# Properties

 Label 74.2.c.b.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

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,2,Mod(47,74)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("74.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: no Analytic conductor: $$0.590892974957$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field 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.b.63.1

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{2} +(1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +2.00000 q^{6} +(2.00000 + 3.46410i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{2} +(1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +2.00000 q^{6} +(2.00000 + 3.46410i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} -3.00000 q^{10} -6.00000 q^{11} +(1.00000 - 1.73205i) q^{12} +(-1.00000 - 1.73205i) q^{13} +4.00000 q^{14} +(3.00000 - 5.19615i) 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} +(-1.50000 + 2.59808i) q^{20} +(-4.00000 + 6.92820i) q^{21} +(-3.00000 + 5.19615i) q^{22} +6.00000 q^{23} +(-1.00000 - 1.73205i) q^{24} +(-2.00000 + 3.46410i) q^{25} -2.00000 q^{26} +4.00000 q^{27} +(2.00000 - 3.46410i) q^{28} +3.00000 q^{29} +(-3.00000 - 5.19615i) q^{30} +2.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-6.00000 - 10.3923i) q^{33} +(1.50000 + 2.59808i) q^{34} +(6.00000 - 10.3923i) q^{35} +1.00000 q^{36} +(5.50000 + 2.59808i) q^{37} -2.00000 q^{38} +(2.00000 - 3.46410i) q^{39} +(1.50000 + 2.59808i) q^{40} +(-1.50000 - 2.59808i) q^{41} +(4.00000 + 6.92820i) q^{42} -4.00000 q^{43} +(3.00000 + 5.19615i) q^{44} +3.00000 q^{45} +(3.00000 - 5.19615i) q^{46} -6.00000 q^{47} -2.00000 q^{48} +(-4.50000 + 7.79423i) q^{49} +(2.00000 + 3.46410i) q^{50} -6.00000 q^{51} +(-1.00000 + 1.73205i) q^{52} +(3.00000 - 5.19615i) q^{53} +(2.00000 - 3.46410i) q^{54} +(9.00000 + 15.5885i) q^{55} +(-2.00000 - 3.46410i) q^{56} +(2.00000 - 3.46410i) q^{57} +(1.50000 - 2.59808i) q^{58} -6.00000 q^{60} +(0.500000 + 0.866025i) q^{61} +(1.00000 - 1.73205i) q^{62} -4.00000 q^{63} +1.00000 q^{64} +(-3.00000 + 5.19615i) q^{65} -12.0000 q^{66} +(-1.00000 - 1.73205i) q^{67} +3.00000 q^{68} +(6.00000 + 10.3923i) q^{69} +(-6.00000 - 10.3923i) q^{70} +(6.00000 + 10.3923i) q^{71} +(0.500000 - 0.866025i) q^{72} -10.0000 q^{73} +(5.00000 - 3.46410i) q^{74} -8.00000 q^{75} +(-1.00000 + 1.73205i) q^{76} +(-12.0000 - 20.7846i) q^{77} +(-2.00000 - 3.46410i) q^{78} +(-7.00000 - 12.1244i) q^{79} +3.00000 q^{80} +(5.50000 + 9.52628i) q^{81} -3.00000 q^{82} +(-3.00000 + 5.19615i) q^{83} +8.00000 q^{84} +9.00000 q^{85} +(-2.00000 + 3.46410i) q^{86} +(3.00000 + 5.19615i) q^{87} +6.00000 q^{88} +(-1.50000 + 2.59808i) q^{89} +(1.50000 - 2.59808i) q^{90} +(4.00000 - 6.92820i) q^{91} +(-3.00000 - 5.19615i) q^{92} +(2.00000 + 3.46410i) q^{93} +(-3.00000 + 5.19615i) q^{94} +(-3.00000 + 5.19615i) q^{95} +(-1.00000 + 1.73205i) q^{96} -13.0000 q^{97} +(4.50000 + 7.79423i) q^{98} +(3.00000 - 5.19615i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{2} + 2 q^{3} - q^{4} - 3 q^{5} + 4 q^{6} + 4 q^{7} - 2 q^{8} - q^{9}+O(q^{10})$$ 2 * q + q^2 + 2 * q^3 - q^4 - 3 * q^5 + 4 * q^6 + 4 * q^7 - 2 * q^8 - q^9 $$2 q + q^{2} + 2 q^{3} - q^{4} - 3 q^{5} + 4 q^{6} + 4 q^{7} - 2 q^{8} - q^{9} - 6 q^{10} - 12 q^{11} + 2 q^{12} - 2 q^{13} + 8 q^{14} + 6 q^{15} - q^{16} - 3 q^{17} + q^{18} - 2 q^{19} - 3 q^{20} - 8 q^{21} - 6 q^{22} + 12 q^{23} - 2 q^{24} - 4 q^{25} - 4 q^{26} + 8 q^{27} + 4 q^{28} + 6 q^{29} - 6 q^{30} + 4 q^{31} + q^{32} - 12 q^{33} + 3 q^{34} + 12 q^{35} + 2 q^{36} + 11 q^{37} - 4 q^{38} + 4 q^{39} + 3 q^{40} - 3 q^{41} + 8 q^{42} - 8 q^{43} + 6 q^{44} + 6 q^{45} + 6 q^{46} - 12 q^{47} - 4 q^{48} - 9 q^{49} + 4 q^{50} - 12 q^{51} - 2 q^{52} + 6 q^{53} + 4 q^{54} + 18 q^{55} - 4 q^{56} + 4 q^{57} + 3 q^{58} - 12 q^{60} + q^{61} + 2 q^{62} - 8 q^{63} + 2 q^{64} - 6 q^{65} - 24 q^{66} - 2 q^{67} + 6 q^{68} + 12 q^{69} - 12 q^{70} + 12 q^{71} + q^{72} - 20 q^{73} + 10 q^{74} - 16 q^{75} - 2 q^{76} - 24 q^{77} - 4 q^{78} - 14 q^{79} + 6 q^{80} + 11 q^{81} - 6 q^{82} - 6 q^{83} + 16 q^{84} + 18 q^{85} - 4 q^{86} + 6 q^{87} + 12 q^{88} - 3 q^{89} + 3 q^{90} + 8 q^{91} - 6 q^{92} + 4 q^{93} - 6 q^{94} - 6 q^{95} - 2 q^{96} - 26 q^{97} + 9 q^{98} + 6 q^{99}+O(q^{100})$$ 2 * q + q^2 + 2 * q^3 - q^4 - 3 * q^5 + 4 * q^6 + 4 * q^7 - 2 * q^8 - q^9 - 6 * q^10 - 12 * q^11 + 2 * q^12 - 2 * q^13 + 8 * q^14 + 6 * q^15 - q^16 - 3 * q^17 + q^18 - 2 * q^19 - 3 * q^20 - 8 * q^21 - 6 * q^22 + 12 * q^23 - 2 * q^24 - 4 * q^25 - 4 * q^26 + 8 * q^27 + 4 * q^28 + 6 * q^29 - 6 * q^30 + 4 * q^31 + q^32 - 12 * q^33 + 3 * q^34 + 12 * q^35 + 2 * q^36 + 11 * q^37 - 4 * q^38 + 4 * q^39 + 3 * q^40 - 3 * q^41 + 8 * q^42 - 8 * q^43 + 6 * q^44 + 6 * q^45 + 6 * q^46 - 12 * q^47 - 4 * q^48 - 9 * q^49 + 4 * q^50 - 12 * q^51 - 2 * q^52 + 6 * q^53 + 4 * q^54 + 18 * q^55 - 4 * q^56 + 4 * q^57 + 3 * q^58 - 12 * q^60 + q^61 + 2 * q^62 - 8 * q^63 + 2 * q^64 - 6 * q^65 - 24 * q^66 - 2 * q^67 + 6 * q^68 + 12 * q^69 - 12 * q^70 + 12 * q^71 + q^72 - 20 * q^73 + 10 * q^74 - 16 * q^75 - 2 * q^76 - 24 * q^77 - 4 * q^78 - 14 * q^79 + 6 * q^80 + 11 * q^81 - 6 * q^82 - 6 * q^83 + 16 * q^84 + 18 * q^85 - 4 * q^86 + 6 * q^87 + 12 * q^88 - 3 * q^89 + 3 * q^90 + 8 * q^91 - 6 * q^92 + 4 * q^93 - 6 * q^94 - 6 * q^95 - 2 * q^96 - 26 * q^97 + 9 * q^98 + 6 * 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 $$0.0292466\pi$$
−0.418432 + 0.908248i $$0.637420\pi$$
$$4$$ −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 $$-0.400725\pi$$
$$6$$ 2.00000 0.816497
$$7$$ 2.00000 + 3.46410i 0.755929 + 1.30931i 0.944911 + 0.327327i $$0.106148\pi$$
−0.188982 + 0.981981i $$0.560519\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ −0.500000 + 0.866025i −0.166667 + 0.288675i
$$10$$ −3.00000 −0.948683
$$11$$ −6.00000 −1.80907 −0.904534 0.426401i $$-0.859781\pi$$
−0.904534 + 0.426401i $$0.859781\pi$$
$$12$$ 1.00000 1.73205i 0.288675 0.500000i
$$13$$ −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i $$-0.256123\pi$$
−0.970725 + 0.240192i $$0.922790\pi$$
$$14$$ 4.00000 1.06904
$$15$$ 3.00000 5.19615i 0.774597 1.34164i
$$16$$ −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 $$0.907015\pi$$
$$20$$ −1.50000 + 2.59808i −0.335410 + 0.580948i
$$21$$ −4.00000 + 6.92820i −0.872872 + 1.51186i
$$22$$ −3.00000 + 5.19615i −0.639602 + 1.10782i
$$23$$ 6.00000 1.25109 0.625543 0.780189i $$-0.284877\pi$$
0.625543 + 0.780189i $$0.284877\pi$$
$$24$$ −1.00000 1.73205i −0.204124 0.353553i
$$25$$ −2.00000 + 3.46410i −0.400000 + 0.692820i
$$26$$ −2.00000 −0.392232
$$27$$ 4.00000 0.769800
$$28$$ 2.00000 3.46410i 0.377964 0.654654i
$$29$$ 3.00000 0.557086 0.278543 0.960424i $$-0.410149\pi$$
0.278543 + 0.960424i $$0.410149\pi$$
$$30$$ −3.00000 5.19615i −0.547723 0.948683i
$$31$$ 2.00000 0.359211 0.179605 0.983739i $$-0.442518\pi$$
0.179605 + 0.983739i $$0.442518\pi$$
$$32$$ 0.500000 + 0.866025i 0.0883883 + 0.153093i
$$33$$ −6.00000 10.3923i −1.04447 1.80907i
$$34$$ 1.50000 + 2.59808i 0.257248 + 0.445566i
$$35$$ 6.00000 10.3923i 1.01419 1.75662i
$$36$$ 1.00000 0.166667
$$37$$ 5.50000 + 2.59808i 0.904194 + 0.427121i
$$38$$ −2.00000 −0.324443
$$39$$ 2.00000 3.46410i 0.320256 0.554700i
$$40$$ 1.50000 + 2.59808i 0.237171 + 0.410792i
$$41$$ −1.50000 2.59808i −0.234261 0.405751i 0.724797 0.688963i $$-0.241934\pi$$
−0.959058 + 0.283211i $$0.908600\pi$$
$$42$$ 4.00000 + 6.92820i 0.617213 + 1.06904i
$$43$$ −4.00000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ 3.00000 + 5.19615i 0.452267 + 0.783349i
$$45$$ 3.00000 0.447214
$$46$$ 3.00000 5.19615i 0.442326 0.766131i
$$47$$ −6.00000 −0.875190 −0.437595 0.899172i $$-0.644170\pi$$
−0.437595 + 0.899172i $$0.644170\pi$$
$$48$$ −2.00000 −0.288675
$$49$$ −4.50000 + 7.79423i −0.642857 + 1.11346i
$$50$$ 2.00000 + 3.46410i 0.282843 + 0.489898i
$$51$$ −6.00000 −0.840168
$$52$$ −1.00000 + 1.73205i −0.138675 + 0.240192i
$$53$$ 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
$$55$$ 9.00000 + 15.5885i 1.21356 + 2.10195i
$$56$$ −2.00000 3.46410i −0.267261 0.462910i
$$57$$ 2.00000 3.46410i 0.264906 0.458831i
$$58$$ 1.50000 2.59808i 0.196960 0.341144i
$$59$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$60$$ −6.00000 −0.774597
$$61$$ 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i $$-0.146275\pi$$
−0.832240 + 0.554416i $$0.812942\pi$$
$$62$$ 1.00000 1.73205i 0.127000 0.219971i
$$63$$ −4.00000 −0.503953
$$64$$ 1.00000 0.125000
$$65$$ −3.00000 + 5.19615i −0.372104 + 0.644503i
$$66$$ −12.0000 −1.47710
$$67$$ −1.00000 1.73205i −0.122169 0.211604i 0.798454 0.602056i $$-0.205652\pi$$
−0.920623 + 0.390453i $$0.872318\pi$$
$$68$$ 3.00000 0.363803
$$69$$ 6.00000 + 10.3923i 0.722315 + 1.25109i
$$70$$ −6.00000 10.3923i −0.717137 1.24212i
$$71$$ 6.00000 + 10.3923i 0.712069 + 1.23334i 0.964079 + 0.265615i $$0.0855750\pi$$
−0.252010 + 0.967725i $$0.581092\pi$$
$$72$$ 0.500000 0.866025i 0.0589256 0.102062i
$$73$$ −10.0000 −1.17041 −0.585206 0.810885i $$-0.698986\pi$$
−0.585206 + 0.810885i $$0.698986\pi$$
$$74$$ 5.00000 3.46410i 0.581238 0.402694i
$$75$$ −8.00000 −0.923760
$$76$$ −1.00000 + 1.73205i −0.114708 + 0.198680i
$$77$$ −12.0000 20.7846i −1.36753 2.36863i
$$78$$ −2.00000 3.46410i −0.226455 0.392232i
$$79$$ −7.00000 12.1244i −0.787562 1.36410i −0.927457 0.373930i $$-0.878010\pi$$
0.139895 0.990166i $$-0.455323\pi$$
$$80$$ 3.00000 0.335410
$$81$$ 5.50000 + 9.52628i 0.611111 + 1.05848i
$$82$$ −3.00000 −0.331295
$$83$$ −3.00000 + 5.19615i −0.329293 + 0.570352i −0.982372 0.186938i $$-0.940144\pi$$
0.653079 + 0.757290i $$0.273477\pi$$
$$84$$ 8.00000 0.872872
$$85$$ 9.00000 0.976187
$$86$$ −2.00000 + 3.46410i −0.215666 + 0.373544i
$$87$$ 3.00000 + 5.19615i 0.321634 + 0.557086i
$$88$$ 6.00000 0.639602
$$89$$ −1.50000 + 2.59808i −0.159000 + 0.275396i −0.934508 0.355942i $$-0.884160\pi$$
0.775509 + 0.631337i $$0.217494\pi$$
$$90$$ 1.50000 2.59808i 0.158114 0.273861i
$$91$$ 4.00000 6.92820i 0.419314 0.726273i
$$92$$ −3.00000 5.19615i −0.312772 0.541736i
$$93$$ 2.00000 + 3.46410i 0.207390 + 0.359211i
$$94$$ −3.00000 + 5.19615i −0.309426 + 0.535942i
$$95$$ −3.00000 + 5.19615i −0.307794 + 0.533114i
$$96$$ −1.00000 + 1.73205i −0.102062 + 0.176777i
$$97$$ −13.0000 −1.31995 −0.659975 0.751288i $$-0.729433\pi$$
−0.659975 + 0.751288i $$0.729433\pi$$
$$98$$ 4.50000 + 7.79423i 0.454569 + 0.787336i
$$99$$ 3.00000 5.19615i 0.301511 0.522233i
$$100$$ 4.00000 0.400000
$$101$$ 3.00000 0.298511 0.149256 0.988799i $$-0.452312\pi$$
0.149256 + 0.988799i $$0.452312\pi$$
$$102$$ −3.00000 + 5.19615i −0.297044 + 0.514496i
$$103$$ −4.00000 −0.394132 −0.197066 0.980390i $$-0.563141\pi$$
−0.197066 + 0.980390i $$0.563141\pi$$
$$104$$ 1.00000 + 1.73205i 0.0980581 + 0.169842i
$$105$$ 24.0000 2.34216
$$106$$ −3.00000 5.19615i −0.291386 0.504695i
$$107$$ 6.00000 + 10.3923i 0.580042 + 1.00466i 0.995474 + 0.0950377i $$0.0302972\pi$$
−0.415432 + 0.909624i $$0.636370\pi$$
$$108$$ −2.00000 3.46410i −0.192450 0.333333i
$$109$$ 0.500000 0.866025i 0.0478913 0.0829502i −0.841086 0.540901i $$-0.818083\pi$$
0.888977 + 0.457951i $$0.151417\pi$$
$$110$$ 18.0000 1.71623
$$111$$ 1.00000 + 12.1244i 0.0949158 + 1.15079i
$$112$$ −4.00000 −0.377964
$$113$$ 9.00000 15.5885i 0.846649 1.46644i −0.0375328 0.999295i $$-0.511950\pi$$
0.884182 0.467143i $$-0.154717\pi$$
$$114$$ −2.00000 3.46410i −0.187317 0.324443i
$$115$$ −9.00000 15.5885i −0.839254 1.45363i
$$116$$ −1.50000 2.59808i −0.139272 0.241225i
$$117$$ 2.00000 0.184900
$$118$$ 0 0
$$119$$ −12.0000 −1.10004
$$120$$ −3.00000 + 5.19615i −0.273861 + 0.474342i
$$121$$ 25.0000 2.27273
$$122$$ 1.00000 0.0905357
$$123$$ 3.00000 5.19615i 0.270501 0.468521i
$$124$$ −1.00000 1.73205i −0.0898027 0.155543i
$$125$$ −3.00000 −0.268328
$$126$$ −2.00000 + 3.46410i −0.178174 + 0.308607i
$$127$$ 5.00000 8.66025i 0.443678 0.768473i −0.554281 0.832330i $$-0.687007\pi$$
0.997959 + 0.0638564i $$0.0203400\pi$$
$$128$$ 0.500000 0.866025i 0.0441942 0.0765466i
$$129$$ −4.00000 6.92820i −0.352180 0.609994i
$$130$$ 3.00000 + 5.19615i 0.263117 + 0.455733i
$$131$$ −9.00000 + 15.5885i −0.786334 + 1.36197i 0.141865 + 0.989886i $$0.454690\pi$$
−0.928199 + 0.372084i $$0.878643\pi$$
$$132$$ −6.00000 + 10.3923i −0.522233 + 0.904534i
$$133$$ 4.00000 6.92820i 0.346844 0.600751i
$$134$$ −2.00000 −0.172774
$$135$$ −6.00000 10.3923i −0.516398 0.894427i
$$136$$ 1.50000 2.59808i 0.128624 0.222783i
$$137$$ 3.00000 0.256307 0.128154 0.991754i $$-0.459095\pi$$
0.128154 + 0.991754i $$0.459095\pi$$
$$138$$ 12.0000 1.02151
$$139$$ −1.00000 + 1.73205i −0.0848189 + 0.146911i −0.905314 0.424743i $$-0.860365\pi$$
0.820495 + 0.571654i $$0.193698\pi$$
$$140$$ −12.0000 −1.01419
$$141$$ −6.00000 10.3923i −0.505291 0.875190i
$$142$$ 12.0000 1.00702
$$143$$ 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
$$146$$ −5.00000 + 8.66025i −0.413803 + 0.716728i
$$147$$ −18.0000 −1.48461
$$148$$ −0.500000 6.06218i −0.0410997 0.498308i
$$149$$ −21.0000 −1.72039 −0.860194 0.509968i $$-0.829657\pi$$
−0.860194 + 0.509968i $$0.829657\pi$$
$$150$$ −4.00000 + 6.92820i −0.326599 + 0.565685i
$$151$$ 11.0000 + 19.0526i 0.895167 + 1.55048i 0.833597 + 0.552372i $$0.186277\pi$$
0.0615699 + 0.998103i $$0.480389\pi$$
$$152$$ 1.00000 + 1.73205i 0.0811107 + 0.140488i
$$153$$ −1.50000 2.59808i −0.121268 0.210042i
$$154$$ −24.0000 −1.93398
$$155$$ −3.00000 5.19615i −0.240966 0.417365i
$$156$$ −4.00000 −0.320256
$$157$$ −5.50000 + 9.52628i −0.438948 + 0.760280i −0.997609 0.0691164i $$-0.977982\pi$$
0.558661 + 0.829396i $$0.311315\pi$$
$$158$$ −14.0000 −1.11378
$$159$$ 12.0000 0.951662
$$160$$ 1.50000 2.59808i 0.118585 0.205396i
$$161$$ 12.0000 + 20.7846i 0.945732 + 1.63806i
$$162$$ 11.0000 0.864242
$$163$$ 8.00000 13.8564i 0.626608 1.08532i −0.361619 0.932326i $$-0.617776\pi$$
0.988227 0.152992i $$-0.0488907\pi$$
$$164$$ −1.50000 + 2.59808i −0.117130 + 0.202876i
$$165$$ −18.0000 + 31.1769i −1.40130 + 2.42712i
$$166$$ 3.00000 + 5.19615i 0.232845 + 0.403300i
$$167$$ −6.00000 10.3923i −0.464294 0.804181i 0.534875 0.844931i $$-0.320359\pi$$
−0.999169 + 0.0407502i $$0.987025\pi$$
$$168$$ 4.00000 6.92820i 0.308607 0.534522i
$$169$$ 4.50000 7.79423i 0.346154 0.599556i
$$170$$ 4.50000 7.79423i 0.345134 0.597790i
$$171$$ 2.00000 0.152944
$$172$$ 2.00000 + 3.46410i 0.152499 + 0.264135i
$$173$$ 10.5000 18.1865i 0.798300 1.38270i −0.122422 0.992478i $$-0.539066\pi$$
0.920722 0.390218i $$-0.127601\pi$$
$$174$$ 6.00000 0.454859
$$175$$ −16.0000 −1.20949
$$176$$ 3.00000 5.19615i 0.226134 0.391675i
$$177$$ 0 0
$$178$$ 1.50000 + 2.59808i 0.112430 + 0.194734i
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ −1.50000 2.59808i −0.111803 0.193649i
$$181$$ 0.500000 + 0.866025i 0.0371647 + 0.0643712i 0.884009 0.467469i $$-0.154834\pi$$
−0.846845 + 0.531840i $$0.821501\pi$$
$$182$$ −4.00000 6.92820i −0.296500 0.513553i
$$183$$ −1.00000 + 1.73205i −0.0739221 + 0.128037i
$$184$$ −6.00000 −0.442326
$$185$$ −1.50000 18.1865i −0.110282 1.33710i
$$186$$ 4.00000 0.293294
$$187$$ 9.00000 15.5885i 0.658145 1.13994i
$$188$$ 3.00000 + 5.19615i 0.218797 + 0.378968i
$$189$$ 8.00000 + 13.8564i 0.581914 + 1.00791i
$$190$$ 3.00000 + 5.19615i 0.217643 + 0.376969i
$$191$$ −6.00000 −0.434145 −0.217072 0.976156i $$-0.569651\pi$$
−0.217072 + 0.976156i $$0.569651\pi$$
$$192$$ 1.00000 + 1.73205i 0.0721688 + 0.125000i
$$193$$ 11.0000 0.791797 0.395899 0.918294i $$-0.370433\pi$$
0.395899 + 0.918294i $$0.370433\pi$$
$$194$$ −6.50000 + 11.2583i −0.466673 + 0.808301i
$$195$$ −12.0000 −0.859338
$$196$$ 9.00000 0.642857
$$197$$ −1.50000 + 2.59808i −0.106871 + 0.185105i −0.914501 0.404584i $$-0.867416\pi$$
0.807630 + 0.589689i $$0.200750\pi$$
$$198$$ −3.00000 5.19615i −0.213201 0.369274i
$$199$$ 8.00000 0.567105 0.283552 0.958957i $$-0.408487\pi$$
0.283552 + 0.958957i $$0.408487\pi$$
$$200$$ 2.00000 3.46410i 0.141421 0.244949i
$$201$$ 2.00000 3.46410i 0.141069 0.244339i
$$202$$ 1.50000 2.59808i 0.105540 0.182800i
$$203$$ 6.00000 + 10.3923i 0.421117 + 0.729397i
$$204$$ 3.00000 + 5.19615i 0.210042 + 0.363803i
$$205$$ −4.50000 + 7.79423i −0.314294 + 0.544373i
$$206$$ −2.00000 + 3.46410i −0.139347 + 0.241355i
$$207$$ −3.00000 + 5.19615i −0.208514 + 0.361158i
$$208$$ 2.00000 0.138675
$$209$$ 6.00000 + 10.3923i 0.415029 + 0.718851i
$$210$$ 12.0000 20.7846i 0.828079 1.43427i
$$211$$ −16.0000 −1.10149 −0.550743 0.834675i $$-0.685655\pi$$
−0.550743 + 0.834675i $$0.685655\pi$$
$$212$$ −6.00000 −0.412082
$$213$$ −12.0000 + 20.7846i −0.822226 + 1.42414i
$$214$$ 12.0000 0.820303
$$215$$ 6.00000 + 10.3923i 0.409197 + 0.708749i
$$216$$ −4.00000 −0.272166
$$217$$ 4.00000 + 6.92820i 0.271538 + 0.470317i
$$218$$ −0.500000 0.866025i −0.0338643 0.0586546i
$$219$$ −10.0000 17.3205i −0.675737 1.17041i
$$220$$ 9.00000 15.5885i 0.606780 1.05097i
$$221$$ 6.00000 0.403604
$$222$$ 11.0000 + 5.19615i 0.738272 + 0.348743i
$$223$$ 14.0000 0.937509 0.468755 0.883328i $$-0.344703\pi$$
0.468755 + 0.883328i $$0.344703\pi$$
$$224$$ −2.00000 + 3.46410i −0.133631 + 0.231455i
$$225$$ −2.00000 3.46410i −0.133333 0.230940i
$$226$$ −9.00000 15.5885i −0.598671 1.03693i
$$227$$ 9.00000 + 15.5885i 0.597351 + 1.03464i 0.993210 + 0.116331i $$0.0371134\pi$$
−0.395860 + 0.918311i $$0.629553\pi$$
$$228$$ −4.00000 −0.264906
$$229$$ −5.50000 9.52628i −0.363450 0.629514i 0.625076 0.780564i $$-0.285068\pi$$
−0.988526 + 0.151050i $$0.951735\pi$$
$$230$$ −18.0000 −1.18688
$$231$$ 24.0000 41.5692i 1.57908 2.73505i
$$232$$ −3.00000 −0.196960
$$233$$ −9.00000 −0.589610 −0.294805 0.955557i $$-0.595255\pi$$
−0.294805 + 0.955557i $$0.595255\pi$$
$$234$$ 1.00000 1.73205i 0.0653720 0.113228i
$$235$$ 9.00000 + 15.5885i 0.587095 + 1.01688i
$$236$$ 0 0
$$237$$ 14.0000 24.2487i 0.909398 1.57512i
$$238$$ −6.00000 + 10.3923i −0.388922 + 0.673633i
$$239$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$240$$ 3.00000 + 5.19615i 0.193649 + 0.335410i
$$241$$ −7.00000 12.1244i −0.450910 0.780998i 0.547533 0.836784i $$-0.315567\pi$$
−0.998443 + 0.0557856i $$0.982234\pi$$
$$242$$ 12.5000 21.6506i 0.803530 1.39176i
$$243$$ −5.00000 + 8.66025i −0.320750 + 0.555556i
$$244$$ 0.500000 0.866025i 0.0320092 0.0554416i
$$245$$ 27.0000 1.72497
$$246$$ −3.00000 5.19615i −0.191273 0.331295i
$$247$$ −2.00000 + 3.46410i −0.127257 + 0.220416i
$$248$$ −2.00000 −0.127000
$$249$$ −12.0000 −0.760469
$$250$$ −1.50000 + 2.59808i −0.0948683 + 0.164317i
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 2.00000 + 3.46410i 0.125988 + 0.218218i
$$253$$ −36.0000 −2.26330
$$254$$ −5.00000 8.66025i −0.313728 0.543393i
$$255$$ 9.00000 + 15.5885i 0.563602 + 0.976187i
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ −13.5000 + 23.3827i −0.842107 + 1.45857i 0.0460033 + 0.998941i $$0.485352\pi$$
−0.888110 + 0.459631i $$0.847982\pi$$
$$258$$ −8.00000 −0.498058
$$259$$ 2.00000 + 24.2487i 0.124274 + 1.50674i
$$260$$ 6.00000 0.372104
$$261$$ −1.50000 + 2.59808i −0.0928477 + 0.160817i
$$262$$ 9.00000 + 15.5885i 0.556022 + 0.963058i
$$263$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$264$$ 6.00000 + 10.3923i 0.369274 + 0.639602i
$$265$$ −18.0000 −1.10573
$$266$$ −4.00000 6.92820i −0.245256 0.424795i
$$267$$ −6.00000 −0.367194
$$268$$ −1.00000 + 1.73205i −0.0610847 + 0.105802i
$$269$$ 18.0000 1.09748 0.548740 0.835993i $$-0.315108\pi$$
0.548740 + 0.835993i $$0.315108\pi$$
$$270$$ −12.0000 −0.730297
$$271$$ 5.00000 8.66025i 0.303728 0.526073i −0.673249 0.739416i $$-0.735102\pi$$
0.976977 + 0.213343i $$0.0684351\pi$$
$$272$$ −1.50000 2.59808i −0.0909509 0.157532i
$$273$$ 16.0000 0.968364
$$274$$ 1.50000 2.59808i 0.0906183 0.156956i
$$275$$ 12.0000 20.7846i 0.723627 1.25336i
$$276$$ 6.00000 10.3923i 0.361158 0.625543i
$$277$$ 0.500000 + 0.866025i 0.0300421 + 0.0520344i 0.880656 0.473757i $$-0.157103\pi$$
−0.850613 + 0.525792i $$0.823769\pi$$
$$278$$ 1.00000 + 1.73205i 0.0599760 + 0.103882i
$$279$$ −1.00000 + 1.73205i −0.0598684 + 0.103695i
$$280$$ −6.00000 + 10.3923i −0.358569 + 0.621059i
$$281$$ −7.50000 + 12.9904i −0.447412 + 0.774941i −0.998217 0.0596933i $$-0.980988\pi$$
0.550804 + 0.834634i $$0.314321\pi$$
$$282$$ −12.0000 −0.714590
$$283$$ 8.00000 + 13.8564i 0.475551 + 0.823678i 0.999608 0.0280052i $$-0.00891551\pi$$
−0.524057 + 0.851683i $$0.675582\pi$$
$$284$$ 6.00000 10.3923i 0.356034 0.616670i
$$285$$ −12.0000 −0.710819
$$286$$ 12.0000 0.709575
$$287$$ 6.00000 10.3923i 0.354169 0.613438i
$$288$$ −1.00000 −0.0589256
$$289$$ 4.00000 + 6.92820i 0.235294 + 0.407541i
$$290$$ −9.00000 −0.528498
$$291$$ −13.0000 22.5167i −0.762073 1.31995i
$$292$$ 5.00000 + 8.66025i 0.292603 + 0.506803i
$$293$$ −1.50000 2.59808i −0.0876309 0.151781i 0.818878 0.573967i $$-0.194596\pi$$
−0.906509 + 0.422186i $$0.861263\pi$$
$$294$$ −9.00000 + 15.5885i −0.524891 + 0.909137i
$$295$$ 0 0
$$296$$ −5.50000 2.59808i −0.319681 0.151010i
$$297$$ −24.0000 −1.39262
$$298$$ −10.5000 + 18.1865i −0.608249 + 1.05352i
$$299$$ −6.00000 10.3923i −0.346989 0.601003i
$$300$$ 4.00000 + 6.92820i 0.230940 + 0.400000i
$$301$$ −8.00000 13.8564i −0.461112 0.798670i
$$302$$ 22.0000 1.26596
$$303$$ 3.00000 + 5.19615i 0.172345 + 0.298511i
$$304$$ 2.00000 0.114708
$$305$$ 1.50000 2.59808i 0.0858898 0.148765i
$$306$$ −3.00000 −0.171499
$$307$$ −28.0000 −1.59804 −0.799022 0.601302i $$-0.794649\pi$$
−0.799022 + 0.601302i $$0.794649\pi$$
$$308$$ −12.0000 + 20.7846i −0.683763 + 1.18431i
$$309$$ −4.00000 6.92820i −0.227552 0.394132i
$$310$$ −6.00000 −0.340777
$$311$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$312$$ −2.00000 + 3.46410i −0.113228 + 0.196116i
$$313$$ 6.50000 11.2583i 0.367402 0.636358i −0.621757 0.783210i $$-0.713581\pi$$
0.989158 + 0.146852i $$0.0469141\pi$$
$$314$$ 5.50000 + 9.52628i 0.310383 + 0.537599i
$$315$$ 6.00000 + 10.3923i 0.338062 + 0.585540i
$$316$$ −7.00000 + 12.1244i −0.393781 + 0.682048i
$$317$$ 10.5000 18.1865i 0.589739 1.02146i −0.404528 0.914526i $$-0.632564\pi$$
0.994266 0.106932i $$-0.0341026\pi$$
$$318$$ 6.00000 10.3923i 0.336463 0.582772i
$$319$$ −18.0000 −1.00781
$$320$$ −1.50000 2.59808i −0.0838525 0.145237i
$$321$$ −12.0000 + 20.7846i −0.669775 + 1.16008i
$$322$$ 24.0000 1.33747
$$323$$ 6.00000 0.333849
$$324$$ 5.50000 9.52628i 0.305556 0.529238i
$$325$$ 8.00000 0.443760
$$326$$ −8.00000 13.8564i −0.443079 0.767435i
$$327$$ 2.00000 0.110600
$$328$$ 1.50000 + 2.59808i 0.0828236 + 0.143455i
$$329$$ −12.0000 20.7846i −0.661581 1.14589i
$$330$$ 18.0000 + 31.1769i 0.990867 + 1.71623i
$$331$$ 2.00000 3.46410i 0.109930 0.190404i −0.805812 0.592172i $$-0.798271\pi$$
0.915742 + 0.401768i $$0.131604\pi$$
$$332$$ 6.00000 0.329293
$$333$$ −5.00000 + 3.46410i −0.273998 + 0.189832i
$$334$$ −12.0000 −0.656611
$$335$$ −3.00000 + 5.19615i −0.163908 + 0.283896i
$$336$$ −4.00000 6.92820i −0.218218 0.377964i
$$337$$ 12.5000 + 21.6506i 0.680918 + 1.17939i 0.974701 + 0.223513i $$0.0717525\pi$$
−0.293783 + 0.955872i $$0.594914\pi$$
$$338$$ −4.50000 7.79423i −0.244768 0.423950i
$$339$$ 36.0000 1.95525
$$340$$ −4.50000 7.79423i −0.244047 0.422701i
$$341$$ −12.0000 −0.649836
$$342$$ 1.00000 1.73205i 0.0540738 0.0936586i
$$343$$ −8.00000 −0.431959
$$344$$ 4.00000 0.215666
$$345$$ 18.0000 31.1769i 0.969087 1.67851i
$$346$$ −10.5000 18.1865i −0.564483 0.977714i
$$347$$ 6.00000 0.322097 0.161048 0.986947i $$-0.448512\pi$$
0.161048 + 0.986947i $$0.448512\pi$$
$$348$$ 3.00000 5.19615i 0.160817 0.278543i
$$349$$ 0.500000 0.866025i 0.0267644 0.0463573i −0.852333 0.523000i $$-0.824813\pi$$
0.879097 + 0.476642i $$0.158146\pi$$
$$350$$ −8.00000 + 13.8564i −0.427618 + 0.740656i
$$351$$ −4.00000 6.92820i −0.213504 0.369800i
$$352$$ −3.00000 5.19615i −0.159901 0.276956i
$$353$$ 10.5000 18.1865i 0.558859 0.967972i −0.438733 0.898617i $$-0.644573\pi$$
0.997592 0.0693543i $$-0.0220939\pi$$
$$354$$ 0 0
$$355$$ 18.0000 31.1769i 0.955341 1.65470i
$$356$$ 3.00000 0.159000
$$357$$ −12.0000 20.7846i −0.635107 1.10004i
$$358$$ 0 0
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ −3.00000 −0.158114
$$361$$ 7.50000 12.9904i 0.394737 0.683704i
$$362$$ 1.00000 0.0525588
$$363$$ 25.0000 + 43.3013i 1.31216 + 2.27273i
$$364$$ −8.00000 −0.419314
$$365$$ 15.0000 + 25.9808i 0.785136 + 1.35990i
$$366$$ 1.00000 + 1.73205i 0.0522708 + 0.0905357i
$$367$$ 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
$$370$$ −16.5000 7.79423i −0.857794 0.405203i
$$371$$ 24.0000 1.24602
$$372$$ 2.00000 3.46410i 0.103695 0.179605i
$$373$$ 12.5000 + 21.6506i 0.647225 + 1.12103i 0.983783 + 0.179364i $$0.0574041\pi$$
−0.336557 + 0.941663i $$0.609263\pi$$
$$374$$ −9.00000 15.5885i −0.465379 0.806060i
$$375$$ −3.00000 5.19615i −0.154919 0.268328i
$$376$$ 6.00000 0.309426
$$377$$ −3.00000 5.19615i −0.154508 0.267615i
$$378$$ 16.0000 0.822951
$$379$$ 8.00000 13.8564i 0.410932 0.711756i −0.584060 0.811711i $$-0.698537\pi$$
0.994992 + 0.0999550i $$0.0318699\pi$$
$$380$$ 6.00000 0.307794
$$381$$ 20.0000 1.02463
$$382$$ −3.00000 + 5.19615i −0.153493 + 0.265858i
$$383$$ −6.00000 10.3923i −0.306586 0.531022i 0.671027 0.741433i $$-0.265853\pi$$
−0.977613 + 0.210411i $$0.932520\pi$$
$$384$$ 2.00000 0.102062
$$385$$ −36.0000 + 62.3538i −1.83473 + 3.17785i
$$386$$ 5.50000 9.52628i 0.279943 0.484875i
$$387$$ 2.00000 3.46410i 0.101666 0.176090i
$$388$$ 6.50000 + 11.2583i 0.329988 + 0.571555i
$$389$$ 4.50000 + 7.79423i 0.228159 + 0.395183i 0.957263 0.289220i $$-0.0933960\pi$$
−0.729103 + 0.684403i $$0.760063\pi$$
$$390$$ −6.00000 + 10.3923i −0.303822 + 0.526235i
$$391$$ −9.00000 + 15.5885i −0.455150 + 0.788342i
$$392$$ 4.50000 7.79423i 0.227284 0.393668i
$$393$$ −36.0000 −1.81596
$$394$$ 1.50000 + 2.59808i 0.0755689 + 0.130889i
$$395$$ −21.0000 + 36.3731i −1.05662 + 1.83013i
$$396$$ −6.00000 −0.301511
$$397$$ 35.0000 1.75660 0.878300 0.478110i $$-0.158678\pi$$
0.878300 + 0.478110i $$0.158678\pi$$
$$398$$ 4.00000 6.92820i 0.200502 0.347279i
$$399$$ 16.0000 0.801002
$$400$$ −2.00000 3.46410i −0.100000 0.173205i
$$401$$ 6.00000 0.299626 0.149813 0.988714i $$-0.452133\pi$$
0.149813 + 0.988714i $$0.452133\pi$$
$$402$$ −2.00000 3.46410i −0.0997509 0.172774i
$$403$$ −2.00000 3.46410i −0.0996271 0.172559i
$$404$$ −1.50000 2.59808i −0.0746278 0.129259i
$$405$$ 16.5000 28.5788i 0.819892 1.42009i
$$406$$ 12.0000 0.595550
$$407$$ −33.0000 15.5885i −1.63575 0.772691i
$$408$$ 6.00000 0.297044
$$409$$ −5.50000 + 9.52628i −0.271957 + 0.471044i −0.969363 0.245633i $$-0.921004\pi$$
0.697406 + 0.716677i $$0.254338\pi$$
$$410$$ 4.50000 + 7.79423i 0.222239 + 0.384930i
$$411$$ 3.00000 + 5.19615i 0.147979 + 0.256307i
$$412$$ 2.00000 + 3.46410i 0.0985329 + 0.170664i
$$413$$ 0 0
$$414$$ 3.00000 + 5.19615i 0.147442 + 0.255377i
$$415$$ 18.0000 0.883585
$$416$$ 1.00000 1.73205i 0.0490290 0.0849208i
$$417$$ −4.00000 −0.195881
$$418$$ 12.0000 0.586939
$$419$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$420$$ −12.0000 20.7846i −0.585540 1.01419i
$$421$$ −37.0000 −1.80327 −0.901635 0.432498i $$-0.857632\pi$$
−0.901635 + 0.432498i $$0.857632\pi$$
$$422$$ −8.00000 + 13.8564i −0.389434 + 0.674519i
$$423$$ 3.00000 5.19615i 0.145865 0.252646i
$$424$$ −3.00000 + 5.19615i −0.145693 + 0.252347i
$$425$$ −6.00000 10.3923i −0.291043 0.504101i
$$426$$ 12.0000 + 20.7846i 0.581402 + 1.00702i
$$427$$ −2.00000 + 3.46410i −0.0967868 + 0.167640i
$$428$$ 6.00000 10.3923i 0.290021 0.502331i
$$429$$ −12.0000 + 20.7846i −0.579365 + 1.00349i
$$430$$ 12.0000 0.578691
$$431$$ −3.00000 5.19615i −0.144505 0.250290i 0.784683 0.619897i $$-0.212826\pi$$
−0.929188 + 0.369607i $$0.879492\pi$$
$$432$$ −2.00000 + 3.46410i −0.0962250 + 0.166667i
$$433$$ −25.0000 −1.20142 −0.600712 0.799466i $$-0.705116\pi$$
−0.600712 + 0.799466i $$0.705116\pi$$
$$434$$ 8.00000 0.384012
$$435$$ 9.00000 15.5885i 0.431517 0.747409i
$$436$$ −1.00000 −0.0478913
$$437$$ −6.00000 10.3923i −0.287019 0.497131i
$$438$$ −20.0000 −0.955637
$$439$$ −16.0000 27.7128i −0.763638 1.32266i −0.940963 0.338508i $$-0.890078\pi$$
0.177325 0.984152i $$-0.443256\pi$$
$$440$$ −9.00000 15.5885i −0.429058 0.743151i
$$441$$ −4.50000 7.79423i −0.214286 0.371154i
$$442$$ 3.00000 5.19615i 0.142695 0.247156i
$$443$$ −24.0000 −1.14027 −0.570137 0.821549i $$-0.693110\pi$$
−0.570137 + 0.821549i $$0.693110\pi$$
$$444$$ 10.0000 6.92820i 0.474579 0.328798i
$$445$$ 9.00000 0.426641
$$446$$ 7.00000 12.1244i 0.331460 0.574105i
$$447$$ −21.0000 36.3731i −0.993266 1.72039i
$$448$$ 2.00000 + 3.46410i 0.0944911 + 0.163663i
$$449$$ −3.00000 5.19615i −0.141579 0.245222i 0.786513 0.617574i $$-0.211885\pi$$
−0.928091 + 0.372353i $$0.878551\pi$$
$$450$$ −4.00000 −0.188562
$$451$$ 9.00000 + 15.5885i 0.423793 + 0.734032i
$$452$$ −18.0000 −0.846649
$$453$$ −22.0000 + 38.1051i −1.03365 + 1.79033i
$$454$$ 18.0000 0.844782
$$455$$ −24.0000 −1.12514
$$456$$ −2.00000 + 3.46410i −0.0936586 + 0.162221i
$$457$$ 18.5000 + 32.0429i 0.865393 + 1.49891i 0.866656 + 0.498906i $$0.166265\pi$$
−0.00126243 + 0.999999i $$0.500402\pi$$
$$458$$ −11.0000 −0.513996
$$459$$ −6.00000 + 10.3923i −0.280056 + 0.485071i
$$460$$ −9.00000 + 15.5885i −0.419627 + 0.726816i
$$461$$ 15.0000 25.9808i 0.698620 1.21004i −0.270326 0.962769i $$-0.587131\pi$$
0.968945 0.247276i $$-0.0795353\pi$$
$$462$$ −24.0000 41.5692i −1.11658 1.93398i
$$463$$ 8.00000 + 13.8564i 0.371792 + 0.643962i 0.989841 0.142177i $$-0.0454103\pi$$
−0.618050 + 0.786139i $$0.712077\pi$$
$$464$$ −1.50000 + 2.59808i −0.0696358 + 0.120613i
$$465$$ 6.00000 10.3923i 0.278243 0.481932i
$$466$$ −4.50000 + 7.79423i −0.208458 + 0.361061i
$$467$$ 36.0000 1.66588 0.832941 0.553362i $$-0.186655\pi$$
0.832941 + 0.553362i $$0.186655\pi$$
$$468$$ −1.00000 1.73205i −0.0462250 0.0800641i
$$469$$ 4.00000 6.92820i 0.184703 0.319915i
$$470$$ 18.0000 0.830278
$$471$$ −22.0000 −1.01371
$$472$$ 0 0
$$473$$ 24.0000 1.10352
$$474$$ −14.0000 24.2487i −0.643041 1.11378i
$$475$$ 8.00000 0.367065
$$476$$ 6.00000 + 10.3923i 0.275010 + 0.476331i
$$477$$ 3.00000 + 5.19615i 0.137361 + 0.237915i
$$478$$ 0 0
$$479$$ −12.0000 + 20.7846i −0.548294 + 0.949673i 0.450098 + 0.892979i $$0.351389\pi$$
−0.998392 + 0.0566937i $$0.981944\pi$$
$$480$$ 6.00000 0.273861
$$481$$ −1.00000 12.1244i −0.0455961 0.552823i
$$482$$ −14.0000 −0.637683
$$483$$ −24.0000 + 41.5692i −1.09204 + 1.89146i
$$484$$ −12.5000 21.6506i −0.568182 0.984120i
$$485$$ 19.5000 + 33.7750i 0.885449 + 1.53364i
$$486$$ 5.00000 + 8.66025i 0.226805 + 0.392837i
$$487$$ 2.00000 0.0906287 0.0453143 0.998973i $$-0.485571\pi$$
0.0453143 + 0.998973i $$0.485571\pi$$
$$488$$ −0.500000 0.866025i −0.0226339 0.0392031i
$$489$$ 32.0000 1.44709
$$490$$ 13.5000 23.3827i 0.609868 1.05632i
$$491$$ 6.00000 0.270776 0.135388 0.990793i $$-0.456772\pi$$
0.135388 + 0.990793i $$0.456772\pi$$
$$492$$ −6.00000 −0.270501
$$493$$ −4.50000 + 7.79423i −0.202670 + 0.351034i
$$494$$ 2.00000 + 3.46410i 0.0899843 + 0.155857i
$$495$$ −18.0000 −0.809040
$$496$$ −1.00000 + 1.73205i −0.0449013 + 0.0777714i
$$497$$ −24.0000 + 41.5692i −1.07655 + 1.86463i
$$498$$ −6.00000 + 10.3923i −0.268866 + 0.465690i
$$499$$ −7.00000 12.1244i −0.313363 0.542761i 0.665725 0.746197i $$-0.268122\pi$$
−0.979088 + 0.203436i $$0.934789\pi$$
$$500$$ 1.50000 + 2.59808i 0.0670820 + 0.116190i
$$501$$ 12.0000 20.7846i 0.536120 0.928588i
$$502$$ 0 0
$$503$$ −15.0000 + 25.9808i −0.668817 + 1.15842i 0.309418 + 0.950926i $$0.399866\pi$$
−0.978235 + 0.207499i $$0.933468\pi$$
$$504$$ 4.00000 0.178174
$$505$$ −4.50000 7.79423i −0.200247 0.346839i
$$506$$ −18.0000 + 31.1769i −0.800198 + 1.38598i
$$507$$ 18.0000 0.799408
$$508$$ −10.0000 −0.443678
$$509$$ −13.5000 + 23.3827i −0.598377 + 1.03642i 0.394684 + 0.918817i $$0.370854\pi$$
−0.993061 + 0.117602i $$0.962479\pi$$
$$510$$ 18.0000 0.797053
$$511$$ −20.0000 34.6410i −0.884748 1.53243i
$$512$$ −1.00000 −0.0441942
$$513$$ −4.00000 6.92820i −0.176604 0.305888i
$$514$$ 13.5000 + 23.3827i 0.595459 + 1.03137i
$$515$$ 6.00000 + 10.3923i 0.264392 + 0.457940i
$$516$$ −4.00000 + 6.92820i −0.176090 + 0.304997i
$$517$$ 36.0000 1.58328
$$518$$ 22.0000 + 10.3923i 0.966625 + 0.456612i
$$519$$ 42.0000 1.84360
$$520$$ 3.00000 5.19615i 0.131559 0.227866i
$$521$$ −3.00000 5.19615i −0.131432 0.227648i 0.792797 0.609486i $$-0.208624\pi$$
−0.924229 + 0.381839i $$0.875291\pi$$
$$522$$ 1.50000 + 2.59808i 0.0656532 + 0.113715i
$$523$$ −13.0000 22.5167i −0.568450 0.984585i −0.996719 0.0809336i $$-0.974210\pi$$
0.428269 0.903651i $$-0.359124\pi$$
$$524$$ 18.0000 0.786334
$$525$$ −16.0000 27.7128i −0.698297 1.20949i
$$526$$ 0 0
$$527$$ −3.00000 + 5.19615i −0.130682 + 0.226348i
$$528$$ 12.0000 0.522233
$$529$$ 13.0000 0.565217
$$530$$ −9.00000 + 15.5885i −0.390935 + 0.677119i
$$531$$ 0 0
$$532$$ −8.00000 −0.346844
$$533$$ −3.00000 + 5.19615i −0.129944 + 0.225070i
$$534$$ −3.00000 + 5.19615i −0.129823 + 0.224860i
$$535$$ 18.0000 31.1769i 0.778208 1.34790i
$$536$$ 1.00000 + 1.73205i 0.0431934 + 0.0748132i
$$537$$ 0 0
$$538$$ 9.00000 15.5885i 0.388018 0.672066i
$$539$$ 27.0000 46.7654i 1.16297 2.01433i
$$540$$ −6.00000 + 10.3923i −0.258199 + 0.447214i
$$541$$ 35.0000 1.50477 0.752384 0.658725i $$-0.228904\pi$$
0.752384 + 0.658725i $$0.228904\pi$$
$$542$$ −5.00000 8.66025i −0.214768 0.371990i
$$543$$ −1.00000 + 1.73205i −0.0429141 + 0.0743294i
$$544$$ −3.00000 −0.128624
$$545$$ −3.00000 −0.128506
$$546$$ 8.00000 13.8564i 0.342368 0.592999i
$$547$$ −22.0000 −0.940652 −0.470326 0.882493i $$-0.655864\pi$$
−0.470326 + 0.882493i $$0.655864\pi$$
$$548$$ −1.50000 2.59808i −0.0640768 0.110984i
$$549$$ −1.00000 −0.0426790
$$550$$ −12.0000 20.7846i −0.511682 0.886259i
$$551$$ −3.00000 5.19615i −0.127804 0.221364i
$$552$$ −6.00000 10.3923i −0.255377 0.442326i
$$553$$ 28.0000 48.4974i 1.19068 2.06232i
$$554$$ 1.00000 0.0424859
$$555$$ 30.0000 20.7846i 1.27343 0.882258i
$$556$$ 2.00000 0.0848189
$$557$$ 16.5000 28.5788i 0.699127 1.21092i −0.269642 0.962961i $$-0.586905\pi$$
0.968769 0.247964i $$-0.0797613\pi$$
$$558$$ 1.00000 + 1.73205i 0.0423334 + 0.0733236i
$$559$$ 4.00000 + 6.92820i 0.169182 + 0.293032i
$$560$$ 6.00000 + 10.3923i 0.253546 + 0.439155i
$$561$$ 36.0000 1.51992
$$562$$ 7.50000 + 12.9904i 0.316368 + 0.547966i
$$563$$ 6.00000 0.252870 0.126435 0.991975i $$-0.459647\pi$$
0.126435 + 0.991975i $$0.459647\pi$$
$$564$$ −6.00000 + 10.3923i −0.252646 + 0.437595i
$$565$$ −54.0000 −2.27180
$$566$$ 16.0000 0.672530
$$567$$ −22.0000 + 38.1051i −0.923913 + 1.60026i
$$568$$ −6.00000 10.3923i −0.251754 0.436051i
$$569$$ 3.00000 0.125767 0.0628833 0.998021i $$-0.479970\pi$$
0.0628833 + 0.998021i $$0.479970\pi$$
$$570$$ −6.00000 + 10.3923i −0.251312 + 0.435286i
$$571$$ −19.0000 + 32.9090i −0.795125 + 1.37720i 0.127634 + 0.991821i $$0.459262\pi$$
−0.922760 + 0.385376i $$0.874072\pi$$
$$572$$ 6.00000 10.3923i 0.250873 0.434524i
$$573$$ −6.00000 10.3923i −0.250654 0.434145i
$$574$$ −6.00000 10.3923i −0.250435 0.433766i
$$575$$ −12.0000 + 20.7846i −0.500435 + 0.866778i
$$576$$ −0.500000 + 0.866025i −0.0208333 + 0.0360844i
$$577$$ 17.0000 29.4449i 0.707719 1.22581i −0.257982 0.966150i $$-0.583058\pi$$
0.965701 0.259656i $$-0.0836092\pi$$
$$578$$ 8.00000 0.332756
$$579$$ 11.0000 + 19.0526i 0.457144 + 0.791797i
$$580$$ −4.50000 + 7.79423i −0.186852 + 0.323638i
$$581$$ −24.0000 −0.995688
$$582$$ −26.0000 −1.07773
$$583$$ −18.0000 + 31.1769i −0.745484 + 1.29122i
$$584$$ 10.0000 0.413803
$$585$$ −3.00000 5.19615i −0.124035 0.214834i
$$586$$ −3.00000 −0.123929
$$587$$ −9.00000 15.5885i −0.371470 0.643404i 0.618322 0.785925i $$-0.287813\pi$$
−0.989792 + 0.142520i $$0.954479\pi$$
$$588$$ 9.00000 + 15.5885i 0.371154 + 0.642857i
$$589$$ −2.00000 3.46410i −0.0824086 0.142736i
$$590$$ 0 0
$$591$$ −6.00000 −0.246807
$$592$$ −5.00000 + 3.46410i −0.205499 + 0.142374i
$$593$$ 27.0000 1.10876 0.554379 0.832265i $$-0.312956\pi$$
0.554379 + 0.832265i $$0.312956\pi$$
$$594$$ −12.0000 + 20.7846i −0.492366 + 0.852803i
$$595$$ 18.0000 + 31.1769i 0.737928 + 1.27813i
$$596$$ 10.5000 + 18.1865i 0.430097 + 0.744949i
$$597$$ 8.00000 + 13.8564i 0.327418 + 0.567105i
$$598$$ −12.0000 −0.490716
$$599$$ 3.00000 + 5.19615i 0.122577 + 0.212309i 0.920783 0.390075i $$-0.127551\pi$$
−0.798206 + 0.602384i $$0.794218\pi$$
$$600$$ 8.00000 0.326599
$$601$$ 6.50000 11.2583i 0.265141 0.459237i −0.702460 0.711723i $$-0.747915\pi$$
0.967600 + 0.252486i $$0.0812483\pi$$
$$602$$ −16.0000 −0.652111
$$603$$ 2.00000 0.0814463
$$604$$ 11.0000 19.0526i 0.447584 0.775238i
$$605$$ −37.5000 64.9519i −1.52459 2.64067i
$$606$$ 6.00000 0.243733
$$607$$ 11.0000 19.0526i 0.446476 0.773320i −0.551678 0.834058i $$-0.686012\pi$$
0.998154 + 0.0607380i $$0.0193454\pi$$
$$608$$ 1.00000 1.73205i 0.0405554 0.0702439i
$$609$$ −12.0000 + 20.7846i −0.486265 + 0.842235i
$$610$$ −1.50000 2.59808i −0.0607332 0.105193i
$$611$$ 6.00000 + 10.3923i 0.242734 + 0.420428i
$$612$$ −1.50000 + 2.59808i −0.0606339 + 0.105021i
$$613$$ 12.5000 21.6506i 0.504870 0.874461i −0.495114 0.868828i $$-0.664874\pi$$
0.999984 0.00563283i $$-0.00179300\pi$$
$$614$$ −14.0000 + 24.2487i −0.564994 + 0.978598i
$$615$$ −18.0000 −0.725830
$$616$$ 12.0000 + 20.7846i 0.483494 + 0.837436i
$$617$$ 9.00000 15.5885i 0.362326 0.627568i −0.626017 0.779809i $$-0.715316\pi$$
0.988343 + 0.152242i $$0.0486493\pi$$
$$618$$ −8.00000 −0.321807
$$619$$ −40.0000 −1.60774 −0.803868 0.594808i $$-0.797228\pi$$
−0.803868 + 0.594808i $$0.797228\pi$$
$$620$$ −3.00000 + 5.19615i −0.120483 + 0.208683i
$$621$$ 24.0000 0.963087
$$622$$ 0 0
$$623$$ −12.0000 −0.480770
$$624$$ 2.00000 + 3.46410i 0.0800641 + 0.138675i
$$625$$ 14.5000 + 25.1147i 0.580000 + 1.00459i
$$626$$ −6.50000 11.2583i −0.259792 0.449973i
$$627$$ −12.0000 + 20.7846i −0.479234 + 0.830057i
$$628$$ 11.0000 0.438948
$$629$$ −15.0000 + 10.3923i −0.598089 + 0.414368i
$$630$$ 12.0000 0.478091
$$631$$ 5.00000 8.66025i 0.199047 0.344759i −0.749173 0.662375i $$-0.769549\pi$$
0.948220 + 0.317615i $$0.102882\pi$$
$$632$$ 7.00000 + 12.1244i 0.278445 + 0.482281i
$$633$$ −16.0000 27.7128i −0.635943 1.10149i
$$634$$ −10.5000 18.1865i −0.417008 0.722280i
$$635$$ −30.0000 −1.19051
$$636$$ −6.00000 10.3923i −0.237915 0.412082i
$$637$$ 18.0000 0.713186
$$638$$ −9.00000 + 15.5885i −0.356313 + 0.617153i
$$639$$ −12.0000 −0.474713
$$640$$ −3.00000 −0.118585
$$641$$ 10.5000 18.1865i 0.414725 0.718325i −0.580674 0.814136i $$-0.697211\pi$$
0.995400 + 0.0958109i $$0.0305444\pi$$
$$642$$ 12.0000 + 20.7846i 0.473602 + 0.820303i
$$643$$ −34.0000 −1.34083 −0.670415 0.741987i $$-0.733884\pi$$
−0.670415 + 0.741987i $$0.733884\pi$$
$$644$$ 12.0000 20.7846i 0.472866 0.819028i
$$645$$ −12.0000 + 20.7846i −0.472500 + 0.818393i
$$646$$ 3.00000 5.19615i 0.118033 0.204440i
$$647$$ −12.0000 20.7846i −0.471769 0.817127i 0.527710 0.849425i $$-0.323051\pi$$
−0.999478 + 0.0322975i $$0.989718\pi$$
$$648$$ −5.50000 9.52628i −0.216060 0.374228i
$$649$$ 0 0
$$650$$ 4.00000 6.92820i 0.156893 0.271746i
$$651$$ −8.00000 + 13.8564i −0.313545 + 0.543075i
$$652$$ −16.0000 −0.626608
$$653$$ −1.50000 2.59808i −0.0586995 0.101671i 0.835182 0.549973i $$-0.185362\pi$$
−0.893882 + 0.448303i $$0.852029\pi$$
$$654$$ 1.00000 1.73205i 0.0391031 0.0677285i
$$655$$ 54.0000 2.10995
$$656$$ 3.00000 0.117130
$$657$$ 5.00000 8.66025i 0.195069 0.337869i
$$658$$ −24.0000 −0.935617
$$659$$ 18.0000 + 31.1769i 0.701180 + 1.21448i 0.968052 + 0.250748i $$0.0806766\pi$$
−0.266872 + 0.963732i $$0.585990\pi$$
$$660$$ 36.0000 1.40130
$$661$$ 12.5000 + 21.6506i 0.486194 + 0.842112i 0.999874 0.0158695i $$-0.00505163\pi$$
−0.513680 + 0.857982i $$0.671718\pi$$
$$662$$ −2.00000 3.46410i −0.0777322 0.134636i
$$663$$ 6.00000 + 10.3923i 0.233021 + 0.403604i
$$664$$ 3.00000 5.19615i 0.116423 0.201650i
$$665$$ −24.0000 −0.930680
$$666$$ 0.500000 + 6.06218i 0.0193746 + 0.234905i
$$667$$ 18.0000 0.696963
$$668$$ −6.00000 + 10.3923i −0.232147 + 0.402090i
$$669$$ 14.0000 + 24.2487i 0.541271 + 0.937509i
$$670$$ 3.00000 + 5.19615i 0.115900 + 0.200745i
$$671$$ −3.00000 5.19615i −0.115814 0.200595i
$$672$$ −8.00000 −0.308607
$$673$$ 5.00000 + 8.66025i 0.192736 + 0.333828i 0.946156 0.323711i $$-0.104931\pi$$
−0.753420 + 0.657539i $$0.771597\pi$$
$$674$$ 25.0000 0.962964
$$675$$ −8.00000 + 13.8564i −0.307920 + 0.533333i
$$676$$ −9.00000 −0.346154
$$677$$ 3.00000 0.115299 0.0576497 0.998337i $$-0.481639\pi$$
0.0576497 + 0.998337i $$0.481639\pi$$
$$678$$ 18.0000 31.1769i 0.691286 1.19734i
$$679$$ −26.0000 45.0333i −0.997788 1.72822i
$$680$$ −9.00000 −0.345134
$$681$$ −18.0000 + 31.1769i −0.689761 + 1.19470i
$$682$$ −6.00000 + 10.3923i −0.229752 + 0.397942i
$$683$$ −6.00000 + 10.3923i −0.229584 + 0.397650i −0.957685 0.287819i $$-0.907070\pi$$
0.728101 + 0.685470i $$0.240403\pi$$
$$684$$ −1.00000 1.73205i −0.0382360 0.0662266i
$$685$$ −4.50000 7.79423i −0.171936 0.297802i
$$686$$ −4.00000 + 6.92820i −0.152721 + 0.264520i
$$687$$ 11.0000 19.0526i 0.419676 0.726900i
$$688$$ 2.00000 3.46410i 0.0762493 0.132068i
$$689$$ −12.0000 −0.457164
$$690$$ −18.0000 31.1769i −0.685248 1.18688i
$$691$$ −25.0000 + 43.3013i −0.951045 + 1.64726i −0.207875 + 0.978155i $$0.566655\pi$$
−0.743170 + 0.669102i $$0.766679\pi$$
$$692$$ −21.0000 −0.798300
$$693$$ 24.0000 0.911685
$$694$$ 3.00000 5.19615i 0.113878 0.197243i
$$695$$ 6.00000 0.227593
$$696$$ −3.00000 5.19615i −0.113715 0.196960i
$$697$$ 9.00000 0.340899
$$698$$ −0.500000 0.866025i −0.0189253 0.0327795i
$$699$$ −9.00000 15.5885i −0.340411 0.589610i
$$700$$ 8.00000 + 13.8564i 0.302372 + 0.523723i
$$701$$ −15.0000 + 25.9808i −0.566542 + 0.981280i 0.430362 + 0.902656i $$0.358386\pi$$
−0.996904 + 0.0786236i $$0.974947\pi$$
$$702$$ −8.00000 −0.301941
$$703$$ −1.00000 12.1244i −0.0377157 0.457279i
$$704$$ −6.00000 −0.226134
$$705$$ −18.0000 + 31.1769i −0.677919 + 1.17419i
$$706$$ −10.5000 18.1865i −0.395173 0.684459i
$$707$$ 6.00000 + 10.3923i 0.225653 + 0.390843i
$$708$$ 0 0
$$709$$ −22.0000 −0.826227 −0.413114 0.910679i $$-0.635559\pi$$
−0.413114 + 0.910679i $$0.635559\pi$$
$$710$$ −18.0000 31.1769i −0.675528 1.17005i
$$711$$ 14.0000 0.525041
$$712$$ 1.50000 2.59808i 0.0562149 0.0973670i
$$713$$ 12.0000 0.449404
$$714$$ −24.0000 −0.898177
$$715$$ 18.0000 31.1769i 0.673162 1.16595i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 21.0000 36.3731i 0.783168 1.35649i −0.146920 0.989148i $$-0.546936\pi$$
0.930087 0.367338i $$-0.119731\pi$$
$$720$$ −1.50000 + 2.59808i −0.0559017 + 0.0968246i
$$721$$ −8.00000 13.8564i −0.297936 0.516040i
$$722$$ −7.50000 12.9904i −0.279121 0.483452i
$$723$$ 14.0000 24.2487i 0.520666 0.901819i
$$724$$ 0.500000 0.866025i 0.0185824 0.0321856i
$$725$$ −6.00000 + 10.3923i −0.222834 + 0.385961i
$$726$$ 50.0000 1.85567
$$727$$ 2.00000 + 3.46410i 0.0741759 + 0.128476i 0.900728 0.434384i $$-0.143034\pi$$
−0.826552 + 0.562861i $$0.809701\pi$$
$$728$$ −4.00000 + 6.92820i −0.148250 + 0.256776i
$$729$$ 13.0000 0.481481
$$730$$ 30.0000 1.11035
$$731$$ 6.00000 10.3923i 0.221918 0.384373i
$$732$$ 2.00000 0.0739221
$$733$$ −1.00000 1.73205i −0.0369358 0.0639748i 0.846967 0.531646i $$-0.178426\pi$$
−0.883902 + 0.467671i $$0.845093\pi$$
$$734$$ 4.00000 0.147643
$$735$$ 27.0000 + 46.7654i 0.995910 + 1.72497i
$$736$$ 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
$$739$$ 38.0000 1.39785 0.698926 0.715194i $$-0.253662\pi$$
0.698926 + 0.715194i $$0.253662\pi$$
$$740$$ −15.0000 + 10.3923i −0.551411 + 0.382029i
$$741$$ −8.00000 −0.293887
$$742$$ 12.0000 20.7846i 0.440534 0.763027i
$$743$$ 3.00000 + 5.19615i 0.110059 + 0.190628i 0.915794 0.401648i $$-0.131563\pi$$
−0.805735 + 0.592277i $$0.798229\pi$$
$$744$$ −2.00000 3.46410i −0.0733236 0.127000i
$$745$$ 31.5000 + 54.5596i 1.15407 + 1.99891i
$$746$$ 25.0000 0.915315
$$747$$ −3.00000 5.19615i −0.109764 0.190117i
$$748$$ −18.0000 −0.658145
$$749$$ −24.0000 + 41.5692i −0.876941 + 1.51891i
$$750$$ −6.00000 −0.219089
$$751$$ −16.0000 −0.583848 −0.291924 0.956441i $$-0.594295\pi$$
−0.291924 + 0.956441i $$0.594295\pi$$
$$752$$ 3.00000 5.19615i 0.109399 0.189484i
$$753$$ 0 0
$$754$$ −6.00000 −0.218507
$$755$$ 33.0000 57.1577i 1.20099 2.08018i
$$756$$ 8.00000 13.8564i 0.290957 0.503953i
$$757$$ −17.5000 + 30.3109i −0.636048 + 1.10167i 0.350244 + 0.936659i $$0.386099\pi$$
−0.986292 + 0.165009i $$0.947235\pi$$
$$758$$ −8.00000 13.8564i −0.290573 0.503287i
$$759$$ −36.0000 62.3538i −1.30672 2.26330i
$$760$$ 3.00000 5.19615i 0.108821 0.188484i
$$761$$ −13.5000 + 23.3827i −0.489375 + 0.847622i −0.999925 0.0122260i $$-0.996108\pi$$
0.510551 + 0.859848i $$0.329442\pi$$
$$762$$ 10.0000 17.3205i 0.362262 0.627456i
$$763$$ 4.00000 0.144810
$$764$$ 3.00000 + 5.19615i 0.108536 + 0.187990i
$$765$$ −4.50000 + 7.79423i −0.162698 + 0.281801i
$$766$$ −12.0000 −0.433578
$$767$$ 0 0
$$768$$ 1.00000 1.73205i 0.0360844 0.0625000i
$$769$$ −34.0000 −1.22607 −0.613036 0.790055i $$-0.710052\pi$$
−0.613036 + 0.790055i $$0.710052\pi$$
$$770$$ 36.0000 + 62.3538i 1.29735 + 2.24708i
$$771$$ −54.0000 −1.94476
$$772$$ −5.50000 9.52628i