Properties

Label 3.39.b.a.2.2
Level 3
Weight 39
Character 3.2
Analytic conductor 27.439
Analytic rank 0
Dimension 12
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 39 \)
Character orbit: \([\chi]\) \(=\) 3.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(27.4390407101\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 17353504902 x^{10} + 111006258614054318328 x^{8} + 323765701965839203118204176384 x^{6} + 420150309279704216298413492838082805760 x^{4} + 190068212511425710374530430459662273636990976000 x^{2} + 27342285412416035125187079526375866471795145886924800000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{75}\cdot 3^{91}\cdot 5^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2.2
Root \(-65373.8i\) of defining polynomial
Character \(\chi\) \(=\) 3.2
Dual form 3.39.b.a.2.11

$q$-expansion

\(f(q)\) \(=\) \(q-784486. i q^{2} +(1.15997e9 + 7.30136e7i) q^{3} -3.40540e11 q^{4} -3.07374e13i q^{5} +(5.72781e13 - 9.09976e14i) q^{6} +1.07708e16 q^{7} +5.15107e16i q^{8} +(1.34019e18 + 1.69386e17i) q^{9} +O(q^{10})\) \(q-784486. i q^{2} +(1.15997e9 + 7.30136e7i) q^{3} -3.40540e11 q^{4} -3.07374e13i q^{5} +(5.72781e13 - 9.09976e14i) q^{6} +1.07708e16 q^{7} +5.15107e16i q^{8} +(1.34019e18 + 1.69386e17i) q^{9} -2.41131e19 q^{10} -2.63951e19i q^{11} +(-3.95014e20 - 2.48640e19i) q^{12} +2.34737e21 q^{13} -8.44954e21i q^{14} +(2.24425e21 - 3.56544e22i) q^{15} -5.31974e22 q^{16} -1.67135e23i q^{17} +(1.32881e23 - 1.05136e24i) q^{18} -9.52513e23 q^{19} +1.04673e25i q^{20} +(1.24938e25 + 7.86415e23i) q^{21} -2.07065e25 q^{22} +4.84019e25i q^{23} +(-3.76098e24 + 5.97506e25i) q^{24} -5.80992e26 q^{25} -1.84148e27i q^{26} +(1.54221e27 + 2.94335e26i) q^{27} -3.66789e27 q^{28} +8.06134e27i q^{29} +(-2.79703e28 - 1.76058e27i) q^{30} -1.15899e28 q^{31} +5.58918e28i q^{32} +(1.92720e27 - 3.06174e28i) q^{33} -1.31115e29 q^{34} -3.31067e29i q^{35} +(-4.56388e29 - 5.76828e28i) q^{36} -4.26694e29 q^{37} +7.47233e29i q^{38} +(2.72287e30 + 1.71390e29i) q^{39} +1.58331e30 q^{40} +7.27638e30i q^{41} +(6.16931e29 - 9.80118e30i) q^{42} +9.82872e30 q^{43} +8.98856e30i q^{44} +(5.20651e30 - 4.11940e31i) q^{45} +3.79706e31 q^{46} -8.44918e29i q^{47} +(-6.17072e31 - 3.88413e30i) q^{48} -1.39246e31 q^{49} +4.55780e32i q^{50} +(1.22031e31 - 1.93871e32i) q^{51} -7.99373e32 q^{52} +6.22306e31i q^{53} +(2.30901e32 - 1.20984e33i) q^{54} -8.11317e32 q^{55} +5.54811e32i q^{56} +(-1.10488e33 - 6.95464e31i) q^{57} +6.32401e33 q^{58} -5.85547e33i q^{59} +(-7.64256e32 + 1.21417e34i) q^{60} -2.26498e33 q^{61} +9.09213e33i q^{62} +(1.44349e34 + 1.82443e33i) q^{63} +2.92235e34 q^{64} -7.21522e34i q^{65} +(-2.40189e34 - 1.51186e33i) q^{66} -2.71859e34 q^{67} +5.69162e34i q^{68} +(-3.53399e33 + 5.61445e34i) q^{69} -2.59717e35 q^{70} -6.76007e34i q^{71} +(-8.72521e33 + 6.90341e34i) q^{72} +4.44073e35 q^{73} +3.34736e35i q^{74} +(-6.73931e35 - 4.24203e34i) q^{75} +3.24368e35 q^{76} -2.84296e35i q^{77} +(1.34453e35 - 2.13605e36i) q^{78} -1.68762e35 q^{79} +1.63515e36i q^{80} +(1.76742e36 + 4.54020e35i) q^{81} +5.70822e36 q^{82} +3.55603e36i q^{83} +(-4.25462e36 - 2.67805e35i) q^{84} -5.13731e36 q^{85} -7.71049e36i q^{86} +(-5.88587e35 + 9.35088e36i) q^{87} +1.35963e36 q^{88} -7.51232e36i q^{89} +(-3.23161e37 - 4.08443e36i) q^{90} +2.52831e37 q^{91} -1.64828e37i q^{92} +(-1.34439e37 - 8.46222e35i) q^{93} -6.62826e35 q^{94} +2.92778e37i q^{95} +(-4.08086e36 + 6.48325e37i) q^{96} +2.81399e37 q^{97} +1.09236e37i q^{98} +(4.47096e36 - 3.53744e37i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 114742404q^{3} - 1699274528448q^{4} - 483611204680128q^{6} + 8107872236538648q^{7} - 424319151461513940q^{9} + O(q^{10}) \) \( 12q - 114742404q^{3} - 1699274528448q^{4} - 483611204680128q^{6} + 8107872236538648q^{7} - 424319151461513940q^{9} + 8521437485093339520q^{10} - 2862564534392665536q^{12} + \)\(10\!\cdots\!52\)\(q^{13} + \)\(63\!\cdots\!80\)\(q^{15} + \)\(67\!\cdots\!56\)\(q^{16} + \)\(14\!\cdots\!20\)\(q^{18} - \)\(46\!\cdots\!60\)\(q^{19} + \)\(33\!\cdots\!52\)\(q^{21} - \)\(13\!\cdots\!60\)\(q^{22} + \)\(78\!\cdots\!84\)\(q^{24} - \)\(12\!\cdots\!20\)\(q^{25} + \)\(35\!\cdots\!04\)\(q^{27} - \)\(77\!\cdots\!68\)\(q^{28} - \)\(31\!\cdots\!40\)\(q^{30} + \)\(62\!\cdots\!84\)\(q^{31} - \)\(20\!\cdots\!40\)\(q^{33} + \)\(27\!\cdots\!04\)\(q^{34} + \)\(52\!\cdots\!44\)\(q^{36} - \)\(10\!\cdots\!52\)\(q^{37} + \)\(37\!\cdots\!68\)\(q^{39} - \)\(86\!\cdots\!40\)\(q^{40} + \)\(37\!\cdots\!80\)\(q^{42} + \)\(10\!\cdots\!92\)\(q^{43} - \)\(61\!\cdots\!20\)\(q^{45} + \)\(13\!\cdots\!64\)\(q^{46} - \)\(16\!\cdots\!64\)\(q^{48} - \)\(74\!\cdots\!52\)\(q^{49} + \)\(71\!\cdots\!72\)\(q^{51} - \)\(99\!\cdots\!32\)\(q^{52} + \)\(12\!\cdots\!12\)\(q^{54} - \)\(14\!\cdots\!40\)\(q^{55} - \)\(19\!\cdots\!12\)\(q^{57} + \)\(54\!\cdots\!20\)\(q^{58} - \)\(21\!\cdots\!80\)\(q^{60} + \)\(19\!\cdots\!24\)\(q^{61} - \)\(68\!\cdots\!88\)\(q^{63} - \)\(33\!\cdots\!44\)\(q^{64} + \)\(29\!\cdots\!20\)\(q^{66} - \)\(12\!\cdots\!52\)\(q^{67} + \)\(14\!\cdots\!32\)\(q^{69} + \)\(13\!\cdots\!80\)\(q^{70} - \)\(84\!\cdots\!40\)\(q^{72} + \)\(90\!\cdots\!72\)\(q^{73} - \)\(19\!\cdots\!60\)\(q^{75} + \)\(37\!\cdots\!48\)\(q^{76} - \)\(47\!\cdots\!80\)\(q^{78} + \)\(33\!\cdots\!20\)\(q^{79} - \)\(38\!\cdots\!88\)\(q^{81} + \)\(97\!\cdots\!60\)\(q^{82} - \)\(23\!\cdots\!52\)\(q^{84} + \)\(16\!\cdots\!60\)\(q^{85} - \)\(46\!\cdots\!20\)\(q^{87} + \)\(11\!\cdots\!20\)\(q^{88} - \)\(16\!\cdots\!20\)\(q^{90} + \)\(12\!\cdots\!24\)\(q^{91} - \)\(17\!\cdots\!28\)\(q^{93} + \)\(32\!\cdots\!64\)\(q^{94} - \)\(45\!\cdots\!24\)\(q^{96} + \)\(24\!\cdots\!28\)\(q^{97} - \)\(34\!\cdots\!40\)\(q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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 (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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 784486.i 1.49629i −0.663537 0.748144i \(-0.730945\pi\)
0.663537 0.748144i \(-0.269055\pi\)
\(3\) 1.15997e9 + 7.30136e7i 0.998025 + 0.0628202i
\(4\) −3.40540e11 −1.23888
\(5\) 3.07374e13i 1.61153i −0.592237 0.805764i \(-0.701755\pi\)
0.592237 0.805764i \(-0.298245\pi\)
\(6\) 5.72781e13 9.09976e14i 0.0939971 1.49333i
\(7\) 1.07708e16 0.944899 0.472449 0.881358i \(-0.343370\pi\)
0.472449 + 0.881358i \(0.343370\pi\)
\(8\) 5.15107e16i 0.357427i
\(9\) 1.34019e18 + 1.69386e17i 0.992107 + 0.125392i
\(10\) −2.41131e19 −2.41131
\(11\) 2.63951e19i 0.431580i −0.976440 0.215790i \(-0.930767\pi\)
0.976440 0.215790i \(-0.0692327\pi\)
\(12\) −3.95014e20 2.48640e19i −1.23643 0.0778265i
\(13\) 2.34737e21 1.60568 0.802839 0.596196i \(-0.203322\pi\)
0.802839 + 0.596196i \(0.203322\pi\)
\(14\) 8.44954e21i 1.41384i
\(15\) 2.24425e21 3.56544e22i 0.101237 1.60834i
\(16\) −5.31974e22 −0.704062
\(17\) 1.67135e23i 0.699099i −0.936918 0.349550i \(-0.886335\pi\)
0.936918 0.349550i \(-0.113665\pi\)
\(18\) 1.32881e23 1.05136e24i 0.187623 1.48448i
\(19\) −9.52513e23 −0.481451 −0.240726 0.970593i \(-0.577385\pi\)
−0.240726 + 0.970593i \(0.577385\pi\)
\(20\) 1.04673e25i 1.99648i
\(21\) 1.24938e25 + 7.86415e23i 0.943033 + 0.0593588i
\(22\) −2.07065e25 −0.645768
\(23\) 4.84019e25i 0.648684i 0.945940 + 0.324342i \(0.105143\pi\)
−0.945940 + 0.324342i \(0.894857\pi\)
\(24\) −3.76098e24 + 5.97506e25i −0.0224537 + 0.356721i
\(25\) −5.80992e26 −1.59702
\(26\) 1.84148e27i 2.40255i
\(27\) 1.54221e27 + 2.94335e26i 0.982271 + 0.187469i
\(28\) −3.66789e27 −1.17061
\(29\) 8.06134e27i 1.32083i 0.750903 + 0.660413i \(0.229619\pi\)
−0.750903 + 0.660413i \(0.770381\pi\)
\(30\) −2.79703e28 1.76058e27i −2.40655 0.151479i
\(31\) −1.15899e28 −0.534821 −0.267411 0.963583i \(-0.586168\pi\)
−0.267411 + 0.963583i \(0.586168\pi\)
\(32\) 5.58918e28i 1.41091i
\(33\) 1.92720e27 3.06174e28i 0.0271120 0.430728i
\(34\) −1.31115e29 −1.04605
\(35\) 3.31067e29i 1.52273i
\(36\) −4.56388e29 5.76828e28i −1.22910 0.155346i
\(37\) −4.26694e29 −0.682785 −0.341393 0.939921i \(-0.610899\pi\)
−0.341393 + 0.939921i \(0.610899\pi\)
\(38\) 7.47233e29i 0.720390i
\(39\) 2.72287e30 + 1.71390e29i 1.60251 + 0.100869i
\(40\) 1.58331e30 0.576003
\(41\) 7.27638e30i 1.65585i 0.560835 + 0.827927i \(0.310480\pi\)
−0.560835 + 0.827927i \(0.689520\pi\)
\(42\) 6.16931e29 9.80118e30i 0.0888178 1.41105i
\(43\) 9.82872e30 0.904891 0.452446 0.891792i \(-0.350552\pi\)
0.452446 + 0.891792i \(0.350552\pi\)
\(44\) 8.98856e30i 0.534674i
\(45\) 5.20651e30 4.11940e31i 0.202073 1.59881i
\(46\) 3.79706e31 0.970618
\(47\) 8.44918e29i 0.0143534i −0.999974 0.00717671i \(-0.997716\pi\)
0.999974 0.00717671i \(-0.00228444\pi\)
\(48\) −6.17072e31 3.88413e30i −0.702672 0.0442294i
\(49\) −1.39246e31 −0.107166
\(50\) 4.55780e32i 2.38960i
\(51\) 1.22031e31 1.93871e32i 0.0439176 0.697718i
\(52\) −7.99373e32 −1.98923
\(53\) 6.22306e31i 0.107836i 0.998545 + 0.0539178i \(0.0171709\pi\)
−0.998545 + 0.0539178i \(0.982829\pi\)
\(54\) 2.30901e32 1.20984e33i 0.280508 1.46976i
\(55\) −8.11317e32 −0.695503
\(56\) 5.54811e32i 0.337732i
\(57\) −1.10488e33 6.95464e31i −0.480501 0.0302449i
\(58\) 6.32401e33 1.97633
\(59\) 5.85547e33i 1.32243i −0.750195 0.661217i \(-0.770040\pi\)
0.750195 0.661217i \(-0.229960\pi\)
\(60\) −7.64256e32 + 1.21417e34i −0.125420 + 1.99254i
\(61\) −2.26498e33 −0.271518 −0.135759 0.990742i \(-0.543347\pi\)
−0.135759 + 0.990742i \(0.543347\pi\)
\(62\) 9.09213e33i 0.800246i
\(63\) 1.44349e34 + 1.82443e33i 0.937441 + 0.118483i
\(64\) 2.92235e34 1.40706
\(65\) 7.21522e34i 2.58759i
\(66\) −2.40189e34 1.51186e33i −0.644493 0.0405673i
\(67\) −2.71859e34 −0.548180 −0.274090 0.961704i \(-0.588377\pi\)
−0.274090 + 0.961704i \(0.588377\pi\)
\(68\) 5.69162e34i 0.866097i
\(69\) −3.53399e33 + 5.61445e34i −0.0407505 + 0.647403i
\(70\) −2.59717e35 −2.27844
\(71\) 6.76007e34i 0.452942i −0.974018 0.226471i \(-0.927281\pi\)
0.974018 0.226471i \(-0.0727189\pi\)
\(72\) −8.72521e33 + 6.90341e34i −0.0448186 + 0.354606i
\(73\) 4.44073e35 1.75517 0.877587 0.479417i \(-0.159152\pi\)
0.877587 + 0.479417i \(0.159152\pi\)
\(74\) 3.34736e35i 1.02164i
\(75\) −6.73931e35 4.24203e34i −1.59387 0.100325i
\(76\) 3.24368e35 0.596459
\(77\) 2.84296e35i 0.407800i
\(78\) 1.34453e35 2.13605e36i 0.150929 2.39781i
\(79\) −1.68762e35 −0.148717 −0.0743584 0.997232i \(-0.523691\pi\)
−0.0743584 + 0.997232i \(0.523691\pi\)
\(80\) 1.63515e36i 1.13462i
\(81\) 1.76742e36 + 4.54020e35i 0.968554 + 0.248805i
\(82\) 5.70822e36 2.47763
\(83\) 3.55603e36i 1.22598i 0.790092 + 0.612988i \(0.210032\pi\)
−0.790092 + 0.612988i \(0.789968\pi\)
\(84\) −4.25462e36 2.67805e35i −1.16830 0.0735382i
\(85\) −5.13731e36 −1.12662
\(86\) 7.71049e36i 1.35398i
\(87\) −5.88587e35 + 9.35088e36i −0.0829746 + 1.31822i
\(88\) 1.35963e36 0.154258
\(89\) 7.51232e36i 0.687644i −0.939035 0.343822i \(-0.888278\pi\)
0.939035 0.343822i \(-0.111722\pi\)
\(90\) −3.23161e37 4.08443e36i −2.39228 0.302360i
\(91\) 2.52831e37 1.51720
\(92\) 1.64828e37i 0.803639i
\(93\) −1.34439e37 8.46222e35i −0.533765 0.0335976i
\(94\) −6.62826e35 −0.0214768
\(95\) 2.92778e37i 0.775872i
\(96\) −4.08086e36 + 6.48325e37i −0.0886335 + 1.40812i
\(97\) 2.81399e37 0.501948 0.250974 0.967994i \(-0.419249\pi\)
0.250974 + 0.967994i \(0.419249\pi\)
\(98\) 1.09236e37i 0.160351i
\(99\) 4.47096e36 3.53744e37i 0.0541169 0.428174i
\(100\) 1.97851e38 1.97851
\(101\) 1.58783e38i 1.31431i −0.753757 0.657153i \(-0.771760\pi\)
0.753757 0.657153i \(-0.228240\pi\)
\(102\) −1.52089e38 9.57319e36i −1.04399 0.0657133i
\(103\) 1.04178e38 0.594110 0.297055 0.954860i \(-0.403995\pi\)
0.297055 + 0.954860i \(0.403995\pi\)
\(104\) 1.20915e38i 0.573912i
\(105\) 2.41724e37 3.84026e38i 0.0956583 1.51972i
\(106\) 4.88190e37 0.161353
\(107\) 5.90450e38i 1.63264i 0.577597 + 0.816322i \(0.303991\pi\)
−0.577597 + 0.816322i \(0.696009\pi\)
\(108\) −5.25183e38 1.00233e38i −1.21691 0.232251i
\(109\) −1.13397e38 −0.220546 −0.110273 0.993901i \(-0.535172\pi\)
−0.110273 + 0.993901i \(0.535172\pi\)
\(110\) 6.36466e38i 1.04067i
\(111\) −4.94951e38 3.11545e37i −0.681437 0.0428927i
\(112\) −5.72979e38 −0.665268
\(113\) 6.92711e38i 0.679300i −0.940552 0.339650i \(-0.889691\pi\)
0.940552 0.339650i \(-0.110309\pi\)
\(114\) −5.45581e37 + 8.66764e38i −0.0452551 + 0.718967i
\(115\) 1.48775e39 1.04537
\(116\) 2.74521e39i 1.63634i
\(117\) 3.14592e39 + 3.97613e38i 1.59300 + 0.201340i
\(118\) −4.59353e39 −1.97874
\(119\) 1.80018e39i 0.660578i
\(120\) 1.83658e39 + 1.15603e38i 0.574866 + 0.0361847i
\(121\) 3.04374e39 0.813738
\(122\) 1.77685e39i 0.406269i
\(123\) −5.31274e38 + 8.44035e39i −0.104021 + 1.65258i
\(124\) 3.94683e39 0.662577
\(125\) 6.67601e39i 0.962114i
\(126\) 1.43124e39 1.13240e40i 0.177285 1.40268i
\(127\) 6.02500e39 0.642224 0.321112 0.947041i \(-0.395943\pi\)
0.321112 + 0.947041i \(0.395943\pi\)
\(128\) 7.56199e39i 0.694459i
\(129\) 1.14010e40 + 7.17630e38i 0.903104 + 0.0568455i
\(130\) −5.66024e40 −3.87178
\(131\) 1.13980e40i 0.674021i −0.941501 0.337011i \(-0.890584\pi\)
0.941501 0.337011i \(-0.109416\pi\)
\(132\) −6.56287e38 + 1.04264e40i −0.0335884 + 0.533618i
\(133\) −1.02593e40 −0.454923
\(134\) 2.13270e40i 0.820235i
\(135\) 9.04709e39 4.74035e40i 0.302112 1.58296i
\(136\) 8.60925e39 0.249877
\(137\) 2.61641e40i 0.660715i 0.943856 + 0.330358i \(0.107169\pi\)
−0.943856 + 0.330358i \(0.892831\pi\)
\(138\) 4.40446e40 + 2.77237e39i 0.968701 + 0.0609745i
\(139\) 1.77183e40 0.339735 0.169867 0.985467i \(-0.445666\pi\)
0.169867 + 0.985467i \(0.445666\pi\)
\(140\) 1.12741e41i 1.88647i
\(141\) 6.16905e37 9.80076e38i 0.000901686 0.0143251i
\(142\) −5.30318e40 −0.677732
\(143\) 6.19590e40i 0.692979i
\(144\) −7.12947e40 9.01093e39i −0.698505 0.0882840i
\(145\) 2.47785e41 2.12855
\(146\) 3.48369e41i 2.62625i
\(147\) −1.61520e40 1.01668e39i −0.106954 0.00673219i
\(148\) 1.45306e41 0.845886
\(149\) 1.85063e40i 0.0947938i 0.998876 + 0.0473969i \(0.0150926\pi\)
−0.998876 + 0.0473969i \(0.984907\pi\)
\(150\) −3.32781e40 + 5.28689e41i −0.150115 + 2.38488i
\(151\) −2.58190e41 −1.02654 −0.513272 0.858226i \(-0.671567\pi\)
−0.513272 + 0.858226i \(0.671567\pi\)
\(152\) 4.90646e40i 0.172084i
\(153\) 2.83105e40 2.23993e41i 0.0876617 0.693581i
\(154\) −2.23026e41 −0.610186
\(155\) 3.56245e41i 0.861879i
\(156\) −9.27246e41 5.83651e40i −1.98531 0.124964i
\(157\) −6.27539e40 −0.119000 −0.0595001 0.998228i \(-0.518951\pi\)
−0.0595001 + 0.998228i \(0.518951\pi\)
\(158\) 1.32391e41i 0.222523i
\(159\) −4.54368e39 + 7.21854e40i −0.00677426 + 0.107623i
\(160\) 1.71797e42 2.27371
\(161\) 5.21327e41i 0.612941i
\(162\) 3.56172e41 1.38651e42i 0.372284 1.44923i
\(163\) −1.58317e42 −1.47219 −0.736094 0.676879i \(-0.763332\pi\)
−0.736094 + 0.676879i \(0.763332\pi\)
\(164\) 2.47790e42i 2.05140i
\(165\) −9.41099e41 5.92371e40i −0.694130 0.0436917i
\(166\) 2.78965e42 1.83441
\(167\) 2.76798e42i 1.62387i 0.583749 + 0.811934i \(0.301585\pi\)
−0.583749 + 0.811934i \(0.698415\pi\)
\(168\) −4.05087e40 + 6.43562e41i −0.0212164 + 0.337065i
\(169\) 3.37294e42 1.57820
\(170\) 4.03015e42i 1.68574i
\(171\) −1.27655e42 1.61343e41i −0.477651 0.0603703i
\(172\) −3.34707e42 −1.12105
\(173\) 4.23364e42i 1.27010i −0.772471 0.635050i \(-0.780979\pi\)
0.772471 0.635050i \(-0.219021\pi\)
\(174\) 7.33563e42 + 4.61738e41i 1.97243 + 0.124154i
\(175\) −6.25776e42 −1.50902
\(176\) 1.40415e42i 0.303859i
\(177\) 4.27529e41 6.79215e42i 0.0830756 1.31982i
\(178\) −5.89330e42 −1.02891
\(179\) 2.84670e42i 0.446821i −0.974724 0.223411i \(-0.928281\pi\)
0.974724 0.223411i \(-0.0717191\pi\)
\(180\) −1.77302e42 + 1.40282e43i −0.250344 + 1.98072i
\(181\) −2.20401e42 −0.280105 −0.140052 0.990144i \(-0.544727\pi\)
−0.140052 + 0.990144i \(0.544727\pi\)
\(182\) 1.98342e43i 2.27017i
\(183\) −2.62730e42 1.65375e41i −0.270981 0.0170568i
\(184\) −2.49321e42 −0.231857
\(185\) 1.31155e43i 1.10033i
\(186\) −6.63849e41 + 1.05466e43i −0.0502717 + 0.798666i
\(187\) −4.41155e42 −0.301717
\(188\) 2.87728e41i 0.0177821i
\(189\) 1.66108e43 + 3.17022e42i 0.928146 + 0.177139i
\(190\) 2.29680e43 1.16093
\(191\) 1.70688e43i 0.780852i 0.920634 + 0.390426i \(0.127672\pi\)
−0.920634 + 0.390426i \(0.872328\pi\)
\(192\) 3.38982e43 + 2.13371e42i 1.40428 + 0.0883918i
\(193\) −2.36210e43 −0.886562 −0.443281 0.896383i \(-0.646186\pi\)
−0.443281 + 0.896383i \(0.646186\pi\)
\(194\) 2.20753e43i 0.751059i
\(195\) 5.26809e42 8.36941e43i 0.162553 2.58248i
\(196\) 4.74187e42 0.132765
\(197\) 5.31510e43i 1.35099i 0.737363 + 0.675497i \(0.236071\pi\)
−0.737363 + 0.675497i \(0.763929\pi\)
\(198\) −2.77507e43 3.50741e42i −0.640671 0.0809744i
\(199\) 2.82826e43 0.593350 0.296675 0.954978i \(-0.404122\pi\)
0.296675 + 0.954978i \(0.404122\pi\)
\(200\) 2.99273e43i 0.570818i
\(201\) −3.15348e43 1.98494e42i −0.547097 0.0344368i
\(202\) −1.24563e44 −1.96658
\(203\) 8.68271e43i 1.24805i
\(204\) −4.15565e42 + 6.60209e43i −0.0544084 + 0.864386i
\(205\) 2.23657e44 2.66845
\(206\) 8.17258e43i 0.888960i
\(207\) −8.19862e42 + 6.48677e43i −0.0813400 + 0.643564i
\(208\) −1.24874e44 −1.13050
\(209\) 2.51416e43i 0.207785i
\(210\) −3.01263e44 1.89629e43i −2.27394 0.143132i
\(211\) −7.14319e43 −0.492636 −0.246318 0.969189i \(-0.579221\pi\)
−0.246318 + 0.969189i \(0.579221\pi\)
\(212\) 2.11920e43i 0.133595i
\(213\) 4.93577e42 7.84145e43i 0.0284539 0.452047i
\(214\) 4.63200e44 2.44290
\(215\) 3.02110e44i 1.45826i
\(216\) −1.51614e43 + 7.94401e43i −0.0670065 + 0.351090i
\(217\) −1.24833e44 −0.505352
\(218\) 8.89584e43i 0.330000i
\(219\) 5.15110e44 + 3.24234e43i 1.75171 + 0.110260i
\(220\) 2.76285e44 0.861642
\(221\) 3.92329e44i 1.12253i
\(222\) −2.44402e43 + 3.88282e44i −0.0641799 + 1.01962i
\(223\) 2.38406e44 0.574811 0.287405 0.957809i \(-0.407207\pi\)
0.287405 + 0.957809i \(0.407207\pi\)
\(224\) 6.01999e44i 1.33316i
\(225\) −7.78640e44 9.84122e43i −1.58441 0.200254i
\(226\) −5.43421e44 −1.01643
\(227\) 7.53137e44i 1.29534i 0.761922 + 0.647668i \(0.224256\pi\)
−0.761922 + 0.647668i \(0.775744\pi\)
\(228\) 3.76256e44 + 2.36833e43i 0.595281 + 0.0374697i
\(229\) −1.95667e44 −0.284867 −0.142434 0.989804i \(-0.545493\pi\)
−0.142434 + 0.989804i \(0.545493\pi\)
\(230\) 1.16712e45i 1.56418i
\(231\) 2.07575e43 3.29774e44i 0.0256181 0.406994i
\(232\) −4.15245e44 −0.472099
\(233\) 8.52785e43i 0.0893464i 0.999002 + 0.0446732i \(0.0142246\pi\)
−0.999002 + 0.0446732i \(0.985775\pi\)
\(234\) 3.11922e44 2.46793e45i 0.301262 2.38359i
\(235\) −2.59706e43 −0.0231309
\(236\) 1.99402e45i 1.63833i
\(237\) −1.95758e44 1.23219e43i −0.148423 0.00934242i
\(238\) −1.41222e45 −0.988415
\(239\) 1.01935e45i 0.658812i 0.944188 + 0.329406i \(0.106849\pi\)
−0.944188 + 0.329406i \(0.893151\pi\)
\(240\) −1.19388e44 + 1.89672e45i −0.0712768 + 1.13237i
\(241\) −1.47874e45 −0.815769 −0.407884 0.913034i \(-0.633733\pi\)
−0.407884 + 0.913034i \(0.633733\pi\)
\(242\) 2.38777e45i 1.21759i
\(243\) 2.01699e45 + 6.55693e44i 0.951010 + 0.309159i
\(244\) 7.71317e44 0.336377
\(245\) 4.28006e44i 0.172701i
\(246\) 6.62134e45 + 4.16777e44i 2.47274 + 0.155646i
\(247\) −2.23590e45 −0.773056
\(248\) 5.97005e44i 0.191160i
\(249\) −2.59638e44 + 4.12487e45i −0.0770161 + 1.22355i
\(250\) 5.23723e45 1.43960
\(251\) 5.02297e45i 1.27985i −0.768436 0.639926i \(-0.778965\pi\)
0.768436 0.639926i \(-0.221035\pi\)
\(252\) −4.91566e45 6.21290e44i −1.16137 0.146786i
\(253\) 1.27757e45 0.279959
\(254\) 4.72653e45i 0.960952i
\(255\) −5.95911e45 3.75093e44i −1.12439 0.0707744i
\(256\) 2.10062e45 0.367950
\(257\) 4.58230e45i 0.745340i −0.927964 0.372670i \(-0.878442\pi\)
0.927964 0.372670i \(-0.121558\pi\)
\(258\) 5.62970e44 8.94390e45i 0.0850572 1.35130i
\(259\) −4.59584e45 −0.645163
\(260\) 2.45707e46i 3.20571i
\(261\) −1.36548e45 + 1.08037e46i −0.165621 + 1.31040i
\(262\) −8.94155e45 −1.00853
\(263\) 3.11142e45i 0.326437i −0.986590 0.163219i \(-0.947812\pi\)
0.986590 0.163219i \(-0.0521876\pi\)
\(264\) 1.57712e45 + 9.92712e43i 0.153954 + 0.00969056i
\(265\) 1.91281e45 0.173780
\(266\) 8.04830e45i 0.680696i
\(267\) 5.48501e44 8.71403e45i 0.0431980 0.686286i
\(268\) 9.25789e45 0.679127
\(269\) 2.16658e46i 1.48075i −0.672193 0.740376i \(-0.734648\pi\)
0.672193 0.740376i \(-0.265352\pi\)
\(270\) −3.71874e46 7.09731e45i −2.36856 0.452046i
\(271\) 1.16365e46 0.690887 0.345444 0.938440i \(-0.387728\pi\)
0.345444 + 0.938440i \(0.387728\pi\)
\(272\) 8.89117e45i 0.492209i
\(273\) 2.93275e46 + 1.84601e45i 1.51421 + 0.0953110i
\(274\) 2.05253e46 0.988620
\(275\) 1.53353e46i 0.689242i
\(276\) 1.20346e45 1.91194e46i 0.0504848 0.802052i
\(277\) −5.19583e45 −0.203488 −0.101744 0.994811i \(-0.532442\pi\)
−0.101744 + 0.994811i \(0.532442\pi\)
\(278\) 1.38997e46i 0.508341i
\(279\) −1.55327e46 1.96318e45i −0.530600 0.0670625i
\(280\) 1.70535e46 0.544265
\(281\) 3.03870e45i 0.0906292i −0.998973 0.0453146i \(-0.985571\pi\)
0.998973 0.0453146i \(-0.0144290\pi\)
\(282\) −7.68856e44 4.83953e43i −0.0214344 0.00134918i
\(283\) 4.82432e46 1.25746 0.628729 0.777624i \(-0.283575\pi\)
0.628729 + 0.777624i \(0.283575\pi\)
\(284\) 2.30207e46i 0.561139i
\(285\) −2.13768e45 + 3.39613e46i −0.0487405 + 0.774340i
\(286\) −4.86060e46 −1.03690
\(287\) 7.83725e46i 1.56462i
\(288\) −9.46731e45 + 7.49056e46i −0.176917 + 1.39977i
\(289\) 2.92214e46 0.511260
\(290\) 1.94384e47i 3.18492i
\(291\) 3.26413e46 + 2.05459e45i 0.500957 + 0.0315325i
\(292\) −1.51225e47 −2.17444
\(293\) 8.65440e46i 1.16614i −0.812421 0.583072i \(-0.801851\pi\)
0.812421 0.583072i \(-0.198149\pi\)
\(294\) −7.97573e44 + 1.26710e46i −0.0100733 + 0.160034i
\(295\) −1.79982e47 −2.13114
\(296\) 2.19793e46i 0.244046i
\(297\) 7.76898e45 4.07066e46i 0.0809080 0.423929i
\(298\) 1.45179e46 0.141839
\(299\) 1.13617e47i 1.04158i
\(300\) 2.29500e47 + 1.44458e46i 1.97460 + 0.124290i
\(301\) 1.05863e47 0.855031
\(302\) 2.02546e47i 1.53600i
\(303\) 1.15933e46 1.84182e47i 0.0825651 1.31171i
\(304\) 5.06713e46 0.338972
\(305\) 6.96198e46i 0.437558i
\(306\) −1.75719e47 2.22091e46i −1.03780 0.131167i
\(307\) 1.80284e46 0.100076 0.0500379 0.998747i \(-0.484066\pi\)
0.0500379 + 0.998747i \(0.484066\pi\)
\(308\) 9.68141e46i 0.505213i
\(309\) 1.20842e47 + 7.60638e45i 0.592937 + 0.0373222i
\(310\) 2.79469e47 1.28962
\(311\) 5.09327e46i 0.221080i −0.993872 0.110540i \(-0.964742\pi\)
0.993872 0.110540i \(-0.0352580\pi\)
\(312\) −8.82841e45 + 1.40257e47i −0.0360533 + 0.572779i
\(313\) −3.91522e47 −1.50458 −0.752288 0.658835i \(-0.771050\pi\)
−0.752288 + 0.658835i \(0.771050\pi\)
\(314\) 4.92295e46i 0.178058i
\(315\) 5.60783e46 4.43693e47i 0.190939 1.51071i
\(316\) 5.74701e46 0.184242
\(317\) 1.16993e47i 0.353212i −0.984282 0.176606i \(-0.943488\pi\)
0.984282 0.176606i \(-0.0565118\pi\)
\(318\) 5.66284e46 + 3.56445e45i 0.161034 + 0.0101362i
\(319\) 2.12780e47 0.570042
\(320\) 8.98255e47i 2.26751i
\(321\) −4.31109e46 + 6.84902e47i −0.102563 + 1.62942i
\(322\) 4.08974e47 0.917136
\(323\) 1.59199e47i 0.336582i
\(324\) −6.01875e47 1.54612e47i −1.19992 0.308239i
\(325\) −1.36381e48 −2.56430
\(326\) 1.24197e48i 2.20282i
\(327\) −1.31537e47 8.27953e45i −0.220110 0.0138547i
\(328\) −3.74811e47 −0.591847
\(329\) 9.10045e45i 0.0135625i
\(330\) −4.64706e46 + 7.38279e47i −0.0653753 + 1.03862i
\(331\) 8.09163e47 1.07474 0.537371 0.843346i \(-0.319418\pi\)
0.537371 + 0.843346i \(0.319418\pi\)
\(332\) 1.21097e48i 1.51883i
\(333\) −5.71851e47 7.22762e46i −0.677396 0.0856160i
\(334\) 2.17144e48 2.42977
\(335\) 8.35626e47i 0.883407i
\(336\) −6.64636e47 4.18353e46i −0.663954 0.0417923i
\(337\) 7.40101e47 0.698751 0.349376 0.936983i \(-0.386394\pi\)
0.349376 + 0.936983i \(0.386394\pi\)
\(338\) 2.64603e48i 2.36144i
\(339\) 5.05773e46 8.03521e47i 0.0426738 0.677958i
\(340\) 1.74946e48 1.39574
\(341\) 3.05917e47i 0.230818i
\(342\) −1.26571e47 + 1.00143e48i −0.0903314 + 0.714704i
\(343\) −1.54948e48 −1.04616
\(344\) 5.06284e47i 0.323433i
\(345\) 1.72574e48 + 1.08626e47i 1.04331 + 0.0656705i
\(346\) −3.32123e48 −1.90044
\(347\) 1.40857e48i 0.762992i 0.924371 + 0.381496i \(0.124591\pi\)
−0.924371 + 0.381496i \(0.875409\pi\)
\(348\) 2.00437e47 3.18435e48i 0.102795 1.63311i
\(349\) 1.01432e48 0.492597 0.246299 0.969194i \(-0.420786\pi\)
0.246299 + 0.969194i \(0.420786\pi\)
\(350\) 4.90912e48i 2.25793i
\(351\) 3.62013e48 + 6.90913e47i 1.57721 + 0.301015i
\(352\) 1.47527e48 0.608919
\(353\) 1.52516e48i 0.596479i −0.954491 0.298240i \(-0.903601\pi\)
0.954491 0.298240i \(-0.0963995\pi\)
\(354\) −5.32834e48 3.35390e47i −1.97483 0.124305i
\(355\) −2.07787e48 −0.729929
\(356\) 2.55824e48i 0.851906i
\(357\) 1.31438e47 2.08815e48i 0.0414977 0.659273i
\(358\) −2.23319e48 −0.668573
\(359\) 2.00126e48i 0.568209i −0.958793 0.284105i \(-0.908304\pi\)
0.958793 0.284105i \(-0.0916963\pi\)
\(360\) 2.12193e48 + 2.68191e47i 0.571457 + 0.0722264i
\(361\) −3.00686e48 −0.768204
\(362\) 1.72901e48i 0.419117i
\(363\) 3.53063e48 + 2.22234e47i 0.812131 + 0.0511193i
\(364\) −8.60989e48 −1.87963
\(365\) 1.36497e49i 2.82851i
\(366\) −1.29734e47 + 2.06108e48i −0.0255219 + 0.405466i
\(367\) 1.39146e48 0.259905 0.129953 0.991520i \(-0.458517\pi\)
0.129953 + 0.991520i \(0.458517\pi\)
\(368\) 2.57486e48i 0.456714i
\(369\) −1.23252e48 + 9.75173e48i −0.207631 + 1.64279i
\(370\) 1.02889e49 1.64641
\(371\) 6.70274e47i 0.101894i
\(372\) 4.57819e48 + 2.88172e47i 0.661268 + 0.0416233i
\(373\) 9.04311e48 1.24122 0.620612 0.784118i \(-0.286884\pi\)
0.620612 + 0.784118i \(0.286884\pi\)
\(374\) 3.46079e48i 0.451456i
\(375\) −4.87439e47 + 7.74394e48i −0.0604402 + 0.960213i
\(376\) 4.35223e46 0.00513030
\(377\) 1.89230e49i 2.12082i
\(378\) 2.48699e48 1.30309e49i 0.265051 1.38877i
\(379\) −1.74074e49 −1.76437 −0.882184 0.470904i \(-0.843928\pi\)
−0.882184 + 0.470904i \(0.843928\pi\)
\(380\) 9.97026e48i 0.961209i
\(381\) 6.98880e48 + 4.39907e47i 0.640956 + 0.0403447i
\(382\) 1.33902e49 1.16838
\(383\) 2.24202e49i 1.86150i −0.365662 0.930748i \(-0.619157\pi\)
0.365662 0.930748i \(-0.380843\pi\)
\(384\) 5.52127e47 8.77165e48i 0.0436261 0.693087i
\(385\) −8.73853e48 −0.657180
\(386\) 1.85303e49i 1.32655i
\(387\) 1.31724e49 + 1.66485e48i 0.897749 + 0.113466i
\(388\) −9.58274e48 −0.621852
\(389\) 6.09185e48i 0.376449i 0.982126 + 0.188225i \(0.0602733\pi\)
−0.982126 + 0.188225i \(0.939727\pi\)
\(390\) −6.56568e49 4.13274e48i −3.86413 0.243226i
\(391\) 8.08966e48 0.453495
\(392\) 7.17265e47i 0.0383040i
\(393\) 8.32207e47 1.32213e49i 0.0423422 0.672690i
\(394\) 4.16962e49 2.02147
\(395\) 5.18731e48i 0.239661i
\(396\) −1.52254e48 + 1.20464e49i −0.0670441 + 0.530454i
\(397\) −2.98327e49 −1.25220 −0.626098 0.779744i \(-0.715349\pi\)
−0.626098 + 0.779744i \(0.715349\pi\)
\(398\) 2.21873e49i 0.887823i
\(399\) −1.19005e49 7.49070e47i −0.454024 0.0285784i
\(400\) 3.09073e49 1.12440
\(401\) 5.09325e49i 1.76706i 0.468371 + 0.883532i \(0.344841\pi\)
−0.468371 + 0.883532i \(0.655159\pi\)
\(402\) −1.55716e48 + 2.47386e49i −0.0515274 + 0.818615i
\(403\) −2.72059e49 −0.858750
\(404\) 5.40717e49i 1.62826i
\(405\) 1.39554e49 5.43259e49i 0.400956 1.56085i
\(406\) 6.81146e49 1.86744
\(407\) 1.12626e49i 0.294677i
\(408\) 9.98644e48 + 6.28592e47i 0.249383 + 0.0156973i
\(409\) −4.95505e49 −1.18115 −0.590575 0.806983i \(-0.701099\pi\)
−0.590575 + 0.806983i \(0.701099\pi\)
\(410\) 1.75456e50i 3.99277i
\(411\) −1.91033e48 + 3.03494e49i −0.0415063 + 0.659410i
\(412\) −3.54766e49 −0.736029
\(413\) 6.30682e49i 1.24957i
\(414\) 5.08878e49 + 6.43170e48i 0.962957 + 0.121708i
\(415\) 1.09303e50 1.97569
\(416\) 1.31199e50i 2.26546i
\(417\) 2.05526e49 + 1.29367e48i 0.339064 + 0.0213422i
\(418\) 1.97232e49 0.310906
\(419\) 1.15930e50i 1.74634i −0.487415 0.873170i \(-0.662060\pi\)
0.487415 0.873170i \(-0.337940\pi\)
\(420\) −8.23165e48 + 1.30776e50i −0.118509 + 1.88275i
\(421\) −1.23857e50 −1.70436 −0.852179 0.523251i \(-0.824719\pi\)
−0.852179 + 0.523251i \(0.824719\pi\)
\(422\) 5.60373e49i 0.737125i
\(423\) 1.43118e47 1.13235e48i 0.00179981 0.0142401i
\(424\) −3.20554e48 −0.0385434
\(425\) 9.71044e49i 1.11648i
\(426\) −6.15151e49 3.87204e48i −0.676393 0.0425753i
\(427\) −2.43957e49 −0.256557
\(428\) 2.01072e50i 2.02264i
\(429\) 4.52385e48 7.18703e49i 0.0435331 0.691610i
\(430\) −2.37001e50 −2.18197
\(431\) 2.16186e50i 1.90441i 0.305463 + 0.952204i \(0.401189\pi\)
−0.305463 + 0.952204i \(0.598811\pi\)
\(432\) −8.20415e49 1.56578e49i −0.691580 0.131990i
\(433\) 2.59340e48 0.0209218 0.0104609 0.999945i \(-0.496670\pi\)
0.0104609 + 0.999945i \(0.496670\pi\)
\(434\) 9.79296e49i 0.756152i
\(435\) 2.87422e50 + 1.80917e49i 2.12434 + 0.133716i
\(436\) 3.86162e49 0.273229
\(437\) 4.61034e49i 0.312310i
\(438\) 2.54357e49 4.04096e50i 0.164981 2.62106i
\(439\) 2.42061e50 1.50348 0.751742 0.659457i \(-0.229214\pi\)
0.751742 + 0.659457i \(0.229214\pi\)
\(440\) 4.17915e49i 0.248592i
\(441\) −1.86616e49 2.35864e48i −0.106320 0.0134378i
\(442\) −3.07776e50 −1.67962
\(443\) 8.62313e49i 0.450811i 0.974265 + 0.225405i \(0.0723707\pi\)
−0.974265 + 0.225405i \(0.927629\pi\)
\(444\) 1.68550e50 + 1.06093e49i 0.844215 + 0.0531388i
\(445\) −2.30909e50 −1.10816
\(446\) 1.87026e50i 0.860082i
\(447\) −1.35121e48 + 2.14667e49i −0.00595497 + 0.0946066i
\(448\) 3.14760e50 1.32953
\(449\) 3.61936e50i 1.46538i 0.680560 + 0.732692i \(0.261736\pi\)
−0.680560 + 0.732692i \(0.738264\pi\)
\(450\) −7.72030e49 + 6.10832e50i −0.299638 + 2.37074i
\(451\) 1.92060e50 0.714634
\(452\) 2.35895e50i 0.841568i
\(453\) −2.99492e50 1.88514e49i −1.02452 0.0644877i
\(454\) 5.90825e50 1.93820
\(455\) 7.77137e50i 2.44501i
\(456\) 3.58238e48 5.69132e49i 0.0108103 0.171744i
\(457\) 2.96698e50 0.858830 0.429415 0.903107i \(-0.358720\pi\)
0.429415 + 0.903107i \(0.358720\pi\)
\(458\) 1.53498e50i 0.426243i
\(459\) 4.91937e49 2.57757e50i 0.131059 0.686704i
\(460\) −5.06638e50 −1.29509
\(461\) 2.23978e50i 0.549399i −0.961530 0.274700i \(-0.911422\pi\)
0.961530 0.274700i \(-0.0885784\pi\)
\(462\) −2.58703e50 1.62839e49i −0.608980 0.0383320i
\(463\) −3.71785e50 −0.839948 −0.419974 0.907536i \(-0.637961\pi\)
−0.419974 + 0.907536i \(0.637961\pi\)
\(464\) 4.28843e50i 0.929943i
\(465\) −2.60107e49 + 4.13232e50i −0.0541434 + 0.860177i
\(466\) 6.68997e49 0.133688
\(467\) 3.00718e50i 0.576950i 0.957487 + 0.288475i \(0.0931482\pi\)
−0.957487 + 0.288475i \(0.906852\pi\)
\(468\) −1.07131e51 1.35403e50i −1.97353 0.249435i
\(469\) −2.92815e50 −0.517975
\(470\) 2.03736e49i 0.0346105i
\(471\) −7.27924e49 4.58189e48i −0.118765 0.00747562i
\(472\) 3.01619e50 0.472673
\(473\) 2.59430e50i 0.390533i
\(474\) −9.66636e48 + 1.53569e50i −0.0139789 + 0.222083i
\(475\) 5.53403e50 0.768888
\(476\) 6.13033e50i 0.818374i
\(477\) −1.05410e49 + 8.34008e49i −0.0135218 + 0.106985i
\(478\) 7.99662e50 0.985772
\(479\) 1.86336e49i 0.0220760i −0.999939 0.0110380i \(-0.996486\pi\)
0.999939 0.0110380i \(-0.00351358\pi\)
\(480\) 1.99279e51 + 1.25435e50i 2.26922 + 0.142835i
\(481\) −1.00161e51 −1.09633
\(482\) 1.16005e51i 1.22062i
\(483\) −3.80639e49 + 6.04722e50i −0.0385051 + 0.611730i
\(484\) −1.03651e51 −1.00812
\(485\) 8.64947e50i 0.808903i
\(486\) 5.14382e50 1.58230e51i 0.462590 1.42298i
\(487\) 1.36286e51 1.17869 0.589347 0.807880i \(-0.299385\pi\)
0.589347 + 0.807880i \(0.299385\pi\)
\(488\) 1.16671e50i 0.0970478i
\(489\) −1.83642e51 1.15593e50i −1.46928 0.0924832i
\(490\) 3.35765e50 0.258410
\(491\) 2.61038e50i 0.193266i 0.995320 + 0.0966330i \(0.0308073\pi\)
−0.995320 + 0.0966330i \(0.969193\pi\)
\(492\) 1.80920e50 2.87428e51i 0.128869 2.04735i
\(493\) 1.34733e51 0.923388
\(494\) 1.75403e51i 1.15671i
\(495\) −1.08732e51 1.37426e50i −0.690014 0.0872108i
\(496\) 6.16555e50 0.376547
\(497\) 7.28114e50i 0.427985i
\(498\) 3.23590e51 + 2.03683e50i 1.83079 + 0.115238i
\(499\) −1.22608e51 −0.667740 −0.333870 0.942619i \(-0.608355\pi\)
−0.333870 + 0.942619i \(0.608355\pi\)
\(500\) 2.27344e51i 1.19194i
\(501\) −2.02100e50 + 3.21077e51i −0.102012 + 1.62066i
\(502\) −3.94045e51 −1.91503
\(503\) 4.03344e51i 1.88749i 0.330680 + 0.943743i \(0.392722\pi\)
−0.330680 + 0.943743i \(0.607278\pi\)
\(504\) −9.39775e49 + 7.43553e50i −0.0423491 + 0.335067i
\(505\) −4.88057e51 −2.11804
\(506\) 1.00224e51i 0.418900i
\(507\) 3.91250e51 + 2.46271e50i 1.57508 + 0.0991429i
\(508\) −2.05175e51 −0.795636
\(509\) 2.06249e51i 0.770467i −0.922819 0.385234i \(-0.874121\pi\)
0.922819 0.385234i \(-0.125879\pi\)
\(510\) −2.94255e50 + 4.67483e51i −0.105899 + 1.68241i
\(511\) 4.78303e51 1.65846
\(512\) 3.72653e51i 1.24502i
\(513\) −1.46897e51 2.80357e50i −0.472916 0.0902573i
\(514\) −3.59475e51 −1.11524
\(515\) 3.20215e51i 0.957425i
\(516\) −3.88249e51 2.44381e50i −1.11883 0.0704245i
\(517\) −2.23017e49 −0.00619465
\(518\) 3.60537e51i 0.965349i
\(519\) 3.09113e50 4.91088e51i 0.0797881 1.26759i
\(520\) 3.71661e51 0.924876
\(521\) 4.54680e51i 1.09091i −0.838140 0.545455i \(-0.816357\pi\)
0.838140 0.545455i \(-0.183643\pi\)
\(522\) 8.47537e51 + 1.07120e51i 1.96074 + 0.247817i
\(523\) 7.86068e51 1.75359 0.876795 0.480865i \(-0.159677\pi\)
0.876795 + 0.480865i \(0.159677\pi\)
\(524\) 3.88147e51i 0.835028i
\(525\) −7.25878e51 4.56901e50i −1.50604 0.0947972i
\(526\) −2.44087e51 −0.488444
\(527\) 1.93709e51i 0.373893i
\(528\) −1.02522e50 + 1.62877e51i −0.0190885 + 0.303259i
\(529\) 3.22473e51 0.579209
\(530\) 1.50057e51i 0.260025i
\(531\) 9.91838e50 7.84744e51i 0.165823 1.31200i
\(532\) 3.49371e51 0.563593
\(533\) 1.70804e52i 2.65877i
\(534\) −6.83603e51 4.30291e50i −1.02688 0.0646366i
\(535\) 1.81489e52 2.63105
\(536\) 1.40037e51i 0.195934i
\(537\) 2.07848e50 3.30207e51i 0.0280694 0.445939i
\(538\) −1.69965e52 −2.21563
\(539\) 3.67540e50i 0.0462507i
\(540\) −3.08089e51 + 1.61428e52i −0.374279 + 1.96109i
\(541\) −1.20983e52 −1.41898 −0.709488 0.704717i \(-0.751074\pi\)
−0.709488 + 0.704717i \(0.751074\pi\)
\(542\) 9.12869e51i 1.03377i
\(543\) −2.55657e51 1.60922e50i −0.279551 0.0175962i
\(544\) 9.34149e51 0.986364
\(545\) 3.48554e51i 0.355415i
\(546\) 1.44817e51 2.30070e52i 0.142613 2.26569i
\(547\) −1.38323e52 −1.31563 −0.657817 0.753178i \(-0.728520\pi\)
−0.657817 + 0.753178i \(0.728520\pi\)
\(548\) 8.90990e51i 0.818545i
\(549\) −3.03551e51 3.83658e50i −0.269375 0.0340462i
\(550\) 1.20303e52 1.03130
\(551\) 7.67853e51i 0.635913i
\(552\) −2.89204e51 1.82038e50i −0.231399 0.0145653i
\(553\) −1.81770e51 −0.140522
\(554\) 4.07606e51i 0.304477i
\(555\) −9.57609e50 + 1.52135e52i −0.0691228 + 1.09815i
\(556\) −6.03377e51 −0.420889
\(557\) 5.55345e50i 0.0374382i −0.999825 0.0187191i \(-0.994041\pi\)
0.999825 0.0187191i \(-0.00595882\pi\)
\(558\) −1.54008e51 + 1.21852e52i −0.100345 + 0.793930i
\(559\) 2.30717e52 1.45296
\(560\) 1.76119e52i 1.07210i
\(561\) −5.11724e51 3.22103e50i −0.301121 0.0189540i
\(562\) −2.38382e51 −0.135607
\(563\) 2.22042e52i 1.22117i 0.791950 + 0.610585i \(0.209066\pi\)
−0.791950 + 0.610585i \(0.790934\pi\)
\(564\) −2.10081e49 + 3.33755e50i −0.00111708 + 0.0177470i
\(565\) −2.12922e52 −1.09471
\(566\) 3.78461e52i 1.88152i
\(567\) 1.90365e52 + 4.89016e51i 0.915185 + 0.235096i
\(568\) 3.48216e51 0.161894
\(569\) 3.40546e52i 1.53124i −0.643295 0.765618i \(-0.722433\pi\)
0.643295 0.765618i \(-0.277567\pi\)
\(570\) 2.66421e52 + 1.67698e51i 1.15863 + 0.0729298i
\(571\) 1.11181e52 0.467676 0.233838 0.972276i \(-0.424871\pi\)
0.233838 + 0.972276i \(0.424871\pi\)
\(572\) 2.10995e52i 0.858514i
\(573\) −1.24625e51 + 1.97992e52i −0.0490533 + 0.779310i
\(574\) 6.14821e52 2.34111
\(575\) 2.81211e52i 1.03596i
\(576\) 3.91650e52 + 4.95006e51i 1.39595 + 0.176434i
\(577\) −4.20380e52 −1.44978 −0.724889 0.688866i \(-0.758109\pi\)
−0.724889 + 0.688866i \(0.758109\pi\)
\(578\) 2.29238e52i 0.764992i
\(579\) −2.73995e52 1.72465e51i −0.884811 0.0556941i
\(580\) −8.43806e52 −2.63700
\(581\) 3.83013e52i 1.15842i
\(582\) 1.61180e51 2.56066e52i 0.0471817 0.749575i
\(583\) 1.64258e51 0.0465398
\(584\) 2.28745e52i 0.627347i
\(585\) 1.22216e52 9.66977e52i 0.324464 2.56717i
\(586\) −6.78925e52 −1.74489
\(587\) 2.39246e52i 0.595280i −0.954678 0.297640i \(-0.903800\pi\)
0.954678 0.297640i \(-0.0961996\pi\)
\(588\) 5.50041e51 + 3.46221e50i 0.132503 + 0.00834035i
\(589\) 1.10396e52 0.257490
\(590\) 1.41193e53i 3.18879i
\(591\) −3.88074e51 + 6.16534e52i −0.0848697 + 1.34832i
\(592\) 2.26990e52 0.480723
\(593\) 3.91007e52i 0.801946i 0.916090 + 0.400973i \(0.131328\pi\)
−0.916090 + 0.400973i \(0.868672\pi\)
\(594\) −3.19338e52 6.09465e51i −0.634319 0.121062i
\(595\) −5.53330e52 −1.06454
\(596\) 6.30212e51i 0.117438i
\(597\) 3.28069e52 + 2.06502e51i 0.592179 + 0.0372744i
\(598\) 8.91311e52 1.55850
\(599\) 2.82304e52i 0.478197i −0.970995 0.239099i \(-0.923148\pi\)
0.970995 0.239099i \(-0.0768519\pi\)
\(600\) 2.18510e51 3.47147e52i 0.0358589 0.569691i
\(601\) 5.62593e52 0.894497 0.447249 0.894410i \(-0.352404\pi\)
0.447249 + 0.894410i \(0.352404\pi\)
\(602\) 8.30482e52i 1.27937i
\(603\) −3.64343e52 4.60493e51i −0.543853 0.0687376i
\(604\) 8.79240e52 1.27176
\(605\) 9.35566e52i 1.31136i
\(606\) −1.44488e53 9.09476e51i −1.96270 0.123541i
\(607\) −1.00427e53 −1.32210 −0.661051 0.750341i \(-0.729889\pi\)
−0.661051 + 0.750341i \(0.729889\pi\)
\(608\) 5.32376e52i 0.679283i
\(609\) −6.33956e51 + 1.00716e53i −0.0784026 + 1.24558i
\(610\) 5.46157e52 0.654713
\(611\) 1.98334e51i 0.0230470i
\(612\) −9.64083e51 + 7.62785e52i −0.108602 + 0.859261i
\(613\) 9.17938e52 1.00245 0.501227 0.865316i \(-0.332882\pi\)
0.501227 + 0.865316i \(0.332882\pi\)
\(614\) 1.41430e52i 0.149742i
\(615\) 2.59435e53 + 1.63300e52i 2.66318 + 0.167633i
\(616\) 1.46443e52 0.145759
\(617\) 1.23754e53i 1.19438i 0.802101 + 0.597189i \(0.203716\pi\)
−0.802101 + 0.597189i \(0.796284\pi\)
\(618\) 5.96709e51 9.47992e52i 0.0558447 0.887204i
\(619\) 1.86035e52 0.168839 0.0844195 0.996430i \(-0.473096\pi\)
0.0844195 + 0.996430i \(0.473096\pi\)
\(620\) 1.21315e53i 1.06776i
\(621\) −1.42463e52 + 7.46457e52i −0.121608 + 0.637183i
\(622\) −3.99560e52 −0.330799
\(623\) 8.09137e52i 0.649754i
\(624\) −1.44850e53 9.11751e51i −1.12826 0.0710181i
\(625\) −6.16050e51 −0.0465474
\(626\) 3.07143e53i 2.25128i
\(627\) −1.83568e51 + 2.91634e52i −0.0130531 + 0.207375i
\(628\) 2.13702e52 0.147426
\(629\) 7.13157e52i 0.477335i
\(630\) −3.48070e53 4.39926e52i −2.26046 0.285699i
\(631\) 7.67791e52 0.483822 0.241911 0.970298i \(-0.422226\pi\)
0.241911 + 0.970298i \(0.422226\pi\)
\(632\) 8.69304e51i 0.0531554i
\(633\) −8.28586e52 5.21550e51i −0.491663 0.0309475i
\(634\) −9.17796e52 −0.528507
\(635\) 1.85193e53i 1.03496i
\(636\) 1.54730e51 2.45820e52i 0.00839247 0.133331i
\(637\) −3.26862e52 −0.172074
\(638\) 1.66922e53i 0.852947i
\(639\) 1.14506e52 9.05978e52i 0.0567955 0.449367i
\(640\) −2.32436e53 −1.11914
\(641\) 8.05357e52i 0.376431i −0.982128 0.188216i \(-0.939730\pi\)
0.982128 0.188216i \(-0.0602704\pi\)
\(642\) 5.37296e53 + 3.38199e52i 2.43808 + 0.153464i
\(643\) −4.12888e52 −0.181896 −0.0909481 0.995856i \(-0.528990\pi\)
−0.0909481 + 0.995856i \(0.528990\pi\)
\(644\) 1.77533e53i 0.759358i
\(645\) 2.20581e52 3.50437e53i 0.0916080 1.45538i
\(646\) 1.24889e53 0.503624
\(647\) 4.04774e53i 1.58501i 0.609867 + 0.792504i \(0.291223\pi\)
−0.609867 + 0.792504i \(0.708777\pi\)
\(648\) −2.33869e52 + 9.10408e52i −0.0889297 + 0.346187i
\(649\) −1.54556e53 −0.570736
\(650\) 1.06989e54i 3.83693i
\(651\) −1.44802e53 9.11449e51i −0.504354 0.0317463i
\(652\) 5.39133e53 1.82386
\(653\) 4.23994e53i 1.39319i −0.717466 0.696593i \(-0.754698\pi\)
0.717466 0.696593i \(-0.245302\pi\)
\(654\) −6.49517e51 + 1.03189e53i −0.0207307 + 0.329348i
\(655\) −3.50345e53 −1.08620
\(656\) 3.87085e53i 1.16582i
\(657\) 5.95142e53 + 7.52200e52i 1.74132 + 0.220085i
\(658\) −7.13917e51 −0.0202934
\(659\) 5.50402e53i 1.52005i 0.649895 + 0.760024i \(0.274813\pi\)
−0.649895 + 0.760024i \(0.725187\pi\)
\(660\) 3.20482e53 + 2.01726e52i 0.859940 + 0.0541286i
\(661\) −2.36596e53 −0.616850 −0.308425 0.951249i \(-0.599802\pi\)
−0.308425 + 0.951249i \(0.599802\pi\)
\(662\) 6.34776e53i 1.60812i
\(663\) 2.86453e52 4.55088e53i 0.0705175 1.12031i
\(664\) −1.83174e53 −0.438197
\(665\) 3.15346e53i 0.733121i
\(666\) −5.66997e52 + 4.48609e53i −0.128106 + 1.01358i
\(667\) −3.90184e53 −0.856798
\(668\) 9.42608e53i 2.01177i
\(669\) 2.76543e53 + 1.74069e52i 0.573675 + 0.0361098i
\(670\) 6.55537e53 1.32183
\(671\) 5.97844e52i 0.117182i
\(672\) −4.39541e52 + 6.98299e53i −0.0837497 + 1.33053i
\(673\) 1.52102e53 0.281740 0.140870 0.990028i \(-0.455010\pi\)
0.140870 + 0.990028i \(0.455010\pi\)
\(674\) 5.80598e53i 1.04553i
\(675\) −8.96011e53 1.71006e53i −1.56871 0.299392i
\(676\) −1.14862e54 −1.95519
\(677\) 4.27880e53i 0.708169i −0.935213 0.354084i \(-0.884793\pi\)
0.935213 0.354084i \(-0.115207\pi\)
\(678\) −6.30350e53 3.96771e52i −1.01442 0.0638522i
\(679\) 3.03089e53 0.474290
\(680\) 2.64626e53i 0.402684i
\(681\) −5.49892e52 + 8.73613e53i −0.0813734 + 1.29278i
\(682\) 2.39987e53 0.345370
\(683\) 6.97682e53i 0.976482i 0.872709 + 0.488241i \(0.162361\pi\)
−0.872709 + 0.488241i \(0.837639\pi\)
\(684\) 4.34715e53 + 5.49436e52i 0.591751 + 0.0747913i
\(685\) 8.04217e53 1.06476
\(686\) 1.21555e54i 1.56536i
\(687\) −2.26966e53 1.42863e52i −0.284305 0.0178954i
\(688\) −5.22863e53 −0.637100
\(689\) 1.46078e53i 0.173149i
\(690\) 8.52154e52 1.35382e54i 0.0982620 1.56109i
\(691\) −1.52764e54 −1.71372 −0.856859 0.515552i \(-0.827587\pi\)
−0.856859 + 0.515552i \(0.827587\pi\)
\(692\) 1.44172e54i 1.57350i
\(693\) 4.81559e52 3.81011e53i 0.0511350 0.404581i
\(694\) 1.10501e54 1.14165
\(695\) 5.44614e53i 0.547492i
\(696\) −4.81670e53 3.03185e52i −0.471166 0.0296574i
\(697\) 1.21614e54 1.15761
\(698\) 7.95719e53i 0.737067i
\(699\) −6.22648e51 + 9.89201e52i −0.00561276 + 0.0891699i
\(700\) 2.13101e54 1.86949
\(701\) 8.65568e53i 0.739024i 0.929226 + 0.369512i \(0.120475\pi\)
−0.929226 + 0.369512i \(0.879525\pi\)
\(702\) 5.42011e53 2.83994e54i 0.450405 2.35996i
\(703\) 4.06432e53 0.328728
\(704\) 7.71355e53i 0.607259i
\(705\) −3.01250e52 1.89621e51i −0.0230852 0.00145309i
\(706\) −1.19646e54 −0.892504
\(707\) 1.71022e54i 1.24189i
\(708\) −1.45591e53 + 2.31300e54i −0.102920 + 1.63509i
\(709\) 1.69444e54 1.16613 0.583066 0.812425i \(-0.301853\pi\)
0.583066 + 0.812425i \(0.301853\pi\)
\(710\) 1.63006e54i 1.09218i
\(711\) −2.26173e53 2.85860e52i −0.147543 0.0186479i
\(712\) 3.86964e53 0.245783
\(713\) 5.60974e53i 0.346930i
\(714\) −1.63812e54 1.03111e53i −0.986462 0.0620925i
\(715\) −1.90446e54 −1.11675
\(716\) 9.69414e53i 0.553556i
\(717\) −7.44261e52 + 1.18241e54i −0.0413867 + 0.657511i
\(718\) −1.56996e54 −0.850205
\(719\) 4.81902e53i 0.254162i 0.991892 + 0.127081i \(0.0405608\pi\)
−0.991892 + 0.127081i \(0.959439\pi\)
\(720\) −2.76973e53 + 2.19142e54i −0.142272 + 1.12566i
\(721\) 1.12208e54 0.561374
\(722\) 2.35884e54i 1.14945i
\(723\) −1.71528e54 1.07968e53i −0.814157 0.0512468i
\(724\) 7.50552e53 0.347015
\(725\) 4.68358e54i 2.10938i
\(726\) 1.74339e53 2.76973e54i 0.0764891 1.21518i
\(727\) 3.91570e54 1.67361 0.836807 0.547498i \(-0.184420\pi\)
0.836807 + 0.547498i \(0.184420\pi\)
\(728\) 1.30235e54i 0.542289i
\(729\) 2.29177e54 + 9.07849e53i 0.929711 + 0.368291i
\(730\) −1.07080e55 −4.23227
\(731\) 1.64273e54i 0.632609i
\(732\) 8.94701e53 + 5.63166e52i 0.335712 + 0.0211313i
\(733\) 3.14878e54 1.15124 0.575621 0.817716i \(-0.304760\pi\)
0.575621 + 0.817716i \(0.304760\pi\)
\(734\) 1.09158e54i 0.388893i
\(735\) −3.12502e52 + 4.96472e53i −0.0108491 + 0.172360i
\(736\) −2.70527e54 −0.915233
\(737\) 7.17575e53i 0.236584i
\(738\) 7.65009e54 + 9.66894e53i 2.45808 + 0.310676i
\(739\) −5.09600e54 −1.59582 −0.797912 0.602774i \(-0.794062\pi\)
−0.797912 + 0.602774i \(0.794062\pi\)
\(740\) 4.46634e54i 1.36317i
\(741\) −2.59357e54 1.63251e53i −0.771529 0.0485635i
\(742\) 5.25820e53 0.152462
\(743\) 3.04691e54i 0.861137i 0.902558 + 0.430569i \(0.141687\pi\)
−0.902558 + 0.430569i \(0.858313\pi\)
\(744\) 4.35895e52 6.92505e53i 0.0120087 0.190782i
\(745\) 5.68836e53 0.152763
\(746\) 7.09419e54i 1.85723i
\(747\) −6.02343e53 + 4.76576e54i −0.153728 + 1.21630i
\(748\) 1.50231e54 0.373790
\(749\) 6.35962e54i 1.54268i
\(750\) 6.07501e54 + 3.82389e53i 1.43676 + 0.0904359i
\(751\) 2.68533e54 0.619211 0.309606 0.950865i \(-0.399803\pi\)
0.309606 + 0.950865i \(0.399803\pi\)
\(752\) 4.49475e52i 0.0101057i
\(753\) 3.66745e53 5.82647e54i 0.0804006 1.27732i
\(754\) 1.48448e55 3.17335
\(755\) 7.93610e54i 1.65430i
\(756\) −5.65664e54 1.07959e54i −1.14986 0.219454i
\(757\) −2.41058e54 −0.477858 −0.238929 0.971037i \(-0.576796\pi\)
−0.238929 + 0.971037i \(0.576796\pi\)