Properties

Label 1.106.a.a.1.2
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 1.2
Root \(-5.83850e13\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-9.55432e15 q^{2} -1.37857e25 q^{3} +5.07201e31 q^{4} -2.80039e36 q^{5} +1.31713e41 q^{6} -2.78207e44 q^{7} -9.70270e46 q^{8} +6.48087e49 q^{9} +O(q^{10})\) \(q-9.55432e15 q^{2} -1.37857e25 q^{3} +5.07201e31 q^{4} -2.80039e36 q^{5} +1.31713e41 q^{6} -2.78207e44 q^{7} -9.70270e46 q^{8} +6.48087e49 q^{9} +2.67558e52 q^{10} +6.08520e53 q^{11} -6.99212e56 q^{12} -5.49066e58 q^{13} +2.65807e60 q^{14} +3.86053e61 q^{15} -1.13043e63 q^{16} -2.90311e64 q^{17} -6.19203e65 q^{18} -1.56027e67 q^{19} -1.42036e68 q^{20} +3.83527e69 q^{21} -5.81399e69 q^{22} +5.72406e71 q^{23} +1.33759e72 q^{24} -1.68097e73 q^{25} +5.24595e74 q^{26} +8.33042e74 q^{27} -1.41107e76 q^{28} -1.76595e76 q^{29} -3.68848e77 q^{30} +1.61443e78 q^{31} +1.47363e79 q^{32} -8.38888e78 q^{33} +2.77372e80 q^{34} +7.79087e80 q^{35} +3.28711e81 q^{36} +1.96604e82 q^{37} +1.49073e83 q^{38} +7.56926e83 q^{39} +2.71714e83 q^{40} +1.17183e83 q^{41} -3.66434e85 q^{42} +1.98821e84 q^{43} +3.08642e85 q^{44} -1.81490e86 q^{45} -5.46895e87 q^{46} +1.10467e88 q^{47} +1.55837e88 q^{48} +2.30371e88 q^{49} +1.60605e89 q^{50} +4.00214e89 q^{51} -2.78487e90 q^{52} -7.34914e89 q^{53} -7.95915e90 q^{54} -1.70409e90 q^{55} +2.69936e91 q^{56} +2.15094e92 q^{57} +1.68724e92 q^{58} -1.37917e93 q^{59} +1.95807e93 q^{60} +1.74942e93 q^{61} -1.54248e94 q^{62} -1.80302e94 q^{63} -9.49400e94 q^{64} +1.53760e95 q^{65} +8.01500e94 q^{66} +1.25972e96 q^{67} -1.47246e96 q^{68} -7.89102e96 q^{69} -7.44364e96 q^{70} -1.81563e97 q^{71} -6.28820e96 q^{72} -2.37938e97 q^{73} -1.87841e98 q^{74} +2.31734e98 q^{75} -7.91371e98 q^{76} -1.69294e98 q^{77} -7.23191e99 q^{78} +8.68206e98 q^{79} +3.16563e99 q^{80} -1.96005e100 q^{81} -1.11961e99 q^{82} +2.69773e100 q^{83} +1.94526e101 q^{84} +8.12984e100 q^{85} -1.89960e100 q^{86} +2.43448e101 q^{87} -5.90429e100 q^{88} -5.78519e101 q^{89} +1.73401e102 q^{90} +1.52754e103 q^{91} +2.90325e103 q^{92} -2.22561e103 q^{93} -1.05543e104 q^{94} +4.36937e103 q^{95} -2.03151e104 q^{96} +1.53726e103 q^{97} -2.20103e104 q^{98} +3.94374e103 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 9175032489175920q^{2} - \)\(35\!\cdots\!80\)\(q^{3} + \)\(12\!\cdots\!76\)\(q^{4} + \)\(74\!\cdots\!00\)\(q^{5} - \)\(13\!\cdots\!64\)\(q^{6} + \)\(70\!\cdots\!00\)\(q^{7} - \)\(70\!\cdots\!60\)\(q^{8} + \)\(31\!\cdots\!84\)\(q^{9} + O(q^{10}) \) \( 8q - 9175032489175920q^{2} - \)\(35\!\cdots\!80\)\(q^{3} + \)\(12\!\cdots\!76\)\(q^{4} + \)\(74\!\cdots\!00\)\(q^{5} - \)\(13\!\cdots\!64\)\(q^{6} + \)\(70\!\cdots\!00\)\(q^{7} - \)\(70\!\cdots\!60\)\(q^{8} + \)\(31\!\cdots\!84\)\(q^{9} + \)\(44\!\cdots\!00\)\(q^{10} - \)\(91\!\cdots\!84\)\(q^{11} + \)\(15\!\cdots\!60\)\(q^{12} + \)\(40\!\cdots\!40\)\(q^{13} - \)\(16\!\cdots\!28\)\(q^{14} - \)\(85\!\cdots\!00\)\(q^{15} + \)\(88\!\cdots\!48\)\(q^{16} - \)\(47\!\cdots\!60\)\(q^{17} - \)\(26\!\cdots\!80\)\(q^{18} - \)\(18\!\cdots\!20\)\(q^{19} - \)\(43\!\cdots\!00\)\(q^{20} + \)\(34\!\cdots\!56\)\(q^{21} + \)\(61\!\cdots\!60\)\(q^{22} + \)\(35\!\cdots\!60\)\(q^{23} - \)\(85\!\cdots\!60\)\(q^{24} + \)\(36\!\cdots\!00\)\(q^{25} - \)\(17\!\cdots\!24\)\(q^{26} + \)\(41\!\cdots\!40\)\(q^{27} - \)\(10\!\cdots\!60\)\(q^{28} - \)\(13\!\cdots\!80\)\(q^{29} + \)\(36\!\cdots\!00\)\(q^{30} + \)\(21\!\cdots\!16\)\(q^{31} + \)\(10\!\cdots\!80\)\(q^{32} - \)\(11\!\cdots\!60\)\(q^{33} + \)\(62\!\cdots\!52\)\(q^{34} - \)\(18\!\cdots\!00\)\(q^{35} + \)\(16\!\cdots\!48\)\(q^{36} - \)\(23\!\cdots\!80\)\(q^{37} + \)\(81\!\cdots\!60\)\(q^{38} + \)\(97\!\cdots\!48\)\(q^{39} + \)\(16\!\cdots\!00\)\(q^{40} - \)\(91\!\cdots\!84\)\(q^{41} - \)\(99\!\cdots\!60\)\(q^{42} + \)\(30\!\cdots\!00\)\(q^{43} - \)\(61\!\cdots\!48\)\(q^{44} - \)\(72\!\cdots\!00\)\(q^{45} - \)\(19\!\cdots\!84\)\(q^{46} - \)\(19\!\cdots\!40\)\(q^{47} + \)\(47\!\cdots\!60\)\(q^{48} + \)\(90\!\cdots\!56\)\(q^{49} + \)\(12\!\cdots\!00\)\(q^{50} - \)\(10\!\cdots\!04\)\(q^{51} + \)\(26\!\cdots\!00\)\(q^{52} - \)\(50\!\cdots\!80\)\(q^{53} - \)\(33\!\cdots\!20\)\(q^{54} + \)\(18\!\cdots\!00\)\(q^{55} + \)\(77\!\cdots\!80\)\(q^{56} - \)\(17\!\cdots\!20\)\(q^{57} + \)\(52\!\cdots\!40\)\(q^{58} - \)\(80\!\cdots\!60\)\(q^{59} - \)\(49\!\cdots\!00\)\(q^{60} + \)\(93\!\cdots\!16\)\(q^{61} - \)\(24\!\cdots\!40\)\(q^{62} - \)\(69\!\cdots\!20\)\(q^{63} - \)\(97\!\cdots\!04\)\(q^{64} - \)\(36\!\cdots\!00\)\(q^{65} + \)\(15\!\cdots\!72\)\(q^{66} - \)\(11\!\cdots\!60\)\(q^{67} - \)\(97\!\cdots\!80\)\(q^{68} - \)\(15\!\cdots\!32\)\(q^{69} - \)\(42\!\cdots\!00\)\(q^{70} - \)\(50\!\cdots\!84\)\(q^{71} - \)\(31\!\cdots\!80\)\(q^{72} - \)\(30\!\cdots\!40\)\(q^{73} - \)\(92\!\cdots\!88\)\(q^{74} - \)\(20\!\cdots\!00\)\(q^{75} - \)\(31\!\cdots\!40\)\(q^{76} - \)\(59\!\cdots\!00\)\(q^{77} - \)\(21\!\cdots\!00\)\(q^{78} - \)\(15\!\cdots\!80\)\(q^{79} - \)\(36\!\cdots\!00\)\(q^{80} - \)\(16\!\cdots\!72\)\(q^{81} + \)\(40\!\cdots\!60\)\(q^{82} - \)\(27\!\cdots\!20\)\(q^{83} + \)\(24\!\cdots\!32\)\(q^{84} + \)\(11\!\cdots\!00\)\(q^{85} + \)\(20\!\cdots\!96\)\(q^{86} + \)\(24\!\cdots\!20\)\(q^{87} + \)\(65\!\cdots\!80\)\(q^{88} + \)\(45\!\cdots\!60\)\(q^{89} + \)\(27\!\cdots\!00\)\(q^{90} + \)\(27\!\cdots\!96\)\(q^{91} + \)\(11\!\cdots\!40\)\(q^{92} - \)\(18\!\cdots\!60\)\(q^{93} - \)\(14\!\cdots\!08\)\(q^{94} - \)\(19\!\cdots\!00\)\(q^{95} - \)\(72\!\cdots\!64\)\(q^{96} - \)\(76\!\cdots\!40\)\(q^{97} - \)\(13\!\cdots\!40\)\(q^{98} - \)\(25\!\cdots\!32\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −9.55432e15 −1.50012 −0.750058 0.661372i \(-0.769974\pi\)
−0.750058 + 0.661372i \(0.769974\pi\)
\(3\) −1.37857e25 −1.23186 −0.615932 0.787799i \(-0.711220\pi\)
−0.615932 + 0.787799i \(0.711220\pi\)
\(4\) 5.07201e31 1.25035
\(5\) −2.80039e36 −0.564018 −0.282009 0.959412i \(-0.591001\pi\)
−0.282009 + 0.959412i \(0.591001\pi\)
\(6\) 1.31713e41 1.84794
\(7\) −2.78207e44 −1.19322 −0.596610 0.802531i \(-0.703486\pi\)
−0.596610 + 0.802531i \(0.703486\pi\)
\(8\) −9.70270e46 −0.375551
\(9\) 6.48087e49 0.517490
\(10\) 2.67558e52 0.846093
\(11\) 6.08520e53 0.129169 0.0645846 0.997912i \(-0.479428\pi\)
0.0645846 + 0.997912i \(0.479428\pi\)
\(12\) −6.99212e56 −1.54026
\(13\) −5.49066e58 −1.80967 −0.904834 0.425764i \(-0.860005\pi\)
−0.904834 + 0.425764i \(0.860005\pi\)
\(14\) 2.65807e60 1.78997
\(15\) 3.86053e61 0.694794
\(16\) −1.13043e63 −0.686978
\(17\) −2.90311e64 −0.731636 −0.365818 0.930686i \(-0.619211\pi\)
−0.365818 + 0.930686i \(0.619211\pi\)
\(18\) −6.19203e65 −0.776295
\(19\) −1.56027e67 −1.14455 −0.572277 0.820061i \(-0.693940\pi\)
−0.572277 + 0.820061i \(0.693940\pi\)
\(20\) −1.42036e68 −0.705219
\(21\) 3.83527e69 1.46988
\(22\) −5.81399e69 −0.193769
\(23\) 5.72406e71 1.84924 0.924620 0.380892i \(-0.124383\pi\)
0.924620 + 0.380892i \(0.124383\pi\)
\(24\) 1.33759e72 0.462627
\(25\) −1.68097e73 −0.681883
\(26\) 5.24595e74 2.71471
\(27\) 8.33042e74 0.594387
\(28\) −1.41107e76 −1.49194
\(29\) −1.76595e76 −0.295857 −0.147929 0.988998i \(-0.547261\pi\)
−0.147929 + 0.988998i \(0.547261\pi\)
\(30\) −3.68848e77 −1.04227
\(31\) 1.61443e78 0.815700 0.407850 0.913049i \(-0.366279\pi\)
0.407850 + 0.913049i \(0.366279\pi\)
\(32\) 1.47363e79 1.40610
\(33\) −8.38888e78 −0.159119
\(34\) 2.77372e80 1.09754
\(35\) 7.79087e80 0.672998
\(36\) 3.28711e81 0.647042
\(37\) 1.96604e82 0.918335 0.459168 0.888350i \(-0.348148\pi\)
0.459168 + 0.888350i \(0.348148\pi\)
\(38\) 1.49073e83 1.71696
\(39\) 7.56926e83 2.22927
\(40\) 2.71714e83 0.211817
\(41\) 1.17183e83 0.0249870 0.0124935 0.999922i \(-0.496023\pi\)
0.0124935 + 0.999922i \(0.496023\pi\)
\(42\) −3.66434e85 −2.20500
\(43\) 1.98821e84 0.0347831 0.0173915 0.999849i \(-0.494464\pi\)
0.0173915 + 0.999849i \(0.494464\pi\)
\(44\) 3.08642e85 0.161506
\(45\) −1.81490e86 −0.291874
\(46\) −5.46895e87 −2.77407
\(47\) 1.10467e88 1.81173 0.905866 0.423564i \(-0.139221\pi\)
0.905866 + 0.423564i \(0.139221\pi\)
\(48\) 1.55837e88 0.846264
\(49\) 2.30371e88 0.423773
\(50\) 1.60605e89 1.02290
\(51\) 4.00214e89 0.901276
\(52\) −2.78487e90 −2.26271
\(53\) −7.34914e89 −0.219661 −0.109831 0.993950i \(-0.535031\pi\)
−0.109831 + 0.993950i \(0.535031\pi\)
\(54\) −7.95915e90 −0.891650
\(55\) −1.70409e90 −0.0728538
\(56\) 2.69936e91 0.448114
\(57\) 2.15094e92 1.40993
\(58\) 1.68724e92 0.443820
\(59\) −1.37917e93 −1.47872 −0.739360 0.673310i \(-0.764872\pi\)
−0.739360 + 0.673310i \(0.764872\pi\)
\(60\) 1.95807e93 0.868734
\(61\) 1.74942e93 0.325894 0.162947 0.986635i \(-0.447900\pi\)
0.162947 + 0.986635i \(0.447900\pi\)
\(62\) −1.54248e94 −1.22365
\(63\) −1.80302e94 −0.617479
\(64\) −9.49400e94 −1.42233
\(65\) 1.53760e95 1.02069
\(66\) 8.01500e94 0.238697
\(67\) 1.25972e96 1.70352 0.851762 0.523929i \(-0.175534\pi\)
0.851762 + 0.523929i \(0.175534\pi\)
\(68\) −1.47246e96 −0.914799
\(69\) −7.89102e96 −2.27801
\(70\) −7.44364e96 −1.00957
\(71\) −1.81563e97 −1.16940 −0.584702 0.811248i \(-0.698788\pi\)
−0.584702 + 0.811248i \(0.698788\pi\)
\(72\) −6.28820e96 −0.194344
\(73\) −2.37938e97 −0.356462 −0.178231 0.983989i \(-0.557037\pi\)
−0.178231 + 0.983989i \(0.557037\pi\)
\(74\) −1.87841e98 −1.37761
\(75\) 2.31734e98 0.839988
\(76\) −7.91371e98 −1.43109
\(77\) −1.69294e98 −0.154127
\(78\) −7.23191e99 −3.34416
\(79\) 8.68206e98 0.205684 0.102842 0.994698i \(-0.467206\pi\)
0.102842 + 0.994698i \(0.467206\pi\)
\(80\) 3.16563e99 0.387468
\(81\) −1.96005e100 −1.24969
\(82\) −1.11961e99 −0.0374834
\(83\) 2.69773e100 0.477968 0.238984 0.971023i \(-0.423186\pi\)
0.238984 + 0.971023i \(0.423186\pi\)
\(84\) 1.94526e101 1.83787
\(85\) 8.12984e100 0.412656
\(86\) −1.89960e100 −0.0521787
\(87\) 2.43448e101 0.364456
\(88\) −5.90429e100 −0.0485096
\(89\) −5.78519e101 −0.262629 −0.131314 0.991341i \(-0.541920\pi\)
−0.131314 + 0.991341i \(0.541920\pi\)
\(90\) 1.73401e102 0.437845
\(91\) 1.52754e103 2.15933
\(92\) 2.90325e103 2.31219
\(93\) −2.22561e103 −1.00483
\(94\) −1.05543e104 −2.71781
\(95\) 4.36937e103 0.645549
\(96\) −2.03151e104 −1.73212
\(97\) 1.53726e103 0.0760730 0.0380365 0.999276i \(-0.487890\pi\)
0.0380365 + 0.999276i \(0.487890\pi\)
\(98\) −2.20103e104 −0.635708
\(99\) 3.94374e103 0.0668438
\(100\) −8.52591e104 −0.852591
\(101\) 2.28689e105 1.35635 0.678177 0.734898i \(-0.262770\pi\)
0.678177 + 0.734898i \(0.262770\pi\)
\(102\) −3.82377e105 −1.35202
\(103\) 3.42402e105 0.725408 0.362704 0.931904i \(-0.381854\pi\)
0.362704 + 0.931904i \(0.381854\pi\)
\(104\) 5.32743e105 0.679622
\(105\) −1.07403e106 −0.829042
\(106\) 7.02160e105 0.329517
\(107\) 2.13857e106 0.613020 0.306510 0.951867i \(-0.400839\pi\)
0.306510 + 0.951867i \(0.400839\pi\)
\(108\) 4.22520e106 0.743191
\(109\) 1.63899e107 1.77699 0.888495 0.458886i \(-0.151751\pi\)
0.888495 + 0.458886i \(0.151751\pi\)
\(110\) 1.62815e106 0.109289
\(111\) −2.71032e107 −1.13126
\(112\) 3.14492e107 0.819716
\(113\) −1.62565e107 −0.265711 −0.132855 0.991135i \(-0.542415\pi\)
−0.132855 + 0.991135i \(0.542415\pi\)
\(114\) −2.05508e108 −2.11506
\(115\) −1.60296e108 −1.04301
\(116\) −8.95690e107 −0.369924
\(117\) −3.55843e108 −0.936485
\(118\) 1.31770e109 2.21825
\(119\) 8.07664e108 0.873002
\(120\) −3.74576e108 −0.260930
\(121\) −2.18235e109 −0.983315
\(122\) −1.67145e109 −0.488879
\(123\) −1.61546e108 −0.0307806
\(124\) 8.18842e109 1.01991
\(125\) 1.16109e110 0.948613
\(126\) 1.72266e110 0.926290
\(127\) −3.88074e109 −0.137790 −0.0688952 0.997624i \(-0.521947\pi\)
−0.0688952 + 0.997624i \(0.521947\pi\)
\(128\) 3.09310e110 0.727564
\(129\) −2.74088e109 −0.0428480
\(130\) −1.46907e111 −1.53115
\(131\) −1.57108e111 −1.09510 −0.547552 0.836772i \(-0.684440\pi\)
−0.547552 + 0.836772i \(0.684440\pi\)
\(132\) −4.25485e110 −0.198954
\(133\) 4.34078e111 1.36570
\(134\) −1.20358e112 −2.55548
\(135\) −2.33284e111 −0.335245
\(136\) 2.81680e111 0.274766
\(137\) −1.76329e111 −0.117083 −0.0585416 0.998285i \(-0.518645\pi\)
−0.0585416 + 0.998285i \(0.518645\pi\)
\(138\) 7.53933e112 3.41728
\(139\) −2.53726e112 −0.787207 −0.393603 0.919280i \(-0.628772\pi\)
−0.393603 + 0.919280i \(0.628772\pi\)
\(140\) 3.95154e112 0.841481
\(141\) −1.52286e113 −2.23181
\(142\) 1.73471e113 1.75424
\(143\) −3.34118e112 −0.233753
\(144\) −7.32615e112 −0.355504
\(145\) 4.94534e112 0.166869
\(146\) 2.27333e113 0.534734
\(147\) −3.17582e113 −0.522031
\(148\) 9.97177e113 1.14824
\(149\) −8.32260e113 −0.672945 −0.336473 0.941693i \(-0.609234\pi\)
−0.336473 + 0.941693i \(0.609234\pi\)
\(150\) −2.21406e114 −1.26008
\(151\) −4.51522e114 −1.81296 −0.906482 0.422245i \(-0.861242\pi\)
−0.906482 + 0.422245i \(0.861242\pi\)
\(152\) 1.51388e114 0.429838
\(153\) −1.88147e114 −0.378614
\(154\) 1.61749e114 0.231209
\(155\) −4.52104e114 −0.460070
\(156\) 3.83914e115 2.78736
\(157\) 2.88320e115 1.49673 0.748364 0.663288i \(-0.230839\pi\)
0.748364 + 0.663288i \(0.230839\pi\)
\(158\) −8.29511e114 −0.308550
\(159\) 1.01313e115 0.270593
\(160\) −4.12675e115 −0.793065
\(161\) −1.59247e116 −2.20655
\(162\) 1.87269e116 1.87469
\(163\) −5.49862e115 −0.398478 −0.199239 0.979951i \(-0.563847\pi\)
−0.199239 + 0.979951i \(0.563847\pi\)
\(164\) 5.94356e114 0.0312424
\(165\) 2.34921e115 0.0897460
\(166\) −2.57750e116 −0.717008
\(167\) −6.07691e116 −1.23330 −0.616649 0.787238i \(-0.711510\pi\)
−0.616649 + 0.787238i \(0.711510\pi\)
\(168\) −3.72125e116 −0.552016
\(169\) 2.09418e117 2.27490
\(170\) −7.76751e116 −0.619032
\(171\) −1.01119e117 −0.592295
\(172\) 1.00842e116 0.0434909
\(173\) 1.52150e117 0.484006 0.242003 0.970275i \(-0.422196\pi\)
0.242003 + 0.970275i \(0.422196\pi\)
\(174\) −2.32598e117 −0.546726
\(175\) 4.67657e117 0.813636
\(176\) −6.87887e116 −0.0887365
\(177\) 1.90128e118 1.82158
\(178\) 5.52735e117 0.393973
\(179\) −1.41887e117 −0.0753629 −0.0376814 0.999290i \(-0.511997\pi\)
−0.0376814 + 0.999290i \(0.511997\pi\)
\(180\) −9.20518e117 −0.364944
\(181\) 2.12802e118 0.630741 0.315370 0.948969i \(-0.397871\pi\)
0.315370 + 0.948969i \(0.397871\pi\)
\(182\) −1.45946e119 −3.23925
\(183\) −2.41169e118 −0.401458
\(184\) −5.55389e118 −0.694483
\(185\) −5.50567e118 −0.517958
\(186\) 2.12641e119 1.50736
\(187\) −1.76660e118 −0.0945049
\(188\) 5.60289e119 2.26530
\(189\) −2.31758e119 −0.709234
\(190\) −4.17463e119 −0.968399
\(191\) 3.26522e119 0.574991 0.287495 0.957782i \(-0.407177\pi\)
0.287495 + 0.957782i \(0.407177\pi\)
\(192\) 1.30881e120 1.75212
\(193\) −1.01008e120 −1.02943 −0.514713 0.857362i \(-0.672102\pi\)
−0.514713 + 0.857362i \(0.672102\pi\)
\(194\) −1.46874e119 −0.114118
\(195\) −2.11969e120 −1.25735
\(196\) 1.16844e120 0.529863
\(197\) 3.20363e120 1.11215 0.556077 0.831130i \(-0.312306\pi\)
0.556077 + 0.831130i \(0.312306\pi\)
\(198\) −3.76798e119 −0.100273
\(199\) 3.54060e120 0.723253 0.361627 0.932323i \(-0.382221\pi\)
0.361627 + 0.932323i \(0.382221\pi\)
\(200\) 1.63100e120 0.256082
\(201\) −1.73662e121 −2.09851
\(202\) −2.18497e121 −2.03469
\(203\) 4.91298e120 0.353023
\(204\) 2.02989e121 1.12691
\(205\) −3.28159e119 −0.0140931
\(206\) −3.27142e121 −1.08820
\(207\) 3.70969e121 0.956962
\(208\) 6.20679e121 1.24320
\(209\) −9.49457e120 −0.147841
\(210\) 1.02616e122 1.24366
\(211\) −3.74411e121 −0.353606 −0.176803 0.984246i \(-0.556576\pi\)
−0.176803 + 0.984246i \(0.556576\pi\)
\(212\) −3.72750e121 −0.274653
\(213\) 2.50297e122 1.44055
\(214\) −2.04325e122 −0.919601
\(215\) −5.56776e120 −0.0196183
\(216\) −8.08276e121 −0.223222
\(217\) −4.49145e122 −0.973310
\(218\) −1.56594e123 −2.66569
\(219\) 3.28014e122 0.439112
\(220\) −8.64319e121 −0.0910926
\(221\) 1.59400e123 1.32402
\(222\) 2.58952e123 1.69703
\(223\) 1.59180e123 0.823918 0.411959 0.911202i \(-0.364845\pi\)
0.411959 + 0.911202i \(0.364845\pi\)
\(224\) −4.09974e123 −1.67778
\(225\) −1.08942e123 −0.352868
\(226\) 1.55320e123 0.398597
\(227\) −6.30732e123 −1.28377 −0.641885 0.766801i \(-0.721847\pi\)
−0.641885 + 0.766801i \(0.721847\pi\)
\(228\) 1.09096e124 1.76291
\(229\) −8.73627e123 −1.12192 −0.560962 0.827842i \(-0.689569\pi\)
−0.560962 + 0.827842i \(0.689569\pi\)
\(230\) 1.53152e124 1.56463
\(231\) 2.33384e123 0.189864
\(232\) 1.71344e123 0.111109
\(233\) −2.69610e123 −0.139492 −0.0697461 0.997565i \(-0.522219\pi\)
−0.0697461 + 0.997565i \(0.522219\pi\)
\(234\) 3.39984e124 1.40484
\(235\) −3.09350e124 −1.02185
\(236\) −6.99515e124 −1.84891
\(237\) −1.19688e124 −0.253375
\(238\) −7.71668e124 −1.30960
\(239\) 4.10469e124 0.558972 0.279486 0.960150i \(-0.409836\pi\)
0.279486 + 0.960150i \(0.409836\pi\)
\(240\) −4.36405e124 −0.477309
\(241\) −4.83839e124 −0.425409 −0.212704 0.977117i \(-0.568227\pi\)
−0.212704 + 0.977117i \(0.568227\pi\)
\(242\) 2.08509e125 1.47509
\(243\) 1.65879e125 0.945066
\(244\) 8.87306e124 0.407481
\(245\) −6.45128e124 −0.239016
\(246\) 1.54346e124 0.0461744
\(247\) 8.56693e125 2.07126
\(248\) −1.56643e125 −0.306337
\(249\) −3.71901e125 −0.588792
\(250\) −1.10934e126 −1.42303
\(251\) 2.38736e125 0.248341 0.124170 0.992261i \(-0.460373\pi\)
0.124170 + 0.992261i \(0.460373\pi\)
\(252\) −9.14495e125 −0.772063
\(253\) 3.48321e125 0.238865
\(254\) 3.70778e125 0.206701
\(255\) −1.12076e126 −0.508337
\(256\) 8.95976e125 0.330901
\(257\) −1.73877e126 −0.523302 −0.261651 0.965163i \(-0.584267\pi\)
−0.261651 + 0.965163i \(0.584267\pi\)
\(258\) 2.61873e125 0.0642770
\(259\) −5.46965e126 −1.09578
\(260\) 7.79873e126 1.27621
\(261\) −1.14449e126 −0.153103
\(262\) 1.50106e127 1.64278
\(263\) −8.47350e126 −0.759252 −0.379626 0.925140i \(-0.623947\pi\)
−0.379626 + 0.925140i \(0.623947\pi\)
\(264\) 8.13948e125 0.0597572
\(265\) 2.05805e126 0.123893
\(266\) −4.14732e127 −2.04871
\(267\) 7.97529e126 0.323523
\(268\) 6.38934e127 2.13000
\(269\) 5.38318e127 1.47586 0.737928 0.674880i \(-0.235805\pi\)
0.737928 + 0.674880i \(0.235805\pi\)
\(270\) 2.22887e127 0.502907
\(271\) −6.18683e127 −1.14969 −0.574845 0.818263i \(-0.694937\pi\)
−0.574845 + 0.818263i \(0.694937\pi\)
\(272\) 3.28175e127 0.502618
\(273\) −2.10582e128 −2.66000
\(274\) 1.68470e127 0.175638
\(275\) −1.02291e127 −0.0880783
\(276\) −4.00234e128 −2.84831
\(277\) 5.28238e127 0.310915 0.155458 0.987843i \(-0.450315\pi\)
0.155458 + 0.987843i \(0.450315\pi\)
\(278\) 2.42418e128 1.18090
\(279\) 1.04629e128 0.422117
\(280\) −7.55925e127 −0.252745
\(281\) 4.88641e128 1.35490 0.677451 0.735568i \(-0.263085\pi\)
0.677451 + 0.735568i \(0.263085\pi\)
\(282\) 1.45499e129 3.34797
\(283\) −4.29397e128 −0.820486 −0.410243 0.911976i \(-0.634556\pi\)
−0.410243 + 0.911976i \(0.634556\pi\)
\(284\) −9.20891e128 −1.46216
\(285\) −6.02348e128 −0.795229
\(286\) 3.19227e128 0.350657
\(287\) −3.26012e127 −0.0298149
\(288\) 9.55043e128 0.727641
\(289\) −7.31674e128 −0.464709
\(290\) −4.72493e128 −0.250323
\(291\) −2.11922e128 −0.0937116
\(292\) −1.20682e129 −0.445701
\(293\) −4.25875e129 −1.31441 −0.657207 0.753710i \(-0.728262\pi\)
−0.657207 + 0.753710i \(0.728262\pi\)
\(294\) 3.03428e129 0.783106
\(295\) 3.86220e129 0.834026
\(296\) −1.90759e129 −0.344881
\(297\) 5.06923e128 0.0767765
\(298\) 7.95167e129 1.00950
\(299\) −3.14289e130 −3.34651
\(300\) 1.17536e130 1.05028
\(301\) −5.53133e128 −0.0415039
\(302\) 4.31398e130 2.71966
\(303\) −3.15264e130 −1.67084
\(304\) 1.76377e130 0.786283
\(305\) −4.89905e129 −0.183810
\(306\) 1.79761e130 0.567965
\(307\) 3.47475e130 0.925036 0.462518 0.886610i \(-0.346946\pi\)
0.462518 + 0.886610i \(0.346946\pi\)
\(308\) −8.58663e129 −0.192713
\(309\) −4.72026e130 −0.893605
\(310\) 4.31954e130 0.690158
\(311\) 4.08993e130 0.551817 0.275908 0.961184i \(-0.411021\pi\)
0.275908 + 0.961184i \(0.411021\pi\)
\(312\) −7.34423e130 −0.837202
\(313\) −1.00853e131 −0.971873 −0.485937 0.873994i \(-0.661521\pi\)
−0.485937 + 0.873994i \(0.661521\pi\)
\(314\) −2.75470e131 −2.24527
\(315\) 5.04916e130 0.348270
\(316\) 4.40355e130 0.257176
\(317\) 7.79846e130 0.385832 0.192916 0.981215i \(-0.438206\pi\)
0.192916 + 0.981215i \(0.438206\pi\)
\(318\) −9.67977e130 −0.405921
\(319\) −1.07461e130 −0.0382157
\(320\) 2.65869e131 0.802221
\(321\) −2.94816e131 −0.755157
\(322\) 1.52150e132 3.31008
\(323\) 4.52964e131 0.837396
\(324\) −9.94140e131 −1.56255
\(325\) 9.22965e131 1.23398
\(326\) 5.25355e131 0.597763
\(327\) −2.25946e132 −2.18901
\(328\) −1.13700e130 −0.00938387
\(329\) −3.07326e132 −2.16179
\(330\) −2.24451e131 −0.134629
\(331\) 1.33736e132 0.684353 0.342176 0.939636i \(-0.388836\pi\)
0.342176 + 0.939636i \(0.388836\pi\)
\(332\) 1.36829e132 0.597627
\(333\) 1.27416e132 0.475229
\(334\) 5.80608e132 1.85009
\(335\) −3.52772e132 −0.960819
\(336\) −4.33549e132 −1.00978
\(337\) 5.42067e132 1.08015 0.540074 0.841618i \(-0.318396\pi\)
0.540074 + 0.841618i \(0.318396\pi\)
\(338\) −2.00085e133 −3.41261
\(339\) 2.24108e132 0.327320
\(340\) 4.12347e132 0.515964
\(341\) 9.82414e131 0.105363
\(342\) 9.66125e132 0.888511
\(343\) 8.71476e132 0.687566
\(344\) −1.92910e131 −0.0130628
\(345\) 2.20979e133 1.28484
\(346\) −1.45369e133 −0.726066
\(347\) 1.25222e132 0.0537506 0.0268753 0.999639i \(-0.491444\pi\)
0.0268753 + 0.999639i \(0.491444\pi\)
\(348\) 1.23477e133 0.455697
\(349\) 4.47790e133 1.42148 0.710738 0.703457i \(-0.248361\pi\)
0.710738 + 0.703457i \(0.248361\pi\)
\(350\) −4.46815e133 −1.22055
\(351\) −4.57396e133 −1.07564
\(352\) 8.96736e132 0.181625
\(353\) 5.25259e133 0.916645 0.458323 0.888786i \(-0.348450\pi\)
0.458323 + 0.888786i \(0.348450\pi\)
\(354\) −1.81654e134 −2.73259
\(355\) 5.08448e133 0.659565
\(356\) −2.93425e133 −0.328377
\(357\) −1.11342e134 −1.07542
\(358\) 1.35563e133 0.113053
\(359\) 1.00745e134 0.725712 0.362856 0.931845i \(-0.381802\pi\)
0.362856 + 0.931845i \(0.381802\pi\)
\(360\) 1.76094e133 0.109613
\(361\) 5.76093e133 0.310002
\(362\) −2.03318e134 −0.946185
\(363\) 3.00852e134 1.21131
\(364\) 7.74770e134 2.69991
\(365\) 6.66318e133 0.201051
\(366\) 2.30421e134 0.602233
\(367\) −8.02021e134 −1.81643 −0.908213 0.418509i \(-0.862553\pi\)
−0.908213 + 0.418509i \(0.862553\pi\)
\(368\) −6.47063e134 −1.27039
\(369\) 7.59451e132 0.0129305
\(370\) 5.26029e134 0.776997
\(371\) 2.04458e134 0.262104
\(372\) −1.12883e135 −1.25639
\(373\) 4.43980e134 0.429190 0.214595 0.976703i \(-0.431157\pi\)
0.214595 + 0.976703i \(0.431157\pi\)
\(374\) 1.68787e134 0.141768
\(375\) −1.60064e135 −1.16856
\(376\) −1.07183e135 −0.680397
\(377\) 9.69621e134 0.535404
\(378\) 2.21429e135 1.06393
\(379\) −6.75431e133 −0.0282502 −0.0141251 0.999900i \(-0.504496\pi\)
−0.0141251 + 0.999900i \(0.504496\pi\)
\(380\) 2.21615e135 0.807161
\(381\) 5.34987e134 0.169739
\(382\) −3.11970e135 −0.862553
\(383\) −5.34001e135 −1.28708 −0.643541 0.765412i \(-0.722535\pi\)
−0.643541 + 0.765412i \(0.722535\pi\)
\(384\) −4.26406e135 −0.896260
\(385\) 4.74090e134 0.0869306
\(386\) 9.65059e135 1.54426
\(387\) 1.28853e134 0.0179999
\(388\) 7.79699e134 0.0951177
\(389\) 1.35889e136 1.44820 0.724102 0.689693i \(-0.242254\pi\)
0.724102 + 0.689693i \(0.242254\pi\)
\(390\) 2.02522e136 1.88617
\(391\) −1.66176e136 −1.35297
\(392\) −2.23522e135 −0.159148
\(393\) 2.16584e136 1.34902
\(394\) −3.06085e136 −1.66836
\(395\) −2.43131e135 −0.116010
\(396\) 2.00027e135 0.0835779
\(397\) −4.74251e136 −1.73583 −0.867914 0.496715i \(-0.834539\pi\)
−0.867914 + 0.496715i \(0.834539\pi\)
\(398\) −3.38280e136 −1.08496
\(399\) −5.98406e136 −1.68236
\(400\) 1.90021e136 0.468439
\(401\) −1.79524e135 −0.0388189 −0.0194094 0.999812i \(-0.506179\pi\)
−0.0194094 + 0.999812i \(0.506179\pi\)
\(402\) 1.65922e137 3.14801
\(403\) −8.86430e136 −1.47615
\(404\) 1.15991e137 1.69591
\(405\) 5.48891e136 0.704851
\(406\) −4.69401e136 −0.529575
\(407\) 1.19637e136 0.118621
\(408\) −3.88316e136 −0.338475
\(409\) −3.15143e136 −0.241565 −0.120783 0.992679i \(-0.538540\pi\)
−0.120783 + 0.992679i \(0.538540\pi\)
\(410\) 3.13534e135 0.0211413
\(411\) 2.43082e136 0.144231
\(412\) 1.73667e137 0.907013
\(413\) 3.83693e137 1.76444
\(414\) −3.54436e137 −1.43555
\(415\) −7.55470e136 −0.269583
\(416\) −8.09123e137 −2.54457
\(417\) 3.49780e137 0.969732
\(418\) 9.07141e136 0.221779
\(419\) −4.51580e137 −0.973864 −0.486932 0.873440i \(-0.661884\pi\)
−0.486932 + 0.873440i \(0.661884\pi\)
\(420\) −5.44747e137 −1.03659
\(421\) 6.83262e137 1.14757 0.573783 0.819008i \(-0.305475\pi\)
0.573783 + 0.819008i \(0.305475\pi\)
\(422\) 3.57724e137 0.530450
\(423\) 7.15921e137 0.937553
\(424\) 7.13066e136 0.0824939
\(425\) 4.88005e137 0.498890
\(426\) −2.39142e138 −2.16099
\(427\) −4.86699e137 −0.388863
\(428\) 1.08468e138 0.766488
\(429\) 4.60605e137 0.287953
\(430\) 5.31961e136 0.0294297
\(431\) 1.34945e137 0.0660846 0.0330423 0.999454i \(-0.489480\pi\)
0.0330423 + 0.999454i \(0.489480\pi\)
\(432\) −9.41693e137 −0.408331
\(433\) 1.24017e138 0.476286 0.238143 0.971230i \(-0.423461\pi\)
0.238143 + 0.971230i \(0.423461\pi\)
\(434\) 4.29128e138 1.46008
\(435\) −6.81749e137 −0.205560
\(436\) 8.31298e138 2.22186
\(437\) −8.93109e138 −2.11655
\(438\) −3.13394e138 −0.658720
\(439\) 6.09549e138 1.13664 0.568318 0.822809i \(-0.307594\pi\)
0.568318 + 0.822809i \(0.307594\pi\)
\(440\) 1.65343e137 0.0273603
\(441\) 1.49300e138 0.219298
\(442\) −1.52296e139 −1.98618
\(443\) −6.29540e138 −0.729168 −0.364584 0.931171i \(-0.618789\pi\)
−0.364584 + 0.931171i \(0.618789\pi\)
\(444\) −1.37468e139 −1.41447
\(445\) 1.62008e138 0.148127
\(446\) −1.52086e139 −1.23597
\(447\) 1.14733e139 0.828977
\(448\) 2.64129e139 1.69715
\(449\) −3.53370e137 −0.0201975 −0.0100987 0.999949i \(-0.503215\pi\)
−0.0100987 + 0.999949i \(0.503215\pi\)
\(450\) 1.04086e139 0.529342
\(451\) 7.13085e136 0.00322755
\(452\) −8.24533e138 −0.332231
\(453\) 6.22454e139 2.23333
\(454\) 6.02621e139 1.92580
\(455\) −4.27771e139 −1.21790
\(456\) −2.08700e139 −0.529502
\(457\) −7.29371e139 −1.64948 −0.824742 0.565510i \(-0.808679\pi\)
−0.824742 + 0.565510i \(0.808679\pi\)
\(458\) 8.34691e139 1.68302
\(459\) −2.41841e139 −0.434875
\(460\) −8.13024e139 −1.30412
\(461\) −1.26835e140 −1.81526 −0.907632 0.419768i \(-0.862112\pi\)
−0.907632 + 0.419768i \(0.862112\pi\)
\(462\) −2.22983e139 −0.284818
\(463\) 1.37630e140 1.56932 0.784660 0.619927i \(-0.212838\pi\)
0.784660 + 0.619927i \(0.212838\pi\)
\(464\) 1.99627e139 0.203248
\(465\) 6.23257e139 0.566744
\(466\) 2.57594e139 0.209254
\(467\) 1.53938e140 1.11740 0.558700 0.829370i \(-0.311300\pi\)
0.558700 + 0.829370i \(0.311300\pi\)
\(468\) −1.80484e140 −1.17093
\(469\) −3.50464e140 −2.03268
\(470\) 2.95563e140 1.53289
\(471\) −3.97469e140 −1.84377
\(472\) 1.33816e140 0.555334
\(473\) 1.20987e138 0.00449290
\(474\) 1.14354e140 0.380091
\(475\) 2.62277e140 0.780452
\(476\) 4.09648e140 1.09156
\(477\) −4.76289e139 −0.113673
\(478\) −3.92175e140 −0.838523
\(479\) 1.64056e140 0.314323 0.157162 0.987573i \(-0.449766\pi\)
0.157162 + 0.987573i \(0.449766\pi\)
\(480\) 5.68901e140 0.976949
\(481\) −1.07949e141 −1.66188
\(482\) 4.62276e140 0.638163
\(483\) 2.19533e141 2.71817
\(484\) −1.10689e141 −1.22949
\(485\) −4.30492e139 −0.0429066
\(486\) −1.58486e141 −1.41771
\(487\) −6.86441e140 −0.551230 −0.275615 0.961268i \(-0.588881\pi\)
−0.275615 + 0.961268i \(0.588881\pi\)
\(488\) −1.69741e140 −0.122390
\(489\) 7.58023e140 0.490871
\(490\) 6.16376e140 0.358551
\(491\) −1.07369e141 −0.561176 −0.280588 0.959828i \(-0.590529\pi\)
−0.280588 + 0.959828i \(0.590529\pi\)
\(492\) −8.19361e139 −0.0384864
\(493\) 5.12673e140 0.216460
\(494\) −8.18511e141 −3.10713
\(495\) −1.10440e140 −0.0377011
\(496\) −1.82500e141 −0.560368
\(497\) 5.05121e141 1.39536
\(498\) 3.55326e141 0.883256
\(499\) 7.22628e141 1.61673 0.808363 0.588685i \(-0.200354\pi\)
0.808363 + 0.588685i \(0.200354\pi\)
\(500\) 5.88905e141 1.18610
\(501\) 8.37745e141 1.51926
\(502\) −2.28096e141 −0.372540
\(503\) −2.57863e140 −0.0379376 −0.0189688 0.999820i \(-0.506038\pi\)
−0.0189688 + 0.999820i \(0.506038\pi\)
\(504\) 1.74942e141 0.231895
\(505\) −6.40419e141 −0.765009
\(506\) −3.32797e141 −0.358325
\(507\) −2.88697e142 −2.80237
\(508\) −1.96831e141 −0.172286
\(509\) 8.55017e141 0.674981 0.337490 0.941329i \(-0.390422\pi\)
0.337490 + 0.941329i \(0.390422\pi\)
\(510\) 1.07080e142 0.762564
\(511\) 6.61958e141 0.425337
\(512\) −2.11076e142 −1.22395
\(513\) −1.29977e142 −0.680308
\(514\) 1.66127e142 0.785013
\(515\) −9.58861e141 −0.409144
\(516\) −1.39018e141 −0.0535749
\(517\) 6.72213e141 0.234020
\(518\) 5.22587e142 1.64379
\(519\) −2.09749e142 −0.596230
\(520\) −1.49189e142 −0.383319
\(521\) −2.86534e141 −0.0665572 −0.0332786 0.999446i \(-0.510595\pi\)
−0.0332786 + 0.999446i \(0.510595\pi\)
\(522\) 1.09348e142 0.229672
\(523\) 4.48660e142 0.852272 0.426136 0.904659i \(-0.359874\pi\)
0.426136 + 0.904659i \(0.359874\pi\)
\(524\) −7.96854e142 −1.36926
\(525\) −6.44698e142 −1.00229
\(526\) 8.09585e142 1.13897
\(527\) −4.68687e142 −0.596796
\(528\) 9.48300e141 0.109311
\(529\) 2.31836e143 2.41969
\(530\) −1.96632e142 −0.185854
\(531\) −8.93820e142 −0.765223
\(532\) 2.20165e143 1.70760
\(533\) −6.43415e141 −0.0452181
\(534\) −7.61984e142 −0.485322
\(535\) −5.98882e142 −0.345754
\(536\) −1.22227e143 −0.639759
\(537\) 1.95601e142 0.0928368
\(538\) −5.14326e143 −2.21395
\(539\) 1.40185e142 0.0547384
\(540\) −1.18322e143 −0.419173
\(541\) −1.97481e143 −0.634847 −0.317424 0.948284i \(-0.602818\pi\)
−0.317424 + 0.948284i \(0.602818\pi\)
\(542\) 5.91109e143 1.72467
\(543\) −2.93363e143 −0.776987
\(544\) −4.27812e143 −1.02875
\(545\) −4.58981e143 −1.00226
\(546\) 2.01197e144 3.99031
\(547\) −1.18448e143 −0.213399 −0.106700 0.994291i \(-0.534028\pi\)
−0.106700 + 0.994291i \(0.534028\pi\)
\(548\) −8.94344e142 −0.146395
\(549\) 1.13377e143 0.168647
\(550\) 9.77316e142 0.132128
\(551\) 2.75535e143 0.338624
\(552\) 7.65642e143 0.855509
\(553\) −2.41541e143 −0.245426
\(554\) −5.04695e143 −0.466409
\(555\) 7.58995e143 0.638054
\(556\) −1.28690e144 −0.984282
\(557\) 1.54722e144 1.07685 0.538423 0.842675i \(-0.319020\pi\)
0.538423 + 0.842675i \(0.319020\pi\)
\(558\) −9.99661e143 −0.633224
\(559\) −1.09166e143 −0.0629458
\(560\) −8.80700e143 −0.462335
\(561\) 2.43538e143 0.116417
\(562\) −4.66863e144 −2.03251
\(563\) 1.70654e144 0.676748 0.338374 0.941012i \(-0.390123\pi\)
0.338374 + 0.941012i \(0.390123\pi\)
\(564\) −7.72397e144 −2.79054
\(565\) 4.55246e143 0.149866
\(566\) 4.10260e144 1.23082
\(567\) 5.45299e144 1.49116
\(568\) 1.76165e144 0.439170
\(569\) −2.55776e144 −0.581388 −0.290694 0.956816i \(-0.593886\pi\)
−0.290694 + 0.956816i \(0.593886\pi\)
\(570\) 5.75502e144 1.19294
\(571\) 7.49648e144 1.41730 0.708650 0.705561i \(-0.249305\pi\)
0.708650 + 0.705561i \(0.249305\pi\)
\(572\) −1.69465e144 −0.292273
\(573\) −4.50134e144 −0.708311
\(574\) 3.11482e143 0.0447259
\(575\) −9.62199e144 −1.26097
\(576\) −6.15294e144 −0.736042
\(577\) −2.51068e144 −0.274196 −0.137098 0.990557i \(-0.543778\pi\)
−0.137098 + 0.990557i \(0.543778\pi\)
\(578\) 6.99064e144 0.697117
\(579\) 1.39246e145 1.26811
\(580\) 2.50828e144 0.208644
\(581\) −7.50527e144 −0.570321
\(582\) 2.02477e144 0.140578
\(583\) −4.47210e143 −0.0283735
\(584\) 2.30864e144 0.133869
\(585\) 9.96499e144 0.528195
\(586\) 4.06895e145 1.97177
\(587\) −1.70386e145 −0.754978 −0.377489 0.926014i \(-0.623212\pi\)
−0.377489 + 0.926014i \(0.623212\pi\)
\(588\) −1.61078e145 −0.652720
\(589\) −2.51895e145 −0.933612
\(590\) −3.69007e145 −1.25114
\(591\) −4.41643e145 −1.37002
\(592\) −2.22246e145 −0.630876
\(593\) 3.57082e145 0.927675 0.463838 0.885920i \(-0.346472\pi\)
0.463838 + 0.885920i \(0.346472\pi\)
\(594\) −4.84330e144 −0.115174
\(595\) −2.26178e145 −0.492389
\(596\) −4.22123e145 −0.841415
\(597\) −4.88097e145 −0.890950
\(598\) 3.00282e146 5.02015
\(599\) 4.04087e145 0.618823 0.309412 0.950928i \(-0.399868\pi\)
0.309412 + 0.950928i \(0.399868\pi\)
\(600\) −2.24844e145 −0.315458
\(601\) −4.23700e145 −0.544689 −0.272345 0.962200i \(-0.587799\pi\)
−0.272345 + 0.962200i \(0.587799\pi\)
\(602\) 5.28481e144 0.0622606
\(603\) 8.16411e145 0.881556
\(604\) −2.29012e146 −2.26683
\(605\) 6.11144e145 0.554608
\(606\) 3.01213e146 2.50646
\(607\) 1.81602e146 1.38584 0.692920 0.721014i \(-0.256324\pi\)
0.692920 + 0.721014i \(0.256324\pi\)
\(608\) −2.29927e146 −1.60935
\(609\) −6.77288e145 −0.434876
\(610\) 4.68070e145 0.275737
\(611\) −6.06536e146 −3.27863
\(612\) −9.54283e145 −0.473399
\(613\) 1.35963e146 0.619079 0.309539 0.950887i \(-0.399825\pi\)
0.309539 + 0.950887i \(0.399825\pi\)
\(614\) −3.31988e146 −1.38766
\(615\) 4.52390e144 0.0173608
\(616\) 1.64261e145 0.0578826
\(617\) 5.10995e146 1.65366 0.826829 0.562453i \(-0.190142\pi\)
0.826829 + 0.562453i \(0.190142\pi\)
\(618\) 4.50988e146 1.34051
\(619\) −2.66391e146 −0.727378 −0.363689 0.931520i \(-0.618483\pi\)
−0.363689 + 0.931520i \(0.618483\pi\)
\(620\) −2.29308e146 −0.575248
\(621\) 4.76839e146 1.09916
\(622\) −3.90764e146 −0.827789
\(623\) 1.60948e146 0.313374
\(624\) −8.55649e146 −1.53146
\(625\) 8.92418e145 0.146848
\(626\) 9.63578e146 1.45792
\(627\) 1.30889e146 0.182120
\(628\) 1.46236e147 1.87143
\(629\) −5.70762e146 −0.671887
\(630\) −4.82413e146 −0.522445
\(631\) −3.13753e146 −0.312641 −0.156321 0.987706i \(-0.549963\pi\)
−0.156321 + 0.987706i \(0.549963\pi\)
\(632\) −8.42394e145 −0.0772447
\(633\) 5.16152e146 0.435595
\(634\) −7.45090e146 −0.578792
\(635\) 1.08676e146 0.0777163
\(636\) 5.13861e146 0.338335
\(637\) −1.26489e147 −0.766888
\(638\) 1.02672e146 0.0573279
\(639\) −1.17669e147 −0.605154
\(640\) −8.66190e146 −0.410359
\(641\) 2.34806e147 1.02486 0.512428 0.858730i \(-0.328746\pi\)
0.512428 + 0.858730i \(0.328746\pi\)
\(642\) 2.81677e147 1.13282
\(643\) 2.81374e147 1.04282 0.521409 0.853307i \(-0.325407\pi\)
0.521409 + 0.853307i \(0.325407\pi\)
\(644\) −8.07704e147 −2.75895
\(645\) 7.67555e145 0.0241671
\(646\) −4.32776e147 −1.25619
\(647\) 2.99199e147 0.800728 0.400364 0.916356i \(-0.368884\pi\)
0.400364 + 0.916356i \(0.368884\pi\)
\(648\) 1.90178e147 0.469323
\(649\) −8.39251e146 −0.191005
\(650\) −8.81830e147 −1.85112
\(651\) 6.19178e147 1.19899
\(652\) −2.78891e147 −0.498236
\(653\) −1.01216e148 −1.66843 −0.834214 0.551441i \(-0.814078\pi\)
−0.834214 + 0.551441i \(0.814078\pi\)
\(654\) 2.15876e148 3.28377
\(655\) 4.39964e147 0.617659
\(656\) −1.32467e146 −0.0171655
\(657\) −1.54204e147 −0.184465
\(658\) 2.93629e148 3.24294
\(659\) 3.85253e146 0.0392881 0.0196441 0.999807i \(-0.493747\pi\)
0.0196441 + 0.999807i \(0.493747\pi\)
\(660\) 1.19152e147 0.112214
\(661\) −2.48731e146 −0.0216348 −0.0108174 0.999941i \(-0.503443\pi\)
−0.0108174 + 0.999941i \(0.503443\pi\)
\(662\) −1.27776e148 −1.02661
\(663\) −2.19744e148 −1.63101
\(664\) −2.61753e147 −0.179501
\(665\) −1.21559e148 −0.770282
\(666\) −1.21738e148 −0.712899
\(667\) −1.01084e148 −0.547111
\(668\) −3.08222e148 −1.54205
\(669\) −2.19441e148 −1.01496
\(670\) 3.37049e148 1.44134
\(671\) 1.06456e147 0.0420955
\(672\) 5.65178e148 2.06680
\(673\) 3.07607e148 1.04041 0.520206 0.854041i \(-0.325855\pi\)
0.520206 + 0.854041i \(0.325855\pi\)
\(674\) −5.17908e148 −1.62035
\(675\) −1.40032e148 −0.405303
\(676\) 1.06217e149 2.84441
\(677\) −5.19092e148 −1.28629 −0.643146 0.765744i \(-0.722371\pi\)
−0.643146 + 0.765744i \(0.722371\pi\)
\(678\) −2.14119e148 −0.491018
\(679\) −4.27675e147 −0.0907718
\(680\) −7.88814e147 −0.154973
\(681\) 8.69508e148 1.58143
\(682\) −9.38630e147 −0.158057
\(683\) 1.89336e148 0.295221 0.147610 0.989046i \(-0.452842\pi\)
0.147610 + 0.989046i \(0.452842\pi\)
\(684\) −5.12878e148 −0.740574
\(685\) 4.93791e147 0.0660371
\(686\) −8.32636e148 −1.03143
\(687\) 1.20436e149 1.38206
\(688\) −2.24752e147 −0.0238952
\(689\) 4.03517e148 0.397514
\(690\) −2.11131e149 −1.92741
\(691\) 5.38718e148 0.455789 0.227894 0.973686i \(-0.426816\pi\)
0.227894 + 0.973686i \(0.426816\pi\)
\(692\) 7.71706e148 0.605176
\(693\) −1.09718e148 −0.0797593
\(694\) −1.19641e148 −0.0806321
\(695\) 7.10533e148 0.443999
\(696\) −2.36210e148 −0.136872
\(697\) −3.40196e147 −0.0182814
\(698\) −4.27833e149 −2.13238
\(699\) 3.71676e148 0.171835
\(700\) 2.37196e149 1.01733
\(701\) −2.86338e149 −1.13942 −0.569708 0.821847i \(-0.692944\pi\)
−0.569708 + 0.821847i \(0.692944\pi\)
\(702\) 4.37010e149 1.61359
\(703\) −3.06755e149 −1.05108
\(704\) −5.77729e148 −0.183721
\(705\) 4.26461e149 1.25878
\(706\) −5.01849e149 −1.37507
\(707\) −6.36228e149 −1.61843
\(708\) 9.64330e149 2.27761
\(709\) 4.90339e149 1.07540 0.537699 0.843137i \(-0.319294\pi\)
0.537699 + 0.843137i \(0.319294\pi\)
\(710\) −4.85787e149 −0.989424
\(711\) 5.62673e148 0.106439
\(712\) 5.61320e148 0.0986303
\(713\) 9.24111e149 1.50843
\(714\) 1.06380e150 1.61326
\(715\) 9.35661e148 0.131841
\(716\) −7.19651e148 −0.0942298
\(717\) −5.65860e149 −0.688578
\(718\) −9.62548e149 −1.08865
\(719\) −6.37999e149 −0.670738 −0.335369 0.942087i \(-0.608861\pi\)
−0.335369 + 0.942087i \(0.608861\pi\)
\(720\) 2.05161e149 0.200511
\(721\) −9.52586e149 −0.865571
\(722\) −5.50418e149 −0.465039
\(723\) 6.67007e149 0.524046
\(724\) 1.07934e150 0.788645
\(725\) 2.96850e149 0.201740
\(726\) −2.87444e150 −1.81711
\(727\) −1.08800e150 −0.639841 −0.319921 0.947444i \(-0.603656\pi\)
−0.319921 + 0.947444i \(0.603656\pi\)
\(728\) −1.48213e150 −0.810938
\(729\) 1.67944e149 0.0855004
\(730\) −6.36621e149 −0.301600
\(731\) −5.77199e148 −0.0254486
\(732\) −1.22321e150 −0.501962
\(733\) 1.12535e150 0.429863 0.214932 0.976629i \(-0.431047\pi\)
0.214932 + 0.976629i \(0.431047\pi\)
\(734\) 7.66276e150 2.72485
\(735\) 8.89354e149 0.294435
\(736\) 8.43517e150 2.60021
\(737\) 7.66568e149 0.220043
\(738\) −7.25603e148 −0.0193973
\(739\) 3.16267e150 0.787446 0.393723 0.919229i \(-0.371187\pi\)
0.393723 + 0.919229i \(0.371187\pi\)
\(740\) −2.79248e150 −0.647628
\(741\) −1.18101e151 −2.55151
\(742\) −1.95346e150 −0.393187
\(743\) −6.22279e150 −1.16701 −0.583503 0.812111i \(-0.698318\pi\)
−0.583503 + 0.812111i \(0.698318\pi\)
\(744\) 2.15944e150 0.377365
\(745\) 2.33065e150 0.379554
\(746\) −4.24192e150 −0.643834
\(747\) 1.74837e150 0.247344
\(748\) −8.96022e149 −0.118164
\(749\) −5.94963e150 −0.731467
\(750\) 1.52930e151 1.75298
\(751\) 1.24977e151 1.33577 0.667886 0.744264i \(-0.267199\pi\)
0.667886 + 0.744264i \(0.267199\pi\)
\(752\) −1.24874e151 −1.24462
\(753\) −3.29115e150 −0.305922
\(754\) −9.26407e150 −0.803167
\(755\) 1.26444e151 1.02254
\(756\) −1.17548e151 −0.886789
\(757\) 1.28207e151 0.902357 0.451178 0.892434i \(-0.351004\pi\)
0.451178 + 0.892434i \(0.351004\pi\)
\(758\) 6.45328e149 0.0423786
\(759\) −4.80185e150 −0.294249
\(760\) −4.23947e150 −0.242436
\(761\) −1.91799e151 −1.02365 −0.511826 0.859089i \(-0.671031\pi\)
−0.511826 + 0.859089i \(0.671031\pi\)
\(762\) −5.11143e150 −0.254628
\(763\) −4.55978e151 −2.12034
\(764\) 1.65613e151 0.718939
\(765\) 5.26885e150 0.213545
\(766\) 5.10201e151 1.93077
\(767\) 7.57254e151 2.67599
\(768\) −1.23517e151 −0.407625
\(769\) −4.55055e150 −0.140259 −0.0701296 0.997538i \(-0.522341\pi\)
−0.0701296 + 0.997538i \(0.522341\pi\)
\(770\) −4.52961e150 −0.130406
\(771\) 2.39701e151 0.644637
\(772\) −5.12312e151 −1.28714
\(773\) 4.52563e151 1.06232 0.531160 0.847272i \(-0.321756\pi\)
0.531160 + 0.847272i \(0.321756\pi\)
\(774\) −1.23111e150 −0.0270019
\(775\) −2.71381e151 −0.556212
\(776\) −1.49156e150 −0.0285693
\(777\) 7.54029e151 1.34985
\(778\) −1.29832e152 −2.17247
\(779\) −1.82838e150 −0.0285989
\(780\) −1.07511e152 −1.57212
\(781\) −1.10485e151 −0.151051
\(782\) 1.58770e152 2.02961
\(783\) −1.47111e151 −0.175854
\(784\) −2.60417e151 −0.291123
\(785\) −8.07409e151 −0.844183
\(786\) −2.06931e152 −2.02368
\(787\) −1.16926e152 −1.06964 −0.534819 0.844967i \(-0.679620\pi\)
−0.534819 + 0.844967i \(0.679620\pi\)
\(788\) 1.62488e152 1.39058
\(789\) 1.16813e152 0.935296
\(790\) 2.32295e151 0.174028
\(791\) 4.52267e151 0.317052
\(792\) −3.82650e150 −0.0251032
\(793\) −9.60546e151 −0.589761
\(794\) 4.53114e152 2.60394
\(795\) −2.83716e151 −0.152619
\(796\) 1.79580e152 0.904318
\(797\) −1.15487e152 −0.544468 −0.272234 0.962231i \(-0.587762\pi\)
−0.272234 + 0.962231i \(0.587762\pi\)
\(798\) 5.71736e152 2.52374
\(799\) −3.20697e152 −1.32553
\(800\) −2.47714e152 −0.958794
\(801\) −3.74931e151 −0.135908
\(802\) 1.71523e151 0.0582328
\(803\) −1.44790e151 −0.0460439
\(804\) −8.80815e152 −2.62387
\(805\) 4.45954e152 1.24453
\(806\) 8.46923e152 2.21439
\(807\) −7.42108e152 −1.81805
\(808\) −2.21890e152 −0.509380
\(809\) −4.63963e152 −0.998127 −0.499064 0.866565i \(-0.666323\pi\)
−0.499064 + 0.866565i \(0.666323\pi\)
\(810\) −5.24427e152 −1.05736
\(811\) 8.65154e151 0.163493 0.0817464 0.996653i \(-0.473950\pi\)
0.0817464 + 0.996653i \(0.473950\pi\)
\(812\) 2.49187e152 0.441401
\(813\) 8.52898e152 1.41626
\(814\) −1.14305e152 −0.177945
\(815\) 1.53983e152 0.224749
\(816\) −4.52412e152 −0.619157
\(817\) −3.10214e151 −0.0398111
\(818\) 3.01098e152 0.362376
\(819\) 9.89979e152 1.11743
\(820\) −1.66443e151 −0.0176213
\(821\) −5.99650e152 −0.595501 −0.297750 0.954644i \(-0.596236\pi\)
−0.297750 + 0.954644i \(0.596236\pi\)
\(822\) −2.32248e152 −0.216363
\(823\) 9.52116e152 0.832144 0.416072 0.909332i \(-0.363406\pi\)
0.416072 + 0.909332i \(0.363406\pi\)
\(824\) −3.32223e152 −0.272428
\(825\) 1.41015e152 0.108501
\(826\) −3.66593e153 −2.64686
\(827\) 1.42933e153 0.968488 0.484244 0.874933i \(-0.339095\pi\)
0.484244 + 0.874933i \(0.339095\pi\)
\(828\) 1.88156e153 1.19654
\(829\) −8.24532e152 −0.492147 −0.246073 0.969251i \(-0.579140\pi\)
−0.246073 + 0.969251i \(0.579140\pi\)
\(830\) 7.21800e152 0.404406
\(831\) −7.28213e152 −0.383005
\(832\) 5.21284e153 2.57395
\(833\) −6.68791e152 −0.310047
\(834\) −3.34190e153 −1.45471
\(835\) 1.70177e153 0.695603
\(836\) −4.81566e152 −0.184853
\(837\) 1.34489e153 0.484842
\(838\) 4.31453e153 1.46091
\(839\) −1.00004e153 −0.318063 −0.159031 0.987274i \(-0.550837\pi\)
−0.159031 + 0.987274i \(0.550837\pi\)
\(840\) 1.04210e153 0.311347
\(841\) −3.25093e153 −0.912468
\(842\) −6.52810e153 −1.72148
\(843\) −6.73625e153 −1.66906
\(844\) −1.89902e153 −0.442131
\(845\) −5.86452e153 −1.28308
\(846\) −6.84014e153 −1.40644
\(847\) 6.07145e153 1.17331
\(848\) 8.30766e152 0.150903
\(849\) 5.91954e153 1.01073
\(850\) −4.66255e153 −0.748393
\(851\) 1.12537e154 1.69822
\(852\) 1.26951e154 1.80118
\(853\) 7.56898e153 1.00975 0.504874 0.863193i \(-0.331539\pi\)
0.504874 + 0.863193i \(0.331539\pi\)
\(854\) 4.65008e153 0.583340
\(855\) 2.83173e153 0.334065
\(856\) −2.07499e153 −0.230220
\(857\) −2.02420e153 −0.211232 −0.105616 0.994407i \(-0.533681\pi\)
−0.105616 + 0.994407i \(0.533681\pi\)
\(858\) −4.40077e153 −0.431962
\(859\) −1.23650e154 −1.14171 −0.570853 0.821053i \(-0.693387\pi\)
−0.570853 + 0.821053i \(0.693387\pi\)
\(860\) −2.82398e152 −0.0245297
\(861\) 4.49430e152 0.0367280
\(862\) −1.28931e153 −0.0991345
\(863\) 1.07223e154 0.775748 0.387874 0.921712i \(-0.373210\pi\)
0.387874 + 0.921712i \(0.373210\pi\)
\(864\) 1.22760e154 0.835766
\(865\) −4.26079e153 −0.272989
\(866\) −1.18490e154 −0.714484
\(867\) 1.00866e154 0.572458
\(868\) −2.27807e154 −1.21698
\(869\) 5.28321e152 0.0265680
\(870\) 6.51364e153 0.308364
\(871\) −6.91672e154 −3.08281
\(872\) −1.59026e154 −0.667350
\(873\) 9.96277e152 0.0393670
\(874\) 8.53305e154 3.17507
\(875\) −3.23022e154 −1.13190
\(876\) 1.66369e154 0.549043
\(877\) 1.27536e154 0.396420 0.198210 0.980160i \(-0.436487\pi\)
0.198210 + 0.980160i \(0.436487\pi\)
\(878\) −5.82382e154 −1.70508
\(879\) 5.87099e154 1.61918
\(880\) 1.92635e153 0.0500490
\(881\) −1.17829e154 −0.288414 −0.144207 0.989548i \(-0.546063\pi\)
−0.144207 + 0.989548i \(0.546063\pi\)
\(882\) −1.42646e154 −0.328973
\(883\) 1.02733e154 0.223241 0.111621 0.993751i \(-0.464396\pi\)
0.111621 + 0.993751i \(0.464396\pi\)
\(884\) 8.08479e154 1.65548
\(885\) −5.32432e154 −1.02741
\(886\) 6.01482e154 1.09384
\(887\) −3.44753e154 −0.590906 −0.295453 0.955357i \(-0.595471\pi\)
−0.295453 + 0.955357i \(0.595471\pi\)
\(888\) 2.62974e154 0.424847
\(889\) 1.07965e154 0.164414
\(890\) −1.54787e154 −0.222208
\(891\) −1.19273e154 −0.161422
\(892\) 8.07365e154 1.03018
\(893\) −1.72358e155 −2.07362
\(894\) −1.09619e155 −1.24356
\(895\) 3.97338e153 0.0425060
\(896\) −8.60522e154 −0.868143
\(897\) 4.33270e155 4.12245
\(898\) 3.37621e153 0.0302985
\(899\) −2.85100e154 −0.241331
\(900\) −5.52553e154 −0.441207
\(901\) 2.13354e154 0.160712
\(902\) −6.81304e152 −0.00484170
\(903\) 7.62532e153 0.0511271
\(904\) 1.57732e154 0.0997879
\(905\) −5.95929e154 −0.355750
\(906\) −5.94713e155 −3.35025
\(907\) 1.66663e155 0.886048 0.443024 0.896510i \(-0.353906\pi\)
0.443024 + 0.896510i \(0.353906\pi\)
\(908\) −3.19908e155 −1.60516
\(909\) 1.48210e155 0.701900
\(910\) 4.08706e155 1.82700
\(911\) −3.43117e155 −1.44786 −0.723931 0.689873i \(-0.757666\pi\)
−0.723931 + 0.689873i \(0.757666\pi\)
\(912\) −2.43148e155 −0.968594
\(913\) 1.64163e154 0.0617388
\(914\) 6.96864e155 2.47442
\(915\) 6.75368e154 0.226429
\(916\) −4.43105e155 −1.40279
\(917\) 4.37085e155 1.30670
\(918\) 2.31063e155 0.652363
\(919\) −1.14534e155 −0.305401 −0.152700 0.988273i \(-0.548797\pi\)
−0.152700 + 0.988273i \(0.548797\pi\)
\(920\) 1.55531e155 0.391701
\(921\) −4.79018e155 −1.13952
\(922\) 1.21182e156 2.72311
\(923\) 9.96902e155 2.11623
\(924\) 1.18373e155 0.237396
\(925\) −3.30485e155 −0.626197
\(926\) −1.31496e156 −2.35416
\(927\) 2.21907e155 0.375391
\(928\) −2.60235e155 −0.416004
\(929\) −2.98166e155 −0.450436 −0.225218 0.974308i \(-0.572309\pi\)
−0.225218 + 0.974308i \(0.572309\pi\)
\(930\) −5.95479e155 −0.850182
\(931\) −3.59441e155 −0.485030
\(932\) −1.36746e155 −0.174414
\(933\) −5.63825e155 −0.679764
\(934\) −1.47077e156 −1.67623
\(935\) 4.94717e154 0.0533025
\(936\) 3.45264e155 0.351697
\(937\) −1.80246e156 −1.73595 −0.867976 0.496605i \(-0.834580\pi\)
−0.867976 + 0.496605i \(0.834580\pi\)
\(938\) 3.34844e156 3.04925
\(939\) 1.39032e156 1.19722
\(940\) −1.56903e156 −1.27767
\(941\) −1.52494e156 −1.17435 −0.587176 0.809460i \(-0.699760\pi\)
−0.587176 + 0.809460i \(0.699760\pi\)
\(942\) 3.79755e156 2.76586
\(943\) 6.70765e154 0.0462069
\(944\) 1.55905e156 1.01585
\(945\) 6.49012e155 0.400021
\(946\) −1.15594e154 −0.00673988
\(947\) −2.42446e156 −1.33734 −0.668670 0.743559i \(-0.733136\pi\)
−0.668670 + 0.743559i \(0.733136\pi\)
\(948\) −6.07060e155 −0.316806
\(949\) 1.30644e156 0.645077
\(950\) −2.50588e156 −1.17077
\(951\) −1.07507e156 −0.475292
\(952\) −7.83653e155 −0.327857
\(953\) 4.23514e156 1.67683 0.838417 0.545029i \(-0.183481\pi\)
0.838417 + 0.545029i \(0.183481\pi\)
\(954\) 4.55061e155 0.170522
\(955\) −9.14390e155 −0.324306
\(956\) 2.08190e156 0.698910
\(957\) 1.48143e155 0.0470765
\(958\) −1.56744e156 −0.471521
\(959\) 4.90560e155 0.139706
\(960\) −3.66519e156 −0.988227
\(961\) −1.31083e156 −0.334633
\(962\) 1.03137e157 2.49302
\(963\) 1.38598e156 0.317231
\(964\) −2.45404e156 −0.531909
\(965\) 2.82861e156 0.580616
\(966\) −2.09749e157 −4.07757
\(967\) 2.95182e156 0.543500 0.271750 0.962368i \(-0.412398\pi\)
0.271750 + 0.962368i \(0.412398\pi\)
\(968\) 2.11747e156 0.369285
\(969\) −6.24442e156 −1.03156
\(970\) 4.11306e155 0.0643648
\(971\) −2.93287e156 −0.434794 −0.217397 0.976083i \(-0.569757\pi\)
−0.217397 + 0.976083i \(0.569757\pi\)
\(972\) 8.41341e156 1.18166
\(973\) 7.05884e156 0.939310
\(974\) 6.55847e156 0.826909
\(975\) −1.27237e157 −1.52010
\(976\) −1.97759e156 −0.223882
\(977\) 1.11036e157 1.19123 0.595617 0.803268i \(-0.296907\pi\)
0.595617 + 0.803268i \(0.296907\pi\)
\(978\) −7.24239e156 −0.736363
\(979\) −3.52040e155 −0.0339235
\(980\) −3.27210e156 −0.298853
\(981\) 1.06221e157 0.919574
\(982\) 1.02583e157 0.841829
\(983\) −2.45904e157 −1.91296 −0.956480 0.291799i \(-0.905746\pi\)
−0.956480 + 0.291799i \(0.905746\pi\)
\(984\) 1.56743e155 0.0115597
\(985\) −8.97141e156 −0.627276
\(986\) −4.89824e156 −0.324715
\(987\) 4.23670e157 2.66304
\(988\) 4.34516e157 2.58980
\(989\) 1.13806e156 0.0643222
\(990\) 1.05518e156 0.0565560
\(991\) −6.63369e156 −0.337201 −0.168600 0.985684i \(-0.553925\pi\)
−0.168600 + 0.985684i \(0.553925\pi\)
\(992\) 2.37908e157 1.14695
\(993\) −1.84365e157 −0.843030
\(994\) −4.82608e157 −2.09319
\(995\) −9.91506e156 −0.407928
\(996\) −1.88629e157 −0.736195
\(997\) 5.95950e156 0.220655 0.110328 0.993895i \(-0.464810\pi\)
0.110328 + 0.993895i \(0.464810\pi\)
\(998\) −6.90422e157 −2.42528
\(999\) 1.63779e157 0.545847
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.1.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.106.a.a.1.2 8 1.1 even 1 trivial