# Properties

 Label 722.2.c.f.653.1 Level $722$ Weight $2$ Character 722.653 Analytic conductor $5.765$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## 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 653.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 722.653 Dual form 722.2.c.f.429.1

## $q$-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 $$\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$$.

 $$n$$ $$363$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$

## 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 $$-0.259881\pi$$
−0.973494 + 0.228714i $$0.926548\pi$$
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ 2.00000 + 3.46410i 0.894427 + 1.54919i 0.834512 + 0.550990i $$0.185750\pi$$
0.0599153 + 0.998203i $$0.480917\pi$$
$$6$$ 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 $$-0.877618\pi$$
0.788320 + 0.615265i $$0.210951\pi$$
$$14$$ 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 0.624780 0.780801i $$-0.285189\pi$$
−0.988583 + 0.150675i $$0.951855\pi$$
$$18$$ 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 −0.809177 0.587565i $$-0.800087\pi$$
0.913434 + 0.406986i $$0.133420\pi$$
$$24$$ 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 $$-0.987005\pi$$
0.534928 + 0.844897i $$0.320339\pi$$
$$30$$ 4.00000 0.730297
$$31$$ 8.00000 1.43684 0.718421 0.695608i $$-0.244865\pi$$
0.718421 + 0.695608i $$0.244865\pi$$
$$32$$ 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 $$-0.447432\pi$$
0.164399 + 0.986394i $$0.447432\pi$$
$$38$$ 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 −0.988600 0.150567i $$-0.951890\pi$$
0.363905 0.931436i $$-0.381443\pi$$
$$42$$ 1.50000 2.59808i 0.231455 0.400892i
$$43$$ −2.00000 3.46410i −0.304997 0.528271i 0.672264 0.740312i $$-0.265322\pi$$
−0.977261 + 0.212041i $$0.931989\pi$$
$$44$$ −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 0.411606 + 0.911362i $$0.364968\pi$$
−0.995066 + 0.0992202i $$0.968365\pi$$
$$48$$ −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 $$-0.855212\pi$$
0.829640 + 0.558298i $$0.188546\pi$$
$$54$$ −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 0.675178 + 0.737655i $$0.264067\pi$$
0.301239 + 0.953549i $$0.402600\pi$$
$$60$$ 2.00000 + 3.46410i 0.258199 + 0.447214i
$$61$$ −1.00000 + 1.73205i −0.128037 + 0.221766i −0.922916 0.385002i $$-0.874201\pi$$
0.794879 + 0.606768i $$0.207534\pi$$
$$62$$ 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 $$-0.774670\pi$$
0.942987 + 0.332830i $$0.108004\pi$$
$$68$$ 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 $$-0.128801\pi$$
−0.800566 + 0.599245i $$0.795468\pi$$
$$72$$ −1.00000 + 1.73205i −0.117851 + 0.204124i
$$73$$ −4.50000 7.79423i −0.526685 0.912245i −0.999517 0.0310925i $$-0.990101\pi$$
0.472831 0.881153i $$-0.343232\pi$$
$$74$$ 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 −0.997274 0.0737937i $$-0.976489\pi$$
0.434730 0.900561i $$-0.356844\pi$$
$$80$$ 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 $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$90$$ 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 $$-0.199042\pi$$
−0.912317 + 0.409484i $$0.865709\pi$$
$$98$$ 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 −0.911479 0.411346i $$-0.865059\pi$$
0.811976 + 0.583691i $$0.198392\pi$$
$$102$$ −3.00000 −0.297044
$$103$$ 6.00000 0.591198 0.295599 0.955312i $$-0.404481\pi$$
0.295599 + 0.955312i $$0.404481\pi$$
$$104$$ 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 $$-0.390129\pi$$
0.338358 + 0.941018i $$0.390129\pi$$
$$108$$ 2.50000 4.33013i 0.240563 0.416667i
$$109$$ −7.50000 12.9904i −0.718370 1.24425i −0.961645 0.274296i $$-0.911555\pi$$
0.243276 0.969957i $$-0.421778\pi$$
$$110$$ −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 $$-0.728811\pi$$
−0.658505 + 0.752577i $$0.728811\pi$$
$$114$$ 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 −0.121894 0.992543i $$-0.538897\pi$$
0.920514 0.390709i $$-0.127770\pi$$
$$128$$ 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 −0.999602 0.0281993i $$-0.991023\pi$$
0.475380 0.879781i $$-0.342311\pi$$
$$132$$ 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 −0.232273 0.972651i $$-0.574616\pi$$
0.958477 0.285171i $$-0.0920506\pi$$
$$138$$ −0.500000 0.866025i −0.0425628 0.0737210i
$$139$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$140$$ −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 $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$150$$ 5.50000 + 9.52628i 0.449073 + 0.777817i
$$151$$ −2.00000 −0.162758 −0.0813788 0.996683i $$-0.525932\pi$$
−0.0813788 + 0.996683i $$0.525932\pi$$
$$152$$ 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 0.903167 0.429289i $$-0.141236\pi$$
−0.823359 + 0.567521i $$0.807902\pi$$
$$158$$ 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 $$-0.987025\pi$$
0.534875 + 0.844931i $$0.320359\pi$$
$$168$$ 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 $$-0.239913\pi$$
−0.957241 + 0.289292i $$0.906580\pi$$
$$174$$ 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 −0.0898051 0.995959i $$-0.528624\pi$$
0.907429 0.420206i $$-0.138042\pi$$
$$182$$ −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 $$-0.235950\pi$$
−0.953564 + 0.301189i $$0.902616\pi$$
$$194$$ 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 0.0416556 0.999132i $$-0.486737\pi$$
0.844446 0.535641i $$-0.179930\pi$$
$$200$$ 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 0.784364 + 0.620301i $$0.212990\pi$$
0.145014 + 0.989430i $$0.453677\pi$$
$$212$$ −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 $$-0.0113695\pi$$
−0.530607 + 0.847618i $$0.678036\pi$$
$$224$$ 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 $$-0.309198\pi$$
0.564165 + 0.825662i $$0.309198\pi$$
$$228$$ 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 0.947403 0.320043i $$-0.103697\pi$$
−0.750867 + 0.660454i $$0.770364\pi$$
$$234$$ −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 $$-0.916286\pi$$
0.707953 + 0.706260i $$0.249619\pi$$
$$242$$ −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 −0.895858 0.444340i $$-0.853438\pi$$
0.832739 + 0.553666i $$0.186772\pi$$
$$252$$ 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 $$-0.753063\pi$$
0.963391 + 0.268101i $$0.0863961\pi$$
$$258$$ −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 −0.952517 0.304487i $$-0.901515\pi$$
0.212565 0.977147i $$-0.431818\pi$$
$$264$$ 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 0.807535 + 0.589819i $$0.200801\pi$$
0.107031 + 0.994256i $$0.465866\pi$$
$$270$$ 10.0000 17.3205i 0.608581 1.05409i
$$271$$ −3.50000 6.06218i −0.212610 0.368251i 0.739921 0.672694i $$-0.234863\pi$$
−0.952531 + 0.304443i $$0.901530\pi$$
$$272$$ −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 $$-0.910028\pi$$
0.721699 + 0.692207i $$0.243362\pi$$
$$282$$ 4.00000 + 6.92820i 0.238197 + 0.412568i
$$283$$ 3.00000 + 5.19615i 0.178331 + 0.308879i 0.941309 0.337546i $$-0.109597\pi$$
−0.762978 + 0.646425i $$0.776263\pi$$
$$284$$ −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 $$-0.584677\pi$$
−0.262893 + 0.964825i $$0.584677\pi$$
$$294$$ 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 $$-0.277919\pi$$
−0.984885 + 0.173210i $$0.944586\pi$$
$$308$$ −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 0.0863973 + 0.996261i $$0.472465\pi$$
−0.905986 + 0.423308i $$0.860869\pi$$
$$314$$ −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 0.185514 + 0.982642i $$0.440605\pi$$
−0.943750 + 0.330661i $$0.892728\pi$$
$$318$$ 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 $$-0.654738\pi$$
−0.467202 + 0.884150i $$0.654738\pi$$
$$332$$ 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 −0.860366 0.509676i $$-0.829765\pi$$
−0.0112091 0.999937i $$-0.503568\pi$$
$$338$$ −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 0.891618 0.452788i $$-0.149571\pi$$
−0.837935 + 0.545770i $$0.816237\pi$$
$$348$$ −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 0.993207 0.116358i $$-0.0371219\pi$$
−0.597372 + 0.801964i $$0.703789\pi$$
$$360$$ −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 0.225750 + 0.974185i $$0.427517\pi$$
−0.956544 + 0.291587i $$0.905817\pi$$
$$368$$ −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 $$-0.770323\pi$$
−0.750782 + 0.660551i $$0.770323\pi$$
$$374$$ 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 $$-0.625884\pi$$
−0.385249 + 0.922813i $$0.625884\pi$$
$$380$$ 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 −0.979483 0.201527i $$-0.935410\pi$$
0.315214 0.949021i $$-0.397924\pi$$
$$384$$ 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 −0.182047 0.983290i $$-0.558272\pi$$
0.942578 0.333987i $$-0.108394\pi$$
$$390$$ −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 0.748017 0.663679i $$-0.231006\pi$$
−0.948772 + 0.315963i $$0.897673\pi$$
$$398$$ 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 $$-0.230680\pi$$
−0.948447 + 0.316934i $$0.897346\pi$$
$$402$$ −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 $$-0.997970\pi$$
0.505511 + 0.862820i $$0.331304\pi$$
$$410$$ 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 $$-0.269272\pi$$
−0.979817 + 0.199899i $$0.935939\pi$$
$$422$$ −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 $$-0.976060\pi$$
0.563658 + 0.826008i $$0.309393\pi$$
$$432$$ 2.50000 + 4.33013i 0.120281 + 0.208333i
$$433$$ 7.00000 12.1244i 0.336399 0.582659i −0.647354 0.762190i $$-0.724124\pi$$
0.983752 + 0.179530i $$0.0574578\pi$$
$$434$$ 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 $$-0.00829161\pi$$
−0.522387 + 0.852709i $$0.674958\pi$$
$$440$$ −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 −0.372265 0.928126i $$-0.621419\pi$$
0.989914 0.141672i $$-0.0452479\pi$$
$$444$$ 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 $$-0.575825\pi$$
−0.235965 + 0.971762i $$0.575825\pi$$
$$450$$ −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 0.982626 + 0.185597i $$0.0594220\pi$$
−0.330581 + 0.943778i $$0.607245\pi$$
$$462$$ 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 −0.541884 0.840453i $$-0.682289\pi$$
0.998796 + 0.0490589i $$0.0156222\pi$$
$$480$$ −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 $$-0.485571\pi$$
0.0453143 + 0.998973i $$0.485571\pi$$
$$488$$ 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 0.987181 + 0.159603i $$0.0510215\pi$$
−0.355370 + 0.934726i $$0.615645\pi$$
$$492$$ −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 −0.833404 0.552664i $$-0.813611\pi$$
−0.0619186 0.998081i $$-0.519722\pi$$
$$500$$ 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 −0.00691465 + 0.999976i $$0.502201\pi$$
−0.862547 + 0.505976i $$0.831132\pi$$
$$504$$ −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 0.314459 + 0.949271i $$0.398177\pi$$
−0.979322 + 0.202306i $$0.935156\pi$$
$$510$$ −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 $$-0.289821\pi$$
0.613351 + 0.789810i $$0.289821\pi$$
$$522$$ −5.00000 + 8.66025i −0.218844 + 0.379049i
$$523$$ 14.5000 25.1147i 0.634041 1.09819i −0.352677 0.935745i $$-0.614728\pi$$
0.986718 0.162446i $$-0.0519382\pi$$
$$524$$ 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 −0.886721 0.462304i $$-0.847023\pi$$
0.843728 + 0.536771i $$0.180356\pi$$
$$542$$ 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 −0.394432 0.918925i $$-0.629059\pi$$
0.993028 0.117875i $$-0.0376081\pi$$
$$548$$ 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 0.400599 + 0.916253i $$0.368802\pi$$
−0.993798 + 0.111198i $$0.964531\pi$$
$$558$$ 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 $$-0.225879\pi$$
0.758610 + 0.651546i $$0.225879\pi$$
$$564$$ −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 $$-0.816534\pi$$
−0.838444 + 0.544988i $$0.816534\pi$$
$$570$$ 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 0.962872 0.269957i $$-0.0870095\pi$$
−0.715226 + 0.698893i $$0.753676\pi$$
$$588$$ 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 0.271016 + 0.962575i $$0.412640\pi$$
−0.969122 + 0.246581i $$0.920693\pi$$
$$594$$ −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 $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$600$$ −11.0000 −0.449073
$$601$$ 8.00000 0.326327 0.163163 0.986599i $$-0.447830\pi$$
0.163163 + 0.986599i $$0.447830\pi$$
$$602$$ 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 $$-0.352679\pi$$
0.446476 + 0.894795i $$0.352679\pi$$
$$608$$ 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 −0.972924 0.231127i $$-0.925759\pi$$
0.286300 0.958140i $$-0.407575\pi$$
$$614$$ 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 −0.988343 0.152242i $$-0.951351\pi$$
0.626017 + 0.779809i $$0.284684\pi$$
$$618$$ 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 0.349148 + 0.937067i $$0.386471\pi$$
−0.986098 + 0.166162i $$0.946862\pi$$
$$632$$ 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 0.898470 + 0.439034i $$0.144679\pi$$
−0.0690201 + 0.997615i $$0.521987\pi$$
$$642$$ 3.50000 6.06218i 0.138134 0.239255i
$$643$$ 13.0000 + 22.5167i 0.512670 + 0.887970i 0.999892 + 0.0146923i $$0.00467688\pi$$
−0.487222 + 0.873278i $$0.661990\pi$$
$$644$$ 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 $$-0.802285\pi$$
0.910602 + 0.413284i $$0.135618\pi$$
$$660$$ 4.00000 + 6.92820i 0.155700 + 0.269680i
$$661$$ −11.5000 + 19.9186i −0.447298 + 0.774743i −0.998209 0.0598209i $$-0.980947\pi$$
0.550911 + 0.834564i $$0.314280\pi$$
$$662$$ −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 $$-0.822216\pi$$
−0.848038 + 0.529936i $$0.822216\pi$$
$$674$$ 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 $$-0.580370\pi$$
−0.249815 + 0.968294i $$0.580370\pi$$
$$678$$ −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 $$-0.524383\pi$$
−0.0765279 + 0.997067i $$0.524383\pi$$
$$684$$ 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 0.999437 + 0.0335489i $$0.0106809\pi$$
−0.470664 + 0.882312i $$0.655986\pi$$
$$702$$ 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 −0.433865 0.900978i $$-0.642851\pi$$
0.997202 0.0747503i $$-0.0238160\pi$$
$$710$$ −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 0.908870 0.417079i $$-0.136946\pi$$
−0.815636 + 0.578565i $$0.803613\pi$$
$$720$$ −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 0.979490 0.201492i $$-0.0645791\pi$$
−0.664243 + 0.747517i $$0.731246\pi$$
$$728$$ 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 0.954410 + 0.298498i $$0.0964856\pi$$
−0.218698 + 0.975793i $$0.570181\pi$$
$$740$$ −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 $$-0.261484\pi$$
−0.974633 + 0.223810i $$0.928151\pi$$
$$744$$ 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 −0.411170 0.911559i $$-0.634880\pi$$
0.995018 0.0996961i $$-0.0317870\pi$$
$$752$$ 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 0.883626 0.468193i $$-0.155095\pi$$
−0.847280 + 0.531146i $$0.821762\pi$$
$$758$$ −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 −0.356268 0.934384i $$-0.615951\pi$$
0.987334 0.158655i $$-0.0507157\pi$$
$$770$$ −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 $$-0.781586\pi$$
0.935534 + 0.353238i $$0.114919\pi$$
$$774$$ −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