# Properties

 Label 4.37.b.b.3.11 Level 4 Weight 37 Character 4.3 Analytic conductor 32.837 Analytic rank 0 Dimension 16 CM no Inner twists 2

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$4 = 2^{2}$$ Weight: $$k$$ $$=$$ $$37$$ Character orbit: $$[\chi]$$ $$=$$ 4.b (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$32.8365034637$$ Analytic rank: $$0$$ Dimension: $$16$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ Defining polynomial: $$x^{16} + 6516989503065492 x^{14} +$$$$17\!\cdots\!98$$$$x^{12} +$$$$23\!\cdots\!44$$$$x^{10} +$$$$17\!\cdots\!45$$$$x^{8} +$$$$72\!\cdots\!20$$$$x^{6} +$$$$15\!\cdots\!00$$$$x^{4} +$$$$15\!\cdots\!00$$$$x^{2} +$$$$51\!\cdots\!00$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: multiple of $$2^{240}\cdot 3^{24}\cdot 5^{6}\cdot 7^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 3.11 Root $$2.95956e7i$$ of defining polynomial Character $$\chi$$ $$=$$ 4.3 Dual form 4.37.b.b.3.12

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(178949. - 191564. i) q^{2} +4.73530e8i q^{3} +(-4.67423e9 - 6.85603e10i) q^{4} +4.97998e11 q^{5} +(9.07113e13 + 8.47375e13i) q^{6} +9.39063e14i q^{7} +(-1.39702e16 - 1.13734e16i) q^{8} -7.41357e16 q^{9} +O(q^{10})$$ $$q+(178949. - 191564. i) q^{2} +4.73530e8i q^{3} +(-4.67423e9 - 6.85603e10i) q^{4} +4.97998e11 q^{5} +(9.07113e13 + 8.47375e13i) q^{6} +9.39063e14i q^{7} +(-1.39702e16 - 1.13734e16i) q^{8} -7.41357e16 q^{9} +(8.91161e16 - 9.53986e16i) q^{10} +1.64809e18i q^{11} +(3.24653e19 - 2.21338e18i) q^{12} +1.14530e20 q^{13} +(1.79891e20 + 1.68044e20i) q^{14} +2.35817e20i q^{15} +(-4.67867e21 + 6.40933e20i) q^{16} -2.29593e22 q^{17} +(-1.32665e22 + 1.42017e22i) q^{18} +1.20463e23i q^{19} +(-2.32776e21 - 3.41429e22i) q^{20} -4.44674e23 q^{21} +(3.15714e23 + 2.94923e23i) q^{22} +2.81335e24i q^{23} +(5.38563e24 - 6.61528e24i) q^{24} -1.43039e25 q^{25} +(2.04950e25 - 2.19398e25i) q^{26} +3.59688e25i q^{27} +(6.43825e25 - 4.38939e24i) q^{28} -1.31366e25 q^{29} +(4.51741e25 + 4.21991e25i) q^{30} +7.15362e26i q^{31} +(-7.14462e26 + 1.01096e27i) q^{32} -7.80418e26 q^{33} +(-4.10853e27 + 4.39817e27i) q^{34} +4.67651e26i q^{35} +(3.46527e26 + 5.08277e27i) q^{36} +2.59863e28 q^{37} +(2.30764e28 + 2.15567e28i) q^{38} +5.42333e28i q^{39} +(-6.95711e27 - 5.66391e27i) q^{40} -1.71112e29 q^{41} +(-7.95738e28 + 8.51837e28i) q^{42} +4.11718e29i q^{43} +(1.12993e29 - 7.70353e27i) q^{44} -3.69194e28 q^{45} +(5.38937e29 + 5.03445e29i) q^{46} -8.93346e29i q^{47} +(-3.03501e29 - 2.21549e30i) q^{48} +1.76989e30 q^{49} +(-2.55967e30 + 2.74012e30i) q^{50} -1.08719e31i q^{51} +(-5.35338e29 - 7.85220e30i) q^{52} +3.45056e30 q^{53} +(6.89034e30 + 6.43657e30i) q^{54} +8.20743e29i q^{55} +(1.06803e31 - 1.31189e31i) q^{56} -5.70428e31 q^{57} +(-2.35078e30 + 2.51651e30i) q^{58} +2.87222e31i q^{59} +(1.61677e31 - 1.10226e30i) q^{60} -1.57408e31 q^{61} +(1.37038e32 + 1.28013e32i) q^{62} -6.96181e31i q^{63} +(6.58117e31 + 3.17775e32i) q^{64} +5.70356e31 q^{65} +(-1.39655e32 + 1.49500e32i) q^{66} -2.63364e32i q^{67} +(1.07317e32 + 1.57409e33i) q^{68} -1.33220e33 q^{69} +(8.95853e31 + 8.36856e31i) q^{70} -2.24092e33i q^{71} +(1.03569e33 + 8.43172e32i) q^{72} -4.63793e33 q^{73} +(4.65022e33 - 4.97805e33i) q^{74} -6.77333e33i q^{75} +(8.25898e33 - 5.63071e32i) q^{76} -1.54766e33 q^{77} +(1.03892e34 + 9.70497e33i) q^{78} -2.60170e34i q^{79} +(-2.32997e33 + 3.19183e32i) q^{80} -2.81597e34 q^{81} +(-3.06203e34 + 3.27790e34i) q^{82} +9.58149e32i q^{83} +(2.07851e33 + 3.04870e34i) q^{84} -1.14337e34 q^{85} +(7.88705e34 + 7.36765e34i) q^{86} -6.22058e33i q^{87} +(1.87443e34 - 2.30240e34i) q^{88} +3.91670e34 q^{89} +(-6.60668e33 + 7.07244e33i) q^{90} +1.07551e35i q^{91} +(1.92884e35 - 1.31502e34i) q^{92} -3.38745e35 q^{93} +(-1.71133e35 - 1.59863e35i) q^{94} +5.99903e34i q^{95} +(-4.78719e35 - 3.38319e35i) q^{96} +5.91294e35 q^{97} +(3.16720e35 - 3.39048e35i) q^{98} -1.22182e35i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16q + 177228q^{2} - 5610707696q^{4} + 5816089539360q^{5} - 217628996575488q^{6} + 11897560228206528q^{8} - 935184460817545968q^{9} + O(q^{10})$$ $$16q + 177228q^{2} - 5610707696q^{4} + 5816089539360q^{5} - 217628996575488q^{6} + 11897560228206528q^{8} - 935184460817545968q^{9} - 2378142919315561000q^{10} - 42882825786868930560q^{12} +$$$$19\!\cdots\!76$$$$q^{13} +$$$$36\!\cdots\!28$$$$q^{14} -$$$$22\!\cdots\!84$$$$q^{16} +$$$$41\!\cdots\!76$$$$q^{17} +$$$$13\!\cdots\!68$$$$q^{18} +$$$$10\!\cdots\!40$$$$q^{20} -$$$$17\!\cdots\!96$$$$q^{21} -$$$$43\!\cdots\!40$$$$q^{22} +$$$$51\!\cdots\!68$$$$q^{24} +$$$$61\!\cdots\!00$$$$q^{25} -$$$$70\!\cdots\!40$$$$q^{26} -$$$$30\!\cdots\!00$$$$q^{28} -$$$$95\!\cdots\!52$$$$q^{29} +$$$$36\!\cdots\!20$$$$q^{30} +$$$$46\!\cdots\!48$$$$q^{32} -$$$$87\!\cdots\!60$$$$q^{33} -$$$$90\!\cdots\!20$$$$q^{34} -$$$$92\!\cdots\!92$$$$q^{36} -$$$$30\!\cdots\!84$$$$q^{37} +$$$$78\!\cdots\!80$$$$q^{38} -$$$$13\!\cdots\!00$$$$q^{40} +$$$$99\!\cdots\!12$$$$q^{41} -$$$$19\!\cdots\!00$$$$q^{42} +$$$$30\!\cdots\!60$$$$q^{44} +$$$$15\!\cdots\!20$$$$q^{45} -$$$$91\!\cdots\!28$$$$q^{46} -$$$$15\!\cdots\!20$$$$q^{48} -$$$$11\!\cdots\!48$$$$q^{49} +$$$$11\!\cdots\!00$$$$q^{50} +$$$$16\!\cdots\!56$$$$q^{52} +$$$$20\!\cdots\!56$$$$q^{53} -$$$$42\!\cdots\!84$$$$q^{54} -$$$$18\!\cdots\!68$$$$q^{56} -$$$$17\!\cdots\!80$$$$q^{57} +$$$$33\!\cdots\!56$$$$q^{58} -$$$$69\!\cdots\!00$$$$q^{60} +$$$$21\!\cdots\!32$$$$q^{61} +$$$$40\!\cdots\!80$$$$q^{62} -$$$$26\!\cdots\!96$$$$q^{64} -$$$$20\!\cdots\!00$$$$q^{65} -$$$$81\!\cdots\!60$$$$q^{66} +$$$$35\!\cdots\!56$$$$q^{68} +$$$$39\!\cdots\!56$$$$q^{69} +$$$$31\!\cdots\!80$$$$q^{70} -$$$$18\!\cdots\!32$$$$q^{72} -$$$$13\!\cdots\!64$$$$q^{73} +$$$$76\!\cdots\!40$$$$q^{74} -$$$$15\!\cdots\!60$$$$q^{76} +$$$$22\!\cdots\!00$$$$q^{77} -$$$$18\!\cdots\!60$$$$q^{78} +$$$$67\!\cdots\!60$$$$q^{80} -$$$$40\!\cdots\!00$$$$q^{81} +$$$$43\!\cdots\!36$$$$q^{82} -$$$$37\!\cdots\!64$$$$q^{84} -$$$$20\!\cdots\!00$$$$q^{85} +$$$$10\!\cdots\!32$$$$q^{86} +$$$$39\!\cdots\!80$$$$q^{88} +$$$$46\!\cdots\!88$$$$q^{89} -$$$$36\!\cdots\!00$$$$q^{90} -$$$$17\!\cdots\!80$$$$q^{92} -$$$$23\!\cdots\!80$$$$q^{93} -$$$$69\!\cdots\!32$$$$q^{94} +$$$$10\!\cdots\!72$$$$q^{96} +$$$$45\!\cdots\!96$$$$q^{97} +$$$$10\!\cdots\!28$$$$q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/4\mathbb{Z}\right)^\times$$.

 $$n$$ $$3$$ $$\chi(n)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 178949. 191564.i 0.682635 0.730760i
$$3$$ 4.73530e8i 1.22226i 0.791529 + 0.611131i $$0.209285\pi$$
−0.791529 + 0.611131i $$0.790715\pi$$
$$4$$ −4.67423e9 6.85603e10i −0.0680190 0.997684i
$$5$$ 4.97998e11 0.130547 0.0652736 0.997867i $$-0.479208\pi$$
0.0652736 + 0.997867i $$0.479208\pi$$
$$6$$ 9.07113e13 + 8.47375e13i 0.893180 + 0.834359i
$$7$$ 9.39063e14i 0.576673i 0.957529 + 0.288337i $$0.0931022\pi$$
−0.957529 + 0.288337i $$0.906898\pi$$
$$8$$ −1.39702e16 1.13734e16i −0.775499 0.631349i
$$9$$ −7.41357e16 −0.493926
$$10$$ 8.91161e16 9.53986e16i 0.0891161 0.0953986i
$$11$$ 1.64809e18i 0.296423i 0.988956 + 0.148211i $$0.0473516\pi$$
−0.988956 + 0.148211i $$0.952648\pi$$
$$12$$ 3.24653e19 2.21338e18i 1.21943 0.0831370i
$$13$$ 1.14530e20 1.01845 0.509223 0.860634i $$-0.329933\pi$$
0.509223 + 0.860634i $$0.329933\pi$$
$$14$$ 1.79891e20 + 1.68044e20i 0.421410 + 0.393657i
$$15$$ 2.35817e20i 0.159563i
$$16$$ −4.67867e21 + 6.40933e20i −0.990747 + 0.135723i
$$17$$ −2.29593e22 −1.63259 −0.816295 0.577635i $$-0.803976\pi$$
−0.816295 + 0.577635i $$0.803976\pi$$
$$18$$ −1.32665e22 + 1.42017e22i −0.337171 + 0.360941i
$$19$$ 1.20463e23i 1.15688i 0.815725 + 0.578440i $$0.196338\pi$$
−0.815725 + 0.578440i $$0.803662\pi$$
$$20$$ −2.32776e21 3.41429e22i −0.00887968 0.130245i
$$21$$ −4.44674e23 −0.704847
$$22$$ 3.15714e23 + 2.94923e23i 0.216614 + 0.202349i
$$23$$ 2.81335e24i 0.867206i 0.901104 + 0.433603i $$0.142758\pi$$
−0.901104 + 0.433603i $$0.857242\pi$$
$$24$$ 5.38563e24 6.61528e24i 0.771674 0.947864i
$$25$$ −1.43039e25 −0.982957
$$26$$ 2.04950e25 2.19398e25i 0.695227 0.744240i
$$27$$ 3.59688e25i 0.618555i
$$28$$ 6.43825e25 4.38939e24i 0.575338 0.0392247i
$$29$$ −1.31366e25 −0.0624194 −0.0312097 0.999513i $$-0.509936\pi$$
−0.0312097 + 0.999513i $$0.509936\pi$$
$$30$$ 4.51741e25 + 4.21991e25i 0.116602 + 0.108923i
$$31$$ 7.15362e26i 1.02333i 0.859185 + 0.511664i $$0.170971\pi$$
−0.859185 + 0.511664i $$0.829029\pi$$
$$32$$ −7.14462e26 + 1.01096e27i −0.577138 + 0.816647i
$$33$$ −7.80418e26 −0.362306
$$34$$ −4.10853e27 + 4.39817e27i −1.11446 + 1.19303i
$$35$$ 4.67651e26i 0.0752831i
$$36$$ 3.46527e26 + 5.08277e27i 0.0335964 + 0.492782i
$$37$$ 2.59863e28 1.53856 0.769279 0.638913i $$-0.220616\pi$$
0.769279 + 0.638913i $$0.220616\pi$$
$$38$$ 2.30764e28 + 2.15567e28i 0.845402 + 0.789727i
$$39$$ 5.42333e28i 1.24481i
$$40$$ −6.95711e27 5.66391e27i −0.101239 0.0824208i
$$41$$ −1.71112e29 −1.59651 −0.798256 0.602318i $$-0.794244\pi$$
−0.798256 + 0.602318i $$0.794244\pi$$
$$42$$ −7.95738e28 + 8.51837e28i −0.481153 + 0.515073i
$$43$$ 4.11718e29i 1.62993i 0.579513 + 0.814963i $$0.303243\pi$$
−0.579513 + 0.814963i $$0.696757\pi$$
$$44$$ 1.12993e29 7.70353e27i 0.295736 0.0201624i
$$45$$ −3.69194e28 −0.0644807
$$46$$ 5.38937e29 + 5.03445e29i 0.633719 + 0.591985i
$$47$$ 8.93346e29i 0.713277i −0.934242 0.356639i $$-0.883923\pi$$
0.934242 0.356639i $$-0.116077\pi$$
$$48$$ −3.03501e29 2.21549e30i −0.165889 1.21095i
$$49$$ 1.76989e30 0.667448
$$50$$ −2.55967e30 + 2.74012e30i −0.671001 + 0.718306i
$$51$$ 1.08719e31i 1.99546i
$$52$$ −5.35338e29 7.85220e30i −0.0692737 1.01609i
$$53$$ 3.45056e30 0.316902 0.158451 0.987367i $$-0.449350\pi$$
0.158451 + 0.987367i $$0.449350\pi$$
$$54$$ 6.89034e30 + 6.43657e30i 0.452015 + 0.422247i
$$55$$ 8.20743e29i 0.0386972i
$$56$$ 1.06803e31 1.31189e31i 0.364082 0.447210i
$$57$$ −5.70428e31 −1.41401
$$58$$ −2.35078e30 + 2.51651e30i −0.0426097 + 0.0456136i
$$59$$ 2.87222e31i 0.382720i 0.981520 + 0.191360i $$0.0612899\pi$$
−0.981520 + 0.191360i $$0.938710\pi$$
$$60$$ 1.61677e31 1.10226e30i 0.159193 0.0108533i
$$61$$ −1.57408e31 −0.115104 −0.0575519 0.998343i $$-0.518329\pi$$
−0.0575519 + 0.998343i $$0.518329\pi$$
$$62$$ 1.37038e32 + 1.28013e32i 0.747807 + 0.698560i
$$63$$ 6.96181e31i 0.284834i
$$64$$ 6.58117e31 + 3.17775e32i 0.202798 + 0.979221i
$$65$$ 5.70356e31 0.132955
$$66$$ −1.39655e32 + 1.49500e32i −0.247323 + 0.264759i
$$67$$ 2.63364e32i 0.355804i −0.984048 0.177902i $$-0.943069\pi$$
0.984048 0.177902i $$-0.0569310\pi$$
$$68$$ 1.07317e32 + 1.57409e33i 0.111047 + 1.62881i
$$69$$ −1.33220e33 −1.05995
$$70$$ 8.95853e31 + 8.36856e31i 0.0550138 + 0.0513909i
$$71$$ 2.24092e33i 1.06604i −0.846101 0.533022i $$-0.821056\pi$$
0.846101 0.533022i $$-0.178944\pi$$
$$72$$ 1.03569e33 + 8.43172e32i 0.383040 + 0.311840i
$$73$$ −4.63793e33 −1.33817 −0.669087 0.743184i $$-0.733315\pi$$
−0.669087 + 0.743184i $$0.733315\pi$$
$$74$$ 4.65022e33 4.97805e33i 1.05027 1.12432i
$$75$$ 6.77333e33i 1.20143i
$$76$$ 8.25898e33 5.63071e32i 1.15420 0.0786898i
$$77$$ −1.54766e33 −0.170939
$$78$$ 1.03892e34 + 9.70497e33i 0.909656 + 0.849751i
$$79$$ 2.60170e34i 1.81121i −0.424119 0.905607i $$-0.639416\pi$$
0.424119 0.905607i $$-0.360584\pi$$
$$80$$ −2.32997e33 + 3.19183e32i −0.129339 + 0.0177182i
$$81$$ −2.81597e34 −1.24996
$$82$$ −3.06203e34 + 3.27790e34i −1.08984 + 1.16667i
$$83$$ 9.58149e32i 0.0274175i 0.999906 + 0.0137087i $$0.00436376\pi$$
−0.999906 + 0.0137087i $$0.995636\pi$$
$$84$$ 2.07851e33 + 3.04870e34i 0.0479429 + 0.703214i
$$85$$ −1.14337e34 −0.213130
$$86$$ 7.88705e34 + 7.36765e34i 1.19108 + 1.11264i
$$87$$ 6.22058e33i 0.0762930i
$$88$$ 1.87443e34 2.30240e34i 0.187146 0.229876i
$$89$$ 3.91670e34 0.319080 0.159540 0.987191i $$-0.448999\pi$$
0.159540 + 0.987191i $$0.448999\pi$$
$$90$$ −6.60668e33 + 7.07244e33i −0.0440168 + 0.0471199i
$$91$$ 1.07551e35i 0.587311i
$$92$$ 1.92884e35 1.31502e34i 0.865198 0.0589864i
$$93$$ −3.38745e35 −1.25078
$$94$$ −1.71133e35 1.59863e35i −0.521234 0.486908i
$$95$$ 5.99903e34i 0.151027i
$$96$$ −4.78719e35 3.38319e35i −0.998157 0.705414i
$$97$$ 5.91294e35 1.02309 0.511543 0.859258i $$-0.329074\pi$$
0.511543 + 0.859258i $$0.329074\pi$$
$$98$$ 3.16720e35 3.39048e35i 0.455623 0.487744i
$$99$$ 1.22182e35i 0.146411i
$$100$$ 6.68597e34 + 9.80681e35i 0.0668597 + 0.980681i
$$101$$ 1.79261e36 1.49865 0.749325 0.662202i $$-0.230378\pi$$
0.749325 + 0.662202i $$0.230378\pi$$
$$102$$ −2.08267e36 1.94551e36i −1.45820 1.36217i
$$103$$ 5.54915e35i 0.325954i −0.986630 0.162977i $$-0.947890\pi$$
0.986630 0.162977i $$-0.0521096\pi$$
$$104$$ −1.60000e36 1.30259e36i −0.789805 0.642995i
$$105$$ −2.21447e35 −0.0920157
$$106$$ 6.17474e35 6.61005e35i 0.216328 0.231579i
$$107$$ 4.04653e36i 1.19722i 0.801040 + 0.598611i $$0.204280\pi$$
−0.801040 + 0.598611i $$0.795720\pi$$
$$108$$ 2.46603e36 1.68126e35i 0.617122 0.0420735i
$$109$$ 3.91818e36 0.830631 0.415315 0.909678i $$-0.363671\pi$$
0.415315 + 0.909678i $$0.363671\pi$$
$$110$$ 1.57225e35 + 1.46871e35i 0.0282783 + 0.0264160i
$$111$$ 1.23053e37i 1.88052i
$$112$$ −6.01876e35 4.39357e36i −0.0782678 0.571337i
$$113$$ −4.45970e36 −0.494189 −0.247095 0.968991i $$-0.579476\pi$$
−0.247095 + 0.968991i $$0.579476\pi$$
$$114$$ −1.02077e37 + 1.09274e37i −0.965254 + 1.03330i
$$115$$ 1.40104e36i 0.113211i
$$116$$ 6.14036e34 + 9.00651e35i 0.00424570 + 0.0622749i
$$117$$ −8.49075e36 −0.503038
$$118$$ 5.50215e36 + 5.13980e36i 0.279677 + 0.261258i
$$119$$ 2.15602e37i 0.941472i
$$120$$ 2.68203e36 3.29440e36i 0.100740 0.123741i
$$121$$ 2.81965e37 0.912134
$$122$$ −2.81679e36 + 3.01537e36i −0.0785739 + 0.0841132i
$$123$$ 8.10268e37i 1.95136i
$$124$$ 4.90454e37 3.34376e36i 1.02096 0.0696057i
$$125$$ −1.43701e37 −0.258869
$$126$$ −1.33363e37 1.24581e37i −0.208145 0.194438i
$$127$$ 2.51694e37i 0.340726i −0.985381 0.170363i $$-0.945506\pi$$
0.985381 0.170363i $$-0.0544940\pi$$
$$128$$ 7.26513e37 + 4.42583e37i 0.854012 + 0.520254i
$$129$$ −1.94961e38 −1.99220
$$130$$ 1.02064e37 1.09260e37i 0.0907600 0.0971584i
$$131$$ 4.39588e37i 0.340535i 0.985398 + 0.170268i $$0.0544632\pi$$
−0.985398 + 0.170268i $$0.945537\pi$$
$$132$$ 3.64785e36 + 5.35057e37i 0.0246437 + 0.361467i
$$133$$ −1.13122e38 −0.667142
$$134$$ −5.04512e37 4.71287e37i −0.260007 0.242884i
$$135$$ 1.79124e37i 0.0807506i
$$136$$ 3.20744e38 + 2.61124e38i 1.26607 + 1.03073i
$$137$$ 2.45741e38 0.850173 0.425086 0.905153i $$-0.360244\pi$$
0.425086 + 0.905153i $$0.360244\pi$$
$$138$$ −2.38396e38 + 2.55203e38i −0.723562 + 0.774571i
$$139$$ 7.52934e37i 0.200674i −0.994954 0.100337i $$-0.968008\pi$$
0.994954 0.100337i $$-0.0319920\pi$$
$$140$$ 3.20623e37 2.18591e36i 0.0751087 0.00512068i
$$141$$ 4.23026e38 0.871812
$$142$$ −4.29279e38 4.01009e38i −0.779022 0.727719i
$$143$$ 1.88755e38i 0.301891i
$$144$$ 3.46856e38 4.75160e37i 0.489356 0.0670371i
$$145$$ −6.54201e36 −0.00814868
$$146$$ −8.29951e38 + 8.88461e38i −0.913484 + 0.977883i
$$147$$ 8.38096e38i 0.815797i
$$148$$ −1.21466e38 1.78163e39i −0.104651 1.53499i
$$149$$ −5.62189e38 −0.429071 −0.214536 0.976716i $$-0.568824\pi$$
−0.214536 + 0.976716i $$0.568824\pi$$
$$150$$ −1.29753e39 1.21208e39i −0.877958 0.820140i
$$151$$ 1.13127e38i 0.0679175i 0.999423 + 0.0339587i $$0.0108115\pi$$
−0.999423 + 0.0339587i $$0.989189\pi$$
$$152$$ 1.37007e39 1.68289e39i 0.730395 0.897160i
$$153$$ 1.70210e39 0.806380
$$154$$ −2.76951e38 + 2.96476e38i −0.116689 + 0.124915i
$$155$$ 3.56249e38i 0.133593i
$$156$$ 3.71825e39 2.53499e38i 1.24193 0.0846706i
$$157$$ 3.45361e39 1.02820 0.514102 0.857729i $$-0.328125\pi$$
0.514102 + 0.857729i $$0.328125\pi$$
$$158$$ −4.98393e39 4.65571e39i −1.32356 1.23640i
$$159$$ 1.63394e39i 0.387337i
$$160$$ −3.55801e38 + 5.03456e38i −0.0753437 + 0.106611i
$$161$$ −2.64191e39 −0.500095
$$162$$ −5.03914e39 + 5.39439e39i −0.853269 + 0.913422i
$$163$$ 5.94810e39i 0.901574i −0.892632 0.450787i $$-0.851143\pi$$
0.892632 0.450787i $$-0.148857\pi$$
$$164$$ 7.99818e38 + 1.17315e40i 0.108593 + 1.59281i
$$165$$ −3.88646e38 −0.0472981
$$166$$ 1.83547e38 + 1.71459e38i 0.0200356 + 0.0187161i
$$167$$ 1.39112e40i 1.36291i 0.731861 + 0.681454i $$0.238652\pi$$
−0.731861 + 0.681454i $$0.761348\pi$$
$$168$$ 6.21217e39 + 5.05744e39i 0.546608 + 0.445004i
$$169$$ 4.70867e38 0.0372338
$$170$$ −2.04604e39 + 2.19028e39i −0.145490 + 0.155747i
$$171$$ 8.93060e39i 0.571414i
$$172$$ 2.82275e40 1.92446e39i 1.62615 0.110866i
$$173$$ −3.29833e40 −1.71185 −0.855923 0.517104i $$-0.827010\pi$$
−0.855923 + 0.517104i $$0.827010\pi$$
$$174$$ −1.19164e39 1.11316e39i −0.0557518 0.0520802i
$$175$$ 1.34323e40i 0.566845i
$$176$$ −1.05631e39 7.71085e39i −0.0402313 0.293680i
$$177$$ −1.36008e40 −0.467785
$$178$$ 7.00888e39 7.50299e39i 0.217815 0.233171i
$$179$$ 5.49966e40i 1.54519i −0.634900 0.772594i $$-0.718959\pi$$
0.634900 0.772594i $$-0.281041\pi$$
$$180$$ 1.72570e38 + 2.53121e39i 0.00438591 + 0.0643314i
$$181$$ 3.46531e40 0.797128 0.398564 0.917141i $$-0.369509\pi$$
0.398564 + 0.917141i $$0.369509\pi$$
$$182$$ 2.06029e40 + 1.92461e40i 0.429183 + 0.400919i
$$183$$ 7.45373e39i 0.140687i
$$184$$ 3.19972e40 3.93029e40i 0.547509 0.672518i
$$185$$ 1.29411e40 0.200854
$$186$$ −6.06180e40 + 6.48914e40i −0.853824 + 0.914017i
$$187$$ 3.78388e40i 0.483937i
$$188$$ −6.12481e40 + 4.17570e39i −0.711625 + 0.0485164i
$$189$$ −3.37770e40 −0.356704
$$190$$ 1.14920e40 + 1.07352e40i 0.110365 + 0.103097i
$$191$$ 1.96526e41i 1.71719i 0.512654 + 0.858595i $$0.328662\pi$$
−0.512654 + 0.858595i $$0.671338\pi$$
$$192$$ −1.50476e41 + 3.11638e40i −1.19686 + 0.247873i
$$193$$ 2.74837e40 0.199087 0.0995437 0.995033i $$-0.468262\pi$$
0.0995437 + 0.995033i $$0.468262\pi$$
$$194$$ 1.05811e41 1.13271e41i 0.698395 0.747630i
$$195$$ 2.70081e40i 0.162506i
$$196$$ −8.27288e39 1.21344e41i −0.0453991 0.665902i
$$197$$ 1.69096e41 0.846725 0.423363 0.905960i $$-0.360850\pi$$
0.423363 + 0.905960i $$0.360850\pi$$
$$198$$ −2.34057e40 2.18643e40i −0.106991 0.0999453i
$$199$$ 4.25960e41i 1.77834i 0.457581 + 0.889168i $$0.348716\pi$$
−0.457581 + 0.889168i $$0.651284\pi$$
$$200$$ 1.99828e41 + 1.62684e41i 0.762283 + 0.620589i
$$201$$ 1.24711e41 0.434886
$$202$$ 3.20785e41 3.43399e41i 1.02303 1.09515i
$$203$$ 1.23361e40i 0.0359956i
$$204$$ −7.45380e41 + 5.08177e40i −1.99083 + 0.135729i
$$205$$ −8.52137e40 −0.208420
$$206$$ −1.06302e41 9.93012e40i −0.238194 0.222508i
$$207$$ 2.08569e41i 0.428336i
$$208$$ −5.35847e41 + 7.34060e40i −1.00902 + 0.138226i
$$209$$ −1.98533e41 −0.342926
$$210$$ −3.96276e40 + 4.24213e40i −0.0628132 + 0.0672414i
$$211$$ 8.66535e41i 1.26096i −0.776205 0.630481i $$-0.782858\pi$$
0.776205 0.630481i $$-0.217142\pi$$
$$212$$ −1.61287e40 2.36572e41i −0.0215553 0.316168i
$$213$$ 1.06114e42 1.30299
$$214$$ 7.75170e41 + 7.24120e41i 0.874881 + 0.817265i
$$215$$ 2.05035e41i 0.212782i
$$216$$ 4.09086e41 5.02490e41i 0.390524 0.479689i
$$217$$ −6.71770e41 −0.590127
$$218$$ 7.01154e41 7.50584e41i 0.567017 0.606991i
$$219$$ 2.19620e42i 1.63560i
$$220$$ 5.62704e40 3.83634e39i 0.0386075 0.00263214i
$$221$$ −2.62952e42 −1.66271
$$222$$ 2.35725e42 + 2.20202e42i 1.37421 + 1.28371i
$$223$$ 3.01760e42i 1.62246i 0.584725 + 0.811231i $$0.301202\pi$$
−0.584725 + 0.811231i $$0.698798\pi$$
$$224$$ −9.49355e41 6.70925e41i −0.470939 0.332820i
$$225$$ 1.06043e42 0.485509
$$226$$ −7.98057e41 + 8.54318e41i −0.337351 + 0.361133i
$$227$$ 2.89079e41i 0.112863i −0.998406 0.0564315i $$-0.982028\pi$$
0.998406 0.0564315i $$-0.0179723\pi$$
$$228$$ 2.66631e41 + 3.91087e42i 0.0961796 + 1.41074i
$$229$$ −4.60426e42 −1.53505 −0.767523 0.641021i $$-0.778511\pi$$
−0.767523 + 0.641021i $$0.778511\pi$$
$$230$$ 2.68389e41 + 2.50714e41i 0.0827302 + 0.0772820i
$$231$$ 7.32861e41i 0.208933i
$$232$$ 1.83521e41 + 1.49408e41i 0.0484062 + 0.0394084i
$$233$$ 2.20539e41 0.0538368 0.0269184 0.999638i $$-0.491431\pi$$
0.0269184 + 0.999638i $$0.491431\pi$$
$$234$$ −1.51941e42 + 1.62652e42i −0.343391 + 0.367600i
$$235$$ 4.44885e41i 0.0931163i
$$236$$ 1.96920e42 1.34254e41i 0.381834 0.0260322i
$$237$$ 1.23198e43 2.21378
$$238$$ −4.13016e42 3.85817e42i −0.687990 0.642682i
$$239$$ 2.95916e42i 0.457094i −0.973533 0.228547i $$-0.926603\pi$$
0.973533 0.228547i $$-0.0733975\pi$$
$$240$$ −1.51143e41 1.10331e42i −0.0216563 0.158086i
$$241$$ −3.45312e42 −0.459097 −0.229549 0.973297i $$-0.573725\pi$$
−0.229549 + 0.973297i $$0.573725\pi$$
$$242$$ 5.04572e42 5.40144e42i 0.622654 0.666550i
$$243$$ 7.93571e42i 0.909228i
$$244$$ 7.35760e40 + 1.07919e42i 0.00782924 + 0.114837i
$$245$$ 8.81402e41 0.0871334
$$246$$ −1.55218e43 1.44996e43i −1.42597 1.33206i
$$247$$ 1.37966e43i 1.17822i
$$248$$ 8.13607e42 9.99371e42i 0.646077 0.793591i
$$249$$ −4.53712e41 −0.0335113
$$250$$ −2.57152e42 + 2.75281e42i −0.176713 + 0.189171i
$$251$$ 2.44151e43i 1.56146i 0.624867 + 0.780731i $$0.285153\pi$$
−0.624867 + 0.780731i $$0.714847\pi$$
$$252$$ −4.77304e42 + 3.25411e41i −0.284175 + 0.0193741i
$$253$$ −4.63664e42 −0.257060
$$254$$ −4.82155e42 4.50402e42i −0.248989 0.232591i
$$255$$ 5.41418e42i 0.260501i
$$256$$ 2.14792e43 5.99743e42i 0.963159 0.268934i
$$257$$ 2.82654e43 1.18157 0.590785 0.806829i $$-0.298818\pi$$
0.590785 + 0.806829i $$0.298818\pi$$
$$258$$ −3.48880e43 + 3.73475e43i −1.35994 + 1.45582i
$$259$$ 2.44028e43i 0.887246i
$$260$$ −2.66597e41 3.91038e42i −0.00904348 0.132647i
$$261$$ 9.73893e41 0.0308306
$$262$$ 8.42093e42 + 7.86636e42i 0.248849 + 0.232461i
$$263$$ 4.72307e43i 1.30323i −0.758551 0.651614i $$-0.774092\pi$$
0.758551 0.651614i $$-0.225908\pi$$
$$264$$ 1.09026e43 + 8.87597e42i 0.280968 + 0.228742i
$$265$$ 1.71837e42 0.0413706
$$266$$ −2.02431e43 + 2.16702e43i −0.455415 + 0.487521i
$$267$$ 1.85467e43i 0.390000i
$$268$$ −1.80563e43 + 1.23102e42i −0.354980 + 0.0242014i
$$269$$ −3.43092e43 −0.630769 −0.315384 0.948964i $$-0.602133\pi$$
−0.315384 + 0.948964i $$0.602133\pi$$
$$270$$ 3.43137e42 + 3.20540e42i 0.0590093 + 0.0551232i
$$271$$ 3.96971e43i 0.638722i −0.947633 0.319361i $$-0.896532\pi$$
0.947633 0.319361i $$-0.103468\pi$$
$$272$$ 1.07419e44 1.47154e43i 1.61748 0.221580i
$$273$$ −5.09285e43 −0.717849
$$274$$ 4.39750e43 4.70752e43i 0.580358 0.621272i
$$275$$ 2.35741e43i 0.291371i
$$276$$ 6.22702e42 + 9.13363e43i 0.0720969 + 1.05750i
$$277$$ 8.05966e42 0.0874341 0.0437170 0.999044i $$-0.486080\pi$$
0.0437170 + 0.999044i $$0.486080\pi$$
$$278$$ −1.44235e43 1.34737e43i −0.146644 0.136987i
$$279$$ 5.30338e43i 0.505449i
$$280$$ 5.31877e42 6.53316e42i 0.0475299 0.0583820i
$$281$$ −1.90752e44 −1.59866 −0.799329 0.600894i $$-0.794812\pi$$
−0.799329 + 0.600894i $$0.794812\pi$$
$$282$$ 7.56999e43 8.10366e43i 0.595130 0.637085i
$$283$$ 7.67667e43i 0.566261i −0.959081 0.283131i $$-0.908627\pi$$
0.959081 0.283131i $$-0.0913730\pi$$
$$284$$ −1.53638e44 + 1.04745e43i −1.06358 + 0.0725112i
$$285$$ −2.84072e43 −0.184595
$$286$$ 3.61587e43 + 3.37775e43i 0.220610 + 0.206081i
$$287$$ 1.60685e44i 0.920666i
$$288$$ 5.29671e43 7.49482e43i 0.285064 0.403363i
$$289$$ 3.29357e44 1.66535
$$290$$ −1.17068e42 + 1.25322e42i −0.00556257 + 0.00595473i
$$291$$ 2.79995e44i 1.25048i
$$292$$ 2.16787e43 + 3.17978e44i 0.0910212 + 1.33507i
$$293$$ 2.66147e44 1.05076 0.525380 0.850868i $$-0.323923\pi$$
0.525380 + 0.850868i $$0.323923\pi$$
$$294$$ 1.60549e44 + 1.49976e44i 0.596151 + 0.556891i
$$295$$ 1.43036e43i 0.0499631i
$$296$$ −3.63033e44 2.95552e44i −1.19315 0.971366i
$$297$$ −5.92797e43 −0.183354
$$298$$ −1.00603e44 + 1.07695e44i −0.292899 + 0.313548i
$$299$$ 3.22212e44i 0.883203i
$$300$$ −4.64382e44 + 3.16601e43i −1.19865 + 0.0817202i
$$301$$ −3.86629e44 −0.939935
$$302$$ 2.16711e43 + 2.02439e43i 0.0496313 + 0.0463628i
$$303$$ 8.48852e44i 1.83174i
$$304$$ −7.72087e43 5.63606e44i −0.157015 1.14618i
$$305$$ −7.83888e42 −0.0150265
$$306$$ 3.04589e44 3.26062e44i 0.550463 0.589270i
$$307$$ 2.07386e44i 0.353418i 0.984263 + 0.176709i $$0.0565451\pi$$
−0.984263 + 0.176709i $$0.943455\pi$$
$$308$$ 7.23410e42 + 1.06108e44i 0.0116271 + 0.170543i
$$309$$ 2.62769e44 0.398401
$$310$$ 6.82445e43 + 6.37502e43i 0.0976241 + 0.0911950i
$$311$$ 1.30713e45i 1.76454i −0.470744 0.882270i $$-0.656014\pi$$
0.470744 0.882270i $$-0.343986\pi$$
$$312$$ 6.16815e44 7.57647e44i 0.785909 0.965349i
$$313$$ 9.40367e44 1.13110 0.565548 0.824716i $$-0.308665\pi$$
0.565548 + 0.824716i $$0.308665\pi$$
$$314$$ 6.18018e44 6.61587e44i 0.701887 0.751369i
$$315$$ 3.46697e43i 0.0371843i
$$316$$ −1.78373e45 + 1.21609e44i −1.80702 + 0.123197i
$$317$$ 1.00608e45 0.962864 0.481432 0.876483i $$-0.340117\pi$$
0.481432 + 0.876483i $$0.340117\pi$$
$$318$$ 3.13005e44 + 2.92392e44i 0.283050 + 0.264410i
$$319$$ 2.16503e43i 0.0185025i
$$320$$ 3.27741e43 + 1.58251e44i 0.0264747 + 0.127834i
$$321$$ −1.91615e45 −1.46332
$$322$$ −4.72766e44 + 5.06095e44i −0.341382 + 0.365449i
$$323$$ 2.76574e45i 1.88871i
$$324$$ 1.31625e44 + 1.93064e45i 0.0850212 + 1.24707i
$$325$$ −1.63822e45 −1.00109
$$326$$ −1.13944e45 1.06440e45i −0.658834 0.615446i
$$327$$ 1.85538e45i 1.01525i
$$328$$ 2.39047e45 + 1.94612e45i 1.23809 + 1.00796i
$$329$$ 8.38908e44 0.411328
$$330$$ −6.95477e43 + 7.44507e43i −0.0322873 + 0.0345635i
$$331$$ 1.31519e45i 0.578210i 0.957297 + 0.289105i $$0.0933577\pi$$
−0.957297 + 0.289105i $$0.906642\pi$$
$$332$$ 6.56910e43 4.47861e42i 0.0273540 0.00186491i
$$333$$ −1.92651e45 −0.759934
$$334$$ 2.66488e45 + 2.48938e45i 0.995958 + 0.930369i
$$335$$ 1.31155e44i 0.0464492i
$$336$$ 2.08048e45 2.85006e44i 0.698324 0.0956638i
$$337$$ −4.63066e44 −0.147334 −0.0736672 0.997283i $$-0.523470\pi$$
−0.0736672 + 0.997283i $$0.523470\pi$$
$$338$$ 8.42610e43 9.02013e43i 0.0254171 0.0272090i
$$339$$ 2.11180e45i 0.604029i
$$340$$ 5.34436e43 + 7.83896e44i 0.0144969 + 0.212637i
$$341$$ −1.17898e45 −0.303338
$$342$$ −1.71078e45 1.59812e45i −0.417566 0.390067i
$$343$$ 4.15218e45i 0.961573i
$$344$$ 4.68262e45 5.75177e45i 1.02905 1.26401i
$$345$$ −6.63435e44 −0.138374
$$346$$ −5.90232e45 + 6.31842e45i −1.16857 + 1.25095i
$$347$$ 8.69234e45i 1.63383i −0.576760 0.816913i $$-0.695683\pi$$
0.576760 0.816913i $$-0.304317\pi$$
$$348$$ −4.26485e44 + 2.90764e43i −0.0761163 + 0.00518937i
$$349$$ 4.23539e45 0.717854 0.358927 0.933366i $$-0.383143\pi$$
0.358927 + 0.933366i $$0.383143\pi$$
$$350$$ −2.57314e45 2.40369e45i −0.414228 0.386949i
$$351$$ 4.11950e45i 0.629965i
$$352$$ −1.66615e45 1.17749e45i −0.242073 0.171077i
$$353$$ 2.46125e45 0.339790 0.169895 0.985462i $$-0.445657\pi$$
0.169895 + 0.985462i $$0.445657\pi$$
$$354$$ −2.43385e45 + 2.60543e45i −0.319326 + 0.341838i
$$355$$ 1.11597e45i 0.139169i
$$356$$ −1.83075e44 2.68530e45i −0.0217035 0.318341i
$$357$$ 1.02094e46 1.15073
$$358$$ −1.05354e46 9.84157e45i −1.12916 1.05480i
$$359$$ 4.62645e45i 0.471572i −0.971805 0.235786i $$-0.924234\pi$$
0.971805 0.235786i $$-0.0757664\pi$$
$$360$$ 5.15770e44 + 4.19898e44i 0.0500047 + 0.0407098i
$$361$$ −3.66881e45 −0.338373
$$362$$ 6.20113e45 6.63830e45i 0.544147 0.582509i
$$363$$ 1.33519e46i 1.11487i
$$364$$ 7.37371e45 5.02717e44i 0.585951 0.0399483i
$$365$$ −2.30968e45 −0.174695
$$366$$ −1.42787e45 1.33384e45i −0.102808 0.0960379i
$$367$$ 1.95361e46i 1.33921i 0.742718 + 0.669604i $$0.233536\pi$$
−0.742718 + 0.669604i $$0.766464\pi$$
$$368$$ −1.80317e45 1.31627e46i −0.117700 0.859182i
$$369$$ 1.26855e46 0.788559
$$370$$ 2.31580e45 2.47906e45i 0.137110 0.146776i
$$371$$ 3.24030e45i 0.182749i
$$372$$ 1.58337e45 + 2.32245e46i 0.0850765 + 1.24788i
$$373$$ −1.78396e46 −0.913325 −0.456662 0.889640i $$-0.650955\pi$$
−0.456662 + 0.889640i $$0.650955\pi$$
$$374$$ −7.24857e45 6.77121e45i −0.353642 0.330352i
$$375$$ 6.80469e45i 0.316407i
$$376$$ −1.01604e46 + 1.24802e46i −0.450327 + 0.553146i
$$377$$ −1.50454e45 −0.0635709
$$378$$ −6.04434e45 + 6.47046e45i −0.243499 + 0.260665i
$$379$$ 1.59965e46i 0.614496i 0.951629 + 0.307248i $$0.0994081\pi$$
−0.951629 + 0.307248i $$0.900592\pi$$
$$380$$ 4.11295e45 2.80408e44i 0.150678 0.0102727i
$$381$$ 1.19184e46 0.416456
$$382$$ 3.76473e46 + 3.51680e46i 1.25485 + 1.17221i
$$383$$ 2.43670e46i 0.774862i −0.921899 0.387431i $$-0.873362\pi$$
0.921899 0.387431i $$-0.126638\pi$$
$$384$$ −2.09576e46 + 3.44025e46i −0.635887 + 1.04383i
$$385$$ −7.70730e44 −0.0223156
$$386$$ 4.91817e45 5.26490e45i 0.135904 0.145485i
$$387$$ 3.05230e46i 0.805064i
$$388$$ −2.76384e45 4.05393e46i −0.0695893 1.02072i
$$389$$ −3.51428e46 −0.844780 −0.422390 0.906414i $$-0.638809\pi$$
−0.422390 + 0.906414i $$0.638809\pi$$
$$390$$ 5.17378e45 + 4.83306e45i 0.118753 + 0.110933i
$$391$$ 6.45924e46i 1.41579i
$$392$$ −2.47257e46 2.01296e46i −0.517605 0.421392i
$$393$$ −2.08158e46 −0.416224
$$394$$ 3.02596e46 3.23928e46i 0.578004 0.618753i
$$395$$ 1.29564e46i 0.236449i
$$396$$ −8.37684e45 + 5.71106e44i −0.146072 + 0.00995872i
$$397$$ 9.09787e45 0.151604 0.0758020 0.997123i $$-0.475848\pi$$
0.0758020 + 0.997123i $$0.475848\pi$$
$$398$$ 8.15987e46 + 7.62250e46i 1.29954 + 1.21395i
$$399$$ 5.35667e46i 0.815423i
$$400$$ 6.69233e46 9.16785e45i 0.973862 0.133410i
$$401$$ −2.80512e46 −0.390259 −0.195129 0.980778i $$-0.562513\pi$$
−0.195129 + 0.980778i $$0.562513\pi$$
$$402$$ 2.23168e46 2.38901e46i 0.296868 0.317797i
$$403$$ 8.19303e46i 1.04221i
$$404$$ −8.37905e45 1.22902e47i −0.101937 1.49518i
$$405$$ −1.40235e46 −0.163179
$$406$$ −2.36316e45 2.20753e45i −0.0263042 0.0245719i
$$407$$ 4.28277e46i 0.456064i
$$408$$ −1.23650e47 + 1.51882e47i −1.25983 + 1.54747i
$$409$$ 2.66506e46 0.259829 0.129914 0.991525i $$-0.458530\pi$$
0.129914 + 0.991525i $$0.458530\pi$$
$$410$$ −1.52489e46 + 1.63239e46i −0.142275 + 0.152305i
$$411$$ 1.16366e47i 1.03913i
$$412$$ −3.80451e46 + 2.59380e45i −0.325199 + 0.0221710i
$$413$$ −2.69720e46 −0.220705
$$414$$ −3.99544e46 3.73232e46i −0.313011 0.292397i
$$415$$ 4.77156e44i 0.00357927i
$$416$$ −8.18272e46 + 1.15785e47i −0.587784 + 0.831711i
$$417$$ 3.56537e46 0.245276
$$418$$ −3.55273e46 + 3.80319e46i −0.234093 + 0.250596i
$$419$$ 2.01039e46i 0.126890i 0.997985 + 0.0634450i $$0.0202087\pi$$
−0.997985 + 0.0634450i $$0.979791\pi$$
$$420$$ 1.03509e45 + 1.51825e46i 0.00625881 + 0.0918026i
$$421$$ 2.31091e47 1.33877 0.669384 0.742916i $$-0.266558\pi$$
0.669384 + 0.742916i $$0.266558\pi$$
$$422$$ −1.65997e47 1.55065e47i −0.921460 0.860777i
$$423$$ 6.62288e46i 0.352306i
$$424$$ −4.82049e46 3.92445e46i −0.245757 0.200075i
$$425$$ 3.28407e47 1.60477
$$426$$ 1.89890e47 2.03276e47i 0.889464 0.952170i
$$427$$ 1.47816e46i 0.0663773i
$$428$$ 2.77431e47 1.89144e46i 1.19445 0.0814337i
$$429$$ −8.93811e46 −0.368990
$$430$$ 3.92774e46 + 3.66907e46i 0.155493 + 0.145253i
$$431$$ 1.16679e47i 0.443000i 0.975160 + 0.221500i $$0.0710952\pi$$
−0.975160 + 0.221500i $$0.928905\pi$$
$$432$$ −2.30536e46 1.68286e47i −0.0839520 0.612831i
$$433$$ −2.80462e47 −0.979697 −0.489848 0.871808i $$-0.662948\pi$$
−0.489848 + 0.871808i $$0.662948\pi$$
$$434$$ −1.20212e47 + 1.28687e47i −0.402841 + 0.431241i
$$435$$ 3.09784e45i 0.00995983i
$$436$$ −1.83145e46 2.68632e47i −0.0564986 0.828707i
$$437$$ −3.38904e47 −1.00325
$$438$$ −4.20713e47 3.93006e47i −1.19523 1.11652i
$$439$$ 1.85002e47i 0.504447i −0.967669 0.252224i $$-0.918838\pi$$
0.967669 0.252224i $$-0.0811618\pi$$
$$440$$ 9.33461e45 1.14659e46i 0.0244314 0.0300096i
$$441$$ −1.31212e47 −0.329670
$$442$$ −4.70549e47 + 5.03722e47i −1.13502 + 1.21504i
$$443$$ 1.13148e47i 0.262048i −0.991379 0.131024i $$-0.958173\pi$$
0.991379 0.131024i $$-0.0418265\pi$$
$$444$$ 8.43655e47 5.75178e46i 1.87617 0.127911i
$$445$$ 1.95051e46 0.0416550
$$446$$ 5.78065e47 + 5.39996e47i 1.18563 + 1.10755i
$$447$$ 2.66213e47i 0.524438i
$$448$$ −2.98411e47 + 6.18014e46i −0.564691 + 0.116948i
$$449$$ 7.27545e47 1.32259 0.661295 0.750126i $$-0.270007\pi$$
0.661295 + 0.750126i $$0.270007\pi$$
$$450$$ 1.89763e47 2.03141e47i 0.331425 0.354790i
$$451$$ 2.82008e47i 0.473242i
$$452$$ 2.08456e46 + 3.05758e47i 0.0336142 + 0.493045i
$$453$$ −5.35690e46 −0.0830130
$$454$$ −5.53773e46 5.17304e46i −0.0824758 0.0770443i
$$455$$ 5.35600e46i 0.0766718i
$$456$$ 7.96896e47 + 6.48768e47i 1.09657 + 0.892734i
$$457$$ −7.18820e47 −0.950886 −0.475443 0.879747i $$-0.657712\pi$$
−0.475443 + 0.879747i $$0.657712\pi$$
$$458$$ −8.23927e47 + 8.82012e47i −1.04788 + 1.12175i
$$459$$ 8.25817e47i 1.00985i
$$460$$ 9.60558e46 6.54878e45i 0.112949 0.00770051i
$$461$$ −6.51911e47 −0.737176 −0.368588 0.929593i $$-0.620159\pi$$
−0.368588 + 0.929593i $$0.620159\pi$$
$$462$$ −1.40390e47 1.31145e47i −0.152679 0.142625i
$$463$$ 7.31141e47i 0.764792i 0.923999 + 0.382396i $$0.124901\pi$$
−0.923999 + 0.382396i $$0.875099\pi$$
$$464$$ 6.14619e46 8.41970e45i 0.0618419 0.00847174i
$$465$$ −1.68694e47 −0.163285
$$466$$ 3.94652e46 4.22474e46i 0.0367509 0.0393417i
$$467$$ 6.00670e47i 0.538185i 0.963114 + 0.269093i $$0.0867238\pi$$
−0.963114 + 0.269093i $$0.913276\pi$$
$$468$$ 3.96877e46 + 5.82129e47i 0.0342161 + 0.501873i
$$469$$ 2.47316e47 0.205183
$$470$$ −8.52240e46 7.96115e46i −0.0680456 0.0635645i
$$471$$ 1.63538e48i 1.25673i
$$472$$ 3.26668e47 4.01254e47i 0.241630 0.296799i
$$473$$ −6.78547e47 −0.483147
$$474$$ 2.20462e48 2.36004e48i 1.51120 1.61774i
$$475$$ 1.72309e48i 1.13716i
$$476$$ −1.47817e48 + 1.00777e47i −0.939291 + 0.0640379i
$$477$$ −2.55810e47 −0.156526
$$478$$ −5.66868e47 5.29537e47i −0.334026 0.312028i
$$479$$ 3.96347e47i 0.224924i 0.993656 + 0.112462i $$0.0358737\pi$$
−0.993656 + 0.112462i $$0.964126\pi$$
$$480$$ −2.38401e47 1.68482e47i −0.130307 0.0920898i
$$481$$ 2.97621e48 1.56694
$$482$$ −6.17931e47 + 6.61494e47i −0.313396 + 0.335490i
$$483$$ 1.25102e48i 0.611247i
$$484$$ −1.31797e47 1.93316e48i −0.0620424 0.910021i
$$485$$ 2.94463e47 0.133561
$$486$$ −1.52020e48 1.42009e48i −0.664427 0.620671i
$$487$$ 1.04806e48i 0.441434i −0.975338 0.220717i $$-0.929160\pi$$
0.975338 0.220717i $$-0.0708397\pi$$
$$488$$ 2.19901e47 + 1.79026e47i 0.0892629 + 0.0726706i
$$489$$ 2.81660e48 1.10196
$$490$$ 1.57726e47 1.68845e47i 0.0594803 0.0636736i
$$491$$ 1.85047e48i 0.672691i 0.941739 + 0.336346i $$0.109191\pi$$
−0.941739 + 0.336346i $$0.890809\pi$$
$$492$$ −5.55523e48 + 3.78738e47i −1.94684 + 0.132729i
$$493$$ 3.01607e47 0.101905
$$494$$ 2.64293e48 + 2.46888e48i 0.860996 + 0.804295i
$$495$$ 6.08464e46i 0.0191135i
$$496$$ −4.58499e47 3.34694e48i −0.138889 1.01386i
$$497$$ 2.10436e48 0.614760
$$498$$ −8.11911e46 + 8.69150e46i −0.0228760 + 0.0244887i
$$499$$ 2.93720e48i 0.798223i 0.916902 + 0.399112i $$0.130681\pi$$
−0.916902 + 0.399112i $$0.869319\pi$$
$$500$$ 6.71693e46 + 9.85222e47i 0.0176080 + 0.258270i
$$501$$ −6.58734e48 −1.66583
$$502$$ 4.67706e48 + 4.36905e48i 1.14105 + 1.06591i
$$503$$ 7.23105e48i 1.70207i 0.525108 + 0.851036i $$0.324025\pi$$
−0.525108 + 0.851036i $$0.675975\pi$$
$$504$$ −7.91792e47 + 9.72575e47i −0.179830 + 0.220889i
$$505$$ 8.92714e47 0.195645
$$506$$ −8.29720e47 + 8.88214e47i −0.175478 + 0.187849i
$$507$$ 2.22970e47i 0.0455095i
$$508$$ −1.72562e48 + 1.17647e47i −0.339937 + 0.0231758i
$$509$$ −1.96709e48 −0.374028 −0.187014 0.982357i $$-0.559881\pi$$
−0.187014 + 0.982357i $$0.559881\pi$$
$$510$$ −1.03716e48 9.68860e47i −0.190364 0.177827i
$$511$$ 4.35531e48i 0.771689i
$$512$$ 2.69477e48 5.18787e48i 0.460960 0.887421i
$$513$$ −4.33291e48 −0.715594
$$514$$ 5.05806e48 5.41465e48i 0.806581 0.863444i
$$515$$ 2.76346e47i 0.0425524i
$$516$$ 9.11291e47 + 1.33666e49i 0.135507 + 1.98758i
$$517$$ 1.47231e48 0.211432
$$518$$ 4.67470e48 + 4.36685e48i 0.648363 + 0.605665i
$$519$$ 1.56186e49i 2.09232i
$$520$$ −7.96796e47 6.48687e47i −0.103107 0.0839412i
$$521$$ −3.03075e48 −0.378854 −0.189427 0.981895i $$-0.560663\pi$$
−0.189427 + 0.981895i $$0.560663\pi$$
$$522$$ 1.74277e47 1.86563e47i 0.0210460 0.0225298i
$$523$$ 3.63953e48i 0.424634i 0.977201 + 0.212317i $$0.0681010\pi$$
−0.977201 + 0.212317i $$0.931899\pi$$
$$524$$ 3.01383e48 2.05473e47i 0.339747 0.0231629i
$$525$$ 6.36058e48 0.692834
$$526$$ −9.04770e48 8.45186e48i −0.952347 0.889629i
$$527$$ 1.64242e49i 1.67068i
$$528$$ 3.65132e48 5.00195e47i 0.358954 0.0491733i
$$529$$ 2.60959e48 0.247954
$$530$$ 3.07501e47 3.29179e47i 0.0282410 0.0302320i
$$531$$ 2.12934e48i 0.189036i
$$532$$ 5.28759e47 + 7.75570e48i 0.0453783 + 0.665597i
$$533$$ −1.95975e49 −1.62596
$$534$$ 3.55289e48 + 3.31891e48i 0.284996 + 0.266228i
$$535$$ 2.01516e48i 0.156294i
$$536$$ −2.99534e48 + 3.67924e48i −0.224636 + 0.275925i
$$537$$ 2.60425e49 1.88863
$$538$$ −6.13959e48 + 6.57242e48i −0.430585 + 0.460940i
$$539$$ 2.91693e48i 0.197847i
$$540$$ 1.22808e48 8.37266e46i 0.0805636 0.00549257i
$$541$$ −2.94812e49 −1.87066 −0.935330 0.353777i $$-0.884897\pi$$
−0.935330 + 0.353777i $$0.884897\pi$$
$$542$$ −7.60455e48 7.10375e48i −0.466752 0.436014i
$$543$$ 1.64093e49i 0.974300i
$$544$$ 1.64035e49 2.32109e49i 0.942230 1.33325i
$$545$$ 1.95125e48 0.108436
$$546$$ −9.11358e48 + 9.75607e48i −0.490029 + 0.524575i
$$547$$ 2.55941e49i 1.33158i 0.746138 + 0.665791i $$0.231906\pi$$
−0.746138 + 0.665791i $$0.768094\pi$$
$$548$$ −1.14865e48 1.68481e49i −0.0578279 0.848204i
$$549$$ 1.16695e48 0.0568528
$$550$$ −4.51595e48 4.21855e48i −0.212922 0.198900i
$$551$$ 1.58248e48i 0.0722118i
$$552$$ 1.86111e49 + 1.51516e49i 0.821993 + 0.669200i
$$553$$ 2.44316e49 1.04448
$$554$$ 1.44226e48 1.54394e48i 0.0596855 0.0638933i
$$555$$ 6.12801e48i 0.245497i
$$556$$ −5.16214e48 + 3.51938e47i −0.200209 + 0.0136496i
$$557$$ 3.13988e49 1.17901 0.589507 0.807763i $$-0.299322\pi$$
0.589507 + 0.807763i $$0.299322\pi$$
$$558$$ −1.01594e49 9.49033e48i −0.369362 0.345037i
$$559$$ 4.71540e49i 1.65999i
$$560$$ −2.99733e47 2.18799e48i −0.0102176 0.0745865i
$$561$$ 1.79178e49 0.591498
$$562$$ −3.41348e49 + 3.65413e49i −1.09130 + 1.16823i
$$563$$ 3.22007e49i 0.997043i −0.866877 0.498521i $$-0.833877\pi$$
0.866877 0.498521i $$-0.166123\pi$$
$$564$$ −1.97732e48 2.90028e49i −0.0592998 0.869793i
$$565$$ −2.22092e48 −0.0645150
$$566$$ −1.47057e49 1.37373e49i −0.413801 0.386550i
$$567$$ 2.64437e49i 0.720821i
$$568$$ −2.54868e49 + 3.13059e49i −0.673046 + 0.826717i
$$569$$ −1.36109e49 −0.348230 −0.174115 0.984725i $$-0.555706\pi$$
−0.174115 + 0.984725i $$0.555706\pi$$
$$570$$ −5.08343e48 + 5.44180e48i −0.126011 + 0.134895i
$$571$$ 1.02069e49i 0.245157i 0.992459 + 0.122579i $$0.0391164\pi$$
−0.992459 + 0.122579i $$0.960884\pi$$
$$572$$ 1.29411e49 8.82284e47i 0.301192 0.0205343i
$$573$$ −9.30607e49 −2.09886
$$574$$ −3.07816e49 2.87544e49i −0.672786 0.628479i
$$575$$ 4.02419e49i 0.852427i
$$576$$ −4.87900e48 2.35585e49i −0.100167 0.483663i
$$577$$ 9.74285e49 1.93875 0.969374 0.245589i $$-0.0789813\pi$$
0.969374 + 0.245589i $$0.0789813\pi$$
$$578$$ 5.89381e49 6.30931e49i 1.13683 1.21697i
$$579$$ 1.30144e49i 0.243337i
$$580$$ 3.05788e46 + 4.48522e47i 0.000554265 + 0.00812981i
$$581$$ −8.99762e47 −0.0158109
$$582$$ 5.36371e49 + 5.01048e49i 0.913801 + 0.853622i
$$583$$ 5.68683e48i 0.0939369i
$$584$$ 6.47926e49 + 5.27488e49i 1.03775 + 0.844854i
$$585$$ −4.22838e48 −0.0656702
$$586$$ 4.76266e49 5.09841e49i 0.717286 0.767853i
$$587$$ 1.32820e50i 1.93989i −0.243333 0.969943i $$-0.578241\pi$$
0.243333 0.969943i $$-0.421759\pi$$
$$588$$ 5.74601e49 3.91745e48i 0.813907 0.0554896i
$$589$$ −8.61745e49 −1.18387
$$590$$ 2.74006e48 + 2.55961e48i 0.0365110 + 0.0341065i
$$591$$ 8.00722e49i 1.03492i
$$592$$ −1.21581e50 + 1.66555e49i −1.52432 + 0.208817i
$$593$$ 1.05208e49 0.127957 0.0639785 0.997951i $$-0.479621\pi$$
0.0639785 + 0.997951i $$0.479621\pi$$
$$594$$ −1.06080e49 + 1.13559e49i −0.125164 + 0.133988i
$$595$$ 1.07369e49i 0.122906i
$$596$$ 2.62780e48 + 3.85438e49i 0.0291850 + 0.428077i
$$597$$ −2.01705e50 −2.17359
$$598$$ 6.17243e49 + 5.76595e49i 0.645409 + 0.602905i
$$599$$ 3.72920e49i 0.378384i 0.981940 + 0.189192i $$0.0605869\pi$$
−0.981940 + 0.189192i $$0.939413\pi$$
$$600$$ −7.70355e49 + 9.46244e49i −0.758523 + 0.931710i
$$601$$ 1.08974e50 1.04131 0.520656 0.853766i $$-0.325687\pi$$
0.520656 + 0.853766i $$0.325687\pi$$
$$602$$ −6.91868e49 + 7.40644e49i −0.641633 + 0.686867i
$$603$$ 1.95247e49i 0.175741i
$$604$$ 7.75603e48 5.28782e47i 0.0677602 0.00461967i
$$605$$ 1.40418e49 0.119076
$$606$$ 1.62610e50 + 1.51901e50i 1.33856 + 1.25041i
$$607$$ 3.62232e48i 0.0289461i 0.999895 + 0.0144730i $$0.00460707\pi$$
−0.999895 + 0.0144730i $$0.995393\pi$$
$$608$$ −1.21783e50 8.60662e49i −0.944763 0.667679i
$$609$$ 5.84152e48 0.0439961
$$610$$ −1.40276e48 + 1.50165e48i −0.0102576 + 0.0109807i
$$611$$ 1.02315e50i 0.726435i
$$612$$ −7.95601e48 1.16697e50i −0.0548491 0.804512i
$$613$$ 1.74376e50 1.16734 0.583672 0.811990i $$-0.301616\pi$$
0.583672 + 0.811990i $$0.301616\pi$$
$$614$$ 3.97277e49 + 3.71114e49i 0.258263 + 0.241255i
$$615$$ 4.03512e49i 0.254744i
$$616$$ 2.16210e49 + 1.76021e49i 0.132563 + 0.107922i
$$617$$ 7.05688e49 0.420223 0.210111 0.977677i $$-0.432617\pi$$
0.210111 + 0.977677i $$0.432617\pi$$
$$618$$ 4.70221e49 5.03370e49i 0.271963 0.291136i
$$619$$ 1.56606e50i 0.879786i 0.898050 + 0.439893i $$0.144984\pi$$
−0.898050 + 0.439893i $$0.855016\pi$$
$$620$$ 2.44245e49 1.66519e48i 0.133283 0.00908683i
$$621$$ −1.01193e50 −0.536415
$$622$$ −2.50399e50 2.33909e50i −1.28945 1.20454i
$$623$$ 3.67803e49i 0.184005i
$$624$$ −3.47599e49 2.53740e50i −0.168949 1.23329i
$$625$$ 2.00993e50 0.949163
$$626$$ 1.68277e50 1.80141e50i 0.772125 0.826559i
$$627$$ 9.40114e49i 0.419145i
$$628$$ −1.61429e49 2.36780e50i −0.0699373 1.02582i
$$629$$ −5.96627e50 −2.51184
$$630$$ −6.64147e48 6.20409e48i −0.0271728 0.0253833i
$$631$$ 1.59388e50i 0.633763i 0.948465 + 0.316881i $$0.102636\pi$$
−0.948465 + 0.316881i $$0.897364\pi$$
$$632$$ −2.95901e50 + 3.63461e50i −1.14351 + 1.40459i
$$633$$ 4.10330e50 1.54123
$$634$$ 1.80036e50 1.92729e50i 0.657285 0.703622i
$$635$$ 1.25343e49i 0.0444808i
$$636$$ 1.12024e50 7.63743e48i 0.386440 0.0263463i
$$637$$ 2.02705e50 0.679760
$$638$$ −4.14742e48 3.87429e48i −0.0135209 0.0126305i
$$639$$ 1.66132e50i 0.526547i
$$640$$ 3.61802e49 + 2.20405e49i 0.111489 + 0.0679176i
$$641$$ 3.35970e50 1.00660 0.503299 0.864112i $$-0.332119\pi$$
0.503299 + 0.864112i $$0.332119\pi$$
$$642$$ −3.42893e50 + 3.67066e50i −0.998913 + 1.06933i
$$643$$ 3.38009e50i 0.957481i 0.877956 + 0.478741i $$0.158907\pi$$
−0.877956 + 0.478741i $$0.841093\pi$$
$$644$$ 1.23489e49 + 1.81130e50i 0.0340159 + 0.498937i
$$645$$ −9.70901e49 −0.260076
$$646$$ −5.29817e50 4.94925e50i −1.38019 1.28930i
$$647$$ 3.22802e50i 0.817823i −0.912574 0.408912i $$-0.865908\pi$$
0.912574 0.408912i $$-0.134092\pi$$
$$648$$ 3.93395e50 + 3.20270e50i 0.969345 + 0.789162i
$$649$$ −4.73367e49 −0.113447
$$650$$ −2.93158e50 + 3.13825e50i −0.683379 + 0.731556i
$$651$$ 3.18103e50i 0.721290i
$$652$$ −4.07804e50 + 2.78028e49i −0.899486 + 0.0613241i
$$653$$ −6.22917e50 −1.33657 −0.668287 0.743904i $$-0.732972\pi$$
−0.668287 + 0.743904i $$0.732972\pi$$
$$654$$ 3.55424e50 + 3.32017e50i 0.741903 + 0.693044i
$$655$$ 2.18914e49i 0.0444559i
$$656$$ 8.00579e50 1.09672e50i 1.58174 0.216683i
$$657$$ 3.43836e50 0.660959
$$658$$ 1.50122e50 1.60705e50i 0.280787 0.300582i
$$659$$ 9.66238e50i 1.75852i 0.476345 + 0.879259i $$0.341961\pi$$
−0.476345 + 0.879259i $$0.658039\pi$$
$$660$$ 1.81662e48 + 2.66457e49i 0.00321717 + 0.0471885i
$$661$$ 1.46714e50 0.252839 0.126420 0.991977i $$-0.459651\pi$$
0.126420 + 0.991977i $$0.459651\pi$$
$$662$$ 2.51944e50 + 2.35352e50i 0.422532 + 0.394706i
$$663$$ 1.24516e51i 2.03226i
$$664$$ 1.08974e49 1.33855e49i 0.0173100 0.0212622i
$$665$$ −5.63347e49 −0.0870935
$$666$$ −3.44747e50 + 3.69051e50i −0.518758 + 0.555329i
$$667$$ 3.69579e49i 0.0541305i
$$668$$ 9.53753e50 6.50239e49i 1.35975 0.0927036i
$$669$$ −1.42893e51 −1.98308
$$670$$ −2.51246e49 2.34700e49i −0.0339432 0.0317078i
$$671$$ 2.59422e49i 0.0341194i
$$672$$ 3.17703e50 4.49548e50i 0.406794 0.575611i
$$673$$ −2.83286e50 −0.353146 −0.176573 0.984288i $$-0.556501\pi$$
−0.176573 + 0.984288i $$0.556501\pi$$
$$674$$ −8.28650e49 + 8.87068e49i −0.100576 + 0.107666i
$$675$$ 5.14495e50i 0.608013i
$$676$$ −2.20094e48 3.22828e49i −0.00253261 0.0371476i
$$677$$ 4.96112e49 0.0555883 0.0277941 0.999614i $$-0.491152\pi$$
0.0277941 + 0.999614i $$0.491152\pi$$
$$678$$ −4.04545e50 3.77903e50i −0.441400 0.412331i
$$679$$ 5.55262e50i 0.589987i
$$680$$ 1.59730e50 + 1.30039e50i 0.165282 + 0.134559i
$$681$$ 1.36888e50 0.137948
$$682$$ −2.10976e50 + 2.25850e50i −0.207069 + 0.221667i
$$683$$ 6.67091e50i 0.637694i −0.947806 0.318847i $$-0.896704\pi$$
0.947806 0.318847i $$-0.103296\pi$$
$$684$$ −6.12285e50 + 4.17437e49i −0.570090 + 0.0388670i
$$685$$ 1.22378e50 0.110988
$$686$$ 7.95409e50 + 7.43027e50i 0.702679 + 0.656403i
$$687$$ 2.18025e51i 1.87623i
$$688$$ −2.63884e50 1.92629e51i −0.221218 1.61484i
$$689$$ 3.95193e50 0.322747
$$690$$ −1.18721e50 + 1.27090e50i −0.0944589 + 0.101118i
$$691$$ 1.46173e51i 1.13308i 0.824034 + 0.566541i $$0.191719\pi$$
−0.824034 + 0.566541i $$0.808281\pi$$
$$692$$ 1.54172e50 + 2.26135e51i 0.116438 + 1.70788i
$$693$$ 1.14737e50 0.0844313
$$694$$ −1.66514e51 1.55548e51i −1.19393 1.11531i
$$695$$ 3.74960e49i 0.0261974i
$$696$$ −7.07489e49 + 8.69025e49i −0.0481674 + 0.0591651i
$$697$$ 3.92862e51 2.60645
$$698$$ 7.57918e50 8.11350e50i 0.490032 0.524579i
$$699$$ 1.04432e50i 0.0658027i
$$700$$ −9.20921e50 + 6.27855e49i −0.565533 + 0.0385562i
$$701$$ −1.22498e51 −0.733172 −0.366586 0.930384i $$-0.619473\pi$$
−0.366586 + 0.930384i $$0.619473\pi$$
$$702$$ 7.89149e50 + 7.37179e50i 0.460353 + 0.430036i
$$703$$ 3.13039e51i 1.77993i
$$704$$ −5.23721e50 + 1.08463e50i −0.290263 + 0.0601140i
$$705$$ 2.10666e50 0.113813
$$706$$ 4.40437e50 4.71487e50i 0.231953 0.248305i
$$707$$ 1.68337e51i 0.864232i
$$708$$ 6.35733e49 + 9.32476e50i 0.0318182 + 0.466702i
$$709$$ −1.49159e51 −0.727811 −0.363905 0.931436i $$-0.618557\pi$$
−0.363905 + 0.931436i $$0.618557\pi$$
$$710$$ −2.13780e50 1.99702e50i −0.101699 0.0950017i
$$711$$ 1.92879e51i 0.894606i
$$712$$ −5.47169e50 4.45460e50i −0.247447 0.201451i
$$713$$ −2.01256e51 −0.887437
$$714$$ 1.82696e51 1.95575e51i 0.785526 0.840904i
$$715$$ 9.39996e49i 0.0394110i
$$716$$ −3.77059e51 + 2.57067e50i −1.54161 + 0.105102i
$$717$$ 1.40125e51 0.558689
$$718$$ −8.86262e50 8.27897e50i −0.344605 0.321911i
$$719$$ 2.75711e51i 1.04553i 0.852478 + 0.522763i $$0.175099\pi$$
−0.852478 + 0.522763i $$0.824901\pi$$
$$720$$ 1.72734e50 2.36629e49i 0.0638840 0.00875150i
$$721$$ 5.21100e50 0.187969
$$722$$ −6.56528e50 + 7.02812e50i −0.230985 + 0.247269i
$$723$$ 1.63515e51i 0.561138i
$$724$$ −1.61977e50 2.37583e51i −0.0542198 0.795282i
$$725$$ 1.87905e50 0.0613556
$$726$$ 2.55774e51 + 2.38930e51i 0.814700 + 0.761047i
$$727$$ 2.75423e51i 0.855817i −0.903822 0.427908i $$-0.859251\pi$$
0.903822 0.427908i $$-0.140749\pi$$
$$728$$ 1.22321e51 1.50250e51i 0.370798 0.455459i
$$729$$ −4.68820e50 −0.138647
$$730$$ −4.13314e50 + 4.42452e50i −0.119253 + 0.127660i
$$731$$ 9.45275e51i 2.66100i
$$732$$ −5.11030e50 + 3.48404e49i −0.140361 + 0.00956939i
$$733$$ 6.09851e51 1.63438 0.817188 0.576371i $$-0.195532\pi$$
0.817188 + 0.576371i $$0.195532\pi$$
$$734$$ 3.74241e51 + 3.49595e51i 0.978639 + 0.914190i
$$735$$ 4.17370e50i 0.106500i
$$736$$ −2.84418e51 2.01003e51i −0.708201 0.500497i
$$737$$ 4.34047e50 0.105468
$$738$$ 2.27006e51 2.43010e51i 0.538298 0.576247i
$$739$$ 5.69250e50i 0.131736i −0.997828 0.0658678i $$-0.979018\pi$$
0.997828 0.0658678i $$-0.0209816\pi$$
$$740$$ −6.04898e49 8.87249e50i −0.0136619 0.200389i
$$741$$ −6.53310e51 −1.44010
$$742$$ 6.20725e50 + 5.79847e50i 0.133545 + 0.124751i
$$743$$ 3.72054e51i 0.781282i −0.920543 0.390641i $$-0.872253\pi$$
0.920543 0.390641i $$-0.127747\pi$$
$$744$$ 4.73232e51 + 3.85267e51i 0.969976 + 0.789676i
$$745$$ −2.79969e50 −0.0560140
$$746$$ −3.19237e51 + 3.41742e51i −0.623468 + 0.667421i
$$747$$ 7.10330e49i 0.0135422i
$$748$$ −2.59424e51 + 1.76867e50i −0.482816 + 0.0329169i
$$749$$ −3.79994e51 −0.690406
$$750$$ −1.30354e51 1.21769e51i −0.231217 0.215990i
$$751$$ 7.88181e51i 1.36492i 0.730923 + 0.682460i $$0.239090\pi$$
−0.730923 + 0.682460i $$0.760910\pi$$
$$752$$ 5.72575e50 + 4.17967e51i 0.0968080 + 0.706677i
$$753$$ −1.15613e52