# Properties

 Label 546.2.e.a.545.1 Level $546$ Weight $2$ Character 546.545 Analytic conductor $4.360$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$546 = 2 \cdot 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 546.e (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.35983195036$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 545.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 546.545 Dual form 546.2.e.a.545.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +(-1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +1.73205i q^{5} +(1.50000 + 0.866025i) q^{6} +(-2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} +(-1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +1.73205i q^{5} +(1.50000 + 0.866025i) q^{6} +(-2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} -1.73205i q^{10} +(-1.50000 - 0.866025i) q^{12} +(1.00000 - 3.46410i) q^{13} +(2.50000 - 0.866025i) q^{14} +(1.50000 - 2.59808i) q^{15} +1.00000 q^{16} -3.00000 q^{17} +(-1.50000 - 2.59808i) q^{18} +2.00000 q^{19} +1.73205i q^{20} +(4.50000 + 0.866025i) q^{21} -3.46410i q^{23} +(1.50000 + 0.866025i) q^{24} +2.00000 q^{25} +(-1.00000 + 3.46410i) q^{26} -5.19615i q^{27} +(-2.50000 + 0.866025i) q^{28} -6.92820i q^{29} +(-1.50000 + 2.59808i) q^{30} -8.00000 q^{31} -1.00000 q^{32} +3.00000 q^{34} +(-1.50000 - 4.33013i) q^{35} +(1.50000 + 2.59808i) q^{36} +1.73205i q^{37} -2.00000 q^{38} +(-4.50000 + 4.33013i) q^{39} -1.73205i q^{40} +(-4.50000 - 0.866025i) q^{42} -11.0000 q^{43} +(-4.50000 + 2.59808i) q^{45} +3.46410i q^{46} -12.1244i q^{47} +(-1.50000 - 0.866025i) q^{48} +(5.50000 - 4.33013i) q^{49} -2.00000 q^{50} +(4.50000 + 2.59808i) q^{51} +(1.00000 - 3.46410i) q^{52} -3.46410i q^{53} +5.19615i q^{54} +(2.50000 - 0.866025i) q^{56} +(-3.00000 - 1.73205i) q^{57} +6.92820i q^{58} -10.3923i q^{59} +(1.50000 - 2.59808i) q^{60} +6.92820i q^{61} +8.00000 q^{62} +(-6.00000 - 5.19615i) q^{63} +1.00000 q^{64} +(6.00000 + 1.73205i) q^{65} -13.8564i q^{67} -3.00000 q^{68} +(-3.00000 + 5.19615i) q^{69} +(1.50000 + 4.33013i) q^{70} -9.00000 q^{71} +(-1.50000 - 2.59808i) q^{72} -2.00000 q^{73} -1.73205i q^{74} +(-3.00000 - 1.73205i) q^{75} +2.00000 q^{76} +(4.50000 - 4.33013i) q^{78} +10.0000 q^{79} +1.73205i q^{80} +(-4.50000 + 7.79423i) q^{81} +3.46410i q^{83} +(4.50000 + 0.866025i) q^{84} -5.19615i q^{85} +11.0000 q^{86} +(-6.00000 + 10.3923i) q^{87} +3.46410i q^{89} +(4.50000 - 2.59808i) q^{90} +(0.500000 + 9.52628i) q^{91} -3.46410i q^{92} +(12.0000 + 6.92820i) q^{93} +12.1244i q^{94} +3.46410i q^{95} +(1.50000 + 0.866025i) q^{96} +8.00000 q^{97} +(-5.50000 + 4.33013i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 2q^{2} - 3q^{3} + 2q^{4} + 3q^{6} - 5q^{7} - 2q^{8} + 3q^{9} + O(q^{10})$$ $$2q - 2q^{2} - 3q^{3} + 2q^{4} + 3q^{6} - 5q^{7} - 2q^{8} + 3q^{9} - 3q^{12} + 2q^{13} + 5q^{14} + 3q^{15} + 2q^{16} - 6q^{17} - 3q^{18} + 4q^{19} + 9q^{21} + 3q^{24} + 4q^{25} - 2q^{26} - 5q^{28} - 3q^{30} - 16q^{31} - 2q^{32} + 6q^{34} - 3q^{35} + 3q^{36} - 4q^{38} - 9q^{39} - 9q^{42} - 22q^{43} - 9q^{45} - 3q^{48} + 11q^{49} - 4q^{50} + 9q^{51} + 2q^{52} + 5q^{56} - 6q^{57} + 3q^{60} + 16q^{62} - 12q^{63} + 2q^{64} + 12q^{65} - 6q^{68} - 6q^{69} + 3q^{70} - 18q^{71} - 3q^{72} - 4q^{73} - 6q^{75} + 4q^{76} + 9q^{78} + 20q^{79} - 9q^{81} + 9q^{84} + 22q^{86} - 12q^{87} + 9q^{90} + q^{91} + 24q^{93} + 3q^{96} + 16q^{97} - 11q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$$.

 $$n$$ $$157$$ $$365$$ $$379$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 −0.707107
$$3$$ −1.50000 0.866025i −0.866025 0.500000i
$$4$$ 1.00000 0.500000
$$5$$ 1.73205i 0.774597i 0.921954 + 0.387298i $$0.126592\pi$$
−0.921954 + 0.387298i $$0.873408\pi$$
$$6$$ 1.50000 + 0.866025i 0.612372 + 0.353553i
$$7$$ −2.50000 + 0.866025i −0.944911 + 0.327327i
$$8$$ −1.00000 −0.353553
$$9$$ 1.50000 + 2.59808i 0.500000 + 0.866025i
$$10$$ 1.73205i 0.547723i
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ −1.50000 0.866025i −0.433013 0.250000i
$$13$$ 1.00000 3.46410i 0.277350 0.960769i
$$14$$ 2.50000 0.866025i 0.668153 0.231455i
$$15$$ 1.50000 2.59808i 0.387298 0.670820i
$$16$$ 1.00000 0.250000
$$17$$ −3.00000 −0.727607 −0.363803 0.931476i $$-0.618522\pi$$
−0.363803 + 0.931476i $$0.618522\pi$$
$$18$$ −1.50000 2.59808i −0.353553 0.612372i
$$19$$ 2.00000 0.458831 0.229416 0.973329i $$-0.426318\pi$$
0.229416 + 0.973329i $$0.426318\pi$$
$$20$$ 1.73205i 0.387298i
$$21$$ 4.50000 + 0.866025i 0.981981 + 0.188982i
$$22$$ 0 0
$$23$$ 3.46410i 0.722315i −0.932505 0.361158i $$-0.882382\pi$$
0.932505 0.361158i $$-0.117618\pi$$
$$24$$ 1.50000 + 0.866025i 0.306186 + 0.176777i
$$25$$ 2.00000 0.400000
$$26$$ −1.00000 + 3.46410i −0.196116 + 0.679366i
$$27$$ 5.19615i 1.00000i
$$28$$ −2.50000 + 0.866025i −0.472456 + 0.163663i
$$29$$ 6.92820i 1.28654i −0.765641 0.643268i $$-0.777578\pi$$
0.765641 0.643268i $$-0.222422\pi$$
$$30$$ −1.50000 + 2.59808i −0.273861 + 0.474342i
$$31$$ −8.00000 −1.43684 −0.718421 0.695608i $$-0.755135\pi$$
−0.718421 + 0.695608i $$0.755135\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 0 0
$$34$$ 3.00000 0.514496
$$35$$ −1.50000 4.33013i −0.253546 0.731925i
$$36$$ 1.50000 + 2.59808i 0.250000 + 0.433013i
$$37$$ 1.73205i 0.284747i 0.989813 + 0.142374i $$0.0454735\pi$$
−0.989813 + 0.142374i $$0.954527\pi$$
$$38$$ −2.00000 −0.324443
$$39$$ −4.50000 + 4.33013i −0.720577 + 0.693375i
$$40$$ 1.73205i 0.273861i
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ −4.50000 0.866025i −0.694365 0.133631i
$$43$$ −11.0000 −1.67748 −0.838742 0.544529i $$-0.816708\pi$$
−0.838742 + 0.544529i $$0.816708\pi$$
$$44$$ 0 0
$$45$$ −4.50000 + 2.59808i −0.670820 + 0.387298i
$$46$$ 3.46410i 0.510754i
$$47$$ 12.1244i 1.76852i −0.466996 0.884260i $$-0.654664\pi$$
0.466996 0.884260i $$-0.345336\pi$$
$$48$$ −1.50000 0.866025i −0.216506 0.125000i
$$49$$ 5.50000 4.33013i 0.785714 0.618590i
$$50$$ −2.00000 −0.282843
$$51$$ 4.50000 + 2.59808i 0.630126 + 0.363803i
$$52$$ 1.00000 3.46410i 0.138675 0.480384i
$$53$$ 3.46410i 0.475831i −0.971286 0.237915i $$-0.923536\pi$$
0.971286 0.237915i $$-0.0764641\pi$$
$$54$$ 5.19615i 0.707107i
$$55$$ 0 0
$$56$$ 2.50000 0.866025i 0.334077 0.115728i
$$57$$ −3.00000 1.73205i −0.397360 0.229416i
$$58$$ 6.92820i 0.909718i
$$59$$ 10.3923i 1.35296i −0.736460 0.676481i $$-0.763504\pi$$
0.736460 0.676481i $$-0.236496\pi$$
$$60$$ 1.50000 2.59808i 0.193649 0.335410i
$$61$$ 6.92820i 0.887066i 0.896258 + 0.443533i $$0.146275\pi$$
−0.896258 + 0.443533i $$0.853725\pi$$
$$62$$ 8.00000 1.01600
$$63$$ −6.00000 5.19615i −0.755929 0.654654i
$$64$$ 1.00000 0.125000
$$65$$ 6.00000 + 1.73205i 0.744208 + 0.214834i
$$66$$ 0 0
$$67$$ 13.8564i 1.69283i −0.532524 0.846415i $$-0.678756\pi$$
0.532524 0.846415i $$-0.321244\pi$$
$$68$$ −3.00000 −0.363803
$$69$$ −3.00000 + 5.19615i −0.361158 + 0.625543i
$$70$$ 1.50000 + 4.33013i 0.179284 + 0.517549i
$$71$$ −9.00000 −1.06810 −0.534052 0.845452i $$-0.679331\pi$$
−0.534052 + 0.845452i $$0.679331\pi$$
$$72$$ −1.50000 2.59808i −0.176777 0.306186i
$$73$$ −2.00000 −0.234082 −0.117041 0.993127i $$-0.537341\pi$$
−0.117041 + 0.993127i $$0.537341\pi$$
$$74$$ 1.73205i 0.201347i
$$75$$ −3.00000 1.73205i −0.346410 0.200000i
$$76$$ 2.00000 0.229416
$$77$$ 0 0
$$78$$ 4.50000 4.33013i 0.509525 0.490290i
$$79$$ 10.0000 1.12509 0.562544 0.826767i $$-0.309823\pi$$
0.562544 + 0.826767i $$0.309823\pi$$
$$80$$ 1.73205i 0.193649i
$$81$$ −4.50000 + 7.79423i −0.500000 + 0.866025i
$$82$$ 0 0
$$83$$ 3.46410i 0.380235i 0.981761 + 0.190117i $$0.0608868\pi$$
−0.981761 + 0.190117i $$0.939113\pi$$
$$84$$ 4.50000 + 0.866025i 0.490990 + 0.0944911i
$$85$$ 5.19615i 0.563602i
$$86$$ 11.0000 1.18616
$$87$$ −6.00000 + 10.3923i −0.643268 + 1.11417i
$$88$$ 0 0
$$89$$ 3.46410i 0.367194i 0.983002 + 0.183597i $$0.0587741\pi$$
−0.983002 + 0.183597i $$0.941226\pi$$
$$90$$ 4.50000 2.59808i 0.474342 0.273861i
$$91$$ 0.500000 + 9.52628i 0.0524142 + 0.998625i
$$92$$ 3.46410i 0.361158i
$$93$$ 12.0000 + 6.92820i 1.24434 + 0.718421i
$$94$$ 12.1244i 1.25053i
$$95$$ 3.46410i 0.355409i
$$96$$ 1.50000 + 0.866025i 0.153093 + 0.0883883i
$$97$$ 8.00000 0.812277 0.406138 0.913812i $$-0.366875\pi$$
0.406138 + 0.913812i $$0.366875\pi$$
$$98$$ −5.50000 + 4.33013i −0.555584 + 0.437409i
$$99$$ 0 0
$$100$$ 2.00000 0.200000
$$101$$ 12.0000 1.19404 0.597022 0.802225i $$-0.296350\pi$$
0.597022 + 0.802225i $$0.296350\pi$$
$$102$$ −4.50000 2.59808i −0.445566 0.257248i
$$103$$ 3.46410i 0.341328i 0.985329 + 0.170664i $$0.0545913\pi$$
−0.985329 + 0.170664i $$0.945409\pi$$
$$104$$ −1.00000 + 3.46410i −0.0980581 + 0.339683i
$$105$$ −1.50000 + 7.79423i −0.146385 + 0.760639i
$$106$$ 3.46410i 0.336463i
$$107$$ 10.3923i 1.00466i 0.864675 + 0.502331i $$0.167524\pi$$
−0.864675 + 0.502331i $$0.832476\pi$$
$$108$$ 5.19615i 0.500000i
$$109$$ 5.19615i 0.497701i −0.968542 0.248851i $$-0.919947\pi$$
0.968542 0.248851i $$-0.0800528\pi$$
$$110$$ 0 0
$$111$$ 1.50000 2.59808i 0.142374 0.246598i
$$112$$ −2.50000 + 0.866025i −0.236228 + 0.0818317i
$$113$$ 6.92820i 0.651751i −0.945413 0.325875i $$-0.894341\pi$$
0.945413 0.325875i $$-0.105659\pi$$
$$114$$ 3.00000 + 1.73205i 0.280976 + 0.162221i
$$115$$ 6.00000 0.559503
$$116$$ 6.92820i 0.643268i
$$117$$ 10.5000 2.59808i 0.970725 0.240192i
$$118$$ 10.3923i 0.956689i
$$119$$ 7.50000 2.59808i 0.687524 0.238165i
$$120$$ −1.50000 + 2.59808i −0.136931 + 0.237171i
$$121$$ −11.0000 −1.00000
$$122$$ 6.92820i 0.627250i
$$123$$ 0 0
$$124$$ −8.00000 −0.718421
$$125$$ 12.1244i 1.08444i
$$126$$ 6.00000 + 5.19615i 0.534522 + 0.462910i
$$127$$ −2.00000 −0.177471 −0.0887357 0.996055i $$-0.528283\pi$$
−0.0887357 + 0.996055i $$0.528283\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ 16.5000 + 9.52628i 1.45274 + 0.838742i
$$130$$ −6.00000 1.73205i −0.526235 0.151911i
$$131$$ 15.0000 1.31056 0.655278 0.755388i $$-0.272551\pi$$
0.655278 + 0.755388i $$0.272551\pi$$
$$132$$ 0 0
$$133$$ −5.00000 + 1.73205i −0.433555 + 0.150188i
$$134$$ 13.8564i 1.19701i
$$135$$ 9.00000 0.774597
$$136$$ 3.00000 0.257248
$$137$$ −18.0000 −1.53784 −0.768922 0.639343i $$-0.779207\pi$$
−0.768922 + 0.639343i $$0.779207\pi$$
$$138$$ 3.00000 5.19615i 0.255377 0.442326i
$$139$$ 19.0526i 1.61602i 0.589171 + 0.808008i $$0.299454\pi$$
−0.589171 + 0.808008i $$0.700546\pi$$
$$140$$ −1.50000 4.33013i −0.126773 0.365963i
$$141$$ −10.5000 + 18.1865i −0.884260 + 1.53158i
$$142$$ 9.00000 0.755263
$$143$$ 0 0
$$144$$ 1.50000 + 2.59808i 0.125000 + 0.216506i
$$145$$ 12.0000 0.996546
$$146$$ 2.00000 0.165521
$$147$$ −12.0000 + 1.73205i −0.989743 + 0.142857i
$$148$$ 1.73205i 0.142374i
$$149$$ −6.00000 −0.491539 −0.245770 0.969328i $$-0.579041\pi$$
−0.245770 + 0.969328i $$0.579041\pi$$
$$150$$ 3.00000 + 1.73205i 0.244949 + 0.141421i
$$151$$ 19.0526i 1.55048i −0.631670 0.775238i $$-0.717630\pi$$
0.631670 0.775238i $$-0.282370\pi$$
$$152$$ −2.00000 −0.162221
$$153$$ −4.50000 7.79423i −0.363803 0.630126i
$$154$$ 0 0
$$155$$ 13.8564i 1.11297i
$$156$$ −4.50000 + 4.33013i −0.360288 + 0.346688i
$$157$$ 10.3923i 0.829396i −0.909959 0.414698i $$-0.863887\pi$$
0.909959 0.414698i $$-0.136113\pi$$
$$158$$ −10.0000 −0.795557
$$159$$ −3.00000 + 5.19615i −0.237915 + 0.412082i
$$160$$ 1.73205i 0.136931i
$$161$$ 3.00000 + 8.66025i 0.236433 + 0.682524i
$$162$$ 4.50000 7.79423i 0.353553 0.612372i
$$163$$ 17.3205i 1.35665i 0.734763 + 0.678323i $$0.237293\pi$$
−0.734763 + 0.678323i $$0.762707\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 3.46410i 0.268866i
$$167$$ 3.46410i 0.268060i −0.990977 0.134030i $$-0.957208\pi$$
0.990977 0.134030i $$-0.0427919\pi$$
$$168$$ −4.50000 0.866025i −0.347183 0.0668153i
$$169$$ −11.0000 6.92820i −0.846154 0.532939i
$$170$$ 5.19615i 0.398527i
$$171$$ 3.00000 + 5.19615i 0.229416 + 0.397360i
$$172$$ −11.0000 −0.838742
$$173$$ 6.00000 0.456172 0.228086 0.973641i $$-0.426753\pi$$
0.228086 + 0.973641i $$0.426753\pi$$
$$174$$ 6.00000 10.3923i 0.454859 0.787839i
$$175$$ −5.00000 + 1.73205i −0.377964 + 0.130931i
$$176$$ 0 0
$$177$$ −9.00000 + 15.5885i −0.676481 + 1.17170i
$$178$$ 3.46410i 0.259645i
$$179$$ 12.1244i 0.906217i 0.891455 + 0.453108i $$0.149685\pi$$
−0.891455 + 0.453108i $$0.850315\pi$$
$$180$$ −4.50000 + 2.59808i −0.335410 + 0.193649i
$$181$$ 3.46410i 0.257485i −0.991678 0.128742i $$-0.958906\pi$$
0.991678 0.128742i $$-0.0410940\pi$$
$$182$$ −0.500000 9.52628i −0.0370625 0.706135i
$$183$$ 6.00000 10.3923i 0.443533 0.768221i
$$184$$ 3.46410i 0.255377i
$$185$$ −3.00000 −0.220564
$$186$$ −12.0000 6.92820i −0.879883 0.508001i
$$187$$ 0 0
$$188$$ 12.1244i 0.884260i
$$189$$ 4.50000 + 12.9904i 0.327327 + 0.944911i
$$190$$ 3.46410i 0.251312i
$$191$$ 20.7846i 1.50392i −0.659208 0.751961i $$-0.729108\pi$$
0.659208 0.751961i $$-0.270892\pi$$
$$192$$ −1.50000 0.866025i −0.108253 0.0625000i
$$193$$ 17.3205i 1.24676i −0.781920 0.623379i $$-0.785760\pi$$
0.781920 0.623379i $$-0.214240\pi$$
$$194$$ −8.00000 −0.574367
$$195$$ −7.50000 7.79423i −0.537086 0.558156i
$$196$$ 5.50000 4.33013i 0.392857 0.309295i
$$197$$ 15.0000 1.06871 0.534353 0.845262i $$-0.320555\pi$$
0.534353 + 0.845262i $$0.320555\pi$$
$$198$$ 0 0
$$199$$ 6.92820i 0.491127i −0.969380 0.245564i $$-0.921027\pi$$
0.969380 0.245564i $$-0.0789730\pi$$
$$200$$ −2.00000 −0.141421
$$201$$ −12.0000 + 20.7846i −0.846415 + 1.46603i
$$202$$ −12.0000 −0.844317
$$203$$ 6.00000 + 17.3205i 0.421117 + 1.21566i
$$204$$ 4.50000 + 2.59808i 0.315063 + 0.181902i
$$205$$ 0 0
$$206$$ 3.46410i 0.241355i
$$207$$ 9.00000 5.19615i 0.625543 0.361158i
$$208$$ 1.00000 3.46410i 0.0693375 0.240192i
$$209$$ 0 0
$$210$$ 1.50000 7.79423i 0.103510 0.537853i
$$211$$ −13.0000 −0.894957 −0.447478 0.894295i $$-0.647678\pi$$
−0.447478 + 0.894295i $$0.647678\pi$$
$$212$$ 3.46410i 0.237915i
$$213$$ 13.5000 + 7.79423i 0.925005 + 0.534052i
$$214$$ 10.3923i 0.710403i
$$215$$ 19.0526i 1.29937i
$$216$$ 5.19615i 0.353553i
$$217$$ 20.0000 6.92820i 1.35769 0.470317i
$$218$$ 5.19615i 0.351928i
$$219$$ 3.00000 + 1.73205i 0.202721 + 0.117041i
$$220$$ 0 0
$$221$$ −3.00000 + 10.3923i −0.201802 + 0.699062i
$$222$$ −1.50000 + 2.59808i −0.100673 + 0.174371i
$$223$$ −7.00000 −0.468755 −0.234377 0.972146i $$-0.575305\pi$$
−0.234377 + 0.972146i $$0.575305\pi$$
$$224$$ 2.50000 0.866025i 0.167038 0.0578638i
$$225$$ 3.00000 + 5.19615i 0.200000 + 0.346410i
$$226$$ 6.92820i 0.460857i
$$227$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$228$$ −3.00000 1.73205i −0.198680 0.114708i
$$229$$ −5.00000 −0.330409 −0.165205 0.986259i $$-0.552828\pi$$
−0.165205 + 0.986259i $$0.552828\pi$$
$$230$$ −6.00000 −0.395628
$$231$$ 0 0
$$232$$ 6.92820i 0.454859i
$$233$$ 8.66025i 0.567352i 0.958920 + 0.283676i $$0.0915540\pi$$
−0.958920 + 0.283676i $$0.908446\pi$$
$$234$$ −10.5000 + 2.59808i −0.686406 + 0.169842i
$$235$$ 21.0000 1.36989
$$236$$ 10.3923i 0.676481i
$$237$$ −15.0000 8.66025i −0.974355 0.562544i
$$238$$ −7.50000 + 2.59808i −0.486153 + 0.168408i
$$239$$ 15.0000 0.970269 0.485135 0.874439i $$-0.338771\pi$$
0.485135 + 0.874439i $$0.338771\pi$$
$$240$$ 1.50000 2.59808i 0.0968246 0.167705i
$$241$$ 10.0000 0.644157 0.322078 0.946713i $$-0.395619\pi$$
0.322078 + 0.946713i $$0.395619\pi$$
$$242$$ 11.0000 0.707107
$$243$$ 13.5000 7.79423i 0.866025 0.500000i
$$244$$ 6.92820i 0.443533i
$$245$$ 7.50000 + 9.52628i 0.479157 + 0.608612i
$$246$$ 0 0
$$247$$ 2.00000 6.92820i 0.127257 0.440831i
$$248$$ 8.00000 0.508001
$$249$$ 3.00000 5.19615i 0.190117 0.329293i
$$250$$ 12.1244i 0.766812i
$$251$$ −12.0000 −0.757433 −0.378717 0.925513i $$-0.623635\pi$$
−0.378717 + 0.925513i $$0.623635\pi$$
$$252$$ −6.00000 5.19615i −0.377964 0.327327i
$$253$$ 0 0
$$254$$ 2.00000 0.125491
$$255$$ −4.50000 + 7.79423i −0.281801 + 0.488094i
$$256$$ 1.00000 0.0625000
$$257$$ −21.0000 −1.30994 −0.654972 0.755653i $$-0.727320\pi$$
−0.654972 + 0.755653i $$0.727320\pi$$
$$258$$ −16.5000 9.52628i −1.02725 0.593080i
$$259$$ −1.50000 4.33013i −0.0932055 0.269061i
$$260$$ 6.00000 + 1.73205i 0.372104 + 0.107417i
$$261$$ 18.0000 10.3923i 1.11417 0.643268i
$$262$$ −15.0000 −0.926703
$$263$$ 13.8564i 0.854423i 0.904152 + 0.427211i $$0.140504\pi$$
−0.904152 + 0.427211i $$0.859496\pi$$
$$264$$ 0 0
$$265$$ 6.00000 0.368577
$$266$$ 5.00000 1.73205i 0.306570 0.106199i
$$267$$ 3.00000 5.19615i 0.183597 0.317999i
$$268$$ 13.8564i 0.846415i
$$269$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$270$$ −9.00000 −0.547723
$$271$$ −1.00000 −0.0607457 −0.0303728 0.999539i $$-0.509669\pi$$
−0.0303728 + 0.999539i $$0.509669\pi$$
$$272$$ −3.00000 −0.181902
$$273$$ 7.50000 14.7224i 0.453921 0.891042i
$$274$$ 18.0000 1.08742
$$275$$ 0 0
$$276$$ −3.00000 + 5.19615i −0.180579 + 0.312772i
$$277$$ −16.0000 −0.961347 −0.480673 0.876900i $$-0.659608\pi$$
−0.480673 + 0.876900i $$0.659608\pi$$
$$278$$ 19.0526i 1.14270i
$$279$$ −12.0000 20.7846i −0.718421 1.24434i
$$280$$ 1.50000 + 4.33013i 0.0896421 + 0.258775i
$$281$$ −30.0000 −1.78965 −0.894825 0.446417i $$-0.852700\pi$$
−0.894825 + 0.446417i $$0.852700\pi$$
$$282$$ 10.5000 18.1865i 0.625266 1.08299i
$$283$$ 10.3923i 0.617758i −0.951101 0.308879i $$-0.900046\pi$$
0.951101 0.308879i $$-0.0999539\pi$$
$$284$$ −9.00000 −0.534052
$$285$$ 3.00000 5.19615i 0.177705 0.307794i
$$286$$ 0 0
$$287$$ 0 0
$$288$$ −1.50000 2.59808i −0.0883883 0.153093i
$$289$$ −8.00000 −0.470588
$$290$$ −12.0000 −0.704664
$$291$$ −12.0000 6.92820i −0.703452 0.406138i
$$292$$ −2.00000 −0.117041
$$293$$ 19.0526i 1.11306i 0.830827 + 0.556531i $$0.187868\pi$$
−0.830827 + 0.556531i $$0.812132\pi$$
$$294$$ 12.0000 1.73205i 0.699854 0.101015i
$$295$$ 18.0000 1.04800
$$296$$ 1.73205i 0.100673i
$$297$$ 0 0
$$298$$ 6.00000 0.347571
$$299$$ −12.0000 3.46410i −0.693978 0.200334i
$$300$$ −3.00000 1.73205i −0.173205 0.100000i
$$301$$ 27.5000 9.52628i 1.58507 0.549086i
$$302$$ 19.0526i 1.09635i
$$303$$ −18.0000 10.3923i −1.03407 0.597022i
$$304$$ 2.00000 0.114708
$$305$$ −12.0000 −0.687118
$$306$$ 4.50000 + 7.79423i 0.257248 + 0.445566i
$$307$$ −14.0000 −0.799022 −0.399511 0.916728i $$-0.630820\pi$$
−0.399511 + 0.916728i $$0.630820\pi$$
$$308$$ 0 0
$$309$$ 3.00000 5.19615i 0.170664 0.295599i
$$310$$ 13.8564i 0.786991i
$$311$$ −30.0000 −1.70114 −0.850572 0.525859i $$-0.823744\pi$$
−0.850572 + 0.525859i $$0.823744\pi$$
$$312$$ 4.50000 4.33013i 0.254762 0.245145i
$$313$$ 8.66025i 0.489506i 0.969585 + 0.244753i $$0.0787070\pi$$
−0.969585 + 0.244753i $$0.921293\pi$$
$$314$$ 10.3923i 0.586472i
$$315$$ 9.00000 10.3923i 0.507093 0.585540i
$$316$$ 10.0000 0.562544
$$317$$ 6.00000 0.336994 0.168497 0.985702i $$-0.446109\pi$$
0.168497 + 0.985702i $$0.446109\pi$$
$$318$$ 3.00000 5.19615i 0.168232 0.291386i
$$319$$ 0 0
$$320$$ 1.73205i 0.0968246i
$$321$$ 9.00000 15.5885i 0.502331 0.870063i
$$322$$ −3.00000 8.66025i −0.167183 0.482617i
$$323$$ −6.00000 −0.333849
$$324$$ −4.50000 + 7.79423i −0.250000 + 0.433013i
$$325$$ 2.00000 6.92820i 0.110940 0.384308i
$$326$$ 17.3205i 0.959294i
$$327$$ −4.50000 + 7.79423i −0.248851 + 0.431022i
$$328$$ 0 0
$$329$$ 10.5000 + 30.3109i 0.578884 + 1.67109i
$$330$$ 0 0
$$331$$ 17.3205i 0.952021i 0.879440 + 0.476011i $$0.157918\pi$$
−0.879440 + 0.476011i $$0.842082\pi$$
$$332$$ 3.46410i 0.190117i
$$333$$ −4.50000 + 2.59808i −0.246598 + 0.142374i
$$334$$ 3.46410i 0.189547i
$$335$$ 24.0000 1.31126
$$336$$ 4.50000 + 0.866025i 0.245495 + 0.0472456i
$$337$$ 5.00000 0.272367 0.136184 0.990684i $$-0.456516\pi$$
0.136184 + 0.990684i $$0.456516\pi$$
$$338$$ 11.0000 + 6.92820i 0.598321 + 0.376845i
$$339$$ −6.00000 + 10.3923i −0.325875 + 0.564433i
$$340$$ 5.19615i 0.281801i
$$341$$ 0 0
$$342$$ −3.00000 5.19615i −0.162221 0.280976i
$$343$$ −10.0000 + 15.5885i −0.539949 + 0.841698i
$$344$$ 11.0000 0.593080
$$345$$ −9.00000 5.19615i −0.484544 0.279751i
$$346$$ −6.00000 −0.322562
$$347$$ 15.5885i 0.836832i 0.908255 + 0.418416i $$0.137415\pi$$
−0.908255 + 0.418416i $$0.862585\pi$$
$$348$$ −6.00000 + 10.3923i −0.321634 + 0.557086i
$$349$$ 1.00000 0.0535288 0.0267644 0.999642i $$-0.491480\pi$$
0.0267644 + 0.999642i $$0.491480\pi$$
$$350$$ 5.00000 1.73205i 0.267261 0.0925820i
$$351$$ −18.0000 5.19615i −0.960769 0.277350i
$$352$$ 0 0
$$353$$ 10.3923i 0.553127i 0.960996 + 0.276563i $$0.0891955\pi$$
−0.960996 + 0.276563i $$0.910804\pi$$
$$354$$ 9.00000 15.5885i 0.478345 0.828517i
$$355$$ 15.5885i 0.827349i
$$356$$ 3.46410i 0.183597i
$$357$$ −13.5000 2.59808i −0.714496 0.137505i
$$358$$ 12.1244i 0.640792i
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 4.50000 2.59808i 0.237171 0.136931i
$$361$$ −15.0000 −0.789474
$$362$$ 3.46410i 0.182069i
$$363$$ 16.5000 + 9.52628i 0.866025 + 0.500000i
$$364$$ 0.500000 + 9.52628i 0.0262071 + 0.499313i
$$365$$ 3.46410i 0.181319i
$$366$$ −6.00000 + 10.3923i −0.313625 + 0.543214i
$$367$$ 34.6410i 1.80825i −0.427272 0.904123i $$-0.640525\pi$$
0.427272 0.904123i $$-0.359475\pi$$
$$368$$ 3.46410i 0.180579i
$$369$$ 0 0
$$370$$ 3.00000 0.155963
$$371$$ 3.00000 + 8.66025i 0.155752 + 0.449618i
$$372$$ 12.0000 + 6.92820i 0.622171 + 0.359211i
$$373$$ 16.0000 0.828449 0.414224 0.910175i $$-0.364053\pi$$
0.414224 + 0.910175i $$0.364053\pi$$
$$374$$ 0 0
$$375$$ 10.5000 18.1865i 0.542218 0.939149i
$$376$$ 12.1244i 0.625266i
$$377$$ −24.0000 6.92820i −1.23606 0.356821i
$$378$$ −4.50000 12.9904i −0.231455 0.668153i
$$379$$ 17.3205i 0.889695i 0.895606 + 0.444847i $$0.146742\pi$$
−0.895606 + 0.444847i $$0.853258\pi$$
$$380$$ 3.46410i 0.177705i
$$381$$ 3.00000 + 1.73205i 0.153695 + 0.0887357i
$$382$$ 20.7846i 1.06343i
$$383$$ 5.19615i 0.265511i −0.991149 0.132755i $$-0.957617\pi$$
0.991149 0.132755i $$-0.0423825\pi$$
$$384$$ 1.50000 + 0.866025i 0.0765466 + 0.0441942i
$$385$$ 0 0
$$386$$ 17.3205i 0.881591i
$$387$$ −16.5000 28.5788i −0.838742 1.45274i
$$388$$ 8.00000 0.406138
$$389$$ 10.3923i 0.526911i −0.964672 0.263455i $$-0.915138\pi$$
0.964672 0.263455i $$-0.0848622\pi$$
$$390$$ 7.50000 + 7.79423i 0.379777 + 0.394676i
$$391$$ 10.3923i 0.525561i
$$392$$ −5.50000 + 4.33013i −0.277792 + 0.218704i
$$393$$ −22.5000 12.9904i −1.13497 0.655278i
$$394$$ −15.0000 −0.755689
$$395$$ 17.3205i 0.871489i
$$396$$ 0 0
$$397$$ −22.0000 −1.10415 −0.552074 0.833795i $$-0.686163\pi$$
−0.552074 + 0.833795i $$0.686163\pi$$
$$398$$ 6.92820i 0.347279i
$$399$$ 9.00000 + 1.73205i 0.450564 + 0.0867110i
$$400$$ 2.00000 0.100000
$$401$$ −6.00000 −0.299626 −0.149813 0.988714i $$-0.547867\pi$$
−0.149813 + 0.988714i $$0.547867\pi$$
$$402$$ 12.0000 20.7846i 0.598506 1.03664i
$$403$$ −8.00000 + 27.7128i −0.398508 + 1.38047i
$$404$$ 12.0000 0.597022
$$405$$ −13.5000 7.79423i −0.670820 0.387298i
$$406$$ −6.00000 17.3205i −0.297775 0.859602i
$$407$$ 0 0
$$408$$ −4.50000 2.59808i −0.222783 0.128624i
$$409$$ 14.0000 0.692255 0.346128 0.938187i $$-0.387496\pi$$
0.346128 + 0.938187i $$0.387496\pi$$
$$410$$ 0 0
$$411$$ 27.0000 + 15.5885i 1.33181 + 0.768922i
$$412$$ 3.46410i 0.170664i
$$413$$ 9.00000 + 25.9808i 0.442861 + 1.27843i
$$414$$ −9.00000 + 5.19615i −0.442326 + 0.255377i
$$415$$ −6.00000 −0.294528
$$416$$ −1.00000 + 3.46410i −0.0490290 + 0.169842i
$$417$$ 16.5000 28.5788i 0.808008 1.39951i
$$418$$ 0 0
$$419$$ 27.0000 1.31904 0.659518 0.751689i $$-0.270760\pi$$
0.659518 + 0.751689i $$0.270760\pi$$
$$420$$ −1.50000 + 7.79423i −0.0731925 + 0.380319i
$$421$$ 32.9090i 1.60388i −0.597401 0.801942i $$-0.703800\pi$$
0.597401 0.801942i $$-0.296200\pi$$
$$422$$ 13.0000 0.632830
$$423$$ 31.5000 18.1865i 1.53158 0.884260i
$$424$$ 3.46410i 0.168232i
$$425$$ −6.00000 −0.291043
$$426$$ −13.5000 7.79423i −0.654077 0.377632i
$$427$$ −6.00000 17.3205i −0.290360 0.838198i
$$428$$ 10.3923i 0.502331i
$$429$$ 0 0
$$430$$ 19.0526i 0.918796i
$$431$$ 33.0000 1.58955 0.794777 0.606902i $$-0.207588\pi$$
0.794777 + 0.606902i $$0.207588\pi$$
$$432$$ 5.19615i 0.250000i
$$433$$ 5.19615i 0.249711i −0.992175 0.124856i $$-0.960153\pi$$
0.992175 0.124856i $$-0.0398468\pi$$
$$434$$ −20.0000 + 6.92820i −0.960031 + 0.332564i
$$435$$ −18.0000 10.3923i −0.863034 0.498273i
$$436$$ 5.19615i 0.248851i
$$437$$ 6.92820i 0.331421i
$$438$$ −3.00000 1.73205i −0.143346 0.0827606i
$$439$$ 31.1769i 1.48799i 0.668184 + 0.743996i $$0.267072\pi$$
−0.668184 + 0.743996i $$0.732928\pi$$
$$440$$ 0 0
$$441$$ 19.5000 + 7.79423i 0.928571 + 0.371154i
$$442$$ 3.00000 10.3923i 0.142695 0.494312i
$$443$$ 22.5167i 1.06980i −0.844916 0.534899i $$-0.820349\pi$$
0.844916 0.534899i $$-0.179651\pi$$
$$444$$ 1.50000 2.59808i 0.0711868 0.123299i
$$445$$ −6.00000 −0.284427
$$446$$ 7.00000 0.331460
$$447$$ 9.00000 + 5.19615i 0.425685 + 0.245770i
$$448$$ −2.50000 + 0.866025i −0.118114 + 0.0409159i
$$449$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$450$$ −3.00000 5.19615i −0.141421 0.244949i
$$451$$ 0 0
$$452$$ 6.92820i 0.325875i
$$453$$ −16.5000 + 28.5788i −0.775238 + 1.34275i
$$454$$ 0 0
$$455$$ −16.5000 + 0.866025i −0.773532 + 0.0405999i
$$456$$ 3.00000 + 1.73205i 0.140488 + 0.0811107i
$$457$$ 10.3923i 0.486132i −0.970010 0.243066i $$-0.921847\pi$$
0.970010 0.243066i $$-0.0781531\pi$$
$$458$$ 5.00000 0.233635
$$459$$ 15.5885i 0.727607i
$$460$$ 6.00000 0.279751
$$461$$ 5.19615i 0.242009i 0.992652 + 0.121004i $$0.0386115\pi$$
−0.992652 + 0.121004i $$0.961388\pi$$
$$462$$ 0 0
$$463$$ 24.2487i 1.12693i 0.826139 + 0.563467i $$0.190533\pi$$
−0.826139 + 0.563467i $$0.809467\pi$$
$$464$$ 6.92820i 0.321634i
$$465$$ −12.0000 + 20.7846i −0.556487 + 0.963863i
$$466$$ 8.66025i 0.401179i
$$467$$ −36.0000 −1.66588 −0.832941 0.553362i $$-0.813345\pi$$
−0.832941 + 0.553362i $$0.813345\pi$$
$$468$$ 10.5000 2.59808i 0.485363 0.120096i
$$469$$ 12.0000 + 34.6410i 0.554109 + 1.59957i
$$470$$ −21.0000 −0.968658
$$471$$ −9.00000 + 15.5885i −0.414698 + 0.718278i
$$472$$ 10.3923i 0.478345i
$$473$$ 0 0
$$474$$ 15.0000 + 8.66025i 0.688973 + 0.397779i
$$475$$ 4.00000 0.183533
$$476$$ 7.50000 2.59808i 0.343762 0.119083i
$$477$$ 9.00000 5.19615i 0.412082 0.237915i
$$478$$ −15.0000 −0.686084
$$479$$ 32.9090i 1.50365i −0.659363 0.751825i $$-0.729174\pi$$
0.659363 0.751825i $$-0.270826\pi$$
$$480$$ −1.50000 + 2.59808i −0.0684653 + 0.118585i
$$481$$ 6.00000 + 1.73205i 0.273576 + 0.0789747i
$$482$$ −10.0000 −0.455488
$$483$$ 3.00000 15.5885i 0.136505 0.709299i
$$484$$ −11.0000 −0.500000
$$485$$ 13.8564i 0.629187i
$$486$$ −13.5000 + 7.79423i −0.612372 + 0.353553i
$$487$$ 24.2487i 1.09881i 0.835555 + 0.549407i $$0.185146\pi$$
−0.835555 + 0.549407i $$0.814854\pi$$
$$488$$ 6.92820i 0.313625i
$$489$$ 15.0000 25.9808i 0.678323 1.17489i
$$490$$ −7.50000 9.52628i −0.338815 0.430353i
$$491$$ 36.3731i 1.64149i 0.571292 + 0.820747i $$0.306442\pi$$
−0.571292 + 0.820747i $$0.693558\pi$$
$$492$$ 0 0
$$493$$ 20.7846i 0.936092i
$$494$$ −2.00000 + 6.92820i −0.0899843 + 0.311715i
$$495$$ 0 0
$$496$$ −8.00000 −0.359211
$$497$$ 22.5000 7.79423i 1.00926 0.349619i
$$498$$ −3.00000 + 5.19615i −0.134433 + 0.232845i
$$499$$ 20.7846i 0.930447i −0.885193 0.465223i $$-0.845974\pi$$
0.885193 0.465223i $$-0.154026\pi$$
$$500$$ 12.1244i 0.542218i
$$501$$ −3.00000 + 5.19615i −0.134030 + 0.232147i
$$502$$ 12.0000 0.535586
$$503$$ 6.00000 0.267527 0.133763 0.991013i $$-0.457294\pi$$
0.133763 + 0.991013i $$0.457294\pi$$
$$504$$ 6.00000 + 5.19615i 0.267261 + 0.231455i
$$505$$ 20.7846i 0.924903i
$$506$$ 0 0
$$507$$ 10.5000 + 19.9186i 0.466321 + 0.884615i
$$508$$ −2.00000 −0.0887357
$$509$$ 27.7128i 1.22835i −0.789170 0.614174i $$-0.789489\pi$$
0.789170 0.614174i $$-0.210511\pi$$
$$510$$ 4.50000 7.79423i 0.199263 0.345134i
$$511$$ 5.00000 1.73205i 0.221187 0.0766214i
$$512$$ −1.00000 −0.0441942
$$513$$ 10.3923i 0.458831i
$$514$$ 21.0000 0.926270
$$515$$ −6.00000 −0.264392
$$516$$ 16.5000 + 9.52628i 0.726372 + 0.419371i
$$517$$ 0 0
$$518$$ 1.50000 + 4.33013i 0.0659062 + 0.190255i
$$519$$ −9.00000 5.19615i −0.395056 0.228086i
$$520$$ −6.00000 1.73205i −0.263117 0.0759555i
$$521$$ 27.0000 1.18289 0.591446 0.806345i $$-0.298557\pi$$
0.591446 + 0.806345i $$0.298557\pi$$
$$522$$ −18.0000 + 10.3923i −0.787839 + 0.454859i
$$523$$ 17.3205i 0.757373i 0.925525 + 0.378686i $$0.123624\pi$$
−0.925525 + 0.378686i $$0.876376\pi$$
$$524$$ 15.0000 0.655278
$$525$$ 9.00000 + 1.73205i 0.392792 + 0.0755929i
$$526$$ 13.8564i 0.604168i
$$527$$ 24.0000 1.04546
$$528$$ 0 0
$$529$$ 11.0000 0.478261
$$530$$ −6.00000 −0.260623
$$531$$ 27.0000 15.5885i 1.17170 0.676481i
$$532$$ −5.00000 + 1.73205i −0.216777 + 0.0750939i
$$533$$ 0 0
$$534$$ −3.00000 + 5.19615i −0.129823 + 0.224860i
$$535$$ −18.0000 −0.778208
$$536$$ 13.8564i 0.598506i
$$537$$ 10.5000 18.1865i 0.453108 0.784807i
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 9.00000 0.387298
$$541$$ 19.0526i 0.819133i 0.912280 + 0.409567i $$0.134320\pi$$
−0.912280 + 0.409567i $$0.865680\pi$$
$$542$$ 1.00000 0.0429537
$$543$$ −3.00000 + 5.19615i −0.128742 + 0.222988i
$$544$$ 3.00000 0.128624
$$545$$ 9.00000 0.385518
$$546$$ −7.50000 + 14.7224i −0.320970 + 0.630062i
$$547$$ 17.0000 0.726868 0.363434 0.931620i $$-0.381604\pi$$
0.363434 + 0.931620i $$0.381604\pi$$
$$548$$ −18.0000 −0.768922
$$549$$ −18.0000 + 10.3923i −0.768221 + 0.443533i
$$550$$ 0 0
$$551$$ 13.8564i 0.590303i
$$552$$ 3.00000 5.19615i 0.127688 0.221163i
$$553$$ −25.0000 + 8.66025i −1.06311 + 0.368271i
$$554$$ 16.0000 0.679775
$$555$$ 4.50000 + 2.59808i 0.191014 + 0.110282i
$$556$$ 19.0526i 0.808008i
$$557$$ 33.0000 1.39825 0.699127 0.714997i $$-0.253572\pi$$
0.699127 + 0.714997i $$0.253572\pi$$
$$558$$ 12.0000 + 20.7846i 0.508001 + 0.879883i
$$559$$ −11.0000 + 38.1051i −0.465250 + 1.61167i
$$560$$ −1.50000 4.33013i −0.0633866 0.182981i
$$561$$ 0 0
$$562$$ 30.0000 1.26547
$$563$$ 21.0000 0.885044 0.442522 0.896758i $$-0.354084\pi$$
0.442522 + 0.896758i $$0.354084\pi$$
$$564$$ −10.5000 + 18.1865i −0.442130 + 0.765791i
$$565$$ 12.0000 0.504844
$$566$$ 10.3923i 0.436821i
$$567$$ 4.50000 23.3827i 0.188982 0.981981i
$$568$$ 9.00000 0.377632
$$569$$ 32.9090i 1.37962i −0.723993 0.689808i $$-0.757695\pi$$
0.723993 0.689808i $$-0.242305\pi$$
$$570$$ −3.00000 + 5.19615i −0.125656 + 0.217643i
$$571$$ 13.0000 0.544033 0.272017 0.962293i $$-0.412309\pi$$
0.272017 + 0.962293i $$0.412309\pi$$
$$572$$ 0 0
$$573$$ −18.0000 + 31.1769i −0.751961 + 1.30243i
$$574$$ 0 0
$$575$$ 6.92820i 0.288926i
$$576$$ 1.50000 + 2.59808i 0.0625000 + 0.108253i
$$577$$ −46.0000 −1.91501 −0.957503 0.288425i $$-0.906868\pi$$
−0.957503 + 0.288425i $$0.906868\pi$$
$$578$$ 8.00000 0.332756
$$579$$ −15.0000 + 25.9808i −0.623379 + 1.07972i
$$580$$ 12.0000 0.498273
$$581$$ −3.00000 8.66025i −0.124461 0.359288i
$$582$$ 12.0000 + 6.92820i 0.497416 + 0.287183i
$$583$$ 0 0
$$584$$ 2.00000 0.0827606
$$585$$ 4.50000 + 18.1865i 0.186052 + 0.751921i
$$586$$ 19.0526i 0.787054i
$$587$$ 38.1051i 1.57277i 0.617739 + 0.786383i $$0.288049\pi$$
−0.617739 + 0.786383i $$0.711951\pi$$
$$588$$ −12.0000 + 1.73205i −0.494872 + 0.0714286i
$$589$$ −16.0000 −0.659269
$$590$$ −18.0000 −0.741048
$$591$$ −22.5000 12.9904i −0.925526 0.534353i
$$592$$ 1.73205i 0.0711868i
$$593$$ 48.4974i 1.99155i −0.0918243 0.995775i $$-0.529270\pi$$
0.0918243 0.995775i $$-0.470730\pi$$
$$594$$ 0 0
$$595$$ 4.50000 + 12.9904i 0.184482 + 0.532554i
$$596$$ −6.00000 −0.245770
$$597$$ −6.00000 + 10.3923i −0.245564 + 0.425329i
$$598$$ 12.0000 + 3.46410i 0.490716 + 0.141658i
$$599$$ 24.2487i 0.990775i 0.868672 + 0.495388i $$0.164974\pi$$
−0.868672 + 0.495388i $$0.835026\pi$$
$$600$$ 3.00000 + 1.73205i 0.122474 + 0.0707107i
$$601$$ 5.19615i 0.211955i 0.994369 + 0.105978i $$0.0337972\pi$$
−0.994369 + 0.105978i $$0.966203\pi$$
$$602$$ −27.5000 + 9.52628i −1.12082 + 0.388262i
$$603$$ 36.0000 20.7846i 1.46603 0.846415i
$$604$$ 19.0526i 0.775238i
$$605$$ 19.0526i 0.774597i
$$606$$ 18.0000 + 10.3923i 0.731200 + 0.422159i
$$607$$ 24.2487i 0.984225i −0.870532 0.492112i $$-0.836225\pi$$
0.870532 0.492112i $$-0.163775\pi$$
$$608$$ −2.00000 −0.0811107
$$609$$ 6.00000 31.1769i 0.243132 1.26335i
$$610$$ 12.0000 0.485866
$$611$$ −42.0000 12.1244i −1.69914 0.490499i
$$612$$ −4.50000 7.79423i −0.181902 0.315063i
$$613$$ 6.92820i 0.279827i 0.990164 + 0.139914i $$0.0446825\pi$$
−0.990164 + 0.139914i $$0.955317\pi$$
$$614$$ 14.0000 0.564994
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 36.0000 1.44931 0.724653 0.689114i $$-0.242000\pi$$
0.724653 + 0.689114i $$0.242000\pi$$
$$618$$ −3.00000 + 5.19615i −0.120678 + 0.209020i
$$619$$ −40.0000 −1.60774 −0.803868 0.594808i $$-0.797228\pi$$
−0.803868 + 0.594808i $$0.797228\pi$$
$$620$$ 13.8564i 0.556487i
$$621$$ −18.0000 −0.722315
$$622$$ 30.0000 1.20289
$$623$$ −3.00000 8.66025i −0.120192 0.346966i
$$624$$ −4.50000 + 4.33013i −0.180144 + 0.173344i
$$625$$ −11.0000 −0.440000
$$626$$ 8.66025i 0.346133i
$$627$$ 0 0
$$628$$ 10.3923i 0.414698i
$$629$$ 5.19615i 0.207184i
$$630$$ −9.00000 + 10.3923i −0.358569 + 0.414039i
$$631$$ 22.5167i 0.896374i −0.893940 0.448187i $$-0.852070\pi$$
0.893940 0.448187i $$-0.147930\pi$$
$$632$$ −10.0000 −0.397779
$$633$$ 19.5000 + 11.2583i 0.775055 + 0.447478i
$$634$$ −6.00000 −0.238290
$$635$$ 3.46410i 0.137469i
$$636$$ −3.00000 + 5.19615i −0.118958 + 0.206041i
$$637$$ −9.50000 23.3827i −0.376404 0.926456i
$$638$$ 0 0
$$639$$ −13.5000 23.3827i −0.534052 0.925005i
$$640$$ 1.73205i 0.0684653i
$$641$$ 34.6410i 1.36824i −0.729370 0.684119i $$-0.760187\pi$$
0.729370 0.684119i $$-0.239813\pi$$
$$642$$ −9.00000 + 15.5885i −0.355202 + 0.615227i
$$643$$ 40.0000 1.57745 0.788723 0.614749i $$-0.210743\pi$$
0.788723 + 0.614749i $$0.210743\pi$$
$$644$$ 3.00000 + 8.66025i 0.118217 + 0.341262i
$$645$$ −16.5000 + 28.5788i −0.649687 + 1.12529i
$$646$$ 6.00000 0.236067
$$647$$ −30.0000 −1.17942 −0.589711 0.807614i $$-0.700758\pi$$
−0.589711 + 0.807614i $$0.700758\pi$$
$$648$$ 4.50000 7.79423i 0.176777 0.306186i
$$649$$ 0 0
$$650$$ −2.00000 + 6.92820i −0.0784465 + 0.271746i
$$651$$ −36.0000 6.92820i −1.41095 0.271538i
$$652$$ 17.3205i 0.678323i
$$653$$ 41.5692i 1.62673i 0.581754 + 0.813365i $$0.302367\pi$$
−0.581754 + 0.813365i $$0.697633\pi$$
$$654$$ 4.50000 7.79423i 0.175964 0.304778i
$$655$$ 25.9808i 1.01515i
$$656$$ 0 0
$$657$$ −3.00000 5.19615i −0.117041 0.202721i
$$658$$ −10.5000 30.3109i −0.409333 1.18164i
$$659$$ 24.2487i 0.944596i −0.881439 0.472298i $$-0.843425\pi$$
0.881439 0.472298i $$-0.156575\pi$$
$$660$$ 0 0
$$661$$ 22.0000 0.855701 0.427850 0.903850i $$-0.359271\pi$$
0.427850 + 0.903850i $$0.359271\pi$$
$$662$$ 17.3205i 0.673181i
$$663$$ 13.5000 12.9904i 0.524297 0.504505i
$$664$$ 3.46410i 0.134433i
$$665$$ −3.00000 8.66025i −0.116335 0.335830i
$$666$$ 4.50000 2.59808i 0.174371 0.100673i
$$667$$ −24.0000 −0.929284
$$668$$ 3.46410i 0.134030i
$$669$$ 10.5000 + 6.06218i 0.405953 + 0.234377i
$$670$$ −24.0000 −0.927201
$$671$$ 0 0
$$672$$ −4.50000 0.866025i −0.173591 0.0334077i
$$673$$ −17.0000 −0.655302 −0.327651 0.944799i $$-0.606257\pi$$
−0.327651 + 0.944799i $$0.606257\pi$$
$$674$$ −5.00000 −0.192593
$$675$$ 10.3923i 0.400000i
$$676$$ −11.0000 6.92820i −0.423077 0.266469i
$$677$$ 18.0000 0.691796 0.345898 0.938272i $$-0.387574\pi$$
0.345898 + 0.938272i $$0.387574\pi$$
$$678$$ 6.00000 10.3923i 0.230429 0.399114i
$$679$$ −20.0000 + 6.92820i −0.767530 + 0.265880i
$$680$$ 5.19615i 0.199263i
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 30.0000 1.14792 0.573959 0.818884i $$-0.305407\pi$$
0.573959 + 0.818884i $$0.305407\pi$$
$$684$$ 3.00000 + 5.19615i 0.114708 + 0.198680i
$$685$$ 31.1769i 1.19121i
$$686$$ 10.0000 15.5885i 0.381802 0.595170i
$$687$$ 7.50000 + 4.33013i 0.286143 + 0.165205i
$$688$$ −11.0000 −0.419371
$$689$$ −12.0000 3.46410i −0.457164 0.131972i
$$690$$ 9.00000 + 5.19615i 0.342624 + 0.197814i
$$691$$ 20.0000 0.760836 0.380418 0.924815i $$-0.375780\pi$$
0.380418 + 0.924815i $$0.375780\pi$$
$$692$$ 6.00000 0.228086
$$693$$ 0 0
$$694$$ 15.5885i 0.591730i
$$695$$ −33.0000 −1.25176
$$696$$ 6.00000 10.3923i 0.227429 0.393919i
$$697$$ 0 0
$$698$$ −1.00000 −0.0378506
$$699$$ 7.50000 12.9904i 0.283676 0.491341i
$$700$$ −5.00000 + 1.73205i −0.188982 + 0.0654654i
$$701$$ 38.1051i 1.43921i −0.694383 0.719605i $$-0.744323\pi$$
0.694383 0.719605i $$-0.255677\pi$$
$$702$$ 18.0000 + 5.19615i 0.679366 + 0.196116i
$$703$$ 3.46410i 0.130651i
$$704$$ 0 0
$$705$$ −31.5000 18.1865i −1.18636 0.684944i
$$706$$ 10.3923i 0.391120i
$$707$$ −30.0000 + 10.3923i −1.12827 + 0.390843i
$$708$$ −9.00000 + 15.5885i −0.338241 + 0.585850i
$$709$$ 34.6410i 1.30097i −0.759519 0.650485i $$-0.774566\pi$$
0.759519 0.650485i $$-0.225434\pi$$
$$710$$ 15.5885i 0.585024i
$$711$$ 15.0000 + 25.9808i 0.562544 + 0.974355i
$$712$$ 3.46410i 0.129823i
$$713$$ 27.7128i 1.03785i
$$714$$ 13.5000 + 2.59808i 0.505225 + 0.0972306i
$$715$$ 0 0
$$716$$ 12.1244i 0.453108i
$$717$$ −22.5000 12.9904i −0.840278 0.485135i
$$718$$ 0 0
$$719$$ −12.0000 −0.447524 −0.223762 0.974644i $$-0.571834\pi$$
−0.223762 + 0.974644i $$0.571834\pi$$
$$720$$ −4.50000 + 2.59808i −0.167705 + 0.0968246i
$$721$$ −3.00000 8.66025i −0.111726 0.322525i
$$722$$ 15.0000 0.558242
$$723$$ −15.0000 8.66025i −0.557856 0.322078i
$$724$$ 3.46410i 0.128742i
$$725$$ 13.8564i 0.514614i
$$726$$ −16.5000 9.52628i −0.612372 0.353553i
$$727$$ 41.5692i 1.54172i −0.637006 0.770859i $$-0.719828\pi$$
0.637006 0.770859i $$-0.280172\pi$$
$$728$$ −0.500000 9.52628i −0.0185312 0.353067i
$$729$$ −27.0000 −1.00000
$$730$$ 3.46410i 0.128212i
$$731$$ 33.0000 1.22055
$$732$$ 6.00000 10.3923i 0.221766 0.384111i
$$733$$ 19.0000 0.701781 0.350891 0.936416i $$-0.385879\pi$$
0.350891 + 0.936416i $$0.385879\pi$$
$$734$$ 34.6410i 1.27862i
$$735$$ −3.00000 20.7846i −0.110657 0.766652i
$$736$$ 3.46410i 0.127688i
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 20.7846i 0.764574i 0.924044 + 0.382287i $$0.124863\pi$$
−0.924044 + 0.382287i $$0.875137\pi$$
$$740$$ −3.00000 −0.110282
$$741$$ −9.00000 + 8.66025i −0.330623 + 0.318142i
$$742$$ −3.00000 8.66025i −0.110133 0.317928i
$$743$$ −33.0000 −1.21065 −0.605326 0.795977i $$-0.706957\pi$$
−0.605326 + 0.795977i $$0.706957\pi$$
$$744$$ −12.0000 6.92820i −0.439941 0.254000i
$$745$$ 10.3923i 0.380745i
$$746$$ −16.0000 −0.585802
$$747$$ −9.00000 + 5.19615i −0.329293 + 0.190117i
$$748$$ 0 0
$$749$$ −9.00000 25.9808i −0.328853 0.949316i
$$750$$ −10.5000 + 18.1865i −0.383406 + 0.664078i
$$751$$ 4.00000 0.145962 0.0729810 0.997333i $$-0.476749\pi$$
0.0729810 + 0.997333i $$0.476749\pi$$
$$752$$ 12.1244i 0.442130i
$$753$$ 18.0000 + 10.3923i 0.655956 + 0.378717i
$$754$$ 24.0000 + 6.92820i 0.874028 + 0.252310i
$$755$$ 33.0000 1.20099
$$756$$ 4.50000 + 12.9904i 0.163663 + 0.472456i
$$757$$ 38.0000 1.38113 0.690567 0.723269i $$-0.257361\pi$$
0.690567 + 0.723269i $$0.257361\pi$$
$$758$$ 17.3205i 0.629109i
$$759$$ 0 0
$$760$$ 3.46410i 0.125656i
$$761$$ 38.1051i 1.38131i 0.723185 + 0.690655i $$0.242678\pi$$
−0.723185 + 0.690655i $$0.757322\pi$$
$$762$$ −3.00000 1.73205i −0.108679 0.0627456i
$$763$$ 4.50000 + 12.9904i 0.162911 + 0.470283i
$$764$$ 20.7846i 0.751961i
$$765$$ 13.5000 7.79423i 0.488094 0.281801i
$$766$$ 5.19615i 0.187745i
$$767$$ −36.0000 10.3923i −1.29988 0.375244i
$$768$$ −1.50000 0.866025i −0.0541266 0.0312500i
$$769$$ 4.00000 0.144244 0.0721218 0.997396i $$-0.477023\pi$$
0.0721218 + 0.997396i $$0.477023\pi$$
$$770$$ 0 0
$$771$$ 31.5000 + 18.1865i 1.13444 + 0.654972i
$$772$$ 17.3205i 0.623379i
$$773$$ 15.5885i 0.560678i 0.959901 + 0.280339i $$0.0904469\pi$$
−0.959901 + 0.280339i $$0.909553\pi$$
$$774$$ 16.5000 + 28.5788i 0.593080 + 1.02725i
$$775$$ −16.0000 −0.574737
$$776$$ −8.00000 −0.287183
$$777$$ −1.50000 + 7.79423i −0.0538122 + 0.279616i
$$778$$ 10.3923i 0.372582i
$$779$$ 0 0
$$780$$ −7.50000 7.79423i −0.268543 0.279078i
$$781$$ 0 0
$$782$$ 10.3923i 0.371628i
$$783$$ −36.0000 −1.28654
$$784$$ 5.50000 4.33013i 0.196429 0.154647i