Properties

Label 3.38.a.a.1.2
Level 3
Weight 38
Character 3.1
Self dual Yes
Analytic conductor 26.014
Analytic rank 1
Dimension 3
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 38 \)
Character orbit: \([\chi]\) = 3.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(26.0142114374\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: \(\mathbb{Q}[x]/(x^{3} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{9}\cdot 3^{5}\cdot 5 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(3724.64\)
Character \(\chi\) = 3.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-148328. q^{2}\) \(-3.87420e8 q^{3}\) \(-1.15438e11 q^{4}\) \(+7.60742e11 q^{5}\) \(+5.74652e13 q^{6}\) \(+2.59260e15 q^{7}\) \(+3.75086e16 q^{8}\) \(+1.50095e17 q^{9}\) \(+O(q^{10})\) \(q\)\(-148328. q^{2}\) \(-3.87420e8 q^{3}\) \(-1.15438e11 q^{4}\) \(+7.60742e11 q^{5}\) \(+5.74652e13 q^{6}\) \(+2.59260e15 q^{7}\) \(+3.75086e16 q^{8}\) \(+1.50095e17 q^{9}\) \(-1.12839e17 q^{10}\) \(+3.65505e18 q^{11}\) \(+4.47230e19 q^{12}\) \(+6.05340e19 q^{13}\) \(-3.84554e20 q^{14}\) \(-2.94727e20 q^{15}\) \(+1.03021e22 q^{16}\) \(+5.25799e22 q^{17}\) \(-2.22632e22 q^{18}\) \(-4.58834e23 q^{19}\) \(-8.78185e22 q^{20}\) \(-1.00443e24 q^{21}\) \(-5.42145e23 q^{22}\) \(+6.97213e24 q^{23}\) \(-1.45316e25 q^{24}\) \(-7.21808e25 q^{25}\) \(-8.97887e24 q^{26}\) \(-5.81497e25 q^{27}\) \(-2.99284e26 q^{28}\) \(-2.14090e27 q^{29}\) \(+4.37162e25 q^{30}\) \(-3.44162e27 q^{31}\) \(-6.68323e27 q^{32}\) \(-1.41604e27 q^{33}\) \(-7.79906e27 q^{34}\) \(+1.97230e27 q^{35}\) \(-1.73266e28 q^{36}\) \(+6.38686e28 q^{37}\) \(+6.80578e28 q^{38}\) \(-2.34521e28 q^{39}\) \(+2.85344e28 q^{40}\) \(+5.40269e29 q^{41}\) \(+1.48984e29 q^{42}\) \(+3.10661e30 q^{43}\) \(-4.21931e29 q^{44}\) \(+1.14183e29 q^{45}\) \(-1.03416e30 q^{46}\) \(-1.05785e31 q^{47}\) \(-3.99124e30 q^{48}\) \(-1.18405e31 q^{49}\) \(+1.07064e31 q^{50}\) \(-2.03705e31 q^{51}\) \(-6.98792e30 q^{52}\) \(-5.28675e31 q^{53}\) \(+8.62521e30 q^{54}\) \(+2.78055e30 q^{55}\) \(+9.72449e31 q^{56}\) \(+1.77762e32 q^{57}\) \(+3.17554e32 q^{58}\) \(+1.00018e32 q^{59}\) \(+3.40227e31 q^{60}\) \(-1.03869e32 q^{61}\) \(+5.10487e32 q^{62}\) \(+3.89135e32 q^{63}\) \(-4.24601e32 q^{64}\) \(+4.60508e31 q^{65}\) \(+2.10038e32 q^{66}\) \(-4.87568e33 q^{67}\) \(-6.06972e33 q^{68}\) \(-2.70115e33 q^{69}\) \(-2.92547e32 q^{70}\) \(-1.97222e34 q^{71}\) \(+5.62984e33 q^{72}\) \(+2.72469e34 q^{73}\) \(-9.47348e33 q^{74}\) \(+2.79643e34 q^{75}\) \(+5.29668e34 q^{76}\) \(+9.47609e33 q^{77}\) \(+3.47860e33 q^{78}\) \(+1.01745e35 q^{79}\) \(+7.83724e33 q^{80}\) \(+2.25284e34 q^{81}\) \(-8.01369e34 q^{82}\) \(-4.82762e35 q^{83}\) \(+1.15949e35 q^{84}\) \(+3.99998e34 q^{85}\) \(-4.60797e35 q^{86}\) \(+8.29427e35 q^{87}\) \(+1.37096e35 q^{88}\) \(-2.01920e36 q^{89}\) \(-1.69365e34 q^{90}\) \(+1.56941e35 q^{91}\) \(-8.04848e35 q^{92}\) \(+1.33335e36 q^{93}\) \(+1.56908e36 q^{94}\) \(-3.49054e35 q^{95}\) \(+2.58922e36 q^{96}\) \(+5.47048e36 q^{97}\) \(+1.75628e36 q^{98}\) \(+5.48604e35 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(3q \) \(\mathstrut -\mathstrut 310908q^{2} \) \(\mathstrut -\mathstrut 1162261467q^{3} \) \(\mathstrut +\mathstrut 338476600848q^{4} \) \(\mathstrut -\mathstrut 9628717886790q^{5} \) \(\mathstrut +\mathstrut 120452129394012q^{6} \) \(\mathstrut -\mathstrut 4621884343701744q^{7} \) \(\mathstrut -\mathstrut 93383909093911488q^{8} \) \(\mathstrut +\mathstrut 450283905890997363q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut -\mathstrut 310908q^{2} \) \(\mathstrut -\mathstrut 1162261467q^{3} \) \(\mathstrut +\mathstrut 338476600848q^{4} \) \(\mathstrut -\mathstrut 9628717886790q^{5} \) \(\mathstrut +\mathstrut 120452129394012q^{6} \) \(\mathstrut -\mathstrut 4621884343701744q^{7} \) \(\mathstrut -\mathstrut 93383909093911488q^{8} \) \(\mathstrut +\mathstrut 450283905890997363q^{9} \) \(\mathstrut +\mathstrut 10698950136741797880q^{10} \) \(\mathstrut +\mathstrut 22673303357139628620q^{11} \) \(\mathstrut -\mathstrut \)\(13\!\cdots\!72\)\(q^{12} \) \(\mathstrut -\mathstrut \)\(16\!\cdots\!10\)\(q^{13} \) \(\mathstrut +\mathstrut \)\(79\!\cdots\!28\)\(q^{14} \) \(\mathstrut +\mathstrut \)\(37\!\cdots\!10\)\(q^{15} \) \(\mathstrut +\mathstrut \)\(32\!\cdots\!56\)\(q^{16} \) \(\mathstrut -\mathstrut \)\(27\!\cdots\!06\)\(q^{17} \) \(\mathstrut -\mathstrut \)\(46\!\cdots\!68\)\(q^{18} \) \(\mathstrut +\mathstrut \)\(58\!\cdots\!04\)\(q^{19} \) \(\mathstrut -\mathstrut \)\(40\!\cdots\!80\)\(q^{20} \) \(\mathstrut +\mathstrut \)\(17\!\cdots\!16\)\(q^{21} \) \(\mathstrut -\mathstrut \)\(44\!\cdots\!52\)\(q^{22} \) \(\mathstrut -\mathstrut \)\(17\!\cdots\!72\)\(q^{23} \) \(\mathstrut +\mathstrut \)\(36\!\cdots\!32\)\(q^{24} \) \(\mathstrut -\mathstrut \)\(24\!\cdots\!75\)\(q^{25} \) \(\mathstrut -\mathstrut \)\(61\!\cdots\!44\)\(q^{26} \) \(\mathstrut -\mathstrut \)\(17\!\cdots\!07\)\(q^{27} \) \(\mathstrut -\mathstrut \)\(20\!\cdots\!88\)\(q^{28} \) \(\mathstrut +\mathstrut \)\(11\!\cdots\!78\)\(q^{29} \) \(\mathstrut -\mathstrut \)\(41\!\cdots\!20\)\(q^{30} \) \(\mathstrut -\mathstrut \)\(11\!\cdots\!36\)\(q^{31} \) \(\mathstrut -\mathstrut \)\(27\!\cdots\!84\)\(q^{32} \) \(\mathstrut -\mathstrut \)\(87\!\cdots\!80\)\(q^{33} \) \(\mathstrut -\mathstrut \)\(18\!\cdots\!64\)\(q^{34} \) \(\mathstrut +\mathstrut \)\(47\!\cdots\!80\)\(q^{35} \) \(\mathstrut +\mathstrut \)\(50\!\cdots\!08\)\(q^{36} \) \(\mathstrut +\mathstrut \)\(60\!\cdots\!66\)\(q^{37} \) \(\mathstrut -\mathstrut \)\(37\!\cdots\!76\)\(q^{38} \) \(\mathstrut +\mathstrut \)\(65\!\cdots\!90\)\(q^{39} \) \(\mathstrut +\mathstrut \)\(17\!\cdots\!00\)\(q^{40} \) \(\mathstrut +\mathstrut \)\(20\!\cdots\!34\)\(q^{41} \) \(\mathstrut -\mathstrut \)\(30\!\cdots\!92\)\(q^{42} \) \(\mathstrut +\mathstrut \)\(24\!\cdots\!44\)\(q^{43} \) \(\mathstrut +\mathstrut \)\(42\!\cdots\!72\)\(q^{44} \) \(\mathstrut -\mathstrut \)\(14\!\cdots\!90\)\(q^{45} \) \(\mathstrut -\mathstrut \)\(43\!\cdots\!56\)\(q^{46} \) \(\mathstrut -\mathstrut \)\(11\!\cdots\!32\)\(q^{47} \) \(\mathstrut -\mathstrut \)\(12\!\cdots\!84\)\(q^{48} \) \(\mathstrut -\mathstrut \)\(22\!\cdots\!73\)\(q^{49} \) \(\mathstrut -\mathstrut \)\(96\!\cdots\!00\)\(q^{50} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!34\)\(q^{51} \) \(\mathstrut +\mathstrut \)\(43\!\cdots\!84\)\(q^{52} \) \(\mathstrut -\mathstrut \)\(11\!\cdots\!82\)\(q^{53} \) \(\mathstrut +\mathstrut \)\(18\!\cdots\!52\)\(q^{54} \) \(\mathstrut -\mathstrut \)\(12\!\cdots\!80\)\(q^{55} \) \(\mathstrut +\mathstrut \)\(63\!\cdots\!60\)\(q^{56} \) \(\mathstrut -\mathstrut \)\(22\!\cdots\!56\)\(q^{57} \) \(\mathstrut +\mathstrut \)\(58\!\cdots\!88\)\(q^{58} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!36\)\(q^{59} \) \(\mathstrut +\mathstrut \)\(15\!\cdots\!20\)\(q^{60} \) \(\mathstrut +\mathstrut \)\(29\!\cdots\!02\)\(q^{61} \) \(\mathstrut +\mathstrut \)\(24\!\cdots\!92\)\(q^{62} \) \(\mathstrut -\mathstrut \)\(69\!\cdots\!24\)\(q^{63} \) \(\mathstrut -\mathstrut \)\(10\!\cdots\!24\)\(q^{64} \) \(\mathstrut -\mathstrut \)\(75\!\cdots\!60\)\(q^{65} \) \(\mathstrut +\mathstrut \)\(17\!\cdots\!28\)\(q^{66} \) \(\mathstrut +\mathstrut \)\(38\!\cdots\!44\)\(q^{67} \) \(\mathstrut -\mathstrut \)\(21\!\cdots\!16\)\(q^{68} \) \(\mathstrut +\mathstrut \)\(66\!\cdots\!08\)\(q^{69} \) \(\mathstrut -\mathstrut \)\(43\!\cdots\!60\)\(q^{70} \) \(\mathstrut -\mathstrut \)\(22\!\cdots\!44\)\(q^{71} \) \(\mathstrut -\mathstrut \)\(14\!\cdots\!48\)\(q^{72} \) \(\mathstrut +\mathstrut \)\(32\!\cdots\!78\)\(q^{73} \) \(\mathstrut +\mathstrut \)\(46\!\cdots\!28\)\(q^{74} \) \(\mathstrut +\mathstrut \)\(96\!\cdots\!75\)\(q^{75} \) \(\mathstrut +\mathstrut \)\(34\!\cdots\!16\)\(q^{76} \) \(\mathstrut -\mathstrut \)\(61\!\cdots\!68\)\(q^{77} \) \(\mathstrut +\mathstrut \)\(23\!\cdots\!16\)\(q^{78} \) \(\mathstrut +\mathstrut \)\(74\!\cdots\!40\)\(q^{79} \) \(\mathstrut -\mathstrut \)\(61\!\cdots\!40\)\(q^{80} \) \(\mathstrut +\mathstrut \)\(67\!\cdots\!23\)\(q^{81} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!12\)\(q^{82} \) \(\mathstrut -\mathstrut \)\(31\!\cdots\!04\)\(q^{83} \) \(\mathstrut +\mathstrut \)\(78\!\cdots\!32\)\(q^{84} \) \(\mathstrut +\mathstrut \)\(21\!\cdots\!80\)\(q^{85} \) \(\mathstrut -\mathstrut \)\(26\!\cdots\!60\)\(q^{86} \) \(\mathstrut -\mathstrut \)\(43\!\cdots\!42\)\(q^{87} \) \(\mathstrut -\mathstrut \)\(13\!\cdots\!28\)\(q^{88} \) \(\mathstrut -\mathstrut \)\(16\!\cdots\!26\)\(q^{89} \) \(\mathstrut +\mathstrut \)\(16\!\cdots\!80\)\(q^{90} \) \(\mathstrut +\mathstrut \)\(45\!\cdots\!04\)\(q^{91} \) \(\mathstrut -\mathstrut \)\(54\!\cdots\!24\)\(q^{92} \) \(\mathstrut +\mathstrut \)\(45\!\cdots\!04\)\(q^{93} \) \(\mathstrut +\mathstrut \)\(15\!\cdots\!00\)\(q^{94} \) \(\mathstrut -\mathstrut \)\(10\!\cdots\!00\)\(q^{95} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!76\)\(q^{96} \) \(\mathstrut +\mathstrut \)\(26\!\cdots\!14\)\(q^{97} \) \(\mathstrut -\mathstrut \)\(16\!\cdots\!00\)\(q^{98} \) \(\mathstrut +\mathstrut \)\(34\!\cdots\!20\)\(q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −148328. −0.400099 −0.200049 0.979786i \(-0.564110\pi\)
−0.200049 + 0.979786i \(0.564110\pi\)
\(3\) −3.87420e8 −0.577350
\(4\) −1.15438e11 −0.839921
\(5\) 7.60742e11 0.0891851 0.0445926 0.999005i \(-0.485801\pi\)
0.0445926 + 0.999005i \(0.485801\pi\)
\(6\) 5.74652e13 0.230997
\(7\) 2.59260e15 0.601758 0.300879 0.953662i \(-0.402720\pi\)
0.300879 + 0.953662i \(0.402720\pi\)
\(8\) 3.75086e16 0.736150
\(9\) 1.50095e17 0.333333
\(10\) −1.12839e17 −0.0356829
\(11\) 3.65505e18 0.198211 0.0991057 0.995077i \(-0.468402\pi\)
0.0991057 + 0.995077i \(0.468402\pi\)
\(12\) 4.47230e19 0.484929
\(13\) 6.05340e19 0.149296 0.0746479 0.997210i \(-0.476217\pi\)
0.0746479 + 0.997210i \(0.476217\pi\)
\(14\) −3.84554e20 −0.240763
\(15\) −2.94727e20 −0.0514911
\(16\) 1.03021e22 0.545388
\(17\) 5.25799e22 0.906808 0.453404 0.891305i \(-0.350210\pi\)
0.453404 + 0.891305i \(0.350210\pi\)
\(18\) −2.22632e22 −0.133366
\(19\) −4.58834e23 −1.01091 −0.505457 0.862852i \(-0.668676\pi\)
−0.505457 + 0.862852i \(0.668676\pi\)
\(20\) −8.78185e22 −0.0749085
\(21\) −1.00443e24 −0.347425
\(22\) −5.42145e23 −0.0793042
\(23\) 6.97213e24 0.448126 0.224063 0.974575i \(-0.428068\pi\)
0.224063 + 0.974575i \(0.428068\pi\)
\(24\) −1.45316e25 −0.425016
\(25\) −7.21808e25 −0.992046
\(26\) −8.97887e24 −0.0597331
\(27\) −5.81497e25 −0.192450
\(28\) −2.99284e26 −0.505429
\(29\) −2.14090e27 −1.88900 −0.944502 0.328506i \(-0.893455\pi\)
−0.944502 + 0.328506i \(0.893455\pi\)
\(30\) 4.37162e25 0.0206015
\(31\) −3.44162e27 −0.884242 −0.442121 0.896955i \(-0.645774\pi\)
−0.442121 + 0.896955i \(0.645774\pi\)
\(32\) −6.68323e27 −0.954359
\(33\) −1.41604e27 −0.114437
\(34\) −7.79906e27 −0.362813
\(35\) 1.97230e27 0.0536678
\(36\) −1.73266e28 −0.279974
\(37\) 6.38686e28 0.621664 0.310832 0.950465i \(-0.399392\pi\)
0.310832 + 0.950465i \(0.399392\pi\)
\(38\) 6.80578e28 0.404465
\(39\) −2.34521e28 −0.0861960
\(40\) 2.85344e28 0.0656536
\(41\) 5.40269e29 0.787243 0.393622 0.919273i \(-0.371222\pi\)
0.393622 + 0.919273i \(0.371222\pi\)
\(42\) 1.48984e29 0.139004
\(43\) 3.10661e30 1.87552 0.937758 0.347288i \(-0.112897\pi\)
0.937758 + 0.347288i \(0.112897\pi\)
\(44\) −4.21931e29 −0.166482
\(45\) 1.14183e29 0.0297284
\(46\) −1.03416e30 −0.179295
\(47\) −1.05785e31 −1.23201 −0.616003 0.787744i \(-0.711249\pi\)
−0.616003 + 0.787744i \(0.711249\pi\)
\(48\) −3.99124e30 −0.314880
\(49\) −1.18405e31 −0.637887
\(50\) 1.07064e31 0.396916
\(51\) −2.03705e31 −0.523546
\(52\) −6.98792e30 −0.125397
\(53\) −5.28675e31 −0.666938 −0.333469 0.942761i \(-0.608219\pi\)
−0.333469 + 0.942761i \(0.608219\pi\)
\(54\) 8.62521e30 0.0769990
\(55\) 2.78055e30 0.0176775
\(56\) 9.72449e31 0.442984
\(57\) 1.77762e32 0.583651
\(58\) 3.17554e32 0.755788
\(59\) 1.00018e32 0.173507 0.0867535 0.996230i \(-0.472351\pi\)
0.0867535 + 0.996230i \(0.472351\pi\)
\(60\) 3.40227e31 0.0432484
\(61\) −1.03869e32 −0.0972490 −0.0486245 0.998817i \(-0.515484\pi\)
−0.0486245 + 0.998817i \(0.515484\pi\)
\(62\) 5.10487e32 0.353784
\(63\) 3.89135e32 0.200586
\(64\) −4.24601e32 −0.163550
\(65\) 4.60508e31 0.0133150
\(66\) 2.10038e32 0.0457863
\(67\) −4.87568e33 −0.804732 −0.402366 0.915479i \(-0.631812\pi\)
−0.402366 + 0.915479i \(0.631812\pi\)
\(68\) −6.06972e33 −0.761647
\(69\) −2.70115e33 −0.258726
\(70\) −2.92547e32 −0.0214724
\(71\) −1.97222e34 −1.11346 −0.556732 0.830692i \(-0.687945\pi\)
−0.556732 + 0.830692i \(0.687945\pi\)
\(72\) 5.62984e33 0.245383
\(73\) 2.72469e34 0.920118 0.460059 0.887888i \(-0.347828\pi\)
0.460059 + 0.887888i \(0.347828\pi\)
\(74\) −9.47348e33 −0.248727
\(75\) 2.79643e34 0.572758
\(76\) 5.29668e34 0.849087
\(77\) 9.47609e33 0.119275
\(78\) 3.47860e33 0.0344869
\(79\) 1.01745e35 0.796915 0.398457 0.917187i \(-0.369546\pi\)
0.398457 + 0.917187i \(0.369546\pi\)
\(80\) 7.83724e33 0.0486405
\(81\) 2.25284e34 0.111111
\(82\) −8.01369e34 −0.314975
\(83\) −4.82762e35 −1.51631 −0.758155 0.652074i \(-0.773899\pi\)
−0.758155 + 0.652074i \(0.773899\pi\)
\(84\) 1.15949e35 0.291810
\(85\) 3.99998e34 0.0808737
\(86\) −4.60797e35 −0.750392
\(87\) 8.29427e35 1.09062
\(88\) 1.37096e35 0.145913
\(89\) −2.01920e36 −1.74367 −0.871837 0.489797i \(-0.837071\pi\)
−0.871837 + 0.489797i \(0.837071\pi\)
\(90\) −1.69365e34 −0.0118943
\(91\) 1.56941e35 0.0898399
\(92\) −8.04848e35 −0.376391
\(93\) 1.33335e36 0.510518
\(94\) 1.56908e36 0.492924
\(95\) −3.49054e35 −0.0901584
\(96\) 2.58922e36 0.551000
\(97\) 5.47048e36 0.961056 0.480528 0.876979i \(-0.340445\pi\)
0.480528 + 0.876979i \(0.340445\pi\)
\(98\) 1.75628e36 0.255218
\(99\) 5.48604e35 0.0660705
\(100\) 8.33240e36 0.833240
\(101\) −2.06698e37 −1.71945 −0.859727 0.510754i \(-0.829366\pi\)
−0.859727 + 0.510754i \(0.829366\pi\)
\(102\) 3.02152e36 0.209470
\(103\) −3.10209e36 −0.179542 −0.0897710 0.995962i \(-0.528614\pi\)
−0.0897710 + 0.995962i \(0.528614\pi\)
\(104\) 2.27055e36 0.109904
\(105\) −7.64110e35 −0.0309851
\(106\) 7.84172e36 0.266841
\(107\) −4.27045e37 −1.22145 −0.610723 0.791844i \(-0.709121\pi\)
−0.610723 + 0.791844i \(0.709121\pi\)
\(108\) 6.71268e36 0.161643
\(109\) −6.16065e37 −1.25094 −0.625470 0.780248i \(-0.715093\pi\)
−0.625470 + 0.780248i \(0.715093\pi\)
\(110\) −4.12433e35 −0.00707275
\(111\) −2.47440e37 −0.358918
\(112\) 2.67092e37 0.328192
\(113\) 1.11410e38 1.16138 0.580690 0.814124i \(-0.302783\pi\)
0.580690 + 0.814124i \(0.302783\pi\)
\(114\) −2.63670e37 −0.233518
\(115\) 5.30399e36 0.0399662
\(116\) 2.47141e38 1.58661
\(117\) 9.08583e36 0.0497653
\(118\) −1.48355e37 −0.0694199
\(119\) 1.36319e38 0.545679
\(120\) −1.10548e37 −0.0379051
\(121\) −3.26680e38 −0.960712
\(122\) 1.54067e37 0.0389092
\(123\) −2.09311e38 −0.454515
\(124\) 3.97293e38 0.742694
\(125\) −1.10262e38 −0.177661
\(126\) −5.77195e37 −0.0802542
\(127\) −1.01769e39 −1.22249 −0.611245 0.791441i \(-0.709331\pi\)
−0.611245 + 0.791441i \(0.709331\pi\)
\(128\) 9.81516e38 1.01980
\(129\) −1.20357e39 −1.08283
\(130\) −6.83060e36 −0.00532730
\(131\) −1.20760e38 −0.0817343 −0.0408672 0.999165i \(-0.513012\pi\)
−0.0408672 + 0.999165i \(0.513012\pi\)
\(132\) 1.63465e38 0.0961184
\(133\) −1.18957e39 −0.608325
\(134\) 7.23198e38 0.321972
\(135\) −4.42370e37 −0.0171637
\(136\) 1.97220e39 0.667546
\(137\) −6.25190e38 −0.184791 −0.0923956 0.995722i \(-0.529452\pi\)
−0.0923956 + 0.995722i \(0.529452\pi\)
\(138\) 4.00655e38 0.103516
\(139\) 3.06556e39 0.693005 0.346503 0.938049i \(-0.387369\pi\)
0.346503 + 0.938049i \(0.387369\pi\)
\(140\) −2.27678e38 −0.0450768
\(141\) 4.09832e39 0.711299
\(142\) 2.92535e39 0.445495
\(143\) 2.21255e38 0.0295921
\(144\) 1.54629e39 0.181796
\(145\) −1.62867e39 −0.168471
\(146\) −4.04146e39 −0.368138
\(147\) 4.58727e39 0.368285
\(148\) −7.37286e39 −0.522148
\(149\) −2.24131e40 −1.40138 −0.700689 0.713467i \(-0.747124\pi\)
−0.700689 + 0.713467i \(0.747124\pi\)
\(150\) −4.14788e39 −0.229160
\(151\) 5.01512e38 0.0245024 0.0122512 0.999925i \(-0.496100\pi\)
0.0122512 + 0.999925i \(0.496100\pi\)
\(152\) −1.72102e40 −0.744184
\(153\) 7.89197e39 0.302269
\(154\) −1.40557e39 −0.0477219
\(155\) −2.61818e39 −0.0788613
\(156\) 2.70726e39 0.0723978
\(157\) 3.93108e40 0.934046 0.467023 0.884245i \(-0.345326\pi\)
0.467023 + 0.884245i \(0.345326\pi\)
\(158\) −1.50916e40 −0.318845
\(159\) 2.04820e40 0.385057
\(160\) −5.08422e39 −0.0851147
\(161\) 1.80759e40 0.269663
\(162\) −3.34158e39 −0.0444554
\(163\) 8.49645e40 1.00871 0.504356 0.863496i \(-0.331730\pi\)
0.504356 + 0.863496i \(0.331730\pi\)
\(164\) −6.23675e40 −0.661222
\(165\) −1.07724e39 −0.0102061
\(166\) 7.16069e40 0.606674
\(167\) 1.99342e41 1.51128 0.755639 0.654989i \(-0.227327\pi\)
0.755639 + 0.654989i \(0.227327\pi\)
\(168\) −3.76747e40 −0.255757
\(169\) −1.60736e41 −0.977711
\(170\) −5.93307e39 −0.0323575
\(171\) −6.88685e40 −0.336971
\(172\) −3.58621e41 −1.57529
\(173\) 1.62039e41 0.639393 0.319697 0.947520i \(-0.396419\pi\)
0.319697 + 0.947520i \(0.396419\pi\)
\(174\) −1.23027e41 −0.436354
\(175\) −1.87136e41 −0.596971
\(176\) 3.76547e40 0.108102
\(177\) −3.87491e40 −0.100174
\(178\) 2.99504e41 0.697641
\(179\) 2.10383e41 0.441804 0.220902 0.975296i \(-0.429100\pi\)
0.220902 + 0.975296i \(0.429100\pi\)
\(180\) −1.31811e40 −0.0249695
\(181\) −4.66595e41 −0.797785 −0.398893 0.916998i \(-0.630605\pi\)
−0.398893 + 0.916998i \(0.630605\pi\)
\(182\) −2.32786e40 −0.0359448
\(183\) 4.02411e40 0.0561468
\(184\) 2.61515e41 0.329888
\(185\) 4.85875e40 0.0554432
\(186\) −1.97773e41 −0.204257
\(187\) 1.92182e41 0.179740
\(188\) 1.22116e42 1.03479
\(189\) −1.50759e41 −0.115808
\(190\) 5.17744e40 0.0360723
\(191\) 9.30968e41 0.588596 0.294298 0.955714i \(-0.404914\pi\)
0.294298 + 0.955714i \(0.404914\pi\)
\(192\) 1.64499e41 0.0944258
\(193\) 1.74256e42 0.908611 0.454306 0.890846i \(-0.349887\pi\)
0.454306 + 0.890846i \(0.349887\pi\)
\(194\) −8.11424e41 −0.384517
\(195\) −1.78410e40 −0.00768740
\(196\) 1.36685e42 0.535775
\(197\) −4.12934e42 −1.47318 −0.736589 0.676341i \(-0.763565\pi\)
−0.736589 + 0.676341i \(0.763565\pi\)
\(198\) −8.13731e40 −0.0264347
\(199\) −5.51808e42 −1.63308 −0.816538 0.577292i \(-0.804109\pi\)
−0.816538 + 0.577292i \(0.804109\pi\)
\(200\) −2.70740e42 −0.730295
\(201\) 1.88894e42 0.464612
\(202\) 3.06590e42 0.687951
\(203\) −5.55049e42 −1.13672
\(204\) 2.35153e42 0.439737
\(205\) 4.11006e41 0.0702104
\(206\) 4.60126e41 0.0718345
\(207\) 1.04648e42 0.149375
\(208\) 6.23627e41 0.0814242
\(209\) −1.67706e42 −0.200375
\(210\) 1.13339e41 0.0123971
\(211\) 6.01151e42 0.602224 0.301112 0.953589i \(-0.402642\pi\)
0.301112 + 0.953589i \(0.402642\pi\)
\(212\) 6.10291e42 0.560175
\(213\) 7.64078e42 0.642858
\(214\) 6.33426e42 0.488699
\(215\) 2.36333e42 0.167268
\(216\) −2.18112e42 −0.141672
\(217\) −8.92274e42 −0.532100
\(218\) 9.13795e42 0.500500
\(219\) −1.05560e43 −0.531230
\(220\) −3.20981e41 −0.0148477
\(221\) 3.18288e42 0.135383
\(222\) 3.67022e42 0.143603
\(223\) −2.40052e42 −0.0864302 −0.0432151 0.999066i \(-0.513760\pi\)
−0.0432151 + 0.999066i \(0.513760\pi\)
\(224\) −1.73269e43 −0.574293
\(225\) −1.08340e43 −0.330682
\(226\) −1.65252e43 −0.464667
\(227\) −2.28689e42 −0.0592607 −0.0296304 0.999561i \(-0.509433\pi\)
−0.0296304 + 0.999561i \(0.509433\pi\)
\(228\) −2.05204e43 −0.490221
\(229\) 3.17158e43 0.698746 0.349373 0.936984i \(-0.386395\pi\)
0.349373 + 0.936984i \(0.386395\pi\)
\(230\) −7.86729e41 −0.0159904
\(231\) −3.67123e42 −0.0688636
\(232\) −8.03021e43 −1.39059
\(233\) 6.37790e43 1.01998 0.509992 0.860179i \(-0.329648\pi\)
0.509992 + 0.860179i \(0.329648\pi\)
\(234\) −1.34768e42 −0.0199110
\(235\) −8.04749e42 −0.109877
\(236\) −1.15459e43 −0.145732
\(237\) −3.94181e43 −0.460099
\(238\) −2.02198e43 −0.218325
\(239\) 1.80775e44 1.80625 0.903124 0.429380i \(-0.141268\pi\)
0.903124 + 0.429380i \(0.141268\pi\)
\(240\) −3.03631e42 −0.0280826
\(241\) 7.69104e43 0.658673 0.329336 0.944213i \(-0.393175\pi\)
0.329336 + 0.944213i \(0.393175\pi\)
\(242\) 4.84557e43 0.384380
\(243\) −8.72796e42 −0.0641500
\(244\) 1.19905e43 0.0816815
\(245\) −9.00760e42 −0.0568901
\(246\) 3.10467e43 0.181851
\(247\) −2.77751e43 −0.150925
\(248\) −1.29090e44 −0.650935
\(249\) 1.87032e44 0.875442
\(250\) 1.63549e43 0.0710819
\(251\) −2.76498e44 −1.11616 −0.558082 0.829786i \(-0.688462\pi\)
−0.558082 + 0.829786i \(0.688462\pi\)
\(252\) −4.49210e43 −0.168476
\(253\) 2.54835e43 0.0888238
\(254\) 1.50951e44 0.489117
\(255\) −1.54967e43 −0.0466925
\(256\) −8.72293e43 −0.244469
\(257\) −6.65338e44 −1.73492 −0.867461 0.497506i \(-0.834249\pi\)
−0.867461 + 0.497506i \(0.834249\pi\)
\(258\) 1.78522e44 0.433239
\(259\) 1.65586e44 0.374091
\(260\) −5.31600e42 −0.0111835
\(261\) −3.21337e44 −0.629668
\(262\) 1.79121e43 0.0327018
\(263\) −4.99229e44 −0.849413 −0.424706 0.905331i \(-0.639623\pi\)
−0.424706 + 0.905331i \(0.639623\pi\)
\(264\) −5.31138e43 −0.0842431
\(265\) −4.02186e43 −0.0594809
\(266\) 1.76447e44 0.243390
\(267\) 7.82281e44 1.00671
\(268\) 5.62838e44 0.675911
\(269\) 3.89715e44 0.436847 0.218424 0.975854i \(-0.429909\pi\)
0.218424 + 0.975854i \(0.429909\pi\)
\(270\) 6.56156e42 0.00686717
\(271\) 1.32142e45 1.29154 0.645772 0.763531i \(-0.276536\pi\)
0.645772 + 0.763531i \(0.276536\pi\)
\(272\) 5.41683e44 0.494562
\(273\) −6.08020e43 −0.0518691
\(274\) 9.27329e43 0.0739347
\(275\) −2.63825e44 −0.196635
\(276\) 3.11814e44 0.217309
\(277\) −1.66934e45 −1.08810 −0.544052 0.839052i \(-0.683111\pi\)
−0.544052 + 0.839052i \(0.683111\pi\)
\(278\) −4.54708e44 −0.277271
\(279\) −5.16568e44 −0.294747
\(280\) 7.39783e43 0.0395076
\(281\) −4.64389e44 −0.232175 −0.116087 0.993239i \(-0.537035\pi\)
−0.116087 + 0.993239i \(0.537035\pi\)
\(282\) −6.07894e44 −0.284590
\(283\) −2.92223e45 −1.28134 −0.640672 0.767815i \(-0.721344\pi\)
−0.640672 + 0.767815i \(0.721344\pi\)
\(284\) 2.27669e45 0.935221
\(285\) 1.35231e44 0.0520530
\(286\) −3.28182e43 −0.0118398
\(287\) 1.40070e45 0.473730
\(288\) −1.00312e45 −0.318120
\(289\) −5.97445e44 −0.177700
\(290\) 2.41577e44 0.0674050
\(291\) −2.11938e45 −0.554866
\(292\) −3.14532e45 −0.772826
\(293\) 2.43231e45 0.561007 0.280503 0.959853i \(-0.409499\pi\)
0.280503 + 0.959853i \(0.409499\pi\)
\(294\) −6.80419e44 −0.147350
\(295\) 7.60881e43 0.0154742
\(296\) 2.39562e45 0.457638
\(297\) −2.12540e44 −0.0381458
\(298\) 3.32448e45 0.560690
\(299\) 4.22051e44 0.0669034
\(300\) −3.22814e45 −0.481071
\(301\) 8.05421e45 1.12861
\(302\) −7.43881e43 −0.00980336
\(303\) 8.00790e45 0.992727
\(304\) −4.72695e45 −0.551340
\(305\) −7.90178e43 −0.00867317
\(306\) −1.17060e45 −0.120938
\(307\) 6.20341e45 0.603351 0.301676 0.953411i \(-0.402454\pi\)
0.301676 + 0.953411i \(0.402454\pi\)
\(308\) −1.09390e45 −0.100182
\(309\) 1.20181e45 0.103659
\(310\) 3.88349e44 0.0315523
\(311\) −7.06086e45 −0.540493 −0.270247 0.962791i \(-0.587105\pi\)
−0.270247 + 0.962791i \(0.587105\pi\)
\(312\) −8.79657e44 −0.0634532
\(313\) 2.19336e45 0.149121 0.0745607 0.997216i \(-0.476245\pi\)
0.0745607 + 0.997216i \(0.476245\pi\)
\(314\) −5.83088e45 −0.373711
\(315\) 2.96032e44 0.0178893
\(316\) −1.17452e46 −0.669345
\(317\) −8.77401e45 −0.471631 −0.235815 0.971798i \(-0.575776\pi\)
−0.235815 + 0.971798i \(0.575776\pi\)
\(318\) −3.03804e45 −0.154061
\(319\) −7.82509e45 −0.374422
\(320\) −3.23012e44 −0.0145862
\(321\) 1.65446e46 0.705202
\(322\) −2.68116e45 −0.107892
\(323\) −2.41255e46 −0.916704
\(324\) −2.60063e45 −0.0933246
\(325\) −4.36940e45 −0.148108
\(326\) −1.26026e46 −0.403584
\(327\) 2.38676e46 0.722231
\(328\) 2.02648e46 0.579529
\(329\) −2.74258e46 −0.741369
\(330\) 1.59785e44 0.00408346
\(331\) 5.90046e46 1.42583 0.712915 0.701250i \(-0.247374\pi\)
0.712915 + 0.701250i \(0.247374\pi\)
\(332\) 5.57290e46 1.27358
\(333\) 9.58634e45 0.207221
\(334\) −2.95679e46 −0.604660
\(335\) −3.70913e45 −0.0717701
\(336\) −1.03477e46 −0.189482
\(337\) 5.49552e46 0.952480 0.476240 0.879315i \(-0.341999\pi\)
0.476240 + 0.879315i \(0.341999\pi\)
\(338\) 2.38417e46 0.391181
\(339\) −4.31627e46 −0.670524
\(340\) −4.61749e45 −0.0679276
\(341\) −1.25793e46 −0.175267
\(342\) 1.02151e46 0.134822
\(343\) −7.88219e46 −0.985612
\(344\) 1.16525e47 1.38066
\(345\) −2.05488e45 −0.0230745
\(346\) −2.40349e46 −0.255820
\(347\) −2.08191e46 −0.210071 −0.105036 0.994468i \(-0.533496\pi\)
−0.105036 + 0.994468i \(0.533496\pi\)
\(348\) −9.57473e46 −0.916032
\(349\) −7.81482e46 −0.709003 −0.354502 0.935055i \(-0.615349\pi\)
−0.354502 + 0.935055i \(0.615349\pi\)
\(350\) 2.77575e46 0.238848
\(351\) −3.52004e45 −0.0287320
\(352\) −2.44276e46 −0.189165
\(353\) −2.52475e47 −1.85518 −0.927591 0.373597i \(-0.878124\pi\)
−0.927591 + 0.373597i \(0.878124\pi\)
\(354\) 5.74757e45 0.0400796
\(355\) −1.50035e46 −0.0993044
\(356\) 2.33093e47 1.46455
\(357\) −5.28127e46 −0.315048
\(358\) −3.12056e46 −0.176765
\(359\) 1.56169e47 0.840133 0.420066 0.907493i \(-0.362007\pi\)
0.420066 + 0.907493i \(0.362007\pi\)
\(360\) 4.28286e45 0.0218845
\(361\) 4.52102e45 0.0219459
\(362\) 6.92089e46 0.319193
\(363\) 1.26563e47 0.554667
\(364\) −1.81169e46 −0.0754584
\(365\) 2.07278e46 0.0820608
\(366\) −5.96887e45 −0.0224642
\(367\) 1.80276e47 0.645083 0.322542 0.946555i \(-0.395463\pi\)
0.322542 + 0.946555i \(0.395463\pi\)
\(368\) 7.18275e46 0.244403
\(369\) 8.10915e46 0.262414
\(370\) −7.20688e45 −0.0221827
\(371\) −1.37064e47 −0.401335
\(372\) −1.53919e47 −0.428794
\(373\) 5.89590e46 0.156292 0.0781460 0.996942i \(-0.475100\pi\)
0.0781460 + 0.996942i \(0.475100\pi\)
\(374\) −2.85060e46 −0.0719136
\(375\) 4.27179e46 0.102573
\(376\) −3.96784e47 −0.906941
\(377\) −1.29597e47 −0.282020
\(378\) 2.23617e46 0.0463348
\(379\) 9.01391e47 1.77864 0.889319 0.457287i \(-0.151179\pi\)
0.889319 + 0.457287i \(0.151179\pi\)
\(380\) 4.02941e46 0.0757260
\(381\) 3.94273e47 0.705805
\(382\) −1.38088e47 −0.235497
\(383\) −7.44373e47 −1.20952 −0.604761 0.796407i \(-0.706731\pi\)
−0.604761 + 0.796407i \(0.706731\pi\)
\(384\) −3.80260e47 −0.588779
\(385\) 7.20886e45 0.0106376
\(386\) −2.58470e47 −0.363534
\(387\) 4.66286e47 0.625172
\(388\) −6.31501e47 −0.807211
\(389\) −1.42792e48 −1.74035 −0.870173 0.492746i \(-0.835993\pi\)
−0.870173 + 0.492746i \(0.835993\pi\)
\(390\) 2.64632e45 0.00307572
\(391\) 3.66594e47 0.406364
\(392\) −4.44122e47 −0.469581
\(393\) 4.67849e46 0.0471893
\(394\) 6.12495e47 0.589417
\(395\) 7.74017e46 0.0710729
\(396\) −6.33296e46 −0.0554940
\(397\) 7.57199e47 0.633265 0.316633 0.948548i \(-0.397448\pi\)
0.316633 + 0.948548i \(0.397448\pi\)
\(398\) 8.18484e47 0.653391
\(399\) 4.60865e47 0.351217
\(400\) −7.43614e47 −0.541050
\(401\) 1.48151e48 1.02928 0.514639 0.857407i \(-0.327926\pi\)
0.514639 + 0.857407i \(0.327926\pi\)
\(402\) −2.80182e47 −0.185891
\(403\) −2.08335e47 −0.132014
\(404\) 2.38608e48 1.44421
\(405\) 1.71383e46 0.00990946
\(406\) 8.23291e47 0.454801
\(407\) 2.33443e47 0.123221
\(408\) −7.64071e47 −0.385408
\(409\) −2.49474e48 −1.20266 −0.601331 0.799000i \(-0.705363\pi\)
−0.601331 + 0.799000i \(0.705363\pi\)
\(410\) −6.09635e46 −0.0280911
\(411\) 2.42211e47 0.106689
\(412\) 3.58099e47 0.150801
\(413\) 2.59307e47 0.104409
\(414\) −1.55222e47 −0.0597649
\(415\) −3.67257e47 −0.135232
\(416\) −4.04563e47 −0.142482
\(417\) −1.18766e48 −0.400107
\(418\) 2.48755e47 0.0801696
\(419\) 3.28563e47 0.101312 0.0506558 0.998716i \(-0.483869\pi\)
0.0506558 + 0.998716i \(0.483869\pi\)
\(420\) 8.82072e46 0.0260251
\(421\) −2.15044e48 −0.607169 −0.303584 0.952805i \(-0.598183\pi\)
−0.303584 + 0.952805i \(0.598183\pi\)
\(422\) −8.91674e47 −0.240949
\(423\) −1.58777e48 −0.410669
\(424\) −1.98299e48 −0.490966
\(425\) −3.79527e48 −0.899595
\(426\) −1.13334e48 −0.257207
\(427\) −2.69292e47 −0.0585204
\(428\) 4.92972e48 1.02592
\(429\) −8.57187e46 −0.0170850
\(430\) −3.50548e47 −0.0669238
\(431\) 5.34912e48 0.978257 0.489129 0.872212i \(-0.337315\pi\)
0.489129 + 0.872212i \(0.337315\pi\)
\(432\) −5.99064e47 −0.104960
\(433\) −5.42893e47 −0.0911357 −0.0455678 0.998961i \(-0.514510\pi\)
−0.0455678 + 0.998961i \(0.514510\pi\)
\(434\) 1.32349e48 0.212892
\(435\) 6.30980e47 0.0972668
\(436\) 7.11173e48 1.05069
\(437\) −3.19905e48 −0.453017
\(438\) 1.56575e48 0.212545
\(439\) 7.01666e48 0.913138 0.456569 0.889688i \(-0.349078\pi\)
0.456569 + 0.889688i \(0.349078\pi\)
\(440\) 1.04295e47 0.0130133
\(441\) −1.77720e48 −0.212629
\(442\) −4.72109e47 −0.0541664
\(443\) −1.97926e48 −0.217788 −0.108894 0.994053i \(-0.534731\pi\)
−0.108894 + 0.994053i \(0.534731\pi\)
\(444\) 2.85640e48 0.301463
\(445\) −1.53609e48 −0.155510
\(446\) 3.56064e47 0.0345806
\(447\) 8.68328e48 0.809086
\(448\) −1.10082e48 −0.0984176
\(449\) −9.61546e48 −0.824922 −0.412461 0.910975i \(-0.635331\pi\)
−0.412461 + 0.910975i \(0.635331\pi\)
\(450\) 1.60698e48 0.132305
\(451\) 1.97471e48 0.156041
\(452\) −1.28610e49 −0.975468
\(453\) −1.94296e47 −0.0141464
\(454\) 3.39209e47 0.0237101
\(455\) 1.19391e47 0.00801238
\(456\) 6.66760e48 0.429655
\(457\) −1.22984e49 −0.761027 −0.380513 0.924775i \(-0.624253\pi\)
−0.380513 + 0.924775i \(0.624253\pi\)
\(458\) −4.70433e48 −0.279568
\(459\) −3.05751e48 −0.174515
\(460\) −6.12281e47 −0.0335684
\(461\) −1.44289e49 −0.759915 −0.379958 0.925004i \(-0.624061\pi\)
−0.379958 + 0.925004i \(0.624061\pi\)
\(462\) 5.44545e47 0.0275523
\(463\) 1.91092e49 0.928952 0.464476 0.885586i \(-0.346243\pi\)
0.464476 + 0.885586i \(0.346243\pi\)
\(464\) −2.20557e49 −1.03024
\(465\) 1.01434e48 0.0455306
\(466\) −9.46019e48 −0.408094
\(467\) 3.89111e49 1.61328 0.806642 0.591041i \(-0.201283\pi\)
0.806642 + 0.591041i \(0.201283\pi\)
\(468\) −1.04885e48 −0.0417989
\(469\) −1.26407e49 −0.484254
\(470\) 1.19367e48 0.0439615
\(471\) −1.52298e49 −0.539272
\(472\) 3.75155e48 0.127727
\(473\) 1.13548e49 0.371749
\(474\) 5.84679e48 0.184085
\(475\) 3.31190e49 1.00287
\(476\) −1.57363e49 −0.458327
\(477\) −7.93513e48 −0.222313
\(478\) −2.68139e49 −0.722677
\(479\) 7.12496e49 1.84746 0.923730 0.383043i \(-0.125124\pi\)
0.923730 + 0.383043i \(0.125124\pi\)
\(480\) 1.96973e48 0.0491410
\(481\) 3.86622e48 0.0928118
\(482\) −1.14079e49 −0.263534
\(483\) −7.00299e48 −0.155690
\(484\) 3.77112e49 0.806922
\(485\) 4.16163e48 0.0857119
\(486\) 1.29460e48 0.0256663
\(487\) 2.21439e49 0.422637 0.211318 0.977417i \(-0.432224\pi\)
0.211318 + 0.977417i \(0.432224\pi\)
\(488\) −3.89599e48 −0.0715899
\(489\) −3.29170e49 −0.582380
\(490\) 1.33608e48 0.0227616
\(491\) 4.50299e49 0.738743 0.369372 0.929282i \(-0.379573\pi\)
0.369372 + 0.929282i \(0.379573\pi\)
\(492\) 2.41625e49 0.381757
\(493\) −1.12568e50 −1.71296
\(494\) 4.11981e48 0.0603849
\(495\) 4.17346e47 0.00589251
\(496\) −3.54559e49 −0.482255
\(497\) −5.11318e49 −0.670035
\(498\) −2.77420e49 −0.350263
\(499\) −1.42699e50 −1.73605 −0.868023 0.496525i \(-0.834609\pi\)
−0.868023 + 0.496525i \(0.834609\pi\)
\(500\) 1.27284e49 0.149221
\(501\) −7.72292e49 −0.872537
\(502\) 4.10123e49 0.446576
\(503\) 6.05148e49 0.635117 0.317559 0.948239i \(-0.397137\pi\)
0.317559 + 0.948239i \(0.397137\pi\)
\(504\) 1.45959e49 0.147661
\(505\) −1.57244e49 −0.153350
\(506\) −3.77991e48 −0.0355383
\(507\) 6.22726e49 0.564482
\(508\) 1.17480e50 1.02680
\(509\) 6.02162e49 0.507498 0.253749 0.967270i \(-0.418336\pi\)
0.253749 + 0.967270i \(0.418336\pi\)
\(510\) 2.29859e48 0.0186816
\(511\) 7.06402e49 0.553688
\(512\) −1.21960e50 −0.921984
\(513\) 2.66811e49 0.194550
\(514\) 9.86881e49 0.694140
\(515\) −2.35989e48 −0.0160125
\(516\) 1.38937e50 0.909492
\(517\) −3.86649e49 −0.244198
\(518\) −2.45609e49 −0.149673
\(519\) −6.27774e49 −0.369154
\(520\) 1.72730e48 0.00980181
\(521\) −1.55956e50 −0.854088 −0.427044 0.904231i \(-0.640445\pi\)
−0.427044 + 0.904231i \(0.640445\pi\)
\(522\) 4.76632e49 0.251929
\(523\) 2.43674e50 1.24316 0.621581 0.783350i \(-0.286491\pi\)
0.621581 + 0.783350i \(0.286491\pi\)
\(524\) 1.39403e49 0.0686504
\(525\) 7.25003e49 0.344662
\(526\) 7.40495e49 0.339849
\(527\) −1.80960e50 −0.801838
\(528\) −1.45882e49 −0.0624128
\(529\) −1.93453e50 −0.799183
\(530\) 5.96552e48 0.0237982
\(531\) 1.50122e49 0.0578357
\(532\) 1.37322e50 0.510945
\(533\) 3.27047e49 0.117532
\(534\) −1.16034e50 −0.402783
\(535\) −3.24871e49 −0.108935
\(536\) −1.82880e50 −0.592403
\(537\) −8.15067e49 −0.255076
\(538\) −5.78055e49 −0.174782
\(539\) −4.32778e49 −0.126437
\(540\) 5.10662e48 0.0144161
\(541\) −2.16130e50 −0.589610 −0.294805 0.955557i \(-0.595255\pi\)
−0.294805 + 0.955557i \(0.595255\pi\)
\(542\) −1.96003e50 −0.516745
\(543\) 1.80768e50 0.460602
\(544\) −3.51404e50 −0.865420
\(545\) −4.68667e49 −0.111565
\(546\) 9.01861e48 0.0207528
\(547\) 1.51748e50 0.337565 0.168782 0.985653i \(-0.446016\pi\)
0.168782 + 0.985653i \(0.446016\pi\)
\(548\) 7.21706e49 0.155210
\(549\) −1.55902e49 −0.0324163
\(550\) 3.91325e49 0.0786734
\(551\) 9.82316e50 1.90962
\(552\) −1.01316e50 −0.190461
\(553\) 2.63784e50 0.479550
\(554\) 2.47610e50 0.435349
\(555\) −1.88238e49 −0.0320101
\(556\) −3.53882e50 −0.582070
\(557\) −2.93619e50 −0.467157 −0.233578 0.972338i \(-0.575044\pi\)
−0.233578 + 0.972338i \(0.575044\pi\)
\(558\) 7.66214e49 0.117928
\(559\) 1.88056e50 0.280007
\(560\) 2.03188e49 0.0292698
\(561\) −7.44554e49 −0.103773
\(562\) 6.88818e49 0.0928929
\(563\) 6.27370e50 0.818688 0.409344 0.912380i \(-0.365758\pi\)
0.409344 + 0.912380i \(0.365758\pi\)
\(564\) −4.73101e50 −0.597435
\(565\) 8.47546e49 0.103578
\(566\) 4.33448e50 0.512664
\(567\) 5.84071e49 0.0668620
\(568\) −7.39753e50 −0.819676
\(569\) 8.59023e50 0.921357 0.460678 0.887567i \(-0.347606\pi\)
0.460678 + 0.887567i \(0.347606\pi\)
\(570\) −2.00585e49 −0.0208263
\(571\) 6.31374e50 0.634627 0.317314 0.948321i \(-0.397219\pi\)
0.317314 + 0.948321i \(0.397219\pi\)
\(572\) −2.55412e49 −0.0248551
\(573\) −3.60676e50 −0.339826
\(574\) −2.07763e50 −0.189539
\(575\) −5.03254e50 −0.444562
\(576\) −6.37303e49 −0.0545168
\(577\) −1.17734e51 −0.975321 −0.487661 0.873033i \(-0.662150\pi\)
−0.487661 + 0.873033i \(0.662150\pi\)
\(578\) 8.86176e49 0.0710976
\(579\) −6.75104e50 −0.524587
\(580\) 1.88010e50 0.141502
\(581\) −1.25161e51 −0.912451
\(582\) 3.14362e50 0.222001
\(583\) −1.93234e50 −0.132195
\(584\) 1.02199e51 0.677345
\(585\) 6.91198e48 0.00443832
\(586\) −3.60779e50 −0.224458
\(587\) −3.20215e51 −1.93035 −0.965176 0.261600i \(-0.915750\pi\)
−0.965176 + 0.261600i \(0.915750\pi\)
\(588\) −5.29544e50 −0.309330
\(589\) 1.57913e51 0.893892
\(590\) −1.12860e49 −0.00619123
\(591\) 1.59979e51 0.850540
\(592\) 6.57980e50 0.339048
\(593\) −1.84366e51 −0.920807 −0.460404 0.887710i \(-0.652295\pi\)
−0.460404 + 0.887710i \(0.652295\pi\)
\(594\) 3.15256e49 0.0152621
\(595\) 1.03703e50 0.0486664
\(596\) 2.58732e51 1.17705
\(597\) 2.13782e51 0.942856
\(598\) −6.26018e49 −0.0267679
\(599\) 5.10057e49 0.0211457 0.0105729 0.999944i \(-0.496634\pi\)
0.0105729 + 0.999944i \(0.496634\pi\)
\(600\) 1.04890e51 0.421636
\(601\) 2.47295e51 0.963911 0.481956 0.876196i \(-0.339927\pi\)
0.481956 + 0.876196i \(0.339927\pi\)
\(602\) −1.19466e51 −0.451554
\(603\) −7.31813e50 −0.268244
\(604\) −5.78935e49 −0.0205800
\(605\) −2.48519e50 −0.0856812
\(606\) −1.18779e51 −0.397189
\(607\) 8.24908e50 0.267556 0.133778 0.991011i \(-0.457289\pi\)
0.133778 + 0.991011i \(0.457289\pi\)
\(608\) 3.06649e51 0.964775
\(609\) 2.15037e51 0.656287
\(610\) 1.17205e49 0.00347012
\(611\) −6.40358e50 −0.183933
\(612\) −9.11032e50 −0.253882
\(613\) −7.67396e50 −0.207492 −0.103746 0.994604i \(-0.533083\pi\)
−0.103746 + 0.994604i \(0.533083\pi\)
\(614\) −9.20137e50 −0.241400
\(615\) −1.59232e50 −0.0405360
\(616\) 3.55435e50 0.0878045
\(617\) −3.86196e51 −0.925832 −0.462916 0.886402i \(-0.653197\pi\)
−0.462916 + 0.886402i \(0.653197\pi\)
\(618\) −1.78262e50 −0.0414737
\(619\) −7.97286e51 −1.80027 −0.900134 0.435613i \(-0.856532\pi\)
−0.900134 + 0.435613i \(0.856532\pi\)
\(620\) 3.02238e50 0.0662372
\(621\) −4.05427e50 −0.0862419
\(622\) 1.04732e51 0.216251
\(623\) −5.23499e51 −1.04927
\(624\) −2.41606e50 −0.0470103
\(625\) 5.16797e51 0.976201
\(626\) −3.25336e50 −0.0596633
\(627\) 6.49728e50 0.115686
\(628\) −4.53796e51 −0.784525
\(629\) 3.35821e51 0.563729
\(630\) −4.39097e49 −0.00715748
\(631\) 3.70656e51 0.586717 0.293358 0.956003i \(-0.405227\pi\)
0.293358 + 0.956003i \(0.405227\pi\)
\(632\) 3.81631e51 0.586649
\(633\) −2.32898e51 −0.347694
\(634\) 1.30143e51 0.188699
\(635\) −7.74198e50 −0.109028
\(636\) −2.36439e51 −0.323417
\(637\) −7.16756e50 −0.0952339
\(638\) 1.16068e51 0.149806
\(639\) −2.96020e51 −0.371154
\(640\) 7.46681e50 0.0909506
\(641\) 1.56704e52 1.85442 0.927210 0.374543i \(-0.122200\pi\)
0.927210 + 0.374543i \(0.122200\pi\)
\(642\) −2.45402e51 −0.282150
\(643\) −6.64937e51 −0.742809 −0.371405 0.928471i \(-0.621124\pi\)
−0.371405 + 0.928471i \(0.621124\pi\)
\(644\) −2.08665e51 −0.226496
\(645\) −9.15604e50 −0.0965723
\(646\) 3.57847e51 0.366772
\(647\) 5.30594e51 0.528485 0.264243 0.964456i \(-0.414878\pi\)
0.264243 + 0.964456i \(0.414878\pi\)
\(648\) 8.45009e50 0.0817945
\(649\) 3.65572e50 0.0343911
\(650\) 6.48102e50 0.0592579
\(651\) 3.45685e51 0.307208
\(652\) −9.80812e51 −0.847238
\(653\) 1.78263e52 1.49682 0.748408 0.663238i \(-0.230818\pi\)
0.748408 + 0.663238i \(0.230818\pi\)
\(654\) −3.54023e51 −0.288964
\(655\) −9.18673e49 −0.00728949
\(656\) 5.56591e51 0.429353
\(657\) 4.08961e51 0.306706
\(658\) 4.06800e51 0.296621
\(659\) −1.76349e52 −1.25024 −0.625120 0.780529i \(-0.714950\pi\)
−0.625120 + 0.780529i \(0.714950\pi\)
\(660\) 1.24355e50 0.00857233
\(661\) 1.76495e52 1.18306 0.591529 0.806284i \(-0.298524\pi\)
0.591529 + 0.806284i \(0.298524\pi\)
\(662\) −8.75201e51 −0.570473
\(663\) −1.23311e51 −0.0781631
\(664\) −1.81077e52 −1.11623
\(665\) −9.04958e50 −0.0542535
\(666\) −1.42192e51 −0.0829090
\(667\) −1.49266e52 −0.846512
\(668\) −2.30116e52 −1.26935
\(669\) 9.30011e50 0.0499005
\(670\) 5.50167e50 0.0287151
\(671\) −3.79648e50 −0.0192759
\(672\) 6.71281e51 0.331568
\(673\) −6.55193e51 −0.314841 −0.157420 0.987532i \(-0.550318\pi\)
−0.157420 + 0.987532i \(0.550318\pi\)
\(674\) −8.15138e51 −0.381086
\(675\) 4.19730e51 0.190919
\(676\) 1.85551e52 0.821200
\(677\) −1.81635e52 −0.782183 −0.391091 0.920352i \(-0.627902\pi\)
−0.391091 + 0.920352i \(0.627902\pi\)
\(678\) 6.40222e51 0.268276
\(679\) 1.41828e52 0.578323
\(680\) 1.50034e51 0.0595352
\(681\) 8.85988e50 0.0342142
\(682\) 1.86586e51 0.0701241
\(683\) 1.58198e51 0.0578653 0.0289327 0.999581i \(-0.490789\pi\)
0.0289327 + 0.999581i \(0.490789\pi\)
\(684\) 7.95003e51 0.283029
\(685\) −4.75608e50 −0.0164806
\(686\) 1.16915e52 0.394342
\(687\) −1.22874e52 −0.403421
\(688\) 3.20046e52 1.02288
\(689\) −3.20028e51 −0.0995710
\(690\) 3.04795e50 0.00923208
\(691\) −3.06206e51 −0.0902963 −0.0451482 0.998980i \(-0.514376\pi\)
−0.0451482 + 0.998980i \(0.514376\pi\)
\(692\) −1.87055e52 −0.537040
\(693\) 1.42231e51 0.0397584
\(694\) 3.08805e51 0.0840493
\(695\) 2.33210e51 0.0618058
\(696\) 3.11107e52 0.802858
\(697\) 2.84073e52 0.713878
\(698\) 1.15915e52 0.283671
\(699\) −2.47093e52 −0.588888
\(700\) 2.16026e52 0.501409
\(701\) 3.61387e52 0.816939 0.408469 0.912772i \(-0.366063\pi\)
0.408469 + 0.912772i \(0.366063\pi\)
\(702\) 5.22119e50 0.0114956
\(703\) −2.93051e52 −0.628448
\(704\) −1.55194e51 −0.0324175
\(705\) 3.11776e51 0.0634373
\(706\) 3.74490e52 0.742256
\(707\) −5.35885e52 −1.03469
\(708\) 4.47312e51 0.0841385
\(709\) −7.65821e52 −1.40337 −0.701684 0.712488i \(-0.747568\pi\)
−0.701684 + 0.712488i \(0.747568\pi\)
\(710\) 2.22544e51 0.0397316
\(711\) 1.52714e52 0.265638
\(712\) −7.57376e52 −1.28361
\(713\) −2.39954e52 −0.396252
\(714\) 7.83358e51 0.126050
\(715\) 1.68318e50 0.00263918
\(716\) −2.42862e52 −0.371081
\(717\) −7.00360e52 −1.04284
\(718\) −2.31642e52 −0.336136
\(719\) 5.00380e52 0.707644 0.353822 0.935313i \(-0.384882\pi\)
0.353822 + 0.935313i \(0.384882\pi\)
\(720\) 1.17633e51 0.0162135
\(721\) −8.04248e51 −0.108041
\(722\) −6.70593e50 −0.00878053
\(723\) −2.97967e52 −0.380285
\(724\) 5.38627e52 0.670077
\(725\) 1.54532e53 1.87398
\(726\) −1.87727e52 −0.221922
\(727\) −1.52054e53 −1.75231 −0.876153 0.482033i \(-0.839898\pi\)
−0.876153 + 0.482033i \(0.839898\pi\)
\(728\) 5.88662e51 0.0661357
\(729\) 3.38139e51 0.0370370
\(730\) −3.07451e51 −0.0328324
\(731\) 1.63346e53 1.70073
\(732\) −4.64535e51 −0.0471588
\(733\) 1.66772e53 1.65082 0.825412 0.564531i \(-0.190943\pi\)
0.825412 + 0.564531i \(0.190943\pi\)
\(734\) −2.67399e52 −0.258097
\(735\) 3.48973e51 0.0328455
\(736\) −4.65963e52 −0.427673
\(737\) −1.78209e52 −0.159507
\(738\) −1.20281e52 −0.104992
\(739\) 4.00559e52 0.340992 0.170496 0.985358i \(-0.445463\pi\)
0.170496 + 0.985358i \(0.445463\pi\)
\(740\) −5.60884e51 −0.0465679
\(741\) 1.07606e52 0.0871366
\(742\) 2.03304e52 0.160574
\(743\) −1.70678e52 −0.131488 −0.0657439 0.997837i \(-0.520942\pi\)
−0.0657439 + 0.997837i \(0.520942\pi\)
\(744\) 5.00122e52 0.375818
\(745\) −1.70506e52 −0.124982
\(746\) −8.74525e51 −0.0625322
\(747\) −7.24599e52 −0.505437
\(748\) −2.21851e52 −0.150967
\(749\) −1.10716e53 −0.735015
\(750\) −6.33624e51 −0.0410392
\(751\) 3.01808e53 1.90718 0.953592 0.301102i \(-0.0973546\pi\)
0.953592 + 0.301102i \(0.0973546\pi\)
\(752\) −1.08980e53 −0.671921
\(753\) 1.07121e53 0.644417
\(754\) 1.92228e52 0.112836
\(755\) 3.81521e50 0.00218525
\(756\) 1.74033e52 0.0972699
\(757\) −2.38775e53 −1.30231 −0.651157 0.758943i \(-0.725716\pi\)
−0.651157 + 0.758943i \(0.725716\pi\)
\(758\) −1.33701e53 −0.711631
\(759\) −9.87282e51 −0.0512824
\(760\) −1.30925e52 −0.0663701
\(761\) 5.79897e52 0.286903 0.143451 0.989657i \(-0.454180\pi\)
0.143451 + 0.989657i \(0.454180\pi\)
\(762\) −5.84816e52 −0.282392
\(763\) −1.59721e53 −0.752763
\(764\) −1.07469e53 −0.494374
\(765\) 6.00375e51 0.0269579
\(766\) 1.10411e53 0.483928
\(767\) 6.05451e51 0.0259039
\(768\) 3.37944e52 0.141144
\(769\) −1.79999e52 −0.0733894 −0.0366947 0.999327i \(-0.511683\pi\)
−0.0366947 + 0.999327i \(0.511683\pi\)
\(770\) −1.06927e51 −0.00425608
\(771\) 2.57766e53 1.00166
\(772\) −2.01158e53 −0.763162
\(773\) −3.51229e53 −1.30098 −0.650488 0.759516i \(-0.725436\pi\)
−0.650488 + 0.759516i \(0.725436\pi\)
\(774\) −6.91631e52 −0.250131
\(775\) 2.48419e53 0.877209
\(776\) 2.05190e53 0.707481
\(777\) −6.41513e52 −0.215982
\(778\) 2.11800e53 0.696311
\(779\) −2.47894e53 −0.795835
\(780\) 2.05953e51 0.00645681
\(781\) −7.20857e52 −0.220701
\(782\) −5.43760e52 −0.162586
\(783\) 1.24493e53 0.363539
\(784\) −1.21982e53 −0.347896
\(785\) 2.99054e52 0.0833030
\(786\) −6.93950e51 −0.0188804
\(787\) 3.07133e53 0.816196 0.408098 0.912938i \(-0.366192\pi\)
0.408098 + 0.912938i \(0.366192\pi\)
\(788\) 4.76682e53 1.23735
\(789\) 1.93412e53 0.490409
\(790\) −1.14808e52 −0.0284362
\(791\) 2.88843e53 0.698870
\(792\) 2.05774e52 0.0486378
\(793\) −6.28763e51 −0.0145189
\(794\) −1.12314e53 −0.253369
\(795\) 1.55815e52 0.0343413
\(796\) 6.36996e53 1.37165
\(797\) −2.70059e53 −0.568171 −0.284086 0.958799i \(-0.591690\pi\)
−0.284086 + 0.958799i \(0.591690\pi\)
\(798\) −6.83590e52 −0.140521
\(799\) −5.56216e53 −1.11719
\(800\) 4.82401e53 0.946768
\(801\) −3.03072e53 −0.581224
\(802\) −2.19748e53 −0.411813
\(803\) 9.95887e52 0.182378
\(804\) −2.18055e53 −0.390237
\(805\) 1.37511e52 0.0240500
\(806\) 3.09018e52 0.0528185
\(807\) −1.50984e53 −0.252214
\(808\) −7.75295e53 −1.26578
\(809\) −9.43604e53 −1.50571 −0.752856 0.658185i \(-0.771325\pi\)
−0.752856 + 0.658185i \(0.771325\pi\)
\(810\) −2.54208e51 −0.00396476
\(811\) 5.48046e53 0.835471 0.417736 0.908569i \(-0.362824\pi\)
0.417736 + 0.908569i \(0.362824\pi\)
\(812\) 6.40737e53 0.954757
\(813\) −5.11945e53 −0.745673
\(814\) −3.46261e52 −0.0493005
\(815\) 6.46361e52 0.0899621
\(816\) −2.09859e53 −0.285536
\(817\) −1.42542e54 −1.89599
\(818\) 3.70038e53 0.481183
\(819\) 2.35559e52 0.0299466
\(820\) −4.74456e52 −0.0589712
\(821\) 8.20887e53 0.997551 0.498775 0.866731i \(-0.333783\pi\)
0.498775 + 0.866731i \(0.333783\pi\)
\(822\) −3.59266e52 −0.0426862
\(823\) 1.02438e54 1.19005 0.595026 0.803707i \(-0.297142\pi\)
0.595026 + 0.803707i \(0.297142\pi\)
\(824\) −1.16355e53 −0.132170
\(825\) 1.02211e53 0.113527
\(826\) −3.84624e52 −0.0417740
\(827\) 2.29267e53 0.243494 0.121747 0.992561i \(-0.461150\pi\)
0.121747 + 0.992561i \(0.461150\pi\)
\(828\) −1.20803e53 −0.125464
\(829\) −4.93570e53 −0.501291 −0.250646 0.968079i \(-0.580643\pi\)
−0.250646 + 0.968079i \(0.580643\pi\)
\(830\) 5.44744e52 0.0541063
\(831\) 6.46738e53 0.628217
\(832\) −2.57028e52 −0.0244174
\(833\) −6.22575e53 −0.578441
\(834\) 1.76163e53 0.160082
\(835\) 1.51648e53 0.134783
\(836\) 1.93596e53 0.168299
\(837\) 2.00129e53 0.170173
\(838\) −4.87350e52 −0.0405346
\(839\) −8.65291e52 −0.0703989 −0.0351995 0.999380i \(-0.511207\pi\)
−0.0351995 + 0.999380i \(0.511207\pi\)
\(840\) −2.86607e52 −0.0228097
\(841\) 3.29896e54 2.56833
\(842\) 3.18970e53 0.242927
\(843\) 1.79914e53 0.134046
\(844\) −6.93956e53 −0.505821
\(845\) −1.22279e53 −0.0871973
\(846\) 2.35511e53 0.164308
\(847\) −8.46951e53 −0.578116
\(848\) −5.44646e53 −0.363740
\(849\) 1.13213e54 0.739784
\(850\) 5.62943e53 0.359927
\(851\) 4.45300e53 0.278584
\(852\) −8.82036e53 −0.539950
\(853\) −1.86556e54 −1.11751 −0.558756 0.829332i \(-0.688721\pi\)
−0.558756 + 0.829332i \(0.688721\pi\)
\(854\) 3.99434e52 0.0234139
\(855\) −5.23912e52 −0.0300528
\(856\) −1.60179e54 −0.899167
\(857\) −2.68028e54 −1.47243 −0.736214 0.676748i \(-0.763388\pi\)
−0.736214 + 0.676748i \(0.763388\pi\)
\(858\) 1.27145e52 0.00683570
\(859\) 2.48268e54 1.30631 0.653156 0.757223i \(-0.273444\pi\)
0.653156 + 0.757223i \(0.273444\pi\)
\(860\) −2.72818e53 −0.140492
\(861\) −5.42661e53 −0.273508
\(862\) −7.93423e53 −0.391399
\(863\) −2.19895e54 −1.06173 −0.530866 0.847456i \(-0.678133\pi\)
−0.530866 + 0.847456i \(0.678133\pi\)
\(864\) 3.88628e53 0.183667
\(865\) 1.23270e53 0.0570244
\(866\) 8.05261e52 0.0364633
\(867\) 2.31462e53 0.102595
\(868\) 1.03002e54 0.446922
\(869\) 3.71883e53 0.157958
\(870\) −9.35918e52 −0.0389163
\(871\) −2.95144e53 −0.120143
\(872\) −2.31078e54 −0.920880
\(873\) 8.21090e53 0.320352
\(874\) 4.74507e53 0.181251
\(875\) −2.85866e53 −0.106909
\(876\) 1.21856e54 0.446192
\(877\) 4.36154e54 1.56368 0.781839 0.623480i \(-0.214282\pi\)
0.781839 + 0.623480i \(0.214282\pi\)
\(878\) −1.04076e54 −0.365346
\(879\) −9.42327e53 −0.323898
\(880\) 2.86455e52 0.00964111
\(881\) 3.09467e54 1.01991 0.509953 0.860202i \(-0.329663\pi\)
0.509953 + 0.860202i \(0.329663\pi\)
\(882\) 2.63608e53 0.0850727
\(883\) −2.65487e54 −0.839016 −0.419508 0.907752i \(-0.637797\pi\)
−0.419508 + 0.907752i \(0.637797\pi\)
\(884\) −3.67424e53 −0.113711
\(885\) −2.94781e52 −0.00893406
\(886\) 2.93579e53 0.0871368
\(887\) 4.89218e53 0.142205 0.0711026 0.997469i \(-0.477348\pi\)
0.0711026 + 0.997469i \(0.477348\pi\)
\(888\) −9.28114e53 −0.264217
\(889\) −2.63846e54 −0.735643
\(890\) 2.27845e53 0.0622192
\(891\) 8.23425e52 0.0220235
\(892\) 2.77111e53 0.0725946
\(893\) 4.85376e54 1.24545
\(894\) −1.28797e54 −0.323714
\(895\) 1.60047e53 0.0394024
\(896\) 2.54468e54 0.613670
\(897\) −1.63511e53 −0.0386267
\(898\) 1.42624e54 0.330050
\(899\) 7.36815e54 1.67034
\(900\) 1.25065e54 0.277747
\(901\) −2.77977e54 −0.604784
\(902\) −2.92904e53 −0.0624317
\(903\) −3.12037e54 −0.651602
\(904\) 4.17885e54 0.854951
\(905\) −3.54958e53 −0.0711506
\(906\) 2.88195e52 0.00565997
\(907\) −7.29269e54 −1.40331 −0.701654 0.712518i \(-0.747555\pi\)
−0.701654 + 0.712518i \(0.747555\pi\)
\(908\) 2.63994e53 0.0497743
\(909\) −3.10242e54 −0.573151
\(910\) −1.77090e52 −0.00320574
\(911\) −5.62240e54 −0.997313 −0.498656 0.866800i \(-0.666173\pi\)
−0.498656 + 0.866800i \(0.666173\pi\)
\(912\) 1.83132e54 0.318316
\(913\) −1.76452e54 −0.300550
\(914\) 1.82420e54 0.304486
\(915\) 3.06131e52 0.00500746
\(916\) −3.66121e54 −0.586892
\(917\) −3.13083e53 −0.0491843
\(918\) 4.53513e53 0.0698233
\(919\) −7.97807e54 −1.20382 −0.601909 0.798564i \(-0.705593\pi\)
−0.601909 + 0.798564i \(0.705593\pi\)
\(920\) 1.98945e53 0.0294211
\(921\) −2.40333e54 −0.348345
\(922\) 2.14020e54 0.304041
\(923\) −1.19386e54 −0.166235
\(924\) 4.23799e53 0.0578400
\(925\) −4.61009e54 −0.616719
\(926\) −2.83442e54 −0.371673
\(927\) −4.65607e53 −0.0598473
\(928\) 1.43081e55 1.80279
\(929\) 1.78826e54 0.220872 0.110436 0.993883i \(-0.464775\pi\)
0.110436 + 0.993883i \(0.464775\pi\)
\(930\) −1.50454e53 −0.0182167
\(931\) 5.43284e54 0.644849
\(932\) −7.36251e54 −0.856706
\(933\) 2.73552e54 0.312054
\(934\) −5.77159e54 −0.645473
\(935\) 1.46201e53 0.0160301
\(936\) 3.40797e53 0.0366347
\(937\) 1.44463e55 1.52256 0.761282 0.648421i \(-0.224571\pi\)
0.761282 + 0.648421i \(0.224571\pi\)
\(938\) 1.87496e54 0.193749
\(939\) −8.49753e53 −0.0860953
\(940\) 9.28985e53 0.0922876
\(941\) 7.66096e54 0.746234 0.373117 0.927784i \(-0.378289\pi\)
0.373117 + 0.927784i \(0.378289\pi\)
\(942\) 2.25900e54 0.215762
\(943\) 3.76683e54 0.352784
\(944\) 1.03040e54 0.0946287
\(945\) −1.14689e53 −0.0103284
\(946\) −1.68424e54 −0.148736
\(947\) −2.84883e54 −0.246713 −0.123357 0.992362i \(-0.539366\pi\)
−0.123357 + 0.992362i \(0.539366\pi\)
\(948\) 4.55034e54 0.386447
\(949\) 1.64936e54 0.137370
\(950\) −4.91247e54 −0.401248
\(951\) 3.39923e54 0.272296
\(952\) 5.11313e54 0.401701
\(953\) 7.19336e54 0.554259 0.277130 0.960833i \(-0.410617\pi\)
0.277130 + 0.960833i \(0.410617\pi\)
\(954\) 1.17700e54 0.0889470
\(955\) 7.08226e53 0.0524940
\(956\) −2.08683e55 −1.51711
\(957\) 3.03160e54 0.216173
\(958\) −1.05683e55 −0.739167
\(959\) −1.62087e54 −0.111200
\(960\) 1.25141e53 0.00842138
\(961\) −3.30422e54 −0.218116
\(962\) −5.73468e53 −0.0371339
\(963\) −6.40972e54 −0.407149
\(964\) −8.87837e54 −0.553233
\(965\) 1.32564e54 0.0810346
\(966\) 1.03874e54 0.0622915
\(967\) 5.29113e54 0.311285 0.155643 0.987813i \(-0.450255\pi\)
0.155643 + 0.987813i \(0.450255\pi\)
\(968\) −1.22533e55 −0.707228
\(969\) 9.34670e54 0.529259
\(970\) −6.17284e53 −0.0342932
\(971\) −2.88478e55 −1.57238 −0.786190 0.617985i \(-0.787949\pi\)
−0.786190 + 0.617985i \(0.787949\pi\)
\(972\) 1.00754e54 0.0538810
\(973\) 7.94778e54 0.417021
\(974\) −3.28455e54 −0.169096
\(975\) 1.69279e54 0.0855104
\(976\) −1.07007e54 −0.0530385
\(977\) 1.74695e55 0.849633 0.424816 0.905280i \(-0.360339\pi\)
0.424816 + 0.905280i \(0.360339\pi\)
\(978\) 4.88250e54 0.233009
\(979\) −7.38029e54 −0.345616
\(980\) 1.03982e54 0.0477832
\(981\) −9.24681e54 −0.416980
\(982\) −6.67918e54 −0.295570
\(983\) 6.87276e54 0.298464 0.149232 0.988802i \(-0.452320\pi\)
0.149232 + 0.988802i \(0.452320\pi\)
\(984\) −7.85098e54 −0.334591
\(985\) −3.14136e54 −0.131386
\(986\) 1.66970e55 0.685354
\(987\) 1.06253e55 0.428030
\(988\) 3.20629e54 0.126765
\(989\) 2.16597e55 0.840468
\(990\) −6.19039e52 −0.00235758
\(991\) −2.63811e55 −0.986121 −0.493061 0.869995i \(-0.664122\pi\)
−0.493061 + 0.869995i \(0.664122\pi\)
\(992\) 2.30011e55 0.843885
\(993\) −2.28596e55 −0.823204
\(994\) 7.58426e54 0.268080
\(995\) −4.19784e54 −0.145646
\(996\) −2.15905e55 −0.735302
\(997\) 4.19948e55 1.40390 0.701948 0.712229i \(-0.252314\pi\)
0.701948 + 0.712229i \(0.252314\pi\)
\(998\) 2.11662e55 0.694590
\(999\) −3.71394e54 −0.119639
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 \(a_p\))