Properties

Label 1.102.a.a.1.3
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 1.3
Root \(1.78363e13\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.76666e15 q^{2} -3.81746e23 q^{3} +5.85773e29 q^{4} -3.44135e35 q^{5} +6.74413e38 q^{6} -5.35995e42 q^{7} +3.44415e45 q^{8} -1.40040e48 q^{9} +O(q^{10})\) \(q-1.76666e15 q^{2} -3.81746e23 q^{3} +5.85773e29 q^{4} -3.44135e35 q^{5} +6.74413e38 q^{6} -5.35995e42 q^{7} +3.44415e45 q^{8} -1.40040e48 q^{9} +6.07967e50 q^{10} -3.44385e52 q^{11} -2.23616e53 q^{12} +3.09748e56 q^{13} +9.46918e57 q^{14} +1.31372e59 q^{15} -7.56973e60 q^{16} -1.06203e62 q^{17} +2.47403e63 q^{18} -6.11425e63 q^{19} -2.01585e65 q^{20} +2.04614e66 q^{21} +6.08410e67 q^{22} -3.47561e68 q^{23} -1.31479e69 q^{24} +7.89855e70 q^{25} -5.47219e71 q^{26} +1.12483e72 q^{27} -3.13971e72 q^{28} +5.28104e73 q^{29} -2.32089e74 q^{30} +2.84133e75 q^{31} +4.64116e75 q^{32} +1.31468e76 q^{33} +1.87624e77 q^{34} +1.84454e78 q^{35} -8.20318e77 q^{36} +1.90109e79 q^{37} +1.08018e79 q^{38} -1.18245e80 q^{39} -1.18525e81 q^{40} +6.25482e80 q^{41} -3.61482e81 q^{42} -1.65073e82 q^{43} -2.01731e82 q^{44} +4.81927e83 q^{45} +6.14021e83 q^{46} -1.59905e84 q^{47} +2.88971e84 q^{48} +6.08770e84 q^{49} -1.39540e86 q^{50} +4.05425e85 q^{51} +1.81442e86 q^{52} +9.26087e86 q^{53} -1.98718e87 q^{54} +1.18515e88 q^{55} -1.84604e88 q^{56} +2.33409e87 q^{57} -9.32978e88 q^{58} -2.36767e89 q^{59} +7.69540e88 q^{60} +8.85775e89 q^{61} -5.01965e90 q^{62} +7.50609e90 q^{63} +1.09922e91 q^{64} -1.06595e92 q^{65} -2.32258e91 q^{66} -3.21574e92 q^{67} -6.22108e91 q^{68} +1.32680e92 q^{69} -3.25867e93 q^{70} +1.94954e93 q^{71} -4.82319e93 q^{72} -1.32770e94 q^{73} -3.35857e94 q^{74} -3.01524e94 q^{75} -3.58156e93 q^{76} +1.84589e95 q^{77} +2.08898e95 q^{78} -3.38956e95 q^{79} +2.60501e96 q^{80} +1.73581e96 q^{81} -1.10501e96 q^{82} -8.23897e95 q^{83} +1.19857e96 q^{84} +3.65481e97 q^{85} +2.91628e97 q^{86} -2.01601e97 q^{87} -1.18611e98 q^{88} +2.68359e98 q^{89} -8.51399e98 q^{90} -1.66023e99 q^{91} -2.03592e98 q^{92} -1.08467e99 q^{93} +2.82498e99 q^{94} +2.10412e99 q^{95} -1.77174e99 q^{96} +1.33729e100 q^{97} -1.07549e100 q^{98} +4.82278e100 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 434989091795040q^{2} - \)\(12\!\cdots\!60\)\(q^{3} + \)\(90\!\cdots\!96\)\(q^{4} + \)\(38\!\cdots\!00\)\(q^{5} + \)\(24\!\cdots\!36\)\(q^{6} - \)\(57\!\cdots\!00\)\(q^{7} - \)\(61\!\cdots\!20\)\(q^{8} + \)\(52\!\cdots\!84\)\(q^{9} + O(q^{10}) \) \( 8q - 434989091795040q^{2} - \)\(12\!\cdots\!60\)\(q^{3} + \)\(90\!\cdots\!96\)\(q^{4} + \)\(38\!\cdots\!00\)\(q^{5} + \)\(24\!\cdots\!36\)\(q^{6} - \)\(57\!\cdots\!00\)\(q^{7} - \)\(61\!\cdots\!20\)\(q^{8} + \)\(52\!\cdots\!84\)\(q^{9} - \)\(37\!\cdots\!00\)\(q^{10} + \)\(46\!\cdots\!96\)\(q^{11} - \)\(72\!\cdots\!80\)\(q^{12} + \)\(25\!\cdots\!80\)\(q^{13} - \)\(48\!\cdots\!88\)\(q^{14} - \)\(29\!\cdots\!00\)\(q^{15} - \)\(10\!\cdots\!72\)\(q^{16} - \)\(39\!\cdots\!20\)\(q^{17} - \)\(72\!\cdots\!60\)\(q^{18} - \)\(21\!\cdots\!80\)\(q^{19} + \)\(17\!\cdots\!00\)\(q^{20} + \)\(40\!\cdots\!36\)\(q^{21} + \)\(61\!\cdots\!20\)\(q^{22} - \)\(13\!\cdots\!80\)\(q^{23} + \)\(10\!\cdots\!60\)\(q^{24} + \)\(77\!\cdots\!00\)\(q^{25} - \)\(97\!\cdots\!44\)\(q^{26} - \)\(59\!\cdots\!20\)\(q^{27} + \)\(92\!\cdots\!80\)\(q^{28} + \)\(15\!\cdots\!80\)\(q^{29} + \)\(11\!\cdots\!00\)\(q^{30} - \)\(65\!\cdots\!44\)\(q^{31} + \)\(12\!\cdots\!60\)\(q^{32} + \)\(43\!\cdots\!80\)\(q^{33} + \)\(95\!\cdots\!12\)\(q^{34} - \)\(11\!\cdots\!00\)\(q^{35} + \)\(19\!\cdots\!08\)\(q^{36} + \)\(39\!\cdots\!40\)\(q^{37} - \)\(70\!\cdots\!80\)\(q^{38} - \)\(26\!\cdots\!32\)\(q^{39} - \)\(76\!\cdots\!00\)\(q^{40} + \)\(56\!\cdots\!36\)\(q^{41} + \)\(30\!\cdots\!80\)\(q^{42} - \)\(28\!\cdots\!00\)\(q^{43} - \)\(20\!\cdots\!48\)\(q^{44} + \)\(71\!\cdots\!00\)\(q^{45} + \)\(10\!\cdots\!76\)\(q^{46} - \)\(45\!\cdots\!80\)\(q^{47} - \)\(58\!\cdots\!80\)\(q^{48} + \)\(12\!\cdots\!56\)\(q^{49} - \)\(40\!\cdots\!00\)\(q^{50} + \)\(11\!\cdots\!36\)\(q^{51} - \)\(73\!\cdots\!00\)\(q^{52} + \)\(13\!\cdots\!40\)\(q^{53} + \)\(68\!\cdots\!20\)\(q^{54} - \)\(14\!\cdots\!00\)\(q^{55} - \)\(23\!\cdots\!80\)\(q^{56} - \)\(66\!\cdots\!40\)\(q^{57} + \)\(29\!\cdots\!80\)\(q^{58} + \)\(21\!\cdots\!60\)\(q^{59} - \)\(34\!\cdots\!00\)\(q^{60} - \)\(33\!\cdots\!04\)\(q^{61} - \)\(58\!\cdots\!80\)\(q^{62} - \)\(20\!\cdots\!40\)\(q^{63} - \)\(74\!\cdots\!04\)\(q^{64} - \)\(16\!\cdots\!00\)\(q^{65} - \)\(74\!\cdots\!68\)\(q^{66} - \)\(61\!\cdots\!20\)\(q^{67} - \)\(21\!\cdots\!60\)\(q^{68} - \)\(53\!\cdots\!72\)\(q^{69} - \)\(12\!\cdots\!00\)\(q^{70} - \)\(15\!\cdots\!24\)\(q^{71} - \)\(55\!\cdots\!60\)\(q^{72} - \)\(20\!\cdots\!80\)\(q^{73} - \)\(14\!\cdots\!88\)\(q^{74} - \)\(20\!\cdots\!00\)\(q^{75} + \)\(64\!\cdots\!40\)\(q^{76} + \)\(25\!\cdots\!00\)\(q^{77} + \)\(12\!\cdots\!00\)\(q^{78} + \)\(14\!\cdots\!80\)\(q^{79} + \)\(60\!\cdots\!00\)\(q^{80} + \)\(14\!\cdots\!08\)\(q^{81} + \)\(30\!\cdots\!20\)\(q^{82} + \)\(33\!\cdots\!60\)\(q^{83} + \)\(57\!\cdots\!32\)\(q^{84} + \)\(17\!\cdots\!00\)\(q^{85} + \)\(67\!\cdots\!16\)\(q^{86} + \)\(25\!\cdots\!40\)\(q^{87} - \)\(36\!\cdots\!40\)\(q^{88} - \)\(62\!\cdots\!60\)\(q^{89} - \)\(47\!\cdots\!00\)\(q^{90} - \)\(36\!\cdots\!44\)\(q^{91} - \)\(46\!\cdots\!20\)\(q^{92} - \)\(39\!\cdots\!20\)\(q^{93} - \)\(17\!\cdots\!88\)\(q^{94} - \)\(26\!\cdots\!00\)\(q^{95} + \)\(46\!\cdots\!56\)\(q^{96} + \)\(64\!\cdots\!20\)\(q^{97} + \)\(20\!\cdots\!20\)\(q^{98} + \)\(22\!\cdots\!08\)\(q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.76666e15 −1.10953 −0.554763 0.832009i \(-0.687191\pi\)
−0.554763 + 0.832009i \(0.687191\pi\)
\(3\) −3.81746e23 −0.307009 −0.153504 0.988148i \(-0.549056\pi\)
−0.153504 + 0.988148i \(0.549056\pi\)
\(4\) 5.85773e29 0.231047
\(5\) −3.44135e35 −1.73278 −0.866389 0.499369i \(-0.833565\pi\)
−0.866389 + 0.499369i \(0.833565\pi\)
\(6\) 6.74413e38 0.340634
\(7\) −5.35995e42 −1.12644 −0.563222 0.826306i \(-0.690438\pi\)
−0.563222 + 0.826306i \(0.690438\pi\)
\(8\) 3.44415e45 0.853173
\(9\) −1.40040e48 −0.905746
\(10\) 6.07967e50 1.92256
\(11\) −3.44385e52 −0.884533 −0.442267 0.896884i \(-0.645825\pi\)
−0.442267 + 0.896884i \(0.645825\pi\)
\(12\) −2.23616e53 −0.0709333
\(13\) 3.09748e56 1.72532 0.862660 0.505785i \(-0.168797\pi\)
0.862660 + 0.505785i \(0.168797\pi\)
\(14\) 9.46918e57 1.24982
\(15\) 1.31372e59 0.531978
\(16\) −7.56973e60 −1.17766
\(17\) −1.06203e62 −0.773510 −0.386755 0.922182i \(-0.626404\pi\)
−0.386755 + 0.922182i \(0.626404\pi\)
\(18\) 2.47403e63 1.00495
\(19\) −6.11425e63 −0.161915 −0.0809574 0.996718i \(-0.525798\pi\)
−0.0809574 + 0.996718i \(0.525798\pi\)
\(20\) −2.01585e65 −0.400352
\(21\) 2.04614e66 0.345828
\(22\) 6.08410e67 0.981412
\(23\) −3.47561e68 −0.593985 −0.296992 0.954880i \(-0.595984\pi\)
−0.296992 + 0.954880i \(0.595984\pi\)
\(24\) −1.31479e69 −0.261932
\(25\) 7.89855e70 2.00252
\(26\) −5.47219e71 −1.91429
\(27\) 1.12483e72 0.585081
\(28\) −3.13971e72 −0.260261
\(29\) 5.28104e73 0.744082 0.372041 0.928216i \(-0.378658\pi\)
0.372041 + 0.928216i \(0.378658\pi\)
\(30\) −2.32089e74 −0.590243
\(31\) 2.84133e75 1.37961 0.689805 0.723996i \(-0.257696\pi\)
0.689805 + 0.723996i \(0.257696\pi\)
\(32\) 4.64116e75 0.453475
\(33\) 1.31468e76 0.271559
\(34\) 1.87624e77 0.858229
\(35\) 1.84454e78 1.95188
\(36\) −8.20318e77 −0.209269
\(37\) 1.90109e79 1.21567 0.607834 0.794064i \(-0.292039\pi\)
0.607834 + 0.794064i \(0.292039\pi\)
\(38\) 1.08018e79 0.179649
\(39\) −1.18245e80 −0.529688
\(40\) −1.18525e81 −1.47836
\(41\) 6.25482e80 0.224197 0.112099 0.993697i \(-0.464243\pi\)
0.112099 + 0.993697i \(0.464243\pi\)
\(42\) −3.61482e81 −0.383705
\(43\) −1.65073e82 −0.533974 −0.266987 0.963700i \(-0.586028\pi\)
−0.266987 + 0.963700i \(0.586028\pi\)
\(44\) −2.01731e82 −0.204368
\(45\) 4.81927e83 1.56946
\(46\) 6.14021e83 0.659041
\(47\) −1.59905e84 −0.579323 −0.289662 0.957129i \(-0.593543\pi\)
−0.289662 + 0.957129i \(0.593543\pi\)
\(48\) 2.88971e84 0.361553
\(49\) 6.08770e84 0.268876
\(50\) −1.39540e86 −2.22185
\(51\) 4.05425e85 0.237474
\(52\) 1.81442e86 0.398629
\(53\) 9.26087e86 0.777536 0.388768 0.921336i \(-0.372901\pi\)
0.388768 + 0.921336i \(0.372901\pi\)
\(54\) −1.98718e87 −0.649162
\(55\) 1.18515e88 1.53270
\(56\) −1.84604e88 −0.961052
\(57\) 2.33409e87 0.0497092
\(58\) −9.32978e88 −0.825578
\(59\) −2.36767e89 −0.883681 −0.441840 0.897094i \(-0.645674\pi\)
−0.441840 + 0.897094i \(0.645674\pi\)
\(60\) 7.69540e88 0.122912
\(61\) 8.85775e89 0.613998 0.306999 0.951710i \(-0.400675\pi\)
0.306999 + 0.951710i \(0.400675\pi\)
\(62\) −5.01965e90 −1.53071
\(63\) 7.50609e90 1.02027
\(64\) 1.09922e91 0.674522
\(65\) −1.06595e92 −2.98960
\(66\) −2.32258e91 −0.301302
\(67\) −3.21574e92 −1.95210 −0.976052 0.217537i \(-0.930198\pi\)
−0.976052 + 0.217537i \(0.930198\pi\)
\(68\) −6.22108e91 −0.178717
\(69\) 1.32680e92 0.182358
\(70\) −3.25867e93 −2.16566
\(71\) 1.94954e93 0.632974 0.316487 0.948597i \(-0.397497\pi\)
0.316487 + 0.948597i \(0.397497\pi\)
\(72\) −4.82319e93 −0.772758
\(73\) −1.32770e94 −1.05998 −0.529988 0.848005i \(-0.677804\pi\)
−0.529988 + 0.848005i \(0.677804\pi\)
\(74\) −3.35857e94 −1.34881
\(75\) −3.01524e94 −0.614791
\(76\) −3.58156e93 −0.0374098
\(77\) 1.84589e95 0.996377
\(78\) 2.08898e95 0.587702
\(79\) −3.38956e95 −0.501158 −0.250579 0.968096i \(-0.580621\pi\)
−0.250579 + 0.968096i \(0.580621\pi\)
\(80\) 2.60501e96 2.04063
\(81\) 1.73581e96 0.726121
\(82\) −1.10501e96 −0.248752
\(83\) −8.23897e95 −0.100561 −0.0502805 0.998735i \(-0.516012\pi\)
−0.0502805 + 0.998735i \(0.516012\pi\)
\(84\) 1.19857e96 0.0799024
\(85\) 3.65481e97 1.34032
\(86\) 2.91628e97 0.592458
\(87\) −2.01601e97 −0.228440
\(88\) −1.18611e98 −0.754660
\(89\) 2.68359e98 0.964985 0.482492 0.875900i \(-0.339732\pi\)
0.482492 + 0.875900i \(0.339732\pi\)
\(90\) −8.51399e98 −1.74135
\(91\) −1.66023e99 −1.94348
\(92\) −2.03592e98 −0.137238
\(93\) −1.08467e99 −0.423552
\(94\) 2.82498e99 0.642774
\(95\) 2.10412e99 0.280562
\(96\) −1.77174e99 −0.139221
\(97\) 1.33729e100 0.622664 0.311332 0.950301i \(-0.399225\pi\)
0.311332 + 0.950301i \(0.399225\pi\)
\(98\) −1.07549e100 −0.298324
\(99\) 4.82278e100 0.801162
\(100\) 4.62676e100 0.462676
\(101\) 3.34535e100 0.202401 0.101200 0.994866i \(-0.467732\pi\)
0.101200 + 0.994866i \(0.467732\pi\)
\(102\) −7.16247e100 −0.263484
\(103\) 3.42996e101 0.770919 0.385459 0.922725i \(-0.374043\pi\)
0.385459 + 0.922725i \(0.374043\pi\)
\(104\) 1.06682e102 1.47200
\(105\) −7.04146e101 −0.599243
\(106\) −1.63608e102 −0.862696
\(107\) −5.39428e102 −1.77032 −0.885162 0.465284i \(-0.845952\pi\)
−0.885162 + 0.465284i \(0.845952\pi\)
\(108\) 6.58893e101 0.135181
\(109\) 1.02335e102 0.131822 0.0659108 0.997826i \(-0.479005\pi\)
0.0659108 + 0.997826i \(0.479005\pi\)
\(110\) −2.09375e103 −1.70057
\(111\) −7.25732e102 −0.373221
\(112\) 4.05734e103 1.32657
\(113\) 3.86042e103 0.805699 0.402850 0.915266i \(-0.368020\pi\)
0.402850 + 0.915266i \(0.368020\pi\)
\(114\) −4.12353e102 −0.0551537
\(115\) 1.19608e104 1.02924
\(116\) 3.09349e103 0.171918
\(117\) −4.33772e104 −1.56270
\(118\) 4.18287e104 0.980466
\(119\) 5.69242e104 0.871316
\(120\) 4.52464e104 0.453870
\(121\) −3.29855e104 −0.217601
\(122\) −1.56486e105 −0.681246
\(123\) −2.38775e104 −0.0688305
\(124\) 1.66437e105 0.318754
\(125\) −1.36079e106 −1.73715
\(126\) −1.32607e106 −1.13202
\(127\) 1.39229e106 0.797339 0.398670 0.917095i \(-0.369472\pi\)
0.398670 + 0.917095i \(0.369472\pi\)
\(128\) −3.11862e106 −1.20187
\(129\) 6.30160e105 0.163935
\(130\) 1.88317e107 3.31703
\(131\) −9.77949e106 −1.16981 −0.584905 0.811102i \(-0.698868\pi\)
−0.584905 + 0.811102i \(0.698868\pi\)
\(132\) 7.70101e105 0.0627429
\(133\) 3.27721e106 0.182388
\(134\) 5.68110e107 2.16591
\(135\) −3.87092e107 −1.01381
\(136\) −3.65778e107 −0.659938
\(137\) −4.26131e107 −0.531073 −0.265537 0.964101i \(-0.585549\pi\)
−0.265537 + 0.964101i \(0.585549\pi\)
\(138\) −2.34400e107 −0.202331
\(139\) −1.67295e107 −0.100285 −0.0501425 0.998742i \(-0.515968\pi\)
−0.0501425 + 0.998742i \(0.515968\pi\)
\(140\) 1.08048e108 0.450975
\(141\) 6.10432e107 0.177857
\(142\) −3.44417e108 −0.702301
\(143\) −1.06673e109 −1.52610
\(144\) 1.06007e109 1.06666
\(145\) −1.81739e109 −1.28933
\(146\) 2.34559e109 1.17607
\(147\) −2.32395e108 −0.0825471
\(148\) 1.11360e109 0.280876
\(149\) 7.26079e109 1.30340 0.651700 0.758477i \(-0.274056\pi\)
0.651700 + 0.758477i \(0.274056\pi\)
\(150\) 5.32689e109 0.682127
\(151\) 2.69592e109 0.246815 0.123408 0.992356i \(-0.460618\pi\)
0.123408 + 0.992356i \(0.460618\pi\)
\(152\) −2.10584e109 −0.138141
\(153\) 1.48727e110 0.700603
\(154\) −3.26105e110 −1.10551
\(155\) −9.77800e110 −2.39056
\(156\) −6.92647e109 −0.122383
\(157\) 4.68140e110 0.599023 0.299511 0.954093i \(-0.403176\pi\)
0.299511 + 0.954093i \(0.403176\pi\)
\(158\) 5.98818e110 0.556048
\(159\) −3.53530e110 −0.238710
\(160\) −1.59719e111 −0.785771
\(161\) 1.86291e111 0.669090
\(162\) −3.06658e111 −0.805649
\(163\) 9.76956e111 1.88105 0.940526 0.339721i \(-0.110333\pi\)
0.940526 + 0.339721i \(0.110333\pi\)
\(164\) 3.66390e110 0.0518000
\(165\) −4.52425e111 −0.470552
\(166\) 1.45554e111 0.111575
\(167\) −2.19092e111 −0.124007 −0.0620034 0.998076i \(-0.519749\pi\)
−0.0620034 + 0.998076i \(0.519749\pi\)
\(168\) 7.04719e111 0.295051
\(169\) 6.37126e112 1.97673
\(170\) −6.45679e112 −1.48712
\(171\) 8.56241e111 0.146654
\(172\) −9.66955e111 −0.123373
\(173\) −1.20621e113 −1.14840 −0.574202 0.818714i \(-0.694688\pi\)
−0.574202 + 0.818714i \(0.694688\pi\)
\(174\) 3.56160e112 0.253460
\(175\) −4.23358e113 −2.25573
\(176\) 2.60691e113 1.04168
\(177\) 9.03850e112 0.271298
\(178\) −4.74098e113 −1.07068
\(179\) 7.66204e113 1.30397 0.651983 0.758234i \(-0.273937\pi\)
0.651983 + 0.758234i \(0.273937\pi\)
\(180\) 2.82300e113 0.362617
\(181\) 5.31499e113 0.516101 0.258051 0.966131i \(-0.416920\pi\)
0.258051 + 0.966131i \(0.416920\pi\)
\(182\) 2.93306e114 2.15633
\(183\) −3.38141e113 −0.188503
\(184\) −1.19705e114 −0.506772
\(185\) −6.54230e114 −2.10648
\(186\) 1.91623e114 0.469942
\(187\) 3.65747e114 0.684195
\(188\) −9.36682e113 −0.133851
\(189\) −6.02901e114 −0.659060
\(190\) −3.71727e114 −0.311291
\(191\) 8.28574e113 0.0532288 0.0266144 0.999646i \(-0.491527\pi\)
0.0266144 + 0.999646i \(0.491527\pi\)
\(192\) −4.19623e114 −0.207084
\(193\) 3.05207e114 0.115865 0.0579323 0.998321i \(-0.481549\pi\)
0.0579323 + 0.998321i \(0.481549\pi\)
\(194\) −2.36254e115 −0.690861
\(195\) 4.06922e115 0.917832
\(196\) 3.56601e114 0.0621228
\(197\) −4.98888e115 −0.672139 −0.336069 0.941837i \(-0.609098\pi\)
−0.336069 + 0.941837i \(0.609098\pi\)
\(198\) −8.52020e115 −0.888910
\(199\) 1.87907e116 1.52006 0.760032 0.649885i \(-0.225183\pi\)
0.760032 + 0.649885i \(0.225183\pi\)
\(200\) 2.72038e116 1.70850
\(201\) 1.22759e116 0.599313
\(202\) −5.91008e115 −0.224569
\(203\) −2.83061e116 −0.838166
\(204\) 2.37487e115 0.0548676
\(205\) −2.15250e116 −0.388484
\(206\) −6.05955e116 −0.855354
\(207\) 4.86725e116 0.537999
\(208\) −2.34471e117 −2.03185
\(209\) 2.10566e116 0.143219
\(210\) 1.24398e117 0.664876
\(211\) −1.37595e117 −0.578548 −0.289274 0.957246i \(-0.593414\pi\)
−0.289274 + 0.957246i \(0.593414\pi\)
\(212\) 5.42477e116 0.179647
\(213\) −7.44229e116 −0.194329
\(214\) 9.52984e117 1.96422
\(215\) 5.68075e117 0.925258
\(216\) 3.87407e117 0.499175
\(217\) −1.52294e118 −1.55405
\(218\) −1.80791e117 −0.146259
\(219\) 5.06845e117 0.325422
\(220\) 6.94228e117 0.354125
\(221\) −3.28962e118 −1.33455
\(222\) 1.28212e118 0.414098
\(223\) 6.07548e118 1.56381 0.781907 0.623396i \(-0.214247\pi\)
0.781907 + 0.623396i \(0.214247\pi\)
\(224\) −2.48764e118 −0.510814
\(225\) −1.10612e119 −1.81377
\(226\) −6.82003e118 −0.893944
\(227\) 1.61334e119 1.69207 0.846037 0.533124i \(-0.178982\pi\)
0.846037 + 0.533124i \(0.178982\pi\)
\(228\) 1.36725e117 0.0114851
\(229\) −7.19765e118 −0.484729 −0.242364 0.970185i \(-0.577923\pi\)
−0.242364 + 0.970185i \(0.577923\pi\)
\(230\) −2.11306e119 −1.14197
\(231\) −7.04659e118 −0.305896
\(232\) 1.81887e119 0.634831
\(233\) 1.46080e119 0.410314 0.205157 0.978729i \(-0.434230\pi\)
0.205157 + 0.978729i \(0.434230\pi\)
\(234\) 7.66326e119 1.73386
\(235\) 5.50289e119 1.00384
\(236\) −1.38692e119 −0.204171
\(237\) 1.29395e119 0.153860
\(238\) −1.00566e120 −0.966747
\(239\) 7.43010e119 0.577964 0.288982 0.957334i \(-0.406683\pi\)
0.288982 + 0.957334i \(0.406683\pi\)
\(240\) −9.94450e119 −0.626491
\(241\) −2.53445e120 −1.29427 −0.647133 0.762377i \(-0.724032\pi\)
−0.647133 + 0.762377i \(0.724032\pi\)
\(242\) 5.82740e119 0.241434
\(243\) −2.40177e120 −0.808006
\(244\) 5.18863e119 0.141862
\(245\) −2.09499e120 −0.465902
\(246\) 4.21833e119 0.0763691
\(247\) −1.89388e120 −0.279355
\(248\) 9.78596e120 1.17705
\(249\) 3.14519e119 0.0308731
\(250\) 2.40405e121 1.92741
\(251\) −2.12075e121 −1.38985 −0.694923 0.719084i \(-0.744562\pi\)
−0.694923 + 0.719084i \(0.744562\pi\)
\(252\) 4.39686e120 0.235730
\(253\) 1.19695e121 0.525399
\(254\) −2.45971e121 −0.884668
\(255\) −1.39521e121 −0.411490
\(256\) 2.72267e121 0.658988
\(257\) 7.82104e121 1.55468 0.777341 0.629079i \(-0.216568\pi\)
0.777341 + 0.629079i \(0.216568\pi\)
\(258\) −1.11328e121 −0.181890
\(259\) −1.01897e122 −1.36938
\(260\) −6.24405e121 −0.690736
\(261\) −7.39559e121 −0.673949
\(262\) 1.72770e122 1.29793
\(263\) −4.46862e121 −0.276954 −0.138477 0.990366i \(-0.544221\pi\)
−0.138477 + 0.990366i \(0.544221\pi\)
\(264\) 4.52794e121 0.231687
\(265\) −3.18699e122 −1.34730
\(266\) −5.78970e121 −0.202364
\(267\) −1.02445e122 −0.296259
\(268\) −1.88369e122 −0.451027
\(269\) 6.09483e122 1.20913 0.604563 0.796557i \(-0.293348\pi\)
0.604563 + 0.796557i \(0.293348\pi\)
\(270\) 6.83858e122 1.12485
\(271\) 2.88488e122 0.393712 0.196856 0.980432i \(-0.436927\pi\)
0.196856 + 0.980432i \(0.436927\pi\)
\(272\) 8.03928e122 0.910935
\(273\) 6.33787e122 0.596664
\(274\) 7.52827e122 0.589239
\(275\) −2.72015e123 −1.77130
\(276\) 7.77202e121 0.0421333
\(277\) −2.29440e123 −1.03619 −0.518097 0.855322i \(-0.673359\pi\)
−0.518097 + 0.855322i \(0.673359\pi\)
\(278\) 2.95553e122 0.111269
\(279\) −3.97901e123 −1.24958
\(280\) 6.35288e123 1.66529
\(281\) −8.87210e123 −1.94248 −0.971242 0.238095i \(-0.923477\pi\)
−0.971242 + 0.238095i \(0.923477\pi\)
\(282\) −1.07842e123 −0.197337
\(283\) 3.63420e123 0.556152 0.278076 0.960559i \(-0.410303\pi\)
0.278076 + 0.960559i \(0.410303\pi\)
\(284\) 1.14199e123 0.146247
\(285\) −8.03241e122 −0.0861351
\(286\) 1.88454e124 1.69325
\(287\) −3.35255e123 −0.252545
\(288\) −6.49950e123 −0.410733
\(289\) −7.57223e123 −0.401682
\(290\) 3.21070e124 1.43054
\(291\) −5.10505e123 −0.191163
\(292\) −7.77732e123 −0.244904
\(293\) −3.97733e124 −1.05384 −0.526922 0.849913i \(-0.676654\pi\)
−0.526922 + 0.849913i \(0.676654\pi\)
\(294\) 4.10563e123 0.0915881
\(295\) 8.14799e124 1.53122
\(296\) 6.54762e124 1.03718
\(297\) −3.87374e124 −0.517523
\(298\) −1.28273e125 −1.44615
\(299\) −1.07656e125 −1.02481
\(300\) −1.76624e124 −0.142045
\(301\) 8.84785e124 0.601492
\(302\) −4.76277e124 −0.273848
\(303\) −1.27707e124 −0.0621388
\(304\) 4.62832e124 0.190681
\(305\) −3.04826e125 −1.06392
\(306\) −2.62749e125 −0.777337
\(307\) 6.37866e125 1.60045 0.800223 0.599702i \(-0.204714\pi\)
0.800223 + 0.599702i \(0.204714\pi\)
\(308\) 1.08127e125 0.230209
\(309\) −1.30937e125 −0.236679
\(310\) 1.72744e126 2.65238
\(311\) 4.16169e124 0.0543088 0.0271544 0.999631i \(-0.491355\pi\)
0.0271544 + 0.999631i \(0.491355\pi\)
\(312\) −4.07253e125 −0.451916
\(313\) 9.78296e125 0.923594 0.461797 0.886986i \(-0.347205\pi\)
0.461797 + 0.886986i \(0.347205\pi\)
\(314\) −8.27042e125 −0.664631
\(315\) −2.58310e126 −1.76790
\(316\) −1.98551e125 −0.115791
\(317\) 1.90344e125 0.0946336 0.0473168 0.998880i \(-0.484933\pi\)
0.0473168 + 0.998880i \(0.484933\pi\)
\(318\) 6.24566e125 0.264855
\(319\) −1.81871e126 −0.658165
\(320\) −3.78280e126 −1.16880
\(321\) 2.05924e126 0.543505
\(322\) −3.29112e126 −0.742373
\(323\) 6.49351e125 0.125243
\(324\) 1.01679e126 0.167768
\(325\) 2.44656e127 3.45499
\(326\) −1.72594e127 −2.08708
\(327\) −3.90660e125 −0.0404704
\(328\) 2.15425e126 0.191279
\(329\) 8.57084e126 0.652575
\(330\) 7.99280e126 0.522090
\(331\) −1.95148e127 −1.09409 −0.547043 0.837105i \(-0.684247\pi\)
−0.547043 + 0.837105i \(0.684247\pi\)
\(332\) −4.82616e125 −0.0232343
\(333\) −2.66229e127 −1.10109
\(334\) 3.87061e126 0.137589
\(335\) 1.10665e128 3.38256
\(336\) −1.54887e127 −0.407269
\(337\) −1.63331e126 −0.0369623 −0.0184811 0.999829i \(-0.505883\pi\)
−0.0184811 + 0.999829i \(0.505883\pi\)
\(338\) −1.12558e128 −2.19323
\(339\) −1.47370e127 −0.247357
\(340\) 2.14089e127 0.309677
\(341\) −9.78512e127 −1.22031
\(342\) −1.51268e127 −0.162716
\(343\) 8.87266e127 0.823571
\(344\) −5.68537e127 −0.455572
\(345\) −4.56597e127 −0.315987
\(346\) 2.13096e128 1.27418
\(347\) −2.36944e128 −1.22464 −0.612319 0.790611i \(-0.709763\pi\)
−0.612319 + 0.790611i \(0.709763\pi\)
\(348\) −1.18093e127 −0.0527802
\(349\) −7.03918e126 −0.0272169 −0.0136084 0.999907i \(-0.504332\pi\)
−0.0136084 + 0.999907i \(0.504332\pi\)
\(350\) 7.47928e128 2.50279
\(351\) 3.48413e128 1.00945
\(352\) −1.59835e128 −0.401113
\(353\) 2.29284e128 0.498599 0.249299 0.968426i \(-0.419800\pi\)
0.249299 + 0.968426i \(0.419800\pi\)
\(354\) −1.59679e128 −0.301012
\(355\) −6.70905e128 −1.09680
\(356\) 1.57197e128 0.222956
\(357\) −2.17306e128 −0.267502
\(358\) −1.35362e129 −1.44678
\(359\) −5.85822e128 −0.543871 −0.271935 0.962316i \(-0.587664\pi\)
−0.271935 + 0.962316i \(0.587664\pi\)
\(360\) 1.65983e129 1.33902
\(361\) −1.38860e129 −0.973784
\(362\) −9.38977e128 −0.572627
\(363\) 1.25921e128 0.0668055
\(364\) −9.72520e128 −0.449033
\(365\) 4.56908e129 1.83671
\(366\) 5.97378e128 0.209148
\(367\) −3.80604e129 −1.16101 −0.580506 0.814256i \(-0.697145\pi\)
−0.580506 + 0.814256i \(0.697145\pi\)
\(368\) 2.63094e129 0.699514
\(369\) −8.75927e128 −0.203066
\(370\) 1.15580e130 2.33720
\(371\) −4.96378e129 −0.875851
\(372\) −6.35367e128 −0.0978602
\(373\) −4.09983e129 −0.551404 −0.275702 0.961243i \(-0.588910\pi\)
−0.275702 + 0.961243i \(0.588910\pi\)
\(374\) −6.46150e129 −0.759132
\(375\) 5.19477e129 0.533319
\(376\) −5.50737e129 −0.494263
\(377\) 1.63579e130 1.28378
\(378\) 1.06512e130 0.731244
\(379\) −1.69783e130 −1.02004 −0.510018 0.860164i \(-0.670361\pi\)
−0.510018 + 0.860164i \(0.670361\pi\)
\(380\) 1.23254e129 0.0648230
\(381\) −5.31502e129 −0.244790
\(382\) −1.46381e129 −0.0590587
\(383\) −2.79558e130 −0.988403 −0.494201 0.869347i \(-0.664539\pi\)
−0.494201 + 0.869347i \(0.664539\pi\)
\(384\) 1.19052e130 0.368986
\(385\) −6.35234e130 −1.72650
\(386\) −5.39196e129 −0.128555
\(387\) 2.31169e130 0.483645
\(388\) 7.83349e129 0.143864
\(389\) 1.02053e131 1.64577 0.822886 0.568206i \(-0.192362\pi\)
0.822886 + 0.568206i \(0.192362\pi\)
\(390\) −7.18891e130 −1.01836
\(391\) 3.69120e130 0.459453
\(392\) 2.09669e130 0.229397
\(393\) 3.73328e130 0.359142
\(394\) 8.81364e130 0.745755
\(395\) 1.16646e131 0.868396
\(396\) 2.82505e130 0.185106
\(397\) 2.41789e131 1.39481 0.697406 0.716676i \(-0.254337\pi\)
0.697406 + 0.716676i \(0.254337\pi\)
\(398\) −3.31967e131 −1.68655
\(399\) −1.25106e130 −0.0559947
\(400\) −5.97899e131 −2.35830
\(401\) −3.05800e131 −1.06328 −0.531638 0.846972i \(-0.678423\pi\)
−0.531638 + 0.846972i \(0.678423\pi\)
\(402\) −2.16874e131 −0.664953
\(403\) 8.80097e131 2.38027
\(404\) 1.95961e130 0.0467640
\(405\) −5.97352e131 −1.25821
\(406\) 5.00072e131 0.929967
\(407\) −6.54706e131 −1.07530
\(408\) 1.39634e131 0.202607
\(409\) 2.88971e131 0.370533 0.185267 0.982688i \(-0.440685\pi\)
0.185267 + 0.982688i \(0.440685\pi\)
\(410\) 3.80273e131 0.431033
\(411\) 1.62674e131 0.163044
\(412\) 2.00917e131 0.178118
\(413\) 1.26906e132 0.995417
\(414\) −8.59876e131 −0.596924
\(415\) 2.83531e131 0.174250
\(416\) 1.43759e132 0.782389
\(417\) 6.38642e130 0.0307884
\(418\) −3.71997e131 −0.158905
\(419\) −4.10257e132 −1.55327 −0.776637 0.629948i \(-0.783076\pi\)
−0.776637 + 0.629948i \(0.783076\pi\)
\(420\) −4.12470e131 −0.138453
\(421\) 9.23486e131 0.274906 0.137453 0.990508i \(-0.456108\pi\)
0.137453 + 0.990508i \(0.456108\pi\)
\(422\) 2.43083e132 0.641913
\(423\) 2.23932e132 0.524720
\(424\) 3.18958e132 0.663373
\(425\) −8.38849e132 −1.54897
\(426\) 1.31480e132 0.215613
\(427\) −4.74771e132 −0.691634
\(428\) −3.15982e132 −0.409027
\(429\) 4.07219e132 0.468527
\(430\) −1.00359e133 −1.02660
\(431\) −4.45061e132 −0.404872 −0.202436 0.979295i \(-0.564886\pi\)
−0.202436 + 0.979295i \(0.564886\pi\)
\(432\) −8.51464e132 −0.689028
\(433\) 1.12944e133 0.813252 0.406626 0.913595i \(-0.366705\pi\)
0.406626 + 0.913595i \(0.366705\pi\)
\(434\) 2.69051e133 1.72426
\(435\) 6.93780e132 0.395835
\(436\) 5.99451e131 0.0304569
\(437\) 2.12507e132 0.0961749
\(438\) −8.95420e132 −0.361064
\(439\) −8.84001e130 −0.00317683 −0.00158842 0.999999i \(-0.500506\pi\)
−0.00158842 + 0.999999i \(0.500506\pi\)
\(440\) 4.08183e133 1.30766
\(441\) −8.52523e132 −0.243533
\(442\) 5.81162e133 1.48072
\(443\) −1.19259e133 −0.271082 −0.135541 0.990772i \(-0.543277\pi\)
−0.135541 + 0.990772i \(0.543277\pi\)
\(444\) −4.25114e132 −0.0862313
\(445\) −9.23515e133 −1.67210
\(446\) −1.07333e134 −1.73509
\(447\) −2.77178e133 −0.400155
\(448\) −5.89177e133 −0.759811
\(449\) −3.96128e133 −0.456452 −0.228226 0.973608i \(-0.573293\pi\)
−0.228226 + 0.973608i \(0.573293\pi\)
\(450\) 1.95413e134 2.01243
\(451\) −2.15407e133 −0.198310
\(452\) 2.26133e133 0.186154
\(453\) −1.02916e133 −0.0757744
\(454\) −2.85021e134 −1.87740
\(455\) 5.71344e134 3.36761
\(456\) 8.03894e132 0.0424106
\(457\) −1.35379e134 −0.639414 −0.319707 0.947516i \(-0.603585\pi\)
−0.319707 + 0.947516i \(0.603585\pi\)
\(458\) 1.27158e134 0.537819
\(459\) −1.19460e134 −0.452566
\(460\) 7.00629e133 0.237803
\(461\) −6.86709e133 −0.208870 −0.104435 0.994532i \(-0.533303\pi\)
−0.104435 + 0.994532i \(0.533303\pi\)
\(462\) 1.24489e134 0.339400
\(463\) 2.52099e134 0.616213 0.308107 0.951352i \(-0.400305\pi\)
0.308107 + 0.951352i \(0.400305\pi\)
\(464\) −3.99761e134 −0.876278
\(465\) 3.73271e134 0.733922
\(466\) −2.58073e134 −0.455253
\(467\) −6.60220e134 −1.04517 −0.522584 0.852588i \(-0.675032\pi\)
−0.522584 + 0.852588i \(0.675032\pi\)
\(468\) −2.54092e134 −0.361057
\(469\) 1.72362e135 2.19894
\(470\) −9.72172e134 −1.11378
\(471\) −1.78710e134 −0.183905
\(472\) −8.15462e134 −0.753933
\(473\) 5.68489e134 0.472318
\(474\) −2.28596e134 −0.170712
\(475\) −4.82937e134 −0.324238
\(476\) 3.33446e134 0.201314
\(477\) −1.29690e135 −0.704250
\(478\) −1.31264e135 −0.641266
\(479\) −1.49265e135 −0.656166 −0.328083 0.944649i \(-0.606403\pi\)
−0.328083 + 0.944649i \(0.606403\pi\)
\(480\) 6.09718e134 0.241239
\(481\) 5.88858e135 2.09741
\(482\) 4.47751e135 1.43602
\(483\) −7.11157e134 −0.205417
\(484\) −1.93220e134 −0.0502760
\(485\) −4.60208e135 −1.07894
\(486\) 4.24310e135 0.896503
\(487\) 1.65892e135 0.315946 0.157973 0.987443i \(-0.449504\pi\)
0.157973 + 0.987443i \(0.449504\pi\)
\(488\) 3.05074e135 0.523847
\(489\) −3.72949e135 −0.577499
\(490\) 3.70112e135 0.516930
\(491\) −5.07962e135 −0.640053 −0.320027 0.947409i \(-0.603692\pi\)
−0.320027 + 0.947409i \(0.603692\pi\)
\(492\) −1.39868e134 −0.0159030
\(493\) −5.60862e135 −0.575555
\(494\) 3.34583e135 0.309951
\(495\) −1.65969e136 −1.38824
\(496\) −2.15081e136 −1.62472
\(497\) −1.04494e136 −0.713010
\(498\) −5.55647e134 −0.0342545
\(499\) 3.25310e136 1.81226 0.906130 0.422999i \(-0.139023\pi\)
0.906130 + 0.422999i \(0.139023\pi\)
\(500\) −7.97115e135 −0.401362
\(501\) 8.36375e134 0.0380712
\(502\) 3.74664e136 1.54207
\(503\) 2.14382e136 0.798006 0.399003 0.916950i \(-0.369356\pi\)
0.399003 + 0.916950i \(0.369356\pi\)
\(504\) 2.58521e136 0.870468
\(505\) −1.15125e136 −0.350716
\(506\) −2.11460e136 −0.582944
\(507\) −2.43220e136 −0.606872
\(508\) 8.15568e135 0.184222
\(509\) −2.39037e136 −0.488897 −0.244448 0.969662i \(-0.578607\pi\)
−0.244448 + 0.969662i \(0.578607\pi\)
\(510\) 2.46485e136 0.456559
\(511\) 7.11642e136 1.19400
\(512\) 3.09661e136 0.470711
\(513\) −6.87748e135 −0.0947332
\(514\) −1.38171e137 −1.72496
\(515\) −1.18037e137 −1.33583
\(516\) 3.69131e135 0.0378765
\(517\) 5.50691e136 0.512431
\(518\) 1.80017e137 1.51936
\(519\) 4.60465e136 0.352570
\(520\) −3.67129e137 −2.55064
\(521\) 1.68827e137 1.06448 0.532239 0.846594i \(-0.321351\pi\)
0.532239 + 0.846594i \(0.321351\pi\)
\(522\) 1.30655e137 0.747763
\(523\) −2.56145e137 −1.33091 −0.665457 0.746436i \(-0.731763\pi\)
−0.665457 + 0.746436i \(0.731763\pi\)
\(524\) −5.72855e136 −0.270281
\(525\) 1.61615e137 0.692528
\(526\) 7.89452e136 0.307288
\(527\) −3.01758e137 −1.06714
\(528\) −9.95175e136 −0.319806
\(529\) −2.21584e137 −0.647182
\(530\) 5.63031e137 1.49486
\(531\) 3.31570e137 0.800390
\(532\) 1.91970e136 0.0421401
\(533\) 1.93742e137 0.386812
\(534\) 1.80985e137 0.328707
\(535\) 1.85636e138 3.06758
\(536\) −1.10755e138 −1.66548
\(537\) −2.92495e137 −0.400329
\(538\) −1.07675e138 −1.34156
\(539\) −2.09652e137 −0.237829
\(540\) −2.26748e137 −0.234238
\(541\) 5.13635e137 0.483273 0.241636 0.970367i \(-0.422316\pi\)
0.241636 + 0.970367i \(0.422316\pi\)
\(542\) −5.09659e137 −0.436833
\(543\) −2.02898e137 −0.158448
\(544\) −4.92905e137 −0.350767
\(545\) −3.52171e137 −0.228418
\(546\) −1.11968e138 −0.662014
\(547\) −1.51606e138 −0.817251 −0.408626 0.912702i \(-0.633992\pi\)
−0.408626 + 0.912702i \(0.633992\pi\)
\(548\) −2.49616e137 −0.122703
\(549\) −1.24044e138 −0.556126
\(550\) 4.80556e138 1.96530
\(551\) −3.22896e137 −0.120478
\(552\) 4.56969e137 0.155583
\(553\) 1.81679e138 0.564527
\(554\) 4.05342e138 1.14968
\(555\) 2.49749e138 0.646709
\(556\) −9.79969e136 −0.0231705
\(557\) −2.27470e138 −0.491175 −0.245588 0.969374i \(-0.578981\pi\)
−0.245588 + 0.969374i \(0.578981\pi\)
\(558\) 7.02954e138 1.38644
\(559\) −5.11312e138 −0.921276
\(560\) −1.39627e139 −2.29866
\(561\) −1.39622e138 −0.210054
\(562\) 1.56740e139 2.15523
\(563\) 2.50855e138 0.315318 0.157659 0.987494i \(-0.449605\pi\)
0.157659 + 0.987494i \(0.449605\pi\)
\(564\) 3.57574e137 0.0410933
\(565\) −1.32850e139 −1.39610
\(566\) −6.42038e138 −0.617065
\(567\) −9.30385e138 −0.817934
\(568\) 6.71451e138 0.540037
\(569\) −5.91124e138 −0.435020 −0.217510 0.976058i \(-0.569793\pi\)
−0.217510 + 0.976058i \(0.569793\pi\)
\(570\) 1.41905e138 0.0955691
\(571\) 2.25293e139 1.38875 0.694375 0.719613i \(-0.255681\pi\)
0.694375 + 0.719613i \(0.255681\pi\)
\(572\) −6.24860e138 −0.352601
\(573\) −3.16305e137 −0.0163417
\(574\) 5.92280e138 0.280206
\(575\) −2.74523e139 −1.18947
\(576\) −1.53935e139 −0.610946
\(577\) 2.94565e139 1.07103 0.535517 0.844525i \(-0.320117\pi\)
0.535517 + 0.844525i \(0.320117\pi\)
\(578\) 1.33775e139 0.445677
\(579\) −1.16512e138 −0.0355715
\(580\) −1.06458e139 −0.297895
\(581\) 4.41605e138 0.113276
\(582\) 9.01887e138 0.212100
\(583\) −3.18931e139 −0.687756
\(584\) −4.57280e139 −0.904344
\(585\) 1.49276e140 2.70781
\(586\) 7.02657e139 1.16927
\(587\) 4.14398e139 0.632694 0.316347 0.948644i \(-0.397544\pi\)
0.316347 + 0.948644i \(0.397544\pi\)
\(588\) −1.36131e138 −0.0190722
\(589\) −1.73726e139 −0.223379
\(590\) −1.43947e140 −1.69893
\(591\) 1.90448e139 0.206352
\(592\) −1.43907e140 −1.43165
\(593\) −4.72697e139 −0.431838 −0.215919 0.976411i \(-0.569275\pi\)
−0.215919 + 0.976411i \(0.569275\pi\)
\(594\) 6.84357e139 0.574205
\(595\) −1.95896e140 −1.50980
\(596\) 4.25317e139 0.301146
\(597\) −7.17326e139 −0.466673
\(598\) 1.90192e140 1.13706
\(599\) −1.54853e139 −0.0850875 −0.0425438 0.999095i \(-0.513546\pi\)
−0.0425438 + 0.999095i \(0.513546\pi\)
\(600\) −1.03849e140 −0.524524
\(601\) −7.43424e139 −0.345204 −0.172602 0.984992i \(-0.555217\pi\)
−0.172602 + 0.984992i \(0.555217\pi\)
\(602\) −1.56311e140 −0.667370
\(603\) 4.50333e140 1.76811
\(604\) 1.57920e139 0.0570258
\(605\) 1.13514e140 0.377055
\(606\) 2.25615e139 0.0689445
\(607\) 6.16048e140 1.73215 0.866076 0.499913i \(-0.166635\pi\)
0.866076 + 0.499913i \(0.166635\pi\)
\(608\) −2.83772e139 −0.0734243
\(609\) 1.08057e140 0.257324
\(610\) 5.38522e140 1.18045
\(611\) −4.95304e140 −0.999518
\(612\) 8.71201e139 0.161872
\(613\) −9.19299e140 −1.57291 −0.786453 0.617650i \(-0.788085\pi\)
−0.786453 + 0.617650i \(0.788085\pi\)
\(614\) −1.12689e141 −1.77574
\(615\) 8.21707e139 0.119268
\(616\) 6.35751e140 0.850082
\(617\) −1.54803e140 −0.190712 −0.0953560 0.995443i \(-0.530399\pi\)
−0.0953560 + 0.995443i \(0.530399\pi\)
\(618\) 2.31321e140 0.262601
\(619\) 5.82380e140 0.609297 0.304648 0.952465i \(-0.401461\pi\)
0.304648 + 0.952465i \(0.401461\pi\)
\(620\) −5.72768e140 −0.552330
\(621\) −3.90946e140 −0.347529
\(622\) −7.35228e139 −0.0602570
\(623\) −1.43839e141 −1.08700
\(624\) 8.95083e140 0.623795
\(625\) 1.56753e141 1.00757
\(626\) −1.72831e141 −1.02475
\(627\) −8.03826e139 −0.0439695
\(628\) 2.74224e140 0.138402
\(629\) −2.01901e141 −0.940331
\(630\) 4.56345e141 1.96153
\(631\) 2.40604e141 0.954597 0.477298 0.878741i \(-0.341616\pi\)
0.477298 + 0.878741i \(0.341616\pi\)
\(632\) −1.16741e141 −0.427575
\(633\) 5.25263e140 0.177619
\(634\) −3.36272e140 −0.104998
\(635\) −4.79137e141 −1.38161
\(636\) −2.07088e140 −0.0551532
\(637\) 1.88565e141 0.463896
\(638\) 3.21304e141 0.730251
\(639\) −2.73014e141 −0.573314
\(640\) 1.07322e142 2.08258
\(641\) 8.62217e140 0.154627 0.0773136 0.997007i \(-0.475366\pi\)
0.0773136 + 0.997007i \(0.475366\pi\)
\(642\) −3.63797e141 −0.603032
\(643\) −4.65858e141 −0.713838 −0.356919 0.934135i \(-0.616173\pi\)
−0.356919 + 0.934135i \(0.616173\pi\)
\(644\) 1.09124e141 0.154591
\(645\) −2.16860e141 −0.284062
\(646\) −1.14718e141 −0.138960
\(647\) −1.01951e142 −1.14216 −0.571078 0.820896i \(-0.693474\pi\)
−0.571078 + 0.820896i \(0.693474\pi\)
\(648\) 5.97839e141 0.619507
\(649\) 8.15393e141 0.781645
\(650\) −4.32223e142 −3.83340
\(651\) 5.81375e141 0.477108
\(652\) 5.72274e141 0.434611
\(653\) −6.34673e141 −0.446102 −0.223051 0.974807i \(-0.571602\pi\)
−0.223051 + 0.974807i \(0.571602\pi\)
\(654\) 6.90162e140 0.0449029
\(655\) 3.36546e142 2.02702
\(656\) −4.73473e141 −0.264029
\(657\) 1.85932e142 0.960069
\(658\) −1.51417e142 −0.724049
\(659\) 2.68625e142 1.18969 0.594844 0.803841i \(-0.297214\pi\)
0.594844 + 0.803841i \(0.297214\pi\)
\(660\) −2.65018e141 −0.108719
\(661\) −1.00522e142 −0.382021 −0.191010 0.981588i \(-0.561176\pi\)
−0.191010 + 0.981588i \(0.561176\pi\)
\(662\) 3.44760e142 1.21392
\(663\) 1.25580e142 0.409719
\(664\) −2.83762e141 −0.0857959
\(665\) −1.12780e142 −0.316038
\(666\) 4.70335e142 1.22168
\(667\) −1.83548e142 −0.441973
\(668\) −1.28338e141 −0.0286513
\(669\) −2.31929e142 −0.480104
\(670\) −1.95506e143 −3.75304
\(671\) −3.05048e142 −0.543101
\(672\) 9.49646e141 0.156824
\(673\) 8.39160e142 1.28554 0.642768 0.766061i \(-0.277786\pi\)
0.642768 + 0.766061i \(0.277786\pi\)
\(674\) 2.88550e141 0.0410106
\(675\) 8.88451e142 1.17164
\(676\) 3.73211e142 0.456716
\(677\) −1.31642e143 −1.49509 −0.747546 0.664210i \(-0.768768\pi\)
−0.747546 + 0.664210i \(0.768768\pi\)
\(678\) 2.60352e142 0.274449
\(679\) −7.16781e142 −0.701396
\(680\) 1.25877e143 1.14353
\(681\) −6.15885e142 −0.519482
\(682\) 1.72869e143 1.35396
\(683\) −1.72479e143 −1.25456 −0.627278 0.778795i \(-0.715831\pi\)
−0.627278 + 0.778795i \(0.715831\pi\)
\(684\) 5.01563e141 0.0338838
\(685\) 1.46646e143 0.920232
\(686\) −1.56749e143 −0.913772
\(687\) 2.74767e142 0.148816
\(688\) 1.24956e143 0.628842
\(689\) 2.86854e143 1.34150
\(690\) 8.06650e142 0.350595
\(691\) −2.96283e143 −1.19692 −0.598461 0.801152i \(-0.704221\pi\)
−0.598461 + 0.801152i \(0.704221\pi\)
\(692\) −7.06565e142 −0.265335
\(693\) −2.58499e143 −0.902464
\(694\) 4.18599e143 1.35877
\(695\) 5.75720e142 0.173772
\(696\) −6.94345e142 −0.194899
\(697\) −6.64280e142 −0.173419
\(698\) 1.24358e142 0.0301978
\(699\) −5.57653e142 −0.125970
\(700\) −2.47992e143 −0.521178
\(701\) 6.60750e143 1.29204 0.646022 0.763319i \(-0.276432\pi\)
0.646022 + 0.763319i \(0.276432\pi\)
\(702\) −6.15526e143 −1.12001
\(703\) −1.16237e143 −0.196835
\(704\) −3.78556e143 −0.596637
\(705\) −2.10071e143 −0.308187
\(706\) −4.05066e143 −0.553208
\(707\) −1.79309e143 −0.227993
\(708\) 5.29450e142 0.0626824
\(709\) −1.19409e144 −1.31644 −0.658221 0.752825i \(-0.728691\pi\)
−0.658221 + 0.752825i \(0.728691\pi\)
\(710\) 1.18526e144 1.21693
\(711\) 4.74675e143 0.453922
\(712\) 9.24267e143 0.823299
\(713\) −9.87535e143 −0.819467
\(714\) 3.83904e143 0.296800
\(715\) 3.67098e144 2.64440
\(716\) 4.48821e143 0.301277
\(717\) −2.83641e143 −0.177440
\(718\) 1.03495e144 0.603438
\(719\) −1.73333e143 −0.0942047 −0.0471023 0.998890i \(-0.514999\pi\)
−0.0471023 + 0.998890i \(0.514999\pi\)
\(720\) −3.64806e144 −1.84829
\(721\) −1.83844e144 −0.868397
\(722\) 2.45317e144 1.08044
\(723\) 9.67517e143 0.397351
\(724\) 3.11338e143 0.119243
\(725\) 4.17126e144 1.49004
\(726\) −2.22458e143 −0.0741224
\(727\) −5.44264e144 −1.69169 −0.845847 0.533425i \(-0.820905\pi\)
−0.845847 + 0.533425i \(0.820905\pi\)
\(728\) −5.71809e144 −1.65812
\(729\) −1.76693e144 −0.478056
\(730\) −8.07200e144 −2.03787
\(731\) 1.75313e144 0.413034
\(732\) −1.98074e143 −0.0435529
\(733\) 3.16959e144 0.650508 0.325254 0.945627i \(-0.394550\pi\)
0.325254 + 0.945627i \(0.394550\pi\)
\(734\) 6.72396e144 1.28817
\(735\) 7.99753e143 0.143036
\(736\) −1.61309e144 −0.269357
\(737\) 1.10745e145 1.72670
\(738\) 1.54746e144 0.225306
\(739\) −3.13110e144 −0.425748 −0.212874 0.977080i \(-0.568282\pi\)
−0.212874 + 0.977080i \(0.568282\pi\)
\(740\) −3.83230e144 −0.486696
\(741\) 7.22980e143 0.0857643
\(742\) 8.76929e144 0.971779
\(743\) 5.48983e144 0.568361 0.284180 0.958771i \(-0.408279\pi\)
0.284180 + 0.958771i \(0.408279\pi\)
\(744\) −3.73575e144 −0.361363
\(745\) −2.49869e145 −2.25850
\(746\) 7.24299e144 0.611797
\(747\) 1.15379e144 0.0910826
\(748\) 2.14245e144 0.158081
\(749\) 2.89131e145 1.99417
\(750\) −9.17737e144 −0.591731
\(751\) −1.26915e145 −0.765061 −0.382531 0.923943i \(-0.624947\pi\)
−0.382531 + 0.923943i \(0.624947\pi\)
\(752\) 1.21044e145 0.682248
\(753\) 8.09588e144 0.426695
\(754\) −2.88988e145 −1.42439
\(755\) −9.27760e144 −0.427676
\(756\) −3.53163e144 −0.152274
\(757\) −4.29701e144 −0.173310 −0.0866552 0.996238i \(-0.527618\pi\)
−0.0866552 + 0.996238i \(0.527618\pi\)
\(758\) 2.99949e145 1.13176
\(759\) −4.56930e144 −0.161302
\(760\) 7.24691e144 0.239368
\(761\) −4.62573e145 −1.42973 −0.714866 0.699261i \(-0.753512\pi\)
−0.714866 + 0.699261i \(0.753512\pi\)
\(762\) 9.38982e144 0.271601
\(763\) −5.48511e144 −0.148490
\(764\) 4.85356e143 0.0122983
\(765\) −5.11821e145 −1.21399
\(766\) 4.93883e145 1.09666
\(767\) −7.33383e145 −1.52463
\(768\) −1.03937e145 −0.202315
\(769\) 5.22254e145 0.951922 0.475961 0.879466i \(-0.342100\pi\)
0.475961 + 0.879466i \(0.342100\pi\)
\(770\) 1.12224e146 1.91560
\(771\) −2.98565e145 −0.477301
\(772\) 1.78782e144 0.0267701
\(773\) 1.02627e145 0.143945 0.0719725 0.997407i \(-0.477071\pi\)
0.0719725 + 0.997407i \(0.477071\pi\)
\(774\) −4.08397e145 −0.536616
\(775\) 2.24424e146 2.76270
\(776\) 4.60583e145 0.531240
\(777\) 3.88988e145 0.420412
\(778\) −1.80292e146 −1.82603
\(779\) −3.82435e144 −0.0363008
\(780\) 2.38364e145 0.212062
\(781\) −6.71394e145 −0.559887
\(782\) −6.52108e145 −0.509775
\(783\) 5.94026e145 0.435348
\(784\) −4.60823e145 −0.316645
\(785\) −1.61103e146 −1.03797
\(786\) −6.59541e145 −0.398477
\(787\) 4.14033e145 0.234591 0.117296 0.993097i \(-0.462578\pi\)
0.117296 + 0.993097i \(0.462578\pi\)
\(788\) −2.92235e145 −0.155295
\(789\) 1.70588e145 0.0850274
\(790\) −2.06074e146 −0.963508
\(791\) −2.06916e146 −0.907575
\(792\) 1.66104e146 0.683530
\(793\) 2.74367e146 1.05934
\(794\) −4.27158e146 −1.54758
\(795\) 1.21662e146 0.413632
\(796\) 1.10071e146 0.351206
\(797\) 5.59586e146 1.67580 0.837899 0.545825i \(-0.183784\pi\)
0.837899 + 0.545825i \(0.183784\pi\)
\(798\) 2.21019e145 0.0621275
\(799\) 1.69824e146 0.448113
\(800\) 3.66585e146 0.908093
\(801\) −3.75810e146 −0.874031
\(802\) 5.40243e146 1.17973
\(803\) 4.57241e146 0.937585
\(804\) 7.19091e145 0.138469
\(805\) −6.41091e146 −1.15939
\(806\) −1.55483e147 −2.64097
\(807\) −2.32668e146 −0.371212
\(808\) 1.15219e146 0.172683
\(809\) 4.55725e146 0.641657 0.320828 0.947137i \(-0.396039\pi\)
0.320828 + 0.947137i \(0.396039\pi\)
\(810\) 1.05532e147 1.39601
\(811\) 2.45816e146 0.305532 0.152766 0.988262i \(-0.451182\pi\)
0.152766 + 0.988262i \(0.451182\pi\)
\(812\) −1.65809e146 −0.193655
\(813\) −1.10129e146 −0.120873
\(814\) 1.15664e147 1.19307
\(815\) −3.36204e147 −3.25945
\(816\) −3.06896e146 −0.279665
\(817\) 1.00930e146 0.0864583
\(818\) −5.10512e146 −0.411116
\(819\) 2.32500e147 1.76029
\(820\) −1.26087e146 −0.0897579
\(821\) 7.99047e146 0.534863 0.267432 0.963577i \(-0.413825\pi\)
0.267432 + 0.963577i \(0.413825\pi\)
\(822\) −2.87388e146 −0.180902
\(823\) −3.10849e147 −1.84017 −0.920084 0.391721i \(-0.871880\pi\)
−0.920084 + 0.391721i \(0.871880\pi\)
\(824\) 1.18133e147 0.657727
\(825\) 1.03840e147 0.543803
\(826\) −2.24199e147 −1.10444
\(827\) 2.11410e147 0.979709 0.489854 0.871804i \(-0.337050\pi\)
0.489854 + 0.871804i \(0.337050\pi\)
\(828\) 2.85110e146 0.124303
\(829\) −1.42947e147 −0.586370 −0.293185 0.956056i \(-0.594715\pi\)
−0.293185 + 0.956056i \(0.594715\pi\)
\(830\) −5.00903e146 −0.193335
\(831\) 8.75878e146 0.318121
\(832\) 3.40482e147 1.16377
\(833\) −6.46532e146 −0.207978
\(834\) −1.12826e146 −0.0341605
\(835\) 7.53972e146 0.214876
\(836\) 1.23344e146 0.0330902
\(837\) 3.19600e147 0.807183
\(838\) 7.24784e147 1.72340
\(839\) 1.47014e145 0.00329138 0.00164569 0.999999i \(-0.499476\pi\)
0.00164569 + 0.999999i \(0.499476\pi\)
\(840\) −2.42518e147 −0.511259
\(841\) −2.24836e147 −0.446342
\(842\) −1.63148e147 −0.305016
\(843\) 3.38689e147 0.596359
\(844\) −8.05994e146 −0.133671
\(845\) −2.19257e148 −3.42523
\(846\) −3.95611e147 −0.582190
\(847\) 1.76800e147 0.245116
\(848\) −7.01023e147 −0.915676
\(849\) −1.38734e147 −0.170744
\(850\) 1.48196e148 1.71862
\(851\) −6.60743e147 −0.722088
\(852\) −4.35949e146 −0.0448990
\(853\) 8.51957e147 0.826974 0.413487 0.910510i \(-0.364311\pi\)
0.413487 + 0.910510i \(0.364311\pi\)
\(854\) 8.38757e147 0.767385
\(855\) −2.94662e147 −0.254118
\(856\) −1.85787e148 −1.51039
\(857\) 2.41123e148 1.84802 0.924010 0.382368i \(-0.124891\pi\)
0.924010 + 0.382368i \(0.124891\pi\)
\(858\) −7.19415e147 −0.519842
\(859\) 1.06941e148 0.728601 0.364300 0.931282i \(-0.381308\pi\)
0.364300 + 0.931282i \(0.381308\pi\)
\(860\) 3.32762e147 0.213778
\(861\) 1.27982e147 0.0775336
\(862\) 7.86270e147 0.449216
\(863\) −2.26991e147 −0.122310 −0.0611552 0.998128i \(-0.519478\pi\)
−0.0611552 + 0.998128i \(0.519478\pi\)
\(864\) 5.22051e147 0.265319
\(865\) 4.15098e148 1.98993
\(866\) −1.99533e148 −0.902323
\(867\) 2.89066e147 0.123320
\(868\) −8.92095e147 −0.359058
\(869\) 1.16731e148 0.443291
\(870\) −1.22567e148 −0.439189
\(871\) −9.96069e148 −3.36800
\(872\) 3.52457e147 0.112467
\(873\) −1.87275e148 −0.563975
\(874\) −3.75428e147 −0.106708
\(875\) 7.29378e148 1.95680
\(876\) 2.96896e147 0.0751877
\(877\) 3.37030e148 0.805728 0.402864 0.915260i \(-0.368015\pi\)
0.402864 + 0.915260i \(0.368015\pi\)
\(878\) 1.56173e146 0.00352478
\(879\) 1.51833e148 0.323540
\(880\) −8.97126e148 −1.80501
\(881\) −7.25925e148 −1.37914 −0.689570 0.724219i \(-0.742201\pi\)
−0.689570 + 0.724219i \(0.742201\pi\)
\(882\) 1.50612e148 0.270206
\(883\) 9.12520e148 1.54606 0.773031 0.634368i \(-0.218740\pi\)
0.773031 + 0.634368i \(0.218740\pi\)
\(884\) −1.92697e148 −0.308344
\(885\) −3.11046e148 −0.470099
\(886\) 2.10689e148 0.300773
\(887\) 5.96302e148 0.804124 0.402062 0.915612i \(-0.368294\pi\)
0.402062 + 0.915612i \(0.368294\pi\)
\(888\) −2.49953e148 −0.318422
\(889\) −7.46262e148 −0.898158
\(890\) 1.63153e149 1.85524
\(891\) −5.97788e148 −0.642278
\(892\) 3.55885e148 0.361314
\(893\) 9.77701e147 0.0938010
\(894\) 4.89677e148 0.443982
\(895\) −2.63677e149 −2.25948
\(896\) 1.67156e149 1.35384
\(897\) 4.10974e148 0.314627
\(898\) 6.99822e148 0.506446
\(899\) 1.50052e149 1.02654
\(900\) −6.47932e148 −0.419066
\(901\) −9.83532e148 −0.601432
\(902\) 3.80550e148 0.220030
\(903\) −3.37763e148 −0.184663
\(904\) 1.32958e149 0.687401
\(905\) −1.82907e149 −0.894289
\(906\) 1.81817e148 0.0840736
\(907\) 2.15967e149 0.944540 0.472270 0.881454i \(-0.343435\pi\)
0.472270 + 0.881454i \(0.343435\pi\)
\(908\) 9.45049e148 0.390948
\(909\) −4.68484e148 −0.183324
\(910\) −1.00937e150 −3.73645
\(911\) −3.54148e149 −1.24024 −0.620121 0.784506i \(-0.712916\pi\)
−0.620121 + 0.784506i \(0.712916\pi\)
\(912\) −1.76684e148 −0.0585408
\(913\) 2.83738e148 0.0889495
\(914\) 2.39168e149 0.709446
\(915\) 1.16366e149 0.326633
\(916\) −4.21618e148 −0.111995
\(917\) 5.24175e149 1.31773
\(918\) 2.11045e149 0.502133
\(919\) −3.46818e149 −0.781032 −0.390516 0.920596i \(-0.627703\pi\)
−0.390516 + 0.920596i \(0.627703\pi\)
\(920\) 4.11947e149 0.878123
\(921\) −2.43502e149 −0.491351
\(922\) 1.21318e149 0.231747
\(923\) 6.03867e149 1.09208
\(924\) −4.12770e148 −0.0706763
\(925\) 1.50158e150 2.43440
\(926\) −4.45372e149 −0.683704
\(927\) −4.80332e149 −0.698256
\(928\) 2.45102e149 0.337422
\(929\) −1.59274e149 −0.207659 −0.103829 0.994595i \(-0.533110\pi\)
−0.103829 + 0.994595i \(0.533110\pi\)
\(930\) −6.59441e149 −0.814305
\(931\) −3.72217e148 −0.0435349
\(932\) 8.55695e148 0.0948015
\(933\) −1.58871e148 −0.0166733
\(934\) 1.16638e150 1.15964
\(935\) −1.25866e150 −1.18556
\(936\) −1.49398e150 −1.33325
\(937\) 9.70291e149 0.820451 0.410226 0.911984i \(-0.365450\pi\)
0.410226 + 0.911984i \(0.365450\pi\)
\(938\) −3.04504e150 −2.43977
\(939\) −3.73460e149 −0.283552
\(940\) 3.22344e149 0.231934
\(941\) 2.18073e149 0.148705 0.0743526 0.997232i \(-0.476311\pi\)
0.0743526 + 0.997232i \(0.476311\pi\)
\(942\) 3.15720e149 0.204048
\(943\) −2.17393e149 −0.133170
\(944\) 1.79227e150 1.04068
\(945\) 2.07479e150 1.14201
\(946\) −1.00432e150 −0.524048
\(947\) 2.56888e150 1.27078 0.635389 0.772192i \(-0.280840\pi\)
0.635389 + 0.772192i \(0.280840\pi\)
\(948\) 7.57960e148 0.0355488
\(949\) −4.11254e150 −1.82880
\(950\) 8.53184e149 0.359750
\(951\) −7.26628e148 −0.0290533
\(952\) 1.96055e150 0.743383
\(953\) −4.47909e150 −1.61064 −0.805319 0.592842i \(-0.798006\pi\)
−0.805319 + 0.592842i \(0.798006\pi\)
\(954\) 2.29117e150 0.781383
\(955\) −2.85141e149 −0.0922337
\(956\) 4.35235e149 0.133537
\(957\) 6.94286e149 0.202062
\(958\) 2.63699e150 0.728033
\(959\) 2.28404e150 0.598224
\(960\) 1.44407e150 0.358831
\(961\) 3.83154e150 0.903322
\(962\) −1.04031e151 −2.32714
\(963\) 7.55416e150 1.60346
\(964\) −1.48461e150 −0.299036
\(965\) −1.05032e150 −0.200768
\(966\) 1.25637e150 0.227915
\(967\) −1.06296e151 −1.83012 −0.915060 0.403318i \(-0.867857\pi\)
−0.915060 + 0.403318i \(0.867857\pi\)
\(968\) −1.13607e150 −0.185652
\(969\) −2.47887e149 −0.0384506
\(970\) 8.13030e150 1.19711
\(971\) 2.05230e150 0.286860 0.143430 0.989660i \(-0.454187\pi\)
0.143430 + 0.989660i \(0.454187\pi\)
\(972\) −1.40689e150 −0.186687
\(973\) 8.96693e149 0.112965
\(974\) −2.93074e150 −0.350550
\(975\) −9.33965e150 −1.06071
\(976\) −6.70508e150 −0.723083
\(977\) −1.45556e150 −0.149058 −0.0745289 0.997219i \(-0.523745\pi\)
−0.0745289 + 0.997219i \(0.523745\pi\)
\(978\) 6.58872e150 0.640750
\(979\) −9.24188e150 −0.853561
\(980\) −1.22719e150 −0.107645
\(981\) −1.43310e150 −0.119397
\(982\) 8.97394e150 0.710155
\(983\) −6.44594e150 −0.484545 −0.242272 0.970208i \(-0.577893\pi\)
−0.242272 + 0.970208i \(0.577893\pi\)
\(984\) −8.22376e149 −0.0587243
\(985\) 1.71685e151 1.16467
\(986\) 9.90851e150 0.638593
\(987\) −3.27188e150 −0.200346
\(988\) −1.10938e150 −0.0645439
\(989\) 5.73731e150 0.317172
\(990\) 2.93209e151 1.54028
\(991\) 1.69874e151 0.848024 0.424012 0.905656i \(-0.360621\pi\)
0.424012 + 0.905656i \(0.360621\pi\)
\(992\) 1.31871e151 0.625618
\(993\) 7.44971e150 0.335894
\(994\) 1.84606e151 0.791103
\(995\) −6.46652e151 −2.63394
\(996\) 1.84237e149 0.00713312
\(997\) −9.31202e150 −0.342719 −0.171360 0.985209i \(-0.554816\pi\)
−0.171360 + 0.985209i \(0.554816\pi\)
\(998\) −5.74712e151 −2.01075
\(999\) 2.13839e151 0.711264
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.1.3 8
3.2 odd 2 9.102.a.b.1.6 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.102.a.a.1.3 8 1.1 even 1 trivial
9.102.a.b.1.6 8 3.2 odd 2