1.02656i
$$94$$ −0.617317 + 0.923880i −0.617317 + 0.923880i
$$95$$ 1.66294i 1.66294i
$$96$$ 0.382683 + 0.923880i 0.382683 + 0.923880i
$$97$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$98$$ 0.831470 + 0.555570i 0.831470 + 0.555570i
$$99$$ 0 0
$$100$$ −1.00000 −1.00000
$$101$$ 0 0 −0.980785 0.195090i $$-0.937500\pi$$
0.980785 + 0.195090i $$0.0625000\pi$$
$$102$$ 0.149316 + 0.360480i 0.149316 + 0.360480i
$$103$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0.541196 0.541196i 0.541196 0.541196i
$$107$$ 1.02656 + 1.53636i 1.02656 + 1.53636i 0.831470 + 0.555570i $$0.187500\pi$$
0.195090 + 0.980785i $$0.437500\pi$$
$$108$$ −0.980785 + 0.195090i −0.980785 + 0.195090i
$$109$$ −1.08979 + 0.216773i −1.08979 + 0.216773i −0.707107 0.707107i $$-0.750000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −0.785695 0.785695i −0.785695 0.785695i 0.195090 0.980785i $$-0.437500\pi$$
−0.980785 + 0.195090i $$0.937500\pi$$
$$114$$ −0.324423 + 1.63099i −0.324423 + 1.63099i
$$115$$ 0.382683 + 1.92388i 0.382683 + 1.92388i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ −0.980785 0.195090i −0.980785 0.195090i
$$121$$ 0.382683 0.923880i 0.382683 0.923880i
$$122$$ 0.636379 1.53636i 0.636379 1.53636i
$$123$$ 0 0
$$124$$ 0.707107 + 1.70711i 0.707107 + 1.70711i
$$125$$ 0.555570 0.831470i 0.555570 0.831470i
$$126$$ 0 0
$$127$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$128$$ −0.195090 + 0.980785i −0.195090 + 0.980785i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 0.555570 0.831470i $$-0.312500\pi$$
−0.555570 + 0.831470i $$0.687500\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0.382683 0.923880i 0.382683 0.923880i
$$136$$ −0.0761205 + 0.382683i −0.0761205 + 0.382683i
$$137$$ −0.425215 1.02656i −0.425215 1.02656i −0.980785 0.195090i $$-0.937500\pi$$
0.555570 0.831470i $$-0.312500\pi$$
$$138$$ 1.96157i 1.96157i
$$139$$ −1.63099 + 1.08979i −1.63099 + 1.08979i −0.707107 + 0.707107i $$0.750000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$140$$ 0 0
$$141$$ −0.216773 1.08979i −0.216773 1.08979i
$$142$$ 0 0
$$143$$ 0 0
$$144$$ −0.923880 0.382683i −0.923880 0.382683i
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −0.980785 + 0.195090i −0.980785 + 0.195090i
$$148$$ 0 0
$$149$$ 0 0 −0.555570 0.831470i $$-0.687500\pi$$
0.555570 + 0.831470i $$0.312500\pi$$
$$150$$ 0.707107 0.707107i 0.707107 0.707107i
$$151$$ −0.707107 + 0.292893i −0.707107 + 0.292893i −0.707107 0.707107i $$-0.750000\pi$$
1.00000i $$0.5\pi$$
$$152$$ −1.17588 + 1.17588i −1.17588 + 1.17588i
$$153$$ −0.360480 0.149316i −0.360480 0.149316i
$$154$$ 0 0
$$155$$ −1.81225 0.360480i −1.81225 0.360480i
$$156$$ 0 0
$$157$$ 0 0 −0.831470 0.555570i $$-0.812500\pi$$
0.831470 + 0.555570i $$0.187500\pi$$
$$158$$ 1.17588 + 0.785695i 1.17588 + 0.785695i
$$159$$ 0.765367i 0.765367i
$$160$$ −0.707107 0.707107i −0.707107 0.707107i
$$161$$ 0 0
$$162$$ 0.555570 0.831470i 0.555570 0.831470i
$$163$$ 0 0 −0.831470 0.555570i $$-0.812500\pi$$
0.831470 + 0.555570i $$0.187500\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0.707107 0.292893i 0.707107 0.292893i
$$167$$ −0.360480 0.149316i −0.360480 0.149316i 0.195090 0.980785i $$-0.437500\pi$$
−0.555570 + 0.831470i $$0.687500\pi$$
$$168$$ 0 0
$$169$$ −0.923880 + 0.382683i −0.923880 + 0.382683i
$$170$$ −0.275899 0.275899i −0.275899 0.275899i
$$171$$ −0.923880 1.38268i −0.923880 1.38268i
$$172$$ 0 0
$$173$$ −1.81225 + 0.360480i −1.81225 + 0.360480i −0.980785 0.195090i $$-0.937500\pi$$
−0.831470 + 0.555570i $$0.812500\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 −0.195090 0.980785i $$-0.562500\pi$$
0.195090 + 0.980785i $$0.437500\pi$$
$$180$$ 0.831470 0.555570i 0.831470 0.555570i
$$181$$ 0.324423 0.216773i 0.324423 0.216773i −0.382683 0.923880i $$-0.625000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$182$$ 0 0
$$183$$ 0.636379 + 1.53636i 0.636379 + 1.53636i
$$184$$ −1.08979 + 1.63099i −1.08979 + 1.63099i
$$185$$ 0 0
$$186$$ −1.70711 0.707107i −1.70711 0.707107i
$$187$$ 0 0
$$188$$ 0.425215 1.02656i 0.425215 1.02656i
$$189$$ 0 0
$$190$$ −0.324423 1.63099i −0.324423 1.63099i
$$191$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$192$$ −0.555570 0.831470i −0.555570 0.831470i
$$193$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ −0.923880 0.382683i −0.923880 0.382683i
$$197$$ −0.275899 + 1.38704i −0.275899 + 1.38704i 0.555570 + 0.831470i $$0.312500\pi$$
−0.831470 + 0.555570i $$0.812500\pi$$
$$198$$ 0 0
$$199$$ 0.541196 1.30656i 0.541196 1.30656i −0.382683 0.923880i $$-0.625000\pi$$
0.923880 0.382683i $$-0.125000\pi$$
$$200$$ 0.980785 0.195090i 0.980785 0.195090i
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ −0.216773 0.324423i −0.216773 0.324423i
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −1.38704 1.38704i −1.38704 1.38704i
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 1.08979 0.216773i 1.08979 0.216773i 0.382683 0.923880i $$-0.375000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$212$$ −0.425215 + 0.636379i −0.425215 + 0.636379i
$$213$$ 0 0
$$214$$ −1.30656 1.30656i −1.30656 1.30656i
$$215$$ 0 0
$$216$$ 0.923880 0.382683i 0.923880 0.382683i
$$217$$ 0 0
$$218$$ 1.02656 0.425215i 1.02656 0.425215i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$224$$ 0 0
$$225$$ 1.00000i 1.00000i
$$226$$ 0.923880 + 0.617317i 0.923880 + 0.617317i
$$227$$ −0.636379 0.425215i −0.636379 0.425215i 0.195090 0.980785i $$-0.437500\pi$$
−0.831470 + 0.555570i $$0.812500\pi$$
$$228$$ 1.66294i 1.66294i
$$229$$ 1.92388 + 0.382683i 1.92388 + 0.382683i 1.00000 $$0$$
0.923880 + 0.382683i $$0.125000\pi$$
$$230$$ −0.750661 1.81225i −0.750661 1.81225i
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −1.81225 + 0.750661i −1.81225 + 0.750661i −0.831470 + 0.555570i $$0.812500\pi$$
−0.980785 + 0.195090i $$0.937500\pi$$
$$234$$ 0 0
$$235$$ 0.617317 + 0.923880i 0.617317 + 0.923880i
$$236$$ 0 0
$$237$$ −1.38704 + 0.275899i −1.38704 + 0.275899i
$$238$$ 0 0
$$239$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$240$$ 1.00000 1.00000
$$241$$ 1.30656 + 1.30656i 1.30656 + 1.30656i 0.923880 + 0.382683i $$0.125000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$242$$ −0.195090 + 0.980785i −0.195090 + 0.980785i
$$243$$ 0.195090 + 0.980785i 0.195090 + 0.980785i
$$244$$ −0.324423 + 1.63099i −0.324423 + 1.63099i
$$245$$ 0.831470 0.555570i 0.831470 0.555570i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ −1.02656 1.53636i −1.02656 1.53636i
$$249$$ −0.292893 + 0.707107i −0.292893 + 0.707107i
$$250$$ −0.382683 + 0.923880i −0.382683 + 0.923880i
$$251$$ 0 0 0.195090 0.980785i $$-0.437500\pi$$
−0.195090 + 0.980785i $$0.562500\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0.390181 0.390181
$$256$$ 1.00000i 1.00000i
$$257$$ 1.96157 1.96157 0.980785 0.195090i $$-0.0625000\pi$$
0.980785 + 0.195090i $$0.0625000\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 0.149316 0.360480i 0.149316 0.360480i −0.831470 0.555570i $$-0.812500\pi$$
0.980785 + 0.195090i $$0.0625000\pi$$
$$264$$ 0 0
$$265$$ −0.292893 0.707107i −0.292893 0.707107i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 0 0 −0.195090 0.980785i $$-0.562500\pi$$
0.195090 + 0.980785i $$0.437500\pi$$
$$270$$ −0.195090 + 0.980785i −0.195090 + 0.980785i
$$271$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$272$$ 0.390181i 0.390181i
$$273$$ 0 0
$$274$$ 0.617317 + 0.923880i 0.617317 + 0.923880i
$$275$$ 0 0
$$276$$ −0.382683 1.92388i −0.382683 1.92388i
$$277$$ 0 0 −0.555570 0.831470i $$-0.687500\pi$$
0.555570 + 0.831470i $$0.312500\pi$$
$$278$$ 1.38704 1.38704i 1.38704 1.38704i
$$279$$ 1.70711 0.707107i 1.70711 0.707107i
$$280$$ 0 0
$$281$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$282$$ 0.425215 + 1.02656i 0.425215 + 1.02656i
$$283$$ 0 0 −0.980785 0.195090i $$-0.937500\pi$$
0.980785 + 0.195090i $$0.0625000\pi$$
$$284$$ 0 0
$$285$$ 1.38268 + 0.923880i 1.38268 + 0.923880i
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0.980785 + 0.195090i 0.980785 + 0.195090i
$$289$$ 0.847759i 0.847759i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −0.750661 0.149316i −0.750661 0.149316i −0.195090 0.980785i $$-0.562500\pi$$
−0.555570 + 0.831470i $$0.687500\pi$$
$$294$$ 0.923880 0.382683i 0.923880 0.382683i
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ −0.555570 + 0.831470i −0.555570 + 0.831470i
$$301$$ 0 0
$$302$$ 0.636379 0.425215i 0.636379 0.425215i
$$303$$ 0 0
$$304$$ 0.923880 1.38268i 0.923880 1.38268i
$$305$$ −1.17588 1.17588i −1.17588 1.17588i
$$306$$ 0.382683 + 0.0761205i 0.382683 + 0.0761205i
$$307$$ 0 0 −0.195090 0.980785i $$-0.562500\pi$$
0.195090 + 0.980785i $$0.437500\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 1.84776 1.84776
$$311$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$312$$ 0 0
$$313$$ 0 0 0.382683 0.923880i $$-0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ −1.30656 0.541196i −1.30656 0.541196i
$$317$$ −0.785695 + 1.17588i −0.785695 + 1.17588i 0.195090 + 0.980785i $$0.437500\pi$$
−0.980785 + 0.195090i $$0.937500\pi$$
$$318$$ −0.149316 0.750661i −0.149316 0.750661i
$$319$$ 0 0
$$320$$ 0.831470 + 0.555570i 0.831470 + 0.555570i
$$321$$ 1.84776 1.84776
$$322$$ 0 0
$$323$$ 0.360480 0.539496i 0.360480 0.539496i
$$324$$ −0.382683 + 0.923880i −0.382683 + 0.923880i
$$325$$ 0 0
$$326$$ 0 0
$$327$$ −0.425215 + 1.02656i −0.425215 + 1.02656i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0.324423 0.216773i 0.324423 0.216773i −0.382683 0.923880i $$-0.625000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$332$$ −0.636379 + 0.425215i −0.636379 + 0.425215i
$$333$$ 0 0
$$334$$ 0.382683 + 0.0761205i 0.382683 + 0.0761205i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$338$$ 0.831470 0.555570i 0.831470 0.555570i
$$339$$ −1.08979 + 0.216773i −1.08979 + 0.216773i
$$340$$ 0.324423 + 0.216773i 0.324423 + 0.216773i
$$341$$ 0 0
$$342$$ 1.17588 + 1.17588i 1.17588 + 1.17588i
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 1.81225 + 0.750661i 1.81225 + 0.750661i
$$346$$ 1.70711 0.707107i 1.70711 0.707107i
$$347$$ 1.38704 + 0.275899i 1.38704 + 0.275899i 0.831470 0.555570i $$-0.187500\pi$$
0.555570 + 0.831470i $$0.312500\pi$$
$$348$$ 0 0
$$349$$ −1.38268 0.923880i −1.38268 0.923880i −0.382683 0.923880i $$-0.625000\pi$$
−1.00000 $$\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 1.66294i 1.66294i 0.555570 + 0.831470i $$0.312500\pi$$
−0.555570 + 0.831470i $$0.687500\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$360$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$361$$ 1.63099 0.675577i 1.63099 0.675577i
$$362$$ −0.275899 + 0.275899i −0.275899 + 0.275899i
$$363$$ −0.555570 0.831470i −0.555570 0.831470i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ −0.923880 1.38268i −0.923880 1.38268i
$$367$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$368$$ 0.750661 1.81225i 0.750661 1.81225i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 1.81225 + 0.360480i 1.81225 + 0.360480i
$$373$$ 0 0 0.831470 0.555570i $$-0.187500\pi$$
−0.831470 + 0.555570i $$0.812500\pi$$
$$374$$ 0 0
$$375$$ −0.382683 0.923880i −0.382683 0.923880i
$$376$$ −0.216773 + 1.08979i −0.216773 + 1.08979i
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 0.0761205 0.382683i 0.0761205 0.382683i −0.923880 0.382683i $$-0.875000\pi$$
1.00000 $$0$$
$$380$$ 0.636379 + 1.53636i 0.636379 + 1.53636i
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 1.66294 1.66294 0.831470 0.555570i $$-0.187500\pi$$
0.831470 + 0.555570i $$0.187500\pi$$
$$384$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 0 0 0.195090 0.980785i $$-0.437500\pi$$
−0.195090 + 0.980785i $$0.562500\pi$$
$$390$$ 0 0
$$391$$ 0.292893 0.707107i 0.292893 0.707107i
$$392$$ 0.980785 + 0.195090i 0.980785 + 0.195090i
$$393$$ 0 0
$$394$$ 1.41421i 1.41421i
$$395$$ 1.17588 0.785695i 1.17588 0.785695i
$$396$$ 0 0
$$397$$ 0 0 −0.195090 0.980785i $$-0.562500\pi$$
0.195090 + 0.980785i $$0.437500\pi$$
$$398$$ −0.275899 + 1.38704i −0.275899 + 1.38704i
$$399$$ 0 0
$$400$$ −0.923880 + 0.382683i −0.923880 + 0.382683i
$$401$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ −0.555570 0.831470i −0.555570 0.831470i
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0.275899 + 0.275899i 0.275899 + 0.275899i
$$409$$ 0.707107 + 0.292893i 0.707107 + 0.292893i 0.707107 0.707107i $$-0.250000\pi$$
1.00000i $$0.5\pi$$
$$410$$ 0 0
$$411$$ −1.08979 0.216773i −1.08979 0.216773i
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 1.63099 + 1.08979i 1.63099 + 1.08979i
$$415$$ 0.765367i 0.765367i
$$416$$ 0 0
$$417$$ 1.96157i 1.96157i
$$418$$ 0 0
$$419$$ 0 0 −0.831470 0.555570i $$-0.812500\pi$$
0.831470 + 0.555570i $$0.187500\pi$$
$$420$$ 0 0
$$421$$ −1.92388 0.382683i −1.92388 0.382683i −0.923880 0.382683i $$-0.875000\pi$$
−1.00000 $$\pi$$
$$422$$ −1.02656 + 0.425215i −1.02656 + 0.425215i
$$423$$ −1.02656 0.425215i −1.02656 0.425215i
$$424$$ 0.292893 0.707107i 0.292893 0.707107i
$$425$$ −0.360480 + 0.149316i −0.360480 + 0.149316i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 1.53636 + 1.02656i 1.53636 + 1.02656i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$432$$ −0.831470 + 0.555570i −0.831470 + 0.555570i
$$433$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −0.923880 + 0.617317i −0.923880 + 0.617317i
$$437$$ 2.71223 1.81225i 2.71223 1.81225i
$$438$$ 0 0
$$439$$ −0.541196 1.30656i −0.541196 1.30656i −0.923880 0.382683i $$-0.875000\pi$$
0.382683 0.923880i $$-0.375000\pi$$
$$440$$ 0 0
$$441$$ −0.382683 + 0.923880i −0.382683 + 0.923880i
$$442$$ 0 0
$$443$$ 0.360480 1.81225i 0.360480 1.81225i −0.195090 0.980785i $$-0.562500\pi$$
0.555570 0.831470i $$-0.312500\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ −0.195090 0.980785i −0.195090 0.980785i
$$451$$ 0 0
$$452$$ −1.02656 0.425215i −1.02656 0.425215i
$$453$$ −0.149316 + 0.750661i −0.149316 + 0.750661i
$$454$$ 0.707107 + 0.292893i 0.707107 + 0.292893i
$$455$$ 0 0
$$456$$ 0.324423 + 1.63099i 0.324423 + 1.63099i
$$457$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$458$$ −1.96157 −1.96157
$$459$$ −0.324423 + 0.216773i −0.324423 + 0.216773i
$$460$$ 1.08979 + 1.63099i 1.08979 + 1.63099i
$$461$$ 0 0 −0.195090 0.980785i $$-0.562500\pi$$
0.195090 + 0.980785i $$0.437500\pi$$
$$462$$ 0 0
$$463$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$464$$ 0 0
$$465$$ −1.30656 + 1.30656i −1.30656 + 1.30656i
$$466$$ 1.63099 1.08979i 1.63099 1.08979i
$$467$$ −1.38704 + 0.275899i −1.38704 + 0.275899i −0.831470 0.555570i $$-0.812500\pi$$
−0.555570 + 0.831470i $$0.687500\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ −0.785695 0.785695i −0.785695 0.785695i
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 1.30656 0.541196i 1.30656 0.541196i
$$475$$ −1.63099 0.324423i −1.63099 0.324423i
$$476$$ 0 0
$$477$$ 0.636379 + 0.425215i 0.636379 + 0.425215i
$$478$$ 0 0
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ −0.980785 + 0.195090i −0.980785 + 0.195090i
$$481$$ 0 0
$$482$$ −1.53636 1.02656i −1.53636 1.02656i
$$483$$ 0 0
$$484$$ 1.00000i 1.00000i
$$485$$ 0 0
$$486$$ −0.382683 0.923880i −0.382683 0.923880i
$$487$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$488$$ 1.66294i 1.66294i
$$489$$ 0 0
$$490$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$491$$ 0 0 −0.555570 0.831470i $$-0.687500\pi$$
0.555570 + 0.831470i $$0.312500\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 1.30656 + 1.30656i 1.30656 + 1.30656i
$$497$$ 0 0
$$498$$ 0.149316 0.750661i 0.149316 0.750661i
$$499$$ −0.382683 1.92388i −0.382683 1.92388i −0.382683 0.923880i $$-0.625000\pi$$
1.00000i $$-0.5\pi$$
$$500$$ 0.195090 0.980785i 0.195090 0.980785i
$$501$$ −0.324423 + 0.216773i −0.324423 + 0.216773i
$$502$$ 0 0
$$503$$ −0.425215 1.02656i −0.425215 1.02656i −0.980785 0.195090i $$-0.937500\pi$$
0.555570 0.831470i $$-0.312500\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −0.195090 + 0.980785i −0.195090 + 0.980785i
$$508$$ 0 0
$$509$$ 0 0 0.555570 0.831470i $$-0.312500\pi$$
−0.555570 + 0.831470i $$0.687500\pi$$
$$510$$ −0.382683 + 0.0761205i −0.382683 + 0.0761205i
$$511$$ 0 0
$$512$$ 0.195090 + 0.980785i 0.195090 + 0.980785i
$$513$$ −1.66294 −1.66294
$$514$$ −1.92388 + 0.382683i −1.92388 + 0.382683i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ −0.707107 + 1.70711i −0.707107 + 1.70711i
$$520$$ 0 0
$$521$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$522$$ 0 0
$$523$$ 0 0 0.831470 0.555570i $$-0.187500\pi$$
−0.831470 + 0.555570i $$0.812500\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ −0.0761205 + 0.382683i −0.0761205 + 0.382683i
$$527$$ 0.509796 + 0.509796i 0.509796 + 0.509796i
$$528$$ 0 0
$$529$$ 2.01367 2.01367i 2.01367 2.01367i
$$530$$ 0.425215 + 0.636379i 0.425215 + 0.636379i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ −1.70711 + 0.707107i −1.70711 + 0.707107i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 1.00000i 1.00000i
$$541$$ 0.324423 + 0.216773i 0.324423 + 0.216773i 0.707107 0.707107i $$-0.250000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$542$$ 0 0
$$543$$ 0.390181i 0.390181i
$$544$$ 0.0761205 + 0.382683i 0.0761205 + 0.382683i
$$545$$ 1.11114i 1.11114i
$$546$$ 0 0
$$547$$ 0 0 −0.831470 0.555570i $$-0.812500\pi$$
0.831470 + 0.555570i $$0.187500\pi$$
$$548$$ −0.785695 0.785695i −0.785695 0.785695i
$$549$$ 1.63099 + 0.324423i 1.63099 + 0.324423i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0.750661 + 1.81225i 0.750661 + 1.81225i
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ −1.08979 + 1.63099i −1.08979 + 1.63099i
$$557$$ −0.750661 + 0.149316i −0.750661 + 0.149316i −0.555570 0.831470i $$-0.687500\pi$$
−0.195090 + 0.980785i $$0.562500\pi$$
$$558$$ −1.53636 + 1.02656i −1.53636 + 1.02656i
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0.275899 + 1.38704i 0.275899 + 1.38704i 0.831470 + 0.555570i $$0.187500\pi$$
−0.555570 + 0.831470i $$0.687500\pi$$
$$564$$ −0.617317 0.923880i −0.617317 0.923880i
$$565$$ 0.923880 0.617317i 0.923880 0.617317i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 0 0 0.382683 0.923880i $$-0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$570$$ −1.53636 0.636379i −1.53636 0.636379i
$$571$$ 0.382683 1.92388i 0.382683 1.92388i 1.00000i $$-0.5\pi$$
0.382683 0.923880i $$-0.375000\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −1.96157 −1.96157
$$576$$ −1.00000 −1.00000
$$577$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$578$$ −0.165390 0.831470i −0.165390 0.831470i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0.765367 0.765367
$$587$$ 1.53636 1.02656i 1.53636 1.02656i 0.555570 0.831470i $$-0.312500\pi$$
0.980785 0.195090i $$-0.0625000\pi$$
$$588$$ −0.831470 + 0.555570i −0.831470 + 0.555570i
$$589$$ 0.599456 + 3.01367i 0.599456 + 3.01367i
$$590$$ 0 0
$$591$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$592$$ 0 0
$$593$$ 1.38704 1.38704i 1.38704 1.38704i 0.555570 0.831470i $$-0.312500\pi$$
0.831470 0.555570i $$-0.187500\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −0.785695 1.17588i −0.785695 1.17588i
$$598$$ 0 0
$$599$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$600$$ 0.382683 0.923880i 0.382683 0.923880i
$$601$$ −0.707107 0.292893i −0.707107 0.292893i 1.00000i $$-0.5\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −0.541196 + 0.541196i −0.541196 + 0.541196i
$$605$$ 0.831470 + 0.555570i 0.831470 + 0.555570i
$$606$$ 0 0
$$607$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$608$$ −0.636379 + 1.53636i −0.636379 + 1.53636i
$$609$$ 0 0
$$610$$ 1.38268 + 0.923880i 1.38268 + 0.923880i
$$611$$ 0 0
$$612$$ −0.390181 −0.390181
$$613$$ 0 0 −0.980785 0.195090i $$-0.937500\pi$$
0.980785 + 0.195090i $$0.0625000\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −1.02656 + 0.425215i −1.02656 + 0.425215i −0.831470 0.555570i $$-0.812500\pi$$
−0.195090 + 0.980785i $$0.562500\pi$$
$$618$$ 0 0
$$619$$ −0.617317 0.923880i −0.617317 0.923880i 0.382683 0.923880i $$-0.375000\pi$$
−1.00000 $$\pi$$
$$620$$ −1.81225 + 0.360480i −1.81225 + 0.360480i
$$621$$ −1.92388 + 0.382683i −1.92388 + 0.382683i
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$632$$ 1.38704 + 0.275899i 1.38704 + 0.275899i
$$633$$ 0.425215 1.02656i 0.425215 1.02656i
$$634$$ 0.541196 1.30656i 0.541196 1.30656i
$$635$$ 0 0
$$636$$ 0.292893 + 0.707107i 0.292893 + 0.707107i
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ −0.923880 0.382683i −0.923880 0.382683i
$$641$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$642$$ −1.81225 + 0.360480i −1.81225 + 0.360480i
$$643$$ 0 0 0.555570 0.831470i $$-0.312500\pi$$
−0.555570 + 0.831470i $$0.687500\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −0.248303 + 0.599456i −0.248303 + 0.599456i
$$647$$ −0.636379 + 1.53636i −0.636379 + 1.53636i 0.195090 + 0.980785i $$0.437500\pi$$
−0.831470 + 0.555570i $$0.812500\pi$$
$$648$$ 0.195090 0.980785i 0.195090 0.980785i
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −0.360480 1.81225i −0.360480 1.81225i −0.555570 0.831470i $$-0.687500\pi$$
0.195090 0.980785i $$-0.437500\pi$$
$$654$$ 0.216773 1.08979i 0.216773 1.08979i
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 0.980785 0.195090i $$-0.0625000\pi$$
−0.980785 + 0.195090i $$0.937500\pi$$
$$660$$ 0 0
$$661$$ −0.617317 0.923880i −0.617317 0.923880i 0.382683 0.923880i $$-0.375000\pi$$
−1.00000 $$\pi$$
$$662$$ −0.275899 + 0.275899i −0.275899 + 0.275899i
$$663$$ 0 0
$$664$$ 0.541196 0.541196i 0.541196 0.541196i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ −0.390181 −0.390181
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$674$$ 0 0
$$675$$ 0.831470 + 0.555570i 0.831470 + 0.555570i
$$676$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$677$$ 1.81225 + 0.360480i 1.81225 + 0.360480i 0.980785 0.195090i $$-0.0625000\pi$$
0.831470 + 0.555570i $$0.187500\pi$$
$$678$$ 1.02656 0.425215i 1.02656 0.425215i
$$679$$ 0 0
$$680$$ −0.360480 0.149316i −0.360480 0.149316i
$$681$$ −0.707107 + 0.292893i −0.707107 + 0.292893i
$$682$$ 0 0
$$683$$ 0.785695 + 1.17588i 0.785695 + 1.17588i 0.980785 + 0.195090i $$0.0625000\pi$$
−0.195090 + 0.980785i $$0.562500\pi$$
$$684$$ −1.38268 0.923880i −1.38268 0.923880i
$$685$$ 1.08979 0.216773i 1.08979 0.216773i
$$686$$ 0 0
$$687$$ 1.38704 1.38704i 1.38704 1.38704i
$$688$$ 0 0
$$689$$ 0 0
$$690$$ −1.92388 0.382683i −1.92388 0.382683i
$$691$$ 0.0761205 + 0.382683i 0.0761205 + 0.382683i 1.00000 $$0$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$692$$ −1.53636 + 1.02656i −1.53636 + 1.02656i
$$693$$ 0 0
$$694$$ −1.41421 −1.41421
$$695$$ −0.750661 1.81225i −0.750661 1.81225i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 1.53636 + 0.636379i 1.53636 + 0.636379i
$$699$$ −0.382683 + 1.92388i −0.382683 + 1.92388i
$$700$$ 0 0
$$701$$ 0 0 0.555570 0.831470i $$-0.312500\pi$$
−0.555570 + 0.831470i $$0.687500\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 1.11114 1.11114
$$706$$ −0.324423 1.63099i −0.324423 1.63099i
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −0.324423 + 1.63099i −0.324423 + 1.63099i 0.382683 + 0.923880i $$0.375000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$710$$ 0 0
$$711$$ −0.541196 + 1.30656i −0.541196 + 1.30656i
$$712$$ 0 0
$$713$$ 1.38704 + 3.34861i 1.38704 + 3.34861i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$720$$ 0.555570 0.831470i 0.555570 0.831470i
$$721$$ 0 0
$$722$$ −1.46785 + 0.980785i −1.46785 + 0.980785i
$$723$$ 1.81225 0.360480i 1.81225 0.360480i
$$724$$ 0.216773 0.324423i 0.216773 0.324423i
$$725$$ 0 0
$$726$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$727$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$728$$ 0 0
$$729$$ 0.923880 + 0.382683i 0.923880 + 0.382683i
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 1.17588 + 1.17588i 1.17588 + 1.17588i
$$733$$ 0 0 −0.831470 0.555570i $$-0.812500\pi$$
0.831470 + 0.555570i $$0.187500\pi$$
$$734$$ 0 0
$$735$$ 1.00000i 1.00000i
$$736$$ −0.382683 + 1.92388i −0.382683 + 1.92388i
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0.923880 + 0.617317i 0.923880 + 0.617317i 0.923880 0.382683i $$-0.125000\pi$$
1.00000i $$0.5\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −1.53636 0.636379i −1.53636 0.636379i −0.555570 0.831470i $$-0.687500\pi$$
−0.980785 + 0.195090i $$0.937500\pi$$
$$744$$ −1.84776 −1.84776
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0.425215 + 0.636379i 0.425215 + 0.636379i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0.555570 + 0.831470i 0.555570 + 0.831470i
$$751$$ −1.30656 + 1.30656i −1.30656 + 1.30656i −0.382683 + 0.923880i $$0.625000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$752$$ 1.11114i 1.11114i
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −0.149316 0.750661i −0.149316 0.750661i
$$756$$ 0 0
$$757$$ 0 0 0.831470 0.555570i $$-0.187500\pi$$
−0.831470 + 0.555570i $$0.812500\pi$$
$$758$$ 0.390181i 0.390181i
$$759$$ 0 0
$$760$$ −0.923880 1.38268i −0.923880 1.38268i
$$761$$ 0 0 0.382683 0.923880i $$-0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0.216773 0.324423i 0.216773 0.324423i
$$766$$ −1.63099 + 0.324423i −1.63099 + 0.324423i
$$767$$ 0 0
$$768$$ −0.831470 0.555570i −0.831470 0.555570i
$$769$$ −1.84776 −1.84776 −0.923880 0.382683i $$-0.875000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$770$$ 0 0
$$771$$ 1.08979 1.63099i 1.08979 1.63099i
$$772$$ 0 0
$$773$$ 0 0 −0.980785 0.195090i $$-0.937500\pi$$
0.980785 + 0.195090i $$0.0625000\pi$$
$$774$$ 0 0
$$775$$ 0.707107 1.70711i 0.707107 1.70711i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ −0.149316 + 0.750661i −0.149316 + 0.750661i
$$783$$ 0 0
$$784$$ −1.00000 −1.00000
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 0 0 0.980785 0.195090i $$-0.0625000\pi$$
−0.980785 + 0.195090i $$0.937500\pi$$
$$788$$ 0.275899 + 1.38704i 0.275899 + 1.38704i
$$789$$ −0.216773 0.324423i −0.216773 0.324423i
$$790$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ −0.750661 0.149316i −0.750661 0.149316i
$$796$$ 1.41421i 1.41421i
$$797$$ −1.17588 0.785695i −1.17588 0.785695i −0.195090 0.980785i $$-0.562500\pi$$
−0.980785 + 0.195090i $$0.937500\pi$$