Properties

Label 2.42.a.b.1.1
Level 2
Weight 42
Character 2.1
Self dual Yes
Analytic conductor 21.294
Analytic rank 0
Dimension 2
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.1
Root \(1.06767e6\)
Character \(\chi\) = 2.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.04858e6 q^{2}\) \(-1.71810e9 q^{3}\) \(+1.09951e12 q^{4}\) \(+3.51885e14 q^{5}\) \(-1.80156e15 q^{6}\) \(-7.89090e16 q^{7}\) \(+1.15292e18 q^{8}\) \(-3.35211e19 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.04858e6 q^{2}\) \(-1.71810e9 q^{3}\) \(+1.09951e12 q^{4}\) \(+3.51885e14 q^{5}\) \(-1.80156e15 q^{6}\) \(-7.89090e16 q^{7}\) \(+1.15292e18 q^{8}\) \(-3.35211e19 q^{9}\) \(+3.68978e20 q^{10}\) \(+1.20679e21 q^{11}\) \(-1.88907e21 q^{12}\) \(+9.23598e22 q^{13}\) \(-8.27420e22 q^{14}\) \(-6.04574e23 q^{15}\) \(+1.20893e24 q^{16}\) \(-4.95668e24 q^{17}\) \(-3.51494e25 q^{18}\) \(+2.41331e26 q^{19}\) \(+3.86902e26 q^{20}\) \(+1.35574e26 q^{21}\) \(+1.26541e27 q^{22}\) \(+8.23610e27 q^{23}\) \(-1.98084e27 q^{24}\) \(+7.83484e28 q^{25}\) \(+9.68462e28 q^{26}\) \(+1.20257e29 q^{27}\) \(-8.67613e28 q^{28}\) \(+2.60718e29 q^{29}\) \(-6.33942e29 q^{30}\) \(-6.40610e30 q^{31}\) \(+1.26765e30 q^{32}\) \(-2.07339e30 q^{33}\) \(-5.19746e30 q^{34}\) \(-2.77669e31 q^{35}\) \(-3.68569e31 q^{36}\) \(+7.38149e31 q^{37}\) \(+2.53054e32 q^{38}\) \(-1.58683e32 q^{39}\) \(+4.05696e32 q^{40}\) \(+2.15386e33 q^{41}\) \(+1.42159e32 q^{42}\) \(-5.67618e33 q^{43}\) \(+1.32688e33 q^{44}\) \(-1.17956e34 q^{45}\) \(+8.63618e33 q^{46}\) \(-6.45458e33 q^{47}\) \(-2.07706e33 q^{48}\) \(-3.83410e34 q^{49}\) \(+8.21542e34 q^{50}\) \(+8.51608e33 q^{51}\) \(+1.01551e35 q^{52}\) \(-9.99163e34 q^{53}\) \(+1.26099e35 q^{54}\) \(+4.24652e35 q^{55}\) \(-9.09758e34 q^{56}\) \(-4.14631e35 q^{57}\) \(+2.73383e35 q^{58}\) \(-3.33277e36 q^{59}\) \(-6.64736e35 q^{60}\) \(+2.08511e36 q^{61}\) \(-6.71729e36 q^{62}\) \(+2.64512e36 q^{63}\) \(+1.32923e36 q^{64}\) \(+3.25000e37 q^{65}\) \(-2.17411e36 q^{66}\) \(+2.21433e36 q^{67}\) \(-5.44993e36 q^{68}\) \(-1.41505e37 q^{69}\) \(-2.91157e37 q^{70}\) \(+5.59105e37 q^{71}\) \(-3.86472e37 q^{72}\) \(-2.02164e38 q^{73}\) \(+7.74006e37 q^{74}\) \(-1.34610e38 q^{75}\) \(+2.65346e38 q^{76}\) \(-9.52266e37 q^{77}\) \(-1.66392e38 q^{78}\) \(-2.46315e38 q^{79}\) \(+4.25403e38 q^{80}\) \(+1.01600e39 q^{81}\) \(+2.25848e39 q^{82}\) \(-3.59771e37 q^{83}\) \(+1.49065e38 q^{84}\) \(-1.74418e39 q^{85}\) \(-5.95190e39 q^{86}\) \(-4.47940e38 q^{87}\) \(+1.39134e39 q^{88}\) \(+5.24223e38 q^{89}\) \(-1.23686e40 q^{90}\) \(-7.28801e39 q^{91}\) \(+9.05569e39 q^{92}\) \(+1.10063e40 q^{93}\) \(-6.76812e39 q^{94}\) \(+8.49208e40 q^{95}\) \(-2.17795e39 q^{96}\) \(-2.35889e40 q^{97}\) \(-4.02035e40 q^{98}\) \(-4.04530e40 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut +\mathstrut 2097152q^{2} \) \(\mathstrut +\mathstrut 8863347528q^{3} \) \(\mathstrut +\mathstrut 2199023255552q^{4} \) \(\mathstrut +\mathstrut 97599184325580q^{5} \) \(\mathstrut +\mathstrut 9293893497520128q^{6} \) \(\mathstrut +\mathstrut 217106802373088656q^{7} \) \(\mathstrut +\mathstrut 2305843009213693952q^{8} \) \(\mathstrut +\mathstrut 41972929616872509786q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 2097152q^{2} \) \(\mathstrut +\mathstrut 8863347528q^{3} \) \(\mathstrut +\mathstrut 2199023255552q^{4} \) \(\mathstrut +\mathstrut 97599184325580q^{5} \) \(\mathstrut +\mathstrut 9293893497520128q^{6} \) \(\mathstrut +\mathstrut 217106802373088656q^{7} \) \(\mathstrut +\mathstrut 2305843009213693952q^{8} \) \(\mathstrut +\mathstrut 41972929616872509786q^{9} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!80\)\(q^{10} \) \(\mathstrut +\mathstrut \)\(11\!\cdots\!84\)\(q^{11} \) \(\mathstrut +\mathstrut \)\(97\!\cdots\!28\)\(q^{12} \) \(\mathstrut +\mathstrut \)\(17\!\cdots\!68\)\(q^{13} \) \(\mathstrut +\mathstrut \)\(22\!\cdots\!56\)\(q^{14} \) \(\mathstrut -\mathstrut \)\(32\!\cdots\!80\)\(q^{15} \) \(\mathstrut +\mathstrut \)\(24\!\cdots\!52\)\(q^{16} \) \(\mathstrut -\mathstrut \)\(10\!\cdots\!04\)\(q^{17} \) \(\mathstrut +\mathstrut \)\(44\!\cdots\!36\)\(q^{18} \) \(\mathstrut +\mathstrut \)\(20\!\cdots\!00\)\(q^{19} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!80\)\(q^{20} \) \(\mathstrut +\mathstrut \)\(32\!\cdots\!84\)\(q^{21} \) \(\mathstrut +\mathstrut \)\(11\!\cdots\!84\)\(q^{22} \) \(\mathstrut +\mathstrut \)\(14\!\cdots\!68\)\(q^{23} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!28\)\(q^{24} \) \(\mathstrut +\mathstrut \)\(97\!\cdots\!50\)\(q^{25} \) \(\mathstrut +\mathstrut \)\(18\!\cdots\!68\)\(q^{26} \) \(\mathstrut +\mathstrut \)\(53\!\cdots\!20\)\(q^{27} \) \(\mathstrut +\mathstrut \)\(23\!\cdots\!56\)\(q^{28} \) \(\mathstrut -\mathstrut \)\(13\!\cdots\!20\)\(q^{29} \) \(\mathstrut -\mathstrut \)\(34\!\cdots\!80\)\(q^{30} \) \(\mathstrut -\mathstrut \)\(36\!\cdots\!16\)\(q^{31} \) \(\mathstrut +\mathstrut \)\(25\!\cdots\!52\)\(q^{32} \) \(\mathstrut -\mathstrut \)\(13\!\cdots\!24\)\(q^{33} \) \(\mathstrut -\mathstrut \)\(10\!\cdots\!04\)\(q^{34} \) \(\mathstrut -\mathstrut \)\(10\!\cdots\!60\)\(q^{35} \) \(\mathstrut +\mathstrut \)\(46\!\cdots\!36\)\(q^{36} \) \(\mathstrut +\mathstrut \)\(12\!\cdots\!36\)\(q^{37} \) \(\mathstrut +\mathstrut \)\(21\!\cdots\!00\)\(q^{38} \) \(\mathstrut +\mathstrut \)\(69\!\cdots\!52\)\(q^{39} \) \(\mathstrut +\mathstrut \)\(11\!\cdots\!80\)\(q^{40} \) \(\mathstrut +\mathstrut \)\(12\!\cdots\!64\)\(q^{41} \) \(\mathstrut +\mathstrut \)\(34\!\cdots\!84\)\(q^{42} \) \(\mathstrut -\mathstrut \)\(60\!\cdots\!52\)\(q^{43} \) \(\mathstrut +\mathstrut \)\(12\!\cdots\!84\)\(q^{44} \) \(\mathstrut -\mathstrut \)\(30\!\cdots\!60\)\(q^{45} \) \(\mathstrut +\mathstrut \)\(15\!\cdots\!68\)\(q^{46} \) \(\mathstrut -\mathstrut \)\(25\!\cdots\!64\)\(q^{47} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!28\)\(q^{48} \) \(\mathstrut +\mathstrut \)\(47\!\cdots\!54\)\(q^{49} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!00\)\(q^{50} \) \(\mathstrut -\mathstrut \)\(47\!\cdots\!56\)\(q^{51} \) \(\mathstrut +\mathstrut \)\(19\!\cdots\!68\)\(q^{52} \) \(\mathstrut -\mathstrut \)\(30\!\cdots\!52\)\(q^{53} \) \(\mathstrut +\mathstrut \)\(55\!\cdots\!20\)\(q^{54} \) \(\mathstrut +\mathstrut \)\(70\!\cdots\!60\)\(q^{55} \) \(\mathstrut +\mathstrut \)\(25\!\cdots\!56\)\(q^{56} \) \(\mathstrut -\mathstrut \)\(78\!\cdots\!00\)\(q^{57} \) \(\mathstrut -\mathstrut \)\(14\!\cdots\!20\)\(q^{58} \) \(\mathstrut -\mathstrut \)\(32\!\cdots\!40\)\(q^{59} \) \(\mathstrut -\mathstrut \)\(36\!\cdots\!80\)\(q^{60} \) \(\mathstrut -\mathstrut \)\(44\!\cdots\!36\)\(q^{61} \) \(\mathstrut -\mathstrut \)\(38\!\cdots\!16\)\(q^{62} \) \(\mathstrut +\mathstrut \)\(24\!\cdots\!08\)\(q^{63} \) \(\mathstrut +\mathstrut \)\(26\!\cdots\!52\)\(q^{64} \) \(\mathstrut +\mathstrut \)\(11\!\cdots\!20\)\(q^{65} \) \(\mathstrut -\mathstrut \)\(14\!\cdots\!24\)\(q^{66} \) \(\mathstrut +\mathstrut \)\(55\!\cdots\!56\)\(q^{67} \) \(\mathstrut -\mathstrut \)\(11\!\cdots\!04\)\(q^{68} \) \(\mathstrut +\mathstrut \)\(56\!\cdots\!52\)\(q^{69} \) \(\mathstrut -\mathstrut \)\(10\!\cdots\!60\)\(q^{70} \) \(\mathstrut -\mathstrut \)\(48\!\cdots\!16\)\(q^{71} \) \(\mathstrut +\mathstrut \)\(48\!\cdots\!36\)\(q^{72} \) \(\mathstrut -\mathstrut \)\(48\!\cdots\!12\)\(q^{73} \) \(\mathstrut +\mathstrut \)\(12\!\cdots\!36\)\(q^{74} \) \(\mathstrut +\mathstrut \)\(68\!\cdots\!00\)\(q^{75} \) \(\mathstrut +\mathstrut \)\(22\!\cdots\!00\)\(q^{76} \) \(\mathstrut -\mathstrut \)\(41\!\cdots\!48\)\(q^{77} \) \(\mathstrut +\mathstrut \)\(73\!\cdots\!52\)\(q^{78} \) \(\mathstrut -\mathstrut \)\(90\!\cdots\!80\)\(q^{79} \) \(\mathstrut +\mathstrut \)\(11\!\cdots\!80\)\(q^{80} \) \(\mathstrut +\mathstrut \)\(26\!\cdots\!22\)\(q^{81} \) \(\mathstrut +\mathstrut \)\(13\!\cdots\!64\)\(q^{82} \) \(\mathstrut +\mathstrut \)\(12\!\cdots\!68\)\(q^{83} \) \(\mathstrut +\mathstrut \)\(35\!\cdots\!84\)\(q^{84} \) \(\mathstrut -\mathstrut \)\(38\!\cdots\!60\)\(q^{85} \) \(\mathstrut -\mathstrut \)\(63\!\cdots\!52\)\(q^{86} \) \(\mathstrut -\mathstrut \)\(17\!\cdots\!80\)\(q^{87} \) \(\mathstrut +\mathstrut \)\(12\!\cdots\!84\)\(q^{88} \) \(\mathstrut +\mathstrut \)\(26\!\cdots\!80\)\(q^{89} \) \(\mathstrut -\mathstrut \)\(32\!\cdots\!60\)\(q^{90} \) \(\mathstrut +\mathstrut \)\(16\!\cdots\!04\)\(q^{91} \) \(\mathstrut +\mathstrut \)\(16\!\cdots\!68\)\(q^{92} \) \(\mathstrut +\mathstrut \)\(40\!\cdots\!76\)\(q^{93} \) \(\mathstrut -\mathstrut \)\(26\!\cdots\!64\)\(q^{94} \) \(\mathstrut +\mathstrut \)\(93\!\cdots\!00\)\(q^{95} \) \(\mathstrut +\mathstrut \)\(11\!\cdots\!28\)\(q^{96} \) \(\mathstrut -\mathstrut \)\(31\!\cdots\!04\)\(q^{97} \) \(\mathstrut +\mathstrut \)\(49\!\cdots\!04\)\(q^{98} \) \(\mathstrut -\mathstrut \)\(12\!\cdots\!88\)\(q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.04858e6 0.707107
\(3\) −1.71810e9 −0.284487 −0.142244 0.989832i \(-0.545432\pi\)
−0.142244 + 0.989832i \(0.545432\pi\)
\(4\) 1.09951e12 0.500000
\(5\) 3.51885e14 1.65012 0.825060 0.565044i \(-0.191141\pi\)
0.825060 + 0.565044i \(0.191141\pi\)
\(6\) −1.80156e15 −0.201163
\(7\) −7.89090e16 −0.373780 −0.186890 0.982381i \(-0.559841\pi\)
−0.186890 + 0.982381i \(0.559841\pi\)
\(8\) 1.15292e18 0.353553
\(9\) −3.35211e19 −0.919067
\(10\) 3.68978e20 1.16681
\(11\) 1.20679e21 0.540856 0.270428 0.962740i \(-0.412835\pi\)
0.270428 + 0.962740i \(0.412835\pi\)
\(12\) −1.88907e21 −0.142244
\(13\) 9.23598e22 1.34786 0.673929 0.738796i \(-0.264605\pi\)
0.673929 + 0.738796i \(0.264605\pi\)
\(14\) −8.27420e22 −0.264303
\(15\) −6.04574e23 −0.469439
\(16\) 1.20893e24 0.250000
\(17\) −4.95668e24 −0.295793 −0.147897 0.989003i \(-0.547250\pi\)
−0.147897 + 0.989003i \(0.547250\pi\)
\(18\) −3.51494e25 −0.649878
\(19\) 2.41331e26 1.47287 0.736435 0.676508i \(-0.236508\pi\)
0.736435 + 0.676508i \(0.236508\pi\)
\(20\) 3.86902e26 0.825060
\(21\) 1.35574e26 0.106336
\(22\) 1.26541e27 0.382443
\(23\) 8.23610e27 1.00069 0.500347 0.865825i \(-0.333206\pi\)
0.500347 + 0.865825i \(0.333206\pi\)
\(24\) −1.98084e27 −0.100581
\(25\) 7.83484e28 1.72290
\(26\) 9.68462e28 0.953079
\(27\) 1.20257e29 0.545950
\(28\) −8.67613e28 −0.186890
\(29\) 2.60718e29 0.273534 0.136767 0.990603i \(-0.456329\pi\)
0.136767 + 0.990603i \(0.456329\pi\)
\(30\) −6.33942e29 −0.331943
\(31\) −6.40610e30 −1.71269 −0.856346 0.516402i \(-0.827271\pi\)
−0.856346 + 0.516402i \(0.827271\pi\)
\(32\) 1.26765e30 0.176777
\(33\) −2.07339e30 −0.153867
\(34\) −5.19746e30 −0.209157
\(35\) −2.77669e31 −0.616783
\(36\) −3.68569e31 −0.459533
\(37\) 7.38149e31 0.524818 0.262409 0.964957i \(-0.415483\pi\)
0.262409 + 0.964957i \(0.415483\pi\)
\(38\) 2.53054e32 1.04148
\(39\) −1.58683e32 −0.383448
\(40\) 4.05696e32 0.583406
\(41\) 2.15386e33 1.86701 0.933507 0.358558i \(-0.116732\pi\)
0.933507 + 0.358558i \(0.116732\pi\)
\(42\) 1.42159e32 0.0751908
\(43\) −5.67618e33 −1.85333 −0.926665 0.375889i \(-0.877337\pi\)
−0.926665 + 0.375889i \(0.877337\pi\)
\(44\) 1.32688e33 0.270428
\(45\) −1.17956e34 −1.51657
\(46\) 8.63618e33 0.707597
\(47\) −6.45458e33 −0.340300 −0.170150 0.985418i \(-0.554425\pi\)
−0.170150 + 0.985418i \(0.554425\pi\)
\(48\) −2.07706e33 −0.0711218
\(49\) −3.83410e34 −0.860288
\(50\) 8.21542e34 1.21827
\(51\) 8.51608e33 0.0841494
\(52\) 1.01551e35 0.673929
\(53\) −9.99163e34 −0.448726 −0.224363 0.974506i \(-0.572030\pi\)
−0.224363 + 0.974506i \(0.572030\pi\)
\(54\) 1.26099e35 0.386045
\(55\) 4.24652e35 0.892479
\(56\) −9.09758e34 −0.132151
\(57\) −4.14631e35 −0.419013
\(58\) 2.73383e35 0.193418
\(59\) −3.33277e36 −1.66088 −0.830442 0.557105i \(-0.811912\pi\)
−0.830442 + 0.557105i \(0.811912\pi\)
\(60\) −6.64736e35 −0.234719
\(61\) 2.08511e36 0.524648 0.262324 0.964980i \(-0.415511\pi\)
0.262324 + 0.964980i \(0.415511\pi\)
\(62\) −6.71729e36 −1.21106
\(63\) 2.64512e36 0.343529
\(64\) 1.32923e36 0.125000
\(65\) 3.25000e37 2.22413
\(66\) −2.17411e36 −0.108800
\(67\) 2.21433e36 0.0814159 0.0407080 0.999171i \(-0.487039\pi\)
0.0407080 + 0.999171i \(0.487039\pi\)
\(68\) −5.44993e36 −0.147897
\(69\) −1.41505e37 −0.284685
\(70\) −2.91157e37 −0.436131
\(71\) 5.59105e37 0.626177 0.313089 0.949724i \(-0.398636\pi\)
0.313089 + 0.949724i \(0.398636\pi\)
\(72\) −3.86472e37 −0.324939
\(73\) −2.02164e38 −1.28110 −0.640552 0.767915i \(-0.721294\pi\)
−0.640552 + 0.767915i \(0.721294\pi\)
\(74\) 7.74006e37 0.371103
\(75\) −1.34610e38 −0.490143
\(76\) 2.65346e38 0.736435
\(77\) −9.52266e37 −0.202162
\(78\) −1.66392e38 −0.271139
\(79\) −2.46315e38 −0.309126 −0.154563 0.987983i \(-0.549397\pi\)
−0.154563 + 0.987983i \(0.549397\pi\)
\(80\) 4.25403e38 0.412530
\(81\) 1.01600e39 0.763751
\(82\) 2.25848e39 1.32018
\(83\) −3.59771e37 −0.0164031 −0.00820154 0.999966i \(-0.502611\pi\)
−0.00820154 + 0.999966i \(0.502611\pi\)
\(84\) 1.49065e38 0.0531679
\(85\) −1.74418e39 −0.488095
\(86\) −5.95190e39 −1.31050
\(87\) −4.47940e38 −0.0778171
\(88\) 1.39134e39 0.191222
\(89\) 5.24223e38 0.0571506 0.0285753 0.999592i \(-0.490903\pi\)
0.0285753 + 0.999592i \(0.490903\pi\)
\(90\) −1.23686e40 −1.07238
\(91\) −7.28801e39 −0.503803
\(92\) 9.05569e39 0.500347
\(93\) 1.10063e40 0.487239
\(94\) −6.76812e39 −0.240628
\(95\) 8.49208e40 2.43041
\(96\) −2.17795e39 −0.0502907
\(97\) −2.35889e40 −0.440441 −0.220221 0.975450i \(-0.570678\pi\)
−0.220221 + 0.975450i \(0.570678\pi\)
\(98\) −4.02035e40 −0.608316
\(99\) −4.04530e40 −0.497083
\(100\) 8.61450e40 0.861450
\(101\) −1.92595e40 −0.157057 −0.0785284 0.996912i \(-0.525022\pi\)
−0.0785284 + 0.996912i \(0.525022\pi\)
\(102\) 8.92976e39 0.0595026
\(103\) −2.65701e41 −1.44954 −0.724770 0.688991i \(-0.758054\pi\)
−0.724770 + 0.688991i \(0.758054\pi\)
\(104\) 1.06484e41 0.476540
\(105\) 4.77063e40 0.175467
\(106\) −1.04770e41 −0.317297
\(107\) −2.47756e41 −0.618951 −0.309476 0.950907i \(-0.600154\pi\)
−0.309476 + 0.950907i \(0.600154\pi\)
\(108\) 1.32224e41 0.272975
\(109\) −5.73631e40 −0.0980369 −0.0490184 0.998798i \(-0.515609\pi\)
−0.0490184 + 0.998798i \(0.515609\pi\)
\(110\) 4.45280e41 0.631078
\(111\) −1.26822e41 −0.149304
\(112\) −9.53951e40 −0.0934451
\(113\) 1.51047e42 1.23312 0.616558 0.787310i \(-0.288527\pi\)
0.616558 + 0.787310i \(0.288527\pi\)
\(114\) −4.34772e41 −0.296287
\(115\) 2.89816e42 1.65127
\(116\) 2.86663e41 0.136767
\(117\) −3.09600e42 −1.23877
\(118\) −3.49466e42 −1.17442
\(119\) 3.91127e41 0.110562
\(120\) −6.97026e41 −0.165972
\(121\) −3.52217e42 −0.707474
\(122\) 2.18640e42 0.370982
\(123\) −3.70054e42 −0.531142
\(124\) −7.04359e42 −0.856346
\(125\) 1.15677e43 1.19287
\(126\) 2.77361e42 0.242912
\(127\) 7.49737e42 0.558384 0.279192 0.960235i \(-0.409933\pi\)
0.279192 + 0.960235i \(0.409933\pi\)
\(128\) 1.39380e42 0.0883883
\(129\) 9.75225e42 0.527249
\(130\) 3.40787e43 1.57270
\(131\) −4.11904e43 −1.62456 −0.812278 0.583271i \(-0.801773\pi\)
−0.812278 + 0.583271i \(0.801773\pi\)
\(132\) −2.27972e42 −0.0769334
\(133\) −1.90432e43 −0.550530
\(134\) 2.32190e42 0.0575698
\(135\) 4.23166e43 0.900884
\(136\) −5.71467e42 −0.104579
\(137\) −3.66801e43 −0.577643 −0.288821 0.957383i \(-0.593263\pi\)
−0.288821 + 0.957383i \(0.593263\pi\)
\(138\) −1.48378e43 −0.201302
\(139\) −8.88436e43 −1.03950 −0.519748 0.854320i \(-0.673974\pi\)
−0.519748 + 0.854320i \(0.673974\pi\)
\(140\) −3.05300e43 −0.308391
\(141\) 1.10896e43 0.0968110
\(142\) 5.86264e43 0.442774
\(143\) 1.11459e44 0.728998
\(144\) −4.05246e43 −0.229767
\(145\) 9.17428e43 0.451365
\(146\) −2.11984e44 −0.905877
\(147\) 6.58737e43 0.244741
\(148\) 8.11604e43 0.262409
\(149\) 3.54730e44 0.999033 0.499517 0.866304i \(-0.333511\pi\)
0.499517 + 0.866304i \(0.333511\pi\)
\(150\) −1.41149e44 −0.346583
\(151\) 4.26711e44 0.914338 0.457169 0.889380i \(-0.348863\pi\)
0.457169 + 0.889380i \(0.348863\pi\)
\(152\) 2.78236e44 0.520738
\(153\) 1.66154e44 0.271854
\(154\) −9.98524e43 −0.142950
\(155\) −2.25421e45 −2.82615
\(156\) −1.74474e44 −0.191724
\(157\) −8.24494e43 −0.0794776 −0.0397388 0.999210i \(-0.512653\pi\)
−0.0397388 + 0.999210i \(0.512653\pi\)
\(158\) −2.58280e44 −0.218585
\(159\) 1.71666e44 0.127657
\(160\) 4.46067e44 0.291703
\(161\) −6.49902e44 −0.374040
\(162\) 1.06536e45 0.540054
\(163\) 1.78991e44 0.0799806 0.0399903 0.999200i \(-0.487267\pi\)
0.0399903 + 0.999200i \(0.487267\pi\)
\(164\) 2.36819e45 0.933507
\(165\) −7.29595e44 −0.253899
\(166\) −3.77248e43 −0.0115987
\(167\) 3.96773e45 1.07859 0.539293 0.842118i \(-0.318692\pi\)
0.539293 + 0.842118i \(0.318692\pi\)
\(168\) 1.56306e44 0.0375954
\(169\) 3.83487e45 0.816721
\(170\) −1.82891e45 −0.345135
\(171\) −8.08969e45 −1.35367
\(172\) −6.24102e45 −0.926665
\(173\) 6.93399e45 0.914193 0.457097 0.889417i \(-0.348889\pi\)
0.457097 + 0.889417i \(0.348889\pi\)
\(174\) −4.69699e44 −0.0550250
\(175\) −6.18239e45 −0.643986
\(176\) 1.45892e45 0.135214
\(177\) 5.72604e45 0.472500
\(178\) 5.49687e44 0.0404116
\(179\) −1.62403e46 −1.06441 −0.532203 0.846617i \(-0.678636\pi\)
−0.532203 + 0.846617i \(0.678636\pi\)
\(180\) −1.29694e46 −0.758286
\(181\) 2.21915e46 1.15818 0.579090 0.815264i \(-0.303408\pi\)
0.579090 + 0.815264i \(0.303408\pi\)
\(182\) −7.64204e45 −0.356242
\(183\) −3.58243e45 −0.149256
\(184\) 9.49558e45 0.353799
\(185\) 2.59744e46 0.866014
\(186\) 1.15410e46 0.344530
\(187\) −5.98168e45 −0.159982
\(188\) −7.09688e45 −0.170150
\(189\) −9.48935e45 −0.204066
\(190\) 8.90459e46 1.71856
\(191\) −4.97685e46 −0.862523 −0.431262 0.902227i \(-0.641931\pi\)
−0.431262 + 0.902227i \(0.641931\pi\)
\(192\) −2.28375e45 −0.0355609
\(193\) 4.02520e46 0.563459 0.281730 0.959494i \(-0.409092\pi\)
0.281730 + 0.959494i \(0.409092\pi\)
\(194\) −2.47348e46 −0.311439
\(195\) −5.58383e46 −0.632736
\(196\) −4.21564e46 −0.430144
\(197\) −7.00300e46 −0.643764 −0.321882 0.946780i \(-0.604315\pi\)
−0.321882 + 0.946780i \(0.604315\pi\)
\(198\) −4.24180e46 −0.351491
\(199\) −1.17193e47 −0.875818 −0.437909 0.899019i \(-0.644281\pi\)
−0.437909 + 0.899019i \(0.644281\pi\)
\(200\) 9.03295e46 0.609137
\(201\) −3.80445e45 −0.0231618
\(202\) −2.01950e46 −0.111056
\(203\) −2.05730e46 −0.102242
\(204\) 9.36353e45 0.0420747
\(205\) 7.57910e47 3.08080
\(206\) −2.78608e47 −1.02498
\(207\) −2.76083e47 −0.919704
\(208\) 1.11656e47 0.336964
\(209\) 2.91236e47 0.796611
\(210\) 5.00237e46 0.124074
\(211\) 5.52367e47 1.24290 0.621452 0.783452i \(-0.286543\pi\)
0.621452 + 0.783452i \(0.286543\pi\)
\(212\) −1.09859e47 −0.224363
\(213\) −9.60599e46 −0.178139
\(214\) −2.59791e47 −0.437665
\(215\) −1.99736e48 −3.05822
\(216\) 1.38647e47 0.193023
\(217\) 5.05499e47 0.640171
\(218\) −6.01496e46 −0.0693225
\(219\) 3.47337e47 0.364458
\(220\) 4.66910e47 0.446239
\(221\) −4.57798e47 −0.398687
\(222\) −1.32982e47 −0.105574
\(223\) 1.20926e48 0.875531 0.437765 0.899089i \(-0.355770\pi\)
0.437765 + 0.899089i \(0.355770\pi\)
\(224\) −1.00029e47 −0.0660757
\(225\) −2.62633e48 −1.58346
\(226\) 1.58384e48 0.871944
\(227\) −1.02944e48 −0.517690 −0.258845 0.965919i \(-0.583342\pi\)
−0.258845 + 0.965919i \(0.583342\pi\)
\(228\) −4.55892e47 −0.209506
\(229\) 2.04406e48 0.858750 0.429375 0.903126i \(-0.358734\pi\)
0.429375 + 0.903126i \(0.358734\pi\)
\(230\) 3.03894e48 1.16762
\(231\) 1.63609e47 0.0575124
\(232\) 3.00587e47 0.0967090
\(233\) 4.38442e48 1.29156 0.645781 0.763523i \(-0.276532\pi\)
0.645781 + 0.763523i \(0.276532\pi\)
\(234\) −3.24639e48 −0.875944
\(235\) −2.27127e48 −0.561536
\(236\) −3.66442e48 −0.830442
\(237\) 4.23194e47 0.0879423
\(238\) 4.10126e47 0.0781789
\(239\) 4.33337e48 0.757999 0.379000 0.925397i \(-0.376268\pi\)
0.379000 + 0.925397i \(0.376268\pi\)
\(240\) −7.30885e47 −0.117360
\(241\) −3.97635e48 −0.586320 −0.293160 0.956063i \(-0.594707\pi\)
−0.293160 + 0.956063i \(0.594707\pi\)
\(242\) −3.69327e48 −0.500260
\(243\) −6.13173e48 −0.763228
\(244\) 2.29260e48 0.262324
\(245\) −1.34916e49 −1.41958
\(246\) −3.88030e48 −0.375574
\(247\) 2.22893e49 1.98522
\(248\) −7.38574e48 −0.605528
\(249\) 6.18123e46 0.00466647
\(250\) 1.21297e49 0.843487
\(251\) 1.35701e49 0.869507 0.434754 0.900549i \(-0.356835\pi\)
0.434754 + 0.900549i \(0.356835\pi\)
\(252\) 2.90834e48 0.171765
\(253\) 9.93926e48 0.541232
\(254\) 7.86156e48 0.394837
\(255\) 2.99668e48 0.138857
\(256\) 1.46150e48 0.0625000
\(257\) −4.30252e49 −1.69861 −0.849304 0.527903i \(-0.822978\pi\)
−0.849304 + 0.527903i \(0.822978\pi\)
\(258\) 1.02260e49 0.372821
\(259\) −5.82466e48 −0.196167
\(260\) 3.57342e49 1.11206
\(261\) −8.73956e48 −0.251397
\(262\) −4.31913e49 −1.14873
\(263\) −1.54140e49 −0.379160 −0.189580 0.981865i \(-0.560713\pi\)
−0.189580 + 0.981865i \(0.560713\pi\)
\(264\) −2.39045e48 −0.0544001
\(265\) −3.51591e49 −0.740452
\(266\) −1.99682e49 −0.389283
\(267\) −9.00667e47 −0.0162586
\(268\) 2.43468e48 0.0407080
\(269\) 2.17495e49 0.336920 0.168460 0.985708i \(-0.446121\pi\)
0.168460 + 0.985708i \(0.446121\pi\)
\(270\) 4.43722e49 0.637021
\(271\) 5.12539e49 0.682113 0.341056 0.940043i \(-0.389215\pi\)
0.341056 + 0.940043i \(0.389215\pi\)
\(272\) −5.99226e48 −0.0739483
\(273\) 1.25215e49 0.143326
\(274\) −3.84619e49 −0.408455
\(275\) 9.45501e49 0.931841
\(276\) −1.55586e49 −0.142342
\(277\) −5.73007e49 −0.486771 −0.243385 0.969930i \(-0.578258\pi\)
−0.243385 + 0.969930i \(0.578258\pi\)
\(278\) −9.31592e49 −0.735034
\(279\) 2.14740e50 1.57408
\(280\) −3.20130e49 −0.218066
\(281\) 1.97230e49 0.124880 0.0624400 0.998049i \(-0.480112\pi\)
0.0624400 + 0.998049i \(0.480112\pi\)
\(282\) 1.16283e49 0.0684557
\(283\) −1.39119e49 −0.0761663 −0.0380832 0.999275i \(-0.512125\pi\)
−0.0380832 + 0.999275i \(0.512125\pi\)
\(284\) 6.14742e49 0.313089
\(285\) −1.45902e50 −0.691422
\(286\) 1.16873e50 0.515479
\(287\) −1.69959e50 −0.697853
\(288\) −4.24931e49 −0.162470
\(289\) −2.56237e50 −0.912506
\(290\) 9.61993e49 0.319163
\(291\) 4.05282e49 0.125300
\(292\) −2.22281e50 −0.640552
\(293\) 3.84683e50 1.03351 0.516757 0.856132i \(-0.327139\pi\)
0.516757 + 0.856132i \(0.327139\pi\)
\(294\) 6.90736e49 0.173058
\(295\) −1.17275e51 −2.74066
\(296\) 8.51028e49 0.185551
\(297\) 1.45125e50 0.295281
\(298\) 3.71962e50 0.706423
\(299\) 7.60684e50 1.34879
\(300\) −1.48006e50 −0.245071
\(301\) 4.47901e50 0.692738
\(302\) 4.47439e50 0.646535
\(303\) 3.30897e49 0.0446807
\(304\) 2.91751e50 0.368217
\(305\) 7.33720e50 0.865732
\(306\) 1.74225e50 0.192230
\(307\) −1.33309e51 −1.37569 −0.687846 0.725856i \(-0.741444\pi\)
−0.687846 + 0.725856i \(0.741444\pi\)
\(308\) −1.04703e50 −0.101081
\(309\) 4.56501e50 0.412376
\(310\) −2.36371e51 −1.99839
\(311\) −3.42217e50 −0.270841 −0.135420 0.990788i \(-0.543239\pi\)
−0.135420 + 0.990788i \(0.543239\pi\)
\(312\) −1.82949e50 −0.135570
\(313\) 8.29482e50 0.575636 0.287818 0.957685i \(-0.407070\pi\)
0.287818 + 0.957685i \(0.407070\pi\)
\(314\) −8.64544e49 −0.0561991
\(315\) 9.30777e50 0.566865
\(316\) −2.70826e50 −0.154563
\(317\) −2.94058e51 −1.57296 −0.786481 0.617615i \(-0.788099\pi\)
−0.786481 + 0.617615i \(0.788099\pi\)
\(318\) 1.80005e50 0.0902670
\(319\) 3.14632e50 0.147943
\(320\) 4.67736e50 0.206265
\(321\) 4.25670e50 0.176084
\(322\) −6.81472e50 −0.264486
\(323\) −1.19620e51 −0.435665
\(324\) 1.11711e51 0.381876
\(325\) 7.23624e51 2.32222
\(326\) 1.87685e50 0.0565548
\(327\) 9.85556e49 0.0278902
\(328\) 2.48323e51 0.660089
\(329\) 5.09324e50 0.127197
\(330\) −7.65035e50 −0.179534
\(331\) −8.47531e51 −1.86931 −0.934656 0.355554i \(-0.884292\pi\)
−0.934656 + 0.355554i \(0.884292\pi\)
\(332\) −3.95573e49 −0.00820154
\(333\) −2.47436e51 −0.482343
\(334\) 4.16047e51 0.762675
\(335\) 7.79191e50 0.134346
\(336\) 1.63898e50 0.0265839
\(337\) 2.49054e51 0.380085 0.190042 0.981776i \(-0.439137\pi\)
0.190042 + 0.981776i \(0.439137\pi\)
\(338\) 4.02116e51 0.577509
\(339\) −2.59514e51 −0.350806
\(340\) −1.91775e51 −0.244047
\(341\) −7.73083e51 −0.926321
\(342\) −8.48265e51 −0.957186
\(343\) 6.54224e51 0.695339
\(344\) −6.54419e51 −0.655251
\(345\) −4.97933e51 −0.469764
\(346\) 7.27082e51 0.646432
\(347\) −1.02424e51 −0.0858314 −0.0429157 0.999079i \(-0.513665\pi\)
−0.0429157 + 0.999079i \(0.513665\pi\)
\(348\) −4.92515e50 −0.0389086
\(349\) 7.39758e51 0.551022 0.275511 0.961298i \(-0.411153\pi\)
0.275511 + 0.961298i \(0.411153\pi\)
\(350\) −6.48271e51 −0.455367
\(351\) 1.11069e52 0.735863
\(352\) 1.52979e51 0.0956108
\(353\) −6.47846e51 −0.382024 −0.191012 0.981588i \(-0.561177\pi\)
−0.191012 + 0.981588i \(0.561177\pi\)
\(354\) 6.00418e51 0.334108
\(355\) 1.96741e52 1.03327
\(356\) 5.76389e50 0.0285753
\(357\) −6.71995e50 −0.0314534
\(358\) −1.70292e52 −0.752648
\(359\) 2.46025e52 1.02693 0.513467 0.858109i \(-0.328361\pi\)
0.513467 + 0.858109i \(0.328361\pi\)
\(360\) −1.35994e52 −0.536189
\(361\) 3.13936e52 1.16935
\(362\) 2.32695e52 0.818957
\(363\) 6.05145e51 0.201267
\(364\) −8.01325e51 −0.251901
\(365\) −7.11383e52 −2.11398
\(366\) −3.75645e51 −0.105540
\(367\) −4.93112e52 −1.31006 −0.655030 0.755603i \(-0.727344\pi\)
−0.655030 + 0.755603i \(0.727344\pi\)
\(368\) 9.95684e51 0.250173
\(369\) −7.21997e52 −1.71591
\(370\) 2.72361e52 0.612364
\(371\) 7.88429e51 0.167725
\(372\) 1.21016e52 0.243620
\(373\) 3.70443e52 0.705815 0.352907 0.935658i \(-0.385193\pi\)
0.352907 + 0.935658i \(0.385193\pi\)
\(374\) −6.27225e51 −0.113124
\(375\) −1.98746e52 −0.339357
\(376\) −7.44162e51 −0.120314
\(377\) 2.40799e52 0.368686
\(378\) −9.95031e51 −0.144296
\(379\) 1.03809e53 1.42604 0.713021 0.701143i \(-0.247327\pi\)
0.713021 + 0.701143i \(0.247327\pi\)
\(380\) 9.33714e52 1.21521
\(381\) −1.28812e52 −0.158853
\(382\) −5.21861e52 −0.609896
\(383\) −1.27369e52 −0.141088 −0.0705440 0.997509i \(-0.522474\pi\)
−0.0705440 + 0.997509i \(0.522474\pi\)
\(384\) −2.39468e51 −0.0251454
\(385\) −3.35088e52 −0.333591
\(386\) 4.22073e52 0.398426
\(387\) 1.90272e53 1.70333
\(388\) −2.59363e52 −0.220221
\(389\) −1.61862e53 −1.30371 −0.651853 0.758346i \(-0.726008\pi\)
−0.651853 + 0.758346i \(0.726008\pi\)
\(390\) −5.85507e52 −0.447412
\(391\) −4.08237e52 −0.295998
\(392\) −4.42042e52 −0.304158
\(393\) 7.07693e52 0.462166
\(394\) −7.34318e52 −0.455210
\(395\) −8.66745e52 −0.510095
\(396\) −4.44785e52 −0.248542
\(397\) 2.20821e53 1.17175 0.585876 0.810401i \(-0.300751\pi\)
0.585876 + 0.810401i \(0.300751\pi\)
\(398\) −1.22886e53 −0.619297
\(399\) 3.27181e52 0.156619
\(400\) 9.47174e52 0.430725
\(401\) −1.18852e52 −0.0513509 −0.0256755 0.999670i \(-0.508174\pi\)
−0.0256755 + 0.999670i \(0.508174\pi\)
\(402\) −3.98925e51 −0.0163779
\(403\) −5.91666e53 −2.30847
\(404\) −2.11760e52 −0.0785284
\(405\) 3.57516e53 1.26028
\(406\) −2.15723e52 −0.0722959
\(407\) 8.90792e52 0.283851
\(408\) 9.81837e51 0.0297513
\(409\) −9.36392e52 −0.269855 −0.134927 0.990856i \(-0.543080\pi\)
−0.134927 + 0.990856i \(0.543080\pi\)
\(410\) 7.94726e53 2.17845
\(411\) 6.30202e52 0.164332
\(412\) −2.92141e53 −0.724770
\(413\) 2.62985e53 0.620806
\(414\) −2.89494e53 −0.650329
\(415\) −1.26598e52 −0.0270671
\(416\) 1.17080e53 0.238270
\(417\) 1.52642e53 0.295723
\(418\) 3.05383e53 0.563289
\(419\) −4.45575e53 −0.782588 −0.391294 0.920266i \(-0.627972\pi\)
−0.391294 + 0.920266i \(0.627972\pi\)
\(420\) 5.24536e52 0.0877335
\(421\) −5.72623e53 −0.912191 −0.456096 0.889931i \(-0.650752\pi\)
−0.456096 + 0.889931i \(0.650752\pi\)
\(422\) 5.79199e53 0.878866
\(423\) 2.16365e53 0.312758
\(424\) −1.15196e53 −0.158649
\(425\) −3.88348e53 −0.509622
\(426\) −1.00726e53 −0.125964
\(427\) −1.64534e53 −0.196103
\(428\) −2.72410e53 −0.309476
\(429\) −1.91498e53 −0.207391
\(430\) −2.09439e54 −2.16249
\(431\) −7.99569e53 −0.787176 −0.393588 0.919287i \(-0.628766\pi\)
−0.393588 + 0.919287i \(0.628766\pi\)
\(432\) 1.45382e53 0.136488
\(433\) 1.41016e54 1.26261 0.631303 0.775536i \(-0.282520\pi\)
0.631303 + 0.775536i \(0.282520\pi\)
\(434\) 5.30054e53 0.452669
\(435\) −1.57623e53 −0.128408
\(436\) −6.30714e52 −0.0490184
\(437\) 1.98763e54 1.47389
\(438\) 3.64210e53 0.257711
\(439\) 9.48293e53 0.640353 0.320177 0.947358i \(-0.396258\pi\)
0.320177 + 0.947358i \(0.396258\pi\)
\(440\) 4.89590e53 0.315539
\(441\) 1.28523e54 0.790662
\(442\) −4.80036e53 −0.281914
\(443\) −1.15125e54 −0.645494 −0.322747 0.946485i \(-0.604606\pi\)
−0.322747 + 0.946485i \(0.604606\pi\)
\(444\) −1.39442e53 −0.0746521
\(445\) 1.84466e53 0.0943054
\(446\) 1.26801e54 0.619094
\(447\) −6.09463e53 −0.284212
\(448\) −1.04888e53 −0.0467225
\(449\) −1.29162e54 −0.549649 −0.274824 0.961494i \(-0.588620\pi\)
−0.274824 + 0.961494i \(0.588620\pi\)
\(450\) −2.75390e54 −1.11968
\(451\) 2.59925e54 1.00979
\(452\) 1.66078e54 0.616558
\(453\) −7.33133e53 −0.260118
\(454\) −1.07944e54 −0.366062
\(455\) −2.56454e54 −0.831336
\(456\) −4.78037e53 −0.148143
\(457\) −5.70144e54 −1.68928 −0.844641 0.535332i \(-0.820186\pi\)
−0.844641 + 0.535332i \(0.820186\pi\)
\(458\) 2.14335e54 0.607228
\(459\) −5.96076e53 −0.161488
\(460\) 3.18656e54 0.825633
\(461\) −5.36766e54 −1.33020 −0.665098 0.746756i \(-0.731610\pi\)
−0.665098 + 0.746756i \(0.731610\pi\)
\(462\) 1.71556e53 0.0406674
\(463\) 6.24453e54 1.41609 0.708043 0.706170i \(-0.249578\pi\)
0.708043 + 0.706170i \(0.249578\pi\)
\(464\) 3.15189e53 0.0683836
\(465\) 3.87296e54 0.804004
\(466\) 4.59739e54 0.913272
\(467\) −8.52716e53 −0.162109 −0.0810547 0.996710i \(-0.525829\pi\)
−0.0810547 + 0.996710i \(0.525829\pi\)
\(468\) −3.40409e54 −0.619386
\(469\) −1.74731e53 −0.0304317
\(470\) −2.38160e54 −0.397066
\(471\) 1.41656e53 0.0226104
\(472\) −3.84242e54 −0.587211
\(473\) −6.84996e54 −1.00239
\(474\) 4.43751e53 0.0621846
\(475\) 1.89079e55 2.53761
\(476\) 4.30048e53 0.0552809
\(477\) 3.34931e54 0.412409
\(478\) 4.54387e54 0.535986
\(479\) −6.54754e54 −0.739947 −0.369973 0.929042i \(-0.620633\pi\)
−0.369973 + 0.929042i \(0.620633\pi\)
\(480\) −7.66389e53 −0.0829858
\(481\) 6.81753e54 0.707380
\(482\) −4.16950e54 −0.414591
\(483\) 1.11660e54 0.106410
\(484\) −3.87267e54 −0.353737
\(485\) −8.30060e54 −0.726781
\(486\) −6.42958e54 −0.539684
\(487\) −4.90744e54 −0.394922 −0.197461 0.980311i \(-0.563270\pi\)
−0.197461 + 0.980311i \(0.563270\pi\)
\(488\) 2.40397e54 0.185491
\(489\) −3.07524e53 −0.0227535
\(490\) −1.41470e55 −1.00379
\(491\) 2.65373e54 0.180587 0.0902935 0.995915i \(-0.471219\pi\)
0.0902935 + 0.995915i \(0.471219\pi\)
\(492\) −4.06879e54 −0.265571
\(493\) −1.29230e54 −0.0809097
\(494\) 2.33720e55 1.40376
\(495\) −1.42348e55 −0.820248
\(496\) −7.74451e54 −0.428173
\(497\) −4.41184e54 −0.234053
\(498\) 6.48149e52 0.00329969
\(499\) 6.02973e53 0.0294603 0.0147301 0.999892i \(-0.495311\pi\)
0.0147301 + 0.999892i \(0.495311\pi\)
\(500\) 1.27189e55 0.596435
\(501\) −6.81696e54 −0.306844
\(502\) 1.42293e55 0.614834
\(503\) 4.08674e55 1.69525 0.847625 0.530596i \(-0.178032\pi\)
0.847625 + 0.530596i \(0.178032\pi\)
\(504\) 3.04961e54 0.121456
\(505\) −6.77713e54 −0.259163
\(506\) 1.04221e55 0.382709
\(507\) −6.58870e54 −0.232347
\(508\) 8.24344e54 0.279192
\(509\) 4.17871e54 0.135934 0.0679670 0.997688i \(-0.478349\pi\)
0.0679670 + 0.997688i \(0.478349\pi\)
\(510\) 3.14225e54 0.0981865
\(511\) 1.59525e55 0.478851
\(512\) 1.53250e54 0.0441942
\(513\) 2.90217e55 0.804114
\(514\) −4.51151e55 −1.20110
\(515\) −9.34962e55 −2.39192
\(516\) 1.07227e55 0.263624
\(517\) −7.78933e54 −0.184053
\(518\) −6.10760e54 −0.138711
\(519\) −1.19133e55 −0.260076
\(520\) 3.74700e55 0.786348
\(521\) 2.55519e55 0.515525 0.257763 0.966208i \(-0.417015\pi\)
0.257763 + 0.966208i \(0.417015\pi\)
\(522\) −9.16409e54 −0.177764
\(523\) −6.45058e55 −1.20314 −0.601568 0.798822i \(-0.705457\pi\)
−0.601568 + 0.798822i \(0.705457\pi\)
\(524\) −4.52893e55 −0.812278
\(525\) 1.06220e55 0.183206
\(526\) −1.61627e55 −0.268107
\(527\) 3.17530e55 0.506603
\(528\) −2.50657e54 −0.0384667
\(529\) 9.40022e52 0.00138770
\(530\) −3.68670e55 −0.523579
\(531\) 1.11718e56 1.52646
\(532\) −2.09382e55 −0.275265
\(533\) 1.98930e56 2.51647
\(534\) −9.44418e53 −0.0114966
\(535\) −8.71816e55 −1.02134
\(536\) 2.55295e54 0.0287849
\(537\) 2.79025e55 0.302810
\(538\) 2.28060e55 0.238238
\(539\) −4.62696e55 −0.465292
\(540\) 4.65276e55 0.450442
\(541\) −1.14581e56 −1.06799 −0.533995 0.845488i \(-0.679310\pi\)
−0.533995 + 0.845488i \(0.679310\pi\)
\(542\) 5.37436e55 0.482327
\(543\) −3.81273e55 −0.329488
\(544\) −6.28334e54 −0.0522894
\(545\) −2.01852e55 −0.161773
\(546\) 1.31298e55 0.101346
\(547\) 6.76717e55 0.503114 0.251557 0.967842i \(-0.419057\pi\)
0.251557 + 0.967842i \(0.419057\pi\)
\(548\) −4.03302e55 −0.288821
\(549\) −6.98953e55 −0.482186
\(550\) 9.91430e55 0.658911
\(551\) 6.29194e55 0.402881
\(552\) −1.63144e55 −0.100651
\(553\) 1.94364e55 0.115545
\(554\) −6.00841e55 −0.344199
\(555\) −4.46266e55 −0.246370
\(556\) −9.76845e55 −0.519748
\(557\) −1.91017e56 −0.979584 −0.489792 0.871839i \(-0.662927\pi\)
−0.489792 + 0.871839i \(0.662927\pi\)
\(558\) 2.25171e56 1.11304
\(559\) −5.24250e56 −2.49802
\(560\) −3.35681e55 −0.154196
\(561\) 1.02771e55 0.0455128
\(562\) 2.06810e55 0.0883035
\(563\) 2.46904e56 1.01650 0.508249 0.861210i \(-0.330293\pi\)
0.508249 + 0.861210i \(0.330293\pi\)
\(564\) 1.21932e55 0.0484055
\(565\) 5.31511e56 2.03479
\(566\) −1.45876e55 −0.0538577
\(567\) −8.01717e55 −0.285475
\(568\) 6.44604e55 0.221387
\(569\) −4.36145e56 −1.44487 −0.722437 0.691437i \(-0.756978\pi\)
−0.722437 + 0.691437i \(0.756978\pi\)
\(570\) −1.52990e56 −0.488909
\(571\) 3.87246e56 1.19384 0.596920 0.802300i \(-0.296391\pi\)
0.596920 + 0.802300i \(0.296391\pi\)
\(572\) 1.22550e56 0.364499
\(573\) 8.55074e55 0.245377
\(574\) −1.78214e56 −0.493457
\(575\) 6.45285e56 1.72409
\(576\) −4.45572e55 −0.114883
\(577\) 3.88180e56 0.965893 0.482947 0.875650i \(-0.339567\pi\)
0.482947 + 0.875650i \(0.339567\pi\)
\(578\) −2.68684e56 −0.645239
\(579\) −6.91570e55 −0.160297
\(580\) 1.00872e56 0.225682
\(581\) 2.83892e54 0.00613115
\(582\) 4.24969e55 0.0886004
\(583\) −1.20578e56 −0.242696
\(584\) −2.33079e56 −0.452938
\(585\) −1.08944e57 −2.04412
\(586\) 4.03369e56 0.730805
\(587\) 5.00890e56 0.876317 0.438158 0.898898i \(-0.355631\pi\)
0.438158 + 0.898898i \(0.355631\pi\)
\(588\) 7.24289e55 0.122371
\(589\) −1.54599e57 −2.52257
\(590\) −1.22972e57 −1.93794
\(591\) 1.20319e56 0.183143
\(592\) 8.92368e55 0.131205
\(593\) 9.63914e56 1.36904 0.684521 0.728993i \(-0.260011\pi\)
0.684521 + 0.728993i \(0.260011\pi\)
\(594\) 1.52175e56 0.208795
\(595\) 1.37632e56 0.182440
\(596\) 3.90030e56 0.499517
\(597\) 2.01350e56 0.249159
\(598\) 7.97635e56 0.953740
\(599\) −1.39170e56 −0.160803 −0.0804016 0.996763i \(-0.525620\pi\)
−0.0804016 + 0.996763i \(0.525620\pi\)
\(600\) −1.55195e56 −0.173292
\(601\) −1.72237e56 −0.185866 −0.0929330 0.995672i \(-0.529624\pi\)
−0.0929330 + 0.995672i \(0.529624\pi\)
\(602\) 4.69659e56 0.489840
\(603\) −7.42269e55 −0.0748267
\(604\) 4.69174e56 0.457169
\(605\) −1.23940e57 −1.16742
\(606\) 3.46971e55 0.0315940
\(607\) 1.22974e57 1.08254 0.541270 0.840849i \(-0.317944\pi\)
0.541270 + 0.840849i \(0.317944\pi\)
\(608\) 3.05923e56 0.260369
\(609\) 3.53465e55 0.0290865
\(610\) 7.69361e56 0.612165
\(611\) −5.96143e56 −0.458676
\(612\) 1.82688e56 0.135927
\(613\) 2.53270e57 1.82240 0.911199 0.411966i \(-0.135158\pi\)
0.911199 + 0.411966i \(0.135158\pi\)
\(614\) −1.39784e57 −0.972762
\(615\) −1.30217e57 −0.876449
\(616\) −1.09789e56 −0.0714749
\(617\) −2.74089e56 −0.172602 −0.0863011 0.996269i \(-0.527505\pi\)
−0.0863011 + 0.996269i \(0.527505\pi\)
\(618\) 4.78676e56 0.291594
\(619\) −1.90431e57 −1.12222 −0.561112 0.827740i \(-0.689626\pi\)
−0.561112 + 0.827740i \(0.689626\pi\)
\(620\) −2.47853e57 −1.41307
\(621\) 9.90449e56 0.546329
\(622\) −3.58841e56 −0.191513
\(623\) −4.13659e55 −0.0213618
\(624\) −1.91836e56 −0.0958621
\(625\) 5.07645e56 0.245482
\(626\) 8.69774e56 0.407036
\(627\) −5.00373e56 −0.226626
\(628\) −9.06541e55 −0.0397388
\(629\) −3.65877e56 −0.155238
\(630\) 9.75991e56 0.400834
\(631\) 1.91059e57 0.759565 0.379782 0.925076i \(-0.375999\pi\)
0.379782 + 0.925076i \(0.375999\pi\)
\(632\) −2.83982e56 −0.109292
\(633\) −9.49023e56 −0.353590
\(634\) −3.08342e57 −1.11225
\(635\) 2.63821e57 0.921400
\(636\) 1.88749e56 0.0638284
\(637\) −3.54117e57 −1.15955
\(638\) 3.29916e56 0.104611
\(639\) −1.87418e57 −0.575499
\(640\) 4.90456e56 0.145851
\(641\) 6.02067e57 1.73403 0.867013 0.498286i \(-0.166037\pi\)
0.867013 + 0.498286i \(0.166037\pi\)
\(642\) 4.46347e56 0.124510
\(643\) 5.41099e57 1.46201 0.731007 0.682370i \(-0.239051\pi\)
0.731007 + 0.682370i \(0.239051\pi\)
\(644\) −7.14575e56 −0.187020
\(645\) 3.43167e57 0.870024
\(646\) −1.25431e57 −0.308062
\(647\) −6.44976e57 −1.53464 −0.767319 0.641266i \(-0.778410\pi\)
−0.767319 + 0.641266i \(0.778410\pi\)
\(648\) 1.17137e57 0.270027
\(649\) −4.02196e57 −0.898300
\(650\) 7.58774e57 1.64206
\(651\) −8.68498e56 −0.182120
\(652\) 1.96802e56 0.0399903
\(653\) 5.84519e57 1.15101 0.575504 0.817799i \(-0.304806\pi\)
0.575504 + 0.817799i \(0.304806\pi\)
\(654\) 1.03343e56 0.0197214
\(655\) −1.44943e58 −2.68071
\(656\) 2.60385e57 0.466754
\(657\) 6.77675e57 1.17742
\(658\) 5.34065e56 0.0899422
\(659\) −3.68490e57 −0.601554 −0.300777 0.953694i \(-0.597246\pi\)
−0.300777 + 0.953694i \(0.597246\pi\)
\(660\) −8.02198e56 −0.126949
\(661\) −6.04679e57 −0.927672 −0.463836 0.885921i \(-0.653527\pi\)
−0.463836 + 0.885921i \(0.653527\pi\)
\(662\) −8.88701e57 −1.32180
\(663\) 7.86543e56 0.113421
\(664\) −4.14788e55 −0.00579937
\(665\) −6.70101e57 −0.908441
\(666\) −2.59455e57 −0.341068
\(667\) 2.14730e57 0.273724
\(668\) 4.36257e57 0.539293
\(669\) −2.07764e57 −0.249077
\(670\) 8.17041e56 0.0949971
\(671\) 2.51629e57 0.283759
\(672\) 1.71860e56 0.0187977
\(673\) 6.56510e57 0.696518 0.348259 0.937398i \(-0.386773\pi\)
0.348259 + 0.937398i \(0.386773\pi\)
\(674\) 2.61152e57 0.268761
\(675\) 9.42194e57 0.940617
\(676\) 4.21649e57 0.408360
\(677\) 1.10721e58 1.04031 0.520155 0.854072i \(-0.325874\pi\)
0.520155 + 0.854072i \(0.325874\pi\)
\(678\) −2.72120e57 −0.248057
\(679\) 1.86138e57 0.164628
\(680\) −2.01091e57 −0.172568
\(681\) 1.76868e57 0.147276
\(682\) −8.10636e57 −0.655008
\(683\) 1.97103e58 1.54550 0.772749 0.634711i \(-0.218881\pi\)
0.772749 + 0.634711i \(0.218881\pi\)
\(684\) −8.89471e57 −0.676833
\(685\) −1.29072e58 −0.953180
\(686\) 6.86003e57 0.491679
\(687\) −3.51190e57 −0.244303
\(688\) −6.86208e57 −0.463332
\(689\) −9.22825e57 −0.604819
\(690\) −5.22121e57 −0.332173
\(691\) 1.78821e58 1.10438 0.552191 0.833718i \(-0.313792\pi\)
0.552191 + 0.833718i \(0.313792\pi\)
\(692\) 7.62400e57 0.457097
\(693\) 3.19210e57 0.185800
\(694\) −1.07399e57 −0.0606920
\(695\) −3.12627e58 −1.71529
\(696\) −5.16440e56 −0.0275125
\(697\) −1.06760e58 −0.552250
\(698\) 7.75693e57 0.389631
\(699\) −7.53287e57 −0.367433
\(700\) −6.79761e57 −0.321993
\(701\) −2.83192e58 −1.30275 −0.651375 0.758756i \(-0.725807\pi\)
−0.651375 + 0.758756i \(0.725807\pi\)
\(702\) 1.16464e58 0.520334
\(703\) 1.78138e58 0.772989
\(704\) 1.60410e57 0.0676071
\(705\) 3.90227e57 0.159750
\(706\) −6.79315e57 −0.270131
\(707\) 1.51975e57 0.0587047
\(708\) 6.29584e57 0.236250
\(709\) 3.01107e58 1.09767 0.548836 0.835930i \(-0.315071\pi\)
0.548836 + 0.835930i \(0.315071\pi\)
\(710\) 2.06298e58 0.730631
\(711\) 8.25675e57 0.284107
\(712\) 6.04388e56 0.0202058
\(713\) −5.27613e58 −1.71388
\(714\) −7.04638e56 −0.0222409
\(715\) 3.92207e58 1.20293
\(716\) −1.78564e58 −0.532203
\(717\) −7.44516e57 −0.215641
\(718\) 2.57976e58 0.726153
\(719\) −3.81485e58 −1.04360 −0.521802 0.853067i \(-0.674740\pi\)
−0.521802 + 0.853067i \(0.674740\pi\)
\(720\) −1.42600e58 −0.379143
\(721\) 2.09662e58 0.541809
\(722\) 3.29185e58 0.826852
\(723\) 6.83176e57 0.166801
\(724\) 2.43998e58 0.579090
\(725\) 2.04268e58 0.471272
\(726\) 6.34540e57 0.142318
\(727\) 3.32784e58 0.725617 0.362808 0.931864i \(-0.381818\pi\)
0.362808 + 0.931864i \(0.381818\pi\)
\(728\) −8.40251e57 −0.178121
\(729\) −2.65217e58 −0.546622
\(730\) −7.45939e58 −1.49481
\(731\) 2.81350e58 0.548202
\(732\) −3.93893e57 −0.0746278
\(733\) −2.73207e58 −0.503338 −0.251669 0.967813i \(-0.580979\pi\)
−0.251669 + 0.967813i \(0.580979\pi\)
\(734\) −5.17065e58 −0.926352
\(735\) 2.31800e58 0.403852
\(736\) 1.04405e58 0.176899
\(737\) 2.67224e57 0.0440343
\(738\) −7.57069e58 −1.21333
\(739\) −2.78923e58 −0.434784 −0.217392 0.976084i \(-0.569755\pi\)
−0.217392 + 0.976084i \(0.569755\pi\)
\(740\) 2.85591e58 0.433007
\(741\) −3.82952e58 −0.564770
\(742\) 8.26728e57 0.118599
\(743\) −5.29149e58 −0.738427 −0.369214 0.929345i \(-0.620373\pi\)
−0.369214 + 0.929345i \(0.620373\pi\)
\(744\) 1.26894e58 0.172265
\(745\) 1.24824e59 1.64853
\(746\) 3.88438e58 0.499086
\(747\) 1.20599e57 0.0150755
\(748\) −6.57693e57 −0.0799908
\(749\) 1.95502e58 0.231352
\(750\) −2.08400e58 −0.239961
\(751\) −1.65688e59 −1.85641 −0.928203 0.372075i \(-0.878647\pi\)
−0.928203 + 0.372075i \(0.878647\pi\)
\(752\) −7.80311e57 −0.0850750
\(753\) −2.33149e58 −0.247364
\(754\) 2.52496e58 0.260700
\(755\) 1.50153e59 1.50877
\(756\) −1.04337e58 −0.102033
\(757\) 1.30792e59 1.24485 0.622424 0.782680i \(-0.286148\pi\)
0.622424 + 0.782680i \(0.286148\pi\)
\(758\) 1.08852e59 1.00836
\(759\) −1.70766e58 −0.153974
\(760\) 9.79070e58 0.859281
\(761\) 8.10267e58 0.692218 0.346109 0.938194i \(-0.387503\pi\)
0.346109 + 0.938194i \(0.387503\pi\)
\(762\) −1.35070e58 −0.112326
\(763\) 4.52646e57 0.0366443
\(764\) −5.47211e58 −0.431262
\(765\) 5.84670e58 0.448592
\(766\) −1.33556e58 −0.0997643
\(767\) −3.07814e59 −2.23863
\(768\) −2.51101e57 −0.0177805
\(769\) −5.87182e58 −0.404839 −0.202420 0.979299i \(-0.564881\pi\)
−0.202420 + 0.979299i \(0.564881\pi\)
\(770\) −3.51366e58 −0.235884
\(771\) 7.39216e58 0.483233
\(772\) 4.42575e58 0.281730
\(773\) −2.32645e59 −1.44216 −0.721081 0.692850i \(-0.756355\pi\)
−0.721081 + 0.692850i \(0.756355\pi\)
\(774\) 1.99515e59 1.20444
\(775\) −5.01908e59 −2.95080
\(776\) −2.71962e58 −0.155719
\(777\) 1.00074e58 0.0558070
\(778\) −1.69725e59 −0.921859
\(779\) 5.19792e59 2.74987
\(780\) −6.13949e58 −0.316368
\(781\) 6.74723e58 0.338672
\(782\) −4.28068e58 −0.209302
\(783\) 3.13532e58 0.149336
\(784\) −4.63514e58 −0.215072
\(785\) −2.90127e58 −0.131148
\(786\) 7.42070e58 0.326800
\(787\) 2.24048e59 0.961299 0.480649 0.876913i \(-0.340401\pi\)
0.480649 + 0.876913i \(0.340401\pi\)
\(788\) −7.69988e58 −0.321882
\(789\) 2.64828e58 0.107866
\(790\) −9.08848e58 −0.360691
\(791\) −1.19190e59 −0.460914
\(792\) −4.66391e58 −0.175745
\(793\) 1.92580e59 0.707150
\(794\) 2.31548e59 0.828553
\(795\) 6.04068e58 0.210649
\(796\) −1.28855e59 −0.437909
\(797\) 3.32067e59 1.09984 0.549921 0.835217i \(-0.314658\pi\)
0.549921 + 0.835217i \(0.314658\pi\)
\(798\) 3.43074e58 0.110746
\(799\) 3.19933e58 0.100658
\(800\) 9.93184e58 0.304568
\(801\) −1.75725e58 −0.0525252
\(802\) −1.24626e58 −0.0363106
\(803\) −2.43969e59 −0.692893
\(804\) −4.18303e57 −0.0115809
\(805\) −2.28691e59 −0.617211
\(806\) −6.20407e59 −1.63233
\(807\) −3.73678e58 −0.0958495
\(808\) −2.22047e58 −0.0555279
\(809\) 7.35141e59 1.79236 0.896182 0.443687i \(-0.146330\pi\)
0.896182 + 0.443687i \(0.146330\pi\)
\(810\) 3.74883e59 0.891154
\(811\) −7.34195e58 −0.170170 −0.0850852 0.996374i \(-0.527116\pi\)
−0.0850852 + 0.996374i \(0.527116\pi\)
\(812\) −2.26202e58 −0.0511209
\(813\) −8.80593e58 −0.194053
\(814\) 9.34063e58 0.200713
\(815\) 6.29842e58 0.131978
\(816\) 1.02953e58 0.0210374
\(817\) −1.36984e60 −2.72971
\(818\) −9.81878e58 −0.190816
\(819\) 2.44302e59 0.463029
\(820\) 8.33331e59 1.54040
\(821\) −7.00875e59 −1.26359 −0.631794 0.775136i \(-0.717681\pi\)
−0.631794 + 0.775136i \(0.717681\pi\)
\(822\) 6.60814e58 0.116200
\(823\) −4.10799e59 −0.704584 −0.352292 0.935890i \(-0.614598\pi\)
−0.352292 + 0.935890i \(0.614598\pi\)
\(824\) −3.06332e59 −0.512490
\(825\) −1.62447e59 −0.265097
\(826\) 2.75760e59 0.438976
\(827\) 2.98123e59 0.462949 0.231474 0.972841i \(-0.425645\pi\)
0.231474 + 0.972841i \(0.425645\pi\)
\(828\) −3.03557e59 −0.459852
\(829\) 3.83752e59 0.567130 0.283565 0.958953i \(-0.408483\pi\)
0.283565 + 0.958953i \(0.408483\pi\)
\(830\) −1.32748e58 −0.0191393
\(831\) 9.84484e58 0.138480
\(832\) 1.22767e59 0.168482
\(833\) 1.90044e59 0.254467
\(834\) 1.60057e59 0.209108
\(835\) 1.39618e60 1.77980
\(836\) 3.20218e59 0.398306
\(837\) −7.70379e59 −0.935045
\(838\) −4.67219e59 −0.553373
\(839\) 9.98054e59 1.15354 0.576772 0.816905i \(-0.304312\pi\)
0.576772 + 0.816905i \(0.304312\pi\)
\(840\) 5.50016e58 0.0620369
\(841\) −8.40511e59 −0.925179
\(842\) −6.00439e59 −0.645017
\(843\) −3.38861e58 −0.0355268
\(844\) 6.07334e59 0.621452
\(845\) 1.34943e60 1.34769
\(846\) 2.26875e59 0.221154
\(847\) 2.77931e59 0.264440
\(848\) −1.20791e59 −0.112181
\(849\) 2.39020e58 0.0216684
\(850\) −4.07212e59 −0.360357
\(851\) 6.07948e59 0.525182
\(852\) −1.05619e59 −0.0890697
\(853\) −1.04133e60 −0.857302 −0.428651 0.903470i \(-0.641011\pi\)
−0.428651 + 0.903470i \(0.641011\pi\)
\(854\) −1.72526e59 −0.138666
\(855\) −2.84664e60 −2.23371
\(856\) −2.85643e59 −0.218832
\(857\) −2.22118e59 −0.166141 −0.0830705 0.996544i \(-0.526473\pi\)
−0.0830705 + 0.996544i \(0.526473\pi\)
\(858\) −2.00800e59 −0.146647
\(859\) 1.83508e60 1.30856 0.654282 0.756250i \(-0.272971\pi\)
0.654282 + 0.756250i \(0.272971\pi\)
\(860\) −2.19612e60 −1.52911
\(861\) 2.92006e59 0.198530
\(862\) −8.38409e59 −0.556618
\(863\) −2.51134e60 −1.62811 −0.814055 0.580788i \(-0.802744\pi\)
−0.814055 + 0.580788i \(0.802744\pi\)
\(864\) 1.52444e59 0.0965113
\(865\) 2.43997e60 1.50853
\(866\) 1.47866e60 0.892797
\(867\) 4.40241e59 0.259597
\(868\) 5.55802e59 0.320085
\(869\) −2.97250e59 −0.167193
\(870\) −1.65280e59 −0.0907979
\(871\) 2.04515e59 0.109737
\(872\) −6.61351e58 −0.0346613
\(873\) 7.90728e59 0.404795
\(874\) 2.08418e60 1.04220
\(875\) −9.12799e59 −0.445872
\(876\) 3.81901e59 0.182229
\(877\) 1.15614e60 0.538913 0.269457 0.963013i \(-0.413156\pi\)
0.269457 + 0.963013i \(0.413156\pi\)
\(878\) 9.94357e59 0.452798
\(879\) −6.60924e59 −0.294022
\(880\) 5.13372e59 0.223120
\(881\) −2.91398e60 −1.23732 −0.618658 0.785661i \(-0.712323\pi\)
−0.618658 + 0.785661i \(0.712323\pi\)
\(882\) 1.34767e60 0.559083
\(883\) 1.84407e60 0.747452 0.373726 0.927539i \(-0.378080\pi\)
0.373726 + 0.927539i \(0.378080\pi\)
\(884\) −5.03354e59 −0.199344
\(885\) 2.01491e60 0.779683
\(886\) −1.20717e60 −0.456433
\(887\) −4.08939e59 −0.151086 −0.0755431 0.997143i \(-0.524069\pi\)
−0.0755431 + 0.997143i \(0.524069\pi\)
\(888\) −1.46215e59 −0.0527870
\(889\) −5.91610e59 −0.208713
\(890\) 1.93427e59 0.0666840
\(891\) 1.22610e60 0.413080
\(892\) 1.32960e60 0.437765
\(893\) −1.55769e60 −0.501217
\(894\) −6.39068e59 −0.200968
\(895\) −5.71472e60 −1.75640
\(896\) −1.09983e59 −0.0330378
\(897\) −1.30693e60 −0.383714
\(898\) −1.35436e60 −0.388660
\(899\) −1.67019e60 −0.468480
\(900\) −2.88768e60 −0.791730
\(901\) 4.95254e59 0.132730
\(902\) 2.72552e60 0.714027
\(903\) −7.69540e59 −0.197075
\(904\) 1.74145e60 0.435972
\(905\) 7.80886e60 1.91114
\(906\) −7.68746e59 −0.183931
\(907\) 1.20769e60 0.282492 0.141246 0.989975i \(-0.454889\pi\)
0.141246 + 0.989975i \(0.454889\pi\)
\(908\) −1.13188e60 −0.258845
\(909\) 6.45600e59 0.144346
\(910\) −2.68912e60 −0.587843
\(911\) 5.09758e59 0.108953 0.0544763 0.998515i \(-0.482651\pi\)
0.0544763 + 0.998515i \(0.482651\pi\)
\(912\) −5.01258e59 −0.104753
\(913\) −4.34169e58 −0.00887172
\(914\) −5.97839e60 −1.19450
\(915\) −1.26060e60 −0.246290
\(916\) 2.24747e60 0.429375
\(917\) 3.25029e60 0.607227
\(918\) −6.25031e59 −0.114190
\(919\) −5.01795e60 −0.896517 −0.448259 0.893904i \(-0.647956\pi\)
−0.448259 + 0.893904i \(0.647956\pi\)
\(920\) 3.34135e60 0.583811
\(921\) 2.29038e60 0.391367
\(922\) −5.62840e60 −0.940591
\(923\) 5.16388e60 0.843998
\(924\) 1.79890e59 0.0287562
\(925\) 5.78328e60 0.904209
\(926\) 6.54787e60 1.00132
\(927\) 8.90660e60 1.33222
\(928\) 3.30499e59 0.0483545
\(929\) −3.15656e60 −0.451744 −0.225872 0.974157i \(-0.572523\pi\)
−0.225872 + 0.974157i \(0.572523\pi\)
\(930\) 4.06110e60 0.568516
\(931\) −9.25288e60 −1.26709
\(932\) 4.82072e60 0.645781
\(933\) 5.87964e59 0.0770508
\(934\) −8.94138e59 −0.114629
\(935\) −2.10486e60 −0.263989
\(936\) −3.56945e60 −0.437972
\(937\) −5.64418e60 −0.677547 −0.338773 0.940868i \(-0.610012\pi\)
−0.338773 + 0.940868i \(0.610012\pi\)
\(938\) −1.83218e59 −0.0215185
\(939\) −1.42513e60 −0.163761
\(940\) −2.49729e60 −0.280768
\(941\) −1.57154e61 −1.72877 −0.864385 0.502831i \(-0.832292\pi\)
−0.864385 + 0.502831i \(0.832292\pi\)
\(942\) 1.48537e59 0.0159879
\(943\) 1.77394e61 1.86831
\(944\) −4.02907e60 −0.415221
\(945\) −3.33916e60 −0.336733
\(946\) −7.18270e60 −0.708793
\(947\) −3.54084e60 −0.341926 −0.170963 0.985277i \(-0.554688\pi\)
−0.170963 + 0.985277i \(0.554688\pi\)
\(948\) 4.65306e59 0.0439712
\(949\) −1.86718e61 −1.72675
\(950\) 1.98264e61 1.79436
\(951\) 5.05221e60 0.447488
\(952\) 4.50938e59 0.0390895
\(953\) −3.82394e60 −0.324420 −0.162210 0.986756i \(-0.551862\pi\)
−0.162210 + 0.986756i \(0.551862\pi\)
\(954\) 3.51200e60 0.291617
\(955\) −1.75128e61 −1.42327
\(956\) 4.76459e60 0.379000
\(957\) −5.40570e59 −0.0420879
\(958\) −6.86560e60 −0.523221
\(959\) 2.89439e60 0.215912
\(960\) −8.03617e59 −0.0586798
\(961\) 2.70478e61 1.93331
\(962\) 7.14870e60 0.500193
\(963\) 8.30505e60 0.568858
\(964\) −4.37204e60 −0.293160
\(965\) 1.41641e61 0.929776
\(966\) 1.17084e60 0.0752429
\(967\) 1.08706e61 0.683930 0.341965 0.939713i \(-0.388908\pi\)
0.341965 + 0.939713i \(0.388908\pi\)
\(968\) −4.06079e60 −0.250130
\(969\) 2.05519e60 0.123941
\(970\) −8.70381e60 −0.513912
\(971\) 1.86961e61 1.08083 0.540416 0.841398i \(-0.318267\pi\)
0.540416 + 0.841398i \(0.318267\pi\)
\(972\) −6.74190e60 −0.381614
\(973\) 7.01055e60 0.388543
\(974\) −5.14582e60 −0.279252
\(975\) −1.24326e61 −0.660643
\(976\) 2.52075e60 0.131162
\(977\) −2.93813e61 −1.49704 −0.748518 0.663115i \(-0.769234\pi\)
−0.748518 + 0.663115i \(0.769234\pi\)
\(978\) −3.22462e59 −0.0160891
\(979\) 6.32627e59 0.0309103
\(980\) −1.48342e61 −0.709790
\(981\) 1.92288e60 0.0901024
\(982\) 2.78264e60 0.127694
\(983\) 2.55719e61 1.14925 0.574626 0.818416i \(-0.305148\pi\)
0.574626 + 0.818416i \(0.305148\pi\)
\(984\) −4.26644e60 −0.187787
\(985\) −2.46425e61 −1.06229
\(986\) −1.35507e60 −0.0572118
\(987\) −8.75070e59 −0.0361861
\(988\) 2.45073e61 0.992610
\(989\) −4.67496e61 −1.85461
\(990\) −1.49263e61 −0.580003
\(991\) 1.53747e61 0.585188 0.292594 0.956237i \(-0.405482\pi\)
0.292594 + 0.956237i \(0.405482\pi\)
\(992\) −8.12070e60 −0.302764
\(993\) 1.45614e61 0.531796
\(994\) −4.62615e60 −0.165500
\(995\) −4.12385e61 −1.44521
\(996\) 6.79634e58 0.00233324
\(997\) 4.42141e61 1.48700 0.743499 0.668737i \(-0.233165\pi\)
0.743499 + 0.668737i \(0.233165\pi\)
\(998\) 6.32263e59 0.0208316
\(999\) 8.87676e60 0.286525
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 \(a_p\))