Properties

Label 1.102.a.a.1.6
Level $1$
Weight $102$
Character 1.1
Self dual yes
Analytic conductor $64.601$
Analytic rank $1$
Dimension $8$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 102 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.6006978936\)
Analytic rank: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - x^{7} - \)\(15\!\cdots\!64\)\( x^{6} - \)\(13\!\cdots\!76\)\( x^{5} + \)\(79\!\cdots\!56\)\( x^{4} + \)\(16\!\cdots\!20\)\( x^{3} - \)\(12\!\cdots\!00\)\( x^{2} - \)\(46\!\cdots\!00\)\( x + \)\(14\!\cdots\!00\)\(\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: multiple of \( 2^{119}\cdot 3^{37}\cdot 5^{14}\cdot 7^{7}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-1.40661e13\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.29597e15 q^{2} -2.26314e24 q^{3} -8.55769e29 q^{4} -1.52987e35 q^{5} -2.93295e39 q^{6} -2.30272e42 q^{7} -4.39472e45 q^{8} +3.57566e48 q^{9} +O(q^{10})\) \(q+1.29597e15 q^{2} -2.26314e24 q^{3} -8.55769e29 q^{4} -1.52987e35 q^{5} -2.93295e39 q^{6} -2.30272e42 q^{7} -4.39472e45 q^{8} +3.57566e48 q^{9} -1.98266e50 q^{10} +7.37923e52 q^{11} +1.93672e54 q^{12} +1.08138e56 q^{13} -2.98425e57 q^{14} +3.46230e59 q^{15} -3.52578e60 q^{16} -7.80096e61 q^{17} +4.63394e63 q^{18} -2.75511e64 q^{19} +1.30921e65 q^{20} +5.21136e66 q^{21} +9.56325e67 q^{22} +8.02073e68 q^{23} +9.94585e69 q^{24} -1.60381e70 q^{25} +1.40143e71 q^{26} -4.59310e72 q^{27} +1.97059e72 q^{28} -4.17708e73 q^{29} +4.48703e74 q^{30} +1.32596e74 q^{31} +6.57264e75 q^{32} -1.67002e77 q^{33} -1.01098e77 q^{34} +3.52285e77 q^{35} -3.05994e78 q^{36} +7.61174e78 q^{37} -3.57054e79 q^{38} -2.44731e80 q^{39} +6.72333e80 q^{40} +4.16079e81 q^{41} +6.75376e81 q^{42} -6.23745e81 q^{43} -6.31492e82 q^{44} -5.47028e83 q^{45} +1.03946e84 q^{46} -9.39126e83 q^{47} +7.97932e84 q^{48} -1.73388e85 q^{49} -2.07849e85 q^{50} +1.76546e86 q^{51} -9.25410e85 q^{52} +1.74117e87 q^{53} -5.95250e87 q^{54} -1.12892e88 q^{55} +1.01198e88 q^{56} +6.23520e88 q^{57} -5.41336e88 q^{58} +2.25849e89 q^{59} -2.96293e89 q^{60} -2.74167e90 q^{61} +1.71840e89 q^{62} -8.23373e90 q^{63} +1.74568e91 q^{64} -1.65436e91 q^{65} -2.16429e92 q^{66} +8.52043e91 q^{67} +6.67582e91 q^{68} -1.81520e93 q^{69} +4.56550e92 q^{70} -3.72400e93 q^{71} -1.57140e94 q^{72} -2.87380e93 q^{73} +9.86457e93 q^{74} +3.62965e94 q^{75} +2.35774e94 q^{76} -1.69923e95 q^{77} -3.17163e95 q^{78} +4.49556e95 q^{79} +5.39397e95 q^{80} +4.86636e96 q^{81} +5.39225e96 q^{82} +1.36723e96 q^{83} -4.45972e96 q^{84} +1.19344e97 q^{85} -8.08353e96 q^{86} +9.45330e97 q^{87} -3.24296e98 q^{88} +2.37256e98 q^{89} -7.08930e98 q^{90} -2.49011e98 q^{91} -6.86390e98 q^{92} -3.00083e98 q^{93} -1.21708e99 q^{94} +4.21495e99 q^{95} -1.48748e100 q^{96} -7.96305e99 q^{97} -2.24706e100 q^{98} +2.63856e101 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 434989091795040q^{2} - \)\(12\!\cdots\!60\)\(q^{3} + \)\(90\!\cdots\!96\)\(q^{4} + \)\(38\!\cdots\!00\)\(q^{5} + \)\(24\!\cdots\!36\)\(q^{6} - \)\(57\!\cdots\!00\)\(q^{7} - \)\(61\!\cdots\!20\)\(q^{8} + \)\(52\!\cdots\!84\)\(q^{9} + O(q^{10}) \) \( 8q - 434989091795040q^{2} - \)\(12\!\cdots\!60\)\(q^{3} + \)\(90\!\cdots\!96\)\(q^{4} + \)\(38\!\cdots\!00\)\(q^{5} + \)\(24\!\cdots\!36\)\(q^{6} - \)\(57\!\cdots\!00\)\(q^{7} - \)\(61\!\cdots\!20\)\(q^{8} + \)\(52\!\cdots\!84\)\(q^{9} - \)\(37\!\cdots\!00\)\(q^{10} + \)\(46\!\cdots\!96\)\(q^{11} - \)\(72\!\cdots\!80\)\(q^{12} + \)\(25\!\cdots\!80\)\(q^{13} - \)\(48\!\cdots\!88\)\(q^{14} - \)\(29\!\cdots\!00\)\(q^{15} - \)\(10\!\cdots\!72\)\(q^{16} - \)\(39\!\cdots\!20\)\(q^{17} - \)\(72\!\cdots\!60\)\(q^{18} - \)\(21\!\cdots\!80\)\(q^{19} + \)\(17\!\cdots\!00\)\(q^{20} + \)\(40\!\cdots\!36\)\(q^{21} + \)\(61\!\cdots\!20\)\(q^{22} - \)\(13\!\cdots\!80\)\(q^{23} + \)\(10\!\cdots\!60\)\(q^{24} + \)\(77\!\cdots\!00\)\(q^{25} - \)\(97\!\cdots\!44\)\(q^{26} - \)\(59\!\cdots\!20\)\(q^{27} + \)\(92\!\cdots\!80\)\(q^{28} + \)\(15\!\cdots\!80\)\(q^{29} + \)\(11\!\cdots\!00\)\(q^{30} - \)\(65\!\cdots\!44\)\(q^{31} + \)\(12\!\cdots\!60\)\(q^{32} + \)\(43\!\cdots\!80\)\(q^{33} + \)\(95\!\cdots\!12\)\(q^{34} - \)\(11\!\cdots\!00\)\(q^{35} + \)\(19\!\cdots\!08\)\(q^{36} + \)\(39\!\cdots\!40\)\(q^{37} - \)\(70\!\cdots\!80\)\(q^{38} - \)\(26\!\cdots\!32\)\(q^{39} - \)\(76\!\cdots\!00\)\(q^{40} + \)\(56\!\cdots\!36\)\(q^{41} + \)\(30\!\cdots\!80\)\(q^{42} - \)\(28\!\cdots\!00\)\(q^{43} - \)\(20\!\cdots\!48\)\(q^{44} + \)\(71\!\cdots\!00\)\(q^{45} + \)\(10\!\cdots\!76\)\(q^{46} - \)\(45\!\cdots\!80\)\(q^{47} - \)\(58\!\cdots\!80\)\(q^{48} + \)\(12\!\cdots\!56\)\(q^{49} - \)\(40\!\cdots\!00\)\(q^{50} + \)\(11\!\cdots\!36\)\(q^{51} - \)\(73\!\cdots\!00\)\(q^{52} + \)\(13\!\cdots\!40\)\(q^{53} + \)\(68\!\cdots\!20\)\(q^{54} - \)\(14\!\cdots\!00\)\(q^{55} - \)\(23\!\cdots\!80\)\(q^{56} - \)\(66\!\cdots\!40\)\(q^{57} + \)\(29\!\cdots\!80\)\(q^{58} + \)\(21\!\cdots\!60\)\(q^{59} - \)\(34\!\cdots\!00\)\(q^{60} - \)\(33\!\cdots\!04\)\(q^{61} - \)\(58\!\cdots\!80\)\(q^{62} - \)\(20\!\cdots\!40\)\(q^{63} - \)\(74\!\cdots\!04\)\(q^{64} - \)\(16\!\cdots\!00\)\(q^{65} - \)\(74\!\cdots\!68\)\(q^{66} - \)\(61\!\cdots\!20\)\(q^{67} - \)\(21\!\cdots\!60\)\(q^{68} - \)\(53\!\cdots\!72\)\(q^{69} - \)\(12\!\cdots\!00\)\(q^{70} - \)\(15\!\cdots\!24\)\(q^{71} - \)\(55\!\cdots\!60\)\(q^{72} - \)\(20\!\cdots\!80\)\(q^{73} - \)\(14\!\cdots\!88\)\(q^{74} - \)\(20\!\cdots\!00\)\(q^{75} + \)\(64\!\cdots\!40\)\(q^{76} + \)\(25\!\cdots\!00\)\(q^{77} + \)\(12\!\cdots\!00\)\(q^{78} + \)\(14\!\cdots\!80\)\(q^{79} + \)\(60\!\cdots\!00\)\(q^{80} + \)\(14\!\cdots\!08\)\(q^{81} + \)\(30\!\cdots\!20\)\(q^{82} + \)\(33\!\cdots\!60\)\(q^{83} + \)\(57\!\cdots\!32\)\(q^{84} + \)\(17\!\cdots\!00\)\(q^{85} + \)\(67\!\cdots\!16\)\(q^{86} + \)\(25\!\cdots\!40\)\(q^{87} - \)\(36\!\cdots\!40\)\(q^{88} - \)\(62\!\cdots\!60\)\(q^{89} - \)\(47\!\cdots\!00\)\(q^{90} - \)\(36\!\cdots\!44\)\(q^{91} - \)\(46\!\cdots\!20\)\(q^{92} - \)\(39\!\cdots\!20\)\(q^{93} - \)\(17\!\cdots\!88\)\(q^{94} - \)\(26\!\cdots\!00\)\(q^{95} + \)\(46\!\cdots\!56\)\(q^{96} + \)\(64\!\cdots\!20\)\(q^{97} + \)\(20\!\cdots\!20\)\(q^{98} + \)\(22\!\cdots\!08\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.29597e15 0.813916 0.406958 0.913447i \(-0.366590\pi\)
0.406958 + 0.913447i \(0.366590\pi\)
\(3\) −2.26314e24 −1.82007 −0.910034 0.414534i \(-0.863945\pi\)
−0.910034 + 0.414534i \(0.863945\pi\)
\(4\) −8.55769e29 −0.337541
\(5\) −1.52987e35 −0.770315 −0.385157 0.922851i \(-0.625853\pi\)
−0.385157 + 0.922851i \(0.625853\pi\)
\(6\) −2.93295e39 −1.48138
\(7\) −2.30272e42 −0.483938 −0.241969 0.970284i \(-0.577793\pi\)
−0.241969 + 0.970284i \(0.577793\pi\)
\(8\) −4.39472e45 −1.08865
\(9\) 3.57566e48 2.31265
\(10\) −1.98266e50 −0.626971
\(11\) 7.37923e52 1.89531 0.947656 0.319293i \(-0.103446\pi\)
0.947656 + 0.319293i \(0.103446\pi\)
\(12\) 1.93672e54 0.614348
\(13\) 1.08138e56 0.602335 0.301167 0.953571i \(-0.402624\pi\)
0.301167 + 0.953571i \(0.402624\pi\)
\(14\) −2.98425e57 −0.393884
\(15\) 3.46230e59 1.40203
\(16\) −3.52578e60 −0.548524
\(17\) −7.80096e61 −0.568169 −0.284084 0.958799i \(-0.591690\pi\)
−0.284084 + 0.958799i \(0.591690\pi\)
\(18\) 4.63394e63 1.88230
\(19\) −2.75511e64 −0.729596 −0.364798 0.931087i \(-0.618862\pi\)
−0.364798 + 0.931087i \(0.618862\pi\)
\(20\) 1.30921e65 0.260013
\(21\) 5.21136e66 0.880799
\(22\) 9.56325e67 1.54262
\(23\) 8.02073e68 1.37075 0.685375 0.728190i \(-0.259638\pi\)
0.685375 + 0.728190i \(0.259638\pi\)
\(24\) 9.94585e69 1.98141
\(25\) −1.60381e70 −0.406615
\(26\) 1.40143e71 0.490250
\(27\) −4.59310e72 −2.38911
\(28\) 1.97059e72 0.163349
\(29\) −4.17708e73 −0.588537 −0.294268 0.955723i \(-0.595076\pi\)
−0.294268 + 0.955723i \(0.595076\pi\)
\(30\) 4.48703e74 1.14113
\(31\) 1.32596e74 0.0643821 0.0321910 0.999482i \(-0.489752\pi\)
0.0321910 + 0.999482i \(0.489752\pi\)
\(32\) 6.57264e75 0.642193
\(33\) −1.67002e77 −3.44960
\(34\) −1.01098e77 −0.462441
\(35\) 3.52285e77 0.372784
\(36\) −3.05994e78 −0.780614
\(37\) 7.61174e78 0.486740 0.243370 0.969934i \(-0.421747\pi\)
0.243370 + 0.969934i \(0.421747\pi\)
\(38\) −3.57054e79 −0.593830
\(39\) −2.44731e80 −1.09629
\(40\) 6.72333e80 0.838600
\(41\) 4.16079e81 1.49139 0.745694 0.666288i \(-0.232118\pi\)
0.745694 + 0.666288i \(0.232118\pi\)
\(42\) 6.75376e81 0.716896
\(43\) −6.23745e81 −0.201767 −0.100883 0.994898i \(-0.532167\pi\)
−0.100883 + 0.994898i \(0.532167\pi\)
\(44\) −6.31492e82 −0.639746
\(45\) −5.47028e83 −1.78147
\(46\) 1.03946e84 1.11568
\(47\) −9.39126e83 −0.340237 −0.170119 0.985424i \(-0.554415\pi\)
−0.170119 + 0.985424i \(0.554415\pi\)
\(48\) 7.97932e84 0.998351
\(49\) −1.73388e85 −0.765804
\(50\) −2.07849e85 −0.330950
\(51\) 1.76546e86 1.03411
\(52\) −9.25410e85 −0.203313
\(53\) 1.74117e87 1.46187 0.730935 0.682447i \(-0.239084\pi\)
0.730935 + 0.682447i \(0.239084\pi\)
\(54\) −5.95250e87 −1.94453
\(55\) −1.12892e88 −1.45999
\(56\) 1.01198e88 0.526837
\(57\) 6.23520e88 1.32791
\(58\) −5.41336e88 −0.479019
\(59\) 2.25849e89 0.842930 0.421465 0.906845i \(-0.361516\pi\)
0.421465 + 0.906845i \(0.361516\pi\)
\(60\) −2.96293e89 −0.473242
\(61\) −2.74167e90 −1.90046 −0.950229 0.311553i \(-0.899151\pi\)
−0.950229 + 0.311553i \(0.899151\pi\)
\(62\) 1.71840e89 0.0524016
\(63\) −8.23373e90 −1.11918
\(64\) 1.74568e91 1.07122
\(65\) −1.65436e91 −0.463988
\(66\) −2.16429e92 −2.80768
\(67\) 8.52043e91 0.517230 0.258615 0.965980i \(-0.416734\pi\)
0.258615 + 0.965980i \(0.416734\pi\)
\(68\) 6.67582e91 0.191780
\(69\) −1.81520e93 −2.49486
\(70\) 4.56550e92 0.303415
\(71\) −3.72400e93 −1.20910 −0.604551 0.796566i \(-0.706648\pi\)
−0.604551 + 0.796566i \(0.706648\pi\)
\(72\) −1.57140e94 −2.51765
\(73\) −2.87380e93 −0.229431 −0.114715 0.993398i \(-0.536596\pi\)
−0.114715 + 0.993398i \(0.536596\pi\)
\(74\) 9.86457e93 0.396165
\(75\) 3.62965e94 0.740067
\(76\) 2.35774e94 0.246269
\(77\) −1.69923e95 −0.917213
\(78\) −3.17163e95 −0.892288
\(79\) 4.49556e95 0.664685 0.332343 0.943159i \(-0.392161\pi\)
0.332343 + 0.943159i \(0.392161\pi\)
\(80\) 5.39397e95 0.422536
\(81\) 4.86636e96 2.03569
\(82\) 5.39225e96 1.21386
\(83\) 1.36723e96 0.166877 0.0834386 0.996513i \(-0.473410\pi\)
0.0834386 + 0.996513i \(0.473410\pi\)
\(84\) −4.45972e96 −0.297306
\(85\) 1.19344e97 0.437669
\(86\) −8.08353e96 −0.164221
\(87\) 9.45330e97 1.07118
\(88\) −3.24296e98 −2.06332
\(89\) 2.37256e98 0.853143 0.426571 0.904454i \(-0.359721\pi\)
0.426571 + 0.904454i \(0.359721\pi\)
\(90\) −7.08930e98 −1.44996
\(91\) −2.49011e98 −0.291493
\(92\) −6.86390e98 −0.462685
\(93\) −3.00083e98 −0.117180
\(94\) −1.21708e99 −0.276924
\(95\) 4.21495e99 0.562019
\(96\) −1.48748e100 −1.16884
\(97\) −7.96305e99 −0.370772 −0.185386 0.982666i \(-0.559354\pi\)
−0.185386 + 0.982666i \(0.559354\pi\)
\(98\) −2.24706e100 −0.623300
\(99\) 2.63856e101 4.38319
\(100\) 1.37249e100 0.137249
\(101\) −7.62399e100 −0.461268 −0.230634 0.973041i \(-0.574080\pi\)
−0.230634 + 0.973041i \(0.574080\pi\)
\(102\) 2.28798e101 0.841675
\(103\) −3.82780e101 −0.860339 −0.430169 0.902748i \(-0.641546\pi\)
−0.430169 + 0.902748i \(0.641546\pi\)
\(104\) −4.75235e101 −0.655729
\(105\) −7.97269e101 −0.678493
\(106\) 2.25649e102 1.18984
\(107\) −2.91169e102 −0.955576 −0.477788 0.878475i \(-0.658561\pi\)
−0.477788 + 0.878475i \(0.658561\pi\)
\(108\) 3.93063e102 0.806422
\(109\) −8.50797e102 −1.09594 −0.547971 0.836497i \(-0.684600\pi\)
−0.547971 + 0.836497i \(0.684600\pi\)
\(110\) −1.46305e103 −1.18831
\(111\) −1.72264e103 −0.885899
\(112\) 8.11887e102 0.265452
\(113\) 5.83476e103 1.21776 0.608880 0.793262i \(-0.291619\pi\)
0.608880 + 0.793262i \(0.291619\pi\)
\(114\) 8.08061e103 1.08081
\(115\) −1.22707e104 −1.05591
\(116\) 3.57461e103 0.198656
\(117\) 3.86664e104 1.39299
\(118\) 2.92693e104 0.686074
\(119\) 1.79634e104 0.274958
\(120\) −1.52158e105 −1.52631
\(121\) 3.92944e105 2.59221
\(122\) −3.55311e105 −1.54681
\(123\) −9.41643e105 −2.71443
\(124\) −1.13472e104 −0.0217316
\(125\) 8.48788e105 1.08354
\(126\) −1.06706e106 −0.910915
\(127\) 9.46785e105 0.542205 0.271102 0.962551i \(-0.412612\pi\)
0.271102 + 0.962551i \(0.412612\pi\)
\(128\) 5.95988e105 0.229686
\(129\) 1.41162e106 0.367230
\(130\) −2.14400e106 −0.377647
\(131\) −9.25172e106 −1.10668 −0.553340 0.832955i \(-0.686647\pi\)
−0.553340 + 0.832955i \(0.686647\pi\)
\(132\) 1.42915e107 1.16438
\(133\) 6.34424e106 0.353079
\(134\) 1.10422e107 0.420982
\(135\) 7.02682e107 1.84036
\(136\) 3.42830e107 0.618534
\(137\) −5.67560e107 −0.707331 −0.353666 0.935372i \(-0.615065\pi\)
−0.353666 + 0.935372i \(0.615065\pi\)
\(138\) −2.35244e108 −2.03060
\(139\) −1.48585e108 −0.890690 −0.445345 0.895359i \(-0.646919\pi\)
−0.445345 + 0.895359i \(0.646919\pi\)
\(140\) −3.01474e107 −0.125830
\(141\) 2.12537e108 0.619255
\(142\) −4.82618e108 −0.984107
\(143\) 7.97974e108 1.14161
\(144\) −1.26070e109 −1.26854
\(145\) 6.39037e108 0.453359
\(146\) −3.72435e108 −0.186737
\(147\) 3.92402e109 1.39382
\(148\) −6.51389e108 −0.164295
\(149\) 2.67615e109 0.480400 0.240200 0.970723i \(-0.422787\pi\)
0.240200 + 0.970723i \(0.422787\pi\)
\(150\) 4.70391e109 0.602352
\(151\) −1.18193e109 −0.108207 −0.0541037 0.998535i \(-0.517230\pi\)
−0.0541037 + 0.998535i \(0.517230\pi\)
\(152\) 1.21079e110 0.794272
\(153\) −2.78936e110 −1.31397
\(154\) −2.20214e110 −0.746534
\(155\) −2.02854e109 −0.0495945
\(156\) 2.09433e110 0.370043
\(157\) 4.49535e110 0.575216 0.287608 0.957748i \(-0.407140\pi\)
0.287608 + 0.957748i \(0.407140\pi\)
\(158\) 5.82611e110 0.540998
\(159\) −3.94050e111 −2.66070
\(160\) −1.00553e111 −0.494691
\(161\) −1.84695e111 −0.663358
\(162\) 6.30665e111 1.65688
\(163\) 2.42594e111 0.467097 0.233548 0.972345i \(-0.424966\pi\)
0.233548 + 0.972345i \(0.424966\pi\)
\(164\) −3.56067e111 −0.503405
\(165\) 2.55491e112 2.65728
\(166\) 1.77188e111 0.135824
\(167\) 5.27032e111 0.298302 0.149151 0.988814i \(-0.452346\pi\)
0.149151 + 0.988814i \(0.452346\pi\)
\(168\) −2.29025e112 −0.958878
\(169\) −2.05376e112 −0.637193
\(170\) 1.54666e112 0.356225
\(171\) −9.85134e112 −1.68730
\(172\) 5.33782e111 0.0681047
\(173\) 2.18981e112 0.208486 0.104243 0.994552i \(-0.466758\pi\)
0.104243 + 0.994552i \(0.466758\pi\)
\(174\) 1.22512e113 0.871848
\(175\) 3.69313e112 0.196776
\(176\) −2.60175e113 −1.03962
\(177\) −5.11127e113 −1.53419
\(178\) 3.07476e113 0.694386
\(179\) 4.11936e113 0.701055 0.350527 0.936553i \(-0.386002\pi\)
0.350527 + 0.936553i \(0.386002\pi\)
\(180\) 4.68130e113 0.601319
\(181\) −3.60610e113 −0.350163 −0.175081 0.984554i \(-0.556019\pi\)
−0.175081 + 0.984554i \(0.556019\pi\)
\(182\) −3.22710e113 −0.237250
\(183\) 6.20477e114 3.45896
\(184\) −3.52489e114 −1.49226
\(185\) −1.16449e114 −0.374943
\(186\) −3.88898e113 −0.0953744
\(187\) −5.75651e114 −1.07686
\(188\) 8.03675e113 0.114844
\(189\) 1.05766e115 1.15618
\(190\) 5.46244e114 0.457436
\(191\) −3.07102e115 −1.97286 −0.986432 0.164171i \(-0.947505\pi\)
−0.986432 + 0.164171i \(0.947505\pi\)
\(192\) −3.95072e115 −1.94968
\(193\) 2.25699e115 0.856811 0.428406 0.903587i \(-0.359075\pi\)
0.428406 + 0.903587i \(0.359075\pi\)
\(194\) −1.03199e115 −0.301777
\(195\) 3.74405e115 0.844489
\(196\) 1.48380e115 0.258491
\(197\) −2.88844e115 −0.389152 −0.194576 0.980887i \(-0.562333\pi\)
−0.194576 + 0.980887i \(0.562333\pi\)
\(198\) 3.41949e116 3.56754
\(199\) −1.43998e116 −1.16486 −0.582432 0.812880i \(-0.697899\pi\)
−0.582432 + 0.812880i \(0.697899\pi\)
\(200\) 7.04831e115 0.442660
\(201\) −1.92829e116 −0.941394
\(202\) −9.88045e115 −0.375433
\(203\) 9.61862e115 0.284815
\(204\) −1.51083e116 −0.349053
\(205\) −6.36545e116 −1.14884
\(206\) −4.96070e116 −0.700243
\(207\) 2.86794e117 3.17006
\(208\) −3.81270e116 −0.330395
\(209\) −2.03306e117 −1.38281
\(210\) −1.03323e117 −0.552236
\(211\) −3.37109e117 −1.41744 −0.708722 0.705488i \(-0.750728\pi\)
−0.708722 + 0.705488i \(0.750728\pi\)
\(212\) −1.49004e117 −0.493442
\(213\) 8.42792e117 2.20065
\(214\) −3.77346e117 −0.777758
\(215\) 9.54246e116 0.155424
\(216\) 2.01854e118 2.60089
\(217\) −3.05331e116 −0.0311569
\(218\) −1.10260e118 −0.892004
\(219\) 6.50380e117 0.417580
\(220\) 9.66099e117 0.492806
\(221\) −8.43578e117 −0.342228
\(222\) −2.23249e118 −0.721047
\(223\) −2.91997e118 −0.751594 −0.375797 0.926702i \(-0.622631\pi\)
−0.375797 + 0.926702i \(0.622631\pi\)
\(224\) −1.51349e118 −0.310781
\(225\) −5.73469e118 −0.940357
\(226\) 7.56166e118 0.991154
\(227\) 4.57961e118 0.480311 0.240155 0.970734i \(-0.422802\pi\)
0.240155 + 0.970734i \(0.422802\pi\)
\(228\) −5.33589e118 −0.448226
\(229\) −1.61593e119 −1.08825 −0.544127 0.839003i \(-0.683139\pi\)
−0.544127 + 0.839003i \(0.683139\pi\)
\(230\) −1.59024e119 −0.859421
\(231\) 3.84559e119 1.66939
\(232\) 1.83571e119 0.640708
\(233\) 1.44890e119 0.406972 0.203486 0.979078i \(-0.434773\pi\)
0.203486 + 0.979078i \(0.434773\pi\)
\(234\) 5.01104e119 1.13377
\(235\) 1.43674e119 0.262090
\(236\) −1.93275e119 −0.284524
\(237\) −1.01741e120 −1.20977
\(238\) 2.32800e119 0.223793
\(239\) −5.74092e118 −0.0446568 −0.0223284 0.999751i \(-0.507108\pi\)
−0.0223284 + 0.999751i \(0.507108\pi\)
\(240\) −1.22073e120 −0.769045
\(241\) −1.31918e120 −0.673666 −0.336833 0.941564i \(-0.609356\pi\)
−0.336833 + 0.941564i \(0.609356\pi\)
\(242\) 5.09243e120 2.10984
\(243\) −3.91172e120 −1.31598
\(244\) 2.34623e120 0.641483
\(245\) 2.65261e120 0.589911
\(246\) −1.22034e121 −2.20932
\(247\) −2.97932e120 −0.439461
\(248\) −5.82722e119 −0.0700893
\(249\) −3.09422e120 −0.303728
\(250\) 1.10000e121 0.881907
\(251\) 8.00520e120 0.524625 0.262313 0.964983i \(-0.415515\pi\)
0.262313 + 0.964983i \(0.415515\pi\)
\(252\) 7.04617e120 0.377768
\(253\) 5.91869e121 2.59800
\(254\) 1.22700e121 0.441309
\(255\) −2.70092e121 −0.796587
\(256\) −3.65345e121 −0.884271
\(257\) −5.16612e121 −1.02693 −0.513466 0.858110i \(-0.671639\pi\)
−0.513466 + 0.858110i \(0.671639\pi\)
\(258\) 1.82941e121 0.298894
\(259\) −1.75277e121 −0.235552
\(260\) 1.41575e121 0.156615
\(261\) −1.49358e122 −1.36108
\(262\) −1.19899e122 −0.900744
\(263\) −1.02351e122 −0.634347 −0.317174 0.948368i \(-0.602734\pi\)
−0.317174 + 0.948368i \(0.602734\pi\)
\(264\) 7.33927e122 3.75539
\(265\) −2.66375e122 −1.12610
\(266\) 8.22193e121 0.287376
\(267\) −5.36943e122 −1.55278
\(268\) −7.29152e121 −0.174587
\(269\) 5.17382e121 0.102641 0.0513205 0.998682i \(-0.483657\pi\)
0.0513205 + 0.998682i \(0.483657\pi\)
\(270\) 9.10653e122 1.49790
\(271\) 4.55314e122 0.621387 0.310693 0.950510i \(-0.399439\pi\)
0.310693 + 0.950510i \(0.399439\pi\)
\(272\) 2.75044e122 0.311654
\(273\) 5.63545e122 0.530536
\(274\) −7.35539e122 −0.575708
\(275\) −1.18349e123 −0.770662
\(276\) 1.55339e123 0.842118
\(277\) −1.61307e123 −0.728490 −0.364245 0.931303i \(-0.618673\pi\)
−0.364245 + 0.931303i \(0.618673\pi\)
\(278\) −1.92561e123 −0.724946
\(279\) 4.74118e122 0.148893
\(280\) −1.54819e123 −0.405830
\(281\) 1.39882e123 0.306263 0.153131 0.988206i \(-0.451064\pi\)
0.153131 + 0.988206i \(0.451064\pi\)
\(282\) 2.75441e123 0.504021
\(283\) −8.50004e123 −1.30079 −0.650394 0.759597i \(-0.725396\pi\)
−0.650394 + 0.759597i \(0.725396\pi\)
\(284\) 3.18688e123 0.408122
\(285\) −9.53902e123 −1.02291
\(286\) 1.03415e124 0.929176
\(287\) −9.58111e123 −0.721739
\(288\) 2.35015e124 1.48517
\(289\) −1.27658e124 −0.677184
\(290\) 8.28171e123 0.368996
\(291\) 1.80215e124 0.674830
\(292\) 2.45931e123 0.0774425
\(293\) 6.76033e124 1.79124 0.895619 0.444822i \(-0.146733\pi\)
0.895619 + 0.444822i \(0.146733\pi\)
\(294\) 5.08540e124 1.13445
\(295\) −3.45519e124 −0.649322
\(296\) −3.34514e124 −0.529887
\(297\) −3.38935e125 −4.52810
\(298\) 3.46820e124 0.391005
\(299\) 8.67344e124 0.825651
\(300\) −3.10614e124 −0.249803
\(301\) 1.43631e124 0.0976426
\(302\) −1.53175e124 −0.0880717
\(303\) 1.72541e125 0.839539
\(304\) 9.71392e124 0.400201
\(305\) 4.19438e125 1.46395
\(306\) −3.61491e125 −1.06946
\(307\) −6.79538e125 −1.70500 −0.852502 0.522723i \(-0.824916\pi\)
−0.852502 + 0.522723i \(0.824916\pi\)
\(308\) 1.45415e125 0.309597
\(309\) 8.66284e125 1.56587
\(310\) −2.62892e124 −0.0403657
\(311\) −5.79067e125 −0.755665 −0.377832 0.925874i \(-0.623330\pi\)
−0.377832 + 0.925874i \(0.623330\pi\)
\(312\) 1.07552e126 1.19347
\(313\) −4.76409e125 −0.449770 −0.224885 0.974385i \(-0.572201\pi\)
−0.224885 + 0.974385i \(0.572201\pi\)
\(314\) 5.82583e125 0.468177
\(315\) 1.25965e126 0.862118
\(316\) −3.84717e125 −0.224359
\(317\) 8.81971e125 0.438492 0.219246 0.975670i \(-0.429640\pi\)
0.219246 + 0.975670i \(0.429640\pi\)
\(318\) −5.10676e126 −2.16559
\(319\) −3.08236e126 −1.11546
\(320\) −2.67066e126 −0.825173
\(321\) 6.58956e126 1.73921
\(322\) −2.39358e126 −0.539917
\(323\) 2.14925e126 0.414534
\(324\) −4.16448e126 −0.687129
\(325\) −1.73433e126 −0.244918
\(326\) 3.14394e126 0.380177
\(327\) 1.92547e127 1.99469
\(328\) −1.82855e127 −1.62359
\(329\) 2.16254e126 0.164654
\(330\) 3.31108e127 2.16280
\(331\) −2.21975e127 −1.24449 −0.622244 0.782823i \(-0.713779\pi\)
−0.622244 + 0.782823i \(0.713779\pi\)
\(332\) −1.17003e126 −0.0563280
\(333\) 2.72170e127 1.12566
\(334\) 6.83017e126 0.242792
\(335\) −1.30351e127 −0.398430
\(336\) −1.83741e127 −0.483140
\(337\) 2.66317e127 0.602684 0.301342 0.953516i \(-0.402565\pi\)
0.301342 + 0.953516i \(0.402565\pi\)
\(338\) −2.66160e127 −0.518621
\(339\) −1.32049e128 −2.21641
\(340\) −1.02131e127 −0.147731
\(341\) 9.78457e126 0.122024
\(342\) −1.27670e128 −1.37332
\(343\) 9.20630e127 0.854539
\(344\) 2.74118e127 0.219653
\(345\) 2.77702e128 1.92183
\(346\) 2.83792e127 0.169690
\(347\) 1.75162e128 0.905317 0.452658 0.891684i \(-0.350476\pi\)
0.452658 + 0.891684i \(0.350476\pi\)
\(348\) −8.08984e127 −0.361567
\(349\) −2.08861e128 −0.807559 −0.403780 0.914856i \(-0.632304\pi\)
−0.403780 + 0.914856i \(0.632304\pi\)
\(350\) 4.78617e127 0.160159
\(351\) −4.96687e128 −1.43904
\(352\) 4.85010e128 1.21716
\(353\) 5.13773e128 1.11725 0.558623 0.829422i \(-0.311330\pi\)
0.558623 + 0.829422i \(0.311330\pi\)
\(354\) −6.62404e128 −1.24870
\(355\) 5.69722e128 0.931390
\(356\) −2.03036e128 −0.287971
\(357\) −4.06536e128 −0.500443
\(358\) 5.33856e128 0.570599
\(359\) −7.54531e128 −0.700499 −0.350250 0.936656i \(-0.613903\pi\)
−0.350250 + 0.936656i \(0.613903\pi\)
\(360\) 2.40403e129 1.93939
\(361\) −6.66916e128 −0.467690
\(362\) −4.67339e128 −0.285003
\(363\) −8.89287e129 −4.71799
\(364\) 2.13096e128 0.0983908
\(365\) 4.39653e128 0.176734
\(366\) 8.04118e129 2.81530
\(367\) −2.00122e129 −0.610463 −0.305231 0.952278i \(-0.598734\pi\)
−0.305231 + 0.952278i \(0.598734\pi\)
\(368\) −2.82793e129 −0.751890
\(369\) 1.48776e130 3.44905
\(370\) −1.50915e129 −0.305172
\(371\) −4.00941e129 −0.707454
\(372\) 2.56802e128 0.0395530
\(373\) 1.38653e130 1.86480 0.932400 0.361428i \(-0.117711\pi\)
0.932400 + 0.361428i \(0.117711\pi\)
\(374\) −7.46025e129 −0.876471
\(375\) −1.92092e130 −1.97211
\(376\) 4.12719e129 0.370398
\(377\) −4.51700e129 −0.354496
\(378\) 1.37069e130 0.941031
\(379\) 1.21170e130 0.727971 0.363986 0.931405i \(-0.381416\pi\)
0.363986 + 0.931405i \(0.381416\pi\)
\(380\) −3.60703e129 −0.189705
\(381\) −2.14270e130 −0.986849
\(382\) −3.97994e130 −1.60574
\(383\) −3.71125e129 −0.131215 −0.0656073 0.997846i \(-0.520898\pi\)
−0.0656073 + 0.997846i \(0.520898\pi\)
\(384\) −1.34880e130 −0.418043
\(385\) 2.59959e130 0.706543
\(386\) 2.92498e130 0.697372
\(387\) −2.23030e130 −0.466616
\(388\) 6.81453e129 0.125151
\(389\) 2.40999e130 0.388651 0.194325 0.980937i \(-0.437748\pi\)
0.194325 + 0.980937i \(0.437748\pi\)
\(390\) 4.85217e130 0.687343
\(391\) −6.25694e130 −0.778817
\(392\) 7.61993e130 0.833690
\(393\) 2.09379e131 2.01423
\(394\) −3.74333e130 −0.316737
\(395\) −6.87761e130 −0.512017
\(396\) −2.25800e131 −1.47951
\(397\) 1.41143e131 0.814216 0.407108 0.913380i \(-0.366537\pi\)
0.407108 + 0.913380i \(0.366537\pi\)
\(398\) −1.86616e131 −0.948100
\(399\) −1.43579e131 −0.642628
\(400\) 5.65469e130 0.223038
\(401\) 5.27775e131 1.83509 0.917546 0.397629i \(-0.130167\pi\)
0.917546 + 0.397629i \(0.130167\pi\)
\(402\) −2.49900e131 −0.766215
\(403\) 1.43386e130 0.0387796
\(404\) 6.52438e130 0.155697
\(405\) −7.44489e131 −1.56812
\(406\) 1.24654e131 0.231815
\(407\) 5.61688e131 0.922524
\(408\) −7.75871e131 −1.12577
\(409\) −6.90731e131 −0.885690 −0.442845 0.896598i \(-0.646031\pi\)
−0.442845 + 0.896598i \(0.646031\pi\)
\(410\) −8.24942e131 −0.935058
\(411\) 1.28447e132 1.28739
\(412\) 3.27571e131 0.290400
\(413\) −5.20066e131 −0.407926
\(414\) 3.71676e132 2.58016
\(415\) −2.09167e131 −0.128548
\(416\) 7.10750e131 0.386815
\(417\) 3.36268e132 1.62112
\(418\) −2.63478e132 −1.12549
\(419\) 1.10295e132 0.417589 0.208795 0.977960i \(-0.433046\pi\)
0.208795 + 0.977960i \(0.433046\pi\)
\(420\) 6.82278e131 0.229019
\(421\) −5.00940e132 −1.49122 −0.745608 0.666385i \(-0.767841\pi\)
−0.745608 + 0.666385i \(0.767841\pi\)
\(422\) −4.36882e132 −1.15368
\(423\) −3.35799e132 −0.786849
\(424\) −7.65193e132 −1.59146
\(425\) 1.25113e132 0.231026
\(426\) 1.09223e133 1.79114
\(427\) 6.31328e132 0.919703
\(428\) 2.49174e132 0.322546
\(429\) −1.80592e133 −2.07781
\(430\) 1.23667e132 0.126502
\(431\) −3.12141e132 −0.283954 −0.141977 0.989870i \(-0.545346\pi\)
−0.141977 + 0.989870i \(0.545346\pi\)
\(432\) 1.61942e133 1.31048
\(433\) 1.09298e133 0.787000 0.393500 0.919325i \(-0.371264\pi\)
0.393500 + 0.919325i \(0.371264\pi\)
\(434\) −3.95699e131 −0.0253591
\(435\) −1.44623e133 −0.825144
\(436\) 7.28085e132 0.369926
\(437\) −2.20980e133 −1.00009
\(438\) 8.42872e132 0.339875
\(439\) 4.51566e133 1.62279 0.811396 0.584497i \(-0.198708\pi\)
0.811396 + 0.584497i \(0.198708\pi\)
\(440\) 4.96130e133 1.58941
\(441\) −6.19977e133 −1.77104
\(442\) −1.09325e133 −0.278545
\(443\) 2.94289e133 0.668938 0.334469 0.942407i \(-0.391443\pi\)
0.334469 + 0.942407i \(0.391443\pi\)
\(444\) 1.47418e133 0.299028
\(445\) −3.62970e133 −0.657188
\(446\) −3.78419e133 −0.611734
\(447\) −6.05649e133 −0.874361
\(448\) −4.01981e133 −0.518401
\(449\) −6.58528e133 −0.758812 −0.379406 0.925230i \(-0.623872\pi\)
−0.379406 + 0.925230i \(0.623872\pi\)
\(450\) −7.43197e133 −0.765371
\(451\) 3.07034e134 2.82665
\(452\) −4.99321e133 −0.411045
\(453\) 2.67488e133 0.196945
\(454\) 5.93502e133 0.390932
\(455\) 3.80953e133 0.224541
\(456\) −2.74019e134 −1.44563
\(457\) −1.30627e134 −0.616971 −0.308486 0.951229i \(-0.599822\pi\)
−0.308486 + 0.951229i \(0.599822\pi\)
\(458\) −2.09419e134 −0.885747
\(459\) 3.58305e134 1.35742
\(460\) 1.05008e134 0.356413
\(461\) 5.34670e134 1.62626 0.813129 0.582084i \(-0.197763\pi\)
0.813129 + 0.582084i \(0.197763\pi\)
\(462\) 4.98376e134 1.35874
\(463\) −3.58951e134 −0.877396 −0.438698 0.898635i \(-0.644560\pi\)
−0.438698 + 0.898635i \(0.644560\pi\)
\(464\) 1.47275e134 0.322827
\(465\) 4.59087e133 0.0902653
\(466\) 1.87773e134 0.331241
\(467\) −8.01039e134 −1.26809 −0.634047 0.773295i \(-0.718607\pi\)
−0.634047 + 0.773295i \(0.718607\pi\)
\(468\) −3.30895e134 −0.470191
\(469\) −1.96201e134 −0.250307
\(470\) 1.86196e134 0.213319
\(471\) −1.01736e135 −1.04693
\(472\) −9.92543e134 −0.917652
\(473\) −4.60276e134 −0.382411
\(474\) −1.31853e135 −0.984652
\(475\) 4.41869e134 0.296665
\(476\) −1.53725e134 −0.0928098
\(477\) 6.22581e135 3.38079
\(478\) −7.44005e133 −0.0363469
\(479\) −1.89509e135 −0.833078 −0.416539 0.909118i \(-0.636757\pi\)
−0.416539 + 0.909118i \(0.636757\pi\)
\(480\) 2.27564e135 0.900371
\(481\) 8.23116e134 0.293180
\(482\) −1.70962e135 −0.548308
\(483\) 4.17990e135 1.20736
\(484\) −3.36270e135 −0.874977
\(485\) 1.21824e135 0.285611
\(486\) −5.06946e135 −1.07110
\(487\) −8.27291e135 −1.57560 −0.787799 0.615932i \(-0.788780\pi\)
−0.787799 + 0.615932i \(0.788780\pi\)
\(488\) 1.20489e136 2.06892
\(489\) −5.49024e135 −0.850147
\(490\) 3.43770e135 0.480137
\(491\) 6.23886e135 0.786122 0.393061 0.919512i \(-0.371416\pi\)
0.393061 + 0.919512i \(0.371416\pi\)
\(492\) 8.05829e135 0.916232
\(493\) 3.25852e135 0.334388
\(494\) −3.86110e135 −0.357684
\(495\) −4.03665e136 −3.37643
\(496\) −4.67504e134 −0.0353151
\(497\) 8.57531e135 0.585130
\(498\) −4.01001e135 −0.247209
\(499\) 1.23647e136 0.688823 0.344411 0.938819i \(-0.388079\pi\)
0.344411 + 0.938819i \(0.388079\pi\)
\(500\) −7.26367e135 −0.365738
\(501\) −1.19275e136 −0.542929
\(502\) 1.03745e136 0.427001
\(503\) −3.60863e136 −1.34326 −0.671628 0.740889i \(-0.734405\pi\)
−0.671628 + 0.740889i \(0.734405\pi\)
\(504\) 3.61849e136 1.21839
\(505\) 1.16637e136 0.355321
\(506\) 7.67043e136 2.11455
\(507\) 4.64794e136 1.15973
\(508\) −8.10229e135 −0.183017
\(509\) −5.84391e136 −1.19524 −0.597621 0.801779i \(-0.703887\pi\)
−0.597621 + 0.801779i \(0.703887\pi\)
\(510\) −3.50031e136 −0.648354
\(511\) 6.61754e135 0.111030
\(512\) −6.24577e136 −0.949407
\(513\) 1.26545e137 1.74308
\(514\) −6.69512e136 −0.835836
\(515\) 5.85602e136 0.662732
\(516\) −1.20802e136 −0.123955
\(517\) −6.93003e136 −0.644856
\(518\) −2.27153e136 −0.191719
\(519\) −4.95583e136 −0.379459
\(520\) 7.27046e136 0.505118
\(521\) −2.75937e137 −1.73982 −0.869912 0.493208i \(-0.835824\pi\)
−0.869912 + 0.493208i \(0.835824\pi\)
\(522\) −1.93563e137 −1.10780
\(523\) 2.02120e137 1.05020 0.525102 0.851039i \(-0.324027\pi\)
0.525102 + 0.851039i \(0.324027\pi\)
\(524\) 7.91734e136 0.373550
\(525\) −8.35805e136 −0.358146
\(526\) −1.32644e137 −0.516305
\(527\) −1.03438e136 −0.0365799
\(528\) 5.88813e137 1.89219
\(529\) 3.00939e137 0.878957
\(530\) −3.45214e137 −0.916550
\(531\) 8.07559e137 1.94940
\(532\) −5.42921e136 −0.119179
\(533\) 4.49938e137 0.898315
\(534\) −6.95860e137 −1.26383
\(535\) 4.45450e137 0.736094
\(536\) −3.74449e137 −0.563081
\(537\) −9.32268e137 −1.27597
\(538\) 6.70510e136 0.0835412
\(539\) −1.27947e138 −1.45144
\(540\) −6.01334e137 −0.621199
\(541\) 7.54522e137 0.709921 0.354960 0.934881i \(-0.384494\pi\)
0.354960 + 0.934881i \(0.384494\pi\)
\(542\) 5.90072e137 0.505756
\(543\) 8.16111e137 0.637320
\(544\) −5.12729e137 −0.364874
\(545\) 1.30160e138 0.844220
\(546\) 7.30336e137 0.431812
\(547\) 1.00720e138 0.542946 0.271473 0.962446i \(-0.412489\pi\)
0.271473 + 0.962446i \(0.412489\pi\)
\(548\) 4.85700e137 0.238754
\(549\) −9.80327e138 −4.39509
\(550\) −1.53377e138 −0.627254
\(551\) 1.15083e138 0.429394
\(552\) 7.97730e138 2.71602
\(553\) −1.03520e138 −0.321666
\(554\) −2.09048e138 −0.592930
\(555\) 2.63541e138 0.682421
\(556\) 1.27154e138 0.300645
\(557\) 3.76306e138 0.812556 0.406278 0.913749i \(-0.366826\pi\)
0.406278 + 0.913749i \(0.366826\pi\)
\(558\) 6.14441e137 0.121186
\(559\) −6.74504e137 −0.121531
\(560\) −1.24208e138 −0.204481
\(561\) 1.30278e139 1.95995
\(562\) 1.81283e138 0.249272
\(563\) −6.33267e138 −0.796000 −0.398000 0.917385i \(-0.630296\pi\)
−0.398000 + 0.917385i \(0.630296\pi\)
\(564\) −1.81883e138 −0.209024
\(565\) −8.92641e138 −0.938059
\(566\) −1.10158e139 −1.05873
\(567\) −1.12059e139 −0.985146
\(568\) 1.63659e139 1.31628
\(569\) −9.81189e138 −0.722077 −0.361038 0.932551i \(-0.617578\pi\)
−0.361038 + 0.932551i \(0.617578\pi\)
\(570\) −1.23623e139 −0.832564
\(571\) −2.82442e139 −1.74103 −0.870515 0.492141i \(-0.836214\pi\)
−0.870515 + 0.492141i \(0.836214\pi\)
\(572\) −6.82881e138 −0.385342
\(573\) 6.95013e139 3.59075
\(574\) −1.24168e139 −0.587435
\(575\) −1.28638e139 −0.557368
\(576\) 6.24197e139 2.47734
\(577\) −8.15873e138 −0.296650 −0.148325 0.988939i \(-0.547388\pi\)
−0.148325 + 0.988939i \(0.547388\pi\)
\(578\) −1.65441e139 −0.551171
\(579\) −5.10787e139 −1.55945
\(580\) −5.46868e138 −0.153027
\(581\) −3.14834e138 −0.0807581
\(582\) 2.33552e139 0.549254
\(583\) 1.28485e140 2.77070
\(584\) 1.26295e139 0.249769
\(585\) −5.91544e139 −1.07304
\(586\) 8.76117e139 1.45792
\(587\) −1.00425e140 −1.53327 −0.766633 0.642086i \(-0.778069\pi\)
−0.766633 + 0.642086i \(0.778069\pi\)
\(588\) −3.35805e139 −0.470471
\(589\) −3.65317e138 −0.0469729
\(590\) −4.47781e139 −0.528493
\(591\) 6.53694e139 0.708283
\(592\) −2.68373e139 −0.266989
\(593\) 8.91714e139 0.814636 0.407318 0.913286i \(-0.366464\pi\)
0.407318 + 0.913286i \(0.366464\pi\)
\(594\) −4.39249e140 −3.68549
\(595\) −2.74816e139 −0.211804
\(596\) −2.29016e139 −0.162155
\(597\) 3.25886e140 2.12013
\(598\) 1.12405e140 0.672010
\(599\) −1.43219e140 −0.786949 −0.393475 0.919335i \(-0.628727\pi\)
−0.393475 + 0.919335i \(0.628727\pi\)
\(600\) −1.59513e140 −0.805671
\(601\) 2.96889e140 1.37859 0.689293 0.724483i \(-0.257921\pi\)
0.689293 + 0.724483i \(0.257921\pi\)
\(602\) 1.86141e139 0.0794728
\(603\) 3.04661e140 1.19617
\(604\) 1.01146e139 0.0365245
\(605\) −6.01152e140 −1.99682
\(606\) 2.23608e140 0.683314
\(607\) 1.14900e140 0.323067 0.161534 0.986867i \(-0.448356\pi\)
0.161534 + 0.986867i \(0.448356\pi\)
\(608\) −1.81084e140 −0.468542
\(609\) −2.17683e140 −0.518383
\(610\) 5.43579e140 1.19153
\(611\) −1.01555e140 −0.204937
\(612\) 2.38704e140 0.443520
\(613\) 2.62097e140 0.448444 0.224222 0.974538i \(-0.428016\pi\)
0.224222 + 0.974538i \(0.428016\pi\)
\(614\) −8.80659e140 −1.38773
\(615\) 1.44059e141 2.09096
\(616\) 7.46763e140 0.998520
\(617\) −1.16164e141 −1.43110 −0.715552 0.698559i \(-0.753825\pi\)
−0.715552 + 0.698559i \(0.753825\pi\)
\(618\) 1.12268e141 1.27449
\(619\) −1.09614e141 −1.14680 −0.573402 0.819274i \(-0.694377\pi\)
−0.573402 + 0.819274i \(0.694377\pi\)
\(620\) 1.73596e139 0.0167402
\(621\) −3.68400e141 −3.27487
\(622\) −7.50452e140 −0.615047
\(623\) −5.46333e140 −0.412868
\(624\) 8.62866e140 0.601342
\(625\) −6.65939e140 −0.428049
\(626\) −6.17410e140 −0.366075
\(627\) 4.60110e141 2.51681
\(628\) −3.84698e140 −0.194159
\(629\) −5.93788e140 −0.276550
\(630\) 1.63247e141 0.701692
\(631\) 1.04696e141 0.415381 0.207691 0.978195i \(-0.433405\pi\)
0.207691 + 0.978195i \(0.433405\pi\)
\(632\) −1.97567e141 −0.723607
\(633\) 7.62923e141 2.57984
\(634\) 1.14301e141 0.356895
\(635\) −1.44845e141 −0.417668
\(636\) 3.37216e141 0.898097
\(637\) −1.87498e141 −0.461271
\(638\) −3.99464e141 −0.907891
\(639\) −1.33158e142 −2.79623
\(640\) −9.11782e140 −0.176930
\(641\) 9.77655e140 0.175329 0.0876647 0.996150i \(-0.472060\pi\)
0.0876647 + 0.996150i \(0.472060\pi\)
\(642\) 8.53986e141 1.41557
\(643\) 5.45078e141 0.835227 0.417614 0.908625i \(-0.362867\pi\)
0.417614 + 0.908625i \(0.362867\pi\)
\(644\) 1.58056e141 0.223911
\(645\) −2.15959e141 −0.282882
\(646\) 2.78536e141 0.337395
\(647\) −1.17949e142 −1.32138 −0.660692 0.750657i \(-0.729737\pi\)
−0.660692 + 0.750657i \(0.729737\pi\)
\(648\) −2.13863e142 −2.21614
\(649\) 1.66659e142 1.59762
\(650\) −2.24763e141 −0.199343
\(651\) 6.91006e140 0.0567077
\(652\) −2.07605e141 −0.157664
\(653\) −1.63413e142 −1.14861 −0.574303 0.818643i \(-0.694727\pi\)
−0.574303 + 0.818643i \(0.694727\pi\)
\(654\) 2.49535e142 1.62351
\(655\) 1.41539e142 0.852492
\(656\) −1.46700e142 −0.818063
\(657\) −1.02757e142 −0.530593
\(658\) 2.80258e141 0.134014
\(659\) 3.81560e142 1.68985 0.844927 0.534881i \(-0.179644\pi\)
0.844927 + 0.534881i \(0.179644\pi\)
\(660\) −2.18641e142 −0.896940
\(661\) 4.39849e142 1.67159 0.835795 0.549041i \(-0.185007\pi\)
0.835795 + 0.549041i \(0.185007\pi\)
\(662\) −2.87673e142 −1.01291
\(663\) 1.90913e142 0.622878
\(664\) −6.00858e141 −0.181670
\(665\) −9.70584e141 −0.271982
\(666\) 3.52723e142 0.916190
\(667\) −3.35032e142 −0.806737
\(668\) −4.51018e141 −0.100689
\(669\) 6.60830e142 1.36795
\(670\) −1.68931e142 −0.324289
\(671\) −2.02314e143 −3.60196
\(672\) 3.42524e142 0.565643
\(673\) −4.95594e140 −0.00759216 −0.00379608 0.999993i \(-0.501208\pi\)
−0.00379608 + 0.999993i \(0.501208\pi\)
\(674\) 3.45139e142 0.490534
\(675\) 7.36647e142 0.971446
\(676\) 1.75754e142 0.215079
\(677\) 8.50309e142 0.965715 0.482857 0.875699i \(-0.339599\pi\)
0.482857 + 0.875699i \(0.339599\pi\)
\(678\) −1.71131e143 −1.80397
\(679\) 1.83366e142 0.179430
\(680\) −5.24484e142 −0.476466
\(681\) −1.03643e143 −0.874198
\(682\) 1.26805e142 0.0993173
\(683\) −2.16958e143 −1.57809 −0.789043 0.614339i \(-0.789423\pi\)
−0.789043 + 0.614339i \(0.789423\pi\)
\(684\) 8.43047e142 0.569533
\(685\) 8.68291e142 0.544868
\(686\) 1.19311e143 0.695523
\(687\) 3.65707e143 1.98070
\(688\) 2.19919e142 0.110674
\(689\) 1.88286e143 0.880535
\(690\) 3.59892e143 1.56420
\(691\) −5.23754e142 −0.211586 −0.105793 0.994388i \(-0.533738\pi\)
−0.105793 + 0.994388i \(0.533738\pi\)
\(692\) −1.87397e142 −0.0703727
\(693\) −6.07586e143 −2.12119
\(694\) 2.27004e143 0.736851
\(695\) 2.27315e143 0.686112
\(696\) −4.15446e143 −1.16613
\(697\) −3.24581e143 −0.847360
\(698\) −2.70678e143 −0.657285
\(699\) −3.27906e143 −0.740716
\(700\) −3.16046e142 −0.0664201
\(701\) −9.46919e141 −0.0185162 −0.00925812 0.999957i \(-0.502947\pi\)
−0.00925812 + 0.999957i \(0.502947\pi\)
\(702\) −6.43690e143 −1.17126
\(703\) −2.09712e143 −0.355123
\(704\) 1.28818e144 2.03029
\(705\) −3.25153e143 −0.477021
\(706\) 6.65833e143 0.909344
\(707\) 1.75559e143 0.223225
\(708\) 4.37407e143 0.517853
\(709\) −1.18469e144 −1.30608 −0.653039 0.757324i \(-0.726506\pi\)
−0.653039 + 0.757324i \(0.726506\pi\)
\(710\) 7.38342e143 0.758072
\(711\) 1.60746e144 1.53718
\(712\) −1.04267e144 −0.928770
\(713\) 1.06352e143 0.0882517
\(714\) −5.26858e143 −0.407318
\(715\) −1.22079e144 −0.879401
\(716\) −3.52522e143 −0.236635
\(717\) 1.29925e143 0.0812784
\(718\) −9.77848e143 −0.570147
\(719\) 3.12750e144 1.69976 0.849881 0.526974i \(-0.176674\pi\)
0.849881 + 0.526974i \(0.176674\pi\)
\(720\) 1.92870e144 0.977178
\(721\) 8.81434e143 0.416350
\(722\) −8.64302e143 −0.380660
\(723\) 2.98550e144 1.22612
\(724\) 3.08599e143 0.118195
\(725\) 6.69925e143 0.239308
\(726\) −1.15249e145 −3.84005
\(727\) 6.15549e143 0.191326 0.0956632 0.995414i \(-0.469503\pi\)
0.0956632 + 0.995414i \(0.469503\pi\)
\(728\) 1.09433e144 0.317332
\(729\) 1.32871e144 0.359492
\(730\) 5.69776e143 0.143847
\(731\) 4.86581e143 0.114638
\(732\) −5.30985e144 −1.16754
\(733\) −2.88576e144 −0.592255 −0.296128 0.955148i \(-0.595695\pi\)
−0.296128 + 0.955148i \(0.595695\pi\)
\(734\) −2.59352e144 −0.496865
\(735\) −6.00322e144 −1.07368
\(736\) 5.27174e144 0.880287
\(737\) 6.28742e144 0.980313
\(738\) 1.92808e145 2.80724
\(739\) −1.27820e145 −1.73802 −0.869008 0.494798i \(-0.835242\pi\)
−0.869008 + 0.494798i \(0.835242\pi\)
\(740\) 9.96538e143 0.126559
\(741\) 6.74260e144 0.799849
\(742\) −5.19607e144 −0.575808
\(743\) −4.61819e144 −0.478120 −0.239060 0.971005i \(-0.576839\pi\)
−0.239060 + 0.971005i \(0.576839\pi\)
\(744\) 1.31878e144 0.127567
\(745\) −4.09415e144 −0.370060
\(746\) 1.79689e145 1.51779
\(747\) 4.88874e144 0.385928
\(748\) 4.92624e144 0.363484
\(749\) 6.70481e144 0.462439
\(750\) −2.48945e145 −1.60513
\(751\) 1.60089e145 0.965041 0.482521 0.875885i \(-0.339721\pi\)
0.482521 + 0.875885i \(0.339721\pi\)
\(752\) 3.31115e144 0.186628
\(753\) −1.81169e145 −0.954854
\(754\) −5.85388e144 −0.288530
\(755\) 1.80820e144 0.0833538
\(756\) −9.05112e144 −0.390258
\(757\) 4.02375e145 1.62289 0.811445 0.584429i \(-0.198681\pi\)
0.811445 + 0.584429i \(0.198681\pi\)
\(758\) 1.57032e145 0.592507
\(759\) −1.33948e146 −4.72854
\(760\) −1.85235e145 −0.611839
\(761\) 2.36459e145 0.730854 0.365427 0.930840i \(-0.380923\pi\)
0.365427 + 0.930840i \(0.380923\pi\)
\(762\) −2.77687e145 −0.803212
\(763\) 1.95914e145 0.530368
\(764\) 2.62808e145 0.665923
\(765\) 4.26734e145 1.01217
\(766\) −4.80966e144 −0.106798
\(767\) 2.44228e145 0.507726
\(768\) 8.26827e145 1.60943
\(769\) −9.23730e145 −1.68370 −0.841851 0.539710i \(-0.818534\pi\)
−0.841851 + 0.539710i \(0.818534\pi\)
\(770\) 3.36899e145 0.575066
\(771\) 1.16916e146 1.86909
\(772\) −1.93146e145 −0.289209
\(773\) −2.95288e145 −0.414173 −0.207086 0.978323i \(-0.566398\pi\)
−0.207086 + 0.978323i \(0.566398\pi\)
\(774\) −2.89039e145 −0.379786
\(775\) −2.12659e144 −0.0261787
\(776\) 3.49953e145 0.403639
\(777\) 3.96675e145 0.428720
\(778\) 3.12326e145 0.316329
\(779\) −1.14634e146 −1.08811
\(780\) −3.20404e145 −0.285050
\(781\) −2.74803e146 −2.29163
\(782\) −8.10879e145 −0.633892
\(783\) 1.91857e146 1.40608
\(784\) 6.11329e145 0.420062
\(785\) −6.87728e145 −0.443098
\(786\) 2.71349e146 1.63942
\(787\) 1.33841e146 0.758343 0.379171 0.925326i \(-0.376209\pi\)
0.379171 + 0.925326i \(0.376209\pi\)
\(788\) 2.47184e145 0.131355
\(789\) 2.31634e146 1.15455
\(790\) −8.91316e145 −0.416739
\(791\) −1.34358e146 −0.589320
\(792\) −1.15957e147 −4.77174
\(793\) −2.96478e146 −1.14471
\(794\) 1.82917e146 0.662703
\(795\) 6.02843e146 2.04958
\(796\) 1.23229e146 0.393190
\(797\) 2.71043e144 0.00811696 0.00405848 0.999992i \(-0.498708\pi\)
0.00405848 + 0.999992i \(0.498708\pi\)
\(798\) −1.86074e146 −0.523045
\(799\) 7.32608e145 0.193312
\(800\) −1.05413e146 −0.261125
\(801\) 8.48346e146 1.97302
\(802\) 6.83979e146 1.49361
\(803\) −2.12064e146 −0.434843
\(804\) 1.65017e146 0.317760
\(805\) 2.82558e146 0.510994
\(806\) 1.85824e145 0.0315633
\(807\) −1.17091e146 −0.186814
\(808\) 3.35053e146 0.502157
\(809\) −7.92293e146 −1.11554 −0.557771 0.829995i \(-0.688343\pi\)
−0.557771 + 0.829995i \(0.688343\pi\)
\(810\) −9.64833e146 −1.27632
\(811\) 4.85339e146 0.603243 0.301621 0.953428i \(-0.402472\pi\)
0.301621 + 0.953428i \(0.402472\pi\)
\(812\) −8.23132e145 −0.0961369
\(813\) −1.03044e147 −1.13097
\(814\) 7.27929e146 0.750856
\(815\) −3.71137e146 −0.359811
\(816\) −6.22463e146 −0.567232
\(817\) 1.71849e146 0.147208
\(818\) −8.95164e146 −0.720877
\(819\) −8.90377e146 −0.674119
\(820\) 5.44736e146 0.387781
\(821\) −1.28716e147 −0.861593 −0.430796 0.902449i \(-0.641767\pi\)
−0.430796 + 0.902449i \(0.641767\pi\)
\(822\) 1.66463e147 1.04783
\(823\) 6.44259e146 0.381389 0.190695 0.981649i \(-0.438926\pi\)
0.190695 + 0.981649i \(0.438926\pi\)
\(824\) 1.68221e147 0.936604
\(825\) 2.67840e147 1.40266
\(826\) −6.73989e146 −0.332017
\(827\) −3.99006e147 −1.84906 −0.924531 0.381107i \(-0.875543\pi\)
−0.924531 + 0.381107i \(0.875543\pi\)
\(828\) −2.45430e147 −1.07003
\(829\) 1.05489e147 0.432717 0.216359 0.976314i \(-0.430582\pi\)
0.216359 + 0.976314i \(0.430582\pi\)
\(830\) −2.71074e146 −0.104627
\(831\) 3.65059e147 1.32590
\(832\) 1.88774e147 0.645231
\(833\) 1.35259e147 0.435106
\(834\) 4.35792e147 1.31945
\(835\) −8.06289e146 −0.229786
\(836\) 1.73983e147 0.466756
\(837\) −6.09026e146 −0.153816
\(838\) 1.42939e147 0.339882
\(839\) −8.81853e147 −1.97432 −0.987160 0.159737i \(-0.948935\pi\)
−0.987160 + 0.159737i \(0.948935\pi\)
\(840\) 3.50377e147 0.738638
\(841\) −3.29250e147 −0.653624
\(842\) −6.49203e147 −1.21372
\(843\) −3.16573e147 −0.557419
\(844\) 2.88487e147 0.478446
\(845\) 3.14198e147 0.490839
\(846\) −4.35185e147 −0.640428
\(847\) −9.04839e147 −1.25447
\(848\) −6.13897e147 −0.801871
\(849\) 1.92368e148 2.36752
\(850\) 1.62142e147 0.188036
\(851\) 6.10517e147 0.667199
\(852\) −7.21236e147 −0.742810
\(853\) −1.29264e148 −1.25474 −0.627369 0.778722i \(-0.715868\pi\)
−0.627369 + 0.778722i \(0.715868\pi\)
\(854\) 8.18181e147 0.748560
\(855\) 1.50712e148 1.29975
\(856\) 1.27961e148 1.04028
\(857\) −1.60312e148 −1.22867 −0.614333 0.789047i \(-0.710575\pi\)
−0.614333 + 0.789047i \(0.710575\pi\)
\(858\) −2.34042e148 −1.69116
\(859\) 5.02898e147 0.342630 0.171315 0.985216i \(-0.445198\pi\)
0.171315 + 0.985216i \(0.445198\pi\)
\(860\) −8.16615e146 −0.0524621
\(861\) 2.16834e148 1.31361
\(862\) −4.04524e147 −0.231115
\(863\) 1.54202e148 0.830890 0.415445 0.909618i \(-0.363626\pi\)
0.415445 + 0.909618i \(0.363626\pi\)
\(864\) −3.01888e148 −1.53427
\(865\) −3.35011e147 −0.160600
\(866\) 1.41647e148 0.640551
\(867\) 2.88908e148 1.23252
\(868\) 2.61293e146 0.0105167
\(869\) 3.31738e148 1.25979
\(870\) −1.87427e148 −0.671597
\(871\) 9.21380e147 0.311546
\(872\) 3.73901e148 1.19309
\(873\) −2.84731e148 −0.857464
\(874\) −2.86383e148 −0.813992
\(875\) −1.95452e148 −0.524364
\(876\) −5.56575e147 −0.140951
\(877\) −7.14743e148 −1.70872 −0.854359 0.519684i \(-0.826050\pi\)
−0.854359 + 0.519684i \(0.826050\pi\)
\(878\) 5.85215e148 1.32082
\(879\) −1.52996e149 −3.26017
\(880\) 3.98034e148 0.800838
\(881\) −2.08981e148 −0.397030 −0.198515 0.980098i \(-0.563612\pi\)
−0.198515 + 0.980098i \(0.563612\pi\)
\(882\) −8.03471e148 −1.44147
\(883\) 1.01269e149 1.71577 0.857886 0.513840i \(-0.171778\pi\)
0.857886 + 0.513840i \(0.171778\pi\)
\(884\) 7.21908e147 0.115516
\(885\) 7.81956e148 1.18181
\(886\) 3.81389e148 0.544459
\(887\) −8.02411e148 −1.08207 −0.541034 0.841001i \(-0.681967\pi\)
−0.541034 + 0.841001i \(0.681967\pi\)
\(888\) 7.57052e148 0.964431
\(889\) −2.18018e148 −0.262393
\(890\) −4.70397e148 −0.534896
\(891\) 3.59100e149 3.85826
\(892\) 2.49882e148 0.253694
\(893\) 2.58740e148 0.248236
\(894\) −7.84901e148 −0.711656
\(895\) −6.30207e148 −0.540033
\(896\) −1.37239e148 −0.111154
\(897\) −1.96292e149 −1.50274
\(898\) −8.53432e148 −0.617609
\(899\) −5.53864e147 −0.0378912
\(900\) 4.90757e148 0.317409
\(901\) −1.35828e149 −0.830589
\(902\) 3.97906e149 2.30065
\(903\) −3.25056e148 −0.177716
\(904\) −2.56421e149 −1.32571
\(905\) 5.51686e148 0.269736
\(906\) 3.46655e148 0.160296
\(907\) 5.06153e148 0.221368 0.110684 0.993856i \(-0.464696\pi\)
0.110684 + 0.993856i \(0.464696\pi\)
\(908\) −3.91909e148 −0.162125
\(909\) −2.72608e149 −1.06675
\(910\) 4.93703e148 0.182757
\(911\) 2.45697e149 0.860444 0.430222 0.902723i \(-0.358435\pi\)
0.430222 + 0.902723i \(0.358435\pi\)
\(912\) −2.19839e149 −0.728393
\(913\) 1.00891e149 0.316284
\(914\) −1.69288e149 −0.502162
\(915\) −9.49247e149 −2.66449
\(916\) 1.38286e149 0.367331
\(917\) 2.13041e149 0.535564
\(918\) 4.64352e149 1.10482
\(919\) −5.29393e149 −1.19219 −0.596095 0.802914i \(-0.703282\pi\)
−0.596095 + 0.802914i \(0.703282\pi\)
\(920\) 5.39260e149 1.14951
\(921\) 1.53789e150 3.10322
\(922\) 6.92915e149 1.32364
\(923\) −4.02705e149 −0.728285
\(924\) −3.29093e149 −0.563488
\(925\) −1.22078e149 −0.197916
\(926\) −4.65189e149 −0.714126
\(927\) −1.36869e150 −1.98966
\(928\) −2.74544e149 −0.377954
\(929\) 1.40418e150 1.83075 0.915376 0.402600i \(-0.131893\pi\)
0.915376 + 0.402600i \(0.131893\pi\)
\(930\) 5.94962e148 0.0734683
\(931\) 4.77704e149 0.558728
\(932\) −1.23992e149 −0.137370
\(933\) 1.31051e150 1.37536
\(934\) −1.03812e150 −1.03212
\(935\) 8.80669e149 0.829519
\(936\) −1.69928e150 −1.51647
\(937\) −1.68453e150 −1.42439 −0.712196 0.701981i \(-0.752299\pi\)
−0.712196 + 0.701981i \(0.752299\pi\)
\(938\) −2.54271e149 −0.203729
\(939\) 1.07818e150 0.818612
\(940\) −1.22952e149 −0.0884662
\(941\) 2.17412e149 0.148254 0.0741272 0.997249i \(-0.476383\pi\)
0.0741272 + 0.997249i \(0.476383\pi\)
\(942\) −1.31846e150 −0.852115
\(943\) 3.33726e150 2.04432
\(944\) −7.96294e149 −0.462368
\(945\) −1.61808e150 −0.890621
\(946\) −5.96503e149 −0.311250
\(947\) −2.61387e150 −1.29303 −0.646516 0.762900i \(-0.723775\pi\)
−0.646516 + 0.762900i \(0.723775\pi\)
\(948\) 8.70666e149 0.408348
\(949\) −3.10766e149 −0.138194
\(950\) 5.72647e149 0.241460
\(951\) −1.99602e150 −0.798085
\(952\) −7.89440e149 −0.299332
\(953\) −2.67818e150 −0.963050 −0.481525 0.876432i \(-0.659917\pi\)
−0.481525 + 0.876432i \(0.659917\pi\)
\(954\) 8.06845e150 2.75168
\(955\) 4.69825e150 1.51973
\(956\) 4.91290e148 0.0150735
\(957\) 6.97581e150 2.03021
\(958\) −2.45597e150 −0.678055
\(959\) 1.30693e150 0.342304
\(960\) 6.04408e150 1.50187
\(961\) −4.22403e150 −0.995855
\(962\) 1.06673e150 0.238624
\(963\) −1.04112e151 −2.20991
\(964\) 1.12892e150 0.227390
\(965\) −3.45289e150 −0.660014
\(966\) 5.41701e150 0.982686
\(967\) −1.44436e150 −0.248678 −0.124339 0.992240i \(-0.539681\pi\)
−0.124339 + 0.992240i \(0.539681\pi\)
\(968\) −1.72688e151 −2.82200
\(969\) −4.86405e150 −0.754479
\(970\) 1.57880e150 0.232463
\(971\) 2.05283e150 0.286934 0.143467 0.989655i \(-0.454175\pi\)
0.143467 + 0.989655i \(0.454175\pi\)
\(972\) 3.34753e150 0.444199
\(973\) 3.42148e150 0.431038
\(974\) −1.07214e151 −1.28240
\(975\) 3.92502e150 0.445768
\(976\) 9.66651e150 1.04245
\(977\) 8.85563e150 0.906868 0.453434 0.891290i \(-0.350199\pi\)
0.453434 + 0.891290i \(0.350199\pi\)
\(978\) −7.11518e150 −0.691948
\(979\) 1.75077e151 1.61697
\(980\) −2.27002e150 −0.199119
\(981\) −3.04216e151 −2.53453
\(982\) 8.08536e150 0.639837
\(983\) −1.64570e151 −1.23708 −0.618542 0.785752i \(-0.712276\pi\)
−0.618542 + 0.785752i \(0.712276\pi\)
\(984\) 4.13826e151 2.95505
\(985\) 4.41893e150 0.299770
\(986\) 4.22294e150 0.272164
\(987\) −4.89412e150 −0.299681
\(988\) 2.54961e150 0.148336
\(989\) −5.00289e150 −0.276572
\(990\) −5.23136e151 −2.74813
\(991\) −1.18475e150 −0.0591437 −0.0295718 0.999563i \(-0.509414\pi\)
−0.0295718 + 0.999563i \(0.509414\pi\)
\(992\) 8.71505e149 0.0413457
\(993\) 5.02360e151 2.26505
\(994\) 1.11133e151 0.476247
\(995\) 2.20297e151 0.897311
\(996\) 2.64794e150 0.102521
\(997\) 2.26170e151 0.832396 0.416198 0.909274i \(-0.363362\pi\)
0.416198 + 0.909274i \(0.363362\pi\)
\(998\) 1.60243e151 0.560644
\(999\) −3.49614e151 −1.16287
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1.102.a.a.1.6 8
3.2 odd 2 9.102.a.b.1.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.102.a.a.1.6 8 1.1 even 1 trivial
9.102.a.b.1.3 8 3.2 odd 2