# Properties

 Label 507.2.j.a.361.1 Level $507$ Weight $2$ Character 507.361 Analytic conductor $4.048$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$507 = 3 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 507.j (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.04841538248$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 39) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 361.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 507.361 Dual form 507.2.j.a.316.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.50000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.50000 - 0.866025i) q^{6} +(-3.00000 - 1.73205i) q^{7} -1.73205i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(-1.50000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.50000 - 0.866025i) q^{6} +(-3.00000 - 1.73205i) q^{7} -1.73205i q^{8} +(-0.500000 + 0.866025i) q^{9} +(3.00000 - 1.73205i) q^{11} +1.00000 q^{12} +6.00000 q^{14} +(2.50000 + 4.33013i) q^{16} +(3.00000 - 5.19615i) q^{17} -1.73205i q^{18} +(3.00000 + 1.73205i) q^{19} -3.46410i q^{21} +(-3.00000 + 5.19615i) q^{22} +(1.50000 - 0.866025i) q^{24} +5.00000 q^{25} -1.00000 q^{27} +(-3.00000 + 1.73205i) q^{28} +(-3.00000 - 5.19615i) q^{29} +3.46410i q^{31} +(-4.50000 - 2.59808i) q^{32} +(3.00000 + 1.73205i) q^{33} +10.3923i q^{34} +(0.500000 + 0.866025i) q^{36} +(-6.00000 + 3.46410i) q^{37} -6.00000 q^{38} +(6.00000 - 3.46410i) q^{41} +(3.00000 + 5.19615i) q^{42} +(2.00000 - 3.46410i) q^{43} -3.46410i q^{44} -3.46410i q^{47} +(-2.50000 + 4.33013i) q^{48} +(2.50000 + 4.33013i) q^{49} +(-7.50000 + 4.33013i) q^{50} +6.00000 q^{51} +6.00000 q^{53} +(1.50000 - 0.866025i) q^{54} +(-3.00000 + 5.19615i) q^{56} +3.46410i q^{57} +(9.00000 + 5.19615i) q^{58} +(9.00000 + 5.19615i) q^{59} +(1.00000 - 1.73205i) q^{61} +(-3.00000 - 5.19615i) q^{62} +(3.00000 - 1.73205i) q^{63} -1.00000 q^{64} -6.00000 q^{66} +(9.00000 - 5.19615i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(3.00000 + 1.73205i) q^{71} +(1.50000 + 0.866025i) q^{72} +(6.00000 - 10.3923i) q^{74} +(2.50000 + 4.33013i) q^{75} +(3.00000 - 1.73205i) q^{76} -12.0000 q^{77} -8.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-6.00000 + 10.3923i) q^{82} +3.46410i q^{83} +(-3.00000 - 1.73205i) q^{84} +6.92820i q^{86} +(3.00000 - 5.19615i) q^{87} +(-3.00000 - 5.19615i) q^{88} +(6.00000 - 3.46410i) q^{89} +(-3.00000 + 1.73205i) q^{93} +(3.00000 + 5.19615i) q^{94} -5.19615i q^{96} +(-12.0000 - 6.92820i) q^{97} +(-7.50000 - 4.33013i) q^{98} +3.46410i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 3 q^{2} + q^{3} + q^{4} - 3 q^{6} - 6 q^{7} - q^{9}+O(q^{10})$$ 2 * q - 3 * q^2 + q^3 + q^4 - 3 * q^6 - 6 * q^7 - q^9 $$2 q - 3 q^{2} + q^{3} + q^{4} - 3 q^{6} - 6 q^{7} - q^{9} + 6 q^{11} + 2 q^{12} + 12 q^{14} + 5 q^{16} + 6 q^{17} + 6 q^{19} - 6 q^{22} + 3 q^{24} + 10 q^{25} - 2 q^{27} - 6 q^{28} - 6 q^{29} - 9 q^{32} + 6 q^{33} + q^{36} - 12 q^{37} - 12 q^{38} + 12 q^{41} + 6 q^{42} + 4 q^{43} - 5 q^{48} + 5 q^{49} - 15 q^{50} + 12 q^{51} + 12 q^{53} + 3 q^{54} - 6 q^{56} + 18 q^{58} + 18 q^{59} + 2 q^{61} - 6 q^{62} + 6 q^{63} - 2 q^{64} - 12 q^{66} + 18 q^{67} - 6 q^{68} + 6 q^{71} + 3 q^{72} + 12 q^{74} + 5 q^{75} + 6 q^{76} - 24 q^{77} - 16 q^{79} - q^{81} - 12 q^{82} - 6 q^{84} + 6 q^{87} - 6 q^{88} + 12 q^{89} - 6 q^{93} + 6 q^{94} - 24 q^{97} - 15 q^{98}+O(q^{100})$$ 2 * q - 3 * q^2 + q^3 + q^4 - 3 * q^6 - 6 * q^7 - q^9 + 6 * q^11 + 2 * q^12 + 12 * q^14 + 5 * q^16 + 6 * q^17 + 6 * q^19 - 6 * q^22 + 3 * q^24 + 10 * q^25 - 2 * q^27 - 6 * q^28 - 6 * q^29 - 9 * q^32 + 6 * q^33 + q^36 - 12 * q^37 - 12 * q^38 + 12 * q^41 + 6 * q^42 + 4 * q^43 - 5 * q^48 + 5 * q^49 - 15 * q^50 + 12 * q^51 + 12 * q^53 + 3 * q^54 - 6 * q^56 + 18 * q^58 + 18 * q^59 + 2 * q^61 - 6 * q^62 + 6 * q^63 - 2 * q^64 - 12 * q^66 + 18 * q^67 - 6 * q^68 + 6 * q^71 + 3 * q^72 + 12 * q^74 + 5 * q^75 + 6 * q^76 - 24 * q^77 - 16 * q^79 - q^81 - 12 * q^82 - 6 * q^84 + 6 * q^87 - 6 * q^88 + 12 * q^89 - 6 * q^93 + 6 * q^94 - 24 * q^97 - 15 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$$.

 $$n$$ $$170$$ $$340$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.50000 + 0.866025i −1.06066 + 0.612372i −0.925615 0.378467i $$-0.876451\pi$$
−0.135045 + 0.990839i $$0.543118\pi$$
$$3$$ 0.500000 + 0.866025i 0.288675 + 0.500000i
$$4$$ 0.500000 0.866025i 0.250000 0.433013i
$$5$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$6$$ −1.50000 0.866025i −0.612372 0.353553i
$$7$$ −3.00000 1.73205i −1.13389 0.654654i −0.188982 0.981981i $$-0.560519\pi$$
−0.944911 + 0.327327i $$0.893852\pi$$
$$8$$ 1.73205i 0.612372i
$$9$$ −0.500000 + 0.866025i −0.166667 + 0.288675i
$$10$$ 0 0
$$11$$ 3.00000 1.73205i 0.904534 0.522233i 0.0258656 0.999665i $$-0.491766\pi$$
0.878668 + 0.477432i $$0.158432\pi$$
$$12$$ 1.00000 0.288675
$$13$$ 0 0
$$14$$ 6.00000 1.60357
$$15$$ 0 0
$$16$$ 2.50000 + 4.33013i 0.625000 + 1.08253i
$$17$$ 3.00000 5.19615i 0.727607 1.26025i −0.230285 0.973123i $$-0.573966\pi$$
0.957892 0.287129i $$-0.0927008\pi$$
$$18$$ 1.73205i 0.408248i
$$19$$ 3.00000 + 1.73205i 0.688247 + 0.397360i 0.802955 0.596040i $$-0.203260\pi$$
−0.114708 + 0.993399i $$0.536593\pi$$
$$20$$ 0 0
$$21$$ 3.46410i 0.755929i
$$22$$ −3.00000 + 5.19615i −0.639602 + 1.10782i
$$23$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$24$$ 1.50000 0.866025i 0.306186 0.176777i
$$25$$ 5.00000 1.00000
$$26$$ 0 0
$$27$$ −1.00000 −0.192450
$$28$$ −3.00000 + 1.73205i −0.566947 + 0.327327i
$$29$$ −3.00000 5.19615i −0.557086 0.964901i −0.997738 0.0672232i $$-0.978586\pi$$
0.440652 0.897678i $$-0.354747\pi$$
$$30$$ 0 0
$$31$$ 3.46410i 0.622171i 0.950382 + 0.311086i $$0.100693\pi$$
−0.950382 + 0.311086i $$0.899307\pi$$
$$32$$ −4.50000 2.59808i −0.795495 0.459279i
$$33$$ 3.00000 + 1.73205i 0.522233 + 0.301511i
$$34$$ 10.3923i 1.78227i
$$35$$ 0 0
$$36$$ 0.500000 + 0.866025i 0.0833333 + 0.144338i
$$37$$ −6.00000 + 3.46410i −0.986394 + 0.569495i −0.904194 0.427121i $$-0.859528\pi$$
−0.0821995 + 0.996616i $$0.526194\pi$$
$$38$$ −6.00000 −0.973329
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 6.00000 3.46410i 0.937043 0.541002i 0.0480106 0.998847i $$-0.484712\pi$$
0.889032 + 0.457845i $$0.151379\pi$$
$$42$$ 3.00000 + 5.19615i 0.462910 + 0.801784i
$$43$$ 2.00000 3.46410i 0.304997 0.528271i −0.672264 0.740312i $$-0.734678\pi$$
0.977261 + 0.212041i $$0.0680112\pi$$
$$44$$ 3.46410i 0.522233i
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 3.46410i 0.505291i −0.967559 0.252646i $$-0.918699\pi$$
0.967559 0.252646i $$-0.0813007\pi$$
$$48$$ −2.50000 + 4.33013i −0.360844 + 0.625000i
$$49$$ 2.50000 + 4.33013i 0.357143 + 0.618590i
$$50$$ −7.50000 + 4.33013i −1.06066 + 0.612372i
$$51$$ 6.00000 0.840168
$$52$$ 0 0
$$53$$ 6.00000 0.824163 0.412082 0.911147i $$-0.364802\pi$$
0.412082 + 0.911147i $$0.364802\pi$$
$$54$$ 1.50000 0.866025i 0.204124 0.117851i
$$55$$ 0 0
$$56$$ −3.00000 + 5.19615i −0.400892 + 0.694365i
$$57$$ 3.46410i 0.458831i
$$58$$ 9.00000 + 5.19615i 1.18176 + 0.682288i
$$59$$ 9.00000 + 5.19615i 1.17170 + 0.676481i 0.954080 0.299552i $$-0.0968372\pi$$
0.217620 + 0.976034i $$0.430171\pi$$
$$60$$ 0 0
$$61$$ 1.00000 1.73205i 0.128037 0.221766i −0.794879 0.606768i $$-0.792466\pi$$
0.922916 + 0.385002i $$0.125799\pi$$
$$62$$ −3.00000 5.19615i −0.381000 0.659912i
$$63$$ 3.00000 1.73205i 0.377964 0.218218i
$$64$$ −1.00000 −0.125000
$$65$$ 0 0
$$66$$ −6.00000 −0.738549
$$67$$ 9.00000 5.19615i 1.09952 0.634811i 0.163429 0.986555i $$-0.447745\pi$$
0.936096 + 0.351744i $$0.114411\pi$$
$$68$$ −3.00000 5.19615i −0.363803 0.630126i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 3.00000 + 1.73205i 0.356034 + 0.205557i 0.667340 0.744753i $$-0.267433\pi$$
−0.311305 + 0.950310i $$0.600766\pi$$
$$72$$ 1.50000 + 0.866025i 0.176777 + 0.102062i
$$73$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$74$$ 6.00000 10.3923i 0.697486 1.20808i
$$75$$ 2.50000 + 4.33013i 0.288675 + 0.500000i
$$76$$ 3.00000 1.73205i 0.344124 0.198680i
$$77$$ −12.0000 −1.36753
$$78$$ 0 0
$$79$$ −8.00000 −0.900070 −0.450035 0.893011i $$-0.648589\pi$$
−0.450035 + 0.893011i $$0.648589\pi$$
$$80$$ 0 0
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ −6.00000 + 10.3923i −0.662589 + 1.14764i
$$83$$ 3.46410i 0.380235i 0.981761 + 0.190117i $$0.0608868\pi$$
−0.981761 + 0.190117i $$0.939113\pi$$
$$84$$ −3.00000 1.73205i −0.327327 0.188982i
$$85$$ 0 0
$$86$$ 6.92820i 0.747087i
$$87$$ 3.00000 5.19615i 0.321634 0.557086i
$$88$$ −3.00000 5.19615i −0.319801 0.553912i
$$89$$ 6.00000 3.46410i 0.635999 0.367194i −0.147073 0.989126i $$-0.546985\pi$$
0.783072 + 0.621932i $$0.213652\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ −3.00000 + 1.73205i −0.311086 + 0.179605i
$$94$$ 3.00000 + 5.19615i 0.309426 + 0.535942i
$$95$$ 0 0
$$96$$ 5.19615i 0.530330i
$$97$$ −12.0000 6.92820i −1.21842 0.703452i −0.253837 0.967247i $$-0.581693\pi$$
−0.964579 + 0.263795i $$0.915026\pi$$
$$98$$ −7.50000 4.33013i −0.757614 0.437409i
$$99$$ 3.46410i 0.348155i
$$100$$ 2.50000 4.33013i 0.250000 0.433013i
$$101$$ −3.00000 5.19615i −0.298511 0.517036i 0.677284 0.735721i $$-0.263157\pi$$
−0.975796 + 0.218685i $$0.929823\pi$$
$$102$$ −9.00000 + 5.19615i −0.891133 + 0.514496i
$$103$$ 8.00000 0.788263 0.394132 0.919054i $$-0.371045\pi$$
0.394132 + 0.919054i $$0.371045\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ −9.00000 + 5.19615i −0.874157 + 0.504695i
$$107$$ −6.00000 10.3923i −0.580042 1.00466i −0.995474 0.0950377i $$-0.969703\pi$$
0.415432 0.909624i $$-0.363630\pi$$
$$108$$ −0.500000 + 0.866025i −0.0481125 + 0.0833333i
$$109$$ 6.92820i 0.663602i −0.943349 0.331801i $$-0.892344\pi$$
0.943349 0.331801i $$-0.107656\pi$$
$$110$$ 0 0
$$111$$ −6.00000 3.46410i −0.569495 0.328798i
$$112$$ 17.3205i 1.63663i
$$113$$ 3.00000 5.19615i 0.282216 0.488813i −0.689714 0.724082i $$-0.742264\pi$$
0.971930 + 0.235269i $$0.0755971\pi$$
$$114$$ −3.00000 5.19615i −0.280976 0.486664i
$$115$$ 0 0
$$116$$ −6.00000 −0.557086
$$117$$ 0 0
$$118$$ −18.0000 −1.65703
$$119$$ −18.0000 + 10.3923i −1.65006 + 0.952661i
$$120$$ 0 0
$$121$$ 0.500000 0.866025i 0.0454545 0.0787296i
$$122$$ 3.46410i 0.313625i
$$123$$ 6.00000 + 3.46410i 0.541002 + 0.312348i
$$124$$ 3.00000 + 1.73205i 0.269408 + 0.155543i
$$125$$ 0 0
$$126$$ −3.00000 + 5.19615i −0.267261 + 0.462910i
$$127$$ 4.00000 + 6.92820i 0.354943 + 0.614779i 0.987108 0.160055i $$-0.0511671\pi$$
−0.632166 + 0.774833i $$0.717834\pi$$
$$128$$ 10.5000 6.06218i 0.928078 0.535826i
$$129$$ 4.00000 0.352180
$$130$$ 0 0
$$131$$ −12.0000 −1.04844 −0.524222 0.851581i $$-0.675644\pi$$
−0.524222 + 0.851581i $$0.675644\pi$$
$$132$$ 3.00000 1.73205i 0.261116 0.150756i
$$133$$ −6.00000 10.3923i −0.520266 0.901127i
$$134$$ −9.00000 + 15.5885i −0.777482 + 1.34664i
$$135$$ 0 0
$$136$$ −9.00000 5.19615i −0.771744 0.445566i
$$137$$ −18.0000 10.3923i −1.53784 0.887875i −0.998965 0.0454914i $$-0.985515\pi$$
−0.538879 0.842383i $$-0.681152\pi$$
$$138$$ 0 0
$$139$$ 2.00000 3.46410i 0.169638 0.293821i −0.768655 0.639664i $$-0.779074\pi$$
0.938293 + 0.345843i $$0.112407\pi$$
$$140$$ 0 0
$$141$$ 3.00000 1.73205i 0.252646 0.145865i
$$142$$ −6.00000 −0.503509
$$143$$ 0 0
$$144$$ −5.00000 −0.416667
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −2.50000 + 4.33013i −0.206197 + 0.357143i
$$148$$ 6.92820i 0.569495i
$$149$$ 12.0000 + 6.92820i 0.983078 + 0.567581i 0.903198 0.429224i $$-0.141213\pi$$
0.0798802 + 0.996804i $$0.474546\pi$$
$$150$$ −7.50000 4.33013i −0.612372 0.353553i
$$151$$ 10.3923i 0.845714i −0.906196 0.422857i $$-0.861027\pi$$
0.906196 0.422857i $$-0.138973\pi$$
$$152$$ 3.00000 5.19615i 0.243332 0.421464i
$$153$$ 3.00000 + 5.19615i 0.242536 + 0.420084i
$$154$$ 18.0000 10.3923i 1.45048 0.837436i
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 14.0000 1.11732 0.558661 0.829396i $$-0.311315\pi$$
0.558661 + 0.829396i $$0.311315\pi$$
$$158$$ 12.0000 6.92820i 0.954669 0.551178i
$$159$$ 3.00000 + 5.19615i 0.237915 + 0.412082i
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 1.50000 + 0.866025i 0.117851 + 0.0680414i
$$163$$ 3.00000 + 1.73205i 0.234978 + 0.135665i 0.612866 0.790186i $$-0.290016\pi$$
−0.377888 + 0.925851i $$0.623350\pi$$
$$164$$ 6.92820i 0.541002i
$$165$$ 0 0
$$166$$ −3.00000 5.19615i −0.232845 0.403300i
$$167$$ −15.0000 + 8.66025i −1.16073 + 0.670151i −0.951480 0.307711i $$-0.900437\pi$$
−0.209255 + 0.977861i $$0.567104\pi$$
$$168$$ −6.00000 −0.462910
$$169$$ 0 0
$$170$$ 0 0
$$171$$ −3.00000 + 1.73205i −0.229416 + 0.132453i
$$172$$ −2.00000 3.46410i −0.152499 0.264135i
$$173$$ 9.00000 15.5885i 0.684257 1.18517i −0.289412 0.957205i $$-0.593460\pi$$
0.973670 0.227964i $$-0.0732068\pi$$
$$174$$ 10.3923i 0.787839i
$$175$$ −15.0000 8.66025i −1.13389 0.654654i
$$176$$ 15.0000 + 8.66025i 1.13067 + 0.652791i
$$177$$ 10.3923i 0.781133i
$$178$$ −6.00000 + 10.3923i −0.449719 + 0.778936i
$$179$$ 6.00000 + 10.3923i 0.448461 + 0.776757i 0.998286 0.0585225i $$-0.0186389\pi$$
−0.549825 + 0.835280i $$0.685306\pi$$
$$180$$ 0 0
$$181$$ −10.0000 −0.743294 −0.371647 0.928374i $$-0.621207\pi$$
−0.371647 + 0.928374i $$0.621207\pi$$
$$182$$ 0 0
$$183$$ 2.00000 0.147844
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 3.00000 5.19615i 0.219971 0.381000i
$$187$$ 20.7846i 1.51992i
$$188$$ −3.00000 1.73205i −0.218797 0.126323i
$$189$$ 3.00000 + 1.73205i 0.218218 + 0.125988i
$$190$$ 0 0
$$191$$ −12.0000 + 20.7846i −0.868290 + 1.50392i −0.00454614 + 0.999990i $$0.501447\pi$$
−0.863743 + 0.503932i $$0.831886\pi$$
$$192$$ −0.500000 0.866025i −0.0360844 0.0625000i
$$193$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$194$$ 24.0000 1.72310
$$195$$ 0 0
$$196$$ 5.00000 0.357143
$$197$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$198$$ −3.00000 5.19615i −0.213201 0.369274i
$$199$$ −8.00000 + 13.8564i −0.567105 + 0.982255i 0.429745 + 0.902950i $$0.358603\pi$$
−0.996850 + 0.0793045i $$0.974730\pi$$
$$200$$ 8.66025i 0.612372i
$$201$$ 9.00000 + 5.19615i 0.634811 + 0.366508i
$$202$$ 9.00000 + 5.19615i 0.633238 + 0.365600i
$$203$$ 20.7846i 1.45879i
$$204$$ 3.00000 5.19615i 0.210042 0.363803i
$$205$$ 0 0
$$206$$ −12.0000 + 6.92820i −0.836080 + 0.482711i
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 12.0000 0.830057
$$210$$ 0 0
$$211$$ 10.0000 + 17.3205i 0.688428 + 1.19239i 0.972346 + 0.233544i $$0.0750324\pi$$
−0.283918 + 0.958849i $$0.591634\pi$$
$$212$$ 3.00000 5.19615i 0.206041 0.356873i
$$213$$ 3.46410i 0.237356i
$$214$$ 18.0000 + 10.3923i 1.23045 + 0.710403i
$$215$$ 0 0
$$216$$ 1.73205i 0.117851i
$$217$$ 6.00000 10.3923i 0.407307 0.705476i
$$218$$ 6.00000 + 10.3923i 0.406371 + 0.703856i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 12.0000 0.805387
$$223$$ 3.00000 1.73205i 0.200895 0.115987i −0.396178 0.918174i $$-0.629664\pi$$
0.597073 + 0.802187i $$0.296330\pi$$
$$224$$ 9.00000 + 15.5885i 0.601338 + 1.04155i
$$225$$ −2.50000 + 4.33013i −0.166667 + 0.288675i
$$226$$ 10.3923i 0.691286i
$$227$$ −15.0000 8.66025i −0.995585 0.574801i −0.0886460 0.996063i $$-0.528254\pi$$
−0.906939 + 0.421262i $$0.861587\pi$$
$$228$$ 3.00000 + 1.73205i 0.198680 + 0.114708i
$$229$$ 6.92820i 0.457829i 0.973447 + 0.228914i $$0.0735176\pi$$
−0.973447 + 0.228914i $$0.926482\pi$$
$$230$$ 0 0
$$231$$ −6.00000 10.3923i −0.394771 0.683763i
$$232$$ −9.00000 + 5.19615i −0.590879 + 0.341144i
$$233$$ −6.00000 −0.393073 −0.196537 0.980497i $$-0.562969\pi$$
−0.196537 + 0.980497i $$0.562969\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 9.00000 5.19615i 0.585850 0.338241i
$$237$$ −4.00000 6.92820i −0.259828 0.450035i
$$238$$ 18.0000 31.1769i 1.16677 2.02090i
$$239$$ 10.3923i 0.672222i 0.941822 + 0.336111i $$0.109112\pi$$
−0.941822 + 0.336111i $$0.890888\pi$$
$$240$$ 0 0
$$241$$ 12.0000 + 6.92820i 0.772988 + 0.446285i 0.833939 0.551856i $$-0.186080\pi$$
−0.0609515 + 0.998141i $$0.519414\pi$$
$$242$$ 1.73205i 0.111340i
$$243$$ 0.500000 0.866025i 0.0320750 0.0555556i
$$244$$ −1.00000 1.73205i −0.0640184 0.110883i
$$245$$ 0 0
$$246$$ −12.0000 −0.765092
$$247$$ 0 0
$$248$$ 6.00000 0.381000
$$249$$ −3.00000 + 1.73205i −0.190117 + 0.109764i
$$250$$ 0 0
$$251$$ 6.00000 10.3923i 0.378717 0.655956i −0.612159 0.790735i $$-0.709699\pi$$
0.990876 + 0.134778i $$0.0430322\pi$$
$$252$$ 3.46410i 0.218218i
$$253$$ 0 0
$$254$$ −12.0000 6.92820i −0.752947 0.434714i
$$255$$ 0 0
$$256$$ −9.50000 + 16.4545i −0.593750 + 1.02841i
$$257$$ −9.00000 15.5885i −0.561405 0.972381i −0.997374 0.0724199i $$-0.976928\pi$$
0.435970 0.899961i $$-0.356405\pi$$
$$258$$ −6.00000 + 3.46410i −0.373544 + 0.215666i
$$259$$ 24.0000 1.49129
$$260$$ 0 0
$$261$$ 6.00000 0.371391
$$262$$ 18.0000 10.3923i 1.11204 0.642039i
$$263$$ 12.0000 + 20.7846i 0.739952 + 1.28163i 0.952517 + 0.304487i $$0.0984850\pi$$
−0.212565 + 0.977147i $$0.568182\pi$$
$$264$$ 3.00000 5.19615i 0.184637 0.319801i
$$265$$ 0 0
$$266$$ 18.0000 + 10.3923i 1.10365 + 0.637193i
$$267$$ 6.00000 + 3.46410i 0.367194 + 0.212000i
$$268$$ 10.3923i 0.634811i
$$269$$ −3.00000 + 5.19615i −0.182913 + 0.316815i −0.942871 0.333157i $$-0.891886\pi$$
0.759958 + 0.649972i $$0.225219\pi$$
$$270$$ 0 0
$$271$$ −9.00000 + 5.19615i −0.546711 + 0.315644i −0.747794 0.663930i $$-0.768887\pi$$
0.201083 + 0.979574i $$0.435554\pi$$
$$272$$ 30.0000 1.81902
$$273$$ 0 0
$$274$$ 36.0000 2.17484
$$275$$ 15.0000 8.66025i 0.904534 0.522233i
$$276$$ 0 0
$$277$$ 5.00000 8.66025i 0.300421 0.520344i −0.675810 0.737075i $$-0.736206\pi$$
0.976231 + 0.216731i $$0.0695395\pi$$
$$278$$ 6.92820i 0.415526i
$$279$$ −3.00000 1.73205i −0.179605 0.103695i
$$280$$ 0 0
$$281$$ 6.92820i 0.413302i −0.978415 0.206651i $$-0.933744\pi$$
0.978415 0.206651i $$-0.0662565\pi$$
$$282$$ −3.00000 + 5.19615i −0.178647 + 0.309426i
$$283$$ −2.00000 3.46410i −0.118888 0.205919i 0.800439 0.599414i $$-0.204600\pi$$
−0.919327 + 0.393494i $$0.871266\pi$$
$$284$$ 3.00000 1.73205i 0.178017 0.102778i
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −24.0000 −1.41668
$$288$$ 4.50000 2.59808i 0.265165 0.153093i
$$289$$ −9.50000 16.4545i −0.558824 0.967911i
$$290$$ 0 0
$$291$$ 13.8564i 0.812277i
$$292$$ 0 0
$$293$$ 24.0000 + 13.8564i 1.40209 + 0.809500i 0.994607 0.103711i $$-0.0330717\pi$$
0.407487 + 0.913211i $$0.366405\pi$$
$$294$$ 8.66025i 0.505076i
$$295$$ 0 0
$$296$$ 6.00000 + 10.3923i 0.348743 + 0.604040i
$$297$$ −3.00000 + 1.73205i −0.174078 + 0.100504i
$$298$$ −24.0000 −1.39028
$$299$$ 0 0
$$300$$ 5.00000 0.288675
$$301$$ −12.0000 + 6.92820i −0.691669 + 0.399335i
$$302$$ 9.00000 + 15.5885i 0.517892 + 0.897015i
$$303$$ 3.00000 5.19615i 0.172345 0.298511i
$$304$$ 17.3205i 0.993399i
$$305$$ 0 0
$$306$$ −9.00000 5.19615i −0.514496 0.297044i
$$307$$ 10.3923i 0.593120i 0.955014 + 0.296560i $$0.0958395\pi$$
−0.955014 + 0.296560i $$0.904160\pi$$
$$308$$ −6.00000 + 10.3923i −0.341882 + 0.592157i
$$309$$ 4.00000 + 6.92820i 0.227552 + 0.394132i
$$310$$ 0 0
$$311$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$312$$ 0 0
$$313$$ 10.0000 0.565233 0.282617 0.959233i $$-0.408798\pi$$
0.282617 + 0.959233i $$0.408798\pi$$
$$314$$ −21.0000 + 12.1244i −1.18510 + 0.684217i
$$315$$ 0 0
$$316$$ −4.00000 + 6.92820i −0.225018 + 0.389742i
$$317$$ 13.8564i 0.778253i −0.921184 0.389127i $$-0.872777\pi$$
0.921184 0.389127i $$-0.127223\pi$$
$$318$$ −9.00000 5.19615i −0.504695 0.291386i
$$319$$ −18.0000 10.3923i −1.00781 0.581857i
$$320$$ 0 0
$$321$$ 6.00000 10.3923i 0.334887 0.580042i
$$322$$ 0 0
$$323$$ 18.0000 10.3923i 1.00155 0.578243i
$$324$$ −1.00000 −0.0555556
$$325$$ 0 0
$$326$$ −6.00000 −0.332309
$$327$$ 6.00000 3.46410i 0.331801 0.191565i
$$328$$ −6.00000 10.3923i −0.331295 0.573819i
$$329$$ −6.00000 + 10.3923i −0.330791 + 0.572946i
$$330$$ 0 0
$$331$$ 3.00000 + 1.73205i 0.164895 + 0.0952021i 0.580176 0.814491i $$-0.302984\pi$$
−0.415282 + 0.909693i $$0.636317\pi$$
$$332$$ 3.00000 + 1.73205i 0.164646 + 0.0950586i
$$333$$ 6.92820i 0.379663i
$$334$$ 15.0000 25.9808i 0.820763 1.42160i
$$335$$ 0 0
$$336$$ 15.0000 8.66025i 0.818317 0.472456i
$$337$$ −14.0000 −0.762629 −0.381314 0.924445i $$-0.624528\pi$$
−0.381314 + 0.924445i $$0.624528\pi$$
$$338$$ 0 0
$$339$$ 6.00000 0.325875
$$340$$ 0 0
$$341$$ 6.00000 + 10.3923i 0.324918 + 0.562775i
$$342$$ 3.00000 5.19615i 0.162221 0.280976i
$$343$$ 6.92820i 0.374088i
$$344$$ −6.00000 3.46410i −0.323498 0.186772i
$$345$$ 0 0
$$346$$ 31.1769i 1.67608i
$$347$$ −18.0000 + 31.1769i −0.966291 + 1.67366i −0.260184 + 0.965559i $$0.583783\pi$$
−0.706107 + 0.708105i $$0.749550\pi$$
$$348$$ −3.00000 5.19615i −0.160817 0.278543i
$$349$$ 6.00000 3.46410i 0.321173 0.185429i −0.330743 0.943721i $$-0.607299\pi$$
0.651915 + 0.758292i $$0.273966\pi$$
$$350$$ 30.0000 1.60357
$$351$$ 0 0
$$352$$ −18.0000 −0.959403
$$353$$ −30.0000 + 17.3205i −1.59674 + 0.921878i −0.604629 + 0.796507i $$0.706679\pi$$
−0.992110 + 0.125370i $$0.959988\pi$$
$$354$$ −9.00000 15.5885i −0.478345 0.828517i
$$355$$ 0 0
$$356$$ 6.92820i 0.367194i
$$357$$ −18.0000 10.3923i −0.952661 0.550019i
$$358$$ −18.0000 10.3923i −0.951330 0.549250i
$$359$$ 17.3205i 0.914141i −0.889430 0.457071i $$-0.848899\pi$$
0.889430 0.457071i $$-0.151101\pi$$
$$360$$ 0 0
$$361$$ −3.50000 6.06218i −0.184211 0.319062i
$$362$$ 15.0000 8.66025i 0.788382 0.455173i
$$363$$ 1.00000 0.0524864
$$364$$ 0 0
$$365$$ 0 0
$$366$$ −3.00000 + 1.73205i −0.156813 + 0.0905357i
$$367$$ 8.00000 + 13.8564i 0.417597 + 0.723299i 0.995697 0.0926670i $$-0.0295392\pi$$
−0.578101 + 0.815966i $$0.696206\pi$$
$$368$$ 0 0
$$369$$ 6.92820i 0.360668i
$$370$$ 0 0
$$371$$ −18.0000 10.3923i −0.934513 0.539542i
$$372$$ 3.46410i 0.179605i
$$373$$ −11.0000 + 19.0526i −0.569558 + 0.986504i 0.427051 + 0.904227i $$0.359552\pi$$
−0.996610 + 0.0822766i $$0.973781\pi$$
$$374$$ 18.0000 + 31.1769i 0.930758 + 1.61212i
$$375$$ 0 0
$$376$$ −6.00000 −0.309426
$$377$$ 0 0
$$378$$ −6.00000 −0.308607
$$379$$ −15.0000 + 8.66025i −0.770498 + 0.444847i −0.833052 0.553194i $$-0.813409\pi$$
0.0625541 + 0.998042i $$0.480075\pi$$
$$380$$ 0 0
$$381$$ −4.00000 + 6.92820i −0.204926 + 0.354943i
$$382$$ 41.5692i 2.12687i
$$383$$ 3.00000 + 1.73205i 0.153293 + 0.0885037i 0.574684 0.818375i $$-0.305125\pi$$
−0.421392 + 0.906879i $$0.638458\pi$$
$$384$$ 10.5000 + 6.06218i 0.535826 + 0.309359i
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 2.00000 + 3.46410i 0.101666 + 0.176090i
$$388$$ −12.0000 + 6.92820i −0.609208 + 0.351726i
$$389$$ −18.0000 −0.912636 −0.456318 0.889817i $$-0.650832\pi$$
−0.456318 + 0.889817i $$0.650832\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 7.50000 4.33013i 0.378807 0.218704i
$$393$$ −6.00000 10.3923i −0.302660 0.524222i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 3.00000 + 1.73205i 0.150756 + 0.0870388i
$$397$$ −30.0000 17.3205i −1.50566 0.869291i −0.999978 0.00656933i $$-0.997909\pi$$
−0.505678 0.862722i $$-0.668758\pi$$
$$398$$ 27.7128i 1.38912i
$$399$$ 6.00000 10.3923i 0.300376 0.520266i
$$400$$ 12.5000 + 21.6506i 0.625000 + 1.08253i
$$401$$ −6.00000 + 3.46410i −0.299626 + 0.172989i −0.642275 0.766475i $$-0.722009\pi$$
0.342649 + 0.939463i $$0.388676\pi$$
$$402$$ −18.0000 −0.897758
$$403$$ 0 0
$$404$$ −6.00000 −0.298511
$$405$$ 0 0
$$406$$ −18.0000 31.1769i −0.893325 1.54728i
$$407$$ −12.0000 + 20.7846i −0.594818 + 1.03025i
$$408$$ 10.3923i 0.514496i
$$409$$ 24.0000 + 13.8564i 1.18672 + 0.685155i 0.957560 0.288233i $$-0.0930677\pi$$
0.229163 + 0.973388i $$0.426401\pi$$
$$410$$ 0 0
$$411$$ 20.7846i 1.02523i
$$412$$ 4.00000 6.92820i 0.197066 0.341328i
$$413$$ −18.0000 31.1769i −0.885722 1.53412i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 4.00000 0.195881
$$418$$ −18.0000 + 10.3923i −0.880409 + 0.508304i
$$419$$ 6.00000 + 10.3923i 0.293119 + 0.507697i 0.974546 0.224189i $$-0.0719734\pi$$
−0.681426 + 0.731887i $$0.738640\pi$$
$$420$$ 0 0
$$421$$ 34.6410i 1.68830i 0.536107 + 0.844150i $$0.319894\pi$$
−0.536107 + 0.844150i $$0.680106\pi$$
$$422$$ −30.0000 17.3205i −1.46038 0.843149i
$$423$$ 3.00000 + 1.73205i 0.145865 + 0.0842152i
$$424$$ 10.3923i 0.504695i
$$425$$ 15.0000 25.9808i 0.727607 1.26025i
$$426$$ −3.00000 5.19615i −0.145350 0.251754i
$$427$$ −6.00000 + 3.46410i −0.290360 + 0.167640i
$$428$$ −12.0000 −0.580042
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 21.0000 12.1244i 1.01153 0.584010i 0.0998939 0.994998i $$-0.468150\pi$$
0.911641 + 0.410988i $$0.134816\pi$$
$$432$$ −2.50000 4.33013i −0.120281 0.208333i
$$433$$ −17.0000 + 29.4449i −0.816968 + 1.41503i 0.0909384 + 0.995857i $$0.471013\pi$$
−0.907906 + 0.419173i $$0.862320\pi$$
$$434$$ 20.7846i 0.997693i
$$435$$ 0 0
$$436$$ −6.00000 3.46410i −0.287348 0.165900i
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −4.00000 6.92820i −0.190910 0.330665i 0.754642 0.656136i $$-0.227810\pi$$
−0.945552 + 0.325471i $$0.894477\pi$$
$$440$$ 0 0
$$441$$ −5.00000 −0.238095
$$442$$ 0 0
$$443$$ −36.0000 −1.71041 −0.855206 0.518289i $$-0.826569\pi$$
−0.855206 + 0.518289i $$0.826569\pi$$
$$444$$ −6.00000 + 3.46410i −0.284747 + 0.164399i
$$445$$ 0 0
$$446$$ −3.00000 + 5.19615i −0.142054 + 0.246045i
$$447$$ 13.8564i 0.655386i
$$448$$ 3.00000 + 1.73205i 0.141737 + 0.0818317i
$$449$$ 6.00000 + 3.46410i 0.283158 + 0.163481i 0.634852 0.772634i $$-0.281061\pi$$
−0.351694 + 0.936115i $$0.614394\pi$$
$$450$$ 8.66025i 0.408248i
$$451$$ 12.0000 20.7846i 0.565058 0.978709i
$$452$$ −3.00000 5.19615i −0.141108 0.244406i
$$453$$ 9.00000 5.19615i 0.422857 0.244137i
$$454$$ 30.0000 1.40797
$$455$$ 0 0
$$456$$ 6.00000 0.280976
$$457$$ 24.0000 13.8564i 1.12267 0.648175i 0.180591 0.983558i $$-0.442199\pi$$
0.942082 + 0.335383i $$0.108866\pi$$
$$458$$ −6.00000 10.3923i −0.280362 0.485601i
$$459$$ −3.00000 + 5.19615i −0.140028 + 0.242536i
$$460$$ 0 0
$$461$$ −12.0000 6.92820i −0.558896 0.322679i 0.193806 0.981040i $$-0.437917\pi$$
−0.752702 + 0.658361i $$0.771250\pi$$
$$462$$ 18.0000 + 10.3923i 0.837436 + 0.483494i
$$463$$ 17.3205i 0.804952i 0.915430 + 0.402476i $$0.131850\pi$$
−0.915430 + 0.402476i $$0.868150\pi$$
$$464$$ 15.0000 25.9808i 0.696358 1.20613i
$$465$$ 0 0
$$466$$ 9.00000 5.19615i 0.416917 0.240707i
$$467$$ 12.0000 0.555294 0.277647 0.960683i $$-0.410445\pi$$
0.277647 + 0.960683i $$0.410445\pi$$
$$468$$ 0 0
$$469$$ −36.0000 −1.66233
$$470$$ 0 0
$$471$$ 7.00000 + 12.1244i 0.322543 + 0.558661i
$$472$$ 9.00000 15.5885i 0.414259 0.717517i
$$473$$ 13.8564i 0.637118i
$$474$$ 12.0000 + 6.92820i 0.551178 + 0.318223i
$$475$$ 15.0000 + 8.66025i 0.688247 + 0.397360i
$$476$$ 20.7846i 0.952661i
$$477$$ −3.00000 + 5.19615i −0.137361 + 0.237915i
$$478$$ −9.00000 15.5885i −0.411650 0.712999i
$$479$$ 9.00000 5.19615i 0.411220 0.237418i −0.280094 0.959973i $$-0.590365\pi$$
0.691314 + 0.722554i $$0.257032\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ −24.0000 −1.09317
$$483$$ 0 0
$$484$$ −0.500000 0.866025i −0.0227273 0.0393648i
$$485$$ 0 0
$$486$$ 1.73205i 0.0785674i
$$487$$ 33.0000 + 19.0526i 1.49537 + 0.863354i 0.999986 0.00531860i $$-0.00169297\pi$$
0.495387 + 0.868672i $$0.335026\pi$$
$$488$$ −3.00000 1.73205i −0.135804 0.0784063i
$$489$$ 3.46410i 0.156652i
$$490$$ 0 0
$$491$$ 6.00000 + 10.3923i 0.270776 + 0.468998i 0.969061 0.246822i $$-0.0793863\pi$$
−0.698285 + 0.715820i $$0.746053\pi$$
$$492$$ 6.00000 3.46410i 0.270501 0.156174i
$$493$$ −36.0000 −1.62136
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −15.0000 + 8.66025i −0.673520 + 0.388857i
$$497$$ −6.00000 10.3923i −0.269137 0.466159i
$$498$$ 3.00000 5.19615i 0.134433 0.232845i
$$499$$ 10.3923i 0.465223i 0.972570 + 0.232612i $$0.0747271\pi$$
−0.972570 + 0.232612i $$0.925273\pi$$
$$500$$ 0 0
$$501$$ −15.0000 8.66025i −0.670151 0.386912i
$$502$$ 20.7846i 0.927663i
$$503$$ −12.0000 + 20.7846i −0.535054 + 0.926740i 0.464107 + 0.885779i $$0.346375\pi$$
−0.999161 + 0.0409609i $$0.986958\pi$$
$$504$$ −3.00000 5.19615i −0.133631 0.231455i
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 8.00000 0.354943
$$509$$ 36.0000 20.7846i 1.59567 0.921262i 0.603364 0.797466i $$-0.293827\pi$$
0.992308 0.123796i $$-0.0395068\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 8.66025i 0.382733i
$$513$$ −3.00000 1.73205i −0.132453 0.0764719i
$$514$$ 27.0000 + 15.5885i 1.19092 + 0.687577i
$$515$$ 0 0
$$516$$ 2.00000 3.46410i 0.0880451 0.152499i
$$517$$ −6.00000 10.3923i −0.263880 0.457053i
$$518$$ −36.0000 + 20.7846i −1.58175 + 0.913223i
$$519$$ 18.0000 0.790112
$$520$$ 0 0
$$521$$ 18.0000 0.788594 0.394297 0.918983i $$-0.370988\pi$$
0.394297 + 0.918983i $$0.370988\pi$$
$$522$$ −9.00000 + 5.19615i −0.393919 + 0.227429i
$$523$$ 2.00000 + 3.46410i 0.0874539 + 0.151475i 0.906434 0.422347i $$-0.138794\pi$$
−0.818980 + 0.573822i $$0.805460\pi$$
$$524$$ −6.00000 + 10.3923i −0.262111 + 0.453990i
$$525$$ 17.3205i 0.755929i
$$526$$ −36.0000 20.7846i −1.56967 0.906252i
$$527$$ 18.0000 + 10.3923i 0.784092 + 0.452696i
$$528$$ 17.3205i 0.753778i
$$529$$ 11.5000 19.9186i 0.500000 0.866025i
$$530$$ 0 0
$$531$$ −9.00000 + 5.19615i −0.390567 + 0.225494i
$$532$$ −12.0000 −0.520266
$$533$$ 0 0
$$534$$ −12.0000 −0.519291
$$535$$ 0 0
$$536$$ −9.00000 15.5885i −0.388741 0.673319i
$$537$$ −6.00000 + 10.3923i −0.258919 + 0.448461i
$$538$$ 10.3923i 0.448044i
$$539$$ 15.0000 + 8.66025i 0.646096 + 0.373024i
$$540$$ 0 0
$$541$$ 6.92820i 0.297867i −0.988847 0.148933i $$-0.952416\pi$$
0.988847 0.148933i $$-0.0475840\pi$$
$$542$$ 9.00000 15.5885i 0.386583 0.669582i
$$543$$ −5.00000 8.66025i −0.214571 0.371647i
$$544$$ −27.0000 + 15.5885i −1.15762 + 0.668350i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 20.0000 0.855138 0.427569 0.903983i $$-0.359370\pi$$
0.427569 + 0.903983i $$0.359370\pi$$
$$548$$ −18.0000 + 10.3923i −0.768922 + 0.443937i
$$549$$ 1.00000 + 1.73205i 0.0426790 + 0.0739221i
$$550$$ −15.0000 + 25.9808i −0.639602 + 1.10782i
$$551$$ 20.7846i 0.885454i
$$552$$ 0 0
$$553$$ 24.0000 + 13.8564i 1.02058 + 0.589234i
$$554$$ 17.3205i 0.735878i
$$555$$ 0 0
$$556$$ −2.00000 3.46410i −0.0848189 0.146911i
$$557$$ −12.0000 + 6.92820i −0.508456 + 0.293557i −0.732199 0.681091i $$-0.761506\pi$$
0.223743 + 0.974648i $$0.428173\pi$$
$$558$$ 6.00000 0.254000
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 18.0000 10.3923i 0.759961 0.438763i
$$562$$ 6.00000 + 10.3923i 0.253095 + 0.438373i
$$563$$ 6.00000 10.3923i 0.252870 0.437983i −0.711445 0.702742i $$-0.751959\pi$$
0.964315 + 0.264758i $$0.0852922\pi$$
$$564$$ 3.46410i 0.145865i
$$565$$ 0 0
$$566$$ 6.00000 + 3.46410i 0.252199 + 0.145607i
$$567$$ 3.46410i 0.145479i
$$568$$ 3.00000 5.19615i 0.125877 0.218026i
$$569$$ 3.00000 + 5.19615i 0.125767 + 0.217834i 0.922032 0.387113i $$-0.126528\pi$$
−0.796266 + 0.604947i $$0.793194\pi$$
$$570$$ 0 0
$$571$$ 4.00000 0.167395 0.0836974 0.996491i $$-0.473327\pi$$
0.0836974 + 0.996491i $$0.473327\pi$$
$$572$$ 0 0
$$573$$ −24.0000 −1.00261
$$574$$ 36.0000 20.7846i 1.50261 0.867533i
$$575$$ 0 0
$$576$$ 0.500000 0.866025i 0.0208333 0.0360844i
$$577$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$578$$ 28.5000 + 16.4545i 1.18544 + 0.684416i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 6.00000 10.3923i 0.248922 0.431145i
$$582$$ 12.0000 + 20.7846i 0.497416 + 0.861550i
$$583$$ 18.0000 10.3923i 0.745484 0.430405i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ −48.0000 −1.98286
$$587$$ −9.00000 + 5.19615i −0.371470 + 0.214468i −0.674100 0.738640i $$-0.735468\pi$$
0.302631 + 0.953108i $$0.402135\pi$$
$$588$$ 2.50000 + 4.33013i 0.103098 + 0.178571i
$$589$$ −6.00000 + 10.3923i −0.247226 + 0.428207i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −30.0000 17.3205i −1.23299 0.711868i
$$593$$ 6.92820i 0.284507i −0.989830 0.142254i $$-0.954565\pi$$
0.989830 0.142254i $$-0.0454349\pi$$
$$594$$ 3.00000 5.19615i 0.123091 0.213201i
$$595$$ 0 0
$$596$$ 12.0000 6.92820i 0.491539 0.283790i
$$597$$ −16.0000 −0.654836
$$598$$ 0 0
$$599$$ 24.0000 0.980613 0.490307 0.871550i $$-0.336885\pi$$
0.490307 + 0.871550i $$0.336885\pi$$
$$600$$ 7.50000 4.33013i 0.306186 0.176777i
$$601$$ −5.00000 8.66025i −0.203954 0.353259i 0.745845 0.666120i $$-0.232046\pi$$
−0.949799 + 0.312861i $$0.898713\pi$$
$$602$$ 12.0000 20.7846i 0.489083 0.847117i
$$603$$ 10.3923i 0.423207i
$$604$$ −9.00000 5.19615i −0.366205 0.211428i
$$605$$ 0 0
$$606$$ 10.3923i 0.422159i
$$607$$ −16.0000 + 27.7128i −0.649420 + 1.12483i 0.333842 + 0.942629i $$0.391655\pi$$
−0.983262 + 0.182199i $$0.941678\pi$$
$$608$$ −9.00000 15.5885i −0.364998 0.632195i
$$609$$ −18.0000 + 10.3923i −0.729397 + 0.421117i
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 6.00000 0.242536
$$613$$ 18.0000 10.3923i 0.727013 0.419741i −0.0903153 0.995913i $$-0.528787\pi$$
0.817328 + 0.576172i $$0.195454\pi$$
$$614$$ −9.00000 15.5885i −0.363210 0.629099i
$$615$$ 0 0
$$616$$ 20.7846i 0.837436i
$$617$$ −6.00000 3.46410i −0.241551 0.139459i 0.374338 0.927292i $$-0.377870\pi$$
−0.615889 + 0.787833i $$0.711203\pi$$
$$618$$ −12.0000 6.92820i −0.482711 0.278693i
$$619$$ 31.1769i 1.25311i −0.779379 0.626553i $$-0.784465\pi$$
0.779379 0.626553i $$-0.215535\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −24.0000 −0.961540
$$624$$ 0 0
$$625$$ 25.0000 1.00000
$$626$$ −15.0000 + 8.66025i −0.599521 + 0.346133i
$$627$$ 6.00000 + 10.3923i 0.239617 + 0.415029i
$$628$$ 7.00000 12.1244i 0.279330 0.483814i
$$629$$ 41.5692i 1.65747i
$$630$$ 0 0
$$631$$ 33.0000 + 19.0526i 1.31371 + 0.758470i 0.982708 0.185160i $$-0.0592804\pi$$
0.331001 + 0.943630i $$0.392614\pi$$
$$632$$ 13.8564i 0.551178i
$$633$$ −10.0000 + 17.3205i −0.397464 + 0.688428i
$$634$$ 12.0000 + 20.7846i 0.476581 + 0.825462i
$$635$$ 0 0
$$636$$ 6.00000 0.237915
$$637$$ 0 0
$$638$$ 36.0000 1.42525
$$639$$ −3.00000 + 1.73205i −0.118678 + 0.0685189i
$$640$$ 0 0
$$641$$ 3.00000 5.19615i 0.118493 0.205236i −0.800678 0.599095i $$-0.795527\pi$$
0.919171 + 0.393860i $$0.128860\pi$$
$$642$$ 20.7846i 0.820303i
$$643$$ −9.00000 5.19615i −0.354925 0.204916i 0.311927 0.950106i $$-0.399026\pi$$
−0.666852 + 0.745190i $$0.732359\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −18.0000 + 31.1769i −0.708201 + 1.22664i
$$647$$ 12.0000 + 20.7846i 0.471769 + 0.817127i 0.999478 0.0322975i $$-0.0102824\pi$$
−0.527710 + 0.849425i $$0.676949\pi$$
$$648$$ −1.50000 + 0.866025i −0.0589256 + 0.0340207i
$$649$$ 36.0000 1.41312
$$650$$ 0 0
$$651$$ 12.0000 0.470317
$$652$$ 3.00000 1.73205i 0.117489 0.0678323i
$$653$$ −3.00000 5.19615i −0.117399 0.203341i 0.801337 0.598213i $$-0.204122\pi$$
−0.918736 + 0.394872i $$0.870789\pi$$
$$654$$ −6.00000 + 10.3923i −0.234619 + 0.406371i
$$655$$ 0 0
$$656$$ 30.0000 + 17.3205i 1.17130 + 0.676252i
$$657$$ 0 0
$$658$$ 20.7846i 0.810268i
$$659$$ −6.00000 + 10.3923i −0.233727 + 0.404827i −0.958902 0.283738i $$-0.908425\pi$$
0.725175 + 0.688565i $$0.241759\pi$$
$$660$$ 0 0
$$661$$ 18.0000 10.3923i 0.700119 0.404214i −0.107273 0.994230i $$-0.534212\pi$$
0.807392 + 0.590016i $$0.200879\pi$$
$$662$$ −6.00000 −0.233197
$$663$$ 0 0
$$664$$ 6.00000 0.232845
$$665$$ 0 0
$$666$$ 6.00000 + 10.3923i 0.232495 + 0.402694i
$$667$$ 0 0
$$668$$ 17.3205i 0.670151i
$$669$$ 3.00000 + 1.73205i 0.115987 + 0.0669650i
$$670$$ 0 0
$$671$$ 6.92820i 0.267460i
$$672$$ −9.00000 + 15.5885i −0.347183 + 0.601338i
$$673$$ 23.0000 + 39.8372i 0.886585 + 1.53561i 0.843886 + 0.536522i $$0.180262\pi$$
0.0426985 + 0.999088i $$0.486405\pi$$
$$674$$ 21.0000 12.1244i 0.808890 0.467013i
$$675$$ −5.00000 −0.192450
$$676$$ 0 0
$$677$$ 6.00000 0.230599 0.115299 0.993331i $$-0.463217\pi$$
0.115299 + 0.993331i $$0.463217\pi$$
$$678$$ −9.00000 + 5.19615i −0.345643 + 0.199557i
$$679$$ 24.0000 + 41.5692i 0.921035 + 1.59528i
$$680$$ 0 0
$$681$$ 17.3205i 0.663723i
$$682$$ −18.0000 10.3923i −0.689256 0.397942i
$$683$$ −27.0000 15.5885i −1.03313 0.596476i −0.115248 0.993337i $$-0.536766\pi$$
−0.917879 + 0.396861i $$0.870099\pi$$
$$684$$ 3.46410i 0.132453i
$$685$$ 0 0
$$686$$ −6.00000 10.3923i −0.229081 0.396780i
$$687$$ −6.00000 + 3.46410i −0.228914 + 0.132164i
$$688$$ 20.0000 0.762493
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −39.0000 + 22.5167i −1.48363 + 0.856574i −0.999827 0.0186028i $$-0.994078\pi$$
−0.483803 + 0.875177i $$0.660745\pi$$
$$692$$ −9.00000 15.5885i −0.342129 0.592584i
$$693$$ 6.00000 10.3923i 0.227921 0.394771i
$$694$$ 62.3538i 2.36692i
$$695$$ 0 0
$$696$$ −9.00000 5.19615i −0.341144 0.196960i
$$697$$ 41.5692i 1.57455i
$$698$$ −6.00000 + 10.3923i −0.227103 + 0.393355i
$$699$$ −3.00000 5.19615i −0.113470 0.196537i
$$700$$ −15.0000 + 8.66025i −0.566947 + 0.327327i
$$701$$ −42.0000 −1.58632 −0.793159 0.609015i $$-0.791565\pi$$
−0.793159 + 0.609015i $$0.791565\pi$$
$$702$$ 0 0
$$703$$ −24.0000 −0.905177
$$704$$ −3.00000 + 1.73205i −0.113067 + 0.0652791i
$$705$$ 0 0
$$706$$ 30.0000 51.9615i 1.12906 1.95560i
$$707$$ 20.7846i 0.781686i
$$708$$ 9.00000 + 5.19615i 0.338241 + 0.195283i
$$709$$ −6.00000 3.46410i −0.225335 0.130097i 0.383083 0.923714i $$-0.374862\pi$$
−0.608418 + 0.793617i $$0.708196\pi$$
$$710$$ 0 0
$$711$$ 4.00000 6.92820i 0.150012 0.259828i
$$712$$ −6.00000 10.3923i −0.224860 0.389468i
$$713$$ 0 0
$$714$$ 36.0000 1.34727
$$715$$ 0 0
$$716$$ 12.0000 0.448461
$$717$$ −9.00000 + 5.19615i −0.336111 + 0.194054i
$$718$$ 15.0000 + 25.9808i 0.559795 + 0.969593i
$$719$$ −12.0000 + 20.7846i −0.447524 + 0.775135i −0.998224 0.0595683i $$-0.981028\pi$$
0.550700 + 0.834703i $$0.314361\pi$$
$$720$$ 0 0
$$721$$ −24.0000 13.8564i −0.893807 0.516040i
$$722$$ 10.5000 + 6.06218i 0.390770 + 0.225611i
$$723$$ 13.8564i 0.515325i
$$724$$ −5.00000 + 8.66025i −0.185824 + 0.321856i
$$725$$ −15.0000 25.9808i −0.557086 0.964901i
$$726$$ −1.50000 + 0.866025i −0.0556702 + 0.0321412i
$$727$$ 16.0000 0.593407 0.296704 0.954970i $$-0.404113\pi$$
0.296704 + 0.954970i $$0.404113\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ −12.0000 20.7846i −0.443836 0.768747i
$$732$$ 1.00000 1.73205i 0.0369611 0.0640184i
$$733$$ 34.6410i 1.27950i −0.768585 0.639748i $$-0.779039\pi$$
0.768585 0.639748i $$-0.220961\pi$$
$$734$$ −24.0000 13.8564i −0.885856 0.511449i
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 18.0000 31.1769i 0.663039 1.14842i
$$738$$ −6.00000 10.3923i −0.220863 0.382546i
$$739$$ 33.0000 19.0526i 1.21392 0.700860i 0.250313 0.968165i $$-0.419467\pi$$
0.963612 + 0.267305i $$0.0861332\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 36.0000 1.32160
$$743$$ −3.00000 + 1.73205i −0.110059 + 0.0635428i −0.554019 0.832504i $$-0.686907\pi$$
0.443960 + 0.896047i $$0.353573\pi$$
$$744$$ 3.00000 + 5.19615i 0.109985 + 0.190500i
$$745$$ 0 0
$$746$$ 38.1051i 1.39513i
$$747$$ −3.00000 1.73205i −0.109764 0.0633724i
$$748$$ −18.0000 10.3923i −0.658145 0.379980i
$$749$$ 41.5692i 1.51891i
$$750$$ 0 0
$$751$$ −16.0000 27.7128i −0.583848 1.01125i −0.995018 0.0996961i $$-0.968213\pi$$
0.411170 0.911559i $$-0.365120\pi$$
$$752$$ 15.0000 8.66025i 0.546994 0.315807i
$$753$$ 12.0000 0.437304
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 3.00000 1.73205i 0.109109 0.0629941i
$$757$$ −11.0000 19.0526i −0.399802 0.692477i 0.593899 0.804539i $$-0.297588\pi$$
−0.993701 + 0.112062i $$0.964254\pi$$
$$758$$ 15.0000 25.9808i 0.544825 0.943664i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −42.0000 24.2487i −1.52250 0.879015i −0.999646 0.0265919i $$-0.991535\pi$$
−0.522852 0.852423i $$-0.675132\pi$$
$$762$$ 13.8564i 0.501965i
$$763$$ −12.0000 + 20.7846i −0.434429 + 0.752453i
$$764$$ 12.0000 + 20.7846i 0.434145 + 0.751961i
$$765$$ 0 0
$$766$$ −6.00000 −0.216789
$$767$$ 0 0
$$768$$ −19.0000 −0.685603
$$769$$ −24.0000 + 13.8564i −0.865462 + 0.499675i −0.865838 0.500325i $$-0.833214\pi$$
0.000375472 1.00000i $$0.499880\pi$$
$$770$$ 0 0
$$771$$ 9.00000 15.5885i 0.324127 0.561405i
$$772$$ 0 0
$$773$$ −12.0000 6.92820i −0.431610 0.249190i 0.268422 0.963301i $$-0.413498\pi$$
−0.700032 + 0.714111i $$0.746831\pi$$
$$774$$ −6.00000 3.46410i −0.215666 0.124515i
$$775$$ 17.3205i 0.622171i
$$776$$ −12.0000 + 20.7846i −0.430775 + 0.746124i
$$777$$ 12.0000 + 20.7846i 0.430498 + 0.745644i
$$778$$ 27.0000 15.5885i 0.967997 0.558873i
$$779$$ 24.0000 0.859889
$$780$$ 0 0
$$781$$ 12.0000 0.429394
$$782$$ 0 0
$$783$$ 3.00000 + 5.19615i 0.107211 + 0.185695i
$$784$$ −12.5000 + 21.6506i −0.446429 + 0.773237i
$$785$$ 0