Properties

Label 2.42.a.b.1.2
Level 2
Weight 42
Character 2.1
Self dual Yes
Analytic conductor 21.294
Analytic rank 0
Dimension 2
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 42 \)
Character orbit: \([\chi]\) = 2.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(21.2943340913\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\mathbb{Q}[x]/(x^{2} - \cdots)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{7}\cdot 3^{2}\cdot 5 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.06767e6\)
Character \(\chi\) = 2.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.04858e6 q^{2}\) \(+1.05814e10 q^{3}\) \(+1.09951e12 q^{4}\) \(-2.54286e14 q^{5}\) \(+1.10955e16 q^{6}\) \(+2.96016e17 q^{7}\) \(+1.15292e18 q^{8}\) \(+7.54941e19 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.04858e6 q^{2}\) \(+1.05814e10 q^{3}\) \(+1.09951e12 q^{4}\) \(-2.54286e14 q^{5}\) \(+1.10955e16 q^{6}\) \(+2.96016e17 q^{7}\) \(+1.15292e18 q^{8}\) \(+7.54941e19 q^{9}\) \(-2.66638e20 q^{10}\) \(-1.09620e21 q^{11}\) \(+1.16344e22 q^{12}\) \(+8.09333e22 q^{13}\) \(+3.10395e23 q^{14}\) \(-2.69071e24 q^{15}\) \(+1.20893e24 q^{16}\) \(-5.33128e24 q^{17}\) \(+7.91613e25 q^{18}\) \(-3.50762e25 q^{19}\) \(-2.79590e26 q^{20}\) \(+3.13228e27 q^{21}\) \(-1.14945e27 q^{22}\) \(+6.68932e27 q^{23}\) \(+1.21996e28 q^{24}\) \(+1.91866e28 q^{25}\) \(+8.48648e28 q^{26}\) \(+4.12899e29 q^{27}\) \(+3.25473e29 q^{28}\) \(-1.63586e30 q^{29}\) \(-2.82142e30 q^{30}\) \(+2.77961e30 q^{31}\) \(+1.26765e30 q^{32}\) \(-1.15993e31 q^{33}\) \(-5.59026e30 q^{34}\) \(-7.52726e31 q^{35}\) \(+8.30066e31 q^{36}\) \(+4.65417e31 q^{37}\) \(-3.67800e31 q^{38}\) \(+8.56392e32 q^{39}\) \(-2.93172e32 q^{40}\) \(-8.83679e32 q^{41}\) \(+3.28443e33 q^{42}\) \(-3.69256e32 q^{43}\) \(-1.20528e33 q^{44}\) \(-1.91971e34 q^{45}\) \(+7.01426e33 q^{46}\) \(-1.89619e34 q^{47}\) \(+1.27922e34 q^{48}\) \(+4.30577e34 q^{49}\) \(+2.01186e34 q^{50}\) \(-5.64127e34 q^{51}\) \(+8.89872e34 q^{52}\) \(-2.01460e35 q^{53}\) \(+4.32956e35 q^{54}\) \(+2.78747e35 q^{55}\) \(+3.41283e35 q^{56}\) \(-3.71157e35 q^{57}\) \(-1.71532e36 q^{58}\) \(+5.07603e34 q^{59}\) \(-2.95847e36 q^{60}\) \(-6.57027e36 q^{61}\) \(+2.91463e36 q^{62}\) \(+2.23474e37 q^{63}\) \(+1.32923e36 q^{64}\) \(-2.05802e37 q^{65}\) \(-1.21628e37 q^{66}\) \(+5.28414e37 q^{67}\) \(-5.86181e36 q^{68}\) \(+7.07827e37 q^{69}\) \(-7.89291e37 q^{70}\) \(-1.04768e38 q^{71}\) \(+8.70387e37 q^{72}\) \(-2.83453e38 q^{73}\) \(+4.88025e37 q^{74}\) \(+2.03022e38 q^{75}\) \(-3.85666e37 q^{76}\) \(-3.24491e38 q^{77}\) \(+8.97992e38 q^{78}\) \(-6.59452e38 q^{79}\) \(-3.07413e38 q^{80}\) \(+1.61558e39 q^{81}\) \(-9.26605e38 q^{82}\) \(+1.30773e39 q^{83}\) \(+3.44397e39 q^{84}\) \(+1.35567e39 q^{85}\) \(-3.87193e38 q^{86}\) \(-1.73098e40 q^{87}\) \(-1.26383e39 q^{88}\) \(+2.16819e39 q^{89}\) \(-2.01296e40 q^{90}\) \(+2.39575e40 q^{91}\) \(+7.35498e39 q^{92}\) \(+2.94123e40 q^{93}\) \(-1.98830e40 q^{94}\) \(+8.91937e39 q^{95}\) \(+1.34136e40 q^{96}\) \(-8.40052e39 q^{97}\) \(+4.51493e40 q^{98}\) \(-8.27563e40 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut +\mathstrut 2097152q^{2} \) \(\mathstrut +\mathstrut 8863347528q^{3} \) \(\mathstrut +\mathstrut 2199023255552q^{4} \) \(\mathstrut +\mathstrut 97599184325580q^{5} \) \(\mathstrut +\mathstrut 9293893497520128q^{6} \) \(\mathstrut +\mathstrut 217106802373088656q^{7} \) \(\mathstrut +\mathstrut 2305843009213693952q^{8} \) \(\mathstrut +\mathstrut 41972929616872509786q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 2097152q^{2} \) \(\mathstrut +\mathstrut 8863347528q^{3} \) \(\mathstrut +\mathstrut 2199023255552q^{4} \) \(\mathstrut +\mathstrut 97599184325580q^{5} \) \(\mathstrut +\mathstrut 9293893497520128q^{6} \) \(\mathstrut +\mathstrut 217106802373088656q^{7} \) \(\mathstrut +\mathstrut 2305843009213693952q^{8} \) \(\mathstrut +\mathstrut 41972929616872509786q^{9} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!80\)\(q^{10} \) \(\mathstrut +\mathstrut \)\(11\!\cdots\!84\)\(q^{11} \) \(\mathstrut +\mathstrut \)\(97\!\cdots\!28\)\(q^{12} \) \(\mathstrut +\mathstrut \)\(17\!\cdots\!68\)\(q^{13} \) \(\mathstrut +\mathstrut \)\(22\!\cdots\!56\)\(q^{14} \) \(\mathstrut -\mathstrut \)\(32\!\cdots\!80\)\(q^{15} \) \(\mathstrut +\mathstrut \)\(24\!\cdots\!52\)\(q^{16} \) \(\mathstrut -\mathstrut \)\(10\!\cdots\!04\)\(q^{17} \) \(\mathstrut +\mathstrut \)\(44\!\cdots\!36\)\(q^{18} \) \(\mathstrut +\mathstrut \)\(20\!\cdots\!00\)\(q^{19} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!80\)\(q^{20} \) \(\mathstrut +\mathstrut \)\(32\!\cdots\!84\)\(q^{21} \) \(\mathstrut +\mathstrut \)\(11\!\cdots\!84\)\(q^{22} \) \(\mathstrut +\mathstrut \)\(14\!\cdots\!68\)\(q^{23} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!28\)\(q^{24} \) \(\mathstrut +\mathstrut \)\(97\!\cdots\!50\)\(q^{25} \) \(\mathstrut +\mathstrut \)\(18\!\cdots\!68\)\(q^{26} \) \(\mathstrut +\mathstrut \)\(53\!\cdots\!20\)\(q^{27} \) \(\mathstrut +\mathstrut \)\(23\!\cdots\!56\)\(q^{28} \) \(\mathstrut -\mathstrut \)\(13\!\cdots\!20\)\(q^{29} \) \(\mathstrut -\mathstrut \)\(34\!\cdots\!80\)\(q^{30} \) \(\mathstrut -\mathstrut \)\(36\!\cdots\!16\)\(q^{31} \) \(\mathstrut +\mathstrut \)\(25\!\cdots\!52\)\(q^{32} \) \(\mathstrut -\mathstrut \)\(13\!\cdots\!24\)\(q^{33} \) \(\mathstrut -\mathstrut \)\(10\!\cdots\!04\)\(q^{34} \) \(\mathstrut -\mathstrut \)\(10\!\cdots\!60\)\(q^{35} \) \(\mathstrut +\mathstrut \)\(46\!\cdots\!36\)\(q^{36} \) \(\mathstrut +\mathstrut \)\(12\!\cdots\!36\)\(q^{37} \) \(\mathstrut +\mathstrut \)\(21\!\cdots\!00\)\(q^{38} \) \(\mathstrut +\mathstrut \)\(69\!\cdots\!52\)\(q^{39} \) \(\mathstrut +\mathstrut \)\(11\!\cdots\!80\)\(q^{40} \) \(\mathstrut +\mathstrut \)\(12\!\cdots\!64\)\(q^{41} \) \(\mathstrut +\mathstrut \)\(34\!\cdots\!84\)\(q^{42} \) \(\mathstrut -\mathstrut \)\(60\!\cdots\!52\)\(q^{43} \) \(\mathstrut +\mathstrut \)\(12\!\cdots\!84\)\(q^{44} \) \(\mathstrut -\mathstrut \)\(30\!\cdots\!60\)\(q^{45} \) \(\mathstrut +\mathstrut \)\(15\!\cdots\!68\)\(q^{46} \) \(\mathstrut -\mathstrut \)\(25\!\cdots\!64\)\(q^{47} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!28\)\(q^{48} \) \(\mathstrut +\mathstrut \)\(47\!\cdots\!54\)\(q^{49} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!00\)\(q^{50} \) \(\mathstrut -\mathstrut \)\(47\!\cdots\!56\)\(q^{51} \) \(\mathstrut +\mathstrut \)\(19\!\cdots\!68\)\(q^{52} \) \(\mathstrut -\mathstrut \)\(30\!\cdots\!52\)\(q^{53} \) \(\mathstrut +\mathstrut \)\(55\!\cdots\!20\)\(q^{54} \) \(\mathstrut +\mathstrut \)\(70\!\cdots\!60\)\(q^{55} \) \(\mathstrut +\mathstrut \)\(25\!\cdots\!56\)\(q^{56} \) \(\mathstrut -\mathstrut \)\(78\!\cdots\!00\)\(q^{57} \) \(\mathstrut -\mathstrut \)\(14\!\cdots\!20\)\(q^{58} \) \(\mathstrut -\mathstrut \)\(32\!\cdots\!40\)\(q^{59} \) \(\mathstrut -\mathstrut \)\(36\!\cdots\!80\)\(q^{60} \) \(\mathstrut -\mathstrut \)\(44\!\cdots\!36\)\(q^{61} \) \(\mathstrut -\mathstrut \)\(38\!\cdots\!16\)\(q^{62} \) \(\mathstrut +\mathstrut \)\(24\!\cdots\!08\)\(q^{63} \) \(\mathstrut +\mathstrut \)\(26\!\cdots\!52\)\(q^{64} \) \(\mathstrut +\mathstrut \)\(11\!\cdots\!20\)\(q^{65} \) \(\mathstrut -\mathstrut \)\(14\!\cdots\!24\)\(q^{66} \) \(\mathstrut +\mathstrut \)\(55\!\cdots\!56\)\(q^{67} \) \(\mathstrut -\mathstrut \)\(11\!\cdots\!04\)\(q^{68} \) \(\mathstrut +\mathstrut \)\(56\!\cdots\!52\)\(q^{69} \) \(\mathstrut -\mathstrut \)\(10\!\cdots\!60\)\(q^{70} \) \(\mathstrut -\mathstrut \)\(48\!\cdots\!16\)\(q^{71} \) \(\mathstrut +\mathstrut \)\(48\!\cdots\!36\)\(q^{72} \) \(\mathstrut -\mathstrut \)\(48\!\cdots\!12\)\(q^{73} \) \(\mathstrut +\mathstrut \)\(12\!\cdots\!36\)\(q^{74} \) \(\mathstrut +\mathstrut \)\(68\!\cdots\!00\)\(q^{75} \) \(\mathstrut +\mathstrut \)\(22\!\cdots\!00\)\(q^{76} \) \(\mathstrut -\mathstrut \)\(41\!\cdots\!48\)\(q^{77} \) \(\mathstrut +\mathstrut \)\(73\!\cdots\!52\)\(q^{78} \) \(\mathstrut -\mathstrut \)\(90\!\cdots\!80\)\(q^{79} \) \(\mathstrut +\mathstrut \)\(11\!\cdots\!80\)\(q^{80} \) \(\mathstrut +\mathstrut \)\(26\!\cdots\!22\)\(q^{81} \) \(\mathstrut +\mathstrut \)\(13\!\cdots\!64\)\(q^{82} \) \(\mathstrut +\mathstrut \)\(12\!\cdots\!68\)\(q^{83} \) \(\mathstrut +\mathstrut \)\(35\!\cdots\!84\)\(q^{84} \) \(\mathstrut -\mathstrut \)\(38\!\cdots\!60\)\(q^{85} \) \(\mathstrut -\mathstrut \)\(63\!\cdots\!52\)\(q^{86} \) \(\mathstrut -\mathstrut \)\(17\!\cdots\!80\)\(q^{87} \) \(\mathstrut +\mathstrut \)\(12\!\cdots\!84\)\(q^{88} \) \(\mathstrut +\mathstrut \)\(26\!\cdots\!80\)\(q^{89} \) \(\mathstrut -\mathstrut \)\(32\!\cdots\!60\)\(q^{90} \) \(\mathstrut +\mathstrut \)\(16\!\cdots\!04\)\(q^{91} \) \(\mathstrut +\mathstrut \)\(16\!\cdots\!68\)\(q^{92} \) \(\mathstrut +\mathstrut \)\(40\!\cdots\!76\)\(q^{93} \) \(\mathstrut -\mathstrut \)\(26\!\cdots\!64\)\(q^{94} \) \(\mathstrut +\mathstrut \)\(93\!\cdots\!00\)\(q^{95} \) \(\mathstrut +\mathstrut \)\(11\!\cdots\!28\)\(q^{96} \) \(\mathstrut -\mathstrut \)\(31\!\cdots\!04\)\(q^{97} \) \(\mathstrut +\mathstrut \)\(49\!\cdots\!04\)\(q^{98} \) \(\mathstrut -\mathstrut \)\(12\!\cdots\!88\)\(q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.04858e6 0.707107
\(3\) 1.05814e10 1.75210 0.876051 0.482218i \(-0.160169\pi\)
0.876051 + 0.482218i \(0.160169\pi\)
\(4\) 1.09951e12 0.500000
\(5\) −2.54286e14 −1.19244 −0.596221 0.802820i \(-0.703332\pi\)
−0.596221 + 0.802820i \(0.703332\pi\)
\(6\) 1.10955e16 1.23892
\(7\) 2.96016e17 1.40218 0.701092 0.713071i \(-0.252696\pi\)
0.701092 + 0.713071i \(0.252696\pi\)
\(8\) 1.15292e18 0.353553
\(9\) 7.54941e19 2.06986
\(10\) −2.66638e20 −0.843184
\(11\) −1.09620e21 −0.491291 −0.245645 0.969360i \(-0.579000\pi\)
−0.245645 + 0.969360i \(0.579000\pi\)
\(12\) 1.16344e22 0.876051
\(13\) 8.09333e22 1.18111 0.590553 0.806999i \(-0.298910\pi\)
0.590553 + 0.806999i \(0.298910\pi\)
\(14\) 3.10395e23 0.991494
\(15\) −2.69071e24 −2.08928
\(16\) 1.20893e24 0.250000
\(17\) −5.33128e24 −0.318148 −0.159074 0.987267i \(-0.550851\pi\)
−0.159074 + 0.987267i \(0.550851\pi\)
\(18\) 7.91613e25 1.46361
\(19\) −3.50762e25 −0.214074 −0.107037 0.994255i \(-0.534136\pi\)
−0.107037 + 0.994255i \(0.534136\pi\)
\(20\) −2.79590e26 −0.596221
\(21\) 3.13228e27 2.45677
\(22\) −1.14945e27 −0.347395
\(23\) 6.68932e27 0.812758 0.406379 0.913705i \(-0.366791\pi\)
0.406379 + 0.913705i \(0.366791\pi\)
\(24\) 1.21996e28 0.619462
\(25\) 1.91866e28 0.421917
\(26\) 8.48648e28 0.835168
\(27\) 4.12899e29 1.87451
\(28\) 3.25473e29 0.701092
\(29\) −1.63586e30 −1.71628 −0.858139 0.513418i \(-0.828379\pi\)
−0.858139 + 0.513418i \(0.828379\pi\)
\(30\) −2.82142e30 −1.47734
\(31\) 2.77961e30 0.743137 0.371568 0.928406i \(-0.378820\pi\)
0.371568 + 0.928406i \(0.378820\pi\)
\(32\) 1.26765e30 0.176777
\(33\) −1.15993e31 −0.860791
\(34\) −5.59026e30 −0.224964
\(35\) −7.52726e31 −1.67202
\(36\) 8.30066e31 1.03493
\(37\) 4.65417e31 0.330908 0.165454 0.986218i \(-0.447091\pi\)
0.165454 + 0.986218i \(0.447091\pi\)
\(38\) −3.67800e31 −0.151373
\(39\) 8.56392e32 2.06942
\(40\) −2.93172e32 −0.421592
\(41\) −8.83679e32 −0.765995 −0.382997 0.923749i \(-0.625108\pi\)
−0.382997 + 0.923749i \(0.625108\pi\)
\(42\) 3.28443e33 1.73720
\(43\) −3.69256e32 −0.120566 −0.0602829 0.998181i \(-0.519200\pi\)
−0.0602829 + 0.998181i \(0.519200\pi\)
\(44\) −1.20528e33 −0.245645
\(45\) −1.91971e34 −2.46819
\(46\) 7.01426e33 0.574707
\(47\) −1.89619e34 −0.999714 −0.499857 0.866108i \(-0.666614\pi\)
−0.499857 + 0.866108i \(0.666614\pi\)
\(48\) 1.27922e34 0.438026
\(49\) 4.30577e34 0.966120
\(50\) 2.01186e34 0.298341
\(51\) −5.64127e34 −0.557427
\(52\) 8.89872e34 0.590553
\(53\) −2.01460e35 −0.904761 −0.452380 0.891825i \(-0.649425\pi\)
−0.452380 + 0.891825i \(0.649425\pi\)
\(54\) 4.32956e35 1.32548
\(55\) 2.78747e35 0.585835
\(56\) 3.41283e35 0.495747
\(57\) −3.71157e35 −0.375079
\(58\) −1.71532e36 −1.21359
\(59\) 5.07603e34 0.0252964 0.0126482 0.999920i \(-0.495974\pi\)
0.0126482 + 0.999920i \(0.495974\pi\)
\(60\) −2.95847e36 −1.04464
\(61\) −6.57027e36 −1.65319 −0.826593 0.562801i \(-0.809724\pi\)
−0.826593 + 0.562801i \(0.809724\pi\)
\(62\) 2.91463e36 0.525477
\(63\) 2.23474e37 2.90233
\(64\) 1.32923e36 0.125000
\(65\) −2.05802e37 −1.40840
\(66\) −1.21628e37 −0.608671
\(67\) 5.28414e37 1.94286 0.971429 0.237332i \(-0.0762729\pi\)
0.971429 + 0.237332i \(0.0762729\pi\)
\(68\) −5.86181e36 −0.159074
\(69\) 7.07827e37 1.42403
\(70\) −7.89291e37 −1.18230
\(71\) −1.04768e38 −1.17337 −0.586684 0.809816i \(-0.699567\pi\)
−0.586684 + 0.809816i \(0.699567\pi\)
\(72\) 8.70387e37 0.731807
\(73\) −2.83453e38 −1.79623 −0.898117 0.439756i \(-0.855065\pi\)
−0.898117 + 0.439756i \(0.855065\pi\)
\(74\) 4.88025e37 0.233987
\(75\) 2.03022e38 0.739242
\(76\) −3.85666e37 −0.107037
\(77\) −3.24491e38 −0.688880
\(78\) 8.97992e38 1.46330
\(79\) −6.59452e38 −0.827614 −0.413807 0.910365i \(-0.635801\pi\)
−0.413807 + 0.910365i \(0.635801\pi\)
\(80\) −3.07413e38 −0.298110
\(81\) 1.61558e39 1.21447
\(82\) −9.26605e38 −0.541640
\(83\) 1.30773e39 0.596236 0.298118 0.954529i \(-0.403641\pi\)
0.298118 + 0.954529i \(0.403641\pi\)
\(84\) 3.44397e39 1.22838
\(85\) 1.35567e39 0.379373
\(86\) −3.87193e38 −0.0852529
\(87\) −1.73098e40 −3.00709
\(88\) −1.26383e39 −0.173697
\(89\) 2.16819e39 0.236376 0.118188 0.992991i \(-0.462292\pi\)
0.118188 + 0.992991i \(0.462292\pi\)
\(90\) −2.01296e40 −1.74527
\(91\) 2.39575e40 1.65613
\(92\) 7.35498e39 0.406379
\(93\) 2.94123e40 1.30205
\(94\) −1.98830e40 −0.706905
\(95\) 8.91937e39 0.255270
\(96\) 1.34136e40 0.309731
\(97\) −8.40052e39 −0.156850 −0.0784252 0.996920i \(-0.524989\pi\)
−0.0784252 + 0.996920i \(0.524989\pi\)
\(98\) 4.51493e40 0.683150
\(99\) −8.27563e40 −1.01690
\(100\) 2.10959e40 0.210959
\(101\) 4.81454e40 0.392615 0.196308 0.980542i \(-0.437105\pi\)
0.196308 + 0.980542i \(0.437105\pi\)
\(102\) −5.91530e40 −0.394161
\(103\) 8.87160e40 0.483992 0.241996 0.970277i \(-0.422198\pi\)
0.241996 + 0.970277i \(0.422198\pi\)
\(104\) 9.33098e40 0.417584
\(105\) −7.96494e41 −2.92955
\(106\) −2.11246e41 −0.639763
\(107\) 5.55682e41 1.38822 0.694111 0.719868i \(-0.255797\pi\)
0.694111 + 0.719868i \(0.255797\pi\)
\(108\) 4.53988e41 0.937253
\(109\) −4.77382e41 −0.815873 −0.407936 0.913010i \(-0.633752\pi\)
−0.407936 + 0.913010i \(0.633752\pi\)
\(110\) 2.92288e41 0.414248
\(111\) 4.92479e41 0.579785
\(112\) 3.57861e41 0.350546
\(113\) 9.67742e41 0.790045 0.395022 0.918672i \(-0.370737\pi\)
0.395022 + 0.918672i \(0.370737\pi\)
\(114\) −3.89186e41 −0.265221
\(115\) −1.70100e42 −0.969167
\(116\) −1.79865e42 −0.858139
\(117\) 6.10999e42 2.44473
\(118\) 5.32261e40 0.0178872
\(119\) −1.57814e42 −0.446102
\(120\) −3.10218e42 −0.738672
\(121\) −3.77687e42 −0.758634
\(122\) −6.88943e42 −1.16898
\(123\) −9.35061e42 −1.34210
\(124\) 3.05621e42 0.371568
\(125\) 6.68471e42 0.689330
\(126\) 2.34330e43 2.05226
\(127\) 1.15659e43 0.861396 0.430698 0.902496i \(-0.358267\pi\)
0.430698 + 0.902496i \(0.358267\pi\)
\(128\) 1.39380e42 0.0883883
\(129\) −3.90726e42 −0.211244
\(130\) −2.15799e43 −0.995889
\(131\) 2.42843e43 0.957776 0.478888 0.877876i \(-0.341040\pi\)
0.478888 + 0.877876i \(0.341040\pi\)
\(132\) −1.27536e43 −0.430396
\(133\) −1.03831e43 −0.300171
\(134\) 5.54082e43 1.37381
\(135\) −1.04994e44 −2.23524
\(136\) −6.14655e42 −0.112482
\(137\) −1.54500e43 −0.243308 −0.121654 0.992573i \(-0.538820\pi\)
−0.121654 + 0.992573i \(0.538820\pi\)
\(138\) 7.42210e43 1.00694
\(139\) 1.40766e44 1.64700 0.823501 0.567315i \(-0.192018\pi\)
0.823501 + 0.567315i \(0.192018\pi\)
\(140\) −8.27631e43 −0.836011
\(141\) −2.00644e44 −1.75160
\(142\) −1.09858e44 −0.829696
\(143\) −8.87189e43 −0.580266
\(144\) 9.12667e43 0.517465
\(145\) 4.15976e44 2.04656
\(146\) −2.97222e44 −1.27013
\(147\) 4.55613e44 1.69274
\(148\) 5.11732e43 0.165454
\(149\) 1.57473e44 0.443493 0.221746 0.975104i \(-0.428824\pi\)
0.221746 + 0.975104i \(0.428824\pi\)
\(150\) 2.12884e44 0.522723
\(151\) −2.82811e44 −0.605994 −0.302997 0.952992i \(-0.597987\pi\)
−0.302997 + 0.952992i \(0.597987\pi\)
\(152\) −4.04401e43 −0.0756865
\(153\) −4.02480e44 −0.658522
\(154\) −3.40254e44 −0.487112
\(155\) −7.06815e44 −0.886147
\(156\) 9.41613e44 1.03471
\(157\) 2.60906e44 0.251502 0.125751 0.992062i \(-0.459866\pi\)
0.125751 + 0.992062i \(0.459866\pi\)
\(158\) −6.91486e44 −0.585212
\(159\) −2.13174e45 −1.58523
\(160\) −3.22346e44 −0.210796
\(161\) 1.98014e45 1.13964
\(162\) 1.69406e45 0.858757
\(163\) −1.61270e45 −0.720621 −0.360310 0.932832i \(-0.617329\pi\)
−0.360310 + 0.932832i \(0.617329\pi\)
\(164\) −9.71616e44 −0.382997
\(165\) 2.94955e45 1.02644
\(166\) 1.37126e45 0.421602
\(167\) −1.22668e43 −0.00333459 −0.00166729 0.999999i \(-0.500531\pi\)
−0.00166729 + 0.999999i \(0.500531\pi\)
\(168\) 3.61127e45 0.868599
\(169\) 1.85475e45 0.395011
\(170\) 1.42152e45 0.268257
\(171\) −2.64804e45 −0.443103
\(172\) −4.06001e44 −0.0602829
\(173\) −6.97298e45 −0.919334 −0.459667 0.888091i \(-0.652031\pi\)
−0.459667 + 0.888091i \(0.652031\pi\)
\(174\) −1.81506e46 −2.12634
\(175\) 5.67953e45 0.591606
\(176\) −1.32522e45 −0.122823
\(177\) 5.37118e44 0.0443218
\(178\) 2.27351e45 0.167143
\(179\) 2.57092e46 1.68501 0.842504 0.538690i \(-0.181080\pi\)
0.842504 + 0.538690i \(0.181080\pi\)
\(180\) −2.11074e46 −1.23409
\(181\) 1.71977e46 0.897553 0.448776 0.893644i \(-0.351860\pi\)
0.448776 + 0.893644i \(0.351860\pi\)
\(182\) 2.51213e46 1.17106
\(183\) −6.95230e46 −2.89655
\(184\) 7.71226e45 0.287353
\(185\) −1.18349e46 −0.394588
\(186\) 3.08410e46 0.920689
\(187\) 5.84413e45 0.156303
\(188\) −2.08488e46 −0.499857
\(189\) 1.22225e47 2.62840
\(190\) 9.35264e45 0.180503
\(191\) −2.15620e46 −0.373684 −0.186842 0.982390i \(-0.559825\pi\)
−0.186842 + 0.982390i \(0.559825\pi\)
\(192\) 1.40652e46 0.219013
\(193\) 2.03359e46 0.284668 0.142334 0.989819i \(-0.454539\pi\)
0.142334 + 0.989819i \(0.454539\pi\)
\(194\) −8.80859e45 −0.110910
\(195\) −2.17768e47 −2.46766
\(196\) 4.73424e46 0.483060
\(197\) −1.48334e47 −1.36359 −0.681793 0.731545i \(-0.738800\pi\)
−0.681793 + 0.731545i \(0.738800\pi\)
\(198\) −8.67763e46 −0.719059
\(199\) −7.47977e46 −0.558985 −0.279493 0.960148i \(-0.590166\pi\)
−0.279493 + 0.960148i \(0.590166\pi\)
\(200\) 2.21206e46 0.149170
\(201\) 5.59139e47 3.40408
\(202\) 5.04842e46 0.277621
\(203\) −4.84241e47 −2.40654
\(204\) −6.20264e46 −0.278714
\(205\) 2.24707e47 0.913404
\(206\) 9.30254e46 0.342234
\(207\) 5.05004e47 1.68230
\(208\) 9.78424e46 0.295276
\(209\) 3.84504e46 0.105172
\(210\) −8.35184e47 −2.07151
\(211\) 8.14889e47 1.83362 0.916808 0.399329i \(-0.130757\pi\)
0.916808 + 0.399329i \(0.130757\pi\)
\(212\) −2.21508e47 −0.452380
\(213\) −1.10860e48 −2.05586
\(214\) 5.82675e47 0.981622
\(215\) 9.38966e46 0.143768
\(216\) 4.76041e47 0.662738
\(217\) 8.22808e47 1.04201
\(218\) −5.00571e47 −0.576909
\(219\) −2.99935e48 −3.14719
\(220\) 3.06486e47 0.292918
\(221\) −4.31479e47 −0.375766
\(222\) 5.16402e47 0.409970
\(223\) −2.94601e45 −0.00213297 −0.00106648 0.999999i \(-0.500339\pi\)
−0.00106648 + 0.999999i \(0.500339\pi\)
\(224\) 3.75245e47 0.247873
\(225\) 1.44847e48 0.873311
\(226\) 1.01475e48 0.558646
\(227\) 1.23961e48 0.623383 0.311691 0.950183i \(-0.399105\pi\)
0.311691 + 0.950183i \(0.399105\pi\)
\(228\) −4.08091e47 −0.187539
\(229\) 2.51277e48 1.05567 0.527833 0.849348i \(-0.323005\pi\)
0.527833 + 0.849348i \(0.323005\pi\)
\(230\) −1.78363e48 −0.685304
\(231\) −3.43359e48 −1.20699
\(232\) −1.88602e48 −0.606796
\(233\) −3.44195e47 −0.101393 −0.0506966 0.998714i \(-0.516144\pi\)
−0.0506966 + 0.998714i \(0.516144\pi\)
\(234\) 6.40679e48 1.72868
\(235\) 4.82174e48 1.19210
\(236\) 5.58116e46 0.0126482
\(237\) −6.97796e48 −1.45006
\(238\) −1.65480e48 −0.315442
\(239\) −1.24157e48 −0.217177 −0.108588 0.994087i \(-0.534633\pi\)
−0.108588 + 0.994087i \(0.534633\pi\)
\(240\) −3.25287e48 −0.522320
\(241\) 8.53681e48 1.25877 0.629385 0.777094i \(-0.283307\pi\)
0.629385 + 0.777094i \(0.283307\pi\)
\(242\) −3.96034e48 −0.536435
\(243\) 2.03549e48 0.253361
\(244\) −7.22409e48 −0.826593
\(245\) −1.09490e49 −1.15204
\(246\) −9.80482e48 −0.949008
\(247\) −2.83883e48 −0.252844
\(248\) 3.20467e48 0.262739
\(249\) 1.38377e49 1.04467
\(250\) 7.00942e48 0.487430
\(251\) 1.82523e49 1.16952 0.584759 0.811207i \(-0.301189\pi\)
0.584759 + 0.811207i \(0.301189\pi\)
\(252\) 2.45713e49 1.45116
\(253\) −7.33281e48 −0.399300
\(254\) 1.21277e49 0.609099
\(255\) 1.43450e49 0.664700
\(256\) 1.46150e48 0.0625000
\(257\) −3.84389e49 −1.51755 −0.758774 0.651354i \(-0.774201\pi\)
−0.758774 + 0.651354i \(0.774201\pi\)
\(258\) −4.09706e48 −0.149372
\(259\) 1.37771e49 0.463994
\(260\) −2.26282e49 −0.704200
\(261\) −1.23498e50 −3.55246
\(262\) 2.54639e49 0.677250
\(263\) 5.88587e49 1.44783 0.723915 0.689889i \(-0.242341\pi\)
0.723915 + 0.689889i \(0.242341\pi\)
\(264\) −1.33731e49 −0.304336
\(265\) 5.12285e49 1.07887
\(266\) −1.08875e49 −0.212253
\(267\) 2.29426e49 0.414154
\(268\) 5.80997e49 0.971429
\(269\) −6.22517e49 −0.964338 −0.482169 0.876078i \(-0.660151\pi\)
−0.482169 + 0.876078i \(0.660151\pi\)
\(270\) −1.10095e50 −1.58055
\(271\) −8.85718e49 −1.17876 −0.589380 0.807856i \(-0.700628\pi\)
−0.589380 + 0.807856i \(0.700628\pi\)
\(272\) −6.44513e48 −0.0795369
\(273\) 2.53506e50 2.90170
\(274\) −1.62005e49 −0.172045
\(275\) −2.10323e49 −0.207284
\(276\) 7.78264e49 0.712017
\(277\) −1.94293e50 −1.65053 −0.825264 0.564747i \(-0.808974\pi\)
−0.825264 + 0.564747i \(0.808974\pi\)
\(278\) 1.47604e50 1.16461
\(279\) 2.09844e50 1.53819
\(280\) −8.67834e49 −0.591149
\(281\) 2.14728e50 1.35960 0.679798 0.733400i \(-0.262068\pi\)
0.679798 + 0.733400i \(0.262068\pi\)
\(282\) −2.10391e50 −1.23857
\(283\) −6.68644e49 −0.366078 −0.183039 0.983106i \(-0.558593\pi\)
−0.183039 + 0.983106i \(0.558593\pi\)
\(284\) −1.15194e50 −0.586684
\(285\) 9.43799e49 0.447260
\(286\) −9.30285e49 −0.410310
\(287\) −2.61583e50 −1.07407
\(288\) 9.57001e49 0.365903
\(289\) −2.52383e50 −0.898782
\(290\) 4.36183e50 1.44714
\(291\) −8.88897e49 −0.274818
\(292\) −3.11660e50 −0.898117
\(293\) −2.93540e50 −0.788644 −0.394322 0.918972i \(-0.629021\pi\)
−0.394322 + 0.918972i \(0.629021\pi\)
\(294\) 4.77745e50 1.19695
\(295\) −1.29076e49 −0.0301645
\(296\) 5.36590e49 0.116994
\(297\) −4.52619e50 −0.920927
\(298\) 1.65122e50 0.313597
\(299\) 5.41389e50 0.959953
\(300\) 2.23225e50 0.369621
\(301\) −1.09306e50 −0.169055
\(302\) −2.96548e50 −0.428502
\(303\) 5.09449e50 0.687902
\(304\) −4.24045e49 −0.0535184
\(305\) 1.67073e51 1.97133
\(306\) −4.22031e50 −0.465645
\(307\) −4.35932e50 −0.449864 −0.224932 0.974374i \(-0.572216\pi\)
−0.224932 + 0.974374i \(0.572216\pi\)
\(308\) −3.56782e50 −0.344440
\(309\) 9.38743e50 0.848004
\(310\) −7.41149e50 −0.626601
\(311\) −2.38798e50 −0.188992 −0.0944958 0.995525i \(-0.530124\pi\)
−0.0944958 + 0.995525i \(0.530124\pi\)
\(312\) 9.87353e50 0.731650
\(313\) −2.03212e51 −1.41023 −0.705117 0.709091i \(-0.749106\pi\)
−0.705117 + 0.709091i \(0.749106\pi\)
\(314\) 2.73580e50 0.177839
\(315\) −5.68264e51 −3.46086
\(316\) −7.25075e50 −0.413807
\(317\) 2.68276e51 1.43505 0.717525 0.696532i \(-0.245275\pi\)
0.717525 + 0.696532i \(0.245275\pi\)
\(318\) −2.23529e51 −1.12093
\(319\) 1.79323e51 0.843191
\(320\) −3.38004e50 −0.149055
\(321\) 5.87993e51 2.43231
\(322\) 2.07633e51 0.805845
\(323\) 1.87001e50 0.0681071
\(324\) 1.77635e51 0.607233
\(325\) 1.55283e51 0.498329
\(326\) −1.69103e51 −0.509556
\(327\) −5.05139e51 −1.42949
\(328\) −1.01881e51 −0.270820
\(329\) −5.61302e51 −1.40178
\(330\) 3.09283e51 0.725805
\(331\) 7.54395e51 1.66389 0.831945 0.554858i \(-0.187227\pi\)
0.831945 + 0.554858i \(0.187227\pi\)
\(332\) 1.43787e51 0.298118
\(333\) 3.51362e51 0.684934
\(334\) −1.28626e49 −0.00235791
\(335\) −1.34368e52 −2.31674
\(336\) 3.78669e51 0.614192
\(337\) −5.36454e51 −0.818689 −0.409345 0.912380i \(-0.634243\pi\)
−0.409345 + 0.912380i \(0.634243\pi\)
\(338\) 1.94485e51 0.279315
\(339\) 1.02401e52 1.38424
\(340\) 1.49058e51 0.189686
\(341\) −3.04700e51 −0.365096
\(342\) −2.77667e51 −0.313321
\(343\) −4.46968e50 −0.0475059
\(344\) −4.25723e50 −0.0426264
\(345\) −1.79990e52 −1.69808
\(346\) −7.31170e51 −0.650068
\(347\) −1.60783e51 −0.134737 −0.0673684 0.997728i \(-0.521460\pi\)
−0.0673684 + 0.997728i \(0.521460\pi\)
\(348\) −1.90323e52 −1.50355
\(349\) 1.51169e52 1.12601 0.563004 0.826454i \(-0.309646\pi\)
0.563004 + 0.826454i \(0.309646\pi\)
\(350\) 5.95542e51 0.418329
\(351\) 3.34173e52 2.21399
\(352\) −1.38959e51 −0.0868487
\(353\) 8.96540e51 0.528675 0.264337 0.964430i \(-0.414847\pi\)
0.264337 + 0.964430i \(0.414847\pi\)
\(354\) 5.63209e50 0.0313403
\(355\) 2.66411e52 1.39917
\(356\) 2.38395e51 0.118188
\(357\) −1.66990e52 −0.781616
\(358\) 2.69581e52 1.19148
\(359\) −2.57092e52 −1.07313 −0.536565 0.843859i \(-0.680278\pi\)
−0.536565 + 0.843859i \(0.680278\pi\)
\(360\) −2.21327e52 −0.872637
\(361\) −2.56168e52 −0.954172
\(362\) 1.80331e52 0.634666
\(363\) −3.99648e52 −1.32920
\(364\) 2.63416e52 0.828064
\(365\) 7.20782e52 2.14191
\(366\) −7.29001e52 −2.04817
\(367\) 4.37801e52 1.16311 0.581557 0.813506i \(-0.302444\pi\)
0.581557 + 0.813506i \(0.302444\pi\)
\(368\) 8.08689e51 0.203189
\(369\) −6.67125e52 −1.58550
\(370\) −1.24098e52 −0.279016
\(371\) −5.96354e52 −1.26864
\(372\) 3.23391e52 0.651026
\(373\) −3.46418e52 −0.660039 −0.330020 0.943974i \(-0.607055\pi\)
−0.330020 + 0.943974i \(0.607055\pi\)
\(374\) 6.12802e51 0.110523
\(375\) 7.07339e52 1.20778
\(376\) −2.18616e52 −0.353452
\(377\) −1.32396e53 −2.02710
\(378\) 1.28162e53 1.85856
\(379\) 3.98009e52 0.546750 0.273375 0.961908i \(-0.411860\pi\)
0.273375 + 0.961908i \(0.411860\pi\)
\(380\) 9.80695e51 0.127635
\(381\) 1.22384e53 1.50925
\(382\) −2.26094e52 −0.264235
\(383\) 4.24383e52 0.470092 0.235046 0.971984i \(-0.424476\pi\)
0.235046 + 0.971984i \(0.424476\pi\)
\(384\) 1.47484e52 0.154865
\(385\) 8.25136e52 0.821449
\(386\) 2.13237e52 0.201290
\(387\) −2.78766e52 −0.249555
\(388\) −9.23647e51 −0.0784252
\(389\) −1.66821e53 −1.34364 −0.671821 0.740713i \(-0.734488\pi\)
−0.671821 + 0.740713i \(0.734488\pi\)
\(390\) −2.28347e53 −1.74490
\(391\) −3.56627e52 −0.258577
\(392\) 4.96421e52 0.341575
\(393\) 2.56963e53 1.67812
\(394\) −1.55539e53 −0.964201
\(395\) 1.67689e53 0.986882
\(396\) −9.09915e52 −0.508452
\(397\) −2.90239e53 −1.54010 −0.770052 0.637981i \(-0.779770\pi\)
−0.770052 + 0.637981i \(0.779770\pi\)
\(398\) −7.84311e52 −0.395262
\(399\) −1.09868e53 −0.525930
\(400\) 2.31952e52 0.105479
\(401\) 1.04436e53 0.451222 0.225611 0.974217i \(-0.427562\pi\)
0.225611 + 0.974217i \(0.427562\pi\)
\(402\) 5.86299e53 2.40705
\(403\) 2.24963e53 0.877723
\(404\) 5.29365e52 0.196308
\(405\) −4.10819e53 −1.44818
\(406\) −5.07763e53 −1.70168
\(407\) −5.10189e52 −0.162572
\(408\) −6.50394e52 −0.197080
\(409\) 2.12912e53 0.613581 0.306790 0.951777i \(-0.400745\pi\)
0.306790 + 0.951777i \(0.400745\pi\)
\(410\) 2.35623e53 0.645874
\(411\) −1.63483e53 −0.426301
\(412\) 9.75442e52 0.241996
\(413\) 1.50259e52 0.0354702
\(414\) 5.29535e53 1.18956
\(415\) −3.32538e53 −0.710976
\(416\) 1.02595e53 0.208792
\(417\) 1.48951e54 2.88571
\(418\) 4.03181e52 0.0743681
\(419\) −8.36673e53 −1.46950 −0.734748 0.678340i \(-0.762700\pi\)
−0.734748 + 0.678340i \(0.762700\pi\)
\(420\) −8.75754e53 −1.46478
\(421\) 1.14983e54 1.83169 0.915845 0.401533i \(-0.131522\pi\)
0.915845 + 0.401533i \(0.131522\pi\)
\(422\) 8.54473e53 1.29656
\(423\) −1.43151e54 −2.06927
\(424\) −2.32268e53 −0.319881
\(425\) −1.02289e53 −0.134232
\(426\) −1.16245e54 −1.45371
\(427\) −1.94490e54 −2.31807
\(428\) 6.10979e53 0.694111
\(429\) −9.38774e53 −1.01669
\(430\) 9.84577e52 0.101659
\(431\) 1.32392e54 1.30340 0.651701 0.758476i \(-0.274056\pi\)
0.651701 + 0.758476i \(0.274056\pi\)
\(432\) 4.99165e53 0.468627
\(433\) −1.08006e54 −0.967046 −0.483523 0.875332i \(-0.660643\pi\)
−0.483523 + 0.875332i \(0.660643\pi\)
\(434\) 8.62776e53 0.736816
\(435\) 4.40163e54 3.58578
\(436\) −5.24887e53 −0.407936
\(437\) −2.34636e53 −0.173990
\(438\) −3.14504e54 −2.22540
\(439\) 1.14481e53 0.0773059 0.0386529 0.999253i \(-0.487693\pi\)
0.0386529 + 0.999253i \(0.487693\pi\)
\(440\) 3.21374e53 0.207124
\(441\) 3.25060e54 1.99973
\(442\) −4.52438e53 −0.265707
\(443\) −9.71784e53 −0.544870 −0.272435 0.962174i \(-0.587829\pi\)
−0.272435 + 0.962174i \(0.587829\pi\)
\(444\) 5.41486e53 0.289892
\(445\) −5.51341e53 −0.281864
\(446\) −3.08911e51 −0.00150823
\(447\) 1.66629e54 0.777045
\(448\) 3.93472e53 0.175273
\(449\) −3.40657e54 −1.44966 −0.724832 0.688926i \(-0.758083\pi\)
−0.724832 + 0.688926i \(0.758083\pi\)
\(450\) 1.51883e54 0.617524
\(451\) 9.68686e53 0.376326
\(452\) 1.06404e54 0.395022
\(453\) −2.99255e54 −1.06176
\(454\) 1.29982e54 0.440798
\(455\) −6.09207e54 −1.97484
\(456\) −4.27914e53 −0.132610
\(457\) 1.58378e54 0.469258 0.234629 0.972085i \(-0.424612\pi\)
0.234629 + 0.972085i \(0.424612\pi\)
\(458\) 2.63484e54 0.746468
\(459\) −2.20128e54 −0.596370
\(460\) −1.87027e54 −0.484583
\(461\) −2.93741e53 −0.0727939 −0.0363970 0.999337i \(-0.511588\pi\)
−0.0363970 + 0.999337i \(0.511588\pi\)
\(462\) −3.60038e54 −0.853469
\(463\) 7.57194e54 1.71711 0.858553 0.512725i \(-0.171364\pi\)
0.858553 + 0.512725i \(0.171364\pi\)
\(464\) −1.97763e54 −0.429069
\(465\) −7.47913e54 −1.55262
\(466\) −3.60915e53 −0.0716958
\(467\) −2.70909e54 −0.515024 −0.257512 0.966275i \(-0.582903\pi\)
−0.257512 + 0.966275i \(0.582903\pi\)
\(468\) 6.71800e54 1.22236
\(469\) 1.56419e55 2.72424
\(470\) 5.05597e54 0.842943
\(471\) 2.76077e54 0.440657
\(472\) 5.85227e52 0.00894362
\(473\) 4.04777e53 0.0592328
\(474\) −7.31692e54 −1.02535
\(475\) −6.72992e53 −0.0903214
\(476\) −1.73519e54 −0.223051
\(477\) −1.52090e55 −1.87273
\(478\) −1.30188e54 −0.153567
\(479\) −7.24145e53 −0.0818366 −0.0409183 0.999162i \(-0.513028\pi\)
−0.0409183 + 0.999162i \(0.513028\pi\)
\(480\) −3.41088e54 −0.369336
\(481\) 3.76678e54 0.390837
\(482\) 8.95149e54 0.890084
\(483\) 2.09528e55 1.99676
\(484\) −4.15271e54 −0.379317
\(485\) 2.13613e54 0.187035
\(486\) 2.13436e54 0.179153
\(487\) 3.33837e54 0.268653 0.134326 0.990937i \(-0.457113\pi\)
0.134326 + 0.990937i \(0.457113\pi\)
\(488\) −7.57500e54 −0.584489
\(489\) −1.70647e55 −1.26260
\(490\) −1.14808e55 −0.814617
\(491\) −1.88223e55 −1.28086 −0.640430 0.768016i \(-0.721244\pi\)
−0.640430 + 0.768016i \(0.721244\pi\)
\(492\) −1.02811e55 −0.671050
\(493\) 8.72124e54 0.546030
\(494\) −2.97673e54 −0.178787
\(495\) 2.10438e55 1.21260
\(496\) 3.36034e54 0.185784
\(497\) −3.10131e55 −1.64528
\(498\) 1.45099e55 0.738690
\(499\) −6.93745e54 −0.338953 −0.169476 0.985534i \(-0.554208\pi\)
−0.169476 + 0.985534i \(0.554208\pi\)
\(500\) 7.34991e54 0.344665
\(501\) −1.29800e53 −0.00584254
\(502\) 1.91390e55 0.826974
\(503\) 2.98925e55 1.23999 0.619995 0.784606i \(-0.287135\pi\)
0.619995 + 0.784606i \(0.287135\pi\)
\(504\) 2.57648e55 1.02613
\(505\) −1.22427e55 −0.468171
\(506\) −7.68901e54 −0.282348
\(507\) 1.96260e55 0.692099
\(508\) 1.27168e55 0.430698
\(509\) 5.65842e55 1.84069 0.920345 0.391108i \(-0.127908\pi\)
0.920345 + 0.391108i \(0.127908\pi\)
\(510\) 1.50418e55 0.470014
\(511\) −8.39067e55 −2.51865
\(512\) 1.53250e54 0.0441942
\(513\) −1.44829e55 −0.401282
\(514\) −4.03061e55 −1.07307
\(515\) −2.25592e55 −0.577133
\(516\) −4.29608e54 −0.105622
\(517\) 2.07860e55 0.491150
\(518\) 1.44463e55 0.328093
\(519\) −7.37843e55 −1.61077
\(520\) −2.37274e55 −0.497945
\(521\) 3.31572e55 0.668967 0.334483 0.942402i \(-0.391438\pi\)
0.334483 + 0.942402i \(0.391438\pi\)
\(522\) −1.29497e56 −2.51197
\(523\) 7.77683e55 1.45050 0.725250 0.688486i \(-0.241724\pi\)
0.725250 + 0.688486i \(0.241724\pi\)
\(524\) 2.67009e55 0.478888
\(525\) 6.00977e55 1.03655
\(526\) 6.17178e55 1.02377
\(527\) −1.48189e55 −0.236427
\(528\) −1.40228e55 −0.215198
\(529\) −2.29924e55 −0.339424
\(530\) 5.37169e55 0.762880
\(531\) 3.83210e54 0.0523600
\(532\) −1.14163e55 −0.150085
\(533\) −7.15191e55 −0.904721
\(534\) 2.40571e55 0.292851
\(535\) −1.41302e56 −1.65538
\(536\) 6.09220e55 0.686904
\(537\) 2.72041e56 2.95231
\(538\) −6.52756e55 −0.681890
\(539\) −4.71997e55 −0.474646
\(540\) −1.15443e56 −1.11762
\(541\) 8.91733e55 0.831172 0.415586 0.909554i \(-0.363577\pi\)
0.415586 + 0.909554i \(0.363577\pi\)
\(542\) −9.28743e55 −0.833509
\(543\) 1.81977e56 1.57260
\(544\) −6.75820e54 −0.0562411
\(545\) 1.21391e56 0.972881
\(546\) 2.65820e56 2.05182
\(547\) −8.97461e55 −0.667230 −0.333615 0.942709i \(-0.608268\pi\)
−0.333615 + 0.942709i \(0.608268\pi\)
\(548\) −1.69875e55 −0.121654
\(549\) −4.96016e56 −3.42186
\(550\) −2.20539e55 −0.146572
\(551\) 5.73797e55 0.367410
\(552\) 8.16069e55 0.503472
\(553\) −1.95208e56 −1.16047
\(554\) −2.03731e56 −1.16710
\(555\) −1.25230e56 −0.691359
\(556\) 1.54774e56 0.823501
\(557\) 3.47843e55 0.178382 0.0891911 0.996015i \(-0.471572\pi\)
0.0891911 + 0.996015i \(0.471572\pi\)
\(558\) 2.20037e56 1.08766
\(559\) −2.98851e55 −0.142401
\(560\) −9.09990e55 −0.418006
\(561\) 6.18394e55 0.273859
\(562\) 2.25159e56 0.961379
\(563\) 2.29948e55 0.0946688 0.0473344 0.998879i \(-0.484927\pi\)
0.0473344 + 0.998879i \(0.484927\pi\)
\(564\) −2.20611e56 −0.875801
\(565\) −2.46083e56 −0.942082
\(566\) −7.01124e55 −0.258856
\(567\) 4.78237e56 1.70290
\(568\) −1.20790e56 −0.414848
\(569\) 3.18790e56 1.05610 0.528048 0.849214i \(-0.322924\pi\)
0.528048 + 0.849214i \(0.322924\pi\)
\(570\) 9.89645e55 0.316260
\(571\) 1.16154e54 0.00358091 0.00179046 0.999998i \(-0.499430\pi\)
0.00179046 + 0.999998i \(0.499430\pi\)
\(572\) −9.75474e55 −0.290133
\(573\) −2.28157e56 −0.654733
\(574\) −2.74290e56 −0.759479
\(575\) 1.28345e56 0.342917
\(576\) 1.00349e56 0.258733
\(577\) 6.45847e56 1.60703 0.803517 0.595281i \(-0.202959\pi\)
0.803517 + 0.595281i \(0.202959\pi\)
\(578\) −2.64643e56 −0.635535
\(579\) 2.15183e56 0.498767
\(580\) 4.57371e56 1.02328
\(581\) 3.87109e56 0.836032
\(582\) −9.32076e55 −0.194326
\(583\) 2.20840e56 0.444500
\(584\) −3.26800e56 −0.635065
\(585\) −1.55368e57 −2.91519
\(586\) −3.07799e56 −0.557656
\(587\) −1.53676e56 −0.268859 −0.134430 0.990923i \(-0.542920\pi\)
−0.134430 + 0.990923i \(0.542920\pi\)
\(588\) 5.00952e56 0.846371
\(589\) −9.74980e55 −0.159086
\(590\) −1.35346e55 −0.0213295
\(591\) −1.56959e57 −2.38914
\(592\) 5.62655e55 0.0827270
\(593\) 7.79761e56 1.10749 0.553746 0.832686i \(-0.313198\pi\)
0.553746 + 0.832686i \(0.313198\pi\)
\(594\) −4.74605e56 −0.651194
\(595\) 4.01300e56 0.531950
\(596\) 1.73143e56 0.221746
\(597\) −7.91468e56 −0.979399
\(598\) 5.67687e56 0.678789
\(599\) −9.18440e56 −1.06121 −0.530605 0.847619i \(-0.678035\pi\)
−0.530605 + 0.847619i \(0.678035\pi\)
\(600\) 2.34068e56 0.261362
\(601\) 1.34315e57 1.44943 0.724714 0.689050i \(-0.241972\pi\)
0.724714 + 0.689050i \(0.241972\pi\)
\(602\) −1.14615e56 −0.119540
\(603\) 3.98921e57 4.02145
\(604\) −3.10954e56 −0.302997
\(605\) 9.60405e56 0.904626
\(606\) 5.34196e56 0.486420
\(607\) −1.37250e56 −0.120821 −0.0604105 0.998174i \(-0.519241\pi\)
−0.0604105 + 0.998174i \(0.519241\pi\)
\(608\) −4.44643e55 −0.0378432
\(609\) −5.12397e57 −4.21650
\(610\) 1.75188e57 1.39394
\(611\) −1.53465e57 −1.18077
\(612\) −4.42532e56 −0.329261
\(613\) −4.58982e56 −0.330260 −0.165130 0.986272i \(-0.552804\pi\)
−0.165130 + 0.986272i \(0.552804\pi\)
\(614\) −4.57107e56 −0.318102
\(615\) 2.37773e57 1.60038
\(616\) −3.74113e56 −0.243556
\(617\) −4.69500e56 −0.295658 −0.147829 0.989013i \(-0.547229\pi\)
−0.147829 + 0.989013i \(0.547229\pi\)
\(618\) 9.84344e56 0.599630
\(619\) −8.01009e56 −0.472040 −0.236020 0.971748i \(-0.575843\pi\)
−0.236020 + 0.971748i \(0.575843\pi\)
\(620\) −7.77151e56 −0.443074
\(621\) 2.76202e57 1.52352
\(622\) −2.50398e56 −0.133637
\(623\) 6.41819e56 0.331442
\(624\) 1.03531e57 0.517354
\(625\) −2.57233e57 −1.24390
\(626\) −2.13084e57 −0.997187
\(627\) 4.06861e56 0.184273
\(628\) 2.86870e56 0.125751
\(629\) −2.48127e56 −0.105278
\(630\) −5.95868e57 −2.44719
\(631\) −1.26000e57 −0.500920 −0.250460 0.968127i \(-0.580582\pi\)
−0.250460 + 0.968127i \(0.580582\pi\)
\(632\) −7.60297e56 −0.292606
\(633\) 8.62271e57 3.21268
\(634\) 2.81308e57 1.01473
\(635\) −2.94104e57 −1.02716
\(636\) −2.34387e57 −0.792617
\(637\) 3.48480e57 1.14109
\(638\) 1.88033e57 0.596226
\(639\) −7.90939e57 −2.42871
\(640\) −3.54423e56 −0.105398
\(641\) 4.29334e57 1.23653 0.618267 0.785968i \(-0.287835\pi\)
0.618267 + 0.785968i \(0.287835\pi\)
\(642\) 6.16555e57 1.71990
\(643\) −3.66649e57 −0.990662 −0.495331 0.868704i \(-0.664953\pi\)
−0.495331 + 0.868704i \(0.664953\pi\)
\(644\) 2.17719e57 0.569818
\(645\) 9.93562e56 0.251896
\(646\) 1.96085e56 0.0481590
\(647\) 7.19666e56 0.171235 0.0856177 0.996328i \(-0.472714\pi\)
0.0856177 + 0.996328i \(0.472714\pi\)
\(648\) 1.86264e57 0.429378
\(649\) −5.56433e55 −0.0124279
\(650\) 1.62827e57 0.352372
\(651\) 8.70650e57 1.82572
\(652\) −1.77318e57 −0.360310
\(653\) 1.77671e56 0.0349862 0.0174931 0.999847i \(-0.494431\pi\)
0.0174931 + 0.999847i \(0.494431\pi\)
\(654\) −5.29677e57 −1.01080
\(655\) −6.17515e57 −1.14209
\(656\) −1.06830e57 −0.191499
\(657\) −2.13990e58 −3.71796
\(658\) −5.88568e57 −0.991210
\(659\) 5.94098e57 0.969855 0.484928 0.874554i \(-0.338846\pi\)
0.484928 + 0.874554i \(0.338846\pi\)
\(660\) 3.24307e57 0.513222
\(661\) 8.22733e57 1.26220 0.631101 0.775700i \(-0.282603\pi\)
0.631101 + 0.775700i \(0.282603\pi\)
\(662\) 7.91040e57 1.17655
\(663\) −4.56567e57 −0.658381
\(664\) 1.50771e57 0.210801
\(665\) 2.64027e57 0.357936
\(666\) 3.68430e57 0.484321
\(667\) −1.09428e58 −1.39492
\(668\) −1.34874e55 −0.00166729
\(669\) −3.11730e55 −0.00373717
\(670\) −1.40895e58 −1.63819
\(671\) 7.20231e57 0.812194
\(672\) 3.97063e57 0.434300
\(673\) 3.40645e57 0.361404 0.180702 0.983538i \(-0.442163\pi\)
0.180702 + 0.983538i \(0.442163\pi\)
\(674\) −5.62512e57 −0.578901
\(675\) 7.92213e57 0.790887
\(676\) 2.03932e57 0.197505
\(677\) −3.42769e57 −0.322058 −0.161029 0.986950i \(-0.551481\pi\)
−0.161029 + 0.986950i \(0.551481\pi\)
\(678\) 1.07375e58 0.978805
\(679\) −2.48669e57 −0.219933
\(680\) 1.56298e57 0.134129
\(681\) 1.31169e58 1.09223
\(682\) −3.19501e57 −0.258162
\(683\) 8.22982e57 0.645306 0.322653 0.946517i \(-0.395425\pi\)
0.322653 + 0.946517i \(0.395425\pi\)
\(684\) −2.91155e57 −0.221551
\(685\) 3.92872e57 0.290131
\(686\) −4.68680e56 −0.0335917
\(687\) 2.65888e58 1.84963
\(688\) −4.46403e56 −0.0301414
\(689\) −1.63048e58 −1.06862
\(690\) −1.88734e58 −1.20072
\(691\) 1.60618e58 0.991960 0.495980 0.868334i \(-0.334809\pi\)
0.495980 + 0.868334i \(0.334809\pi\)
\(692\) −7.66688e57 −0.459667
\(693\) −2.44972e58 −1.42589
\(694\) −1.68593e57 −0.0952733
\(695\) −3.57948e58 −1.96395
\(696\) −1.99568e58 −1.06317
\(697\) 4.71115e57 0.243699
\(698\) 1.58512e58 0.796208
\(699\) −3.64208e57 −0.177651
\(700\) 6.24471e57 0.295803
\(701\) −3.61228e58 −1.66174 −0.830869 0.556468i \(-0.812156\pi\)
−0.830869 + 0.556468i \(0.812156\pi\)
\(702\) 3.50406e58 1.56553
\(703\) −1.63251e57 −0.0708387
\(704\) −1.45710e57 −0.0614113
\(705\) 5.10210e58 2.08868
\(706\) 9.40091e57 0.373829
\(707\) 1.42518e58 0.550519
\(708\) 5.90567e56 0.0221609
\(709\) −2.71836e58 −0.990965 −0.495483 0.868618i \(-0.665009\pi\)
−0.495483 + 0.868618i \(0.665009\pi\)
\(710\) 2.79352e58 0.989364
\(711\) −4.97847e58 −1.71305
\(712\) 2.49976e57 0.0835714
\(713\) 1.85937e58 0.603990
\(714\) −1.75102e58 −0.552686
\(715\) 2.25600e58 0.691934
\(716\) 2.82676e58 0.842504
\(717\) −1.31376e58 −0.380516
\(718\) −2.69580e58 −0.758817
\(719\) −1.95054e58 −0.533595 −0.266797 0.963753i \(-0.585965\pi\)
−0.266797 + 0.963753i \(0.585965\pi\)
\(720\) −2.32078e58 −0.617047
\(721\) 2.62613e58 0.678647
\(722\) −2.68611e58 −0.674702
\(723\) 9.03318e58 2.20549
\(724\) 1.89091e58 0.448776
\(725\) −3.13866e58 −0.724127
\(726\) −4.19061e58 −0.939889
\(727\) 6.41681e58 1.39915 0.699575 0.714560i \(-0.253373\pi\)
0.699575 + 0.714560i \(0.253373\pi\)
\(728\) 2.76212e58 0.585530
\(729\) −3.73866e58 −0.770552
\(730\) 7.55795e58 1.51456
\(731\) 1.96861e57 0.0383577
\(732\) −7.64413e58 −1.44827
\(733\) 1.98495e58 0.365695 0.182847 0.983141i \(-0.441469\pi\)
0.182847 + 0.983141i \(0.441469\pi\)
\(734\) 4.59067e58 0.822445
\(735\) −1.15856e59 −2.01850
\(736\) 8.47972e57 0.143677
\(737\) −5.79246e58 −0.954507
\(738\) −6.99532e58 −1.12112
\(739\) 9.09593e58 1.41787 0.708934 0.705275i \(-0.249176\pi\)
0.708934 + 0.705275i \(0.249176\pi\)
\(740\) −1.30126e58 −0.197294
\(741\) −3.00389e58 −0.443008
\(742\) −6.25322e58 −0.897065
\(743\) −1.22229e59 −1.70570 −0.852849 0.522158i \(-0.825127\pi\)
−0.852849 + 0.522158i \(0.825127\pi\)
\(744\) 3.39100e58 0.460345
\(745\) −4.00431e58 −0.528839
\(746\) −3.63246e58 −0.466718
\(747\) 9.87260e58 1.23413
\(748\) 6.42569e57 0.0781515
\(749\) 1.64491e59 1.94654
\(750\) 7.41698e58 0.854027
\(751\) −3.17979e57 −0.0356270 −0.0178135 0.999841i \(-0.505671\pi\)
−0.0178135 + 0.999841i \(0.505671\pi\)
\(752\) −2.29235e58 −0.249929
\(753\) 1.93136e59 2.04912
\(754\) −1.38827e59 −1.43338
\(755\) 7.19147e58 0.722612
\(756\) 1.34387e59 1.31420
\(757\) −5.74234e58 −0.546542 −0.273271 0.961937i \(-0.588106\pi\)
−0.273271 + 0.961937i \(0.588106\pi\)
\(758\) 4.17343e58 0.386611
\(759\) −7.75917e58 −0.699615
\(760\) 1.02833e58 0.0902517
\(761\) −1.47303e59 −1.25842 −0.629209 0.777236i \(-0.716621\pi\)
−0.629209 + 0.777236i \(0.716621\pi\)
\(762\) 1.28329e59 1.06720
\(763\) −1.41313e59 −1.14400
\(764\) −2.37077e58 −0.186842
\(765\) 1.02345e59 0.785249
\(766\) 4.44998e58 0.332405
\(767\) 4.10820e57 0.0298777
\(768\) 1.54648e58 0.109506
\(769\) −1.33564e59 −0.920873 −0.460437 0.887693i \(-0.652307\pi\)
−0.460437 + 0.887693i \(0.652307\pi\)
\(770\) 8.65218e58 0.580852
\(771\) −4.06740e59 −2.65890
\(772\) 2.23595e58 0.142334
\(773\) 2.25801e59 1.39974 0.699868 0.714272i \(-0.253242\pi\)
0.699868 + 0.714272i \(0.253242\pi\)
\(774\) −2.92308e58 −0.176462
\(775\) 5.33312e58 0.313542
\(776\) −9.68514e57 −0.0554550
\(777\) 1.45782e59 0.812965
\(778\) −1.74924e59 −0.950099
\(779\) 3.09961e58 0.163979
\(780\) −2.39439e59 −1.23383
\(781\) 1.14847e59 0.576464
\(782\) −3.73950e58 −0.182842
\(783\) −6.75446e59 −3.21717
\(784\) 5.20536e58 0.241530
\(785\) −6.63448e58 −0.299902
\(786\) 2.69445e59 1.18661
\(787\) 3.77733e59 1.62070 0.810351 0.585945i \(-0.199277\pi\)
0.810351 + 0.585945i \(0.199277\pi\)
\(788\) −1.63095e59 −0.681793
\(789\) 6.22810e59 2.53675
\(790\) 1.75835e59 0.697831
\(791\) 2.86467e59 1.10779
\(792\) −9.54115e58 −0.359530
\(793\) −5.31754e59 −1.95259
\(794\) −3.04337e59 −1.08902
\(795\) 5.42071e59 1.89030
\(796\) −8.22410e58 −0.279493
\(797\) −1.32373e59 −0.438433 −0.219217 0.975676i \(-0.570350\pi\)
−0.219217 + 0.975676i \(0.570350\pi\)
\(798\) −1.15205e59 −0.371888
\(799\) 1.01091e59 0.318057
\(800\) 2.43219e58 0.0745852
\(801\) 1.63686e59 0.489265
\(802\) 1.09509e59 0.319062
\(803\) 3.10721e59 0.882473
\(804\) 6.14779e59 1.70204
\(805\) −5.03523e59 −1.35895
\(806\) 2.35891e59 0.620644
\(807\) −6.58713e59 −1.68962
\(808\) 5.55079e58 0.138810
\(809\) 8.51729e58 0.207662 0.103831 0.994595i \(-0.466890\pi\)
0.103831 + 0.994595i \(0.466890\pi\)
\(810\) −4.30775e59 −1.02402
\(811\) −1.20156e59 −0.278496 −0.139248 0.990258i \(-0.544469\pi\)
−0.139248 + 0.990258i \(0.544469\pi\)
\(812\) −5.32428e59 −1.20327
\(813\) −9.37218e59 −2.06531
\(814\) −5.34972e58 −0.114956
\(815\) 4.10086e59 0.859298
\(816\) −6.81988e58 −0.139357
\(817\) 1.29521e58 0.0258100
\(818\) 2.23254e59 0.433867
\(819\) 1.80865e60 3.42796
\(820\) 2.47068e59 0.456702
\(821\) −1.35794e59 −0.244820 −0.122410 0.992480i \(-0.539062\pi\)
−0.122410 + 0.992480i \(0.539062\pi\)
\(822\) −1.71425e59 −0.301440
\(823\) −8.83563e59 −1.51545 −0.757724 0.652575i \(-0.773689\pi\)
−0.757724 + 0.652575i \(0.773689\pi\)
\(824\) 1.02283e59 0.171117
\(825\) −2.22552e59 −0.363183
\(826\) 1.57558e58 0.0250812
\(827\) −2.24391e59 −0.348451 −0.174226 0.984706i \(-0.555742\pi\)
−0.174226 + 0.984706i \(0.555742\pi\)
\(828\) 5.55258e59 0.841148
\(829\) −8.39406e58 −0.124052 −0.0620260 0.998075i \(-0.519756\pi\)
−0.0620260 + 0.998075i \(0.519756\pi\)
\(830\) −3.48691e59 −0.502736
\(831\) −2.05591e60 −2.89189
\(832\) 1.07579e59 0.147638
\(833\) −2.29553e59 −0.307369
\(834\) 1.56186e60 2.04051
\(835\) 3.11926e57 0.00397630
\(836\) 4.22766e58 0.0525862
\(837\) 1.14770e60 1.39301
\(838\) −8.77315e59 −1.03909
\(839\) 7.27294e59 0.840600 0.420300 0.907385i \(-0.361925\pi\)
0.420300 + 0.907385i \(0.361925\pi\)
\(840\) −9.18295e59 −1.03575
\(841\) 1.76756e60 1.94561
\(842\) 1.20569e60 1.29520
\(843\) 2.27214e60 2.38215
\(844\) 8.95980e59 0.916808
\(845\) −4.71638e59 −0.471027
\(846\) −1.50105e60 −1.46319
\(847\) −1.11801e60 −1.06374
\(848\) −2.43550e59 −0.226190
\(849\) −7.07522e59 −0.641405
\(850\) −1.07258e59 −0.0949164
\(851\) 3.11332e59 0.268948
\(852\) −1.21892e60 −1.02793
\(853\) 9.33512e58 0.0768537 0.0384269 0.999261i \(-0.487765\pi\)
0.0384269 + 0.999261i \(0.487765\pi\)
\(854\) −2.03938e60 −1.63912
\(855\) 6.73360e59 0.528374
\(856\) 6.40658e59 0.490811
\(857\) −1.10562e60 −0.826990 −0.413495 0.910506i \(-0.635692\pi\)
−0.413495 + 0.910506i \(0.635692\pi\)
\(858\) −9.84376e59 −0.718905
\(859\) −6.75499e59 −0.481687 −0.240844 0.970564i \(-0.577424\pi\)
−0.240844 + 0.970564i \(0.577424\pi\)
\(860\) 1.03240e59 0.0718838
\(861\) −2.76793e60 −1.88187
\(862\) 1.38823e60 0.921644
\(863\) 5.90285e59 0.382684 0.191342 0.981523i \(-0.438716\pi\)
0.191342 + 0.981523i \(0.438716\pi\)
\(864\) 5.23412e59 0.331369
\(865\) 1.77313e60 1.09625
\(866\) −1.13253e60 −0.683805
\(867\) −2.67058e60 −1.57476
\(868\) 9.04687e59 0.521007
\(869\) 7.22889e59 0.406599
\(870\) 4.61545e60 2.53553
\(871\) 4.27663e60 2.29472
\(872\) −5.50384e59 −0.288455
\(873\) −6.34190e59 −0.324659
\(874\) −2.46033e59 −0.123030
\(875\) 1.97878e60 0.966567
\(876\) −3.29782e60 −1.57359
\(877\) −2.63402e60 −1.22780 −0.613900 0.789384i \(-0.710400\pi\)
−0.613900 + 0.789384i \(0.710400\pi\)
\(878\) 1.20042e59 0.0546635
\(879\) −3.10608e60 −1.38179
\(880\) 3.36985e59 0.146459
\(881\) 1.68258e60 0.714445 0.357223 0.934019i \(-0.383724\pi\)
0.357223 + 0.934019i \(0.383724\pi\)
\(882\) 3.40850e60 1.41403
\(883\) 2.43606e60 0.987400 0.493700 0.869632i \(-0.335644\pi\)
0.493700 + 0.869632i \(0.335644\pi\)
\(884\) −4.74416e59 −0.187883
\(885\) −1.36582e59 −0.0528512
\(886\) −1.01899e60 −0.385282
\(887\) −2.73192e60 −1.00933 −0.504666 0.863315i \(-0.668384\pi\)
−0.504666 + 0.863315i \(0.668384\pi\)
\(888\) 5.67790e59 0.204985
\(889\) 3.42369e60 1.20784
\(890\) −5.78123e59 −0.199308
\(891\) −1.77099e60 −0.596655
\(892\) −3.23917e57 −0.00106648
\(893\) 6.65111e59 0.214012
\(894\) 1.74723e60 0.549454
\(895\) −6.53750e60 −2.00927
\(896\) 4.12586e59 0.123937
\(897\) 5.72868e60 1.68194
\(898\) −3.57205e60 −1.02507
\(899\) −4.54705e60 −1.27543
\(900\) 1.59261e60 0.436655
\(901\) 1.07404e60 0.287848
\(902\) 1.01574e60 0.266103
\(903\) −1.15661e60 −0.296202
\(904\) 1.11573e60 0.279323
\(905\) −4.37314e60 −1.07028
\(906\) −3.13791e60 −0.750780
\(907\) −9.66132e59 −0.225989 −0.112994 0.993596i \(-0.536044\pi\)
−0.112994 + 0.993596i \(0.536044\pi\)
\(908\) 1.36296e60 0.311691
\(909\) 3.63469e60 0.812659
\(910\) −6.38799e60 −1.39642
\(911\) −3.27643e60 −0.700284 −0.350142 0.936697i \(-0.613867\pi\)
−0.350142 + 0.936697i \(0.613867\pi\)
\(912\) −4.48701e59 −0.0937697
\(913\) −1.43353e60 −0.292925
\(914\) 1.66071e60 0.331815
\(915\) 1.76787e61 3.45397
\(916\) 2.76283e60 0.527833
\(917\) 7.18853e60 1.34298
\(918\) −2.30821e60 −0.421697
\(919\) 2.29076e60 0.409271 0.204636 0.978838i \(-0.434399\pi\)
0.204636 + 0.978838i \(0.434399\pi\)
\(920\) −1.96112e60 −0.342652
\(921\) −4.61279e60 −0.788208
\(922\) −3.08009e59 −0.0514731
\(923\) −8.47926e60 −1.38587
\(924\) −3.77527e60 −0.603494
\(925\) 8.92977e59 0.139616
\(926\) 7.93976e60 1.21418
\(927\) 6.69753e60 1.00180
\(928\) −2.07370e60 −0.303398
\(929\) 6.62994e60 0.948828 0.474414 0.880302i \(-0.342660\pi\)
0.474414 + 0.880302i \(0.342660\pi\)
\(930\) −7.84243e60 −1.09787
\(931\) −1.51030e60 −0.206821
\(932\) −3.78447e59 −0.0506966
\(933\) −2.52683e60 −0.331133
\(934\) −2.84069e60 −0.364177
\(935\) −1.48608e60 −0.186382
\(936\) 7.04434e60 0.864341
\(937\) −2.63986e60 −0.316898 −0.158449 0.987367i \(-0.550649\pi\)
−0.158449 + 0.987367i \(0.550649\pi\)
\(938\) 1.64017e61 1.92633
\(939\) −2.15028e61 −2.47088
\(940\) 5.30156e60 0.596050
\(941\) 1.40617e61 1.54685 0.773427 0.633885i \(-0.218541\pi\)
0.773427 + 0.633885i \(0.218541\pi\)
\(942\) 2.89487e60 0.311592
\(943\) −5.91121e60 −0.622568
\(944\) 6.13655e58 0.00632409
\(945\) −3.10800e61 −3.13422
\(946\) 4.24439e59 0.0418839
\(947\) 1.18800e61 1.14721 0.573606 0.819131i \(-0.305544\pi\)
0.573606 + 0.819131i \(0.305544\pi\)
\(948\) −7.67235e60 −0.725032
\(949\) −2.29408e61 −2.12154
\(950\) −7.05683e59 −0.0638669
\(951\) 2.83875e61 2.51436
\(952\) −1.81948e60 −0.157721
\(953\) −1.12712e61 −0.956235 −0.478117 0.878296i \(-0.658681\pi\)
−0.478117 + 0.878296i \(0.658681\pi\)
\(954\) −1.59478e61 −1.32422
\(955\) 5.48291e60 0.445597
\(956\) −1.36512e60 −0.108588
\(957\) 1.89749e61 1.47736
\(958\) −7.59321e59 −0.0578672
\(959\) −4.57345e60 −0.341163
\(960\) −3.57657e60 −0.261160
\(961\) −6.26416e60 −0.447748
\(962\) 3.94975e60 0.276364
\(963\) 4.19507e61 2.87343
\(964\) 9.38632e60 0.629385
\(965\) −5.17113e60 −0.339450
\(966\) 2.19706e61 1.41192
\(967\) −6.94733e60 −0.437095 −0.218547 0.975826i \(-0.570132\pi\)
−0.218547 + 0.975826i \(0.570132\pi\)
\(968\) −4.35444e60 −0.268217
\(969\) 1.97874e60 0.119331
\(970\) 2.23990e60 0.132254
\(971\) −2.12424e61 −1.22803 −0.614016 0.789294i \(-0.710447\pi\)
−0.614016 + 0.789294i \(0.710447\pi\)
\(972\) 2.23804e60 0.126680
\(973\) 4.16689e61 2.30940
\(974\) 3.50054e60 0.189966
\(975\) 1.64312e61 0.873124
\(976\) −7.94297e60 −0.413296
\(977\) −2.72440e61 −1.38814 −0.694068 0.719909i \(-0.744183\pi\)
−0.694068 + 0.719909i \(0.744183\pi\)
\(978\) −1.78936e61 −0.892794
\(979\) −2.37676e60 −0.116129
\(980\) −1.20385e61 −0.576021
\(981\) −3.60395e61 −1.68874
\(982\) −1.97366e61 −0.905705
\(983\) −6.88350e60 −0.309359 −0.154679 0.987965i \(-0.549434\pi\)
−0.154679 + 0.987965i \(0.549434\pi\)
\(984\) −1.07805e61 −0.474504
\(985\) 3.77192e61 1.62600
\(986\) 9.14488e60 0.386101
\(987\) −5.93939e61 −2.45607
\(988\) −3.12133e60 −0.126422
\(989\) −2.47007e60 −0.0979908
\(990\) 2.20660e61 0.857436
\(991\) −1.65448e60 −0.0629727 −0.0314864 0.999504i \(-0.510024\pi\)
−0.0314864 + 0.999504i \(0.510024\pi\)
\(992\) 3.52357e60 0.131369
\(993\) 7.98259e61 2.91531
\(994\) −3.25196e61 −1.16339
\(995\) 1.90200e61 0.666557
\(996\) 1.52147e61 0.522333
\(997\) 3.62868e60 0.122039 0.0610193 0.998137i \(-0.480565\pi\)
0.0610193 + 0.998137i \(0.480565\pi\)
\(998\) −7.27445e60 −0.239676
\(999\) 1.92170e61 0.620289
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 \(a_p\))