# Properties

 Label 722.2.c.d.429.1 Level $722$ Weight $2$ Character 722.429 Analytic conductor $5.765$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$722 = 2 \cdot 19^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 722.c (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.76519902594$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 38) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 429.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 722.429 Dual form 722.2.c.d.653.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.00000 - 3.46410i) q^{5} +(0.500000 + 0.866025i) q^{6} +3.00000 q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.00000 - 3.46410i) q^{5} +(0.500000 + 0.866025i) q^{6} +3.00000 q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(2.00000 + 3.46410i) q^{10} +2.00000 q^{11} -1.00000 q^{12} +(0.500000 + 0.866025i) q^{13} +(-1.50000 + 2.59808i) q^{14} +(-2.00000 - 3.46410i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} -2.00000 q^{18} -4.00000 q^{20} +(1.50000 - 2.59808i) q^{21} +(-1.00000 + 1.73205i) q^{22} +(0.500000 + 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-5.50000 - 9.52628i) q^{25} -1.00000 q^{26} +5.00000 q^{27} +(-1.50000 - 2.59808i) q^{28} +(2.50000 + 4.33013i) q^{29} +4.00000 q^{30} -8.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.00000 - 1.73205i) q^{33} +(-1.50000 - 2.59808i) q^{34} +(6.00000 - 10.3923i) q^{35} +(1.00000 - 1.73205i) q^{36} -2.00000 q^{37} +1.00000 q^{39} +(2.00000 - 3.46410i) q^{40} +(4.00000 - 6.92820i) q^{41} +(1.50000 + 2.59808i) q^{42} +(-2.00000 + 3.46410i) q^{43} +(-1.00000 - 1.73205i) q^{44} +8.00000 q^{45} -1.00000 q^{46} +(-4.00000 - 6.92820i) q^{47} +(0.500000 + 0.866025i) q^{48} +2.00000 q^{49} +11.0000 q^{50} +(1.50000 + 2.59808i) q^{51} +(0.500000 - 0.866025i) q^{52} +(0.500000 + 0.866025i) q^{53} +(-2.50000 + 4.33013i) q^{54} +(4.00000 - 6.92820i) q^{55} +3.00000 q^{56} -5.00000 q^{58} +(-7.50000 + 12.9904i) q^{59} +(-2.00000 + 3.46410i) q^{60} +(-1.00000 - 1.73205i) q^{61} +(4.00000 - 6.92820i) q^{62} +(3.00000 + 5.19615i) q^{63} +1.00000 q^{64} +4.00000 q^{65} +(1.00000 + 1.73205i) q^{66} +(-1.50000 - 2.59808i) q^{67} +3.00000 q^{68} +1.00000 q^{69} +(6.00000 + 10.3923i) q^{70} +(-1.00000 + 1.73205i) q^{71} +(1.00000 + 1.73205i) q^{72} +(-4.50000 + 7.79423i) q^{73} +(1.00000 - 1.73205i) q^{74} -11.0000 q^{75} +6.00000 q^{77} +(-0.500000 + 0.866025i) q^{78} +(5.00000 - 8.66025i) q^{79} +(2.00000 + 3.46410i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.00000 + 6.92820i) q^{82} -6.00000 q^{83} -3.00000 q^{84} +(6.00000 + 10.3923i) q^{85} +(-2.00000 - 3.46410i) q^{86} +5.00000 q^{87} +2.00000 q^{88} +(-4.00000 + 6.92820i) q^{90} +(1.50000 + 2.59808i) q^{91} +(0.500000 - 0.866025i) q^{92} +(-4.00000 + 6.92820i) q^{93} +8.00000 q^{94} -1.00000 q^{96} +(1.00000 - 1.73205i) q^{97} +(-1.00000 + 1.73205i) q^{98} +(2.00000 + 3.46410i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - q^{2} + q^{3} - q^{4} + 4q^{5} + q^{6} + 6q^{7} + 2q^{8} + 2q^{9} + O(q^{10})$$ $$2q - q^{2} + q^{3} - q^{4} + 4q^{5} + q^{6} + 6q^{7} + 2q^{8} + 2q^{9} + 4q^{10} + 4q^{11} - 2q^{12} + q^{13} - 3q^{14} - 4q^{15} - q^{16} - 3q^{17} - 4q^{18} - 8q^{20} + 3q^{21} - 2q^{22} + q^{23} + q^{24} - 11q^{25} - 2q^{26} + 10q^{27} - 3q^{28} + 5q^{29} + 8q^{30} - 16q^{31} - q^{32} + 2q^{33} - 3q^{34} + 12q^{35} + 2q^{36} - 4q^{37} + 2q^{39} + 4q^{40} + 8q^{41} + 3q^{42} - 4q^{43} - 2q^{44} + 16q^{45} - 2q^{46} - 8q^{47} + q^{48} + 4q^{49} + 22q^{50} + 3q^{51} + q^{52} + q^{53} - 5q^{54} + 8q^{55} + 6q^{56} - 10q^{58} - 15q^{59} - 4q^{60} - 2q^{61} + 8q^{62} + 6q^{63} + 2q^{64} + 8q^{65} + 2q^{66} - 3q^{67} + 6q^{68} + 2q^{69} + 12q^{70} - 2q^{71} + 2q^{72} - 9q^{73} + 2q^{74} - 22q^{75} + 12q^{77} - q^{78} + 10q^{79} + 4q^{80} - q^{81} + 8q^{82} - 12q^{83} - 6q^{84} + 12q^{85} - 4q^{86} + 10q^{87} + 4q^{88} - 8q^{90} + 3q^{91} + q^{92} - 8q^{93} + 16q^{94} - 2q^{96} + 2q^{97} - 2q^{98} + 4q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$$.

 $$n$$ $$363$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.500000 + 0.866025i −0.353553 + 0.612372i
$$3$$ 0.500000 0.866025i 0.288675 0.500000i −0.684819 0.728714i $$-0.740119\pi$$
0.973494 + 0.228714i $$0.0734519\pi$$
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ 2.00000 3.46410i 0.894427 1.54919i 0.0599153 0.998203i $$-0.480917\pi$$
0.834512 0.550990i $$-0.185750\pi$$
$$6$$ 0.500000 + 0.866025i 0.204124 + 0.353553i
$$7$$ 3.00000 1.13389 0.566947 0.823754i $$-0.308125\pi$$
0.566947 + 0.823754i $$0.308125\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 1.00000 + 1.73205i 0.333333 + 0.577350i
$$10$$ 2.00000 + 3.46410i 0.632456 + 1.09545i
$$11$$ 2.00000 0.603023 0.301511 0.953463i $$-0.402509\pi$$
0.301511 + 0.953463i $$0.402509\pi$$
$$12$$ −1.00000 −0.288675
$$13$$ 0.500000 + 0.866025i 0.138675 + 0.240192i 0.926995 0.375073i $$-0.122382\pi$$
−0.788320 + 0.615265i $$0.789049\pi$$
$$14$$ −1.50000 + 2.59808i −0.400892 + 0.694365i
$$15$$ −2.00000 3.46410i −0.516398 0.894427i
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i $$-0.951855\pi$$
0.624780 + 0.780801i $$0.285189\pi$$
$$18$$ −2.00000 −0.471405
$$19$$ 0 0
$$20$$ −4.00000 −0.894427
$$21$$ 1.50000 2.59808i 0.327327 0.566947i
$$22$$ −1.00000 + 1.73205i −0.213201 + 0.369274i
$$23$$ 0.500000 + 0.866025i 0.104257 + 0.180579i 0.913434 0.406986i $$-0.133420\pi$$
−0.809177 + 0.587565i $$0.800087\pi$$
$$24$$ 0.500000 0.866025i 0.102062 0.176777i
$$25$$ −5.50000 9.52628i −1.10000 1.90526i
$$26$$ −1.00000 −0.196116
$$27$$ 5.00000 0.962250
$$28$$ −1.50000 2.59808i −0.283473 0.490990i
$$29$$ 2.50000 + 4.33013i 0.464238 + 0.804084i 0.999167 0.0408130i $$-0.0129948\pi$$
−0.534928 + 0.844897i $$0.679661\pi$$
$$30$$ 4.00000 0.730297
$$31$$ −8.00000 −1.43684 −0.718421 0.695608i $$-0.755135\pi$$
−0.718421 + 0.695608i $$0.755135\pi$$
$$32$$ −0.500000 0.866025i −0.0883883 0.153093i
$$33$$ 1.00000 1.73205i 0.174078 0.301511i
$$34$$ −1.50000 2.59808i −0.257248 0.445566i
$$35$$ 6.00000 10.3923i 1.01419 1.75662i
$$36$$ 1.00000 1.73205i 0.166667 0.288675i
$$37$$ −2.00000 −0.328798 −0.164399 0.986394i $$-0.552568\pi$$
−0.164399 + 0.986394i $$0.552568\pi$$
$$38$$ 0 0
$$39$$ 1.00000 0.160128
$$40$$ 2.00000 3.46410i 0.316228 0.547723i
$$41$$ 4.00000 6.92820i 0.624695 1.08200i −0.363905 0.931436i $$-0.618557\pi$$
0.988600 0.150567i $$-0.0481100\pi$$
$$42$$ 1.50000 + 2.59808i 0.231455 + 0.400892i
$$43$$ −2.00000 + 3.46410i −0.304997 + 0.528271i −0.977261 0.212041i $$-0.931989\pi$$
0.672264 + 0.740312i $$0.265322\pi$$
$$44$$ −1.00000 1.73205i −0.150756 0.261116i
$$45$$ 8.00000 1.19257
$$46$$ −1.00000 −0.147442
$$47$$ −4.00000 6.92820i −0.583460 1.01058i −0.995066 0.0992202i $$-0.968365\pi$$
0.411606 0.911362i $$-0.364968\pi$$
$$48$$ 0.500000 + 0.866025i 0.0721688 + 0.125000i
$$49$$ 2.00000 0.285714
$$50$$ 11.0000 1.55563
$$51$$ 1.50000 + 2.59808i 0.210042 + 0.363803i
$$52$$ 0.500000 0.866025i 0.0693375 0.120096i
$$53$$ 0.500000 + 0.866025i 0.0686803 + 0.118958i 0.898321 0.439340i $$-0.144788\pi$$
−0.829640 + 0.558298i $$0.811454\pi$$
$$54$$ −2.50000 + 4.33013i −0.340207 + 0.589256i
$$55$$ 4.00000 6.92820i 0.539360 0.934199i
$$56$$ 3.00000 0.400892
$$57$$ 0 0
$$58$$ −5.00000 −0.656532
$$59$$ −7.50000 + 12.9904i −0.976417 + 1.69120i −0.301239 + 0.953549i $$0.597400\pi$$
−0.675178 + 0.737655i $$0.735933\pi$$
$$60$$ −2.00000 + 3.46410i −0.258199 + 0.447214i
$$61$$ −1.00000 1.73205i −0.128037 0.221766i 0.794879 0.606768i $$-0.207534\pi$$
−0.922916 + 0.385002i $$0.874201\pi$$
$$62$$ 4.00000 6.92820i 0.508001 0.879883i
$$63$$ 3.00000 + 5.19615i 0.377964 + 0.654654i
$$64$$ 1.00000 0.125000
$$65$$ 4.00000 0.496139
$$66$$ 1.00000 + 1.73205i 0.123091 + 0.213201i
$$67$$ −1.50000 2.59808i −0.183254 0.317406i 0.759733 0.650236i $$-0.225330\pi$$
−0.942987 + 0.332830i $$0.891996\pi$$
$$68$$ 3.00000 0.363803
$$69$$ 1.00000 0.120386
$$70$$ 6.00000 + 10.3923i 0.717137 + 1.24212i
$$71$$ −1.00000 + 1.73205i −0.118678 + 0.205557i −0.919244 0.393688i $$-0.871199\pi$$
0.800566 + 0.599245i $$0.204532\pi$$
$$72$$ 1.00000 + 1.73205i 0.117851 + 0.204124i
$$73$$ −4.50000 + 7.79423i −0.526685 + 0.912245i 0.472831 + 0.881153i $$0.343232\pi$$
−0.999517 + 0.0310925i $$0.990101\pi$$
$$74$$ 1.00000 1.73205i 0.116248 0.201347i
$$75$$ −11.0000 −1.27017
$$76$$ 0 0
$$77$$ 6.00000 0.683763
$$78$$ −0.500000 + 0.866025i −0.0566139 + 0.0980581i
$$79$$ 5.00000 8.66025i 0.562544 0.974355i −0.434730 0.900561i $$-0.643156\pi$$
0.997274 0.0737937i $$-0.0235106\pi$$
$$80$$ 2.00000 + 3.46410i 0.223607 + 0.387298i
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 4.00000 + 6.92820i 0.441726 + 0.765092i
$$83$$ −6.00000 −0.658586 −0.329293 0.944228i $$-0.606810\pi$$
−0.329293 + 0.944228i $$0.606810\pi$$
$$84$$ −3.00000 −0.327327
$$85$$ 6.00000 + 10.3923i 0.650791 + 1.12720i
$$86$$ −2.00000 3.46410i −0.215666 0.373544i
$$87$$ 5.00000 0.536056
$$88$$ 2.00000 0.213201
$$89$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$90$$ −4.00000 + 6.92820i −0.421637 + 0.730297i
$$91$$ 1.50000 + 2.59808i 0.157243 + 0.272352i
$$92$$ 0.500000 0.866025i 0.0521286 0.0902894i
$$93$$ −4.00000 + 6.92820i −0.414781 + 0.718421i
$$94$$ 8.00000 0.825137
$$95$$ 0 0
$$96$$ −1.00000 −0.102062
$$97$$ 1.00000 1.73205i 0.101535 0.175863i −0.810782 0.585348i $$-0.800958\pi$$
0.912317 + 0.409484i $$0.134291\pi$$
$$98$$ −1.00000 + 1.73205i −0.101015 + 0.174964i
$$99$$ 2.00000 + 3.46410i 0.201008 + 0.348155i
$$100$$ −5.50000 + 9.52628i −0.550000 + 0.952628i
$$101$$ −1.00000 1.73205i −0.0995037 0.172345i 0.811976 0.583691i $$-0.198392\pi$$
−0.911479 + 0.411346i $$0.865059\pi$$
$$102$$ −3.00000 −0.297044
$$103$$ −6.00000 −0.591198 −0.295599 0.955312i $$-0.595519\pi$$
−0.295599 + 0.955312i $$0.595519\pi$$
$$104$$ 0.500000 + 0.866025i 0.0490290 + 0.0849208i
$$105$$ −6.00000 10.3923i −0.585540 1.01419i
$$106$$ −1.00000 −0.0971286
$$107$$ −7.00000 −0.676716 −0.338358 0.941018i $$-0.609871\pi$$
−0.338358 + 0.941018i $$0.609871\pi$$
$$108$$ −2.50000 4.33013i −0.240563 0.416667i
$$109$$ 7.50000 12.9904i 0.718370 1.24425i −0.243276 0.969957i $$-0.578222\pi$$
0.961645 0.274296i $$-0.0884447\pi$$
$$110$$ 4.00000 + 6.92820i 0.381385 + 0.660578i
$$111$$ −1.00000 + 1.73205i −0.0949158 + 0.164399i
$$112$$ −1.50000 + 2.59808i −0.141737 + 0.245495i
$$113$$ 14.0000 1.31701 0.658505 0.752577i $$-0.271189\pi$$
0.658505 + 0.752577i $$0.271189\pi$$
$$114$$ 0 0
$$115$$ 4.00000 0.373002
$$116$$ 2.50000 4.33013i 0.232119 0.402042i
$$117$$ −1.00000 + 1.73205i −0.0924500 + 0.160128i
$$118$$ −7.50000 12.9904i −0.690431 1.19586i
$$119$$ −4.50000 + 7.79423i −0.412514 + 0.714496i
$$120$$ −2.00000 3.46410i −0.182574 0.316228i
$$121$$ −7.00000 −0.636364
$$122$$ 2.00000 0.181071
$$123$$ −4.00000 6.92820i −0.360668 0.624695i
$$124$$ 4.00000 + 6.92820i 0.359211 + 0.622171i
$$125$$ −24.0000 −2.14663
$$126$$ −6.00000 −0.534522
$$127$$ −9.00000 15.5885i −0.798621 1.38325i −0.920514 0.390709i $$-0.872230\pi$$
0.121894 0.992543i $$-0.461103\pi$$
$$128$$ −0.500000 + 0.866025i −0.0441942 + 0.0765466i
$$129$$ 2.00000 + 3.46410i 0.176090 + 0.304997i
$$130$$ −2.00000 + 3.46410i −0.175412 + 0.303822i
$$131$$ −6.00000 + 10.3923i −0.524222 + 0.907980i 0.475380 + 0.879781i $$0.342311\pi$$
−0.999602 + 0.0281993i $$0.991023\pi$$
$$132$$ −2.00000 −0.174078
$$133$$ 0 0
$$134$$ 3.00000 0.259161
$$135$$ 10.0000 17.3205i 0.860663 1.49071i
$$136$$ −1.50000 + 2.59808i −0.128624 + 0.222783i
$$137$$ 8.50000 + 14.7224i 0.726204 + 1.25782i 0.958477 + 0.285171i $$0.0920506\pi$$
−0.232273 + 0.972651i $$0.574616\pi$$
$$138$$ −0.500000 + 0.866025i −0.0425628 + 0.0737210i
$$139$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$140$$ −12.0000 −1.01419
$$141$$ −8.00000 −0.673722
$$142$$ −1.00000 1.73205i −0.0839181 0.145350i
$$143$$ 1.00000 + 1.73205i 0.0836242 + 0.144841i
$$144$$ −2.00000 −0.166667
$$145$$ 20.0000 1.66091
$$146$$ −4.50000 7.79423i −0.372423 0.645055i
$$147$$ 1.00000 1.73205i 0.0824786 0.142857i
$$148$$ 1.00000 + 1.73205i 0.0821995 + 0.142374i
$$149$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$150$$ 5.50000 9.52628i 0.449073 0.777817i
$$151$$ 2.00000 0.162758 0.0813788 0.996683i $$-0.474068\pi$$
0.0813788 + 0.996683i $$0.474068\pi$$
$$152$$ 0 0
$$153$$ −6.00000 −0.485071
$$154$$ −3.00000 + 5.19615i −0.241747 + 0.418718i
$$155$$ −16.0000 + 27.7128i −1.28515 + 2.22595i
$$156$$ −0.500000 0.866025i −0.0400320 0.0693375i
$$157$$ 1.00000 1.73205i 0.0798087 0.138233i −0.823359 0.567521i $$-0.807902\pi$$
0.903167 + 0.429289i $$0.141236\pi$$
$$158$$ 5.00000 + 8.66025i 0.397779 + 0.688973i
$$159$$ 1.00000 0.0793052
$$160$$ −4.00000 −0.316228
$$161$$ 1.50000 + 2.59808i 0.118217 + 0.204757i
$$162$$ −0.500000 0.866025i −0.0392837 0.0680414i
$$163$$ −16.0000 −1.25322 −0.626608 0.779334i $$-0.715557\pi$$
−0.626608 + 0.779334i $$0.715557\pi$$
$$164$$ −8.00000 −0.624695
$$165$$ −4.00000 6.92820i −0.311400 0.539360i
$$166$$ 3.00000 5.19615i 0.232845 0.403300i
$$167$$ 6.00000 + 10.3923i 0.464294 + 0.804181i 0.999169 0.0407502i $$-0.0129748\pi$$
−0.534875 + 0.844931i $$0.679641\pi$$
$$168$$ 1.50000 2.59808i 0.115728 0.200446i
$$169$$ 6.00000 10.3923i 0.461538 0.799408i
$$170$$ −12.0000 −0.920358
$$171$$ 0 0
$$172$$ 4.00000 0.304997
$$173$$ 3.00000 5.19615i 0.228086 0.395056i −0.729155 0.684349i $$-0.760087\pi$$
0.957241 + 0.289292i $$0.0934200\pi$$
$$174$$ −2.50000 + 4.33013i −0.189525 + 0.328266i
$$175$$ −16.5000 28.5788i −1.24728 2.16036i
$$176$$ −1.00000 + 1.73205i −0.0753778 + 0.130558i
$$177$$ 7.50000 + 12.9904i 0.563735 + 0.976417i
$$178$$ 0 0
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ −4.00000 6.92820i −0.298142 0.516398i
$$181$$ −11.0000 19.0526i −0.817624 1.41617i −0.907429 0.420206i $$-0.861958\pi$$
0.0898051 0.995959i $$-0.471376\pi$$
$$182$$ −3.00000 −0.222375
$$183$$ −2.00000 −0.147844
$$184$$ 0.500000 + 0.866025i 0.0368605 + 0.0638442i
$$185$$ −4.00000 + 6.92820i −0.294086 + 0.509372i
$$186$$ −4.00000 6.92820i −0.293294 0.508001i
$$187$$ −3.00000 + 5.19615i −0.219382 + 0.379980i
$$188$$ −4.00000 + 6.92820i −0.291730 + 0.505291i
$$189$$ 15.0000 1.09109
$$190$$ 0 0
$$191$$ 7.00000 0.506502 0.253251 0.967401i $$-0.418500\pi$$
0.253251 + 0.967401i $$0.418500\pi$$
$$192$$ 0.500000 0.866025i 0.0360844 0.0625000i
$$193$$ 3.00000 5.19615i 0.215945 0.374027i −0.737620 0.675216i $$-0.764050\pi$$
0.953564 + 0.301189i $$0.0973836\pi$$
$$194$$ 1.00000 + 1.73205i 0.0717958 + 0.124354i
$$195$$ 2.00000 3.46410i 0.143223 0.248069i
$$196$$ −1.00000 1.73205i −0.0714286 0.123718i
$$197$$ 8.00000 0.569976 0.284988 0.958531i $$-0.408010\pi$$
0.284988 + 0.958531i $$0.408010\pi$$
$$198$$ −4.00000 −0.284268
$$199$$ 12.5000 + 21.6506i 0.886102 + 1.53477i 0.844446 + 0.535641i $$0.179930\pi$$
0.0416556 + 0.999132i $$0.486737\pi$$
$$200$$ −5.50000 9.52628i −0.388909 0.673610i
$$201$$ −3.00000 −0.211604
$$202$$ 2.00000 0.140720
$$203$$ 7.50000 + 12.9904i 0.526397 + 0.911746i
$$204$$ 1.50000 2.59808i 0.105021 0.181902i
$$205$$ −16.0000 27.7128i −1.11749 1.93555i
$$206$$ 3.00000 5.19615i 0.209020 0.362033i
$$207$$ −1.00000 + 1.73205i −0.0695048 + 0.120386i
$$208$$ −1.00000 −0.0693375
$$209$$ 0 0
$$210$$ 12.0000 0.828079
$$211$$ −13.5000 + 23.3827i −0.929378 + 1.60973i −0.145014 + 0.989430i $$0.546323\pi$$
−0.784364 + 0.620301i $$0.787010\pi$$
$$212$$ 0.500000 0.866025i 0.0343401 0.0594789i
$$213$$ 1.00000 + 1.73205i 0.0685189 + 0.118678i
$$214$$ 3.50000 6.06218i 0.239255 0.414402i
$$215$$ 8.00000 + 13.8564i 0.545595 + 0.944999i
$$216$$ 5.00000 0.340207
$$217$$ −24.0000 −1.62923
$$218$$ 7.50000 + 12.9904i 0.507964 + 0.879820i
$$219$$ 4.50000 + 7.79423i 0.304082 + 0.526685i
$$220$$ −8.00000 −0.539360
$$221$$ −3.00000 −0.201802
$$222$$ −1.00000 1.73205i −0.0671156 0.116248i
$$223$$ −7.00000 + 12.1244i −0.468755 + 0.811907i −0.999362 0.0357107i $$-0.988630\pi$$
0.530607 + 0.847618i $$0.321964\pi$$
$$224$$ −1.50000 2.59808i −0.100223 0.173591i
$$225$$ 11.0000 19.0526i 0.733333 1.27017i
$$226$$ −7.00000 + 12.1244i −0.465633 + 0.806500i
$$227$$ −17.0000 −1.12833 −0.564165 0.825662i $$-0.690802\pi$$
−0.564165 + 0.825662i $$0.690802\pi$$
$$228$$ 0 0
$$229$$ −10.0000 −0.660819 −0.330409 0.943838i $$-0.607187\pi$$
−0.330409 + 0.943838i $$0.607187\pi$$
$$230$$ −2.00000 + 3.46410i −0.131876 + 0.228416i
$$231$$ 3.00000 5.19615i 0.197386 0.341882i
$$232$$ 2.50000 + 4.33013i 0.164133 + 0.284287i
$$233$$ 3.00000 5.19615i 0.196537 0.340411i −0.750867 0.660454i $$-0.770364\pi$$
0.947403 + 0.320043i $$0.103697\pi$$
$$234$$ −1.00000 1.73205i −0.0653720 0.113228i
$$235$$ −32.0000 −2.08745
$$236$$ 15.0000 0.976417
$$237$$ −5.00000 8.66025i −0.324785 0.562544i
$$238$$ −4.50000 7.79423i −0.291692 0.505225i
$$239$$ 15.0000 0.970269 0.485135 0.874439i $$-0.338771\pi$$
0.485135 + 0.874439i $$0.338771\pi$$
$$240$$ 4.00000 0.258199
$$241$$ 4.00000 + 6.92820i 0.257663 + 0.446285i 0.965615 0.259975i $$-0.0837143\pi$$
−0.707953 + 0.706260i $$0.750381\pi$$
$$242$$ 3.50000 6.06218i 0.224989 0.389692i
$$243$$ 8.00000 + 13.8564i 0.513200 + 0.888889i
$$244$$ −1.00000 + 1.73205i −0.0640184 + 0.110883i
$$245$$ 4.00000 6.92820i 0.255551 0.442627i
$$246$$ 8.00000 0.510061
$$247$$ 0 0
$$248$$ −8.00000 −0.508001
$$249$$ −3.00000 + 5.19615i −0.190117 + 0.329293i
$$250$$ 12.0000 20.7846i 0.758947 1.31453i
$$251$$ −1.00000 1.73205i −0.0631194 0.109326i 0.832739 0.553666i $$-0.186772\pi$$
−0.895858 + 0.444340i $$0.853438\pi$$
$$252$$ 3.00000 5.19615i 0.188982 0.327327i
$$253$$ 1.00000 + 1.73205i 0.0628695 + 0.108893i
$$254$$ 18.0000 1.12942
$$255$$ 12.0000 0.751469
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ −4.00000 6.92820i −0.249513 0.432169i 0.713878 0.700270i $$-0.246937\pi$$
−0.963391 + 0.268101i $$0.913604\pi$$
$$258$$ −4.00000 −0.249029
$$259$$ −6.00000 −0.372822
$$260$$ −2.00000 3.46410i −0.124035 0.214834i
$$261$$ −5.00000 + 8.66025i −0.309492 + 0.536056i
$$262$$ −6.00000 10.3923i −0.370681 0.642039i
$$263$$ −12.0000 + 20.7846i −0.739952 + 1.28163i 0.212565 + 0.977147i $$0.431818\pi$$
−0.952517 + 0.304487i $$0.901515\pi$$
$$264$$ 1.00000 1.73205i 0.0615457 0.106600i
$$265$$ 4.00000 0.245718
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −1.50000 + 2.59808i −0.0916271 + 0.158703i
$$269$$ −15.0000 + 25.9808i −0.914566 + 1.58408i −0.107031 + 0.994256i $$0.534134\pi$$
−0.807535 + 0.589819i $$0.799199\pi$$
$$270$$ 10.0000 + 17.3205i 0.608581 + 1.05409i
$$271$$ −3.50000 + 6.06218i −0.212610 + 0.368251i −0.952531 0.304443i $$-0.901530\pi$$
0.739921 + 0.672694i $$0.234863\pi$$
$$272$$ −1.50000 2.59808i −0.0909509 0.157532i
$$273$$ 3.00000 0.181568
$$274$$ −17.0000 −1.02701
$$275$$ −11.0000 19.0526i −0.663325 1.14891i
$$276$$ −0.500000 0.866025i −0.0300965 0.0521286i
$$277$$ 28.0000 1.68236 0.841178 0.540758i $$-0.181862\pi$$
0.841178 + 0.540758i $$0.181862\pi$$
$$278$$ 0 0
$$279$$ −8.00000 13.8564i −0.478947 0.829561i
$$280$$ 6.00000 10.3923i 0.358569 0.621059i
$$281$$ 4.00000 + 6.92820i 0.238620 + 0.413302i 0.960319 0.278906i $$-0.0899716\pi$$
−0.721699 + 0.692207i $$0.756638\pi$$
$$282$$ 4.00000 6.92820i 0.238197 0.412568i
$$283$$ 3.00000 5.19615i 0.178331 0.308879i −0.762978 0.646425i $$-0.776263\pi$$
0.941309 + 0.337546i $$0.109597\pi$$
$$284$$ 2.00000 0.118678
$$285$$ 0 0
$$286$$ −2.00000 −0.118262
$$287$$ 12.0000 20.7846i 0.708338 1.22688i
$$288$$ 1.00000 1.73205i 0.0589256 0.102062i
$$289$$ 4.00000 + 6.92820i 0.235294 + 0.407541i
$$290$$ −10.0000 + 17.3205i −0.587220 + 1.01710i
$$291$$ −1.00000 1.73205i −0.0586210 0.101535i
$$292$$ 9.00000 0.526685
$$293$$ 9.00000 0.525786 0.262893 0.964825i $$-0.415323\pi$$
0.262893 + 0.964825i $$0.415323\pi$$
$$294$$ 1.00000 + 1.73205i 0.0583212 + 0.101015i
$$295$$ 30.0000 + 51.9615i 1.74667 + 3.02532i
$$296$$ −2.00000 −0.116248
$$297$$ 10.0000 0.580259
$$298$$ 0 0
$$299$$ −0.500000 + 0.866025i −0.0289157 + 0.0500835i
$$300$$ 5.50000 + 9.52628i 0.317543 + 0.550000i
$$301$$ −6.00000 + 10.3923i −0.345834 + 0.599002i
$$302$$ −1.00000 + 1.73205i −0.0575435 + 0.0996683i
$$303$$ −2.00000 −0.114897
$$304$$ 0 0
$$305$$ −8.00000 −0.458079
$$306$$ 3.00000 5.19615i 0.171499 0.297044i
$$307$$ 6.00000 10.3923i 0.342438 0.593120i −0.642447 0.766330i $$-0.722081\pi$$
0.984885 + 0.173210i $$0.0554140\pi$$
$$308$$ −3.00000 5.19615i −0.170941 0.296078i
$$309$$ −3.00000 + 5.19615i −0.170664 + 0.295599i
$$310$$ −16.0000 27.7128i −0.908739 1.57398i
$$311$$ 7.00000 0.396934 0.198467 0.980108i $$-0.436404\pi$$
0.198467 + 0.980108i $$0.436404\pi$$
$$312$$ 1.00000 0.0566139
$$313$$ −14.5000 25.1147i −0.819588 1.41957i −0.905986 0.423308i $$-0.860869\pi$$
0.0863973 0.996261i $$-0.472465\pi$$
$$314$$ 1.00000 + 1.73205i 0.0564333 + 0.0977453i
$$315$$ 24.0000 1.35225
$$316$$ −10.0000 −0.562544
$$317$$ 13.5000 + 23.3827i 0.758236 + 1.31330i 0.943750 + 0.330661i $$0.107272\pi$$
−0.185514 + 0.982642i $$0.559395\pi$$
$$318$$ −0.500000 + 0.866025i −0.0280386 + 0.0485643i
$$319$$ 5.00000 + 8.66025i 0.279946 + 0.484881i
$$320$$ 2.00000 3.46410i 0.111803 0.193649i
$$321$$ −3.50000 + 6.06218i −0.195351 + 0.338358i
$$322$$ −3.00000 −0.167183
$$323$$ 0 0
$$324$$ 1.00000 0.0555556
$$325$$ 5.50000 9.52628i 0.305085 0.528423i
$$326$$ 8.00000 13.8564i 0.443079 0.767435i
$$327$$ −7.50000 12.9904i −0.414751 0.718370i
$$328$$ 4.00000 6.92820i 0.220863 0.382546i
$$329$$ −12.0000 20.7846i −0.661581 1.14589i
$$330$$ 8.00000 0.440386
$$331$$ 17.0000 0.934405 0.467202 0.884150i $$-0.345262\pi$$
0.467202 + 0.884150i $$0.345262\pi$$
$$332$$ 3.00000 + 5.19615i 0.164646 + 0.285176i
$$333$$ −2.00000 3.46410i −0.109599 0.189832i
$$334$$ −12.0000 −0.656611
$$335$$ −12.0000 −0.655630
$$336$$ 1.50000 + 2.59808i 0.0818317 + 0.141737i
$$337$$ 16.0000 27.7128i 0.871576 1.50961i 0.0112091 0.999937i $$-0.496432\pi$$
0.860366 0.509676i $$-0.170235\pi$$
$$338$$ 6.00000 + 10.3923i 0.326357 + 0.565267i
$$339$$ 7.00000 12.1244i 0.380188 0.658505i
$$340$$ 6.00000 10.3923i 0.325396 0.563602i
$$341$$ −16.0000 −0.866449
$$342$$ 0 0
$$343$$ −15.0000 −0.809924
$$344$$ −2.00000 + 3.46410i −0.107833 + 0.186772i
$$345$$ 2.00000 3.46410i 0.107676 0.186501i
$$346$$ 3.00000 + 5.19615i 0.161281 + 0.279347i
$$347$$ 1.00000 1.73205i 0.0536828 0.0929814i −0.837935 0.545770i $$-0.816237\pi$$
0.891618 + 0.452788i $$0.149571\pi$$
$$348$$ −2.50000 4.33013i −0.134014 0.232119i
$$349$$ 10.0000 0.535288 0.267644 0.963518i $$-0.413755\pi$$
0.267644 + 0.963518i $$0.413755\pi$$
$$350$$ 33.0000 1.76392
$$351$$ 2.50000 + 4.33013i 0.133440 + 0.231125i
$$352$$ −1.00000 1.73205i −0.0533002 0.0923186i
$$353$$ 9.00000 0.479022 0.239511 0.970894i $$-0.423013\pi$$
0.239511 + 0.970894i $$0.423013\pi$$
$$354$$ −15.0000 −0.797241
$$355$$ 4.00000 + 6.92820i 0.212298 + 0.367711i
$$356$$ 0 0
$$357$$ 4.50000 + 7.79423i 0.238165 + 0.412514i
$$358$$ 0 0
$$359$$ 7.50000 12.9904i 0.395835 0.685606i −0.597372 0.801964i $$-0.703789\pi$$
0.993207 + 0.116358i $$0.0371219\pi$$
$$360$$ 8.00000 0.421637
$$361$$ 0 0
$$362$$ 22.0000 1.15629
$$363$$ −3.50000 + 6.06218i −0.183702 + 0.318182i
$$364$$ 1.50000 2.59808i 0.0786214 0.136176i
$$365$$ 18.0000 + 31.1769i 0.942163 + 1.63187i
$$366$$ 1.00000 1.73205i 0.0522708 0.0905357i
$$367$$ −14.0000 24.2487i −0.730794 1.26577i −0.956544 0.291587i $$-0.905817\pi$$
0.225750 0.974185i $$-0.427517\pi$$
$$368$$ −1.00000 −0.0521286
$$369$$ 16.0000 0.832927
$$370$$ −4.00000 6.92820i −0.207950 0.360180i
$$371$$ 1.50000 + 2.59808i 0.0778761 + 0.134885i
$$372$$ 8.00000 0.414781
$$373$$ 29.0000 1.50156 0.750782 0.660551i $$-0.229677\pi$$
0.750782 + 0.660551i $$0.229677\pi$$
$$374$$ −3.00000 5.19615i −0.155126 0.268687i
$$375$$ −12.0000 + 20.7846i −0.619677 + 1.07331i
$$376$$ −4.00000 6.92820i −0.206284 0.357295i
$$377$$ −2.50000 + 4.33013i −0.128757 + 0.223013i
$$378$$ −7.50000 + 12.9904i −0.385758 + 0.668153i
$$379$$ 15.0000 0.770498 0.385249 0.922813i $$-0.374116\pi$$
0.385249 + 0.922813i $$0.374116\pi$$
$$380$$ 0 0
$$381$$ −18.0000 −0.922168
$$382$$ −3.50000 + 6.06218i −0.179076 + 0.310168i
$$383$$ 13.0000 22.5167i 0.664269 1.15055i −0.315214 0.949021i $$-0.602076\pi$$
0.979483 0.201527i $$-0.0645904\pi$$
$$384$$ 0.500000 + 0.866025i 0.0255155 + 0.0441942i
$$385$$ 12.0000 20.7846i 0.611577 1.05928i
$$386$$ 3.00000 + 5.19615i 0.152696 + 0.264477i
$$387$$ −8.00000 −0.406663
$$388$$ −2.00000 −0.101535
$$389$$ 15.0000 + 25.9808i 0.760530 + 1.31728i 0.942578 + 0.333987i $$0.108394\pi$$
−0.182047 + 0.983290i $$0.558272\pi$$
$$390$$ 2.00000 + 3.46410i 0.101274 + 0.175412i
$$391$$ −3.00000 −0.151717
$$392$$ 2.00000 0.101015
$$393$$ 6.00000 + 10.3923i 0.302660 + 0.524222i
$$394$$ −4.00000 + 6.92820i −0.201517 + 0.349038i
$$395$$ −20.0000 34.6410i −1.00631 1.74298i
$$396$$ 2.00000 3.46410i 0.100504 0.174078i
$$397$$ −4.00000 + 6.92820i −0.200754 + 0.347717i −0.948772 0.315963i $$-0.897673\pi$$
0.748017 + 0.663679i $$0.231006\pi$$
$$398$$ −25.0000 −1.25314
$$399$$ 0 0
$$400$$ 11.0000 0.550000
$$401$$ 4.00000 6.92820i 0.199750 0.345978i −0.748697 0.662912i $$-0.769320\pi$$
0.948447 + 0.316934i $$0.102654\pi$$
$$402$$ 1.50000 2.59808i 0.0748132 0.129580i
$$403$$ −4.00000 6.92820i −0.199254 0.345118i
$$404$$ −1.00000 + 1.73205i −0.0497519 + 0.0861727i
$$405$$ 2.00000 + 3.46410i 0.0993808 + 0.172133i
$$406$$ −15.0000 −0.744438
$$407$$ −4.00000 −0.198273
$$408$$ 1.50000 + 2.59808i 0.0742611 + 0.128624i
$$409$$ 10.0000 + 17.3205i 0.494468 + 0.856444i 0.999980 0.00637586i $$-0.00202951\pi$$
−0.505511 + 0.862820i $$0.668696\pi$$
$$410$$ 32.0000 1.58037
$$411$$ 17.0000 0.838548
$$412$$ 3.00000 + 5.19615i 0.147799 + 0.255996i
$$413$$ −22.5000 + 38.9711i −1.10715 + 1.91764i
$$414$$ −1.00000 1.73205i −0.0491473 0.0851257i
$$415$$ −12.0000 + 20.7846i −0.589057 + 1.02028i
$$416$$ 0.500000 0.866025i 0.0245145 0.0424604i
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ −6.00000 + 10.3923i −0.292770 + 0.507093i
$$421$$ 6.50000 11.2583i 0.316791 0.548697i −0.663026 0.748596i $$-0.730728\pi$$
0.979817 + 0.199899i $$0.0640614\pi$$
$$422$$ −13.5000 23.3827i −0.657170 1.13825i
$$423$$ 8.00000 13.8564i 0.388973 0.673722i
$$424$$ 0.500000 + 0.866025i 0.0242821 + 0.0420579i
$$425$$ 33.0000 1.60074
$$426$$ −2.00000 −0.0969003
$$427$$ −3.00000 5.19615i −0.145180 0.251459i
$$428$$ 3.50000 + 6.06218i 0.169179 + 0.293026i
$$429$$ 2.00000 0.0965609
$$430$$ −16.0000 −0.771589
$$431$$ 9.00000 + 15.5885i 0.433515 + 0.750870i 0.997173 0.0751385i $$-0.0239399\pi$$
−0.563658 + 0.826008i $$0.690607\pi$$
$$432$$ −2.50000 + 4.33013i −0.120281 + 0.208333i
$$433$$ −7.00000 12.1244i −0.336399 0.582659i 0.647354 0.762190i $$-0.275876\pi$$
−0.983752 + 0.179530i $$0.942542\pi$$
$$434$$ 12.0000 20.7846i 0.576018 0.997693i
$$435$$ 10.0000 17.3205i 0.479463 0.830455i
$$436$$ −15.0000 −0.718370
$$437$$ 0 0
$$438$$ −9.00000 −0.430037
$$439$$ −10.0000 + 17.3205i −0.477274 + 0.826663i −0.999661 0.0260459i $$-0.991708\pi$$
0.522387 + 0.852709i $$0.325042\pi$$
$$440$$ 4.00000 6.92820i 0.190693 0.330289i
$$441$$ 2.00000 + 3.46410i 0.0952381 + 0.164957i
$$442$$ 1.50000 2.59808i 0.0713477 0.123578i
$$443$$ 13.0000 + 22.5167i 0.617649 + 1.06980i 0.989914 + 0.141672i $$0.0452479\pi$$
−0.372265 + 0.928126i $$0.621419\pi$$
$$444$$ 2.00000 0.0949158
$$445$$ 0 0
$$446$$ −7.00000 12.1244i −0.331460 0.574105i
$$447$$ 0 0
$$448$$ 3.00000 0.141737
$$449$$ 10.0000 0.471929 0.235965 0.971762i $$-0.424175\pi$$
0.235965 + 0.971762i $$0.424175\pi$$
$$450$$ 11.0000 + 19.0526i 0.518545 + 0.898146i
$$451$$ 8.00000 13.8564i 0.376705 0.652473i
$$452$$ −7.00000 12.1244i −0.329252 0.570282i
$$453$$ 1.00000 1.73205i 0.0469841 0.0813788i
$$454$$ 8.50000 14.7224i 0.398925 0.690958i
$$455$$ 12.0000 0.562569
$$456$$ 0 0
$$457$$ −7.00000 −0.327446 −0.163723 0.986506i $$-0.552350\pi$$
−0.163723 + 0.986506i $$0.552350\pi$$
$$458$$ 5.00000 8.66025i 0.233635 0.404667i
$$459$$ −7.50000 + 12.9904i −0.350070 + 0.606339i
$$460$$ −2.00000 3.46410i −0.0932505 0.161515i
$$461$$ 14.0000 24.2487i 0.652045 1.12938i −0.330581 0.943778i $$-0.607245\pi$$
0.982626 0.185597i $$-0.0594220\pi$$
$$462$$ 3.00000 + 5.19615i 0.139573 + 0.241747i
$$463$$ 4.00000 0.185896 0.0929479 0.995671i $$-0.470371\pi$$
0.0929479 + 0.995671i $$0.470371\pi$$
$$464$$ −5.00000 −0.232119
$$465$$ 16.0000 + 27.7128i 0.741982 + 1.28515i
$$466$$ 3.00000 + 5.19615i 0.138972 + 0.240707i
$$467$$ −2.00000 −0.0925490 −0.0462745 0.998929i $$-0.514735\pi$$
−0.0462745 + 0.998929i $$0.514735\pi$$
$$468$$ 2.00000 0.0924500
$$469$$ −4.50000 7.79423i −0.207791 0.359904i
$$470$$ 16.0000 27.7128i 0.738025 1.27830i
$$471$$ −1.00000 1.73205i −0.0460776 0.0798087i
$$472$$ −7.50000 + 12.9904i −0.345215 + 0.597931i
$$473$$ −4.00000 + 6.92820i −0.183920 + 0.318559i
$$474$$ 10.0000 0.459315
$$475$$ 0 0
$$476$$ 9.00000 0.412514
$$477$$ −1.00000 + 1.73205i −0.0457869 + 0.0793052i
$$478$$ −7.50000 + 12.9904i −0.343042 + 0.594166i
$$479$$ 10.0000 + 17.3205i 0.456912 + 0.791394i 0.998796 0.0490589i $$-0.0156222\pi$$
−0.541884 + 0.840453i $$0.682289\pi$$
$$480$$ −2.00000 + 3.46410i −0.0912871 + 0.158114i
$$481$$ −1.00000 1.73205i −0.0455961 0.0789747i
$$482$$ −8.00000 −0.364390
$$483$$ 3.00000 0.136505
$$484$$ 3.50000 + 6.06218i 0.159091 + 0.275554i
$$485$$ −4.00000 6.92820i −0.181631 0.314594i
$$486$$ −16.0000 −0.725775
$$487$$ −2.00000 −0.0906287 −0.0453143 0.998973i $$-0.514429\pi$$
−0.0453143 + 0.998973i $$0.514429\pi$$
$$488$$ −1.00000 1.73205i −0.0452679 0.0784063i
$$489$$ −8.00000 + 13.8564i −0.361773 + 0.626608i
$$490$$ 4.00000 + 6.92820i 0.180702 + 0.312984i
$$491$$ 14.0000 24.2487i 0.631811 1.09433i −0.355370 0.934726i $$-0.615645\pi$$
0.987181 0.159603i $$-0.0510215\pi$$
$$492$$ −4.00000 + 6.92820i −0.180334 + 0.312348i
$$493$$ −15.0000 −0.675566
$$494$$ 0 0
$$495$$ 16.0000 0.719147
$$496$$ 4.00000 6.92820i 0.179605 0.311086i
$$497$$ −3.00000 + 5.19615i −0.134568 + 0.233079i
$$498$$ −3.00000 5.19615i −0.134433 0.232845i
$$499$$ −20.0000 + 34.6410i −0.895323 + 1.55074i −0.0619186 + 0.998081i $$0.519722\pi$$
−0.833404 + 0.552664i $$0.813611\pi$$
$$500$$ 12.0000 + 20.7846i 0.536656 + 0.929516i
$$501$$ 12.0000 0.536120
$$502$$ 2.00000 0.0892644
$$503$$ −19.5000 33.7750i −0.869462 1.50595i −0.862547 0.505976i $$-0.831132\pi$$
−0.00691465 0.999976i $$-0.502201\pi$$
$$504$$ 3.00000 + 5.19615i 0.133631 + 0.231455i
$$505$$ −8.00000 −0.355995
$$506$$ −2.00000 −0.0889108
$$507$$ −6.00000 10.3923i −0.266469 0.461538i
$$508$$ −9.00000 + 15.5885i −0.399310 + 0.691626i
$$509$$ 15.0000 + 25.9808i 0.664863 + 1.15158i 0.979322 + 0.202306i $$0.0648436\pi$$
−0.314459 + 0.949271i $$0.601823\pi$$
$$510$$ −6.00000 + 10.3923i −0.265684 + 0.460179i
$$511$$ −13.5000 + 23.3827i −0.597205 + 1.03439i
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ 8.00000 0.352865
$$515$$ −12.0000 + 20.7846i −0.528783 + 0.915879i
$$516$$ 2.00000 3.46410i 0.0880451 0.152499i
$$517$$ −8.00000 13.8564i −0.351840 0.609404i
$$518$$ 3.00000 5.19615i 0.131812 0.228306i
$$519$$ −3.00000 5.19615i −0.131685 0.228086i
$$520$$ 4.00000 0.175412
$$521$$ −28.0000 −1.22670 −0.613351 0.789810i $$-0.710179\pi$$
−0.613351 + 0.789810i $$0.710179\pi$$
$$522$$ −5.00000 8.66025i −0.218844 0.379049i
$$523$$ −14.5000 25.1147i −0.634041 1.09819i −0.986718 0.162446i $$-0.948062\pi$$
0.352677 0.935745i $$-0.385272\pi$$
$$524$$ 12.0000 0.524222
$$525$$ −33.0000 −1.44024
$$526$$ −12.0000 20.7846i −0.523225 0.906252i
$$527$$ 12.0000 20.7846i 0.522728 0.905392i
$$528$$ 1.00000 + 1.73205i 0.0435194 + 0.0753778i
$$529$$ 11.0000 19.0526i 0.478261 0.828372i
$$530$$ −2.00000 + 3.46410i −0.0868744 + 0.150471i
$$531$$ −30.0000 −1.30189
$$532$$ 0 0
$$533$$ 8.00000 0.346518
$$534$$ 0 0
$$535$$ −14.0000 + 24.2487i −0.605273 + 1.04836i
$$536$$ −1.50000 2.59808i −0.0647901 0.112220i
$$537$$ 0 0
$$538$$ −15.0000 25.9808i −0.646696 1.12011i
$$539$$ 4.00000 0.172292
$$540$$ −20.0000 −0.860663
$$541$$ −1.00000 1.73205i −0.0429934 0.0744667i 0.843728 0.536771i $$-0.180356\pi$$
−0.886721 + 0.462304i $$0.847023\pi$$
$$542$$ −3.50000 6.06218i −0.150338 0.260393i
$$543$$ −22.0000 −0.944110
$$544$$ 3.00000 0.128624
$$545$$ −30.0000 51.9615i −1.28506 2.22579i
$$546$$ −1.50000 + 2.59808i −0.0641941 + 0.111187i
$$547$$ −14.0000 24.2487i −0.598597 1.03680i −0.993028 0.117875i $$-0.962392\pi$$
0.394432 0.918925i $$-0.370941\pi$$
$$548$$ 8.50000 14.7224i 0.363102 0.628911i
$$549$$ 2.00000 3.46410i 0.0853579 0.147844i
$$550$$ 22.0000 0.938083
$$551$$ 0 0
$$552$$ 1.00000 0.0425628
$$553$$ 15.0000 25.9808i 0.637865 1.10481i
$$554$$ −14.0000 + 24.2487i −0.594803 + 1.03023i
$$555$$ 4.00000 + 6.92820i 0.169791 + 0.294086i
$$556$$ 0 0
$$557$$ −14.0000 24.2487i −0.593199 1.02745i −0.993798 0.111198i $$-0.964531\pi$$
0.400599 0.916253i $$-0.368802\pi$$
$$558$$ 16.0000 0.677334
$$559$$ −4.00000 −0.169182
$$560$$ 6.00000 + 10.3923i 0.253546 + 0.439155i
$$561$$ 3.00000 + 5.19615i 0.126660 + 0.219382i
$$562$$ −8.00000 −0.337460
$$563$$ −36.0000 −1.51722 −0.758610 0.651546i $$-0.774121\pi$$
−0.758610 + 0.651546i $$0.774121\pi$$
$$564$$ 4.00000 + 6.92820i 0.168430 + 0.291730i
$$565$$ 28.0000 48.4974i 1.17797 2.04030i
$$566$$ 3.00000 + 5.19615i 0.126099 + 0.218411i
$$567$$ −1.50000 + 2.59808i −0.0629941 + 0.109109i
$$568$$ −1.00000 + 1.73205i −0.0419591 + 0.0726752i
$$569$$ 40.0000 1.67689 0.838444 0.544988i $$-0.183466\pi$$
0.838444 + 0.544988i $$0.183466\pi$$
$$570$$ 0 0
$$571$$ −28.0000 −1.17176 −0.585882 0.810397i $$-0.699252\pi$$
−0.585882 + 0.810397i $$0.699252\pi$$
$$572$$ 1.00000 1.73205i 0.0418121 0.0724207i
$$573$$ 3.50000 6.06218i 0.146215 0.253251i
$$574$$ 12.0000 + 20.7846i 0.500870 + 0.867533i
$$575$$ 5.50000 9.52628i 0.229366 0.397273i
$$576$$ 1.00000 + 1.73205i 0.0416667 + 0.0721688i
$$577$$ −37.0000 −1.54033 −0.770165 0.637845i $$-0.779826\pi$$
−0.770165 + 0.637845i $$0.779826\pi$$
$$578$$ −8.00000 −0.332756
$$579$$ −3.00000 5.19615i −0.124676 0.215945i
$$580$$ −10.0000 17.3205i −0.415227 0.719195i
$$581$$ −18.0000 −0.746766
$$582$$ 2.00000 0.0829027
$$583$$ 1.00000 + 1.73205i 0.0414158 + 0.0717342i
$$584$$ −4.50000 + 7.79423i −0.186211 + 0.322527i
$$585$$ 4.00000 + 6.92820i 0.165380 + 0.286446i
$$586$$ −4.50000 + 7.79423i −0.185893 + 0.321977i
$$587$$ 6.00000 10.3923i 0.247647 0.428936i −0.715226 0.698893i $$-0.753676\pi$$
0.962872 + 0.269957i $$0.0870095\pi$$
$$588$$ −2.00000 −0.0824786
$$589$$ 0 0
$$590$$ −60.0000 −2.47016
$$591$$ 4.00000 6.92820i 0.164538 0.284988i
$$592$$ 1.00000 1.73205i 0.0410997 0.0711868i
$$593$$ −17.0000 29.4449i −0.698106 1.20916i −0.969122 0.246581i $$-0.920693\pi$$
0.271016 0.962575i $$-0.412640\pi$$
$$594$$ −5.00000 + 8.66025i −0.205152 + 0.355335i
$$595$$ 18.0000 + 31.1769i 0.737928 + 1.27813i
$$596$$ 0 0
$$597$$ 25.0000 1.02318
$$598$$ −0.500000 0.866025i −0.0204465 0.0354144i
$$599$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$600$$ −11.0000 −0.449073
$$601$$ −8.00000 −0.326327 −0.163163 0.986599i $$-0.552170\pi$$
−0.163163 + 0.986599i $$0.552170\pi$$
$$602$$ −6.00000 10.3923i −0.244542 0.423559i
$$603$$ 3.00000 5.19615i 0.122169 0.211604i
$$604$$ −1.00000 1.73205i −0.0406894 0.0704761i
$$605$$ −14.0000 + 24.2487i −0.569181 + 0.985850i
$$606$$ 1.00000 1.73205i 0.0406222 0.0703598i
$$607$$ −22.0000 −0.892952 −0.446476 0.894795i $$-0.647321\pi$$
−0.446476 + 0.894795i $$0.647321\pi$$
$$608$$ 0 0
$$609$$ 15.0000 0.607831
$$610$$ 4.00000 6.92820i 0.161955 0.280515i
$$611$$ 4.00000 6.92820i 0.161823 0.280285i
$$612$$ 3.00000 + 5.19615i 0.121268 + 0.210042i
$$613$$ −17.0000 + 29.4449i −0.686624 + 1.18927i 0.286300 + 0.958140i $$0.407575\pi$$
−0.972924 + 0.231127i $$0.925759\pi$$
$$614$$ 6.00000 + 10.3923i 0.242140 + 0.419399i
$$615$$ −32.0000 −1.29036
$$616$$ 6.00000 0.241747
$$617$$ −9.00000 15.5885i −0.362326 0.627568i 0.626017 0.779809i $$-0.284684\pi$$
−0.988343 + 0.152242i $$0.951351\pi$$
$$618$$ −3.00000 5.19615i −0.120678 0.209020i
$$619$$ 10.0000 0.401934 0.200967 0.979598i $$-0.435592\pi$$
0.200967 + 0.979598i $$0.435592\pi$$
$$620$$ 32.0000 1.28515
$$621$$ 2.50000 + 4.33013i 0.100322 + 0.173762i
$$622$$ −3.50000 + 6.06218i −0.140337 + 0.243071i
$$623$$ 0 0
$$624$$ −0.500000 + 0.866025i −0.0200160 + 0.0346688i
$$625$$ −20.5000 + 35.5070i −0.820000 + 1.42028i
$$626$$ 29.0000 1.15907
$$627$$ 0 0
$$628$$ −2.00000 −0.0798087
$$629$$ 3.00000 5.19615i 0.119618 0.207184i
$$630$$ −12.0000 + 20.7846i −0.478091 + 0.828079i
$$631$$ −16.0000 27.7128i −0.636950 1.10323i −0.986098 0.166162i $$-0.946862\pi$$
0.349148 0.937067i $$-0.386471\pi$$
$$632$$ 5.00000 8.66025i 0.198889 0.344486i
$$633$$ 13.5000 + 23.3827i 0.536577 + 0.929378i
$$634$$ −27.0000 −1.07231
$$635$$ −72.0000 −2.85723
$$636$$ −0.500000 0.866025i −0.0198263 0.0343401i
$$637$$ 1.00000 + 1.73205i 0.0396214 + 0.0686264i
$$638$$ −10.0000 −0.395904
$$639$$ −4.00000 −0.158238
$$640$$ 2.00000 + 3.46410i 0.0790569 + 0.136931i
$$641$$ −21.0000 + 36.3731i −0.829450 + 1.43665i 0.0690201 + 0.997615i $$0.478013\pi$$
−0.898470 + 0.439034i $$0.855321\pi$$
$$642$$ −3.50000 6.06218i −0.138134 0.239255i
$$643$$ 13.0000 22.5167i 0.512670 0.887970i −0.487222 0.873278i $$-0.661990\pi$$
0.999892 0.0146923i $$-0.00467688\pi$$
$$644$$ 1.50000 2.59808i 0.0591083 0.102379i
$$645$$ 16.0000 0.629999
$$646$$ 0 0
$$647$$ 23.0000 0.904223 0.452112 0.891961i $$-0.350671\pi$$
0.452112 + 0.891961i $$0.350671\pi$$
$$648$$ −0.500000 + 0.866025i −0.0196419 + 0.0340207i
$$649$$ −15.0000 + 25.9808i −0.588802 + 1.01983i
$$650$$ 5.50000 + 9.52628i 0.215728 + 0.373651i
$$651$$ −12.0000 + 20.7846i −0.470317 + 0.814613i
$$652$$ 8.00000 + 13.8564i 0.313304 + 0.542659i
$$653$$ −36.0000 −1.40879 −0.704394 0.709809i $$-0.748781\pi$$
−0.704394 + 0.709809i $$0.748781\pi$$
$$654$$ 15.0000 0.586546
$$655$$ 24.0000 + 41.5692i 0.937758 + 1.62424i
$$656$$ 4.00000 + 6.92820i 0.156174 + 0.270501i
$$657$$ −18.0000 −0.702247
$$658$$ 24.0000 0.935617
$$659$$ −2.50000 4.33013i −0.0973862 0.168678i 0.813216 0.581962i $$-0.197715\pi$$
−0.910602 + 0.413284i $$0.864382\pi$$
$$660$$ −4.00000 + 6.92820i −0.155700 + 0.269680i
$$661$$ 11.5000 + 19.9186i 0.447298 + 0.774743i 0.998209 0.0598209i $$-0.0190530\pi$$
−0.550911 + 0.834564i $$0.685720\pi$$
$$662$$ −8.50000 + 14.7224i −0.330362 + 0.572204i
$$663$$ −1.50000 + 2.59808i −0.0582552 + 0.100901i
$$664$$ −6.00000 −0.232845
$$665$$ 0 0
$$666$$ 4.00000 0.154997
$$667$$ −2.50000 + 4.33013i −0.0968004 + 0.167663i
$$668$$ 6.00000 10.3923i 0.232147 0.402090i
$$669$$ 7.00000 + 12.1244i 0.270636 + 0.468755i
$$670$$ 6.00000 10.3923i 0.231800 0.401490i
$$671$$ −2.00000 3.46410i −0.0772091 0.133730i
$$672$$ −3.00000 −0.115728
$$673$$ 44.0000 1.69608 0.848038 0.529936i $$-0.177784\pi$$
0.848038 + 0.529936i $$0.177784\pi$$
$$674$$ 16.0000 + 27.7128i 0.616297 + 1.06746i
$$675$$ −27.5000 47.6314i −1.05848 1.83333i
$$676$$ −12.0000 −0.461538
$$677$$ 13.0000 0.499631 0.249815 0.968294i $$-0.419630\pi$$
0.249815 + 0.968294i $$0.419630\pi$$
$$678$$ 7.00000 + 12.1244i 0.268833 + 0.465633i
$$679$$ 3.00000 5.19615i 0.115129 0.199410i
$$680$$ 6.00000 + 10.3923i 0.230089 + 0.398527i
$$681$$ −8.50000 + 14.7224i −0.325721 + 0.564165i
$$682$$ 8.00000 13.8564i 0.306336 0.530589i
$$683$$ 4.00000 0.153056 0.0765279 0.997067i $$-0.475617\pi$$
0.0765279 + 0.997067i $$0.475617\pi$$
$$684$$ 0 0
$$685$$ 68.0000 2.59815
$$686$$ 7.50000 12.9904i 0.286351 0.495975i
$$687$$ −5.00000 + 8.66025i −0.190762 + 0.330409i
$$688$$ −2.00000 3.46410i −0.0762493 0.132068i
$$689$$ −0.500000 + 0.866025i −0.0190485 + 0.0329929i
$$690$$ 2.00000 + 3.46410i 0.0761387 + 0.131876i
$$691$$ 42.0000 1.59776 0.798878 0.601494i $$-0.205427\pi$$
0.798878 + 0.601494i $$0.205427\pi$$
$$692$$ −6.00000 −0.228086
$$693$$ 6.00000 + 10.3923i 0.227921 + 0.394771i
$$694$$ 1.00000 + 1.73205i 0.0379595 + 0.0657477i
$$695$$ 0 0
$$696$$ 5.00000 0.189525
$$697$$ 12.0000 + 20.7846i 0.454532 + 0.787273i
$$698$$ −5.00000 + 8.66025i −0.189253 + 0.327795i
$$699$$ −3.00000 5.19615i −0.113470 0.196537i
$$700$$ −16.5000 + 28.5788i −0.623641 + 1.08018i
$$701$$ 14.0000 24.2487i 0.528773 0.915861i −0.470664 0.882312i $$-0.655986\pi$$
0.999437 0.0335489i $$-0.0106809\pi$$
$$702$$ −5.00000 −0.188713
$$703$$ 0 0
$$704$$ 2.00000 0.0753778
$$705$$ −16.0000 + 27.7128i −0.602595 + 1.04372i
$$706$$ −4.50000 + 7.79423i −0.169360 + 0.293340i
$$707$$ −3.00000 5.19615i −0.112827 0.195421i
$$708$$ 7.50000 12.9904i 0.281867 0.488208i
$$709$$ 15.0000 + 25.9808i 0.563337 + 0.975728i 0.997202 + 0.0747503i $$0.0238160\pi$$
−0.433865 + 0.900978i $$0.642851\pi$$
$$710$$ −8.00000 −0.300235
$$711$$ 20.0000 0.750059
$$712$$ 0 0
$$713$$ −4.00000 6.92820i −0.149801 0.259463i
$$714$$ −9.00000 −0.336817
$$715$$ 8.00000 0.299183
$$716$$ 0 0
$$717$$ 7.50000 12.9904i 0.280093 0.485135i
$$718$$ 7.50000 + 12.9904i 0.279898 + 0.484797i
$$719$$ 2.50000 4.33013i 0.0932343 0.161486i −0.815636 0.578565i $$-0.803613\pi$$
0.908870 + 0.417079i $$0.136946\pi$$
$$720$$ −4.00000 + 6.92820i −0.149071 + 0.258199i
$$721$$ −18.0000 −0.670355
$$722$$ 0 0
$$723$$ 8.00000 0.297523
$$724$$ −11.0000 + 19.0526i −0.408812 + 0.708083i
$$725$$ 27.5000 47.6314i 1.02132 1.76899i
$$726$$ −3.50000 6.06218i −0.129897 0.224989i
$$727$$ 8.50000 14.7224i 0.315248 0.546025i −0.664243 0.747517i $$-0.731246\pi$$
0.979490 + 0.201492i $$0.0645791\pi$$
$$728$$ 1.50000 + 2.59808i 0.0555937 + 0.0962911i
$$729$$ 13.0000 0.481481
$$730$$ −36.0000 −1.33242
$$731$$ −6.00000 10.3923i −0.221918 0.384373i
$$732$$ 1.00000 + 1.73205i 0.0369611 + 0.0640184i
$$733$$ −36.0000 −1.32969 −0.664845 0.746981i $$-0.731502\pi$$
−0.664845 + 0.746981i $$0.731502\pi$$
$$734$$ 28.0000 1.03350
$$735$$ −4.00000 6.92820i −0.147542 0.255551i
$$736$$ 0.500000 0.866025i 0.0184302 0.0319221i
$$737$$ −3.00000 5.19615i −0.110506 0.191403i
$$738$$ −8.00000 + 13.8564i −0.294484 + 0.510061i
$$739$$ 20.0000 34.6410i 0.735712 1.27429i −0.218698 0.975793i $$-0.570181\pi$$
0.954410 0.298498i $$-0.0964856\pi$$
$$740$$ 8.00000 0.294086
$$741$$ 0 0
$$742$$ −3.00000 −0.110133
$$743$$ 8.00000 13.8564i 0.293492 0.508342i −0.681141 0.732152i $$-0.738516\pi$$
0.974633 + 0.223810i $$0.0718494\pi$$
$$744$$ −4.00000 + 6.92820i −0.146647 + 0.254000i
$$745$$ 0 0
$$746$$ −14.5000 + 25.1147i −0.530883 + 0.919516i
$$747$$ −6.00000 10.3923i −0.219529 0.380235i
$$748$$ 6.00000 0.219382
$$749$$ −21.0000 −0.767323
$$750$$ −12.0000 20.7846i −0.438178 0.758947i
$$751$$ −16.0000 27.7128i −0.583848 1.01125i −0.995018 0.0996961i $$-0.968213\pi$$
0.411170 0.911559i $$-0.365120\pi$$
$$752$$ 8.00000 0.291730
$$753$$ −2.00000 −0.0728841
$$754$$ −2.50000 4.33013i −0.0910446 0.157694i
$$755$$ 4.00000 6.92820i 0.145575 0.252143i
$$756$$ −7.50000 12.9904i −0.272772 0.472456i
$$757$$ 1.00000 1.73205i 0.0363456 0.0629525i −0.847280 0.531146i $$-0.821762\pi$$
0.883626 + 0.468193i $$0.155095\pi$$
$$758$$ −7.50000 + 12.9904i −0.272412 + 0.471832i
$$759$$ 2.00000 0.0725954
$$760$$ 0 0
$$761$$ 27.0000 0.978749 0.489375 0.872074i $$-0.337225\pi$$
0.489375 + 0.872074i $$0.337225\pi$$
$$762$$ 9.00000 15.5885i 0.326036 0.564710i
$$763$$ 22.5000 38.9711i 0.814555 1.41085i
$$764$$ −3.50000 6.06218i −0.126626 0.219322i
$$765$$ −12.0000 + 20.7846i −0.433861 + 0.751469i
$$766$$ 13.0000 + 22.5167i 0.469709 + 0.813560i
$$767$$ −15.0000 −0.541619
$$768$$ −1.00000 −0.0360844
$$769$$ 17.5000 + 30.3109i 0.631066 + 1.09304i 0.987334 + 0.158655i $$0.0507157\pi$$
−0.356268 + 0.934384i $$0.615951\pi$$
$$770$$ 12.0000 + 20.7846i 0.432450 + 0.749025i
$$771$$ −8.00000 −0.288113
$$772$$ −6.00000 −0.215945
$$773$$ −4.50000 7.79423i −0.161854 0.280339i 0.773680 0.633577i $$-0.218414\pi$$
−0.935534 + 0.353238i $$0.885081\pi$$
$$774$$ 4.00000 6.92820i 0.143777 0.249029i
$$775$$ 44.0000 + 76.2102i 1.58053 + 2.73755i
$$776$$ 1.00000 1.73205i 0.0358979 0.0621770i
$$777$$ −3.00000 + 5.19615i −0.107624 + 0.186411i
$$778$$ −30.0000 −1.07555
$$779$$ 0 0
$$780$$ −4.00000 −0.143223
$$781$$ −2.00000 + 3.46410i −0.0715656 + 0.123955i