# Properties

 Label 114.2.b.b.113.1 Level $114$ Weight $2$ Character 114.113 Analytic conductor $0.910$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$114 = 2 \cdot 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 114.b (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.910294583043$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 113.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 114.113 Dual form 114.2.b.b.113.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +(1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +3.46410i q^{5} +(-1.50000 + 0.866025i) q^{6} +1.00000 q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} +(1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +3.46410i q^{5} +(-1.50000 + 0.866025i) q^{6} +1.00000 q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} -3.46410i q^{10} -3.46410i q^{11} +(1.50000 - 0.866025i) q^{12} +1.73205i q^{13} -1.00000 q^{14} +(3.00000 + 5.19615i) q^{15} +1.00000 q^{16} +1.73205i q^{17} +(-1.50000 + 2.59808i) q^{18} +(-4.00000 - 1.73205i) q^{19} +3.46410i q^{20} +(1.50000 - 0.866025i) q^{21} +3.46410i q^{22} -5.19615i q^{23} +(-1.50000 + 0.866025i) q^{24} -7.00000 q^{25} -1.73205i q^{26} -5.19615i q^{27} +1.00000 q^{28} -9.00000 q^{29} +(-3.00000 - 5.19615i) q^{30} +10.3923i q^{31} -1.00000 q^{32} +(-3.00000 - 5.19615i) q^{33} -1.73205i q^{34} +3.46410i q^{35} +(1.50000 - 2.59808i) q^{36} -6.92820i q^{37} +(4.00000 + 1.73205i) q^{38} +(1.50000 + 2.59808i) q^{39} -3.46410i q^{40} +(-1.50000 + 0.866025i) q^{42} +2.00000 q^{43} -3.46410i q^{44} +(9.00000 + 5.19615i) q^{45} +5.19615i q^{46} +3.46410i q^{47} +(1.50000 - 0.866025i) q^{48} -6.00000 q^{49} +7.00000 q^{50} +(1.50000 + 2.59808i) q^{51} +1.73205i q^{52} +9.00000 q^{53} +5.19615i q^{54} +12.0000 q^{55} -1.00000 q^{56} +(-7.50000 + 0.866025i) q^{57} +9.00000 q^{58} +3.00000 q^{59} +(3.00000 + 5.19615i) q^{60} -8.00000 q^{61} -10.3923i q^{62} +(1.50000 - 2.59808i) q^{63} +1.00000 q^{64} -6.00000 q^{65} +(3.00000 + 5.19615i) q^{66} -8.66025i q^{67} +1.73205i q^{68} +(-4.50000 - 7.79423i) q^{69} -3.46410i q^{70} +12.0000 q^{71} +(-1.50000 + 2.59808i) q^{72} +11.0000 q^{73} +6.92820i q^{74} +(-10.5000 + 6.06218i) q^{75} +(-4.00000 - 1.73205i) q^{76} -3.46410i q^{77} +(-1.50000 - 2.59808i) q^{78} -6.92820i q^{79} +3.46410i q^{80} +(-4.50000 - 7.79423i) q^{81} +10.3923i q^{83} +(1.50000 - 0.866025i) q^{84} -6.00000 q^{85} -2.00000 q^{86} +(-13.5000 + 7.79423i) q^{87} +3.46410i q^{88} -6.00000 q^{89} +(-9.00000 - 5.19615i) q^{90} +1.73205i q^{91} -5.19615i q^{92} +(9.00000 + 15.5885i) q^{93} -3.46410i q^{94} +(6.00000 - 13.8564i) q^{95} +(-1.50000 + 0.866025i) q^{96} +13.8564i q^{97} +6.00000 q^{98} +(-9.00000 - 5.19615i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 2 q^{2} + 3 q^{3} + 2 q^{4} - 3 q^{6} + 2 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10})$$ 2 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 - 3 * q^6 + 2 * q^7 - 2 * q^8 + 3 * q^9 $$2 q - 2 q^{2} + 3 q^{3} + 2 q^{4} - 3 q^{6} + 2 q^{7} - 2 q^{8} + 3 q^{9} + 3 q^{12} - 2 q^{14} + 6 q^{15} + 2 q^{16} - 3 q^{18} - 8 q^{19} + 3 q^{21} - 3 q^{24} - 14 q^{25} + 2 q^{28} - 18 q^{29} - 6 q^{30} - 2 q^{32} - 6 q^{33} + 3 q^{36} + 8 q^{38} + 3 q^{39} - 3 q^{42} + 4 q^{43} + 18 q^{45} + 3 q^{48} - 12 q^{49} + 14 q^{50} + 3 q^{51} + 18 q^{53} + 24 q^{55} - 2 q^{56} - 15 q^{57} + 18 q^{58} + 6 q^{59} + 6 q^{60} - 16 q^{61} + 3 q^{63} + 2 q^{64} - 12 q^{65} + 6 q^{66} - 9 q^{69} + 24 q^{71} - 3 q^{72} + 22 q^{73} - 21 q^{75} - 8 q^{76} - 3 q^{78} - 9 q^{81} + 3 q^{84} - 12 q^{85} - 4 q^{86} - 27 q^{87} - 12 q^{89} - 18 q^{90} + 18 q^{93} + 12 q^{95} - 3 q^{96} + 12 q^{98} - 18 q^{99}+O(q^{100})$$ 2 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 - 3 * q^6 + 2 * q^7 - 2 * q^8 + 3 * q^9 + 3 * q^12 - 2 * q^14 + 6 * q^15 + 2 * q^16 - 3 * q^18 - 8 * q^19 + 3 * q^21 - 3 * q^24 - 14 * q^25 + 2 * q^28 - 18 * q^29 - 6 * q^30 - 2 * q^32 - 6 * q^33 + 3 * q^36 + 8 * q^38 + 3 * q^39 - 3 * q^42 + 4 * q^43 + 18 * q^45 + 3 * q^48 - 12 * q^49 + 14 * q^50 + 3 * q^51 + 18 * q^53 + 24 * q^55 - 2 * q^56 - 15 * q^57 + 18 * q^58 + 6 * q^59 + 6 * q^60 - 16 * q^61 + 3 * q^63 + 2 * q^64 - 12 * q^65 + 6 * q^66 - 9 * q^69 + 24 * q^71 - 3 * q^72 + 22 * q^73 - 21 * q^75 - 8 * q^76 - 3 * q^78 - 9 * q^81 + 3 * q^84 - 12 * q^85 - 4 * q^86 - 27 * q^87 - 12 * q^89 - 18 * q^90 + 18 * q^93 + 12 * q^95 - 3 * q^96 + 12 * q^98 - 18 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$$.

 $$n$$ $$77$$ $$97$$ $$\chi(n)$$ $$-1$$ $$-1$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 −0.707107
$$3$$ 1.50000 0.866025i 0.866025 0.500000i
$$4$$ 1.00000 0.500000
$$5$$ 3.46410i 1.54919i 0.632456 + 0.774597i $$0.282047\pi$$
−0.632456 + 0.774597i $$0.717953\pi$$
$$6$$ −1.50000 + 0.866025i −0.612372 + 0.353553i
$$7$$ 1.00000 0.377964 0.188982 0.981981i $$-0.439481\pi$$
0.188982 + 0.981981i $$0.439481\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ 1.50000 2.59808i 0.500000 0.866025i
$$10$$ 3.46410i 1.09545i
$$11$$ 3.46410i 1.04447i −0.852803 0.522233i $$-0.825099\pi$$
0.852803 0.522233i $$-0.174901\pi$$
$$12$$ 1.50000 0.866025i 0.433013 0.250000i
$$13$$ 1.73205i 0.480384i 0.970725 + 0.240192i $$0.0772105\pi$$
−0.970725 + 0.240192i $$0.922790\pi$$
$$14$$ −1.00000 −0.267261
$$15$$ 3.00000 + 5.19615i 0.774597 + 1.34164i
$$16$$ 1.00000 0.250000
$$17$$ 1.73205i 0.420084i 0.977692 + 0.210042i $$0.0673601\pi$$
−0.977692 + 0.210042i $$0.932640\pi$$
$$18$$ −1.50000 + 2.59808i −0.353553 + 0.612372i
$$19$$ −4.00000 1.73205i −0.917663 0.397360i
$$20$$ 3.46410i 0.774597i
$$21$$ 1.50000 0.866025i 0.327327 0.188982i
$$22$$ 3.46410i 0.738549i
$$23$$ 5.19615i 1.08347i −0.840548 0.541736i $$-0.817767\pi$$
0.840548 0.541736i $$-0.182233\pi$$
$$24$$ −1.50000 + 0.866025i −0.306186 + 0.176777i
$$25$$ −7.00000 −1.40000
$$26$$ 1.73205i 0.339683i
$$27$$ 5.19615i 1.00000i
$$28$$ 1.00000 0.188982
$$29$$ −9.00000 −1.67126 −0.835629 0.549294i $$-0.814897\pi$$
−0.835629 + 0.549294i $$0.814897\pi$$
$$30$$ −3.00000 5.19615i −0.547723 0.948683i
$$31$$ 10.3923i 1.86651i 0.359211 + 0.933257i $$0.383046\pi$$
−0.359211 + 0.933257i $$0.616954\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ −3.00000 5.19615i −0.522233 0.904534i
$$34$$ 1.73205i 0.297044i
$$35$$ 3.46410i 0.585540i
$$36$$ 1.50000 2.59808i 0.250000 0.433013i
$$37$$ 6.92820i 1.13899i −0.821995 0.569495i $$-0.807139\pi$$
0.821995 0.569495i $$-0.192861\pi$$
$$38$$ 4.00000 + 1.73205i 0.648886 + 0.280976i
$$39$$ 1.50000 + 2.59808i 0.240192 + 0.416025i
$$40$$ 3.46410i 0.547723i
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ −1.50000 + 0.866025i −0.231455 + 0.133631i
$$43$$ 2.00000 0.304997 0.152499 0.988304i $$-0.451268\pi$$
0.152499 + 0.988304i $$0.451268\pi$$
$$44$$ 3.46410i 0.522233i
$$45$$ 9.00000 + 5.19615i 1.34164 + 0.774597i
$$46$$ 5.19615i 0.766131i
$$47$$ 3.46410i 0.505291i 0.967559 + 0.252646i $$0.0813007\pi$$
−0.967559 + 0.252646i $$0.918699\pi$$
$$48$$ 1.50000 0.866025i 0.216506 0.125000i
$$49$$ −6.00000 −0.857143
$$50$$ 7.00000 0.989949
$$51$$ 1.50000 + 2.59808i 0.210042 + 0.363803i
$$52$$ 1.73205i 0.240192i
$$53$$ 9.00000 1.23625 0.618123 0.786082i $$-0.287894\pi$$
0.618123 + 0.786082i $$0.287894\pi$$
$$54$$ 5.19615i 0.707107i
$$55$$ 12.0000 1.61808
$$56$$ −1.00000 −0.133631
$$57$$ −7.50000 + 0.866025i −0.993399 + 0.114708i
$$58$$ 9.00000 1.18176
$$59$$ 3.00000 0.390567 0.195283 0.980747i $$-0.437437\pi$$
0.195283 + 0.980747i $$0.437437\pi$$
$$60$$ 3.00000 + 5.19615i 0.387298 + 0.670820i
$$61$$ −8.00000 −1.02430 −0.512148 0.858898i $$-0.671150\pi$$
−0.512148 + 0.858898i $$0.671150\pi$$
$$62$$ 10.3923i 1.31982i
$$63$$ 1.50000 2.59808i 0.188982 0.327327i
$$64$$ 1.00000 0.125000
$$65$$ −6.00000 −0.744208
$$66$$ 3.00000 + 5.19615i 0.369274 + 0.639602i
$$67$$ 8.66025i 1.05802i −0.848616 0.529009i $$-0.822564\pi$$
0.848616 0.529009i $$-0.177436\pi$$
$$68$$ 1.73205i 0.210042i
$$69$$ −4.50000 7.79423i −0.541736 0.938315i
$$70$$ 3.46410i 0.414039i
$$71$$ 12.0000 1.42414 0.712069 0.702109i $$-0.247758\pi$$
0.712069 + 0.702109i $$0.247758\pi$$
$$72$$ −1.50000 + 2.59808i −0.176777 + 0.306186i
$$73$$ 11.0000 1.28745 0.643726 0.765256i $$-0.277388\pi$$
0.643726 + 0.765256i $$0.277388\pi$$
$$74$$ 6.92820i 0.805387i
$$75$$ −10.5000 + 6.06218i −1.21244 + 0.700000i
$$76$$ −4.00000 1.73205i −0.458831 0.198680i
$$77$$ 3.46410i 0.394771i
$$78$$ −1.50000 2.59808i −0.169842 0.294174i
$$79$$ 6.92820i 0.779484i −0.920924 0.389742i $$-0.872564\pi$$
0.920924 0.389742i $$-0.127436\pi$$
$$80$$ 3.46410i 0.387298i
$$81$$ −4.50000 7.79423i −0.500000 0.866025i
$$82$$ 0 0
$$83$$ 10.3923i 1.14070i 0.821401 + 0.570352i $$0.193193\pi$$
−0.821401 + 0.570352i $$0.806807\pi$$
$$84$$ 1.50000 0.866025i 0.163663 0.0944911i
$$85$$ −6.00000 −0.650791
$$86$$ −2.00000 −0.215666
$$87$$ −13.5000 + 7.79423i −1.44735 + 0.835629i
$$88$$ 3.46410i 0.369274i
$$89$$ −6.00000 −0.635999 −0.317999 0.948091i $$-0.603011\pi$$
−0.317999 + 0.948091i $$0.603011\pi$$
$$90$$ −9.00000 5.19615i −0.948683 0.547723i
$$91$$ 1.73205i 0.181568i
$$92$$ 5.19615i 0.541736i
$$93$$ 9.00000 + 15.5885i 0.933257 + 1.61645i
$$94$$ 3.46410i 0.357295i
$$95$$ 6.00000 13.8564i 0.615587 1.42164i
$$96$$ −1.50000 + 0.866025i −0.153093 + 0.0883883i
$$97$$ 13.8564i 1.40690i 0.710742 + 0.703452i $$0.248359\pi$$
−0.710742 + 0.703452i $$0.751641\pi$$
$$98$$ 6.00000 0.606092
$$99$$ −9.00000 5.19615i −0.904534 0.522233i
$$100$$ −7.00000 −0.700000
$$101$$ 10.3923i 1.03407i −0.855963 0.517036i $$-0.827035\pi$$
0.855963 0.517036i $$-0.172965\pi$$
$$102$$ −1.50000 2.59808i −0.148522 0.257248i
$$103$$ 3.46410i 0.341328i −0.985329 0.170664i $$-0.945409\pi$$
0.985329 0.170664i $$-0.0545913\pi$$
$$104$$ 1.73205i 0.169842i
$$105$$ 3.00000 + 5.19615i 0.292770 + 0.507093i
$$106$$ −9.00000 −0.874157
$$107$$ −3.00000 −0.290021 −0.145010 0.989430i $$-0.546322\pi$$
−0.145010 + 0.989430i $$0.546322\pi$$
$$108$$ 5.19615i 0.500000i
$$109$$ 15.5885i 1.49310i 0.665327 + 0.746552i $$0.268292\pi$$
−0.665327 + 0.746552i $$0.731708\pi$$
$$110$$ −12.0000 −1.14416
$$111$$ −6.00000 10.3923i −0.569495 0.986394i
$$112$$ 1.00000 0.0944911
$$113$$ 12.0000 1.12887 0.564433 0.825479i $$-0.309095\pi$$
0.564433 + 0.825479i $$0.309095\pi$$
$$114$$ 7.50000 0.866025i 0.702439 0.0811107i
$$115$$ 18.0000 1.67851
$$116$$ −9.00000 −0.835629
$$117$$ 4.50000 + 2.59808i 0.416025 + 0.240192i
$$118$$ −3.00000 −0.276172
$$119$$ 1.73205i 0.158777i
$$120$$ −3.00000 5.19615i −0.273861 0.474342i
$$121$$ −1.00000 −0.0909091
$$122$$ 8.00000 0.724286
$$123$$ 0 0
$$124$$ 10.3923i 0.933257i
$$125$$ 6.92820i 0.619677i
$$126$$ −1.50000 + 2.59808i −0.133631 + 0.231455i
$$127$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ 3.00000 1.73205i 0.264135 0.152499i
$$130$$ 6.00000 0.526235
$$131$$ 3.46410i 0.302660i 0.988483 + 0.151330i $$0.0483556\pi$$
−0.988483 + 0.151330i $$0.951644\pi$$
$$132$$ −3.00000 5.19615i −0.261116 0.452267i
$$133$$ −4.00000 1.73205i −0.346844 0.150188i
$$134$$ 8.66025i 0.748132i
$$135$$ 18.0000 1.54919
$$136$$ 1.73205i 0.148522i
$$137$$ 8.66025i 0.739895i 0.929053 + 0.369948i $$0.120624\pi$$
−0.929053 + 0.369948i $$0.879376\pi$$
$$138$$ 4.50000 + 7.79423i 0.383065 + 0.663489i
$$139$$ −14.0000 −1.18746 −0.593732 0.804663i $$-0.702346\pi$$
−0.593732 + 0.804663i $$0.702346\pi$$
$$140$$ 3.46410i 0.292770i
$$141$$ 3.00000 + 5.19615i 0.252646 + 0.437595i
$$142$$ −12.0000 −1.00702
$$143$$ 6.00000 0.501745
$$144$$ 1.50000 2.59808i 0.125000 0.216506i
$$145$$ 31.1769i 2.58910i
$$146$$ −11.0000 −0.910366
$$147$$ −9.00000 + 5.19615i −0.742307 + 0.428571i
$$148$$ 6.92820i 0.569495i
$$149$$ 6.92820i 0.567581i 0.958886 + 0.283790i $$0.0915919\pi$$
−0.958886 + 0.283790i $$0.908408\pi$$
$$150$$ 10.5000 6.06218i 0.857321 0.494975i
$$151$$ 3.46410i 0.281905i 0.990016 + 0.140952i $$0.0450164\pi$$
−0.990016 + 0.140952i $$0.954984\pi$$
$$152$$ 4.00000 + 1.73205i 0.324443 + 0.140488i
$$153$$ 4.50000 + 2.59808i 0.363803 + 0.210042i
$$154$$ 3.46410i 0.279145i
$$155$$ −36.0000 −2.89159
$$156$$ 1.50000 + 2.59808i 0.120096 + 0.208013i
$$157$$ 4.00000 0.319235 0.159617 0.987179i $$-0.448974\pi$$
0.159617 + 0.987179i $$0.448974\pi$$
$$158$$ 6.92820i 0.551178i
$$159$$ 13.5000 7.79423i 1.07062 0.618123i
$$160$$ 3.46410i 0.273861i
$$161$$ 5.19615i 0.409514i
$$162$$ 4.50000 + 7.79423i 0.353553 + 0.612372i
$$163$$ 10.0000 0.783260 0.391630 0.920123i $$-0.371911\pi$$
0.391630 + 0.920123i $$0.371911\pi$$
$$164$$ 0 0
$$165$$ 18.0000 10.3923i 1.40130 0.809040i
$$166$$ 10.3923i 0.806599i
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ −1.50000 + 0.866025i −0.115728 + 0.0668153i
$$169$$ 10.0000 0.769231
$$170$$ 6.00000 0.460179
$$171$$ −10.5000 + 7.79423i −0.802955 + 0.596040i
$$172$$ 2.00000 0.152499
$$173$$ −6.00000 −0.456172 −0.228086 0.973641i $$-0.573247\pi$$
−0.228086 + 0.973641i $$0.573247\pi$$
$$174$$ 13.5000 7.79423i 1.02343 0.590879i
$$175$$ −7.00000 −0.529150
$$176$$ 3.46410i 0.261116i
$$177$$ 4.50000 2.59808i 0.338241 0.195283i
$$178$$ 6.00000 0.449719
$$179$$ −12.0000 −0.896922 −0.448461 0.893802i $$-0.648028\pi$$
−0.448461 + 0.893802i $$0.648028\pi$$
$$180$$ 9.00000 + 5.19615i 0.670820 + 0.387298i
$$181$$ 13.8564i 1.02994i 0.857209 + 0.514969i $$0.172197\pi$$
−0.857209 + 0.514969i $$0.827803\pi$$
$$182$$ 1.73205i 0.128388i
$$183$$ −12.0000 + 6.92820i −0.887066 + 0.512148i
$$184$$ 5.19615i 0.383065i
$$185$$ 24.0000 1.76452
$$186$$ −9.00000 15.5885i −0.659912 1.14300i
$$187$$ 6.00000 0.438763
$$188$$ 3.46410i 0.252646i
$$189$$ 5.19615i 0.377964i
$$190$$ −6.00000 + 13.8564i −0.435286 + 1.00525i
$$191$$ 19.0526i 1.37859i 0.724479 + 0.689297i $$0.242081\pi$$
−0.724479 + 0.689297i $$0.757919\pi$$
$$192$$ 1.50000 0.866025i 0.108253 0.0625000i
$$193$$ 3.46410i 0.249351i 0.992198 + 0.124676i $$0.0397891\pi$$
−0.992198 + 0.124676i $$0.960211\pi$$
$$194$$ 13.8564i 0.994832i
$$195$$ −9.00000 + 5.19615i −0.644503 + 0.372104i
$$196$$ −6.00000 −0.428571
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 9.00000 + 5.19615i 0.639602 + 0.369274i
$$199$$ 11.0000 0.779769 0.389885 0.920864i $$-0.372515\pi$$
0.389885 + 0.920864i $$0.372515\pi$$
$$200$$ 7.00000 0.494975
$$201$$ −7.50000 12.9904i −0.529009 0.916271i
$$202$$ 10.3923i 0.731200i
$$203$$ −9.00000 −0.631676
$$204$$ 1.50000 + 2.59808i 0.105021 + 0.181902i
$$205$$ 0 0
$$206$$ 3.46410i 0.241355i
$$207$$ −13.5000 7.79423i −0.938315 0.541736i
$$208$$ 1.73205i 0.120096i
$$209$$ −6.00000 + 13.8564i −0.415029 + 0.958468i
$$210$$ −3.00000 5.19615i −0.207020 0.358569i
$$211$$ 12.1244i 0.834675i −0.908752 0.417338i $$-0.862963\pi$$
0.908752 0.417338i $$-0.137037\pi$$
$$212$$ 9.00000 0.618123
$$213$$ 18.0000 10.3923i 1.23334 0.712069i
$$214$$ 3.00000 0.205076
$$215$$ 6.92820i 0.472500i
$$216$$ 5.19615i 0.353553i
$$217$$ 10.3923i 0.705476i
$$218$$ 15.5885i 1.05578i
$$219$$ 16.5000 9.52628i 1.11497 0.643726i
$$220$$ 12.0000 0.809040
$$221$$ −3.00000 −0.201802
$$222$$ 6.00000 + 10.3923i 0.402694 + 0.697486i
$$223$$ 10.3923i 0.695920i −0.937509 0.347960i $$-0.886874\pi$$
0.937509 0.347960i $$-0.113126\pi$$
$$224$$ −1.00000 −0.0668153
$$225$$ −10.5000 + 18.1865i −0.700000 + 1.21244i
$$226$$ −12.0000 −0.798228
$$227$$ 3.00000 0.199117 0.0995585 0.995032i $$-0.468257\pi$$
0.0995585 + 0.995032i $$0.468257\pi$$
$$228$$ −7.50000 + 0.866025i −0.496700 + 0.0573539i
$$229$$ −8.00000 −0.528655 −0.264327 0.964433i $$-0.585150\pi$$
−0.264327 + 0.964433i $$0.585150\pi$$
$$230$$ −18.0000 −1.18688
$$231$$ −3.00000 5.19615i −0.197386 0.341882i
$$232$$ 9.00000 0.590879
$$233$$ 6.92820i 0.453882i 0.973909 + 0.226941i $$0.0728724\pi$$
−0.973909 + 0.226941i $$0.927128\pi$$
$$234$$ −4.50000 2.59808i −0.294174 0.169842i
$$235$$ −12.0000 −0.782794
$$236$$ 3.00000 0.195283
$$237$$ −6.00000 10.3923i −0.389742 0.675053i
$$238$$ 1.73205i 0.112272i
$$239$$ 12.1244i 0.784259i −0.919910 0.392130i $$-0.871738\pi$$
0.919910 0.392130i $$-0.128262\pi$$
$$240$$ 3.00000 + 5.19615i 0.193649 + 0.335410i
$$241$$ 13.8564i 0.892570i −0.894891 0.446285i $$-0.852747\pi$$
0.894891 0.446285i $$-0.147253\pi$$
$$242$$ 1.00000 0.0642824
$$243$$ −13.5000 7.79423i −0.866025 0.500000i
$$244$$ −8.00000 −0.512148
$$245$$ 20.7846i 1.32788i
$$246$$ 0 0
$$247$$ 3.00000 6.92820i 0.190885 0.440831i
$$248$$ 10.3923i 0.659912i
$$249$$ 9.00000 + 15.5885i 0.570352 + 0.987878i
$$250$$ 6.92820i 0.438178i
$$251$$ 13.8564i 0.874609i −0.899314 0.437304i $$-0.855933\pi$$
0.899314 0.437304i $$-0.144067\pi$$
$$252$$ 1.50000 2.59808i 0.0944911 0.163663i
$$253$$ −18.0000 −1.13165
$$254$$ 0 0
$$255$$ −9.00000 + 5.19615i −0.563602 + 0.325396i
$$256$$ 1.00000 0.0625000
$$257$$ −6.00000 −0.374270 −0.187135 0.982334i $$-0.559920\pi$$
−0.187135 + 0.982334i $$0.559920\pi$$
$$258$$ −3.00000 + 1.73205i −0.186772 + 0.107833i
$$259$$ 6.92820i 0.430498i
$$260$$ −6.00000 −0.372104
$$261$$ −13.5000 + 23.3827i −0.835629 + 1.44735i
$$262$$ 3.46410i 0.214013i
$$263$$ 3.46410i 0.213606i −0.994280 0.106803i $$-0.965939\pi$$
0.994280 0.106803i $$-0.0340614\pi$$
$$264$$ 3.00000 + 5.19615i 0.184637 + 0.319801i
$$265$$ 31.1769i 1.91518i
$$266$$ 4.00000 + 1.73205i 0.245256 + 0.106199i
$$267$$ −9.00000 + 5.19615i −0.550791 + 0.317999i
$$268$$ 8.66025i 0.529009i
$$269$$ −18.0000 −1.09748 −0.548740 0.835993i $$-0.684892\pi$$
−0.548740 + 0.835993i $$0.684892\pi$$
$$270$$ −18.0000 −1.09545
$$271$$ −1.00000 −0.0607457 −0.0303728 0.999539i $$-0.509669\pi$$
−0.0303728 + 0.999539i $$0.509669\pi$$
$$272$$ 1.73205i 0.105021i
$$273$$ 1.50000 + 2.59808i 0.0907841 + 0.157243i
$$274$$ 8.66025i 0.523185i
$$275$$ 24.2487i 1.46225i
$$276$$ −4.50000 7.79423i −0.270868 0.469157i
$$277$$ −2.00000 −0.120168 −0.0600842 0.998193i $$-0.519137\pi$$
−0.0600842 + 0.998193i $$0.519137\pi$$
$$278$$ 14.0000 0.839664
$$279$$ 27.0000 + 15.5885i 1.61645 + 0.933257i
$$280$$ 3.46410i 0.207020i
$$281$$ 12.0000 0.715860 0.357930 0.933748i $$-0.383483\pi$$
0.357930 + 0.933748i $$0.383483\pi$$
$$282$$ −3.00000 5.19615i −0.178647 0.309426i
$$283$$ −10.0000 −0.594438 −0.297219 0.954809i $$-0.596059\pi$$
−0.297219 + 0.954809i $$0.596059\pi$$
$$284$$ 12.0000 0.712069
$$285$$ −3.00000 25.9808i −0.177705 1.53897i
$$286$$ −6.00000 −0.354787
$$287$$ 0 0
$$288$$ −1.50000 + 2.59808i −0.0883883 + 0.153093i
$$289$$ 14.0000 0.823529
$$290$$ 31.1769i 1.83077i
$$291$$ 12.0000 + 20.7846i 0.703452 + 1.21842i
$$292$$ 11.0000 0.643726
$$293$$ 21.0000 1.22683 0.613417 0.789760i $$-0.289795\pi$$
0.613417 + 0.789760i $$0.289795\pi$$
$$294$$ 9.00000 5.19615i 0.524891 0.303046i
$$295$$ 10.3923i 0.605063i
$$296$$ 6.92820i 0.402694i
$$297$$ −18.0000 −1.04447
$$298$$ 6.92820i 0.401340i
$$299$$ 9.00000 0.520483
$$300$$ −10.5000 + 6.06218i −0.606218 + 0.350000i
$$301$$ 2.00000 0.115278
$$302$$ 3.46410i 0.199337i
$$303$$ −9.00000 15.5885i −0.517036 0.895533i
$$304$$ −4.00000 1.73205i −0.229416 0.0993399i
$$305$$ 27.7128i 1.58683i
$$306$$ −4.50000 2.59808i −0.257248 0.148522i
$$307$$ 10.3923i 0.593120i −0.955014 0.296560i $$-0.904160\pi$$
0.955014 0.296560i $$-0.0958395\pi$$
$$308$$ 3.46410i 0.197386i
$$309$$ −3.00000 5.19615i −0.170664 0.295599i
$$310$$ 36.0000 2.04466
$$311$$ 22.5167i 1.27680i −0.769704 0.638401i $$-0.779596\pi$$
0.769704 0.638401i $$-0.220404\pi$$
$$312$$ −1.50000 2.59808i −0.0849208 0.147087i
$$313$$ 13.0000 0.734803 0.367402 0.930062i $$-0.380247\pi$$
0.367402 + 0.930062i $$0.380247\pi$$
$$314$$ −4.00000 −0.225733
$$315$$ 9.00000 + 5.19615i 0.507093 + 0.292770i
$$316$$ 6.92820i 0.389742i
$$317$$ −3.00000 −0.168497 −0.0842484 0.996445i $$-0.526849\pi$$
−0.0842484 + 0.996445i $$0.526849\pi$$
$$318$$ −13.5000 + 7.79423i −0.757042 + 0.437079i
$$319$$ 31.1769i 1.74557i
$$320$$ 3.46410i 0.193649i
$$321$$ −4.50000 + 2.59808i −0.251166 + 0.145010i
$$322$$ 5.19615i 0.289570i
$$323$$ 3.00000 6.92820i 0.166924 0.385496i
$$324$$ −4.50000 7.79423i −0.250000 0.433013i
$$325$$ 12.1244i 0.672538i
$$326$$ −10.0000 −0.553849
$$327$$ 13.5000 + 23.3827i 0.746552 + 1.29307i
$$328$$ 0 0
$$329$$ 3.46410i 0.190982i
$$330$$ −18.0000 + 10.3923i −0.990867 + 0.572078i
$$331$$ 19.0526i 1.04722i −0.851957 0.523612i $$-0.824584\pi$$
0.851957 0.523612i $$-0.175416\pi$$
$$332$$ 10.3923i 0.570352i
$$333$$ −18.0000 10.3923i −0.986394 0.569495i
$$334$$ 0 0
$$335$$ 30.0000 1.63908
$$336$$ 1.50000 0.866025i 0.0818317 0.0472456i
$$337$$ 24.2487i 1.32091i −0.750865 0.660456i $$-0.770363\pi$$
0.750865 0.660456i $$-0.229637\pi$$
$$338$$ −10.0000 −0.543928
$$339$$ 18.0000 10.3923i 0.977626 0.564433i
$$340$$ −6.00000 −0.325396
$$341$$ 36.0000 1.94951
$$342$$ 10.5000 7.79423i 0.567775 0.421464i
$$343$$ −13.0000 −0.701934
$$344$$ −2.00000 −0.107833
$$345$$ 27.0000 15.5885i 1.45363 0.839254i
$$346$$ 6.00000 0.322562
$$347$$ 27.7128i 1.48770i −0.668346 0.743851i $$-0.732997\pi$$
0.668346 0.743851i $$-0.267003\pi$$
$$348$$ −13.5000 + 7.79423i −0.723676 + 0.417815i
$$349$$ −28.0000 −1.49881 −0.749403 0.662114i $$-0.769659\pi$$
−0.749403 + 0.662114i $$0.769659\pi$$
$$350$$ 7.00000 0.374166
$$351$$ 9.00000 0.480384
$$352$$ 3.46410i 0.184637i
$$353$$ 25.9808i 1.38282i 0.722464 + 0.691408i $$0.243009\pi$$
−0.722464 + 0.691408i $$0.756991\pi$$
$$354$$ −4.50000 + 2.59808i −0.239172 + 0.138086i
$$355$$ 41.5692i 2.20627i
$$356$$ −6.00000 −0.317999
$$357$$ 1.50000 + 2.59808i 0.0793884 + 0.137505i
$$358$$ 12.0000 0.634220
$$359$$ 19.0526i 1.00556i 0.864416 + 0.502778i $$0.167689\pi$$
−0.864416 + 0.502778i $$0.832311\pi$$
$$360$$ −9.00000 5.19615i −0.474342 0.273861i
$$361$$ 13.0000 + 13.8564i 0.684211 + 0.729285i
$$362$$ 13.8564i 0.728277i
$$363$$ −1.50000 + 0.866025i −0.0787296 + 0.0454545i
$$364$$ 1.73205i 0.0907841i
$$365$$ 38.1051i 1.99451i
$$366$$ 12.0000 6.92820i 0.627250 0.362143i
$$367$$ 32.0000 1.67039 0.835193 0.549957i $$-0.185356\pi$$
0.835193 + 0.549957i $$0.185356\pi$$
$$368$$ 5.19615i 0.270868i
$$369$$ 0 0
$$370$$ −24.0000 −1.24770
$$371$$ 9.00000 0.467257
$$372$$ 9.00000 + 15.5885i 0.466628 + 0.808224i
$$373$$ 29.4449i 1.52460i 0.647225 + 0.762299i $$0.275929\pi$$
−0.647225 + 0.762299i $$0.724071\pi$$
$$374$$ −6.00000 −0.310253
$$375$$ −6.00000 10.3923i −0.309839 0.536656i
$$376$$ 3.46410i 0.178647i
$$377$$ 15.5885i 0.802846i
$$378$$ 5.19615i 0.267261i
$$379$$ 12.1244i 0.622786i −0.950281 0.311393i $$-0.899204\pi$$
0.950281 0.311393i $$-0.100796\pi$$
$$380$$ 6.00000 13.8564i 0.307794 0.710819i
$$381$$ 0 0
$$382$$ 19.0526i 0.974814i
$$383$$ −6.00000 −0.306586 −0.153293 0.988181i $$-0.548988\pi$$
−0.153293 + 0.988181i $$0.548988\pi$$
$$384$$ −1.50000 + 0.866025i −0.0765466 + 0.0441942i
$$385$$ 12.0000 0.611577
$$386$$ 3.46410i 0.176318i
$$387$$ 3.00000 5.19615i 0.152499 0.264135i
$$388$$ 13.8564i 0.703452i
$$389$$ 3.46410i 0.175637i −0.996136 0.0878185i $$-0.972010\pi$$
0.996136 0.0878185i $$-0.0279895\pi$$
$$390$$ 9.00000 5.19615i 0.455733 0.263117i
$$391$$ 9.00000 0.455150
$$392$$ 6.00000 0.303046
$$393$$ 3.00000 + 5.19615i 0.151330 + 0.262111i
$$394$$ 0 0
$$395$$ 24.0000 1.20757
$$396$$ −9.00000 5.19615i −0.452267 0.261116i
$$397$$ −22.0000 −1.10415 −0.552074 0.833795i $$-0.686163\pi$$
−0.552074 + 0.833795i $$0.686163\pi$$
$$398$$ −11.0000 −0.551380
$$399$$ −7.50000 + 0.866025i −0.375470 + 0.0433555i
$$400$$ −7.00000 −0.350000
$$401$$ −24.0000 −1.19850 −0.599251 0.800561i $$-0.704535\pi$$
−0.599251 + 0.800561i $$0.704535\pi$$
$$402$$ 7.50000 + 12.9904i 0.374066 + 0.647901i
$$403$$ −18.0000 −0.896644
$$404$$ 10.3923i 0.517036i
$$405$$ 27.0000 15.5885i 1.34164 0.774597i
$$406$$ 9.00000 0.446663
$$407$$ −24.0000 −1.18964
$$408$$ −1.50000 2.59808i −0.0742611 0.128624i
$$409$$ 38.1051i 1.88418i −0.335365 0.942088i $$-0.608860\pi$$
0.335365 0.942088i $$-0.391140\pi$$
$$410$$ 0 0
$$411$$ 7.50000 + 12.9904i 0.369948 + 0.640768i
$$412$$ 3.46410i 0.170664i
$$413$$ 3.00000 0.147620
$$414$$ 13.5000 + 7.79423i 0.663489 + 0.383065i
$$415$$ −36.0000 −1.76717
$$416$$ 1.73205i 0.0849208i
$$417$$ −21.0000 + 12.1244i −1.02837 + 0.593732i
$$418$$ 6.00000 13.8564i 0.293470 0.677739i
$$419$$ 10.3923i 0.507697i 0.967244 + 0.253849i $$0.0816965\pi$$
−0.967244 + 0.253849i $$0.918303\pi$$
$$420$$ 3.00000 + 5.19615i 0.146385 + 0.253546i
$$421$$ 12.1244i 0.590905i 0.955357 + 0.295452i $$0.0954704\pi$$
−0.955357 + 0.295452i $$0.904530\pi$$
$$422$$ 12.1244i 0.590204i
$$423$$ 9.00000 + 5.19615i 0.437595 + 0.252646i
$$424$$ −9.00000 −0.437079
$$425$$ 12.1244i 0.588118i
$$426$$ −18.0000 + 10.3923i −0.872103 + 0.503509i
$$427$$ −8.00000 −0.387147
$$428$$ −3.00000 −0.145010
$$429$$ 9.00000 5.19615i 0.434524 0.250873i
$$430$$ 6.92820i 0.334108i
$$431$$ −12.0000 −0.578020 −0.289010 0.957326i $$-0.593326\pi$$
−0.289010 + 0.957326i $$0.593326\pi$$
$$432$$ 5.19615i 0.250000i
$$433$$ 10.3923i 0.499422i −0.968320 0.249711i $$-0.919664\pi$$
0.968320 0.249711i $$-0.0803357\pi$$
$$434$$ 10.3923i 0.498847i
$$435$$ −27.0000 46.7654i −1.29455 2.24223i
$$436$$ 15.5885i 0.746552i
$$437$$ −9.00000 + 20.7846i −0.430528 + 0.994263i
$$438$$ −16.5000 + 9.52628i −0.788400 + 0.455183i
$$439$$ 20.7846i 0.991995i 0.868324 + 0.495998i $$0.165198\pi$$
−0.868324 + 0.495998i $$0.834802\pi$$
$$440$$ −12.0000 −0.572078
$$441$$ −9.00000 + 15.5885i −0.428571 + 0.742307i
$$442$$ 3.00000 0.142695
$$443$$ 17.3205i 0.822922i −0.911427 0.411461i $$-0.865019\pi$$
0.911427 0.411461i $$-0.134981\pi$$
$$444$$ −6.00000 10.3923i −0.284747 0.493197i
$$445$$ 20.7846i 0.985285i
$$446$$ 10.3923i 0.492090i
$$447$$ 6.00000 + 10.3923i 0.283790 + 0.491539i
$$448$$ 1.00000 0.0472456
$$449$$ −30.0000 −1.41579 −0.707894 0.706319i $$-0.750354\pi$$
−0.707894 + 0.706319i $$0.750354\pi$$
$$450$$ 10.5000 18.1865i 0.494975 0.857321i
$$451$$ 0 0
$$452$$ 12.0000 0.564433
$$453$$ 3.00000 + 5.19615i 0.140952 + 0.244137i
$$454$$ −3.00000 −0.140797
$$455$$ −6.00000 −0.281284
$$456$$ 7.50000 0.866025i 0.351220 0.0405554i
$$457$$ −25.0000 −1.16945 −0.584725 0.811231i $$-0.698798\pi$$
−0.584725 + 0.811231i $$0.698798\pi$$
$$458$$ 8.00000 0.373815
$$459$$ 9.00000 0.420084
$$460$$ 18.0000 0.839254
$$461$$ 13.8564i 0.645357i −0.946509 0.322679i $$-0.895417\pi$$
0.946509 0.322679i $$-0.104583\pi$$
$$462$$ 3.00000 + 5.19615i 0.139573 + 0.241747i
$$463$$ −40.0000 −1.85896 −0.929479 0.368875i $$-0.879743\pi$$
−0.929479 + 0.368875i $$0.879743\pi$$
$$464$$ −9.00000 −0.417815
$$465$$ −54.0000 + 31.1769i −2.50419 + 1.44579i
$$466$$ 6.92820i 0.320943i
$$467$$ 27.7128i 1.28240i 0.767375 + 0.641198i $$0.221562\pi$$
−0.767375 + 0.641198i $$0.778438\pi$$
$$468$$ 4.50000 + 2.59808i 0.208013 + 0.120096i
$$469$$ 8.66025i 0.399893i
$$470$$ 12.0000 0.553519
$$471$$ 6.00000 3.46410i 0.276465 0.159617i
$$472$$ −3.00000 −0.138086
$$473$$ 6.92820i 0.318559i
$$474$$ 6.00000 + 10.3923i 0.275589 + 0.477334i
$$475$$ 28.0000 + 12.1244i 1.28473 + 0.556304i
$$476$$ 1.73205i 0.0793884i
$$477$$ 13.5000 23.3827i 0.618123 1.07062i
$$478$$ 12.1244i 0.554555i
$$479$$ 10.3923i 0.474837i −0.971408 0.237418i $$-0.923699\pi$$
0.971408 0.237418i $$-0.0763012\pi$$
$$480$$ −3.00000 5.19615i −0.136931 0.237171i
$$481$$ 12.0000 0.547153
$$482$$ 13.8564i 0.631142i
$$483$$ −4.50000 7.79423i −0.204757 0.354650i
$$484$$ −1.00000 −0.0454545
$$485$$ −48.0000 −2.17957
$$486$$ 13.5000 + 7.79423i 0.612372 + 0.353553i
$$487$$ 3.46410i 0.156973i 0.996915 + 0.0784867i $$0.0250088\pi$$
−0.996915 + 0.0784867i $$0.974991\pi$$
$$488$$ 8.00000 0.362143
$$489$$ 15.0000 8.66025i 0.678323 0.391630i
$$490$$ 20.7846i 0.938953i
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ 15.5885i 0.702069i
$$494$$ −3.00000 + 6.92820i −0.134976 + 0.311715i
$$495$$ 18.0000 31.1769i 0.809040 1.40130i
$$496$$ 10.3923i 0.466628i
$$497$$ 12.0000 0.538274
$$498$$ −9.00000 15.5885i −0.403300 0.698535i
$$499$$ 10.0000 0.447661 0.223831 0.974628i $$-0.428144\pi$$
0.223831 + 0.974628i $$0.428144\pi$$
$$500$$ 6.92820i 0.309839i
$$501$$ 0 0
$$502$$ 13.8564i 0.618442i
$$503$$ 25.9808i 1.15842i −0.815177 0.579212i $$-0.803360\pi$$
0.815177 0.579212i $$-0.196640\pi$$
$$504$$ −1.50000 + 2.59808i −0.0668153 + 0.115728i
$$505$$ 36.0000 1.60198
$$506$$ 18.0000 0.800198
$$507$$ 15.0000 8.66025i 0.666173 0.384615i
$$508$$ 0 0
$$509$$ −6.00000 −0.265945 −0.132973 0.991120i $$-0.542452\pi$$
−0.132973 + 0.991120i $$0.542452\pi$$
$$510$$ 9.00000 5.19615i 0.398527 0.230089i
$$511$$ 11.0000 0.486611
$$512$$ −1.00000 −0.0441942
$$513$$ −9.00000 + 20.7846i −0.397360 + 0.917663i
$$514$$ 6.00000 0.264649
$$515$$ 12.0000 0.528783
$$516$$ 3.00000 1.73205i 0.132068 0.0762493i
$$517$$ 12.0000 0.527759
$$518$$ 6.92820i 0.304408i
$$519$$ −9.00000 + 5.19615i −0.395056 + 0.228086i
$$520$$ 6.00000 0.263117
$$521$$ 24.0000 1.05146 0.525730 0.850652i $$-0.323792\pi$$
0.525730 + 0.850652i $$0.323792\pi$$
$$522$$ 13.5000 23.3827i 0.590879 1.02343i
$$523$$ 32.9090i 1.43901i 0.694488 + 0.719504i $$0.255631\pi$$
−0.694488 + 0.719504i $$0.744369\pi$$
$$524$$ 3.46410i 0.151330i
$$525$$ −10.5000 + 6.06218i −0.458258 + 0.264575i
$$526$$ 3.46410i 0.151042i
$$527$$ −18.0000 −0.784092
$$528$$ −3.00000 5.19615i −0.130558 0.226134i
$$529$$ −4.00000 −0.173913
$$530$$ 31.1769i 1.35424i
$$531$$ 4.50000 7.79423i 0.195283 0.338241i
$$532$$ −4.00000 1.73205i −0.173422 0.0750939i
$$533$$ 0 0
$$534$$ 9.00000 5.19615i 0.389468 0.224860i
$$535$$ 10.3923i 0.449299i
$$536$$ 8.66025i 0.374066i
$$537$$ −18.0000 + 10.3923i −0.776757 + 0.448461i
$$538$$ 18.0000 0.776035
$$539$$ 20.7846i 0.895257i
$$540$$ 18.0000 0.774597
$$541$$ 38.0000 1.63375 0.816874 0.576816i $$-0.195705\pi$$
0.816874 + 0.576816i $$0.195705\pi$$
$$542$$ 1.00000 0.0429537
$$543$$ 12.0000 + 20.7846i 0.514969 + 0.891953i
$$544$$ 1.73205i 0.0742611i
$$545$$ −54.0000 −2.31311
$$546$$ −1.50000 2.59808i −0.0641941 0.111187i
$$547$$ 24.2487i 1.03680i −0.855138 0.518400i $$-0.826528\pi$$
0.855138 0.518400i $$-0.173472\pi$$
$$548$$ 8.66025i 0.369948i
$$549$$ −12.0000 + 20.7846i −0.512148 + 0.887066i
$$550$$ 24.2487i 1.03397i
$$551$$ 36.0000 + 15.5885i 1.53365 + 0.664091i
$$552$$ 4.50000 + 7.79423i 0.191533 + 0.331744i
$$553$$ 6.92820i 0.294617i
$$554$$ 2.00000 0.0849719
$$555$$ 36.0000 20.7846i 1.52811 0.882258i
$$556$$ −14.0000 −0.593732
$$557$$ 45.0333i 1.90812i 0.299611 + 0.954062i $$0.403143\pi$$
−0.299611 + 0.954062i $$0.596857\pi$$
$$558$$ −27.0000 15.5885i −1.14300 0.659912i
$$559$$ 3.46410i 0.146516i
$$560$$ 3.46410i 0.146385i
$$561$$ 9.00000 5.19615i 0.379980 0.219382i
$$562$$ −12.0000 −0.506189
$$563$$ 24.0000 1.01148 0.505740 0.862686i $$-0.331220\pi$$
0.505740 + 0.862686i $$0.331220\pi$$
$$564$$ 3.00000 + 5.19615i 0.126323 + 0.218797i
$$565$$ 41.5692i 1.74883i
$$566$$ 10.0000 0.420331
$$567$$ −4.50000 7.79423i −0.188982 0.327327i
$$568$$ −12.0000 −0.503509
$$569$$ −24.0000 −1.00613 −0.503066 0.864248i $$-0.667795\pi$$
−0.503066 + 0.864248i $$0.667795\pi$$
$$570$$ 3.00000 + 25.9808i 0.125656 + 1.08821i
$$571$$ −16.0000 −0.669579 −0.334790 0.942293i $$-0.608665\pi$$
−0.334790 + 0.942293i $$0.608665\pi$$
$$572$$ 6.00000 0.250873
$$573$$ 16.5000 + 28.5788i 0.689297 + 1.19390i
$$574$$ 0 0
$$575$$ 36.3731i 1.51686i
$$576$$ 1.50000 2.59808i 0.0625000 0.108253i
$$577$$ 25.0000 1.04076 0.520382 0.853934i $$-0.325790\pi$$
0.520382 + 0.853934i $$0.325790\pi$$
$$578$$ −14.0000 −0.582323
$$579$$ 3.00000 + 5.19615i 0.124676 + 0.215945i
$$580$$ 31.1769i 1.29455i
$$581$$ 10.3923i 0.431145i
$$582$$ −12.0000 20.7846i −0.497416 0.861550i
$$583$$ 31.1769i 1.29122i
$$584$$ −11.0000 −0.455183
$$585$$ −9.00000 + 15.5885i −0.372104 + 0.644503i
$$586$$ −21.0000 −0.867502
$$587$$ 13.8564i 0.571915i −0.958242 0.285958i $$-0.907688\pi$$
0.958242 0.285958i $$-0.0923116\pi$$
$$588$$ −9.00000 + 5.19615i −0.371154 + 0.214286i
$$589$$ 18.0000 41.5692i 0.741677 1.71283i
$$590$$ 10.3923i 0.427844i
$$591$$ 0 0
$$592$$ 6.92820i 0.284747i
$$593$$ 20.7846i 0.853522i −0.904365 0.426761i $$-0.859655\pi$$
0.904365 0.426761i $$-0.140345\pi$$
$$594$$ 18.0000 0.738549
$$595$$ −6.00000 −0.245976
$$596$$ 6.92820i 0.283790i
$$597$$ 16.5000 9.52628i 0.675300 0.389885i
$$598$$ −9.00000 −0.368037
$$599$$ −12.0000 −0.490307 −0.245153 0.969484i $$-0.578838\pi$$
−0.245153 + 0.969484i $$0.578838\pi$$
$$600$$ 10.5000 6.06218i 0.428661 0.247487i
$$601$$ 10.3923i 0.423911i −0.977279 0.211955i $$-0.932017\pi$$
0.977279 0.211955i $$-0.0679832\pi$$
$$602$$ −2.00000 −0.0815139
$$603$$ −22.5000 12.9904i −0.916271 0.529009i
$$604$$ 3.46410i 0.140952i
$$605$$ 3.46410i 0.140836i
$$606$$ 9.00000 + 15.5885i 0.365600 + 0.633238i
$$607$$ 27.7128i 1.12483i −0.826856 0.562414i $$-0.809873\pi$$
0.826856 0.562414i $$-0.190127\pi$$
$$608$$ 4.00000 + 1.73205i 0.162221 + 0.0702439i
$$609$$ −13.5000 + 7.79423i −0.547048 + 0.315838i
$$610$$ 27.7128i 1.12206i
$$611$$ −6.00000 −0.242734
$$612$$ 4.50000 + 2.59808i 0.181902 + 0.105021i
$$613$$ −2.00000 −0.0807792 −0.0403896 0.999184i $$-0.512860\pi$$
−0.0403896 + 0.999184i $$0.512860\pi$$
$$614$$ 10.3923i 0.419399i
$$615$$ 0 0
$$616$$ 3.46410i 0.139573i
$$617$$ 48.4974i 1.95243i −0.216799 0.976216i $$-0.569561\pi$$
0.216799 0.976216i $$-0.430439\pi$$
$$618$$ 3.00000 + 5.19615i 0.120678 + 0.209020i
$$619$$ 4.00000 0.160774 0.0803868 0.996764i $$-0.474384\pi$$
0.0803868 + 0.996764i $$0.474384\pi$$
$$620$$ −36.0000 −1.44579
$$621$$ −27.0000 −1.08347
$$622$$ 22.5167i 0.902836i
$$623$$ −6.00000 −0.240385
$$624$$ 1.50000 + 2.59808i 0.0600481 + 0.104006i
$$625$$ −11.0000 −0.440000
$$626$$ −13.0000 −0.519584
$$627$$ 3.00000 + 25.9808i 0.119808 + 1.03757i
$$628$$ 4.00000 0.159617
$$629$$ 12.0000 0.478471
$$630$$ −9.00000 5.19615i −0.358569 0.207020i
$$631$$ 16.0000 0.636950 0.318475 0.947931i $$-0.396829\pi$$
0.318475 + 0.947931i $$0.396829\pi$$
$$632$$ 6.92820i 0.275589i
$$633$$ −10.5000 18.1865i −0.417338 0.722850i
$$634$$ 3.00000 0.119145
$$635$$ 0 0
$$636$$ 13.5000 7.79423i 0.535310 0.309061i
$$637$$ 10.3923i 0.411758i
$$638$$ 31.1769i 1.23431i
$$639$$ 18.0000 31.1769i 0.712069 1.23334i
$$640$$ 3.46410i 0.136931i
$$641$$ 30.0000 1.18493 0.592464 0.805597i $$-0.298155\pi$$
0.592464 + 0.805597i $$0.298155\pi$$
$$642$$ 4.50000 2.59808i 0.177601 0.102538i
$$643$$ −28.0000 −1.10421 −0.552106 0.833774i $$-0.686176\pi$$
−0.552106 + 0.833774i $$0.686176\pi$$
$$644$$ 5.19615i 0.204757i
$$645$$ 6.00000 + 10.3923i 0.236250 + 0.409197i
$$646$$ −3.00000 + 6.92820i −0.118033 + 0.272587i
$$647$$ 1.73205i 0.0680939i 0.999420 + 0.0340470i $$0.0108396\pi$$
−0.999420 + 0.0340470i $$0.989160\pi$$
$$648$$ 4.50000 + 7.79423i 0.176777 + 0.306186i
$$649$$ 10.3923i 0.407934i
$$650$$ 12.1244i 0.475556i
$$651$$ 9.00000 + 15.5885i 0.352738 + 0.610960i
$$652$$ 10.0000 0.391630
$$653$$ 17.3205i 0.677804i −0.940822 0.338902i $$-0.889945\pi$$
0.940822 0.338902i $$-0.110055\pi$$
$$654$$ −13.5000 23.3827i −0.527892 0.914335i
$$655$$ −12.0000 −0.468879
$$656$$ 0 0
$$657$$ 16.5000 28.5788i 0.643726 1.11497i
$$658$$ 3.46410i 0.135045i
$$659$$ 33.0000 1.28550 0.642749 0.766077i $$-0.277794\pi$$
0.642749 + 0.766077i $$0.277794\pi$$
$$660$$ 18.0000 10.3923i 0.700649 0.404520i
$$661$$ 22.5167i 0.875797i 0.899025 + 0.437898i $$0.144277\pi$$
−0.899025 + 0.437898i $$0.855723\pi$$
$$662$$ 19.0526i 0.740499i
$$663$$ −4.50000 + 2.59808i −0.174766 + 0.100901i
$$664$$ 10.3923i 0.403300i
$$665$$ 6.00000 13.8564i 0.232670 0.537328i
$$666$$ 18.0000 + 10.3923i 0.697486 + 0.402694i
$$667$$ 46.7654i 1.81076i
$$668$$ 0 0
$$669$$ −9.00000 15.5885i −0.347960 0.602685i
$$670$$ −30.0000 −1.15900
$$671$$ 27.7128i 1.06984i
$$672$$ −1.50000 + 0.866025i −0.0578638 + 0.0334077i
$$673$$ 48.4974i 1.86944i 0.355387 + 0.934719i $$0.384349\pi$$
−0.355387 + 0.934719i $$0.615651\pi$$
$$674$$ 24.2487i 0.934025i
$$675$$ 36.3731i 1.40000i
$$676$$ 10.0000 0.384615
$$677$$ 15.0000 0.576497 0.288248 0.957556i $$-0.406927\pi$$
0.288248 + 0.957556i $$0.406927\pi$$
$$678$$ −18.0000 + 10.3923i −0.691286 + 0.399114i
$$679$$ 13.8564i 0.531760i
$$680$$ 6.00000 0.230089
$$681$$ 4.50000 2.59808i 0.172440 0.0995585i
$$682$$ −36.0000 −1.37851
$$683$$ −12.0000 −0.459167 −0.229584 0.973289i $$-0.573736\pi$$
−0.229584 + 0.973289i $$0.573736\pi$$
$$684$$ −10.5000 + 7.79423i −0.401478 + 0.298020i
$$685$$ −30.0000 −1.14624
$$686$$ 13.0000 0.496342
$$687$$ −12.0000 + 6.92820i −0.457829 + 0.264327i
$$688$$ 2.00000 0.0762493
$$689$$ 15.5885i 0.593873i
$$690$$ −27.0000 + 15.5885i −1.02787 + 0.593442i
$$691$$ 20.0000 0.760836 0.380418 0.924815i $$-0.375780\pi$$
0.380418 + 0.924815i $$0.375780\pi$$
$$692$$ −6.00000 −0.228086
$$693$$ −9.00000 5.19615i −0.341882 0.197386i
$$694$$ 27.7128i 1.05196i
$$695$$ 48.4974i 1.83961i
$$696$$ 13.5000 7.79423i 0.511716 0.295439i
$$697$$ 0 0
$$698$$ 28.0000 1.05982
$$699$$ 6.00000 + 10.3923i 0.226941 + 0.393073i
$$700$$ −7.00000 −0.264575
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ −9.00000 −0.339683
$$703$$ −12.0000 + 27.7128i −0.452589 + 1.04521i
$$704$$ 3.46410i 0.130558i
$$705$$ −18.0000 + 10.3923i −0.677919 + 0.391397i
$$706$$ 25.9808i 0.977799i
$$707$$ 10.3923i 0.390843i
$$708$$ 4.50000 2.59808i 0.169120 0.0976417i
$$709$$ −4.00000 −0.150223 −0.0751116 0.997175i $$-0.523931\pi$$
−0.0751116 + 0.997175i $$0.523931\pi$$
$$710$$ 41.5692i 1.56007i
$$711$$ −18.0000 10.3923i −0.675053 0.389742i
$$712$$ 6.00000 0.224860
$$713$$ 54.0000 2.02232
$$714$$ −1.50000 2.59808i −0.0561361 0.0972306i
$$715$$ 20.7846i 0.777300i
$$716$$ −12.0000 −0.448461
$$717$$ −10.5000 18.1865i −0.392130 0.679189i
$$718$$ 19.0526i 0.711035i
$$719$$ 8.66025i 0.322973i −0.986875 0.161486i $$-0.948371\pi$$
0.986875 0.161486i $$-0.0516288\pi$$
$$720$$ 9.00000 + 5.19615i 0.335410 + 0.193649i
$$721$$ 3.46410i 0.129010i
$$722$$ −13.0000 13.8564i −0.483810 0.515682i
$$723$$ −12.0000 20.7846i −0.446285 0.772988i
$$724$$ 13.8564i 0.514969i
$$725$$ 63.0000 2.33976
$$726$$ 1.50000 0.866025i 0.0556702 0.0321412i
$$727$$ −7.00000 −0.259616 −0.129808 0.991539i $$-0.541436\pi$$
−0.129808 + 0.991539i $$0.541436\pi$$
$$728$$ 1.73205i 0.0641941i
$$729$$ −27.0000 −1.00000
$$730$$ 38.1051i 1.41033i
$$731$$ 3.46410i 0.128124i
$$732$$ −12.0000 + 6.92820i −0.443533 + 0.256074i
$$733$$ −22.0000 −0.812589 −0.406294 0.913742i $$-0.633179\pi$$
−0.406294 + 0.913742i $$0.633179\pi$$
$$734$$ −32.0000 −1.18114
$$735$$ −18.0000 31.1769i −0.663940 1.14998i
$$736$$ 5.19615i 0.191533i
$$737$$ −30.0000 −1.10506
$$738$$ 0 0
$$739$$ 40.0000 1.47142 0.735712 0.677295i $$-0.236848\pi$$
0.735712 + 0.677295i $$0.236848\pi$$
$$740$$ 24.0000 0.882258
$$741$$ −1.50000 12.9904i −0.0551039 0.477214i
$$742$$ −9.00000 −0.330400
$$743$$ −30.0000 −1.10059 −0.550297 0.834969i $$-0.685485\pi$$
−0.550297 + 0.834969i $$0.685485\pi$$
$$744$$ −9.00000 15.5885i −0.329956 0.571501i
$$745$$ −24.0000 −0.879292
$$746$$ 29.4449i 1.07805i
$$747$$ 27.0000 + 15.5885i 0.987878 + 0.570352i
$$748$$ 6.00000 0.219382
$$749$$ −3.00000 −0.109618
$$750$$ 6.00000 + 10.3923i 0.219089 + 0.379473i
$$751$$ 6.92820i 0.252814i −0.991978 0.126407i $$-0.959656\pi$$
0.991978 0.126407i $$-0.0403445\pi$$
$$752$$ 3.46410i 0.126323i
$$753$$ −12.0000 20.7846i −0.437304 0.757433i
$$754$$ 15.5885i 0.567698i
$$755$$ −12.0000 −0.436725
$$756$$ 5.19615i 0.188982i
$$757$$ 16.0000 0.581530 0.290765 0.956795i $$-0.406090\pi$$
0.290765 + 0.956795i $$0.406090\pi$$
$$758$$ 12.1244i 0.440376i
$$759$$ −27.0000 + 15.5885i −0.980038 + 0.565825i
$$760$$ −6.00000 + 13.8564i −0.217643 + 0.502625i
$$761$$ 8.66025i 0.313934i −0.987604 0.156967i $$-0.949828\pi$$
0.987604 0.156967i $$-0.0501716\pi$$
$$762$$ 0 0
$$763$$ 15.5885i 0.564340i
$$764$$ 19.0526i 0.689297i
$$765$$ −9.00000 + 15.5885i −0.325396 + 0.563602i
$$766$$ 6.00000 0.216789
$$767$$ 5.19615i 0.187622i
$$768$$ 1.50000 0.866025i 0.0541266 0.0312500i
$$769$$ 49.0000 1.76699 0.883493 0.468445i $$-0.155186\pi$$
0.883493 + 0.468445i $$0.155186\pi$$
$$770$$ −12.0000 −0.432450
$$771$$ −9.00000 + 5.19615i −0.324127 + 0.187135i
$$772$$ 3.46410i 0.124676i
$$773$$ 3.00000 0.107903 0.0539513 0.998544i $$-0.482818\pi$$
0.0539513 + 0.998544i $$0.482818\pi$$
$$774$$ −3.00000 + 5.19615i −0.107833 + 0.186772i
$$775$$ 72.7461i 2.61312i
$$776$$ 13.8564i 0.497416i
$$777$$ −6.00000 10.3923i −0.215249 0.372822i
$$778$$ 3.46410i 0.124194i
$$779$$ 0 0
$$780$$ −9.00000 + 5.19615i −0.322252 + 0.186052i
$$781$$ 41.5692i 1.48746i
$$782$$ −9.00000 −0.321839
$$783$$ 46.7654i 1.67126i
$$784$$ −6.00000