Properties

Label 1.102.a.a.1.8
Level $1$
Weight $102$
Character 1.1
Self dual yes
Analytic conductor $64.601$
Analytic rank $1$
Dimension $8$
CM no
Inner twists $1$

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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 1.8
Root \(-2.72721e13\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.56375e15 q^{2} -2.60728e23 q^{3} +4.03750e30 q^{4} +2.88877e35 q^{5} -6.68439e38 q^{6} -6.25978e42 q^{7} +3.85125e45 q^{8} -1.47815e48 q^{9} +O(q^{10})\) \(q+2.56375e15 q^{2} -2.60728e23 q^{3} +4.03750e30 q^{4} +2.88877e35 q^{5} -6.68439e38 q^{6} -6.25978e42 q^{7} +3.85125e45 q^{8} -1.47815e48 q^{9} +7.40607e50 q^{10} -2.44501e52 q^{11} -1.05269e54 q^{12} -8.21796e55 q^{13} -1.60485e58 q^{14} -7.53182e58 q^{15} -3.62648e59 q^{16} -1.73969e62 q^{17} -3.78961e63 q^{18} -3.05406e64 q^{19} +1.16634e66 q^{20} +1.63210e66 q^{21} -6.26838e67 q^{22} +2.17017e68 q^{23} -1.00413e69 q^{24} +4.40068e70 q^{25} -2.10688e71 q^{26} +7.88515e71 q^{27} -2.52738e73 q^{28} +1.39854e74 q^{29} -1.93097e74 q^{30} -3.23973e75 q^{31} -1.06938e76 q^{32} +6.37481e75 q^{33} -4.46012e77 q^{34} -1.80831e78 q^{35} -5.96804e78 q^{36} +1.43241e79 q^{37} -7.82984e79 q^{38} +2.14265e79 q^{39} +1.11254e81 q^{40} +4.24481e81 q^{41} +4.18428e81 q^{42} +1.21927e82 q^{43} -9.87171e82 q^{44} -4.27005e83 q^{45} +5.56377e83 q^{46} -3.72383e84 q^{47} +9.45523e82 q^{48} +1.65435e85 q^{49} +1.12822e86 q^{50} +4.53585e85 q^{51} -3.31800e86 q^{52} -1.31257e87 q^{53} +2.02155e87 q^{54} -7.06306e87 q^{55} -2.41080e88 q^{56} +7.96278e87 q^{57} +3.58550e89 q^{58} -2.92483e89 q^{59} -3.04097e89 q^{60} -4.65268e89 q^{61} -8.30584e90 q^{62} +9.25292e90 q^{63} -2.64968e91 q^{64} -2.37398e91 q^{65} +1.63434e91 q^{66} +1.13200e92 q^{67} -7.02398e92 q^{68} -5.65824e91 q^{69} -4.63604e93 q^{70} -1.95260e93 q^{71} -5.69273e93 q^{72} -9.13236e93 q^{73} +3.67234e94 q^{74} -1.14738e94 q^{75} -1.23308e95 q^{76} +1.53052e95 q^{77} +5.49321e94 q^{78} -4.27479e95 q^{79} -1.04761e95 q^{80} +2.07983e96 q^{81} +1.08826e97 q^{82} +1.25026e97 q^{83} +6.58959e96 q^{84} -5.02556e97 q^{85} +3.12590e97 q^{86} -3.64638e97 q^{87} -9.41633e97 q^{88} +1.65813e98 q^{89} -1.09473e99 q^{90} +5.14426e98 q^{91} +8.76206e98 q^{92} +8.44686e98 q^{93} -9.54696e99 q^{94} -8.82247e99 q^{95} +2.78817e99 q^{96} +1.54750e100 q^{97} +4.24133e100 q^{98} +3.61410e100 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 434989091795040q^{2} - \)\(12\!\cdots\!60\)\(q^{3} + \)\(90\!\cdots\!96\)\(q^{4} + \)\(38\!\cdots\!00\)\(q^{5} + \)\(24\!\cdots\!36\)\(q^{6} - \)\(57\!\cdots\!00\)\(q^{7} - \)\(61\!\cdots\!20\)\(q^{8} + \)\(52\!\cdots\!84\)\(q^{9} + O(q^{10}) \) \( 8q - 434989091795040q^{2} - \)\(12\!\cdots\!60\)\(q^{3} + \)\(90\!\cdots\!96\)\(q^{4} + \)\(38\!\cdots\!00\)\(q^{5} + \)\(24\!\cdots\!36\)\(q^{6} - \)\(57\!\cdots\!00\)\(q^{7} - \)\(61\!\cdots\!20\)\(q^{8} + \)\(52\!\cdots\!84\)\(q^{9} - \)\(37\!\cdots\!00\)\(q^{10} + \)\(46\!\cdots\!96\)\(q^{11} - \)\(72\!\cdots\!80\)\(q^{12} + \)\(25\!\cdots\!80\)\(q^{13} - \)\(48\!\cdots\!88\)\(q^{14} - \)\(29\!\cdots\!00\)\(q^{15} - \)\(10\!\cdots\!72\)\(q^{16} - \)\(39\!\cdots\!20\)\(q^{17} - \)\(72\!\cdots\!60\)\(q^{18} - \)\(21\!\cdots\!80\)\(q^{19} + \)\(17\!\cdots\!00\)\(q^{20} + \)\(40\!\cdots\!36\)\(q^{21} + \)\(61\!\cdots\!20\)\(q^{22} - \)\(13\!\cdots\!80\)\(q^{23} + \)\(10\!\cdots\!60\)\(q^{24} + \)\(77\!\cdots\!00\)\(q^{25} - \)\(97\!\cdots\!44\)\(q^{26} - \)\(59\!\cdots\!20\)\(q^{27} + \)\(92\!\cdots\!80\)\(q^{28} + \)\(15\!\cdots\!80\)\(q^{29} + \)\(11\!\cdots\!00\)\(q^{30} - \)\(65\!\cdots\!44\)\(q^{31} + \)\(12\!\cdots\!60\)\(q^{32} + \)\(43\!\cdots\!80\)\(q^{33} + \)\(95\!\cdots\!12\)\(q^{34} - \)\(11\!\cdots\!00\)\(q^{35} + \)\(19\!\cdots\!08\)\(q^{36} + \)\(39\!\cdots\!40\)\(q^{37} - \)\(70\!\cdots\!80\)\(q^{38} - \)\(26\!\cdots\!32\)\(q^{39} - \)\(76\!\cdots\!00\)\(q^{40} + \)\(56\!\cdots\!36\)\(q^{41} + \)\(30\!\cdots\!80\)\(q^{42} - \)\(28\!\cdots\!00\)\(q^{43} - \)\(20\!\cdots\!48\)\(q^{44} + \)\(71\!\cdots\!00\)\(q^{45} + \)\(10\!\cdots\!76\)\(q^{46} - \)\(45\!\cdots\!80\)\(q^{47} - \)\(58\!\cdots\!80\)\(q^{48} + \)\(12\!\cdots\!56\)\(q^{49} - \)\(40\!\cdots\!00\)\(q^{50} + \)\(11\!\cdots\!36\)\(q^{51} - \)\(73\!\cdots\!00\)\(q^{52} + \)\(13\!\cdots\!40\)\(q^{53} + \)\(68\!\cdots\!20\)\(q^{54} - \)\(14\!\cdots\!00\)\(q^{55} - \)\(23\!\cdots\!80\)\(q^{56} - \)\(66\!\cdots\!40\)\(q^{57} + \)\(29\!\cdots\!80\)\(q^{58} + \)\(21\!\cdots\!60\)\(q^{59} - \)\(34\!\cdots\!00\)\(q^{60} - \)\(33\!\cdots\!04\)\(q^{61} - \)\(58\!\cdots\!80\)\(q^{62} - \)\(20\!\cdots\!40\)\(q^{63} - \)\(74\!\cdots\!04\)\(q^{64} - \)\(16\!\cdots\!00\)\(q^{65} - \)\(74\!\cdots\!68\)\(q^{66} - \)\(61\!\cdots\!20\)\(q^{67} - \)\(21\!\cdots\!60\)\(q^{68} - \)\(53\!\cdots\!72\)\(q^{69} - \)\(12\!\cdots\!00\)\(q^{70} - \)\(15\!\cdots\!24\)\(q^{71} - \)\(55\!\cdots\!60\)\(q^{72} - \)\(20\!\cdots\!80\)\(q^{73} - \)\(14\!\cdots\!88\)\(q^{74} - \)\(20\!\cdots\!00\)\(q^{75} + \)\(64\!\cdots\!40\)\(q^{76} + \)\(25\!\cdots\!00\)\(q^{77} + \)\(12\!\cdots\!00\)\(q^{78} + \)\(14\!\cdots\!80\)\(q^{79} + \)\(60\!\cdots\!00\)\(q^{80} + \)\(14\!\cdots\!08\)\(q^{81} + \)\(30\!\cdots\!20\)\(q^{82} + \)\(33\!\cdots\!60\)\(q^{83} + \)\(57\!\cdots\!32\)\(q^{84} + \)\(17\!\cdots\!00\)\(q^{85} + \)\(67\!\cdots\!16\)\(q^{86} + \)\(25\!\cdots\!40\)\(q^{87} - \)\(36\!\cdots\!40\)\(q^{88} - \)\(62\!\cdots\!60\)\(q^{89} - \)\(47\!\cdots\!00\)\(q^{90} - \)\(36\!\cdots\!44\)\(q^{91} - \)\(46\!\cdots\!20\)\(q^{92} - \)\(39\!\cdots\!20\)\(q^{93} - \)\(17\!\cdots\!88\)\(q^{94} - \)\(26\!\cdots\!00\)\(q^{95} + \)\(46\!\cdots\!56\)\(q^{96} + \)\(64\!\cdots\!20\)\(q^{97} + \)\(20\!\cdots\!20\)\(q^{98} + \)\(22\!\cdots\!08\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.56375e15 1.61013 0.805064 0.593188i \(-0.202131\pi\)
0.805064 + 0.593188i \(0.202131\pi\)
\(3\) −2.60728e23 −0.209683 −0.104842 0.994489i \(-0.533434\pi\)
−0.104842 + 0.994489i \(0.533434\pi\)
\(4\) 4.03750e30 1.59251
\(5\) 2.88877e35 1.45455 0.727273 0.686348i \(-0.240787\pi\)
0.727273 + 0.686348i \(0.240787\pi\)
\(6\) −6.68439e38 −0.337617
\(7\) −6.25978e42 −1.31555 −0.657776 0.753214i \(-0.728503\pi\)
−0.657776 + 0.753214i \(0.728503\pi\)
\(8\) 3.85125e45 0.954019
\(9\) −1.47815e48 −0.956033
\(10\) 7.40607e50 2.34201
\(11\) −2.44501e52 −0.627986 −0.313993 0.949425i \(-0.601667\pi\)
−0.313993 + 0.949425i \(0.601667\pi\)
\(12\) −1.05269e54 −0.333923
\(13\) −8.21796e55 −0.457746 −0.228873 0.973456i \(-0.573504\pi\)
−0.228873 + 0.973456i \(0.573504\pi\)
\(14\) −1.60485e58 −2.11821
\(15\) −7.53182e58 −0.304994
\(16\) −3.62648e59 −0.0564191
\(17\) −1.73969e62 −1.26707 −0.633535 0.773714i \(-0.718397\pi\)
−0.633535 + 0.773714i \(0.718397\pi\)
\(18\) −3.78961e63 −1.53934
\(19\) −3.05406e64 −0.808762 −0.404381 0.914591i \(-0.632513\pi\)
−0.404381 + 0.914591i \(0.632513\pi\)
\(20\) 1.16634e66 2.31638
\(21\) 1.63210e66 0.275849
\(22\) −6.26838e67 −1.01114
\(23\) 2.17017e68 0.370884 0.185442 0.982655i \(-0.440628\pi\)
0.185442 + 0.982655i \(0.440628\pi\)
\(24\) −1.00413e69 −0.200042
\(25\) 4.40068e70 1.11571
\(26\) −2.10688e71 −0.737030
\(27\) 7.88515e71 0.410147
\(28\) −2.52738e73 −2.09503
\(29\) 1.39854e74 1.97050 0.985249 0.171125i \(-0.0547401\pi\)
0.985249 + 0.171125i \(0.0547401\pi\)
\(30\) −1.93097e74 −0.491079
\(31\) −3.23973e75 −1.57305 −0.786526 0.617557i \(-0.788122\pi\)
−0.786526 + 0.617557i \(0.788122\pi\)
\(32\) −1.06938e76 −1.04486
\(33\) 6.37481e75 0.131678
\(34\) −4.46012e77 −2.04015
\(35\) −1.80831e78 −1.91353
\(36\) −5.96804e78 −1.52249
\(37\) 1.43241e79 0.915968 0.457984 0.888960i \(-0.348572\pi\)
0.457984 + 0.888960i \(0.348572\pi\)
\(38\) −7.82984e79 −1.30221
\(39\) 2.14265e79 0.0959817
\(40\) 1.11254e81 1.38766
\(41\) 4.24481e81 1.52151 0.760753 0.649041i \(-0.224830\pi\)
0.760753 + 0.649041i \(0.224830\pi\)
\(42\) 4.18428e81 0.444152
\(43\) 1.21927e82 0.394405 0.197202 0.980363i \(-0.436814\pi\)
0.197202 + 0.980363i \(0.436814\pi\)
\(44\) −9.87171e82 −1.00007
\(45\) −4.27005e83 −1.39059
\(46\) 5.56377e83 0.597171
\(47\) −3.72383e84 −1.34911 −0.674556 0.738223i \(-0.735665\pi\)
−0.674556 + 0.738223i \(0.735665\pi\)
\(48\) 9.45523e82 0.0118301
\(49\) 1.65435e85 0.730677
\(50\) 1.12822e86 1.79643
\(51\) 4.53585e85 0.265683
\(52\) −3.31800e86 −0.728966
\(53\) −1.31257e87 −1.10203 −0.551013 0.834497i \(-0.685758\pi\)
−0.551013 + 0.834497i \(0.685758\pi\)
\(54\) 2.02155e87 0.660389
\(55\) −7.06306e87 −0.913434
\(56\) −2.41080e88 −1.25506
\(57\) 7.96278e87 0.169584
\(58\) 3.58550e89 3.17275
\(59\) −2.92483e89 −1.09163 −0.545813 0.837907i \(-0.683779\pi\)
−0.545813 + 0.837907i \(0.683779\pi\)
\(60\) −3.04097e89 −0.485706
\(61\) −4.65268e89 −0.322513 −0.161256 0.986913i \(-0.551555\pi\)
−0.161256 + 0.986913i \(0.551555\pi\)
\(62\) −8.30584e90 −2.53281
\(63\) 9.25292e90 1.25771
\(64\) −2.64968e91 −1.62594
\(65\) −2.37398e91 −0.665813
\(66\) 1.63434e91 0.212018
\(67\) 1.13200e92 0.687180 0.343590 0.939120i \(-0.388357\pi\)
0.343590 + 0.939120i \(0.388357\pi\)
\(68\) −7.02398e92 −2.01782
\(69\) −5.65824e91 −0.0777682
\(70\) −4.63604e93 −3.08103
\(71\) −1.95260e93 −0.633967 −0.316984 0.948431i \(-0.602670\pi\)
−0.316984 + 0.948431i \(0.602670\pi\)
\(72\) −5.69273e93 −0.912073
\(73\) −9.13236e93 −0.729086 −0.364543 0.931187i \(-0.618775\pi\)
−0.364543 + 0.931187i \(0.618775\pi\)
\(74\) 3.67234e94 1.47483
\(75\) −1.14738e94 −0.233945
\(76\) −1.23308e95 −1.28796
\(77\) 1.53052e95 0.826148
\(78\) 5.49321e94 0.154543
\(79\) −4.27479e95 −0.632043 −0.316022 0.948752i \(-0.602347\pi\)
−0.316022 + 0.948752i \(0.602347\pi\)
\(80\) −1.04761e95 −0.0820642
\(81\) 2.07983e96 0.870032
\(82\) 1.08826e97 2.44982
\(83\) 1.25026e97 1.52601 0.763005 0.646392i \(-0.223723\pi\)
0.763005 + 0.646392i \(0.223723\pi\)
\(84\) 6.58959e96 0.439293
\(85\) −5.02556e97 −1.84301
\(86\) 3.12590e97 0.635042
\(87\) −3.64638e97 −0.413180
\(88\) −9.41633e97 −0.599110
\(89\) 1.65813e98 0.596242 0.298121 0.954528i \(-0.403640\pi\)
0.298121 + 0.954528i \(0.403640\pi\)
\(90\) −1.09473e99 −2.23903
\(91\) 5.14426e98 0.602189
\(92\) 8.76206e98 0.590638
\(93\) 8.44686e98 0.329842
\(94\) −9.54696e99 −2.17224
\(95\) −8.82247e99 −1.17638
\(96\) 2.78817e99 0.219090
\(97\) 1.54750e100 0.720539 0.360269 0.932848i \(-0.382685\pi\)
0.360269 + 0.932848i \(0.382685\pi\)
\(98\) 4.24133e100 1.17648
\(99\) 3.61410e100 0.600375
\(100\) 1.77677e101 1.77677
\(101\) −3.42264e100 −0.207077 −0.103538 0.994625i \(-0.533016\pi\)
−0.103538 + 0.994625i \(0.533016\pi\)
\(102\) 1.16288e101 0.427784
\(103\) −3.65070e101 −0.820534 −0.410267 0.911965i \(-0.634564\pi\)
−0.410267 + 0.911965i \(0.634564\pi\)
\(104\) −3.16494e101 −0.436699
\(105\) 4.71475e101 0.401235
\(106\) −3.36510e102 −1.77440
\(107\) 1.09596e102 0.359679 0.179839 0.983696i \(-0.442442\pi\)
0.179839 + 0.983696i \(0.442442\pi\)
\(108\) 3.18363e102 0.653164
\(109\) 1.89257e102 0.243788 0.121894 0.992543i \(-0.461103\pi\)
0.121894 + 0.992543i \(0.461103\pi\)
\(110\) −1.81079e103 −1.47075
\(111\) −3.73469e102 −0.192063
\(112\) 2.27010e102 0.0742223
\(113\) −6.23836e103 −1.30199 −0.650997 0.759080i \(-0.725649\pi\)
−0.650997 + 0.759080i \(0.725649\pi\)
\(114\) 2.04145e103 0.273052
\(115\) 6.26913e103 0.539469
\(116\) 5.64660e104 3.13804
\(117\) 1.21474e104 0.437621
\(118\) −7.49853e104 −1.75766
\(119\) 1.08901e105 1.66690
\(120\) −2.90069e104 −0.290970
\(121\) −9.18061e104 −0.605634
\(122\) −1.19283e105 −0.519287
\(123\) −1.10674e105 −0.319034
\(124\) −1.30804e106 −2.50510
\(125\) 1.31837e105 0.168300
\(126\) 2.37221e106 2.02508
\(127\) 1.87262e106 1.07241 0.536205 0.844088i \(-0.319857\pi\)
0.536205 + 0.844088i \(0.319857\pi\)
\(128\) −4.08190e106 −1.57311
\(129\) −3.17897e105 −0.0827001
\(130\) −6.08628e106 −1.07204
\(131\) 5.76238e106 0.689290 0.344645 0.938733i \(-0.387999\pi\)
0.344645 + 0.938733i \(0.387999\pi\)
\(132\) 2.57383e106 0.209699
\(133\) 1.91177e107 1.06397
\(134\) 2.90217e107 1.10645
\(135\) 2.27784e107 0.596578
\(136\) −6.69997e107 −1.20881
\(137\) 7.34857e107 0.915829 0.457914 0.888996i \(-0.348597\pi\)
0.457914 + 0.888996i \(0.348597\pi\)
\(138\) −1.45063e107 −0.125217
\(139\) 8.70128e106 0.0521598 0.0260799 0.999660i \(-0.491698\pi\)
0.0260799 + 0.999660i \(0.491698\pi\)
\(140\) −7.30103e108 −3.04732
\(141\) 9.70906e107 0.282886
\(142\) −5.00597e108 −1.02077
\(143\) 2.00930e108 0.287458
\(144\) 5.36049e107 0.0539385
\(145\) 4.04006e109 2.86618
\(146\) −2.34131e109 −1.17392
\(147\) −4.31335e108 −0.153211
\(148\) 5.78335e109 1.45869
\(149\) −3.67441e109 −0.659600 −0.329800 0.944051i \(-0.606981\pi\)
−0.329800 + 0.944051i \(0.606981\pi\)
\(150\) −2.94159e109 −0.376681
\(151\) 4.20738e109 0.385191 0.192595 0.981278i \(-0.438309\pi\)
0.192595 + 0.981278i \(0.438309\pi\)
\(152\) −1.17619e110 −0.771574
\(153\) 2.57153e110 1.21136
\(154\) 3.92387e110 1.33020
\(155\) −9.35883e110 −2.28808
\(156\) 8.65094e109 0.152852
\(157\) 2.25516e110 0.288566 0.144283 0.989536i \(-0.453912\pi\)
0.144283 + 0.989536i \(0.453912\pi\)
\(158\) −1.09595e111 −1.01767
\(159\) 3.42224e110 0.231076
\(160\) −3.08919e111 −1.51980
\(161\) −1.35848e111 −0.487918
\(162\) 5.33217e111 1.40086
\(163\) −5.79305e111 −1.11541 −0.557703 0.830040i \(-0.688317\pi\)
−0.557703 + 0.830040i \(0.688317\pi\)
\(164\) 1.71384e112 2.42302
\(165\) 1.84154e111 0.191532
\(166\) 3.20536e112 2.45707
\(167\) −2.04226e112 −1.15592 −0.577961 0.816064i \(-0.696152\pi\)
−0.577961 + 0.816064i \(0.696152\pi\)
\(168\) 6.28561e111 0.263165
\(169\) −2.54779e112 −0.790468
\(170\) −1.28843e113 −2.96749
\(171\) 4.51437e112 0.773203
\(172\) 4.92279e112 0.628094
\(173\) 1.08886e113 1.03668 0.518340 0.855174i \(-0.326550\pi\)
0.518340 + 0.855174i \(0.326550\pi\)
\(174\) −9.34840e112 −0.665273
\(175\) −2.75473e113 −1.46777
\(176\) 8.86677e111 0.0354304
\(177\) 7.62584e112 0.228896
\(178\) 4.25102e113 0.960026
\(179\) 8.45466e113 1.43886 0.719429 0.694566i \(-0.244403\pi\)
0.719429 + 0.694566i \(0.244403\pi\)
\(180\) −1.72403e114 −2.21454
\(181\) −2.55677e113 −0.248269 −0.124135 0.992265i \(-0.539615\pi\)
−0.124135 + 0.992265i \(0.539615\pi\)
\(182\) 1.31886e114 0.969601
\(183\) 1.21308e113 0.0676255
\(184\) 8.35787e113 0.353831
\(185\) 4.13790e114 1.33232
\(186\) 2.16556e114 0.531089
\(187\) 4.25355e114 0.795702
\(188\) −1.50350e115 −2.14848
\(189\) −4.93593e114 −0.539570
\(190\) −2.26186e115 −1.89413
\(191\) 7.87385e114 0.505827 0.252914 0.967489i \(-0.418611\pi\)
0.252914 + 0.967489i \(0.418611\pi\)
\(192\) 6.90844e114 0.340932
\(193\) −4.31049e115 −1.63637 −0.818187 0.574952i \(-0.805021\pi\)
−0.818187 + 0.574952i \(0.805021\pi\)
\(194\) 3.96739e115 1.16016
\(195\) 6.18962e114 0.139610
\(196\) 6.67943e115 1.16361
\(197\) 1.14002e115 0.153591 0.0767957 0.997047i \(-0.475531\pi\)
0.0767957 + 0.997047i \(0.475531\pi\)
\(198\) 9.26563e115 0.966680
\(199\) −5.38798e115 −0.435859 −0.217929 0.975965i \(-0.569930\pi\)
−0.217929 + 0.975965i \(0.569930\pi\)
\(200\) 1.69481e116 1.06440
\(201\) −2.95145e115 −0.144090
\(202\) −8.77478e115 −0.333420
\(203\) −8.75456e116 −2.59229
\(204\) 1.83135e116 0.423104
\(205\) 1.22623e117 2.21310
\(206\) −9.35948e116 −1.32116
\(207\) −3.20785e116 −0.354578
\(208\) 2.98023e115 0.0258256
\(209\) 7.46720e116 0.507891
\(210\) 1.20874e117 0.646040
\(211\) −2.73700e117 −1.15083 −0.575414 0.817862i \(-0.695159\pi\)
−0.575414 + 0.817862i \(0.695159\pi\)
\(212\) −5.29950e117 −1.75499
\(213\) 5.09097e116 0.132932
\(214\) 2.80977e117 0.579129
\(215\) 3.52218e117 0.573680
\(216\) 3.03676e117 0.391288
\(217\) 2.02800e118 2.06943
\(218\) 4.85206e117 0.392530
\(219\) 2.38106e117 0.152877
\(220\) −2.85171e118 −1.45465
\(221\) 1.42967e118 0.579997
\(222\) −9.57479e117 −0.309246
\(223\) −5.94409e118 −1.52999 −0.764997 0.644034i \(-0.777259\pi\)
−0.764997 + 0.644034i \(0.777259\pi\)
\(224\) 6.69409e118 1.37457
\(225\) −6.50489e118 −1.06665
\(226\) −1.59936e119 −2.09638
\(227\) 1.51279e118 0.158662 0.0793309 0.996848i \(-0.474722\pi\)
0.0793309 + 0.996848i \(0.474722\pi\)
\(228\) 3.21497e118 0.270064
\(229\) 1.06684e119 0.718465 0.359232 0.933248i \(-0.383039\pi\)
0.359232 + 0.933248i \(0.383039\pi\)
\(230\) 1.60725e119 0.868614
\(231\) −3.99049e118 −0.173229
\(232\) 5.38612e119 1.87989
\(233\) 2.66360e118 0.0748160 0.0374080 0.999300i \(-0.488090\pi\)
0.0374080 + 0.999300i \(0.488090\pi\)
\(234\) 3.11429e119 0.704625
\(235\) −1.07573e120 −1.96235
\(236\) −1.18090e120 −1.73843
\(237\) 1.11456e119 0.132529
\(238\) 2.79194e120 2.68392
\(239\) −1.14147e119 −0.0887912 −0.0443956 0.999014i \(-0.514136\pi\)
−0.0443956 + 0.999014i \(0.514136\pi\)
\(240\) 2.73140e118 0.0172075
\(241\) −4.01998e119 −0.205288 −0.102644 0.994718i \(-0.532730\pi\)
−0.102644 + 0.994718i \(0.532730\pi\)
\(242\) −2.35368e120 −0.975148
\(243\) −1.76142e120 −0.592578
\(244\) −1.87852e120 −0.513605
\(245\) 4.77904e120 1.06280
\(246\) −2.83740e120 −0.513686
\(247\) 2.50982e120 0.370208
\(248\) −1.24770e121 −1.50072
\(249\) −3.25978e120 −0.319979
\(250\) 3.37998e120 0.270984
\(251\) 6.98915e120 0.458038 0.229019 0.973422i \(-0.426448\pi\)
0.229019 + 0.973422i \(0.426448\pi\)
\(252\) 3.73586e121 2.00292
\(253\) −5.30609e120 −0.232910
\(254\) 4.80092e121 1.72672
\(255\) 1.31030e121 0.386449
\(256\) −3.74723e121 −0.906969
\(257\) −1.41846e121 −0.281964 −0.140982 0.990012i \(-0.545026\pi\)
−0.140982 + 0.990012i \(0.545026\pi\)
\(258\) −8.15007e120 −0.133158
\(259\) −8.96657e121 −1.20500
\(260\) −9.58493e121 −1.06032
\(261\) −2.06726e122 −1.88386
\(262\) 1.47733e122 1.10984
\(263\) 2.18472e122 1.35403 0.677017 0.735967i \(-0.263272\pi\)
0.677017 + 0.735967i \(0.263272\pi\)
\(264\) 2.45510e121 0.125623
\(265\) −3.79172e122 −1.60295
\(266\) 4.90130e122 1.71313
\(267\) −4.32320e121 −0.125022
\(268\) 4.57046e122 1.09434
\(269\) −5.08484e122 −1.00876 −0.504379 0.863482i \(-0.668279\pi\)
−0.504379 + 0.863482i \(0.668279\pi\)
\(270\) 5.83980e122 0.960567
\(271\) −5.98554e122 −0.816872 −0.408436 0.912787i \(-0.633926\pi\)
−0.408436 + 0.912787i \(0.633926\pi\)
\(272\) 6.30894e121 0.0714870
\(273\) −1.34125e122 −0.126269
\(274\) 1.88399e123 1.47460
\(275\) −1.07597e123 −0.700647
\(276\) −2.28451e122 −0.123847
\(277\) −1.50383e123 −0.679156 −0.339578 0.940578i \(-0.610284\pi\)
−0.339578 + 0.940578i \(0.610284\pi\)
\(278\) 2.23079e122 0.0839839
\(279\) 4.78882e123 1.50389
\(280\) −6.96423e123 −1.82555
\(281\) 2.37882e123 0.520827 0.260413 0.965497i \(-0.416141\pi\)
0.260413 + 0.965497i \(0.416141\pi\)
\(282\) 2.48916e123 0.455483
\(283\) −8.85918e123 −1.35575 −0.677874 0.735178i \(-0.737098\pi\)
−0.677874 + 0.735178i \(0.737098\pi\)
\(284\) −7.88362e123 −1.00960
\(285\) 2.30026e123 0.246668
\(286\) 5.15133e123 0.462844
\(287\) −2.65716e124 −2.00162
\(288\) 1.58071e124 0.998921
\(289\) 1.14139e124 0.605468
\(290\) 1.03577e125 4.61492
\(291\) −4.03475e123 −0.151085
\(292\) −3.68719e124 −1.16108
\(293\) −7.86213e123 −0.208317 −0.104159 0.994561i \(-0.533215\pi\)
−0.104159 + 0.994561i \(0.533215\pi\)
\(294\) −1.10583e124 −0.246689
\(295\) −8.44916e124 −1.58782
\(296\) 5.51656e124 0.873851
\(297\) −1.92792e124 −0.257567
\(298\) −9.42025e124 −1.06204
\(299\) −1.78344e124 −0.169771
\(300\) −4.63254e124 −0.372560
\(301\) −7.63235e124 −0.518860
\(302\) 1.07867e125 0.620207
\(303\) 8.92376e123 0.0434205
\(304\) 1.10755e124 0.0456296
\(305\) −1.34405e125 −0.469110
\(306\) 6.59274e125 1.95045
\(307\) 5.07790e124 0.127408 0.0637039 0.997969i \(-0.479709\pi\)
0.0637039 + 0.997969i \(0.479709\pi\)
\(308\) 6.17947e125 1.31565
\(309\) 9.51839e124 0.172052
\(310\) −2.39937e126 −3.68410
\(311\) 8.66949e125 1.13134 0.565671 0.824631i \(-0.308617\pi\)
0.565671 + 0.824631i \(0.308617\pi\)
\(312\) 8.25187e124 0.0915684
\(313\) −2.59518e125 −0.245007 −0.122504 0.992468i \(-0.539092\pi\)
−0.122504 + 0.992468i \(0.539092\pi\)
\(314\) 5.78167e125 0.464629
\(315\) 2.67295e126 1.82940
\(316\) −1.72594e126 −1.00654
\(317\) 2.15142e126 1.06963 0.534813 0.844971i \(-0.320382\pi\)
0.534813 + 0.844971i \(0.320382\pi\)
\(318\) 8.77375e125 0.372062
\(319\) −3.41944e126 −1.23744
\(320\) −7.65431e126 −2.36501
\(321\) −2.85748e125 −0.0754186
\(322\) −3.48280e126 −0.785610
\(323\) 5.31311e126 1.02476
\(324\) 8.39732e126 1.38554
\(325\) −3.61647e126 −0.510710
\(326\) −1.48519e127 −1.79595
\(327\) −4.93444e125 −0.0511183
\(328\) 1.63478e127 1.45155
\(329\) 2.33104e127 1.77483
\(330\) 4.72123e126 0.308391
\(331\) −1.15240e127 −0.646085 −0.323042 0.946385i \(-0.604706\pi\)
−0.323042 + 0.946385i \(0.604706\pi\)
\(332\) 5.04793e127 2.43019
\(333\) −2.11732e127 −0.875696
\(334\) −5.23583e127 −1.86118
\(335\) 3.27010e127 0.999536
\(336\) −5.91877e125 −0.0155632
\(337\) −3.11810e127 −0.705635 −0.352817 0.935692i \(-0.614776\pi\)
−0.352817 + 0.935692i \(0.614776\pi\)
\(338\) −6.53188e127 −1.27275
\(339\) 1.62651e127 0.273006
\(340\) −2.02907e128 −2.93502
\(341\) 7.92116e127 0.987854
\(342\) 1.15737e128 1.24496
\(343\) 3.81711e127 0.354308
\(344\) 4.69570e127 0.376270
\(345\) −1.63453e127 −0.113118
\(346\) 2.79157e128 1.66919
\(347\) −1.04259e128 −0.538858 −0.269429 0.963020i \(-0.586835\pi\)
−0.269429 + 0.963020i \(0.586835\pi\)
\(348\) −1.47222e128 −0.657995
\(349\) 4.27486e128 1.65287 0.826433 0.563036i \(-0.190367\pi\)
0.826433 + 0.563036i \(0.190367\pi\)
\(350\) −7.06243e128 −2.36330
\(351\) −6.47999e127 −0.187743
\(352\) 2.61464e128 0.656157
\(353\) 3.37741e128 0.734449 0.367224 0.930132i \(-0.380308\pi\)
0.367224 + 0.930132i \(0.380308\pi\)
\(354\) 1.95507e128 0.368551
\(355\) −5.64061e128 −0.922135
\(356\) 6.69469e128 0.949523
\(357\) −2.83934e128 −0.349520
\(358\) 2.16756e129 2.31675
\(359\) −2.13662e129 −1.98362 −0.991810 0.127724i \(-0.959233\pi\)
−0.991810 + 0.127724i \(0.959233\pi\)
\(360\) −1.64450e129 −1.32665
\(361\) −4.93253e128 −0.345904
\(362\) −6.55490e128 −0.399745
\(363\) 2.39364e128 0.126991
\(364\) 2.07699e129 0.958993
\(365\) −2.63813e129 −1.06049
\(366\) 3.11004e128 0.108886
\(367\) −8.11750e128 −0.247620 −0.123810 0.992306i \(-0.539511\pi\)
−0.123810 + 0.992306i \(0.539511\pi\)
\(368\) −7.87009e127 −0.0209250
\(369\) −6.27449e129 −1.45461
\(370\) 1.06085e130 2.14520
\(371\) 8.21641e129 1.44977
\(372\) 3.41042e129 0.525278
\(373\) 4.08727e129 0.549714 0.274857 0.961485i \(-0.411369\pi\)
0.274857 + 0.961485i \(0.411369\pi\)
\(374\) 1.09050e130 1.28118
\(375\) −3.43736e128 −0.0352896
\(376\) −1.43414e130 −1.28708
\(377\) −1.14932e130 −0.901989
\(378\) −1.26545e130 −0.868777
\(379\) −5.94249e129 −0.357017 −0.178508 0.983938i \(-0.557127\pi\)
−0.178508 + 0.983938i \(0.557127\pi\)
\(380\) −3.56207e130 −1.87340
\(381\) −4.88243e129 −0.224867
\(382\) 2.01866e130 0.814447
\(383\) 3.05852e130 1.08137 0.540684 0.841226i \(-0.318166\pi\)
0.540684 + 0.841226i \(0.318166\pi\)
\(384\) 1.06426e130 0.329855
\(385\) 4.42132e130 1.20167
\(386\) −1.10510e131 −2.63477
\(387\) −1.80227e130 −0.377064
\(388\) 6.24801e130 1.14747
\(389\) 7.76173e130 1.25171 0.625855 0.779940i \(-0.284750\pi\)
0.625855 + 0.779940i \(0.284750\pi\)
\(390\) 1.58686e130 0.224790
\(391\) −3.77542e130 −0.469937
\(392\) 6.37131e130 0.697080
\(393\) −1.50241e130 −0.144532
\(394\) 2.92271e130 0.247302
\(395\) −1.23489e131 −0.919336
\(396\) 1.45919e131 0.956104
\(397\) −1.13551e131 −0.655044 −0.327522 0.944844i \(-0.606214\pi\)
−0.327522 + 0.944844i \(0.606214\pi\)
\(398\) −1.38134e131 −0.701789
\(399\) −4.98452e130 −0.223096
\(400\) −1.59590e130 −0.0629471
\(401\) 4.48151e131 1.55824 0.779119 0.626876i \(-0.215667\pi\)
0.779119 + 0.626876i \(0.215667\pi\)
\(402\) −7.56677e130 −0.232004
\(403\) 2.66240e131 0.720059
\(404\) −1.38189e131 −0.329772
\(405\) 6.00816e131 1.26550
\(406\) −2.24445e132 −4.17392
\(407\) −3.50225e131 −0.575215
\(408\) 1.74687e131 0.253467
\(409\) −1.25927e132 −1.61469 −0.807347 0.590077i \(-0.799098\pi\)
−0.807347 + 0.590077i \(0.799098\pi\)
\(410\) 3.14374e132 3.56338
\(411\) −1.91598e131 −0.192034
\(412\) −1.47397e132 −1.30671
\(413\) 1.83088e132 1.43609
\(414\) −8.22411e131 −0.570916
\(415\) 3.61172e132 2.21965
\(416\) 8.78813e131 0.478281
\(417\) −2.26866e130 −0.0109370
\(418\) 1.91440e132 0.817769
\(419\) −2.46484e132 −0.933214 −0.466607 0.884465i \(-0.654524\pi\)
−0.466607 + 0.884465i \(0.654524\pi\)
\(420\) 1.90358e132 0.638972
\(421\) −4.71464e132 −1.40347 −0.701734 0.712439i \(-0.747590\pi\)
−0.701734 + 0.712439i \(0.747590\pi\)
\(422\) −7.01697e132 −1.85298
\(423\) 5.50440e132 1.28980
\(424\) −5.05504e132 −1.05135
\(425\) −7.65582e132 −1.41368
\(426\) 1.30520e132 0.214038
\(427\) 2.91248e132 0.424282
\(428\) 4.42494e132 0.572793
\(429\) −5.23879e131 −0.0602751
\(430\) 9.02999e132 0.923699
\(431\) −1.67772e133 −1.52622 −0.763111 0.646268i \(-0.776329\pi\)
−0.763111 + 0.646268i \(0.776329\pi\)
\(432\) −2.85953e131 −0.0231401
\(433\) −6.18307e129 −0.000445211 0 −0.000222605 1.00000i \(-0.500071\pi\)
−0.000222605 1.00000i \(0.500071\pi\)
\(434\) 5.19927e133 3.33205
\(435\) −1.05336e133 −0.600990
\(436\) 7.64123e132 0.388236
\(437\) −6.62784e132 −0.299957
\(438\) 6.10443e132 0.246152
\(439\) −3.77735e133 −1.35747 −0.678733 0.734385i \(-0.737470\pi\)
−0.678733 + 0.734385i \(0.737470\pi\)
\(440\) −2.72016e133 −0.871433
\(441\) −2.44538e133 −0.698551
\(442\) 3.66531e133 0.933869
\(443\) 6.56580e133 1.49245 0.746224 0.665695i \(-0.231865\pi\)
0.746224 + 0.665695i \(0.231865\pi\)
\(444\) −1.50788e133 −0.305863
\(445\) 4.78995e133 0.867262
\(446\) −1.52391e134 −2.46348
\(447\) 9.58019e132 0.138307
\(448\) 1.65864e134 2.13901
\(449\) 7.19767e133 0.829377 0.414688 0.909963i \(-0.363891\pi\)
0.414688 + 0.909963i \(0.363891\pi\)
\(450\) −1.66769e134 −1.71745
\(451\) −1.03786e134 −0.955484
\(452\) −2.51874e134 −2.07344
\(453\) −1.09698e133 −0.0807681
\(454\) 3.87840e133 0.255466
\(455\) 1.48606e134 0.875912
\(456\) 3.06666e133 0.161786
\(457\) 1.64631e134 0.777576 0.388788 0.921327i \(-0.372894\pi\)
0.388788 + 0.921327i \(0.372894\pi\)
\(458\) 2.73509e134 1.15682
\(459\) −1.37177e134 −0.519686
\(460\) 2.53116e134 0.859110
\(461\) −1.97585e134 −0.600976 −0.300488 0.953786i \(-0.597150\pi\)
−0.300488 + 0.953786i \(0.597150\pi\)
\(462\) −1.02306e134 −0.278921
\(463\) 5.15727e134 1.26061 0.630303 0.776349i \(-0.282930\pi\)
0.630303 + 0.776349i \(0.282930\pi\)
\(464\) −5.07178e133 −0.111174
\(465\) 2.44010e134 0.479771
\(466\) 6.82879e133 0.120463
\(467\) 2.94920e133 0.0466876 0.0233438 0.999727i \(-0.492569\pi\)
0.0233438 + 0.999727i \(0.492569\pi\)
\(468\) 4.90451e134 0.696916
\(469\) −7.08610e134 −0.904021
\(470\) −2.75790e135 −3.15963
\(471\) −5.87984e133 −0.0605075
\(472\) −1.12642e135 −1.04143
\(473\) −2.98112e134 −0.247681
\(474\) 2.85744e134 0.213388
\(475\) −1.34400e135 −0.902340
\(476\) 4.39686e135 2.65455
\(477\) 1.94018e135 1.05357
\(478\) −2.92643e134 −0.142965
\(479\) 2.46547e135 1.08382 0.541909 0.840437i \(-0.317702\pi\)
0.541909 + 0.840437i \(0.317702\pi\)
\(480\) 8.05438e134 0.318676
\(481\) −1.17715e135 −0.419281
\(482\) −1.03062e135 −0.330540
\(483\) 3.54193e134 0.102308
\(484\) −3.70667e135 −0.964479
\(485\) 4.47036e135 1.04806
\(486\) −4.51583e135 −0.954127
\(487\) 1.02728e134 0.0195649 0.00978245 0.999952i \(-0.496886\pi\)
0.00978245 + 0.999952i \(0.496886\pi\)
\(488\) −1.79186e135 −0.307683
\(489\) 1.51041e135 0.233882
\(490\) 1.22522e136 1.71125
\(491\) −8.92443e134 −0.112451 −0.0562257 0.998418i \(-0.517907\pi\)
−0.0562257 + 0.998418i \(0.517907\pi\)
\(492\) −4.46846e135 −0.508066
\(493\) −2.43302e136 −2.49676
\(494\) 6.43453e135 0.596082
\(495\) 1.04403e136 0.873273
\(496\) 1.17488e135 0.0887502
\(497\) 1.22229e136 0.834017
\(498\) −8.35725e135 −0.515207
\(499\) −3.42871e136 −1.91009 −0.955044 0.296464i \(-0.904192\pi\)
−0.955044 + 0.296464i \(0.904192\pi\)
\(500\) 5.32293e135 0.268019
\(501\) 5.32473e135 0.242378
\(502\) 1.79184e136 0.737499
\(503\) −4.02932e136 −1.49985 −0.749926 0.661522i \(-0.769911\pi\)
−0.749926 + 0.661522i \(0.769911\pi\)
\(504\) 3.56353e136 1.19988
\(505\) −9.88721e135 −0.301203
\(506\) −1.36035e136 −0.375015
\(507\) 6.64278e135 0.165748
\(508\) 7.56069e136 1.70783
\(509\) 1.18185e136 0.241721 0.120861 0.992669i \(-0.461435\pi\)
0.120861 + 0.992669i \(0.461435\pi\)
\(510\) 3.35928e136 0.622232
\(511\) 5.71666e136 0.959151
\(512\) 7.41901e135 0.112775
\(513\) −2.40817e136 −0.331711
\(514\) −3.63657e136 −0.453999
\(515\) −1.05460e137 −1.19350
\(516\) −1.28351e136 −0.131701
\(517\) 9.10480e136 0.847223
\(518\) −2.29880e137 −1.94021
\(519\) −2.83897e136 −0.217374
\(520\) −9.14278e136 −0.635199
\(521\) 9.59448e136 0.604946 0.302473 0.953158i \(-0.402188\pi\)
0.302473 + 0.953158i \(0.402188\pi\)
\(522\) −5.29993e137 −3.03326
\(523\) 1.10209e137 0.572642 0.286321 0.958134i \(-0.407568\pi\)
0.286321 + 0.958134i \(0.407568\pi\)
\(524\) 2.32656e137 1.09770
\(525\) 7.18234e136 0.307766
\(526\) 5.60106e137 2.18017
\(527\) 5.63612e137 1.99317
\(528\) −2.31181e135 −0.00742915
\(529\) −2.95286e137 −0.862445
\(530\) −9.72100e137 −2.58095
\(531\) 4.32335e137 1.04363
\(532\) 7.71878e137 1.69438
\(533\) −3.48837e137 −0.696464
\(534\) −1.10836e137 −0.201301
\(535\) 3.16598e137 0.523170
\(536\) 4.35963e137 0.655583
\(537\) −2.20436e137 −0.301704
\(538\) −1.30362e138 −1.62423
\(539\) −4.04490e137 −0.458855
\(540\) 9.19676e137 0.950058
\(541\) −6.70930e137 −0.631270 −0.315635 0.948881i \(-0.602218\pi\)
−0.315635 + 0.948881i \(0.602218\pi\)
\(542\) −1.53454e138 −1.31527
\(543\) 6.66619e136 0.0520579
\(544\) 1.86039e138 1.32391
\(545\) 5.46719e137 0.354601
\(546\) −3.43863e137 −0.203309
\(547\) −8.05553e137 −0.434244 −0.217122 0.976144i \(-0.569667\pi\)
−0.217122 + 0.976144i \(0.569667\pi\)
\(548\) 2.96698e138 1.45847
\(549\) 6.87738e137 0.308333
\(550\) −2.75852e138 −1.12813
\(551\) −4.27123e138 −1.59366
\(552\) −2.17913e137 −0.0741924
\(553\) 2.67592e138 0.831486
\(554\) −3.85543e138 −1.09353
\(555\) −1.07887e138 −0.279365
\(556\) 3.51314e137 0.0830651
\(557\) 6.47956e138 1.39913 0.699565 0.714569i \(-0.253377\pi\)
0.699565 + 0.714569i \(0.253377\pi\)
\(558\) 1.22773e139 2.42145
\(559\) −1.00199e138 −0.180537
\(560\) 6.55778e137 0.107960
\(561\) −1.10902e138 −0.166845
\(562\) 6.09870e138 0.838598
\(563\) 4.45055e138 0.559423 0.279711 0.960084i \(-0.409761\pi\)
0.279711 + 0.960084i \(0.409761\pi\)
\(564\) 3.92003e138 0.450500
\(565\) −1.80212e139 −1.89381
\(566\) −2.27127e139 −2.18293
\(567\) −1.30193e139 −1.14457
\(568\) −7.51995e138 −0.604817
\(569\) 1.34965e139 0.993237 0.496618 0.867969i \(-0.334575\pi\)
0.496618 + 0.867969i \(0.334575\pi\)
\(570\) 5.89729e138 0.397166
\(571\) 1.08594e139 0.669396 0.334698 0.942325i \(-0.391366\pi\)
0.334698 + 0.942325i \(0.391366\pi\)
\(572\) 8.11253e138 0.457780
\(573\) −2.05293e138 −0.106063
\(574\) −6.81229e139 −3.22287
\(575\) 9.55024e138 0.413798
\(576\) 3.91663e139 1.55445
\(577\) −2.62894e139 −0.955876 −0.477938 0.878394i \(-0.658616\pi\)
−0.477938 + 0.878394i \(0.658616\pi\)
\(578\) 2.92622e139 0.974881
\(579\) 1.12386e139 0.343120
\(580\) 1.63117e140 4.56443
\(581\) −7.82637e139 −2.00755
\(582\) −1.03441e139 −0.243266
\(583\) 3.20925e139 0.692056
\(584\) −3.51710e139 −0.695562
\(585\) 3.50911e139 0.636540
\(586\) −2.01565e139 −0.335417
\(587\) −1.05231e140 −1.60664 −0.803321 0.595546i \(-0.796936\pi\)
−0.803321 + 0.595546i \(0.796936\pi\)
\(588\) −1.74151e139 −0.243990
\(589\) 9.89432e139 1.27222
\(590\) −2.16615e140 −2.55660
\(591\) −2.97234e138 −0.0322055
\(592\) −5.19461e138 −0.0516781
\(593\) 6.79702e139 0.620950 0.310475 0.950582i \(-0.399512\pi\)
0.310475 + 0.950582i \(0.399512\pi\)
\(594\) −4.94271e139 −0.414715
\(595\) 3.14589e140 2.42458
\(596\) −1.48354e140 −1.05042
\(597\) 1.40480e139 0.0913923
\(598\) −4.57229e139 −0.273353
\(599\) −1.50842e140 −0.828835 −0.414417 0.910087i \(-0.636015\pi\)
−0.414417 + 0.910087i \(0.636015\pi\)
\(600\) −4.41884e139 −0.223188
\(601\) 3.83968e140 1.78293 0.891464 0.453091i \(-0.149679\pi\)
0.891464 + 0.453091i \(0.149679\pi\)
\(602\) −1.95674e140 −0.835431
\(603\) −1.67328e140 −0.656967
\(604\) 1.69873e140 0.613421
\(605\) −2.65207e140 −0.880923
\(606\) 2.28783e139 0.0699126
\(607\) 8.64913e139 0.243189 0.121594 0.992580i \(-0.461199\pi\)
0.121594 + 0.992580i \(0.461199\pi\)
\(608\) 3.26595e140 0.845044
\(609\) 2.28255e140 0.543560
\(610\) −3.44581e140 −0.755327
\(611\) 3.06023e140 0.617551
\(612\) 1.03825e141 1.92911
\(613\) −7.96669e140 −1.36309 −0.681544 0.731777i \(-0.738691\pi\)
−0.681544 + 0.731777i \(0.738691\pi\)
\(614\) 1.30184e140 0.205143
\(615\) −3.19712e140 −0.464050
\(616\) 5.89441e140 0.788160
\(617\) 4.02335e140 0.495664 0.247832 0.968803i \(-0.420282\pi\)
0.247832 + 0.968803i \(0.420282\pi\)
\(618\) 2.44027e140 0.277026
\(619\) −8.10256e140 −0.847705 −0.423852 0.905731i \(-0.639322\pi\)
−0.423852 + 0.905731i \(0.639322\pi\)
\(620\) −3.77862e141 −3.64379
\(621\) 1.71121e140 0.152117
\(622\) 2.22264e141 1.82161
\(623\) −1.03795e141 −0.784388
\(624\) −7.77027e138 −0.00541520
\(625\) −1.35492e141 −0.870906
\(626\) −6.65339e140 −0.394493
\(627\) −1.94691e140 −0.106496
\(628\) 9.10522e140 0.459545
\(629\) −2.49195e141 −1.16060
\(630\) 6.85278e141 2.94557
\(631\) 1.26653e141 0.502496 0.251248 0.967923i \(-0.419159\pi\)
0.251248 + 0.967923i \(0.419159\pi\)
\(632\) −1.64633e141 −0.602981
\(633\) 7.13610e140 0.241309
\(634\) 5.51569e141 1.72223
\(635\) 5.40956e141 1.55987
\(636\) 1.38173e141 0.367991
\(637\) −1.35954e141 −0.334465
\(638\) −8.76658e141 −1.99244
\(639\) 2.88624e141 0.606094
\(640\) −1.17917e142 −2.28816
\(641\) 2.46708e141 0.442438 0.221219 0.975224i \(-0.428996\pi\)
0.221219 + 0.975224i \(0.428996\pi\)
\(642\) −7.32585e140 −0.121434
\(643\) −1.00891e142 −1.54596 −0.772981 0.634430i \(-0.781235\pi\)
−0.772981 + 0.634430i \(0.781235\pi\)
\(644\) −5.48486e141 −0.777015
\(645\) −9.18331e140 −0.120291
\(646\) 1.36215e142 1.64999
\(647\) 5.47711e141 0.613600 0.306800 0.951774i \(-0.400742\pi\)
0.306800 + 0.951774i \(0.400742\pi\)
\(648\) 8.00995e141 0.830027
\(649\) 7.15123e141 0.685526
\(650\) −9.27170e141 −0.822309
\(651\) −5.28755e141 −0.433925
\(652\) −2.33894e142 −1.77630
\(653\) −1.55247e141 −0.109121 −0.0545605 0.998510i \(-0.517376\pi\)
−0.0545605 + 0.998510i \(0.517376\pi\)
\(654\) −1.26507e141 −0.0823070
\(655\) 1.66462e142 1.00260
\(656\) −1.53937e141 −0.0858420
\(657\) 1.34990e142 0.697030
\(658\) 5.97619e142 2.85770
\(659\) −3.76071e142 −1.66554 −0.832772 0.553616i \(-0.813248\pi\)
−0.832772 + 0.553616i \(0.813248\pi\)
\(660\) 7.43519e141 0.305017
\(661\) −3.14082e142 −1.19363 −0.596815 0.802379i \(-0.703567\pi\)
−0.596815 + 0.802379i \(0.703567\pi\)
\(662\) −2.95446e142 −1.04028
\(663\) −3.72754e141 −0.121616
\(664\) 4.81507e142 1.45584
\(665\) 5.52267e142 1.54759
\(666\) −5.42828e142 −1.40998
\(667\) 3.03508e142 0.730827
\(668\) −8.24561e142 −1.84082
\(669\) 1.54979e142 0.320814
\(670\) 8.38371e142 1.60938
\(671\) 1.13758e142 0.202533
\(672\) −1.74533e142 −0.288224
\(673\) 5.72017e142 0.876290 0.438145 0.898904i \(-0.355636\pi\)
0.438145 + 0.898904i \(0.355636\pi\)
\(674\) −7.99402e142 −1.13616
\(675\) 3.47000e142 0.457604
\(676\) −1.02867e143 −1.25883
\(677\) −1.68388e143 −1.91242 −0.956211 0.292679i \(-0.905453\pi\)
−0.956211 + 0.292679i \(0.905453\pi\)
\(678\) 4.16997e142 0.439575
\(679\) −9.68699e142 −0.947906
\(680\) −1.93547e143 −1.75827
\(681\) −3.94426e141 −0.0332687
\(682\) 2.03078e143 1.59057
\(683\) 9.75485e142 0.709537 0.354769 0.934954i \(-0.384560\pi\)
0.354769 + 0.934954i \(0.384560\pi\)
\(684\) 1.82268e143 1.23133
\(685\) 2.12283e143 1.33212
\(686\) 9.78610e142 0.570482
\(687\) −2.78153e142 −0.150650
\(688\) −4.42165e141 −0.0222520
\(689\) 1.07867e143 0.504448
\(690\) −4.19053e142 −0.182134
\(691\) −9.67210e142 −0.390732 −0.195366 0.980730i \(-0.562590\pi\)
−0.195366 + 0.980730i \(0.562590\pi\)
\(692\) 4.39628e143 1.65093
\(693\) −2.26235e143 −0.789824
\(694\) −2.67293e143 −0.867630
\(695\) 2.51360e142 0.0758689
\(696\) −1.40431e143 −0.394182
\(697\) −7.38465e143 −1.92786
\(698\) 1.09596e144 2.66132
\(699\) −6.94473e141 −0.0156877
\(700\) −1.11222e144 −2.33744
\(701\) −6.48692e143 −1.26847 −0.634233 0.773142i \(-0.718684\pi\)
−0.634233 + 0.773142i \(0.718684\pi\)
\(702\) −1.66130e143 −0.302291
\(703\) −4.37467e143 −0.740800
\(704\) 6.47849e143 1.02107
\(705\) 2.80472e143 0.411471
\(706\) 8.65883e143 1.18256
\(707\) 2.14250e143 0.272420
\(708\) 3.07893e143 0.364519
\(709\) 8.63719e143 0.952221 0.476111 0.879385i \(-0.342046\pi\)
0.476111 + 0.879385i \(0.342046\pi\)
\(710\) −1.44611e144 −1.48476
\(711\) 6.31880e143 0.604254
\(712\) 6.38586e143 0.568826
\(713\) −7.03077e143 −0.583420
\(714\) −7.27935e143 −0.562772
\(715\) 5.80440e143 0.418121
\(716\) 3.41357e144 2.29140
\(717\) 2.97612e142 0.0186180
\(718\) −5.47776e144 −3.19388
\(719\) 1.28977e143 0.0700975 0.0350488 0.999386i \(-0.488841\pi\)
0.0350488 + 0.999386i \(0.488841\pi\)
\(720\) 1.54852e143 0.0784561
\(721\) 2.28526e144 1.07946
\(722\) −1.26457e144 −0.556950
\(723\) 1.04812e143 0.0430454
\(724\) −1.03229e144 −0.395372
\(725\) 6.15453e144 2.19850
\(726\) 6.13668e143 0.204472
\(727\) −1.32206e144 −0.410925 −0.205462 0.978665i \(-0.565870\pi\)
−0.205462 + 0.978665i \(0.565870\pi\)
\(728\) 1.98118e144 0.574500
\(729\) −2.75645e144 −0.745778
\(730\) −6.76350e144 −1.70752
\(731\) −2.12115e144 −0.499739
\(732\) 4.89782e143 0.107694
\(733\) 2.44219e144 0.501220 0.250610 0.968088i \(-0.419369\pi\)
0.250610 + 0.968088i \(0.419369\pi\)
\(734\) −2.08112e144 −0.398700
\(735\) −1.24603e144 −0.222852
\(736\) −2.32074e144 −0.387523
\(737\) −2.76776e144 −0.431539
\(738\) −1.60862e145 −2.34211
\(739\) 6.04415e144 0.821847 0.410924 0.911670i \(-0.365206\pi\)
0.410924 + 0.911670i \(0.365206\pi\)
\(740\) 1.67068e145 2.12173
\(741\) −6.54378e143 −0.0776264
\(742\) 2.10648e145 2.33432
\(743\) 4.51166e144 0.467091 0.233546 0.972346i \(-0.424967\pi\)
0.233546 + 0.972346i \(0.424967\pi\)
\(744\) 3.25310e144 0.314676
\(745\) −1.06145e145 −0.959419
\(746\) 1.04787e145 0.885110
\(747\) −1.84808e145 −1.45892
\(748\) 1.71737e145 1.26716
\(749\) −6.86048e144 −0.473176
\(750\) −8.81253e143 −0.0568207
\(751\) 1.45207e145 0.875326 0.437663 0.899139i \(-0.355806\pi\)
0.437663 + 0.899139i \(0.355806\pi\)
\(752\) 1.35044e144 0.0761157
\(753\) −1.82226e144 −0.0960428
\(754\) −2.94655e145 −1.45232
\(755\) 1.21542e145 0.560278
\(756\) −1.99288e145 −0.859271
\(757\) −1.20161e145 −0.484641 −0.242320 0.970196i \(-0.577909\pi\)
−0.242320 + 0.970196i \(0.577909\pi\)
\(758\) −1.52351e145 −0.574843
\(759\) 1.38344e144 0.0488373
\(760\) −3.39775e145 −1.12229
\(761\) −3.90026e145 −1.20550 −0.602751 0.797929i \(-0.705929\pi\)
−0.602751 + 0.797929i \(0.705929\pi\)
\(762\) −1.25173e145 −0.362064
\(763\) −1.18470e145 −0.320716
\(764\) 3.17906e145 0.805536
\(765\) 7.42855e145 1.76198
\(766\) 7.84127e145 1.74114
\(767\) 2.40362e145 0.499688
\(768\) 9.77007e144 0.190176
\(769\) 4.51695e144 0.0823313 0.0411656 0.999152i \(-0.486893\pi\)
0.0411656 + 0.999152i \(0.486893\pi\)
\(770\) 1.13351e146 1.93484
\(771\) 3.69831e144 0.0591232
\(772\) −1.74036e146 −2.60594
\(773\) 1.00998e145 0.141661 0.0708303 0.997488i \(-0.477435\pi\)
0.0708303 + 0.997488i \(0.477435\pi\)
\(774\) −4.62055e145 −0.607121
\(775\) −1.42570e146 −1.75506
\(776\) 5.95979e145 0.687408
\(777\) 2.33783e145 0.252669
\(778\) 1.98991e146 2.01541
\(779\) −1.29639e146 −1.23054
\(780\) 2.49906e145 0.222330
\(781\) 4.77412e145 0.398122
\(782\) −9.67923e145 −0.756658
\(783\) 1.10277e146 0.808195
\(784\) −5.99947e144 −0.0412241
\(785\) 6.51465e145 0.419733
\(786\) −3.85180e145 −0.232716
\(787\) −2.76862e146 −1.56870 −0.784350 0.620319i \(-0.787003\pi\)
−0.784350 + 0.620319i \(0.787003\pi\)
\(788\) 4.60281e145 0.244596
\(789\) −5.69615e145 −0.283918
\(790\) −3.16594e146 −1.48025
\(791\) 3.90508e146 1.71284
\(792\) 1.39188e146 0.572769
\(793\) 3.82356e145 0.147629
\(794\) −2.91116e146 −1.05470
\(795\) 9.88605e145 0.336111
\(796\) −2.17540e146 −0.694110
\(797\) −1.73951e146 −0.520932 −0.260466 0.965483i \(-0.583876\pi\)
−0.260466 + 0.965483i \(0.583876\pi\)
\(798\) −1.27791e146 −0.359214
\(799\) 6.47831e146 1.70942
\(800\) −4.70601e146 −1.16576
\(801\) −2.45097e146 −0.570027
\(802\) 1.14895e147 2.50896
\(803\) 2.23287e146 0.457855
\(804\) −1.19165e146 −0.229465
\(805\) −3.92434e146 −0.709699
\(806\) 6.82571e146 1.15939
\(807\) 1.32576e146 0.211520
\(808\) −1.31814e146 −0.197555
\(809\) 6.19950e146 0.872883 0.436442 0.899733i \(-0.356239\pi\)
0.436442 + 0.899733i \(0.356239\pi\)
\(810\) 1.54034e147 2.03762
\(811\) 9.95522e146 1.23736 0.618682 0.785641i \(-0.287667\pi\)
0.618682 + 0.785641i \(0.287667\pi\)
\(812\) −3.53465e147 −4.12826
\(813\) 1.56059e146 0.171284
\(814\) −8.97889e146 −0.926169
\(815\) −1.67348e147 −1.62241
\(816\) −1.64492e145 −0.0149896
\(817\) −3.72372e146 −0.318980
\(818\) −3.22844e147 −2.59986
\(819\) −7.60401e146 −0.575713
\(820\) 4.95089e147 3.52439
\(821\) 1.00145e147 0.670349 0.335174 0.942156i \(-0.391205\pi\)
0.335174 + 0.942156i \(0.391205\pi\)
\(822\) −4.91208e146 −0.309199
\(823\) −3.42968e146 −0.203031 −0.101515 0.994834i \(-0.532369\pi\)
−0.101515 + 0.994834i \(0.532369\pi\)
\(824\) −1.40598e147 −0.782805
\(825\) 2.80535e146 0.146914
\(826\) 4.69391e147 2.31229
\(827\) −2.19408e147 −1.01677 −0.508386 0.861129i \(-0.669758\pi\)
−0.508386 + 0.861129i \(0.669758\pi\)
\(828\) −1.29517e147 −0.564669
\(829\) −1.42397e147 −0.584113 −0.292057 0.956401i \(-0.594340\pi\)
−0.292057 + 0.956401i \(0.594340\pi\)
\(830\) 9.25953e147 3.57393
\(831\) 3.92089e146 0.142408
\(832\) 2.17750e147 0.744268
\(833\) −2.87805e147 −0.925819
\(834\) −5.81628e145 −0.0176100
\(835\) −5.89961e147 −1.68134
\(836\) 3.01488e147 0.808822
\(837\) −2.55457e147 −0.645183
\(838\) −6.31924e147 −1.50259
\(839\) 2.17760e147 0.487528 0.243764 0.969835i \(-0.421618\pi\)
0.243764 + 0.969835i \(0.421618\pi\)
\(840\) 1.81577e147 0.382786
\(841\) 1.45219e148 2.88287
\(842\) −1.20871e148 −2.25976
\(843\) −6.20225e146 −0.109209
\(844\) −1.10506e148 −1.83271
\(845\) −7.35997e147 −1.14977
\(846\) 1.41119e148 2.07674
\(847\) 5.74686e147 0.796743
\(848\) 4.76001e146 0.0621753
\(849\) 2.30983e147 0.284277
\(850\) −1.96276e148 −2.27620
\(851\) 3.10858e147 0.339718
\(852\) 2.05548e147 0.211696
\(853\) 2.39847e147 0.232814 0.116407 0.993202i \(-0.462862\pi\)
0.116407 + 0.993202i \(0.462862\pi\)
\(854\) 7.46685e147 0.683149
\(855\) 1.30410e148 1.12466
\(856\) 4.22082e147 0.343140
\(857\) −1.77495e148 −1.36037 −0.680183 0.733042i \(-0.738100\pi\)
−0.680183 + 0.733042i \(0.738100\pi\)
\(858\) −1.34309e147 −0.0970506
\(859\) −1.76032e148 −1.19933 −0.599664 0.800252i \(-0.704699\pi\)
−0.599664 + 0.800252i \(0.704699\pi\)
\(860\) 1.42208e148 0.913592
\(861\) 6.92795e147 0.419706
\(862\) −4.30125e148 −2.45741
\(863\) 2.64645e148 1.42600 0.712998 0.701166i \(-0.247337\pi\)
0.712998 + 0.701166i \(0.247337\pi\)
\(864\) −8.43223e147 −0.428547
\(865\) 3.14547e148 1.50790
\(866\) −1.58518e145 −0.000716846 0
\(867\) −2.97591e147 −0.126957
\(868\) 8.18803e148 3.29559
\(869\) 1.04519e148 0.396914
\(870\) −2.70054e148 −0.967671
\(871\) −9.30277e147 −0.314554
\(872\) 7.28874e147 0.232579
\(873\) −2.28744e148 −0.688859
\(874\) −1.69921e148 −0.482969
\(875\) −8.25273e147 −0.221407
\(876\) 9.61352e147 0.243458
\(877\) −7.77572e148 −1.85892 −0.929461 0.368920i \(-0.879728\pi\)
−0.929461 + 0.368920i \(0.879728\pi\)
\(878\) −9.68416e148 −2.18569
\(879\) 2.04987e147 0.0436806
\(880\) 2.56141e147 0.0515351
\(881\) 5.10744e148 0.970332 0.485166 0.874422i \(-0.338759\pi\)
0.485166 + 0.874422i \(0.338759\pi\)
\(882\) −6.26934e148 −1.12476
\(883\) −4.89678e148 −0.829650 −0.414825 0.909901i \(-0.636157\pi\)
−0.414825 + 0.909901i \(0.636157\pi\)
\(884\) 5.77228e148 0.923652
\(885\) 2.20293e148 0.332940
\(886\) 1.68330e149 2.40303
\(887\) 8.91966e148 1.20283 0.601416 0.798936i \(-0.294603\pi\)
0.601416 + 0.798936i \(0.294603\pi\)
\(888\) −1.43832e148 −0.183232
\(889\) −1.17222e149 −1.41081
\(890\) 1.22802e149 1.39640
\(891\) −5.08521e148 −0.546367
\(892\) −2.39992e149 −2.43653
\(893\) 1.13728e149 1.09111
\(894\) 2.45612e148 0.222692
\(895\) 2.44236e149 2.09289
\(896\) 2.55518e149 2.06951
\(897\) 4.64992e147 0.0355981
\(898\) 1.84530e149 1.33540
\(899\) −4.53089e149 −3.09970
\(900\) −2.62635e149 −1.69865
\(901\) 2.28347e149 1.39634
\(902\) −2.66081e149 −1.53845
\(903\) 1.98996e148 0.108796
\(904\) −2.40255e149 −1.24213
\(905\) −7.38591e148 −0.361119
\(906\) −2.81238e148 −0.130047
\(907\) −2.11629e149 −0.925567 −0.462784 0.886471i \(-0.653149\pi\)
−0.462784 + 0.886471i \(0.653149\pi\)
\(908\) 6.10787e148 0.252671
\(909\) 5.05919e148 0.197972
\(910\) 3.80988e149 1.41033
\(911\) 2.22931e149 0.780715 0.390358 0.920663i \(-0.372351\pi\)
0.390358 + 0.920663i \(0.372351\pi\)
\(912\) −2.88768e147 −0.00956776
\(913\) −3.05690e149 −0.958312
\(914\) 4.22072e149 1.25200
\(915\) 3.50432e148 0.0983644
\(916\) 4.30734e149 1.14416
\(917\) −3.60712e149 −0.906796
\(918\) −3.51687e149 −0.836760
\(919\) −4.28888e149 −0.965852 −0.482926 0.875661i \(-0.660426\pi\)
−0.482926 + 0.875661i \(0.660426\pi\)
\(920\) 2.41440e149 0.514663
\(921\) −1.32395e148 −0.0267153
\(922\) −5.06558e149 −0.967648
\(923\) 1.60464e149 0.290196
\(924\) −1.61116e149 −0.275870
\(925\) 6.30358e149 1.02195
\(926\) 1.32219e150 2.02974
\(927\) 5.39630e149 0.784457
\(928\) −1.49557e150 −2.05890
\(929\) 1.69023e149 0.220370 0.110185 0.993911i \(-0.464856\pi\)
0.110185 + 0.993911i \(0.464856\pi\)
\(930\) 6.25581e149 0.772493
\(931\) −5.05249e149 −0.590944
\(932\) 1.07543e149 0.119145
\(933\) −2.26038e149 −0.237223
\(934\) 7.56099e148 0.0751729
\(935\) 1.22875e150 1.15739
\(936\) 4.67827e149 0.417498
\(937\) −1.59055e148 −0.0134492 −0.00672461 0.999977i \(-0.502141\pi\)
−0.00672461 + 0.999977i \(0.502141\pi\)
\(938\) −1.81670e150 −1.45559
\(939\) 6.76636e148 0.0513739
\(940\) −4.34325e150 −3.12506
\(941\) 2.35520e150 1.60602 0.803012 0.595962i \(-0.203229\pi\)
0.803012 + 0.595962i \(0.203229\pi\)
\(942\) −1.50744e149 −0.0974248
\(943\) 9.21198e149 0.564303
\(944\) 1.06068e149 0.0615886
\(945\) −1.42588e150 −0.784830
\(946\) −7.64284e149 −0.398797
\(947\) −1.39047e150 −0.687838 −0.343919 0.938999i \(-0.611755\pi\)
−0.343919 + 0.938999i \(0.611755\pi\)
\(948\) 4.50001e149 0.211054
\(949\) 7.50494e149 0.333736
\(950\) −3.44566e150 −1.45288
\(951\) −5.60934e149 −0.224283
\(952\) 4.19403e150 1.59025
\(953\) 9.30332e149 0.334539 0.167269 0.985911i \(-0.446505\pi\)
0.167269 + 0.985911i \(0.446505\pi\)
\(954\) 4.97414e150 1.69639
\(955\) 2.27457e150 0.735749
\(956\) −4.60867e149 −0.141401
\(957\) 8.91543e149 0.259471
\(958\) 6.32084e150 1.74509
\(959\) −4.60004e150 −1.20482
\(960\) 1.99569e150 0.495902
\(961\) 6.25422e150 1.47449
\(962\) −3.01791e150 −0.675096
\(963\) −1.62000e150 −0.343865
\(964\) −1.62307e150 −0.326923
\(965\) −1.24520e151 −2.38018
\(966\) 9.08062e149 0.164729
\(967\) −5.17125e150 −0.890345 −0.445172 0.895445i \(-0.646858\pi\)
−0.445172 + 0.895445i \(0.646858\pi\)
\(968\) −3.53568e150 −0.577786
\(969\) −1.38527e150 −0.214875
\(970\) 1.14609e151 1.68751
\(971\) −1.02064e151 −1.42660 −0.713302 0.700857i \(-0.752801\pi\)
−0.713302 + 0.700857i \(0.752801\pi\)
\(972\) −7.11172e150 −0.943688
\(973\) −5.44681e149 −0.0686189
\(974\) 2.63370e149 0.0315020
\(975\) 9.42912e149 0.107087
\(976\) 1.68729e149 0.0181959
\(977\) 1.19151e151 1.22017 0.610087 0.792334i \(-0.291134\pi\)
0.610087 + 0.792334i \(0.291134\pi\)
\(978\) 3.87230e150 0.376580
\(979\) −4.05414e150 −0.374432
\(980\) 1.92953e151 1.69253
\(981\) −2.79750e150 −0.233070
\(982\) −2.28800e150 −0.181061
\(983\) 2.64030e151 1.98473 0.992364 0.123343i \(-0.0393617\pi\)
0.992364 + 0.123343i \(0.0393617\pi\)
\(984\) −4.26233e150 −0.304365
\(985\) 3.29324e150 0.223406
\(986\) −6.23766e151 −4.02010
\(987\) −6.07766e150 −0.372152
\(988\) 1.01334e151 0.589560
\(989\) 2.64602e150 0.146279
\(990\) 2.67663e151 1.40608
\(991\) −1.12820e151 −0.563205 −0.281603 0.959531i \(-0.590866\pi\)
−0.281603 + 0.959531i \(0.590866\pi\)
\(992\) 3.46450e151 1.64362
\(993\) 3.00462e150 0.135473
\(994\) 3.13363e151 1.34287
\(995\) −1.55646e151 −0.633977
\(996\) −1.31613e151 −0.509570
\(997\) 1.50434e151 0.553656 0.276828 0.960920i \(-0.410717\pi\)
0.276828 + 0.960920i \(0.410717\pi\)
\(998\) −8.79035e151 −3.07549
\(999\) 1.12948e151 0.375682
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.1.8 8
3.2 odd 2 9.102.a.b.1.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.102.a.a.1.8 8 1.1 even 1 trivial
9.102.a.b.1.1 8 3.2 odd 2