Properties

Label 1.104.a.a.1.6
Level 1
Weight 104
Character 1.1
Self dual Yes
Analytic conductor 67.184
Analytic rank 0
Dimension 8
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 104 \)
Character orbit: \([\chi]\) = 1.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(67.1843880807\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: multiple of \( 2^{104}\cdot 3^{40}\cdot 5^{12}\cdot 7^{8}\cdot 11\cdot 13^{3}\cdot 17^{2} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-1.05899e14\)
Character \(\chi\) = 1.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+3.09018e15 q^{2}\) \(-9.30646e23 q^{3}\) \(-5.91967e29 q^{4}\) \(-7.61227e35 q^{5}\) \(-2.87587e39 q^{6}\) \(-3.39343e43 q^{7}\) \(-3.31675e46 q^{8}\) \(-1.30491e49 q^{9}\) \(+O(q^{10})\) \(q\)\(+3.09018e15 q^{2}\) \(-9.30646e23 q^{3}\) \(-5.91967e29 q^{4}\) \(-7.61227e35 q^{5}\) \(-2.87587e39 q^{6}\) \(-3.39343e43 q^{7}\) \(-3.31675e46 q^{8}\) \(-1.30491e49 q^{9}\) \(-2.35233e51 q^{10}\) \(-1.54885e53 q^{11}\) \(+5.50912e53 q^{12}\) \(-6.78771e56 q^{13}\) \(-1.04863e59 q^{14}\) \(+7.08433e59 q^{15}\) \(-9.64903e61 q^{16}\) \(+3.47857e63 q^{17}\) \(-4.03241e64 q^{18}\) \(-3.44755e64 q^{19}\) \(+4.50622e65 q^{20}\) \(+3.15808e67 q^{21}\) \(-4.78622e68 q^{22}\) \(-5.84642e69 q^{23}\) \(+3.08672e70 q^{24}\) \(-4.06609e71 q^{25}\) \(-2.09753e72 q^{26}\) \(+2.50942e73 q^{27}\) \(+2.00880e73 q^{28}\) \(+3.50391e73 q^{29}\) \(+2.18919e75 q^{30}\) \(+1.38875e76 q^{31}\) \(+3.81852e76 q^{32}\) \(+1.44143e77 q^{33}\) \(+1.07494e79 q^{34}\) \(+2.58317e79 q^{35}\) \(+7.72464e78 q^{36}\) \(+1.03572e81 q^{37}\) \(-1.06536e80 q^{38}\) \(+6.31696e80 q^{39}\) \(+2.52480e82 q^{40}\) \(-1.61257e83 q^{41}\) \(+9.75906e82 q^{42}\) \(-2.10970e84 q^{43}\) \(+9.16867e82 q^{44}\) \(+9.93333e84 q^{45}\) \(-1.80665e85 q^{46}\) \(+1.62802e86 q^{47}\) \(+8.97984e85 q^{48}\) \(+4.21120e85 q^{49}\) \(-1.25650e87 q^{50}\) \(-3.23732e87 q^{51}\) \(+4.01810e86 q^{52}\) \(-6.47734e88 q^{53}\) \(+7.75457e88 q^{54}\) \(+1.17902e89 q^{55}\) \(+1.12552e90 q^{56}\) \(+3.20845e88 q^{57}\) \(+1.08277e89 q^{58}\) \(-7.57677e90 q^{59}\) \(-4.19369e89 q^{60}\) \(-4.94411e91 q^{61}\) \(+4.29149e91 q^{62}\) \(+4.42812e92 q^{63}\) \(+1.09653e93 q^{64}\) \(+5.16699e92 q^{65}\) \(+4.45428e92 q^{66}\) \(+1.38891e94 q^{67}\) \(-2.05920e93 q^{68}\) \(+5.44094e93 q^{69}\) \(+7.98248e94 q^{70}\) \(+3.57169e95 q^{71}\) \(+4.32805e95 q^{72}\) \(+8.65911e95 q^{73}\) \(+3.20056e96 q^{74}\) \(+3.78409e95 q^{75}\) \(+2.04084e94 q^{76}\) \(+5.25590e96 q^{77}\) \(+1.95206e96 q^{78}\) \(-9.98014e96 q^{79}\) \(+7.34511e97 q^{80}\) \(+1.58227e98 q^{81}\) \(-4.98315e98 q^{82}\) \(-8.18903e98 q^{83}\) \(-1.86948e97 q^{84}\) \(-2.64798e99 q^{85}\) \(-6.51936e99 q^{86}\) \(-3.26090e97 q^{87}\) \(+5.13713e99 q^{88}\) \(-7.53893e99 q^{89}\) \(+3.06958e100 q^{90}\) \(+2.30336e100 q^{91}\) \(+3.46089e99 q^{92}\) \(-1.29243e100 q^{93}\) \(+5.03087e101 q^{94}\) \(+2.62437e100 q^{95}\) \(-3.55370e100 q^{96}\) \(+3.33364e102 q^{97}\) \(+1.30134e101 q^{98}\) \(+2.02110e102 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(8q \) \(\mathstrut +\mathstrut 4388929556680440q^{2} \) \(\mathstrut +\mathstrut \)\(50\!\cdots\!40\)\(q^{3} \) \(\mathstrut +\mathstrut \)\(48\!\cdots\!64\)\(q^{4} \) \(\mathstrut +\mathstrut \)\(55\!\cdots\!20\)\(q^{5} \) \(\mathstrut +\mathstrut \)\(26\!\cdots\!36\)\(q^{6} \) \(\mathstrut +\mathstrut \)\(41\!\cdots\!00\)\(q^{7} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!80\)\(q^{8} \) \(\mathstrut +\mathstrut \)\(35\!\cdots\!16\)\(q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut +\mathstrut 4388929556680440q^{2} \) \(\mathstrut +\mathstrut \)\(50\!\cdots\!40\)\(q^{3} \) \(\mathstrut +\mathstrut \)\(48\!\cdots\!64\)\(q^{4} \) \(\mathstrut +\mathstrut \)\(55\!\cdots\!20\)\(q^{5} \) \(\mathstrut +\mathstrut \)\(26\!\cdots\!36\)\(q^{6} \) \(\mathstrut +\mathstrut \)\(41\!\cdots\!00\)\(q^{7} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!80\)\(q^{8} \) \(\mathstrut +\mathstrut \)\(35\!\cdots\!16\)\(q^{9} \) \(\mathstrut +\mathstrut \)\(20\!\cdots\!20\)\(q^{10} \) \(\mathstrut -\mathstrut \)\(53\!\cdots\!44\)\(q^{11} \) \(\mathstrut +\mathstrut \)\(25\!\cdots\!80\)\(q^{12} \) \(\mathstrut -\mathstrut \)\(15\!\cdots\!20\)\(q^{13} \) \(\mathstrut +\mathstrut \)\(20\!\cdots\!08\)\(q^{14} \) \(\mathstrut -\mathstrut \)\(30\!\cdots\!60\)\(q^{15} \) \(\mathstrut +\mathstrut \)\(36\!\cdots\!88\)\(q^{16} \) \(\mathstrut +\mathstrut \)\(20\!\cdots\!20\)\(q^{17} \) \(\mathstrut +\mathstrut \)\(26\!\cdots\!40\)\(q^{18} \) \(\mathstrut +\mathstrut \)\(14\!\cdots\!00\)\(q^{19} \) \(\mathstrut +\mathstrut \)\(25\!\cdots\!60\)\(q^{20} \) \(\mathstrut -\mathstrut \)\(46\!\cdots\!04\)\(q^{21} \) \(\mathstrut -\mathstrut \)\(13\!\cdots\!20\)\(q^{22} \) \(\mathstrut +\mathstrut \)\(40\!\cdots\!20\)\(q^{23} \) \(\mathstrut +\mathstrut \)\(41\!\cdots\!00\)\(q^{24} \) \(\mathstrut -\mathstrut \)\(36\!\cdots\!00\)\(q^{25} \) \(\mathstrut -\mathstrut \)\(14\!\cdots\!84\)\(q^{26} \) \(\mathstrut +\mathstrut \)\(63\!\cdots\!20\)\(q^{27} \) \(\mathstrut +\mathstrut \)\(51\!\cdots\!80\)\(q^{28} \) \(\mathstrut -\mathstrut \)\(11\!\cdots\!00\)\(q^{29} \) \(\mathstrut -\mathstrut \)\(31\!\cdots\!60\)\(q^{30} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!36\)\(q^{31} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!40\)\(q^{32} \) \(\mathstrut +\mathstrut \)\(16\!\cdots\!80\)\(q^{33} \) \(\mathstrut -\mathstrut \)\(16\!\cdots\!32\)\(q^{34} \) \(\mathstrut -\mathstrut \)\(15\!\cdots\!80\)\(q^{35} \) \(\mathstrut +\mathstrut \)\(80\!\cdots\!28\)\(q^{36} \) \(\mathstrut -\mathstrut \)\(92\!\cdots\!40\)\(q^{37} \) \(\mathstrut +\mathstrut \)\(19\!\cdots\!20\)\(q^{38} \) \(\mathstrut -\mathstrut \)\(78\!\cdots\!08\)\(q^{39} \) \(\mathstrut +\mathstrut \)\(19\!\cdots\!00\)\(q^{40} \) \(\mathstrut +\mathstrut \)\(22\!\cdots\!76\)\(q^{41} \) \(\mathstrut -\mathstrut \)\(18\!\cdots\!80\)\(q^{42} \) \(\mathstrut +\mathstrut \)\(96\!\cdots\!00\)\(q^{43} \) \(\mathstrut +\mathstrut \)\(26\!\cdots\!48\)\(q^{44} \) \(\mathstrut -\mathstrut \)\(14\!\cdots\!60\)\(q^{45} \) \(\mathstrut +\mathstrut \)\(27\!\cdots\!96\)\(q^{46} \) \(\mathstrut -\mathstrut \)\(29\!\cdots\!20\)\(q^{47} \) \(\mathstrut +\mathstrut \)\(12\!\cdots\!20\)\(q^{48} \) \(\mathstrut +\mathstrut \)\(26\!\cdots\!44\)\(q^{49} \) \(\mathstrut -\mathstrut \)\(65\!\cdots\!00\)\(q^{50} \) \(\mathstrut -\mathstrut \)\(20\!\cdots\!84\)\(q^{51} \) \(\mathstrut -\mathstrut \)\(36\!\cdots\!00\)\(q^{52} \) \(\mathstrut +\mathstrut \)\(16\!\cdots\!40\)\(q^{53} \) \(\mathstrut +\mathstrut \)\(24\!\cdots\!00\)\(q^{54} \) \(\mathstrut -\mathstrut \)\(60\!\cdots\!60\)\(q^{55} \) \(\mathstrut -\mathstrut \)\(50\!\cdots\!00\)\(q^{56} \) \(\mathstrut +\mathstrut \)\(55\!\cdots\!40\)\(q^{57} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!80\)\(q^{58} \) \(\mathstrut -\mathstrut \)\(37\!\cdots\!00\)\(q^{59} \) \(\mathstrut -\mathstrut \)\(44\!\cdots\!80\)\(q^{60} \) \(\mathstrut +\mathstrut \)\(56\!\cdots\!56\)\(q^{61} \) \(\mathstrut +\mathstrut \)\(70\!\cdots\!80\)\(q^{62} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!60\)\(q^{63} \) \(\mathstrut +\mathstrut \)\(26\!\cdots\!04\)\(q^{64} \) \(\mathstrut +\mathstrut \)\(51\!\cdots\!40\)\(q^{65} \) \(\mathstrut +\mathstrut \)\(36\!\cdots\!52\)\(q^{66} \) \(\mathstrut +\mathstrut \)\(36\!\cdots\!20\)\(q^{67} \) \(\mathstrut +\mathstrut \)\(12\!\cdots\!40\)\(q^{68} \) \(\mathstrut +\mathstrut \)\(14\!\cdots\!52\)\(q^{69} \) \(\mathstrut +\mathstrut \)\(85\!\cdots\!20\)\(q^{70} \) \(\mathstrut +\mathstrut \)\(13\!\cdots\!96\)\(q^{71} \) \(\mathstrut +\mathstrut \)\(56\!\cdots\!60\)\(q^{72} \) \(\mathstrut +\mathstrut \)\(44\!\cdots\!20\)\(q^{73} \) \(\mathstrut +\mathstrut \)\(94\!\cdots\!88\)\(q^{74} \) \(\mathstrut +\mathstrut \)\(15\!\cdots\!00\)\(q^{75} \) \(\mathstrut +\mathstrut \)\(62\!\cdots\!00\)\(q^{76} \) \(\mathstrut +\mathstrut \)\(37\!\cdots\!00\)\(q^{77} \) \(\mathstrut +\mathstrut \)\(44\!\cdots\!00\)\(q^{78} \) \(\mathstrut +\mathstrut \)\(24\!\cdots\!00\)\(q^{79} \) \(\mathstrut -\mathstrut \)\(25\!\cdots\!80\)\(q^{80} \) \(\mathstrut -\mathstrut \)\(31\!\cdots\!32\)\(q^{81} \) \(\mathstrut -\mathstrut \)\(34\!\cdots\!20\)\(q^{82} \) \(\mathstrut -\mathstrut \)\(25\!\cdots\!40\)\(q^{83} \) \(\mathstrut -\mathstrut \)\(14\!\cdots\!32\)\(q^{84} \) \(\mathstrut -\mathstrut \)\(77\!\cdots\!80\)\(q^{85} \) \(\mathstrut -\mathstrut \)\(22\!\cdots\!44\)\(q^{86} \) \(\mathstrut -\mathstrut \)\(19\!\cdots\!40\)\(q^{87} \) \(\mathstrut -\mathstrut \)\(40\!\cdots\!40\)\(q^{88} \) \(\mathstrut -\mathstrut \)\(24\!\cdots\!00\)\(q^{89} \) \(\mathstrut +\mathstrut \)\(19\!\cdots\!40\)\(q^{90} \) \(\mathstrut +\mathstrut \)\(15\!\cdots\!76\)\(q^{91} \) \(\mathstrut +\mathstrut \)\(77\!\cdots\!20\)\(q^{92} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!80\)\(q^{93} \) \(\mathstrut +\mathstrut \)\(72\!\cdots\!48\)\(q^{94} \) \(\mathstrut +\mathstrut \)\(27\!\cdots\!00\)\(q^{95} \) \(\mathstrut +\mathstrut \)\(88\!\cdots\!96\)\(q^{96} \) \(\mathstrut +\mathstrut \)\(50\!\cdots\!80\)\(q^{97} \) \(\mathstrut +\mathstrut \)\(88\!\cdots\!20\)\(q^{98} \) \(\mathstrut -\mathstrut \)\(72\!\cdots\!88\)\(q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.09018e15 0.970375 0.485187 0.874410i \(-0.338751\pi\)
0.485187 + 0.874410i \(0.338751\pi\)
\(3\) −9.30646e23 −0.249482 −0.124741 0.992189i \(-0.539810\pi\)
−0.124741 + 0.992189i \(0.539810\pi\)
\(4\) −5.91967e29 −0.0583725
\(5\) −7.61227e35 −0.766583 −0.383292 0.923627i \(-0.625210\pi\)
−0.383292 + 0.923627i \(0.625210\pi\)
\(6\) −2.87587e39 −0.242091
\(7\) −3.39343e43 −1.01880 −0.509401 0.860529i \(-0.670133\pi\)
−0.509401 + 0.860529i \(0.670133\pi\)
\(8\) −3.31675e46 −1.02702
\(9\) −1.30491e49 −0.937759
\(10\) −2.35233e51 −0.743873
\(11\) −1.54885e53 −0.361647 −0.180824 0.983516i \(-0.557876\pi\)
−0.180824 + 0.983516i \(0.557876\pi\)
\(12\) 5.50912e53 0.0145629
\(13\) −6.78771e56 −0.290831 −0.145415 0.989371i \(-0.546452\pi\)
−0.145415 + 0.989371i \(0.546452\pi\)
\(14\) −1.04863e59 −0.988620
\(15\) 7.08433e59 0.191249
\(16\) −9.64903e61 −0.938220
\(17\) 3.47857e63 1.49033 0.745163 0.666883i \(-0.232372\pi\)
0.745163 + 0.666883i \(0.232372\pi\)
\(18\) −4.03241e64 −0.909977
\(19\) −3.44755e64 −0.0480507 −0.0240254 0.999711i \(-0.507648\pi\)
−0.0240254 + 0.999711i \(0.507648\pi\)
\(20\) 4.50622e65 0.0447474
\(21\) 3.15808e67 0.254173
\(22\) −4.78622e68 −0.350933
\(23\) −5.84642e69 −0.434416 −0.217208 0.976125i \(-0.569695\pi\)
−0.217208 + 0.976125i \(0.569695\pi\)
\(24\) 3.08672e70 0.256223
\(25\) −4.06609e71 −0.412350
\(26\) −2.09753e72 −0.282215
\(27\) 2.50942e73 0.483437
\(28\) 2.00880e73 0.0594700
\(29\) 3.50391e73 0.0170238 0.00851190 0.999964i \(-0.497291\pi\)
0.00851190 + 0.999964i \(0.497291\pi\)
\(30\) 2.18919e75 0.185583
\(31\) 1.38875e76 0.217519 0.108759 0.994068i \(-0.465312\pi\)
0.108759 + 0.994068i \(0.465312\pi\)
\(32\) 3.81852e76 0.116593
\(33\) 1.44143e77 0.0902246
\(34\) 1.07494e79 1.44617
\(35\) 2.58317e79 0.780997
\(36\) 7.72464e78 0.0547393
\(37\) 1.03572e81 1.79000 0.895000 0.446066i \(-0.147175\pi\)
0.895000 + 0.446066i \(0.147175\pi\)
\(38\) −1.06536e80 −0.0466272
\(39\) 6.31696e80 0.0725572
\(40\) 2.52480e82 0.787295
\(41\) −1.61257e83 −1.40978 −0.704889 0.709317i \(-0.749003\pi\)
−0.704889 + 0.709317i \(0.749003\pi\)
\(42\) 9.75906e82 0.246643
\(43\) −2.10970e84 −1.58707 −0.793533 0.608527i \(-0.791761\pi\)
−0.793533 + 0.608527i \(0.791761\pi\)
\(44\) 9.16867e82 0.0211103
\(45\) 9.93333e84 0.718870
\(46\) −1.80665e85 −0.421547
\(47\) 1.62802e86 1.25493 0.627465 0.778645i \(-0.284093\pi\)
0.627465 + 0.778645i \(0.284093\pi\)
\(48\) 8.97984e85 0.234069
\(49\) 4.21120e85 0.0379584
\(50\) −1.25650e87 −0.400135
\(51\) −3.23732e87 −0.371810
\(52\) 4.01810e86 0.0169765
\(53\) −6.47734e88 −1.02610 −0.513049 0.858359i \(-0.671484\pi\)
−0.513049 + 0.858359i \(0.671484\pi\)
\(54\) 7.75457e88 0.469115
\(55\) 1.17902e89 0.277233
\(56\) 1.12552e90 1.04633
\(57\) 3.20845e88 0.0119878
\(58\) 1.08277e89 0.0165195
\(59\) −7.57677e90 −0.479298 −0.239649 0.970860i \(-0.577032\pi\)
−0.239649 + 0.970860i \(0.577032\pi\)
\(60\) −4.19369e89 −0.0111637
\(61\) −4.94411e91 −0.561826 −0.280913 0.959733i \(-0.590637\pi\)
−0.280913 + 0.959733i \(0.590637\pi\)
\(62\) 4.29149e91 0.211075
\(63\) 4.42812e92 0.955391
\(64\) 1.09653e93 1.05136
\(65\) 5.16699e92 0.222946
\(66\) 4.45428e92 0.0875517
\(67\) 1.38891e94 1.25841 0.629205 0.777239i \(-0.283380\pi\)
0.629205 + 0.777239i \(0.283380\pi\)
\(68\) −2.05920e93 −0.0869940
\(69\) 5.44094e93 0.108379
\(70\) 7.98248e94 0.757860
\(71\) 3.57169e95 1.63331 0.816656 0.577124i \(-0.195825\pi\)
0.816656 + 0.577124i \(0.195825\pi\)
\(72\) 4.32805e95 0.963095
\(73\) 8.65911e95 0.946992 0.473496 0.880796i \(-0.342992\pi\)
0.473496 + 0.880796i \(0.342992\pi\)
\(74\) 3.20056e96 1.73697
\(75\) 3.78409e95 0.102874
\(76\) 2.04084e94 0.00280484
\(77\) 5.25590e96 0.368447
\(78\) 1.95206e96 0.0704077
\(79\) −9.98014e96 −0.186785 −0.0933924 0.995629i \(-0.529771\pi\)
−0.0933924 + 0.995629i \(0.529771\pi\)
\(80\) 7.34511e97 0.719224
\(81\) 1.58227e98 0.817150
\(82\) −4.98315e98 −1.36801
\(83\) −8.18903e98 −1.20423 −0.602117 0.798408i \(-0.705676\pi\)
−0.602117 + 0.798408i \(0.705676\pi\)
\(84\) −1.86948e97 −0.0148367
\(85\) −2.64798e99 −1.14246
\(86\) −6.51936e99 −1.54005
\(87\) −3.26090e97 −0.00424714
\(88\) 5.13713e99 0.371418
\(89\) −7.53893e99 −0.304596 −0.152298 0.988335i \(-0.548667\pi\)
−0.152298 + 0.988335i \(0.548667\pi\)
\(90\) 3.06958e100 0.697573
\(91\) 2.30336e100 0.296299
\(92\) 3.46089e99 0.0253580
\(93\) −1.29243e100 −0.0542671
\(94\) 5.03087e101 1.21775
\(95\) 2.62437e100 0.0368349
\(96\) −3.55370e100 −0.0290879
\(97\) 3.33364e102 1.60020 0.800100 0.599867i \(-0.204780\pi\)
0.800100 + 0.599867i \(0.204780\pi\)
\(98\) 1.30134e101 0.0368339
\(99\) 2.02110e102 0.339138
\(100\) 2.40699e101 0.0240699
\(101\) −3.07503e103 −1.84204 −0.921020 0.389515i \(-0.872643\pi\)
−0.921020 + 0.389515i \(0.872643\pi\)
\(102\) −1.00039e103 −0.360795
\(103\) −5.88557e103 −1.28431 −0.642157 0.766573i \(-0.721960\pi\)
−0.642157 + 0.766573i \(0.721960\pi\)
\(104\) 2.25131e103 0.298689
\(105\) −2.40402e103 −0.194845
\(106\) −2.00162e104 −0.995700
\(107\) 4.99845e104 1.53310 0.766551 0.642184i \(-0.221971\pi\)
0.766551 + 0.642184i \(0.221971\pi\)
\(108\) −1.48549e103 −0.0282194
\(109\) −9.22156e103 −0.108978 −0.0544891 0.998514i \(-0.517353\pi\)
−0.0544891 + 0.998514i \(0.517353\pi\)
\(110\) 3.64340e104 0.269020
\(111\) −9.63888e104 −0.446574
\(112\) 3.27433e105 0.955861
\(113\) 5.74183e105 1.06050 0.530249 0.847842i \(-0.322098\pi\)
0.530249 + 0.847842i \(0.322098\pi\)
\(114\) 9.91469e103 0.0116327
\(115\) 4.45045e105 0.333016
\(116\) −2.07420e103 −0.000993721 0
\(117\) 8.85735e105 0.272729
\(118\) −2.34136e106 −0.465098
\(119\) −1.18043e107 −1.51835
\(120\) −2.34969e106 −0.196416
\(121\) −1.59431e107 −0.869211
\(122\) −1.52782e107 −0.545181
\(123\) 1.50073e107 0.351715
\(124\) −8.22094e105 −0.0126971
\(125\) 1.06015e108 1.08268
\(126\) 1.36837e108 0.927087
\(127\) −2.37665e108 −1.07170 −0.535851 0.844313i \(-0.680009\pi\)
−0.535851 + 0.844313i \(0.680009\pi\)
\(128\) 3.00123e108 0.903620
\(129\) 1.96338e108 0.395945
\(130\) 1.59670e108 0.216341
\(131\) −3.88226e108 −0.354498 −0.177249 0.984166i \(-0.556720\pi\)
−0.177249 + 0.984166i \(0.556720\pi\)
\(132\) −8.53278e106 −0.00526664
\(133\) 1.16990e108 0.0489542
\(134\) 4.29199e109 1.22113
\(135\) −1.91024e109 −0.370594
\(136\) −1.15375e110 −1.53059
\(137\) −1.01353e110 −0.921991 −0.460995 0.887403i \(-0.652508\pi\)
−0.460995 + 0.887403i \(0.652508\pi\)
\(138\) 1.68135e109 0.105168
\(139\) −1.76086e110 −0.759385 −0.379692 0.925113i \(-0.623970\pi\)
−0.379692 + 0.925113i \(0.623970\pi\)
\(140\) −1.52915e109 −0.0455887
\(141\) −1.51511e110 −0.313083
\(142\) 1.10372e111 1.58493
\(143\) 1.05131e110 0.105178
\(144\) 1.25911e111 0.879824
\(145\) −2.66727e109 −0.0130501
\(146\) 2.67583e111 0.918937
\(147\) −3.91914e109 −0.00946996
\(148\) −6.13112e110 −0.104487
\(149\) −1.09933e112 −1.32445 −0.662226 0.749304i \(-0.730388\pi\)
−0.662226 + 0.749304i \(0.730388\pi\)
\(150\) 1.16935e111 0.0998265
\(151\) 6.03159e111 0.365695 0.182848 0.983141i \(-0.441469\pi\)
0.182848 + 0.983141i \(0.441469\pi\)
\(152\) 1.14346e111 0.0493490
\(153\) −4.53922e112 −1.39757
\(154\) 1.62417e112 0.357532
\(155\) −1.05715e112 −0.166746
\(156\) −3.73943e110 −0.00423535
\(157\) −3.47276e112 −0.283037 −0.141518 0.989936i \(-0.545198\pi\)
−0.141518 + 0.989936i \(0.545198\pi\)
\(158\) −3.08405e112 −0.181251
\(159\) 6.02811e112 0.255994
\(160\) −2.90677e112 −0.0893781
\(161\) 1.98394e113 0.442584
\(162\) 4.88950e113 0.792941
\(163\) 1.33487e114 1.57680 0.788402 0.615160i \(-0.210909\pi\)
0.788402 + 0.615160i \(0.210909\pi\)
\(164\) 9.54591e112 0.0822923
\(165\) −1.09725e113 −0.0691647
\(166\) −2.53056e114 −1.16856
\(167\) 2.11932e113 0.0718289 0.0359144 0.999355i \(-0.488566\pi\)
0.0359144 + 0.999355i \(0.488566\pi\)
\(168\) −1.04746e114 −0.261041
\(169\) −4.98637e114 −0.915417
\(170\) −8.18275e114 −1.10861
\(171\) 4.49874e113 0.0450600
\(172\) 1.24887e114 0.0926410
\(173\) 1.25212e115 0.689081 0.344540 0.938772i \(-0.388035\pi\)
0.344540 + 0.938772i \(0.388035\pi\)
\(174\) −1.00768e113 −0.00412131
\(175\) 1.37980e115 0.420104
\(176\) 1.49449e115 0.339305
\(177\) 7.05129e114 0.119576
\(178\) −2.32967e115 −0.295572
\(179\) 6.23982e115 0.593255 0.296627 0.954993i \(-0.404138\pi\)
0.296627 + 0.954993i \(0.404138\pi\)
\(180\) −5.88020e114 −0.0419622
\(181\) 3.59924e115 0.193092 0.0965460 0.995329i \(-0.469221\pi\)
0.0965460 + 0.995329i \(0.469221\pi\)
\(182\) 7.11782e115 0.287521
\(183\) 4.60121e115 0.140166
\(184\) 1.93911e116 0.446153
\(185\) −7.88418e116 −1.37218
\(186\) −3.99386e115 −0.0526594
\(187\) −5.38777e116 −0.538972
\(188\) −9.63733e115 −0.0732534
\(189\) −8.51555e116 −0.492526
\(190\) 8.10978e115 0.0357436
\(191\) −3.05068e117 −1.02607 −0.513037 0.858367i \(-0.671480\pi\)
−0.513037 + 0.858367i \(0.671480\pi\)
\(192\) −1.02048e117 −0.262296
\(193\) 8.06071e117 1.58552 0.792760 0.609534i \(-0.208643\pi\)
0.792760 + 0.609534i \(0.208643\pi\)
\(194\) 1.03016e118 1.55279
\(195\) −4.80864e116 −0.0556211
\(196\) −2.49290e115 −0.00221573
\(197\) 8.16653e117 0.558505 0.279252 0.960218i \(-0.409913\pi\)
0.279252 + 0.960218i \(0.409913\pi\)
\(198\) 6.24558e117 0.329091
\(199\) −2.29387e118 −0.932470 −0.466235 0.884661i \(-0.654390\pi\)
−0.466235 + 0.884661i \(0.654390\pi\)
\(200\) 1.34862e118 0.423491
\(201\) −1.29259e118 −0.313951
\(202\) −9.50242e118 −1.78747
\(203\) −1.18903e117 −0.0173439
\(204\) 1.91639e117 0.0217035
\(205\) 1.22754e119 1.08071
\(206\) −1.81875e119 −1.24627
\(207\) 7.62904e118 0.407378
\(208\) 6.54949e118 0.272863
\(209\) 5.33972e117 0.0173774
\(210\) −7.42886e118 −0.189073
\(211\) 1.64335e118 0.0327478 0.0163739 0.999866i \(-0.494788\pi\)
0.0163739 + 0.999866i \(0.494788\pi\)
\(212\) 3.83437e118 0.0598959
\(213\) −3.32398e119 −0.407483
\(214\) 1.54461e120 1.48768
\(215\) 1.60596e120 1.21662
\(216\) −8.32311e119 −0.496498
\(217\) −4.71262e119 −0.221608
\(218\) −2.84963e119 −0.105750
\(219\) −8.05857e119 −0.236258
\(220\) −6.97944e118 −0.0161828
\(221\) −2.36115e120 −0.433433
\(222\) −2.97859e120 −0.433344
\(223\) −1.63017e121 −1.88163 −0.940813 0.338927i \(-0.889936\pi\)
−0.940813 + 0.338927i \(0.889936\pi\)
\(224\) −1.29579e120 −0.118785
\(225\) 5.30588e120 0.386685
\(226\) 1.77433e121 1.02908
\(227\) −2.48101e120 −0.114630 −0.0573149 0.998356i \(-0.518254\pi\)
−0.0573149 + 0.998356i \(0.518254\pi\)
\(228\) −1.89930e118 −0.000699758 0
\(229\) 4.69922e121 1.38197 0.690984 0.722870i \(-0.257177\pi\)
0.690984 + 0.722870i \(0.257177\pi\)
\(230\) 1.37527e121 0.323151
\(231\) −4.89139e120 −0.0919211
\(232\) −1.16216e120 −0.0174837
\(233\) 3.18301e121 0.383715 0.191857 0.981423i \(-0.438549\pi\)
0.191857 + 0.981423i \(0.438549\pi\)
\(234\) 2.73708e121 0.264650
\(235\) −1.23929e122 −0.962008
\(236\) 4.48520e120 0.0279778
\(237\) 9.28798e120 0.0465995
\(238\) −3.64774e122 −1.47337
\(239\) 1.30194e122 0.423738 0.211869 0.977298i \(-0.432045\pi\)
0.211869 + 0.977298i \(0.432045\pi\)
\(240\) −6.83570e121 −0.179434
\(241\) 5.92699e122 1.25590 0.627952 0.778252i \(-0.283893\pi\)
0.627952 + 0.778252i \(0.283893\pi\)
\(242\) −4.92670e122 −0.843461
\(243\) −4.96444e122 −0.687301
\(244\) 2.92675e121 0.0327952
\(245\) −3.20568e121 −0.0290983
\(246\) 4.63755e122 0.341295
\(247\) 2.34010e121 0.0139746
\(248\) −4.60613e122 −0.223396
\(249\) 7.62109e122 0.300435
\(250\) 3.27606e123 1.05061
\(251\) 4.58935e123 1.19827 0.599134 0.800648i \(-0.295512\pi\)
0.599134 + 0.800648i \(0.295512\pi\)
\(252\) −2.62130e122 −0.0557685
\(253\) 9.05520e122 0.157105
\(254\) −7.34429e123 −1.03995
\(255\) 2.46433e123 0.285023
\(256\) −1.84577e123 −0.174509
\(257\) −1.50678e124 −1.16545 −0.582725 0.812670i \(-0.698013\pi\)
−0.582725 + 0.812670i \(0.698013\pi\)
\(258\) 6.06721e123 0.384215
\(259\) −3.51464e124 −1.82366
\(260\) −3.05869e122 −0.0130139
\(261\) −4.57229e122 −0.0159642
\(262\) −1.19969e124 −0.343996
\(263\) 7.65944e124 1.80499 0.902497 0.430696i \(-0.141732\pi\)
0.902497 + 0.430696i \(0.141732\pi\)
\(264\) −4.78085e123 −0.0926623
\(265\) 4.93073e124 0.786590
\(266\) 3.61521e123 0.0475039
\(267\) 7.01607e123 0.0759913
\(268\) −8.22191e123 −0.0734566
\(269\) 2.10976e124 0.155593 0.0777965 0.996969i \(-0.475212\pi\)
0.0777965 + 0.996969i \(0.475212\pi\)
\(270\) −5.90299e124 −0.359615
\(271\) 3.54564e125 1.78557 0.892784 0.450485i \(-0.148749\pi\)
0.892784 + 0.450485i \(0.148749\pi\)
\(272\) −3.35648e125 −1.39825
\(273\) −2.14362e124 −0.0739215
\(274\) −3.13199e125 −0.894677
\(275\) 6.29775e124 0.149125
\(276\) −3.22086e123 −0.00632637
\(277\) 4.60382e125 0.750603 0.375302 0.926903i \(-0.377539\pi\)
0.375302 + 0.926903i \(0.377539\pi\)
\(278\) −5.44137e125 −0.736888
\(279\) −1.81219e125 −0.203980
\(280\) −8.56773e125 −0.802098
\(281\) 4.92394e125 0.383652 0.191826 0.981429i \(-0.438559\pi\)
0.191826 + 0.981429i \(0.438559\pi\)
\(282\) −4.68196e125 −0.303808
\(283\) 5.29101e125 0.286113 0.143056 0.989715i \(-0.454307\pi\)
0.143056 + 0.989715i \(0.454307\pi\)
\(284\) −2.11433e125 −0.0953405
\(285\) −2.44236e124 −0.00918965
\(286\) 3.24875e125 0.102062
\(287\) 5.47216e126 1.43629
\(288\) −4.98283e125 −0.109336
\(289\) 6.65242e126 1.22107
\(290\) −8.24237e124 −0.0126635
\(291\) −3.10244e126 −0.399222
\(292\) −5.12591e125 −0.0552783
\(293\) −6.26659e126 −0.566694 −0.283347 0.959017i \(-0.591445\pi\)
−0.283347 + 0.959017i \(0.591445\pi\)
\(294\) −1.21109e125 −0.00918941
\(295\) 5.76764e126 0.367421
\(296\) −3.43522e127 −1.83836
\(297\) −3.88671e126 −0.174834
\(298\) −3.39714e127 −1.28522
\(299\) 3.96838e126 0.126342
\(300\) −2.24006e125 −0.00600502
\(301\) 7.15912e127 1.61691
\(302\) 1.86387e127 0.354861
\(303\) 2.86177e127 0.459557
\(304\) 3.32655e126 0.0450822
\(305\) 3.76359e127 0.430686
\(306\) −1.40270e128 −1.35616
\(307\) 1.74147e128 1.42328 0.711640 0.702544i \(-0.247953\pi\)
0.711640 + 0.702544i \(0.247953\pi\)
\(308\) −3.11132e126 −0.0215072
\(309\) 5.47738e127 0.320414
\(310\) −3.26680e127 −0.161806
\(311\) −2.61176e128 −1.09590 −0.547952 0.836510i \(-0.684592\pi\)
−0.547952 + 0.836510i \(0.684592\pi\)
\(312\) −2.09517e127 −0.0745176
\(313\) 3.82086e128 1.15246 0.576232 0.817286i \(-0.304522\pi\)
0.576232 + 0.817286i \(0.304522\pi\)
\(314\) −1.07315e128 −0.274652
\(315\) −3.37081e128 −0.732386
\(316\) 5.90792e126 0.0109031
\(317\) −3.08293e128 −0.483516 −0.241758 0.970337i \(-0.577724\pi\)
−0.241758 + 0.970337i \(0.577724\pi\)
\(318\) 1.86280e128 0.248410
\(319\) −5.42702e126 −0.00615661
\(320\) −8.34707e128 −0.805954
\(321\) −4.65179e128 −0.382482
\(322\) 6.13074e128 0.429473
\(323\) −1.19925e128 −0.0716112
\(324\) −9.36651e127 −0.0476991
\(325\) 2.75994e128 0.119924
\(326\) 4.12500e129 1.53009
\(327\) 8.58201e127 0.0271881
\(328\) 5.34850e129 1.44787
\(329\) −5.52457e129 −1.27853
\(330\) −3.39072e128 −0.0671157
\(331\) 8.63187e129 1.46205 0.731027 0.682349i \(-0.239042\pi\)
0.731027 + 0.682349i \(0.239042\pi\)
\(332\) 4.84764e128 0.0702941
\(333\) −1.35152e130 −1.67859
\(334\) 6.54910e128 0.0697009
\(335\) −1.05728e130 −0.964676
\(336\) −3.04725e129 −0.238471
\(337\) 2.49506e129 0.167549 0.0837744 0.996485i \(-0.473302\pi\)
0.0837744 + 0.996485i \(0.473302\pi\)
\(338\) −1.54088e130 −0.888298
\(339\) −5.34361e129 −0.264576
\(340\) 1.56752e129 0.0666881
\(341\) −2.15096e129 −0.0786650
\(342\) 1.39019e129 0.0437251
\(343\) 3.62185e130 0.980130
\(344\) 6.99734e130 1.62995
\(345\) −4.14180e129 −0.0830817
\(346\) 3.86927e130 0.668667
\(347\) −1.05028e131 −1.56436 −0.782181 0.623051i \(-0.785893\pi\)
−0.782181 + 0.623051i \(0.785893\pi\)
\(348\) 1.93035e127 0.000247916 0
\(349\) 3.77219e130 0.417911 0.208956 0.977925i \(-0.432994\pi\)
0.208956 + 0.977925i \(0.432994\pi\)
\(350\) 4.26383e130 0.407658
\(351\) −1.70332e130 −0.140598
\(352\) −5.91431e129 −0.0421655
\(353\) −5.95150e129 −0.0366631 −0.0183315 0.999832i \(-0.505835\pi\)
−0.0183315 + 0.999832i \(0.505835\pi\)
\(354\) 2.17898e130 0.116034
\(355\) −2.71887e131 −1.25207
\(356\) 4.46280e129 0.0177800
\(357\) 1.09856e131 0.378801
\(358\) 1.92822e131 0.575680
\(359\) −5.18908e130 −0.134192 −0.0670959 0.997747i \(-0.521373\pi\)
−0.0670959 + 0.997747i \(0.521373\pi\)
\(360\) −3.29463e131 −0.738292
\(361\) −5.13591e131 −0.997691
\(362\) 1.11223e131 0.187372
\(363\) 1.48374e131 0.216853
\(364\) −1.36352e130 −0.0172957
\(365\) −6.59156e131 −0.725948
\(366\) 1.42186e131 0.136013
\(367\) 2.04929e132 1.70334 0.851670 0.524079i \(-0.175590\pi\)
0.851670 + 0.524079i \(0.175590\pi\)
\(368\) 5.64123e131 0.407578
\(369\) 2.10426e132 1.32203
\(370\) −2.43636e132 −1.33153
\(371\) 2.19804e132 1.04539
\(372\) 7.65078e129 0.00316770
\(373\) 8.75779e131 0.315784 0.157892 0.987456i \(-0.449530\pi\)
0.157892 + 0.987456i \(0.449530\pi\)
\(374\) −1.66492e132 −0.523005
\(375\) −9.86624e131 −0.270111
\(376\) −5.39972e132 −1.28884
\(377\) −2.37835e130 −0.00495105
\(378\) −2.63146e132 −0.477935
\(379\) −2.47269e132 −0.391967 −0.195984 0.980607i \(-0.562790\pi\)
−0.195984 + 0.980607i \(0.562790\pi\)
\(380\) −1.55354e130 −0.00215014
\(381\) 2.21182e132 0.267371
\(382\) −9.42717e132 −0.995676
\(383\) 6.52492e132 0.602335 0.301168 0.953571i \(-0.402624\pi\)
0.301168 + 0.953571i \(0.402624\pi\)
\(384\) −2.79308e132 −0.225437
\(385\) −4.00094e132 −0.282445
\(386\) 2.49091e133 1.53855
\(387\) 2.75296e133 1.48828
\(388\) −1.97341e132 −0.0934076
\(389\) −5.81266e132 −0.240974 −0.120487 0.992715i \(-0.538446\pi\)
−0.120487 + 0.992715i \(0.538446\pi\)
\(390\) −1.48596e132 −0.0539733
\(391\) −2.03372e133 −0.647422
\(392\) −1.39675e132 −0.0389840
\(393\) 3.61301e132 0.0884409
\(394\) 2.52361e133 0.541959
\(395\) 7.59716e132 0.143186
\(396\) −1.19643e132 −0.0197963
\(397\) −4.10497e133 −0.596485 −0.298242 0.954490i \(-0.596400\pi\)
−0.298242 + 0.954490i \(0.596400\pi\)
\(398\) −7.08847e133 −0.904845
\(399\) −1.08876e132 −0.0122132
\(400\) 3.92338e133 0.386875
\(401\) 1.48258e133 0.128553 0.0642767 0.997932i \(-0.479526\pi\)
0.0642767 + 0.997932i \(0.479526\pi\)
\(402\) −3.99433e133 −0.304651
\(403\) −9.42642e132 −0.0632611
\(404\) 1.82032e133 0.107524
\(405\) −1.20447e134 −0.626413
\(406\) −3.67432e132 −0.0168301
\(407\) −1.60417e134 −0.647349
\(408\) 1.07374e134 0.381856
\(409\) −1.69483e133 −0.0531345 −0.0265672 0.999647i \(-0.508458\pi\)
−0.0265672 + 0.999647i \(0.508458\pi\)
\(410\) 3.79331e134 1.04870
\(411\) 9.43236e133 0.230020
\(412\) 3.48406e133 0.0749686
\(413\) 2.57112e134 0.488310
\(414\) 2.35751e134 0.395309
\(415\) 6.23372e134 0.923145
\(416\) −2.59190e133 −0.0339088
\(417\) 1.63873e134 0.189453
\(418\) 1.65007e133 0.0168626
\(419\) −1.96923e135 −1.77940 −0.889700 0.456546i \(-0.849086\pi\)
−0.889700 + 0.456546i \(0.849086\pi\)
\(420\) 1.42310e133 0.0113736
\(421\) −1.41262e135 −0.998841 −0.499420 0.866360i \(-0.666454\pi\)
−0.499420 + 0.866360i \(0.666454\pi\)
\(422\) 5.07824e133 0.0317777
\(423\) −2.12442e135 −1.17682
\(424\) 2.14837e135 1.05382
\(425\) −1.41442e135 −0.614536
\(426\) −1.02717e135 −0.395411
\(427\) 1.67775e135 0.572389
\(428\) −2.95892e134 −0.0894909
\(429\) −9.78400e133 −0.0262401
\(430\) 4.96271e135 1.18058
\(431\) 3.87417e135 0.817709 0.408855 0.912600i \(-0.365928\pi\)
0.408855 + 0.912600i \(0.365928\pi\)
\(432\) −2.42135e135 −0.453570
\(433\) 5.39175e135 0.896610 0.448305 0.893881i \(-0.352028\pi\)
0.448305 + 0.893881i \(0.352028\pi\)
\(434\) −1.45629e135 −0.215043
\(435\) 2.48229e133 0.00325578
\(436\) 5.45886e133 0.00636133
\(437\) 2.01558e134 0.0208740
\(438\) −2.49025e135 −0.229259
\(439\) −3.84644e135 −0.314873 −0.157437 0.987529i \(-0.550323\pi\)
−0.157437 + 0.987529i \(0.550323\pi\)
\(440\) −3.91053e135 −0.284723
\(441\) −5.49524e134 −0.0355958
\(442\) −7.29639e135 −0.420592
\(443\) 1.84814e136 0.948293 0.474146 0.880446i \(-0.342757\pi\)
0.474146 + 0.880446i \(0.342757\pi\)
\(444\) 5.70590e134 0.0260676
\(445\) 5.73884e135 0.233498
\(446\) −5.03753e136 −1.82588
\(447\) 1.02309e136 0.330427
\(448\) −3.72099e136 −1.07113
\(449\) 2.03484e136 0.522209 0.261105 0.965310i \(-0.415913\pi\)
0.261105 + 0.965310i \(0.415913\pi\)
\(450\) 1.63961e136 0.375230
\(451\) 2.49763e136 0.509842
\(452\) −3.39897e135 −0.0619040
\(453\) −5.61328e135 −0.0912345
\(454\) −7.66679e135 −0.111234
\(455\) −1.75338e136 −0.227138
\(456\) −1.06416e135 −0.0123117
\(457\) −1.04378e136 −0.107876 −0.0539379 0.998544i \(-0.517177\pi\)
−0.0539379 + 0.998544i \(0.517177\pi\)
\(458\) 1.45214e137 1.34103
\(459\) 8.72919e136 0.720478
\(460\) −2.63452e135 −0.0194390
\(461\) 2.02664e137 1.33715 0.668574 0.743645i \(-0.266905\pi\)
0.668574 + 0.743645i \(0.266905\pi\)
\(462\) −1.51153e136 −0.0891979
\(463\) −3.03753e137 −1.60361 −0.801806 0.597584i \(-0.796128\pi\)
−0.801806 + 0.597584i \(0.796128\pi\)
\(464\) −3.38094e135 −0.0159721
\(465\) 9.83836e135 0.0416002
\(466\) 9.83609e136 0.372347
\(467\) −3.51688e137 −1.19217 −0.596085 0.802921i \(-0.703278\pi\)
−0.596085 + 0.802921i \(0.703278\pi\)
\(468\) −5.24326e135 −0.0159199
\(469\) −4.71318e137 −1.28207
\(470\) −3.82964e137 −0.933508
\(471\) 3.23191e136 0.0706127
\(472\) 2.51302e137 0.492247
\(473\) 3.26760e137 0.573958
\(474\) 2.87016e136 0.0452190
\(475\) 1.40180e136 0.0198137
\(476\) 6.98775e136 0.0886297
\(477\) 8.45233e137 0.962233
\(478\) 4.02322e137 0.411185
\(479\) 6.63006e137 0.608469 0.304235 0.952597i \(-0.401599\pi\)
0.304235 + 0.952597i \(0.401599\pi\)
\(480\) 2.70517e136 0.0222983
\(481\) −7.03016e137 −0.520587
\(482\) 1.83155e138 1.21870
\(483\) −1.84635e137 −0.110417
\(484\) 9.43778e136 0.0507380
\(485\) −2.53766e138 −1.22669
\(486\) −1.53410e138 −0.666940
\(487\) −6.31224e137 −0.246855 −0.123427 0.992354i \(-0.539389\pi\)
−0.123427 + 0.992354i \(0.539389\pi\)
\(488\) 1.63984e138 0.577005
\(489\) −1.24229e138 −0.393385
\(490\) −9.90616e136 −0.0282363
\(491\) 1.20288e138 0.308692 0.154346 0.988017i \(-0.450673\pi\)
0.154346 + 0.988017i \(0.450673\pi\)
\(492\) −8.88386e136 −0.0205305
\(493\) 1.21886e137 0.0253710
\(494\) 7.23133e136 0.0135606
\(495\) −1.53852e138 −0.259977
\(496\) −1.34001e138 −0.204080
\(497\) −1.21203e139 −1.66402
\(498\) 2.35506e138 0.291535
\(499\) 1.17929e139 1.31656 0.658281 0.752772i \(-0.271284\pi\)
0.658281 + 0.752772i \(0.271284\pi\)
\(500\) −6.27574e137 −0.0631990
\(501\) −1.97234e137 −0.0179200
\(502\) 1.41819e139 1.16277
\(503\) −9.85276e138 −0.729133 −0.364566 0.931177i \(-0.618783\pi\)
−0.364566 + 0.931177i \(0.618783\pi\)
\(504\) −1.46870e139 −0.981204
\(505\) 2.34080e139 1.41208
\(506\) 2.79822e138 0.152451
\(507\) 4.64054e138 0.228381
\(508\) 1.40690e138 0.0625579
\(509\) 3.90438e139 1.56887 0.784434 0.620213i \(-0.212954\pi\)
0.784434 + 0.620213i \(0.212954\pi\)
\(510\) 7.61524e138 0.276579
\(511\) −2.93841e139 −0.964797
\(512\) −3.61398e139 −1.07296
\(513\) −8.65135e137 −0.0232295
\(514\) −4.65622e139 −1.13092
\(515\) 4.48026e139 0.984534
\(516\) −1.16226e138 −0.0231123
\(517\) −2.52155e139 −0.453842
\(518\) −1.08609e140 −1.76963
\(519\) −1.16528e139 −0.171913
\(520\) −1.71376e139 −0.228970
\(521\) 5.34960e139 0.647408 0.323704 0.946158i \(-0.395072\pi\)
0.323704 + 0.946158i \(0.395072\pi\)
\(522\) −1.41292e138 −0.0154913
\(523\) 7.87355e139 0.782228 0.391114 0.920342i \(-0.372090\pi\)
0.391114 + 0.920342i \(0.372090\pi\)
\(524\) 2.29817e138 0.0206929
\(525\) −1.28410e139 −0.104808
\(526\) 2.36691e140 1.75152
\(527\) 4.83086e139 0.324173
\(528\) −1.39084e139 −0.0846506
\(529\) −1.46940e140 −0.811282
\(530\) 1.52368e140 0.763287
\(531\) 9.88699e139 0.449465
\(532\) −6.92544e137 −0.00285758
\(533\) 1.09457e140 0.410007
\(534\) 2.16810e139 0.0737401
\(535\) −3.80496e140 −1.17525
\(536\) −4.60667e140 −1.29241
\(537\) −5.80707e139 −0.148007
\(538\) 6.51954e139 0.150983
\(539\) −6.52251e138 −0.0137276
\(540\) 1.13080e139 0.0216325
\(541\) −7.84823e140 −1.36494 −0.682468 0.730915i \(-0.739093\pi\)
−0.682468 + 0.730915i \(0.739093\pi\)
\(542\) 1.09567e141 1.73267
\(543\) −3.34962e139 −0.0481730
\(544\) 1.32830e140 0.173761
\(545\) 7.01970e139 0.0835408
\(546\) −6.62417e139 −0.0717315
\(547\) −1.20441e141 −1.18693 −0.593466 0.804859i \(-0.702241\pi\)
−0.593466 + 0.804859i \(0.702241\pi\)
\(548\) 5.99976e139 0.0538189
\(549\) 6.45161e140 0.526857
\(550\) 1.94612e140 0.144708
\(551\) −1.20799e138 −0.000818005 0
\(552\) −1.80462e140 −0.111307
\(553\) 3.38669e140 0.190297
\(554\) 1.42267e141 0.728367
\(555\) 7.33738e140 0.342336
\(556\) 1.04237e140 0.0443272
\(557\) 1.34802e141 0.522580 0.261290 0.965260i \(-0.415852\pi\)
0.261290 + 0.965260i \(0.415852\pi\)
\(558\) −5.60000e140 −0.197937
\(559\) 1.43200e141 0.461568
\(560\) −2.49251e141 −0.732747
\(561\) 5.01411e140 0.134464
\(562\) 1.52159e141 0.372286
\(563\) −1.30404e141 −0.291144 −0.145572 0.989348i \(-0.546502\pi\)
−0.145572 + 0.989348i \(0.546502\pi\)
\(564\) 8.96895e139 0.0182754
\(565\) −4.37084e141 −0.812960
\(566\) 1.63502e141 0.277637
\(567\) −5.36932e141 −0.832514
\(568\) −1.18464e142 −1.67744
\(569\) −4.65743e141 −0.602372 −0.301186 0.953565i \(-0.597383\pi\)
−0.301186 + 0.953565i \(0.597383\pi\)
\(570\) −7.54734e139 −0.00891741
\(571\) 9.58062e141 1.03427 0.517135 0.855904i \(-0.326998\pi\)
0.517135 + 0.855904i \(0.326998\pi\)
\(572\) −6.22343e139 −0.00613951
\(573\) 2.83910e141 0.255987
\(574\) 1.69100e142 1.39374
\(575\) 2.37720e141 0.179132
\(576\) −1.43087e142 −0.985921
\(577\) 1.26876e142 0.799514 0.399757 0.916621i \(-0.369095\pi\)
0.399757 + 0.916621i \(0.369095\pi\)
\(578\) 2.05572e142 1.18490
\(579\) −7.50167e141 −0.395559
\(580\) 1.57894e139 0.000761770 0
\(581\) 2.77889e142 1.22688
\(582\) −9.58710e141 −0.387395
\(583\) 1.00324e142 0.371086
\(584\) −2.87201e142 −0.972578
\(585\) −6.74245e141 −0.209070
\(586\) −1.93649e142 −0.549906
\(587\) −1.60821e142 −0.418294 −0.209147 0.977884i \(-0.567069\pi\)
−0.209147 + 0.977884i \(0.567069\pi\)
\(588\) 2.32000e139 0.000552785 0
\(589\) −4.78778e140 −0.0104519
\(590\) 1.78231e142 0.356537
\(591\) −7.60015e141 −0.139337
\(592\) −9.99369e142 −1.67941
\(593\) −1.19977e142 −0.184834 −0.0924169 0.995720i \(-0.529459\pi\)
−0.0924169 + 0.995720i \(0.529459\pi\)
\(594\) −1.20106e142 −0.169654
\(595\) 8.98574e142 1.16394
\(596\) 6.50769e141 0.0773116
\(597\) 2.13478e142 0.232635
\(598\) 1.22630e142 0.122599
\(599\) 1.21247e143 1.11222 0.556108 0.831110i \(-0.312294\pi\)
0.556108 + 0.831110i \(0.312294\pi\)
\(600\) −1.25509e142 −0.105654
\(601\) −2.28866e143 −1.76826 −0.884131 0.467239i \(-0.845249\pi\)
−0.884131 + 0.467239i \(0.845249\pi\)
\(602\) 2.21230e143 1.56901
\(603\) −1.81240e143 −1.18009
\(604\) −3.57051e141 −0.0213465
\(605\) 1.21363e143 0.666323
\(606\) 8.84339e142 0.445942
\(607\) 1.17644e143 0.544945 0.272473 0.962164i \(-0.412159\pi\)
0.272473 + 0.962164i \(0.412159\pi\)
\(608\) −1.31645e141 −0.00560237
\(609\) 1.10656e141 0.00432699
\(610\) 1.16302e143 0.417927
\(611\) −1.10505e143 −0.364972
\(612\) 2.68707e142 0.0815794
\(613\) −4.43772e143 −1.23864 −0.619320 0.785139i \(-0.712592\pi\)
−0.619320 + 0.785139i \(0.712592\pi\)
\(614\) 5.38147e143 1.38112
\(615\) −1.14240e143 −0.269619
\(616\) −1.74325e143 −0.378402
\(617\) −3.29116e142 −0.0657147 −0.0328574 0.999460i \(-0.510461\pi\)
−0.0328574 + 0.999460i \(0.510461\pi\)
\(618\) 1.69261e143 0.310922
\(619\) −9.92293e143 −1.67715 −0.838574 0.544788i \(-0.816610\pi\)
−0.838574 + 0.544788i \(0.816610\pi\)
\(620\) 6.25800e141 0.00973338
\(621\) −1.46711e143 −0.210013
\(622\) −8.07081e143 −1.06344
\(623\) 2.55828e143 0.310323
\(624\) −6.09525e142 −0.0680746
\(625\) −4.06068e143 −0.417617
\(626\) 1.18072e144 1.11832
\(627\) −4.96939e141 −0.00433536
\(628\) 2.05576e142 0.0165216
\(629\) 3.60282e144 2.66768
\(630\) −1.04164e144 −0.710689
\(631\) 8.95555e143 0.563093 0.281547 0.959548i \(-0.409153\pi\)
0.281547 + 0.959548i \(0.409153\pi\)
\(632\) 3.31016e143 0.191831
\(633\) −1.52937e142 −0.00817001
\(634\) −9.52681e143 −0.469192
\(635\) 1.80917e144 0.821549
\(636\) −3.56844e142 −0.0149430
\(637\) −2.85844e142 −0.0110395
\(638\) −1.67705e142 −0.00597422
\(639\) −4.66074e144 −1.53165
\(640\) −2.28462e144 −0.692699
\(641\) −1.80207e144 −0.504178 −0.252089 0.967704i \(-0.581118\pi\)
−0.252089 + 0.967704i \(0.581118\pi\)
\(642\) −1.43749e144 −0.371151
\(643\) 3.33669e144 0.795152 0.397576 0.917569i \(-0.369851\pi\)
0.397576 + 0.917569i \(0.369851\pi\)
\(644\) −1.17443e143 −0.0258348
\(645\) −1.49458e144 −0.303525
\(646\) −3.70591e143 −0.0694897
\(647\) 1.92009e144 0.332469 0.166235 0.986086i \(-0.446839\pi\)
0.166235 + 0.986086i \(0.446839\pi\)
\(648\) −5.24798e144 −0.839227
\(649\) 1.17352e144 0.173337
\(650\) 8.52873e143 0.116372
\(651\) 4.38578e143 0.0552874
\(652\) −7.90200e143 −0.0920420
\(653\) 1.26374e145 1.36029 0.680143 0.733079i \(-0.261918\pi\)
0.680143 + 0.733079i \(0.261918\pi\)
\(654\) 2.65200e143 0.0263827
\(655\) 2.95529e144 0.271752
\(656\) 1.55598e145 1.32268
\(657\) −1.12994e145 −0.888050
\(658\) −1.70719e145 −1.24065
\(659\) 1.69140e144 0.113671 0.0568353 0.998384i \(-0.481899\pi\)
0.0568353 + 0.998384i \(0.481899\pi\)
\(660\) 6.49539e142 0.00403731
\(661\) −9.69697e144 −0.557521 −0.278760 0.960361i \(-0.589924\pi\)
−0.278760 + 0.960361i \(0.589924\pi\)
\(662\) 2.66741e145 1.41874
\(663\) 2.19740e144 0.108134
\(664\) 2.71610e145 1.23677
\(665\) −8.90561e143 −0.0375275
\(666\) −4.17644e145 −1.62886
\(667\) −2.04853e143 −0.00739541
\(668\) −1.25457e143 −0.00419283
\(669\) 1.51711e145 0.469432
\(670\) −3.26718e145 −0.936098
\(671\) 7.65767e144 0.203183
\(672\) 1.20592e144 0.0296348
\(673\) −5.58858e145 −1.27211 −0.636057 0.771642i \(-0.719436\pi\)
−0.636057 + 0.771642i \(0.719436\pi\)
\(674\) 7.71020e144 0.162585
\(675\) −1.02035e145 −0.199345
\(676\) 2.95177e144 0.0534352
\(677\) 3.97647e145 0.667086 0.333543 0.942735i \(-0.391756\pi\)
0.333543 + 0.942735i \(0.391756\pi\)
\(678\) −1.65127e145 −0.256738
\(679\) −1.13125e146 −1.63029
\(680\) 8.78269e145 1.17333
\(681\) 2.30895e144 0.0285981
\(682\) −6.64686e144 −0.0763345
\(683\) 6.61264e145 0.704220 0.352110 0.935959i \(-0.385464\pi\)
0.352110 + 0.935959i \(0.385464\pi\)
\(684\) −2.66311e143 −0.00263026
\(685\) 7.71525e145 0.706782
\(686\) 1.11922e146 0.951094
\(687\) −4.37331e145 −0.344777
\(688\) 2.03566e146 1.48902
\(689\) 4.39663e145 0.298421
\(690\) −1.27989e145 −0.0806204
\(691\) −1.17807e146 −0.688733 −0.344366 0.938835i \(-0.611906\pi\)
−0.344366 + 0.938835i \(0.611906\pi\)
\(692\) −7.41211e144 −0.0402234
\(693\) −6.85848e145 −0.345514
\(694\) −3.24556e146 −1.51802
\(695\) 1.34041e146 0.582131
\(696\) 1.08156e144 0.00436189
\(697\) −5.60945e146 −2.10103
\(698\) 1.16568e146 0.405531
\(699\) −2.96226e145 −0.0957300
\(700\) −8.16796e144 −0.0245225
\(701\) 7.11768e145 0.198546 0.0992728 0.995060i \(-0.468348\pi\)
0.0992728 + 0.995060i \(0.468348\pi\)
\(702\) −5.26358e145 −0.136433
\(703\) −3.57069e145 −0.0860108
\(704\) −1.69835e146 −0.380221
\(705\) 1.15334e146 0.240004
\(706\) −1.83912e145 −0.0355769
\(707\) 1.04349e147 1.87668
\(708\) −4.17413e144 −0.00697997
\(709\) 6.25496e146 0.972620 0.486310 0.873786i \(-0.338343\pi\)
0.486310 + 0.873786i \(0.338343\pi\)
\(710\) −8.40181e146 −1.21498
\(711\) 1.30232e146 0.175159
\(712\) 2.50047e146 0.312826
\(713\) −8.11920e145 −0.0944936
\(714\) 3.39476e146 0.367579
\(715\) −8.00288e145 −0.0806278
\(716\) −3.69377e145 −0.0346298
\(717\) −1.21164e146 −0.105715
\(718\) −1.60352e146 −0.130216
\(719\) 1.25794e146 0.0950876 0.0475438 0.998869i \(-0.484861\pi\)
0.0475438 + 0.998869i \(0.484861\pi\)
\(720\) −9.58470e146 −0.674458
\(721\) 1.99723e147 1.30846
\(722\) −1.58709e147 −0.968134
\(723\) −5.51593e146 −0.313326
\(724\) −2.13063e145 −0.0112713
\(725\) −1.42472e145 −0.00701977
\(726\) 4.58502e146 0.210429
\(727\) 2.64267e147 1.12985 0.564926 0.825142i \(-0.308905\pi\)
0.564926 + 0.825142i \(0.308905\pi\)
\(728\) −7.63967e146 −0.304305
\(729\) −1.73974e147 −0.645680
\(730\) −2.03691e147 −0.704442
\(731\) −7.33873e147 −2.36524
\(732\) −2.72377e145 −0.00818181
\(733\) 1.86567e147 0.522372 0.261186 0.965289i \(-0.415886\pi\)
0.261186 + 0.965289i \(0.415886\pi\)
\(734\) 6.33269e147 1.65288
\(735\) 2.98336e145 0.00725951
\(736\) −2.23247e146 −0.0506498
\(737\) −2.15121e147 −0.455101
\(738\) 6.50256e147 1.28287
\(739\) −3.72257e147 −0.684943 −0.342472 0.939528i \(-0.611264\pi\)
−0.342472 + 0.939528i \(0.611264\pi\)
\(740\) 4.66717e146 0.0800978
\(741\) −2.17780e145 −0.00348643
\(742\) 6.79235e147 1.01442
\(743\) −1.87751e147 −0.261612 −0.130806 0.991408i \(-0.541757\pi\)
−0.130806 + 0.991408i \(0.541757\pi\)
\(744\) 4.28667e146 0.0557332
\(745\) 8.36842e147 1.01530
\(746\) 2.70632e147 0.306429
\(747\) 1.06859e148 1.12928
\(748\) 3.18938e146 0.0314611
\(749\) −1.69619e148 −1.56193
\(750\) −3.04885e147 −0.262109
\(751\) 9.93437e146 0.0797413 0.0398707 0.999205i \(-0.487305\pi\)
0.0398707 + 0.999205i \(0.487305\pi\)
\(752\) −1.57088e148 −1.17740
\(753\) −4.27106e147 −0.298947
\(754\) −7.34955e145 −0.00480437
\(755\) −4.59141e147 −0.280336
\(756\) 5.04092e146 0.0287500
\(757\) −1.88500e148 −1.00432 −0.502161 0.864774i \(-0.667461\pi\)
−0.502161 + 0.864774i \(0.667461\pi\)
\(758\) −7.64106e147 −0.380355
\(759\) −8.42719e146 −0.0391951
\(760\) −8.70437e146 −0.0378301
\(761\) 1.09839e148 0.446116 0.223058 0.974805i \(-0.428396\pi\)
0.223058 + 0.974805i \(0.428396\pi\)
\(762\) 6.83494e147 0.259450
\(763\) 3.12927e147 0.111027
\(764\) 1.80590e147 0.0598945
\(765\) 3.45538e148 1.07135
\(766\) 2.01632e148 0.584491
\(767\) 5.14289e147 0.139395
\(768\) 1.71775e147 0.0435370
\(769\) 2.13006e148 0.504876 0.252438 0.967613i \(-0.418768\pi\)
0.252438 + 0.967613i \(0.418768\pi\)
\(770\) −1.23636e148 −0.274078
\(771\) 1.40228e148 0.290759
\(772\) −4.77168e147 −0.0925508
\(773\) −3.96679e148 −0.719772 −0.359886 0.932996i \(-0.617184\pi\)
−0.359886 + 0.932996i \(0.617184\pi\)
\(774\) 8.50717e148 1.44419
\(775\) −5.64677e147 −0.0896939
\(776\) −1.10568e149 −1.64343
\(777\) 3.27089e148 0.454970
\(778\) −1.79622e148 −0.233835
\(779\) 5.55942e147 0.0677409
\(780\) 2.84656e146 0.00324674
\(781\) −5.53201e148 −0.590683
\(782\) −6.28456e148 −0.628242
\(783\) 8.79279e146 0.00822992
\(784\) −4.06341e147 −0.0356134
\(785\) 2.64356e148 0.216971
\(786\) 1.11649e148 0.0858209
\(787\) 1.51510e149 1.09079 0.545396 0.838178i \(-0.316379\pi\)
0.545396 + 0.838178i \(0.316379\pi\)
\(788\) −4.83432e147 −0.0326013
\(789\) −7.12823e148 −0.450314
\(790\) 2.34766e148 0.138944
\(791\) −1.94845e149 −1.08044
\(792\) −6.70349e148 −0.348301
\(793\) 3.35592e148 0.163396
\(794\) −1.26851e149 −0.578814
\(795\) −4.58876e148 −0.196240
\(796\) 1.35789e148 0.0544306
\(797\) 2.69553e149 1.01284 0.506419 0.862288i \(-0.330969\pi\)
0.506419 + 0.862288i \(0.330969\pi\)
\(798\) −3.36448e147 −0.0118514
\(799\) 5.66317e149 1.87025
\(800\) −1.55265e148 −0.0480771
\(801\) 9.83761e148 0.285637
\(802\) 4.58145e148 0.124745
\(803\) −1.34116e149 −0.342477
\(804\) 7.65168e147 0.0183261
\(805\) −1.51023e149 −0.339278
\(806\) −2.91294e148 −0.0613870
\(807\) −1.96344e148 −0.0388177
\(808\) 1.01991e150 1.89181
\(809\) −1.21477e149 −0.211420 −0.105710 0.994397i \(-0.533712\pi\)
−0.105710 + 0.994397i \(0.533712\pi\)
\(810\) −3.72202e149 −0.607855
\(811\) −9.32412e149 −1.42900 −0.714502 0.699633i \(-0.753347\pi\)
−0.714502 + 0.699633i \(0.753347\pi\)
\(812\) 7.03866e146 0.00101241
\(813\) −3.29974e149 −0.445468
\(814\) −4.95718e149 −0.628171
\(815\) −1.01614e150 −1.20875
\(816\) 3.12370e149 0.348840
\(817\) 7.27329e148 0.0762597
\(818\) −5.23734e148 −0.0515603
\(819\) −3.00568e149 −0.277857
\(820\) −7.26661e148 −0.0630839
\(821\) 3.43581e149 0.280128 0.140064 0.990142i \(-0.455269\pi\)
0.140064 + 0.990142i \(0.455269\pi\)
\(822\) 2.91477e149 0.223206
\(823\) −3.27566e149 −0.235617 −0.117809 0.993036i \(-0.537587\pi\)
−0.117809 + 0.993036i \(0.537587\pi\)
\(824\) 1.95209e150 1.31901
\(825\) −5.86098e148 −0.0372042
\(826\) 7.94524e149 0.473843
\(827\) 2.51231e150 1.40779 0.703897 0.710302i \(-0.251442\pi\)
0.703897 + 0.710302i \(0.251442\pi\)
\(828\) −4.51614e148 −0.0237796
\(829\) −1.69501e150 −0.838715 −0.419357 0.907821i \(-0.637745\pi\)
−0.419357 + 0.907821i \(0.637745\pi\)
\(830\) 1.92633e150 0.895797
\(831\) −4.28453e149 −0.187262
\(832\) −7.44291e149 −0.305768
\(833\) 1.46490e149 0.0565704
\(834\) 5.06399e149 0.183841
\(835\) −1.61329e149 −0.0550628
\(836\) −3.16094e147 −0.00101436
\(837\) 3.48495e149 0.105156
\(838\) −6.08527e150 −1.72668
\(839\) 3.72041e150 0.992773 0.496387 0.868102i \(-0.334660\pi\)
0.496387 + 0.868102i \(0.334660\pi\)
\(840\) 7.97353e149 0.200109
\(841\) −4.23514e150 −0.999710
\(842\) −4.36524e150 −0.969250
\(843\) −4.58244e149 −0.0957144
\(844\) −9.72807e147 −0.00191157
\(845\) 3.79576e150 0.701743
\(846\) −6.56483e150 −1.14196
\(847\) 5.41017e150 0.885555
\(848\) 6.25000e150 0.962706
\(849\) −4.92406e149 −0.0713801
\(850\) −4.37081e150 −0.596331
\(851\) −6.05524e150 −0.777605
\(852\) 1.96769e149 0.0237858
\(853\) 1.00654e151 1.14539 0.572697 0.819767i \(-0.305897\pi\)
0.572697 + 0.819767i \(0.305897\pi\)
\(854\) 5.18455e150 0.555432
\(855\) −3.42456e149 −0.0345422
\(856\) −1.65786e151 −1.57452
\(857\) 1.71589e151 1.53453 0.767267 0.641328i \(-0.221616\pi\)
0.767267 + 0.641328i \(0.221616\pi\)
\(858\) −3.02344e149 −0.0254628
\(859\) −1.00890e151 −0.800204 −0.400102 0.916471i \(-0.631025\pi\)
−0.400102 + 0.916471i \(0.631025\pi\)
\(860\) −9.50676e149 −0.0710170
\(861\) −5.09264e150 −0.358328
\(862\) 1.19719e151 0.793485
\(863\) 2.30280e151 1.43780 0.718902 0.695111i \(-0.244645\pi\)
0.718902 + 0.695111i \(0.244645\pi\)
\(864\) 9.58228e149 0.0563652
\(865\) −9.53145e150 −0.528238
\(866\) 1.66615e151 0.870048
\(867\) −6.19104e150 −0.304635
\(868\) 2.78972e149 0.0129358
\(869\) 1.54577e150 0.0675502
\(870\) 7.67073e148 0.00315933
\(871\) −9.42753e150 −0.365985
\(872\) 3.05856e150 0.111923
\(873\) −4.35010e151 −1.50060
\(874\) 6.22851e149 0.0202556
\(875\) −3.59755e151 −1.10304
\(876\) 4.77041e149 0.0137910
\(877\) 3.15300e151 0.859497 0.429749 0.902949i \(-0.358602\pi\)
0.429749 + 0.902949i \(0.358602\pi\)
\(878\) −1.18862e151 −0.305545
\(879\) 5.83198e150 0.141380
\(880\) −1.13764e151 −0.260105
\(881\) −7.29314e151 −1.57273 −0.786367 0.617760i \(-0.788040\pi\)
−0.786367 + 0.617760i \(0.788040\pi\)
\(882\) −1.69813e150 −0.0345413
\(883\) 1.46757e151 0.281593 0.140796 0.990039i \(-0.455034\pi\)
0.140796 + 0.990039i \(0.455034\pi\)
\(884\) 1.39772e150 0.0253006
\(885\) −5.36763e150 −0.0916652
\(886\) 5.71108e151 0.920199
\(887\) 1.03249e152 1.56972 0.784858 0.619676i \(-0.212736\pi\)
0.784858 + 0.619676i \(0.212736\pi\)
\(888\) 3.19697e151 0.458639
\(889\) 8.06501e151 1.09185
\(890\) 1.77341e151 0.226581
\(891\) −2.45069e151 −0.295520
\(892\) 9.65009e150 0.109835
\(893\) −5.61267e150 −0.0603003
\(894\) 3.16153e151 0.320639
\(895\) −4.74993e151 −0.454779
\(896\) −1.01845e152 −0.920610
\(897\) −3.69316e150 −0.0315200
\(898\) 6.28804e151 0.506739
\(899\) 4.86605e149 0.00370299
\(900\) −3.14091e150 −0.0225718
\(901\) −2.25319e152 −1.52922
\(902\) 7.71813e151 0.494738
\(903\) −6.66260e151 −0.403390
\(904\) −1.90442e152 −1.08915
\(905\) −2.73984e151 −0.148021
\(906\) −1.73461e151 −0.0885317
\(907\) 5.53998e151 0.267136 0.133568 0.991040i \(-0.457356\pi\)
0.133568 + 0.991040i \(0.457356\pi\)
\(908\) 1.46868e150 0.00669123
\(909\) 4.01264e152 1.72739
\(910\) −5.41828e151 −0.220409
\(911\) −3.31225e152 −1.27329 −0.636643 0.771159i \(-0.719678\pi\)
−0.636643 + 0.771159i \(0.719678\pi\)
\(912\) −3.09584e150 −0.0112472
\(913\) 1.26836e152 0.435508
\(914\) −3.22547e151 −0.104680
\(915\) −3.50257e151 −0.107449
\(916\) −2.78178e151 −0.0806689
\(917\) 1.31742e152 0.361163
\(918\) 2.69748e152 0.699134
\(919\) 3.61151e152 0.884992 0.442496 0.896770i \(-0.354093\pi\)
0.442496 + 0.896770i \(0.354093\pi\)
\(920\) −1.47610e152 −0.342014
\(921\) −1.62070e152 −0.355084
\(922\) 6.26270e152 1.29754
\(923\) −2.42436e152 −0.475018
\(924\) 2.89554e150 0.00536566
\(925\) −4.21132e152 −0.738107
\(926\) −9.38653e152 −1.55611
\(927\) 7.68013e152 1.20438
\(928\) 1.33798e150 0.00198485
\(929\) 8.45797e152 1.18702 0.593508 0.804828i \(-0.297742\pi\)
0.593508 + 0.804828i \(0.297742\pi\)
\(930\) 3.04023e151 0.0403678
\(931\) −1.45183e150 −0.00182393
\(932\) −1.88424e151 −0.0223984
\(933\) 2.43062e152 0.273409
\(934\) −1.08678e153 −1.15685
\(935\) 4.10132e152 0.413167
\(936\) −2.93776e152 −0.280098
\(937\) 4.31161e152 0.389091 0.194545 0.980894i \(-0.437677\pi\)
0.194545 + 0.980894i \(0.437677\pi\)
\(938\) −1.45646e153 −1.24409
\(939\) −3.55587e152 −0.287520
\(940\) 7.33620e151 0.0561548
\(941\) −2.36826e153 −1.71618 −0.858092 0.513496i \(-0.828350\pi\)
−0.858092 + 0.513496i \(0.828350\pi\)
\(942\) 9.98720e151 0.0685208
\(943\) 9.42777e152 0.612431
\(944\) 7.31085e152 0.449687
\(945\) 6.48227e152 0.377562
\(946\) 1.00975e153 0.556954
\(947\) −1.66395e153 −0.869193 −0.434596 0.900625i \(-0.643109\pi\)
−0.434596 + 0.900625i \(0.643109\pi\)
\(948\) −5.49818e150 −0.00272013
\(949\) −5.87756e152 −0.275415
\(950\) 4.33183e151 0.0192268
\(951\) 2.86911e152 0.120629
\(952\) 3.91518e153 1.55937
\(953\) −1.09805e153 −0.414322 −0.207161 0.978307i \(-0.566422\pi\)
−0.207161 + 0.978307i \(0.566422\pi\)
\(954\) 2.61193e153 0.933727
\(955\) 2.32226e153 0.786570
\(956\) −7.70703e151 −0.0247347
\(957\) 5.05064e150 0.00153597
\(958\) 2.04881e153 0.590443
\(959\) 3.43934e153 0.939326
\(960\) 7.76817e152 0.201071
\(961\) −3.88333e153 −0.952686
\(962\) −2.17245e153 −0.505165
\(963\) −6.52252e153 −1.43768
\(964\) −3.50859e152 −0.0733103
\(965\) −6.13603e153 −1.21543
\(966\) −5.70555e152 −0.107146
\(967\) −6.60714e151 −0.0117639 −0.00588193 0.999983i \(-0.501872\pi\)
−0.00588193 + 0.999983i \(0.501872\pi\)
\(968\) 5.28791e153 0.892696
\(969\) 1.11608e152 0.0178657
\(970\) −7.84183e153 −1.19035
\(971\) −7.08512e153 −1.01990 −0.509949 0.860205i \(-0.670336\pi\)
−0.509949 + 0.860205i \(0.670336\pi\)
\(972\) 2.93879e152 0.0401195
\(973\) 5.97535e153 0.773663
\(974\) −1.95060e153 −0.239542
\(975\) −2.56853e152 −0.0299190
\(976\) 4.77059e153 0.527116
\(977\) 1.38503e154 1.45174 0.725868 0.687834i \(-0.241438\pi\)
0.725868 + 0.687834i \(0.241438\pi\)
\(978\) −3.83891e153 −0.381731
\(979\) 1.16766e153 0.110156
\(980\) 1.89766e151 0.00169854
\(981\) 1.20333e153 0.102195
\(982\) 3.71712e153 0.299547
\(983\) 8.88217e153 0.679224 0.339612 0.940566i \(-0.389704\pi\)
0.339612 + 0.940566i \(0.389704\pi\)
\(984\) −4.97756e153 −0.361218
\(985\) −6.21658e153 −0.428140
\(986\) 3.76650e152 0.0246194
\(987\) 5.14142e153 0.318970
\(988\) −1.38526e151 −0.000815734 0
\(989\) 1.23342e154 0.689447
\(990\) −4.75431e153 −0.252275
\(991\) 4.72938e153 0.238238 0.119119 0.992880i \(-0.461993\pi\)
0.119119 + 0.992880i \(0.461993\pi\)
\(992\) 5.30297e152 0.0253611
\(993\) −8.03321e153 −0.364757
\(994\) −3.74540e154 −1.61473
\(995\) 1.74615e154 0.714815
\(996\) −4.51144e152 −0.0175371
\(997\) −1.51373e154 −0.558788 −0.279394 0.960177i \(-0.590134\pi\)
−0.279394 + 0.960177i \(0.590134\pi\)
\(998\) 3.64421e154 1.27756
\(999\) 2.59905e154 0.865352
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 \(a_p\))