Properties

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

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.1
Root \(2.71282e13\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.65868e15 q^{2} -2.23967e24 q^{3} +4.53328e30 q^{4} +2.85912e35 q^{5} +5.95456e39 q^{6} +3.30273e41 q^{7} -5.31200e45 q^{8} +3.46997e48 q^{9} +O(q^{10})\) \(q-2.65868e15 q^{2} -2.23967e24 q^{3} +4.53328e30 q^{4} +2.85912e35 q^{5} +5.95456e39 q^{6} +3.30273e41 q^{7} -5.31200e45 q^{8} +3.46997e48 q^{9} -7.60148e50 q^{10} -4.96610e52 q^{11} -1.01530e55 q^{12} +5.64410e55 q^{13} -8.78091e56 q^{14} -6.40347e59 q^{15} +2.62967e60 q^{16} -1.94858e61 q^{17} -9.22556e63 q^{18} +3.52128e64 q^{19} +1.29612e66 q^{20} -7.39702e65 q^{21} +1.32033e68 q^{22} -1.63800e68 q^{23} +1.18971e70 q^{24} +4.23025e70 q^{25} -1.50059e71 q^{26} -4.30876e72 q^{27} +1.49722e72 q^{28} -5.40160e73 q^{29} +1.70248e75 q^{30} -3.00633e75 q^{31} +6.47607e75 q^{32} +1.11224e77 q^{33} +5.18065e76 q^{34} +9.44290e76 q^{35} +1.57304e79 q^{36} +2.08004e79 q^{37} -9.36197e79 q^{38} -1.26409e80 q^{39} -1.51876e81 q^{40} +6.19514e80 q^{41} +1.96663e81 q^{42} -1.29205e82 q^{43} -2.25127e83 q^{44} +9.92107e83 q^{45} +4.35492e83 q^{46} +3.59319e84 q^{47} -5.88958e84 q^{48} -2.25323e85 q^{49} -1.12469e86 q^{50} +4.36417e85 q^{51} +2.55863e86 q^{52} -9.51793e86 q^{53} +1.14556e88 q^{54} -1.41987e88 q^{55} -1.75441e87 q^{56} -7.88650e88 q^{57} +1.43611e89 q^{58} +2.90108e89 q^{59} -2.90288e90 q^{60} +9.18299e89 q^{61} +7.99286e90 q^{62} +1.14604e90 q^{63} -2.38848e91 q^{64} +1.61371e91 q^{65} -2.95709e92 q^{66} -1.99314e92 q^{67} -8.83346e91 q^{68} +3.66857e92 q^{69} -2.51057e92 q^{70} -1.96946e93 q^{71} -1.84325e94 q^{72} +2.27832e94 q^{73} -5.53017e94 q^{74} -9.47435e94 q^{75} +1.59630e95 q^{76} -1.64017e94 q^{77} +3.36081e95 q^{78} +2.24448e95 q^{79} +7.51853e95 q^{80} +4.28516e96 q^{81} -1.64709e96 q^{82} +1.11393e96 q^{83} -3.35328e96 q^{84} -5.57122e96 q^{85} +3.43516e97 q^{86} +1.20978e98 q^{87} +2.63799e98 q^{88} -1.83015e98 q^{89} -2.63770e99 q^{90} +1.86409e97 q^{91} -7.42551e98 q^{92} +6.73317e99 q^{93} -9.55315e99 q^{94} +1.00678e100 q^{95} -1.45042e100 q^{96} +2.50182e100 q^{97} +5.99061e100 q^{98} -1.72322e101 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 434989091795040q^{2} - \)\(12\!\cdots\!60\)\(q^{3} + \)\(90\!\cdots\!96\)\(q^{4} + \)\(38\!\cdots\!00\)\(q^{5} + \)\(24\!\cdots\!36\)\(q^{6} - \)\(57\!\cdots\!00\)\(q^{7} - \)\(61\!\cdots\!20\)\(q^{8} + \)\(52\!\cdots\!84\)\(q^{9} + O(q^{10}) \) \( 8q - 434989091795040q^{2} - \)\(12\!\cdots\!60\)\(q^{3} + \)\(90\!\cdots\!96\)\(q^{4} + \)\(38\!\cdots\!00\)\(q^{5} + \)\(24\!\cdots\!36\)\(q^{6} - \)\(57\!\cdots\!00\)\(q^{7} - \)\(61\!\cdots\!20\)\(q^{8} + \)\(52\!\cdots\!84\)\(q^{9} - \)\(37\!\cdots\!00\)\(q^{10} + \)\(46\!\cdots\!96\)\(q^{11} - \)\(72\!\cdots\!80\)\(q^{12} + \)\(25\!\cdots\!80\)\(q^{13} - \)\(48\!\cdots\!88\)\(q^{14} - \)\(29\!\cdots\!00\)\(q^{15} - \)\(10\!\cdots\!72\)\(q^{16} - \)\(39\!\cdots\!20\)\(q^{17} - \)\(72\!\cdots\!60\)\(q^{18} - \)\(21\!\cdots\!80\)\(q^{19} + \)\(17\!\cdots\!00\)\(q^{20} + \)\(40\!\cdots\!36\)\(q^{21} + \)\(61\!\cdots\!20\)\(q^{22} - \)\(13\!\cdots\!80\)\(q^{23} + \)\(10\!\cdots\!60\)\(q^{24} + \)\(77\!\cdots\!00\)\(q^{25} - \)\(97\!\cdots\!44\)\(q^{26} - \)\(59\!\cdots\!20\)\(q^{27} + \)\(92\!\cdots\!80\)\(q^{28} + \)\(15\!\cdots\!80\)\(q^{29} + \)\(11\!\cdots\!00\)\(q^{30} - \)\(65\!\cdots\!44\)\(q^{31} + \)\(12\!\cdots\!60\)\(q^{32} + \)\(43\!\cdots\!80\)\(q^{33} + \)\(95\!\cdots\!12\)\(q^{34} - \)\(11\!\cdots\!00\)\(q^{35} + \)\(19\!\cdots\!08\)\(q^{36} + \)\(39\!\cdots\!40\)\(q^{37} - \)\(70\!\cdots\!80\)\(q^{38} - \)\(26\!\cdots\!32\)\(q^{39} - \)\(76\!\cdots\!00\)\(q^{40} + \)\(56\!\cdots\!36\)\(q^{41} + \)\(30\!\cdots\!80\)\(q^{42} - \)\(28\!\cdots\!00\)\(q^{43} - \)\(20\!\cdots\!48\)\(q^{44} + \)\(71\!\cdots\!00\)\(q^{45} + \)\(10\!\cdots\!76\)\(q^{46} - \)\(45\!\cdots\!80\)\(q^{47} - \)\(58\!\cdots\!80\)\(q^{48} + \)\(12\!\cdots\!56\)\(q^{49} - \)\(40\!\cdots\!00\)\(q^{50} + \)\(11\!\cdots\!36\)\(q^{51} - \)\(73\!\cdots\!00\)\(q^{52} + \)\(13\!\cdots\!40\)\(q^{53} + \)\(68\!\cdots\!20\)\(q^{54} - \)\(14\!\cdots\!00\)\(q^{55} - \)\(23\!\cdots\!80\)\(q^{56} - \)\(66\!\cdots\!40\)\(q^{57} + \)\(29\!\cdots\!80\)\(q^{58} + \)\(21\!\cdots\!60\)\(q^{59} - \)\(34\!\cdots\!00\)\(q^{60} - \)\(33\!\cdots\!04\)\(q^{61} - \)\(58\!\cdots\!80\)\(q^{62} - \)\(20\!\cdots\!40\)\(q^{63} - \)\(74\!\cdots\!04\)\(q^{64} - \)\(16\!\cdots\!00\)\(q^{65} - \)\(74\!\cdots\!68\)\(q^{66} - \)\(61\!\cdots\!20\)\(q^{67} - \)\(21\!\cdots\!60\)\(q^{68} - \)\(53\!\cdots\!72\)\(q^{69} - \)\(12\!\cdots\!00\)\(q^{70} - \)\(15\!\cdots\!24\)\(q^{71} - \)\(55\!\cdots\!60\)\(q^{72} - \)\(20\!\cdots\!80\)\(q^{73} - \)\(14\!\cdots\!88\)\(q^{74} - \)\(20\!\cdots\!00\)\(q^{75} + \)\(64\!\cdots\!40\)\(q^{76} + \)\(25\!\cdots\!00\)\(q^{77} + \)\(12\!\cdots\!00\)\(q^{78} + \)\(14\!\cdots\!80\)\(q^{79} + \)\(60\!\cdots\!00\)\(q^{80} + \)\(14\!\cdots\!08\)\(q^{81} + \)\(30\!\cdots\!20\)\(q^{82} + \)\(33\!\cdots\!60\)\(q^{83} + \)\(57\!\cdots\!32\)\(q^{84} + \)\(17\!\cdots\!00\)\(q^{85} + \)\(67\!\cdots\!16\)\(q^{86} + \)\(25\!\cdots\!40\)\(q^{87} - \)\(36\!\cdots\!40\)\(q^{88} - \)\(62\!\cdots\!60\)\(q^{89} - \)\(47\!\cdots\!00\)\(q^{90} - \)\(36\!\cdots\!44\)\(q^{91} - \)\(46\!\cdots\!20\)\(q^{92} - \)\(39\!\cdots\!20\)\(q^{93} - \)\(17\!\cdots\!88\)\(q^{94} - \)\(26\!\cdots\!00\)\(q^{95} + \)\(46\!\cdots\!56\)\(q^{96} + \)\(64\!\cdots\!20\)\(q^{97} + \)\(20\!\cdots\!20\)\(q^{98} + \)\(22\!\cdots\!08\)\(q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.65868e15 −1.66975 −0.834875 0.550440i \(-0.814460\pi\)
−0.834875 + 0.550440i \(0.814460\pi\)
\(3\) −2.23967e24 −1.80119 −0.900596 0.434657i \(-0.856870\pi\)
−0.900596 + 0.434657i \(0.856870\pi\)
\(4\) 4.53328e30 1.78807
\(5\) 2.85912e35 1.43962 0.719808 0.694173i \(-0.244230\pi\)
0.719808 + 0.694173i \(0.244230\pi\)
\(6\) 5.95456e39 3.00754
\(7\) 3.30273e41 0.0694100 0.0347050 0.999398i \(-0.488951\pi\)
0.0347050 + 0.999398i \(0.488951\pi\)
\(8\) −5.31200e45 −1.31587
\(9\) 3.46997e48 2.24429
\(10\) −7.60148e50 −2.40380
\(11\) −4.96610e52 −1.27551 −0.637756 0.770238i \(-0.720137\pi\)
−0.637756 + 0.770238i \(0.720137\pi\)
\(12\) −1.01530e55 −3.22065
\(13\) 5.64410e55 0.314380 0.157190 0.987568i \(-0.449756\pi\)
0.157190 + 0.987568i \(0.449756\pi\)
\(14\) −8.78091e56 −0.115897
\(15\) −6.40347e59 −2.59303
\(16\) 2.62967e60 0.409112
\(17\) −1.94858e61 −0.141921 −0.0709606 0.997479i \(-0.522606\pi\)
−0.0709606 + 0.997479i \(0.522606\pi\)
\(18\) −9.22556e63 −3.74741
\(19\) 3.52128e64 0.932490 0.466245 0.884656i \(-0.345606\pi\)
0.466245 + 0.884656i \(0.345606\pi\)
\(20\) 1.29612e66 2.57413
\(21\) −7.39702e65 −0.125021
\(22\) 1.32033e68 2.12979
\(23\) −1.63800e68 −0.279935 −0.139968 0.990156i \(-0.544700\pi\)
−0.139968 + 0.990156i \(0.544700\pi\)
\(24\) 1.18971e70 2.37014
\(25\) 4.23025e70 1.07250
\(26\) −1.50059e71 −0.524936
\(27\) −4.30876e72 −2.24121
\(28\) 1.49722e72 0.124110
\(29\) −5.40160e73 −0.761068 −0.380534 0.924767i \(-0.624260\pi\)
−0.380534 + 0.924767i \(0.624260\pi\)
\(30\) 1.70248e75 4.32971
\(31\) −3.00633e75 −1.45972 −0.729862 0.683595i \(-0.760416\pi\)
−0.729862 + 0.683595i \(0.760416\pi\)
\(32\) 6.47607e75 0.632758
\(33\) 1.11224e77 2.29744
\(34\) 5.18065e76 0.236973
\(35\) 9.44290e76 0.0999238
\(36\) 1.57304e79 4.01294
\(37\) 2.08004e79 1.33010 0.665052 0.746797i \(-0.268410\pi\)
0.665052 + 0.746797i \(0.268410\pi\)
\(38\) −9.36197e79 −1.55703
\(39\) −1.26409e80 −0.566259
\(40\) −1.51876e81 −1.89435
\(41\) 6.19514e80 0.222058 0.111029 0.993817i \(-0.464585\pi\)
0.111029 + 0.993817i \(0.464585\pi\)
\(42\) 1.96663e81 0.208753
\(43\) −1.29205e82 −0.417950 −0.208975 0.977921i \(-0.567013\pi\)
−0.208975 + 0.977921i \(0.567013\pi\)
\(44\) −2.25127e83 −2.28070
\(45\) 9.92107e83 3.23092
\(46\) 4.35492e83 0.467422
\(47\) 3.59319e84 1.30178 0.650891 0.759171i \(-0.274395\pi\)
0.650891 + 0.759171i \(0.274395\pi\)
\(48\) −5.88958e84 −0.736889
\(49\) −2.25323e85 −0.995182
\(50\) −1.12469e86 −1.79080
\(51\) 4.36417e85 0.255627
\(52\) 2.55863e86 0.562132
\(53\) −9.51793e86 −0.799118 −0.399559 0.916707i \(-0.630837\pi\)
−0.399559 + 0.916707i \(0.630837\pi\)
\(54\) 1.14556e88 3.74226
\(55\) −1.41987e88 −1.83625
\(56\) −1.75441e87 −0.0913347
\(57\) −7.88650e88 −1.67959
\(58\) 1.43611e89 1.27079
\(59\) 2.90108e89 1.08276 0.541382 0.840777i \(-0.317901\pi\)
0.541382 + 0.840777i \(0.317901\pi\)
\(60\) −2.90288e90 −4.63650
\(61\) 9.18299e89 0.636543 0.318271 0.948000i \(-0.396898\pi\)
0.318271 + 0.948000i \(0.396898\pi\)
\(62\) 7.99286e90 2.43737
\(63\) 1.14604e90 0.155776
\(64\) −2.38848e91 −1.46566
\(65\) 1.61371e91 0.452587
\(66\) −2.95709e92 −3.83616
\(67\) −1.99314e92 −1.20993 −0.604966 0.796251i \(-0.706813\pi\)
−0.604966 + 0.796251i \(0.706813\pi\)
\(68\) −8.83346e91 −0.253764
\(69\) 3.66857e92 0.504218
\(70\) −2.51057e92 −0.166848
\(71\) −1.96946e93 −0.639442 −0.319721 0.947512i \(-0.603589\pi\)
−0.319721 + 0.947512i \(0.603589\pi\)
\(72\) −1.84325e94 −2.95320
\(73\) 2.27832e94 1.81891 0.909453 0.415806i \(-0.136501\pi\)
0.909453 + 0.415806i \(0.136501\pi\)
\(74\) −5.53017e94 −2.22094
\(75\) −9.47435e94 −1.93177
\(76\) 1.59630e95 1.66735
\(77\) −1.64017e94 −0.0885334
\(78\) 3.36081e95 0.945511
\(79\) 2.24448e95 0.331854 0.165927 0.986138i \(-0.446938\pi\)
0.165927 + 0.986138i \(0.446938\pi\)
\(80\) 7.51853e95 0.588964
\(81\) 4.28516e96 1.79256
\(82\) −1.64709e96 −0.370782
\(83\) 1.11393e96 0.135961 0.0679805 0.997687i \(-0.478344\pi\)
0.0679805 + 0.997687i \(0.478344\pi\)
\(84\) −3.35328e96 −0.223545
\(85\) −5.57122e96 −0.204312
\(86\) 3.43516e97 0.697871
\(87\) 1.20978e98 1.37083
\(88\) 2.63799e98 1.67841
\(89\) −1.83015e98 −0.658099 −0.329050 0.944313i \(-0.606728\pi\)
−0.329050 + 0.944313i \(0.606728\pi\)
\(90\) −2.63770e99 −5.39483
\(91\) 1.86409e97 0.0218211
\(92\) −7.42551e98 −0.500543
\(93\) 6.73317e99 2.62924
\(94\) −9.55315e99 −2.17365
\(95\) 1.00678e100 1.34243
\(96\) −1.45042e100 −1.13972
\(97\) 2.50182e100 1.16489 0.582443 0.812872i \(-0.302097\pi\)
0.582443 + 0.812872i \(0.302097\pi\)
\(98\) 5.99061e100 1.66171
\(99\) −1.72322e101 −2.86262
\(100\) 1.91769e101 1.91769
\(101\) 1.66188e101 1.00547 0.502735 0.864441i \(-0.332327\pi\)
0.502735 + 0.864441i \(0.332327\pi\)
\(102\) −1.16029e101 −0.426834
\(103\) 4.49375e101 1.01002 0.505009 0.863114i \(-0.331489\pi\)
0.505009 + 0.863114i \(0.331489\pi\)
\(104\) −2.99814e101 −0.413684
\(105\) −2.11489e101 −0.179982
\(106\) 2.53051e102 1.33433
\(107\) −1.40440e102 −0.460903 −0.230451 0.973084i \(-0.574020\pi\)
−0.230451 + 0.973084i \(0.574020\pi\)
\(108\) −1.95329e103 −4.00743
\(109\) −7.42040e102 −0.955849 −0.477924 0.878401i \(-0.658611\pi\)
−0.477924 + 0.878401i \(0.658611\pi\)
\(110\) 3.77497e103 3.06608
\(111\) −4.65860e103 −2.39577
\(112\) 8.68509e101 0.0283964
\(113\) 5.70765e103 1.19123 0.595615 0.803270i \(-0.296908\pi\)
0.595615 + 0.803270i \(0.296908\pi\)
\(114\) 2.09677e104 2.80450
\(115\) −4.68323e103 −0.403000
\(116\) −2.44870e104 −1.36084
\(117\) 1.95849e104 0.705561
\(118\) −7.71305e104 −1.80794
\(119\) −6.43563e102 −0.00985075
\(120\) 3.40152e105 3.41209
\(121\) 9.50347e104 0.626933
\(122\) −2.44147e105 −1.06287
\(123\) −1.38751e105 −0.399969
\(124\) −1.36285e106 −2.61008
\(125\) 8.17554e104 0.104366
\(126\) −3.04695e105 −0.260108
\(127\) −2.11472e106 −1.21106 −0.605528 0.795824i \(-0.707038\pi\)
−0.605528 + 0.795824i \(0.707038\pi\)
\(128\) 4.70833e106 1.81453
\(129\) 2.89377e106 0.752808
\(130\) −4.29035e106 −0.755707
\(131\) −1.59542e107 −1.90843 −0.954213 0.299129i \(-0.903304\pi\)
−0.954213 + 0.299129i \(0.903304\pi\)
\(132\) 5.04210e107 4.10798
\(133\) 1.16299e106 0.0647242
\(134\) 5.29913e107 2.02028
\(135\) −1.23193e108 −3.22648
\(136\) 1.03508e107 0.186750
\(137\) −5.11141e107 −0.637018 −0.318509 0.947920i \(-0.603182\pi\)
−0.318509 + 0.947920i \(0.603182\pi\)
\(138\) −9.75356e107 −0.841917
\(139\) 3.25384e108 1.95051 0.975256 0.221078i \(-0.0709575\pi\)
0.975256 + 0.221078i \(0.0709575\pi\)
\(140\) 4.28073e107 0.178670
\(141\) −8.04755e108 −2.34476
\(142\) 5.23617e108 1.06771
\(143\) −2.80291e108 −0.400996
\(144\) 9.12488e108 0.918166
\(145\) −1.54438e109 −1.09565
\(146\) −6.05733e109 −3.03712
\(147\) 5.04647e109 1.79251
\(148\) 9.42943e109 2.37831
\(149\) −2.84162e109 −0.510104 −0.255052 0.966927i \(-0.582093\pi\)
−0.255052 + 0.966927i \(0.582093\pi\)
\(150\) 2.51893e110 3.22558
\(151\) −5.37944e109 −0.492494 −0.246247 0.969207i \(-0.579197\pi\)
−0.246247 + 0.969207i \(0.579197\pi\)
\(152\) −1.87051e110 −1.22704
\(153\) −6.76152e109 −0.318513
\(154\) 4.36069e109 0.147829
\(155\) −8.59544e110 −2.10144
\(156\) −5.73048e110 −1.01251
\(157\) 6.87958e110 0.880298 0.440149 0.897925i \(-0.354926\pi\)
0.440149 + 0.897925i \(0.354926\pi\)
\(158\) −5.96734e110 −0.554113
\(159\) 2.13170e111 1.43937
\(160\) 1.85158e111 0.910928
\(161\) −5.40987e109 −0.0194303
\(162\) −1.13929e112 −2.99312
\(163\) 2.92192e111 0.562594 0.281297 0.959621i \(-0.409235\pi\)
0.281297 + 0.959621i \(0.409235\pi\)
\(164\) 2.80843e111 0.397054
\(165\) 3.18003e112 3.30744
\(166\) −2.96158e111 −0.227021
\(167\) −2.55509e112 −1.44619 −0.723094 0.690749i \(-0.757281\pi\)
−0.723094 + 0.690749i \(0.757281\pi\)
\(168\) 3.92929e111 0.164511
\(169\) −2.90458e112 −0.901165
\(170\) 1.48121e112 0.341150
\(171\) 1.22188e113 2.09278
\(172\) −5.85725e112 −0.747321
\(173\) −5.66260e110 −0.00539122 −0.00269561 0.999996i \(-0.500858\pi\)
−0.00269561 + 0.999996i \(0.500858\pi\)
\(174\) −3.21641e113 −2.28894
\(175\) 1.39714e112 0.0744420
\(176\) −1.30592e113 −0.521827
\(177\) −6.49746e113 −1.95026
\(178\) 4.86579e113 1.09886
\(179\) −3.56632e113 −0.606936 −0.303468 0.952842i \(-0.598145\pi\)
−0.303468 + 0.952842i \(0.598145\pi\)
\(180\) 4.49750e114 5.77710
\(181\) −1.18458e114 −1.15026 −0.575131 0.818061i \(-0.695049\pi\)
−0.575131 + 0.818061i \(0.695049\pi\)
\(182\) −4.95603e112 −0.0364358
\(183\) −2.05668e114 −1.14654
\(184\) 8.70105e113 0.368359
\(185\) 5.94709e114 1.91484
\(186\) −1.79014e115 −4.39018
\(187\) 9.67683e113 0.181022
\(188\) 1.62889e115 2.32767
\(189\) −1.42307e114 −0.155562
\(190\) −2.67670e115 −2.24152
\(191\) −2.94775e114 −0.189367 −0.0946837 0.995507i \(-0.530184\pi\)
−0.0946837 + 0.995507i \(0.530184\pi\)
\(192\) 5.34940e115 2.63993
\(193\) 1.45178e115 0.551134 0.275567 0.961282i \(-0.411134\pi\)
0.275567 + 0.961282i \(0.411134\pi\)
\(194\) −6.65154e115 −1.94507
\(195\) −3.61418e115 −0.815196
\(196\) −1.02145e116 −1.77945
\(197\) −3.67802e115 −0.495529 −0.247765 0.968820i \(-0.579696\pi\)
−0.247765 + 0.968820i \(0.579696\pi\)
\(198\) 4.58150e116 4.77987
\(199\) 4.98786e115 0.403491 0.201746 0.979438i \(-0.435339\pi\)
0.201746 + 0.979438i \(0.435339\pi\)
\(200\) −2.24711e116 −1.41127
\(201\) 4.46398e116 2.17932
\(202\) −4.41840e116 −1.67888
\(203\) −1.78400e115 −0.0528257
\(204\) 1.97840e116 0.457078
\(205\) 1.77126e116 0.319679
\(206\) −1.19475e117 −1.68648
\(207\) −5.68381e116 −0.628257
\(208\) 1.48421e116 0.128617
\(209\) −1.74870e117 −1.18940
\(210\) 5.62283e116 0.300525
\(211\) 2.38874e117 1.00439 0.502197 0.864753i \(-0.332525\pi\)
0.502197 + 0.864753i \(0.332525\pi\)
\(212\) −4.31475e117 −1.42888
\(213\) 4.41094e117 1.15176
\(214\) 3.73385e117 0.769593
\(215\) −3.69414e117 −0.601687
\(216\) 2.28881e118 2.94915
\(217\) −9.92909e116 −0.101319
\(218\) 1.97285e118 1.59603
\(219\) −5.10268e118 −3.27620
\(220\) −6.43666e118 −3.28333
\(221\) −1.09980e117 −0.0446172
\(222\) 1.23857e119 4.00034
\(223\) −3.35176e118 −0.862734 −0.431367 0.902177i \(-0.641969\pi\)
−0.431367 + 0.902177i \(0.641969\pi\)
\(224\) 2.13887e117 0.0439197
\(225\) 1.46789e119 2.40700
\(226\) −1.51748e119 −1.98906
\(227\) −5.26256e118 −0.551939 −0.275969 0.961166i \(-0.588999\pi\)
−0.275969 + 0.961166i \(0.588999\pi\)
\(228\) −3.57518e119 −3.00322
\(229\) 7.34834e118 0.494877 0.247439 0.968904i \(-0.420411\pi\)
0.247439 + 0.968904i \(0.420411\pi\)
\(230\) 1.24512e119 0.672909
\(231\) 3.67343e118 0.159466
\(232\) 2.86933e119 1.00147
\(233\) 2.38643e119 0.670307 0.335154 0.942163i \(-0.391212\pi\)
0.335154 + 0.942163i \(0.391212\pi\)
\(234\) −5.20699e119 −1.17811
\(235\) 1.02734e120 1.87407
\(236\) 1.31514e120 1.93605
\(237\) −5.02688e119 −0.597732
\(238\) 1.71103e118 0.0164483
\(239\) −1.95496e120 −1.52070 −0.760352 0.649511i \(-0.774974\pi\)
−0.760352 + 0.649511i \(0.774974\pi\)
\(240\) −1.68390e120 −1.06084
\(241\) 1.17898e120 0.602066 0.301033 0.953614i \(-0.402669\pi\)
0.301033 + 0.953614i \(0.402669\pi\)
\(242\) −2.52667e120 −1.04682
\(243\) −2.93540e120 −0.987531
\(244\) 4.16291e120 1.13818
\(245\) −6.44224e120 −1.43268
\(246\) 3.68894e120 0.667849
\(247\) 1.98745e120 0.293156
\(248\) 1.59696e121 1.92081
\(249\) −2.49483e120 −0.244892
\(250\) −2.17361e120 −0.174266
\(251\) −1.91657e121 −1.25603 −0.628017 0.778200i \(-0.716133\pi\)
−0.628017 + 0.778200i \(0.716133\pi\)
\(252\) 5.19532e120 0.278538
\(253\) 8.13446e120 0.357061
\(254\) 5.62236e121 2.02216
\(255\) 1.24777e121 0.368005
\(256\) −6.46242e121 −1.56415
\(257\) −4.00544e120 −0.0796211 −0.0398105 0.999207i \(-0.512675\pi\)
−0.0398105 + 0.999207i \(0.512675\pi\)
\(258\) −7.69362e121 −1.25700
\(259\) 6.86982e120 0.0923225
\(260\) 7.31542e121 0.809255
\(261\) −1.87434e122 −1.70806
\(262\) 4.24172e122 3.18659
\(263\) 1.20762e122 0.748452 0.374226 0.927337i \(-0.377908\pi\)
0.374226 + 0.927337i \(0.377908\pi\)
\(264\) −5.90822e122 −3.02314
\(265\) −2.72129e122 −1.15042
\(266\) −3.09201e121 −0.108073
\(267\) 4.09893e122 1.18536
\(268\) −9.03548e122 −2.16344
\(269\) −7.02503e122 −1.39366 −0.696832 0.717234i \(-0.745408\pi\)
−0.696832 + 0.717234i \(0.745408\pi\)
\(270\) 3.27530e123 5.38742
\(271\) 4.75544e122 0.648995 0.324497 0.945887i \(-0.394805\pi\)
0.324497 + 0.945887i \(0.394805\pi\)
\(272\) −5.12411e121 −0.0580616
\(273\) −4.17495e121 −0.0393041
\(274\) 1.35896e123 1.06366
\(275\) −2.10078e123 −1.36798
\(276\) 1.66307e123 0.901574
\(277\) 4.65434e122 0.210198 0.105099 0.994462i \(-0.466484\pi\)
0.105099 + 0.994462i \(0.466484\pi\)
\(278\) −8.65092e123 −3.25687
\(279\) −1.04319e124 −3.27605
\(280\) −5.01606e122 −0.131487
\(281\) 8.19421e123 1.79406 0.897032 0.441966i \(-0.145719\pi\)
0.897032 + 0.441966i \(0.145719\pi\)
\(282\) 2.13959e124 3.91516
\(283\) 2.01371e123 0.308164 0.154082 0.988058i \(-0.450758\pi\)
0.154082 + 0.988058i \(0.450758\pi\)
\(284\) −8.92813e123 −1.14336
\(285\) −2.25484e124 −2.41797
\(286\) 7.45205e123 0.669563
\(287\) 2.04609e122 0.0154131
\(288\) 2.24718e124 1.42009
\(289\) −1.84716e124 −0.979858
\(290\) 4.10601e124 1.82945
\(291\) −5.60324e124 −2.09818
\(292\) 1.03283e125 3.25232
\(293\) −2.49149e124 −0.660154 −0.330077 0.943954i \(-0.607075\pi\)
−0.330077 + 0.943954i \(0.607075\pi\)
\(294\) −1.34170e125 −2.99305
\(295\) 8.29454e124 1.55876
\(296\) −1.10492e125 −1.75025
\(297\) 2.13978e125 2.85869
\(298\) 7.55496e124 0.851747
\(299\) −9.24502e123 −0.0880061
\(300\) −4.29499e125 −3.45413
\(301\) −4.26731e123 −0.0290099
\(302\) 1.43022e125 0.822342
\(303\) −3.72205e125 −1.81104
\(304\) 9.25981e124 0.381493
\(305\) 2.62553e125 0.916378
\(306\) 1.79767e125 0.531837
\(307\) 1.07629e125 0.270049 0.135024 0.990842i \(-0.456889\pi\)
0.135024 + 0.990842i \(0.456889\pi\)
\(308\) −7.43535e124 −0.158303
\(309\) −1.00645e126 −1.81924
\(310\) 2.28525e126 3.50888
\(311\) −2.71674e125 −0.354527 −0.177263 0.984163i \(-0.556724\pi\)
−0.177263 + 0.984163i \(0.556724\pi\)
\(312\) 6.71484e125 0.745124
\(313\) 1.08086e126 1.02043 0.510214 0.860048i \(-0.329566\pi\)
0.510214 + 0.860048i \(0.329566\pi\)
\(314\) −1.82906e126 −1.46988
\(315\) 3.27666e125 0.224258
\(316\) 1.01748e126 0.593376
\(317\) −3.10015e126 −1.54131 −0.770656 0.637252i \(-0.780071\pi\)
−0.770656 + 0.637252i \(0.780071\pi\)
\(318\) −5.66751e126 −2.40338
\(319\) 2.68249e126 0.970751
\(320\) −6.82894e126 −2.10999
\(321\) 3.14538e126 0.830175
\(322\) 1.43831e125 0.0324438
\(323\) −6.86150e125 −0.132340
\(324\) 1.94258e127 3.20521
\(325\) 2.38759e126 0.337171
\(326\) −7.76846e126 −0.939391
\(327\) 1.66192e127 1.72167
\(328\) −3.29086e126 −0.292200
\(329\) 1.18673e126 0.0903567
\(330\) −8.45468e127 −5.52259
\(331\) 2.31485e127 1.29780 0.648902 0.760872i \(-0.275228\pi\)
0.648902 + 0.760872i \(0.275228\pi\)
\(332\) 5.04976e126 0.243107
\(333\) 7.21770e127 2.98514
\(334\) 6.79318e127 2.41477
\(335\) −5.69863e127 −1.74184
\(336\) −1.94517e126 −0.0511474
\(337\) −5.17085e127 −1.17018 −0.585089 0.810969i \(-0.698940\pi\)
−0.585089 + 0.810969i \(0.698940\pi\)
\(338\) 7.72234e127 1.50472
\(339\) −1.27832e128 −2.14563
\(340\) −2.52559e127 −0.365323
\(341\) 1.49297e128 1.86190
\(342\) −3.24858e128 −3.49442
\(343\) −1.49196e127 −0.138486
\(344\) 6.86339e127 0.549968
\(345\) 1.04889e128 0.725880
\(346\) 1.50550e126 0.00900200
\(347\) −1.81398e128 −0.937549 −0.468775 0.883318i \(-0.655304\pi\)
−0.468775 + 0.883318i \(0.655304\pi\)
\(348\) 5.48426e128 2.45113
\(349\) 3.13313e128 1.21142 0.605710 0.795686i \(-0.292889\pi\)
0.605710 + 0.795686i \(0.292889\pi\)
\(350\) −3.71454e127 −0.124299
\(351\) −2.43191e128 −0.704592
\(352\) −3.21608e128 −0.807090
\(353\) −1.25997e128 −0.273992 −0.136996 0.990572i \(-0.543745\pi\)
−0.136996 + 0.990572i \(0.543745\pi\)
\(354\) 1.72747e129 3.25645
\(355\) −5.63093e128 −0.920551
\(356\) −8.29659e128 −1.17672
\(357\) 1.44137e127 0.0177431
\(358\) 9.48172e128 1.01343
\(359\) −7.76594e128 −0.720982 −0.360491 0.932763i \(-0.617391\pi\)
−0.360491 + 0.932763i \(0.617391\pi\)
\(360\) −5.27007e129 −4.25148
\(361\) −1.86036e128 −0.130462
\(362\) 3.14942e129 1.92065
\(363\) −2.12846e129 −1.12923
\(364\) 8.45046e127 0.0390176
\(365\) 6.51399e129 2.61853
\(366\) 5.46807e129 1.91443
\(367\) −4.50811e129 −1.37518 −0.687588 0.726101i \(-0.741331\pi\)
−0.687588 + 0.726101i \(0.741331\pi\)
\(368\) −4.30739e128 −0.114525
\(369\) 2.14970e129 0.498363
\(370\) −1.58114e130 −3.19730
\(371\) −3.14352e128 −0.0554668
\(372\) 3.05234e130 4.70126
\(373\) −7.42600e129 −0.998754 −0.499377 0.866385i \(-0.666438\pi\)
−0.499377 + 0.866385i \(0.666438\pi\)
\(374\) −2.57276e129 −0.302262
\(375\) −1.83105e129 −0.187984
\(376\) −1.90870e130 −1.71298
\(377\) −3.04871e129 −0.239265
\(378\) 3.78349e129 0.259750
\(379\) −1.86901e130 −1.12288 −0.561439 0.827518i \(-0.689752\pi\)
−0.561439 + 0.827518i \(0.689752\pi\)
\(380\) 4.56400e130 2.40035
\(381\) 4.73626e130 2.18135
\(382\) 7.83712e129 0.316196
\(383\) −3.78544e130 −1.33838 −0.669188 0.743093i \(-0.733358\pi\)
−0.669188 + 0.743093i \(0.733358\pi\)
\(384\) −1.05451e131 −3.26831
\(385\) −4.68944e129 −0.127454
\(386\) −3.85982e130 −0.920256
\(387\) −4.48340e130 −0.938001
\(388\) 1.13415e131 2.08289
\(389\) −9.11393e130 −1.46977 −0.734887 0.678189i \(-0.762765\pi\)
−0.734887 + 0.678189i \(0.762765\pi\)
\(390\) 9.60895e130 1.36117
\(391\) 3.19177e129 0.0397288
\(392\) 1.19691e131 1.30953
\(393\) 3.57321e131 3.43744
\(394\) 9.77868e130 0.827410
\(395\) 6.41722e130 0.477742
\(396\) −7.81186e131 −5.11856
\(397\) 2.61893e131 1.51079 0.755393 0.655272i \(-0.227446\pi\)
0.755393 + 0.655272i \(0.227446\pi\)
\(398\) −1.32611e131 −0.673729
\(399\) −2.60470e130 −0.116581
\(400\) 1.11242e131 0.438771
\(401\) 4.94826e130 0.172053 0.0860265 0.996293i \(-0.472583\pi\)
0.0860265 + 0.996293i \(0.472583\pi\)
\(402\) −1.18683e132 −3.63892
\(403\) −1.69680e131 −0.458908
\(404\) 7.53375e131 1.79785
\(405\) 1.22518e132 2.58060
\(406\) 4.74309e130 0.0882057
\(407\) −1.03297e132 −1.69656
\(408\) −2.31824e131 −0.336373
\(409\) −7.74861e131 −0.993566 −0.496783 0.867875i \(-0.665485\pi\)
−0.496783 + 0.867875i \(0.665485\pi\)
\(410\) −4.70923e131 −0.533783
\(411\) 1.14479e132 1.14739
\(412\) 2.03715e132 1.80598
\(413\) 9.58149e130 0.0751546
\(414\) 1.51114e132 1.04903
\(415\) 3.18486e131 0.195732
\(416\) 3.65515e131 0.198926
\(417\) −7.28752e132 −3.51325
\(418\) 4.64925e132 1.98601
\(419\) 5.87287e131 0.222353 0.111176 0.993801i \(-0.464538\pi\)
0.111176 + 0.993801i \(0.464538\pi\)
\(420\) −9.58741e131 −0.321820
\(421\) −3.52135e132 −1.04825 −0.524123 0.851643i \(-0.675607\pi\)
−0.524123 + 0.851643i \(0.675607\pi\)
\(422\) −6.35089e132 −1.67709
\(423\) 1.24683e133 2.92158
\(424\) 5.05592e132 1.05154
\(425\) −8.24298e131 −0.152210
\(426\) −1.17273e133 −1.92315
\(427\) 3.03290e131 0.0441824
\(428\) −6.36653e132 −0.824124
\(429\) 6.27759e132 0.722271
\(430\) 9.82153e132 1.00467
\(431\) −1.61351e133 −1.46781 −0.733905 0.679252i \(-0.762304\pi\)
−0.733905 + 0.679252i \(0.762304\pi\)
\(432\) −1.13306e133 −0.916905
\(433\) −9.85490e132 −0.709600 −0.354800 0.934942i \(-0.615451\pi\)
−0.354800 + 0.934942i \(0.615451\pi\)
\(434\) 2.63983e132 0.169178
\(435\) 3.45890e133 1.97347
\(436\) −3.36388e133 −1.70912
\(437\) −5.76786e132 −0.261037
\(438\) 1.35664e134 5.47044
\(439\) −3.01466e133 −1.08338 −0.541689 0.840579i \(-0.682215\pi\)
−0.541689 + 0.840579i \(0.682215\pi\)
\(440\) 7.54233e133 2.41627
\(441\) −7.81864e133 −2.23348
\(442\) 2.92401e132 0.0744996
\(443\) 3.73898e133 0.849894 0.424947 0.905218i \(-0.360293\pi\)
0.424947 + 0.905218i \(0.360293\pi\)
\(444\) −2.11188e134 −4.28380
\(445\) −5.23262e133 −0.947411
\(446\) 8.91125e133 1.44055
\(447\) 6.36428e133 0.918796
\(448\) −7.88850e132 −0.101731
\(449\) −4.28883e132 −0.0494195 −0.0247098 0.999695i \(-0.507866\pi\)
−0.0247098 + 0.999695i \(0.507866\pi\)
\(450\) −3.90264e134 −4.01908
\(451\) −3.07657e133 −0.283238
\(452\) 2.58744e134 2.13000
\(453\) 1.20481e134 0.887076
\(454\) 1.39915e134 0.921600
\(455\) 5.32966e132 0.0314141
\(456\) 4.18931e134 2.21013
\(457\) 4.13841e133 0.195464 0.0977318 0.995213i \(-0.468841\pi\)
0.0977318 + 0.995213i \(0.468841\pi\)
\(458\) −1.95369e134 −0.826322
\(459\) 8.39597e133 0.318075
\(460\) −2.12304e134 −0.720590
\(461\) −5.95323e134 −1.81074 −0.905369 0.424625i \(-0.860406\pi\)
−0.905369 + 0.424625i \(0.860406\pi\)
\(462\) −9.76648e133 −0.266268
\(463\) −3.95798e134 −0.967461 −0.483731 0.875217i \(-0.660719\pi\)
−0.483731 + 0.875217i \(0.660719\pi\)
\(464\) −1.42044e134 −0.311362
\(465\) 1.92509e135 3.78510
\(466\) −6.34474e134 −1.11925
\(467\) 1.18548e135 1.87668 0.938341 0.345712i \(-0.112363\pi\)
0.938341 + 0.345712i \(0.112363\pi\)
\(468\) 8.87838e134 1.26159
\(469\) −6.58282e133 −0.0839814
\(470\) −2.73136e135 −3.12922
\(471\) −1.54080e135 −1.58559
\(472\) −1.54105e135 −1.42478
\(473\) 6.41647e134 0.533100
\(474\) 1.33649e135 0.998064
\(475\) 1.48959e135 1.00009
\(476\) −2.91745e133 −0.0176138
\(477\) −3.30270e135 −1.79346
\(478\) 5.19763e135 2.53920
\(479\) 4.57007e134 0.200900 0.100450 0.994942i \(-0.467972\pi\)
0.100450 + 0.994942i \(0.467972\pi\)
\(480\) −4.14693e135 −1.64076
\(481\) 1.17400e135 0.418158
\(482\) −3.13452e135 −1.00530
\(483\) 1.21163e134 0.0349977
\(484\) 4.30819e135 1.12100
\(485\) 7.15299e135 1.67699
\(486\) 7.80430e135 1.64893
\(487\) −7.30705e135 −1.39165 −0.695824 0.718212i \(-0.744961\pi\)
−0.695824 + 0.718212i \(0.744961\pi\)
\(488\) −4.87800e135 −0.837609
\(489\) −6.54414e135 −1.01334
\(490\) 1.71279e136 2.39222
\(491\) 4.01652e135 0.506098 0.253049 0.967453i \(-0.418567\pi\)
0.253049 + 0.967453i \(0.418567\pi\)
\(492\) −6.28996e135 −0.715171
\(493\) 1.05254e135 0.108012
\(494\) −5.28399e135 −0.489498
\(495\) −4.92690e136 −4.12108
\(496\) −7.90564e135 −0.597190
\(497\) −6.50460e134 −0.0443837
\(498\) 6.63296e135 0.408908
\(499\) −6.63017e135 −0.369358 −0.184679 0.982799i \(-0.559125\pi\)
−0.184679 + 0.982799i \(0.559125\pi\)
\(500\) 3.70620e135 0.186614
\(501\) 5.72256e136 2.60486
\(502\) 5.09554e136 2.09726
\(503\) −2.86457e136 −1.06629 −0.533145 0.846024i \(-0.678990\pi\)
−0.533145 + 0.846024i \(0.678990\pi\)
\(504\) −6.08776e135 −0.204982
\(505\) 4.75150e136 1.44749
\(506\) −2.16269e136 −0.596203
\(507\) 6.50529e136 1.62317
\(508\) −9.58662e136 −2.16545
\(509\) −1.28096e136 −0.261991 −0.130996 0.991383i \(-0.541817\pi\)
−0.130996 + 0.991383i \(0.541817\pi\)
\(510\) −3.31741e136 −0.614477
\(511\) 7.52468e135 0.126250
\(512\) 5.24450e136 0.797207
\(513\) −1.51724e137 −2.08991
\(514\) 1.06492e136 0.132947
\(515\) 1.28482e137 1.45404
\(516\) 1.31183e137 1.34607
\(517\) −1.78441e137 −1.66044
\(518\) −1.82647e136 −0.154155
\(519\) 1.26823e135 0.00971063
\(520\) −8.57204e136 −0.595546
\(521\) 7.26006e136 0.457757 0.228878 0.973455i \(-0.426494\pi\)
0.228878 + 0.973455i \(0.426494\pi\)
\(522\) 4.98327e137 2.85203
\(523\) −1.02612e137 −0.533167 −0.266584 0.963812i \(-0.585895\pi\)
−0.266584 + 0.963812i \(0.585895\pi\)
\(524\) −7.23250e137 −3.41239
\(525\) −3.12912e136 −0.134084
\(526\) −3.21067e137 −1.24973
\(527\) 5.85806e136 0.207166
\(528\) 2.92482e137 0.939911
\(529\) −3.15552e137 −0.921636
\(530\) 7.23504e137 1.92092
\(531\) 1.00667e138 2.43004
\(532\) 5.27214e136 0.115731
\(533\) 3.49660e136 0.0698107
\(534\) −1.08977e138 −1.97926
\(535\) −4.01534e137 −0.663524
\(536\) 1.05876e138 1.59212
\(537\) 7.98738e137 1.09321
\(538\) 1.86773e138 2.32707
\(539\) 1.11897e138 1.26937
\(540\) −5.58467e138 −5.76916
\(541\) −1.45489e138 −1.36889 −0.684446 0.729064i \(-0.739956\pi\)
−0.684446 + 0.729064i \(0.739956\pi\)
\(542\) −1.26432e138 −1.08366
\(543\) 2.65307e138 2.07184
\(544\) −1.26191e137 −0.0898017
\(545\) −2.12158e138 −1.37606
\(546\) 1.10999e137 0.0656279
\(547\) 1.17665e138 0.634292 0.317146 0.948377i \(-0.397276\pi\)
0.317146 + 0.948377i \(0.397276\pi\)
\(548\) −2.31715e138 −1.13903
\(549\) 3.18648e138 1.42859
\(550\) 5.58532e138 2.28419
\(551\) −1.90206e138 −0.709688
\(552\) −1.94874e138 −0.663486
\(553\) 7.41290e136 0.0230340
\(554\) −1.23744e138 −0.350979
\(555\) −1.33195e139 −3.44899
\(556\) 1.47506e139 3.48764
\(557\) −3.44720e138 −0.744354 −0.372177 0.928162i \(-0.621389\pi\)
−0.372177 + 0.928162i \(0.621389\pi\)
\(558\) 2.77350e139 5.47018
\(559\) −7.29248e137 −0.131395
\(560\) 2.48317e137 0.0408800
\(561\) −2.16729e138 −0.326056
\(562\) −2.17858e139 −2.99564
\(563\) −2.08998e138 −0.262705 −0.131353 0.991336i \(-0.541932\pi\)
−0.131353 + 0.991336i \(0.541932\pi\)
\(564\) −3.64818e139 −4.19258
\(565\) 1.63188e139 1.71491
\(566\) −5.35381e138 −0.514556
\(567\) 1.41527e138 0.124421
\(568\) 1.04618e139 0.841423
\(569\) −8.60079e138 −0.632949 −0.316475 0.948601i \(-0.602499\pi\)
−0.316475 + 0.948601i \(0.602499\pi\)
\(570\) 5.99491e139 4.03741
\(571\) −9.38577e138 −0.578557 −0.289279 0.957245i \(-0.593415\pi\)
−0.289279 + 0.957245i \(0.593415\pi\)
\(572\) −1.27064e139 −0.717007
\(573\) 6.60197e138 0.341087
\(574\) −5.43990e137 −0.0257360
\(575\) −6.92915e138 −0.300230
\(576\) −8.28796e139 −3.28937
\(577\) 2.84386e139 1.03402 0.517010 0.855979i \(-0.327045\pi\)
0.517010 + 0.855979i \(0.327045\pi\)
\(578\) 4.91101e139 1.63612
\(579\) −3.25151e139 −0.992698
\(580\) −7.00111e139 −1.95909
\(581\) 3.67901e137 0.00943705
\(582\) 1.48972e140 3.50344
\(583\) 4.72670e139 1.01929
\(584\) −1.21024e140 −2.39345
\(585\) 5.59955e139 1.01574
\(586\) 6.62409e139 1.10229
\(587\) −1.57271e139 −0.240118 −0.120059 0.992767i \(-0.538308\pi\)
−0.120059 + 0.992767i \(0.538308\pi\)
\(588\) 2.28771e140 3.20513
\(589\) −1.05861e140 −1.36118
\(590\) −2.20525e140 −2.60275
\(591\) 8.23753e139 0.892544
\(592\) 5.46982e139 0.544161
\(593\) 9.51778e139 0.869508 0.434754 0.900549i \(-0.356835\pi\)
0.434754 + 0.900549i \(0.356835\pi\)
\(594\) −5.68898e140 −4.77330
\(595\) −1.84002e138 −0.0141813
\(596\) −1.28819e140 −0.912100
\(597\) −1.11711e140 −0.726765
\(598\) 2.45796e139 0.146948
\(599\) 1.75385e140 0.963692 0.481846 0.876256i \(-0.339966\pi\)
0.481846 + 0.876256i \(0.339966\pi\)
\(600\) 5.03277e140 2.54196
\(601\) 2.44735e140 1.13641 0.568205 0.822887i \(-0.307638\pi\)
0.568205 + 0.822887i \(0.307638\pi\)
\(602\) 1.13454e139 0.0484393
\(603\) −6.91616e140 −2.71544
\(604\) −2.43865e140 −0.880611
\(605\) 2.71715e140 0.902542
\(606\) 9.89573e140 3.02399
\(607\) 2.18152e140 0.613382 0.306691 0.951809i \(-0.400778\pi\)
0.306691 + 0.951809i \(0.400778\pi\)
\(608\) 2.28041e140 0.590040
\(609\) 3.99557e139 0.0951493
\(610\) −6.98044e140 −1.53012
\(611\) 2.02803e140 0.409255
\(612\) −3.06519e140 −0.569522
\(613\) −3.77369e140 −0.645672 −0.322836 0.946455i \(-0.604636\pi\)
−0.322836 + 0.946455i \(0.604636\pi\)
\(614\) −2.86152e140 −0.450914
\(615\) −3.96704e140 −0.575802
\(616\) 8.71257e139 0.116499
\(617\) −1.61490e141 −1.98950 −0.994752 0.102315i \(-0.967375\pi\)
−0.994752 + 0.102315i \(0.967375\pi\)
\(618\) 2.67583e141 3.03767
\(619\) 1.70112e141 1.77974 0.889869 0.456217i \(-0.150796\pi\)
0.889869 + 0.456217i \(0.150796\pi\)
\(620\) −3.89656e141 −3.75752
\(621\) 7.05775e140 0.627394
\(622\) 7.22296e140 0.591971
\(623\) −6.04450e139 −0.0456787
\(624\) −3.32414e140 −0.231663
\(625\) −1.43479e141 −0.922248
\(626\) −2.87367e141 −1.70386
\(627\) 3.91652e141 2.14234
\(628\) 3.11871e141 1.57403
\(629\) −4.05313e140 −0.188770
\(630\) −8.71160e140 −0.374455
\(631\) 1.57092e141 0.623265 0.311632 0.950203i \(-0.399124\pi\)
0.311632 + 0.950203i \(0.399124\pi\)
\(632\) −1.19226e141 −0.436677
\(633\) −5.34997e141 −1.80911
\(634\) 8.24232e141 2.57361
\(635\) −6.04623e141 −1.74346
\(636\) 9.66360e141 2.57368
\(637\) −1.27174e141 −0.312866
\(638\) −7.13188e141 −1.62091
\(639\) −6.83398e141 −1.43510
\(640\) 1.34617e142 2.61222
\(641\) 9.21834e139 0.0165319 0.00826594 0.999966i \(-0.497369\pi\)
0.00826594 + 0.999966i \(0.497369\pi\)
\(642\) −8.36257e141 −1.38618
\(643\) 6.37723e141 0.977187 0.488594 0.872511i \(-0.337510\pi\)
0.488594 + 0.872511i \(0.337510\pi\)
\(644\) −2.45245e140 −0.0347427
\(645\) 8.27364e141 1.08375
\(646\) 1.82425e141 0.220975
\(647\) 5.48721e141 0.614732 0.307366 0.951591i \(-0.400552\pi\)
0.307366 + 0.951591i \(0.400552\pi\)
\(648\) −2.27627e142 −2.35878
\(649\) −1.44071e142 −1.38108
\(650\) −6.34785e141 −0.562992
\(651\) 2.22378e141 0.182496
\(652\) 1.32459e142 1.00595
\(653\) 2.39345e141 0.168232 0.0841161 0.996456i \(-0.473193\pi\)
0.0841161 + 0.996456i \(0.473193\pi\)
\(654\) −4.41852e142 −2.87475
\(655\) −4.56150e142 −2.74740
\(656\) 1.62912e141 0.0908465
\(657\) 7.90571e142 4.08216
\(658\) −3.15515e141 −0.150873
\(659\) 4.27600e142 1.89376 0.946879 0.321591i \(-0.104218\pi\)
0.946879 + 0.321591i \(0.104218\pi\)
\(660\) 1.44160e143 5.91391
\(661\) −1.93362e141 −0.0734849 −0.0367424 0.999325i \(-0.511698\pi\)
−0.0367424 + 0.999325i \(0.511698\pi\)
\(662\) −6.15445e142 −2.16701
\(663\) 2.46318e141 0.0803642
\(664\) −5.91719e141 −0.178907
\(665\) 3.32511e141 0.0931780
\(666\) −1.91896e143 −4.98444
\(667\) 8.84781e141 0.213050
\(668\) −1.15830e143 −2.58588
\(669\) 7.50682e142 1.55395
\(670\) 1.51508e143 2.90843
\(671\) −4.56037e142 −0.811918
\(672\) −4.79036e141 −0.0791078
\(673\) 6.44088e141 0.0986698 0.0493349 0.998782i \(-0.484290\pi\)
0.0493349 + 0.998782i \(0.484290\pi\)
\(674\) 1.37476e143 1.95390
\(675\) −1.82272e143 −2.40369
\(676\) −1.31673e143 −1.61134
\(677\) −1.37829e143 −1.56536 −0.782680 0.622424i \(-0.786148\pi\)
−0.782680 + 0.622424i \(0.786148\pi\)
\(678\) 3.39865e143 3.58267
\(679\) 8.26283e141 0.0808547
\(680\) 2.95943e142 0.268849
\(681\) 1.17864e143 0.994148
\(682\) −3.96934e143 −3.10890
\(683\) −2.02521e142 −0.147307 −0.0736537 0.997284i \(-0.523466\pi\)
−0.0736537 + 0.997284i \(0.523466\pi\)
\(684\) 5.53911e143 3.74203
\(685\) −1.46141e143 −0.917062
\(686\) 3.96665e142 0.231236
\(687\) −1.64578e143 −0.891369
\(688\) −3.39768e142 −0.170988
\(689\) −5.37201e142 −0.251227
\(690\) −2.78866e143 −1.21204
\(691\) 3.53577e143 1.42837 0.714187 0.699955i \(-0.246797\pi\)
0.714187 + 0.699955i \(0.246797\pi\)
\(692\) −2.56702e141 −0.00963986
\(693\) −5.69134e142 −0.198695
\(694\) 4.82280e143 1.56547
\(695\) 9.30311e143 2.80799
\(696\) −6.42634e143 −1.80383
\(697\) −1.20717e142 −0.0315148
\(698\) −8.33000e143 −2.02277
\(699\) −5.34480e143 −1.20735
\(700\) 6.33362e142 0.133107
\(701\) −4.97697e143 −0.973207 −0.486603 0.873623i \(-0.661764\pi\)
−0.486603 + 0.873623i \(0.661764\pi\)
\(702\) 6.46567e143 1.17649
\(703\) 7.32442e143 1.24031
\(704\) 1.18614e144 1.86947
\(705\) −2.30089e144 −3.37556
\(706\) 3.34986e143 0.457499
\(707\) 5.48873e142 0.0697897
\(708\) −2.94548e144 −3.48720
\(709\) 4.41508e143 0.486748 0.243374 0.969933i \(-0.421746\pi\)
0.243374 + 0.969933i \(0.421746\pi\)
\(710\) 1.49708e144 1.53709
\(711\) 7.78827e143 0.744777
\(712\) 9.72176e143 0.865974
\(713\) 4.92436e143 0.408628
\(714\) −3.83213e142 −0.0296265
\(715\) −8.01386e143 −0.577280
\(716\) −1.61672e144 −1.08524
\(717\) 4.37847e144 2.73908
\(718\) 2.06472e144 1.20386
\(719\) −1.90598e144 −1.03588 −0.517940 0.855417i \(-0.673301\pi\)
−0.517940 + 0.855417i \(0.673301\pi\)
\(720\) 2.60891e144 1.32181
\(721\) 1.48417e143 0.0701054
\(722\) 4.94611e143 0.217839
\(723\) −2.64051e144 −1.08444
\(724\) −5.37004e144 −2.05674
\(725\) −2.28501e144 −0.816242
\(726\) 5.65890e144 1.88552
\(727\) 1.74840e144 0.543441 0.271721 0.962376i \(-0.412407\pi\)
0.271721 + 0.962376i \(0.412407\pi\)
\(728\) −9.90206e142 −0.0287138
\(729\) −5.10998e142 −0.0138255
\(730\) −1.73186e145 −4.37229
\(731\) 2.51767e143 0.0593159
\(732\) −9.32353e144 −2.05008
\(733\) −2.17870e144 −0.447142 −0.223571 0.974688i \(-0.571772\pi\)
−0.223571 + 0.974688i \(0.571772\pi\)
\(734\) 1.19856e145 2.29620
\(735\) 1.44285e145 2.58053
\(736\) −1.06078e144 −0.177131
\(737\) 9.89815e144 1.54328
\(738\) −5.71536e144 −0.832142
\(739\) 2.47719e144 0.336833 0.168417 0.985716i \(-0.446135\pi\)
0.168417 + 0.985716i \(0.446135\pi\)
\(740\) 2.69598e145 3.42386
\(741\) −4.45122e144 −0.528031
\(742\) 8.35761e143 0.0926157
\(743\) −1.41653e145 −1.46653 −0.733266 0.679942i \(-0.762005\pi\)
−0.733266 + 0.679942i \(0.762005\pi\)
\(744\) −3.57666e145 −3.45975
\(745\) −8.12452e144 −0.734355
\(746\) 1.97434e145 1.66767
\(747\) 3.86531e144 0.305136
\(748\) 4.38678e144 0.323680
\(749\) −4.63835e143 −0.0319913
\(750\) 4.86817e144 0.313886
\(751\) −2.99869e145 −1.80765 −0.903827 0.427898i \(-0.859254\pi\)
−0.903827 + 0.427898i \(0.859254\pi\)
\(752\) 9.44890e144 0.532574
\(753\) 4.29247e145 2.26236
\(754\) 8.10556e144 0.399512
\(755\) −1.53804e145 −0.709002
\(756\) −6.45118e144 −0.278156
\(757\) 2.01628e145 0.813223 0.406611 0.913601i \(-0.366710\pi\)
0.406611 + 0.913601i \(0.366710\pi\)
\(758\) 4.96911e145 1.87492
\(759\) −1.82185e145 −0.643136
\(760\) −5.34800e145 −1.76646
\(761\) −2.47328e145 −0.764449 −0.382225 0.924069i \(-0.624842\pi\)
−0.382225 + 0.924069i \(0.624842\pi\)
\(762\) −1.25922e146 −3.64230
\(763\) −2.45076e144 −0.0663455
\(764\) −1.33630e145 −0.338601
\(765\) −1.93320e145 −0.458536
\(766\) 1.00643e146 2.23475
\(767\) 1.63740e145 0.340399
\(768\) 1.44737e146 2.81733
\(769\) −6.52736e145 −1.18976 −0.594878 0.803816i \(-0.702799\pi\)
−0.594878 + 0.803816i \(0.702799\pi\)
\(770\) 1.24677e145 0.212816
\(771\) 8.97086e144 0.143413
\(772\) 6.58134e145 0.985463
\(773\) −1.86502e145 −0.261589 −0.130794 0.991410i \(-0.541753\pi\)
−0.130794 + 0.991410i \(0.541753\pi\)
\(774\) 1.19199e146 1.56623
\(775\) −1.27175e146 −1.56555
\(776\) −1.32897e146 −1.53284
\(777\) −1.53861e145 −0.166291
\(778\) 2.42310e146 2.45416
\(779\) 2.18149e145 0.207067
\(780\) −1.63841e146 −1.45762
\(781\) 9.78055e145 0.815616
\(782\) −8.48590e144 −0.0663371
\(783\) 2.32742e146 1.70571
\(784\) −5.92523e145 −0.407141
\(785\) 1.96695e146 1.26729
\(786\) −9.50004e146 −5.73967
\(787\) 1.31860e146 0.747117 0.373558 0.927607i \(-0.378138\pi\)
0.373558 + 0.927607i \(0.378138\pi\)
\(788\) −1.66735e146 −0.886039
\(789\) −2.70466e146 −1.34811
\(790\) −1.70613e146 −0.797710
\(791\) 1.88508e145 0.0826833
\(792\) 9.15376e146 3.76685
\(793\) 5.18297e145 0.200116
\(794\) −6.96289e146 −2.52263
\(795\) 6.09478e146 2.07213
\(796\) 2.26114e146 0.721468
\(797\) 2.99469e146 0.896823 0.448412 0.893827i \(-0.351990\pi\)
0.448412 + 0.893827i \(0.351990\pi\)
\(798\) 6.92507e145 0.194661
\(799\) −7.00161e145 −0.184751
\(800\) 2.73954e146 0.678630
\(801\) −6.35058e146 −1.47697
\(802\) −1.31559e146 −0.287285
\(803\) −1.13144e147 −2.32004
\(804\) 2.02365e147 3.89677
\(805\) −1.54675e145 −0.0279722
\(806\) 4.51125e146 0.766262
\(807\) 1.57337e147 2.51026
\(808\) −8.82788e146 −1.32307
\(809\) −5.73712e146 −0.807781 −0.403891 0.914807i \(-0.632342\pi\)
−0.403891 + 0.914807i \(0.632342\pi\)
\(810\) −3.25735e147 −4.30895
\(811\) −6.28300e146 −0.780933 −0.390466 0.920617i \(-0.627686\pi\)
−0.390466 + 0.920617i \(0.627686\pi\)
\(812\) −8.08739e145 −0.0944558
\(813\) −1.06506e147 −1.16896
\(814\) 2.74634e147 2.83284
\(815\) 8.35412e146 0.809919
\(816\) 1.14763e146 0.104580
\(817\) −4.54969e146 −0.389734
\(818\) 2.06011e147 1.65901
\(819\) 6.46836e145 0.0489730
\(820\) 8.02965e146 0.571606
\(821\) −1.21835e147 −0.815533 −0.407767 0.913086i \(-0.633692\pi\)
−0.407767 + 0.913086i \(0.633692\pi\)
\(822\) −3.04362e147 −1.91586
\(823\) −1.61951e145 −0.00958719 −0.00479359 0.999989i \(-0.501526\pi\)
−0.00479359 + 0.999989i \(0.501526\pi\)
\(824\) −2.38708e147 −1.32905
\(825\) 4.70506e147 2.46400
\(826\) −2.54741e146 −0.125489
\(827\) −1.74500e147 −0.808662 −0.404331 0.914613i \(-0.632496\pi\)
−0.404331 + 0.914613i \(0.632496\pi\)
\(828\) −2.57663e147 −1.12336
\(829\) 1.16559e147 0.478125 0.239063 0.971004i \(-0.423160\pi\)
0.239063 + 0.971004i \(0.423160\pi\)
\(830\) −8.46752e146 −0.326823
\(831\) −1.04242e147 −0.378608
\(832\) −1.34808e147 −0.460774
\(833\) 4.39059e146 0.141237
\(834\) 1.93752e148 5.86624
\(835\) −7.30531e147 −2.08196
\(836\) −7.92737e147 −2.12673
\(837\) 1.29536e148 3.27155
\(838\) −1.56141e147 −0.371273
\(839\) 2.66604e147 0.596880 0.298440 0.954428i \(-0.403534\pi\)
0.298440 + 0.954428i \(0.403534\pi\)
\(840\) 1.12343e147 0.236833
\(841\) −2.11958e147 −0.420776
\(842\) 9.36214e147 1.75031
\(843\) −1.83523e148 −3.23145
\(844\) 1.08288e148 1.79592
\(845\) −8.30453e147 −1.29733
\(846\) −3.31492e148 −4.87831
\(847\) 3.13874e146 0.0435154
\(848\) −2.50290e147 −0.326929
\(849\) −4.51003e147 −0.555062
\(850\) 2.19154e147 0.254153
\(851\) −3.40711e147 −0.372343
\(852\) 1.99960e148 2.05942
\(853\) 1.18019e148 1.14558 0.572790 0.819702i \(-0.305861\pi\)
0.572790 + 0.819702i \(0.305861\pi\)
\(854\) −8.06350e146 −0.0737736
\(855\) 3.49349e148 3.01280
\(856\) 7.46016e147 0.606489
\(857\) −1.85191e148 −1.41934 −0.709672 0.704532i \(-0.751157\pi\)
−0.709672 + 0.704532i \(0.751157\pi\)
\(858\) −1.66901e148 −1.20601
\(859\) 5.32758e147 0.362974 0.181487 0.983393i \(-0.441909\pi\)
0.181487 + 0.983393i \(0.441909\pi\)
\(860\) −1.67466e148 −1.07586
\(861\) −4.58256e146 −0.0277619
\(862\) 4.28981e148 2.45088
\(863\) −7.09562e147 −0.382336 −0.191168 0.981557i \(-0.561228\pi\)
−0.191168 + 0.981557i \(0.561228\pi\)
\(864\) −2.79038e148 −1.41814
\(865\) −1.61900e146 −0.00776130
\(866\) 2.62010e148 1.18485
\(867\) 4.13702e148 1.76491
\(868\) −4.50114e147 −0.181166
\(869\) −1.11463e148 −0.423284
\(870\) −9.19610e148 −3.29520
\(871\) −1.12495e148 −0.380379
\(872\) 3.94172e148 1.25777
\(873\) 8.68125e148 2.61434
\(874\) 1.53349e148 0.435867
\(875\) 2.70016e146 0.00724407
\(876\) −2.31319e149 −5.85806
\(877\) −5.98242e148 −1.43020 −0.715101 0.699021i \(-0.753619\pi\)
−0.715101 + 0.699021i \(0.753619\pi\)
\(878\) 8.01501e148 1.80897
\(879\) 5.58012e148 1.18906
\(880\) −3.73378e148 −0.751231
\(881\) −5.93085e147 −0.112677 −0.0563383 0.998412i \(-0.517943\pi\)
−0.0563383 + 0.998412i \(0.517943\pi\)
\(882\) 2.07873e149 3.72935
\(883\) 1.68283e148 0.285118 0.142559 0.989786i \(-0.454467\pi\)
0.142559 + 0.989786i \(0.454467\pi\)
\(884\) −4.98569e147 −0.0797785
\(885\) −1.85770e149 −2.80763
\(886\) −9.94075e148 −1.41911
\(887\) 6.72744e148 0.907208 0.453604 0.891203i \(-0.350138\pi\)
0.453604 + 0.891203i \(0.350138\pi\)
\(888\) 2.47465e149 3.15253
\(889\) −6.98434e147 −0.0840595
\(890\) 1.39119e149 1.58194
\(891\) −2.12805e149 −2.28643
\(892\) −1.51945e149 −1.54262
\(893\) 1.26526e149 1.21390
\(894\) −1.69206e149 −1.53416
\(895\) −1.01965e149 −0.873755
\(896\) 1.55503e148 0.125946
\(897\) 2.07058e148 0.158516
\(898\) 1.14026e148 0.0825183
\(899\) 1.62390e149 1.11095
\(900\) 6.65434e149 4.30386
\(901\) 1.85464e148 0.113412
\(902\) 8.17962e148 0.472937
\(903\) 9.55735e147 0.0522524
\(904\) −3.03190e149 −1.56751
\(905\) −3.38686e149 −1.65594
\(906\) −3.20322e149 −1.48120
\(907\) −2.64086e149 −1.15499 −0.577494 0.816395i \(-0.695969\pi\)
−0.577494 + 0.816395i \(0.695969\pi\)
\(908\) −2.38567e149 −0.986903
\(909\) 5.76666e149 2.25657
\(910\) −1.41699e148 −0.0524536
\(911\) 6.18346e148 0.216548 0.108274 0.994121i \(-0.465468\pi\)
0.108274 + 0.994121i \(0.465468\pi\)
\(912\) −2.07389e149 −0.687141
\(913\) −5.53189e148 −0.173420
\(914\) −1.10027e149 −0.326375
\(915\) −5.88030e149 −1.65057
\(916\) 3.33121e149 0.884873
\(917\) −5.26925e148 −0.132464
\(918\) −2.23222e149 −0.531106
\(919\) 5.43382e148 0.122369 0.0611845 0.998126i \(-0.480512\pi\)
0.0611845 + 0.998126i \(0.480512\pi\)
\(920\) 2.48773e149 0.530296
\(921\) −2.41053e149 −0.486409
\(922\) 1.58277e150 3.02348
\(923\) −1.11158e149 −0.201028
\(924\) 1.66527e149 0.285135
\(925\) 8.79911e149 1.42653
\(926\) 1.05230e150 1.61542
\(927\) 1.55932e150 2.26678
\(928\) −3.49811e149 −0.481571
\(929\) 8.18039e149 1.06655 0.533274 0.845942i \(-0.320961\pi\)
0.533274 + 0.845942i \(0.320961\pi\)
\(930\) −5.11821e150 −6.32017
\(931\) −7.93425e149 −0.927998
\(932\) 1.08183e150 1.19855
\(933\) 6.08460e149 0.638571
\(934\) −3.15180e150 −3.13359
\(935\) 2.76672e149 0.260603
\(936\) −1.04035e150 −0.928428
\(937\) 1.21825e150 1.03011 0.515057 0.857156i \(-0.327771\pi\)
0.515057 + 0.857156i \(0.327771\pi\)
\(938\) 1.75016e149 0.140228
\(939\) −2.42078e150 −1.83799
\(940\) 4.65720e150 3.35095
\(941\) −2.26501e150 −1.54452 −0.772261 0.635306i \(-0.780874\pi\)
−0.772261 + 0.635306i \(0.780874\pi\)
\(942\) 4.09649e150 2.64753
\(943\) −1.01476e149 −0.0621619
\(944\) 7.62888e149 0.442971
\(945\) −4.06872e149 −0.223950
\(946\) −1.70594e150 −0.890144
\(947\) −2.06929e150 −1.02364 −0.511820 0.859093i \(-0.671028\pi\)
−0.511820 + 0.859093i \(0.671028\pi\)
\(948\) −2.27883e150 −1.06878
\(949\) 1.28591e150 0.571828
\(950\) −3.96035e150 −1.66990
\(951\) 6.94331e150 2.77620
\(952\) 3.41861e148 0.0129623
\(953\) −5.31863e149 −0.191253 −0.0956265 0.995417i \(-0.530485\pi\)
−0.0956265 + 0.995417i \(0.530485\pi\)
\(954\) 8.78082e150 2.99462
\(955\) −8.42796e149 −0.272617
\(956\) −8.86241e150 −2.71912
\(957\) −6.00788e150 −1.74851
\(958\) −1.21504e150 −0.335453
\(959\) −1.68816e149 −0.0442155
\(960\) 1.52946e151 3.80049
\(961\) 4.79639e150 1.13079
\(962\) −3.12128e150 −0.698219
\(963\) −4.87323e150 −1.03440
\(964\) 5.34463e150 1.07653
\(965\) 4.15081e150 0.793421
\(966\) −3.22134e149 −0.0584375
\(967\) −6.29354e150 −1.08357 −0.541786 0.840516i \(-0.682252\pi\)
−0.541786 + 0.840516i \(0.682252\pi\)
\(968\) −5.04824e150 −0.824963
\(969\) 1.53675e150 0.238370
\(970\) −1.90175e151 −2.80015
\(971\) 6.77300e150 0.946694 0.473347 0.880876i \(-0.343046\pi\)
0.473347 + 0.880876i \(0.343046\pi\)
\(972\) −1.33070e151 −1.76577
\(973\) 1.07466e150 0.135385
\(974\) 1.94271e151 2.32371
\(975\) −5.34742e150 −0.607311
\(976\) 2.41482e150 0.260417
\(977\) 6.16617e150 0.631451 0.315726 0.948851i \(-0.397752\pi\)
0.315726 + 0.948851i \(0.397752\pi\)
\(978\) 1.73988e151 1.69202
\(979\) 9.08871e150 0.839414
\(980\) −2.92045e151 −2.56173
\(981\) −2.57486e151 −2.14520
\(982\) −1.06787e151 −0.845057
\(983\) 9.36727e150 0.704142 0.352071 0.935973i \(-0.385478\pi\)
0.352071 + 0.935973i \(0.385478\pi\)
\(984\) 7.37043e150 0.526308
\(985\) −1.05159e151 −0.713372
\(986\) −2.79838e150 −0.180352
\(987\) −2.65789e150 −0.162750
\(988\) 9.00966e150 0.524183
\(989\) 2.11638e150 0.116999
\(990\) 1.30991e152 6.88118
\(991\) 8.64302e150 0.431465 0.215733 0.976452i \(-0.430786\pi\)
0.215733 + 0.976452i \(0.430786\pi\)
\(992\) −1.94692e151 −0.923651
\(993\) −5.18449e151 −2.33759
\(994\) 1.72937e150 0.0741096
\(995\) 1.42609e151 0.580873
\(996\) −1.13098e151 −0.437882
\(997\) 3.72625e151 1.37141 0.685703 0.727881i \(-0.259495\pi\)
0.685703 + 0.727881i \(0.259495\pi\)
\(998\) 1.76275e151 0.616735
\(999\) −8.96242e151 −2.98104
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1.102.a.a.1.1 8
3.2 odd 2 9.102.a.b.1.8 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.102.a.a.1.1 8 1.1 even 1 trivial
9.102.a.b.1.8 8 3.2 odd 2