# Properties

 Label 74.2.c.a.47.1 Level $74$ Weight $2$ Character 74.47 Analytic conductor $0.591$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$74 = 2 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 74.c (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.590892974957$$ 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: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 47.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 74.47 Dual form 74.2.c.a.63.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -2.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -2.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} +2.00000 q^{11} +(-1.00000 + 1.73205i) q^{12} +(3.00000 + 5.19615i) q^{13} +(1.00000 - 1.73205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-1.00000 - 1.73205i) q^{19} +(0.500000 - 0.866025i) q^{20} +(1.00000 - 1.73205i) q^{22} -6.00000 q^{23} +(1.00000 + 1.73205i) q^{24} +(2.00000 - 3.46410i) q^{25} +6.00000 q^{26} -4.00000 q^{27} -9.00000 q^{29} +(-1.00000 - 1.73205i) q^{30} +10.0000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.00000 - 3.46410i) q^{33} +(1.50000 + 2.59808i) q^{34} +1.00000 q^{36} +(-0.500000 + 6.06218i) q^{37} -2.00000 q^{38} +(6.00000 - 10.3923i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-1.50000 - 2.59808i) q^{41} -8.00000 q^{43} +(-1.00000 - 1.73205i) q^{44} -1.00000 q^{45} +(-3.00000 + 5.19615i) q^{46} +2.00000 q^{47} +2.00000 q^{48} +(3.50000 - 6.06218i) q^{49} +(-2.00000 - 3.46410i) q^{50} +6.00000 q^{51} +(3.00000 - 5.19615i) q^{52} +(3.00000 - 5.19615i) q^{53} +(-2.00000 + 3.46410i) q^{54} +(1.00000 + 1.73205i) q^{55} +(-2.00000 + 3.46410i) q^{57} +(-4.50000 + 7.79423i) q^{58} +(-4.00000 + 6.92820i) q^{59} -2.00000 q^{60} +(2.50000 + 4.33013i) q^{61} +(5.00000 - 8.66025i) q^{62} +1.00000 q^{64} +(-3.00000 + 5.19615i) q^{65} -4.00000 q^{66} +(3.00000 + 5.19615i) q^{67} +3.00000 q^{68} +(6.00000 + 10.3923i) q^{69} +(0.500000 - 0.866025i) q^{72} -2.00000 q^{73} +(5.00000 + 3.46410i) q^{74} -8.00000 q^{75} +(-1.00000 + 1.73205i) q^{76} +(-6.00000 - 10.3923i) q^{78} +(-3.00000 - 5.19615i) q^{79} -1.00000 q^{80} +(5.50000 + 9.52628i) q^{81} -3.00000 q^{82} +(-1.00000 + 1.73205i) q^{83} -3.00000 q^{85} +(-4.00000 + 6.92820i) q^{86} +(9.00000 + 15.5885i) q^{87} -2.00000 q^{88} +(6.50000 - 11.2583i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(3.00000 + 5.19615i) q^{92} +(-10.0000 - 17.3205i) q^{93} +(1.00000 - 1.73205i) q^{94} +(1.00000 - 1.73205i) q^{95} +(1.00000 - 1.73205i) q^{96} +3.00000 q^{97} +(-3.50000 - 6.06218i) q^{98} +(-1.00000 + 1.73205i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{2} - 2 q^{3} - q^{4} + q^{5} - 4 q^{6} - 2 q^{8} - q^{9}+O(q^{10})$$ 2 * q + q^2 - 2 * q^3 - q^4 + q^5 - 4 * q^6 - 2 * q^8 - q^9 $$2 q + q^{2} - 2 q^{3} - q^{4} + q^{5} - 4 q^{6} - 2 q^{8} - q^{9} + 2 q^{10} + 4 q^{11} - 2 q^{12} + 6 q^{13} + 2 q^{15} - q^{16} - 3 q^{17} + q^{18} - 2 q^{19} + q^{20} + 2 q^{22} - 12 q^{23} + 2 q^{24} + 4 q^{25} + 12 q^{26} - 8 q^{27} - 18 q^{29} - 2 q^{30} + 20 q^{31} + q^{32} - 4 q^{33} + 3 q^{34} + 2 q^{36} - q^{37} - 4 q^{38} + 12 q^{39} - q^{40} - 3 q^{41} - 16 q^{43} - 2 q^{44} - 2 q^{45} - 6 q^{46} + 4 q^{47} + 4 q^{48} + 7 q^{49} - 4 q^{50} + 12 q^{51} + 6 q^{52} + 6 q^{53} - 4 q^{54} + 2 q^{55} - 4 q^{57} - 9 q^{58} - 8 q^{59} - 4 q^{60} + 5 q^{61} + 10 q^{62} + 2 q^{64} - 6 q^{65} - 8 q^{66} + 6 q^{67} + 6 q^{68} + 12 q^{69} + q^{72} - 4 q^{73} + 10 q^{74} - 16 q^{75} - 2 q^{76} - 12 q^{78} - 6 q^{79} - 2 q^{80} + 11 q^{81} - 6 q^{82} - 2 q^{83} - 6 q^{85} - 8 q^{86} + 18 q^{87} - 4 q^{88} + 13 q^{89} - q^{90} + 6 q^{92} - 20 q^{93} + 2 q^{94} + 2 q^{95} + 2 q^{96} + 6 q^{97} - 7 q^{98} - 2 q^{99}+O(q^{100})$$ 2 * q + q^2 - 2 * q^3 - q^4 + q^5 - 4 * q^6 - 2 * q^8 - q^9 + 2 * q^10 + 4 * q^11 - 2 * q^12 + 6 * q^13 + 2 * q^15 - q^16 - 3 * q^17 + q^18 - 2 * q^19 + q^20 + 2 * q^22 - 12 * q^23 + 2 * q^24 + 4 * q^25 + 12 * q^26 - 8 * q^27 - 18 * q^29 - 2 * q^30 + 20 * q^31 + q^32 - 4 * q^33 + 3 * q^34 + 2 * q^36 - q^37 - 4 * q^38 + 12 * q^39 - q^40 - 3 * q^41 - 16 * q^43 - 2 * q^44 - 2 * q^45 - 6 * q^46 + 4 * q^47 + 4 * q^48 + 7 * q^49 - 4 * q^50 + 12 * q^51 + 6 * q^52 + 6 * q^53 - 4 * q^54 + 2 * q^55 - 4 * q^57 - 9 * q^58 - 8 * q^59 - 4 * q^60 + 5 * q^61 + 10 * q^62 + 2 * q^64 - 6 * q^65 - 8 * q^66 + 6 * q^67 + 6 * q^68 + 12 * q^69 + q^72 - 4 * q^73 + 10 * q^74 - 16 * q^75 - 2 * q^76 - 12 * q^78 - 6 * q^79 - 2 * q^80 + 11 * q^81 - 6 * q^82 - 2 * q^83 - 6 * q^85 - 8 * q^86 + 18 * q^87 - 4 * q^88 + 13 * q^89 - q^90 + 6 * q^92 - 20 * q^93 + 2 * q^94 + 2 * q^95 + 2 * q^96 + 6 * q^97 - 7 * q^98 - 2 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$$.

 $$n$$ $$39$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.500000 0.866025i 0.353553 0.612372i
$$3$$ −1.00000 1.73205i −0.577350 1.00000i −0.995782 0.0917517i $$-0.970753\pi$$
0.418432 0.908248i $$-0.362580\pi$$
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ 0.500000 + 0.866025i 0.223607 + 0.387298i 0.955901 0.293691i $$-0.0948835\pi$$
−0.732294 + 0.680989i $$0.761550\pi$$
$$6$$ −2.00000 −0.816497
$$7$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ −0.500000 + 0.866025i −0.166667 + 0.288675i
$$10$$ 1.00000 0.316228
$$11$$ 2.00000 0.603023 0.301511 0.953463i $$-0.402509\pi$$
0.301511 + 0.953463i $$0.402509\pi$$
$$12$$ −1.00000 + 1.73205i −0.288675 + 0.500000i
$$13$$ 3.00000 + 5.19615i 0.832050 + 1.44115i 0.896410 + 0.443227i $$0.146166\pi$$
−0.0643593 + 0.997927i $$0.520500\pi$$
$$14$$ 0 0
$$15$$ 1.00000 1.73205i 0.258199 0.447214i
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i $$-0.951855\pi$$
0.624780 + 0.780801i $$0.285189\pi$$
$$18$$ 0.500000 + 0.866025i 0.117851 + 0.204124i
$$19$$ −1.00000 1.73205i −0.229416 0.397360i 0.728219 0.685344i $$-0.240348\pi$$
−0.957635 + 0.287984i $$0.907015\pi$$
$$20$$ 0.500000 0.866025i 0.111803 0.193649i
$$21$$ 0 0
$$22$$ 1.00000 1.73205i 0.213201 0.369274i
$$23$$ −6.00000 −1.25109 −0.625543 0.780189i $$-0.715123\pi$$
−0.625543 + 0.780189i $$0.715123\pi$$
$$24$$ 1.00000 + 1.73205i 0.204124 + 0.353553i
$$25$$ 2.00000 3.46410i 0.400000 0.692820i
$$26$$ 6.00000 1.17670
$$27$$ −4.00000 −0.769800
$$28$$ 0 0
$$29$$ −9.00000 −1.67126 −0.835629 0.549294i $$-0.814897\pi$$
−0.835629 + 0.549294i $$0.814897\pi$$
$$30$$ −1.00000 1.73205i −0.182574 0.316228i
$$31$$ 10.0000 1.79605 0.898027 0.439941i $$-0.145001\pi$$
0.898027 + 0.439941i $$0.145001\pi$$
$$32$$ 0.500000 + 0.866025i 0.0883883 + 0.153093i
$$33$$ −2.00000 3.46410i −0.348155 0.603023i
$$34$$ 1.50000 + 2.59808i 0.257248 + 0.445566i
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ −0.500000 + 6.06218i −0.0821995 + 0.996616i
$$38$$ −2.00000 −0.324443
$$39$$ 6.00000 10.3923i 0.960769 1.66410i
$$40$$ −0.500000 0.866025i −0.0790569 0.136931i
$$41$$ −1.50000 2.59808i −0.234261 0.405751i 0.724797 0.688963i $$-0.241934\pi$$
−0.959058 + 0.283211i $$0.908600\pi$$
$$42$$ 0 0
$$43$$ −8.00000 −1.21999 −0.609994 0.792406i $$-0.708828\pi$$
−0.609994 + 0.792406i $$0.708828\pi$$
$$44$$ −1.00000 1.73205i −0.150756 0.261116i
$$45$$ −1.00000 −0.149071
$$46$$ −3.00000 + 5.19615i −0.442326 + 0.766131i
$$47$$ 2.00000 0.291730 0.145865 0.989305i $$-0.453403\pi$$
0.145865 + 0.989305i $$0.453403\pi$$
$$48$$ 2.00000 0.288675
$$49$$ 3.50000 6.06218i 0.500000 0.866025i
$$50$$ −2.00000 3.46410i −0.282843 0.489898i
$$51$$ 6.00000 0.840168
$$52$$ 3.00000 5.19615i 0.416025 0.720577i
$$53$$ 3.00000 5.19615i 0.412082 0.713746i −0.583036 0.812447i $$-0.698135\pi$$
0.995117 + 0.0987002i $$0.0314685\pi$$
$$54$$ −2.00000 + 3.46410i −0.272166 + 0.471405i
$$55$$ 1.00000 + 1.73205i 0.134840 + 0.233550i
$$56$$ 0 0
$$57$$ −2.00000 + 3.46410i −0.264906 + 0.458831i
$$58$$ −4.50000 + 7.79423i −0.590879 + 1.02343i
$$59$$ −4.00000 + 6.92820i −0.520756 + 0.901975i 0.478953 + 0.877841i $$0.341016\pi$$
−0.999709 + 0.0241347i $$0.992317\pi$$
$$60$$ −2.00000 −0.258199
$$61$$ 2.50000 + 4.33013i 0.320092 + 0.554416i 0.980507 0.196485i $$-0.0629528\pi$$
−0.660415 + 0.750901i $$0.729619\pi$$
$$62$$ 5.00000 8.66025i 0.635001 1.09985i
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ −3.00000 + 5.19615i −0.372104 + 0.644503i
$$66$$ −4.00000 −0.492366
$$67$$ 3.00000 + 5.19615i 0.366508 + 0.634811i 0.989017 0.147802i $$-0.0472198\pi$$
−0.622509 + 0.782613i $$0.713886\pi$$
$$68$$ 3.00000 0.363803
$$69$$ 6.00000 + 10.3923i 0.722315 + 1.25109i
$$70$$ 0 0
$$71$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$72$$ 0.500000 0.866025i 0.0589256 0.102062i
$$73$$ −2.00000 −0.234082 −0.117041 0.993127i $$-0.537341\pi$$
−0.117041 + 0.993127i $$0.537341\pi$$
$$74$$ 5.00000 + 3.46410i 0.581238 + 0.402694i
$$75$$ −8.00000 −0.923760
$$76$$ −1.00000 + 1.73205i −0.114708 + 0.198680i
$$77$$ 0 0
$$78$$ −6.00000 10.3923i −0.679366 1.17670i
$$79$$ −3.00000 5.19615i −0.337526 0.584613i 0.646440 0.762964i $$-0.276257\pi$$
−0.983967 + 0.178352i $$0.942924\pi$$
$$80$$ −1.00000 −0.111803
$$81$$ 5.50000 + 9.52628i 0.611111 + 1.05848i
$$82$$ −3.00000 −0.331295
$$83$$ −1.00000 + 1.73205i −0.109764 + 0.190117i −0.915675 0.401920i $$-0.868343\pi$$
0.805910 + 0.592037i $$0.201676\pi$$
$$84$$ 0 0
$$85$$ −3.00000 −0.325396
$$86$$ −4.00000 + 6.92820i −0.431331 + 0.747087i
$$87$$ 9.00000 + 15.5885i 0.964901 + 1.67126i
$$88$$ −2.00000 −0.213201
$$89$$ 6.50000 11.2583i 0.688999 1.19338i −0.283164 0.959072i $$-0.591384\pi$$
0.972162 0.234309i $$-0.0752827\pi$$
$$90$$ −0.500000 + 0.866025i −0.0527046 + 0.0912871i
$$91$$ 0 0
$$92$$ 3.00000 + 5.19615i 0.312772 + 0.541736i
$$93$$ −10.0000 17.3205i −1.03695 1.79605i
$$94$$ 1.00000 1.73205i 0.103142 0.178647i
$$95$$ 1.00000 1.73205i 0.102598 0.177705i
$$96$$ 1.00000 1.73205i 0.102062 0.176777i
$$97$$ 3.00000 0.304604 0.152302 0.988334i $$-0.451331\pi$$
0.152302 + 0.988334i $$0.451331\pi$$
$$98$$ −3.50000 6.06218i −0.353553 0.612372i
$$99$$ −1.00000 + 1.73205i −0.100504 + 0.174078i
$$100$$ −4.00000 −0.400000
$$101$$ 7.00000 0.696526 0.348263 0.937397i $$-0.386772\pi$$
0.348263 + 0.937397i $$0.386772\pi$$
$$102$$ 3.00000 5.19615i 0.297044 0.514496i
$$103$$ −8.00000 −0.788263 −0.394132 0.919054i $$-0.628955\pi$$
−0.394132 + 0.919054i $$0.628955\pi$$
$$104$$ −3.00000 5.19615i −0.294174 0.509525i
$$105$$ 0 0
$$106$$ −3.00000 5.19615i −0.291386 0.504695i
$$107$$ −4.00000 6.92820i −0.386695 0.669775i 0.605308 0.795991i $$-0.293050\pi$$
−0.992003 + 0.126217i $$0.959717\pi$$
$$108$$ 2.00000 + 3.46410i 0.192450 + 0.333333i
$$109$$ 6.50000 11.2583i 0.622587 1.07835i −0.366415 0.930451i $$-0.619415\pi$$
0.989002 0.147901i $$-0.0472517\pi$$
$$110$$ 2.00000 0.190693
$$111$$ 11.0000 5.19615i 1.04407 0.493197i
$$112$$ 0 0
$$113$$ 5.00000 8.66025i 0.470360 0.814688i −0.529065 0.848581i $$-0.677457\pi$$
0.999425 + 0.0338931i $$0.0107906\pi$$
$$114$$ 2.00000 + 3.46410i 0.187317 + 0.324443i
$$115$$ −3.00000 5.19615i −0.279751 0.484544i
$$116$$ 4.50000 + 7.79423i 0.417815 + 0.723676i
$$117$$ −6.00000 −0.554700
$$118$$ 4.00000 + 6.92820i 0.368230 + 0.637793i
$$119$$ 0 0
$$120$$ −1.00000 + 1.73205i −0.0912871 + 0.158114i
$$121$$ −7.00000 −0.636364
$$122$$ 5.00000 0.452679
$$123$$ −3.00000 + 5.19615i −0.270501 + 0.468521i
$$124$$ −5.00000 8.66025i −0.449013 0.777714i
$$125$$ 9.00000 0.804984
$$126$$ 0 0
$$127$$ 7.00000 12.1244i 0.621150 1.07586i −0.368122 0.929777i $$-0.619999\pi$$
0.989272 0.146085i $$-0.0466674\pi$$
$$128$$ 0.500000 0.866025i 0.0441942 0.0765466i
$$129$$ 8.00000 + 13.8564i 0.704361 + 1.21999i
$$130$$ 3.00000 + 5.19615i 0.263117 + 0.455733i
$$131$$ −7.00000 + 12.1244i −0.611593 + 1.05931i 0.379379 + 0.925241i $$0.376138\pi$$
−0.990972 + 0.134069i $$0.957196\pi$$
$$132$$ −2.00000 + 3.46410i −0.174078 + 0.301511i
$$133$$ 0 0
$$134$$ 6.00000 0.518321
$$135$$ −2.00000 3.46410i −0.172133 0.298142i
$$136$$ 1.50000 2.59808i 0.128624 0.222783i
$$137$$ −21.0000 −1.79415 −0.897076 0.441877i $$-0.854313\pi$$
−0.897076 + 0.441877i $$0.854313\pi$$
$$138$$ 12.0000 1.02151
$$139$$ −7.00000 + 12.1244i −0.593732 + 1.02837i 0.399992 + 0.916519i $$0.369013\pi$$
−0.993724 + 0.111856i $$0.964321\pi$$
$$140$$ 0 0
$$141$$ −2.00000 3.46410i −0.168430 0.291730i
$$142$$ 0 0
$$143$$ 6.00000 + 10.3923i 0.501745 + 0.869048i
$$144$$ −0.500000 0.866025i −0.0416667 0.0721688i
$$145$$ −4.50000 7.79423i −0.373705 0.647275i
$$146$$ −1.00000 + 1.73205i −0.0827606 + 0.143346i
$$147$$ −14.0000 −1.15470
$$148$$ 5.50000 2.59808i 0.452097 0.213561i
$$149$$ −9.00000 −0.737309 −0.368654 0.929567i $$-0.620181\pi$$
−0.368654 + 0.929567i $$0.620181\pi$$
$$150$$ −4.00000 + 6.92820i −0.326599 + 0.565685i
$$151$$ −3.00000 5.19615i −0.244137 0.422857i 0.717752 0.696299i $$-0.245171\pi$$
−0.961888 + 0.273442i $$0.911838\pi$$
$$152$$ 1.00000 + 1.73205i 0.0811107 + 0.140488i
$$153$$ −1.50000 2.59808i −0.121268 0.210042i
$$154$$ 0 0
$$155$$ 5.00000 + 8.66025i 0.401610 + 0.695608i
$$156$$ −12.0000 −0.960769
$$157$$ 8.50000 14.7224i 0.678374 1.17498i −0.297097 0.954847i $$-0.596018\pi$$
0.975470 0.220131i $$-0.0706483\pi$$
$$158$$ −6.00000 −0.477334
$$159$$ −12.0000 −0.951662
$$160$$ −0.500000 + 0.866025i −0.0395285 + 0.0684653i
$$161$$ 0 0
$$162$$ 11.0000 0.864242
$$163$$ −2.00000 + 3.46410i −0.156652 + 0.271329i −0.933659 0.358162i $$-0.883403\pi$$
0.777007 + 0.629492i $$0.216737\pi$$
$$164$$ −1.50000 + 2.59808i −0.117130 + 0.202876i
$$165$$ 2.00000 3.46410i 0.155700 0.269680i
$$166$$ 1.00000 + 1.73205i 0.0776151 + 0.134433i
$$167$$ 10.0000 + 17.3205i 0.773823 + 1.34030i 0.935454 + 0.353450i $$0.114991\pi$$
−0.161630 + 0.986851i $$0.551675\pi$$
$$168$$ 0 0
$$169$$ −11.5000 + 19.9186i −0.884615 + 1.53220i
$$170$$ −1.50000 + 2.59808i −0.115045 + 0.199263i
$$171$$ 2.00000 0.152944
$$172$$ 4.00000 + 6.92820i 0.304997 + 0.528271i
$$173$$ −3.50000 + 6.06218i −0.266100 + 0.460899i −0.967851 0.251523i $$-0.919068\pi$$
0.701751 + 0.712422i $$0.252402\pi$$
$$174$$ 18.0000 1.36458
$$175$$ 0 0
$$176$$ −1.00000 + 1.73205i −0.0753778 + 0.130558i
$$177$$ 16.0000 1.20263
$$178$$ −6.50000 11.2583i −0.487196 0.843848i
$$179$$ 24.0000 1.79384 0.896922 0.442189i $$-0.145798\pi$$
0.896922 + 0.442189i $$0.145798\pi$$
$$180$$ 0.500000 + 0.866025i 0.0372678 + 0.0645497i
$$181$$ −5.50000 9.52628i −0.408812 0.708083i 0.585945 0.810351i $$-0.300723\pi$$
−0.994757 + 0.102268i $$0.967390\pi$$
$$182$$ 0 0
$$183$$ 5.00000 8.66025i 0.369611 0.640184i
$$184$$ 6.00000 0.442326
$$185$$ −5.50000 + 2.59808i −0.404368 + 0.191014i
$$186$$ −20.0000 −1.46647
$$187$$ −3.00000 + 5.19615i −0.219382 + 0.379980i
$$188$$ −1.00000 1.73205i −0.0729325 0.126323i
$$189$$ 0 0
$$190$$ −1.00000 1.73205i −0.0725476 0.125656i
$$191$$ 22.0000 1.59186 0.795932 0.605386i $$-0.206981\pi$$
0.795932 + 0.605386i $$0.206981\pi$$
$$192$$ −1.00000 1.73205i −0.0721688 0.125000i
$$193$$ 11.0000 0.791797 0.395899 0.918294i $$-0.370433\pi$$
0.395899 + 0.918294i $$0.370433\pi$$
$$194$$ 1.50000 2.59808i 0.107694 0.186531i
$$195$$ 12.0000 0.859338
$$196$$ −7.00000 −0.500000
$$197$$ 4.50000 7.79423i 0.320612 0.555316i −0.660003 0.751263i $$-0.729445\pi$$
0.980614 + 0.195947i $$0.0627782\pi$$
$$198$$ 1.00000 + 1.73205i 0.0710669 + 0.123091i
$$199$$ −20.0000 −1.41776 −0.708881 0.705328i $$-0.750800\pi$$
−0.708881 + 0.705328i $$0.750800\pi$$
$$200$$ −2.00000 + 3.46410i −0.141421 + 0.244949i
$$201$$ 6.00000 10.3923i 0.423207 0.733017i
$$202$$ 3.50000 6.06218i 0.246259 0.426533i
$$203$$ 0 0
$$204$$ −3.00000 5.19615i −0.210042 0.363803i
$$205$$ 1.50000 2.59808i 0.104765 0.181458i
$$206$$ −4.00000 + 6.92820i −0.278693 + 0.482711i
$$207$$ 3.00000 5.19615i 0.208514 0.361158i
$$208$$ −6.00000 −0.416025
$$209$$ −2.00000 3.46410i −0.138343 0.239617i
$$210$$ 0 0
$$211$$ −12.0000 −0.826114 −0.413057 0.910705i $$-0.635539\pi$$
−0.413057 + 0.910705i $$0.635539\pi$$
$$212$$ −6.00000 −0.412082
$$213$$ 0 0
$$214$$ −8.00000 −0.546869
$$215$$ −4.00000 6.92820i −0.272798 0.472500i
$$216$$ 4.00000 0.272166
$$217$$ 0 0
$$218$$ −6.50000 11.2583i −0.440236 0.762510i
$$219$$ 2.00000 + 3.46410i 0.135147 + 0.234082i
$$220$$ 1.00000 1.73205i 0.0674200 0.116775i
$$221$$ −18.0000 −1.21081
$$222$$ 1.00000 12.1244i 0.0671156 0.813733i
$$223$$ 2.00000 0.133930 0.0669650 0.997755i $$-0.478668\pi$$
0.0669650 + 0.997755i $$0.478668\pi$$
$$224$$ 0 0
$$225$$ 2.00000 + 3.46410i 0.133333 + 0.230940i
$$226$$ −5.00000 8.66025i −0.332595 0.576072i
$$227$$ −15.0000 25.9808i −0.995585 1.72440i −0.579082 0.815270i $$-0.696589\pi$$
−0.416503 0.909134i $$-0.636745\pi$$
$$228$$ 4.00000 0.264906
$$229$$ 8.50000 + 14.7224i 0.561696 + 0.972886i 0.997349 + 0.0727709i $$0.0231842\pi$$
−0.435653 + 0.900115i $$0.643482\pi$$
$$230$$ −6.00000 −0.395628
$$231$$ 0 0
$$232$$ 9.00000 0.590879
$$233$$ −1.00000 −0.0655122 −0.0327561 0.999463i $$-0.510428\pi$$
−0.0327561 + 0.999463i $$0.510428\pi$$
$$234$$ −3.00000 + 5.19615i −0.196116 + 0.339683i
$$235$$ 1.00000 + 1.73205i 0.0652328 + 0.112987i
$$236$$ 8.00000 0.520756
$$237$$ −6.00000 + 10.3923i −0.389742 + 0.675053i
$$238$$ 0 0
$$239$$ −2.00000 + 3.46410i −0.129369 + 0.224074i −0.923432 0.383761i $$-0.874629\pi$$
0.794063 + 0.607835i $$0.207962\pi$$
$$240$$ 1.00000 + 1.73205i 0.0645497 + 0.111803i
$$241$$ 5.00000 + 8.66025i 0.322078 + 0.557856i 0.980917 0.194429i $$-0.0622852\pi$$
−0.658838 + 0.752285i $$0.728952\pi$$
$$242$$ −3.50000 + 6.06218i −0.224989 + 0.389692i
$$243$$ 5.00000 8.66025i 0.320750 0.555556i
$$244$$ 2.50000 4.33013i 0.160046 0.277208i
$$245$$ 7.00000 0.447214
$$246$$ 3.00000 + 5.19615i 0.191273 + 0.331295i
$$247$$ 6.00000 10.3923i 0.381771 0.661247i
$$248$$ −10.0000 −0.635001
$$249$$ 4.00000 0.253490
$$250$$ 4.50000 7.79423i 0.284605 0.492950i
$$251$$ 20.0000 1.26239 0.631194 0.775625i $$-0.282565\pi$$
0.631194 + 0.775625i $$0.282565\pi$$
$$252$$ 0 0
$$253$$ −12.0000 −0.754434
$$254$$ −7.00000 12.1244i −0.439219 0.760750i
$$255$$ 3.00000 + 5.19615i 0.187867 + 0.325396i
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ −9.50000 + 16.4545i −0.592594 + 1.02640i 0.401288 + 0.915952i $$0.368563\pi$$
−0.993882 + 0.110450i $$0.964771\pi$$
$$258$$ 16.0000 0.996116
$$259$$ 0 0
$$260$$ 6.00000 0.372104
$$261$$ 4.50000 7.79423i 0.278543 0.482451i
$$262$$ 7.00000 + 12.1244i 0.432461 + 0.749045i
$$263$$ 12.0000 + 20.7846i 0.739952 + 1.28163i 0.952517 + 0.304487i $$0.0984850\pi$$
−0.212565 + 0.977147i $$0.568182\pi$$
$$264$$ 2.00000 + 3.46410i 0.123091 + 0.213201i
$$265$$ 6.00000 0.368577
$$266$$ 0 0
$$267$$ −26.0000 −1.59117
$$268$$ 3.00000 5.19615i 0.183254 0.317406i
$$269$$ 2.00000 0.121942 0.0609711 0.998140i $$-0.480580\pi$$
0.0609711 + 0.998140i $$0.480580\pi$$
$$270$$ −4.00000 −0.243432
$$271$$ −3.00000 + 5.19615i −0.182237 + 0.315644i −0.942642 0.333805i $$-0.891667\pi$$
0.760405 + 0.649449i $$0.225000\pi$$
$$272$$ −1.50000 2.59808i −0.0909509 0.157532i
$$273$$ 0 0
$$274$$ −10.5000 + 18.1865i −0.634328 + 1.09869i
$$275$$ 4.00000 6.92820i 0.241209 0.417786i
$$276$$ 6.00000 10.3923i 0.361158 0.625543i
$$277$$ 10.5000 + 18.1865i 0.630884 + 1.09272i 0.987371 + 0.158423i $$0.0506409\pi$$
−0.356488 + 0.934300i $$0.616026\pi$$
$$278$$ 7.00000 + 12.1244i 0.419832 + 0.727171i
$$279$$ −5.00000 + 8.66025i −0.299342 + 0.518476i
$$280$$ 0 0
$$281$$ 4.50000 7.79423i 0.268447 0.464965i −0.700014 0.714130i $$-0.746823\pi$$
0.968461 + 0.249165i $$0.0801561\pi$$
$$282$$ −4.00000 −0.238197
$$283$$ −2.00000 3.46410i −0.118888 0.205919i 0.800439 0.599414i $$-0.204600\pi$$
−0.919327 + 0.393494i $$0.871266\pi$$
$$284$$ 0 0
$$285$$ −4.00000 −0.236940
$$286$$ 12.0000 0.709575
$$287$$ 0 0
$$288$$ −1.00000 −0.0589256
$$289$$ 4.00000 + 6.92820i 0.235294 + 0.407541i
$$290$$ −9.00000 −0.528498
$$291$$ −3.00000 5.19615i −0.175863 0.304604i
$$292$$ 1.00000 + 1.73205i 0.0585206 + 0.101361i
$$293$$ −3.50000 6.06218i −0.204472 0.354156i 0.745492 0.666514i $$-0.232214\pi$$
−0.949964 + 0.312358i $$0.898881\pi$$
$$294$$ −7.00000 + 12.1244i −0.408248 + 0.707107i
$$295$$ −8.00000 −0.465778
$$296$$ 0.500000 6.06218i 0.0290619 0.352357i
$$297$$ −8.00000 −0.464207
$$298$$ −4.50000 + 7.79423i −0.260678 + 0.451508i
$$299$$ −18.0000 31.1769i −1.04097 1.80301i
$$300$$ 4.00000 + 6.92820i 0.230940 + 0.400000i
$$301$$ 0 0
$$302$$ −6.00000 −0.345261
$$303$$ −7.00000 12.1244i −0.402139 0.696526i
$$304$$ 2.00000 0.114708
$$305$$ −2.50000 + 4.33013i −0.143150 + 0.247942i
$$306$$ −3.00000 −0.171499
$$307$$ 32.0000 1.82634 0.913168 0.407583i $$-0.133628\pi$$
0.913168 + 0.407583i $$0.133628\pi$$
$$308$$ 0 0
$$309$$ 8.00000 + 13.8564i 0.455104 + 0.788263i
$$310$$ 10.0000 0.567962
$$311$$ 6.00000 10.3923i 0.340229 0.589294i −0.644246 0.764818i $$-0.722829\pi$$
0.984475 + 0.175525i $$0.0561621\pi$$
$$312$$ −6.00000 + 10.3923i −0.339683 + 0.588348i
$$313$$ −9.50000 + 16.4545i −0.536972 + 0.930062i 0.462093 + 0.886831i $$0.347098\pi$$
−0.999065 + 0.0432311i $$0.986235\pi$$
$$314$$ −8.50000 14.7224i −0.479683 0.830835i
$$315$$ 0 0
$$316$$ −3.00000 + 5.19615i −0.168763 + 0.292306i
$$317$$ −3.50000 + 6.06218i −0.196580 + 0.340486i −0.947417 0.320001i $$-0.896317\pi$$
0.750838 + 0.660487i $$0.229650\pi$$
$$318$$ −6.00000 + 10.3923i −0.336463 + 0.582772i
$$319$$ −18.0000 −1.00781
$$320$$ 0.500000 + 0.866025i 0.0279508 + 0.0484123i
$$321$$ −8.00000 + 13.8564i −0.446516 + 0.773389i
$$322$$ 0 0
$$323$$ 6.00000 0.333849
$$324$$ 5.50000 9.52628i 0.305556 0.529238i
$$325$$ 24.0000 1.33128
$$326$$ 2.00000 + 3.46410i 0.110770 + 0.191859i
$$327$$ −26.0000 −1.43780
$$328$$ 1.50000 + 2.59808i 0.0828236 + 0.143455i
$$329$$ 0 0
$$330$$ −2.00000 3.46410i −0.110096 0.190693i
$$331$$ 10.0000 17.3205i 0.549650 0.952021i −0.448649 0.893708i $$-0.648095\pi$$
0.998298 0.0583130i $$-0.0185721\pi$$
$$332$$ 2.00000 0.109764
$$333$$ −5.00000 3.46410i −0.273998 0.189832i
$$334$$ 20.0000 1.09435
$$335$$ −3.00000 + 5.19615i −0.163908 + 0.283896i
$$336$$ 0 0
$$337$$ −7.50000 12.9904i −0.408551 0.707631i 0.586177 0.810183i $$-0.300632\pi$$
−0.994728 + 0.102552i $$0.967299\pi$$
$$338$$ 11.5000 + 19.9186i 0.625518 + 1.08343i
$$339$$ −20.0000 −1.08625
$$340$$ 1.50000 + 2.59808i 0.0813489 + 0.140900i
$$341$$ 20.0000 1.08306
$$342$$ 1.00000 1.73205i 0.0540738 0.0936586i
$$343$$ 0 0
$$344$$ 8.00000 0.431331
$$345$$ −6.00000 + 10.3923i −0.323029 + 0.559503i
$$346$$ 3.50000 + 6.06218i 0.188161 + 0.325905i
$$347$$ −6.00000 −0.322097 −0.161048 0.986947i $$-0.551488\pi$$
−0.161048 + 0.986947i $$0.551488\pi$$
$$348$$ 9.00000 15.5885i 0.482451 0.835629i
$$349$$ −9.50000 + 16.4545i −0.508523 + 0.880788i 0.491428 + 0.870918i $$0.336475\pi$$
−0.999951 + 0.00987003i $$0.996858\pi$$
$$350$$ 0 0
$$351$$ −12.0000 20.7846i −0.640513 1.10940i
$$352$$ 1.00000 + 1.73205i 0.0533002 + 0.0923186i
$$353$$ 10.5000 18.1865i 0.558859 0.967972i −0.438733 0.898617i $$-0.644573\pi$$
0.997592 0.0693543i $$-0.0220939\pi$$
$$354$$ 8.00000 13.8564i 0.425195 0.736460i
$$355$$ 0 0
$$356$$ −13.0000 −0.688999
$$357$$ 0 0
$$358$$ 12.0000 20.7846i 0.634220 1.09850i
$$359$$ 16.0000 0.844448 0.422224 0.906492i $$-0.361250\pi$$
0.422224 + 0.906492i $$0.361250\pi$$
$$360$$ 1.00000 0.0527046
$$361$$ 7.50000 12.9904i 0.394737 0.683704i
$$362$$ −11.0000 −0.578147
$$363$$ 7.00000 + 12.1244i 0.367405 + 0.636364i
$$364$$ 0 0
$$365$$ −1.00000 1.73205i −0.0523424 0.0906597i
$$366$$ −5.00000 8.66025i −0.261354 0.452679i
$$367$$ 2.00000 + 3.46410i 0.104399 + 0.180825i 0.913493 0.406855i $$-0.133375\pi$$
−0.809093 + 0.587680i $$0.800041\pi$$
$$368$$ 3.00000 5.19615i 0.156386 0.270868i
$$369$$ 3.00000 0.156174
$$370$$ −0.500000 + 6.06218i −0.0259938 + 0.315158i
$$371$$ 0 0
$$372$$ −10.0000 + 17.3205i −0.518476 + 0.898027i
$$373$$ 18.5000 + 32.0429i 0.957894 + 1.65912i 0.727603 + 0.685999i $$0.240634\pi$$
0.230291 + 0.973122i $$0.426032\pi$$
$$374$$ 3.00000 + 5.19615i 0.155126 + 0.268687i
$$375$$ −9.00000 15.5885i −0.464758 0.804984i
$$376$$ −2.00000 −0.103142
$$377$$ −27.0000 46.7654i −1.39057 2.40854i
$$378$$ 0 0
$$379$$ 10.0000 17.3205i 0.513665 0.889695i −0.486209 0.873843i $$-0.661621\pi$$
0.999874 0.0158521i $$-0.00504609\pi$$
$$380$$ −2.00000 −0.102598
$$381$$ −28.0000 −1.43448
$$382$$ 11.0000 19.0526i 0.562809 0.974814i
$$383$$ −4.00000 6.92820i −0.204390 0.354015i 0.745548 0.666452i $$-0.232188\pi$$
−0.949938 + 0.312437i $$0.898855\pi$$
$$384$$ −2.00000 −0.102062
$$385$$ 0 0
$$386$$ 5.50000 9.52628i 0.279943 0.484875i
$$387$$ 4.00000 6.92820i 0.203331 0.352180i
$$388$$ −1.50000 2.59808i −0.0761510 0.131897i
$$389$$ −5.50000 9.52628i −0.278861 0.483002i 0.692241 0.721666i $$-0.256624\pi$$
−0.971102 + 0.238665i $$0.923290\pi$$
$$390$$ 6.00000 10.3923i 0.303822 0.526235i
$$391$$ 9.00000 15.5885i 0.455150 0.788342i
$$392$$ −3.50000 + 6.06218i −0.176777 + 0.306186i
$$393$$ 28.0000 1.41241
$$394$$ −4.50000 7.79423i −0.226707 0.392668i
$$395$$ 3.00000 5.19615i 0.150946 0.261447i
$$396$$ 2.00000 0.100504
$$397$$ −25.0000 −1.25471 −0.627357 0.778732i $$-0.715863\pi$$
−0.627357 + 0.778732i $$0.715863\pi$$
$$398$$ −10.0000 + 17.3205i −0.501255 + 0.868199i
$$399$$ 0 0
$$400$$ 2.00000 + 3.46410i 0.100000 + 0.173205i
$$401$$ −18.0000 −0.898877 −0.449439 0.893311i $$-0.648376\pi$$
−0.449439 + 0.893311i $$0.648376\pi$$
$$402$$ −6.00000 10.3923i −0.299253 0.518321i
$$403$$ 30.0000 + 51.9615i 1.49441 + 2.58839i
$$404$$ −3.50000 6.06218i −0.174132 0.301605i
$$405$$ −5.50000 + 9.52628i −0.273297 + 0.473365i
$$406$$ 0 0
$$407$$ −1.00000 + 12.1244i −0.0495682 + 0.600982i
$$408$$ −6.00000 −0.297044
$$409$$ 10.5000 18.1865i 0.519192 0.899266i −0.480560 0.876962i $$-0.659566\pi$$
0.999751 0.0223042i $$-0.00710022\pi$$
$$410$$ −1.50000 2.59808i −0.0740797 0.128310i
$$411$$ 21.0000 + 36.3731i 1.03585 + 1.79415i
$$412$$ 4.00000 + 6.92820i 0.197066 + 0.341328i
$$413$$ 0 0
$$414$$ −3.00000 5.19615i −0.147442 0.255377i
$$415$$ −2.00000 −0.0981761
$$416$$ −3.00000 + 5.19615i −0.147087 + 0.254762i
$$417$$ 28.0000 1.37117
$$418$$ −4.00000 −0.195646
$$419$$ 2.00000 3.46410i 0.0977064 0.169232i −0.813029 0.582224i $$-0.802183\pi$$
0.910735 + 0.412991i $$0.135516\pi$$
$$420$$ 0 0
$$421$$ −25.0000 −1.21843 −0.609213 0.793007i $$-0.708514\pi$$
−0.609213 + 0.793007i $$0.708514\pi$$
$$422$$ −6.00000 + 10.3923i −0.292075 + 0.505889i
$$423$$ −1.00000 + 1.73205i −0.0486217 + 0.0842152i
$$424$$ −3.00000 + 5.19615i −0.145693 + 0.252347i
$$425$$ 6.00000 + 10.3923i 0.291043 + 0.504101i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −4.00000 + 6.92820i −0.193347 + 0.334887i
$$429$$ 12.0000 20.7846i 0.579365 1.00349i
$$430$$ −8.00000 −0.385794
$$431$$ 1.00000 + 1.73205i 0.0481683 + 0.0834300i 0.889104 0.457705i $$-0.151328\pi$$
−0.840936 + 0.541135i $$0.817995\pi$$
$$432$$ 2.00000 3.46410i 0.0962250 0.166667i
$$433$$ −9.00000 −0.432512 −0.216256 0.976337i $$-0.569385\pi$$
−0.216256 + 0.976337i $$0.569385\pi$$
$$434$$ 0 0
$$435$$ −9.00000 + 15.5885i −0.431517 + 0.747409i
$$436$$ −13.0000 −0.622587
$$437$$ 6.00000 + 10.3923i 0.287019 + 0.497131i
$$438$$ 4.00000 0.191127
$$439$$ 4.00000 + 6.92820i 0.190910 + 0.330665i 0.945552 0.325471i $$-0.105523\pi$$
−0.754642 + 0.656136i $$0.772190\pi$$
$$440$$ −1.00000 1.73205i −0.0476731 0.0825723i
$$441$$ 3.50000 + 6.06218i 0.166667 + 0.288675i
$$442$$ −9.00000 + 15.5885i −0.428086 + 0.741467i
$$443$$ 24.0000 1.14027 0.570137 0.821549i $$-0.306890\pi$$
0.570137 + 0.821549i $$0.306890\pi$$
$$444$$ −10.0000 6.92820i −0.474579 0.328798i
$$445$$ 13.0000 0.616259
$$446$$ 1.00000 1.73205i 0.0473514 0.0820150i
$$447$$ 9.00000 + 15.5885i 0.425685 + 0.737309i
$$448$$ 0 0
$$449$$ 17.0000 + 29.4449i 0.802280 + 1.38959i 0.918112 + 0.396320i $$0.129713\pi$$
−0.115833 + 0.993269i $$0.536954\pi$$
$$450$$ 4.00000 0.188562
$$451$$ −3.00000 5.19615i −0.141264 0.244677i
$$452$$ −10.0000 −0.470360
$$453$$ −6.00000 + 10.3923i −0.281905 + 0.488273i
$$454$$ −30.0000 −1.40797
$$455$$ 0 0
$$456$$ 2.00000 3.46410i 0.0936586 0.162221i
$$457$$ −13.5000 23.3827i −0.631503 1.09380i −0.987245 0.159211i $$-0.949105\pi$$
0.355741 0.934585i $$-0.384228\pi$$
$$458$$ 17.0000 0.794358
$$459$$ 6.00000 10.3923i 0.280056 0.485071i
$$460$$ −3.00000 + 5.19615i −0.139876 + 0.242272i
$$461$$ −13.0000 + 22.5167i −0.605470 + 1.04871i 0.386507 + 0.922287i $$0.373682\pi$$
−0.991977 + 0.126419i $$0.959652\pi$$
$$462$$ 0 0
$$463$$ 10.0000 + 17.3205i 0.464739 + 0.804952i 0.999190 0.0402476i $$-0.0128147\pi$$
−0.534450 + 0.845200i $$0.679481\pi$$
$$464$$ 4.50000 7.79423i 0.208907 0.361838i
$$465$$ 10.0000 17.3205i 0.463739 0.803219i
$$466$$ −0.500000 + 0.866025i −0.0231621 + 0.0401179i
$$467$$ 12.0000 0.555294 0.277647 0.960683i $$-0.410445\pi$$
0.277647 + 0.960683i $$0.410445\pi$$
$$468$$ 3.00000 + 5.19615i 0.138675 + 0.240192i
$$469$$ 0 0
$$470$$ 2.00000 0.0922531
$$471$$ −34.0000 −1.56664
$$472$$ 4.00000 6.92820i 0.184115 0.318896i
$$473$$ −16.0000 −0.735681
$$474$$ 6.00000 + 10.3923i 0.275589 + 0.477334i
$$475$$ −8.00000 −0.367065
$$476$$ 0 0
$$477$$ 3.00000 + 5.19615i 0.137361 + 0.237915i
$$478$$ 2.00000 + 3.46410i 0.0914779 + 0.158444i
$$479$$ −16.0000 + 27.7128i −0.731059 + 1.26623i 0.225372 + 0.974273i $$0.427640\pi$$
−0.956431 + 0.291958i $$0.905693\pi$$
$$480$$ 2.00000 0.0912871
$$481$$ −33.0000 + 15.5885i −1.50467 + 0.710772i
$$482$$ 10.0000 0.455488
$$483$$ 0 0
$$484$$ 3.50000 + 6.06218i 0.159091 + 0.275554i
$$485$$ 1.50000 + 2.59808i 0.0681115 + 0.117973i
$$486$$ −5.00000 8.66025i −0.226805 0.392837i
$$487$$ −2.00000 −0.0906287 −0.0453143 0.998973i $$-0.514429\pi$$
−0.0453143 + 0.998973i $$0.514429\pi$$
$$488$$ −2.50000 4.33013i −0.113170 0.196016i
$$489$$ 8.00000 0.361773
$$490$$ 3.50000 6.06218i 0.158114 0.273861i
$$491$$ −18.0000 −0.812329 −0.406164 0.913800i $$-0.633134\pi$$
−0.406164 + 0.913800i $$0.633134\pi$$
$$492$$ 6.00000 0.270501
$$493$$ 13.5000 23.3827i 0.608009 1.05310i
$$494$$ −6.00000 10.3923i −0.269953 0.467572i
$$495$$ −2.00000 −0.0898933
$$496$$ −5.00000 + 8.66025i −0.224507 + 0.388857i
$$497$$ 0 0
$$498$$ 2.00000 3.46410i 0.0896221 0.155230i
$$499$$ −15.0000 25.9808i −0.671492 1.16306i −0.977481 0.211024i $$-0.932320\pi$$
0.305989 0.952035i $$-0.401013\pi$$
$$500$$ −4.50000 7.79423i −0.201246 0.348569i
$$501$$ 20.0000 34.6410i 0.893534 1.54765i
$$502$$ 10.0000 17.3205i 0.446322 0.773052i
$$503$$ −7.00000 + 12.1244i −0.312115 + 0.540598i −0.978820 0.204723i $$-0.934371\pi$$
0.666705 + 0.745321i $$0.267704\pi$$
$$504$$ 0 0
$$505$$ 3.50000 + 6.06218i 0.155748 + 0.269763i
$$506$$ −6.00000 + 10.3923i −0.266733 + 0.461994i
$$507$$ 46.0000 2.04293
$$508$$ −14.0000 −0.621150
$$509$$ 4.50000 7.79423i 0.199459 0.345473i −0.748894 0.662690i $$-0.769415\pi$$
0.948353 + 0.317217i $$0.102748\pi$$
$$510$$ 6.00000 0.265684
$$511$$ 0 0
$$512$$ −1.00000 −0.0441942
$$513$$ 4.00000 + 6.92820i 0.176604 + 0.305888i
$$514$$ 9.50000 + 16.4545i 0.419027 + 0.725776i
$$515$$ −4.00000 6.92820i −0.176261 0.305293i
$$516$$ 8.00000 13.8564i 0.352180 0.609994i
$$517$$ 4.00000 0.175920
$$518$$ 0 0
$$519$$ 14.0000 0.614532
$$520$$ 3.00000 5.19615i 0.131559 0.227866i
$$521$$ −15.0000 25.9808i −0.657162 1.13824i −0.981347 0.192244i $$-0.938423\pi$$
0.324185 0.945994i $$-0.394910\pi$$
$$522$$ −4.50000 7.79423i −0.196960 0.341144i
$$523$$ −3.00000 5.19615i −0.131181 0.227212i 0.792951 0.609285i $$-0.208544\pi$$
−0.924132 + 0.382073i $$0.875210\pi$$
$$524$$ 14.0000 0.611593
$$525$$ 0 0
$$526$$ 24.0000 1.04645
$$527$$ −15.0000 + 25.9808i −0.653410 + 1.13174i
$$528$$ 4.00000 0.174078
$$529$$ 13.0000 0.565217
$$530$$ 3.00000 5.19615i 0.130312 0.225706i
$$531$$ −4.00000 6.92820i −0.173585 0.300658i
$$532$$ 0 0
$$533$$ 9.00000 15.5885i 0.389833 0.675211i
$$534$$ −13.0000 + 22.5167i −0.562565 + 0.974391i
$$535$$ 4.00000 6.92820i 0.172935 0.299532i
$$536$$ −3.00000 5.19615i −0.129580 0.224440i
$$537$$ −24.0000 41.5692i −1.03568 1.79384i
$$538$$ 1.00000 1.73205i 0.0431131 0.0746740i
$$539$$ 7.00000 12.1244i 0.301511 0.522233i
$$540$$ −2.00000 + 3.46410i −0.0860663 + 0.149071i
$$541$$ −9.00000 −0.386940 −0.193470 0.981106i $$-0.561974\pi$$
−0.193470 + 0.981106i $$0.561974\pi$$
$$542$$ 3.00000 + 5.19615i 0.128861 + 0.223194i
$$543$$ −11.0000 + 19.0526i −0.472055 + 0.817624i
$$544$$ −3.00000 −0.128624
$$545$$ 13.0000 0.556859
$$546$$ 0 0
$$547$$ −6.00000 −0.256541 −0.128271 0.991739i $$-0.540943\pi$$
−0.128271 + 0.991739i $$0.540943\pi$$
$$548$$ 10.5000 + 18.1865i 0.448538 + 0.776890i
$$549$$ −5.00000 −0.213395
$$550$$ −4.00000 6.92820i −0.170561 0.295420i
$$551$$ 9.00000 + 15.5885i 0.383413 + 0.664091i
$$552$$ −6.00000 10.3923i −0.255377 0.442326i
$$553$$ 0 0
$$554$$ 21.0000 0.892205
$$555$$ 10.0000 + 6.92820i 0.424476 + 0.294086i
$$556$$ 14.0000 0.593732
$$557$$ −17.5000 + 30.3109i −0.741499 + 1.28431i 0.210314 + 0.977634i $$0.432551\pi$$
−0.951813 + 0.306680i $$0.900782\pi$$
$$558$$ 5.00000 + 8.66025i 0.211667 + 0.366618i
$$559$$ −24.0000 41.5692i −1.01509 1.75819i
$$560$$ 0 0
$$561$$ 12.0000 0.506640
$$562$$ −4.50000 7.79423i −0.189821 0.328780i
$$563$$ 10.0000 0.421450 0.210725 0.977545i $$-0.432418\pi$$
0.210725 + 0.977545i $$0.432418\pi$$
$$564$$ −2.00000 + 3.46410i −0.0842152 + 0.145865i
$$565$$ 10.0000 0.420703
$$566$$ −4.00000 −0.168133
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 11.0000 0.461144 0.230572 0.973055i $$-0.425940\pi$$
0.230572 + 0.973055i $$0.425940\pi$$
$$570$$ −2.00000 + 3.46410i −0.0837708 + 0.145095i
$$571$$ −9.00000 + 15.5885i −0.376638 + 0.652357i −0.990571 0.137002i $$-0.956253\pi$$
0.613933 + 0.789359i $$0.289587\pi$$
$$572$$ 6.00000 10.3923i 0.250873 0.434524i
$$573$$ −22.0000 38.1051i −0.919063 1.59186i
$$574$$ 0 0
$$575$$ −12.0000 + 20.7846i −0.500435 + 0.866778i
$$576$$ −0.500000 + 0.866025i −0.0208333 + 0.0360844i
$$577$$ 1.00000 1.73205i 0.0416305 0.0721062i −0.844459 0.535620i $$-0.820078\pi$$
0.886090 + 0.463513i $$0.153411\pi$$
$$578$$ 8.00000 0.332756
$$579$$ −11.0000 19.0526i −0.457144 0.791797i
$$580$$ −4.50000 + 7.79423i −0.186852 + 0.323638i
$$581$$ 0 0
$$582$$ −6.00000 −0.248708
$$583$$ 6.00000 10.3923i 0.248495 0.430405i
$$584$$ 2.00000 0.0827606
$$585$$ −3.00000 5.19615i −0.124035 0.214834i
$$586$$ −7.00000 −0.289167
$$587$$ −15.0000 25.9808i −0.619116 1.07234i −0.989647 0.143521i $$-0.954158\pi$$
0.370531 0.928820i $$-0.379176\pi$$
$$588$$ 7.00000 + 12.1244i 0.288675 + 0.500000i
$$589$$ −10.0000 17.3205i −0.412043 0.713679i
$$590$$ −4.00000 + 6.92820i −0.164677 + 0.285230i
$$591$$ −18.0000 −0.740421
$$592$$ −5.00000 3.46410i −0.205499 0.142374i
$$593$$ 19.0000 0.780236 0.390118 0.920765i $$-0.372434\pi$$
0.390118 + 0.920765i $$0.372434\pi$$
$$594$$ −4.00000 + 6.92820i −0.164122 + 0.284268i
$$595$$ 0 0
$$596$$ 4.50000 + 7.79423i 0.184327 + 0.319264i
$$597$$ 20.0000 + 34.6410i 0.818546 + 1.41776i
$$598$$ −36.0000 −1.47215
$$599$$ −5.00000 8.66025i −0.204294 0.353848i 0.745613 0.666379i $$-0.232157\pi$$
−0.949908 + 0.312531i $$0.898823\pi$$
$$600$$ 8.00000 0.326599
$$601$$ 2.50000 4.33013i 0.101977 0.176630i −0.810522 0.585708i $$-0.800816\pi$$
0.912499 + 0.409079i $$0.134150\pi$$
$$602$$ 0 0
$$603$$ −6.00000 −0.244339
$$604$$ −3.00000 + 5.19615i −0.122068 + 0.211428i
$$605$$ −3.50000 6.06218i −0.142295 0.246463i
$$606$$ −14.0000 −0.568711
$$607$$ −5.00000 + 8.66025i −0.202944 + 0.351509i −0.949476 0.313841i $$-0.898384\pi$$
0.746532 + 0.665350i $$0.231718\pi$$
$$608$$ 1.00000 1.73205i 0.0405554 0.0702439i
$$609$$ 0 0
$$610$$ 2.50000 + 4.33013i 0.101222 + 0.175322i
$$611$$ 6.00000 + 10.3923i 0.242734 + 0.420428i
$$612$$ −1.50000 + 2.59808i −0.0606339 + 0.105021i
$$613$$ −5.50000 + 9.52628i −0.222143 + 0.384763i −0.955458 0.295126i $$-0.904638\pi$$
0.733316 + 0.679888i $$0.237972\pi$$
$$614$$ 16.0000 27.7128i 0.645707 1.11840i
$$615$$ −6.00000 −0.241943
$$616$$ 0 0
$$617$$ −7.00000 + 12.1244i −0.281809 + 0.488108i −0.971830 0.235681i $$-0.924268\pi$$
0.690021 + 0.723789i $$0.257601\pi$$
$$618$$ 16.0000 0.643614
$$619$$ 4.00000 0.160774 0.0803868 0.996764i $$-0.474384\pi$$
0.0803868 + 0.996764i $$0.474384\pi$$
$$620$$ 5.00000 8.66025i 0.200805 0.347804i
$$621$$ 24.0000 0.963087
$$622$$ −6.00000 10.3923i −0.240578 0.416693i
$$623$$ 0 0
$$624$$ 6.00000 + 10.3923i 0.240192 + 0.416025i
$$625$$ −5.50000 9.52628i −0.220000 0.381051i
$$626$$ 9.50000 + 16.4545i 0.379696 + 0.657653i
$$627$$ −4.00000 + 6.92820i −0.159745 + 0.276686i
$$628$$ −17.0000 −0.678374
$$629$$ −15.0000 10.3923i −0.598089 0.414368i
$$630$$ 0 0
$$631$$ −5.00000 + 8.66025i −0.199047 + 0.344759i −0.948220 0.317615i $$-0.897118\pi$$
0.749173 + 0.662375i $$0.230451\pi$$
$$632$$ 3.00000 + 5.19615i 0.119334 + 0.206692i
$$633$$ 12.0000 + 20.7846i 0.476957 + 0.826114i
$$634$$ 3.50000 + 6.06218i 0.139003 + 0.240760i
$$635$$ 14.0000 0.555573
$$636$$ 6.00000 + 10.3923i 0.237915 + 0.412082i
$$637$$ 42.0000 1.66410
$$638$$ −9.00000 + 15.5885i −0.356313 + 0.617153i
$$639$$ 0 0
$$640$$ 1.00000 0.0395285
$$641$$ −9.50000 + 16.4545i −0.375227 + 0.649913i −0.990361 0.138510i $$-0.955769\pi$$
0.615134 + 0.788423i $$0.289102\pi$$
$$642$$ 8.00000 + 13.8564i 0.315735 + 0.546869i
$$643$$ −34.0000 −1.34083 −0.670415 0.741987i $$-0.733884\pi$$
−0.670415 + 0.741987i $$0.733884\pi$$
$$644$$ 0 0
$$645$$ −8.00000 + 13.8564i −0.315000 + 0.545595i
$$646$$ 3.00000 5.19615i 0.118033 0.204440i
$$647$$ −2.00000 3.46410i −0.0786281 0.136188i 0.824030 0.566546i $$-0.191721\pi$$
−0.902658 + 0.430358i $$0.858387\pi$$
$$648$$ −5.50000 9.52628i −0.216060 0.374228i
$$649$$ −8.00000 + 13.8564i −0.314027 + 0.543912i
$$650$$ 12.0000 20.7846i 0.470679 0.815239i
$$651$$ 0 0
$$652$$ 4.00000 0.156652
$$653$$ −7.50000 12.9904i −0.293498 0.508353i 0.681137 0.732156i $$-0.261486\pi$$
−0.974634 + 0.223803i $$0.928153\pi$$
$$654$$ −13.0000 + 22.5167i −0.508340 + 0.880471i
$$655$$ −14.0000 −0.547025
$$656$$ 3.00000 0.117130
$$657$$ 1.00000 1.73205i 0.0390137 0.0675737i
$$658$$ 0 0
$$659$$ 10.0000 + 17.3205i 0.389545 + 0.674711i 0.992388 0.123148i $$-0.0392990\pi$$
−0.602844 + 0.797859i $$0.705966\pi$$
$$660$$ −4.00000 −0.155700
$$661$$ −13.5000 23.3827i −0.525089 0.909481i −0.999573 0.0292169i $$-0.990699\pi$$
0.474484 0.880264i $$-0.342635\pi$$
$$662$$ −10.0000 17.3205i −0.388661 0.673181i
$$663$$ 18.0000 + 31.1769i 0.699062 + 1.21081i
$$664$$ 1.00000 1.73205i 0.0388075 0.0672166i
$$665$$ 0 0
$$666$$ −5.50000 + 2.59808i −0.213121 + 0.100673i
$$667$$ 54.0000 2.09089
$$668$$ 10.0000 17.3205i 0.386912 0.670151i
$$669$$ −2.00000 3.46410i −0.0773245 0.133930i
$$670$$ 3.00000 + 5.19615i 0.115900 + 0.200745i
$$671$$ 5.00000 + 8.66025i 0.193023 + 0.334325i
$$672$$ 0 0
$$673$$ 1.00000 + 1.73205i 0.0385472 + 0.0667657i 0.884655 0.466246i $$-0.154394\pi$$
−0.846108 + 0.533011i $$0.821060\pi$$
$$674$$ −15.0000 −0.577778
$$675$$ −8.00000 + 13.8564i −0.307920 + 0.533333i
$$676$$ 23.0000 0.884615
$$677$$ 47.0000 1.80636 0.903178 0.429265i $$-0.141228\pi$$
0.903178 + 0.429265i $$0.141228\pi$$
$$678$$ −10.0000 + 17.3205i −0.384048 + 0.665190i
$$679$$ 0 0
$$680$$ 3.00000 0.115045
$$681$$ −30.0000 + 51.9615i −1.14960 + 1.99117i
$$682$$ 10.0000 17.3205i 0.382920 0.663237i
$$683$$ 12.0000 20.7846i 0.459167 0.795301i −0.539750 0.841825i $$-0.681481\pi$$
0.998917 + 0.0465244i $$0.0148145\pi$$
$$684$$ −1.00000 1.73205i −0.0382360 0.0662266i
$$685$$ −10.5000 18.1865i −0.401184 0.694872i
$$686$$ 0 0
$$687$$ 17.0000 29.4449i 0.648590 1.12339i
$$688$$ 4.00000 6.92820i 0.152499 0.264135i
$$689$$ 36.0000 1.37149
$$690$$ 6.00000 + 10.3923i 0.228416 + 0.395628i
$$691$$ −25.0000 + 43.3013i −0.951045 + 1.64726i −0.207875 + 0.978155i $$0.566655\pi$$
−0.743170 + 0.669102i $$0.766679\pi$$
$$692$$ 7.00000 0.266100
$$693$$ 0 0
$$694$$ −3.00000 + 5.19615i −0.113878 + 0.197243i
$$695$$ −14.0000 −0.531050
$$696$$ −9.00000 15.5885i −0.341144 0.590879i
$$697$$ 9.00000 0.340899
$$698$$ 9.50000 + 16.4545i 0.359580 + 0.622811i
$$699$$ 1.00000 + 1.73205i 0.0378235 + 0.0655122i
$$700$$ 0 0
$$701$$ 1.00000 1.73205i 0.0377695 0.0654187i −0.846523 0.532353i $$-0.821308\pi$$
0.884292 + 0.466934i $$0.154641\pi$$
$$702$$ −24.0000 −0.905822
$$703$$ 11.0000 5.19615i 0.414873 0.195977i
$$704$$ 2.00000 0.0753778
$$705$$ 2.00000 3.46410i 0.0753244 0.130466i
$$706$$ −10.5000 18.1865i −0.395173 0.684459i
$$707$$ 0 0
$$708$$ −8.00000 13.8564i −0.300658 0.520756i
$$709$$ −6.00000 −0.225335 −0.112667 0.993633i $$-0.535939\pi$$
−0.112667 + 0.993633i $$0.535939\pi$$
$$710$$ 0 0
$$711$$ 6.00000 0.225018
$$712$$ −6.50000 + 11.2583i −0.243598 + 0.421924i
$$713$$ −60.0000 −2.24702
$$714$$ 0 0
$$715$$ −6.00000 + 10.3923i −0.224387 + 0.388650i
$$716$$ −12.0000 20.7846i −0.448461 0.776757i
$$717$$ 8.00000 0.298765
$$718$$ 8.00000 13.8564i 0.298557 0.517116i
$$719$$ −9.00000 + 15.5885i −0.335643 + 0.581351i −0.983608 0.180319i $$-0.942287\pi$$
0.647965 + 0.761670i $$0.275620\pi$$
$$720$$ 0.500000 0.866025i 0.0186339 0.0322749i
$$721$$ 0 0
$$722$$ −7.50000 12.9904i −0.279121 0.483452i
$$723$$ 10.0000 17.3205i 0.371904 0.644157i
$$724$$ −5.50000 + 9.52628i −0.204406 + 0.354041i
$$725$$ −18.0000 + 31.1769i −0.668503 + 1.15788i
$$726$$ 14.0000 0.519589
$$727$$ 14.0000 + 24.2487i 0.519231 + 0.899335i 0.999750 + 0.0223506i $$0.00711500\pi$$
−0.480519 + 0.876984i $$0.659552\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ −2.00000 −0.0740233
$$731$$ 12.0000 20.7846i 0.443836 0.768747i
$$732$$ −10.0000 −0.369611
$$733$$ −13.0000 22.5167i −0.480166 0.831672i 0.519575 0.854425i $$-0.326090\pi$$
−0.999741 + 0.0227529i $$0.992757\pi$$
$$734$$ 4.00000 0.147643
$$735$$ −7.00000 12.1244i −0.258199 0.447214i
$$736$$ −3.00000 5.19615i −0.110581 0.191533i
$$737$$ 6.00000 + 10.3923i 0.221013 + 0.382805i
$$738$$ 1.50000 2.59808i 0.0552158 0.0956365i
$$739$$ 34.0000 1.25071 0.625355 0.780340i $$-0.284954\pi$$
0.625355 + 0.780340i $$0.284954\pi$$
$$740$$ 5.00000 + 3.46410i 0.183804 + 0.127343i
$$741$$ −24.0000 −0.881662
$$742$$ 0 0
$$743$$ −9.00000 15.5885i −0.330178 0.571885i 0.652369 0.757902i $$-0.273775\pi$$
−0.982547 + 0.186017i $$0.940442\pi$$
$$744$$ 10.0000 + 17.3205i 0.366618 + 0.635001i
$$745$$ −4.50000 7.79423i −0.164867 0.285558i
$$746$$ 37.0000 1.35467
$$747$$ −1.00000 1.73205i −0.0365881 0.0633724i
$$748$$ 6.00000 0.219382
$$749$$ 0 0
$$750$$ −18.0000 −0.657267
$$751$$ −4.00000 −0.145962 −0.0729810 0.997333i $$-0.523251\pi$$
−0.0729810 + 0.997333i $$0.523251\pi$$
$$752$$ −1.00000 + 1.73205i −0.0364662 + 0.0631614i
$$753$$ −20.0000 34.6410i −0.728841 1.26239i
$$754$$ −54.0000 −1.96656
$$755$$ 3.00000 5.19615i 0.109181 0.189107i
$$756$$ 0 0
$$757$$ 8.50000 14.7224i 0.308938 0.535096i −0.669193 0.743089i $$-0.733360\pi$$
0.978130 + 0.207993i $$0.0666932\pi$$
$$758$$ −10.0000 17.3205i −0.363216 0.629109i
$$759$$ 12.0000 + 20.7846i 0.435572 + 0.754434i
$$760$$ −1.00000 + 1.73205i −0.0362738 + 0.0628281i
$$761$$ 6.50000 11.2583i 0.235625 0.408114i −0.723829 0.689979i $$-0.757620\pi$$
0.959454 + 0.281865i $$0.0909530\pi$$
$$762$$ −14.0000 + 24.2487i −0.507166 + 0.878438i
$$763$$ 0 0
$$764$$ −11.0000 19.0526i −0.397966 0.689297i
$$765$$ 1.50000 2.59808i 0.0542326 0.0939336i
$$766$$ −8.00000 −0.289052
$$767$$ −48.0000 −1.73318
$$768$$ −1.00000 + 1.73205i −0.0360844 + 0.0625000i
$$769$$ −10.0000 −0.360609 −0.180305 0.983611i $$-0.557708\pi$$
−0.180305 + 0.983611i $$0.557708\pi$$
$$770$$ 0 0
$$771$$ 38.0000 1.36854
$$772$$ −5.50000 9.52628i −0.197949 0.342858i
$$773$$ −11.5000 19.9186i −0.413626 0.716422i 0.581657 0.813434i $$-0.302405\pi$$
−0.995283 + 0.0970125i $$0.969071\pi$$
$$774$$ −4.00000 6.92820i −0.143777 0.249029i
$$775$$ 20.0000 34.6410i 0.718421 1.24434i
$$776$$ −3.00000 −0.107694
$$777$$ 0 0
$$778$$ −11.0000 −0.394369
$$779$$ −3.00000 + 5.19615i −0.107486 + 0.186171i
$$780$$ −6.00000