Properties

Label 21.33.h.b.2.14
Level $21$
Weight $33$
Character 21.2
Analytic conductor $136.220$
Analytic rank $0$
Dimension $164$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 33 \)
Character orbit: \([\chi]\) \(=\) 21.h (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(136.219975799\)
Analytic rank: \(0\)
Dimension: \(164\)
Relative dimension: \(82\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 2.14
Character \(\chi\) \(=\) 21.2
Dual form 21.33.h.b.11.14

$q$-expansion

\(f(q)\) \(=\) \(q+(-81147.0 - 46850.3i) q^{2} +(2.92478e7 + 3.15846e7i) q^{3} +(2.24241e9 + 3.88397e9i) q^{4} +(1.46995e10 + 8.48674e9i) q^{5} +(-8.93631e11 - 3.93326e12i) q^{6} +(5.53322e12 - 3.27691e13i) q^{7} -1.77891e13i q^{8} +(-1.42148e14 + 1.84756e15i) q^{9} +O(q^{10})\) \(q+(-81147.0 - 46850.3i) q^{2} +(2.92478e7 + 3.15846e7i) q^{3} +(2.24241e9 + 3.88397e9i) q^{4} +(1.46995e10 + 8.48674e9i) q^{5} +(-8.93631e11 - 3.93326e12i) q^{6} +(5.53322e12 - 3.27691e13i) q^{7} -1.77891e13i q^{8} +(-1.42148e14 + 1.84756e15i) q^{9} +(-7.95212e14 - 1.37735e15i) q^{10} +(3.46655e16 - 2.00141e16i) q^{11} +(-5.70877e16 + 1.84423e17i) q^{12} +7.68983e17 q^{13} +(-1.98424e18 + 2.39988e18i) q^{14} +(1.61878e17 + 7.12495e17i) q^{15} +(8.79765e18 - 1.52380e19i) q^{16} +(-5.61030e19 + 3.23911e19i) q^{17} +(9.80935e19 - 1.43264e20i) q^{18} +(-9.39650e19 + 1.62752e20i) q^{19} +7.61230e19i q^{20} +(1.19683e21 - 7.83660e20i) q^{21} -3.75066e21 q^{22} +(-5.77728e21 - 3.33551e21i) q^{23} +(5.61859e20 - 5.20291e20i) q^{24} +(-1.14975e22 - 1.99142e22i) q^{25} +(-6.24006e22 - 3.60270e22i) q^{26} +(-6.25119e22 + 4.95475e22i) q^{27} +(1.39682e23 - 5.19908e22i) q^{28} -2.09025e23i q^{29} +(2.02447e22 - 6.54009e22i) q^{30} +(4.76006e23 + 8.24466e23i) q^{31} +(-1.49397e24 + 8.62546e23i) q^{32} +(1.64603e24 + 5.09523e23i) q^{33} +6.07013e24 q^{34} +(3.59438e23 - 4.34729e23i) q^{35} +(-7.49461e24 + 3.59089e24i) q^{36} +(-1.05619e25 + 1.82938e25i) q^{37} +(1.52500e25 - 8.80457e24i) q^{38} +(2.24911e25 + 2.42880e25i) q^{39} +(1.50971e23 - 2.61490e23i) q^{40} +5.73927e25i q^{41} +(-1.33834e26 + 7.51983e24i) q^{42} +2.04424e26 q^{43} +(1.55468e26 + 8.97596e25i) q^{44} +(-1.77693e25 + 2.59518e25i) q^{45} +(3.12539e26 + 5.41334e26i) q^{46} +(-9.38645e26 - 5.41927e26i) q^{47} +(7.38597e26 - 1.67808e26i) q^{48} +(-1.04319e27 - 3.62637e26i) q^{49} +2.15464e27i q^{50} +(-2.66395e27 - 8.24619e26i) q^{51} +(1.72437e27 + 2.98670e27i) q^{52} +(4.08500e27 - 2.35848e27i) q^{53} +(7.39396e27 - 1.09193e27i) q^{54} +6.79418e26 q^{55} +(-5.82931e26 - 9.84308e25i) q^{56} +(-7.88873e27 + 1.79231e27i) q^{57} +(-9.79287e27 + 1.69618e28i) q^{58} +(-2.39983e28 + 1.38554e28i) q^{59} +(-2.40431e27 + 2.22643e27i) q^{60} +(1.45150e28 - 2.51406e28i) q^{61} -8.92040e28i q^{62} +(5.97563e28 + 1.48810e28i) q^{63} +8.60708e28 q^{64} +(1.13036e28 + 6.52616e27i) q^{65} +(-1.09699e29 - 1.18463e29i) q^{66} +(9.49210e28 + 1.64408e29i) q^{67} +(-2.51612e29 - 1.45268e29i) q^{68} +(-6.36222e28 - 2.80029e29i) q^{69} +(-4.95345e28 + 1.84372e28i) q^{70} +3.98539e28i q^{71} +(3.28663e28 + 2.52868e27i) q^{72} +(1.07588e29 + 1.86348e29i) q^{73} +(1.71414e30 - 9.89660e29i) q^{74} +(2.92705e29 - 9.45591e29i) q^{75} -8.42832e29 q^{76} +(-4.64032e29 - 1.24670e30i) q^{77} +(-6.87186e29 - 3.02461e30i) q^{78} +(8.54185e27 - 1.47949e28i) q^{79} +(2.58642e29 - 1.49327e29i) q^{80} +(-3.39327e30 - 5.25253e29i) q^{81} +(2.68886e30 - 4.65725e30i) q^{82} -9.34369e30i q^{83} +(5.72749e30 + 2.89116e30i) q^{84} -1.09958e30 q^{85} +(-1.65884e31 - 9.57732e30i) q^{86} +(6.60196e30 - 6.11353e30i) q^{87} +(-3.56032e29 - 6.16666e29i) q^{88} +(8.59311e30 + 4.96124e30i) q^{89} +(2.65777e30 - 1.27342e30i) q^{90} +(4.25495e30 - 2.51988e31i) q^{91} -2.99183e31i q^{92} +(-1.21183e31 + 3.91483e31i) q^{93} +(5.07788e31 + 8.79515e31i) q^{94} +(-2.76247e30 + 1.59491e30i) q^{95} +(-7.09386e31 - 2.19589e31i) q^{96} -3.16826e31 q^{97} +(6.76625e31 + 7.83008e31i) q^{98} +(3.20496e31 + 6.68915e31i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 164q + 43046720q^{3} + 176093659134q^{4} + 3915256954876q^{6} - 41868332499126q^{7} + 1232720974221986q^{9} + O(q^{10}) \) \( 164q + 43046720q^{3} + 176093659134q^{4} + 3915256954876q^{6} - 41868332499126q^{7} + 1232720974221986q^{9} - 653609167486978q^{10} - 80283770812252892q^{12} + 930128021838524592q^{13} + 295985739739384604q^{15} - \)\(35\!\cdots\!98\)\(q^{16} - \)\(28\!\cdots\!84\)\(q^{18} - \)\(55\!\cdots\!32\)\(q^{19} - \)\(63\!\cdots\!60\)\(q^{21} - \)\(13\!\cdots\!96\)\(q^{22} + \)\(10\!\cdots\!46\)\(q^{24} + \)\(37\!\cdots\!44\)\(q^{25} - \)\(46\!\cdots\!76\)\(q^{27} + \)\(47\!\cdots\!58\)\(q^{28} - \)\(33\!\cdots\!80\)\(q^{30} + \)\(52\!\cdots\!26\)\(q^{31} - \)\(73\!\cdots\!26\)\(q^{33} - \)\(22\!\cdots\!96\)\(q^{34} - \)\(58\!\cdots\!40\)\(q^{36} - \)\(47\!\cdots\!40\)\(q^{37} + \)\(80\!\cdots\!20\)\(q^{39} - \)\(45\!\cdots\!26\)\(q^{40} + \)\(10\!\cdots\!78\)\(q^{42} - \)\(82\!\cdots\!28\)\(q^{43} + \)\(88\!\cdots\!80\)\(q^{45} + \)\(30\!\cdots\!92\)\(q^{46} - \)\(10\!\cdots\!00\)\(q^{48} + \)\(42\!\cdots\!90\)\(q^{49} + \)\(89\!\cdots\!16\)\(q^{51} + \)\(39\!\cdots\!84\)\(q^{52} + \)\(16\!\cdots\!78\)\(q^{54} + \)\(55\!\cdots\!00\)\(q^{55} - \)\(88\!\cdots\!80\)\(q^{57} + \)\(63\!\cdots\!34\)\(q^{58} + \)\(69\!\cdots\!10\)\(q^{60} - \)\(49\!\cdots\!48\)\(q^{61} + \)\(38\!\cdots\!20\)\(q^{63} - \)\(17\!\cdots\!24\)\(q^{64} + \)\(20\!\cdots\!84\)\(q^{66} + \)\(41\!\cdots\!36\)\(q^{67} - \)\(54\!\cdots\!68\)\(q^{69} - \)\(18\!\cdots\!50\)\(q^{70} + \)\(88\!\cdots\!12\)\(q^{72} + \)\(14\!\cdots\!40\)\(q^{73} - \)\(13\!\cdots\!24\)\(q^{75} - \)\(13\!\cdots\!12\)\(q^{76} - \)\(15\!\cdots\!20\)\(q^{78} + \)\(11\!\cdots\!98\)\(q^{79} + \)\(41\!\cdots\!98\)\(q^{81} - \)\(17\!\cdots\!72\)\(q^{82} + \)\(23\!\cdots\!36\)\(q^{84} - \)\(11\!\cdots\!64\)\(q^{85} + \)\(25\!\cdots\!98\)\(q^{87} - \)\(10\!\cdots\!90\)\(q^{88} - \)\(13\!\cdots\!64\)\(q^{90} + \)\(33\!\cdots\!84\)\(q^{91} - \)\(88\!\cdots\!00\)\(q^{93} - \)\(96\!\cdots\!24\)\(q^{94} + \)\(14\!\cdots\!10\)\(q^{96} - \)\(26\!\cdots\!24\)\(q^{97} - \)\(24\!\cdots\!32\)\(q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −81147.0 46850.3i −1.23821 0.714878i −0.269478 0.963007i \(-0.586851\pi\)
−0.968727 + 0.248128i \(0.920185\pi\)
\(3\) 2.92478e7 + 3.15846e7i 0.679444 + 0.733727i
\(4\) 2.24241e9 + 3.88397e9i 0.522101 + 0.904306i
\(5\) 1.46995e10 + 8.48674e9i 0.0963345 + 0.0556187i 0.547393 0.836876i \(-0.315620\pi\)
−0.451059 + 0.892494i \(0.648954\pi\)
\(6\) −8.93631e11 3.93326e12i −0.316766 1.39422i
\(7\) 5.53322e12 3.27691e13i 0.166498 0.986042i
\(8\) 1.77891e13i 0.0631994i
\(9\) −1.42148e14 + 1.84756e15i −0.0767114 + 0.997053i
\(10\) −7.95212e14 1.37735e15i −0.0795212 0.137735i
\(11\) 3.46655e16 2.00141e16i 0.754421 0.435565i −0.0728679 0.997342i \(-0.523215\pi\)
0.827289 + 0.561776i \(0.189882\pi\)
\(12\) −5.70877e16 + 1.84423e17i −0.308775 + 0.997506i
\(13\) 7.68983e17 1.15564 0.577820 0.816164i \(-0.303903\pi\)
0.577820 + 0.816164i \(0.303903\pi\)
\(14\) −1.98424e18 + 2.39988e18i −0.911059 + 1.10190i
\(15\) 1.61878e17 + 7.12495e17i 0.0246449 + 0.108473i
\(16\) 8.79765e18 1.52380e19i 0.476922 0.826052i
\(17\) −5.61030e19 + 3.23911e19i −1.15293 + 0.665645i −0.949600 0.313464i \(-0.898510\pi\)
−0.203332 + 0.979110i \(0.565177\pi\)
\(18\) 9.80935e19 1.43264e20i 0.807756 1.17972i
\(19\) −9.39650e19 + 1.62752e20i −0.325768 + 0.564247i −0.981668 0.190601i \(-0.938956\pi\)
0.655899 + 0.754848i \(0.272290\pi\)
\(20\) 7.61230e19i 0.116154i
\(21\) 1.19683e21 7.83660e20i 0.836612 0.547796i
\(22\) −3.75066e21 −1.24550
\(23\) −5.77728e21 3.33551e21i −0.942058 0.543898i −0.0514534 0.998675i \(-0.516385\pi\)
−0.890605 + 0.454778i \(0.849719\pi\)
\(24\) 5.61859e20 5.20291e20i 0.0463711 0.0429405i
\(25\) −1.14975e22 1.99142e22i −0.493813 0.855309i
\(26\) −6.24006e22 3.60270e22i −1.43092 0.826142i
\(27\) −6.25119e22 + 4.95475e22i −0.783686 + 0.621157i
\(28\) 1.39682e23 5.19908e22i 0.978613 0.364249i
\(29\) 2.09025e23i 0.835277i −0.908613 0.417638i \(-0.862858\pi\)
0.908613 0.417638i \(-0.137142\pi\)
\(30\) 2.02447e22 6.54009e22i 0.0470295 0.151930i
\(31\) 4.76006e23 + 8.24466e23i 0.654373 + 1.13341i 0.982051 + 0.188617i \(0.0604005\pi\)
−0.327678 + 0.944789i \(0.606266\pi\)
\(32\) −1.49397e24 + 8.62546e23i −1.23579 + 0.713481i
\(33\) 1.64603e24 + 5.09523e23i 0.832173 + 0.257597i
\(34\) 6.07013e24 1.90342
\(35\) 3.59438e23 4.34729e23i 0.0708819 0.0857294i
\(36\) −7.49461e24 + 3.59089e24i −0.941693 + 0.451192i
\(37\) −1.05619e25 + 1.82938e25i −0.856084 + 1.48278i 0.0195512 + 0.999809i \(0.493776\pi\)
−0.875635 + 0.482973i \(0.839557\pi\)
\(38\) 1.52500e25 8.80457e24i 0.806736 0.465769i
\(39\) 2.24911e25 + 2.42880e25i 0.785193 + 0.847925i
\(40\) 1.50971e23 2.61490e23i 0.00351507 0.00608828i
\(41\) 5.73927e25i 0.900151i 0.892991 + 0.450075i \(0.148603\pi\)
−0.892991 + 0.450075i \(0.851397\pi\)
\(42\) −1.33834e26 + 7.51983e24i −1.42750 + 0.0802084i
\(43\) 2.04424e26 1.49636 0.748181 0.663494i \(-0.230927\pi\)
0.748181 + 0.663494i \(0.230927\pi\)
\(44\) 1.55468e26 + 8.97596e25i 0.787769 + 0.454819i
\(45\) −1.77693e25 + 2.59518e25i −0.0628448 + 0.0917840i
\(46\) 3.12539e26 + 5.41334e26i 0.777641 + 1.34691i
\(47\) −9.38645e26 5.41927e26i −1.65552 0.955817i −0.974743 0.223330i \(-0.928307\pi\)
−0.680781 0.732487i \(-0.738359\pi\)
\(48\) 7.38597e26 1.67808e26i 0.930139 0.211326i
\(49\) −1.04319e27 3.62637e26i −0.944557 0.328348i
\(50\) 2.15464e27i 1.41206i
\(51\) −2.66395e27 8.24619e26i −1.27175 0.393669i
\(52\) 1.72437e27 + 2.98670e27i 0.603362 + 1.04505i
\(53\) 4.08500e27 2.35848e27i 1.05385 0.608440i 0.130125 0.991498i \(-0.458462\pi\)
0.923725 + 0.383057i \(0.125129\pi\)
\(54\) 7.39396e27 1.09193e27i 1.41442 0.208879i
\(55\) 6.79418e26 0.0969024
\(56\) −5.82931e26 9.84308e25i −0.0623173 0.0105226i
\(57\) −7.88873e27 + 1.79231e27i −0.635345 + 0.144349i
\(58\) −9.79287e27 + 1.69618e28i −0.597121 + 1.03424i
\(59\) −2.39983e28 + 1.38554e28i −1.11314 + 0.642670i −0.939640 0.342164i \(-0.888840\pi\)
−0.173497 + 0.984834i \(0.555507\pi\)
\(60\) −2.40431e27 + 2.22643e27i −0.0852257 + 0.0789205i
\(61\) 1.45150e28 2.51406e28i 0.394947 0.684068i −0.598148 0.801386i \(-0.704096\pi\)
0.993094 + 0.117318i \(0.0374298\pi\)
\(62\) 8.92040e28i 1.87119i
\(63\) 5.97563e28 + 1.48810e28i 0.970364 + 0.241648i
\(64\) 8.60708e28 1.08637
\(65\) 1.13036e28 + 6.52616e27i 0.111328 + 0.0642753i
\(66\) −1.09699e29 1.18463e29i −0.846251 0.913861i
\(67\) 9.49210e28 + 1.64408e29i 0.575659 + 0.997071i 0.995970 + 0.0896908i \(0.0285879\pi\)
−0.420310 + 0.907380i \(0.638079\pi\)
\(68\) −2.51612e29 1.45268e29i −1.20389 0.695069i
\(69\) −6.36222e28 2.80029e29i −0.241003 1.06076i
\(70\) −4.95345e28 + 1.84372e28i −0.149052 + 0.0554787i
\(71\) 3.98539e28i 0.0955735i 0.998858 + 0.0477867i \(0.0152168\pi\)
−0.998858 + 0.0477867i \(0.984783\pi\)
\(72\) 3.28663e28 + 2.52868e27i 0.0630132 + 0.00484812i
\(73\) 1.07588e29 + 1.86348e29i 0.165424 + 0.286522i 0.936806 0.349850i \(-0.113767\pi\)
−0.771382 + 0.636373i \(0.780434\pi\)
\(74\) 1.71414e30 9.89660e29i 2.12002 1.22399i
\(75\) 2.92705e29 9.45591e29i 0.292045 0.943459i
\(76\) −8.42832e29 −0.680336
\(77\) −4.64032e29 1.24670e30i −0.303876 0.816412i
\(78\) −6.87186e29 3.02461e30i −0.366067 1.61122i
\(79\) 8.54185e27 1.47949e28i 0.00371123 0.00642805i −0.864164 0.503211i \(-0.832152\pi\)
0.867875 + 0.496783i \(0.165485\pi\)
\(80\) 2.58642e29 1.49327e29i 0.0918880 0.0530515i
\(81\) −3.39327e30 5.25253e29i −0.988231 0.152971i
\(82\) 2.68886e30 4.65725e30i 0.643498 1.11457i
\(83\) 9.34369e30i 1.84191i −0.389665 0.920957i \(-0.627409\pi\)
0.389665 0.920957i \(-0.372591\pi\)
\(84\) 5.72749e30 + 2.89116e30i 0.932172 + 0.470548i
\(85\) −1.09958e30 −0.148089
\(86\) −1.65884e31 9.57732e30i −1.85280 1.06972i
\(87\) 6.60196e30 6.11353e30i 0.612865 0.567524i
\(88\) −3.56032e29 6.16666e29i −0.0275275 0.0476790i
\(89\) 8.59311e30 + 4.96124e30i 0.554511 + 0.320147i 0.750940 0.660371i \(-0.229601\pi\)
−0.196428 + 0.980518i \(0.562934\pi\)
\(90\) 2.65777e30 1.27342e30i 0.143429 0.0687211i
\(91\) 4.25495e30 2.51988e31i 0.192412 1.13951i
\(92\) 2.99183e31i 1.13588i
\(93\) −1.21183e31 + 3.91483e31i −0.387002 + 1.25022i
\(94\) 5.07788e31 + 8.79515e31i 1.36659 + 2.36700i
\(95\) −2.76247e30 + 1.59491e30i −0.0627654 + 0.0362376i
\(96\) −7.09386e31 2.19589e31i −1.36315 0.421959i
\(97\) −3.16826e31 −0.515790 −0.257895 0.966173i \(-0.583029\pi\)
−0.257895 + 0.966173i \(0.583029\pi\)
\(98\) 6.76625e31 + 7.83008e31i 0.934826 + 1.08181i
\(99\) 3.20496e31 + 6.68915e31i 0.376409 + 0.785611i
\(100\) 5.15641e31 8.93117e31i 0.515641 0.893117i
\(101\) −9.46056e31 + 5.46206e31i −0.806817 + 0.465816i −0.845849 0.533422i \(-0.820906\pi\)
0.0390325 + 0.999238i \(0.487572\pi\)
\(102\) 1.77538e32 + 1.91722e32i 1.29327 + 1.39659i
\(103\) 8.94112e31 1.54865e32i 0.557181 0.965066i −0.440549 0.897729i \(-0.645216\pi\)
0.997730 0.0673378i \(-0.0214505\pi\)
\(104\) 1.36795e31i 0.0730358i
\(105\) 2.42435e31 1.36219e30i 0.111062 0.00624035i
\(106\) −4.41981e32 −1.73984
\(107\) 1.05494e32 + 6.09070e31i 0.357345 + 0.206313i 0.667915 0.744237i \(-0.267187\pi\)
−0.310571 + 0.950550i \(0.600520\pi\)
\(108\) −3.32618e32 1.31688e32i −0.970880 0.384386i
\(109\) −8.73960e31 1.51374e32i −0.220124 0.381266i 0.734721 0.678369i \(-0.237313\pi\)
−0.954845 + 0.297103i \(0.903980\pi\)
\(110\) −5.51328e31 3.18309e31i −0.119985 0.0692734i
\(111\) −8.86717e32 + 2.01461e32i −1.66962 + 0.379335i
\(112\) −4.50655e32 3.72606e32i −0.735116 0.607801i
\(113\) 8.13421e32i 1.15096i 0.817816 + 0.575480i \(0.195185\pi\)
−0.817816 + 0.575480i \(0.804815\pi\)
\(114\) 7.24117e32 + 2.24149e32i 0.889879 + 0.275460i
\(115\) −5.66153e31 9.80605e31i −0.0605018 0.104792i
\(116\) 8.11846e32 4.68719e32i 0.755346 0.436099i
\(117\) −1.09309e32 + 1.42074e33i −0.0886509 + 1.15224i
\(118\) 2.59652e33 1.83772
\(119\) 7.50995e32 + 2.01767e33i 0.464393 + 1.24767i
\(120\) 1.26746e31 2.87965e30i 0.00685543 0.00155754i
\(121\) −2.54560e32 + 4.40910e32i −0.120566 + 0.208826i
\(122\) −2.35569e33 + 1.36006e33i −0.978050 + 0.564677i
\(123\) −1.81272e33 + 1.67861e33i −0.660465 + 0.611602i
\(124\) −2.13480e33 + 3.69758e33i −0.683298 + 1.18351i
\(125\) 7.85500e32i 0.221098i
\(126\) −4.15186e33 4.00715e33i −1.02876 0.992902i
\(127\) 1.37273e33 0.299728 0.149864 0.988707i \(-0.452116\pi\)
0.149864 + 0.988707i \(0.452116\pi\)
\(128\) −5.67818e32 3.27830e32i −0.109358 0.0631377i
\(129\) 5.97896e33 + 6.45664e33i 1.01669 + 1.09792i
\(130\) −6.11504e32 1.05916e33i −0.0918980 0.159172i
\(131\) −6.52544e33 3.76747e33i −0.867500 0.500851i −0.000983206 1.00000i \(-0.500313\pi\)
−0.866517 + 0.499148i \(0.833646\pi\)
\(132\) 1.71209e33 + 7.53567e33i 0.201532 + 0.887031i
\(133\) 4.81331e33 + 3.97969e33i 0.502131 + 0.415167i
\(134\) 1.77883e34i 1.64611i
\(135\) −1.33939e33 + 1.97799e32i −0.110044 + 0.0162512i
\(136\) 5.76207e32 + 9.98020e32i 0.0420684 + 0.0728646i
\(137\) −5.96159e33 + 3.44192e33i −0.387109 + 0.223497i −0.680907 0.732370i \(-0.738414\pi\)
0.293798 + 0.955868i \(0.405081\pi\)
\(138\) −7.95669e33 + 2.57043e34i −0.459904 + 1.48573i
\(139\) −4.19805e33 −0.216178 −0.108089 0.994141i \(-0.534473\pi\)
−0.108089 + 0.994141i \(0.534473\pi\)
\(140\) 2.49448e33 + 4.21205e32i 0.114533 + 0.0193395i
\(141\) −1.03368e34 4.54969e34i −0.423527 1.86413i
\(142\) 1.86717e33 3.23403e33i 0.0683234 0.118340i
\(143\) 2.66571e34 1.53905e34i 0.871840 0.503357i
\(144\) 2.69025e34 + 1.84202e34i 0.787033 + 0.538884i
\(145\) 1.77394e33 3.07256e33i 0.0464570 0.0804659i
\(146\) 2.01621e34i 0.473031i
\(147\) −1.90575e34 4.35552e34i −0.400855 0.916141i
\(148\) −9.47368e34 −1.78785
\(149\) −5.14207e34 2.96877e34i −0.871279 0.503033i −0.00350619 0.999994i \(-0.501116\pi\)
−0.867773 + 0.496960i \(0.834449\pi\)
\(150\) −6.80533e34 + 6.30186e34i −1.03607 + 0.959419i
\(151\) 1.23757e34 + 2.14354e34i 0.169410 + 0.293427i 0.938213 0.346059i \(-0.112480\pi\)
−0.768802 + 0.639486i \(0.779147\pi\)
\(152\) 2.89521e33 + 1.67155e33i 0.0356601 + 0.0205884i
\(153\) −5.18696e34 1.08258e35i −0.575241 1.20060i
\(154\) −2.07533e34 + 1.22906e35i −0.207374 + 1.22812i
\(155\) 1.61590e34i 0.145581i
\(156\) −4.38995e34 + 1.41818e35i −0.356833 + 1.15276i
\(157\) 6.62985e34 + 1.14832e35i 0.486529 + 0.842693i 0.999880 0.0154854i \(-0.00492936\pi\)
−0.513351 + 0.858179i \(0.671596\pi\)
\(158\) −1.38629e33 + 8.00375e32i −0.00919054 + 0.00530616i
\(159\) 1.93969e35 + 6.00426e34i 1.16246 + 0.359837i
\(160\) −2.92808e34 −0.158732
\(161\) −1.41269e35 + 1.70860e35i −0.693157 + 0.838351i
\(162\) 2.50746e35 + 2.01598e35i 1.11428 + 0.895874i
\(163\) −2.27101e35 + 3.93350e35i −0.914571 + 1.58408i −0.107042 + 0.994254i \(0.534138\pi\)
−0.807528 + 0.589829i \(0.799195\pi\)
\(164\) −2.22911e35 + 1.28698e35i −0.814012 + 0.469970i
\(165\) 1.98715e34 + 2.14591e34i 0.0658397 + 0.0710999i
\(166\) −4.37754e35 + 7.58213e35i −1.31674 + 2.28067i
\(167\) 2.95669e35i 0.807872i 0.914787 + 0.403936i \(0.132358\pi\)
−0.914787 + 0.403936i \(0.867642\pi\)
\(168\) −1.39406e34 2.12905e34i −0.0346204 0.0528734i
\(169\) 1.48555e35 0.335506
\(170\) 8.92276e34 + 5.15156e34i 0.183365 + 0.105866i
\(171\) −2.87338e35 1.96741e35i −0.537594 0.368093i
\(172\) 4.58402e35 + 7.93976e35i 0.781253 + 1.35317i
\(173\) 5.90448e35 + 3.40895e35i 0.917157 + 0.529521i 0.882727 0.469886i \(-0.155705\pi\)
0.0344300 + 0.999407i \(0.489038\pi\)
\(174\) −8.22150e35 + 1.86791e35i −1.16456 + 0.264587i
\(175\) −7.16188e35 + 2.66572e35i −0.925590 + 0.344513i
\(176\) 7.04309e35i 0.830922i
\(177\) −1.13952e36 3.52735e35i −1.22786 0.380081i
\(178\) −4.64870e35 8.05179e35i −0.457733 0.792816i
\(179\) −4.73227e35 + 2.73218e35i −0.426011 + 0.245958i −0.697646 0.716443i \(-0.745769\pi\)
0.271635 + 0.962400i \(0.412436\pi\)
\(180\) −1.40642e35 1.08207e34i −0.115812 0.00891038i
\(181\) 2.15687e35 0.162542 0.0812711 0.996692i \(-0.474102\pi\)
0.0812711 + 0.996692i \(0.474102\pi\)
\(182\) −1.52585e36 + 1.84546e36i −1.05286 + 1.27340i
\(183\) 1.21859e36 2.76861e35i 0.770263 0.175003i
\(184\) −5.93356e34 + 1.02772e35i −0.0343740 + 0.0595376i
\(185\) −3.10510e35 + 1.79273e35i −0.164941 + 0.0952286i
\(186\) 2.81747e36 2.60902e36i 1.37294 1.27137i
\(187\) −1.29656e36 + 2.24570e36i −0.579864 + 1.00435i
\(188\) 4.86088e36i 1.99613i
\(189\) 1.27773e36 + 2.32261e36i 0.482004 + 0.876169i
\(190\) 2.98889e35 0.103622
\(191\) −2.30238e36 1.32928e36i −0.733911 0.423724i 0.0859404 0.996300i \(-0.472611\pi\)
−0.819851 + 0.572577i \(0.805944\pi\)
\(192\) 2.51738e36 + 2.71851e36i 0.738125 + 0.797096i
\(193\) 4.25663e35 + 7.37270e35i 0.114855 + 0.198934i 0.917722 0.397224i \(-0.130026\pi\)
−0.802867 + 0.596158i \(0.796693\pi\)
\(194\) 2.57095e36 + 1.48434e36i 0.638654 + 0.368727i
\(195\) 1.24481e35 + 5.47896e35i 0.0284807 + 0.125356i
\(196\) −9.30799e35 4.86491e36i −0.196227 1.02560i
\(197\) 4.77659e36i 0.928236i −0.885773 0.464118i \(-0.846371\pi\)
0.885773 0.464118i \(-0.153629\pi\)
\(198\) 5.33149e35 6.92958e36i 0.0955444 1.24183i
\(199\) −2.30380e36 3.99029e36i −0.380886 0.659714i 0.610303 0.792168i \(-0.291048\pi\)
−0.991189 + 0.132454i \(0.957714\pi\)
\(200\) −3.54255e35 + 2.04529e35i −0.0540551 + 0.0312087i
\(201\) −2.41652e36 + 7.80662e36i −0.340450 + 1.09983i
\(202\) 1.02360e37 1.33201
\(203\) −6.84955e36 1.15658e36i −0.823618 0.139072i
\(204\) −2.77087e36 1.21958e37i −0.307988 1.35559i
\(205\) −4.87077e35 + 8.43643e35i −0.0500652 + 0.0867155i
\(206\) −1.45109e37 + 8.37788e36i −1.37981 + 0.796633i
\(207\) 6.98379e36 1.01997e37i 0.614562 0.897559i
\(208\) 6.76524e36 1.17177e37i 0.551150 0.954620i
\(209\) 7.52251e36i 0.567573i
\(210\) −2.03111e36 1.02528e36i −0.141979 0.0716692i
\(211\) 4.29291e36 0.278120 0.139060 0.990284i \(-0.455592\pi\)
0.139060 + 0.990284i \(0.455592\pi\)
\(212\) 1.83205e37 + 1.05773e37i 1.10043 + 0.635335i
\(213\) −1.25877e36 + 1.16564e36i −0.0701249 + 0.0649368i
\(214\) −5.70701e36 9.88484e36i −0.294977 0.510916i
\(215\) 3.00493e36 + 1.73489e36i 0.144151 + 0.0832258i
\(216\) 8.81403e35 + 1.11203e36i 0.0392567 + 0.0495285i
\(217\) 2.96508e37 1.10363e37i 1.22654 0.456529i
\(218\) 1.63781e37i 0.629447i
\(219\) −2.73900e36 + 8.84839e36i −0.0978331 + 0.316052i
\(220\) 1.52353e36 + 2.63884e36i 0.0505929 + 0.0876294i
\(221\) −4.31423e37 + 2.49082e37i −1.33237 + 0.769247i
\(222\) 8.13929e37 + 2.51950e37i 2.33851 + 0.723880i
\(223\) −4.34313e37 −1.16125 −0.580624 0.814172i \(-0.697191\pi\)
−0.580624 + 0.814172i \(0.697191\pi\)
\(224\) 1.99983e37 + 5.37288e37i 0.497766 + 1.33733i
\(225\) 3.84271e37 1.84115e37i 0.890670 0.426746i
\(226\) 3.81090e37 6.60067e37i 0.822796 1.42512i
\(227\) −2.71259e37 + 1.56611e37i −0.545720 + 0.315072i −0.747394 0.664381i \(-0.768695\pi\)
0.201674 + 0.979453i \(0.435362\pi\)
\(228\) −2.46510e37 2.66205e37i −0.462250 0.499181i
\(229\) −1.67395e37 + 2.89936e37i −0.292667 + 0.506914i −0.974439 0.224650i \(-0.927876\pi\)
0.681772 + 0.731564i \(0.261209\pi\)
\(230\) 1.06098e37i 0.173006i
\(231\) 2.58044e37 5.11194e37i 0.392557 0.777668i
\(232\) −3.71836e36 −0.0527890
\(233\) −3.18758e37 1.84035e37i −0.422441 0.243896i 0.273680 0.961821i \(-0.411759\pi\)
−0.696121 + 0.717924i \(0.745092\pi\)
\(234\) 7.54322e37 1.10168e38i 0.933476 1.36333i
\(235\) −9.19839e36 1.59321e37i −0.106323 0.184156i
\(236\) −1.07628e38 6.21391e37i −1.16234 0.671078i
\(237\) 7.17121e35 1.62929e35i 0.00723801 0.00164446i
\(238\) 3.35873e37 1.98912e38i 0.316916 1.87685i
\(239\) 1.74017e38i 1.53542i 0.640800 + 0.767708i \(0.278603\pi\)
−0.640800 + 0.767708i \(0.721397\pi\)
\(240\) 1.22811e37 + 3.80159e36i 0.101358 + 0.0313751i
\(241\) −2.42589e36 4.20176e36i −0.0187326 0.0324458i 0.856507 0.516135i \(-0.172630\pi\)
−0.875240 + 0.483689i \(0.839296\pi\)
\(242\) 4.13135e37 2.38524e37i 0.298570 0.172380i
\(243\) −8.26560e37 1.22537e38i −0.559209 0.829027i
\(244\) 1.30194e38 0.824809
\(245\) −1.22568e37 1.41839e37i −0.0727310 0.0841663i
\(246\) 2.25741e38 5.12879e37i 1.25501 0.285137i
\(247\) −7.22575e37 + 1.25154e38i −0.376471 + 0.652067i
\(248\) 1.46665e37 8.46769e36i 0.0716306 0.0413560i
\(249\) 2.95116e38 2.73283e38i 1.35146 1.25148i
\(250\) −3.68009e37 + 6.37409e37i −0.158058 + 0.273765i
\(251\) 8.10306e37i 0.326490i 0.986586 + 0.163245i \(0.0521960\pi\)
−0.986586 + 0.163245i \(0.947804\pi\)
\(252\) 7.62006e37 + 2.65461e38i 0.288104 + 1.00367i
\(253\) −2.67029e38 −0.947612
\(254\) −1.11393e38 6.43129e37i −0.371124 0.214269i
\(255\) −3.21603e37 3.47297e37i −0.100618 0.108657i
\(256\) −1.54118e38 2.66940e38i −0.452911 0.784465i
\(257\) −4.95180e38 2.85892e38i −1.36720 0.789355i −0.376632 0.926363i \(-0.622918\pi\)
−0.990570 + 0.137008i \(0.956251\pi\)
\(258\) −1.82680e38 8.04053e38i −0.473996 2.08627i
\(259\) 5.41030e38 + 4.47329e38i 1.31955 + 1.09102i
\(260\) 5.85373e37i 0.134233i
\(261\) 3.86186e38 + 2.97125e37i 0.832815 + 0.0640753i
\(262\) 3.53014e38 + 6.11437e38i 0.716095 + 1.24031i
\(263\) −8.10698e38 + 4.68056e38i −1.54727 + 0.893318i −0.548924 + 0.835872i \(0.684962\pi\)
−0.998349 + 0.0574463i \(0.981704\pi\)
\(264\) 9.06394e36 2.92813e37i 0.0162800 0.0525929i
\(265\) 8.00632e37 0.135363
\(266\) −2.04136e38 5.48445e38i −0.324948 0.873025i
\(267\) 9.46316e37 + 4.16515e38i 0.141859 + 0.624382i
\(268\) −4.25703e38 + 7.37340e38i −0.601105 + 1.04114i
\(269\) 1.75328e38 1.01226e38i 0.233247 0.134665i −0.378822 0.925469i \(-0.623671\pi\)
0.612069 + 0.790804i \(0.290338\pi\)
\(270\) 1.17954e38 + 4.66999e37i 0.147875 + 0.0585457i
\(271\) −8.24666e38 + 1.42836e39i −0.974472 + 1.68783i −0.292805 + 0.956172i \(0.594589\pi\)
−0.681667 + 0.731663i \(0.738745\pi\)
\(272\) 1.13986e39i 1.26984i
\(273\) 9.20342e38 6.02621e38i 0.966823 0.633055i
\(274\) 6.45020e38 0.639093
\(275\) −7.97131e38 4.60224e38i −0.745086 0.430176i
\(276\) 9.44957e38 8.75047e38i 0.833425 0.771766i
\(277\) −1.09151e39 1.89055e39i −0.908554 1.57366i −0.816074 0.577947i \(-0.803854\pi\)
−0.0924795 0.995715i \(-0.529479\pi\)
\(278\) 3.40659e38 + 1.96680e38i 0.267672 + 0.154541i
\(279\) −1.59091e39 + 7.62253e38i −1.18026 + 0.565499i
\(280\) −7.73342e36 6.39406e36i −0.00541805 0.00447969i
\(281\) 2.81895e39i 1.86546i 0.360571 + 0.932732i \(0.382582\pi\)
−0.360571 + 0.932732i \(0.617418\pi\)
\(282\) −1.29274e39 + 4.17622e39i −0.808211 + 2.61094i
\(283\) 2.84826e38 + 4.93333e38i 0.168266 + 0.291445i 0.937810 0.347148i \(-0.112850\pi\)
−0.769544 + 0.638594i \(0.779517\pi\)
\(284\) −1.54791e38 + 8.93688e37i −0.0864277 + 0.0498991i
\(285\) −1.31171e38 4.06037e37i −0.0692341 0.0214313i
\(286\) −2.88420e39 −1.43936
\(287\) 1.88071e39 + 3.17567e38i 0.887586 + 0.149873i
\(288\) −1.38124e39 2.88281e39i −0.616580 1.28688i
\(289\) 9.14411e38 1.58381e39i 0.386168 0.668862i
\(290\) −2.87900e38 + 1.66219e38i −0.115047 + 0.0664222i
\(291\) −9.26647e38 1.00068e39i −0.350451 0.378449i
\(292\) −4.82513e38 + 8.35736e38i −0.172736 + 0.299188i
\(293\) 1.33635e39i 0.452936i 0.974019 + 0.226468i \(0.0727179\pi\)
−0.974019 + 0.226468i \(0.927282\pi\)
\(294\) −4.94115e38 + 4.42722e39i −0.158588 + 1.42093i
\(295\) −4.70350e38 −0.142978
\(296\) 3.25430e38 + 1.87887e38i 0.0937109 + 0.0541040i
\(297\) −1.17535e39 + 2.96870e39i −0.320675 + 0.809960i
\(298\) 2.78176e39 + 4.81814e39i 0.719215 + 1.24572i
\(299\) −4.44263e39 2.56495e39i −1.08868 0.628550i
\(300\) 4.32901e39 9.83544e38i 1.00565 0.228483i
\(301\) 1.13112e39 6.69878e39i 0.249142 1.47548i
\(302\) 2.31922e39i 0.484431i
\(303\) −4.49218e39 1.39054e39i −0.889969 0.275488i
\(304\) 1.65334e39 + 2.86367e39i 0.310732 + 0.538203i
\(305\) 4.26724e38 2.46369e38i 0.0760939 0.0439329i
\(306\) −8.62855e38 + 1.12149e40i −0.146014 + 1.89781i
\(307\) 4.42716e39 0.711068 0.355534 0.934663i \(-0.384299\pi\)
0.355534 + 0.934663i \(0.384299\pi\)
\(308\) 3.80158e39 4.59789e39i 0.579632 0.701047i
\(309\) 7.50642e39 1.70545e39i 1.08667 0.246890i
\(310\) 7.57051e38 1.31125e39i 0.104073 0.180260i
\(311\) −1.82694e39 + 1.05478e39i −0.238538 + 0.137720i −0.614505 0.788913i \(-0.710644\pi\)
0.375967 + 0.926633i \(0.377311\pi\)
\(312\) 4.32060e38 4.00095e38i 0.0535884 0.0496238i
\(313\) −4.43871e39 + 7.68807e39i −0.523055 + 0.905957i 0.476585 + 0.879128i \(0.341874\pi\)
−0.999640 + 0.0268292i \(0.991459\pi\)
\(314\) 1.24244e40i 1.39124i
\(315\) 7.52094e38 + 7.25879e38i 0.0800393 + 0.0772495i
\(316\) 7.66172e37 0.00775056
\(317\) 4.92456e39 + 2.84319e39i 0.473608 + 0.273438i 0.717749 0.696302i \(-0.245173\pi\)
−0.244141 + 0.969740i \(0.578506\pi\)
\(318\) −1.29270e40 1.39598e40i −1.18213 1.27657i
\(319\) −4.18345e39 7.24595e39i −0.363818 0.630150i
\(320\) 1.26519e39 + 7.30460e38i 0.104654 + 0.0604223i
\(321\) 1.16175e39 + 5.11338e39i 0.0914182 + 0.402372i
\(322\) 1.94683e40 7.24630e39i 1.45759 0.542528i
\(323\) 1.21745e40i 0.867385i
\(324\) −5.56904e39 1.43572e40i −0.377624 0.973529i
\(325\) −8.84136e39 1.53137e40i −0.570671 0.988430i
\(326\) 3.68571e40 2.12795e40i 2.26485 1.30761i
\(327\) 2.22494e39 7.18773e39i 0.130183 0.420560i
\(328\) 1.02096e39 0.0568890
\(329\) −2.29522e40 + 2.77599e40i −1.21812 + 1.47327i
\(330\) −6.07149e38 2.67233e39i −0.0306953 0.135104i
\(331\) −5.02647e39 + 8.70611e39i −0.242112 + 0.419350i −0.961316 0.275449i \(-0.911173\pi\)
0.719204 + 0.694799i \(0.244507\pi\)
\(332\) 3.62906e40 2.09524e40i 1.66565 0.961666i
\(333\) −3.22976e40 2.21143e40i −1.41274 0.967308i
\(334\) 1.38522e40 2.39927e40i 0.577530 1.00031i
\(335\) 3.22228e39i 0.128070i
\(336\) −1.41209e39 2.51316e40i −0.0535100 0.952341i
\(337\) 1.69205e40 0.611413 0.305706 0.952126i \(-0.401107\pi\)
0.305706 + 0.952126i \(0.401107\pi\)
\(338\) −1.20548e40 6.95984e39i −0.415425 0.239846i
\(339\) −2.56915e40 + 2.37908e40i −0.844491 + 0.782013i
\(340\) −2.46571e39 4.27073e39i −0.0773177 0.133918i
\(341\) 3.30019e40 + 1.90537e40i 0.987345 + 0.570044i
\(342\) 1.40992e40 + 2.94268e40i 0.402511 + 0.840088i
\(343\) −1.76555e40 + 3.21780e40i −0.481032 + 0.876703i
\(344\) 3.63651e39i 0.0945692i
\(345\) 1.44132e39 4.65623e39i 0.0357813 0.115592i
\(346\) −3.19420e40 5.53252e40i −0.757086 1.31131i
\(347\) −4.75970e40 + 2.74801e40i −1.07723 + 0.621938i −0.930147 0.367186i \(-0.880321\pi\)
−0.147081 + 0.989124i \(0.546988\pi\)
\(348\) 3.85490e40 + 1.19328e40i 0.833193 + 0.257913i
\(349\) 5.08865e40 1.05050 0.525249 0.850948i \(-0.323972\pi\)
0.525249 + 0.850948i \(0.323972\pi\)
\(350\) 7.06055e40 + 1.19221e40i 1.39235 + 0.235106i
\(351\) −4.80705e40 + 3.81011e40i −0.905660 + 0.717834i
\(352\) −3.45262e40 + 5.98011e40i −0.621535 + 1.07653i
\(353\) 2.39222e40 1.38115e40i 0.411535 0.237600i −0.279914 0.960025i \(-0.590306\pi\)
0.691449 + 0.722425i \(0.256973\pi\)
\(354\) 7.59427e40 + 8.20101e40i 1.24863 + 1.34839i
\(355\) −3.38230e38 + 5.85831e38i −0.00531567 + 0.00920702i
\(356\) 4.45005e40i 0.668598i
\(357\) −4.17622e40 + 8.27324e40i −0.599919 + 1.18846i
\(358\) 5.12012e40 0.703319
\(359\) 2.32461e40 + 1.34211e40i 0.305379 + 0.176310i 0.644857 0.764304i \(-0.276917\pi\)
−0.339478 + 0.940614i \(0.610250\pi\)
\(360\) 4.61658e38 + 3.16098e38i 0.00580070 + 0.00397175i
\(361\) 2.39404e40 + 4.14659e40i 0.287750 + 0.498398i
\(362\) −1.75023e40 1.01050e40i −0.201261 0.116198i
\(363\) −2.13713e40 + 4.85552e39i −0.235139 + 0.0534232i
\(364\) 1.07413e41 3.99800e40i 1.13092 0.420940i
\(365\) 3.65229e39i 0.0368026i
\(366\) −1.11856e41 3.46247e40i −1.07885 0.333955i
\(367\) −6.20792e40 1.07524e41i −0.573178 0.992773i −0.996237 0.0866711i \(-0.972377\pi\)
0.423059 0.906102i \(-0.360956\pi\)
\(368\) −1.01653e41 + 5.86893e40i −0.898576 + 0.518793i
\(369\) −1.06037e41 8.15825e39i −0.897498 0.0690519i
\(370\) 3.35960e40 0.272307
\(371\) −5.46819e40 1.46912e41i −0.424484 1.14044i
\(372\) −1.79225e41 + 4.07196e40i −1.33263 + 0.302772i
\(373\) 2.02928e40 3.51482e40i 0.144545 0.250358i −0.784658 0.619928i \(-0.787162\pi\)
0.929203 + 0.369570i \(0.120495\pi\)
\(374\) 2.10424e41 1.21488e41i 1.43598 0.829064i
\(375\) 2.48097e40 2.29742e40i 0.162226 0.150224i
\(376\) −9.64036e39 + 1.66976e40i −0.0604071 + 0.104628i
\(377\) 1.60737e41i 0.965280i
\(378\) 5.13086e39 2.48335e41i 0.0295339 1.42945i
\(379\) −2.17035e41 −1.19757 −0.598787 0.800909i \(-0.704350\pi\)
−0.598787 + 0.800909i \(0.704350\pi\)
\(380\) −1.23892e40 7.15290e39i −0.0655398 0.0378394i
\(381\) 4.01495e40 + 4.33572e40i 0.203648 + 0.219918i
\(382\) 1.24554e41 + 2.15734e41i 0.605821 + 1.04931i
\(383\) −1.01117e41 5.83802e40i −0.471678 0.272323i 0.245264 0.969456i \(-0.421125\pi\)
−0.716942 + 0.697133i \(0.754459\pi\)
\(384\) −6.25308e39 2.75226e40i −0.0279766 0.123137i
\(385\) 3.75937e39 2.22639e40i 0.0161341 0.0955498i
\(386\) 7.97696e40i 0.328428i
\(387\) −2.90584e40 + 3.77686e41i −0.114788 + 1.49195i
\(388\) −7.10453e40 1.23054e41i −0.269295 0.466432i
\(389\) −3.04550e40 + 1.75832e40i −0.110781 + 0.0639594i −0.554367 0.832273i \(-0.687039\pi\)
0.443586 + 0.896232i \(0.353706\pi\)
\(390\) 1.55678e40 5.02921e40i 0.0543493 0.175576i
\(391\) 4.32164e41 1.44817
\(392\) −6.45097e39 + 1.85574e40i −0.0207514 + 0.0596954i
\(393\) −7.18614e40 3.16294e41i −0.221929 0.976809i
\(394\) −2.23785e41 + 3.87606e41i −0.663576 + 1.14935i
\(395\) 2.51121e38 1.44985e38i 0.000715039 0.000412828i
\(396\) −1.87936e41 + 2.74478e41i −0.513909 + 0.750558i
\(397\) 2.96737e40 5.13963e40i 0.0779333 0.134984i −0.824425 0.565971i \(-0.808501\pi\)
0.902358 + 0.430987i \(0.141835\pi\)
\(398\) 4.31734e41i 1.08915i
\(399\) 1.50821e40 + 2.68424e41i 0.0365508 + 0.650510i
\(400\) −4.04603e41 −0.942041
\(401\) −6.15596e41 3.55414e41i −1.37716 0.795106i −0.385346 0.922772i \(-0.625918\pi\)
−0.991817 + 0.127666i \(0.959251\pi\)
\(402\) 5.61835e41 5.20269e41i 1.20779 1.11844i
\(403\) 3.66040e41 + 6.34000e41i 0.756220 + 1.30981i
\(404\) −4.24289e41 2.44963e41i −0.842480 0.486406i
\(405\) −4.54216e40 3.65188e40i −0.0866926 0.0697005i
\(406\) 5.01635e41 + 4.14756e41i 0.920388 + 0.760986i
\(407\) 8.45552e41i 1.49152i
\(408\) −1.46692e40 + 4.73892e40i −0.0248796 + 0.0803742i
\(409\) 3.44309e40 + 5.96360e40i 0.0561533 + 0.0972603i 0.892736 0.450581i \(-0.148783\pi\)
−0.836582 + 0.547841i \(0.815450\pi\)
\(410\) 7.90498e40 4.56394e40i 0.123982 0.0715811i
\(411\) −2.83075e41 8.76252e40i −0.427005 0.132178i
\(412\) 8.01986e41 1.16362
\(413\) 3.21242e41 + 8.63068e41i 0.448364 + 1.20460i
\(414\) −1.04457e42 + 5.00486e41i −1.40260 + 0.672026i
\(415\) 7.92975e40 1.37347e41i 0.102445 0.177440i
\(416\) −1.14884e42 + 6.63283e41i −1.42812 + 0.824528i
\(417\) −1.22784e41 1.32594e41i −0.146881 0.158615i
\(418\) 3.52431e41 6.10429e41i 0.405746 0.702772i
\(419\) 5.74093e41i 0.636147i 0.948066 + 0.318074i \(0.103036\pi\)
−0.948066 + 0.318074i \(0.896964\pi\)
\(420\) 5.96545e40 + 9.11063e40i 0.0636290 + 0.0971762i
\(421\) −7.76042e41 −0.796841 −0.398421 0.917203i \(-0.630442\pi\)
−0.398421 + 0.917203i \(0.630442\pi\)
\(422\) −3.48357e41 2.01124e41i −0.344370 0.198822i
\(423\) 1.13467e42 1.65717e42i 1.08000 1.57732i
\(424\) −4.19551e40 7.26684e40i −0.0384531 0.0666027i
\(425\) 1.29009e42 + 7.44832e41i 1.13867 + 0.657409i
\(426\) 1.56756e41 3.56147e40i 0.133251 0.0302744i
\(427\) −7.43521e41 6.14750e41i −0.608761 0.503330i
\(428\) 5.46313e41i 0.430865i
\(429\) 1.26577e42 + 3.91815e41i 0.961693 + 0.297690i
\(430\) −1.62561e41 2.81563e41i −0.118993 0.206101i
\(431\) 2.68703e41 1.55136e41i 0.189511 0.109415i −0.402242 0.915533i \(-0.631769\pi\)
0.591754 + 0.806119i \(0.298436\pi\)
\(432\) 2.05046e41 + 1.38846e42i 0.139351 + 0.943609i
\(433\) −2.85462e41 −0.186957 −0.0934786 0.995621i \(-0.529799\pi\)
−0.0934786 + 0.995621i \(0.529799\pi\)
\(434\) −2.92313e42 4.93585e41i −1.84507 0.311549i
\(435\) 1.48929e41 3.38365e40i 0.0906050 0.0205853i
\(436\) 3.91955e41 6.78886e41i 0.229854 0.398119i
\(437\) 1.08572e42 6.26843e41i 0.613785 0.354369i
\(438\) 6.36811e41 5.89698e41i 0.347076 0.321398i
\(439\) 9.06797e41 1.57062e42i 0.476516 0.825350i −0.523122 0.852258i \(-0.675233\pi\)
0.999638 + 0.0269078i \(0.00856606\pi\)
\(440\) 1.20862e40i 0.00612417i
\(441\) 8.18281e41 1.87582e42i 0.399839 0.916585i
\(442\) 4.66782e42 2.19967
\(443\) −1.11394e42 6.43132e41i −0.506292 0.292308i 0.225016 0.974355i \(-0.427756\pi\)
−0.731308 + 0.682047i \(0.761090\pi\)
\(444\) −2.77085e42 2.99222e42i −1.21475 1.31180i
\(445\) 8.42095e40 + 1.45855e41i 0.0356124 + 0.0616824i
\(446\) 3.52432e42 + 2.03477e42i 1.43786 + 0.830150i
\(447\) −5.66270e41 2.49240e42i −0.222896 0.981064i
\(448\) 4.76249e41 2.82046e42i 0.180878 1.07120i
\(449\) 2.10415e42i 0.771144i −0.922678 0.385572i \(-0.874004\pi\)
0.922678 0.385572i \(-0.125996\pi\)
\(450\) −3.98083e42 3.06277e41i −1.40790 0.108322i
\(451\) 1.14866e42 + 1.98955e42i 0.392074 + 0.679093i
\(452\) −3.15930e42 + 1.82402e42i −1.04082 + 0.600918i
\(453\) −3.15064e41 + 1.01782e42i −0.100191 + 0.323668i
\(454\) 2.93491e42 0.900951
\(455\) 2.76402e41 3.34299e41i 0.0819140 0.0990724i
\(456\) 3.18835e40 + 1.40333e41i 0.00912280 + 0.0401534i
\(457\) 1.66341e42 2.88111e42i 0.459557 0.795976i −0.539380 0.842062i \(-0.681342\pi\)
0.998937 + 0.0460861i \(0.0146749\pi\)
\(458\) 2.71672e42 1.56850e42i 0.724764 0.418443i
\(459\) 1.90221e42 4.80459e42i 0.490067 1.23781i
\(460\) 2.53909e41 4.39784e41i 0.0631761 0.109424i
\(461\) 5.86215e42i 1.40878i −0.709814 0.704389i \(-0.751221\pi\)
0.709814 0.704389i \(-0.248779\pi\)
\(462\) −4.48891e42 + 2.93925e42i −1.04200 + 0.682282i
\(463\) 3.03791e42 0.681207 0.340604 0.940207i \(-0.389369\pi\)
0.340604 + 0.940207i \(0.389369\pi\)
\(464\) −3.18512e42 1.83893e42i −0.689982 0.398361i
\(465\) −5.10373e41 + 4.72615e41i −0.106817 + 0.0989145i
\(466\) 1.72442e42 + 2.98678e42i 0.348713 + 0.603988i
\(467\) −1.96268e41 1.13316e41i −0.0383513 0.0221421i 0.480702 0.876884i \(-0.340382\pi\)
−0.519053 + 0.854742i \(0.673715\pi\)
\(468\) −5.76323e42 + 2.76133e42i −1.08826 + 0.521416i
\(469\) 5.91272e42 2.20077e42i 1.07900 0.401614i
\(470\) 1.72379e42i 0.304031i
\(471\) −1.68784e42 + 5.45260e42i −0.287738 + 0.929543i
\(472\) 2.46475e41 + 4.26908e41i 0.0406164 + 0.0703497i
\(473\) 7.08645e42 4.09137e42i 1.12889 0.651764i
\(474\) −6.58255e40 2.03761e40i −0.0101377 0.00313811i
\(475\) 4.32145e42 0.643474
\(476\) −6.15253e42 + 7.44128e42i −0.885813 + 1.07136i
\(477\) 3.77676e42 + 7.88254e42i 0.525805 + 1.09742i
\(478\) 8.15275e42 1.41210e43i 1.09764 1.90116i
\(479\) 6.44850e42 3.72304e42i 0.839634 0.484763i −0.0175055 0.999847i \(-0.505572\pi\)
0.857140 + 0.515084i \(0.172239\pi\)
\(480\) −8.56401e41 9.24822e41i −0.107849 0.116466i
\(481\) −8.12196e42 + 1.40676e43i −0.989326 + 1.71356i
\(482\) 4.54614e41i 0.0535661i
\(483\) −9.52833e42 + 5.35376e41i −1.08608 + 0.0610246i
\(484\) −2.28331e42 −0.251790
\(485\) −4.65717e41 2.68882e41i −0.0496884 0.0286876i
\(486\) 9.66374e41 + 1.38160e43i 0.0997619 + 1.42627i
\(487\) −9.25798e42 1.60353e43i −0.924811 1.60182i −0.791865 0.610696i \(-0.790890\pi\)
−0.132946 0.991123i \(-0.542444\pi\)
\(488\) −4.47228e41 2.58207e41i −0.0432327 0.0249604i
\(489\) −1.90660e43 + 4.33177e42i −1.78368 + 0.405250i
\(490\) 3.30084e41 + 1.72522e42i 0.0298873 + 0.156209i
\(491\) 1.67841e43i 1.47093i 0.677560 + 0.735467i \(0.263037\pi\)
−0.677560 + 0.735467i \(0.736963\pi\)
\(492\) −1.05845e43 3.27642e42i −0.897906 0.277944i
\(493\) 6.77055e42 + 1.17269e43i 0.555998 + 0.963017i
\(494\) 1.17270e43 6.77056e42i 0.932297 0.538262i
\(495\) −9.65779e40 + 1.25527e42i −0.00743352 + 0.0966168i
\(496\) 1.67509e43 1.24834
\(497\) 1.30598e42 + 2.20521e41i 0.0942394 + 0.0159128i
\(498\) −3.67512e43 + 8.34981e42i −2.56804 + 0.583455i
\(499\) −8.28040e42 + 1.43421e43i −0.560328 + 0.970517i 0.437139 + 0.899394i \(0.355992\pi\)
−0.997468 + 0.0711231i \(0.977342\pi\)
\(500\) 3.05085e42 1.76141e42i 0.199941 0.115436i
\(501\) −9.33858e42 + 8.64769e42i −0.592758 + 0.548904i
\(502\) 3.79630e42 6.57539e42i 0.233400 0.404261i
\(503\) 1.48927e43i 0.886923i −0.896293 0.443462i \(-0.853750\pi\)
0.896293 0.443462i \(-0.146250\pi\)
\(504\) 2.64719e41 1.06301e42i 0.0152720 0.0613264i
\(505\) −1.85420e42 −0.103632
\(506\) 2.16686e43 + 1.25104e43i 1.17334 + 0.677427i
\(507\) 4.34491e42 + 4.69204e42i 0.227957 + 0.246170i
\(508\) 3.07823e42 + 5.33165e42i 0.156488 + 0.271046i
\(509\) 3.18004e42 + 1.83600e42i 0.156656 + 0.0904455i 0.576279 0.817253i \(-0.304504\pi\)
−0.419623 + 0.907699i \(0.637838\pi\)
\(510\) 9.82618e41 + 4.32493e42i 0.0469096 + 0.206470i
\(511\) 6.70175e42 2.49445e42i 0.310066 0.115409i
\(512\) 3.16979e43i 1.42138i
\(513\) −2.19003e42 1.48297e43i −0.0951858 0.644546i
\(514\) 2.67882e43 + 4.63986e43i 1.12858 + 1.95477i
\(515\) 2.62860e42 1.51762e42i 0.107352 0.0619794i
\(516\) −1.16701e43 + 3.77005e43i −0.462040 + 1.49263i
\(517\) −4.33847e43 −1.66528
\(518\) −2.29455e43 6.16468e43i −0.853928 2.29422i
\(519\) 6.50230e42 + 2.86195e43i 0.234633 + 1.03272i
\(520\) 1.16094e41 2.01081e41i 0.00406216 0.00703587i
\(521\) 1.82705e43 1.05485e43i 0.619936 0.357921i −0.156908 0.987613i \(-0.550153\pi\)
0.776844 + 0.629693i \(0.216819\pi\)
\(522\) −2.99458e43 2.05040e43i −0.985390 0.674700i
\(523\) −1.84570e42 + 3.19684e42i −0.0589025 + 0.102022i −0.893973 0.448121i \(-0.852093\pi\)
0.835071 + 0.550143i \(0.185427\pi\)
\(524\) 3.37928e43i 1.04598i
\(525\) −2.93665e43 1.48238e43i −0.881665 0.445053i
\(526\) 8.77143e43 2.55446
\(527\) −5.34107e43 3.08367e43i −1.50889 0.871160i
\(528\) 2.22453e43 2.05995e43i 0.609670 0.564565i
\(529\) 3.44683e42 + 5.97009e42i 0.0916494 + 0.158741i
\(530\) −6.49689e42 3.75098e42i −0.167607 0.0967678i
\(531\) −2.21875e43 4.63079e43i −0.555386 1.15916i
\(532\) −4.66358e42 + 2.76188e43i −0.113275 + 0.670840i
\(533\) 4.41340e43i 1.04025i
\(534\) 1.18348e43 3.82325e43i 0.270707 0.874525i
\(535\) 1.03380e42 + 1.79060e42i 0.0229497 + 0.0397501i
\(536\) 2.92466e42 1.68856e42i 0.0630143 0.0363813i
\(537\) −2.24703e43 6.95563e42i −0.469916 0.145461i
\(538\) −1.89698e43 −0.385076
\(539\) −4.34207e43 + 8.30764e42i −0.855611 + 0.163703i
\(540\) −3.77170e42 4.75859e42i −0.0721501 0.0910287i
\(541\) −4.99261e42 + 8.64745e42i −0.0927195 + 0.160595i −0.908655 0.417549i \(-0.862889\pi\)
0.815935 + 0.578144i \(0.196223\pi\)
\(542\) 1.33838e44 7.72716e43i 2.41319 1.39326i
\(543\) 6.30837e42 + 6.81237e42i 0.110438 + 0.119262i
\(544\) 5.58776e43 9.67829e43i 0.949851 1.64519i
\(545\) 2.96683e42i 0.0489721i
\(546\) −1.02916e44 + 5.78262e42i −1.64968 + 0.0926920i
\(547\) −3.77308e43 −0.587353 −0.293676 0.955905i \(-0.594879\pi\)
−0.293676 + 0.955905i \(0.594879\pi\)
\(548\) −2.67366e43 1.54364e43i −0.404220 0.233377i
\(549\) 4.43856e43 + 3.03909e43i 0.651755 + 0.446259i
\(550\) 4.31232e43 + 7.46916e43i 0.615046 + 1.06529i
\(551\) 3.40193e43 + 1.96410e43i 0.471302 + 0.272107i
\(552\) −4.98146e42 + 1.13178e42i −0.0670396 + 0.0152313i
\(553\) −4.37551e41 3.61772e41i −0.00572041 0.00472969i
\(554\) 2.04550e44i 2.59802i
\(555\) −1.47440e43 4.56397e42i −0.181940 0.0563191i
\(556\) −9.41375e42 1.63051e43i −0.112867 0.195491i
\(557\) 2.24414e42 1.29565e42i 0.0261437 0.0150941i −0.486871 0.873474i \(-0.661862\pi\)
0.513015 + 0.858380i \(0.328529\pi\)
\(558\) 1.64810e44 + 1.26801e43i 1.86567 + 0.143541i
\(559\) 1.57199e44 1.72926
\(560\) −3.46218e42 9.30170e42i −0.0370119 0.0994383i
\(561\) −1.08851e44 + 2.47308e43i −1.13091 + 0.256940i
\(562\) 1.32069e44 2.28750e44i 1.33358 2.30983i
\(563\) −5.18860e43 + 2.99564e43i −0.509232 + 0.294005i −0.732518 0.680748i \(-0.761655\pi\)
0.223286 + 0.974753i \(0.428322\pi\)
\(564\) 1.53529e44 1.42170e44i 1.46462 1.35626i
\(565\) −6.90329e42 + 1.19569e43i −0.0640149 + 0.110877i
\(566\) 5.33767e43i 0.481159i
\(567\) −3.59878e43 + 1.08288e44i −0.315374 + 0.948967i
\(568\) 7.08964e41 0.00604019
\(569\) −1.28777e44 7.43497e43i −1.06670 0.615861i −0.139424 0.990233i \(-0.544525\pi\)
−0.927279 + 0.374371i \(0.877859\pi\)
\(570\) 8.74185e42 + 9.44026e42i 0.0704053 + 0.0760302i
\(571\) −9.52986e43 1.65062e44i −0.746292 1.29262i −0.949589 0.313498i \(-0.898499\pi\)
0.203297 0.979117i \(-0.434834\pi\)
\(572\) 1.19552e44 + 6.90236e43i 0.910378 + 0.525607i
\(573\) −2.53549e43 1.11598e44i −0.187754 0.826387i
\(574\) −1.37736e44 1.13881e44i −0.991873 0.820090i
\(575\) 1.53400e44i 1.07434i
\(576\) −1.22348e43 + 1.59021e44i −0.0833367 + 1.08316i
\(577\) −7.58531e43 1.31381e44i −0.502528 0.870404i −0.999996 0.00292177i \(-0.999070\pi\)
0.497468 0.867483i \(-0.334263\pi\)
\(578\) −1.48403e44 + 8.56808e43i −0.956310 + 0.552126i
\(579\) −1.08366e43 + 3.50079e43i −0.0679261 + 0.219437i
\(580\) 1.59116e43 0.0970211
\(581\) −3.06184e44 5.17007e43i −1.81620 0.306675i
\(582\) 2.83125e43 + 1.24616e44i 0.163385 + 0.719127i
\(583\) 9.44057e43 1.63515e44i 0.530031 0.918041i
\(584\) 3.31495e42 1.91389e42i 0.0181081 0.0104547i
\(585\) −1.36643e43 + 1.99565e43i −0.0726260 + 0.106069i
\(586\) 6.26081e43 1.08440e44i 0.323794 0.560828i
\(587\) 3.13400e44i 1.57721i 0.614899 + 0.788606i \(0.289197\pi\)
−0.614899 + 0.788606i \(0.710803\pi\)
\(588\) 1.26432e44 1.71687e44i 0.619185 0.840815i
\(589\) −1.78912e44 −0.852695
\(590\) 3.81675e43 + 2.20360e43i 0.177036 + 0.102212i
\(591\) 1.50867e44 1.39705e44i 0.681072 0.630685i
\(592\) 1.85841e44 + 3.21886e44i 0.816570 + 1.41434i
\(593\) 3.78102e44 + 2.18297e44i 1.61709 + 0.933626i 0.987668 + 0.156560i \(0.0500406\pi\)
0.629420 + 0.777066i \(0.283293\pi\)
\(594\) 2.34461e44 1.85836e44i 0.976085 0.773654i
\(595\) −6.08422e42 + 3.60322e43i −0.0246566 + 0.146022i
\(596\) 2.66288e44i 1.05054i
\(597\) 5.86505e43 1.89472e44i 0.225259 0.727705i
\(598\) 2.40337e44 + 4.16276e44i 0.898674 + 1.55655i
\(599\) 3.21360e44 1.85538e44i 1.16994 0.675465i 0.216273 0.976333i \(-0.430610\pi\)
0.953666 + 0.300868i \(0.0972764\pi\)
\(600\) −1.68212e43 5.20695e42i −0.0596261 0.0184571i
\(601\) −8.98519e42 −0.0310124 −0.0155062 0.999880i \(-0.504936\pi\)
−0.0155062 + 0.999880i \(0.504936\pi\)
\(602\) −4.05627e44 + 4.90593e44i −1.36327 + 1.64884i
\(603\) −3.17247e44 + 1.52002e44i −1.03829 + 0.497476i
\(604\) −5.55029e43 + 9.61338e43i −0.176899 + 0.306398i
\(605\) −7.48378e42 + 4.32076e42i −0.0232293 + 0.0134114i
\(606\) 2.99379e44 + 3.23298e44i 0.905024 + 0.977329i
\(607\) −2.30405e44 + 3.99073e44i −0.678379 + 1.17499i 0.297090 + 0.954850i \(0.403984\pi\)
−0.975469 + 0.220137i \(0.929349\pi\)
\(608\) 3.24197e44i 0.929718i
\(609\) −1.63805e44 2.50168e44i −0.457561 0.698802i
\(610\) −4.61699e43 −0.125627
\(611\) −7.21801e44 4.16732e44i −1.91319 1.10458i
\(612\) 3.04158e44 4.44218e44i 0.785373 1.14703i
\(613\) 1.90436e44 + 3.29845e44i 0.479051 + 0.829740i 0.999711 0.0240234i \(-0.00764763\pi\)
−0.520661 + 0.853764i \(0.674314\pi\)
\(614\) −3.59251e44 2.07413e44i −0.880448 0.508327i
\(615\) −4.08921e43 + 9.29061e42i −0.0976421 + 0.0221841i
\(616\) −2.21776e43 + 8.25469e42i −0.0515968 + 0.0192048i
\(617\) 4.78475e44i 1.08467i 0.840163 + 0.542334i \(0.182459\pi\)
−0.840163 + 0.542334i \(0.817541\pi\)
\(618\) −6.89024e44 2.13286e44i −1.52202 0.471136i
\(619\) −3.07708e44 5.32965e44i −0.662351 1.14722i −0.979996 0.199015i \(-0.936226\pi\)
0.317646 0.948209i \(-0.397108\pi\)
\(620\) −6.27608e43 + 3.62350e43i −0.131650 + 0.0760083i
\(621\) 5.26415e44 7.77403e43i 1.07612 0.158921i
\(622\) 1.97668e44 0.393812
\(623\) 2.10123e44 2.54137e44i 0.408004 0.493468i
\(624\) 5.67968e44 1.29041e44i 1.07491 0.244217i
\(625\) −2.61030e44 + 4.52118e44i −0.481516 + 0.834010i
\(626\) 7.20376e44 4.15909e44i 1.29530 0.747841i
\(627\) −2.37595e44 + 2.20017e44i −0.416444 + 0.385634i
\(628\) −2.97336e44 + 5.15002e44i −0.508035 + 0.879943i
\(629\) 1.36845e45i 2.27939i
\(630\) −2.70226e43 9.41387e43i −0.0438812 0.152869i
\(631\) −3.47143e44 −0.549590 −0.274795 0.961503i \(-0.588610\pi\)
−0.274795 + 0.961503i \(0.588610\pi\)
\(632\) −2.63188e41 1.51951e41i −0.000406249 0.000234548i
\(633\) 1.25558e44 + 1.35590e44i 0.188967 + 0.204064i
\(634\) −2.66409e44 4.61433e44i −0.390949 0.677144i
\(635\) 2.01785e43 + 1.16500e43i 0.0288741 + 0.0166705i
\(636\) 2.01754e44 + 8.88009e44i 0.281520 + 1.23909i
\(637\) −8.02198e44 2.78861e44i −1.09157 0.379453i
\(638\) 7.83983e44i 1.04034i
\(639\) −7.36325e43 5.66515e42i −0.0952919 0.00733158i
\(640\) −5.56441e42 9.63784e42i −0.00702327 0.0121647i
\(641\) −4.20898e44 + 2.43005e44i −0.518141 + 0.299149i −0.736174 0.676793i \(-0.763369\pi\)
0.218033 + 0.975941i \(0.430036\pi\)
\(642\) 1.45290e44 4.69364e44i 0.174452 0.563571i
\(643\) −6.72727e44 −0.787885 −0.393943 0.919135i \(-0.628889\pi\)
−0.393943 + 0.919135i \(0.628889\pi\)
\(644\) −9.80395e44 1.65545e44i −1.12002 0.189122i
\(645\) 3.30917e43 + 1.45651e44i 0.0368777 + 0.162315i
\(646\) −5.70380e44 + 9.87926e44i −0.620074 + 1.07400i
\(647\) 1.58709e45 9.16307e44i 1.68319 0.971790i 0.723670 0.690146i \(-0.242454\pi\)
0.959519 0.281644i \(-0.0908798\pi\)
\(648\) −9.34376e42 + 6.03631e43i −0.00966767 + 0.0624556i
\(649\) −5.54609e44 + 9.60611e44i −0.559850 + 0.969688i
\(650\) 1.65688e45i 1.63184i
\(651\) 1.21580e45 + 6.13720e44i 1.16833 + 0.589759i
\(652\) −2.03701e45 −1.91000
\(653\) 9.50583e44 + 5.48819e44i 0.869719 + 0.502133i 0.867255 0.497864i \(-0.165882\pi\)
0.00246441 + 0.999997i \(0.499216\pi\)
\(654\) −5.17295e44 + 4.79024e44i −0.461843 + 0.427674i
\(655\) −6.39471e43 1.10760e44i −0.0557134 0.0964985i
\(656\) 8.74549e44 + 5.04921e44i 0.743572 + 0.429301i
\(657\) −3.59582e44 + 1.72286e44i −0.298368 + 0.142957i
\(658\) 3.16306e45 1.17732e45i 2.56149 0.953410i
\(659\) 4.45430e44i 0.352057i 0.984385 + 0.176028i \(0.0563251\pi\)
−0.984385 + 0.176028i \(0.943675\pi\)
\(660\) −3.87864e43 + 1.25300e44i −0.0299211 + 0.0966606i
\(661\) 1.64422e44 + 2.84788e44i 0.123805 + 0.214436i 0.921265 0.388935i \(-0.127157\pi\)
−0.797460 + 0.603371i \(0.793824\pi\)
\(662\) 8.15767e44 4.70983e44i 0.599568 0.346161i
\(663\) −2.04853e45 6.34118e44i −1.46969 0.454939i
\(664\) −1.66216e44 −0.116408
\(665\) 3.69785e43 + 9.93487e43i 0.0252815 + 0.0679228i
\(666\) 1.58479e45 + 3.30766e45i 1.05776 + 2.20766i
\(667\) −6.97206e44 + 1.20760e45i −0.454305 + 0.786879i
\(668\) −1.14837e45 + 6.63011e44i −0.730564 + 0.421791i
\(669\) −1.27027e45 1.37176e45i −0.789003 0.852039i
\(670\) 1.50965e44 2.61479e44i 0.0915543 0.158577i
\(671\) 1.16202e45i 0.688100i
\(672\) −1.11209e45 + 2.20309e45i −0.643031 + 1.27387i
\(673\) −9.96066e44 −0.562402 −0.281201 0.959649i \(-0.590733\pi\)
−0.281201 + 0.959649i \(0.590733\pi\)
\(674\) −1.37305e45 7.92729e44i −0.757055 0.437086i
\(675\) 1.70543e45 + 6.75204e44i 0.918276 + 0.363559i
\(676\) 3.33121e44 + 5.76982e44i 0.175168 + 0.303400i
\(677\) 7.72559e44 + 4.46037e44i 0.396746 + 0.229062i 0.685079 0.728469i \(-0.259768\pi\)
−0.288333 + 0.957530i \(0.593101\pi\)
\(678\) 3.19940e45 7.26898e44i 1.60470 0.364585i
\(679\) −1.75307e44 + 1.03821e45i −0.0858781 + 0.508591i
\(680\) 1.95605e43i 0.00935917i
\(681\) −1.28802e45 3.98704e44i −0.601963 0.186336i
\(682\) −1.78534e45 3.09230e45i −0.815024 1.41166i
\(683\) −1.62002e43 + 9.35320e42i −0.00722420 + 0.00417089i −0.503608 0.863932i \(-0.667994\pi\)
0.496384 + 0.868103i \(0.334661\pi\)
\(684\) 1.19807e44 1.55718e45i 0.0521896 0.678332i
\(685\) −1.16843e44 −0.0497225
\(686\) 2.94024e45 1.78398e45i 1.22235 0.741659i
\(687\) −1.40534e45 + 3.19292e44i −0.570788 + 0.129682i
\(688\) 1.79845e45 3.11501e45i 0.713647 1.23607i
\(689\) 3.14130e45 1.81363e45i 1.21787 0.703138i
\(690\) −3.35105e44 + 3.10313e44i −0.126939 + 0.117548i
\(691\) −4.63651e44 + 8.03067e44i −0.171610 + 0.297237i −0.938983 0.343964i \(-0.888230\pi\)
0.767373 + 0.641201i \(0.221564\pi\)
\(692\) 3.05770e45i 1.10585i
\(693\) 2.36931e45 6.80111e44i 0.837317 0.240352i
\(694\) 5.14981e45 1.77844
\(695\) −6.17091e43 3.56278e43i −0.0208254 0.0120235i
\(696\) −1.08754e44 1.17443e44i −0.0358672 0.0387327i
\(697\) −1.85901e45 3.21991e45i −0.599181 1.03781i
\(698\) −4.12929e45 2.38404e45i −1.30073 0.750979i
\(699\) −3.51032e44 1.54504e45i −0.108072 0.475671i
\(700\) −2.64134e45 2.18389e45i −0.794797 0.657146i
\(701\) 4.02850e45i 1.18483i −0.805634 0.592414i \(-0.798175\pi\)
0.805634 0.592414i \(-0.201825\pi\)
\(702\) 5.68583e45 8.39677e44i 1.63456 0.241389i
\(703\) −1.98491e45 3.43796e45i −0.557770 0.966086i
\(704\) 2.98368e45 1.72263e45i 0.819577 0.473183i
\(705\) 2.34174e44 7.56506e44i 0.0628802 0.203136i
\(706\) −2.58829e45 −0.679419
\(707\) 1.26639e45 + 3.40236e45i 0.324980 + 0.873112i
\(708\) −1.18525e45 5.21682e45i −0.297358 1.30880i
\(709\) −1.27710e45 + 2.21200e45i −0.313245 + 0.542556i −0.979063 0.203558i \(-0.934749\pi\)
0.665818 + 0.746114i \(0.268083\pi\)
\(710\) 5.48927e43 3.16923e43i 0.0131638 0.00760012i
\(711\) 2.61203e43 + 1.78846e43i 0.00612441 + 0.00419340i
\(712\) 8.82557e43 1.52863e44i 0.0202331 0.0350448i
\(713\) 6.35089e45i 1.42365i
\(714\) 7.26491e45 4.75691e45i 1.59243 1.04269i
\(715\) 5.22461e44 0.111984
\(716\) −2.12234e45 1.22533e45i −0.444842 0.256830i
\(717\) −5.49626e45 + 5.08963e45i −1.12658 + 1.04323i
\(718\) −1.25757e45 2.17817e45i −0.252081 0.436617i
\(719\) 3.99691e45 + 2.30762e45i 0.783541 + 0.452378i 0.837684 0.546155i \(-0.183909\pi\)
−0.0541425 + 0.998533i \(0.517243\pi\)
\(720\) 2.39125e44 + 4.99082e44i 0.0458464 + 0.0956869i
\(721\) −4.58004e45 3.78682e45i −0.858826 0.710086i
\(722\) 4.48645e45i 0.822825i
\(723\) 6.17588e43 1.99513e44i 0.0110786 0.0357897i
\(724\) 4.83658e44 + 8.37720e44i 0.0848636 + 0.146988i
\(725\) −4.16257e45 + 2.40326e45i −0.714420 + 0.412471i
\(726\) 1.96170e45 + 6.07239e44i 0.329341 + 0.101947i
\(727\) 3.40492e45 0.559187 0.279593 0.960119i \(-0.409800\pi\)
0.279593 + 0.960119i \(0.409800\pi\)
\(728\) −4.48263e44 7.56916e43i −0.0720164 0.0121603i
\(729\) 1.45278e45 6.19461e45i 0.228329 0.973584i
\(730\) 1.71111e44 2.96372e44i 0.0263094 0.0455692i
\(731\) −1.14688e46 + 6.62152e45i −1.72520 + 0.996047i
\(732\) 3.80789e45 + 4.11211e45i 0.560411 + 0.605185i
\(733\) −3.98421e45 + 6.90085e45i −0.573692 + 0.993663i 0.422491 + 0.906367i \(0.361156\pi\)
−0.996182 + 0.0872959i \(0.972177\pi\)
\(734\) 1.16337e46i 1.63901i
\(735\) 8.95070e43 8.01974e44i 0.0123384 0.110551i
\(736\) 1.15081e46 1.55224
\(737\) 6.58096e45 + 3.79952e45i 0.868579 + 0.501475i
\(738\) 8.22233e45 + 5.62986e45i 1.06192 + 0.727102i
\(739\) 4.91904e45 + 8.52003e45i 0.621684 + 1.07679i 0.989172 + 0.146760i \(0.0468844\pi\)
−0.367489 + 0.930028i