# Properties

 Label 712.1.y.a.539.1 Level $712$ Weight $1$ Character 712.539 Analytic conductor $0.355$ Analytic rank $0$ Dimension $20$ Projective image $D_{44}$ CM discriminant -8 Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$712 = 2^{3} \cdot 89$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 712.y (of order $$44$$, degree $$20$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.355334288995$$ Analytic rank: $$0$$ Dimension: $$20$$ Coefficient field: $$\Q(\zeta_{44})$$ Defining polynomial: $$x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{44}$$ Projective field: Galois closure of $$\mathbb{Q}[x]/(x^{44} - \cdots)$$

## Embedding invariants

 Embedding label 539.1 Root $$0.909632 + 0.415415i$$ of defining polynomial Character $$\chi$$ $$=$$ 712.539 Dual form 712.1.y.a.107.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.654861 - 0.755750i) q^{2} +(0.559521 - 0.418852i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.0498610 - 0.697148i) q^{6} +(-0.841254 - 0.540641i) q^{8} +(-0.144106 + 0.490780i) q^{9} +O(q^{10})$$ $$q+(0.654861 - 0.755750i) q^{2} +(0.559521 - 0.418852i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.0498610 - 0.697148i) q^{6} +(-0.841254 - 0.540641i) q^{8} +(-0.144106 + 0.490780i) q^{9} +(0.909632 - 0.584585i) q^{11} +(-0.494217 - 0.494217i) q^{12} +(-0.959493 + 0.281733i) q^{16} +(-0.989821 + 0.857685i) q^{17} +(0.276537 + 0.430300i) q^{18} +(-0.373128 + 0.203743i) q^{19} +(0.153882 - 1.07028i) q^{22} +(-0.697148 + 0.0498610i) q^{24} +(-0.415415 - 0.909632i) q^{25} +(0.369184 + 0.989821i) q^{27} +(-0.415415 + 0.909632i) q^{32} +(0.264103 - 0.708089i) q^{33} +1.30972i q^{34} +(0.506293 + 0.0727939i) q^{36} +(-0.0903680 + 0.415415i) q^{38} +(-0.847507 + 1.13214i) q^{41} +(1.94931 + 0.424047i) q^{43} +(-0.708089 - 0.817178i) q^{44} +(-0.418852 + 0.559521i) q^{48} +(-0.909632 + 0.415415i) q^{49} +(-0.959493 - 0.281733i) q^{50} +(-0.194583 + 0.894482i) q^{51} +(0.989821 + 0.369184i) q^{54} +(-0.123435 + 0.270284i) q^{57} +(-0.114220 - 0.0855040i) q^{59} +(0.415415 + 0.909632i) q^{64} +(-0.362187 - 0.663296i) q^{66} +(0.0801894 - 0.557730i) q^{67} +(0.989821 + 0.857685i) q^{68} +(0.386565 - 0.334961i) q^{72} +(1.74557 - 0.512546i) q^{73} +(-0.613435 - 0.334961i) q^{75} +(0.254771 + 0.340335i) q^{76} +(0.190855 + 0.122655i) q^{81} +(0.300613 + 1.38189i) q^{82} +(0.114220 - 1.59700i) q^{83} +(1.59700 - 1.19550i) q^{86} -1.08128 q^{88} +(-0.415415 + 0.909632i) q^{89} +(0.148568 + 0.682956i) q^{96} +(-1.61435 - 1.03748i) q^{97} +(-0.281733 + 0.959493i) q^{98} +(0.155819 + 0.530671i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$20q + 2q^{2} - 2q^{3} - 2q^{4} + 2q^{6} + 2q^{8} + O(q^{10})$$ $$20q + 2q^{2} - 2q^{3} - 2q^{4} + 2q^{6} + 2q^{8} - 2q^{12} - 2q^{16} - 2q^{19} + 2q^{24} + 2q^{25} - 22q^{27} + 2q^{32} - 20q^{38} + 2q^{41} + 2q^{43} - 2q^{48} - 2q^{50} + 4q^{51} - 4q^{57} - 2q^{59} - 2q^{64} + 22q^{72} + 2q^{75} - 2q^{76} - 2q^{81} - 2q^{82} + 2q^{83} - 2q^{86} + 2q^{89} + 2q^{96} - 4q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/712\mathbb{Z}\right)^\times$$.

 $$n$$ $$357$$ $$535$$ $$537$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$e\left(\frac{35}{44}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.654861 0.755750i 0.654861 0.755750i
$$3$$ 0.559521 0.418852i 0.559521 0.418852i −0.281733 0.959493i $$-0.590909\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$4$$ −0.142315 0.989821i −0.142315 0.989821i
$$5$$ 0 0 0.540641 0.841254i $$-0.318182\pi$$
−0.540641 + 0.841254i $$0.681818\pi$$
$$6$$ 0.0498610 0.697148i 0.0498610 0.697148i
$$7$$ 0 0 −0.212565 0.977147i $$-0.568182\pi$$
0.212565 + 0.977147i $$0.431818\pi$$
$$8$$ −0.841254 0.540641i −0.841254 0.540641i
$$9$$ −0.144106 + 0.490780i −0.144106 + 0.490780i
$$10$$ 0 0
$$11$$ 0.909632 0.584585i 0.909632 0.584585i 1.00000i $$-0.5\pi$$
0.909632 + 0.415415i $$0.136364\pi$$
$$12$$ −0.494217 0.494217i −0.494217 0.494217i
$$13$$ 0 0 −0.599278 0.800541i $$-0.704545\pi$$
0.599278 + 0.800541i $$0.295455\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −0.959493 + 0.281733i −0.959493 + 0.281733i
$$17$$ −0.989821 + 0.857685i −0.989821 + 0.857685i −0.989821 0.142315i $$-0.954545\pi$$
1.00000i $$0.5\pi$$
$$18$$ 0.276537 + 0.430300i 0.276537 + 0.430300i
$$19$$ −0.373128 + 0.203743i −0.373128 + 0.203743i −0.654861 0.755750i $$-0.727273\pi$$
0.281733 + 0.959493i $$0.409091\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0.153882 1.07028i 0.153882 1.07028i
$$23$$ 0 0 −0.479249 0.877679i $$-0.659091\pi$$
0.479249 + 0.877679i $$0.340909\pi$$
$$24$$ −0.697148 + 0.0498610i −0.697148 + 0.0498610i
$$25$$ −0.415415 0.909632i −0.415415 0.909632i
$$26$$ 0 0
$$27$$ 0.369184 + 0.989821i 0.369184 + 0.989821i
$$28$$ 0 0
$$29$$ 0 0 0.977147 0.212565i $$-0.0681818\pi$$
−0.977147 + 0.212565i $$0.931818\pi$$
$$30$$ 0 0
$$31$$ 0 0 0.479249 0.877679i $$-0.340909\pi$$
−0.479249 + 0.877679i $$0.659091\pi$$
$$32$$ −0.415415 + 0.909632i −0.415415 + 0.909632i
$$33$$ 0.264103 0.708089i 0.264103 0.708089i
$$34$$ 1.30972i 1.30972i
$$35$$ 0 0
$$36$$ 0.506293 + 0.0727939i 0.506293 + 0.0727939i
$$37$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$38$$ −0.0903680 + 0.415415i −0.0903680 + 0.415415i
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −0.847507 + 1.13214i −0.847507 + 1.13214i 0.142315 + 0.989821i $$0.454545\pi$$
−0.989821 + 0.142315i $$0.954545\pi$$
$$42$$ 0 0
$$43$$ 1.94931 + 0.424047i 1.94931 + 0.424047i 0.989821 + 0.142315i $$0.0454545\pi$$
0.959493 + 0.281733i $$0.0909091\pi$$
$$44$$ −0.708089 0.817178i −0.708089 0.817178i
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 0.989821 0.142315i $$-0.0454545\pi$$
−0.989821 + 0.142315i $$0.954545\pi$$
$$48$$ −0.418852 + 0.559521i −0.418852 + 0.559521i
$$49$$ −0.909632 + 0.415415i −0.909632 + 0.415415i
$$50$$ −0.959493 0.281733i −0.959493 0.281733i
$$51$$ −0.194583 + 0.894482i −0.194583 + 0.894482i
$$52$$ 0 0
$$53$$ 0 0 −0.989821 0.142315i $$-0.954545\pi$$
0.989821 + 0.142315i $$0.0454545\pi$$
$$54$$ 0.989821 + 0.369184i 0.989821 + 0.369184i
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −0.123435 + 0.270284i −0.123435 + 0.270284i
$$58$$ 0 0
$$59$$ −0.114220 0.0855040i −0.114220 0.0855040i 0.540641 0.841254i $$-0.318182\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$60$$ 0 0
$$61$$ 0 0 0.936950 0.349464i $$-0.113636\pi$$
−0.936950 + 0.349464i $$0.886364\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0.415415 + 0.909632i 0.415415 + 0.909632i
$$65$$ 0 0
$$66$$ −0.362187 0.663296i −0.362187 0.663296i
$$67$$ 0.0801894 0.557730i 0.0801894 0.557730i −0.909632 0.415415i $$-0.863636\pi$$
0.989821 0.142315i $$-0.0454545\pi$$
$$68$$ 0.989821 + 0.857685i 0.989821 + 0.857685i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 −0.540641 0.841254i $$-0.681818\pi$$
0.540641 + 0.841254i $$0.318182\pi$$
$$72$$ 0.386565 0.334961i 0.386565 0.334961i
$$73$$ 1.74557 0.512546i 1.74557 0.512546i 0.755750 0.654861i $$-0.227273\pi$$
0.989821 + 0.142315i $$0.0454545\pi$$
$$74$$ 0 0
$$75$$ −0.613435 0.334961i −0.613435 0.334961i
$$76$$ 0.254771 + 0.340335i 0.254771 + 0.340335i
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 −0.281733 0.959493i $$-0.590909\pi$$
0.281733 + 0.959493i $$0.409091\pi$$
$$80$$ 0 0
$$81$$ 0.190855 + 0.122655i 0.190855 + 0.122655i
$$82$$ 0.300613 + 1.38189i 0.300613 + 1.38189i
$$83$$ 0.114220 1.59700i 0.114220 1.59700i −0.540641 0.841254i $$-0.681818\pi$$
0.654861 0.755750i $$-0.272727\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 1.59700 1.19550i 1.59700 1.19550i
$$87$$ 0 0
$$88$$ −1.08128 −1.08128
$$89$$ −0.415415 + 0.909632i −0.415415 + 0.909632i
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0.148568 + 0.682956i 0.148568 + 0.682956i
$$97$$ −1.61435 1.03748i −1.61435 1.03748i −0.959493 0.281733i $$-0.909091\pi$$
−0.654861 0.755750i $$-0.727273\pi$$
$$98$$ −0.281733 + 0.959493i −0.281733 + 0.959493i
$$99$$ 0.155819 + 0.530671i 0.155819 + 0.530671i
$$100$$ −0.841254 + 0.540641i −0.841254 + 0.540641i
$$101$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$102$$ 0.548580 + 0.732817i 0.548580 + 0.732817i
$$103$$ 0 0 −0.877679 0.479249i $$-0.840909\pi$$
0.877679 + 0.479249i $$0.159091\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 0.841254 0.540641i $$-0.181818\pi$$
−0.841254 + 0.540641i $$0.818182\pi$$
$$108$$ 0.927206 0.506293i 0.927206 0.506293i
$$109$$ 0 0 −0.909632 0.415415i $$-0.863636\pi$$
0.909632 + 0.415415i $$0.136364\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −1.59700 + 0.114220i −1.59700 + 0.114220i −0.841254 0.540641i $$-0.818182\pi$$
−0.755750 + 0.654861i $$0.772727\pi$$
$$114$$ 0.123435 + 0.270284i 0.123435 + 0.270284i
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ −0.139418 + 0.0303285i −0.139418 + 0.0303285i
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 0.0702757 0.153882i 0.0702757 0.153882i
$$122$$ 0 0
$$123$$ 0.988434i 0.988434i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 0 0 0.212565 0.977147i $$-0.431818\pi$$
−0.212565 + 0.977147i $$0.568182\pi$$
$$128$$ 0.959493 + 0.281733i 0.959493 + 0.281733i
$$129$$ 1.26830 0.579211i 1.26830 0.579211i
$$130$$ 0 0
$$131$$ −0.822373 + 0.118239i −0.822373 + 0.118239i −0.540641 0.841254i $$-0.681818\pi$$
−0.281733 + 0.959493i $$0.590909\pi$$
$$132$$ −0.738467 0.160644i −0.738467 0.160644i
$$133$$ 0 0
$$134$$ −0.368991 0.425839i −0.368991 0.425839i
$$135$$ 0 0
$$136$$ 1.29639 0.186393i 1.29639 0.186393i
$$137$$ 0.0855040 0.114220i 0.0855040 0.114220i −0.755750 0.654861i $$-0.772727\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$138$$ 0 0
$$139$$ 1.61435 + 0.474017i 1.61435 + 0.474017i 0.959493 0.281733i $$-0.0909091\pi$$
0.654861 + 0.755750i $$0.272727\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0.511499i 0.511499i
$$145$$ 0 0
$$146$$ 0.755750 1.65486i 0.755750 1.65486i
$$147$$ −0.334961 + 0.613435i −0.334961 + 0.613435i
$$148$$ 0 0
$$149$$ 0 0 0.977147 0.212565i $$-0.0681818\pi$$
−0.977147 + 0.212565i $$0.931818\pi$$
$$150$$ −0.654861 + 0.244250i −0.654861 + 0.244250i
$$151$$ 0 0 −0.349464 0.936950i $$-0.613636\pi$$
0.349464 + 0.936950i $$0.386364\pi$$
$$152$$ 0.424047 + 0.0303285i 0.424047 + 0.0303285i
$$153$$ −0.278295 0.609382i −0.278295 0.609382i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0 0 −0.755750 0.654861i $$-0.772727\pi$$
0.755750 + 0.654861i $$0.227273\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0.217680 0.0639165i 0.217680 0.0639165i
$$163$$ −0.133682 1.86912i −0.133682 1.86912i −0.415415 0.909632i $$-0.636364\pi$$
0.281733 0.959493i $$-0.409091\pi$$
$$164$$ 1.24123 + 0.677760i 1.24123 + 0.677760i
$$165$$ 0 0
$$166$$ −1.13214 1.13214i −1.13214 1.13214i
$$167$$ 0 0 0.841254 0.540641i $$-0.181818\pi$$
−0.841254 + 0.540641i $$0.818182\pi$$
$$168$$ 0 0
$$169$$ −0.281733 + 0.959493i −0.281733 + 0.959493i
$$170$$ 0 0
$$171$$ −0.0462232 0.212484i −0.0462232 0.212484i
$$172$$ 0.142315 1.98982i 0.142315 1.98982i
$$173$$ 0 0 0.540641 0.841254i $$-0.318182\pi$$
−0.540641 + 0.841254i $$0.681818\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −0.708089 + 0.817178i −0.708089 + 0.817178i
$$177$$ −0.0997220 −0.0997220
$$178$$ 0.415415 + 0.909632i 0.415415 + 0.909632i
$$179$$ −1.91899 −1.91899 −0.959493 0.281733i $$-0.909091\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$180$$ 0 0
$$181$$ 0 0 0.800541 0.599278i $$-0.204545\pi$$
−0.800541 + 0.599278i $$0.795455\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −0.398983 + 1.35881i −0.398983 + 1.35881i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 −0.599278 0.800541i $$-0.704545\pi$$
0.599278 + 0.800541i $$0.295455\pi$$
$$192$$ 0.613435 + 0.334961i 0.613435 + 0.334961i
$$193$$ −0.0683785 0.956056i −0.0683785 0.956056i −0.909632 0.415415i $$-0.863636\pi$$
0.841254 0.540641i $$-0.181818\pi$$
$$194$$ −1.84125 + 0.540641i −1.84125 + 0.540641i
$$195$$ 0 0
$$196$$ 0.540641 + 0.841254i 0.540641 + 0.841254i
$$197$$ 0 0 0.877679 0.479249i $$-0.159091\pi$$
−0.877679 + 0.479249i $$0.840909\pi$$
$$198$$ 0.503094 + 0.229756i 0.503094 + 0.229756i
$$199$$ 0 0 −0.755750 0.654861i $$-0.772727\pi$$
0.755750 + 0.654861i $$0.227273\pi$$
$$200$$ −0.142315 + 0.989821i −0.142315 + 0.989821i
$$201$$ −0.188739 0.345649i −0.188739 0.345649i
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0.913069 + 0.0653040i 0.913069 + 0.0653040i
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −0.220304 + 0.403457i −0.220304 + 0.403457i
$$210$$ 0 0
$$211$$ 0.697148 1.86912i 0.697148 1.86912i 0.281733 0.959493i $$-0.409091\pi$$
0.415415 0.909632i $$-0.363636\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0.224560 1.03229i 0.224560 1.03229i
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0.762003 1.01792i 0.762003 1.01792i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0 0 −0.654861 0.755750i $$-0.727273\pi$$
0.654861 + 0.755750i $$0.272727\pi$$
$$224$$ 0 0
$$225$$ 0.506293 0.0727939i 0.506293 0.0727939i
$$226$$ −0.959493 + 1.28173i −0.959493 + 1.28173i
$$227$$ −1.65486 + 0.755750i −1.65486 + 0.755750i −0.654861 + 0.755750i $$0.727273\pi$$
−1.00000 $$\pi$$
$$228$$ 0.285100 + 0.0837128i 0.285100 + 0.0837128i
$$229$$ 0 0 0.212565 0.977147i $$-0.431818\pi$$
−0.212565 + 0.977147i $$0.568182\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0.284630i 0.284630i −0.989821 0.142315i $$-0.954545\pi$$
0.989821 0.142315i $$-0.0454545\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −0.0683785 + 0.125226i −0.0683785 + 0.125226i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 0.936950 0.349464i $$-0.113636\pi$$
−0.936950 + 0.349464i $$0.886364\pi$$
$$240$$ 0 0
$$241$$ 1.19550 + 0.0855040i 1.19550 + 0.0855040i 0.654861 0.755750i $$-0.272727\pi$$
0.540641 + 0.841254i $$0.318182\pi$$
$$242$$ −0.0702757 0.153882i −0.0702757 0.153882i
$$243$$ −0.895576 + 0.0640529i −0.895576 + 0.0640529i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0.747009 + 0.647287i 0.747009 + 0.647287i
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −0.605000 0.941398i −0.605000 0.941398i
$$250$$ 0 0
$$251$$ 0.273100 0.0801894i 0.273100 0.0801894i −0.142315 0.989821i $$-0.545455\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0.841254 0.540641i 0.841254 0.540641i
$$257$$ −0.474017 1.61435i −0.474017 1.61435i −0.755750 0.654861i $$-0.772727\pi$$
0.281733 0.959493i $$-0.409091\pi$$
$$258$$ 0.392818 1.33782i 0.392818 1.33782i
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −0.449181 + 0.698939i −0.449181 + 0.698939i
$$263$$ 0 0 −0.142315 0.989821i $$-0.545455\pi$$
0.142315 + 0.989821i $$0.454545\pi$$
$$264$$ −0.605000 + 0.452897i −0.605000 + 0.452897i
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0.148568 + 0.682956i 0.148568 + 0.682956i
$$268$$ −0.563465 −0.563465
$$269$$ 0 0 0.654861 0.755750i $$-0.272727\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$270$$ 0 0
$$271$$ 0 0 −0.142315 0.989821i $$-0.545455\pi$$
0.142315 + 0.989821i $$0.454545\pi$$
$$272$$ 0.708089 1.10181i 0.708089 1.10181i
$$273$$ 0 0
$$274$$ −0.0303285 0.139418i −0.0303285 0.139418i
$$275$$ −0.909632 0.584585i −0.909632 0.584585i
$$276$$ 0 0
$$277$$ 0 0 −0.281733 0.959493i $$-0.590909\pi$$
0.281733 + 0.959493i $$0.409091\pi$$
$$278$$ 1.41542 0.909632i 1.41542 0.909632i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 1.71524 + 0.936593i 1.71524 + 0.936593i 0.959493 + 0.281733i $$0.0909091\pi$$
0.755750 + 0.654861i $$0.227273\pi$$
$$282$$ 0 0
$$283$$ −1.89945 + 0.557730i −1.89945 + 0.557730i −0.909632 + 0.415415i $$0.863636\pi$$
−0.989821 + 0.142315i $$0.954545\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ −0.386565 0.334961i −0.386565 0.334961i
$$289$$ 0.101808 0.708089i 0.101808 0.708089i
$$290$$ 0 0
$$291$$ −1.33782 + 0.0956825i −1.33782 + 0.0956825i
$$292$$ −0.755750 1.65486i −0.755750 1.65486i
$$293$$ 0 0 −0.997452 0.0713392i $$-0.977273\pi$$
0.997452 + 0.0713392i $$0.0227273\pi$$
$$294$$ 0.244250 + 0.654861i 0.244250 + 0.654861i
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0.914457 + 0.684554i 0.914457 + 0.684554i
$$298$$ 0 0
$$299$$ 0 0
$$300$$ −0.244250 + 0.654861i −0.244250 + 0.654861i
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0.300613 0.300613i 0.300613 0.300613i
$$305$$ 0 0
$$306$$ −0.642785 0.188739i −0.642785 0.188739i
$$307$$ 0.258908 0.118239i 0.258908 0.118239i −0.281733 0.959493i $$-0.590909\pi$$
0.540641 + 0.841254i $$0.318182\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 −0.654861 0.755750i $$-0.727273\pi$$
0.654861 + 0.755750i $$0.272727\pi$$
$$312$$ 0 0
$$313$$ 0.936593 + 0.203743i 0.936593 + 0.203743i 0.654861 0.755750i $$-0.272727\pi$$
0.281733 + 0.959493i $$0.409091\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 0 0 −0.959493 0.281733i $$-0.909091\pi$$
0.959493 + 0.281733i $$0.0909091\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0.194583 0.521696i 0.194583 0.521696i
$$324$$ 0.0942450 0.206368i 0.0942450 0.206368i
$$325$$ 0 0
$$326$$ −1.50013 1.12299i −1.50013 1.12299i
$$327$$ 0 0
$$328$$ 1.32505 0.494217i 1.32505 0.494217i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −0.698939 1.53046i −0.698939 1.53046i −0.841254 0.540641i $$-0.818182\pi$$
0.142315 0.989821i $$-0.454545\pi$$
$$332$$ −1.59700 + 0.114220i −1.59700 + 0.114220i
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 1.71524 0.936593i 1.71524 0.936593i 0.755750 0.654861i $$-0.227273\pi$$
0.959493 0.281733i $$-0.0909091\pi$$
$$338$$ 0.540641 + 0.841254i 0.540641 + 0.841254i
$$339$$ −0.845715 + 0.732817i −0.845715 + 0.732817i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ −0.190855 0.104215i −0.190855 0.104215i
$$343$$ 0 0
$$344$$ −1.41061 1.41061i −1.41061 1.41061i
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0.557730 1.89945i 0.557730 1.89945i 0.142315 0.989821i $$-0.454545\pi$$
0.415415 0.909632i $$-0.363636\pi$$
$$348$$ 0 0
$$349$$ 0 0 −0.212565 0.977147i $$-0.568182\pi$$
0.212565 + 0.977147i $$0.431818\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0.153882 + 1.07028i 0.153882 + 1.07028i
$$353$$ −0.767317 + 0.574406i −0.767317 + 0.574406i −0.909632 0.415415i $$-0.863636\pi$$
0.142315 + 0.989821i $$0.454545\pi$$
$$354$$ −0.0653040 + 0.0753648i −0.0653040 + 0.0753648i
$$355$$ 0 0
$$356$$ 0.959493 + 0.281733i 0.959493 + 0.281733i
$$357$$ 0 0
$$358$$ −1.25667 + 1.45027i −1.25667 + 1.45027i
$$359$$ 0 0 0.800541 0.599278i $$-0.204545\pi$$
−0.800541 + 0.599278i $$0.795455\pi$$
$$360$$ 0 0
$$361$$ −0.442928 + 0.689209i −0.442928 + 0.689209i
$$362$$ 0 0
$$363$$ −0.0251332 0.115536i −0.0251332 0.115536i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 0.841254 0.540641i $$-0.181818\pi$$
−0.841254 + 0.540641i $$0.818182\pi$$
$$368$$ 0 0
$$369$$ −0.433499 0.579087i −0.433499 0.579087i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 0.755750 0.654861i $$-0.227273\pi$$
−0.755750 + 0.654861i $$0.772727\pi$$
$$374$$ 0.765644 + 1.19136i 0.765644 + 1.19136i
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 0.841254 + 1.54064i 0.841254 + 1.54064i 0.841254 + 0.540641i $$0.181818\pi$$
1.00000i $$0.500000\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 −0.349464 0.936950i $$-0.613636\pi$$
0.349464 + 0.936950i $$0.386364\pi$$
$$384$$ 0.654861 0.244250i 0.654861 0.244250i
$$385$$ 0 0
$$386$$ −0.767317 0.574406i −0.767317 0.574406i
$$387$$ −0.489022 + 0.895576i −0.489022 + 0.895576i
$$388$$ −0.797176 + 1.74557i −0.797176 + 1.74557i
$$389$$ 0 0 0.349464 0.936950i $$-0.386364\pi$$
−0.349464 + 0.936950i $$0.613636\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0.989821 + 0.142315i 0.989821 + 0.142315i
$$393$$ −0.410610 + 0.410610i −0.410610 + 0.410610i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0.503094 0.229756i 0.503094 0.229756i
$$397$$ 0 0 0.599278 0.800541i $$-0.295455\pi$$
−0.599278 + 0.800541i $$0.704545\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0.654861 + 0.755750i 0.654861 + 0.755750i
$$401$$ 0.368991 + 0.425839i 0.368991 + 0.425839i 0.909632 0.415415i $$-0.136364\pi$$
−0.540641 + 0.841254i $$0.681818\pi$$
$$402$$ −0.384822 0.0837128i −0.384822 0.0837128i
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0.647287 0.647287i 0.647287 0.647287i
$$409$$ 1.89945 + 0.273100i 1.89945 + 0.273100i 0.989821 0.142315i $$-0.0454545\pi$$
0.909632 + 0.415415i $$0.136364\pi$$
$$410$$ 0 0
$$411$$ 0.0997220i 0.0997220i
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 1.10181 0.410953i 1.10181 0.410953i
$$418$$ 0.160644 + 0.430703i 0.160644 + 0.430703i
$$419$$ −0.956056 0.0683785i −0.956056 0.0683785i −0.415415 0.909632i $$-0.636364\pi$$
−0.540641 + 0.841254i $$0.681818\pi$$
$$420$$ 0 0
$$421$$ 0 0 0.997452 0.0713392i $$-0.0227273\pi$$
−0.997452 + 0.0713392i $$0.977273\pi$$
$$422$$ −0.956056 1.75089i −0.956056 1.75089i
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 1.19136 + 0.544078i 1.19136 + 0.544078i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 −0.877679 0.479249i $$-0.840909\pi$$
0.877679 + 0.479249i $$0.159091\pi$$
$$432$$ −0.633095 0.845715i −0.633095 0.845715i
$$433$$ 1.32505 + 1.32505i 1.32505 + 1.32505i 0.909632 + 0.415415i $$0.136364\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ −0.270284 1.24248i −0.270284 1.24248i
$$439$$ 0 0 0.0713392 0.997452i $$-0.477273\pi$$
−0.0713392 + 0.997452i $$0.522727\pi$$
$$440$$ 0 0
$$441$$ −0.0727939 0.506293i −0.0727939 0.506293i
$$442$$ 0 0
$$443$$ 1.29639 1.49611i 1.29639 1.49611i 0.540641 0.841254i $$-0.318182\pi$$
0.755750 0.654861i $$-0.227273\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 0.281733 + 1.95949i 0.281733 + 1.95949i 0.281733 + 0.959493i $$0.409091\pi$$
1.00000i $$0.500000\pi$$
$$450$$ 0.276537 0.430300i 0.276537 0.430300i
$$451$$ −0.109089 + 1.52527i −0.109089 + 1.52527i
$$452$$ 0.340335 + 1.56449i 0.340335 + 1.56449i
$$453$$ 0 0
$$454$$ −0.512546 + 1.74557i −0.512546 + 1.74557i
$$455$$ 0 0
$$456$$ 0.249967 0.160644i 0.249967 0.160644i
$$457$$ −1.24123 1.24123i −1.24123 1.24123i −0.959493 0.281733i $$-0.909091\pi$$
−0.281733 0.959493i $$-0.590909\pi$$
$$458$$ 0 0
$$459$$ −1.21438 0.663103i −1.21438 0.663103i
$$460$$ 0 0
$$461$$ 0 0 0.959493 0.281733i $$-0.0909091\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$462$$ 0 0
$$463$$ 0 0 −0.540641 0.841254i $$-0.681818\pi$$
0.540641 + 0.841254i $$0.318182\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ −0.215109 0.186393i −0.215109 0.186393i
$$467$$ −0.186393 + 1.29639i −0.186393 + 1.29639i 0.654861 + 0.755750i $$0.272727\pi$$
−0.841254 + 0.540641i $$0.818182\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0.0498610 + 0.133682i 0.0498610 + 0.133682i
$$473$$ 2.02105 0.753813i 2.02105 0.753813i
$$474$$ 0 0
$$475$$ 0.340335 + 0.254771i 0.340335 + 0.254771i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0.847507 0.847507i 0.847507 0.847507i
$$483$$ 0 0
$$484$$ −0.162317 0.0476607i −0.162317 0.0476607i
$$485$$ 0 0
$$486$$ −0.538070 + 0.718777i −0.538070 + 0.718777i
$$487$$ 0 0 0.989821 0.142315i $$-0.0454545\pi$$
−0.989821 + 0.142315i $$0.954545\pi$$
$$488$$ 0 0
$$489$$ −0.857685 0.989821i −0.857685 0.989821i
$$490$$ 0 0
$$491$$ 1.90963 + 0.415415i 1.90963 + 0.415415i 1.00000 $$0$$
0.909632 + 0.415415i $$0.136364\pi$$
$$492$$ 0.978373 0.140669i 0.978373 0.140669i
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ −1.10765 0.159256i −1.10765 0.159256i
$$499$$ 1.12299 + 0.418852i 1.12299 + 0.418852i 0.841254 0.540641i $$-0.181818\pi$$
0.281733 + 0.959493i $$0.409091\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0.118239 0.258908i 0.118239 0.258908i
$$503$$ 0 0 0.479249 0.877679i $$-0.340909\pi$$
−0.479249 + 0.877679i $$0.659091\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0.244250 + 0.654861i 0.244250 + 0.654861i
$$508$$ 0 0
$$509$$ 0 0 −0.415415 0.909632i $$-0.636364\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0.142315 0.989821i 0.142315 0.989821i
$$513$$ −0.339423 0.294111i −0.339423 0.294111i
$$514$$ −1.53046 0.698939i −1.53046 0.698939i
$$515$$ 0 0
$$516$$ −0.753813 1.17296i −0.753813 1.17296i
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 1.19550 + 1.59700i 1.19550 + 1.59700i 0.654861 + 0.755750i $$0.272727\pi$$
0.540641 + 0.841254i $$0.318182\pi$$
$$522$$ 0 0
$$523$$ −1.53046 + 0.983568i −1.53046 + 0.983568i −0.540641 + 0.841254i $$0.681818\pi$$
−0.989821 + 0.142315i $$0.954545\pi$$
$$524$$ 0.234072 + 0.797176i 0.234072 + 0.797176i
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ −0.0539138 + 0.753813i −0.0539138 + 0.753813i
$$529$$ −0.540641 + 0.841254i −0.540641 + 0.841254i
$$530$$ 0 0
$$531$$ 0.0584234 0.0437352i 0.0584234 0.0437352i
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0.613435 + 0.334961i 0.613435 + 0.334961i
$$535$$ 0 0
$$536$$ −0.368991 + 0.425839i −0.368991 + 0.425839i
$$537$$ −1.07371 + 0.803771i −1.07371 + 0.803771i
$$538$$ 0 0
$$539$$ −0.584585 + 0.909632i −0.584585 + 0.909632i
$$540$$ 0 0
$$541$$ 0 0 −0.212565 0.977147i $$-0.568182\pi$$
0.212565 + 0.977147i $$0.431818\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ −0.368991 1.25667i −0.368991 1.25667i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 1.17116 + 1.56449i 1.17116 + 1.56449i 0.755750 + 0.654861i $$0.227273\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$548$$ −0.125226 0.0683785i −0.125226 0.0683785i
$$549$$ 0 0
$$550$$ −1.03748 + 0.304632i −1.03748 + 0.304632i
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0.239446 1.66538i 0.239446 1.66538i
$$557$$ 0 0 −0.479249 0.877679i $$-0.659091\pi$$
0.479249 + 0.877679i $$0.340909\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0.345902 + 0.927399i 0.345902 + 0.927399i
$$562$$ 1.83107 0.682956i 1.83107 0.682956i
$$563$$ 1.90963 0.415415i 1.90963 0.415415i 0.909632 0.415415i $$-0.136364\pi$$
1.00000 $$0$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ −0.822373 + 1.80075i −0.822373 + 1.80075i
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −1.64468 0.613435i −1.64468 0.613435i −0.654861 0.755750i $$-0.727273\pi$$
−0.989821 + 0.142315i $$0.954545\pi$$
$$570$$ 0 0
$$571$$ −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i $$0.5\pi$$
−1.00000 $$\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −0.506293 + 0.0727939i −0.506293 + 0.0727939i
$$577$$ −0.415415 0.0903680i −0.415415 0.0903680i 1.00000i $$-0.5\pi$$
−0.415415 + 0.909632i $$0.636364\pi$$
$$578$$ −0.468468 0.540641i −0.468468 0.540641i
$$579$$ −0.438705 0.506293i −0.438705 0.506293i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ −0.803771 + 1.07371i −0.803771 + 1.07371i
$$583$$ 0 0
$$584$$ −1.74557 0.512546i −1.74557 0.512546i
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 1.66538 + 0.239446i 1.66538 + 0.239446i 0.909632 0.415415i $$-0.136364\pi$$
0.755750 + 0.654861i $$0.227273\pi$$
$$588$$ 0.654861 + 0.244250i 0.654861 + 0.244250i
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 1.40524 + 1.05195i 1.40524 + 1.05195i 0.989821 + 0.142315i $$0.0454545\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$594$$ 1.11619 0.242813i 1.11619 0.242813i
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 0.997452 0.0713392i $$-0.0227273\pi$$
−0.997452 + 0.0713392i $$0.977273\pi$$
$$600$$ 0.334961 + 0.613435i 0.334961 + 0.613435i
$$601$$ −0.118239 + 0.822373i −0.118239 + 0.822373i 0.841254 + 0.540641i $$0.181818\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$602$$ 0 0
$$603$$ 0.262167 + 0.119728i 0.262167 + 0.119728i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 0 0 0.959493 0.281733i $$-0.0909091\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$608$$ −0.0303285 0.424047i −0.0303285 0.424047i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ −0.563574 + 0.362187i −0.563574 + 0.362187i
$$613$$ 0 0 −0.281733 0.959493i $$-0.590909\pi$$
0.281733 + 0.959493i $$0.409091\pi$$
$$614$$ 0.0801894 0.273100i 0.0801894 0.273100i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0.133682 1.86912i 0.133682 1.86912i −0.281733 0.959493i $$-0.590909\pi$$
0.415415 0.909632i $$-0.363636\pi$$
$$618$$ 0 0
$$619$$ 0.118239 + 0.822373i 0.118239 + 0.822373i 0.959493 + 0.281733i $$0.0909091\pi$$
−0.841254 + 0.540641i $$0.818182\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −0.654861 + 0.755750i −0.654861 + 0.755750i
$$626$$ 0.767317 0.574406i 0.767317 0.574406i
$$627$$ 0.0457240 + 0.318017i 0.0457240 + 0.318017i
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 −0.841254 0.540641i $$-0.818182\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$632$$ 0 0
$$633$$ −0.392818 1.33782i −0.392818 1.33782i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0.449181 + 0.698939i 0.449181 + 0.698939i 0.989821 0.142315i $$-0.0454545\pi$$
−0.540641 + 0.841254i $$0.681818\pi$$
$$642$$ 0 0
$$643$$ −1.74557 0.797176i −1.74557 0.797176i −0.989821 0.142315i $$-0.954545\pi$$
−0.755750 0.654861i $$-0.772727\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −0.266847 0.488694i −0.266847 0.488694i
$$647$$ 0 0 0.997452 0.0713392i $$-0.0227273\pi$$
−0.997452 + 0.0713392i $$0.977273\pi$$
$$648$$ −0.0942450 0.206368i −0.0942450 0.206368i
$$649$$ −0.153882 0.0110059i −0.153882 0.0110059i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −1.83107 + 0.398326i −1.83107 + 0.398326i
$$653$$ 0 0 −0.800541 0.599278i $$-0.795455\pi$$
0.800541 + 0.599278i $$0.204545\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0.494217 1.32505i 0.494217 1.32505i
$$657$$ 0.930552i 0.930552i
$$658$$ 0 0
$$659$$ −0.822373 0.118239i −0.822373 0.118239i −0.281733 0.959493i $$-0.590909\pi$$
−0.540641 + 0.841254i $$0.681818\pi$$
$$660$$ 0 0
$$661$$ 0 0 0.212565 0.977147i $$-0.431818\pi$$
−0.212565 + 0.977147i $$0.568182\pi$$
$$662$$ −1.61435 0.474017i −1.61435 0.474017i
$$663$$ 0 0
$$664$$ −0.959493 + 1.28173i −0.959493 + 1.28173i
$$665$$ 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 0 0.281733 0.959493i $$-0.409091\pi$$
−0.281733 + 0.959493i $$0.590909\pi$$
$$674$$ 0.415415 1.90963i 0.415415 1.90963i
$$675$$ 0.747009 0.747009i 0.747009 0.747009i
$$676$$ 0.989821 + 0.142315i 0.989821 + 0.142315i
$$677$$ 0 0 −0.936950 0.349464i $$-0.886364\pi$$
0.936950 + 0.349464i $$0.113636\pi$$
$$678$$ 1.11904i 1.11904i
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −0.609382 + 1.11600i −0.609382 + 1.11600i
$$682$$ 0 0
$$683$$ 1.83107 0.398326i 1.83107 0.398326i 0.841254 0.540641i $$-0.181818\pi$$
0.989821 + 0.142315i $$0.0454545\pi$$
$$684$$ −0.203743 + 0.0759924i −0.203743 + 0.0759924i
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ −1.98982 + 0.142315i −1.98982 + 0.142315i
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −0.215109 0.186393i −0.215109 0.186393i 0.540641 0.841254i $$-0.318182\pi$$
−0.755750 + 0.654861i $$0.772727\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ −1.07028 1.66538i −1.07028 1.66538i
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −0.132136 1.84751i −0.132136 1.84751i
$$698$$ 0 0
$$699$$ −0.119218 0.159256i −0.119218 0.159256i
$$700$$ 0 0
$$701$$ 0 0 0.841254 0.540641i $$-0.181818\pi$$
−0.841254 + 0.540641i $$0.818182\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0.909632 + 0.584585i 0.909632 + 0.584585i
$$705$$ 0 0
$$706$$ −0.0683785 + 0.956056i −0.0683785 + 0.956056i
$$707$$ 0 0
$$708$$ 0.0141919 + 0.0987069i 0.0141919 + 0.0987069i
$$709$$ 0 0 0.800541 0.599278i $$-0.204545\pi$$
−0.800541 + 0.599278i $$0.795455\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0.841254 0.540641i 0.841254 0.540641i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0.273100 + 1.89945i 0.273100 + 1.89945i
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 −0.212565 0.977147i $$-0.568182\pi$$
0.212565 + 0.977147i $$0.431818\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0.230813 + 0.786078i 0.230813 + 0.786078i
$$723$$ 0.704722 0.452897i 0.704722 0.452897i
$$724$$ 0 0
$$725$$ 0 0
$$726$$ −0.103775 0.0566653i −0.103775 0.0566653i
$$727$$ 0 0 −0.0713392 0.997452i $$-0.522727\pi$$
0.0713392 + 0.997452i $$0.477273\pi$$
$$728$$ 0 0
$$729$$ −0.645722 + 0.559521i −0.645722 + 0.559521i
$$730$$ 0 0
$$731$$ −2.29317 + 1.25217i −2.29317 + 1.25217i
$$732$$ 0 0
$$733$$ 0 0 −0.755750 0.654861i $$-0.772727\pi$$
0.755750 + 0.654861i $$0.227273\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −0.253098 0.554206i −0.253098 0.554206i
$$738$$ −0.721526 0.0516046i −0.721526 0.0516046i
$$739$$ −0.334961 0.898064i −0.334961 0.898064i −0.989821 0.142315i $$-0.954545\pi$$
0.654861 0.755750i $$-0.272727\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 0.479249 0.877679i $$-0.340909\pi$$
−0.479249 + 0.877679i $$0.659091\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0.767317 + 0.286195i 0.767317 + 0.286195i
$$748$$ 1.40176 + 0.201543i 1.40176 + 0.201543i
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 −0.959493 0.281733i $$-0.909091\pi$$
0.959493 + 0.281733i $$0.0909091\pi$$
$$752$$ 0 0
$$753$$ 0.119218 0.159256i 0.119218 0.159256i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0 0 −0.654861 0.755750i $$-0.727273\pi$$
0.654861 + 0.755750i $$0.272727\pi$$
$$758$$ 1.71524 + 0.373128i 1.71524 + 0.373128i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −0.983568 + 0.449181i −0.983568 + 0.449181i −0.841254 0.540641i $$-0.818182\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0.244250 0.654861i 0.244250 0.654861i
$$769$$ 0.822373 1.80075i 0.822373 1.80075i 0.281733 0.959493i $$-0.409091\pi$$
0.540641 0.841254i $$-0.318182\pi$$
$$770$$ 0 0
$$771$$ −0.941398 0.704722i −0.941398 0.704722i
$$772$$ −0.936593 + 0.203743i −0.936593 + 0.203743i
$$773$$ 0 0 0.936950 0.349464i $$-0.113636\pi$$
−0.936950 + 0.349464i $$0.886364\pi$$
$$774$$ 0.356590 + 0.956056i 0.356590 + 0.956056i
$$775$$ 0 0
$$776$$ 0.797176 + 1.74557i 0.797176 + 1.74557i
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0.0855633 0.595106i 0.0855633 0.595106i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0.755750 0.654861i 0.755750 0.654861i
$$785$$ 0 0
$$786$$ 0.0414260 + 0.579211i 0.0414260 + 0.579211i
$$787$$ 1.05195 + 0.574406i 1.05195 + 0.574406i 0.909632 0.415415i $$-0.136364\pi$$
0.142315 + 0.989821i $$0.454545\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0.155819 0.530671i 0.155819 0.530671i
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0