# Properties

 Label 585.2.i.b.391.1 Level $585$ Weight $2$ Character 585.391 Analytic conductor $4.671$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$585 = 3^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 585.i (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.67124851824$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 391.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 585.391 Dual form 585.2.i.b.196.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 + 0.866025i) q^{2} -1.73205i q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.50000 - 0.866025i) q^{6} +(-1.00000 - 1.73205i) q^{7} +3.00000 q^{8} -3.00000 q^{9} +O(q^{10})$$ $$q+(0.500000 + 0.866025i) q^{2} -1.73205i q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.50000 - 0.866025i) q^{6} +(-1.00000 - 1.73205i) q^{7} +3.00000 q^{8} -3.00000 q^{9} +1.00000 q^{10} +(0.500000 + 0.866025i) q^{11} +(-1.50000 - 0.866025i) q^{12} +(0.500000 - 0.866025i) q^{13} +(1.00000 - 1.73205i) q^{14} +(-1.50000 - 0.866025i) q^{15} +(0.500000 + 0.866025i) q^{16} +2.00000 q^{17} +(-1.50000 - 2.59808i) q^{18} -3.00000 q^{19} +(-0.500000 - 0.866025i) q^{20} +(-3.00000 + 1.73205i) q^{21} +(-0.500000 + 0.866025i) q^{22} -5.19615i q^{24} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{26} +5.19615i q^{27} -2.00000 q^{28} +(-2.50000 - 4.33013i) q^{29} -1.73205i q^{30} +(0.500000 - 0.866025i) q^{31} +(2.50000 - 4.33013i) q^{32} +(1.50000 - 0.866025i) q^{33} +(1.00000 + 1.73205i) q^{34} -2.00000 q^{35} +(-1.50000 + 2.59808i) q^{36} -5.00000 q^{37} +(-1.50000 - 2.59808i) q^{38} +(-1.50000 - 0.866025i) q^{39} +(1.50000 - 2.59808i) q^{40} +(-3.00000 - 1.73205i) q^{42} +(4.00000 + 6.92820i) q^{43} +1.00000 q^{44} +(-1.50000 + 2.59808i) q^{45} +(1.00000 + 1.73205i) q^{47} +(1.50000 - 0.866025i) q^{48} +(1.50000 - 2.59808i) q^{49} +(0.500000 - 0.866025i) q^{50} -3.46410i q^{51} +(-0.500000 - 0.866025i) q^{52} +14.0000 q^{53} +(-4.50000 + 2.59808i) q^{54} +1.00000 q^{55} +(-3.00000 - 5.19615i) q^{56} +5.19615i q^{57} +(2.50000 - 4.33013i) q^{58} +(4.50000 - 7.79423i) q^{59} +(-1.50000 + 0.866025i) q^{60} +(0.500000 + 0.866025i) q^{61} +1.00000 q^{62} +(3.00000 + 5.19615i) q^{63} +7.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} +(1.50000 + 0.866025i) q^{66} +(-7.00000 + 12.1244i) q^{67} +(1.00000 - 1.73205i) q^{68} +(-1.00000 - 1.73205i) q^{70} -9.00000 q^{72} +6.00000 q^{73} +(-2.50000 - 4.33013i) q^{74} +(-1.50000 + 0.866025i) q^{75} +(-1.50000 + 2.59808i) q^{76} +(1.00000 - 1.73205i) q^{77} -1.73205i q^{78} +(6.00000 + 10.3923i) q^{79} +1.00000 q^{80} +9.00000 q^{81} +(5.00000 + 8.66025i) q^{83} +3.46410i q^{84} +(1.00000 - 1.73205i) q^{85} +(-4.00000 + 6.92820i) q^{86} +(-7.50000 + 4.33013i) q^{87} +(1.50000 + 2.59808i) q^{88} +2.00000 q^{89} -3.00000 q^{90} -2.00000 q^{91} +(-1.50000 - 0.866025i) q^{93} +(-1.00000 + 1.73205i) q^{94} +(-1.50000 + 2.59808i) q^{95} +(-7.50000 - 4.33013i) q^{96} +(-0.500000 - 0.866025i) q^{97} +3.00000 q^{98} +(-1.50000 - 2.59808i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{2} + q^{4} + q^{5} + 3 q^{6} - 2 q^{7} + 6 q^{8} - 6 q^{9}+O(q^{10})$$ 2 * q + q^2 + q^4 + q^5 + 3 * q^6 - 2 * q^7 + 6 * q^8 - 6 * q^9 $$2 q + q^{2} + q^{4} + q^{5} + 3 q^{6} - 2 q^{7} + 6 q^{8} - 6 q^{9} + 2 q^{10} + q^{11} - 3 q^{12} + q^{13} + 2 q^{14} - 3 q^{15} + q^{16} + 4 q^{17} - 3 q^{18} - 6 q^{19} - q^{20} - 6 q^{21} - q^{22} - q^{25} + 2 q^{26} - 4 q^{28} - 5 q^{29} + q^{31} + 5 q^{32} + 3 q^{33} + 2 q^{34} - 4 q^{35} - 3 q^{36} - 10 q^{37} - 3 q^{38} - 3 q^{39} + 3 q^{40} - 6 q^{42} + 8 q^{43} + 2 q^{44} - 3 q^{45} + 2 q^{47} + 3 q^{48} + 3 q^{49} + q^{50} - q^{52} + 28 q^{53} - 9 q^{54} + 2 q^{55} - 6 q^{56} + 5 q^{58} + 9 q^{59} - 3 q^{60} + q^{61} + 2 q^{62} + 6 q^{63} + 14 q^{64} - q^{65} + 3 q^{66} - 14 q^{67} + 2 q^{68} - 2 q^{70} - 18 q^{72} + 12 q^{73} - 5 q^{74} - 3 q^{75} - 3 q^{76} + 2 q^{77} + 12 q^{79} + 2 q^{80} + 18 q^{81} + 10 q^{83} + 2 q^{85} - 8 q^{86} - 15 q^{87} + 3 q^{88} + 4 q^{89} - 6 q^{90} - 4 q^{91} - 3 q^{93} - 2 q^{94} - 3 q^{95} - 15 q^{96} - q^{97} + 6 q^{98} - 3 q^{99}+O(q^{100})$$ 2 * q + q^2 + q^4 + q^5 + 3 * q^6 - 2 * q^7 + 6 * q^8 - 6 * q^9 + 2 * q^10 + q^11 - 3 * q^12 + q^13 + 2 * q^14 - 3 * q^15 + q^16 + 4 * q^17 - 3 * q^18 - 6 * q^19 - q^20 - 6 * q^21 - q^22 - q^25 + 2 * q^26 - 4 * q^28 - 5 * q^29 + q^31 + 5 * q^32 + 3 * q^33 + 2 * q^34 - 4 * q^35 - 3 * q^36 - 10 * q^37 - 3 * q^38 - 3 * q^39 + 3 * q^40 - 6 * q^42 + 8 * q^43 + 2 * q^44 - 3 * q^45 + 2 * q^47 + 3 * q^48 + 3 * q^49 + q^50 - q^52 + 28 * q^53 - 9 * q^54 + 2 * q^55 - 6 * q^56 + 5 * q^58 + 9 * q^59 - 3 * q^60 + q^61 + 2 * q^62 + 6 * q^63 + 14 * q^64 - q^65 + 3 * q^66 - 14 * q^67 + 2 * q^68 - 2 * q^70 - 18 * q^72 + 12 * q^73 - 5 * q^74 - 3 * q^75 - 3 * q^76 + 2 * q^77 + 12 * q^79 + 2 * q^80 + 18 * q^81 + 10 * q^83 + 2 * q^85 - 8 * q^86 - 15 * q^87 + 3 * q^88 + 4 * q^89 - 6 * q^90 - 4 * q^91 - 3 * q^93 - 2 * q^94 - 3 * q^95 - 15 * q^96 - q^97 + 6 * q^98 - 3 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$$.

 $$n$$ $$326$$ $$352$$ $$496$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.500000 + 0.866025i 0.353553 + 0.612372i 0.986869 0.161521i $$-0.0516399\pi$$
−0.633316 + 0.773893i $$0.718307\pi$$
$$3$$ 1.73205i 1.00000i
$$4$$ 0.500000 0.866025i 0.250000 0.433013i
$$5$$ 0.500000 0.866025i 0.223607 0.387298i
$$6$$ 1.50000 0.866025i 0.612372 0.353553i
$$7$$ −1.00000 1.73205i −0.377964 0.654654i 0.612801 0.790237i $$-0.290043\pi$$
−0.990766 + 0.135583i $$0.956709\pi$$
$$8$$ 3.00000 1.06066
$$9$$ −3.00000 −1.00000
$$10$$ 1.00000 0.316228
$$11$$ 0.500000 + 0.866025i 0.150756 + 0.261116i 0.931505 0.363727i $$-0.118496\pi$$
−0.780750 + 0.624844i $$0.785163\pi$$
$$12$$ −1.50000 0.866025i −0.433013 0.250000i
$$13$$ 0.500000 0.866025i 0.138675 0.240192i
$$14$$ 1.00000 1.73205i 0.267261 0.462910i
$$15$$ −1.50000 0.866025i −0.387298 0.223607i
$$16$$ 0.500000 + 0.866025i 0.125000 + 0.216506i
$$17$$ 2.00000 0.485071 0.242536 0.970143i $$-0.422021\pi$$
0.242536 + 0.970143i $$0.422021\pi$$
$$18$$ −1.50000 2.59808i −0.353553 0.612372i
$$19$$ −3.00000 −0.688247 −0.344124 0.938924i $$-0.611824\pi$$
−0.344124 + 0.938924i $$0.611824\pi$$
$$20$$ −0.500000 0.866025i −0.111803 0.193649i
$$21$$ −3.00000 + 1.73205i −0.654654 + 0.377964i
$$22$$ −0.500000 + 0.866025i −0.106600 + 0.184637i
$$23$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$24$$ 5.19615i 1.06066i
$$25$$ −0.500000 0.866025i −0.100000 0.173205i
$$26$$ 1.00000 0.196116
$$27$$ 5.19615i 1.00000i
$$28$$ −2.00000 −0.377964
$$29$$ −2.50000 4.33013i −0.464238 0.804084i 0.534928 0.844897i $$-0.320339\pi$$
−0.999167 + 0.0408130i $$0.987005\pi$$
$$30$$ 1.73205i 0.316228i
$$31$$ 0.500000 0.866025i 0.0898027 0.155543i −0.817625 0.575751i $$-0.804710\pi$$
0.907428 + 0.420208i $$0.138043\pi$$
$$32$$ 2.50000 4.33013i 0.441942 0.765466i
$$33$$ 1.50000 0.866025i 0.261116 0.150756i
$$34$$ 1.00000 + 1.73205i 0.171499 + 0.297044i
$$35$$ −2.00000 −0.338062
$$36$$ −1.50000 + 2.59808i −0.250000 + 0.433013i
$$37$$ −5.00000 −0.821995 −0.410997 0.911636i $$-0.634819\pi$$
−0.410997 + 0.911636i $$0.634819\pi$$
$$38$$ −1.50000 2.59808i −0.243332 0.421464i
$$39$$ −1.50000 0.866025i −0.240192 0.138675i
$$40$$ 1.50000 2.59808i 0.237171 0.410792i
$$41$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$42$$ −3.00000 1.73205i −0.462910 0.267261i
$$43$$ 4.00000 + 6.92820i 0.609994 + 1.05654i 0.991241 + 0.132068i $$0.0421616\pi$$
−0.381246 + 0.924473i $$0.624505\pi$$
$$44$$ 1.00000 0.150756
$$45$$ −1.50000 + 2.59808i −0.223607 + 0.387298i
$$46$$ 0 0
$$47$$ 1.00000 + 1.73205i 0.145865 + 0.252646i 0.929695 0.368329i $$-0.120070\pi$$
−0.783830 + 0.620975i $$0.786737\pi$$
$$48$$ 1.50000 0.866025i 0.216506 0.125000i
$$49$$ 1.50000 2.59808i 0.214286 0.371154i
$$50$$ 0.500000 0.866025i 0.0707107 0.122474i
$$51$$ 3.46410i 0.485071i
$$52$$ −0.500000 0.866025i −0.0693375 0.120096i
$$53$$ 14.0000 1.92305 0.961524 0.274721i $$-0.0885855\pi$$
0.961524 + 0.274721i $$0.0885855\pi$$
$$54$$ −4.50000 + 2.59808i −0.612372 + 0.353553i
$$55$$ 1.00000 0.134840
$$56$$ −3.00000 5.19615i −0.400892 0.694365i
$$57$$ 5.19615i 0.688247i
$$58$$ 2.50000 4.33013i 0.328266 0.568574i
$$59$$ 4.50000 7.79423i 0.585850 1.01472i −0.408919 0.912571i $$-0.634094\pi$$
0.994769 0.102151i $$-0.0325726\pi$$
$$60$$ −1.50000 + 0.866025i −0.193649 + 0.111803i
$$61$$ 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i $$-0.146275\pi$$
−0.832240 + 0.554416i $$0.812942\pi$$
$$62$$ 1.00000 0.127000
$$63$$ 3.00000 + 5.19615i 0.377964 + 0.654654i
$$64$$ 7.00000 0.875000
$$65$$ −0.500000 0.866025i −0.0620174 0.107417i
$$66$$ 1.50000 + 0.866025i 0.184637 + 0.106600i
$$67$$ −7.00000 + 12.1244i −0.855186 + 1.48123i 0.0212861 + 0.999773i $$0.493224\pi$$
−0.876472 + 0.481452i $$0.840109\pi$$
$$68$$ 1.00000 1.73205i 0.121268 0.210042i
$$69$$ 0 0
$$70$$ −1.00000 1.73205i −0.119523 0.207020i
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ −9.00000 −1.06066
$$73$$ 6.00000 0.702247 0.351123 0.936329i $$-0.385800\pi$$
0.351123 + 0.936329i $$0.385800\pi$$
$$74$$ −2.50000 4.33013i −0.290619 0.503367i
$$75$$ −1.50000 + 0.866025i −0.173205 + 0.100000i
$$76$$ −1.50000 + 2.59808i −0.172062 + 0.298020i
$$77$$ 1.00000 1.73205i 0.113961 0.197386i
$$78$$ 1.73205i 0.196116i
$$79$$ 6.00000 + 10.3923i 0.675053 + 1.16923i 0.976453 + 0.215728i $$0.0692125\pi$$
−0.301401 + 0.953498i $$0.597454\pi$$
$$80$$ 1.00000 0.111803
$$81$$ 9.00000 1.00000
$$82$$ 0 0
$$83$$ 5.00000 + 8.66025i 0.548821 + 0.950586i 0.998356 + 0.0573233i $$0.0182566\pi$$
−0.449534 + 0.893263i $$0.648410\pi$$
$$84$$ 3.46410i 0.377964i
$$85$$ 1.00000 1.73205i 0.108465 0.187867i
$$86$$ −4.00000 + 6.92820i −0.431331 + 0.747087i
$$87$$ −7.50000 + 4.33013i −0.804084 + 0.464238i
$$88$$ 1.50000 + 2.59808i 0.159901 + 0.276956i
$$89$$ 2.00000 0.212000 0.106000 0.994366i $$-0.466196\pi$$
0.106000 + 0.994366i $$0.466196\pi$$
$$90$$ −3.00000 −0.316228
$$91$$ −2.00000 −0.209657
$$92$$ 0 0
$$93$$ −1.50000 0.866025i −0.155543 0.0898027i
$$94$$ −1.00000 + 1.73205i −0.103142 + 0.178647i
$$95$$ −1.50000 + 2.59808i −0.153897 + 0.266557i
$$96$$ −7.50000 4.33013i −0.765466 0.441942i
$$97$$ −0.500000 0.866025i −0.0507673 0.0879316i 0.839525 0.543321i $$-0.182833\pi$$
−0.890292 + 0.455389i $$0.849500\pi$$
$$98$$ 3.00000 0.303046
$$99$$ −1.50000 2.59808i −0.150756 0.261116i
$$100$$ −1.00000 −0.100000
$$101$$ −1.50000 2.59808i −0.149256 0.258518i 0.781697 0.623658i $$-0.214354\pi$$
−0.930953 + 0.365140i $$0.881021\pi$$
$$102$$ 3.00000 1.73205i 0.297044 0.171499i
$$103$$ 0.500000 0.866025i 0.0492665 0.0853320i −0.840341 0.542059i $$-0.817645\pi$$
0.889607 + 0.456727i $$0.150978\pi$$
$$104$$ 1.50000 2.59808i 0.147087 0.254762i
$$105$$ 3.46410i 0.338062i
$$106$$ 7.00000 + 12.1244i 0.679900 + 1.17762i
$$107$$ 19.0000 1.83680 0.918400 0.395654i $$-0.129482\pi$$
0.918400 + 0.395654i $$0.129482\pi$$
$$108$$ 4.50000 + 2.59808i 0.433013 + 0.250000i
$$109$$ −14.0000 −1.34096 −0.670478 0.741929i $$-0.733911\pi$$
−0.670478 + 0.741929i $$0.733911\pi$$
$$110$$ 0.500000 + 0.866025i 0.0476731 + 0.0825723i
$$111$$ 8.66025i 0.821995i
$$112$$ 1.00000 1.73205i 0.0944911 0.163663i
$$113$$ −5.00000 + 8.66025i −0.470360 + 0.814688i −0.999425 0.0338931i $$-0.989209\pi$$
0.529065 + 0.848581i $$0.322543\pi$$
$$114$$ −4.50000 + 2.59808i −0.421464 + 0.243332i
$$115$$ 0 0
$$116$$ −5.00000 −0.464238
$$117$$ −1.50000 + 2.59808i −0.138675 + 0.240192i
$$118$$ 9.00000 0.828517
$$119$$ −2.00000 3.46410i −0.183340 0.317554i
$$120$$ −4.50000 2.59808i −0.410792 0.237171i
$$121$$ 5.00000 8.66025i 0.454545 0.787296i
$$122$$ −0.500000 + 0.866025i −0.0452679 + 0.0784063i
$$123$$ 0 0
$$124$$ −0.500000 0.866025i −0.0449013 0.0777714i
$$125$$ −1.00000 −0.0894427
$$126$$ −3.00000 + 5.19615i −0.267261 + 0.462910i
$$127$$ −8.00000 −0.709885 −0.354943 0.934888i $$-0.615500\pi$$
−0.354943 + 0.934888i $$0.615500\pi$$
$$128$$ −1.50000 2.59808i −0.132583 0.229640i
$$129$$ 12.0000 6.92820i 1.05654 0.609994i
$$130$$ 0.500000 0.866025i 0.0438529 0.0759555i
$$131$$ 2.00000 3.46410i 0.174741 0.302660i −0.765331 0.643637i $$-0.777425\pi$$
0.940072 + 0.340977i $$0.110758\pi$$
$$132$$ 1.73205i 0.150756i
$$133$$ 3.00000 + 5.19615i 0.260133 + 0.450564i
$$134$$ −14.0000 −1.20942
$$135$$ 4.50000 + 2.59808i 0.387298 + 0.223607i
$$136$$ 6.00000 0.514496
$$137$$ 2.50000 + 4.33013i 0.213589 + 0.369948i 0.952835 0.303488i $$-0.0981512\pi$$
−0.739246 + 0.673436i $$0.764818\pi$$
$$138$$ 0 0
$$139$$ −6.00000 + 10.3923i −0.508913 + 0.881464i 0.491033 + 0.871141i $$0.336619\pi$$
−0.999947 + 0.0103230i $$0.996714\pi$$
$$140$$ −1.00000 + 1.73205i −0.0845154 + 0.146385i
$$141$$ 3.00000 1.73205i 0.252646 0.145865i
$$142$$ 0 0
$$143$$ 1.00000 0.0836242
$$144$$ −1.50000 2.59808i −0.125000 0.216506i
$$145$$ −5.00000 −0.415227
$$146$$ 3.00000 + 5.19615i 0.248282 + 0.430037i
$$147$$ −4.50000 2.59808i −0.371154 0.214286i
$$148$$ −2.50000 + 4.33013i −0.205499 + 0.355934i
$$149$$ −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i $$-0.912374\pi$$
0.716578 + 0.697507i $$0.245707\pi$$
$$150$$ −1.50000 0.866025i −0.122474 0.0707107i
$$151$$ 4.00000 + 6.92820i 0.325515 + 0.563809i 0.981617 0.190864i $$-0.0611289\pi$$
−0.656101 + 0.754673i $$0.727796\pi$$
$$152$$ −9.00000 −0.729996
$$153$$ −6.00000 −0.485071
$$154$$ 2.00000 0.161165
$$155$$ −0.500000 0.866025i −0.0401610 0.0695608i
$$156$$ −1.50000 + 0.866025i −0.120096 + 0.0693375i
$$157$$ 3.00000 5.19615i 0.239426 0.414698i −0.721124 0.692806i $$-0.756374\pi$$
0.960550 + 0.278108i $$0.0897074\pi$$
$$158$$ −6.00000 + 10.3923i −0.477334 + 0.826767i
$$159$$ 24.2487i 1.92305i
$$160$$ −2.50000 4.33013i −0.197642 0.342327i
$$161$$ 0 0
$$162$$ 4.50000 + 7.79423i 0.353553 + 0.612372i
$$163$$ −12.0000 −0.939913 −0.469956 0.882690i $$-0.655730\pi$$
−0.469956 + 0.882690i $$0.655730\pi$$
$$164$$ 0 0
$$165$$ 1.73205i 0.134840i
$$166$$ −5.00000 + 8.66025i −0.388075 + 0.672166i
$$167$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$168$$ −9.00000 + 5.19615i −0.694365 + 0.400892i
$$169$$ −0.500000 0.866025i −0.0384615 0.0666173i
$$170$$ 2.00000 0.153393
$$171$$ 9.00000 0.688247
$$172$$ 8.00000 0.609994
$$173$$ −6.00000 10.3923i −0.456172 0.790112i 0.542583 0.840002i $$-0.317446\pi$$
−0.998755 + 0.0498898i $$0.984113\pi$$
$$174$$ −7.50000 4.33013i −0.568574 0.328266i
$$175$$ −1.00000 + 1.73205i −0.0755929 + 0.130931i
$$176$$ −0.500000 + 0.866025i −0.0376889 + 0.0652791i
$$177$$ −13.5000 7.79423i −1.01472 0.585850i
$$178$$ 1.00000 + 1.73205i 0.0749532 + 0.129823i
$$179$$ −18.0000 −1.34538 −0.672692 0.739923i $$-0.734862\pi$$
−0.672692 + 0.739923i $$0.734862\pi$$
$$180$$ 1.50000 + 2.59808i 0.111803 + 0.193649i
$$181$$ 17.0000 1.26360 0.631800 0.775131i $$-0.282316\pi$$
0.631800 + 0.775131i $$0.282316\pi$$
$$182$$ −1.00000 1.73205i −0.0741249 0.128388i
$$183$$ 1.50000 0.866025i 0.110883 0.0640184i
$$184$$ 0 0
$$185$$ −2.50000 + 4.33013i −0.183804 + 0.318357i
$$186$$ 1.73205i 0.127000i
$$187$$ 1.00000 + 1.73205i 0.0731272 + 0.126660i
$$188$$ 2.00000 0.145865
$$189$$ 9.00000 5.19615i 0.654654 0.377964i
$$190$$ −3.00000 −0.217643
$$191$$ −9.00000 15.5885i −0.651217 1.12794i −0.982828 0.184525i $$-0.940925\pi$$
0.331611 0.943416i $$-0.392408\pi$$
$$192$$ 12.1244i 0.875000i
$$193$$ −6.50000 + 11.2583i −0.467880 + 0.810392i −0.999326 0.0366998i $$-0.988315\pi$$
0.531446 + 0.847092i $$0.321649\pi$$
$$194$$ 0.500000 0.866025i 0.0358979 0.0621770i
$$195$$ −1.50000 + 0.866025i −0.107417 + 0.0620174i
$$196$$ −1.50000 2.59808i −0.107143 0.185577i
$$197$$ 15.0000 1.06871 0.534353 0.845262i $$-0.320555\pi$$
0.534353 + 0.845262i $$0.320555\pi$$
$$198$$ 1.50000 2.59808i 0.106600 0.184637i
$$199$$ −22.0000 −1.55954 −0.779769 0.626067i $$-0.784664\pi$$
−0.779769 + 0.626067i $$0.784664\pi$$
$$200$$ −1.50000 2.59808i −0.106066 0.183712i
$$201$$ 21.0000 + 12.1244i 1.48123 + 0.855186i
$$202$$ 1.50000 2.59808i 0.105540 0.182800i
$$203$$ −5.00000 + 8.66025i −0.350931 + 0.607831i
$$204$$ −3.00000 1.73205i −0.210042 0.121268i
$$205$$ 0 0
$$206$$ 1.00000 0.0696733
$$207$$ 0 0
$$208$$ 1.00000 0.0693375
$$209$$ −1.50000 2.59808i −0.103757 0.179713i
$$210$$ −3.00000 + 1.73205i −0.207020 + 0.119523i
$$211$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$212$$ 7.00000 12.1244i 0.480762 0.832704i
$$213$$ 0 0
$$214$$ 9.50000 + 16.4545i 0.649407 + 1.12481i
$$215$$ 8.00000 0.545595
$$216$$ 15.5885i 1.06066i
$$217$$ −2.00000 −0.135769
$$218$$ −7.00000 12.1244i −0.474100 0.821165i
$$219$$ 10.3923i 0.702247i
$$220$$ 0.500000 0.866025i 0.0337100 0.0583874i
$$221$$ 1.00000 1.73205i 0.0672673 0.116510i
$$222$$ −7.50000 + 4.33013i −0.503367 + 0.290619i
$$223$$ 13.0000 + 22.5167i 0.870544 + 1.50783i 0.861435 + 0.507869i $$0.169566\pi$$
0.00910984 + 0.999959i $$0.497100\pi$$
$$224$$ −10.0000 −0.668153
$$225$$ 1.50000 + 2.59808i 0.100000 + 0.173205i
$$226$$ −10.0000 −0.665190
$$227$$ 13.0000 + 22.5167i 0.862840 + 1.49448i 0.869176 + 0.494503i $$0.164650\pi$$
−0.00633544 + 0.999980i $$0.502017\pi$$
$$228$$ 4.50000 + 2.59808i 0.298020 + 0.172062i
$$229$$ 8.00000 13.8564i 0.528655 0.915657i −0.470787 0.882247i $$-0.656030\pi$$
0.999442 0.0334101i $$-0.0106368\pi$$
$$230$$ 0 0
$$231$$ −3.00000 1.73205i −0.197386 0.113961i
$$232$$ −7.50000 12.9904i −0.492399 0.852860i
$$233$$ −14.0000 −0.917170 −0.458585 0.888650i $$-0.651644\pi$$
−0.458585 + 0.888650i $$0.651644\pi$$
$$234$$ −3.00000 −0.196116
$$235$$ 2.00000 0.130466
$$236$$ −4.50000 7.79423i −0.292925 0.507361i
$$237$$ 18.0000 10.3923i 1.16923 0.675053i
$$238$$ 2.00000 3.46410i 0.129641 0.224544i
$$239$$ −7.50000 + 12.9904i −0.485135 + 0.840278i −0.999854 0.0170808i $$-0.994563\pi$$
0.514719 + 0.857359i $$0.327896\pi$$
$$240$$ 1.73205i 0.111803i
$$241$$ −5.00000 8.66025i −0.322078 0.557856i 0.658838 0.752285i $$-0.271048\pi$$
−0.980917 + 0.194429i $$0.937715\pi$$
$$242$$ 10.0000 0.642824
$$243$$ 15.5885i 1.00000i
$$244$$ 1.00000 0.0640184
$$245$$ −1.50000 2.59808i −0.0958315 0.165985i
$$246$$ 0 0
$$247$$ −1.50000 + 2.59808i −0.0954427 + 0.165312i
$$248$$ 1.50000 2.59808i 0.0952501 0.164978i
$$249$$ 15.0000 8.66025i 0.950586 0.548821i
$$250$$ −0.500000 0.866025i −0.0316228 0.0547723i
$$251$$ 12.0000 0.757433 0.378717 0.925513i $$-0.376365\pi$$
0.378717 + 0.925513i $$0.376365\pi$$
$$252$$ 6.00000 0.377964
$$253$$ 0 0
$$254$$ −4.00000 6.92820i −0.250982 0.434714i
$$255$$ −3.00000 1.73205i −0.187867 0.108465i
$$256$$ 8.50000 14.7224i 0.531250 0.920152i
$$257$$ 14.0000 24.2487i 0.873296 1.51259i 0.0147291 0.999892i $$-0.495311\pi$$
0.858567 0.512702i $$-0.171355\pi$$
$$258$$ 12.0000 + 6.92820i 0.747087 + 0.431331i
$$259$$ 5.00000 + 8.66025i 0.310685 + 0.538122i
$$260$$ −1.00000 −0.0620174
$$261$$ 7.50000 + 12.9904i 0.464238 + 0.804084i
$$262$$ 4.00000 0.247121
$$263$$ 8.00000 + 13.8564i 0.493301 + 0.854423i 0.999970 0.00771799i $$-0.00245674\pi$$
−0.506669 + 0.862141i $$0.669123\pi$$
$$264$$ 4.50000 2.59808i 0.276956 0.159901i
$$265$$ 7.00000 12.1244i 0.430007 0.744793i
$$266$$ −3.00000 + 5.19615i −0.183942 + 0.318597i
$$267$$ 3.46410i 0.212000i
$$268$$ 7.00000 + 12.1244i 0.427593 + 0.740613i
$$269$$ 3.00000 0.182913 0.0914566 0.995809i $$-0.470848\pi$$
0.0914566 + 0.995809i $$0.470848\pi$$
$$270$$ 5.19615i 0.316228i
$$271$$ −7.00000 −0.425220 −0.212610 0.977137i $$-0.568196\pi$$
−0.212610 + 0.977137i $$0.568196\pi$$
$$272$$ 1.00000 + 1.73205i 0.0606339 + 0.105021i
$$273$$ 3.46410i 0.209657i
$$274$$ −2.50000 + 4.33013i −0.151031 + 0.261593i
$$275$$ 0.500000 0.866025i 0.0301511 0.0522233i
$$276$$ 0 0
$$277$$ −5.00000 8.66025i −0.300421 0.520344i 0.675810 0.737075i $$-0.263794\pi$$
−0.976231 + 0.216731i $$0.930460\pi$$
$$278$$ −12.0000 −0.719712
$$279$$ −1.50000 + 2.59808i −0.0898027 + 0.155543i
$$280$$ −6.00000 −0.358569
$$281$$ 6.00000 + 10.3923i 0.357930 + 0.619953i 0.987615 0.156898i $$-0.0501493\pi$$
−0.629685 + 0.776851i $$0.716816\pi$$
$$282$$ 3.00000 + 1.73205i 0.178647 + 0.103142i
$$283$$ 12.5000 21.6506i 0.743048 1.28700i −0.208053 0.978117i $$-0.566713\pi$$
0.951101 0.308879i $$-0.0999539\pi$$
$$284$$ 0 0
$$285$$ 4.50000 + 2.59808i 0.266557 + 0.153897i
$$286$$ 0.500000 + 0.866025i 0.0295656 + 0.0512092i
$$287$$ 0 0
$$288$$ −7.50000 + 12.9904i −0.441942 + 0.765466i
$$289$$ −13.0000 −0.764706
$$290$$ −2.50000 4.33013i −0.146805 0.254274i
$$291$$ −1.50000 + 0.866025i −0.0879316 + 0.0507673i
$$292$$ 3.00000 5.19615i 0.175562 0.304082i
$$293$$ −0.500000 + 0.866025i −0.0292103 + 0.0505937i −0.880261 0.474490i $$-0.842633\pi$$
0.851051 + 0.525084i $$0.175966\pi$$
$$294$$ 5.19615i 0.303046i
$$295$$ −4.50000 7.79423i −0.262000 0.453798i
$$296$$ −15.0000 −0.871857
$$297$$ −4.50000 + 2.59808i −0.261116 + 0.150756i
$$298$$ −6.00000 −0.347571
$$299$$ 0 0
$$300$$ 1.73205i 0.100000i
$$301$$ 8.00000 13.8564i 0.461112 0.798670i
$$302$$ −4.00000 + 6.92820i −0.230174 + 0.398673i
$$303$$ −4.50000 + 2.59808i −0.258518 + 0.149256i
$$304$$ −1.50000 2.59808i −0.0860309 0.149010i
$$305$$ 1.00000 0.0572598
$$306$$ −3.00000 5.19615i −0.171499 0.297044i
$$307$$ 2.00000 0.114146 0.0570730 0.998370i $$-0.481823\pi$$
0.0570730 + 0.998370i $$0.481823\pi$$
$$308$$ −1.00000 1.73205i −0.0569803 0.0986928i
$$309$$ −1.50000 0.866025i −0.0853320 0.0492665i
$$310$$ 0.500000 0.866025i 0.0283981 0.0491869i
$$311$$ 2.00000 3.46410i 0.113410 0.196431i −0.803733 0.594990i $$-0.797156\pi$$
0.917143 + 0.398559i $$0.130489\pi$$
$$312$$ −4.50000 2.59808i −0.254762 0.147087i
$$313$$ 14.0000 + 24.2487i 0.791327 + 1.37062i 0.925146 + 0.379612i $$0.123943\pi$$
−0.133819 + 0.991006i $$0.542724\pi$$
$$314$$ 6.00000 0.338600
$$315$$ 6.00000 0.338062
$$316$$ 12.0000 0.675053
$$317$$ 13.5000 + 23.3827i 0.758236 + 1.31330i 0.943750 + 0.330661i $$0.107272\pi$$
−0.185514 + 0.982642i $$0.559395\pi$$
$$318$$ 21.0000 12.1244i 1.17762 0.679900i
$$319$$ 2.50000 4.33013i 0.139973 0.242441i
$$320$$ 3.50000 6.06218i 0.195656 0.338886i
$$321$$ 32.9090i 1.83680i
$$322$$ 0 0
$$323$$ −6.00000 −0.333849
$$324$$ 4.50000 7.79423i 0.250000 0.433013i
$$325$$ −1.00000 −0.0554700
$$326$$ −6.00000 10.3923i −0.332309 0.575577i
$$327$$ 24.2487i 1.34096i
$$328$$ 0 0
$$329$$ 2.00000 3.46410i 0.110264 0.190982i
$$330$$ 1.50000 0.866025i 0.0825723 0.0476731i
$$331$$ −13.5000 23.3827i −0.742027 1.28523i −0.951571 0.307429i $$-0.900531\pi$$
0.209544 0.977799i $$-0.432802\pi$$
$$332$$ 10.0000 0.548821
$$333$$ 15.0000 0.821995
$$334$$ 0 0
$$335$$ 7.00000 + 12.1244i 0.382451 + 0.662424i
$$336$$ −3.00000 1.73205i −0.163663 0.0944911i
$$337$$ 11.0000 19.0526i 0.599208 1.03786i −0.393730 0.919226i $$-0.628816\pi$$
0.992938 0.118633i $$-0.0378512\pi$$
$$338$$ 0.500000 0.866025i 0.0271964 0.0471056i
$$339$$ 15.0000 + 8.66025i 0.814688 + 0.470360i
$$340$$ −1.00000 1.73205i −0.0542326 0.0939336i
$$341$$ 1.00000 0.0541530
$$342$$ 4.50000 + 7.79423i 0.243332 + 0.421464i
$$343$$ −20.0000 −1.07990
$$344$$ 12.0000 + 20.7846i 0.646997 + 1.12063i
$$345$$ 0 0
$$346$$ 6.00000 10.3923i 0.322562 0.558694i
$$347$$ −8.50000 + 14.7224i −0.456304 + 0.790342i −0.998762 0.0497412i $$-0.984160\pi$$
0.542458 + 0.840083i $$0.317494\pi$$
$$348$$ 8.66025i 0.464238i
$$349$$ −6.00000 10.3923i −0.321173 0.556287i 0.659558 0.751654i $$-0.270744\pi$$
−0.980730 + 0.195367i $$0.937410\pi$$
$$350$$ −2.00000 −0.106904
$$351$$ 4.50000 + 2.59808i 0.240192 + 0.138675i
$$352$$ 5.00000 0.266501
$$353$$ 1.50000 + 2.59808i 0.0798369 + 0.138282i 0.903179 0.429263i $$-0.141227\pi$$
−0.823343 + 0.567545i $$0.807893\pi$$
$$354$$ 15.5885i 0.828517i
$$355$$ 0 0
$$356$$ 1.00000 1.73205i 0.0529999 0.0917985i
$$357$$ −6.00000 + 3.46410i −0.317554 + 0.183340i
$$358$$ −9.00000 15.5885i −0.475665 0.823876i
$$359$$ −31.0000 −1.63612 −0.818059 0.575135i $$-0.804950\pi$$
−0.818059 + 0.575135i $$0.804950\pi$$
$$360$$ −4.50000 + 7.79423i −0.237171 + 0.410792i
$$361$$ −10.0000 −0.526316
$$362$$ 8.50000 + 14.7224i 0.446750 + 0.773794i
$$363$$ −15.0000 8.66025i −0.787296 0.454545i
$$364$$ −1.00000 + 1.73205i −0.0524142 + 0.0907841i
$$365$$ 3.00000 5.19615i 0.157027 0.271979i
$$366$$ 1.50000 + 0.866025i 0.0784063 + 0.0452679i
$$367$$ −12.5000 21.6506i −0.652495 1.13015i −0.982516 0.186180i $$-0.940389\pi$$
0.330021 0.943974i $$-0.392944\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ −5.00000 −0.259938
$$371$$ −14.0000 24.2487i −0.726844 1.25893i
$$372$$ −1.50000 + 0.866025i −0.0777714 + 0.0449013i
$$373$$ 10.0000 17.3205i 0.517780 0.896822i −0.482006 0.876168i $$-0.660092\pi$$
0.999787 0.0206542i $$-0.00657489\pi$$
$$374$$ −1.00000 + 1.73205i −0.0517088 + 0.0895622i
$$375$$ 1.73205i 0.0894427i
$$376$$ 3.00000 + 5.19615i 0.154713 + 0.267971i
$$377$$ −5.00000 −0.257513
$$378$$ 9.00000 + 5.19615i 0.462910 + 0.267261i
$$379$$ −23.0000 −1.18143 −0.590715 0.806880i $$-0.701154\pi$$
−0.590715 + 0.806880i $$0.701154\pi$$
$$380$$ 1.50000 + 2.59808i 0.0769484 + 0.133278i
$$381$$ 13.8564i 0.709885i
$$382$$ 9.00000 15.5885i 0.460480 0.797575i
$$383$$ 6.00000 10.3923i 0.306586 0.531022i −0.671027 0.741433i $$-0.734147\pi$$
0.977613 + 0.210411i $$0.0674801\pi$$
$$384$$ −4.50000 + 2.59808i −0.229640 + 0.132583i
$$385$$ −1.00000 1.73205i −0.0509647 0.0882735i
$$386$$ −13.0000 −0.661683
$$387$$ −12.0000 20.7846i −0.609994 1.05654i
$$388$$ −1.00000 −0.0507673
$$389$$ 11.0000 + 19.0526i 0.557722 + 0.966003i 0.997686 + 0.0679877i $$0.0216579\pi$$
−0.439964 + 0.898015i $$0.645009\pi$$
$$390$$ −1.50000 0.866025i −0.0759555 0.0438529i
$$391$$ 0 0
$$392$$ 4.50000 7.79423i 0.227284 0.393668i
$$393$$ −6.00000 3.46410i −0.302660 0.174741i
$$394$$ 7.50000 + 12.9904i 0.377845 + 0.654446i
$$395$$ 12.0000 0.603786
$$396$$ −3.00000 −0.150756
$$397$$ −30.0000 −1.50566 −0.752828 0.658217i $$-0.771311\pi$$
−0.752828 + 0.658217i $$0.771311\pi$$
$$398$$ −11.0000 19.0526i −0.551380 0.955018i
$$399$$ 9.00000 5.19615i 0.450564 0.260133i
$$400$$ 0.500000 0.866025i 0.0250000 0.0433013i
$$401$$ −14.0000 + 24.2487i −0.699127 + 1.21092i 0.269643 + 0.962960i $$0.413094\pi$$
−0.968770 + 0.247962i $$0.920239\pi$$
$$402$$ 24.2487i 1.20942i
$$403$$ −0.500000 0.866025i −0.0249068 0.0431398i
$$404$$ −3.00000 −0.149256
$$405$$ 4.50000 7.79423i 0.223607 0.387298i
$$406$$ −10.0000 −0.496292
$$407$$ −2.50000 4.33013i −0.123920 0.214636i
$$408$$ 10.3923i 0.514496i
$$409$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$410$$ 0 0
$$411$$ 7.50000 4.33013i 0.369948 0.213589i
$$412$$ −0.500000 0.866025i −0.0246332 0.0426660i
$$413$$ −18.0000 −0.885722
$$414$$ 0 0
$$415$$ 10.0000 0.490881
$$416$$ −2.50000 4.33013i −0.122573 0.212302i
$$417$$ 18.0000 + 10.3923i 0.881464 + 0.508913i
$$418$$ 1.50000 2.59808i 0.0733674 0.127076i
$$419$$ −10.0000 + 17.3205i −0.488532 + 0.846162i −0.999913 0.0131919i $$-0.995801\pi$$
0.511381 + 0.859354i $$0.329134\pi$$
$$420$$ 3.00000 + 1.73205i 0.146385 + 0.0845154i
$$421$$ −5.00000 8.66025i −0.243685 0.422075i 0.718076 0.695965i $$-0.245023\pi$$
−0.961761 + 0.273890i $$0.911690\pi$$
$$422$$ 0 0
$$423$$ −3.00000 5.19615i −0.145865 0.252646i
$$424$$ 42.0000 2.03970
$$425$$ −1.00000 1.73205i −0.0485071 0.0840168i
$$426$$ 0 0
$$427$$ 1.00000 1.73205i 0.0483934 0.0838198i
$$428$$ 9.50000 16.4545i 0.459200 0.795357i
$$429$$ 1.73205i 0.0836242i
$$430$$ 4.00000 + 6.92820i 0.192897 + 0.334108i
$$431$$ 17.0000 0.818861 0.409431 0.912341i $$-0.365727\pi$$
0.409431 + 0.912341i $$0.365727\pi$$
$$432$$ −4.50000 + 2.59808i −0.216506 + 0.125000i
$$433$$ −38.0000 −1.82616 −0.913082 0.407777i $$-0.866304\pi$$
−0.913082 + 0.407777i $$0.866304\pi$$
$$434$$ −1.00000 1.73205i −0.0480015 0.0831411i
$$435$$ 8.66025i 0.415227i
$$436$$ −7.00000 + 12.1244i −0.335239 + 0.580651i
$$437$$ 0 0
$$438$$ 9.00000 5.19615i 0.430037 0.248282i
$$439$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$440$$ 3.00000 0.143019
$$441$$ −4.50000 + 7.79423i −0.214286 + 0.371154i
$$442$$ 2.00000 0.0951303
$$443$$ 3.50000 + 6.06218i 0.166290 + 0.288023i 0.937113 0.349027i $$-0.113488\pi$$
−0.770823 + 0.637050i $$0.780155\pi$$
$$444$$ 7.50000 + 4.33013i 0.355934 + 0.205499i
$$445$$ 1.00000 1.73205i 0.0474045 0.0821071i
$$446$$ −13.0000 + 22.5167i −0.615568 + 1.06619i
$$447$$ 9.00000 + 5.19615i 0.425685 + 0.245770i
$$448$$ −7.00000 12.1244i −0.330719 0.572822i
$$449$$ −30.0000 −1.41579 −0.707894 0.706319i $$-0.750354\pi$$
−0.707894 + 0.706319i $$0.750354\pi$$
$$450$$ −1.50000 + 2.59808i −0.0707107 + 0.122474i
$$451$$ 0 0
$$452$$ 5.00000 + 8.66025i 0.235180 + 0.407344i
$$453$$ 12.0000 6.92820i 0.563809 0.325515i
$$454$$ −13.0000 + 22.5167i −0.610120 + 1.05676i
$$455$$ −1.00000 + 1.73205i −0.0468807 + 0.0811998i
$$456$$ 15.5885i 0.729996i
$$457$$ −13.0000 22.5167i −0.608114 1.05328i −0.991551 0.129718i $$-0.958593\pi$$
0.383437 0.923567i $$-0.374740\pi$$
$$458$$ 16.0000 0.747631
$$459$$ 10.3923i 0.485071i
$$460$$ 0 0
$$461$$ 13.0000 + 22.5167i 0.605470 + 1.04871i 0.991977 + 0.126419i $$0.0403483\pi$$
−0.386507 + 0.922287i $$0.626318\pi$$
$$462$$ 3.46410i 0.161165i
$$463$$ 3.00000 5.19615i 0.139422 0.241486i −0.787856 0.615859i $$-0.788809\pi$$
0.927278 + 0.374374i $$0.122142\pi$$
$$464$$ 2.50000 4.33013i 0.116060 0.201021i
$$465$$ −1.50000 + 0.866025i −0.0695608 + 0.0401610i
$$466$$ −7.00000 12.1244i −0.324269 0.561650i
$$467$$ −28.0000 −1.29569 −0.647843 0.761774i $$-0.724329\pi$$
−0.647843 + 0.761774i $$0.724329\pi$$
$$468$$ 1.50000 + 2.59808i 0.0693375 + 0.120096i
$$469$$ 28.0000 1.29292
$$470$$ 1.00000 + 1.73205i 0.0461266 + 0.0798935i
$$471$$ −9.00000 5.19615i −0.414698 0.239426i
$$472$$ 13.5000 23.3827i 0.621388 1.07628i
$$473$$ −4.00000 + 6.92820i −0.183920 + 0.318559i
$$474$$ 18.0000 + 10.3923i 0.826767 + 0.477334i
$$475$$ 1.50000 + 2.59808i 0.0688247 + 0.119208i
$$476$$ −4.00000 −0.183340
$$477$$ −42.0000 −1.92305
$$478$$ −15.0000 −0.686084
$$479$$ −7.50000 12.9904i −0.342684 0.593546i 0.642246 0.766498i $$-0.278003\pi$$
−0.984930 + 0.172953i $$0.944669\pi$$
$$480$$ −7.50000 + 4.33013i −0.342327 + 0.197642i
$$481$$ −2.50000 + 4.33013i −0.113990 + 0.197437i
$$482$$ 5.00000 8.66025i 0.227744 0.394464i
$$483$$ 0 0
$$484$$ −5.00000 8.66025i −0.227273 0.393648i
$$485$$ −1.00000 −0.0454077
$$486$$ 13.5000 7.79423i 0.612372 0.353553i
$$487$$ −34.0000 −1.54069 −0.770344 0.637629i $$-0.779915\pi$$
−0.770344 + 0.637629i $$0.779915\pi$$
$$488$$ 1.50000 + 2.59808i 0.0679018 + 0.117609i
$$489$$ 20.7846i 0.939913i
$$490$$ 1.50000 2.59808i 0.0677631 0.117369i
$$491$$ 3.00000 5.19615i 0.135388 0.234499i −0.790358 0.612646i $$-0.790105\pi$$
0.925746 + 0.378147i $$0.123439\pi$$
$$492$$ 0 0
$$493$$ −5.00000 8.66025i −0.225189 0.390038i
$$494$$ −3.00000 −0.134976
$$495$$ −3.00000 −0.134840
$$496$$ 1.00000 0.0449013
$$497$$ 0 0
$$498$$ 15.0000 + 8.66025i 0.672166 + 0.388075i
$$499$$ −14.0000 + 24.2487i −0.626726 + 1.08552i 0.361478 + 0.932381i $$0.382272\pi$$
−0.988204 + 0.153141i $$0.951061\pi$$
$$500$$ −0.500000 + 0.866025i −0.0223607 + 0.0387298i
$$501$$ 0 0
$$502$$ 6.00000 + 10.3923i 0.267793 + 0.463831i
$$503$$ −9.00000 −0.401290 −0.200645 0.979664i $$-0.564304\pi$$
−0.200645 + 0.979664i $$0.564304\pi$$
$$504$$ 9.00000 + 15.5885i 0.400892 + 0.694365i
$$505$$ −3.00000 −0.133498
$$506$$ 0 0
$$507$$ −1.50000 + 0.866025i −0.0666173 + 0.0384615i
$$508$$ −4.00000 + 6.92820i −0.177471 + 0.307389i
$$509$$ 12.0000 20.7846i 0.531891 0.921262i −0.467416 0.884037i $$-0.654815\pi$$
0.999307 0.0372243i $$-0.0118516\pi$$
$$510$$ 3.46410i 0.153393i
$$511$$ −6.00000 10.3923i −0.265424 0.459728i
$$512$$ 11.0000 0.486136
$$513$$ 15.5885i 0.688247i
$$514$$ 28.0000 1.23503
$$515$$ −0.500000 0.866025i −0.0220326 0.0381616i
$$516$$ 13.8564i 0.609994i
$$517$$ −1.00000 + 1.73205i −0.0439799 + 0.0761755i
$$518$$ −5.00000 + 8.66025i −0.219687 + 0.380510i
$$519$$ −18.0000 + 10.3923i −0.790112 + 0.456172i
$$520$$ −1.50000 2.59808i −0.0657794 0.113933i
$$521$$ 6.00000 0.262865 0.131432 0.991325i $$-0.458042\pi$$
0.131432 + 0.991325i $$0.458042\pi$$
$$522$$ −7.50000 + 12.9904i −0.328266 + 0.568574i
$$523$$ −15.0000 −0.655904 −0.327952 0.944694i $$-0.606358\pi$$
−0.327952 + 0.944694i $$0.606358\pi$$
$$524$$ −2.00000 3.46410i −0.0873704 0.151330i
$$525$$ 3.00000 + 1.73205i 0.130931 + 0.0755929i
$$526$$ −8.00000 + 13.8564i −0.348817 + 0.604168i
$$527$$ 1.00000 1.73205i 0.0435607 0.0754493i
$$528$$ 1.50000 + 0.866025i 0.0652791 + 0.0376889i
$$529$$ 11.5000 + 19.9186i 0.500000 + 0.866025i
$$530$$ 14.0000 0.608121
$$531$$ −13.5000 + 23.3827i −0.585850 + 1.01472i
$$532$$ 6.00000 0.260133
$$533$$ 0 0
$$534$$ 3.00000 1.73205i 0.129823 0.0749532i
$$535$$ 9.50000 16.4545i 0.410721 0.711389i
$$536$$ −21.0000 + 36.3731i −0.907062 + 1.57108i
$$537$$ 31.1769i 1.34538i
$$538$$ 1.50000 + 2.59808i 0.0646696 + 0.112011i
$$539$$ 3.00000 0.129219
$$540$$ 4.50000 2.59808i 0.193649 0.111803i
$$541$$ 32.0000 1.37579 0.687894 0.725811i $$-0.258536\pi$$
0.687894 + 0.725811i $$0.258536\pi$$
$$542$$ −3.50000 6.06218i −0.150338 0.260393i
$$543$$ 29.4449i 1.26360i
$$544$$ 5.00000 8.66025i 0.214373 0.371305i
$$545$$ −7.00000 + 12.1244i −0.299847 + 0.519350i
$$546$$ −3.00000 + 1.73205i −0.128388 + 0.0741249i
$$547$$ 7.50000 + 12.9904i 0.320677 + 0.555429i 0.980628 0.195880i $$-0.0627563\pi$$
−0.659951 + 0.751309i $$0.729423\pi$$
$$548$$ 5.00000 0.213589
$$549$$ −1.50000 2.59808i −0.0640184 0.110883i
$$550$$ 1.00000 0.0426401
$$551$$ 7.50000 + 12.9904i 0.319511 + 0.553409i
$$552$$ 0 0
$$553$$ 12.0000 20.7846i 0.510292 0.883852i
$$554$$ 5.00000 8.66025i 0.212430 0.367939i
$$555$$ 7.50000 + 4.33013i 0.318357 + 0.183804i
$$556$$ 6.00000 + 10.3923i 0.254457 + 0.440732i
$$557$$ −5.00000 −0.211857 −0.105928 0.994374i $$-0.533781\pi$$
−0.105928 + 0.994374i $$0.533781\pi$$
$$558$$ −3.00000 −0.127000
$$559$$ 8.00000 0.338364
$$560$$ −1.00000 1.73205i −0.0422577 0.0731925i
$$561$$ 3.00000 1.73205i 0.126660 0.0731272i
$$562$$ −6.00000 + 10.3923i −0.253095 + 0.438373i
$$563$$ 9.50000 16.4545i 0.400377 0.693474i −0.593394 0.804912i $$-0.702212\pi$$
0.993771 + 0.111438i $$0.0355457\pi$$
$$564$$ 3.46410i 0.145865i
$$565$$ 5.00000 + 8.66025i 0.210352 + 0.364340i
$$566$$ 25.0000 1.05083
$$567$$ −9.00000 15.5885i −0.377964 0.654654i
$$568$$ 0 0
$$569$$ 5.50000 + 9.52628i 0.230572 + 0.399362i 0.957977 0.286846i $$-0.0926069\pi$$
−0.727405 + 0.686209i $$0.759274\pi$$
$$570$$ 5.19615i 0.217643i
$$571$$ −6.00000 + 10.3923i −0.251092 + 0.434904i −0.963827 0.266529i $$-0.914123\pi$$
0.712735 + 0.701434i $$0.247456\pi$$
$$572$$ 0.500000 0.866025i 0.0209061 0.0362103i
$$573$$ −27.0000 + 15.5885i −1.12794 + 0.651217i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −21.0000 −0.875000
$$577$$ 11.0000 0.457936 0.228968 0.973434i $$-0.426465\pi$$
0.228968 + 0.973434i $$0.426465\pi$$
$$578$$ −6.50000 11.2583i −0.270364 0.468285i
$$579$$ 19.5000 + 11.2583i 0.810392 + 0.467880i
$$580$$ −2.50000 + 4.33013i −0.103807 + 0.179799i
$$581$$ 10.0000 17.3205i 0.414870 0.718576i
$$582$$ −1.50000 0.866025i −0.0621770 0.0358979i
$$583$$ 7.00000 + 12.1244i 0.289910 + 0.502140i
$$584$$ 18.0000 0.744845
$$585$$ 1.50000 + 2.59808i 0.0620174 + 0.107417i
$$586$$ −1.00000 −0.0413096
$$587$$ 7.00000 + 12.1244i 0.288921 + 0.500426i 0.973552 0.228464i $$-0.0733702\pi$$
−0.684632 + 0.728889i $$0.740037\pi$$
$$588$$ −4.50000 + 2.59808i −0.185577 + 0.107143i
$$589$$ −1.50000 + 2.59808i −0.0618064 + 0.107052i
$$590$$ 4.50000 7.79423i 0.185262 0.320883i
$$591$$ 25.9808i 1.06871i
$$592$$ −2.50000 4.33013i −0.102749 0.177967i
$$593$$ −31.0000 −1.27302 −0.636509 0.771270i $$-0.719622\pi$$
−0.636509 + 0.771270i $$0.719622\pi$$
$$594$$ −4.50000 2.59808i −0.184637 0.106600i
$$595$$ −4.00000 −0.163984
$$596$$ 3.00000 + 5.19615i 0.122885 + 0.212843i
$$597$$ 38.1051i 1.55954i
$$598$$ 0 0
$$599$$ −7.00000 + 12.1244i −0.286012 + 0.495388i −0.972854 0.231419i $$-0.925663\pi$$
0.686842 + 0.726807i $$0.258996\pi$$
$$600$$ −4.50000 + 2.59808i −0.183712 + 0.106066i
$$601$$ 8.50000 + 14.7224i 0.346722 + 0.600541i 0.985665 0.168714i $$-0.0539613\pi$$
−0.638943 + 0.769254i $$0.720628\pi$$
$$602$$ 16.0000 0.652111
$$603$$ 21.0000 36.3731i 0.855186 1.48123i
$$604$$ 8.00000 0.325515
$$605$$ −5.00000 8.66025i −0.203279 0.352089i
$$606$$ −4.50000 2.59808i −0.182800 0.105540i
$$607$$ 4.00000 6.92820i 0.162355 0.281207i −0.773358 0.633970i $$-0.781424\pi$$
0.935713 + 0.352763i $$0.114758\pi$$
$$608$$ −7.50000 + 12.9904i −0.304165 + 0.526830i
$$609$$ 15.0000 + 8.66025i 0.607831 + 0.350931i
$$610$$ 0.500000 + 0.866025i 0.0202444 + 0.0350643i
$$611$$ 2.00000 0.0809113
$$612$$ −3.00000 + 5.19615i −0.121268 + 0.210042i
$$613$$ 30.0000 1.21169 0.605844 0.795583i $$-0.292835\pi$$
0.605844 + 0.795583i $$0.292835\pi$$
$$614$$ 1.00000 + 1.73205i 0.0403567 + 0.0698999i
$$615$$ 0 0
$$616$$ 3.00000 5.19615i 0.120873 0.209359i
$$617$$ −4.50000 + 7.79423i −0.181163 + 0.313784i −0.942277 0.334835i $$-0.891320\pi$$
0.761114 + 0.648618i $$0.224653\pi$$
$$618$$ 1.73205i 0.0696733i
$$619$$ 5.50000 + 9.52628i 0.221064 + 0.382893i 0.955131 0.296183i $$-0.0957138\pi$$
−0.734068 + 0.679076i $$0.762380\pi$$
$$620$$ −1.00000 −0.0401610
$$621$$ 0 0
$$622$$ 4.00000 0.160385
$$623$$ −2.00000 3.46410i −0.0801283 0.138786i
$$624$$ 1.73205i 0.0693375i
$$625$$ −0.500000 + 0.866025i −0.0200000 + 0.0346410i
$$626$$ −14.0000 + 24.2487i −0.559553 + 0.969173i
$$627$$ −4.50000 + 2.59808i −0.179713 + 0.103757i
$$628$$ −3.00000 5.19615i −0.119713 0.207349i
$$629$$ −10.0000 −0.398726
$$630$$ 3.00000 + 5.19615i 0.119523 + 0.207020i
$$631$$ −5.00000 −0.199047 −0.0995234 0.995035i $$-0.531732\pi$$
−0.0995234 + 0.995035i $$0.531732\pi$$
$$632$$ 18.0000 + 31.1769i 0.716002 + 1.24015i
$$633$$ 0 0
$$634$$ −13.5000 + 23.3827i −0.536153 + 0.928645i
$$635$$ −4.00000 + 6.92820i −0.158735 + 0.274937i
$$636$$ −21.0000 12.1244i −0.832704 0.480762i
$$637$$ −1.50000 2.59808i −0.0594322 0.102940i
$$638$$ 5.00000 0.197952
$$639$$ 0 0
$$640$$ −3.00000 −0.118585
$$641$$ −8.50000 14.7224i −0.335730 0.581501i 0.647895 0.761730i $$-0.275650\pi$$
−0.983625 + 0.180229i $$0.942316\pi$$
$$642$$ 28.5000 16.4545i 1.12481 0.649407i
$$643$$ −16.0000 + 27.7128i −0.630978 + 1.09289i 0.356374 + 0.934344i $$0.384013\pi$$
−0.987352 + 0.158543i $$0.949320\pi$$
$$644$$ 0 0
$$645$$ 13.8564i 0.545595i
$$646$$ −3.00000 5.19615i −0.118033 0.204440i
$$647$$ 41.0000 1.61188 0.805938 0.592000i $$-0.201661\pi$$
0.805938 + 0.592000i $$0.201661\pi$$
$$648$$ 27.0000 1.06066
$$649$$ 9.00000 0.353281
$$650$$ −0.500000 0.866025i −0.0196116 0.0339683i
$$651$$ 3.46410i 0.135769i
$$652$$ −6.00000 + 10.3923i −0.234978 + 0.406994i
$$653$$ −24.0000 + 41.5692i −0.939193 + 1.62673i −0.172211 + 0.985060i $$0.555091\pi$$
−0.766982 + 0.641669i $$0.778242\pi$$
$$654$$ −21.0000 + 12.1244i −0.821165 + 0.474100i
$$655$$ −2.00000 3.46410i −0.0781465 0.135354i
$$656$$ 0 0
$$657$$ −18.0000 −0.702247
$$658$$ 4.00000 0.155936
$$659$$ 18.0000 + 31.1769i 0.701180 + 1.21448i 0.968052 + 0.250748i $$0.0806766\pi$$
−0.266872 + 0.963732i $$0.585990\pi$$
$$660$$ −1.50000 0.866025i −0.0583874 0.0337100i
$$661$$ −19.0000 + 32.9090i −0.739014 + 1.28001i 0.213925 + 0.976850i $$0.431375\pi$$
−0.952940 + 0.303160i $$0.901958\pi$$
$$662$$ 13.5000 23.3827i 0.524692 0.908794i
$$663$$ −3.00000 1.73205i −0.116510 0.0672673i
$$664$$ 15.0000 + 25.9808i 0.582113 + 1.00825i
$$665$$ 6.00000 0.232670
$$666$$ 7.50000 + 12.9904i 0.290619 + 0.503367i
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 39.0000 22.5167i 1.50783 0.870544i
$$670$$ −7.00000 + 12.1244i −0.270434 + 0.468405i
$$671$$ −0.500000 + 0.866025i −0.0193023 + 0.0334325i
$$672$$ 17.3205i 0.668153i
$$673$$ −12.0000 20.7846i −0.462566 0.801188i 0.536522 0.843886i $$-0.319738\pi$$
−0.999088 + 0.0426985i $$0.986405\pi$$
$$674$$ 22.0000 0.847408
$$675$$ 4.50000 2.59808i 0.173205 0.100000i
$$676$$ −1.00000 −0.0384615
$$677$$ −3.00000 5.19615i −0.115299 0.199704i 0.802600 0.596518i $$-0.203449\pi$$
−0.917899 + 0.396813i $$0.870116\pi$$
$$678$$ 17.3205i 0.665190i
$$679$$ −1.00000 + 1.73205i −0.0383765 + 0.0664700i
$$680$$ 3.00000 5.19615i 0.115045 0.199263i
$$681$$ 39.0000 22.5167i 1.49448 0.862840i
$$682$$ 0.500000 + 0.866025i 0.0191460 + 0.0331618i
$$683$$ −20.0000 −0.765279 −0.382639 0.923898i $$-0.624985\pi$$
−0.382639 + 0.923898i $$0.624985\pi$$
$$684$$ 4.50000 7.79423i 0.172062 0.298020i
$$685$$ 5.00000 0.191040
$$686$$ −10.0000 17.3205i −0.381802 0.661300i
$$687$$ −24.0000 13.8564i −0.915657 0.528655i
$$688$$ −4.00000 + 6.92820i −0.152499 + 0.264135i
$$689$$ 7.00000 12.1244i 0.266679 0.461901i
$$690$$ 0 0
$$691$$ −0.500000 0.866025i −0.0190209 0.0329452i 0.856358 0.516382i $$-0.172722\pi$$
−0.875379 + 0.483437i $$0.839388\pi$$
$$692$$ −12.0000 −0.456172
$$693$$ −3.00000 + 5.19615i −0.113961 + 0.197386i
$$694$$ −17.0000 −0.645311
$$695$$ 6.00000 + 10.3923i 0.227593 + 0.394203i
$$696$$ −22.5000 + 12.9904i −0.852860 + 0.492399i
$$697$$ 0 0
$$698$$ 6.00000 10.3923i 0.227103 0.393355i
$$699$$ 24.2487i 0.917170i
$$700$$ 1.00000 + 1.73205i 0.0377964 + 0.0654654i
$$701$$ −5.00000 −0.188847 −0.0944237 0.995532i $$-0.530101\pi$$
−0.0944237 + 0.995532i $$0.530101\pi$$
$$702$$ 5.19615i 0.196116i
$$703$$ 15.0000 0.565736
$$704$$ 3.50000 + 6.06218i 0.131911 + 0.228477i
$$705$$ 3.46410i 0.130466i
$$706$$ −1.50000 + 2.59808i −0.0564532 + 0.0977799i
$$707$$ −3.00000 + 5.19615i −0.112827 + 0.195421i
$$708$$ −13.5000 + 7.79423i −0.507361 + 0.292925i
$$709$$ −2.00000 3.46410i −0.0751116 0.130097i 0.826023 0.563636i $$-0.190598\pi$$
−0.901135 + 0.433539i $$0.857265\pi$$
$$710$$ 0 0
$$711$$ −18.0000 31.1769i −0.675053 1.16923i
$$712$$ 6.00000 0.224860
$$713$$ 0 0
$$714$$ −6.00000 3.46410i −0.224544 0.129641i
$$715$$ 0.500000 0.866025i 0.0186989 0.0323875i
$$716$$ −9.00000 + 15.5885i −0.336346 + 0.582568i
$$717$$ 22.5000 + 12.9904i 0.840278 + 0.485135i
$$718$$ −15.5000 26.8468i −0.578455 1.00191i
$$719$$ −2.00000 −0.0745874 −0.0372937 0.999304i $$-0.511874\pi$$
−0.0372937 + 0.999304i $$0.511874\pi$$
$$720$$ −3.00000 −0.111803
$$721$$ −2.00000 −0.0744839
$$722$$ −5.00000 8.66025i −0.186081 0.322301i
$$723$$ −15.0000 + 8.66025i −0.557856 + 0.322078i
$$724$$ 8.50000 14.7224i 0.315900 0.547155i
$$725$$ −2.50000 + 4.33013i −0.0928477 + 0.160817i
$$726$$ 17.3205i 0.642824i
$$727$$ −24.0000 41.5692i −0.890111 1.54172i −0.839742 0.542986i $$-0.817294\pi$$
−0.0503692 0.998731i $$-0.516040\pi$$
$$728$$ −6.00000 −0.222375
$$729$$ −27.0000 −1.00000
$$730$$ 6.00000 0.222070
$$731$$ 8.00000 + 13.8564i 0.295891 + 0.512498i
$$732$$ 1.73205i 0.0640184i
$$733$$ −6.50000 + 11.2583i −0.240083 + 0.415836i −0.960738 0.277458i $$-0.910508\pi$$
0.720655 + 0.693294i $$0.243841\pi$$
$$734$$ 12.5000 21.6506i 0.461383 0.799140i
$$735$$ −4.50000 + 2.59808i −0.165985 + 0.0958315i
$$736$$ 0 0
$$737$$ −14.0000 −0.515697
$$738$$ 0 0
$$739$$ 9.00000 0.331070 0.165535 0.986204i $$-0.447065\pi$$
0.165535 + 0.986204i $$0.447065\pi$$
$$740$$ 2.50000 + 4.33013i 0.0919018 + 0.159179i
$$741$$ 4.50000 + 2.59808i 0.165312 + 0.0954427i
$$742$$ 14.0000 24.2487i 0.513956 0.890198i
$$743$$ 24.0000 41.5692i 0.880475 1.52503i 0.0296605 0.999560i $$-0.490557\pi$$
0.850814 0.525467i $$-0.176109\pi$$
$$744$$ −4.50000 2.59808i −0.164978 0.0952501i
$$745$$ 3.00000 + 5.19615i 0.109911 + 0.190372i
$$746$$ 20.0000 0.732252
$$747$$ −15.0000 25.9808i −0.548821 0.950586i
$$748$$ 2.00000 0.0731272
$$749$$ −19.0000 32.9090i −0.694245 1.20247i
$$750$$ −1.50000 + 0.866025i −0.0547723 + 0.0316228i
$$751$$ −1.00000 + 1.73205i −0.0364905 + 0.0632034i −0.883694 0.468065i $$-0.844951\pi$$
0.847203 + 0.531269i $$0.178285\pi$$
$$752$$ −1.00000 + 1.73205i −0.0364662 + 0.0631614i
$$753$$ 20.7846i 0.757433i
$$754$$ −2.50000 4.33013i −0.0910446 0.157694i
$$755$$ 8.00000 0.291150
$$756$$ 10.3923i 0.377964i
$$757$$ −16.0000 −0.581530 −0.290765 0.956795i $$-0.593910\pi$$
−0.290765 + 0.956795i $$0.593910\pi$$
$$758$$ −11.5000 19.9186i −0.417699 0.723476i
$$759$$ 0 0
$$760$$ −4.50000 + 7.79423i −0.163232 + 0.282726i
$$761$$ 18.0000 31.1769i 0.652499 1.13016i −0.330015 0.943976i $$-0.607054\pi$$
0.982514 0.186187i $$-0.0596129\pi$$
$$762$$ −12.0000 + 6.92820i −0.434714 + 0.250982i
$$763$$ 14.0000 + 24.2487i 0.506834 + 0.877862i
$$764$$ −18.0000 −0.651217
$$765$$ −3.00000 + 5.19615i −0.108465 + 0.187867i
$$766$$ 12.0000 0.433578
$$767$$ −4.50000 7.79423i −0.162486 0.281433i
$$768$$ −25.5000 14.7224i −0.920152 0.531250i
$$769$$ 20.0000 34.6410i 0.721218 1.24919i −0.239293 0.970947i $$-0.576916\pi$$
0.960512 0.278240i $$-0.0897509\pi$$
$$770$$ 1.00000 1.73205i 0.0360375 0.0624188i
$$771$$ −42.0000 24.2487i −1.51259 0.873296i
$$772$$ 6.50000 + 11.2583i 0.233940 + 0.405196i
$$773$$ 31.0000 1.11499 0.557496 0.830179i $$-0.311762\pi$$
0.557496 + 0.830179i $$0.311762\pi$$
$$774$$ 12.0000 20.7846i 0.431331 0.747087i
$$775$$ −1.00000 −0.0359211
$$776$$ −1.50000 2.59808i −0.0538469 0.0932655i
$$777$$ 15.0000 8.66025i 0.538122 0.310685i