Properties

 Label 42.2.e.b.25.1 Level $42$ Weight $2$ Character 42.25 Analytic conductor $0.335$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$42 = 2 \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 42.e (of order $$3$$, degree $$2$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$0.335371688489$$ 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: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

 Embedding label 25.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 42.25 Dual form 42.2.e.b.37.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} -1.00000 q^{6} +(2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} -1.00000 q^{6} +(2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.50000 - 2.59808i) q^{10} +(-1.50000 + 2.59808i) q^{11} +(-0.500000 - 0.866025i) q^{12} -4.00000 q^{13} +(2.00000 + 1.73205i) q^{14} +3.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.500000 - 0.866025i) q^{18} +(2.00000 + 3.46410i) q^{19} +3.00000 q^{20} +(-0.500000 + 2.59808i) q^{21} -3.00000 q^{22} +(0.500000 - 0.866025i) q^{24} +(-2.00000 + 3.46410i) q^{25} +(-2.00000 - 3.46410i) q^{26} +1.00000 q^{27} +(-0.500000 + 2.59808i) q^{28} +9.00000 q^{29} +(1.50000 + 2.59808i) q^{30} +(0.500000 - 0.866025i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{33} +(-6.00000 - 5.19615i) q^{35} +1.00000 q^{36} +(-4.00000 - 6.92820i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(2.00000 - 3.46410i) q^{39} +(1.50000 + 2.59808i) q^{40} +(-2.50000 + 0.866025i) q^{42} -10.0000 q^{43} +(-1.50000 - 2.59808i) q^{44} +(-1.50000 + 2.59808i) q^{45} +(3.00000 + 5.19615i) q^{47} +1.00000 q^{48} +(5.50000 - 4.33013i) q^{49} -4.00000 q^{50} +(2.00000 - 3.46410i) q^{52} +(1.50000 - 2.59808i) q^{53} +(0.500000 + 0.866025i) q^{54} +9.00000 q^{55} +(-2.50000 + 0.866025i) q^{56} -4.00000 q^{57} +(4.50000 + 7.79423i) q^{58} +(-1.50000 + 2.59808i) q^{59} +(-1.50000 + 2.59808i) q^{60} +(5.00000 + 8.66025i) q^{61} +1.00000 q^{62} +(-2.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(6.00000 + 10.3923i) q^{65} +(1.50000 - 2.59808i) q^{66} +(5.00000 - 8.66025i) q^{67} +(1.50000 - 7.79423i) q^{70} -6.00000 q^{71} +(0.500000 + 0.866025i) q^{72} +(-1.00000 + 1.73205i) q^{73} +(4.00000 - 6.92820i) q^{74} +(-2.00000 - 3.46410i) q^{75} -4.00000 q^{76} +(-1.50000 + 7.79423i) q^{77} +4.00000 q^{78} +(0.500000 + 0.866025i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} -9.00000 q^{83} +(-2.00000 - 1.73205i) q^{84} +(-5.00000 - 8.66025i) q^{86} +(-4.50000 + 7.79423i) q^{87} +(1.50000 - 2.59808i) q^{88} +(-3.00000 - 5.19615i) q^{89} -3.00000 q^{90} +(-10.0000 + 3.46410i) q^{91} +(0.500000 + 0.866025i) q^{93} +(-3.00000 + 5.19615i) q^{94} +(6.00000 - 10.3923i) q^{95} +(0.500000 + 0.866025i) q^{96} -1.00000 q^{97} +(6.50000 + 2.59808i) q^{98} +3.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + q^{2} - q^{3} - q^{4} - 3q^{5} - 2q^{6} + 5q^{7} - 2q^{8} - q^{9} + O(q^{10})$$ $$2q + q^{2} - q^{3} - q^{4} - 3q^{5} - 2q^{6} + 5q^{7} - 2q^{8} - q^{9} + 3q^{10} - 3q^{11} - q^{12} - 8q^{13} + 4q^{14} + 6q^{15} - q^{16} + q^{18} + 4q^{19} + 6q^{20} - q^{21} - 6q^{22} + q^{24} - 4q^{25} - 4q^{26} + 2q^{27} - q^{28} + 18q^{29} + 3q^{30} + q^{31} + q^{32} - 3q^{33} - 12q^{35} + 2q^{36} - 8q^{37} - 4q^{38} + 4q^{39} + 3q^{40} - 5q^{42} - 20q^{43} - 3q^{44} - 3q^{45} + 6q^{47} + 2q^{48} + 11q^{49} - 8q^{50} + 4q^{52} + 3q^{53} + q^{54} + 18q^{55} - 5q^{56} - 8q^{57} + 9q^{58} - 3q^{59} - 3q^{60} + 10q^{61} + 2q^{62} - 4q^{63} + 2q^{64} + 12q^{65} + 3q^{66} + 10q^{67} + 3q^{70} - 12q^{71} + q^{72} - 2q^{73} + 8q^{74} - 4q^{75} - 8q^{76} - 3q^{77} + 8q^{78} + q^{79} - 3q^{80} - q^{81} - 18q^{83} - 4q^{84} - 10q^{86} - 9q^{87} + 3q^{88} - 6q^{89} - 6q^{90} - 20q^{91} + q^{93} - 6q^{94} + 12q^{95} + q^{96} - 2q^{97} + 13q^{98} + 6q^{99} + O(q^{100})$$

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$31$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.500000 + 0.866025i 0.353553 + 0.612372i
$$3$$ −0.500000 + 0.866025i −0.288675 + 0.500000i
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ −1.50000 2.59808i −0.670820 1.16190i −0.977672 0.210138i $$-0.932609\pi$$
0.306851 0.951757i $$-0.400725\pi$$
$$6$$ −1.00000 −0.408248
$$7$$ 2.50000 0.866025i 0.944911 0.327327i
$$8$$ −1.00000 −0.353553
$$9$$ −0.500000 0.866025i −0.166667 0.288675i
$$10$$ 1.50000 2.59808i 0.474342 0.821584i
$$11$$ −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i $$-0.982718\pi$$
0.546259 + 0.837616i $$0.316051\pi$$
$$12$$ −0.500000 0.866025i −0.144338 0.250000i
$$13$$ −4.00000 −1.10940 −0.554700 0.832050i $$-0.687167\pi$$
−0.554700 + 0.832050i $$0.687167\pi$$
$$14$$ 2.00000 + 1.73205i 0.534522 + 0.462910i
$$15$$ 3.00000 0.774597
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$18$$ 0.500000 0.866025i 0.117851 0.204124i
$$19$$ 2.00000 + 3.46410i 0.458831 + 0.794719i 0.998899 0.0469020i $$-0.0149348\pi$$
−0.540068 + 0.841621i $$0.681602\pi$$
$$20$$ 3.00000 0.670820
$$21$$ −0.500000 + 2.59808i −0.109109 + 0.566947i
$$22$$ −3.00000 −0.639602
$$23$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$24$$ 0.500000 0.866025i 0.102062 0.176777i
$$25$$ −2.00000 + 3.46410i −0.400000 + 0.692820i
$$26$$ −2.00000 3.46410i −0.392232 0.679366i
$$27$$ 1.00000 0.192450
$$28$$ −0.500000 + 2.59808i −0.0944911 + 0.490990i
$$29$$ 9.00000 1.67126 0.835629 0.549294i $$-0.185103\pi$$
0.835629 + 0.549294i $$0.185103\pi$$
$$30$$ 1.50000 + 2.59808i 0.273861 + 0.474342i
$$31$$ 0.500000 0.866025i 0.0898027 0.155543i −0.817625 0.575751i $$-0.804710\pi$$
0.907428 + 0.420208i $$0.138043\pi$$
$$32$$ 0.500000 0.866025i 0.0883883 0.153093i
$$33$$ −1.50000 2.59808i −0.261116 0.452267i
$$34$$ 0 0
$$35$$ −6.00000 5.19615i −1.01419 0.878310i
$$36$$ 1.00000 0.166667
$$37$$ −4.00000 6.92820i −0.657596 1.13899i −0.981236 0.192809i $$-0.938240\pi$$
0.323640 0.946180i $$-0.395093\pi$$
$$38$$ −2.00000 + 3.46410i −0.324443 + 0.561951i
$$39$$ 2.00000 3.46410i 0.320256 0.554700i
$$40$$ 1.50000 + 2.59808i 0.237171 + 0.410792i
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ −2.50000 + 0.866025i −0.385758 + 0.133631i
$$43$$ −10.0000 −1.52499 −0.762493 0.646997i $$-0.776025\pi$$
−0.762493 + 0.646997i $$0.776025\pi$$
$$44$$ −1.50000 2.59808i −0.226134 0.391675i
$$45$$ −1.50000 + 2.59808i −0.223607 + 0.387298i
$$46$$ 0 0
$$47$$ 3.00000 + 5.19615i 0.437595 + 0.757937i 0.997503 0.0706177i $$-0.0224970\pi$$
−0.559908 + 0.828554i $$0.689164\pi$$
$$48$$ 1.00000 0.144338
$$49$$ 5.50000 4.33013i 0.785714 0.618590i
$$50$$ −4.00000 −0.565685
$$51$$ 0 0
$$52$$ 2.00000 3.46410i 0.277350 0.480384i
$$53$$ 1.50000 2.59808i 0.206041 0.356873i −0.744423 0.667708i $$-0.767275\pi$$
0.950464 + 0.310835i $$0.100609\pi$$
$$54$$ 0.500000 + 0.866025i 0.0680414 + 0.117851i
$$55$$ 9.00000 1.21356
$$56$$ −2.50000 + 0.866025i −0.334077 + 0.115728i
$$57$$ −4.00000 −0.529813
$$58$$ 4.50000 + 7.79423i 0.590879 + 1.02343i
$$59$$ −1.50000 + 2.59808i −0.195283 + 0.338241i −0.946993 0.321253i $$-0.895896\pi$$
0.751710 + 0.659494i $$0.229229\pi$$
$$60$$ −1.50000 + 2.59808i −0.193649 + 0.335410i
$$61$$ 5.00000 + 8.66025i 0.640184 + 1.10883i 0.985391 + 0.170305i $$0.0544754\pi$$
−0.345207 + 0.938527i $$0.612191\pi$$
$$62$$ 1.00000 0.127000
$$63$$ −2.00000 1.73205i −0.251976 0.218218i
$$64$$ 1.00000 0.125000
$$65$$ 6.00000 + 10.3923i 0.744208 + 1.28901i
$$66$$ 1.50000 2.59808i 0.184637 0.319801i
$$67$$ 5.00000 8.66025i 0.610847 1.05802i −0.380251 0.924883i $$-0.624162\pi$$
0.991098 0.133135i $$-0.0425044\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 1.50000 7.79423i 0.179284 0.931589i
$$71$$ −6.00000 −0.712069 −0.356034 0.934473i $$-0.615871\pi$$
−0.356034 + 0.934473i $$0.615871\pi$$
$$72$$ 0.500000 + 0.866025i 0.0589256 + 0.102062i
$$73$$ −1.00000 + 1.73205i −0.117041 + 0.202721i −0.918594 0.395203i $$-0.870674\pi$$
0.801553 + 0.597924i $$0.204008\pi$$
$$74$$ 4.00000 6.92820i 0.464991 0.805387i
$$75$$ −2.00000 3.46410i −0.230940 0.400000i
$$76$$ −4.00000 −0.458831
$$77$$ −1.50000 + 7.79423i −0.170941 + 0.888235i
$$78$$ 4.00000 0.452911
$$79$$ 0.500000 + 0.866025i 0.0562544 + 0.0974355i 0.892781 0.450490i $$-0.148751\pi$$
−0.836527 + 0.547926i $$0.815418\pi$$
$$80$$ −1.50000 + 2.59808i −0.167705 + 0.290474i
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 0 0
$$83$$ −9.00000 −0.987878 −0.493939 0.869496i $$-0.664443\pi$$
−0.493939 + 0.869496i $$0.664443\pi$$
$$84$$ −2.00000 1.73205i −0.218218 0.188982i
$$85$$ 0 0
$$86$$ −5.00000 8.66025i −0.539164 0.933859i
$$87$$ −4.50000 + 7.79423i −0.482451 + 0.835629i
$$88$$ 1.50000 2.59808i 0.159901 0.276956i
$$89$$ −3.00000 5.19615i −0.317999 0.550791i 0.662071 0.749441i $$-0.269678\pi$$
−0.980071 + 0.198650i $$0.936344\pi$$
$$90$$ −3.00000 −0.316228
$$91$$ −10.0000 + 3.46410i −1.04828 + 0.363137i
$$92$$ 0 0
$$93$$ 0.500000 + 0.866025i 0.0518476 + 0.0898027i
$$94$$ −3.00000 + 5.19615i −0.309426 + 0.535942i
$$95$$ 6.00000 10.3923i 0.615587 1.06623i
$$96$$ 0.500000 + 0.866025i 0.0510310 + 0.0883883i
$$97$$ −1.00000 −0.101535 −0.0507673 0.998711i $$-0.516167\pi$$
−0.0507673 + 0.998711i $$0.516167\pi$$
$$98$$ 6.50000 + 2.59808i 0.656599 + 0.262445i
$$99$$ 3.00000 0.301511
$$100$$ −2.00000 3.46410i −0.200000 0.346410i
$$101$$ 9.00000 15.5885i 0.895533 1.55111i 0.0623905 0.998052i $$-0.480128\pi$$
0.833143 0.553058i $$-0.186539\pi$$
$$102$$ 0 0
$$103$$ −4.00000 6.92820i −0.394132 0.682656i 0.598858 0.800855i $$-0.295621\pi$$
−0.992990 + 0.118199i $$0.962288\pi$$
$$104$$ 4.00000 0.392232
$$105$$ 7.50000 2.59808i 0.731925 0.253546i
$$106$$ 3.00000 0.291386
$$107$$ 1.50000 + 2.59808i 0.145010 + 0.251166i 0.929377 0.369132i $$-0.120345\pi$$
−0.784366 + 0.620298i $$0.787012\pi$$
$$108$$ −0.500000 + 0.866025i −0.0481125 + 0.0833333i
$$109$$ −7.00000 + 12.1244i −0.670478 + 1.16130i 0.307290 + 0.951616i $$0.400578\pi$$
−0.977769 + 0.209687i $$0.932756\pi$$
$$110$$ 4.50000 + 7.79423i 0.429058 + 0.743151i
$$111$$ 8.00000 0.759326
$$112$$ −2.00000 1.73205i −0.188982 0.163663i
$$113$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$114$$ −2.00000 3.46410i −0.187317 0.324443i
$$115$$ 0 0
$$116$$ −4.50000 + 7.79423i −0.417815 + 0.723676i
$$117$$ 2.00000 + 3.46410i 0.184900 + 0.320256i
$$118$$ −3.00000 −0.276172
$$119$$ 0 0
$$120$$ −3.00000 −0.273861
$$121$$ 1.00000 + 1.73205i 0.0909091 + 0.157459i
$$122$$ −5.00000 + 8.66025i −0.452679 + 0.784063i
$$123$$ 0 0
$$124$$ 0.500000 + 0.866025i 0.0449013 + 0.0777714i
$$125$$ −3.00000 −0.268328
$$126$$ 0.500000 2.59808i 0.0445435 0.231455i
$$127$$ 5.00000 0.443678 0.221839 0.975083i $$-0.428794\pi$$
0.221839 + 0.975083i $$0.428794\pi$$
$$128$$ 0.500000 + 0.866025i 0.0441942 + 0.0765466i
$$129$$ 5.00000 8.66025i 0.440225 0.762493i
$$130$$ −6.00000 + 10.3923i −0.526235 + 0.911465i
$$131$$ 4.50000 + 7.79423i 0.393167 + 0.680985i 0.992865 0.119241i $$-0.0380462\pi$$
−0.599699 + 0.800226i $$0.704713\pi$$
$$132$$ 3.00000 0.261116
$$133$$ 8.00000 + 6.92820i 0.693688 + 0.600751i
$$134$$ 10.0000 0.863868
$$135$$ −1.50000 2.59808i −0.129099 0.223607i
$$136$$ 0 0
$$137$$ −9.00000 + 15.5885i −0.768922 + 1.33181i 0.169226 + 0.985577i $$0.445873\pi$$
−0.938148 + 0.346235i $$0.887460\pi$$
$$138$$ 0 0
$$139$$ 2.00000 0.169638 0.0848189 0.996396i $$-0.472969\pi$$
0.0848189 + 0.996396i $$0.472969\pi$$
$$140$$ 7.50000 2.59808i 0.633866 0.219578i
$$141$$ −6.00000 −0.505291
$$142$$ −3.00000 5.19615i −0.251754 0.436051i
$$143$$ 6.00000 10.3923i 0.501745 0.869048i
$$144$$ −0.500000 + 0.866025i −0.0416667 + 0.0721688i
$$145$$ −13.5000 23.3827i −1.12111 1.94183i
$$146$$ −2.00000 −0.165521
$$147$$ 1.00000 + 6.92820i 0.0824786 + 0.571429i
$$148$$ 8.00000 0.657596
$$149$$ −9.00000 15.5885i −0.737309 1.27706i −0.953703 0.300750i $$-0.902763\pi$$
0.216394 0.976306i $$-0.430570\pi$$
$$150$$ 2.00000 3.46410i 0.163299 0.282843i
$$151$$ 0.500000 0.866025i 0.0406894 0.0704761i −0.844963 0.534824i $$-0.820378\pi$$
0.885653 + 0.464348i $$0.153711\pi$$
$$152$$ −2.00000 3.46410i −0.162221 0.280976i
$$153$$ 0 0
$$154$$ −7.50000 + 2.59808i −0.604367 + 0.209359i
$$155$$ −3.00000 −0.240966
$$156$$ 2.00000 + 3.46410i 0.160128 + 0.277350i
$$157$$ 2.00000 3.46410i 0.159617 0.276465i −0.775113 0.631822i $$-0.782307\pi$$
0.934731 + 0.355357i $$0.115641\pi$$
$$158$$ −0.500000 + 0.866025i −0.0397779 + 0.0688973i
$$159$$ 1.50000 + 2.59808i 0.118958 + 0.206041i
$$160$$ −3.00000 −0.237171
$$161$$ 0 0
$$162$$ −1.00000 −0.0785674
$$163$$ 8.00000 + 13.8564i 0.626608 + 1.08532i 0.988227 + 0.152992i $$0.0488907\pi$$
−0.361619 + 0.932326i $$0.617776\pi$$
$$164$$ 0 0
$$165$$ −4.50000 + 7.79423i −0.350325 + 0.606780i
$$166$$ −4.50000 7.79423i −0.349268 0.604949i
$$167$$ 6.00000 0.464294 0.232147 0.972681i $$-0.425425\pi$$
0.232147 + 0.972681i $$0.425425\pi$$
$$168$$ 0.500000 2.59808i 0.0385758 0.200446i
$$169$$ 3.00000 0.230769
$$170$$ 0 0
$$171$$ 2.00000 3.46410i 0.152944 0.264906i
$$172$$ 5.00000 8.66025i 0.381246 0.660338i
$$173$$ −9.00000 15.5885i −0.684257 1.18517i −0.973670 0.227964i $$-0.926793\pi$$
0.289412 0.957205i $$-0.406540\pi$$
$$174$$ −9.00000 −0.682288
$$175$$ −2.00000 + 10.3923i −0.151186 + 0.785584i
$$176$$ 3.00000 0.226134
$$177$$ −1.50000 2.59808i −0.112747 0.195283i
$$178$$ 3.00000 5.19615i 0.224860 0.389468i
$$179$$ −6.00000 + 10.3923i −0.448461 + 0.776757i −0.998286 0.0585225i $$-0.981361\pi$$
0.549825 + 0.835280i $$0.314694\pi$$
$$180$$ −1.50000 2.59808i −0.111803 0.193649i
$$181$$ 8.00000 0.594635 0.297318 0.954779i $$-0.403908\pi$$
0.297318 + 0.954779i $$0.403908\pi$$
$$182$$ −8.00000 6.92820i −0.592999 0.513553i
$$183$$ −10.0000 −0.739221
$$184$$ 0 0
$$185$$ −12.0000 + 20.7846i −0.882258 + 1.52811i
$$186$$ −0.500000 + 0.866025i −0.0366618 + 0.0635001i
$$187$$ 0 0
$$188$$ −6.00000 −0.437595
$$189$$ 2.50000 0.866025i 0.181848 0.0629941i
$$190$$ 12.0000 0.870572
$$191$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$192$$ −0.500000 + 0.866025i −0.0360844 + 0.0625000i
$$193$$ 9.50000 16.4545i 0.683825 1.18442i −0.289980 0.957033i $$-0.593649\pi$$
0.973805 0.227387i $$-0.0730182\pi$$
$$194$$ −0.500000 0.866025i −0.0358979 0.0621770i
$$195$$ −12.0000 −0.859338
$$196$$ 1.00000 + 6.92820i 0.0714286 + 0.494872i
$$197$$ 6.00000 0.427482 0.213741 0.976890i $$-0.431435\pi$$
0.213741 + 0.976890i $$0.431435\pi$$
$$198$$ 1.50000 + 2.59808i 0.106600 + 0.184637i
$$199$$ −10.0000 + 17.3205i −0.708881 + 1.22782i 0.256391 + 0.966573i $$0.417466\pi$$
−0.965272 + 0.261245i $$0.915867\pi$$
$$200$$ 2.00000 3.46410i 0.141421 0.244949i
$$201$$ 5.00000 + 8.66025i 0.352673 + 0.610847i
$$202$$ 18.0000 1.26648
$$203$$ 22.5000 7.79423i 1.57919 0.547048i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 4.00000 6.92820i 0.278693 0.482711i
$$207$$ 0 0
$$208$$ 2.00000 + 3.46410i 0.138675 + 0.240192i
$$209$$ −12.0000 −0.830057
$$210$$ 6.00000 + 5.19615i 0.414039 + 0.358569i
$$211$$ 14.0000 0.963800 0.481900 0.876226i $$-0.339947\pi$$
0.481900 + 0.876226i $$0.339947\pi$$
$$212$$ 1.50000 + 2.59808i 0.103020 + 0.178437i
$$213$$ 3.00000 5.19615i 0.205557 0.356034i
$$214$$ −1.50000 + 2.59808i −0.102538 + 0.177601i
$$215$$ 15.0000 + 25.9808i 1.02299 + 1.77187i
$$216$$ −1.00000 −0.0680414
$$217$$ 0.500000 2.59808i 0.0339422 0.176369i
$$218$$ −14.0000 −0.948200
$$219$$ −1.00000 1.73205i −0.0675737 0.117041i
$$220$$ −4.50000 + 7.79423i −0.303390 + 0.525487i
$$221$$ 0 0
$$222$$ 4.00000 + 6.92820i 0.268462 + 0.464991i
$$223$$ −19.0000 −1.27233 −0.636167 0.771551i $$-0.719481\pi$$
−0.636167 + 0.771551i $$0.719481\pi$$
$$224$$ 0.500000 2.59808i 0.0334077 0.173591i
$$225$$ 4.00000 0.266667
$$226$$ 0 0
$$227$$ 13.5000 23.3827i 0.896026 1.55196i 0.0634974 0.997982i $$-0.479775\pi$$
0.832529 0.553981i $$-0.186892\pi$$
$$228$$ 2.00000 3.46410i 0.132453 0.229416i
$$229$$ 2.00000 + 3.46410i 0.132164 + 0.228914i 0.924510 0.381157i $$-0.124474\pi$$
−0.792347 + 0.610071i $$0.791141\pi$$
$$230$$ 0 0
$$231$$ −6.00000 5.19615i −0.394771 0.341882i
$$232$$ −9.00000 −0.590879
$$233$$ 12.0000 + 20.7846i 0.786146 + 1.36165i 0.928312 + 0.371802i $$0.121260\pi$$
−0.142166 + 0.989843i $$0.545407\pi$$
$$234$$ −2.00000 + 3.46410i −0.130744 + 0.226455i
$$235$$ 9.00000 15.5885i 0.587095 1.01688i
$$236$$ −1.50000 2.59808i −0.0976417 0.169120i
$$237$$ −1.00000 −0.0649570
$$238$$ 0 0
$$239$$ −24.0000 −1.55243 −0.776215 0.630468i $$-0.782863\pi$$
−0.776215 + 0.630468i $$0.782863\pi$$
$$240$$ −1.50000 2.59808i −0.0968246 0.167705i
$$241$$ 0.500000 0.866025i 0.0322078 0.0557856i −0.849472 0.527633i $$-0.823079\pi$$
0.881680 + 0.471848i $$0.156413\pi$$
$$242$$ −1.00000 + 1.73205i −0.0642824 + 0.111340i
$$243$$ −0.500000 0.866025i −0.0320750 0.0555556i
$$244$$ −10.0000 −0.640184
$$245$$ −19.5000 7.79423i −1.24581 0.497955i
$$246$$ 0 0
$$247$$ −8.00000 13.8564i −0.509028 0.881662i
$$248$$ −0.500000 + 0.866025i −0.0317500 + 0.0549927i
$$249$$ 4.50000 7.79423i 0.285176 0.493939i
$$250$$ −1.50000 2.59808i −0.0948683 0.164317i
$$251$$ 27.0000 1.70422 0.852112 0.523359i $$-0.175321\pi$$
0.852112 + 0.523359i $$0.175321\pi$$
$$252$$ 2.50000 0.866025i 0.157485 0.0545545i
$$253$$ 0 0
$$254$$ 2.50000 + 4.33013i 0.156864 + 0.271696i
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −3.00000 5.19615i −0.187135 0.324127i 0.757159 0.653231i $$-0.226587\pi$$
−0.944294 + 0.329104i $$0.893253\pi$$
$$258$$ 10.0000 0.622573
$$259$$ −16.0000 13.8564i −0.994192 0.860995i
$$260$$ −12.0000 −0.744208
$$261$$ −4.50000 7.79423i −0.278543 0.482451i
$$262$$ −4.50000 + 7.79423i −0.278011 + 0.481529i
$$263$$ 3.00000 5.19615i 0.184988 0.320408i −0.758585 0.651575i $$-0.774109\pi$$
0.943572 + 0.331166i $$0.107442\pi$$
$$264$$ 1.50000 + 2.59808i 0.0923186 + 0.159901i
$$265$$ −9.00000 −0.552866
$$266$$ −2.00000 + 10.3923i −0.122628 + 0.637193i
$$267$$ 6.00000 0.367194
$$268$$ 5.00000 + 8.66025i 0.305424 + 0.529009i
$$269$$ −10.5000 + 18.1865i −0.640196 + 1.10885i 0.345192 + 0.938532i $$0.387814\pi$$
−0.985389 + 0.170321i $$0.945520\pi$$
$$270$$ 1.50000 2.59808i 0.0912871 0.158114i
$$271$$ −5.50000 9.52628i −0.334101 0.578680i 0.649211 0.760609i $$-0.275099\pi$$
−0.983312 + 0.181928i $$0.941766\pi$$
$$272$$ 0 0
$$273$$ 2.00000 10.3923i 0.121046 0.628971i
$$274$$ −18.0000 −1.08742
$$275$$ −6.00000 10.3923i −0.361814 0.626680i
$$276$$ 0 0
$$277$$ −4.00000 + 6.92820i −0.240337 + 0.416275i −0.960810 0.277207i $$-0.910591\pi$$
0.720473 + 0.693482i $$0.243925\pi$$
$$278$$ 1.00000 + 1.73205i 0.0599760 + 0.103882i
$$279$$ −1.00000 −0.0598684
$$280$$ 6.00000 + 5.19615i 0.358569 + 0.310530i
$$281$$ 6.00000 0.357930 0.178965 0.983855i $$-0.442725\pi$$
0.178965 + 0.983855i $$0.442725\pi$$
$$282$$ −3.00000 5.19615i −0.178647 0.309426i
$$283$$ −7.00000 + 12.1244i −0.416107 + 0.720718i −0.995544 0.0942988i $$-0.969939\pi$$
0.579437 + 0.815017i $$0.303272\pi$$
$$284$$ 3.00000 5.19615i 0.178017 0.308335i
$$285$$ 6.00000 + 10.3923i 0.355409 + 0.615587i
$$286$$ 12.0000 0.709575
$$287$$ 0 0
$$288$$ −1.00000 −0.0589256
$$289$$ 8.50000 + 14.7224i 0.500000 + 0.866025i
$$290$$ 13.5000 23.3827i 0.792747 1.37308i
$$291$$ 0.500000 0.866025i 0.0293105 0.0507673i
$$292$$ −1.00000 1.73205i −0.0585206 0.101361i
$$293$$ 33.0000 1.92788 0.963940 0.266119i $$-0.0857413\pi$$
0.963940 + 0.266119i $$0.0857413\pi$$
$$294$$ −5.50000 + 4.33013i −0.320767 + 0.252538i
$$295$$ 9.00000 0.524000
$$296$$ 4.00000 + 6.92820i 0.232495 + 0.402694i
$$297$$ −1.50000 + 2.59808i −0.0870388 + 0.150756i
$$298$$ 9.00000 15.5885i 0.521356 0.903015i
$$299$$ 0 0
$$300$$ 4.00000 0.230940
$$301$$ −25.0000 + 8.66025i −1.44098 + 0.499169i
$$302$$ 1.00000 0.0575435
$$303$$ 9.00000 + 15.5885i 0.517036 + 0.895533i
$$304$$ 2.00000 3.46410i 0.114708 0.198680i
$$305$$ 15.0000 25.9808i 0.858898 1.48765i
$$306$$ 0 0
$$307$$ 8.00000 0.456584 0.228292 0.973593i $$-0.426686\pi$$
0.228292 + 0.973593i $$0.426686\pi$$
$$308$$ −6.00000 5.19615i −0.341882 0.296078i
$$309$$ 8.00000 0.455104
$$310$$ −1.50000 2.59808i −0.0851943 0.147561i
$$311$$ −12.0000 + 20.7846i −0.680458 + 1.17859i 0.294384 + 0.955687i $$0.404886\pi$$
−0.974841 + 0.222900i $$0.928448\pi$$
$$312$$ −2.00000 + 3.46410i −0.113228 + 0.196116i
$$313$$ 15.5000 + 26.8468i 0.876112 + 1.51747i 0.855574 + 0.517681i $$0.173205\pi$$
0.0205381 + 0.999789i $$0.493462\pi$$
$$314$$ 4.00000 0.225733
$$315$$ −1.50000 + 7.79423i −0.0845154 + 0.439155i
$$316$$ −1.00000 −0.0562544
$$317$$ −4.50000 7.79423i −0.252745 0.437767i 0.711535 0.702650i $$-0.248000\pi$$
−0.964281 + 0.264883i $$0.914667\pi$$
$$318$$ −1.50000 + 2.59808i −0.0841158 + 0.145693i
$$319$$ −13.5000 + 23.3827i −0.755855 + 1.30918i
$$320$$ −1.50000 2.59808i −0.0838525 0.145237i
$$321$$ −3.00000 −0.167444
$$322$$ 0 0
$$323$$ 0 0
$$324$$ −0.500000 0.866025i −0.0277778 0.0481125i
$$325$$ 8.00000 13.8564i 0.443760 0.768615i
$$326$$ −8.00000 + 13.8564i −0.443079 + 0.767435i
$$327$$ −7.00000 12.1244i −0.387101 0.670478i
$$328$$ 0 0
$$329$$ 12.0000 + 10.3923i 0.661581 + 0.572946i
$$330$$ −9.00000 −0.495434
$$331$$ −10.0000 17.3205i −0.549650 0.952021i −0.998298 0.0583130i $$-0.981428\pi$$
0.448649 0.893708i $$-0.351905\pi$$
$$332$$ 4.50000 7.79423i 0.246970 0.427764i
$$333$$ −4.00000 + 6.92820i −0.219199 + 0.379663i
$$334$$ 3.00000 + 5.19615i 0.164153 + 0.284321i
$$335$$ −30.0000 −1.63908
$$336$$ 2.50000 0.866025i 0.136386 0.0472456i
$$337$$ −7.00000 −0.381314 −0.190657 0.981657i $$-0.561062\pi$$
−0.190657 + 0.981657i $$0.561062\pi$$
$$338$$ 1.50000 + 2.59808i 0.0815892 + 0.141317i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 1.50000 + 2.59808i 0.0812296 + 0.140694i
$$342$$ 4.00000 0.216295
$$343$$ 10.0000 15.5885i 0.539949 0.841698i
$$344$$ 10.0000 0.539164
$$345$$ 0 0
$$346$$ 9.00000 15.5885i 0.483843 0.838041i
$$347$$ −6.00000 + 10.3923i −0.322097 + 0.557888i −0.980921 0.194409i $$-0.937721\pi$$
0.658824 + 0.752297i $$0.271054\pi$$
$$348$$ −4.50000 7.79423i −0.241225 0.417815i
$$349$$ 26.0000 1.39175 0.695874 0.718164i $$-0.255017\pi$$
0.695874 + 0.718164i $$0.255017\pi$$
$$350$$ −10.0000 + 3.46410i −0.534522 + 0.185164i
$$351$$ −4.00000 −0.213504
$$352$$ 1.50000 + 2.59808i 0.0799503 + 0.138478i
$$353$$ −12.0000 + 20.7846i −0.638696 + 1.10625i 0.347024 + 0.937856i $$0.387192\pi$$
−0.985719 + 0.168397i $$0.946141\pi$$
$$354$$ 1.50000 2.59808i 0.0797241 0.138086i
$$355$$ 9.00000 + 15.5885i 0.477670 + 0.827349i
$$356$$ 6.00000 0.317999
$$357$$ 0 0
$$358$$ −12.0000 −0.634220
$$359$$ −15.0000 25.9808i −0.791670 1.37121i −0.924932 0.380131i $$-0.875879\pi$$
0.133263 0.991081i $$-0.457455\pi$$
$$360$$ 1.50000 2.59808i 0.0790569 0.136931i
$$361$$ 1.50000 2.59808i 0.0789474 0.136741i
$$362$$ 4.00000 + 6.92820i 0.210235 + 0.364138i
$$363$$ −2.00000 −0.104973
$$364$$ 2.00000 10.3923i 0.104828 0.544705i
$$365$$ 6.00000 0.314054
$$366$$ −5.00000 8.66025i −0.261354 0.452679i
$$367$$ 9.50000 16.4545i 0.495896 0.858917i −0.504093 0.863649i $$-0.668173\pi$$
0.999989 + 0.00473247i $$0.00150640\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ −24.0000 −1.24770
$$371$$ 1.50000 7.79423i 0.0778761 0.404656i
$$372$$ −1.00000 −0.0518476
$$373$$ −4.00000 6.92820i −0.207112 0.358729i 0.743691 0.668523i $$-0.233073\pi$$
−0.950804 + 0.309794i $$0.899740\pi$$
$$374$$ 0 0
$$375$$ 1.50000 2.59808i 0.0774597 0.134164i
$$376$$ −3.00000 5.19615i −0.154713 0.267971i
$$377$$ −36.0000 −1.85409
$$378$$ 2.00000 + 1.73205i 0.102869 + 0.0890871i
$$379$$ 8.00000 0.410932 0.205466 0.978664i $$-0.434129\pi$$
0.205466 + 0.978664i $$0.434129\pi$$
$$380$$ 6.00000 + 10.3923i 0.307794 + 0.533114i
$$381$$ −2.50000 + 4.33013i −0.128079 + 0.221839i
$$382$$ 0 0
$$383$$ −9.00000 15.5885i −0.459879 0.796533i 0.539076 0.842257i $$-0.318774\pi$$
−0.998954 + 0.0457244i $$0.985440\pi$$
$$384$$ −1.00000 −0.0510310
$$385$$ 22.5000 7.79423i 1.14671 0.397231i
$$386$$ 19.0000 0.967075
$$387$$ 5.00000 + 8.66025i 0.254164 + 0.440225i
$$388$$ 0.500000 0.866025i 0.0253837 0.0439658i
$$389$$ 3.00000 5.19615i 0.152106 0.263455i −0.779895 0.625910i $$-0.784728\pi$$
0.932002 + 0.362454i $$0.118061\pi$$
$$390$$ −6.00000 10.3923i −0.303822 0.526235i
$$391$$ 0 0
$$392$$ −5.50000 + 4.33013i −0.277792 + 0.218704i
$$393$$ −9.00000 −0.453990
$$394$$ 3.00000 + 5.19615i 0.151138 + 0.261778i
$$395$$ 1.50000 2.59808i 0.0754732 0.130723i
$$396$$ −1.50000 + 2.59808i −0.0753778 + 0.130558i
$$397$$ 2.00000 + 3.46410i 0.100377 + 0.173858i 0.911840 0.410546i $$-0.134662\pi$$
−0.811463 + 0.584404i $$0.801328\pi$$
$$398$$ −20.0000 −1.00251
$$399$$ −10.0000 + 3.46410i −0.500626 + 0.173422i
$$400$$ 4.00000 0.200000
$$401$$ −12.0000 20.7846i −0.599251 1.03793i −0.992932 0.118686i $$-0.962132\pi$$
0.393680 0.919247i $$-0.371202\pi$$
$$402$$ −5.00000 + 8.66025i −0.249377 + 0.431934i
$$403$$ −2.00000 + 3.46410i −0.0996271 + 0.172559i
$$404$$ 9.00000 + 15.5885i 0.447767 + 0.775555i
$$405$$ 3.00000 0.149071
$$406$$ 18.0000 + 15.5885i 0.893325 + 0.773642i
$$407$$ 24.0000 1.18964
$$408$$ 0 0
$$409$$ 12.5000 21.6506i 0.618085 1.07056i −0.371750 0.928333i $$-0.621242\pi$$
0.989835 0.142222i $$-0.0454247\pi$$
$$410$$ 0 0
$$411$$ −9.00000 15.5885i −0.443937 0.768922i
$$412$$ 8.00000 0.394132
$$413$$ −1.50000 + 7.79423i −0.0738102 + 0.383529i
$$414$$ 0 0
$$415$$ 13.5000 + 23.3827i 0.662689 + 1.14781i
$$416$$ −2.00000 + 3.46410i −0.0980581 + 0.169842i
$$417$$ −1.00000 + 1.73205i −0.0489702 + 0.0848189i
$$418$$ −6.00000 10.3923i −0.293470 0.508304i
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ −1.50000 + 7.79423i −0.0731925 + 0.380319i
$$421$$ −22.0000 −1.07221 −0.536107 0.844150i $$-0.680106\pi$$
−0.536107 + 0.844150i $$0.680106\pi$$
$$422$$ 7.00000 + 12.1244i 0.340755 + 0.590204i
$$423$$ 3.00000 5.19615i 0.145865 0.252646i
$$424$$ −1.50000 + 2.59808i −0.0728464 + 0.126174i
$$425$$ 0 0
$$426$$ 6.00000 0.290701
$$427$$ 20.0000 + 17.3205i 0.967868 + 0.838198i
$$428$$ −3.00000 −0.145010
$$429$$ 6.00000 + 10.3923i 0.289683 + 0.501745i
$$430$$ −15.0000 + 25.9808i −0.723364 + 1.25290i
$$431$$ −6.00000 + 10.3923i −0.289010 + 0.500580i −0.973574 0.228373i $$-0.926659\pi$$
0.684564 + 0.728953i $$0.259993\pi$$
$$432$$ −0.500000 0.866025i −0.0240563 0.0416667i
$$433$$ −34.0000 −1.63394 −0.816968 0.576683i $$-0.804347\pi$$
−0.816968 + 0.576683i $$0.804347\pi$$
$$434$$ 2.50000 0.866025i 0.120004 0.0415705i
$$435$$ 27.0000 1.29455
$$436$$ −7.00000 12.1244i −0.335239 0.580651i
$$437$$ 0 0
$$438$$ 1.00000 1.73205i 0.0477818 0.0827606i
$$439$$ −17.5000 30.3109i −0.835229 1.44666i −0.893843 0.448379i $$-0.852001\pi$$
0.0586141 0.998281i $$-0.481332\pi$$
$$440$$ −9.00000 −0.429058
$$441$$ −6.50000 2.59808i −0.309524 0.123718i
$$442$$ 0 0
$$443$$ 16.5000 + 28.5788i 0.783939 + 1.35782i 0.929631 + 0.368492i $$0.120126\pi$$
−0.145692 + 0.989330i $$0.546541\pi$$
$$444$$ −4.00000 + 6.92820i −0.189832 + 0.328798i
$$445$$ −9.00000 + 15.5885i −0.426641 + 0.738964i
$$446$$ −9.50000 16.4545i −0.449838 0.779142i
$$447$$ 18.0000 0.851371
$$448$$ 2.50000 0.866025i 0.118114 0.0409159i
$$449$$ 12.0000 0.566315 0.283158 0.959073i $$-0.408618\pi$$
0.283158 + 0.959073i $$0.408618\pi$$
$$450$$ 2.00000 + 3.46410i 0.0942809 + 0.163299i
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0.500000 + 0.866025i 0.0234920 + 0.0406894i
$$454$$ 27.0000 1.26717
$$455$$ 24.0000 + 20.7846i 1.12514 + 0.974398i
$$456$$ 4.00000 0.187317
$$457$$ 0.500000 + 0.866025i 0.0233890 + 0.0405110i 0.877483 0.479608i $$-0.159221\pi$$
−0.854094 + 0.520119i $$0.825888\pi$$
$$458$$ −2.00000 + 3.46410i −0.0934539 + 0.161867i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 30.0000 1.39724 0.698620 0.715493i $$-0.253798\pi$$
0.698620 + 0.715493i $$0.253798\pi$$
$$462$$ 1.50000 7.79423i 0.0697863 0.362620i
$$463$$ 8.00000 0.371792 0.185896 0.982569i $$-0.440481\pi$$
0.185896 + 0.982569i $$0.440481\pi$$
$$464$$ −4.50000 7.79423i −0.208907 0.361838i
$$465$$ 1.50000 2.59808i 0.0695608 0.120483i
$$466$$ −12.0000 + 20.7846i −0.555889 + 0.962828i
$$467$$ −18.0000 31.1769i −0.832941 1.44270i −0.895696 0.444667i $$-0.853322\pi$$
0.0627555 0.998029i $$-0.480011\pi$$
$$468$$ −4.00000 −0.184900
$$469$$ 5.00000 25.9808i 0.230879 1.19968i
$$470$$ 18.0000 0.830278
$$471$$ 2.00000 + 3.46410i 0.0921551 + 0.159617i
$$472$$ 1.50000 2.59808i 0.0690431 0.119586i
$$473$$ 15.0000 25.9808i 0.689701 1.19460i
$$474$$ −0.500000 0.866025i −0.0229658 0.0397779i
$$475$$ −16.0000 −0.734130
$$476$$ 0 0
$$477$$ −3.00000 −0.137361
$$478$$ −12.0000 20.7846i −0.548867 0.950666i
$$479$$ 9.00000 15.5885i 0.411220 0.712255i −0.583803 0.811895i $$-0.698436\pi$$
0.995023 + 0.0996406i $$0.0317693\pi$$
$$480$$ 1.50000 2.59808i 0.0684653 0.118585i
$$481$$ 16.0000 + 27.7128i 0.729537 + 1.26360i
$$482$$ 1.00000 0.0455488
$$483$$ 0 0
$$484$$ −2.00000 −0.0909091
$$485$$ 1.50000 + 2.59808i 0.0681115 + 0.117973i
$$486$$ 0.500000 0.866025i 0.0226805 0.0392837i
$$487$$ −20.5000 + 35.5070i −0.928944 + 1.60898i −0.143851 + 0.989599i $$0.545949\pi$$
−0.785093 + 0.619378i $$0.787385\pi$$
$$488$$ −5.00000 8.66025i −0.226339 0.392031i
$$489$$ −16.0000 −0.723545
$$490$$ −3.00000 20.7846i −0.135526 0.938953i
$$491$$ −33.0000 −1.48927 −0.744635 0.667472i $$-0.767376\pi$$
−0.744635 + 0.667472i $$0.767376\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 8.00000 13.8564i 0.359937 0.623429i
$$495$$ −4.50000 7.79423i −0.202260 0.350325i
$$496$$ −1.00000 −0.0449013
$$497$$ −15.0000 + 5.19615i −0.672842 + 0.233079i
$$498$$ 9.00000 0.403300
$$499$$ −1.00000 1.73205i −0.0447661 0.0775372i 0.842774 0.538267i $$-0.180921\pi$$
−0.887540 + 0.460730i $$0.847588\pi$$
$$500$$ 1.50000 2.59808i 0.0670820 0.116190i
$$501$$ −3.00000 + 5.19615i −0.134030 + 0.232147i
$$502$$ 13.5000 + 23.3827i 0.602534 + 1.04362i
$$503$$ −12.0000 −0.535054 −0.267527 0.963550i $$-0.586206\pi$$
−0.267527 + 0.963550i $$0.586206\pi$$
$$504$$ 2.00000 + 1.73205i 0.0890871 + 0.0771517i
$$505$$ −54.0000 −2.40297
$$506$$ 0 0
$$507$$ −1.50000 + 2.59808i −0.0666173 + 0.115385i
$$508$$ −2.50000 + 4.33013i −0.110920 + 0.192118i
$$509$$ 1.50000 + 2.59808i 0.0664863 + 0.115158i 0.897352 0.441315i $$-0.145488\pi$$
−0.830866 + 0.556473i $$0.812154\pi$$
$$510$$ 0 0
$$511$$ −1.00000 + 5.19615i −0.0442374 + 0.229864i
$$512$$ −1.00000 −0.0441942
$$513$$ 2.00000 + 3.46410i 0.0883022 + 0.152944i
$$514$$ 3.00000 5.19615i 0.132324 0.229192i
$$515$$ −12.0000 + 20.7846i −0.528783 + 0.915879i
$$516$$ 5.00000 + 8.66025i 0.220113 + 0.381246i
$$517$$ −18.0000 −0.791639
$$518$$ 4.00000 20.7846i 0.175750 0.913223i
$$519$$ 18.0000 0.790112
$$520$$ −6.00000 10.3923i −0.263117 0.455733i
$$521$$ 9.00000 15.5885i 0.394297 0.682943i −0.598714 0.800963i $$-0.704321\pi$$
0.993011 + 0.118020i $$0.0376547\pi$$
$$522$$ 4.50000 7.79423i 0.196960 0.341144i
$$523$$ 2.00000 + 3.46410i 0.0874539 + 0.151475i 0.906434 0.422347i $$-0.138794\pi$$
−0.818980 + 0.573822i $$0.805460\pi$$
$$524$$ −9.00000 −0.393167
$$525$$ −8.00000 6.92820i −0.349149 0.302372i
$$526$$ 6.00000 0.261612
$$527$$ 0 0
$$528$$ −1.50000 + 2.59808i −0.0652791 + 0.113067i
$$529$$ 11.5000 19.9186i 0.500000 0.866025i
$$530$$ −4.50000 7.79423i −0.195468 0.338560i
$$531$$ 3.00000 0.130189
$$532$$ −10.0000 + 3.46410i −0.433555 + 0.150188i
$$533$$ 0 0
$$534$$ 3.00000 + 5.19615i 0.129823 + 0.224860i
$$535$$ 4.50000 7.79423i 0.194552 0.336974i
$$536$$ −5.00000 + 8.66025i −0.215967 + 0.374066i
$$537$$ −6.00000 10.3923i −0.258919 0.448461i
$$538$$ −21.0000 −0.905374
$$539$$ 3.00000 + 20.7846i 0.129219 + 0.895257i
$$540$$ 3.00000 0.129099
$$541$$ −13.0000 22.5167i −0.558914 0.968067i −0.997587 0.0694205i $$-0.977885\pi$$
0.438674 0.898646i $$-0.355448\pi$$
$$542$$ 5.50000 9.52628i 0.236245 0.409189i
$$543$$ −4.00000 + 6.92820i −0.171656 + 0.297318i
$$544$$ 0 0
$$545$$ 42.0000 1.79908
$$546$$ 10.0000 3.46410i 0.427960 0.148250i
$$547$$ 8.00000 0.342055 0.171028 0.985266i $$-0.445291\pi$$
0.171028 + 0.985266i $$0.445291\pi$$
$$548$$ −9.00000 15.5885i −0.384461 0.665906i
$$549$$ 5.00000 8.66025i 0.213395 0.369611i
$$550$$ 6.00000 10.3923i 0.255841 0.443129i
$$551$$ 18.0000 + 31.1769i 0.766826 + 1.32818i
$$552$$ 0 0
$$553$$ 2.00000 + 1.73205i 0.0850487 + 0.0736543i
$$554$$ −8.00000 −0.339887
$$555$$ −12.0000 20.7846i −0.509372 0.882258i
$$556$$ −1.00000 + 1.73205i −0.0424094 + 0.0734553i
$$557$$ −1.50000 + 2.59808i −0.0635570 + 0.110084i −0.896053 0.443947i $$-0.853578\pi$$
0.832496 + 0.554031i $$0.186911\pi$$
$$558$$ −0.500000 0.866025i −0.0211667 0.0366618i
$$559$$ 40.0000 1.69182
$$560$$ −1.50000 + 7.79423i −0.0633866 + 0.329366i
$$561$$ 0 0
$$562$$ 3.00000 + 5.19615i 0.126547 + 0.219186i
$$563$$ −19.5000 + 33.7750i −0.821827 + 1.42345i 0.0824933 + 0.996592i $$0.473712\pi$$
−0.904320 + 0.426855i $$0.859622\pi$$
$$564$$ 3.00000 5.19615i 0.126323 0.218797i
$$565$$ 0 0
$$566$$ −14.0000 −0.588464
$$567$$ −0.500000 + 2.59808i −0.0209980 + 0.109109i
$$568$$ 6.00000 0.251754
$$569$$ 18.0000 + 31.1769i 0.754599 + 1.30700i 0.945573 + 0.325409i $$0.105502\pi$$
−0.190974 + 0.981595i $$0.561165\pi$$
$$570$$ −6.00000 + 10.3923i −0.251312 + 0.435286i
$$571$$ 17.0000 29.4449i 0.711428 1.23223i −0.252893 0.967494i $$-0.581382\pi$$
0.964321 0.264735i $$-0.0852845\pi$$
$$572$$ 6.00000 + 10.3923i 0.250873 + 0.434524i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −0.500000 0.866025i −0.0208333 0.0360844i
$$577$$ −11.5000 + 19.9186i −0.478751 + 0.829222i −0.999703 0.0243645i $$-0.992244\pi$$
0.520952 + 0.853586i $$0.325577\pi$$
$$578$$ −8.50000 + 14.7224i −0.353553 + 0.612372i
$$579$$ 9.50000 + 16.4545i 0.394807 + 0.683825i
$$580$$ 27.0000 1.12111
$$581$$ −22.5000 + 7.79423i −0.933457 + 0.323359i
$$582$$ 1.00000 0.0414513
$$583$$ 4.50000 + 7.79423i 0.186371 + 0.322804i
$$584$$ 1.00000 1.73205i 0.0413803 0.0716728i
$$585$$ 6.00000 10.3923i 0.248069 0.429669i
$$586$$ 16.5000 + 28.5788i 0.681609 + 1.18058i
$$587$$ 21.0000 0.866763 0.433381 0.901211i $$-0.357320\pi$$
0.433381 + 0.901211i $$0.357320\pi$$
$$588$$ −6.50000 2.59808i −0.268055 0.107143i
$$589$$ 4.00000 0.164817
$$590$$ 4.50000 + 7.79423i 0.185262 + 0.320883i
$$591$$ −3.00000 + 5.19615i −0.123404 + 0.213741i
$$592$$ −4.00000 + 6.92820i −0.164399 + 0.284747i
$$593$$ −12.0000 20.7846i −0.492781 0.853522i 0.507184 0.861838i $$-0.330686\pi$$
−0.999965 + 0.00831589i $$0.997353\pi$$
$$594$$ −3.00000 −0.123091
$$595$$ 0 0
$$596$$ 18.0000 0.737309
$$597$$ −10.0000 17.3205i −0.409273 0.708881i
$$598$$ 0 0
$$599$$ 9.00000 15.5885i 0.367730 0.636927i −0.621480 0.783430i $$-0.713468\pi$$
0.989210 + 0.146503i $$0.0468017\pi$$
$$600$$ 2.00000 + 3.46410i 0.0816497 + 0.141421i
$$601$$ 11.0000 0.448699 0.224350 0.974509i $$-0.427974\pi$$
0.224350 + 0.974509i $$0.427974\pi$$
$$602$$ −20.0000 17.3205i −0.815139 0.705931i
$$603$$ −10.0000 −0.407231
$$604$$ 0.500000 + 0.866025i 0.0203447 + 0.0352381i
$$605$$ 3.00000 5.19615i 0.121967 0.211254i
$$606$$ −9.00000 + 15.5885i −0.365600 + 0.633238i
$$607$$ 3.50000 + 6.06218i 0.142061 + 0.246056i 0.928272 0.371901i $$-0.121294\pi$$
−0.786212 + 0.617957i $$0.787961\pi$$
$$608$$ 4.00000 0.162221
$$609$$ −4.50000 + 23.3827i −0.182349 + 0.947514i
$$610$$ 30.0000 1.21466
$$611$$ −12.0000 20.7846i −0.485468 0.840855i
$$612$$ 0 0
$$613$$ 8.00000 13.8564i 0.323117 0.559655i −0.658012 0.753007i $$-0.728603\pi$$
0.981129 + 0.193352i $$0.0619359\pi$$
$$614$$ 4.00000 + 6.92820i 0.161427 + 0.279600i
$$615$$ 0 0
$$616$$ 1.50000 7.79423i 0.0604367 0.314038i
$$617$$ −6.00000 −0.241551 −0.120775 0.992680i $$-0.538538\pi$$
−0.120775 + 0.992680i $$0.538538\pi$$
$$618$$ 4.00000 + 6.92820i 0.160904 + 0.278693i
$$619$$ 17.0000 29.4449i 0.683288 1.18349i −0.290684 0.956819i $$-0.593883\pi$$
0.973972 0.226670i $$-0.0727838\pi$$
$$620$$ 1.50000 2.59808i 0.0602414 0.104341i
$$621$$ 0 0
$$622$$ −24.0000 −0.962312
$$623$$ −12.0000 10.3923i −0.480770 0.416359i
$$624$$ −4.00000 −0.160128
$$625$$ 14.5000 + 25.1147i 0.580000 + 1.00459i
$$626$$ −15.5000 + 26.8468i −0.619505 + 1.07301i
$$627$$ 6.00000 10.3923i 0.239617 0.415029i
$$628$$ 2.00000 + 3.46410i 0.0798087 + 0.138233i
$$629$$ 0 0
$$630$$ −7.50000 + 2.59808i −0.298807 + 0.103510i
$$631$$ −7.00000 −0.278666 −0.139333 0.990246i $$-0.544496\pi$$
−0.139333 + 0.990246i $$0.544496\pi$$
$$632$$ −0.500000 0.866025i −0.0198889 0.0344486i
$$633$$ −7.00000 + 12.1244i −0.278225 + 0.481900i
$$634$$ 4.50000 7.79423i 0.178718 0.309548i
$$635$$ −7.50000 12.9904i −0.297628 0.515508i
$$636$$ −3.00000 −0.118958
$$637$$ −22.0000 + 17.3205i −0.871672 + 0.686264i
$$638$$ −27.0000 −1.06894
$$639$$ 3.00000 + 5.19615i 0.118678 + 0.205557i
$$640$$ 1.50000 2.59808i 0.0592927 0.102698i
$$641$$ 15.0000 25.9808i 0.592464 1.02618i −0.401435 0.915888i $$-0.631488\pi$$
0.993899 0.110291i $$-0.0351782\pi$$
$$642$$ −1.50000 2.59808i −0.0592003 0.102538i
$$643$$ −34.0000 −1.34083 −0.670415 0.741987i $$-0.733884\pi$$
−0.670415 + 0.741987i $$0.733884\pi$$
$$644$$ 0 0
$$645$$ −30.0000 −1.18125
$$646$$ 0 0
$$647$$ 9.00000 15.5885i 0.353827 0.612845i −0.633090 0.774078i $$-0.718214\pi$$
0.986916 + 0.161233i $$0.0515470\pi$$
$$648$$ 0.500000 0.866025i 0.0196419 0.0340207i
$$649$$ −4.50000 7.79423i −0.176640 0.305950i
$$650$$ 16.0000 0.627572
$$651$$ 2.00000 + 1.73205i 0.0783862 + 0.0678844i
$$652$$ −16.0000 −0.626608
$$653$$ −1.50000 2.59808i −0.0586995 0.101671i 0.835182 0.549973i $$-0.185362\pi$$
−0.893882 + 0.448303i $$0.852029\pi$$
$$654$$ 7.00000 12.1244i 0.273722 0.474100i
$$655$$ 13.5000 23.3827i 0.527489 0.913637i
$$656$$ 0 0
$$657$$ 2.00000 0.0780274
$$658$$ −3.00000 + 15.5885i −0.116952 + 0.607701i
$$659$$ −24.0000 −0.934907 −0.467454 0.884018i $$-0.654829\pi$$
−0.467454 + 0.884018i $$0.654829\pi$$
$$660$$ −4.50000 7.79423i −0.175162 0.303390i
$$661$$ −7.00000 + 12.1244i −0.272268 + 0.471583i −0.969442 0.245319i $$-0.921107\pi$$
0.697174 + 0.716902i $$0.254441\pi$$
$$662$$ 10.0000 17.3205i 0.388661 0.673181i
$$663$$ 0 0
$$664$$ 9.00000 0.349268
$$665$$ 6.00000 31.1769i 0.232670 1.20899i
$$666$$ −8.00000 −0.309994
$$667$$ 0 0
$$668$$ −3.00000 + 5.19615i −0.116073 + 0.201045i
$$669$$ 9.50000 16.4545i 0.367291 0.636167i
$$670$$ −15.0000 25.9808i −0.579501 1.00372i
$$671$$ −30.0000 −1.15814
$$672$$ 2.00000 + 1.73205i 0.0771517 + 0.0668153i
$$673$$ 29.0000 1.11787 0.558934 0.829212i $$-0.311211\pi$$
0.558934 + 0.829212i $$0.311211\pi$$
$$674$$ −3.50000 6.06218i −0.134815 0.233506i
$$675$$ −2.00000 + 3.46410i −0.0769800 + 0.133333i
$$676$$ −1.50000 + 2.59808i −0.0576923 + 0.0999260i
$$677$$ 16.5000 + 28.5788i 0.634147 + 1.09837i 0.986695 + 0.162581i $$0.0519817\pi$$
−0.352549 + 0.935793i $$0.614685\pi$$
$$678$$ 0 0
$$679$$ −2.50000 + 0.866025i −0.0959412 + 0.0332350i
$$680$$ 0 0
$$681$$ 13.5000 + 23.3827i 0.517321 + 0.896026i
$$682$$ −1.50000 + 2.59808i −0.0574380 + 0.0994855i
$$683$$ −16.5000 + 28.5788i −0.631355 + 1.09354i 0.355920 + 0.934516i $$0.384168\pi$$
−0.987275 + 0.159022i $$0.949166\pi$$
$$684$$ 2.00000 + 3.46410i 0.0764719 + 0.132453i
$$685$$ 54.0000 2.06323
$$686$$ 18.5000 + 0.866025i 0.706333 + 0.0330650i
$$687$$ −4.00000 −0.152610
$$688$$ 5.00000 + 8.66025i 0.190623 + 0.330169i
$$689$$ −6.00000 + 10.3923i −0.228582 + 0.395915i
$$690$$ 0 0
$$691$$ −4.00000 6.92820i −0.152167 0.263561i 0.779857 0.625958i $$-0.215292\pi$$
−0.932024 + 0.362397i $$0.881959\pi$$
$$692$$ 18.0000 0.684257
$$693$$ 7.50000 2.59808i 0.284901 0.0986928i
$$694$$ −12.0000 −0.455514
$$695$$ −3.00000 5.19615i −0.113796 0.197101i
$$696$$ 4.50000 7.79423i 0.170572 0.295439i
$$697$$ 0 0
$$698$$ 13.0000 + 22.5167i 0.492057 + 0.852268i
$$699$$ −24.0000 −0.907763
$$700$$ −8.00000 6.92820i −0.302372 0.261861i
$$701$$ −15.0000 −0.566542 −0.283271 0.959040i $$-0.591420\pi$$
−0.283271 + 0.959040i $$0.591420\pi$$
$$702$$ −2.00000 3.46410i −0.0754851 0.130744i
$$703$$ 16.0000 27.7128i 0.603451 1.04521i
$$704$$ −1.50000 + 2.59808i −0.0565334 + 0.0979187i
$$705$$ 9.00000 + 15.5885i 0.338960 + 0.587095i
$$706$$ −24.0000 −0.903252
$$707$$ 9.00000 46.7654i 0.338480 1.75879i
$$708$$ 3.00000 0.112747
$$709$$ 5.00000 + 8.66025i 0.187779 + 0.325243i 0.944509 0.328484i $$-0.106538\pi$$
−0.756730 + 0.653727i $$0.773204\pi$$
$$710$$ −9.00000 + 15.5885i −0.337764 + 0.585024i
$$711$$ 0.500000 0.866025i 0.0187515 0.0324785i
$$712$$ 3.00000 + 5.19615i 0.112430 + 0.194734i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ −36.0000 −1.34632
$$716$$ −6.00000 10.3923i −0.224231 0.388379i
$$717$$ 12.0000 20.7846i 0.448148 0.776215i
$$718$$ 15.0000 25.9808i 0.559795 0.969593i
$$719$$ 9.00000 + 15.5885i 0.335643 + 0.581351i 0.983608 0.180319i $$-0.0577130\pi$$
−0.647965 + 0.761670i $$0.724380\pi$$
$$720$$ 3.00000 0.111803
$$721$$ −16.0000 13.8564i −0.595871 0.516040i
$$722$$ 3.00000 0.111648
$$723$$ 0.500000 + 0.866025i 0.0185952 + 0.0322078i
$$724$$ −4.00000 + 6.92820i −0.148659 + 0.257485i
$$725$$ −18.0000 + 31.1769i −0.668503 + 1.15788i
$$726$$ −1.00000 1.73205i −0.0371135 0.0642824i
$$727$$ −13.0000 −0.482143 −0.241072 0.970507i $$-0.577499\pi$$
−0.241072 + 0.970507i $$0.577499\pi$$
$$728$$ 10.0000 3.46410i 0.370625 0.128388i
$$729$$ 1.00000 0.0370370
$$730$$ 3.00000 + 5.19615i 0.111035 + 0.192318i
$$731$$ 0 0
$$732$$ 5.00000 8.66025i 0.184805 0.320092i
$$733$$ 5.00000 + 8.66025i 0.184679 + 0.319874i 0.943468 0.331463i $$-0.107542\pi$$
−0.758789 + 0.651336i $$0.774209\pi$$
$$734$$ 19.0000 0.701303
$$735$$ 16.5000 12.9904i 0.608612 0.479157i
$$736$$ 0 0
$$737$$ 15.0000 + 25.9808i 0.552532 + 0.957014i
$$738$$ 0 0
$$739$$ −25.0000 + 43.3013i −0.919640 + 1.59286i −0.119677 + 0.992813i $$0.538186\pi$$
−0.799962 + 0.600050i $$0.795147\pi$$
$$740$$ −12.0000 20.7846i −0.441129 0.764057i
$$741$$ 16.0000 0.587775
$$742$$ 7.50000 2.59808i 0.275334 0.0953784i
$$743$$ 42.0000 1.54083 0.770415 0.637542i $$-0.220049\pi$$
0.770415 + 0.637542i $$0.220049\pi$$
$$744$$ −0.500000 0.866025i −0.0183309 0.0317500i
$$745$$ −27.0000 + 46.7654i −0.989203 + 1.71335i
$$746$$ 4.00000 6.92820i 0.146450 0.253660i
$$747$$ 4.50000 + 7.79423i 0.164646 + 0.285176i
$$748$$ 0 0
$$749$$ 6.00000 + 5.19615i 0.219235 + 0.189863i
$$750$$ 3.00000 0.109545
$$751$$ 3.50000 + 6.06218i 0.127717 + 0.221212i 0.922792 0.385299i $$-0.125902\pi$$
−0.795075 + 0.606511i $$0.792568\pi$$
$$752$$ 3.00000 5.19615i 0.109399 0.189484i
$$753$$ −13.5000 + 23.3827i −0.491967 + 0.852112i
$$754$$ −18.0000 31.1769i −0.655521 1.13540i
$$755$$ −3.00000 −0.109181
$$756$$ −0.500000 + 2.59808i −0.0181848 + 0.0944911i
$$757$$ 38.0000 1.38113 0.690567 0.723269i $$-0.257361\pi$$
0.690567 + 0.723269i $$0.257361\pi$$
$$758$$ 4.00000 + 6.92820i 0.145287 + 0.251644i
$$759$$ 0 0
$$760$$ −6.00000 + 10.3923i −0.217643 + 0.376969i
$$761$$ −6.00000 10.3923i −0.217500 0.376721i 0.736543 0.676391i $$-0.236457\pi$$
−0.954043 + 0.299670i $$0.903123\pi$$
$$762$$ −5.00000 −0.181131
$$763$$ −7.00000 + 36.3731i −0.253417 + 1.31679i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 9.00000 15.5885i 0.325183 0.563234i
$$767$$ 6.00000 10.3923i 0.216647 0.375244i
$$768$$ −0.500000 0.866025i −0.0180422 0.0312500i
$$769$$ −19.0000 −0.685158 −0.342579 0.939489i $$-0.611300\pi$$
−0.342579 + 0.939489i $$0.611300\pi$$
$$770$$ 18.0000 + 15.5885i 0.648675 + 0.561769i
$$771$$ 6.00000 0.216085
$$772$$ 9.50000 + 16.4545i 0.341912 + 0.592210i
$$773$$ −3.00000 + 5.19615i −0.107903 + 0.186893i −0.914920 0.403634i $$-0.867747\pi$$
0.807018 + 0.590527i $$0.201080\pi$$
$$774$$ −5.00000 + 8.66025i −0.179721 + 0.311286i
$$775$$ 2.00000 + 3.46410i 0.0718421 + 0.124434i
$$776$$ 1.00000 0.0358979
$$777$$ 20.0000 6.92820i 0.717496 0.248548i
$$778$$ 6.00000 0.215110
$$779$$ 0 0
$$780$$ 6.00000 10.3923i 0.214834 0.372104i
$$781$$ 9.00000 15.5885i