Properties

Label 1.106.a.a.1.3
Level 1
Weight 106
Character 1.1
Self dual yes
Analytic conductor 69.819
Analytic rank 1
Dimension 8
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 106 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(69.8187388595\)
Analytic rank: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - x^{7} - \)\(10\!\cdots\!04\)\( x^{6} - \)\(62\!\cdots\!96\)\( x^{5} + \)\(32\!\cdots\!36\)\( x^{4} - \)\(88\!\cdots\!20\)\( x^{3} - \)\(32\!\cdots\!00\)\( x^{2} + \)\(21\!\cdots\!00\)\( x + \)\(48\!\cdots\!00\)\(\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: multiple of \( 2^{111}\cdot 3^{44}\cdot 5^{13}\cdot 7^{7}\cdot 11\cdot 13^{3}\cdot 17 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-4.32050e13\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-7.36840e15 q^{2} -8.33754e23 q^{3} +1.37285e31 q^{4} +6.83377e36 q^{5} +6.14343e39 q^{6} +4.41963e44 q^{7} +1.97741e47 q^{8} -1.24542e50 q^{9} +O(q^{10})\) \(q-7.36840e15 q^{2} -8.33754e23 q^{3} +1.37285e31 q^{4} +6.83377e36 q^{5} +6.14343e39 q^{6} +4.41963e44 q^{7} +1.97741e47 q^{8} -1.24542e50 q^{9} -5.03539e52 q^{10} -4.48414e54 q^{11} -1.14462e55 q^{12} +1.91848e58 q^{13} -3.25656e60 q^{14} -5.69768e60 q^{15} -2.01393e63 q^{16} +1.58211e64 q^{17} +9.17672e65 q^{18} -2.66912e67 q^{19} +9.38173e67 q^{20} -3.68489e68 q^{21} +3.30409e70 q^{22} -2.81725e71 q^{23} -1.64867e71 q^{24} +2.20485e73 q^{25} -1.41362e74 q^{26} +2.08254e74 q^{27} +6.06749e75 q^{28} -4.39751e76 q^{29} +4.19828e76 q^{30} +4.22496e77 q^{31} +6.81810e78 q^{32} +3.73867e78 q^{33} -1.16576e80 q^{34} +3.02028e81 q^{35} -1.70977e81 q^{36} +1.25411e82 q^{37} +1.96671e83 q^{38} -1.59954e82 q^{39} +1.35132e84 q^{40} -2.50078e84 q^{41} +2.71517e84 q^{42} -6.45716e85 q^{43} -6.15605e85 q^{44} -8.51089e86 q^{45} +2.07586e87 q^{46} -3.82379e87 q^{47} +1.67912e87 q^{48} +1.40970e89 q^{49} -1.62462e89 q^{50} -1.31909e88 q^{51} +2.63379e89 q^{52} -3.23348e90 q^{53} -1.53450e90 q^{54} -3.06436e91 q^{55} +8.73942e91 q^{56} +2.22539e91 q^{57} +3.24026e92 q^{58} -3.76398e92 q^{59} -7.82206e91 q^{60} -9.74654e92 q^{61} -3.11312e93 q^{62} -5.50428e94 q^{63} +3.14561e94 q^{64} +1.31105e95 q^{65} -2.75480e94 q^{66} -4.90505e95 q^{67} +2.17199e95 q^{68} +2.34889e95 q^{69} -2.22546e97 q^{70} -2.06839e96 q^{71} -2.46270e97 q^{72} -4.35765e97 q^{73} -9.24075e97 q^{74} -1.83830e97 q^{75} -3.66429e98 q^{76} -1.98183e99 q^{77} +1.17861e98 q^{78} -6.86400e99 q^{79} -1.37627e100 q^{80} +1.54236e100 q^{81} +1.84267e100 q^{82} +1.96175e100 q^{83} -5.05880e99 q^{84} +1.08117e101 q^{85} +4.75790e101 q^{86} +3.66644e100 q^{87} -8.86698e101 q^{88} +1.19123e102 q^{89} +6.27116e102 q^{90} +8.47900e102 q^{91} -3.86765e102 q^{92} -3.52258e101 q^{93} +2.81752e103 q^{94} -1.82401e104 q^{95} -5.68462e102 q^{96} +1.02974e104 q^{97} -1.03872e105 q^{98} +5.58462e104 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 9175032489175920q^{2} - \)\(35\!\cdots\!80\)\(q^{3} + \)\(12\!\cdots\!76\)\(q^{4} + \)\(74\!\cdots\!00\)\(q^{5} - \)\(13\!\cdots\!64\)\(q^{6} + \)\(70\!\cdots\!00\)\(q^{7} - \)\(70\!\cdots\!60\)\(q^{8} + \)\(31\!\cdots\!84\)\(q^{9} + O(q^{10}) \) \( 8q - 9175032489175920q^{2} - \)\(35\!\cdots\!80\)\(q^{3} + \)\(12\!\cdots\!76\)\(q^{4} + \)\(74\!\cdots\!00\)\(q^{5} - \)\(13\!\cdots\!64\)\(q^{6} + \)\(70\!\cdots\!00\)\(q^{7} - \)\(70\!\cdots\!60\)\(q^{8} + \)\(31\!\cdots\!84\)\(q^{9} + \)\(44\!\cdots\!00\)\(q^{10} - \)\(91\!\cdots\!84\)\(q^{11} + \)\(15\!\cdots\!60\)\(q^{12} + \)\(40\!\cdots\!40\)\(q^{13} - \)\(16\!\cdots\!28\)\(q^{14} - \)\(85\!\cdots\!00\)\(q^{15} + \)\(88\!\cdots\!48\)\(q^{16} - \)\(47\!\cdots\!60\)\(q^{17} - \)\(26\!\cdots\!80\)\(q^{18} - \)\(18\!\cdots\!20\)\(q^{19} - \)\(43\!\cdots\!00\)\(q^{20} + \)\(34\!\cdots\!56\)\(q^{21} + \)\(61\!\cdots\!60\)\(q^{22} + \)\(35\!\cdots\!60\)\(q^{23} - \)\(85\!\cdots\!60\)\(q^{24} + \)\(36\!\cdots\!00\)\(q^{25} - \)\(17\!\cdots\!24\)\(q^{26} + \)\(41\!\cdots\!40\)\(q^{27} - \)\(10\!\cdots\!60\)\(q^{28} - \)\(13\!\cdots\!80\)\(q^{29} + \)\(36\!\cdots\!00\)\(q^{30} + \)\(21\!\cdots\!16\)\(q^{31} + \)\(10\!\cdots\!80\)\(q^{32} - \)\(11\!\cdots\!60\)\(q^{33} + \)\(62\!\cdots\!52\)\(q^{34} - \)\(18\!\cdots\!00\)\(q^{35} + \)\(16\!\cdots\!48\)\(q^{36} - \)\(23\!\cdots\!80\)\(q^{37} + \)\(81\!\cdots\!60\)\(q^{38} + \)\(97\!\cdots\!48\)\(q^{39} + \)\(16\!\cdots\!00\)\(q^{40} - \)\(91\!\cdots\!84\)\(q^{41} - \)\(99\!\cdots\!60\)\(q^{42} + \)\(30\!\cdots\!00\)\(q^{43} - \)\(61\!\cdots\!48\)\(q^{44} - \)\(72\!\cdots\!00\)\(q^{45} - \)\(19\!\cdots\!84\)\(q^{46} - \)\(19\!\cdots\!40\)\(q^{47} + \)\(47\!\cdots\!60\)\(q^{48} + \)\(90\!\cdots\!56\)\(q^{49} + \)\(12\!\cdots\!00\)\(q^{50} - \)\(10\!\cdots\!04\)\(q^{51} + \)\(26\!\cdots\!00\)\(q^{52} - \)\(50\!\cdots\!80\)\(q^{53} - \)\(33\!\cdots\!20\)\(q^{54} + \)\(18\!\cdots\!00\)\(q^{55} + \)\(77\!\cdots\!80\)\(q^{56} - \)\(17\!\cdots\!20\)\(q^{57} + \)\(52\!\cdots\!40\)\(q^{58} - \)\(80\!\cdots\!60\)\(q^{59} - \)\(49\!\cdots\!00\)\(q^{60} + \)\(93\!\cdots\!16\)\(q^{61} - \)\(24\!\cdots\!40\)\(q^{62} - \)\(69\!\cdots\!20\)\(q^{63} - \)\(97\!\cdots\!04\)\(q^{64} - \)\(36\!\cdots\!00\)\(q^{65} + \)\(15\!\cdots\!72\)\(q^{66} - \)\(11\!\cdots\!60\)\(q^{67} - \)\(97\!\cdots\!80\)\(q^{68} - \)\(15\!\cdots\!32\)\(q^{69} - \)\(42\!\cdots\!00\)\(q^{70} - \)\(50\!\cdots\!84\)\(q^{71} - \)\(31\!\cdots\!80\)\(q^{72} - \)\(30\!\cdots\!40\)\(q^{73} - \)\(92\!\cdots\!88\)\(q^{74} - \)\(20\!\cdots\!00\)\(q^{75} - \)\(31\!\cdots\!40\)\(q^{76} - \)\(59\!\cdots\!00\)\(q^{77} - \)\(21\!\cdots\!00\)\(q^{78} - \)\(15\!\cdots\!80\)\(q^{79} - \)\(36\!\cdots\!00\)\(q^{80} - \)\(16\!\cdots\!72\)\(q^{81} + \)\(40\!\cdots\!60\)\(q^{82} - \)\(27\!\cdots\!20\)\(q^{83} + \)\(24\!\cdots\!32\)\(q^{84} + \)\(11\!\cdots\!00\)\(q^{85} + \)\(20\!\cdots\!96\)\(q^{86} + \)\(24\!\cdots\!20\)\(q^{87} + \)\(65\!\cdots\!80\)\(q^{88} + \)\(45\!\cdots\!60\)\(q^{89} + \)\(27\!\cdots\!00\)\(q^{90} + \)\(27\!\cdots\!96\)\(q^{91} + \)\(11\!\cdots\!40\)\(q^{92} - \)\(18\!\cdots\!60\)\(q^{93} - \)\(14\!\cdots\!08\)\(q^{94} - \)\(19\!\cdots\!00\)\(q^{95} - \)\(72\!\cdots\!64\)\(q^{96} - \)\(76\!\cdots\!40\)\(q^{97} - \)\(13\!\cdots\!40\)\(q^{98} - \)\(25\!\cdots\!32\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −7.36840e15 −1.15691 −0.578453 0.815715i \(-0.696344\pi\)
−0.578453 + 0.815715i \(0.696344\pi\)
\(3\) −8.33754e23 −0.0745027 −0.0372514 0.999306i \(-0.511860\pi\)
−0.0372514 + 0.999306i \(0.511860\pi\)
\(4\) 1.37285e31 0.338433
\(5\) 6.83377e36 1.37637 0.688185 0.725535i \(-0.258408\pi\)
0.688185 + 0.725535i \(0.258408\pi\)
\(6\) 6.14343e39 0.0861927
\(7\) 4.41963e44 1.89557 0.947784 0.318914i \(-0.103318\pi\)
0.947784 + 0.318914i \(0.103318\pi\)
\(8\) 1.97741e47 0.765371
\(9\) −1.24542e50 −0.994449
\(10\) −5.03539e52 −1.59233
\(11\) −4.48414e54 −0.951839 −0.475919 0.879489i \(-0.657885\pi\)
−0.475919 + 0.879489i \(0.657885\pi\)
\(12\) −1.14462e55 −0.0252142
\(13\) 1.91848e58 0.632313 0.316157 0.948707i \(-0.397607\pi\)
0.316157 + 0.948707i \(0.397607\pi\)
\(14\) −3.25656e60 −2.19300
\(15\) −5.69768e60 −0.102543
\(16\) −2.01393e63 −1.22390
\(17\) 1.58211e64 0.398719 0.199360 0.979926i \(-0.436114\pi\)
0.199360 + 0.979926i \(0.436114\pi\)
\(18\) 9.17672e65 1.15049
\(19\) −2.66912e67 −1.95796 −0.978979 0.203960i \(-0.934619\pi\)
−0.978979 + 0.203960i \(0.934619\pi\)
\(20\) 9.38173e67 0.465809
\(21\) −3.68489e68 −0.141225
\(22\) 3.30409e70 1.10119
\(23\) −2.81725e71 −0.910151 −0.455075 0.890453i \(-0.650388\pi\)
−0.455075 + 0.890453i \(0.650388\pi\)
\(24\) −1.64867e71 −0.0570222
\(25\) 2.20485e73 0.894394
\(26\) −1.41362e74 −0.731528
\(27\) 2.08254e74 0.148592
\(28\) 6.06749e75 0.641523
\(29\) −4.39751e76 −0.736736 −0.368368 0.929680i \(-0.620083\pi\)
−0.368368 + 0.929680i \(0.620083\pi\)
\(30\) 4.19828e76 0.118633
\(31\) 4.22496e77 0.213468 0.106734 0.994288i \(-0.465961\pi\)
0.106734 + 0.994288i \(0.465961\pi\)
\(32\) 6.81810e78 0.650563
\(33\) 3.73867e78 0.0709146
\(34\) −1.16576e80 −0.461281
\(35\) 3.02028e81 2.60900
\(36\) −1.70977e81 −0.336555
\(37\) 1.25411e82 0.585792 0.292896 0.956144i \(-0.405381\pi\)
0.292896 + 0.956144i \(0.405381\pi\)
\(38\) 1.96671e83 2.26518
\(39\) −1.59954e82 −0.0471091
\(40\) 1.35132e84 1.05343
\(41\) −2.50078e84 −0.533240 −0.266620 0.963802i \(-0.585907\pi\)
−0.266620 + 0.963802i \(0.585907\pi\)
\(42\) 2.71517e84 0.163384
\(43\) −6.45716e85 −1.12966 −0.564830 0.825207i \(-0.691058\pi\)
−0.564830 + 0.825207i \(0.691058\pi\)
\(44\) −6.15605e85 −0.322134
\(45\) −8.51089e86 −1.36873
\(46\) 2.07586e87 1.05296
\(47\) −3.82379e87 −0.627129 −0.313564 0.949567i \(-0.601523\pi\)
−0.313564 + 0.949567i \(0.601523\pi\)
\(48\) 1.67912e87 0.0911836
\(49\) 1.40970e89 2.59318
\(50\) −1.62462e89 −1.03473
\(51\) −1.31909e88 −0.0297057
\(52\) 2.63379e89 0.213996
\(53\) −3.23348e90 −0.966467 −0.483234 0.875491i \(-0.660538\pi\)
−0.483234 + 0.875491i \(0.660538\pi\)
\(54\) −1.53450e90 −0.171907
\(55\) −3.06436e91 −1.31008
\(56\) 8.73942e91 1.45081
\(57\) 2.22539e91 0.145873
\(58\) 3.24026e92 0.852334
\(59\) −3.76398e92 −0.403568 −0.201784 0.979430i \(-0.564674\pi\)
−0.201784 + 0.979430i \(0.564674\pi\)
\(60\) −7.82206e91 −0.0347041
\(61\) −9.74654e92 −0.181566 −0.0907829 0.995871i \(-0.528937\pi\)
−0.0907829 + 0.995871i \(0.528937\pi\)
\(62\) −3.11312e93 −0.246963
\(63\) −5.50428e94 −1.88505
\(64\) 3.14561e94 0.471256
\(65\) 1.31105e95 0.870297
\(66\) −2.75480e94 −0.0820416
\(67\) −4.90505e95 −0.663309 −0.331655 0.943401i \(-0.607607\pi\)
−0.331655 + 0.943401i \(0.607607\pi\)
\(68\) 2.17199e95 0.134940
\(69\) 2.34889e95 0.0678087
\(70\) −2.22546e97 −3.01837
\(71\) −2.06839e96 −0.133220 −0.0666098 0.997779i \(-0.521218\pi\)
−0.0666098 + 0.997779i \(0.521218\pi\)
\(72\) −2.46270e97 −0.761123
\(73\) −4.35765e97 −0.652833 −0.326417 0.945226i \(-0.605841\pi\)
−0.326417 + 0.945226i \(0.605841\pi\)
\(74\) −9.24075e97 −0.677707
\(75\) −1.83830e97 −0.0666348
\(76\) −3.66429e98 −0.662638
\(77\) −1.98183e99 −1.80427
\(78\) 1.17861e98 0.0545008
\(79\) −6.86400e99 −1.62613 −0.813064 0.582174i \(-0.802202\pi\)
−0.813064 + 0.582174i \(0.802202\pi\)
\(80\) −1.37627e100 −1.68453
\(81\) 1.54236e100 0.983379
\(82\) 1.84267e100 0.616910
\(83\) 1.96175e100 0.347572 0.173786 0.984783i \(-0.444400\pi\)
0.173786 + 0.984783i \(0.444400\pi\)
\(84\) −5.05880e99 −0.0477952
\(85\) 1.08117e101 0.548785
\(86\) 4.75790e101 1.30691
\(87\) 3.66644e100 0.0548888
\(88\) −8.86698e101 −0.728510
\(89\) 1.19123e102 0.540780 0.270390 0.962751i \(-0.412847\pi\)
0.270390 + 0.962751i \(0.412847\pi\)
\(90\) 6.27116e102 1.58349
\(91\) 8.47900e102 1.19859
\(92\) −3.86765e102 −0.308025
\(93\) −3.52258e101 −0.0159040
\(94\) 2.81752e103 0.725530
\(95\) −1.82401e104 −2.69487
\(96\) −5.68462e102 −0.0484687
\(97\) 1.02974e104 0.509580 0.254790 0.966996i \(-0.417994\pi\)
0.254790 + 0.966996i \(0.417994\pi\)
\(98\) −1.03872e105 −3.00006
\(99\) 5.58462e104 0.946555
\(100\) 3.02693e104 0.302693
\(101\) 3.13638e104 0.186019 0.0930094 0.995665i \(-0.470351\pi\)
0.0930094 + 0.995665i \(0.470351\pi\)
\(102\) 9.71956e103 0.0343667
\(103\) −3.39113e105 −0.718439 −0.359219 0.933253i \(-0.616957\pi\)
−0.359219 + 0.933253i \(0.616957\pi\)
\(104\) 3.79363e105 0.483954
\(105\) −2.51817e105 −0.194378
\(106\) 2.38256e106 1.11811
\(107\) 1.15787e106 0.331904 0.165952 0.986134i \(-0.446930\pi\)
0.165952 + 0.986134i \(0.446930\pi\)
\(108\) 2.85901e105 0.0502885
\(109\) 1.01283e107 1.09811 0.549055 0.835786i \(-0.314988\pi\)
0.549055 + 0.835786i \(0.314988\pi\)
\(110\) 2.25794e107 1.51564
\(111\) −1.04562e106 −0.0436431
\(112\) −8.90082e107 −2.31998
\(113\) 4.58630e106 0.0749626 0.0374813 0.999297i \(-0.488067\pi\)
0.0374813 + 0.999297i \(0.488067\pi\)
\(114\) −1.63975e107 −0.168762
\(115\) −1.92524e108 −1.25270
\(116\) −6.03711e107 −0.249336
\(117\) −2.38931e108 −0.628804
\(118\) 2.77345e108 0.466891
\(119\) 6.99233e108 0.755799
\(120\) −1.12666e108 −0.0784837
\(121\) −2.08629e108 −0.0940030
\(122\) 7.18164e108 0.210055
\(123\) 2.08504e108 0.0397279
\(124\) 5.80023e108 0.0722448
\(125\) −1.77910e109 −0.145353
\(126\) 4.05578e110 2.18082
\(127\) 2.26248e110 0.803320 0.401660 0.915789i \(-0.368433\pi\)
0.401660 + 0.915789i \(0.368433\pi\)
\(128\) −5.08356e110 −1.19576
\(129\) 5.38369e109 0.0841628
\(130\) −9.66033e110 −1.00685
\(131\) 9.11375e110 0.635264 0.317632 0.948214i \(-0.397112\pi\)
0.317632 + 0.948214i \(0.397112\pi\)
\(132\) 5.13263e109 0.0239999
\(133\) −1.17965e112 −3.71144
\(134\) 3.61424e111 0.767387
\(135\) 1.42316e111 0.204517
\(136\) 3.12847e111 0.305168
\(137\) 1.96095e112 1.30208 0.651039 0.759044i \(-0.274333\pi\)
0.651039 + 0.759044i \(0.274333\pi\)
\(138\) −1.73076e111 −0.0784484
\(139\) −5.25948e111 −0.163180 −0.0815899 0.996666i \(-0.526000\pi\)
−0.0815899 + 0.996666i \(0.526000\pi\)
\(140\) 4.14638e112 0.882973
\(141\) 3.18810e111 0.0467228
\(142\) 1.52407e112 0.154123
\(143\) −8.60276e112 −0.601860
\(144\) 2.50818e113 1.21710
\(145\) −3.00515e113 −1.01402
\(146\) 3.21089e113 0.755267
\(147\) −1.17534e113 −0.193199
\(148\) 1.72170e113 0.198252
\(149\) −1.63050e114 −1.31838 −0.659190 0.751976i \(-0.729101\pi\)
−0.659190 + 0.751976i \(0.729101\pi\)
\(150\) 1.35454e113 0.0770902
\(151\) −1.72555e114 −0.692846 −0.346423 0.938078i \(-0.612604\pi\)
−0.346423 + 0.938078i \(0.612604\pi\)
\(152\) −5.27793e114 −1.49856
\(153\) −1.97038e114 −0.396506
\(154\) 1.46029e115 2.08738
\(155\) 2.88724e114 0.293812
\(156\) −2.19593e113 −0.0159433
\(157\) 9.78183e113 0.0507795 0.0253897 0.999678i \(-0.491917\pi\)
0.0253897 + 0.999678i \(0.491917\pi\)
\(158\) 5.05767e115 1.88128
\(159\) 2.69593e114 0.0720044
\(160\) 4.65933e115 0.895415
\(161\) −1.24512e116 −1.72525
\(162\) −1.13647e116 −1.13768
\(163\) 7.23022e115 0.523965 0.261983 0.965073i \(-0.415624\pi\)
0.261983 + 0.965073i \(0.415624\pi\)
\(164\) −3.43319e115 −0.180466
\(165\) 2.55492e115 0.0976047
\(166\) −1.44550e116 −0.402108
\(167\) −3.73133e115 −0.0757268 −0.0378634 0.999283i \(-0.512055\pi\)
−0.0378634 + 0.999283i \(0.512055\pi\)
\(168\) −7.28653e115 −0.108089
\(169\) −5.52501e116 −0.600180
\(170\) −7.96652e116 −0.634893
\(171\) 3.32416e117 1.94709
\(172\) −8.86471e116 −0.382315
\(173\) −3.68706e117 −1.17290 −0.586449 0.809986i \(-0.699474\pi\)
−0.586449 + 0.809986i \(0.699474\pi\)
\(174\) −2.70158e116 −0.0635012
\(175\) 9.74464e117 1.69538
\(176\) 9.03073e117 1.16495
\(177\) 3.13823e116 0.0300669
\(178\) −8.77746e117 −0.625632
\(179\) 2.91163e118 1.54651 0.773253 0.634098i \(-0.218628\pi\)
0.773253 + 0.634098i \(0.218628\pi\)
\(180\) −1.16842e118 −0.463224
\(181\) −5.31349e118 −1.57491 −0.787454 0.616374i \(-0.788601\pi\)
−0.787454 + 0.616374i \(0.788601\pi\)
\(182\) −6.24767e118 −1.38666
\(183\) 8.12622e116 0.0135271
\(184\) −5.57085e118 −0.696603
\(185\) 8.57027e118 0.806267
\(186\) 2.59558e117 0.0183994
\(187\) −7.09438e118 −0.379516
\(188\) −5.24949e118 −0.212241
\(189\) 9.20405e118 0.281666
\(190\) 1.34401e120 3.11772
\(191\) −6.62984e119 −1.16749 −0.583743 0.811939i \(-0.698412\pi\)
−0.583743 + 0.811939i \(0.698412\pi\)
\(192\) −2.62267e118 −0.0351098
\(193\) −2.46353e119 −0.251072 −0.125536 0.992089i \(-0.540065\pi\)
−0.125536 + 0.992089i \(0.540065\pi\)
\(194\) −7.58756e119 −0.589537
\(195\) −1.09309e119 −0.0648395
\(196\) 1.93530e120 0.877617
\(197\) 3.61918e120 1.25641 0.628207 0.778046i \(-0.283789\pi\)
0.628207 + 0.778046i \(0.283789\pi\)
\(198\) −4.11497e120 −1.09508
\(199\) −6.75502e120 −1.37988 −0.689938 0.723868i \(-0.742362\pi\)
−0.689938 + 0.723868i \(0.742362\pi\)
\(200\) 4.35989e120 0.684543
\(201\) 4.08960e119 0.0494184
\(202\) −2.31101e120 −0.215206
\(203\) −1.94354e121 −1.39653
\(204\) −1.81091e119 −0.0100534
\(205\) −1.70898e121 −0.733936
\(206\) 2.49872e121 0.831166
\(207\) 3.50864e121 0.905099
\(208\) −3.86369e121 −0.773886
\(209\) 1.19687e122 1.86366
\(210\) 1.85549e121 0.224877
\(211\) 1.13421e122 1.07118 0.535592 0.844477i \(-0.320089\pi\)
0.535592 + 0.844477i \(0.320089\pi\)
\(212\) −4.43908e121 −0.327085
\(213\) 1.72452e120 0.00992522
\(214\) −8.53167e121 −0.383982
\(215\) −4.41268e122 −1.55483
\(216\) 4.11803e121 0.113728
\(217\) 1.86728e122 0.404644
\(218\) −7.46295e122 −1.27041
\(219\) 3.63321e121 0.0486379
\(220\) −4.20690e122 −0.443375
\(221\) 3.03524e122 0.252115
\(222\) 7.70452e121 0.0504910
\(223\) 1.67124e123 0.865035 0.432517 0.901626i \(-0.357625\pi\)
0.432517 + 0.901626i \(0.357625\pi\)
\(224\) 3.01335e123 1.23319
\(225\) −2.74596e123 −0.889429
\(226\) −3.37937e122 −0.0867247
\(227\) −4.72016e123 −0.960725 −0.480363 0.877070i \(-0.659495\pi\)
−0.480363 + 0.877070i \(0.659495\pi\)
\(228\) 3.05512e122 0.0493684
\(229\) 8.23914e123 1.05808 0.529040 0.848597i \(-0.322552\pi\)
0.529040 + 0.848597i \(0.322552\pi\)
\(230\) 1.41859e124 1.44926
\(231\) 1.65236e123 0.134423
\(232\) −8.69567e123 −0.563876
\(233\) −1.55779e124 −0.805977 −0.402988 0.915205i \(-0.632029\pi\)
−0.402988 + 0.915205i \(0.632029\pi\)
\(234\) 1.76054e124 0.727467
\(235\) −2.61309e124 −0.863161
\(236\) −5.16738e123 −0.136581
\(237\) 5.72289e123 0.121151
\(238\) −5.15223e124 −0.874389
\(239\) −1.18903e125 −1.61921 −0.809607 0.586972i \(-0.800320\pi\)
−0.809607 + 0.586972i \(0.800320\pi\)
\(240\) 1.14747e124 0.125502
\(241\) 1.11462e125 0.980017 0.490009 0.871718i \(-0.336994\pi\)
0.490009 + 0.871718i \(0.336994\pi\)
\(242\) 1.53726e124 0.108753
\(243\) −3.89405e124 −0.221856
\(244\) −1.33805e124 −0.0614479
\(245\) 9.63356e125 3.56917
\(246\) −1.53634e124 −0.0459614
\(247\) −5.12066e125 −1.23804
\(248\) 8.35447e124 0.163383
\(249\) −1.63562e124 −0.0258951
\(250\) 1.31091e125 0.168160
\(251\) −1.11133e126 −1.15604 −0.578019 0.816023i \(-0.696174\pi\)
−0.578019 + 0.816023i \(0.696174\pi\)
\(252\) −7.55655e125 −0.637962
\(253\) 1.26329e126 0.866317
\(254\) −1.66708e126 −0.929367
\(255\) −9.01434e124 −0.0408860
\(256\) 2.46976e126 0.912129
\(257\) −5.66215e126 −1.70409 −0.852044 0.523470i \(-0.824637\pi\)
−0.852044 + 0.523470i \(0.824637\pi\)
\(258\) −3.96692e125 −0.0973685
\(259\) 5.54269e126 1.11041
\(260\) 1.79987e126 0.294537
\(261\) 5.47672e126 0.732646
\(262\) −6.71538e126 −0.734941
\(263\) −9.17187e126 −0.821828 −0.410914 0.911674i \(-0.634790\pi\)
−0.410914 + 0.911674i \(0.634790\pi\)
\(264\) 7.39288e125 0.0542760
\(265\) −2.20969e127 −1.33022
\(266\) 8.69215e127 4.29379
\(267\) −9.93194e125 −0.0402896
\(268\) −6.73389e126 −0.224486
\(269\) −4.82313e127 −1.32231 −0.661156 0.750248i \(-0.729934\pi\)
−0.661156 + 0.750248i \(0.729934\pi\)
\(270\) −1.04864e127 −0.236608
\(271\) 6.98433e127 1.29789 0.648943 0.760837i \(-0.275211\pi\)
0.648943 + 0.760837i \(0.275211\pi\)
\(272\) −3.18624e127 −0.487991
\(273\) −7.06940e126 −0.0892984
\(274\) −1.44491e128 −1.50638
\(275\) −9.88687e127 −0.851319
\(276\) 3.22467e126 0.0229487
\(277\) −1.33380e128 −0.785058 −0.392529 0.919740i \(-0.628400\pi\)
−0.392529 + 0.919740i \(0.628400\pi\)
\(278\) 3.87540e127 0.188784
\(279\) −5.26183e127 −0.212284
\(280\) 5.97232e128 1.99685
\(281\) 1.71423e128 0.475321 0.237660 0.971348i \(-0.423619\pi\)
0.237660 + 0.971348i \(0.423619\pi\)
\(282\) −2.34912e127 −0.0540539
\(283\) 4.21932e128 0.806221 0.403111 0.915151i \(-0.367929\pi\)
0.403111 + 0.915151i \(0.367929\pi\)
\(284\) −2.83958e127 −0.0450859
\(285\) 1.52078e128 0.200776
\(286\) 6.33885e128 0.696296
\(287\) −1.10525e129 −1.01079
\(288\) −8.49137e128 −0.646952
\(289\) −1.32417e129 −0.841023
\(290\) 2.21432e129 1.17313
\(291\) −8.58552e127 −0.0379651
\(292\) −5.98239e128 −0.220941
\(293\) −3.79428e129 −1.17106 −0.585530 0.810651i \(-0.699114\pi\)
−0.585530 + 0.810651i \(0.699114\pi\)
\(294\) 8.66039e128 0.223513
\(295\) −2.57222e129 −0.555459
\(296\) 2.47988e129 0.448348
\(297\) −9.33839e128 −0.141436
\(298\) 1.20141e130 1.52524
\(299\) −5.40484e129 −0.575500
\(300\) −2.52371e128 −0.0225514
\(301\) −2.85383e130 −2.14135
\(302\) 1.27145e130 0.801559
\(303\) −2.61497e128 −0.0138589
\(304\) 5.37540e130 2.39634
\(305\) −6.66056e129 −0.249902
\(306\) 1.45185e130 0.458720
\(307\) 2.81819e130 0.750249 0.375125 0.926974i \(-0.377600\pi\)
0.375125 + 0.926974i \(0.377600\pi\)
\(308\) −2.72075e130 −0.610627
\(309\) 2.82737e129 0.0535256
\(310\) −2.12743e130 −0.339913
\(311\) −1.12349e131 −1.51583 −0.757914 0.652355i \(-0.773781\pi\)
−0.757914 + 0.652355i \(0.773781\pi\)
\(312\) −3.16295e129 −0.0360559
\(313\) 9.89355e130 0.953398 0.476699 0.879067i \(-0.341833\pi\)
0.476699 + 0.879067i \(0.341833\pi\)
\(314\) −7.20764e129 −0.0587471
\(315\) −3.76150e131 −2.59452
\(316\) −9.42323e130 −0.550336
\(317\) 2.02522e131 1.00198 0.500992 0.865452i \(-0.332969\pi\)
0.500992 + 0.865452i \(0.332969\pi\)
\(318\) −1.98647e130 −0.0833024
\(319\) 1.97190e131 0.701253
\(320\) 2.14964e131 0.648622
\(321\) −9.65381e129 −0.0247278
\(322\) 9.17454e131 1.99596
\(323\) −4.22282e131 −0.780675
\(324\) 2.11742e131 0.332808
\(325\) 4.22997e131 0.565537
\(326\) −5.32752e131 −0.606179
\(327\) −8.44453e130 −0.0818122
\(328\) −4.94506e131 −0.408127
\(329\) −1.68998e132 −1.18876
\(330\) −1.88257e131 −0.112920
\(331\) 2.08449e132 1.06667 0.533336 0.845904i \(-0.320938\pi\)
0.533336 + 0.845904i \(0.320938\pi\)
\(332\) 2.69319e131 0.117630
\(333\) −1.56188e132 −0.582541
\(334\) 2.74940e131 0.0876088
\(335\) −3.35200e132 −0.912959
\(336\) 7.42110e131 0.172845
\(337\) −1.43308e132 −0.285563 −0.142781 0.989754i \(-0.545605\pi\)
−0.142781 + 0.989754i \(0.545605\pi\)
\(338\) 4.07105e132 0.694352
\(339\) −3.82385e130 −0.00558491
\(340\) 1.48429e132 0.185727
\(341\) −1.89453e132 −0.203188
\(342\) −2.44937e133 −2.25260
\(343\) 3.82776e133 3.01997
\(344\) −1.27684e133 −0.864609
\(345\) 1.60518e132 0.0933299
\(346\) 2.71677e133 1.35693
\(347\) 1.61500e133 0.693228 0.346614 0.938008i \(-0.387331\pi\)
0.346614 + 0.938008i \(0.387331\pi\)
\(348\) 5.03347e131 0.0185762
\(349\) 3.42631e133 1.08766 0.543829 0.839196i \(-0.316974\pi\)
0.543829 + 0.839196i \(0.316974\pi\)
\(350\) −7.18024e133 −1.96140
\(351\) 3.99532e132 0.0939566
\(352\) −3.05733e133 −0.619231
\(353\) −4.49817e133 −0.784990 −0.392495 0.919754i \(-0.628388\pi\)
−0.392495 + 0.919754i \(0.628388\pi\)
\(354\) −2.31238e132 −0.0347846
\(355\) −1.41349e133 −0.183359
\(356\) 1.63538e133 0.183018
\(357\) −5.82988e132 −0.0563091
\(358\) −2.14540e134 −1.78916
\(359\) −2.93840e132 −0.0211667 −0.0105833 0.999944i \(-0.503369\pi\)
−0.0105833 + 0.999944i \(0.503369\pi\)
\(360\) −1.68295e134 −1.04759
\(361\) 5.26583e134 2.83360
\(362\) 3.91519e134 1.82202
\(363\) 1.73945e132 0.00700348
\(364\) 1.16404e134 0.405644
\(365\) −2.97792e134 −0.898540
\(366\) −5.98772e132 −0.0156496
\(367\) −2.14897e134 −0.486700 −0.243350 0.969939i \(-0.578246\pi\)
−0.243350 + 0.969939i \(0.578246\pi\)
\(368\) 5.67373e134 1.11393
\(369\) 3.11451e134 0.530281
\(370\) −6.31492e134 −0.932776
\(371\) −1.42908e135 −1.83200
\(372\) −4.83597e132 −0.00538244
\(373\) 8.60799e134 0.832124 0.416062 0.909336i \(-0.363410\pi\)
0.416062 + 0.909336i \(0.363410\pi\)
\(374\) 5.22743e134 0.439065
\(375\) 1.48333e133 0.0108292
\(376\) −7.56120e134 −0.479986
\(377\) −8.43655e134 −0.465848
\(378\) −6.78191e134 −0.325861
\(379\) 9.16019e134 0.383130 0.191565 0.981480i \(-0.438644\pi\)
0.191565 + 0.981480i \(0.438644\pi\)
\(380\) −2.50409e135 −0.912035
\(381\) −1.88635e134 −0.0598496
\(382\) 4.88513e135 1.35067
\(383\) 3.16438e135 0.762699 0.381349 0.924431i \(-0.375459\pi\)
0.381349 + 0.924431i \(0.375459\pi\)
\(384\) 4.23844e134 0.0890875
\(385\) −1.35434e136 −2.48335
\(386\) 1.81523e135 0.290467
\(387\) 8.04185e135 1.12339
\(388\) 1.41368e135 0.172459
\(389\) 1.36629e136 1.45609 0.728045 0.685529i \(-0.240429\pi\)
0.728045 + 0.685529i \(0.240429\pi\)
\(390\) 8.05434e134 0.0750133
\(391\) −4.45718e135 −0.362895
\(392\) 2.78755e136 1.98474
\(393\) −7.59863e134 −0.0473289
\(394\) −2.66675e136 −1.45355
\(395\) −4.69070e136 −2.23815
\(396\) 7.66684e135 0.320346
\(397\) −4.44670e136 −1.62756 −0.813778 0.581176i \(-0.802593\pi\)
−0.813778 + 0.581176i \(0.802593\pi\)
\(398\) 4.97737e136 1.59639
\(399\) 9.83540e135 0.276513
\(400\) −4.44041e136 −1.09465
\(401\) −2.66460e136 −0.576171 −0.288086 0.957605i \(-0.593019\pi\)
−0.288086 + 0.957605i \(0.593019\pi\)
\(402\) −3.01338e135 −0.0571724
\(403\) 8.10552e135 0.134979
\(404\) 4.30578e135 0.0629549
\(405\) 1.05401e137 1.35349
\(406\) 1.43208e137 1.61566
\(407\) −5.62359e136 −0.557580
\(408\) −2.60837e135 −0.0227358
\(409\) 2.73574e136 0.209701 0.104851 0.994488i \(-0.466564\pi\)
0.104851 + 0.994488i \(0.466564\pi\)
\(410\) 1.25924e137 0.849096
\(411\) −1.63495e136 −0.0970084
\(412\) −4.65550e136 −0.243144
\(413\) −1.66354e137 −0.764990
\(414\) −2.58531e137 −1.04712
\(415\) 1.34062e137 0.478387
\(416\) 1.30804e137 0.411360
\(417\) 4.38512e135 0.0121573
\(418\) −8.81901e137 −2.15608
\(419\) 6.16363e137 1.32923 0.664616 0.747186i \(-0.268595\pi\)
0.664616 + 0.747186i \(0.268595\pi\)
\(420\) −3.45706e136 −0.0657839
\(421\) 4.88353e137 0.820207 0.410104 0.912039i \(-0.365492\pi\)
0.410104 + 0.912039i \(0.365492\pi\)
\(422\) −8.35730e137 −1.23926
\(423\) 4.76221e137 0.623648
\(424\) −6.39391e137 −0.739706
\(425\) 3.48831e137 0.356612
\(426\) −1.27070e136 −0.0114826
\(427\) −4.30761e137 −0.344170
\(428\) 1.58958e137 0.112327
\(429\) 7.17258e136 0.0448402
\(430\) 3.25144e138 1.79879
\(431\) −2.78682e138 −1.36475 −0.682375 0.731002i \(-0.739053\pi\)
−0.682375 + 0.731002i \(0.739053\pi\)
\(432\) −4.19408e137 −0.181861
\(433\) 3.64338e138 1.39923 0.699617 0.714518i \(-0.253354\pi\)
0.699617 + 0.714518i \(0.253354\pi\)
\(434\) −1.37589e138 −0.468135
\(435\) 2.50556e137 0.0755473
\(436\) 1.39046e138 0.371637
\(437\) 7.51956e138 1.78204
\(438\) −2.67709e137 −0.0562695
\(439\) −1.56099e138 −0.291080 −0.145540 0.989352i \(-0.546492\pi\)
−0.145540 + 0.989352i \(0.546492\pi\)
\(440\) −6.05949e138 −1.00270
\(441\) −1.75566e139 −2.57878
\(442\) −2.23649e138 −0.291674
\(443\) 1.04375e138 0.120893 0.0604467 0.998171i \(-0.480747\pi\)
0.0604467 + 0.998171i \(0.480747\pi\)
\(444\) −1.43547e137 −0.0147703
\(445\) 8.14060e138 0.744313
\(446\) −1.23144e139 −1.00076
\(447\) 1.35943e138 0.0982229
\(448\) 1.39025e139 0.893297
\(449\) −1.68684e139 −0.964142 −0.482071 0.876132i \(-0.660115\pi\)
−0.482071 + 0.876132i \(0.660115\pi\)
\(450\) 2.02333e139 1.02899
\(451\) 1.12139e139 0.507559
\(452\) 6.29630e137 0.0253698
\(453\) 1.43868e138 0.0516190
\(454\) 3.47800e139 1.11147
\(455\) 5.79435e139 1.64971
\(456\) 4.40050e138 0.111647
\(457\) −4.28923e139 −0.970015 −0.485008 0.874510i \(-0.661183\pi\)
−0.485008 + 0.874510i \(0.661183\pi\)
\(458\) −6.07092e139 −1.22410
\(459\) 3.29479e138 0.0592464
\(460\) −2.64306e139 −0.423957
\(461\) −3.43285e139 −0.491311 −0.245656 0.969357i \(-0.579003\pi\)
−0.245656 + 0.969357i \(0.579003\pi\)
\(462\) −1.21752e139 −0.155515
\(463\) −7.65195e139 −0.872510 −0.436255 0.899823i \(-0.643695\pi\)
−0.436255 + 0.899823i \(0.643695\pi\)
\(464\) 8.85626e139 0.901688
\(465\) −2.40725e138 −0.0218898
\(466\) 1.14784e140 0.932440
\(467\) −7.91580e139 −0.574590 −0.287295 0.957842i \(-0.592756\pi\)
−0.287295 + 0.957842i \(0.592756\pi\)
\(468\) −3.28016e139 −0.212808
\(469\) −2.16785e140 −1.25735
\(470\) 1.92543e140 0.998597
\(471\) −8.15564e137 −0.00378321
\(472\) −7.44293e139 −0.308879
\(473\) 2.89548e140 1.07525
\(474\) −4.21685e139 −0.140160
\(475\) −5.88500e140 −1.75119
\(476\) 9.59941e139 0.255788
\(477\) 4.02703e140 0.961103
\(478\) 8.76127e140 1.87328
\(479\) −1.70702e140 −0.327057 −0.163529 0.986539i \(-0.552288\pi\)
−0.163529 + 0.986539i \(0.552288\pi\)
\(480\) −3.88474e139 −0.0667109
\(481\) 2.40598e140 0.370404
\(482\) −8.21300e140 −1.13379
\(483\) 1.03812e140 0.128536
\(484\) −2.86415e139 −0.0318138
\(485\) 7.03703e140 0.701371
\(486\) 2.86929e140 0.256667
\(487\) 7.74854e140 0.622228 0.311114 0.950373i \(-0.399298\pi\)
0.311114 + 0.950373i \(0.399298\pi\)
\(488\) −1.92729e140 −0.138965
\(489\) −6.02823e139 −0.0390368
\(490\) −7.09839e141 −4.12920
\(491\) −6.91335e140 −0.361335 −0.180668 0.983544i \(-0.557826\pi\)
−0.180668 + 0.983544i \(0.557826\pi\)
\(492\) 2.86244e139 0.0134452
\(493\) −6.95732e140 −0.293750
\(494\) 3.77311e141 1.43230
\(495\) 3.81640e141 1.30281
\(496\) −8.50876e140 −0.261263
\(497\) −9.14151e140 −0.252527
\(498\) 1.20519e140 0.0299582
\(499\) 3.99593e141 0.894003 0.447001 0.894533i \(-0.352492\pi\)
0.447001 + 0.894533i \(0.352492\pi\)
\(500\) −2.44243e140 −0.0491923
\(501\) 3.11102e139 0.00564185
\(502\) 8.18871e141 1.33743
\(503\) 1.07217e142 1.57741 0.788705 0.614772i \(-0.210752\pi\)
0.788705 + 0.614772i \(0.210752\pi\)
\(504\) −1.08842e142 −1.44276
\(505\) 2.14333e141 0.256031
\(506\) −9.30845e141 −1.00225
\(507\) 4.60650e140 0.0447150
\(508\) 3.10604e141 0.271870
\(509\) −1.71358e142 −1.35276 −0.676381 0.736552i \(-0.736453\pi\)
−0.676381 + 0.736552i \(0.736453\pi\)
\(510\) 6.64212e140 0.0473013
\(511\) −1.92592e142 −1.23749
\(512\) 2.42321e141 0.140513
\(513\) −5.55853e141 −0.290937
\(514\) 4.17210e142 1.97147
\(515\) −2.31742e142 −0.988837
\(516\) 7.39099e140 0.0284835
\(517\) 1.71464e142 0.596925
\(518\) −4.08408e142 −1.28464
\(519\) 3.07410e141 0.0873841
\(520\) 2.59248e142 0.666100
\(521\) 5.71915e142 1.32847 0.664234 0.747525i \(-0.268758\pi\)
0.664234 + 0.747525i \(0.268758\pi\)
\(522\) −4.03547e142 −0.847603
\(523\) −3.96164e142 −0.752552 −0.376276 0.926508i \(-0.622796\pi\)
−0.376276 + 0.926508i \(0.622796\pi\)
\(524\) 1.25118e142 0.214995
\(525\) −8.12463e141 −0.126311
\(526\) 6.75820e142 0.950779
\(527\) 6.68433e141 0.0851139
\(528\) −7.52941e141 −0.0867921
\(529\) −1.64439e142 −0.171625
\(530\) 1.62819e143 1.53894
\(531\) 4.68772e142 0.401328
\(532\) −1.61948e143 −1.25608
\(533\) −4.79771e142 −0.337175
\(534\) 7.31825e141 0.0466113
\(535\) 7.91264e142 0.456823
\(536\) −9.69928e142 −0.507678
\(537\) −2.42758e142 −0.115219
\(538\) 3.55387e143 1.52979
\(539\) −6.32129e143 −2.46829
\(540\) 1.95378e142 0.0692155
\(541\) −3.06037e143 −0.983823 −0.491912 0.870645i \(-0.663702\pi\)
−0.491912 + 0.870645i \(0.663702\pi\)
\(542\) −5.14633e143 −1.50153
\(543\) 4.43015e142 0.117335
\(544\) 1.07869e143 0.259392
\(545\) 6.92146e143 1.51141
\(546\) 5.20902e142 0.103310
\(547\) 3.58490e143 0.645865 0.322933 0.946422i \(-0.395331\pi\)
0.322933 + 0.946422i \(0.395331\pi\)
\(548\) 2.69209e143 0.440667
\(549\) 1.21385e143 0.180558
\(550\) 7.28504e143 0.984897
\(551\) 1.17375e144 1.44250
\(552\) 4.64472e142 0.0518988
\(553\) −3.03364e144 −3.08244
\(554\) 9.82795e143 0.908239
\(555\) −7.14550e142 −0.0600691
\(556\) −7.22048e142 −0.0552255
\(557\) 2.76592e144 1.92505 0.962524 0.271198i \(-0.0874199\pi\)
0.962524 + 0.271198i \(0.0874199\pi\)
\(558\) 3.87713e143 0.245592
\(559\) −1.23880e144 −0.714299
\(560\) −6.08262e144 −3.19315
\(561\) 5.91497e142 0.0282750
\(562\) −1.26311e144 −0.549902
\(563\) 1.21160e144 0.480473 0.240237 0.970714i \(-0.422775\pi\)
0.240237 + 0.970714i \(0.422775\pi\)
\(564\) 4.37678e142 0.0158126
\(565\) 3.13417e143 0.103176
\(566\) −3.10896e144 −0.932723
\(567\) 6.81665e144 1.86406
\(568\) −4.09004e143 −0.101962
\(569\) 3.93949e144 0.895459 0.447730 0.894169i \(-0.352233\pi\)
0.447730 + 0.894169i \(0.352233\pi\)
\(570\) −1.12057e144 −0.232279
\(571\) −2.37657e144 −0.449320 −0.224660 0.974437i \(-0.572127\pi\)
−0.224660 + 0.974437i \(0.572127\pi\)
\(572\) −1.18103e144 −0.203690
\(573\) 5.52766e143 0.0869809
\(574\) 8.14395e144 1.16939
\(575\) −6.21161e144 −0.814033
\(576\) −3.91760e144 −0.468640
\(577\) −6.30933e143 −0.0689054 −0.0344527 0.999406i \(-0.510969\pi\)
−0.0344527 + 0.999406i \(0.510969\pi\)
\(578\) 9.75703e144 0.972985
\(579\) 2.05398e143 0.0187056
\(580\) −4.12562e144 −0.343178
\(581\) 8.67023e144 0.658846
\(582\) 6.32616e143 0.0439221
\(583\) 1.44994e145 0.919921
\(584\) −8.61685e144 −0.499660
\(585\) −1.63280e145 −0.865466
\(586\) 2.79578e145 1.35481
\(587\) −4.42324e145 −1.95993 −0.979963 0.199179i \(-0.936172\pi\)
−0.979963 + 0.199179i \(0.936172\pi\)
\(588\) −1.61357e144 −0.0653849
\(589\) −1.12769e145 −0.417962
\(590\) 1.89531e145 0.642614
\(591\) −3.01750e144 −0.0936063
\(592\) −2.52568e145 −0.716949
\(593\) −5.28905e145 −1.37406 −0.687031 0.726628i \(-0.741086\pi\)
−0.687031 + 0.726628i \(0.741086\pi\)
\(594\) 6.88090e144 0.163628
\(595\) 4.77840e145 1.04026
\(596\) −2.23842e145 −0.446184
\(597\) 5.63203e144 0.102805
\(598\) 3.98250e145 0.665800
\(599\) −7.53160e145 −1.15340 −0.576699 0.816957i \(-0.695659\pi\)
−0.576699 + 0.816957i \(0.695659\pi\)
\(600\) −3.63508e144 −0.0510003
\(601\) 1.21435e146 1.56111 0.780553 0.625090i \(-0.214938\pi\)
0.780553 + 0.625090i \(0.214938\pi\)
\(602\) 2.10282e146 2.47734
\(603\) 6.10883e145 0.659628
\(604\) −2.36891e145 −0.234482
\(605\) −1.42572e145 −0.129383
\(606\) 1.92681e144 0.0160335
\(607\) −1.55972e146 −1.19026 −0.595130 0.803630i \(-0.702899\pi\)
−0.595130 + 0.803630i \(0.702899\pi\)
\(608\) −1.81983e146 −1.27377
\(609\) 1.62043e145 0.104045
\(610\) 4.90777e145 0.289113
\(611\) −7.33589e145 −0.396542
\(612\) −2.70503e145 −0.134191
\(613\) 1.58307e146 0.720816 0.360408 0.932795i \(-0.382638\pi\)
0.360408 + 0.932795i \(0.382638\pi\)
\(614\) −2.07655e146 −0.867968
\(615\) 1.42487e145 0.0546802
\(616\) −3.91888e146 −1.38094
\(617\) −4.02502e146 −1.30256 −0.651279 0.758838i \(-0.725767\pi\)
−0.651279 + 0.758838i \(0.725767\pi\)
\(618\) −2.08332e145 −0.0619242
\(619\) 6.53348e146 1.78396 0.891981 0.452073i \(-0.149315\pi\)
0.891981 + 0.452073i \(0.149315\pi\)
\(620\) 3.96374e145 0.0994356
\(621\) −5.86702e145 −0.135241
\(622\) 8.27834e146 1.75367
\(623\) 5.26480e146 1.02508
\(624\) 3.22137e145 0.0576566
\(625\) −6.65117e146 −1.09445
\(626\) −7.28996e146 −1.10299
\(627\) −9.97895e145 −0.138848
\(628\) 1.34290e145 0.0171855
\(629\) 1.98413e146 0.233567
\(630\) 2.77162e147 3.00162
\(631\) −9.04534e146 −0.901329 −0.450664 0.892693i \(-0.648813\pi\)
−0.450664 + 0.892693i \(0.648813\pi\)
\(632\) −1.35729e147 −1.24459
\(633\) −9.45651e145 −0.0798061
\(634\) −1.49226e147 −1.15920
\(635\) 1.54612e147 1.10567
\(636\) 3.70110e145 0.0243687
\(637\) 2.70449e147 1.63970
\(638\) −1.45298e147 −0.811285
\(639\) 2.57600e146 0.132480
\(640\) −3.47399e147 −1.64581
\(641\) 1.32664e147 0.579039 0.289520 0.957172i \(-0.406504\pi\)
0.289520 + 0.957172i \(0.406504\pi\)
\(642\) 7.11331e145 0.0286077
\(643\) −2.59325e147 −0.961100 −0.480550 0.876967i \(-0.659563\pi\)
−0.480550 + 0.876967i \(0.659563\pi\)
\(644\) −1.70936e147 −0.583883
\(645\) 3.67909e146 0.115839
\(646\) 3.11154e147 0.903169
\(647\) −5.34417e147 −1.43023 −0.715115 0.699007i \(-0.753626\pi\)
−0.715115 + 0.699007i \(0.753626\pi\)
\(648\) 3.04987e147 0.752650
\(649\) 1.68782e147 0.384132
\(650\) −3.11681e147 −0.654274
\(651\) −1.55685e146 −0.0301471
\(652\) 9.92600e146 0.177327
\(653\) 6.55280e146 0.108015 0.0540076 0.998541i \(-0.482800\pi\)
0.0540076 + 0.998541i \(0.482800\pi\)
\(654\) 6.22226e146 0.0946491
\(655\) 6.22813e147 0.874358
\(656\) 5.03639e147 0.652631
\(657\) 5.42709e147 0.649210
\(658\) 1.24524e148 1.37529
\(659\) −6.28428e147 −0.640872 −0.320436 0.947270i \(-0.603829\pi\)
−0.320436 + 0.947270i \(0.603829\pi\)
\(660\) 3.50752e146 0.0330327
\(661\) 1.52889e148 1.32984 0.664920 0.746914i \(-0.268465\pi\)
0.664920 + 0.746914i \(0.268465\pi\)
\(662\) −1.53594e148 −1.23404
\(663\) −2.53065e146 −0.0187833
\(664\) 3.87919e147 0.266021
\(665\) −8.06147e148 −5.10832
\(666\) 1.15086e148 0.673945
\(667\) 1.23889e148 0.670540
\(668\) −5.12256e146 −0.0256285
\(669\) −1.39340e147 −0.0644474
\(670\) 2.46989e148 1.05621
\(671\) 4.37049e147 0.172821
\(672\) −2.51239e147 −0.0918757
\(673\) −4.68333e148 −1.58403 −0.792016 0.610501i \(-0.790968\pi\)
−0.792016 + 0.610501i \(0.790968\pi\)
\(674\) 1.05595e148 0.330370
\(675\) 4.59169e147 0.132900
\(676\) −7.58501e147 −0.203121
\(677\) 5.48314e148 1.35870 0.679351 0.733814i \(-0.262261\pi\)
0.679351 + 0.733814i \(0.262261\pi\)
\(678\) 2.81756e146 0.00646123
\(679\) 4.55109e148 0.965944
\(680\) 2.13792e148 0.420024
\(681\) 3.93545e147 0.0715766
\(682\) 1.39597e148 0.235069
\(683\) −5.85471e148 −0.912890 −0.456445 0.889752i \(-0.650877\pi\)
−0.456445 + 0.889752i \(0.650877\pi\)
\(684\) 4.56357e148 0.658960
\(685\) 1.34007e149 1.79214
\(686\) −2.82045e149 −3.49383
\(687\) −6.86942e147 −0.0788299
\(688\) 1.30043e149 1.38259
\(689\) −6.20338e148 −0.611110
\(690\) −1.18276e148 −0.107974
\(691\) −5.99911e147 −0.0507562 −0.0253781 0.999678i \(-0.508079\pi\)
−0.0253781 + 0.999678i \(0.508079\pi\)
\(692\) −5.06178e148 −0.396948
\(693\) 2.46820e149 1.79426
\(694\) −1.19000e149 −0.802000
\(695\) −3.59421e148 −0.224596
\(696\) 7.25005e147 0.0420103
\(697\) −3.95650e148 −0.212613
\(698\) −2.52464e149 −1.25832
\(699\) 1.29881e148 0.0600475
\(700\) 1.33779e149 0.573775
\(701\) 5.70124e148 0.226868 0.113434 0.993546i \(-0.463815\pi\)
0.113434 + 0.993546i \(0.463815\pi\)
\(702\) −2.94391e148 −0.108699
\(703\) −3.34735e149 −1.14696
\(704\) −1.41054e149 −0.448559
\(705\) 2.17868e148 0.0643079
\(706\) 3.31443e149 0.908161
\(707\) 1.38617e149 0.352611
\(708\) 4.30832e147 0.0101756
\(709\) −6.68298e146 −0.00146569 −0.000732846 1.00000i \(-0.500233\pi\)
−0.000732846 1.00000i \(0.500233\pi\)
\(710\) 1.04151e149 0.212130
\(711\) 8.54853e149 1.61710
\(712\) 2.35555e149 0.413897
\(713\) −1.19028e149 −0.194289
\(714\) 4.29569e148 0.0651444
\(715\) −5.87893e149 −0.828382
\(716\) 3.99722e149 0.523389
\(717\) 9.91362e148 0.120636
\(718\) 2.16513e148 0.0244879
\(719\) 5.00706e149 0.526400 0.263200 0.964741i \(-0.415222\pi\)
0.263200 + 0.964741i \(0.415222\pi\)
\(720\) 1.71403e150 1.67518
\(721\) −1.49875e150 −1.36185
\(722\) −3.88007e150 −3.27821
\(723\) −9.29323e148 −0.0730140
\(724\) −7.29462e149 −0.533001
\(725\) −9.69585e149 −0.658932
\(726\) −1.28170e148 −0.00810237
\(727\) 6.05190e149 0.355906 0.177953 0.984039i \(-0.443053\pi\)
0.177953 + 0.984039i \(0.443053\pi\)
\(728\) 1.67664e150 0.917368
\(729\) −1.89913e150 −0.966850
\(730\) 2.19425e150 1.03953
\(731\) −1.02159e150 −0.450417
\(732\) 1.11561e148 0.00457804
\(733\) 4.46401e150 1.70516 0.852582 0.522594i \(-0.175036\pi\)
0.852582 + 0.522594i \(0.175036\pi\)
\(734\) 1.58344e150 0.563066
\(735\) −8.03202e149 −0.265913
\(736\) −1.92083e150 −0.592110
\(737\) 2.19949e150 0.631364
\(738\) −2.29490e150 −0.613485
\(739\) 3.56099e150 0.886621 0.443311 0.896368i \(-0.353804\pi\)
0.443311 + 0.896368i \(0.353804\pi\)
\(740\) 1.17657e150 0.272868
\(741\) 4.26937e149 0.0922376
\(742\) 1.05300e151 2.11946
\(743\) −6.98622e150 −1.31018 −0.655088 0.755553i \(-0.727368\pi\)
−0.655088 + 0.755553i \(0.727368\pi\)
\(744\) −6.96558e148 −0.0121724
\(745\) −1.11424e151 −1.81458
\(746\) −6.34271e150 −0.962690
\(747\) −2.44320e150 −0.345643
\(748\) −9.73952e149 −0.128441
\(749\) 5.11737e150 0.629146
\(750\) −1.09298e149 −0.0125284
\(751\) 1.18621e150 0.126784 0.0633920 0.997989i \(-0.479808\pi\)
0.0633920 + 0.997989i \(0.479808\pi\)
\(752\) 7.70084e150 0.767541
\(753\) 9.26575e149 0.0861280
\(754\) 6.21639e150 0.538942
\(755\) −1.17920e151 −0.953613
\(756\) 1.26358e150 0.0953252
\(757\) −5.00625e150 −0.352354 −0.176177 0.984359i \(-0.556373\pi\)
−0.176177 + 0.984359i \(0.556373\pi\)
\(758\) −6.74959e150 −0.443245
\(759\) −1.05328e150 −0.0645430
\(760\) −3.60682e151 −2.06258
\(761\) 2.83818e151 1.51476 0.757382 0.652972i \(-0.226478\pi\)
0.757382 + 0.652972i \(0.226478\pi\)
\(762\) 1.38994e150 0.0692404
\(763\) 4.47635e151 2.08154
\(764\) −9.10177e150 −0.395116
\(765\) −1.34651e151 −0.545739
\(766\) −2.33164e151 −0.882371
\(767\) −7.22114e150 −0.255181
\(768\) −2.05917e150 −0.0679561
\(769\) 3.01681e151 0.929853 0.464927 0.885349i \(-0.346081\pi\)
0.464927 + 0.885349i \(0.346081\pi\)
\(770\) 9.97928e151 2.87300
\(771\) 4.72084e150 0.126959
\(772\) −3.38205e150 −0.0849713
\(773\) −2.17459e151 −0.510452 −0.255226 0.966881i \(-0.582150\pi\)
−0.255226 + 0.966881i \(0.582150\pi\)
\(774\) −5.92556e151 −1.29966
\(775\) 9.31541e150 0.190925
\(776\) 2.03622e151 0.390018
\(777\) −4.62124e150 −0.0827285
\(778\) −1.00674e152 −1.68456
\(779\) 6.67487e151 1.04406
\(780\) −1.50065e150 −0.0219438
\(781\) 9.27493e150 0.126804
\(782\) 3.28423e151 0.419835
\(783\) −9.15797e150 −0.109473
\(784\) −2.83903e152 −3.17378
\(785\) 6.68468e150 0.0698914
\(786\) 5.59897e150 0.0547551
\(787\) −1.84640e152 −1.68909 −0.844544 0.535486i \(-0.820128\pi\)
−0.844544 + 0.535486i \(0.820128\pi\)
\(788\) 4.96858e151 0.425212
\(789\) 7.64708e150 0.0612284
\(790\) 3.45629e152 2.58933
\(791\) 2.02698e151 0.142097
\(792\) 1.10431e152 0.724466
\(793\) −1.86986e151 −0.114806
\(794\) 3.27650e152 1.88293
\(795\) 1.84234e151 0.0991047
\(796\) −9.27362e151 −0.466996
\(797\) −7.49684e151 −0.353440 −0.176720 0.984261i \(-0.556549\pi\)
−0.176720 + 0.984261i \(0.556549\pi\)
\(798\) −7.24711e151 −0.319899
\(799\) −6.04964e151 −0.250048
\(800\) 1.50329e152 0.581859
\(801\) −1.48358e152 −0.537778
\(802\) 1.96338e152 0.666577
\(803\) 1.95403e152 0.621392
\(804\) 5.61441e150 0.0167248
\(805\) −8.50886e152 −2.37459
\(806\) −5.97247e151 −0.156158
\(807\) 4.02130e151 0.0985159
\(808\) 6.20190e151 0.142373
\(809\) 7.83353e152 1.68523 0.842617 0.538513i \(-0.181014\pi\)
0.842617 + 0.538513i \(0.181014\pi\)
\(810\) −7.76637e152 −1.56587
\(811\) −7.46411e152 −1.41053 −0.705267 0.708942i \(-0.749173\pi\)
−0.705267 + 0.708942i \(0.749173\pi\)
\(812\) −2.66818e152 −0.472633
\(813\) −5.82321e151 −0.0966961
\(814\) 4.14368e152 0.645068
\(815\) 4.94097e152 0.721170
\(816\) 2.65654e151 0.0363566
\(817\) 1.72349e153 2.21183
\(818\) −2.01580e152 −0.242605
\(819\) −1.05599e153 −1.19194
\(820\) −2.34617e152 −0.248388
\(821\) −1.02758e153 −1.02047 −0.510233 0.860036i \(-0.670441\pi\)
−0.510233 + 0.860036i \(0.670441\pi\)
\(822\) 1.20470e152 0.112230
\(823\) 9.91017e152 0.866143 0.433072 0.901359i \(-0.357430\pi\)
0.433072 + 0.901359i \(0.357430\pi\)
\(824\) −6.70564e152 −0.549872
\(825\) 8.24322e151 0.0634256
\(826\) 1.22576e153 0.885023
\(827\) 5.69334e152 0.385770 0.192885 0.981221i \(-0.438216\pi\)
0.192885 + 0.981221i \(0.438216\pi\)
\(828\) 4.81684e152 0.306316
\(829\) −2.36891e152 −0.141396 −0.0706979 0.997498i \(-0.522523\pi\)
−0.0706979 + 0.997498i \(0.522523\pi\)
\(830\) −9.87820e152 −0.553450
\(831\) 1.11206e152 0.0584890
\(832\) 6.03481e152 0.297981
\(833\) 2.23029e153 1.03395
\(834\) −3.23113e151 −0.0140649
\(835\) −2.54991e152 −0.104228
\(836\) 1.64312e153 0.630725
\(837\) 8.79864e151 0.0317197
\(838\) −4.54161e153 −1.53780
\(839\) 2.95617e152 0.0940214 0.0470107 0.998894i \(-0.485031\pi\)
0.0470107 + 0.998894i \(0.485031\pi\)
\(840\) −4.97945e152 −0.148771
\(841\) −1.62898e153 −0.457221
\(842\) −3.59838e153 −0.948904
\(843\) −1.42924e152 −0.0354127
\(844\) 1.55710e153 0.362524
\(845\) −3.77567e153 −0.826070
\(846\) −3.50899e153 −0.721502
\(847\) −9.22062e152 −0.178189
\(848\) 6.51199e153 1.18286
\(849\) −3.51787e152 −0.0600657
\(850\) −2.57032e153 −0.412567
\(851\) −3.53312e153 −0.533159
\(852\) 2.36751e151 0.00335903
\(853\) 6.28821e153 0.838886 0.419443 0.907782i \(-0.362225\pi\)
0.419443 + 0.907782i \(0.362225\pi\)
\(854\) 3.17402e153 0.398173
\(855\) 2.27165e154 2.67992
\(856\) 2.28959e153 0.254030
\(857\) −3.80402e153 −0.396962 −0.198481 0.980105i \(-0.563601\pi\)
−0.198481 + 0.980105i \(0.563601\pi\)
\(858\) −5.28505e152 −0.0518760
\(859\) 6.93239e153 0.640091 0.320046 0.947402i \(-0.396302\pi\)
0.320046 + 0.947402i \(0.396302\pi\)
\(860\) −6.05794e153 −0.526206
\(861\) 9.21510e152 0.0753069
\(862\) 2.05344e154 1.57889
\(863\) −2.25684e154 −1.63280 −0.816401 0.577486i \(-0.804034\pi\)
−0.816401 + 0.577486i \(0.804034\pi\)
\(864\) 1.41989e153 0.0966684
\(865\) −2.51965e154 −1.61434
\(866\) −2.68459e154 −1.61878
\(867\) 1.10403e153 0.0626585
\(868\) 2.56349e153 0.136945
\(869\) 3.07791e154 1.54781
\(870\) −1.84620e153 −0.0874012
\(871\) −9.41026e153 −0.419419
\(872\) 2.00278e154 0.840462
\(873\) −1.28246e154 −0.506752
\(874\) −5.54071e154 −2.06165
\(875\) −7.86296e153 −0.275526
\(876\) 4.98785e152 0.0164607
\(877\) 9.58540e153 0.297942 0.148971 0.988842i \(-0.452404\pi\)
0.148971 + 0.988842i \(0.452404\pi\)
\(878\) 1.15020e154 0.336752
\(879\) 3.16350e153 0.0872472
\(880\) 6.17140e154 1.60340
\(881\) −4.25775e154 −1.04219 −0.521093 0.853500i \(-0.674475\pi\)
−0.521093 + 0.853500i \(0.674475\pi\)
\(882\) 1.29364e155 2.98341
\(883\) −5.65508e154 −1.22886 −0.614429 0.788972i \(-0.710614\pi\)
−0.614429 + 0.788972i \(0.710614\pi\)
\(884\) 4.16693e153 0.0853242
\(885\) 2.14460e153 0.0413832
\(886\) −7.69079e153 −0.139862
\(887\) −8.11925e154 −1.39164 −0.695819 0.718218i \(-0.744958\pi\)
−0.695819 + 0.718218i \(0.744958\pi\)
\(888\) −2.06761e153 −0.0334032
\(889\) 9.99932e154 1.52275
\(890\) −5.99832e154 −0.861101
\(891\) −6.91614e154 −0.936018
\(892\) 2.29436e154 0.292757
\(893\) 1.02061e155 1.22789
\(894\) −1.00168e154 −0.113635
\(895\) 1.98974e155 2.12856
\(896\) −2.24675e155 −2.26665
\(897\) 4.50631e153 0.0428764
\(898\) 1.24293e155 1.11542
\(899\) −1.85793e154 −0.157270
\(900\) −3.76978e154 −0.301013
\(901\) −5.11571e154 −0.385349
\(902\) −8.26282e154 −0.587198
\(903\) 2.37939e154 0.159536
\(904\) 9.06899e153 0.0573742
\(905\) −3.63112e155 −2.16765
\(906\) −1.06008e154 −0.0597183
\(907\) 2.73085e155 1.45183 0.725914 0.687785i \(-0.241417\pi\)
0.725914 + 0.687785i \(0.241417\pi\)
\(908\) −6.48006e154 −0.325141
\(909\) −3.90610e154 −0.184986
\(910\) −4.26951e155 −1.90856
\(911\) 3.00572e155 1.26833 0.634167 0.773196i \(-0.281343\pi\)
0.634167 + 0.773196i \(0.281343\pi\)
\(912\) −4.48177e154 −0.178534
\(913\) −8.79678e154 −0.330832
\(914\) 3.16047e155 1.12222
\(915\) 5.55327e153 0.0186184
\(916\) 1.13111e155 0.358090
\(917\) 4.02795e155 1.20419
\(918\) −2.42774e154 −0.0685426
\(919\) 4.20926e155 1.12238 0.561192 0.827686i \(-0.310343\pi\)
0.561192 + 0.827686i \(0.310343\pi\)
\(920\) −3.80699e155 −0.958784
\(921\) −2.34968e154 −0.0558956
\(922\) 2.52946e155 0.568401
\(923\) −3.96816e154 −0.0842365
\(924\) 2.26844e154 0.0454934
\(925\) 2.76512e155 0.523929
\(926\) 5.63827e155 1.00941
\(927\) 4.22336e155 0.714451
\(928\) −2.99826e155 −0.479293
\(929\) −2.46842e155 −0.372901 −0.186451 0.982464i \(-0.559698\pi\)
−0.186451 + 0.982464i \(0.559698\pi\)
\(930\) 1.77376e154 0.0253244
\(931\) −3.76265e156 −5.07733
\(932\) −2.13861e155 −0.272769
\(933\) 9.36717e154 0.112933
\(934\) 5.83268e155 0.664748
\(935\) −4.84814e155 −0.522355
\(936\) −4.72464e155 −0.481268
\(937\) 1.82249e156 1.75524 0.877621 0.479356i \(-0.159130\pi\)
0.877621 + 0.479356i \(0.159130\pi\)
\(938\) 1.59736e156 1.45463
\(939\) −8.24879e154 −0.0710308
\(940\) −3.58738e155 −0.292122
\(941\) −1.54822e156 −1.19228 −0.596138 0.802882i \(-0.703299\pi\)
−0.596138 + 0.802882i \(0.703299\pi\)
\(942\) 6.00940e153 0.00437682
\(943\) 7.04531e155 0.485329
\(944\) 7.58038e155 0.493925
\(945\) 6.28984e155 0.387677
\(946\) −2.13351e156 −1.24397
\(947\) 2.52207e156 1.39118 0.695589 0.718440i \(-0.255144\pi\)
0.695589 + 0.718440i \(0.255144\pi\)
\(948\) 7.85666e154 0.0410015
\(949\) −8.36009e155 −0.412795
\(950\) 4.33631e156 2.02596
\(951\) −1.68853e155 −0.0746505
\(952\) 1.38267e156 0.578467
\(953\) −3.92414e155 −0.155370 −0.0776850 0.996978i \(-0.524753\pi\)
−0.0776850 + 0.996978i \(0.524753\pi\)
\(954\) −2.96727e156 −1.11191
\(955\) −4.53068e156 −1.60689
\(956\) −1.63236e156 −0.547996
\(957\) −1.64408e155 −0.0522453
\(958\) 1.25780e156 0.378375
\(959\) 8.66669e156 2.46818
\(960\) −1.79227e155 −0.0483241
\(961\) −3.73872e156 −0.954431
\(962\) −1.77282e156 −0.428523
\(963\) −1.44203e156 −0.330062
\(964\) 1.53021e156 0.331671
\(965\) −1.68352e156 −0.345569
\(966\) −7.64931e155 −0.148704
\(967\) 3.51079e156 0.646421 0.323210 0.946327i \(-0.395238\pi\)
0.323210 + 0.946327i \(0.395238\pi\)
\(968\) −4.12544e155 −0.0719472
\(969\) 3.52080e155 0.0581624
\(970\) −5.18516e156 −0.811421
\(971\) −4.15598e156 −0.616118 −0.308059 0.951367i \(-0.599679\pi\)
−0.308059 + 0.951367i \(0.599679\pi\)
\(972\) −5.34594e155 −0.0750836
\(973\) −2.32450e156 −0.309318
\(974\) −5.70943e156 −0.719860
\(975\) −3.52676e155 −0.0421341
\(976\) 1.96288e156 0.222218
\(977\) 1.31466e157 1.41042 0.705209 0.708999i \(-0.250853\pi\)
0.705209 + 0.708999i \(0.250853\pi\)
\(978\) 4.44184e155 0.0451620
\(979\) −5.34165e156 −0.514735
\(980\) 1.32254e157 1.20793
\(981\) −1.26140e157 −1.09202
\(982\) 5.09403e156 0.418031
\(983\) 1.46640e156 0.114076 0.0570378 0.998372i \(-0.481834\pi\)
0.0570378 + 0.998372i \(0.481834\pi\)
\(984\) 4.12297e155 0.0304066
\(985\) 2.47326e157 1.72929
\(986\) 5.12643e156 0.339842
\(987\) 1.40903e156 0.0885662
\(988\) −7.02989e156 −0.418995
\(989\) 1.81914e157 1.02816
\(990\) −2.81208e157 −1.50723
\(991\) 1.77420e157 0.901854 0.450927 0.892561i \(-0.351093\pi\)
0.450927 + 0.892561i \(0.351093\pi\)
\(992\) 2.88062e156 0.138875
\(993\) −1.73795e156 −0.0794699
\(994\) 6.73583e156 0.292150
\(995\) −4.61623e157 −1.89922
\(996\) −2.24546e155 −0.00876375
\(997\) −5.26632e156 −0.194990 −0.0974948 0.995236i \(-0.531083\pi\)
−0.0974948 + 0.995236i \(0.531083\pi\)
\(998\) −2.94436e157 −1.03428
\(999\) 2.61172e156 0.0870440
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 1.106.a.a.1.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.106.a.a.1.3 8 1.1 even 1 trivial