# Properties

 Label 420.2.l.f.239.3 Level $420$ Weight $2$ Character 420.239 Analytic conductor $3.354$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$420 = 2^{2} \cdot 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 420.l (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.35371688489$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: 8.0.386672896.3 Defining polynomial: $$x^{8} - x^{6} - 2x^{5} + 2x^{4} - 4x^{3} - 4x^{2} + 16$$ x^8 - x^6 - 2*x^5 + 2*x^4 - 4*x^3 - 4*x^2 + 16 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 239.3 Root $$0.621372 - 1.27039i$$ of defining polynomial Character $$\chi$$ $$=$$ 420.239 Dual form 420.2.l.f.239.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.621372 - 1.27039i) q^{2} +(1.72779 + 0.121372i) q^{3} +(-1.22779 + 1.57877i) q^{4} +(1.00000 - 2.00000i) q^{5} +(-0.919412 - 2.27039i) q^{6} +1.00000 q^{7} +(2.76858 + 0.578773i) q^{8} +(2.97054 + 0.419412i) q^{9} +O(q^{10})$$ $$q+(-0.621372 - 1.27039i) q^{2} +(1.72779 + 0.121372i) q^{3} +(-1.22779 + 1.57877i) q^{4} +(1.00000 - 2.00000i) q^{5} +(-0.919412 - 2.27039i) q^{6} +1.00000 q^{7} +(2.76858 + 0.578773i) q^{8} +(2.97054 + 0.419412i) q^{9} +(-3.16216 - 0.0276478i) q^{10} +3.45559 q^{11} +(-2.31299 + 2.57877i) q^{12} +4.83882i q^{13} +(-0.621372 - 1.27039i) q^{14} +(1.97054 - 3.33421i) q^{15} +(-0.985049 - 3.87681i) q^{16} -5.94108 q^{17} +(-1.31299 - 4.03436i) q^{18} -1.08157i q^{19} +(1.92975 + 4.03436i) q^{20} +(1.72779 + 0.121372i) q^{21} +(-2.14721 - 4.38995i) q^{22} +0.596080i q^{23} +(4.71328 + 1.33603i) q^{24} +(-3.00000 - 4.00000i) q^{25} +(6.14721 - 3.00671i) q^{26} +(5.08157 + 1.08520i) q^{27} +(-1.22779 + 1.57877i) q^{28} -4.83882i q^{29} +(-5.46020 - 0.431568i) q^{30} -9.56706i q^{31} +(-4.31299 + 3.66034i) q^{32} +(5.97054 + 0.419412i) q^{33} +(3.69162 + 7.54750i) q^{34} +(1.00000 - 2.00000i) q^{35} +(-4.30936 + 4.17485i) q^{36} +2.91117i q^{37} +(-1.37402 + 0.672057i) q^{38} +(-0.587299 + 8.36049i) q^{39} +(3.92612 - 4.95838i) q^{40} +6.91117i q^{41} +(-0.919412 - 2.27039i) q^{42} +7.39666 q^{43} +(-4.24274 + 5.45559i) q^{44} +(3.80936 - 5.52166i) q^{45} +(0.757255 - 0.370388i) q^{46} -0.242745i q^{47} +(-1.23142 - 6.81789i) q^{48} +1.00000 q^{49} +(-3.21745 + 6.29667i) q^{50} +(-10.2649 - 0.721082i) q^{51} +(-7.63941 - 5.94108i) q^{52} -11.8223 q^{53} +(-1.77892 - 7.12990i) q^{54} +(3.45559 - 6.91117i) q^{55} +(2.76858 + 0.578773i) q^{56} +(0.131272 - 1.86873i) q^{57} +(-6.14721 + 3.00671i) q^{58} +3.25197 q^{59} +(2.84455 + 7.20476i) q^{60} -12.6486 q^{61} +(-12.1539 + 5.94470i) q^{62} +(2.97054 + 0.419412i) q^{63} +(7.33004 + 3.20476i) q^{64} +(9.67765 + 4.83882i) q^{65} +(-3.17711 - 7.84554i) q^{66} -5.71901 q^{67} +(7.29441 - 9.37961i) q^{68} +(-0.0723476 + 1.02990i) q^{69} +(-3.16216 - 0.0276478i) q^{70} -8.00000 q^{71} +(7.98142 + 2.88044i) q^{72} +8.00000i q^{73} +(3.69833 - 1.80892i) q^{74} +(-4.69789 - 7.27529i) q^{75} +(1.70755 + 1.32794i) q^{76} +3.45559 q^{77} +(10.9860 - 4.44887i) q^{78} +0.949416i q^{79} +(-8.73867 - 1.90672i) q^{80} +(8.64819 + 2.49176i) q^{81} +(8.77990 - 4.29441i) q^{82} +16.9637i q^{83} +(-2.31299 + 2.57877i) q^{84} +(-5.94108 + 11.8822i) q^{85} +(-4.59608 - 9.39666i) q^{86} +(0.587299 - 8.36049i) q^{87} +(9.56706 + 2.00000i) q^{88} +5.23352i q^{89} +(-9.38171 - 1.40838i) q^{90} +4.83882i q^{91} +(-0.941075 - 0.731863i) q^{92} +(1.16118 - 16.5299i) q^{93} +(-0.308381 + 0.150835i) q^{94} +(-2.16314 - 1.08157i) q^{95} +(-7.89622 + 5.80084i) q^{96} -3.30587i q^{97} +(-0.621372 - 1.27039i) q^{98} +(10.2649 + 1.44932i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q + 2 q^{3} + 2 q^{4} + 8 q^{5} + 4 q^{6} + 8 q^{7} - 6 q^{8} + 2 q^{9}+O(q^{10})$$ 8 * q + 2 * q^3 + 2 * q^4 + 8 * q^5 + 4 * q^6 + 8 * q^7 - 6 * q^8 + 2 * q^9 $$8 q + 2 q^{3} + 2 q^{4} + 8 q^{5} + 4 q^{6} + 8 q^{7} - 6 q^{8} + 2 q^{9} - 4 q^{10} + 4 q^{11} - 14 q^{12} - 6 q^{15} - 6 q^{16} - 4 q^{17} - 6 q^{18} + 10 q^{20} + 2 q^{21} + 6 q^{22} + 6 q^{24} - 24 q^{25} + 26 q^{26} + 8 q^{27} + 2 q^{28} - 16 q^{30} - 30 q^{32} + 26 q^{33} + 30 q^{34} + 8 q^{35} + 10 q^{36} - 20 q^{38} + 18 q^{39} - 14 q^{40} + 4 q^{42} - 8 q^{43} - 24 q^{44} - 14 q^{45} + 16 q^{46} - 38 q^{48} + 8 q^{49} - 8 q^{50} - 14 q^{51} + 16 q^{52} + 8 q^{54} + 4 q^{55} - 6 q^{56} + 20 q^{57} - 26 q^{58} + 8 q^{59} + 10 q^{60} - 16 q^{61} - 40 q^{62} + 2 q^{63} + 26 q^{64} + 32 q^{65} - 6 q^{66} - 24 q^{67} + 12 q^{68} + 24 q^{69} - 4 q^{70} - 64 q^{71} + 22 q^{72} - 4 q^{74} - 22 q^{75} - 28 q^{76} + 4 q^{77} + 42 q^{78} - 38 q^{80} + 2 q^{81} + 4 q^{82} - 14 q^{84} - 4 q^{85} - 24 q^{86} - 18 q^{87} + 24 q^{88} - 6 q^{90} + 36 q^{92} + 32 q^{93} - 2 q^{94} + 48 q^{95} - 14 q^{96} + 14 q^{99}+O(q^{100})$$ 8 * q + 2 * q^3 + 2 * q^4 + 8 * q^5 + 4 * q^6 + 8 * q^7 - 6 * q^8 + 2 * q^9 - 4 * q^10 + 4 * q^11 - 14 * q^12 - 6 * q^15 - 6 * q^16 - 4 * q^17 - 6 * q^18 + 10 * q^20 + 2 * q^21 + 6 * q^22 + 6 * q^24 - 24 * q^25 + 26 * q^26 + 8 * q^27 + 2 * q^28 - 16 * q^30 - 30 * q^32 + 26 * q^33 + 30 * q^34 + 8 * q^35 + 10 * q^36 - 20 * q^38 + 18 * q^39 - 14 * q^40 + 4 * q^42 - 8 * q^43 - 24 * q^44 - 14 * q^45 + 16 * q^46 - 38 * q^48 + 8 * q^49 - 8 * q^50 - 14 * q^51 + 16 * q^52 + 8 * q^54 + 4 * q^55 - 6 * q^56 + 20 * q^57 - 26 * q^58 + 8 * q^59 + 10 * q^60 - 16 * q^61 - 40 * q^62 + 2 * q^63 + 26 * q^64 + 32 * q^65 - 6 * q^66 - 24 * q^67 + 12 * q^68 + 24 * q^69 - 4 * q^70 - 64 * q^71 + 22 * q^72 - 4 * q^74 - 22 * q^75 - 28 * q^76 + 4 * q^77 + 42 * q^78 - 38 * q^80 + 2 * q^81 + 4 * q^82 - 14 * q^84 - 4 * q^85 - 24 * q^86 - 18 * q^87 + 24 * q^88 - 6 * q^90 + 36 * q^92 + 32 * q^93 - 2 * q^94 + 48 * q^95 - 14 * q^96 + 14 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$$.

 $$n$$ $$211$$ $$241$$ $$281$$ $$337$$ $$\chi(n)$$ $$-1$$ $$1$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.621372 1.27039i −0.439377 0.898303i
$$3$$ 1.72779 + 0.121372i 0.997542 + 0.0700743i
$$4$$ −1.22779 + 1.57877i −0.613897 + 0.789387i
$$5$$ 1.00000 2.00000i 0.447214 0.894427i
$$6$$ −0.919412 2.27039i −0.375348 0.926884i
$$7$$ 1.00000 0.377964
$$8$$ 2.76858 + 0.578773i 0.978840 + 0.204627i
$$9$$ 2.97054 + 0.419412i 0.990179 + 0.139804i
$$10$$ −3.16216 0.0276478i −0.999962 0.00874299i
$$11$$ 3.45559 1.04190 0.520949 0.853588i $$-0.325578\pi$$
0.520949 + 0.853588i $$0.325578\pi$$
$$12$$ −2.31299 + 2.57877i −0.667703 + 0.744428i
$$13$$ 4.83882i 1.34205i 0.741435 + 0.671024i $$0.234145\pi$$
−0.741435 + 0.671024i $$0.765855\pi$$
$$14$$ −0.621372 1.27039i −0.166069 0.339527i
$$15$$ 1.97054 3.33421i 0.508791 0.860890i
$$16$$ −0.985049 3.87681i −0.246262 0.969203i
$$17$$ −5.94108 −1.44092 −0.720461 0.693495i $$-0.756070\pi$$
−0.720461 + 0.693495i $$0.756070\pi$$
$$18$$ −1.31299 4.03436i −0.309475 0.950908i
$$19$$ 1.08157i 0.248129i −0.992274 0.124064i $$-0.960407\pi$$
0.992274 0.124064i $$-0.0395930\pi$$
$$20$$ 1.92975 + 4.03436i 0.431506 + 0.902110i
$$21$$ 1.72779 + 0.121372i 0.377035 + 0.0264856i
$$22$$ −2.14721 4.38995i −0.457786 0.935940i
$$23$$ 0.596080i 0.124291i 0.998067 + 0.0621456i $$0.0197943\pi$$
−0.998067 + 0.0621456i $$0.980206\pi$$
$$24$$ 4.71328 + 1.33603i 0.962095 + 0.272716i
$$25$$ −3.00000 4.00000i −0.600000 0.800000i
$$26$$ 6.14721 3.00671i 1.20557 0.589665i
$$27$$ 5.08157 + 1.08520i 0.977948 + 0.208847i
$$28$$ −1.22779 + 1.57877i −0.232031 + 0.298360i
$$29$$ 4.83882i 0.898547i −0.893394 0.449274i $$-0.851683\pi$$
0.893394 0.449274i $$-0.148317\pi$$
$$30$$ −5.46020 0.431568i −0.996891 0.0787931i
$$31$$ 9.56706i 1.71829i −0.511729 0.859147i $$-0.670995\pi$$
0.511729 0.859147i $$-0.329005\pi$$
$$32$$ −4.31299 + 3.66034i −0.762436 + 0.647063i
$$33$$ 5.97054 + 0.419412i 1.03934 + 0.0730103i
$$34$$ 3.69162 + 7.54750i 0.633107 + 1.29438i
$$35$$ 1.00000 2.00000i 0.169031 0.338062i
$$36$$ −4.30936 + 4.17485i −0.718227 + 0.695809i
$$37$$ 2.91117i 0.478594i 0.970946 + 0.239297i $$0.0769169\pi$$
−0.970946 + 0.239297i $$0.923083\pi$$
$$38$$ −1.37402 + 0.672057i −0.222895 + 0.109022i
$$39$$ −0.587299 + 8.36049i −0.0940431 + 1.33875i
$$40$$ 3.92612 4.95838i 0.620775 0.783989i
$$41$$ 6.91117i 1.07934i 0.841875 + 0.539672i $$0.181452\pi$$
−0.841875 + 0.539672i $$0.818548\pi$$
$$42$$ −0.919412 2.27039i −0.141868 0.350329i
$$43$$ 7.39666 1.12798 0.563990 0.825782i $$-0.309266\pi$$
0.563990 + 0.825782i $$0.309266\pi$$
$$44$$ −4.24274 + 5.45559i −0.639618 + 0.822461i
$$45$$ 3.80936 5.52166i 0.567866 0.823121i
$$46$$ 0.757255 0.370388i 0.111651 0.0546107i
$$47$$ 0.242745i 0.0354079i −0.999843 0.0177040i $$-0.994364\pi$$
0.999843 0.0177040i $$-0.00563564\pi$$
$$48$$ −1.23142 6.81789i −0.177741 0.984077i
$$49$$ 1.00000 0.142857
$$50$$ −3.21745 + 6.29667i −0.455016 + 0.890483i
$$51$$ −10.2649 0.721082i −1.43738 0.100972i
$$52$$ −7.63941 5.94108i −1.05939 0.823879i
$$53$$ −11.8223 −1.62392 −0.811962 0.583710i $$-0.801600\pi$$
−0.811962 + 0.583710i $$0.801600\pi$$
$$54$$ −1.77892 7.12990i −0.242080 0.970256i
$$55$$ 3.45559 6.91117i 0.465951 0.931902i
$$56$$ 2.76858 + 0.578773i 0.369967 + 0.0773418i
$$57$$ 0.131272 1.86873i 0.0173875 0.247519i
$$58$$ −6.14721 + 3.00671i −0.807168 + 0.394801i
$$59$$ 3.25197 0.423370 0.211685 0.977338i $$-0.432105\pi$$
0.211685 + 0.977338i $$0.432105\pi$$
$$60$$ 2.84455 + 7.20476i 0.367230 + 0.930130i
$$61$$ −12.6486 −1.61949 −0.809745 0.586781i $$-0.800395\pi$$
−0.809745 + 0.586781i $$0.800395\pi$$
$$62$$ −12.1539 + 5.94470i −1.54355 + 0.754978i
$$63$$ 2.97054 + 0.419412i 0.374253 + 0.0528410i
$$64$$ 7.33004 + 3.20476i 0.916255 + 0.400595i
$$65$$ 9.67765 + 4.83882i 1.20036 + 0.600182i
$$66$$ −3.17711 7.84554i −0.391075 0.965719i
$$67$$ −5.71901 −0.698689 −0.349344 0.936994i $$-0.613596\pi$$
−0.349344 + 0.936994i $$0.613596\pi$$
$$68$$ 7.29441 9.37961i 0.884577 1.13744i
$$69$$ −0.0723476 + 1.02990i −0.00870963 + 0.123986i
$$70$$ −3.16216 0.0276478i −0.377950 0.00330454i
$$71$$ −8.00000 −0.949425 −0.474713 0.880141i $$-0.657448\pi$$
−0.474713 + 0.880141i $$0.657448\pi$$
$$72$$ 7.98142 + 2.88044i 0.940619 + 0.339463i
$$73$$ 8.00000i 0.936329i 0.883641 + 0.468165i $$0.155085\pi$$
−0.883641 + 0.468165i $$0.844915\pi$$
$$74$$ 3.69833 1.80892i 0.429922 0.210283i
$$75$$ −4.69789 7.27529i −0.542466 0.840078i
$$76$$ 1.70755 + 1.32794i 0.195870 + 0.152326i
$$77$$ 3.45559 0.393801
$$78$$ 10.9860 4.44887i 1.24392 0.503736i
$$79$$ 0.949416i 0.106818i 0.998573 + 0.0534088i $$0.0170086\pi$$
−0.998573 + 0.0534088i $$0.982991\pi$$
$$80$$ −8.73867 1.90672i −0.977014 0.213177i
$$81$$ 8.64819 + 2.49176i 0.960910 + 0.276862i
$$82$$ 8.77990 4.29441i 0.969578 0.474238i
$$83$$ 16.9637i 1.86201i 0.365006 + 0.931005i $$0.381067\pi$$
−0.365006 + 0.931005i $$0.618933\pi$$
$$84$$ −2.31299 + 2.57877i −0.252368 + 0.281367i
$$85$$ −5.94108 + 11.8822i −0.644400 + 1.28880i
$$86$$ −4.59608 9.39666i −0.495608 1.01327i
$$87$$ 0.587299 8.36049i 0.0629651 0.896338i
$$88$$ 9.56706 + 2.00000i 1.01985 + 0.213201i
$$89$$ 5.23352i 0.554752i 0.960761 + 0.277376i $$0.0894648\pi$$
−0.960761 + 0.277376i $$0.910535\pi$$
$$90$$ −9.38171 1.40838i −0.988919 0.148456i
$$91$$ 4.83882i 0.507247i
$$92$$ −0.941075 0.731863i −0.0981139 0.0763020i
$$93$$ 1.16118 16.5299i 0.120408 1.71407i
$$94$$ −0.308381 + 0.150835i −0.0318070 + 0.0155574i
$$95$$ −2.16314 1.08157i −0.221933 0.110967i
$$96$$ −7.89622 + 5.80084i −0.805905 + 0.592045i
$$97$$ 3.30587i 0.335660i −0.985816 0.167830i $$-0.946324\pi$$
0.985816 0.167830i $$-0.0536760\pi$$
$$98$$ −0.621372 1.27039i −0.0627681 0.128329i
$$99$$ 10.2649 + 1.44932i 1.03167 + 0.145662i
$$100$$ 9.99847 + 0.174853i 0.999847 + 0.0174853i
$$101$$ 7.73746i 0.769906i 0.922936 + 0.384953i $$0.125782\pi$$
−0.922936 + 0.384953i $$0.874218\pi$$
$$102$$ 5.46230 + 13.4886i 0.540848 + 1.33557i
$$103$$ −5.61872 −0.553629 −0.276815 0.960923i $$-0.589279\pi$$
−0.276815 + 0.960923i $$0.589279\pi$$
$$104$$ −2.80058 + 13.3967i −0.274620 + 1.31365i
$$105$$ 1.97054 3.33421i 0.192305 0.325386i
$$106$$ 7.34608 + 15.0190i 0.713514 + 1.45878i
$$107$$ 1.68491i 0.162886i −0.996678 0.0814431i $$-0.974047\pi$$
0.996678 0.0814431i $$-0.0259529\pi$$
$$108$$ −7.95240 + 6.69025i −0.765220 + 0.643769i
$$109$$ 9.94108 0.952182 0.476091 0.879396i $$-0.342053\pi$$
0.476091 + 0.879396i $$0.342053\pi$$
$$110$$ −10.9271 0.0955392i −1.04186 0.00910931i
$$111$$ −0.353336 + 5.02990i −0.0335371 + 0.477417i
$$112$$ −0.985049 3.87681i −0.0930783 0.366324i
$$113$$ 3.23352 0.304184 0.152092 0.988366i $$-0.451399\pi$$
0.152092 + 0.988366i $$0.451399\pi$$
$$114$$ −2.45559 + 0.994408i −0.229987 + 0.0931348i
$$115$$ 1.19216 + 0.596080i 0.111170 + 0.0555848i
$$116$$ 7.63941 + 5.94108i 0.709301 + 0.551615i
$$117$$ −2.02946 + 14.3739i −0.187624 + 1.32887i
$$118$$ −2.02068 4.13127i −0.186019 0.380314i
$$119$$ −5.94108 −0.544617
$$120$$ 7.38534 8.09054i 0.674186 0.738561i
$$121$$ 0.941075 0.0855523
$$122$$ 7.85951 + 16.0687i 0.711566 + 1.45479i
$$123$$ −0.838825 + 11.9411i −0.0756343 + 1.07669i
$$124$$ 15.1042 + 11.7464i 1.35640 + 1.05485i
$$125$$ −11.0000 + 2.00000i −0.983870 + 0.178885i
$$126$$ −1.31299 4.03436i −0.116971 0.359409i
$$127$$ 1.08883 0.0966178 0.0483089 0.998832i $$-0.484617\pi$$
0.0483089 + 0.998832i $$0.484617\pi$$
$$128$$ −0.483388 11.3034i −0.0427259 0.999087i
$$129$$ 12.7799 + 0.897749i 1.12521 + 0.0790424i
$$130$$ 0.133783 15.3011i 0.0117335 1.34200i
$$131$$ 6.30783 0.551118 0.275559 0.961284i $$-0.411137\pi$$
0.275559 + 0.961284i $$0.411137\pi$$
$$132$$ −7.99274 + 8.91117i −0.695679 + 0.775618i
$$133$$ 1.08157i 0.0937839i
$$134$$ 3.55364 + 7.26539i 0.306987 + 0.627634i
$$135$$ 7.25197 9.07794i 0.624150 0.781305i
$$136$$ −16.4483 3.43853i −1.41043 0.294852i
$$137$$ 8.64863 0.738902 0.369451 0.929250i $$-0.379546\pi$$
0.369451 + 0.929250i $$0.379546\pi$$
$$138$$ 1.35334 0.548043i 0.115204 0.0466525i
$$139$$ 5.82960i 0.494460i 0.968957 + 0.247230i $$0.0795204\pi$$
−0.968957 + 0.247230i $$0.920480\pi$$
$$140$$ 1.92975 + 4.03436i 0.163094 + 0.340966i
$$141$$ 0.0294624 0.419412i 0.00248119 0.0353209i
$$142$$ 4.97098 + 10.1631i 0.417155 + 0.852872i
$$143$$ 16.7210i 1.39828i
$$144$$ −1.30014 11.9294i −0.108345 0.994113i
$$145$$ −9.67765 4.83882i −0.803685 0.401843i
$$146$$ 10.1631 4.97098i 0.841107 0.411401i
$$147$$ 1.72779 + 0.121372i 0.142506 + 0.0100106i
$$148$$ −4.59608 3.57432i −0.377795 0.293807i
$$149$$ 17.8223i 1.46006i −0.683413 0.730032i $$-0.739505\pi$$
0.683413 0.730032i $$-0.260495\pi$$
$$150$$ −6.32333 + 10.4888i −0.516298 + 0.856409i
$$151$$ 15.7427i 1.28113i 0.767906 + 0.640563i $$0.221299\pi$$
−0.767906 + 0.640563i $$0.778701\pi$$
$$152$$ 0.625983 2.99441i 0.0507739 0.242879i
$$153$$ −17.6482 2.49176i −1.42677 0.201447i
$$154$$ −2.14721 4.38995i −0.173027 0.353752i
$$155$$ −19.1341 9.56706i −1.53689 0.768445i
$$156$$ −12.4782 11.1922i −0.999058 0.896090i
$$157$$ 17.8223i 1.42238i −0.703001 0.711189i $$-0.748157\pi$$
0.703001 0.711189i $$-0.251843\pi$$
$$158$$ 1.20613 0.589941i 0.0959546 0.0469331i
$$159$$ −20.4266 1.43490i −1.61993 0.113795i
$$160$$ 3.00769 + 12.2863i 0.237779 + 0.971319i
$$161$$ 0.596080i 0.0469777i
$$162$$ −2.20823 12.5349i −0.173495 0.984835i
$$163$$ −11.2520 −0.881322 −0.440661 0.897674i $$-0.645256\pi$$
−0.440661 + 0.897674i $$0.645256\pi$$
$$164$$ −10.9112 8.48549i −0.852019 0.662605i
$$165$$ 6.80936 11.5217i 0.530108 0.896960i
$$166$$ 21.5506 10.5408i 1.67265 0.818124i
$$167$$ 16.7137i 1.29335i −0.762767 0.646673i $$-0.776160\pi$$
0.762767 0.646673i $$-0.223840\pi$$
$$168$$ 4.71328 + 1.33603i 0.363638 + 0.103077i
$$169$$ −10.4142 −0.801094
$$170$$ 18.7866 + 0.164257i 1.44087 + 0.0125980i
$$171$$ 0.453623 3.21284i 0.0346894 0.245692i
$$172$$ −9.08157 + 11.6776i −0.692463 + 0.890412i
$$173$$ −1.94108 −0.147577 −0.0737886 0.997274i $$-0.523509\pi$$
−0.0737886 + 0.997274i $$0.523509\pi$$
$$174$$ −10.9860 + 4.44887i −0.832849 + 0.337268i
$$175$$ −3.00000 4.00000i −0.226779 0.302372i
$$176$$ −3.40392 13.3967i −0.256580 1.00981i
$$177$$ 5.61872 + 0.394698i 0.422329 + 0.0296674i
$$178$$ 6.64863 3.25197i 0.498336 0.243745i
$$179$$ 6.80784 0.508842 0.254421 0.967094i $$-0.418115\pi$$
0.254421 + 0.967094i $$0.418115\pi$$
$$180$$ 4.04034 + 12.7936i 0.301149 + 0.953577i
$$181$$ −2.97098 −0.220831 −0.110416 0.993886i $$-0.535218\pi$$
−0.110416 + 0.993886i $$0.535218\pi$$
$$182$$ 6.14721 3.00671i 0.455661 0.222872i
$$183$$ −21.8542 1.53519i −1.61551 0.113485i
$$184$$ −0.344995 + 1.65029i −0.0254334 + 0.121661i
$$185$$ 5.82234 + 2.91117i 0.428067 + 0.214034i
$$186$$ −21.7210 + 8.79607i −1.59266 + 0.644959i
$$187$$ −20.5299 −1.50129
$$188$$ 0.383238 + 0.298040i 0.0279505 + 0.0217368i
$$189$$ 5.08157 + 1.08520i 0.369630 + 0.0789366i
$$190$$ −0.0299030 + 3.42009i −0.00216939 + 0.248119i
$$191$$ 20.6477 1.49402 0.747009 0.664814i $$-0.231489\pi$$
0.747009 + 0.664814i $$0.231489\pi$$
$$192$$ 12.2758 + 6.42682i 0.885932 + 0.463816i
$$193$$ 9.55980i 0.688129i −0.938946 0.344065i $$-0.888196\pi$$
0.938946 0.344065i $$-0.111804\pi$$
$$194$$ −4.19975 + 2.05418i −0.301525 + 0.147481i
$$195$$ 16.1337 + 9.53509i 1.15536 + 0.682822i
$$196$$ −1.22779 + 1.57877i −0.0876995 + 0.112770i
$$197$$ 11.5598 0.823602 0.411801 0.911274i $$-0.364900\pi$$
0.411801 + 0.911274i $$0.364900\pi$$
$$198$$ −4.53716 13.9411i −0.322442 0.990749i
$$199$$ 16.9637i 1.20253i 0.799051 + 0.601263i $$0.205336\pi$$
−0.799051 + 0.601263i $$0.794664\pi$$
$$200$$ −5.99064 12.8106i −0.423602 0.905848i
$$201$$ −9.88127 0.694129i −0.696971 0.0489601i
$$202$$ 9.82960 4.80784i 0.691608 0.338278i
$$203$$ 4.83882i 0.339619i
$$204$$ 13.7417 15.3207i 0.962108 1.07266i
$$205$$ 13.8223 + 6.91117i 0.965394 + 0.482697i
$$206$$ 3.49132 + 7.13798i 0.243252 + 0.497327i
$$207$$ −0.250003 + 1.77068i −0.0173764 + 0.123071i
$$208$$ 18.7592 4.76648i 1.30072 0.330496i
$$209$$ 3.73746i 0.258525i
$$210$$ −5.46020 0.431568i −0.376789 0.0297810i
$$211$$ 16.7137i 1.15062i −0.817936 0.575310i $$-0.804881\pi$$
0.817936 0.575310i $$-0.195119\pi$$
$$212$$ 14.5154 18.6648i 0.996921 1.28190i
$$213$$ −13.8223 0.970978i −0.947091 0.0665303i
$$214$$ −2.14049 + 1.04696i −0.146321 + 0.0715684i
$$215$$ 7.39666 14.7933i 0.504448 1.00890i
$$216$$ 13.4406 + 5.94553i 0.914519 + 0.404542i
$$217$$ 9.56706i 0.649454i
$$218$$ −6.17711 12.6291i −0.418367 0.855348i
$$219$$ −0.970978 + 13.8223i −0.0656126 + 0.934027i
$$220$$ 6.66843 + 13.9411i 0.449585 + 0.939907i
$$221$$ 28.7478i 1.93379i
$$222$$ 6.60950 2.67657i 0.443601 0.179639i
$$223$$ −8.76736 −0.587106 −0.293553 0.955943i $$-0.594838\pi$$
−0.293553 + 0.955943i $$0.594838\pi$$
$$224$$ −4.31299 + 3.66034i −0.288174 + 0.244567i
$$225$$ −7.23396 13.1404i −0.482264 0.876026i
$$226$$ −2.00922 4.10784i −0.133651 0.273250i
$$227$$ 0.242745i 0.0161115i 0.999968 + 0.00805576i $$0.00256426\pi$$
−0.999968 + 0.00805576i $$0.997436\pi$$
$$228$$ 2.78912 + 2.50166i 0.184714 + 0.165676i
$$229$$ −26.3531 −1.74146 −0.870732 0.491758i $$-0.836354\pi$$
−0.870732 + 0.491758i $$0.836354\pi$$
$$230$$ 0.0164803 1.88490i 0.00108668 0.124287i
$$231$$ 5.97054 + 0.419412i 0.392833 + 0.0275953i
$$232$$ 2.80058 13.3967i 0.183867 0.879534i
$$233$$ −6.44413 −0.422169 −0.211084 0.977468i $$-0.567699\pi$$
−0.211084 + 0.977468i $$0.567699\pi$$
$$234$$ 19.5216 6.35334i 1.27616 0.415331i
$$235$$ −0.485489 0.242745i −0.0316698 0.0158349i
$$236$$ −3.99274 + 5.13412i −0.259905 + 0.334202i
$$237$$ −0.115233 + 1.64039i −0.00748517 + 0.106555i
$$238$$ 3.69162 + 7.54750i 0.239292 + 0.489231i
$$239$$ 16.6495 1.07697 0.538484 0.842636i $$-0.318997\pi$$
0.538484 + 0.842636i $$0.318997\pi$$
$$240$$ −14.8672 4.35504i −0.959674 0.281117i
$$241$$ −5.61784 −0.361877 −0.180939 0.983494i $$-0.557914\pi$$
−0.180939 + 0.983494i $$0.557914\pi$$
$$242$$ −0.584758 1.19553i −0.0375897 0.0768519i
$$243$$ 14.6398 + 5.35490i 0.939147 + 0.343517i
$$244$$ 15.5299 19.9693i 0.994200 1.27840i
$$245$$ 1.00000 2.00000i 0.0638877 0.127775i
$$246$$ 15.6911 6.35422i 1.00043 0.405130i
$$247$$ 5.23352 0.333001
$$248$$ 5.53716 26.4871i 0.351610 1.68194i
$$249$$ −2.05892 + 29.3098i −0.130479 + 1.85743i
$$250$$ 9.37588 + 12.7316i 0.592983 + 0.805215i
$$251$$ 3.25197 0.205262 0.102631 0.994719i $$-0.467274\pi$$
0.102631 + 0.994719i $$0.467274\pi$$
$$252$$ −4.30936 + 4.17485i −0.271464 + 0.262991i
$$253$$ 2.05981i 0.129499i
$$254$$ −0.676567 1.38324i −0.0424516 0.0867921i
$$255$$ −11.7071 + 19.8088i −0.733128 + 1.24048i
$$256$$ −14.0594 + 7.63770i −0.878710 + 0.477356i
$$257$$ 0.467046 0.0291335 0.0145668 0.999894i $$-0.495363\pi$$
0.0145668 + 0.999894i $$0.495363\pi$$
$$258$$ −6.80058 16.7933i −0.423386 1.04551i
$$259$$ 2.91117i 0.180891i
$$260$$ −19.5216 + 9.33774i −1.21068 + 0.579102i
$$261$$ 2.02946 14.3739i 0.125621 0.889723i
$$262$$ −3.91951 8.01342i −0.242148 0.495071i
$$263$$ 8.47823i 0.522790i 0.965232 + 0.261395i $$0.0841825\pi$$
−0.965232 + 0.261395i $$0.915817\pi$$
$$264$$ 16.2872 + 4.61676i 1.00240 + 0.284142i
$$265$$ −11.8223 + 23.6447i −0.726241 + 1.45248i
$$266$$ −1.37402 + 0.672057i −0.0842464 + 0.0412065i
$$267$$ −0.635205 + 9.04244i −0.0388739 + 0.553389i
$$268$$ 7.02176 9.02902i 0.428922 0.551535i
$$269$$ 0.144695i 0.00882222i 0.999990 + 0.00441111i $$0.00140410\pi$$
−0.999990 + 0.00441111i $$0.998596\pi$$
$$270$$ −16.0387 3.57206i −0.976085 0.217389i
$$271$$ 23.1251i 1.40475i −0.711807 0.702375i $$-0.752123\pi$$
0.711807 0.702375i $$-0.247877\pi$$
$$272$$ 5.85225 + 23.0324i 0.354845 + 1.39655i
$$273$$ −0.587299 + 8.36049i −0.0355450 + 0.506000i
$$274$$ −5.37402 10.9871i −0.324656 0.663758i
$$275$$ −10.3668 13.8223i −0.625139 0.833519i
$$276$$ −1.53716 1.37873i −0.0925259 0.0829897i
$$277$$ 0.826283i 0.0496465i 0.999692 + 0.0248233i $$0.00790230\pi$$
−0.999692 + 0.0248233i $$0.992098\pi$$
$$278$$ 7.40588 3.62235i 0.444175 0.217254i
$$279$$ 4.01254 28.4193i 0.240225 1.70142i
$$280$$ 3.92612 4.95838i 0.234631 0.296320i
$$281$$ 14.6612i 0.874612i 0.899313 + 0.437306i $$0.144067\pi$$
−0.899313 + 0.437306i $$0.855933\pi$$
$$282$$ −0.551125 + 0.223182i −0.0328190 + 0.0132903i
$$283$$ 20.4266 1.21423 0.607117 0.794613i $$-0.292326\pi$$
0.607117 + 0.794613i $$0.292326\pi$$
$$284$$ 9.82234 12.6302i 0.582849 0.749464i
$$285$$ −3.60618 2.13127i −0.213612 0.126246i
$$286$$ 21.2422 10.3899i 1.25608 0.614371i
$$287$$ 6.91117i 0.407954i
$$288$$ −14.3471 + 9.06426i −0.845411 + 0.534117i
$$289$$ 18.2964 1.07626
$$290$$ −0.133783 + 15.3011i −0.00785599 + 0.898513i
$$291$$ 0.401241 5.71186i 0.0235212 0.334835i
$$292$$ −12.6302 9.82234i −0.739126 0.574809i
$$293$$ −5.41422 −0.316302 −0.158151 0.987415i $$-0.550553\pi$$
−0.158151 + 0.987415i $$0.550553\pi$$
$$294$$ −0.919412 2.27039i −0.0536212 0.132412i
$$295$$ 3.25197 6.50393i 0.189337 0.378674i
$$296$$ −1.68491 + 8.05981i −0.0979333 + 0.468467i
$$297$$ 17.5598 + 3.75000i 1.01892 + 0.217597i
$$298$$ −22.6414 + 11.0743i −1.31158 + 0.641518i
$$299$$ −2.88433 −0.166805
$$300$$ 17.2541 + 1.51565i 0.996164 + 0.0875059i
$$301$$ 7.39666 0.426336
$$302$$ 19.9995 9.78210i 1.15084 0.562897i
$$303$$ −0.939112 + 13.3687i −0.0539506 + 0.768013i
$$304$$ −4.19304 + 1.06540i −0.240487 + 0.0611048i
$$305$$ −12.6486 + 25.2973i −0.724258 + 1.44852i
$$306$$ 7.80058 + 23.9684i 0.445930 + 1.37018i
$$307$$ −16.3070 −0.930687 −0.465343 0.885130i $$-0.654069\pi$$
−0.465343 + 0.885130i $$0.654069\pi$$
$$308$$ −4.24274 + 5.45559i −0.241753 + 0.310861i
$$309$$ −9.70799 0.681957i −0.552268 0.0387952i
$$310$$ −0.264508 + 30.2525i −0.0150230 + 1.71823i
$$311$$ −24.3531 −1.38094 −0.690469 0.723362i $$-0.742596\pi$$
−0.690469 + 0.723362i $$0.742596\pi$$
$$312$$ −6.46481 + 22.8067i −0.365998 + 1.29118i
$$313$$ 30.6612i 1.73307i 0.499115 + 0.866536i $$0.333659\pi$$
−0.499115 + 0.866536i $$0.666341\pi$$
$$314$$ −22.6414 + 11.0743i −1.27773 + 0.624959i
$$315$$ 3.80936 5.52166i 0.214633 0.311110i
$$316$$ −1.49891 1.16569i −0.0843204 0.0655750i
$$317$$ −13.8822 −0.779699 −0.389850 0.920879i $$-0.627473\pi$$
−0.389850 + 0.920879i $$0.627473\pi$$
$$318$$ 10.8696 + 26.8414i 0.609537 + 1.50519i
$$319$$ 16.7210i 0.936195i
$$320$$ 13.7396 11.4553i 0.768065 0.640372i
$$321$$ 0.204501 2.91117i 0.0114141 0.162486i
$$322$$ 0.757255 0.370388i 0.0422002 0.0206409i
$$323$$ 6.42568i 0.357535i
$$324$$ −14.5521 + 10.5942i −0.808450 + 0.588564i
$$325$$ 19.3553 14.5165i 1.07364 0.805229i
$$326$$ 6.99166 + 14.2944i 0.387232 + 0.791694i
$$327$$ 17.1761 + 1.20657i 0.949842 + 0.0667235i
$$328$$ −4.00000 + 19.1341i −0.220863 + 1.05650i
$$329$$ 0.242745i 0.0133829i
$$330$$ −18.8682 1.49132i −1.03866 0.0820944i
$$331$$ 18.1559i 0.997937i 0.866620 + 0.498969i $$0.166288\pi$$
−0.866620 + 0.498969i $$0.833712\pi$$
$$332$$ −26.7819 20.8279i −1.46985 1.14308i
$$333$$ −1.22098 + 8.64775i −0.0669094 + 0.473894i
$$334$$ −21.2330 + 10.3854i −1.16182 + 0.568266i
$$335$$ −5.71901 + 11.4380i −0.312463 + 0.624926i
$$336$$ −1.23142 6.81789i −0.0671796 0.371946i
$$337$$ 17.4419i 0.950124i 0.879952 + 0.475062i $$0.157574\pi$$
−0.879952 + 0.475062i $$0.842426\pi$$
$$338$$ 6.47111 + 13.2301i 0.351982 + 0.719625i
$$339$$ 5.58686 + 0.392460i 0.303437 + 0.0213155i
$$340$$ −11.4648 23.9684i −0.621766 1.29987i
$$341$$ 33.0598i 1.79029i
$$342$$ −4.36344 + 1.42009i −0.235948 + 0.0767897i
$$343$$ 1.00000 0.0539949
$$344$$ 20.4782 + 4.28099i 1.10411 + 0.230815i
$$345$$ 1.98746 + 1.17460i 0.107001 + 0.0632382i
$$346$$ 1.20613 + 2.46593i 0.0648420 + 0.132569i
$$347$$ 33.8564i 1.81751i −0.417331 0.908755i $$-0.637034\pi$$
0.417331 0.908755i $$-0.362966\pi$$
$$348$$ 12.4782 + 11.1922i 0.668903 + 0.599963i
$$349$$ −9.29333 −0.497460 −0.248730 0.968573i $$-0.580013\pi$$
−0.248730 + 0.968573i $$0.580013\pi$$
$$350$$ −3.21745 + 6.29667i −0.171980 + 0.336571i
$$351$$ −5.25108 + 24.5888i −0.280282 + 1.31245i
$$352$$ −14.9039 + 12.6486i −0.794381 + 0.674174i
$$353$$ 7.47403 0.397802 0.198901 0.980020i $$-0.436263\pi$$
0.198901 + 0.980020i $$0.436263\pi$$
$$354$$ −2.98990 7.38324i −0.158911 0.392415i
$$355$$ −8.00000 + 16.0000i −0.424596 + 0.849192i
$$356$$ −8.26254 6.42568i −0.437914 0.340561i
$$357$$ −10.2649 0.721082i −0.543279 0.0381637i
$$358$$ −4.23020 8.64863i −0.223573 0.457094i
$$359$$ −11.3553 −0.599310 −0.299655 0.954048i $$-0.596872\pi$$
−0.299655 + 0.954048i $$0.596872\pi$$
$$360$$ 13.7423 13.0824i 0.724283 0.689503i
$$361$$ 17.8302 0.938432
$$362$$ 1.84608 + 3.77431i 0.0970280 + 0.198373i
$$363$$ 1.62598 + 0.114220i 0.0853420 + 0.00599502i
$$364$$ −7.63941 5.94108i −0.400414 0.311397i
$$365$$ 16.0000 + 8.00000i 0.837478 + 0.418739i
$$366$$ 11.6293 + 28.7173i 0.607873 + 1.50108i
$$367$$ 4.24051 0.221353 0.110676 0.993857i $$-0.464698\pi$$
0.110676 + 0.993857i $$0.464698\pi$$
$$368$$ 2.31089 0.587168i 0.120464 0.0306082i
$$369$$ −2.89863 + 20.5299i −0.150897 + 1.06874i
$$370$$ 0.0804874 9.20558i 0.00418434 0.478575i
$$371$$ −11.8223 −0.613786
$$372$$ 24.6713 + 22.1285i 1.27915 + 1.14731i
$$373$$ 23.0559i 1.19379i −0.802320 0.596894i $$-0.796401\pi$$
0.802320 0.596894i $$-0.203599\pi$$
$$374$$ 12.7567 + 26.0810i 0.659634 + 1.34862i
$$375$$ −19.2485 + 2.12049i −0.993987 + 0.109502i
$$376$$ 0.140494 0.672057i 0.00724542 0.0346587i
$$377$$ 23.4142 1.20589
$$378$$ −1.77892 7.12990i −0.0914977 0.366722i
$$379$$ 28.8441i 1.48162i −0.671713 0.740811i $$-0.734441\pi$$
0.671713 0.740811i $$-0.265559\pi$$
$$380$$ 4.36344 2.08716i 0.223840 0.107069i
$$381$$ 1.88127 + 0.132153i 0.0963803 + 0.00677043i
$$382$$ −12.8299 26.2307i −0.656437 1.34208i
$$383$$ 6.51119i 0.332706i 0.986066 + 0.166353i $$0.0531992\pi$$
−0.986066 + 0.166353i $$0.946801\pi$$
$$384$$ 0.536721 19.5886i 0.0273894 0.999625i
$$385$$ 3.45559 6.91117i 0.176113 0.352226i
$$386$$ −12.1447 + 5.94019i −0.618149 + 0.302348i
$$387$$ 21.9721 + 3.10225i 1.11690 + 0.157696i
$$388$$ 5.21922 + 4.05892i 0.264966 + 0.206061i
$$389$$ 22.8059i 1.15630i −0.815929 0.578152i $$-0.803774\pi$$
0.815929 0.578152i $$-0.196226\pi$$
$$390$$ 2.08828 26.4209i 0.105744 1.33788i
$$391$$ 3.54136i 0.179094i
$$392$$ 2.76858 + 0.578773i 0.139834 + 0.0292325i
$$393$$ 10.8986 + 0.765596i 0.549763 + 0.0386192i
$$394$$ −7.18294 14.6855i −0.361871 0.739844i
$$395$$ 1.89883 + 0.949416i 0.0955406 + 0.0477703i
$$396$$ −14.8914 + 14.4266i −0.748320 + 0.724962i
$$397$$ 13.1031i 0.657627i −0.944395 0.328814i $$-0.893351\pi$$
0.944395 0.328814i $$-0.106649\pi$$
$$398$$ 21.5506 10.5408i 1.08023 0.528362i
$$399$$ 0.131272 1.86873i 0.00657184 0.0935534i
$$400$$ −12.5521 + 15.5706i −0.627605 + 0.778532i
$$401$$ 10.7808i 0.538366i 0.963089 + 0.269183i $$0.0867537\pi$$
−0.963089 + 0.269183i $$0.913246\pi$$
$$402$$ 5.25813 + 12.9844i 0.262252 + 0.647603i
$$403$$ 46.2933 2.30603
$$404$$ −12.2157 9.49999i −0.607753 0.472642i
$$405$$ 13.6317 14.8046i 0.677365 0.735647i
$$406$$ −6.14721 + 3.00671i −0.305081 + 0.149221i
$$407$$ 10.0598i 0.498646i
$$408$$ −28.0020 7.93745i −1.38630 0.392962i
$$409$$ 15.7045 0.776537 0.388269 0.921546i $$-0.373073\pi$$
0.388269 + 0.921546i $$0.373073\pi$$
$$410$$ 0.191078 21.8542i 0.00943669 1.07930i
$$411$$ 14.9430 + 1.04970i 0.737086 + 0.0517781i
$$412$$ 6.89863 8.87069i 0.339871 0.437028i
$$413$$ 3.25197 0.160019
$$414$$ 2.40480 0.782648i 0.118190 0.0384651i
$$415$$ 33.9274 + 16.9637i 1.66543 + 0.832716i
$$416$$ −17.7118 20.8698i −0.868390 1.02323i
$$417$$ −0.707552 + 10.0723i −0.0346490 + 0.493245i
$$418$$ −4.74803 + 2.32235i −0.232234 + 0.113590i
$$419$$ −33.0743 −1.61579 −0.807893 0.589329i $$-0.799392\pi$$
−0.807893 + 0.589329i $$0.799392\pi$$
$$420$$ 2.84455 + 7.20476i 0.138800 + 0.351556i
$$421$$ 7.88127 0.384110 0.192055 0.981384i $$-0.438485\pi$$
0.192055 + 0.981384i $$0.438485\pi$$
$$422$$ −21.2330 + 10.3854i −1.03361 + 0.505555i
$$423$$ 0.101810 0.721082i 0.00495017 0.0350602i
$$424$$ −32.7311 6.84245i −1.58956 0.332299i
$$425$$ 17.8232 + 23.7643i 0.864553 + 1.15274i
$$426$$ 7.35530 + 18.1631i 0.356365 + 0.880007i
$$427$$ −12.6486 −0.612110
$$428$$ 2.66009 + 2.06872i 0.128580 + 0.0999953i
$$429$$ −2.02946 + 28.8904i −0.0979834 + 1.39484i
$$430$$ −23.3894 0.204501i −1.12794 0.00986192i
$$431$$ 26.3522 1.26934 0.634671 0.772782i $$-0.281135\pi$$
0.634671 + 0.772782i $$0.281135\pi$$
$$432$$ −0.798481 20.7693i −0.0384169 0.999262i
$$433$$ 37.2973i 1.79239i −0.443659 0.896196i $$-0.646320\pi$$
0.443659 0.896196i $$-0.353680\pi$$
$$434$$ −12.1539 + 5.94470i −0.583407 + 0.285355i
$$435$$ −16.1337 9.53509i −0.773551 0.457172i
$$436$$ −12.2056 + 15.6947i −0.584541 + 0.751640i
$$437$$ 0.644702 0.0308403
$$438$$ 18.1631 7.35530i 0.867868 0.351450i
$$439$$ 12.6229i 0.602459i −0.953552 0.301230i $$-0.902603\pi$$
0.953552 0.301230i $$-0.0973971\pi$$
$$440$$ 13.5671 17.1341i 0.646784 0.816837i
$$441$$ 2.97054 + 0.419412i 0.141454 + 0.0199720i
$$442$$ −36.5210 + 17.8631i −1.73713 + 0.849661i
$$443$$ 21.7118i 1.03156i −0.856722 0.515778i $$-0.827503\pi$$
0.856722 0.515778i $$-0.172497\pi$$
$$444$$ −7.50725 6.73352i −0.356278 0.319559i
$$445$$ 10.4670 + 5.23352i 0.496186 + 0.248093i
$$446$$ 5.44779 + 11.1380i 0.257960 + 0.527399i
$$447$$ 2.16314 30.7933i 0.102313 1.45647i
$$448$$ 7.33004 + 3.20476i 0.346312 + 0.151410i
$$449$$ 14.6361i 0.690720i −0.938470 0.345360i $$-0.887757\pi$$
0.938470 0.345360i $$-0.112243\pi$$
$$450$$ −12.1985 + 17.3550i −0.575041 + 0.818125i
$$451$$ 23.8822i 1.12457i
$$452$$ −3.97010 + 5.10500i −0.186738 + 0.240119i
$$453$$ −1.91073 + 27.2002i −0.0897740 + 1.27798i
$$454$$ 0.308381 0.150835i 0.0144730 0.00707902i
$$455$$ 9.67765 + 4.83882i 0.453695 + 0.226848i
$$456$$ 1.44501 5.09774i 0.0676687 0.238724i
$$457$$ 4.00176i 0.187195i −0.995610 0.0935973i $$-0.970163\pi$$
0.995610 0.0935973i $$-0.0298366\pi$$
$$458$$ 16.3751 + 33.4788i 0.765158 + 1.56436i
$$459$$ −30.1900 6.44725i −1.40915 0.300932i
$$460$$ −2.40480 + 1.15029i −0.112124 + 0.0536324i
$$461$$ 36.9419i 1.72056i 0.509824 + 0.860279i $$0.329711\pi$$
−0.509824 + 0.860279i $$0.670289\pi$$
$$462$$ −3.17711 7.84554i −0.147812 0.365007i
$$463$$ 6.12178 0.284503 0.142252 0.989831i $$-0.454566\pi$$
0.142252 + 0.989831i $$0.454566\pi$$
$$464$$ −18.7592 + 4.76648i −0.870875 + 0.221278i
$$465$$ −31.8986 18.8522i −1.47926 0.874252i
$$466$$ 4.00420 + 8.18657i 0.185491 + 0.379235i
$$467$$ 14.0651i 0.650855i 0.945567 + 0.325427i $$0.105508\pi$$
−0.945567 + 0.325427i $$0.894492\pi$$
$$468$$ −20.2014 20.8522i −0.933809 0.963895i
$$469$$ −5.71901 −0.264079
$$470$$ −0.00671134 + 0.767596i −0.000309571 + 0.0354066i
$$471$$ 2.16314 30.7933i 0.0996721 1.41888i
$$472$$ 9.00332 + 1.88215i 0.414411 + 0.0866330i
$$473$$ 25.5598 1.17524
$$474$$ 2.15555 0.872904i 0.0990075 0.0400938i
$$475$$ −4.32628 + 3.24471i −0.198503 + 0.148877i
$$476$$ 7.29441 9.37961i 0.334339 0.429914i
$$477$$ −35.1187 4.95844i −1.60798 0.227031i
$$478$$ −10.3455 21.1514i −0.473194 0.967443i
$$479$$ 33.4419 1.52800 0.764001 0.645215i $$-0.223232\pi$$
0.764001 + 0.645215i $$0.223232\pi$$
$$480$$ 3.70545 + 21.5933i 0.169130 + 0.985594i
$$481$$ −14.0867 −0.642296
$$482$$ 3.49077 + 7.13686i 0.159000 + 0.325075i
$$483$$ −0.0723476 + 1.02990i −0.00329193 + 0.0468622i
$$484$$ −1.15545 + 1.48574i −0.0525202 + 0.0675338i
$$485$$ −6.61174 3.30587i −0.300224 0.150112i
$$486$$ −2.29398 21.9257i −0.104057 0.994571i
$$487$$ 17.8241 0.807687 0.403844 0.914828i $$-0.367674\pi$$
0.403844 + 0.914828i $$0.367674\pi$$
$$488$$ −35.0187 7.32068i −1.58522 0.331392i
$$489$$ −19.4411 1.36568i −0.879156 0.0617580i
$$490$$ −3.16216 0.0276478i −0.142852 0.00124900i
$$491$$ −12.3087 −0.555485 −0.277742 0.960656i $$-0.589586\pi$$
−0.277742 + 0.960656i $$0.589586\pi$$
$$492$$ −17.8223 15.9855i −0.803493 0.720681i
$$493$$ 28.7478i 1.29474i
$$494$$ −3.25197 6.64863i −0.146313 0.299136i
$$495$$ 13.1636 19.0806i 0.591659 0.857608i
$$496$$ −37.0897 + 9.42402i −1.66538 + 0.423151i
$$497$$ −8.00000 −0.358849
$$498$$ 38.5143 15.5967i 1.72587 0.698903i
$$499$$ 13.0941i 0.586173i −0.956086 0.293086i $$-0.905318\pi$$
0.956086 0.293086i $$-0.0946824\pi$$
$$500$$ 10.3482 19.8221i 0.462785 0.886471i
$$501$$ 2.02858 28.8778i 0.0906303 1.29017i
$$502$$ −2.02068 4.13127i −0.0901874 0.184388i
$$503$$ 15.9639i 0.711796i 0.934525 + 0.355898i $$0.115825\pi$$
−0.934525 + 0.355898i $$0.884175\pi$$
$$504$$ 7.98142 + 2.88044i 0.355521 + 0.128305i
$$505$$ 15.4749 + 7.73746i 0.688624 + 0.344312i
$$506$$ 2.61676 1.27991i 0.116329 0.0568988i
$$507$$ −17.9936 1.26400i −0.799125 0.0561361i
$$508$$ −1.33686 + 1.71901i −0.0593134 + 0.0762688i
$$509$$ 13.6776i 0.606251i −0.952951 0.303126i $$-0.901970\pi$$
0.952951 0.303126i $$-0.0980302\pi$$
$$510$$ 32.4394 + 2.56398i 1.43644 + 0.113535i
$$511$$ 8.00000i 0.353899i
$$512$$ 18.4390 + 13.1150i 0.814895 + 0.579609i
$$513$$ 1.17372 5.49607i 0.0518209 0.242657i
$$514$$ −0.290209 0.593332i −0.0128006 0.0261707i
$$515$$ −5.61872 + 11.2374i −0.247591 + 0.495181i
$$516$$ −17.1084 + 19.0743i −0.753156 + 0.839700i
$$517$$ 0.838825i 0.0368915i
$$518$$ 3.69833 1.80892i 0.162495 0.0794795i
$$519$$ −3.35378 0.235593i −0.147214 0.0103414i
$$520$$ 23.9927 + 18.9978i 1.05215 + 0.833110i
$$521$$ 22.4112i 0.981851i 0.871202 + 0.490925i $$0.163341\pi$$
−0.871202 + 0.490925i $$0.836659\pi$$
$$522$$ −19.5216 + 6.35334i −0.854435 + 0.278078i
$$523$$ 8.74980 0.382602 0.191301 0.981531i $$-0.438729\pi$$
0.191301 + 0.981531i $$0.438729\pi$$
$$524$$ −7.74471 + 9.95864i −0.338329 + 0.435045i
$$525$$ −4.69789 7.27529i −0.205033 0.317520i
$$526$$ 10.7707 5.26814i 0.469624 0.229702i
$$527$$ 56.8386i 2.47593i
$$528$$ −4.25529 23.5598i −0.185188 1.02531i
$$529$$ 22.6447 0.984552
$$530$$ 37.3841 + 0.326861i 1.62386 + 0.0141979i
$$531$$ 9.66009 + 1.36391i 0.419212 + 0.0591888i
$$532$$ 1.70755 + 1.32794i 0.0740318 + 0.0575736i
$$533$$ −33.4419 −1.44853
$$534$$ 11.8822 4.81177i 0.514191 0.208225i
$$535$$ −3.36982 1.68491i −0.145690 0.0728449i
$$536$$ −15.8335 3.31001i −0.683904 0.142971i
$$537$$ 11.7625 + 0.826283i 0.507591 + 0.0356567i
$$538$$ 0.183820 0.0899096i 0.00792503 0.00387628i
$$539$$ 3.45559 0.148843
$$540$$ 5.42809 + 22.5950i 0.233588 + 0.972336i
$$541$$ 23.3562 1.00416 0.502080 0.864821i $$-0.332568\pi$$
0.502080 + 0.864821i $$0.332568\pi$$
$$542$$ −29.3779 + 14.3693i −1.26189 + 0.617214i
$$543$$ −5.13324 0.360594i −0.220288 0.0154746i
$$544$$ 25.6238 21.7464i 1.09861 0.932368i
$$545$$ 9.94108 19.8822i 0.425829 0.851658i
$$546$$ 10.9860 4.44887i 0.470159 0.190394i
$$547$$ 27.7229 1.18535 0.592674 0.805443i $$-0.298072\pi$$
0.592674 + 0.805443i $$0.298072\pi$$
$$548$$ −10.6187 + 13.6542i −0.453609 + 0.583279i
$$549$$ −37.5732 5.30499i −1.60359 0.226411i
$$550$$ −11.1182 + 21.7587i −0.474081 + 0.927793i
$$551$$ −5.23352 −0.222956
$$552$$ −0.796380 + 2.80949i −0.0338962 + 0.119580i
$$553$$ 0.949416i 0.0403733i
$$554$$ 1.04970 0.513429i 0.0445976 0.0218135i
$$555$$ 9.70647 + 5.73657i 0.412017 + 0.243504i
$$556$$ −9.20362 7.15755i −0.390320 0.303548i
$$557$$ −15.8241 −0.670489 −0.335244 0.942131i $$-0.608819\pi$$
−0.335244 + 0.942131i $$0.608819\pi$$
$$558$$ −38.5969 + 12.5615i −1.63394 + 0.531769i
$$559$$ 35.7911i 1.51380i
$$560$$ −8.73867 1.90672i −0.369276 0.0805735i
$$561$$ −35.4714 2.49176i −1.49760 0.105202i
$$562$$ 18.6254 9.11004i 0.785667 0.384284i
$$563$$ 37.5112i 1.58091i −0.612522 0.790454i $$-0.709845\pi$$
0.612522 0.790454i $$-0.290155\pi$$
$$564$$ 0.625983 + 0.561466i 0.0263586 + 0.0236420i
$$565$$ 3.23352 6.46705i 0.136035 0.272071i
$$566$$ −12.6925 25.9497i −0.533506 1.09075i
$$567$$ 8.64819 + 2.49176i 0.363190 + 0.104644i
$$568$$ −22.1486 4.63018i −0.929335 0.194278i
$$569$$ 19.8804i 0.833429i 0.909037 + 0.416715i $$0.136819\pi$$
−0.909037 + 0.416715i $$0.863181\pi$$
$$570$$ −0.466770 + 5.90558i −0.0195509 + 0.247358i
$$571$$ 3.37707i 0.141326i −0.997500 0.0706631i $$-0.977488\pi$$
0.997500 0.0706631i $$-0.0225115\pi$$
$$572$$ −26.3986 20.5299i −1.10378 0.858398i
$$573$$ 35.6750 + 2.50606i 1.49035 + 0.104692i
$$574$$ 8.77990 4.29441i 0.366466 0.179245i
$$575$$ 2.38432 1.78824i 0.0994330 0.0745748i
$$576$$ 20.4301 + 12.5942i 0.851252 + 0.524757i
$$577$$ 6.66117i 0.277308i −0.990341 0.138654i $$-0.955722\pi$$
0.990341 0.138654i $$-0.0442776\pi$$
$$578$$ −11.3689 23.2436i −0.472882 0.966805i
$$579$$ 1.16029 16.5174i 0.0482202 0.686438i
$$580$$ 19.5216 9.33774i 0.810588 0.387728i
$$581$$ 16.9637i 0.703774i
$$582$$ −7.50562 + 3.03946i −0.311118 + 0.125990i
$$583$$ −40.8531 −1.69196
$$584$$ −4.63018 + 22.1486i −0.191598 + 0.916516i
$$585$$ 26.7184 + 18.4328i 1.10467 + 0.762104i
$$586$$ 3.36425 + 6.87819i 0.138976 + 0.284135i
$$587$$ 31.7716i 1.31135i −0.755042 0.655676i $$-0.772384\pi$$
0.755042 0.655676i $$-0.227616\pi$$
$$588$$ −2.31299 + 2.57877i −0.0953862 + 0.106347i
$$589$$ −10.3474 −0.426359
$$590$$ −10.2832 0.0899096i −0.423354 0.00370152i
$$591$$ 19.9729 + 1.40304i 0.821577 + 0.0577133i
$$592$$ 11.2861 2.86765i 0.463855 0.117860i
$$593$$ −24.2903 −0.997482 −0.498741 0.866751i $$-0.666204\pi$$
−0.498741 + 0.866751i $$0.666204\pi$$
$$594$$ −6.14721 24.6380i −0.252223 1.01091i
$$595$$ −5.94108 + 11.8822i −0.243560 + 0.487121i
$$596$$ 28.1374 + 21.8822i 1.15255 + 0.896328i
$$597$$ −2.05892 + 29.3098i −0.0842662 + 1.19957i
$$598$$ 1.79224 + 3.66423i 0.0732902 + 0.149841i
$$599$$ 34.0277 1.39034 0.695168 0.718848i $$-0.255330\pi$$
0.695168 + 0.718848i $$0.255330\pi$$
$$600$$ −8.79573 22.8612i −0.359084 0.933305i
$$601$$ 8.99390 0.366869 0.183434 0.983032i $$-0.441279\pi$$
0.183434 + 0.983032i $$0.441279\pi$$
$$602$$ −4.59608 9.39666i −0.187322 0.382979i
$$603$$ −16.9885 2.39862i −0.691827 0.0976795i
$$604$$ −24.8542 19.3288i −1.01130 0.786479i
$$605$$ 0.941075 1.88215i 0.0382601 0.0765203i
$$606$$ 17.5671 7.11391i 0.713613 0.288983i
$$607$$ −0.649508 −0.0263627 −0.0131814 0.999913i $$-0.504196\pi$$
−0.0131814 + 0.999913i $$0.504196\pi$$
$$608$$ 3.95891 + 4.66480i 0.160555 + 0.189183i
$$609$$ 0.587299 8.36049i 0.0237986 0.338784i
$$610$$ 39.9969 + 0.349706i 1.61943 + 0.0141592i
$$611$$ 1.17460 0.0475192
$$612$$ 25.6022 24.8031i 1.03491 1.00261i
$$613$$ 24.6157i 0.994217i 0.867688 + 0.497109i $$0.165605\pi$$
−0.867688 + 0.497109i $$0.834395\pi$$
$$614$$ 10.1327 + 20.7162i 0.408922 + 0.836039i
$$615$$ 23.0433 + 13.6187i 0.929197 + 0.549160i
$$616$$ 9.56706 + 2.00000i 0.385468 + 0.0805823i
$$617$$ −26.9710 −1.08581 −0.542905 0.839794i $$-0.682676\pi$$
−0.542905 + 0.839794i $$0.682676\pi$$
$$618$$ 5.16592 + 12.7567i 0.207804 + 0.513150i
$$619$$ 35.7302i 1.43612i −0.695982 0.718059i $$-0.745031\pi$$
0.695982 0.718059i $$-0.254969\pi$$
$$620$$ 38.5969 18.4621i 1.55009 0.741454i
$$621$$ −0.646865 + 3.02902i −0.0259578 + 0.121550i
$$622$$ 15.1324 + 30.9380i 0.606752 + 1.24050i
$$623$$ 5.23352i 0.209677i
$$624$$ 32.9906 5.95864i 1.32068 0.238536i
$$625$$ −7.00000 + 24.0000i −0.280000 + 0.960000i
$$626$$ 38.9517 19.0520i 1.55682 0.761471i
$$627$$ 0.453623 6.45755i 0.0181160 0.257890i
$$628$$ 28.1374 + 21.8822i 1.12281 + 0.873193i
$$629$$ 17.2955i 0.689616i
$$630$$ −9.38171 1.40838i −0.373776 0.0561110i
$$631$$ 28.1517i 1.12070i 0.828255 + 0.560352i $$0.189334\pi$$
−0.828255 + 0.560352i $$0.810666\pi$$
$$632$$ −0.549496 + 2.62853i −0.0218578 + 0.104557i
$$633$$ 2.02858 28.8778i 0.0806289 1.14779i
$$634$$ 8.62598 + 17.6358i 0.342582 + 0.700406i
$$635$$ 1.08883 2.17766i 0.0432088 0.0864176i
$$636$$ 27.3450 30.4871i 1.08430 1.20889i
$$637$$ 4.83882i 0.191721i
$$638$$ −21.2422 + 10.3899i −0.840987 + 0.411342i
$$639$$ −23.7643 3.35530i −0.940101 0.132734i
$$640$$ −23.0901 10.3366i −0.912718 0.408590i
$$641$$ 36.5329i 1.44296i −0.692433 0.721482i $$-0.743461\pi$$
0.692433 0.721482i $$-0.256539\pi$$
$$642$$ −3.82540 + 1.54913i −0.150977 + 0.0611391i
$$643$$ −29.7221 −1.17212 −0.586062 0.810266i $$-0.699322\pi$$
−0.586062 + 0.810266i $$0.699322\pi$$
$$644$$ −0.941075 0.731863i −0.0370836 0.0288394i
$$645$$ 14.5754 24.6620i 0.573906 0.971067i
$$646$$ 8.16314 3.99274i 0.321174 0.157092i
$$647$$ 6.11899i 0.240562i 0.992740 + 0.120281i $$0.0383796\pi$$
−0.992740 + 0.120281i $$0.961620\pi$$
$$648$$ 22.5010 + 11.9040i 0.883923 + 0.467632i
$$649$$ 11.2374 0.441108
$$650$$ −30.4685 15.5687i −1.19507 0.610654i
$$651$$ 1.16118 16.5299i 0.0455101 0.647858i
$$652$$ 13.8151 17.7643i 0.541041 0.695704i
$$653$$ 21.9090 0.857365 0.428683 0.903455i $$-0.358978\pi$$
0.428683 + 0.903455i $$0.358978\pi$$
$$654$$ −9.13995 22.5701i −0.357400 0.882562i
$$655$$ 6.30783 12.6157i 0.246467 0.492935i
$$656$$ 26.7933 6.80784i 1.04610 0.265801i
$$657$$ −3.35530 + 23.7643i −0.130903 + 0.927134i
$$658$$ −0.308381 + 0.150835i −0.0120219 + 0.00588015i
$$659$$ 45.4864 1.77190 0.885948 0.463784i $$-0.153509\pi$$
0.885948 + 0.463784i $$0.153509\pi$$
$$660$$ 9.82960 + 24.8967i 0.382617 + 0.969101i
$$661$$ 18.7335 0.728649 0.364325 0.931272i $$-0.381300\pi$$
0.364325 + 0.931272i $$0.381300\pi$$
$$662$$ 23.0651 11.2816i 0.896450 0.438470i
$$663$$ 3.48919 49.6703i 0.135509 1.92903i
$$664$$ −9.81814 + 46.9654i −0.381018 + 1.82261i
$$665$$ −2.16314 1.08157i −0.0838829 0.0419414i
$$666$$ 11.7447 3.82234i 0.455098 0.148113i
$$667$$ 2.88433 0.111682
$$668$$ 26.3872 + 20.5210i 1.02095 + 0.793981i
$$669$$ −15.1482 1.06411i −0.585662 0.0411410i
$$670$$ 18.0844 + 0.158118i 0.698662 + 0.00610863i
$$671$$ −43.7084 −1.68734
$$672$$ −7.89622 + 5.80084i −0.304603 + 0.223772i
$$673$$ 5.67589i 0.218789i −0.993998 0.109395i $$-0.965109\pi$$
0.993998 0.109395i $$-0.0348912\pi$$
$$674$$ 22.1581 10.8379i 0.853499 0.417462i
$$675$$ −10.9039 23.5819i −0.419692 0.907667i
$$676$$ 12.7865 16.4417i 0.491789 0.632373i
$$677$$ −29.7036 −1.14160 −0.570801 0.821088i $$-0.693367\pi$$
−0.570801 + 0.821088i $$0.693367\pi$$
$$678$$ −2.97294 7.34137i −0.114175 0.281943i
$$679$$ 3.30587i 0.126868i
$$680$$ −23.3254 + 29.4581i −0.894488 + 1.12967i
$$681$$ −0.0294624 + 0.419412i −0.00112900 + 0.0160719i
$$682$$ −41.9989 + 20.5424i −1.60822 + 0.786611i
$$683$$ 44.4223i 1.69977i −0.526965 0.849887i $$-0.676670\pi$$
0.526965 0.849887i $$-0.323330\pi$$
$$684$$ 4.51539 + 4.66087i 0.172650 + 0.178213i
$$685$$ 8.64863 17.2973i 0.330447 0.660894i
$$686$$ −0.621372 1.27039i −0.0237241 0.0485038i
$$687$$ −45.5327 3.19854i −1.73718 0.122032i
$$688$$ −7.28607 28.6755i −0.277779 1.09324i
$$689$$ 57.2062i 2.17938i
$$690$$ 0.257249 3.25471i 0.00979330 0.123905i
$$691$$ 6.30057i 0.239685i 0.992793 + 0.119843i $$0.0382390\pi$$
−0.992793 + 0.119843i $$0.961761\pi$$
$$692$$ 2.38324 3.06452i 0.0905971 0.116495i
$$693$$ 10.2649 + 1.44932i 0.389933 + 0.0550549i
$$694$$ −43.0110 + 21.0375i −1.63267 + 0.798571i
$$695$$ 11.6592 + 5.82960i 0.442259 + 0.221129i
$$696$$ 6.46481 22.8067i 0.245048 0.864487i
$$697$$ 41.0598i 1.55525i
$$698$$ 5.77462 + 11.8062i 0.218572 + 0.446870i
$$699$$ −11.1341 0.782138i −0.421131 0.0295832i
$$700$$ 9.99847 + 0.174853i 0.377907 + 0.00660882i
$$701$$ 40.7478i 1.53902i 0.638632 + 0.769512i $$0.279500\pi$$
−0.638632 + 0.769512i $$0.720500\pi$$
$$702$$ 34.5003 8.60787i 1.30213 0.324883i
$$703$$ 3.14863 0.118753
$$704$$ 25.3296 + 11.0743i 0.954645 + 0.417379i
$$705$$ −0.809362 0.478337i −0.0304823 0.0180152i
$$706$$ −4.64415 9.49495i −0.174785 0.357347i
$$707$$ 7.73746i 0.290997i
$$708$$ −7.52177 + 8.38608i −0.282685 + 0.315168i
$$709$$ −38.8830 −1.46028 −0.730141 0.683296i $$-0.760546\pi$$
−0.730141 + 0.683296i $$0.760546\pi$$
$$710$$ 25.2973 + 0.221182i 0.949389 + 0.00830081i
$$711$$ −0.398197 + 2.82027i −0.0149335 + 0.105769i
$$712$$ −3.02902 + 14.4894i −0.113517 + 0.543014i
$$713$$ 5.70273 0.213569
$$714$$ 5.46230 + 13.4886i 0.204421 + 0.504797i
$$715$$ 33.4419 + 16.7210i 1.25066 + 0.625329i
$$716$$ −8.35862 + 10.7480i −0.312376 + 0.401673i
$$717$$ 28.7669 + 2.02079i 1.07432 + 0.0754677i
$$718$$ 7.05587 + 14.4257i 0.263323 + 0.538362i
$$719$$ −5.03295 −0.187697 −0.0938486 0.995586i $$-0.529917\pi$$
−0.0938486 + 0.995586i $$0.529917\pi$$
$$720$$ −25.1589 9.32908i −0.937615 0.347674i
$$721$$ −5.61872 −0.209252
$$722$$ −11.0792 22.6514i −0.412325 0.842996i
$$723$$ −9.70647 0.681850i −0.360988 0.0253583i
$$724$$ 3.64775 4.69050i 0.135567 0.174321i
$$725$$ −19.3553 + 14.5165i −0.718838 + 0.539128i
$$726$$ −0.865236 2.13661i −0.0321119 0.0792970i
$$727$$ −11.3553 −0.421145 −0.210572 0.977578i $$-0.567533\pi$$
−0.210572 + 0.977578i $$0.567533\pi$$
$$728$$ −2.80058 + 13.3967i −0.103796 + 0.496513i
$$729$$ 24.6447 + 11.0290i 0.912766 + 0.408482i
$$730$$ 0.221182 25.2973i 0.00818631 0.936293i
$$731$$ −43.9441 −1.62533
$$732$$ 29.2562 32.6179i 1.08134 1.20559i
$$733$$ 14.7808i 0.545941i −0.962022 0.272970i $$-0.911994\pi$$
0.962022 0.272970i $$-0.0880061\pi$$
$$734$$ −2.63493 5.38711i −0.0972571 0.198842i
$$735$$ 1.97054 3.33421i 0.0726844 0.122984i
$$736$$ −2.18186 2.57089i −0.0804243 0.0947642i
$$737$$ −19.7625 −0.727962
$$738$$ 27.8822 9.07431i 1.02636 0.334030i
$$739$$ 36.3478i 1.33708i 0.743678 + 0.668538i $$0.233080\pi$$
−0.743678 + 0.668538i $$0.766920\pi$$
$$740$$ −11.7447 + 5.61784i −0.431744 + 0.206516i
$$741$$ 9.04244 + 0.635205i 0.332183 + 0.0233348i
$$742$$ 7.34608 + 15.0190i 0.269683 + 0.551365i
$$743$$ 1.48881i 0.0546191i −0.999627 0.0273096i $$-0.991306\pi$$
0.999627 0.0273096i $$-0.00869398\pi$$
$$744$$ 12.7819 45.0922i 0.468606 1.65316i
$$745$$ −35.6447 17.8223i −1.30592 0.652960i
$$746$$ −29.2900 + 14.3263i −1.07238 + 0.524522i
$$747$$ −7.11479 + 50.3914i −0.260317 + 1.84372i
$$748$$ 25.2065 32.4120i 0.921640 1.18510i
$$749$$ 1.68491i 0.0615652i
$$750$$ 14.6543 + 23.1355i 0.535100 + 0.844789i
$$751$$ 7.56116i 0.275911i 0.990438 + 0.137955i $$0.0440530\pi$$
−0.990438 + 0.137955i $$0.955947\pi$$
$$752$$ −0.941075 + 0.239115i −0.0343175 + 0.00871963i
$$753$$ 5.61872 + 0.394698i 0.204758 + 0.0143836i
$$754$$ −14.5489 29.7452i −0.529841 1.08326i
$$755$$ 31.4855 + 15.7427i 1.14587 + 0.572937i
$$756$$ −7.95240 + 6.69025i −0.289226 + 0.243322i
$$757$$ 9.61568i 0.349488i 0.984614 + 0.174744i $$0.0559098\pi$$
−0.984614 + 0.174744i $$0.944090\pi$$
$$758$$ −36.6433 + 17.9229i −1.33095 + 0.650990i
$$759$$ −0.250003 + 3.55892i −0.00907454 + 0.129181i
$$760$$ −5.36283 4.24637i −0.194530 0.154032i
$$761$$ 26.2665i 0.952159i 0.879402 + 0.476079i $$0.157943\pi$$
−0.879402 + 0.476079i $$0.842057\pi$$
$$762$$ −1.00108 2.47207i −0.0362654 0.0895535i
$$763$$ 9.94108 0.359891
$$764$$ −25.3512 + 32.5981i −0.917173 + 1.17936i
$$765$$ −22.6317 + 32.8046i −0.818251 + 1.18605i
$$766$$ 8.27177 4.04587i 0.298871 0.146183i
$$767$$ 15.7357i 0.568183i
$$768$$ −25.2187 + 11.4899i −0.910000 + 0.414608i
$$769$$ 35.5849 1.28322 0.641612 0.767029i $$-0.278266\pi$$
0.641612 + 0.767029i $$0.278266\pi$$
$$770$$ −10.9271 0.0955392i −0.393786 0.00344299i
$$771$$ 0.806959 + 0.0566864i 0.0290619 + 0.00204151i
$$772$$ 15.0928 + 11.7375i 0.543200 + 0.422440i
$$773$$ 28.5338 1.02629