# Properties

 Label 546.2.s.e.127.2 Level $546$ Weight $2$ Character 546.127 Analytic conductor $4.360$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(43,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("546.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$546 = 2 \cdot 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 546.s (of order $$6$$, 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: $$4.35983195036$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{6})$$ Coefficient field: 8.0.195105024.2 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{8} - 4x^{7} + 5x^{6} + 4x^{5} - 20x^{4} + 12x^{3} + 45x^{2} - 108x + 81$$ x^8 - 4*x^7 + 5*x^6 + 4*x^5 - 20*x^4 + 12*x^3 + 45*x^2 - 108*x + 81 Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 127.2 Root $$0.560908 - 1.63871i$$ of defining polynomial Character $$\chi$$ $$=$$ 546.127 Dual form 546.2.s.e.43.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -0.332808i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -0.332808i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.166404 + 0.288220i) q^{10} +(2.26053 - 1.30512i) q^{11} +1.00000 q^{12} +(3.41140 - 1.16719i) q^{13} +1.00000 q^{14} +(0.288220 - 0.166404i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.94383 + 3.36681i) q^{17} -1.00000i q^{18} +(4.85997 + 2.80591i) q^{19} +(-0.288220 - 0.166404i) q^{20} -1.00000i q^{21} +(-1.30512 + 2.26053i) q^{22} +(2.10628 + 3.64819i) q^{23} +(-0.866025 + 0.500000i) q^{24} +4.88924 q^{25} +(-2.37076 + 2.71652i) q^{26} -1.00000 q^{27} +(-0.866025 + 0.500000i) q^{28} +(0.593337 + 1.02769i) q^{29} +(-0.166404 + 0.288220i) q^{30} -7.07434i q^{31} +(0.866025 + 0.500000i) q^{32} +(2.26053 + 1.30512i) q^{33} -3.88766i q^{34} +(-0.166404 + 0.288220i) q^{35} +(0.500000 + 0.866025i) q^{36} +(0.499211 - 0.288220i) q^{37} -5.61181 q^{38} +(2.71652 + 2.37076i) q^{39} +0.332808 q^{40} +(0.451251 - 0.260530i) q^{41} +(0.500000 + 0.866025i) q^{42} +(1.53717 - 2.66245i) q^{43} -2.61023i q^{44} +(0.288220 + 0.166404i) q^{45} +(-3.64819 - 2.10628i) q^{46} +12.0528i q^{47} +(0.500000 - 0.866025i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-4.23421 + 2.44462i) q^{50} -3.88766 q^{51} +(0.694883 - 3.53796i) q^{52} -9.71047 q^{53} +(0.866025 - 0.500000i) q^{54} +(-0.434353 - 0.752321i) q^{55} +(0.500000 - 0.866025i) q^{56} +5.61181i q^{57} +(-1.02769 - 0.593337i) q^{58} +(9.07175 + 5.23758i) q^{59} -0.332808i q^{60} +(-3.71989 + 6.44304i) q^{61} +(3.53717 + 6.12656i) q^{62} +(0.866025 - 0.500000i) q^{63} -1.00000 q^{64} +(-0.388451 - 1.13534i) q^{65} -2.61023 q^{66} +(10.3233 - 5.96015i) q^{67} +(1.94383 + 3.36681i) q^{68} +(-2.10628 + 3.64819i) q^{69} -0.332808i q^{70} +(-0.818065 - 0.472310i) q^{71} +(-0.866025 - 0.500000i) q^{72} +4.66562i q^{73} +(-0.288220 + 0.499211i) q^{74} +(2.44462 + 4.23421i) q^{75} +(4.85997 - 2.80591i) q^{76} -2.61023 q^{77} +(-3.53796 - 0.694883i) q^{78} -0.943042 q^{79} +(-0.288220 + 0.166404i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.260530 + 0.451251i) q^{82} -13.7172i q^{83} +(-0.866025 - 0.500000i) q^{84} +(1.12050 + 0.646922i) q^{85} +3.07434i q^{86} +(-0.593337 + 1.02769i) q^{87} +(1.30512 + 2.26053i) q^{88} +(2.92741 - 1.69014i) q^{89} -0.332808 q^{90} +(-3.53796 - 0.694883i) q^{91} +4.21257 q^{92} +(6.12656 - 3.53717i) q^{93} +(-6.02638 - 10.4380i) q^{94} +(0.933827 - 1.61744i) q^{95} +1.00000i q^{96} +(-5.03669 - 2.90793i) q^{97} +(-0.866025 - 0.500000i) q^{98} +2.61023i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q + 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10})$$ 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9 $$8 q + 4 q^{3} + 4 q^{4} - 4 q^{9} + 6 q^{10} + 6 q^{11} + 8 q^{12} + 12 q^{13} + 8 q^{14} + 6 q^{15} - 4 q^{16} + 2 q^{17} - 12 q^{19} - 6 q^{20} - 4 q^{22} + 8 q^{23} - 24 q^{25} + 6 q^{26} - 8 q^{27} + 2 q^{29} - 6 q^{30} + 6 q^{33} - 6 q^{35} + 4 q^{36} + 18 q^{37} - 4 q^{38} + 12 q^{40} + 12 q^{41} + 4 q^{42} - 8 q^{43} + 6 q^{45} + 18 q^{46} + 4 q^{48} + 4 q^{49} + 12 q^{50} + 4 q^{51} + 12 q^{52} - 12 q^{53} - 22 q^{55} + 4 q^{56} - 24 q^{58} + 18 q^{59} - 8 q^{61} + 8 q^{62} - 8 q^{64} + 46 q^{65} - 8 q^{66} + 18 q^{67} - 2 q^{68} - 8 q^{69} + 6 q^{71} - 6 q^{74} - 12 q^{75} - 12 q^{76} - 8 q^{77} + 6 q^{78} - 4 q^{79} - 6 q^{80} - 4 q^{81} + 10 q^{82} - 54 q^{85} - 2 q^{87} + 4 q^{88} - 18 q^{89} - 12 q^{90} + 6 q^{91} + 16 q^{92} + 30 q^{93} - 2 q^{94} - 50 q^{95} - 54 q^{97}+O(q^{100})$$ 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9 + 6 * q^10 + 6 * q^11 + 8 * q^12 + 12 * q^13 + 8 * q^14 + 6 * q^15 - 4 * q^16 + 2 * q^17 - 12 * q^19 - 6 * q^20 - 4 * q^22 + 8 * q^23 - 24 * q^25 + 6 * q^26 - 8 * q^27 + 2 * q^29 - 6 * q^30 + 6 * q^33 - 6 * q^35 + 4 * q^36 + 18 * q^37 - 4 * q^38 + 12 * q^40 + 12 * q^41 + 4 * q^42 - 8 * q^43 + 6 * q^45 + 18 * q^46 + 4 * q^48 + 4 * q^49 + 12 * q^50 + 4 * q^51 + 12 * q^52 - 12 * q^53 - 22 * q^55 + 4 * q^56 - 24 * q^58 + 18 * q^59 - 8 * q^61 + 8 * q^62 - 8 * q^64 + 46 * q^65 - 8 * q^66 + 18 * q^67 - 2 * q^68 - 8 * q^69 + 6 * q^71 - 6 * q^74 - 12 * q^75 - 12 * q^76 - 8 * q^77 + 6 * q^78 - 4 * q^79 - 6 * q^80 - 4 * q^81 + 10 * q^82 - 54 * q^85 - 2 * q^87 + 4 * q^88 - 18 * q^89 - 12 * q^90 + 6 * q^91 + 16 * q^92 + 30 * q^93 - 2 * q^94 - 50 * q^95 - 54 * q^97

## Character values

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

 $$n$$ $$157$$ $$365$$ $$379$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.866025 + 0.500000i −0.612372 + 0.353553i
$$3$$ 0.500000 + 0.866025i 0.288675 + 0.500000i
$$4$$ 0.500000 0.866025i 0.250000 0.433013i
$$5$$ 0.332808i 0.148836i −0.997227 0.0744180i $$-0.976290\pi$$
0.997227 0.0744180i $$-0.0237099\pi$$
$$6$$ −0.866025 0.500000i −0.353553 0.204124i
$$7$$ −0.866025 0.500000i −0.327327 0.188982i
$$8$$ 1.00000i 0.353553i
$$9$$ −0.500000 + 0.866025i −0.166667 + 0.288675i
$$10$$ 0.166404 + 0.288220i 0.0526215 + 0.0911431i
$$11$$ 2.26053 1.30512i 0.681575 0.393508i −0.118873 0.992909i $$-0.537928\pi$$
0.800448 + 0.599402i $$0.204595\pi$$
$$12$$ 1.00000 0.288675
$$13$$ 3.41140 1.16719i 0.946153 0.323721i
$$14$$ 1.00000 0.267261
$$15$$ 0.288220 0.166404i 0.0744180 0.0429653i
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ −1.94383 + 3.36681i −0.471448 + 0.816572i −0.999466 0.0326607i $$-0.989602\pi$$
0.528018 + 0.849233i $$0.322935\pi$$
$$18$$ 1.00000i 0.235702i
$$19$$ 4.85997 + 2.80591i 1.11495 + 0.643719i 0.940108 0.340877i $$-0.110724\pi$$
0.174846 + 0.984596i $$0.444057\pi$$
$$20$$ −0.288220 0.166404i −0.0644479 0.0372090i
$$21$$ 1.00000i 0.218218i
$$22$$ −1.30512 + 2.26053i −0.278252 + 0.481947i
$$23$$ 2.10628 + 3.64819i 0.439191 + 0.760701i 0.997627 0.0688467i $$-0.0219319\pi$$
−0.558437 + 0.829547i $$0.688599\pi$$
$$24$$ −0.866025 + 0.500000i −0.176777 + 0.102062i
$$25$$ 4.88924 0.977848
$$26$$ −2.37076 + 2.71652i −0.464945 + 0.532753i
$$27$$ −1.00000 −0.192450
$$28$$ −0.866025 + 0.500000i −0.163663 + 0.0944911i
$$29$$ 0.593337 + 1.02769i 0.110180 + 0.190837i 0.915843 0.401537i $$-0.131524\pi$$
−0.805663 + 0.592374i $$0.798191\pi$$
$$30$$ −0.166404 + 0.288220i −0.0303810 + 0.0526215i
$$31$$ 7.07434i 1.27059i −0.772270 0.635294i $$-0.780879\pi$$
0.772270 0.635294i $$-0.219121\pi$$
$$32$$ 0.866025 + 0.500000i 0.153093 + 0.0883883i
$$33$$ 2.26053 + 1.30512i 0.393508 + 0.227192i
$$34$$ 3.88766i 0.666729i
$$35$$ −0.166404 + 0.288220i −0.0281274 + 0.0487180i
$$36$$ 0.500000 + 0.866025i 0.0833333 + 0.144338i
$$37$$ 0.499211 0.288220i 0.0820699 0.0473831i −0.458403 0.888744i $$-0.651579\pi$$
0.540473 + 0.841361i $$0.318245\pi$$
$$38$$ −5.61181 −0.910356
$$39$$ 2.71652 + 2.37076i 0.434991 + 0.379626i
$$40$$ 0.332808 0.0526215
$$41$$ 0.451251 0.260530i 0.0704735 0.0406879i −0.464349 0.885652i $$-0.653712\pi$$
0.534823 + 0.844964i $$0.320378\pi$$
$$42$$ 0.500000 + 0.866025i 0.0771517 + 0.133631i
$$43$$ 1.53717 2.66245i 0.234416 0.406020i −0.724687 0.689078i $$-0.758016\pi$$
0.959103 + 0.283058i $$0.0913489\pi$$
$$44$$ 2.61023i 0.393508i
$$45$$ 0.288220 + 0.166404i 0.0429653 + 0.0248060i
$$46$$ −3.64819 2.10628i −0.537896 0.310555i
$$47$$ 12.0528i 1.75807i 0.476753 + 0.879037i $$0.341814\pi$$
−0.476753 + 0.879037i $$0.658186\pi$$
$$48$$ 0.500000 0.866025i 0.0721688 0.125000i
$$49$$ 0.500000 + 0.866025i 0.0714286 + 0.123718i
$$50$$ −4.23421 + 2.44462i −0.598807 + 0.345721i
$$51$$ −3.88766 −0.544382
$$52$$ 0.694883 3.53796i 0.0963629 0.490626i
$$53$$ −9.71047 −1.33384 −0.666918 0.745132i $$-0.732387\pi$$
−0.666918 + 0.745132i $$0.732387\pi$$
$$54$$ 0.866025 0.500000i 0.117851 0.0680414i
$$55$$ −0.434353 0.752321i −0.0585681 0.101443i
$$56$$ 0.500000 0.866025i 0.0668153 0.115728i
$$57$$ 5.61181i 0.743303i
$$58$$ −1.02769 0.593337i −0.134942 0.0779090i
$$59$$ 9.07175 + 5.23758i 1.18104 + 0.681875i 0.956255 0.292533i $$-0.0944983\pi$$
0.224786 + 0.974408i $$0.427832\pi$$
$$60$$ 0.332808i 0.0429653i
$$61$$ −3.71989 + 6.44304i −0.476283 + 0.824947i −0.999631 0.0271724i $$-0.991350\pi$$
0.523347 + 0.852119i $$0.324683\pi$$
$$62$$ 3.53717 + 6.12656i 0.449221 + 0.778073i
$$63$$ 0.866025 0.500000i 0.109109 0.0629941i
$$64$$ −1.00000 −0.125000
$$65$$ −0.388451 1.13534i −0.0481814 0.140822i
$$66$$ −2.61023 −0.321298
$$67$$ 10.3233 5.96015i 1.26119 0.728148i 0.287885 0.957665i $$-0.407048\pi$$
0.973305 + 0.229517i $$0.0737145\pi$$
$$68$$ 1.94383 + 3.36681i 0.235724 + 0.408286i
$$69$$ −2.10628 + 3.64819i −0.253567 + 0.439191i
$$70$$ 0.332808i 0.0397781i
$$71$$ −0.818065 0.472310i −0.0970864 0.0560529i 0.450671 0.892690i $$-0.351185\pi$$
−0.547757 + 0.836637i $$0.684518\pi$$
$$72$$ −0.866025 0.500000i −0.102062 0.0589256i
$$73$$ 4.66562i 0.546069i 0.962004 + 0.273034i $$0.0880273\pi$$
−0.962004 + 0.273034i $$0.911973\pi$$
$$74$$ −0.288220 + 0.499211i −0.0335049 + 0.0580321i
$$75$$ 2.44462 + 4.23421i 0.282280 + 0.488924i
$$76$$ 4.85997 2.80591i 0.557477 0.321859i
$$77$$ −2.61023 −0.297464
$$78$$ −3.53796 0.694883i −0.400595 0.0786800i
$$79$$ −0.943042 −0.106101 −0.0530503 0.998592i $$-0.516894\pi$$
−0.0530503 + 0.998592i $$0.516894\pi$$
$$80$$ −0.288220 + 0.166404i −0.0322240 + 0.0186045i
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ −0.260530 + 0.451251i −0.0287707 + 0.0498323i
$$83$$ 13.7172i 1.50566i −0.658215 0.752830i $$-0.728688\pi$$
0.658215 0.752830i $$-0.271312\pi$$
$$84$$ −0.866025 0.500000i −0.0944911 0.0545545i
$$85$$ 1.12050 + 0.646922i 0.121535 + 0.0701685i
$$86$$ 3.07434i 0.331514i
$$87$$ −0.593337 + 1.02769i −0.0636124 + 0.110180i
$$88$$ 1.30512 + 2.26053i 0.139126 + 0.240973i
$$89$$ 2.92741 1.69014i 0.310305 0.179155i −0.336758 0.941591i $$-0.609330\pi$$
0.647063 + 0.762436i $$0.275997\pi$$
$$90$$ −0.332808 −0.0350810
$$91$$ −3.53796 0.694883i −0.370879 0.0728435i
$$92$$ 4.21257 0.439191
$$93$$ 6.12656 3.53717i 0.635294 0.366787i
$$94$$ −6.02638 10.4380i −0.621573 1.07660i
$$95$$ 0.933827 1.61744i 0.0958086 0.165945i
$$96$$ 1.00000i 0.102062i
$$97$$ −5.03669 2.90793i −0.511398 0.295256i 0.222010 0.975044i $$-0.428738\pi$$
−0.733408 + 0.679789i $$0.762072\pi$$
$$98$$ −0.866025 0.500000i −0.0874818 0.0505076i
$$99$$ 2.61023i 0.262338i
$$100$$ 2.44462 4.23421i 0.244462 0.423421i
$$101$$ −7.98516 13.8307i −0.794553 1.37621i −0.923122 0.384506i $$-0.874372\pi$$
0.128569 0.991701i $$-0.458962\pi$$
$$102$$ 3.36681 1.94383i 0.333364 0.192468i
$$103$$ −7.50641 −0.739629 −0.369814 0.929106i $$-0.620579\pi$$
−0.369814 + 0.929106i $$0.620579\pi$$
$$104$$ 1.16719 + 3.41140i 0.114453 + 0.334515i
$$105$$ −0.332808 −0.0324787
$$106$$ 8.40951 4.85523i 0.816804 0.471582i
$$107$$ −4.32539 7.49179i −0.418151 0.724259i 0.577602 0.816318i $$-0.303988\pi$$
−0.995754 + 0.0920593i $$0.970655\pi$$
$$108$$ −0.500000 + 0.866025i −0.0481125 + 0.0833333i
$$109$$ 18.6144i 1.78293i −0.453088 0.891466i $$-0.649678\pi$$
0.453088 0.891466i $$-0.350322\pi$$
$$110$$ 0.752321 + 0.434353i 0.0717310 + 0.0414139i
$$111$$ 0.499211 + 0.288220i 0.0473831 + 0.0273566i
$$112$$ 1.00000i 0.0944911i
$$113$$ −4.57512 + 7.92435i −0.430392 + 0.745460i −0.996907 0.0785911i $$-0.974958\pi$$
0.566515 + 0.824051i $$0.308291\pi$$
$$114$$ −2.80591 4.85997i −0.262797 0.455178i
$$115$$ 1.21415 0.700987i 0.113220 0.0653674i
$$116$$ 1.18667 0.110180
$$117$$ −0.694883 + 3.53796i −0.0642419 + 0.327084i
$$118$$ −10.4752 −0.964316
$$119$$ 3.36681 1.94383i 0.308635 0.178191i
$$120$$ 0.166404 + 0.288220i 0.0151905 + 0.0263108i
$$121$$ −2.09334 + 3.62577i −0.190303 + 0.329615i
$$122$$ 7.43978i 0.673566i
$$123$$ 0.451251 + 0.260530i 0.0406879 + 0.0234912i
$$124$$ −6.12656 3.53717i −0.550181 0.317647i
$$125$$ 3.29121i 0.294375i
$$126$$ −0.500000 + 0.866025i −0.0445435 + 0.0771517i
$$127$$ 3.38977 + 5.87125i 0.300793 + 0.520989i 0.976316 0.216350i $$-0.0694153\pi$$
−0.675523 + 0.737339i $$0.736082\pi$$
$$128$$ 0.866025 0.500000i 0.0765466 0.0441942i
$$129$$ 3.07434 0.270680
$$130$$ 0.904078 + 0.789008i 0.0792929 + 0.0692006i
$$131$$ 7.22879 0.631583 0.315791 0.948829i $$-0.397730\pi$$
0.315791 + 0.948829i $$0.397730\pi$$
$$132$$ 2.26053 1.30512i 0.196754 0.113596i
$$133$$ −2.80591 4.85997i −0.243303 0.421413i
$$134$$ −5.96015 + 10.3233i −0.514879 + 0.891796i
$$135$$ 0.332808i 0.0286435i
$$136$$ −3.36681 1.94383i −0.288702 0.166682i
$$137$$ −10.2964 5.94462i −0.879679 0.507883i −0.00912669 0.999958i $$-0.502905\pi$$
−0.870553 + 0.492075i $$0.836238\pi$$
$$138$$ 4.21257i 0.358598i
$$139$$ −7.16056 + 12.4025i −0.607351 + 1.05196i 0.384324 + 0.923198i $$0.374434\pi$$
−0.991675 + 0.128764i $$0.958899\pi$$
$$140$$ 0.166404 + 0.288220i 0.0140637 + 0.0243590i
$$141$$ −10.4380 + 6.02638i −0.879037 + 0.507512i
$$142$$ 0.944620 0.0792707
$$143$$ 6.18825 7.09075i 0.517488 0.592959i
$$144$$ 1.00000 0.0833333
$$145$$ 0.342023 0.197467i 0.0284035 0.0163988i
$$146$$ −2.33281 4.04054i −0.193065 0.334398i
$$147$$ −0.500000 + 0.866025i −0.0412393 + 0.0714286i
$$148$$ 0.576440i 0.0473831i
$$149$$ −5.24548 3.02848i −0.429726 0.248103i 0.269504 0.962999i $$-0.413140\pi$$
−0.699230 + 0.714897i $$0.746474\pi$$
$$150$$ −4.23421 2.44462i −0.345721 0.199602i
$$151$$ 21.4953i 1.74926i −0.484791 0.874630i $$-0.661104\pi$$
0.484791 0.874630i $$-0.338896\pi$$
$$152$$ −2.80591 + 4.85997i −0.227589 + 0.394196i
$$153$$ −1.94383 3.36681i −0.157149 0.272191i
$$154$$ 2.26053 1.30512i 0.182159 0.105169i
$$155$$ −2.35439 −0.189109
$$156$$ 3.41140 1.16719i 0.273131 0.0934502i
$$157$$ 2.29227 0.182943 0.0914714 0.995808i $$-0.470843\pi$$
0.0914714 + 0.995808i $$0.470843\pi$$
$$158$$ 0.816699 0.471521i 0.0649731 0.0375122i
$$159$$ −4.85523 8.40951i −0.385045 0.666918i
$$160$$ 0.166404 0.288220i 0.0131554 0.0227858i
$$161$$ 4.21257i 0.331997i
$$162$$ 0.866025 + 0.500000i 0.0680414 + 0.0392837i
$$163$$ 2.89314 + 1.67035i 0.226608 + 0.130832i 0.609006 0.793165i $$-0.291568\pi$$
−0.382398 + 0.923998i $$0.624902\pi$$
$$164$$ 0.521059i 0.0406879i
$$165$$ 0.434353 0.752321i 0.0338143 0.0585681i
$$166$$ 6.85861 + 11.8795i 0.532331 + 0.922024i
$$167$$ 5.57802 3.22047i 0.431640 0.249207i −0.268405 0.963306i $$-0.586497\pi$$
0.700045 + 0.714099i $$0.253163\pi$$
$$168$$ 1.00000 0.0771517
$$169$$ 10.2753 7.96352i 0.790410 0.612579i
$$170$$ −1.29384 −0.0992333
$$171$$ −4.85997 + 2.80591i −0.371651 + 0.214573i
$$172$$ −1.53717 2.66245i −0.117208 0.203010i
$$173$$ −9.30718 + 16.1205i −0.707611 + 1.22562i 0.258129 + 0.966110i $$0.416894\pi$$
−0.965741 + 0.259509i $$0.916439\pi$$
$$174$$ 1.18667i 0.0899616i
$$175$$ −4.23421 2.44462i −0.320076 0.184796i
$$176$$ −2.26053 1.30512i −0.170394 0.0983769i
$$177$$ 10.4752i 0.787361i
$$178$$ −1.69014 + 2.92741i −0.126682 + 0.219419i
$$179$$ −11.1081 19.2398i −0.830261 1.43805i −0.897831 0.440339i $$-0.854858\pi$$
0.0675707 0.997714i $$-0.478475\pi$$
$$180$$ 0.288220 0.166404i 0.0214826 0.0124030i
$$181$$ −4.05853 −0.301669 −0.150834 0.988559i $$-0.548196\pi$$
−0.150834 + 0.988559i $$0.548196\pi$$
$$182$$ 3.41140 1.16719i 0.252870 0.0865181i
$$183$$ −7.43978 −0.549965
$$184$$ −3.64819 + 2.10628i −0.268948 + 0.155277i
$$185$$ −0.0959218 0.166141i −0.00705231 0.0122150i
$$186$$ −3.53717 + 6.12656i −0.259358 + 0.449221i
$$187$$ 10.1477i 0.742074i
$$188$$ 10.4380 + 6.02638i 0.761269 + 0.439519i
$$189$$ 0.866025 + 0.500000i 0.0629941 + 0.0363696i
$$190$$ 1.86765i 0.135494i
$$191$$ 5.86018 10.1501i 0.424028 0.734438i −0.572301 0.820044i $$-0.693949\pi$$
0.996329 + 0.0856056i $$0.0272825\pi$$
$$192$$ −0.500000 0.866025i −0.0360844 0.0625000i
$$193$$ −20.6123 + 11.9005i −1.48371 + 0.856618i −0.999829 0.0185185i $$-0.994105\pi$$
−0.483877 + 0.875136i $$0.660772\pi$$
$$194$$ 5.81587 0.417555
$$195$$ 0.789008 0.904078i 0.0565021 0.0647424i
$$196$$ 1.00000 0.0714286
$$197$$ 8.73184 5.04133i 0.622118 0.359180i −0.155575 0.987824i $$-0.549723\pi$$
0.777693 + 0.628644i $$0.216390\pi$$
$$198$$ −1.30512 2.26053i −0.0927507 0.160649i
$$199$$ 6.92504 11.9945i 0.490903 0.850269i −0.509042 0.860742i $$-0.670000\pi$$
0.999945 + 0.0104725i $$0.00333355\pi$$
$$200$$ 4.88924i 0.345721i
$$201$$ 10.3233 + 5.96015i 0.728148 + 0.420397i
$$202$$ 13.8307 + 7.98516i 0.973125 + 0.561834i
$$203$$ 1.18667i 0.0832882i
$$204$$ −1.94383 + 3.36681i −0.136095 + 0.235724i
$$205$$ −0.0867062 0.150180i −0.00605583 0.0104890i
$$206$$ 6.50074 3.75321i 0.452928 0.261498i
$$207$$ −4.21257 −0.292794
$$208$$ −2.71652 2.37076i −0.188357 0.164383i
$$209$$ 14.6481 1.01323
$$210$$ 0.288220 0.166404i 0.0198891 0.0114830i
$$211$$ −2.27743 3.94462i −0.156785 0.271559i 0.776923 0.629596i $$-0.216779\pi$$
−0.933707 + 0.358037i $$0.883446\pi$$
$$212$$ −4.85523 + 8.40951i −0.333459 + 0.577568i
$$213$$ 0.944620i 0.0647243i
$$214$$ 7.49179 + 4.32539i 0.512128 + 0.295677i
$$215$$ −0.886085 0.511581i −0.0604305 0.0348896i
$$216$$ 1.00000i 0.0680414i
$$217$$ −3.53717 + 6.12656i −0.240119 + 0.415898i
$$218$$ 9.30718 + 16.1205i 0.630361 + 1.09182i
$$219$$ −4.04054 + 2.33281i −0.273034 + 0.157637i
$$220$$ −0.868706 −0.0585681
$$221$$ −2.70147 + 13.7544i −0.181720 + 0.925220i
$$222$$ −0.576440 −0.0386881
$$223$$ −7.30359 + 4.21673i −0.489085 + 0.282373i −0.724195 0.689596i $$-0.757788\pi$$
0.235110 + 0.971969i $$0.424455\pi$$
$$224$$ −0.500000 0.866025i −0.0334077 0.0578638i
$$225$$ −2.44462 + 4.23421i −0.162975 + 0.282280i
$$226$$ 9.15025i 0.608666i
$$227$$ 24.2394 + 13.9946i 1.60883 + 0.928857i 0.989633 + 0.143619i $$0.0458739\pi$$
0.619194 + 0.785238i $$0.287459\pi$$
$$228$$ 4.85997 + 2.80591i 0.321859 + 0.185826i
$$229$$ 28.7785i 1.90174i 0.309598 + 0.950868i $$0.399806\pi$$
−0.309598 + 0.950868i $$0.600194\pi$$
$$230$$ −0.700987 + 1.21415i −0.0462217 + 0.0800584i
$$231$$ −1.30512 2.26053i −0.0858704 0.148732i
$$232$$ −1.02769 + 0.593337i −0.0674712 + 0.0389545i
$$233$$ −18.8877 −1.23737 −0.618686 0.785638i $$-0.712335\pi$$
−0.618686 + 0.785638i $$0.712335\pi$$
$$234$$ −1.16719 3.41140i −0.0763018 0.223010i
$$235$$ 4.01125 0.261665
$$236$$ 9.07175 5.23758i 0.590521 0.340937i
$$237$$ −0.471521 0.816699i −0.0306286 0.0530503i
$$238$$ −1.94383 + 3.36681i −0.126000 + 0.218238i
$$239$$ 11.0933i 0.717565i −0.933421 0.358783i $$-0.883192\pi$$
0.933421 0.358783i $$-0.116808\pi$$
$$240$$ −0.288220 0.166404i −0.0186045 0.0107413i
$$241$$ −7.02686 4.05696i −0.452640 0.261332i 0.256305 0.966596i $$-0.417495\pi$$
−0.708944 + 0.705264i $$0.750828\pi$$
$$242$$ 4.18667i 0.269130i
$$243$$ 0.500000 0.866025i 0.0320750 0.0555556i
$$244$$ 3.71989 + 6.44304i 0.238142 + 0.412474i
$$245$$ 0.288220 0.166404i 0.0184137 0.0106311i
$$246$$ −0.521059 −0.0332215
$$247$$ 19.8543 + 3.89955i 1.26330 + 0.248122i
$$248$$ 7.07434 0.449221
$$249$$ 11.8795 6.85861i 0.752830 0.434646i
$$250$$ 1.64561 + 2.85027i 0.104077 + 0.180267i
$$251$$ −1.58465 + 2.74469i −0.100022 + 0.173243i −0.911694 0.410871i $$-0.865225\pi$$
0.811671 + 0.584114i $$0.198558\pi$$
$$252$$ 1.00000i 0.0629941i
$$253$$ 9.52264 + 5.49790i 0.598683 + 0.345650i
$$254$$ −5.87125 3.38977i −0.368395 0.212693i
$$255$$ 1.29384i 0.0810236i
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −0.0967103 0.167507i −0.00603263 0.0104488i 0.862993 0.505215i $$-0.168587\pi$$
−0.869026 + 0.494766i $$0.835254\pi$$
$$258$$ −2.66245 + 1.53717i −0.165757 + 0.0956999i
$$259$$ −0.576440 −0.0358182
$$260$$ −1.17746 0.231262i −0.0730229 0.0143423i
$$261$$ −1.18667 −0.0734533
$$262$$ −6.26032 + 3.61440i −0.386764 + 0.223298i
$$263$$ −6.02185 10.4301i −0.371323 0.643150i 0.618446 0.785827i $$-0.287762\pi$$
−0.989769 + 0.142677i $$0.954429\pi$$
$$264$$ −1.30512 + 2.26053i −0.0803244 + 0.139126i
$$265$$ 3.23172i 0.198523i
$$266$$ 4.85997 + 2.80591i 0.297984 + 0.172041i
$$267$$ 2.92741 + 1.69014i 0.179155 + 0.103435i
$$268$$ 11.9203i 0.728148i
$$269$$ −8.60487 + 14.9041i −0.524648 + 0.908718i 0.474940 + 0.880018i $$0.342470\pi$$
−0.999588 + 0.0286993i $$0.990863\pi$$
$$270$$ −0.166404 0.288220i −0.0101270 0.0175405i
$$271$$ −14.8453 + 8.57096i −0.901790 + 0.520649i −0.877781 0.479063i $$-0.840977\pi$$
−0.0240098 + 0.999712i $$0.507643\pi$$
$$272$$ 3.88766 0.235724
$$273$$ −1.16719 3.41140i −0.0706417 0.206467i
$$274$$ 11.8892 0.718255
$$275$$ 11.0523 6.38103i 0.666477 0.384791i
$$276$$ 2.10628 + 3.64819i 0.126783 + 0.219595i
$$277$$ −7.85660 + 13.6080i −0.472057 + 0.817627i −0.999489 0.0319704i $$-0.989822\pi$$
0.527432 + 0.849598i $$0.323155\pi$$
$$278$$ 14.3211i 0.858924i
$$279$$ 6.12656 + 3.53717i 0.366787 + 0.211765i
$$280$$ −0.288220 0.166404i −0.0172244 0.00994453i
$$281$$ 4.07337i 0.242997i 0.992592 + 0.121499i $$0.0387700\pi$$
−0.992592 + 0.121499i $$0.961230\pi$$
$$282$$ 6.02638 10.4380i 0.358865 0.621573i
$$283$$ 10.7674 + 18.6497i 0.640057 + 1.10861i 0.985420 + 0.170142i $$0.0544226\pi$$
−0.345363 + 0.938469i $$0.612244\pi$$
$$284$$ −0.818065 + 0.472310i −0.0485432 + 0.0280264i
$$285$$ 1.86765 0.110630
$$286$$ −1.81381 + 9.23490i −0.107253 + 0.546071i
$$287$$ −0.521059 −0.0307572
$$288$$ −0.866025 + 0.500000i −0.0510310 + 0.0294628i
$$289$$ 0.943042 + 1.63340i 0.0554731 + 0.0960822i
$$290$$ −0.197467 + 0.342023i −0.0115957 + 0.0200843i
$$291$$ 5.81587i 0.340932i
$$292$$ 4.04054 + 2.33281i 0.236455 + 0.136517i
$$293$$ 0.152457 + 0.0880210i 0.00890662 + 0.00514224i 0.504447 0.863443i $$-0.331697\pi$$
−0.495540 + 0.868585i $$0.665030\pi$$
$$294$$ 1.00000i 0.0583212i
$$295$$ 1.74311 3.01915i 0.101488 0.175782i
$$296$$ 0.288220 + 0.499211i 0.0167524 + 0.0290161i
$$297$$ −2.26053 + 1.30512i −0.131169 + 0.0757306i
$$298$$ 6.05696 0.350870
$$299$$ 11.4435 + 9.98701i 0.661796 + 0.577564i
$$300$$ 4.88924 0.282280
$$301$$ −2.66245 + 1.53717i −0.153461 + 0.0886009i
$$302$$ 10.7476 + 18.6154i 0.618457 + 1.07120i
$$303$$ 7.98516 13.8307i 0.458736 0.794553i
$$304$$ 5.61181i 0.321859i
$$305$$ 2.14429 + 1.23801i 0.122782 + 0.0708882i
$$306$$ 3.36681 + 1.94383i 0.192468 + 0.111121i
$$307$$ 20.7405i 1.18372i 0.806040 + 0.591861i $$0.201606\pi$$
−0.806040 + 0.591861i $$0.798394\pi$$
$$308$$ −1.30512 + 2.26053i −0.0743660 + 0.128806i
$$309$$ −3.75321 6.50074i −0.213512 0.369814i
$$310$$ 2.03896 1.17720i 0.115805 0.0668603i
$$311$$ 10.9678 0.621926 0.310963 0.950422i $$-0.399348\pi$$
0.310963 + 0.950422i $$0.399348\pi$$
$$312$$ −2.37076 + 2.71652i −0.134218 + 0.153793i
$$313$$ 16.2189 0.916746 0.458373 0.888760i $$-0.348432\pi$$
0.458373 + 0.888760i $$0.348432\pi$$
$$314$$ −1.98516 + 1.14613i −0.112029 + 0.0646800i
$$315$$ −0.166404 0.288220i −0.00937579 0.0162393i
$$316$$ −0.471521 + 0.816699i −0.0265251 + 0.0459429i
$$317$$ 10.5358i 0.591750i −0.955227 0.295875i $$-0.904389\pi$$
0.955227 0.295875i $$-0.0956112\pi$$
$$318$$ 8.40951 + 4.85523i 0.471582 + 0.272268i
$$319$$ 2.68251 + 1.54875i 0.150192 + 0.0867133i
$$320$$ 0.332808i 0.0186045i
$$321$$ 4.32539 7.49179i 0.241420 0.418151i
$$322$$ 2.10628 + 3.64819i 0.117379 + 0.203306i
$$323$$ −18.8939 + 10.9084i −1.05129 + 0.606960i
$$324$$ −1.00000 −0.0555556
$$325$$ 16.6792 5.70668i 0.925193 0.316550i
$$326$$ −3.34071 −0.185025
$$327$$ 16.1205 9.30718i 0.891466 0.514688i
$$328$$ 0.260530 + 0.451251i 0.0143853 + 0.0249161i
$$329$$ 6.02638 10.4380i 0.332245 0.575465i
$$330$$ 0.868706i 0.0478207i
$$331$$ −13.9687 8.06486i −0.767792 0.443285i 0.0642946 0.997931i $$-0.479520\pi$$
−0.832086 + 0.554646i $$0.812854\pi$$
$$332$$ −11.8795 6.85861i −0.651970 0.376415i
$$333$$ 0.576440i 0.0315887i
$$334$$ −3.22047 + 5.57802i −0.176216 + 0.305216i
$$335$$ −1.98358 3.43567i −0.108375 0.187711i
$$336$$ −0.866025 + 0.500000i −0.0472456 + 0.0272772i
$$337$$ 1.78785 0.0973906 0.0486953 0.998814i $$-0.484494\pi$$
0.0486953 + 0.998814i $$0.484494\pi$$
$$338$$ −4.91693 + 12.0343i −0.267446 + 0.654578i
$$339$$ −9.15025 −0.496973
$$340$$ 1.12050 0.646922i 0.0607677 0.0350843i
$$341$$ −9.23284 15.9917i −0.499986 0.866002i
$$342$$ 2.80591 4.85997i 0.151726 0.262797i
$$343$$ 1.00000i 0.0539949i
$$344$$ 2.66245 + 1.53717i 0.143550 + 0.0828786i
$$345$$ 1.21415 + 0.700987i 0.0653674 + 0.0377399i
$$346$$ 18.6144i 1.00071i
$$347$$ −12.7030 + 22.0023i −0.681935 + 1.18115i 0.292454 + 0.956280i $$0.405528\pi$$
−0.974389 + 0.224867i $$0.927805\pi$$
$$348$$ 0.593337 + 1.02769i 0.0318062 + 0.0550900i
$$349$$ −24.5419 + 14.1693i −1.31370 + 0.758463i −0.982706 0.185172i $$-0.940716\pi$$
−0.330990 + 0.943634i $$0.607383\pi$$
$$350$$ 4.88924 0.261341
$$351$$ −3.41140 + 1.16719i −0.182087 + 0.0623001i
$$352$$ 2.61023 0.139126
$$353$$ −1.69146 + 0.976568i −0.0900276 + 0.0519774i −0.544338 0.838866i $$-0.683219\pi$$
0.454310 + 0.890843i $$0.349886\pi$$
$$354$$ −5.23758 9.07175i −0.278374 0.482158i
$$355$$ −0.157188 + 0.272258i −0.00834269 + 0.0144500i
$$356$$ 3.38029i 0.179155i
$$357$$ 3.36681 + 1.94383i 0.178191 + 0.102878i
$$358$$ 19.2398 + 11.1081i 1.01686 + 0.587083i
$$359$$ 27.6565i 1.45965i −0.683633 0.729826i $$-0.739601\pi$$
0.683633 0.729826i $$-0.260399\pi$$
$$360$$ −0.166404 + 0.288220i −0.00877025 + 0.0151905i
$$361$$ 6.24622 + 10.8188i 0.328748 + 0.569409i
$$362$$ 3.51479 2.02927i 0.184733 0.106656i
$$363$$ −4.18667 −0.219743
$$364$$ −2.37076 + 2.71652i −0.124262 + 0.142384i
$$365$$ 1.55275 0.0812748
$$366$$ 6.44304 3.71989i 0.336783 0.194442i
$$367$$ −2.87888 4.98636i −0.150276 0.260286i 0.781053 0.624465i $$-0.214683\pi$$
−0.931329 + 0.364179i $$0.881350\pi$$
$$368$$ 2.10628 3.64819i 0.109798 0.190175i
$$369$$ 0.521059i 0.0271253i
$$370$$ 0.166141 + 0.0959218i 0.00863728 + 0.00498673i
$$371$$ 8.40951 + 4.85523i 0.436600 + 0.252071i
$$372$$ 7.07434i 0.366787i
$$373$$ −13.9243 + 24.1177i −0.720975 + 1.24877i 0.239634 + 0.970863i $$0.422973\pi$$
−0.960609 + 0.277903i $$0.910361\pi$$
$$374$$ −5.07386 8.78817i −0.262363 0.454426i
$$375$$ 2.85027 1.64561i 0.147188 0.0849788i
$$376$$ −12.0528 −0.621573
$$377$$ 3.22362 + 2.81333i 0.166025 + 0.144894i
$$378$$ −1.00000 −0.0514344
$$379$$ −10.7836 + 6.22590i −0.553915 + 0.319803i −0.750700 0.660644i $$-0.770283\pi$$
0.196784 + 0.980447i $$0.436950\pi$$
$$380$$ −0.933827 1.61744i −0.0479043 0.0829727i
$$381$$ −3.38977 + 5.87125i −0.173663 + 0.300793i
$$382$$ 11.7204i 0.599666i
$$383$$ −8.42273 4.86286i −0.430381 0.248481i 0.269128 0.963104i $$-0.413265\pi$$
−0.699509 + 0.714624i $$0.746598\pi$$
$$384$$ 0.866025 + 0.500000i 0.0441942 + 0.0255155i
$$385$$ 0.868706i 0.0442734i
$$386$$ 11.9005 20.6123i 0.605720 1.04914i
$$387$$ 1.53717 + 2.66245i 0.0781387 + 0.135340i
$$388$$ −5.03669 + 2.90793i −0.255699 + 0.147628i
$$389$$ −13.8910 −0.704302 −0.352151 0.935943i $$-0.614550\pi$$
−0.352151 + 0.935943i $$0.614550\pi$$
$$390$$ −0.231262 + 1.17746i −0.0117104 + 0.0596230i
$$391$$ −16.3770 −0.828223
$$392$$ −0.866025 + 0.500000i −0.0437409 + 0.0252538i
$$393$$ 3.61440 + 6.26032i 0.182322 + 0.315791i
$$394$$ −5.04133 + 8.73184i −0.253979 + 0.439904i
$$395$$ 0.313852i 0.0157916i
$$396$$ 2.26053 + 1.30512i 0.113596 + 0.0655846i
$$397$$ 5.87033 + 3.38924i 0.294624 + 0.170101i 0.640025 0.768354i $$-0.278924\pi$$
−0.345401 + 0.938455i $$0.612257\pi$$
$$398$$ 13.8501i 0.694242i
$$399$$ 2.80591 4.85997i 0.140471 0.243303i
$$400$$ −2.44462 4.23421i −0.122231 0.211710i
$$401$$ 12.5254 7.23152i 0.625487 0.361125i −0.153515 0.988146i $$-0.549059\pi$$
0.779002 + 0.627021i $$0.215726\pi$$
$$402$$ −11.9203 −0.594531
$$403$$ −8.25711 24.1334i −0.411316 1.20217i
$$404$$ −15.9703 −0.794553
$$405$$ −0.288220 + 0.166404i −0.0143218 + 0.00826867i
$$406$$ 0.593337 + 1.02769i 0.0294468 + 0.0510034i
$$407$$ 0.752321 1.30306i 0.0372912 0.0645902i
$$408$$ 3.88766i 0.192468i
$$409$$ 20.2032 + 11.6643i 0.998982 + 0.576763i 0.907947 0.419085i $$-0.137649\pi$$
0.0910351 + 0.995848i $$0.470982\pi$$
$$410$$ 0.150180 + 0.0867062i 0.00741684 + 0.00428212i
$$411$$ 11.8892i 0.586453i
$$412$$ −3.75321 + 6.50074i −0.184907 + 0.320269i
$$413$$ −5.23758 9.07175i −0.257724 0.446392i
$$414$$ 3.64819 2.10628i 0.179299 0.103518i
$$415$$ −4.56519 −0.224096
$$416$$ 3.53796 + 0.694883i 0.173463 + 0.0340694i
$$417$$ −14.3211 −0.701308
$$418$$ −12.6857 + 7.32407i −0.620476 + 0.358232i
$$419$$ 11.2898 + 19.5544i 0.551540 + 0.955296i 0.998164 + 0.0605740i $$0.0192931\pi$$
−0.446623 + 0.894722i $$0.647374\pi$$
$$420$$ −0.166404 + 0.288220i −0.00811967 + 0.0140637i
$$421$$ 34.1708i 1.66538i −0.553738 0.832691i $$-0.686799\pi$$
0.553738 0.832691i $$-0.313201\pi$$
$$422$$ 3.94462 + 2.27743i 0.192021 + 0.110863i
$$423$$ −10.4380 6.02638i −0.507512 0.293012i
$$424$$ 9.71047i 0.471582i
$$425$$ −9.50385 + 16.4612i −0.461005 + 0.798483i
$$426$$ 0.472310 + 0.818065i 0.0228835 + 0.0396354i
$$427$$ 6.44304 3.71989i 0.311801 0.180018i
$$428$$ −8.65078 −0.418151
$$429$$ 9.23490 + 1.81381i 0.445865 + 0.0875714i
$$430$$ 1.02316 0.0493413
$$431$$ 4.53528 2.61844i 0.218457 0.126126i −0.386779 0.922173i $$-0.626412\pi$$
0.605235 + 0.796047i $$0.293079\pi$$
$$432$$ 0.500000 + 0.866025i 0.0240563 + 0.0416667i
$$433$$ 8.41030 14.5671i 0.404173 0.700048i −0.590052 0.807365i $$-0.700893\pi$$
0.994225 + 0.107317i $$0.0342260\pi$$
$$434$$ 7.07434i 0.339579i
$$435$$ 0.342023 + 0.197467i 0.0163988 + 0.00946782i
$$436$$ −16.1205 9.30718i −0.772032 0.445733i
$$437$$ 23.6401i 1.13086i
$$438$$ 2.33281 4.04054i 0.111466 0.193065i
$$439$$ −7.36282 12.7528i −0.351408 0.608657i 0.635088 0.772440i $$-0.280964\pi$$
−0.986496 + 0.163783i $$0.947630\pi$$
$$440$$ 0.752321 0.434353i 0.0358655 0.0207070i
$$441$$ −1.00000 −0.0476190
$$442$$ −4.53765 13.2624i −0.215834 0.630827i
$$443$$ 36.2393 1.72178 0.860891 0.508789i $$-0.169907\pi$$
0.860891 + 0.508789i $$0.169907\pi$$
$$444$$ 0.499211 0.288220i 0.0236915 0.0136783i
$$445$$ −0.562493 0.974266i −0.0266647 0.0461846i
$$446$$ 4.21673 7.30359i 0.199668 0.345835i
$$447$$ 6.05696i 0.286484i
$$448$$ 0.866025 + 0.500000i 0.0409159 + 0.0236228i
$$449$$ −21.0351 12.1446i −0.992708 0.573140i −0.0866255 0.996241i $$-0.527608\pi$$
−0.906083 + 0.423101i $$0.860942\pi$$
$$450$$ 4.88924i 0.230481i
$$451$$ 0.680043 1.17787i 0.0320220 0.0554637i
$$452$$ 4.57512 + 7.92435i 0.215196 + 0.372730i
$$453$$ 18.6154 10.7476i 0.874630 0.504968i
$$454$$ −27.9893 −1.31360
$$455$$ −0.231262 + 1.17746i −0.0108417 + 0.0552001i
$$456$$ −5.61181 −0.262797
$$457$$ −28.8744 + 16.6706i −1.35069 + 0.779819i −0.988345 0.152227i $$-0.951355\pi$$
−0.362340 + 0.932046i $$0.618022\pi$$
$$458$$ −14.3892 24.9229i −0.672365 1.16457i
$$459$$ 1.94383 3.36681i 0.0907303 0.157149i
$$460$$ 1.40197i 0.0653674i
$$461$$ −25.6317 14.7985i −1.19379 0.689234i −0.234625 0.972086i $$-0.575386\pi$$
−0.959164 + 0.282852i $$0.908720\pi$$
$$462$$ 2.26053 + 1.30512i 0.105169 + 0.0607196i
$$463$$ 36.6027i 1.70107i −0.525918 0.850535i $$-0.676278\pi$$
0.525918 0.850535i $$-0.323722\pi$$
$$464$$ 0.593337 1.02769i 0.0275450 0.0477093i
$$465$$ −1.17720 2.03896i −0.0545912 0.0945547i
$$466$$ 16.3572 9.44383i 0.757732 0.437477i
$$467$$ −6.21635 −0.287658 −0.143829 0.989603i $$-0.545942\pi$$
−0.143829 + 0.989603i $$0.545942\pi$$
$$468$$ 2.71652 + 2.37076i 0.125571 + 0.109589i
$$469$$ −11.9203 −0.550428
$$470$$ −3.47384 + 2.00562i −0.160236 + 0.0925125i
$$471$$ 1.14613 + 1.98516i 0.0528110 + 0.0914714i
$$472$$ −5.23758 + 9.07175i −0.241079 + 0.417561i
$$473$$ 8.02474i 0.368978i
$$474$$ 0.816699 + 0.471521i 0.0375122 + 0.0216577i
$$475$$ 23.7616 + 13.7187i 1.09026 + 0.629459i
$$476$$ 3.88766i 0.178191i
$$477$$ 4.85523 8.40951i 0.222306 0.385045i
$$478$$ 5.54665 + 9.60707i 0.253698 + 0.439417i
$$479$$ −29.0757 + 16.7869i −1.32850 + 0.767011i −0.985068 0.172165i $$-0.944924\pi$$
−0.343434 + 0.939177i $$0.611590\pi$$
$$480$$ 0.332808 0.0151905
$$481$$ 1.36660 1.56591i 0.0623117 0.0713993i
$$482$$ 8.11392 0.369579
$$483$$ 3.64819 2.10628i 0.165998 0.0958393i
$$484$$ 2.09334 + 3.62577i 0.0951517 + 0.164808i
$$485$$ −0.967782 + 1.67625i −0.0439447 + 0.0761145i
$$486$$ 1.00000i 0.0453609i
$$487$$ 17.5020 + 10.1048i 0.793089 + 0.457890i 0.841049 0.540959i $$-0.181939\pi$$
−0.0479597 + 0.998849i $$0.515272\pi$$
$$488$$ −6.44304 3.71989i −0.291663 0.168392i
$$489$$ 3.34071i 0.151072i
$$490$$ −0.166404 + 0.288220i −0.00751736 + 0.0130204i
$$491$$ −3.38977 5.87125i −0.152978 0.264966i 0.779343 0.626598i $$-0.215553\pi$$
−0.932321 + 0.361632i $$0.882220\pi$$
$$492$$ 0.451251 0.260530i 0.0203439 0.0117456i
$$493$$ −4.61339 −0.207777
$$494$$ −19.1441 + 6.55006i −0.861336 + 0.294701i
$$495$$ 0.868706 0.0390454
$$496$$ −6.12656 + 3.53717i −0.275090 + 0.158824i
$$497$$ 0.472310 + 0.818065i 0.0211860 + 0.0366952i
$$498$$ −6.85861 + 11.8795i −0.307341 + 0.532331i
$$499$$ 11.0813i 0.496066i 0.968752 + 0.248033i $$0.0797841\pi$$
−0.968752 + 0.248033i $$0.920216\pi$$
$$500$$ −2.85027 1.64561i −0.127468 0.0735938i
$$501$$ 5.57802 + 3.22047i 0.249207 + 0.143880i
$$502$$ 3.16930i 0.141453i
$$503$$ 14.9958 25.9735i 0.668629 1.15810i −0.309658 0.950848i $$-0.600215\pi$$
0.978288 0.207252i $$-0.0664520\pi$$
$$504$$ 0.500000 + 0.866025i 0.0222718 + 0.0385758i
$$505$$ −4.60296 + 2.65752i −0.204829 + 0.118258i
$$506$$ −10.9958 −0.488823
$$507$$ 12.0343 + 4.91693i 0.534461 + 0.218368i
$$508$$ 6.77953 0.300793
$$509$$ 27.2629 15.7402i 1.20840 0.697673i 0.245994 0.969271i $$-0.420886\pi$$
0.962411 + 0.271599i $$0.0875523\pi$$
$$510$$ −0.646922 1.12050i −0.0286462 0.0496166i
$$511$$ 2.33281 4.04054i 0.103197 0.178743i
$$512$$ 1.00000i 0.0441942i
$$513$$ −4.85997 2.80591i −0.214573 0.123884i
$$514$$ 0.167507 + 0.0967103i 0.00738843 + 0.00426571i
$$515$$ 2.49819i 0.110083i
$$516$$ 1.53717 2.66245i 0.0676701 0.117208i
$$517$$ 15.7303 + 27.2456i 0.691816 + 1.19826i
$$518$$ 0.499211 0.288220i 0.0219341 0.0126637i
$$519$$ −18.6144 −0.817079
$$520$$ 1.13534 0.388451i 0.0497880 0.0170347i
$$521$$ 17.8010 0.779877 0.389939 0.920841i $$-0.372496\pi$$
0.389939 + 0.920841i $$0.372496\pi$$
$$522$$ 1.02769 0.593337i 0.0449808 0.0259697i
$$523$$ −16.4702 28.5272i −0.720192 1.24741i −0.960923 0.276817i $$-0.910720\pi$$
0.240731 0.970592i $$-0.422613\pi$$
$$524$$ 3.61440 6.26032i 0.157896 0.273483i
$$525$$ 4.88924i 0.213384i
$$526$$ 10.4301 + 6.02185i 0.454776 + 0.262565i
$$527$$ 23.8180 + 13.7513i 1.03753 + 0.599017i
$$528$$ 2.61023i 0.113596i
$$529$$ 2.62713 4.55033i 0.114223 0.197840i
$$530$$ −1.61586 2.79875i −0.0701884 0.121570i
$$531$$ −9.07175 + 5.23758i −0.393680 + 0.227292i
$$532$$ −5.61181 −0.243303
$$533$$ 1.23531 1.41547i 0.0535072 0.0613107i
$$534$$ −3.38029 −0.146279
$$535$$ −2.49333 + 1.43952i −0.107796 + 0.0622360i
$$536$$ 5.96015 + 10.3233i 0.257439 + 0.445898i
$$537$$ 11.1081 19.2398i 0.479351 0.830261i
$$538$$ 17.2097i 0.741965i
$$539$$ 2.26053 + 1.30512i 0.0973679 + 0.0562154i
$$540$$ 0.288220 + 0.166404i 0.0124030 + 0.00716088i
$$541$$ 15.5204i 0.667276i −0.942701 0.333638i $$-0.891724\pi$$
0.942701 0.333638i $$-0.108276\pi$$
$$542$$ 8.57096 14.8453i 0.368154 0.637662i
$$543$$ −2.02927 3.51479i −0.0870842 0.150834i
$$544$$ −3.36681 + 1.94383i −0.144351 + 0.0833411i
$$545$$ −6.19500 −0.265365
$$546$$ 2.71652 + 2.37076i 0.116256 + 0.101459i
$$547$$ 22.9529 0.981397 0.490698 0.871329i $$-0.336742\pi$$
0.490698 + 0.871329i $$0.336742\pi$$
$$548$$ −10.2964 + 5.94462i −0.439840 + 0.253942i
$$549$$ −3.71989 6.44304i −0.158761 0.274982i
$$550$$ −6.38103 + 11.0523i −0.272088 + 0.471270i
$$551$$ 6.65939i 0.283700i
$$552$$ −3.64819 2.10628i −0.155277 0.0896494i
$$553$$ 0.816699 + 0.471521i 0.0347296 + 0.0200511i
$$554$$ 15.7132i 0.667590i
$$555$$ 0.0959218 0.166141i 0.00407165 0.00705231i
$$556$$ 7.16056 + 12.4025i 0.303675 + 0.525981i
$$557$$ −20.8161 + 12.0182i −0.882005 + 0.509226i −0.871319 0.490717i $$-0.836735\pi$$
−0.0106863 + 0.999943i $$0.503402\pi$$
$$558$$ −7.07434 −0.299481
$$559$$ 2.13630 10.8769i 0.0903560 0.460043i
$$560$$ 0.332808 0.0140637
$$561$$ −8.78817 + 5.07386i −0.371037 + 0.214218i
$$562$$ −2.03669 3.52765i −0.0859125 0.148805i
$$563$$ −18.9379 + 32.8015i −0.798139 + 1.38242i 0.122687 + 0.992445i $$0.460849\pi$$
−0.920827 + 0.389972i $$0.872485\pi$$
$$564$$ 12.0528i 0.507512i
$$565$$ 2.63728 + 1.52264i 0.110951 + 0.0640578i
$$566$$ −18.6497 10.7674i −0.783906 0.452589i
$$567$$ 1.00000i 0.0419961i
$$568$$ 0.472310 0.818065i 0.0198177 0.0343252i
$$569$$ −13.6833 23.7001i −0.573632 0.993560i −0.996189 0.0872233i $$-0.972201\pi$$
0.422557 0.906336i $$-0.361133\pi$$
$$570$$ −1.61744 + 0.933827i −0.0677469 + 0.0391137i
$$571$$ 17.6639 0.739213 0.369607 0.929188i $$-0.379492\pi$$
0.369607 + 0.929188i $$0.379492\pi$$
$$572$$ −3.04665 8.90456i −0.127387 0.372318i
$$573$$ 11.7204 0.489625
$$574$$ 0.451251 0.260530i 0.0188348 0.0108743i
$$575$$ 10.2981 + 17.8369i 0.429462 + 0.743849i
$$576$$ 0.500000 0.866025i 0.0208333 0.0360844i
$$577$$ 11.3804i 0.473772i 0.971537 + 0.236886i $$0.0761268\pi$$
−0.971537 + 0.236886i $$0.923873\pi$$
$$578$$ −1.63340 0.943042i −0.0679404 0.0392254i
$$579$$ −20.6123 11.9005i −0.856618 0.494568i
$$580$$ 0.394934i 0.0163988i
$$581$$ −6.85861 + 11.8795i −0.284543 + 0.492843i
$$582$$ 2.90793 + 5.03669i 0.120538 + 0.208777i
$$583$$ −21.9508 + 12.6733i −0.909109 + 0.524874i
$$584$$ −4.66562 −0.193065
$$585$$ 1.17746 + 0.231262i 0.0486819 + 0.00956152i
$$586$$ −0.176042 −0.00727222
$$587$$ 15.9949 9.23469i 0.660182 0.381156i −0.132164 0.991228i $$-0.542193\pi$$
0.792346 + 0.610072i $$0.208859\pi$$
$$588$$ 0.500000 + 0.866025i 0.0206197 + 0.0357143i
$$589$$ 19.8499 34.3811i 0.817902 1.41665i
$$590$$ 3.48621i 0.143525i
$$591$$ 8.73184 + 5.04133i 0.359180 + 0.207373i
$$592$$ −0.499211 0.288220i −0.0205175 0.0118458i
$$593$$ 19.3561i 0.794859i −0.917633 0.397429i $$-0.869902\pi$$
0.917633 0.397429i $$-0.130098\pi$$
$$594$$ 1.30512 2.26053i 0.0535496 0.0927507i
$$595$$ −0.646922 1.12050i −0.0265212 0.0459361i
$$596$$ −5.24548 + 3.02848i −0.214863 + 0.124051i
$$597$$ 13.8501 0.566846
$$598$$ −14.9039 2.92724i −0.609465 0.119704i
$$599$$ 21.1818 0.865466 0.432733 0.901522i $$-0.357549\pi$$
0.432733 + 0.901522i $$0.357549\pi$$
$$600$$ −4.23421 + 2.44462i −0.172861 + 0.0998012i
$$601$$ −11.0721 19.1774i −0.451639 0.782261i 0.546849 0.837231i $$-0.315827\pi$$
−0.998488 + 0.0549699i $$0.982494\pi$$
$$602$$ 1.53717 2.66245i 0.0626503 0.108513i
$$603$$ 11.9203i 0.485432i
$$604$$ −18.6154 10.7476i −0.757452 0.437315i
$$605$$ 1.20668 + 0.696679i 0.0490586 + 0.0283240i
$$606$$ 15.9703i 0.648750i
$$607$$ −17.1439 + 29.6942i −0.695851 + 1.20525i 0.274042 + 0.961718i $$0.411639\pi$$
−0.969893 + 0.243531i $$0.921694\pi$$
$$608$$ 2.80591 + 4.85997i 0.113795 + 0.197098i
$$609$$ 1.02769 0.593337i 0.0416441 0.0240432i
$$610$$ −2.47602 −0.100251
$$611$$ 14.0679 + 41.1168i 0.569125 + 1.66341i
$$612$$ −3.88766 −0.157149
$$613$$ 14.7308 8.50484i 0.594972 0.343507i −0.172089 0.985081i $$-0.555052\pi$$
0.767061 + 0.641574i $$0.221718\pi$$
$$614$$ −10.3702 17.9618i −0.418509 0.724878i
$$615$$ 0.0867062 0.150180i 0.00349633 0.00605583i
$$616$$ 2.61023i 0.105169i
$$617$$ 15.0005 + 8.66052i 0.603896 + 0.348659i 0.770573 0.637352i $$-0.219970\pi$$
−0.166677 + 0.986012i $$0.553304\pi$$
$$618$$ 6.50074 + 3.75321i 0.261498 + 0.150976i
$$619$$ 0.621482i 0.0249795i 0.999922 + 0.0124897i $$0.00397571\pi$$
−0.999922 + 0.0124897i $$0.996024\pi$$
$$620$$ −1.17720 + 2.03896i −0.0472773 + 0.0818868i
$$621$$ −2.10628 3.64819i −0.0845223 0.146397i
$$622$$ −9.49838 + 5.48389i −0.380850 + 0.219884i
$$623$$ −3.38029 −0.135428
$$624$$ 0.694883 3.53796i 0.0278176 0.141632i
$$625$$ 23.3509 0.934034
$$626$$ −14.0460 + 8.10945i −0.561390 + 0.324119i
$$627$$ 7.32407 + 12.6857i 0.292495 + 0.506617i
$$628$$ 1.14613 1.98516i 0.0457357 0.0792165i
$$629$$ 2.24100i 0.0893546i
$$630$$ 0.288220 + 0.166404i 0.0114830 + 0.00662969i
$$631$$ 11.7575 + 6.78817i 0.468057 + 0.270233i 0.715426 0.698688i $$-0.246233\pi$$
−0.247369 + 0.968921i $$0.579566\pi$$
$$632$$ 0.943042i 0.0375122i
$$633$$ 2.27743 3.94462i 0.0905196 0.156785i
$$634$$ 5.26790 + 9.12428i 0.209215 + 0.362371i
$$635$$ 1.95400 1.12814i 0.0775419 0.0447689i
$$636$$ −9.71047 −0.385045
$$637$$ 2.71652 + 2.37076i 0.107632 + 0.0939331i
$$638$$ −3.09750 −0.122631
$$639$$ 0.818065 0.472310i 0.0323621 0.0186843i
$$640$$ −0.166404 0.288220i −0.00657769 0.0113929i
$$641$$ −10.2558 + 17.7636i −0.405081 + 0.701622i −0.994331 0.106330i $$-0.966090\pi$$
0.589250 + 0.807951i $$0.299423\pi$$
$$642$$ 8.65078i 0.341419i
$$643$$ −37.0253 21.3766i −1.46013 0.843009i −0.461118 0.887339i $$-0.652552\pi$$
−0.999017 + 0.0443295i $$0.985885\pi$$
$$644$$ −3.64819 2.10628i −0.143759 0.0829992i
$$645$$ 1.02316i 0.0402870i
$$646$$ 10.9084 18.8939i 0.429186 0.743372i
$$647$$ −13.1115 22.7098i −0.515466 0.892814i −0.999839 0.0179521i $$-0.994285\pi$$
0.484372 0.874862i $$-0.339048\pi$$
$$648$$ 0.866025 0.500000i 0.0340207 0.0196419i
$$649$$ 27.3426 1.07329
$$650$$ −11.5912 + 13.2817i −0.454646 + 0.520952i
$$651$$ −7.07434 −0.277265
$$652$$ 2.89314 1.67035i 0.113304 0.0654161i
$$653$$ 4.36935 + 7.56794i 0.170986 + 0.296156i 0.938765 0.344558i $$-0.111971\pi$$
−0.767779 + 0.640715i $$0.778638\pi$$
$$654$$ −9.30718 + 16.1205i −0.363939 + 0.630361i
$$655$$ 2.40580i 0.0940023i
$$656$$ −0.451251 0.260530i −0.0176184 0.0101720i
$$657$$ −4.04054 2.33281i −0.157637 0.0910115i
$$658$$ 12.0528i 0.469865i
$$659$$ −0.251052 + 0.434834i −0.00977958 + 0.0169387i −0.870874 0.491507i $$-0.836446\pi$$
0.861094 + 0.508445i $$0.169780\pi$$
$$660$$ −0.434353 0.752321i −0.0169072 0.0292841i
$$661$$ 27.1062 15.6498i 1.05431 0.608705i 0.130456 0.991454i $$-0.458356\pi$$
0.923853 + 0.382749i $$0.125022\pi$$
$$662$$ 16.1297 0.626899
$$663$$ −13.2624 + 4.53765i −0.515068 + 0.176228i
$$664$$ 13.7172 0.532331
$$665$$ −1.61744 + 0.933827i −0.0627215 + 0.0362123i
$$666$$ −0.288220 0.499211i −0.0111683 0.0193440i
$$667$$ −2.49947 + 4.32922i −0.0967800 + 0.167628i
$$668$$ 6.44094i 0.249207i
$$669$$ −7.30359 4.21673i −0.282373 0.163028i
$$670$$ 3.43567 + 1.98358i 0.132731 + 0.0766325i
$$671$$ 19.4196i 0.749685i
$$672$$ 0.500000 0.866025i 0.0192879 0.0334077i
$$673$$ −11.8585 20.5395i −0.457112 0.791741i 0.541695 0.840575i $$-0.317783\pi$$
−0.998807 + 0.0488340i $$0.984449\pi$$
$$674$$ −1.54833 + 0.893927i −0.0596393 + 0.0344328i
$$675$$ −4.88924 −0.188187
$$676$$ −1.75895 12.8805i −0.0676520 0.495402i
$$677$$ 17.8136 0.684631 0.342315 0.939585i $$-0.388789\pi$$
0.342315 + 0.939585i $$0.388789\pi$$
$$678$$ 7.92435 4.57512i 0.304333 0.175707i
$$679$$ 2.90793 + 5.03669i 0.111596 + 0.193290i
$$680$$ −0.646922 + 1.12050i −0.0248083 + 0.0429693i
$$681$$ 27.9893i 1.07255i
$$682$$ 15.9917 + 9.23284i 0.612356 + 0.353544i
$$683$$ 10.3174 + 5.95673i 0.394783 + 0.227928i 0.684230 0.729266i $$-0.260138\pi$$
−0.289448 + 0.957194i $$0.593472\pi$$
$$684$$ 5.61181i 0.214573i
$$685$$ −1.97841 + 3.42671i −0.0755913 + 0.130928i
$$686$$ 0.500000 + 0.866025i 0.0190901 + 0.0330650i
$$687$$ −24.9229 + 14.3892i −0.950868 + 0.548984i
$$688$$ −3.07434 −0.117208
$$689$$ −33.1263 + 11.3340i −1.26201 + 0.431790i
$$690$$ −1.40197 −0.0533723
$$691$$ −17.3085 + 9.99306i −0.658446 + 0.380154i −0.791685 0.610930i $$-0.790796\pi$$
0.133239 + 0.991084i $$0.457462\pi$$
$$692$$ 9.30718 + 16.1205i 0.353806 + 0.612810i
$$693$$ 1.30512 2.26053i 0.0495773 0.0858704i
$$694$$ 25.4061i 0.964402i
$$695$$ 4.12763 + 2.38309i 0.156570 + 0.0903957i
$$696$$ −1.02769 0.593337i −0.0389545 0.0224904i
$$697$$ 2.02570i 0.0767289i
$$698$$ 14.1693 24.5419i 0.536314 0.928923i
$$699$$ −9.44383 16.3572i −0.357198 0.618686i
$$700$$ −4.23421 + 2.44462i −0.160038 + 0.0923979i
$$701$$ −23.9244 −0.903613 −0.451806 0.892116i $$-0.649220\pi$$
−0.451806 + 0.892116i $$0.649220\pi$$
$$702$$ 2.37076 2.71652i 0.0894787 0.102528i
$$703$$ 3.23487 0.122005
$$704$$ −2.26053 + 1.30512i −0.0851969 + 0.0491885i
$$705$$ 2.00562 + 3.47384i 0.0755362 + 0.130832i
$$706$$ 0.976568 1.69146i 0.0367536 0.0636591i
$$707$$ 15.9703i 0.600626i
$$708$$ 9.07175 + 5.23758i 0.340937 + 0.196840i
$$709$$ 30.7406 + 17.7481i 1.15449 + 0.666544i 0.949977 0.312320i $$-0.101106\pi$$
0.204512 + 0.978864i $$0.434439\pi$$
$$710$$ 0.314377i 0.0117983i
$$711$$ 0.471521 0.816699i 0.0176834 0.0306286i
$$712$$ 1.69014 + 2.92741i 0.0633408 + 0.109710i
$$713$$ 25.8085 14.9006i 0.966537 0.558031i
$$714$$ −3.88766 −0.145492
$$715$$ −2.35986 2.05950i −0.0882536 0.0770208i
$$716$$ −22.2163 −0.830261
$$717$$ 9.60707 5.54665i 0.358783 0.207143i
$$718$$ 13.8282 + 23.9512i 0.516065 + 0.893851i
$$719$$ −3.09097 + 5.35372i −0.115274 + 0.199660i −0.917889 0.396837i $$-0.870108\pi$$
0.802615 + 0.596497i $$0.203441\pi$$
$$720$$ 0.332808i 0.0124030i
$$721$$ 6.50074 + 3.75321i 0.242100 + 0.139777i
$$722$$ −10.8188 6.24622i −0.402633 0.232460i
$$723$$ 8.11392i 0.301760i
$$724$$ −2.02927 + 3.51479i −0.0754171 + 0.130626i
$$725$$ 2.90097 + 5.02462i 0.107739 + 0.186610i
$$726$$ 3.62577 2.09334i 0.134565 0.0776910i
$$727$$ −43.2387 −1.60363 −0.801817 0.597569i $$-0.796133\pi$$
−0.801817 + 0.597569i $$0.796133\pi$$
$$728$$ 0.694883 3.53796i 0.0257541 0.131125i
$$729$$ 1.00000 0.0370370
$$730$$ −1.34472 + 0.776376i −0.0497704 + 0.0287350i
$$731$$ 5.97599 + 10.3507i 0.221030 + 0.382835i
$$732$$ −3.71989 + 6.44304i −0.137491 + 0.238142i
$$733$$ 32.0306i 1.18308i −0.806277 0.591538i $$-0.798521\pi$$
0.806277 0.591538i $$-0.201479\pi$$
$$734$$ 4.98636 + 2.87888i 0.184050 + 0.106261i
$$735$$ 0.288220 + 0.166404i 0.0106311 + 0.00613790i
$$736$$ 4.21257i 0.155277i
$$737$$ 15.5574 26.9462i 0.573064 0.992576i
$$738$$ −0.260530 0.451251i −0.00959023 0.0166108i
$$739$$ −22.0558 + 12.7339i −0.811334 + 0.468424i −0.847419 0.530925i $$-0.821845\pi$$
0.0360848 + 0.999349i $$0.488511\pi$$
$$740$$ −0.191844 −0.00705231
$$741$$ 6.55006 + 19.1441i 0.240623 + 0.703278i
$$742$$ −9.71047 −0.356482
$$743$$ −12.5533 + 7.24763i −0.460535 + 0.265890i −0.712269 0.701906i $$-0.752332\pi$$
0.251734 + 0.967796i $$0.418999\pi$$
$$744$$ 3.53717 + 6.12656i 0.129679 + 0.224610i
$$745$$ −1.00790 + 1.74574i −0.0369266 + 0.0639588i
$$746$$ 27.8487i 1.01961i
$$747$$ 11.8795 + 6.85861i 0.434646 + 0.250943i
$$748$$ 8.78817 + 5.07386i 0.321327 + 0.185519i
$$749$$ 8.65078i 0.316092i
$$750$$ −1.64561 + 2.85027i −0.0600891 + 0.104077i
$$751$$ 14.5632 + 25.2243i 0.531420 + 0.920447i 0.999327 + 0.0366690i $$0.0116747\pi$$
−0.467907 + 0.883777i $$0.654992\pi$$
$$752$$ 10.4380 6.02638i 0.380634 0.219759i
$$753$$ −3.16930 −0.115496
$$754$$ −4.19840 0.824599i −0.152897 0.0300301i
$$755$$ −7.15379 −0.260353
$$756$$ 0.866025 0.500000i 0.0314970 0.0181848i
$$757$$ 10.0230 + 17.3603i 0.364292 + 0.630973i 0.988662 0.150156i $$-0.0479776\pi$$
−0.624370 + 0.781129i $$0.714644\pi$$
$$758$$ 6.22590 10.7836i 0.226135 0.391677i
$$759$$ 10.9958i 0.399122i
$$760$$ 1.61744 + 0.933827i 0.0586706 + 0.0338735i
$$761$$ 16.4954 + 9.52360i 0.597956 + 0.345230i 0.768237 0.640165i $$-0.221134\pi$$
−0.170281 + 0.985396i $$0.554468\pi$$
$$762$$ 6.77953i 0.245596i
$$763$$ −9.30718 + 16.1205i −0.336942 + 0.583601i
$$764$$ −5.86018 10.1501i −0.212014 0.367219i
$$765$$ −1.12050 + 0.646922i −0.0405118 + 0.0233895i
$$766$$ 9.72573 0.351405
$$767$$ 37.0607 + 7.27900i 1.33818 + 0.262830i
$$768$$ −1.00000 −0.0360844
$$769$$ 13.2055 7.62418i 0.476201 0.274935i −0.242631 0.970119i $$-0.578010\pi$$
0.718832 + 0.695184i $$0.244677\pi$$
$$770$$ −0.434353 0.752321i −0.0156530 0.0271118i
$$771$$ 0.0967103