Properties

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

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.1
Root \(-7.21371e13\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.15346e16 q^{2} +2.00325e25 q^{3} +9.24825e31 q^{4} -4.02660e36 q^{5} -2.31067e41 q^{6} -1.49411e43 q^{7} -5.98851e47 q^{8} +2.76064e50 q^{9} +O(q^{10})\) \(q-1.15346e16 q^{2} +2.00325e25 q^{3} +9.24825e31 q^{4} -4.02660e36 q^{5} -2.31067e41 q^{6} -1.49411e43 q^{7} -5.98851e47 q^{8} +2.76064e50 q^{9} +4.64453e52 q^{10} -4.19278e54 q^{11} +1.85266e57 q^{12} +4.35724e58 q^{13} +1.72340e59 q^{14} -8.06629e61 q^{15} +3.15598e63 q^{16} -5.45067e64 q^{17} -3.18429e66 q^{18} +5.82286e66 q^{19} -3.72391e68 q^{20} -2.99307e68 q^{21} +4.83621e70 q^{22} -5.38565e70 q^{23} -1.19965e73 q^{24} -8.43836e72 q^{25} -5.02591e74 q^{26} +3.02144e75 q^{27} -1.38179e75 q^{28} -5.63591e76 q^{29} +9.30415e77 q^{30} +1.44648e78 q^{31} -1.21107e79 q^{32} -8.39919e79 q^{33} +6.28714e80 q^{34} +6.01618e79 q^{35} +2.55311e82 q^{36} -2.11238e81 q^{37} -6.71645e82 q^{38} +8.72864e83 q^{39} +2.41134e84 q^{40} -5.42415e84 q^{41} +3.45239e84 q^{42} -3.33535e85 q^{43} -3.87759e86 q^{44} -1.11160e87 q^{45} +6.21214e86 q^{46} +2.06871e87 q^{47} +6.32221e88 q^{48} -5.41386e88 q^{49} +9.73333e88 q^{50} -1.09190e90 q^{51} +4.02969e90 q^{52} -1.52093e90 q^{53} -3.48512e91 q^{54} +1.68827e91 q^{55} +8.94748e90 q^{56} +1.16646e92 q^{57} +6.50081e92 q^{58} +1.70773e93 q^{59} -7.45991e93 q^{60} +2.17269e93 q^{61} -1.66846e94 q^{62} -4.12469e93 q^{63} +1.16707e94 q^{64} -1.75449e95 q^{65} +9.68814e95 q^{66} +8.39741e94 q^{67} -5.04092e96 q^{68} -1.07888e96 q^{69} -6.93944e95 q^{70} +1.45834e97 q^{71} -1.65321e98 q^{72} +3.40172e97 q^{73} +2.43655e97 q^{74} -1.69041e98 q^{75} +5.38513e98 q^{76} +6.26447e97 q^{77} -1.00682e100 q^{78} -3.48037e99 q^{79} -1.27079e100 q^{80} +2.59537e100 q^{81} +6.25655e100 q^{82} -4.88553e100 q^{83} -2.76807e100 q^{84} +2.19477e101 q^{85} +3.84720e101 q^{86} -1.12901e102 q^{87} +2.51085e102 q^{88} -3.37399e102 q^{89} +1.28219e103 q^{90} -6.51020e101 q^{91} -4.98078e102 q^{92} +2.89766e103 q^{93} -2.38617e103 q^{94} -2.34464e103 q^{95} -2.42608e104 q^{96} -3.41463e104 q^{97} +6.24468e104 q^{98} -1.15748e105 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 9175032489175920q^{2} - \)\(35\!\cdots\!80\)\(q^{3} + \)\(12\!\cdots\!76\)\(q^{4} + \)\(74\!\cdots\!00\)\(q^{5} - \)\(13\!\cdots\!64\)\(q^{6} + \)\(70\!\cdots\!00\)\(q^{7} - \)\(70\!\cdots\!60\)\(q^{8} + \)\(31\!\cdots\!84\)\(q^{9} + O(q^{10}) \) \( 8q - 9175032489175920q^{2} - \)\(35\!\cdots\!80\)\(q^{3} + \)\(12\!\cdots\!76\)\(q^{4} + \)\(74\!\cdots\!00\)\(q^{5} - \)\(13\!\cdots\!64\)\(q^{6} + \)\(70\!\cdots\!00\)\(q^{7} - \)\(70\!\cdots\!60\)\(q^{8} + \)\(31\!\cdots\!84\)\(q^{9} + \)\(44\!\cdots\!00\)\(q^{10} - \)\(91\!\cdots\!84\)\(q^{11} + \)\(15\!\cdots\!60\)\(q^{12} + \)\(40\!\cdots\!40\)\(q^{13} - \)\(16\!\cdots\!28\)\(q^{14} - \)\(85\!\cdots\!00\)\(q^{15} + \)\(88\!\cdots\!48\)\(q^{16} - \)\(47\!\cdots\!60\)\(q^{17} - \)\(26\!\cdots\!80\)\(q^{18} - \)\(18\!\cdots\!20\)\(q^{19} - \)\(43\!\cdots\!00\)\(q^{20} + \)\(34\!\cdots\!56\)\(q^{21} + \)\(61\!\cdots\!60\)\(q^{22} + \)\(35\!\cdots\!60\)\(q^{23} - \)\(85\!\cdots\!60\)\(q^{24} + \)\(36\!\cdots\!00\)\(q^{25} - \)\(17\!\cdots\!24\)\(q^{26} + \)\(41\!\cdots\!40\)\(q^{27} - \)\(10\!\cdots\!60\)\(q^{28} - \)\(13\!\cdots\!80\)\(q^{29} + \)\(36\!\cdots\!00\)\(q^{30} + \)\(21\!\cdots\!16\)\(q^{31} + \)\(10\!\cdots\!80\)\(q^{32} - \)\(11\!\cdots\!60\)\(q^{33} + \)\(62\!\cdots\!52\)\(q^{34} - \)\(18\!\cdots\!00\)\(q^{35} + \)\(16\!\cdots\!48\)\(q^{36} - \)\(23\!\cdots\!80\)\(q^{37} + \)\(81\!\cdots\!60\)\(q^{38} + \)\(97\!\cdots\!48\)\(q^{39} + \)\(16\!\cdots\!00\)\(q^{40} - \)\(91\!\cdots\!84\)\(q^{41} - \)\(99\!\cdots\!60\)\(q^{42} + \)\(30\!\cdots\!00\)\(q^{43} - \)\(61\!\cdots\!48\)\(q^{44} - \)\(72\!\cdots\!00\)\(q^{45} - \)\(19\!\cdots\!84\)\(q^{46} - \)\(19\!\cdots\!40\)\(q^{47} + \)\(47\!\cdots\!60\)\(q^{48} + \)\(90\!\cdots\!56\)\(q^{49} + \)\(12\!\cdots\!00\)\(q^{50} - \)\(10\!\cdots\!04\)\(q^{51} + \)\(26\!\cdots\!00\)\(q^{52} - \)\(50\!\cdots\!80\)\(q^{53} - \)\(33\!\cdots\!20\)\(q^{54} + \)\(18\!\cdots\!00\)\(q^{55} + \)\(77\!\cdots\!80\)\(q^{56} - \)\(17\!\cdots\!20\)\(q^{57} + \)\(52\!\cdots\!40\)\(q^{58} - \)\(80\!\cdots\!60\)\(q^{59} - \)\(49\!\cdots\!00\)\(q^{60} + \)\(93\!\cdots\!16\)\(q^{61} - \)\(24\!\cdots\!40\)\(q^{62} - \)\(69\!\cdots\!20\)\(q^{63} - \)\(97\!\cdots\!04\)\(q^{64} - \)\(36\!\cdots\!00\)\(q^{65} + \)\(15\!\cdots\!72\)\(q^{66} - \)\(11\!\cdots\!60\)\(q^{67} - \)\(97\!\cdots\!80\)\(q^{68} - \)\(15\!\cdots\!32\)\(q^{69} - \)\(42\!\cdots\!00\)\(q^{70} - \)\(50\!\cdots\!84\)\(q^{71} - \)\(31\!\cdots\!80\)\(q^{72} - \)\(30\!\cdots\!40\)\(q^{73} - \)\(92\!\cdots\!88\)\(q^{74} - \)\(20\!\cdots\!00\)\(q^{75} - \)\(31\!\cdots\!40\)\(q^{76} - \)\(59\!\cdots\!00\)\(q^{77} - \)\(21\!\cdots\!00\)\(q^{78} - \)\(15\!\cdots\!80\)\(q^{79} - \)\(36\!\cdots\!00\)\(q^{80} - \)\(16\!\cdots\!72\)\(q^{81} + \)\(40\!\cdots\!60\)\(q^{82} - \)\(27\!\cdots\!20\)\(q^{83} + \)\(24\!\cdots\!32\)\(q^{84} + \)\(11\!\cdots\!00\)\(q^{85} + \)\(20\!\cdots\!96\)\(q^{86} + \)\(24\!\cdots\!20\)\(q^{87} + \)\(65\!\cdots\!80\)\(q^{88} + \)\(45\!\cdots\!60\)\(q^{89} + \)\(27\!\cdots\!00\)\(q^{90} + \)\(27\!\cdots\!96\)\(q^{91} + \)\(11\!\cdots\!40\)\(q^{92} - \)\(18\!\cdots\!60\)\(q^{93} - \)\(14\!\cdots\!08\)\(q^{94} - \)\(19\!\cdots\!00\)\(q^{95} - \)\(72\!\cdots\!64\)\(q^{96} - \)\(76\!\cdots\!40\)\(q^{97} - \)\(13\!\cdots\!40\)\(q^{98} - \)\(25\!\cdots\!32\)\(q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.15346e16 −1.81104 −0.905521 0.424302i \(-0.860519\pi\)
−0.905521 + 0.424302i \(0.860519\pi\)
\(3\) 2.00325e25 1.79007 0.895033 0.446000i \(-0.147152\pi\)
0.895033 + 0.446000i \(0.147152\pi\)
\(4\) 9.24825e31 2.27987
\(5\) −4.02660e36 −0.810987 −0.405493 0.914098i \(-0.632900\pi\)
−0.405493 + 0.914098i \(0.632900\pi\)
\(6\) −2.31067e41 −3.24188
\(7\) −1.49411e43 −0.0640819 −0.0320409 0.999487i \(-0.510201\pi\)
−0.0320409 + 0.999487i \(0.510201\pi\)
\(8\) −5.98851e47 −2.31790
\(9\) 2.76064e50 2.20434
\(10\) 4.64453e52 1.46873
\(11\) −4.19278e54 −0.889993 −0.444996 0.895532i \(-0.646795\pi\)
−0.444996 + 0.895532i \(0.646795\pi\)
\(12\) 1.85266e57 4.08112
\(13\) 4.35724e58 1.43610 0.718052 0.695990i \(-0.245034\pi\)
0.718052 + 0.695990i \(0.245034\pi\)
\(14\) 1.72340e59 0.116055
\(15\) −8.06629e61 −1.45172
\(16\) 3.15598e63 1.91794
\(17\) −5.45067e64 −1.37367 −0.686833 0.726815i \(-0.741000\pi\)
−0.686833 + 0.726815i \(0.741000\pi\)
\(18\) −3.18429e66 −3.99214
\(19\) 5.82286e66 0.427142 0.213571 0.976928i \(-0.431490\pi\)
0.213571 + 0.976928i \(0.431490\pi\)
\(20\) −3.72391e68 −1.84894
\(21\) −2.99307e68 −0.114711
\(22\) 4.83621e70 1.61181
\(23\) −5.38565e70 −0.173991 −0.0869954 0.996209i \(-0.527727\pi\)
−0.0869954 + 0.996209i \(0.527727\pi\)
\(24\) −1.19965e73 −4.14919
\(25\) −8.43836e72 −0.342301
\(26\) −5.02591e74 −2.60084
\(27\) 3.02144e75 2.15584
\(28\) −1.38179e75 −0.146098
\(29\) −5.63591e76 −0.944211 −0.472106 0.881542i \(-0.656506\pi\)
−0.472106 + 0.881542i \(0.656506\pi\)
\(30\) 9.30415e77 2.62912
\(31\) 1.44648e78 0.730841 0.365421 0.930843i \(-0.380925\pi\)
0.365421 + 0.930843i \(0.380925\pi\)
\(32\) −1.21107e79 −1.15557
\(33\) −8.39919e79 −1.59315
\(34\) 6.28714e80 2.48777
\(35\) 6.01618e79 0.0519695
\(36\) 2.55311e82 5.02560
\(37\) −2.11238e81 −0.0986693 −0.0493347 0.998782i \(-0.515710\pi\)
−0.0493347 + 0.998782i \(0.515710\pi\)
\(38\) −6.71645e82 −0.773572
\(39\) 8.72864e83 2.57072
\(40\) 2.41134e84 1.87978
\(41\) −5.42415e84 −1.15659 −0.578295 0.815828i \(-0.696282\pi\)
−0.578295 + 0.815828i \(0.696282\pi\)
\(42\) 3.45239e84 0.207746
\(43\) −3.33535e85 −0.583509 −0.291755 0.956493i \(-0.594239\pi\)
−0.291755 + 0.956493i \(0.594239\pi\)
\(44\) −3.87759e86 −2.02907
\(45\) −1.11160e87 −1.78769
\(46\) 6.21214e86 0.315105
\(47\) 2.06871e87 0.339282 0.169641 0.985506i \(-0.445739\pi\)
0.169641 + 0.985506i \(0.445739\pi\)
\(48\) 6.32221e88 3.43324
\(49\) −5.41386e88 −0.995894
\(50\) 9.73333e88 0.619921
\(51\) −1.09190e90 −2.45895
\(52\) 4.02969e90 3.27413
\(53\) −1.52093e90 −0.454596 −0.227298 0.973825i \(-0.572989\pi\)
−0.227298 + 0.973825i \(0.572989\pi\)
\(54\) −3.48512e91 −3.90432
\(55\) 1.68827e91 0.721772
\(56\) 8.94748e90 0.148535
\(57\) 1.16646e92 0.764613
\(58\) 6.50081e92 1.71001
\(59\) 1.70773e93 1.83100 0.915499 0.402320i \(-0.131796\pi\)
0.915499 + 0.402320i \(0.131796\pi\)
\(60\) −7.45991e93 −3.30973
\(61\) 2.17269e93 0.404745 0.202372 0.979309i \(-0.435135\pi\)
0.202372 + 0.979309i \(0.435135\pi\)
\(62\) −1.66846e94 −1.32358
\(63\) −4.12469e93 −0.141258
\(64\) 1.16707e94 0.174843
\(65\) −1.75449e95 −1.16466
\(66\) 9.68814e95 2.88525
\(67\) 8.39741e94 0.113558 0.0567791 0.998387i \(-0.481917\pi\)
0.0567791 + 0.998387i \(0.481917\pi\)
\(68\) −5.04092e96 −3.13178
\(69\) −1.07888e96 −0.311455
\(70\) −6.93944e95 −0.0941190
\(71\) 1.45834e97 0.939278 0.469639 0.882859i \(-0.344384\pi\)
0.469639 + 0.882859i \(0.344384\pi\)
\(72\) −1.65321e98 −5.10943
\(73\) 3.40172e97 0.509622 0.254811 0.966991i \(-0.417987\pi\)
0.254811 + 0.966991i \(0.417987\pi\)
\(74\) 2.43655e97 0.178694
\(75\) −1.69041e98 −0.612741
\(76\) 5.38513e98 0.973829
\(77\) 6.26447e97 0.0570324
\(78\) −1.00682e100 −4.65568
\(79\) −3.48037e99 −0.824523 −0.412261 0.911066i \(-0.635261\pi\)
−0.412261 + 0.911066i \(0.635261\pi\)
\(80\) −1.27079e100 −1.55542
\(81\) 2.59537e100 1.65476
\(82\) 6.25655e100 2.09463
\(83\) −4.88553e100 −0.865589 −0.432795 0.901493i \(-0.642472\pi\)
−0.432795 + 0.901493i \(0.642472\pi\)
\(84\) −2.76807e100 −0.261526
\(85\) 2.19477e101 1.11403
\(86\) 3.84720e101 1.05676
\(87\) −1.12901e102 −1.69020
\(88\) 2.51085e102 2.06291
\(89\) −3.37399e102 −1.53168 −0.765841 0.643030i \(-0.777677\pi\)
−0.765841 + 0.643030i \(0.777677\pi\)
\(90\) 1.28219e103 3.23757
\(91\) −6.51020e101 −0.0920282
\(92\) −4.98078e102 −0.396677
\(93\) 2.89766e103 1.30825
\(94\) −2.38617e103 −0.614454
\(95\) −2.34464e103 −0.346407
\(96\) −2.42608e104 −2.06854
\(97\) −3.41463e104 −1.68977 −0.844885 0.534948i \(-0.820331\pi\)
−0.844885 + 0.534948i \(0.820331\pi\)
\(98\) 6.24468e104 1.80360
\(99\) −1.15748e105 −1.96184
\(100\) −7.80401e104 −0.780401
\(101\) 9.40507e104 0.557814 0.278907 0.960318i \(-0.410028\pi\)
0.278907 + 0.960318i \(0.410028\pi\)
\(102\) 1.25947e106 4.45327
\(103\) −7.48693e105 −1.58617 −0.793084 0.609112i \(-0.791526\pi\)
−0.793084 + 0.609112i \(0.791526\pi\)
\(104\) −2.60934e106 −3.32874
\(105\) 1.20519e105 0.0930289
\(106\) 1.75433e106 0.823291
\(107\) 1.11641e106 0.320020 0.160010 0.987115i \(-0.448847\pi\)
0.160010 + 0.987115i \(0.448847\pi\)
\(108\) 2.79431e107 4.91504
\(109\) −6.08327e106 −0.659548 −0.329774 0.944060i \(-0.606973\pi\)
−0.329774 + 0.944060i \(0.606973\pi\)
\(110\) −1.94735e107 −1.30716
\(111\) −4.23163e106 −0.176625
\(112\) −4.71537e106 −0.122905
\(113\) −1.91150e107 −0.312432 −0.156216 0.987723i \(-0.549930\pi\)
−0.156216 + 0.987723i \(0.549930\pi\)
\(114\) −1.34547e108 −1.38475
\(115\) 2.16859e107 0.141104
\(116\) −5.21223e108 −2.15268
\(117\) 1.20288e109 3.16566
\(118\) −1.96980e109 −3.31601
\(119\) 8.14389e107 0.0880271
\(120\) 4.83050e109 3.36494
\(121\) −4.61438e108 −0.207913
\(122\) −2.50611e109 −0.733009
\(123\) −1.08659e110 −2.07037
\(124\) 1.33774e110 1.66622
\(125\) 1.33241e110 1.08859
\(126\) 4.75768e109 0.255824
\(127\) 7.03101e109 0.249645 0.124822 0.992179i \(-0.460164\pi\)
0.124822 + 0.992179i \(0.460164\pi\)
\(128\) 3.56652e110 0.838921
\(129\) −6.68154e110 −1.04452
\(130\) 2.02374e111 2.10925
\(131\) −1.77240e111 −1.23543 −0.617717 0.786401i \(-0.711942\pi\)
−0.617717 + 0.786401i \(0.711942\pi\)
\(132\) −7.76778e111 −3.63217
\(133\) −8.69999e109 −0.0273721
\(134\) −9.68609e110 −0.205658
\(135\) −1.21662e112 −1.74836
\(136\) 3.26414e112 3.18402
\(137\) 1.65935e112 1.10181 0.550907 0.834567i \(-0.314282\pi\)
0.550907 + 0.834567i \(0.314282\pi\)
\(138\) 1.24445e112 0.564058
\(139\) −2.84779e112 −0.883551 −0.441775 0.897126i \(-0.645651\pi\)
−0.441775 + 0.897126i \(0.645651\pi\)
\(140\) 5.56392e111 0.118484
\(141\) 4.14413e112 0.607338
\(142\) −1.68213e113 −1.70107
\(143\) −1.82690e113 −1.27812
\(144\) 8.71251e113 4.22778
\(145\) 2.26936e113 0.765743
\(146\) −3.92375e113 −0.922946
\(147\) −1.08453e114 −1.78272
\(148\) −1.95359e113 −0.224953
\(149\) −1.97570e114 −1.59750 −0.798752 0.601661i \(-0.794506\pi\)
−0.798752 + 0.601661i \(0.794506\pi\)
\(150\) 1.94983e114 1.10970
\(151\) 3.99582e114 1.60441 0.802207 0.597046i \(-0.203659\pi\)
0.802207 + 0.597046i \(0.203659\pi\)
\(152\) −3.48703e114 −0.990072
\(153\) −1.50473e115 −3.02802
\(154\) −7.22583e113 −0.103288
\(155\) −5.82439e114 −0.592702
\(156\) 8.07247e115 5.86091
\(157\) −3.24507e115 −1.68458 −0.842290 0.539024i \(-0.818793\pi\)
−0.842290 + 0.539024i \(0.818793\pi\)
\(158\) 4.01447e115 1.49325
\(159\) −3.04680e115 −0.813756
\(160\) 4.87650e115 0.937150
\(161\) 8.04674e113 0.0111497
\(162\) −2.99366e116 −2.99684
\(163\) 1.98748e116 1.44030 0.720150 0.693818i \(-0.244073\pi\)
0.720150 + 0.693818i \(0.244073\pi\)
\(164\) −5.01639e116 −2.63687
\(165\) 3.38202e116 1.29202
\(166\) 5.63527e116 1.56762
\(167\) −6.79873e116 −1.37979 −0.689895 0.723910i \(-0.742343\pi\)
−0.689895 + 0.723910i \(0.742343\pi\)
\(168\) 1.79240e116 0.265888
\(169\) 9.77997e116 1.06239
\(170\) −2.53158e117 −2.01755
\(171\) 1.60748e117 0.941565
\(172\) −3.08462e117 −1.33033
\(173\) −3.33164e117 −1.05983 −0.529917 0.848049i \(-0.677777\pi\)
−0.529917 + 0.848049i \(0.677777\pi\)
\(174\) 1.30227e118 3.06102
\(175\) 1.26078e116 0.0219353
\(176\) −1.32323e118 −1.70695
\(177\) 3.42100e118 3.27761
\(178\) 3.89177e118 2.77394
\(179\) −1.92920e118 −1.02469 −0.512345 0.858780i \(-0.671223\pi\)
−0.512345 + 0.858780i \(0.671223\pi\)
\(180\) −1.02804e119 −4.07569
\(181\) −3.92801e118 −1.16425 −0.582126 0.813099i \(-0.697779\pi\)
−0.582126 + 0.813099i \(0.697779\pi\)
\(182\) 7.50926e117 0.166667
\(183\) 4.35244e118 0.724520
\(184\) 3.22520e118 0.403293
\(185\) 8.50573e117 0.0800195
\(186\) −3.34233e119 −2.36930
\(187\) 2.28535e119 1.22255
\(188\) 1.91319e119 0.773520
\(189\) −4.51436e118 −0.138150
\(190\) 2.70445e119 0.627357
\(191\) 5.36723e119 0.945145 0.472573 0.881292i \(-0.343325\pi\)
0.472573 + 0.881292i \(0.343325\pi\)
\(192\) 2.33793e119 0.312980
\(193\) −1.23058e120 −1.25416 −0.627079 0.778956i \(-0.715750\pi\)
−0.627079 + 0.778956i \(0.715750\pi\)
\(194\) 3.93865e120 3.06024
\(195\) −3.51468e120 −2.08482
\(196\) −5.00688e120 −2.27051
\(197\) −3.21266e120 −1.11529 −0.557644 0.830080i \(-0.688295\pi\)
−0.557644 + 0.830080i \(0.688295\pi\)
\(198\) 1.33510e121 3.55298
\(199\) −2.12151e120 −0.433369 −0.216685 0.976242i \(-0.569524\pi\)
−0.216685 + 0.976242i \(0.569524\pi\)
\(200\) 5.05332e120 0.793418
\(201\) 1.68221e120 0.203277
\(202\) −1.08484e121 −1.01023
\(203\) 8.42066e119 0.0605068
\(204\) −1.00982e122 −5.60610
\(205\) 2.18409e121 0.937979
\(206\) 8.63588e121 2.87262
\(207\) −1.48678e121 −0.383534
\(208\) 1.37514e122 2.75436
\(209\) −2.44140e121 −0.380153
\(210\) −1.39014e121 −0.168479
\(211\) 1.16118e122 1.09665 0.548327 0.836264i \(-0.315265\pi\)
0.548327 + 0.836264i \(0.315265\pi\)
\(212\) −1.40659e122 −1.03642
\(213\) 2.92141e122 1.68137
\(214\) −1.28774e122 −0.579570
\(215\) 1.34301e122 0.473218
\(216\) −1.80939e123 −4.99702
\(217\) −2.16120e121 −0.0468336
\(218\) 7.01682e122 1.19447
\(219\) 6.81449e122 0.912257
\(220\) 1.56135e123 1.64555
\(221\) −2.37499e123 −1.97273
\(222\) 4.88102e122 0.319874
\(223\) 7.24098e122 0.374793 0.187397 0.982284i \(-0.439995\pi\)
0.187397 + 0.982284i \(0.439995\pi\)
\(224\) 1.80947e122 0.0740510
\(225\) −2.32953e123 −0.754546
\(226\) 2.20484e123 0.565828
\(227\) −2.60705e123 −0.530630 −0.265315 0.964162i \(-0.585476\pi\)
−0.265315 + 0.964162i \(0.585476\pi\)
\(228\) 1.07878e124 1.74322
\(229\) −3.82412e123 −0.491098 −0.245549 0.969384i \(-0.578968\pi\)
−0.245549 + 0.969384i \(0.578968\pi\)
\(230\) −2.50138e123 −0.255546
\(231\) 1.25493e123 0.102092
\(232\) 3.37507e124 2.18859
\(233\) 2.49183e124 1.28923 0.644617 0.764505i \(-0.277017\pi\)
0.644617 + 0.764505i \(0.277017\pi\)
\(234\) −1.38747e125 −5.73313
\(235\) −8.32986e123 −0.275153
\(236\) 1.57935e125 4.17444
\(237\) −6.97204e124 −1.47595
\(238\) −9.39366e123 −0.159421
\(239\) −7.40706e123 −0.100869 −0.0504343 0.998727i \(-0.516061\pi\)
−0.0504343 + 0.998727i \(0.516061\pi\)
\(240\) −2.54570e125 −2.78431
\(241\) −4.19382e124 −0.368735 −0.184368 0.982857i \(-0.559024\pi\)
−0.184368 + 0.982857i \(0.559024\pi\)
\(242\) 5.32251e124 0.376539
\(243\) 1.41521e125 0.806290
\(244\) 2.00936e125 0.922765
\(245\) 2.17995e125 0.807656
\(246\) 1.25334e126 3.74953
\(247\) 2.53716e125 0.613421
\(248\) −8.66225e125 −1.69402
\(249\) −9.78693e125 −1.54946
\(250\) −1.53689e126 −1.97148
\(251\) 2.46814e125 0.256744 0.128372 0.991726i \(-0.459025\pi\)
0.128372 + 0.991726i \(0.459025\pi\)
\(252\) −3.81462e125 −0.322050
\(253\) 2.25809e125 0.154851
\(254\) −8.10999e125 −0.452117
\(255\) 4.39667e126 1.99418
\(256\) −4.58726e126 −1.69416
\(257\) 1.85222e126 0.557448 0.278724 0.960371i \(-0.410089\pi\)
0.278724 + 0.960371i \(0.410089\pi\)
\(258\) 7.70690e126 1.89167
\(259\) 3.15613e124 0.00632291
\(260\) −1.62260e127 −2.65528
\(261\) −1.55587e127 −2.08136
\(262\) 2.04440e127 2.23742
\(263\) −1.47726e127 −1.32367 −0.661834 0.749650i \(-0.730222\pi\)
−0.661834 + 0.749650i \(0.730222\pi\)
\(264\) 5.02986e127 3.69275
\(265\) 6.12417e126 0.368671
\(266\) 1.00351e126 0.0495719
\(267\) −6.75894e127 −2.74181
\(268\) 7.76614e126 0.258898
\(269\) 4.07814e127 1.11807 0.559033 0.829145i \(-0.311172\pi\)
0.559033 + 0.829145i \(0.311172\pi\)
\(270\) 1.40332e128 3.16635
\(271\) −2.10498e127 −0.391165 −0.195582 0.980687i \(-0.562660\pi\)
−0.195582 + 0.980687i \(0.562660\pi\)
\(272\) −1.72022e128 −2.63461
\(273\) −1.30415e127 −0.164737
\(274\) −1.91400e128 −1.99543
\(275\) 3.53802e127 0.304645
\(276\) −9.97775e127 −0.710077
\(277\) −1.88787e128 −1.11118 −0.555590 0.831456i \(-0.687508\pi\)
−0.555590 + 0.831456i \(0.687508\pi\)
\(278\) 3.28482e128 1.60015
\(279\) 3.99320e128 1.61102
\(280\) −3.60280e127 −0.120460
\(281\) 1.51465e128 0.419982 0.209991 0.977703i \(-0.432657\pi\)
0.209991 + 0.977703i \(0.432657\pi\)
\(282\) −4.78010e128 −1.09991
\(283\) −9.04953e127 −0.172917 −0.0864586 0.996255i \(-0.527555\pi\)
−0.0864586 + 0.996255i \(0.527555\pi\)
\(284\) 1.34871e129 2.14143
\(285\) −4.69689e128 −0.620091
\(286\) 2.10726e129 2.31473
\(287\) 8.10427e127 0.0741164
\(288\) −3.34333e129 −2.54726
\(289\) 1.39650e129 0.886960
\(290\) −2.61762e129 −1.38679
\(291\) −6.84036e129 −3.02480
\(292\) 3.14599e129 1.16187
\(293\) 6.96245e128 0.214888 0.107444 0.994211i \(-0.465733\pi\)
0.107444 + 0.994211i \(0.465733\pi\)
\(294\) 1.25096e130 3.22857
\(295\) −6.87634e129 −1.48491
\(296\) 1.26500e129 0.228705
\(297\) −1.26683e130 −1.91868
\(298\) 2.27889e130 2.89314
\(299\) −2.34666e129 −0.249869
\(300\) −1.56334e130 −1.39697
\(301\) 4.98338e128 0.0373923
\(302\) −4.60903e130 −2.90566
\(303\) 1.88407e130 0.998525
\(304\) 1.83768e130 0.819233
\(305\) −8.74856e129 −0.328243
\(306\) 1.73565e131 5.48387
\(307\) 4.13248e129 0.110014 0.0550068 0.998486i \(-0.482482\pi\)
0.0550068 + 0.998486i \(0.482482\pi\)
\(308\) 5.79354e129 0.130026
\(309\) −1.49982e131 −2.83935
\(310\) 6.71821e130 1.07341
\(311\) −3.52591e130 −0.475719 −0.237859 0.971300i \(-0.576446\pi\)
−0.237859 + 0.971300i \(0.576446\pi\)
\(312\) −5.22716e131 −5.95867
\(313\) 1.39264e131 1.34202 0.671011 0.741447i \(-0.265860\pi\)
0.671011 + 0.741447i \(0.265860\pi\)
\(314\) 3.74306e131 3.05084
\(315\) 1.66085e130 0.114558
\(316\) −3.21873e131 −1.87981
\(317\) −2.13768e131 −1.05762 −0.528812 0.848739i \(-0.677362\pi\)
−0.528812 + 0.848739i \(0.677362\pi\)
\(318\) 3.51436e131 1.47375
\(319\) 2.36301e131 0.840341
\(320\) −4.69932e130 −0.141795
\(321\) 2.23646e131 0.572857
\(322\) −9.28161e129 −0.0201925
\(323\) −3.17385e131 −0.586751
\(324\) 2.40026e132 3.77264
\(325\) −3.67680e131 −0.491579
\(326\) −2.29248e132 −2.60844
\(327\) −1.21863e132 −1.18063
\(328\) 3.24826e132 2.68086
\(329\) −3.09087e130 −0.0217418
\(330\) −3.90103e132 −2.33990
\(331\) 1.84900e132 0.946166 0.473083 0.881018i \(-0.343141\pi\)
0.473083 + 0.881018i \(0.343141\pi\)
\(332\) −4.51826e132 −1.97343
\(333\) −5.83153e131 −0.217500
\(334\) 7.84207e132 2.49886
\(335\) −3.38130e131 −0.0920941
\(336\) −9.44606e131 −0.220008
\(337\) 1.77864e132 0.354421 0.177210 0.984173i \(-0.443293\pi\)
0.177210 + 0.984173i \(0.443293\pi\)
\(338\) −1.12808e133 −1.92404
\(339\) −3.82921e132 −0.559275
\(340\) 2.02978e133 2.53983
\(341\) −6.06477e132 −0.650443
\(342\) −1.85417e133 −1.70521
\(343\) 1.62111e132 0.127901
\(344\) 1.99738e133 1.35251
\(345\) 4.34422e132 0.252586
\(346\) 3.84292e133 1.91940
\(347\) 1.92289e133 0.825387 0.412694 0.910870i \(-0.364588\pi\)
0.412694 + 0.910870i \(0.364588\pi\)
\(348\) −1.04414e134 −3.85344
\(349\) 2.67204e133 0.848220 0.424110 0.905611i \(-0.360587\pi\)
0.424110 + 0.905611i \(0.360587\pi\)
\(350\) −1.45427e132 −0.0397257
\(351\) 1.31652e134 3.09601
\(352\) 5.07776e133 1.02845
\(353\) 7.63262e133 1.33199 0.665996 0.745955i \(-0.268007\pi\)
0.665996 + 0.745955i \(0.268007\pi\)
\(354\) −3.94599e134 −5.93588
\(355\) −5.87214e133 −0.761742
\(356\) −3.12035e134 −3.49204
\(357\) 1.63142e133 0.157574
\(358\) 2.22526e134 1.85576
\(359\) −3.74967e133 −0.270106 −0.135053 0.990838i \(-0.543120\pi\)
−0.135053 + 0.990838i \(0.543120\pi\)
\(360\) 6.65682e134 4.14368
\(361\) −1.51930e134 −0.817549
\(362\) 4.53080e134 2.10851
\(363\) −9.24376e133 −0.372178
\(364\) −6.02079e133 −0.209812
\(365\) −1.36974e134 −0.413297
\(366\) −5.02037e134 −1.31213
\(367\) 8.36768e134 1.89512 0.947560 0.319578i \(-0.103541\pi\)
0.947560 + 0.319578i \(0.103541\pi\)
\(368\) −1.69970e134 −0.333704
\(369\) −1.49741e135 −2.54951
\(370\) −9.81103e133 −0.144919
\(371\) 2.27243e133 0.0291313
\(372\) 2.67983e135 2.98265
\(373\) −3.45717e134 −0.334200 −0.167100 0.985940i \(-0.553440\pi\)
−0.167100 + 0.985940i \(0.553440\pi\)
\(374\) −2.63606e135 −2.21409
\(375\) 2.66916e135 1.94864
\(376\) −1.23885e135 −0.786422
\(377\) −2.45570e135 −1.35599
\(378\) 5.20714e134 0.250196
\(379\) 8.50571e134 0.355756 0.177878 0.984053i \(-0.443077\pi\)
0.177878 + 0.984053i \(0.443077\pi\)
\(380\) −2.16838e135 −0.789762
\(381\) 1.40849e135 0.446880
\(382\) −6.19090e135 −1.71170
\(383\) 5.56925e135 1.34234 0.671168 0.741305i \(-0.265793\pi\)
0.671168 + 0.741305i \(0.265793\pi\)
\(384\) 7.14462e135 1.50172
\(385\) −2.52246e134 −0.0462525
\(386\) 1.41943e136 2.27133
\(387\) −9.20770e135 −1.28625
\(388\) −3.15794e136 −3.85246
\(389\) −3.38533e135 −0.360784 −0.180392 0.983595i \(-0.557737\pi\)
−0.180392 + 0.983595i \(0.557737\pi\)
\(390\) 4.05405e136 3.77569
\(391\) 2.93554e135 0.239005
\(392\) 3.24210e136 2.30838
\(393\) −3.55056e136 −2.21151
\(394\) 3.70568e136 2.01983
\(395\) 1.40141e136 0.668677
\(396\) −1.07046e137 −4.47275
\(397\) −4.90612e136 −1.79571 −0.897856 0.440290i \(-0.854876\pi\)
−0.897856 + 0.440290i \(0.854876\pi\)
\(398\) 2.44708e136 0.784849
\(399\) −1.74282e135 −0.0489978
\(400\) −2.66313e136 −0.656512
\(401\) 1.98317e136 0.428826 0.214413 0.976743i \(-0.431216\pi\)
0.214413 + 0.976743i \(0.431216\pi\)
\(402\) −1.94036e136 −0.368142
\(403\) 6.30266e136 1.04956
\(404\) 8.69804e136 1.27174
\(405\) −1.04505e137 −1.34199
\(406\) −9.71291e135 −0.109580
\(407\) 8.85677e135 0.0878150
\(408\) 6.53888e137 5.69960
\(409\) −1.84011e137 −1.41049 −0.705246 0.708963i \(-0.749163\pi\)
−0.705246 + 0.708963i \(0.749163\pi\)
\(410\) −2.51926e137 −1.69872
\(411\) 3.32409e137 1.97232
\(412\) −6.92410e137 −3.61626
\(413\) −2.55153e136 −0.117334
\(414\) 1.71495e137 0.694597
\(415\) 1.96721e137 0.701981
\(416\) −5.27693e137 −1.65952
\(417\) −5.70484e137 −1.58161
\(418\) 2.81606e137 0.688474
\(419\) 4.70201e137 1.01402 0.507011 0.861940i \(-0.330750\pi\)
0.507011 + 0.861940i \(0.330750\pi\)
\(420\) 1.11459e137 0.212094
\(421\) 1.06651e138 1.79124 0.895622 0.444817i \(-0.146731\pi\)
0.895622 + 0.444817i \(0.146731\pi\)
\(422\) −1.33937e138 −1.98609
\(423\) 5.71095e137 0.747892
\(424\) 9.10809e137 1.05371
\(425\) 4.59947e137 0.470207
\(426\) −3.36973e138 −3.04503
\(427\) −3.24623e136 −0.0259368
\(428\) 1.03249e138 0.729604
\(429\) −3.65973e138 −2.28792
\(430\) −1.54911e138 −0.857017
\(431\) 2.22553e138 1.08987 0.544937 0.838477i \(-0.316554\pi\)
0.544937 + 0.838477i \(0.316554\pi\)
\(432\) 9.53560e138 4.13477
\(433\) 2.56876e138 0.986525 0.493263 0.869880i \(-0.335804\pi\)
0.493263 + 0.869880i \(0.335804\pi\)
\(434\) 2.49286e137 0.0848177
\(435\) 4.54609e138 1.37073
\(436\) −5.62597e138 −1.50368
\(437\) −3.13599e137 −0.0743189
\(438\) −7.86025e138 −1.65213
\(439\) −1.19025e138 −0.221947 −0.110973 0.993823i \(-0.535397\pi\)
−0.110973 + 0.993823i \(0.535397\pi\)
\(440\) −1.01102e139 −1.67299
\(441\) −1.49457e139 −2.19528
\(442\) 2.73946e139 3.57269
\(443\) −1.45385e138 −0.168393 −0.0841963 0.996449i \(-0.526832\pi\)
−0.0841963 + 0.996449i \(0.526832\pi\)
\(444\) −3.91352e138 −0.402681
\(445\) 1.35857e139 1.24217
\(446\) −8.35219e138 −0.678766
\(447\) −3.95782e139 −2.85964
\(448\) −1.74373e137 −0.0112042
\(449\) −1.37731e138 −0.0787227 −0.0393613 0.999225i \(-0.512532\pi\)
−0.0393613 + 0.999225i \(0.512532\pi\)
\(450\) 2.68702e139 1.36651
\(451\) 2.27423e139 1.02936
\(452\) −1.76780e139 −0.712306
\(453\) 8.00463e139 2.87201
\(454\) 3.00713e139 0.960993
\(455\) 2.62140e138 0.0746336
\(456\) −6.98538e139 −1.77229
\(457\) 3.38698e139 0.765970 0.382985 0.923755i \(-0.374896\pi\)
0.382985 + 0.923755i \(0.374896\pi\)
\(458\) 4.41097e139 0.889399
\(459\) −1.64689e140 −2.96141
\(460\) 2.00556e139 0.321699
\(461\) 2.63171e139 0.376651 0.188325 0.982107i \(-0.439694\pi\)
0.188325 + 0.982107i \(0.439694\pi\)
\(462\) −1.44751e139 −0.184892
\(463\) 1.79225e139 0.204360 0.102180 0.994766i \(-0.467418\pi\)
0.102180 + 0.994766i \(0.467418\pi\)
\(464\) −1.77868e140 −1.81094
\(465\) −1.16677e140 −1.06098
\(466\) −2.87423e140 −2.33486
\(467\) 1.27444e140 0.925087 0.462543 0.886597i \(-0.346937\pi\)
0.462543 + 0.886597i \(0.346937\pi\)
\(468\) 1.11245e141 7.21728
\(469\) −1.25466e138 −0.00727702
\(470\) 9.60817e139 0.498314
\(471\) −6.50067e140 −3.01551
\(472\) −1.02267e141 −4.24407
\(473\) 1.39844e140 0.519319
\(474\) 8.04198e140 2.67301
\(475\) −4.91354e139 −0.146211
\(476\) 7.53168e139 0.200690
\(477\) −4.19873e140 −1.00208
\(478\) 8.54375e139 0.182677
\(479\) 2.18412e140 0.418467 0.209233 0.977866i \(-0.432903\pi\)
0.209233 + 0.977866i \(0.432903\pi\)
\(480\) 9.76885e140 1.67756
\(481\) −9.20417e139 −0.141699
\(482\) 4.83741e140 0.667795
\(483\) 1.61196e139 0.0199586
\(484\) −4.26750e140 −0.474015
\(485\) 1.37494e141 1.37038
\(486\) −1.63239e141 −1.46023
\(487\) −6.62572e140 −0.532062 −0.266031 0.963964i \(-0.585712\pi\)
−0.266031 + 0.963964i \(0.585712\pi\)
\(488\) −1.30112e141 −0.938157
\(489\) 3.98141e141 2.57823
\(490\) −2.51449e141 −1.46270
\(491\) −1.37473e141 −0.718518 −0.359259 0.933238i \(-0.616971\pi\)
−0.359259 + 0.933238i \(0.616971\pi\)
\(492\) −1.00491e142 −4.72018
\(493\) 3.07195e141 1.29703
\(494\) −2.92652e141 −1.11093
\(495\) 4.66070e141 1.59103
\(496\) 4.56505e141 1.40171
\(497\) −2.17891e140 −0.0601907
\(498\) 1.12888e142 2.80614
\(499\) 3.23152e141 0.722983 0.361491 0.932375i \(-0.382268\pi\)
0.361491 + 0.932375i \(0.382268\pi\)
\(500\) 1.23225e142 2.48184
\(501\) −1.36195e142 −2.46991
\(502\) −2.84691e141 −0.464974
\(503\) −9.98096e141 −1.46843 −0.734215 0.678917i \(-0.762450\pi\)
−0.734215 + 0.678917i \(0.762450\pi\)
\(504\) 2.47008e141 0.327422
\(505\) −3.78705e141 −0.452380
\(506\) −2.60461e141 −0.280441
\(507\) 1.95917e142 1.90176
\(508\) 6.50245e141 0.569157
\(509\) −9.19610e141 −0.725972 −0.362986 0.931795i \(-0.618243\pi\)
−0.362986 + 0.931795i \(0.618243\pi\)
\(510\) −5.07139e142 −3.61154
\(511\) −5.08254e140 −0.0326575
\(512\) 3.84448e142 2.22928
\(513\) 1.75934e142 0.920851
\(514\) −2.13647e142 −1.00956
\(515\) 3.01469e142 1.28636
\(516\) −6.17925e142 −2.38137
\(517\) −8.67363e141 −0.301959
\(518\) −3.64047e140 −0.0114511
\(519\) −6.67411e142 −1.89717
\(520\) 1.05068e143 2.69957
\(521\) −3.87902e142 −0.901034 −0.450517 0.892768i \(-0.648760\pi\)
−0.450517 + 0.892768i \(0.648760\pi\)
\(522\) 1.79464e143 3.76943
\(523\) 3.97356e142 0.754815 0.377408 0.926047i \(-0.376816\pi\)
0.377408 + 0.926047i \(0.376816\pi\)
\(524\) −1.63916e143 −2.81663
\(525\) 2.52566e141 0.0392656
\(526\) 1.70396e143 2.39722
\(527\) −7.88427e142 −1.00393
\(528\) −2.65076e143 −3.05556
\(529\) −9.29121e142 −0.969727
\(530\) −7.06400e142 −0.667678
\(531\) 4.71442e143 4.03613
\(532\) −8.04597e141 −0.0624048
\(533\) −2.36343e143 −1.66098
\(534\) 7.79618e143 4.96553
\(535\) −4.49536e142 −0.259532
\(536\) −5.02880e142 −0.263216
\(537\) −3.86466e143 −1.83426
\(538\) −4.70398e143 −2.02486
\(539\) 2.26991e143 0.886338
\(540\) −1.12516e144 −3.98603
\(541\) 2.44851e143 0.787129 0.393564 0.919297i \(-0.371242\pi\)
0.393564 + 0.919297i \(0.371242\pi\)
\(542\) 2.42801e143 0.708416
\(543\) −7.86877e143 −2.08409
\(544\) 6.60114e143 1.58737
\(545\) 2.44949e143 0.534884
\(546\) 1.50429e143 0.298345
\(547\) −3.00103e142 −0.0540675 −0.0270337 0.999635i \(-0.508606\pi\)
−0.0270337 + 0.999635i \(0.508606\pi\)
\(548\) 1.53461e144 2.51199
\(549\) 5.99801e143 0.892193
\(550\) −4.08097e143 −0.551725
\(551\) −3.28171e143 −0.403313
\(552\) 6.46088e143 0.721921
\(553\) 5.20005e142 0.0528370
\(554\) 2.17759e144 2.01239
\(555\) 1.70391e143 0.143240
\(556\) −2.63371e144 −2.01438
\(557\) −5.76286e143 −0.401089 −0.200544 0.979685i \(-0.564271\pi\)
−0.200544 + 0.979685i \(0.564271\pi\)
\(558\) −4.60601e144 −2.91762
\(559\) −1.45329e144 −0.837980
\(560\) 1.89869e143 0.0996744
\(561\) 4.57812e144 2.18845
\(562\) −1.74709e144 −0.760605
\(563\) −2.14485e144 −0.850564 −0.425282 0.905061i \(-0.639825\pi\)
−0.425282 + 0.905061i \(0.639825\pi\)
\(564\) 3.83260e144 1.38465
\(565\) 7.69686e143 0.253379
\(566\) 1.04383e144 0.313160
\(567\) −3.87776e143 −0.106040
\(568\) −8.73325e144 −2.17715
\(569\) 4.55830e144 1.03612 0.518059 0.855345i \(-0.326655\pi\)
0.518059 + 0.855345i \(0.326655\pi\)
\(570\) 5.41768e144 1.12301
\(571\) 8.13053e144 1.53717 0.768587 0.639745i \(-0.220960\pi\)
0.768587 + 0.639745i \(0.220960\pi\)
\(572\) −1.68956e145 −2.91395
\(573\) 1.07519e145 1.69187
\(574\) −9.34796e143 −0.134228
\(575\) 4.54461e143 0.0595572
\(576\) 3.22185e144 0.385412
\(577\) 6.19944e143 0.0677052 0.0338526 0.999427i \(-0.489222\pi\)
0.0338526 + 0.999427i \(0.489222\pi\)
\(578\) −1.61081e145 −1.60632
\(579\) −2.46516e145 −2.24503
\(580\) 2.09876e145 1.74579
\(581\) 7.29951e143 0.0554686
\(582\) 7.89009e145 5.47804
\(583\) 6.37692e144 0.404587
\(584\) −2.03712e145 −1.18125
\(585\) −4.84351e145 −2.56730
\(586\) −8.03092e144 −0.389171
\(587\) 1.70804e145 0.756828 0.378414 0.925636i \(-0.376470\pi\)
0.378414 + 0.925636i \(0.376470\pi\)
\(588\) −1.00300e146 −4.06436
\(589\) 8.42264e144 0.312173
\(590\) 7.93159e145 2.68924
\(591\) −6.43575e145 −1.99644
\(592\) −6.66663e144 −0.189242
\(593\) 2.00221e145 0.520160 0.260080 0.965587i \(-0.416251\pi\)
0.260080 + 0.965587i \(0.416251\pi\)
\(594\) 1.46123e146 3.47481
\(595\) −3.27922e144 −0.0713888
\(596\) −1.82718e146 −3.64210
\(597\) −4.24991e145 −0.775759
\(598\) 2.70678e145 0.452523
\(599\) −7.83512e144 −0.119988 −0.0599940 0.998199i \(-0.519108\pi\)
−0.0599940 + 0.998199i \(0.519108\pi\)
\(600\) 1.01231e146 1.42027
\(601\) 7.00949e144 0.0901108 0.0450554 0.998984i \(-0.485654\pi\)
0.0450554 + 0.998984i \(0.485654\pi\)
\(602\) −5.74813e144 −0.0677191
\(603\) 2.31822e145 0.250320
\(604\) 3.69544e146 3.65786
\(605\) 1.85803e145 0.168615
\(606\) −2.17320e146 −1.80837
\(607\) 2.12280e146 1.61996 0.809978 0.586460i \(-0.199479\pi\)
0.809978 + 0.586460i \(0.199479\pi\)
\(608\) −7.05190e145 −0.493592
\(609\) 1.68687e145 0.108311
\(610\) 1.00911e146 0.594461
\(611\) 9.01386e145 0.487245
\(612\) −1.39161e147 −6.90350
\(613\) −2.40584e146 −1.09545 −0.547725 0.836658i \(-0.684506\pi\)
−0.547725 + 0.836658i \(0.684506\pi\)
\(614\) −4.76666e145 −0.199239
\(615\) 4.37528e146 1.67904
\(616\) −3.75149e145 −0.132195
\(617\) −2.96563e146 −0.959723 −0.479861 0.877344i \(-0.659313\pi\)
−0.479861 + 0.877344i \(0.659313\pi\)
\(618\) 1.72998e147 5.14217
\(619\) −3.44019e146 −0.939340 −0.469670 0.882842i \(-0.655627\pi\)
−0.469670 + 0.882842i \(0.655627\pi\)
\(620\) −5.38655e146 −1.35128
\(621\) −1.62724e146 −0.375097
\(622\) 4.06700e146 0.861547
\(623\) 5.04111e145 0.0981530
\(624\) 2.75474e147 4.93048
\(625\) −3.28489e146 −0.540530
\(626\) −1.60635e147 −2.43046
\(627\) −4.89073e146 −0.680500
\(628\) −3.00112e147 −3.84062
\(629\) 1.15139e146 0.135539
\(630\) −1.91573e146 −0.207470
\(631\) 8.24712e146 0.821790 0.410895 0.911683i \(-0.365216\pi\)
0.410895 + 0.911683i \(0.365216\pi\)
\(632\) 2.08422e147 1.91116
\(633\) 2.32613e147 1.96308
\(634\) 2.46573e147 1.91540
\(635\) −2.83111e146 −0.202458
\(636\) −2.81775e147 −1.85526
\(637\) −2.35895e147 −1.43021
\(638\) −2.72565e147 −1.52189
\(639\) 4.02594e147 2.07048
\(640\) −1.43610e147 −0.680353
\(641\) 2.02276e147 0.882871 0.441436 0.897293i \(-0.354469\pi\)
0.441436 + 0.897293i \(0.354469\pi\)
\(642\) −2.57967e147 −1.03747
\(643\) −2.37322e147 −0.879553 −0.439776 0.898107i \(-0.644942\pi\)
−0.439776 + 0.898107i \(0.644942\pi\)
\(644\) 7.44183e145 0.0254198
\(645\) 2.69039e147 0.847091
\(646\) 3.66091e147 1.06263
\(647\) 5.29062e146 0.141590 0.0707949 0.997491i \(-0.477446\pi\)
0.0707949 + 0.997491i \(0.477446\pi\)
\(648\) −1.55424e148 −3.83557
\(649\) −7.16013e147 −1.62957
\(650\) 4.24105e147 0.890271
\(651\) −4.32941e146 −0.0838353
\(652\) 1.83807e148 3.28370
\(653\) −4.21757e146 −0.0695218 −0.0347609 0.999396i \(-0.511067\pi\)
−0.0347609 + 0.999396i \(0.511067\pi\)
\(654\) 1.40564e148 2.13818
\(655\) 7.13677e147 1.00192
\(656\) −1.71185e148 −2.21827
\(657\) 9.39091e147 1.12338
\(658\) 3.56520e146 0.0393754
\(659\) −1.62818e148 −1.66042 −0.830212 0.557448i \(-0.811781\pi\)
−0.830212 + 0.557448i \(0.811781\pi\)
\(660\) 3.12778e148 2.94564
\(661\) 6.87944e147 0.598380 0.299190 0.954194i \(-0.403284\pi\)
0.299190 + 0.954194i \(0.403284\pi\)
\(662\) −2.13275e148 −1.71355
\(663\) −4.75769e148 −3.53131
\(664\) 2.92570e148 2.00635
\(665\) 3.50314e146 0.0221984
\(666\) 6.72644e147 0.393902
\(667\) 3.03530e147 0.164284
\(668\) −6.28763e148 −3.14574
\(669\) 1.45055e148 0.670905
\(670\) 3.90020e147 0.166786
\(671\) −9.10961e147 −0.360220
\(672\) 3.62482e147 0.132556
\(673\) −4.65685e147 −0.157508 −0.0787538 0.996894i \(-0.525094\pi\)
−0.0787538 + 0.996894i \(0.525094\pi\)
\(674\) −2.05160e148 −0.641871
\(675\) −2.54960e148 −0.737946
\(676\) 9.04477e148 2.42212
\(677\) 6.98042e148 1.72972 0.864861 0.502012i \(-0.167407\pi\)
0.864861 + 0.502012i \(0.167407\pi\)
\(678\) 4.41685e148 1.01287
\(679\) 5.10183e147 0.108284
\(680\) −1.31434e149 −2.58220
\(681\) −5.22257e148 −0.949863
\(682\) 6.99548e148 1.17798
\(683\) 8.39022e148 1.30824 0.654118 0.756392i \(-0.273040\pi\)
0.654118 + 0.756392i \(0.273040\pi\)
\(684\) 1.48664e149 2.14665
\(685\) −6.68154e148 −0.893556
\(686\) −1.86989e148 −0.231633
\(687\) −7.66065e148 −0.879098
\(688\) −1.05263e149 −1.11913
\(689\) −6.62705e148 −0.652847
\(690\) −5.01089e148 −0.457444
\(691\) 1.77282e149 1.49992 0.749959 0.661484i \(-0.230073\pi\)
0.749959 + 0.661484i \(0.230073\pi\)
\(692\) −3.08119e149 −2.41629
\(693\) 1.72939e148 0.125719
\(694\) −2.21798e149 −1.49481
\(695\) 1.14669e149 0.716548
\(696\) 6.76110e149 3.91771
\(697\) 2.95652e149 1.58877
\(698\) −3.08210e149 −1.53616
\(699\) 4.99175e149 2.30782
\(700\) 1.16600e148 0.0500096
\(701\) −2.47268e149 −0.983948 −0.491974 0.870610i \(-0.663725\pi\)
−0.491974 + 0.870610i \(0.663725\pi\)
\(702\) −1.51855e150 −5.60700
\(703\) −1.23001e148 −0.0421458
\(704\) −4.89326e148 −0.155609
\(705\) −1.66868e149 −0.492543
\(706\) −8.80394e149 −2.41229
\(707\) −1.40522e148 −0.0357458
\(708\) 3.16383e150 7.47252
\(709\) −6.59385e149 −1.44614 −0.723072 0.690772i \(-0.757271\pi\)
−0.723072 + 0.690772i \(0.757271\pi\)
\(710\) 6.77329e149 1.37955
\(711\) −9.60803e149 −1.81753
\(712\) 2.02052e150 3.55028
\(713\) −7.79022e148 −0.127160
\(714\) −1.88178e149 −0.285374
\(715\) 7.35619e149 1.03654
\(716\) −1.78417e150 −2.33616
\(717\) −1.48382e149 −0.180561
\(718\) 4.32510e149 0.489173
\(719\) 6.21958e149 0.653875 0.326937 0.945046i \(-0.393983\pi\)
0.326937 + 0.945046i \(0.393983\pi\)
\(720\) −3.50818e150 −3.42867
\(721\) 1.11863e149 0.101645
\(722\) 1.75245e150 1.48062
\(723\) −8.40126e149 −0.660061
\(724\) −3.63272e150 −2.65434
\(725\) 4.75579e149 0.323204
\(726\) 1.06623e150 0.674030
\(727\) −2.32064e149 −0.136474 −0.0682372 0.997669i \(-0.521737\pi\)
−0.0682372 + 0.997669i \(0.521737\pi\)
\(728\) 3.89864e149 0.213312
\(729\) −4.15335e149 −0.211448
\(730\) 1.57994e150 0.748497
\(731\) 1.81799e150 0.801547
\(732\) 4.02524e150 1.65181
\(733\) −1.28759e150 −0.491833 −0.245917 0.969291i \(-0.579089\pi\)
−0.245917 + 0.969291i \(0.579089\pi\)
\(734\) −9.65180e150 −3.43214
\(735\) 4.36698e150 1.44576
\(736\) 6.52240e149 0.201058
\(737\) −3.52085e149 −0.101066
\(738\) 1.72721e151 4.61727
\(739\) −7.51915e150 −1.87213 −0.936064 0.351830i \(-0.885559\pi\)
−0.936064 + 0.351830i \(0.885559\pi\)
\(740\) 7.86632e149 0.182434
\(741\) 5.08257e150 1.09806
\(742\) −2.62116e149 −0.0527580
\(743\) −8.03286e150 −1.50646 −0.753229 0.657758i \(-0.771505\pi\)
−0.753229 + 0.657758i \(0.771505\pi\)
\(744\) −1.73526e151 −3.03240
\(745\) 7.95536e150 1.29555
\(746\) 3.98771e150 0.605250
\(747\) −1.34872e151 −1.90805
\(748\) 2.11355e151 2.78726
\(749\) −1.66805e149 −0.0205075
\(750\) −3.07877e151 −3.52907
\(751\) 6.97978e150 0.746010 0.373005 0.927829i \(-0.378327\pi\)
0.373005 + 0.927829i \(0.378327\pi\)
\(752\) 6.52879e150 0.650723
\(753\) 4.94431e150 0.459589
\(754\) 2.83256e151 2.45575
\(755\) −1.60896e151 −1.30116
\(756\) −4.17500e150 −0.314965
\(757\) −1.00145e151 −0.704851 −0.352426 0.935840i \(-0.614643\pi\)
−0.352426 + 0.935840i \(0.614643\pi\)
\(758\) −9.81101e150 −0.644288
\(759\) 4.52351e150 0.277193
\(760\) 1.40409e151 0.802935
\(761\) −3.09059e151 −1.64948 −0.824741 0.565511i \(-0.808679\pi\)
−0.824741 + 0.565511i \(0.808679\pi\)
\(762\) −1.62463e151 −0.809318
\(763\) 9.08907e149 0.0422650
\(764\) 4.96375e151 2.15481
\(765\) 6.05896e151 2.45569
\(766\) −6.42392e151 −2.43103
\(767\) 7.44098e151 2.62950
\(768\) −9.18942e151 −3.03266
\(769\) 2.69582e150 0.0830917 0.0415459 0.999137i \(-0.486772\pi\)
0.0415459 + 0.999137i \(0.486772\pi\)
\(770\) 2.90956e150 0.0837652
\(771\) 3.71046e151 0.997869
\(772\) −1.13807e152 −2.85932
\(773\) 3.50661e151 0.823122 0.411561 0.911382i \(-0.364984\pi\)
0.411561 + 0.911382i \(0.364984\pi\)
\(774\) 1.06207e152 2.32945
\(775\) −1.22059e151 −0.250167
\(776\) 2.04485e152 3.91672
\(777\) 6.32251e149 0.0113184
\(778\) 3.90485e151 0.653394
\(779\) −3.15841e151 −0.494028
\(780\) −3.25046e152 −4.75312
\(781\) −6.11448e151 −0.835951
\(782\) −3.38603e151 −0.432849
\(783\) −1.70286e152 −2.03557
\(784\) −1.70860e152 −1.91006
\(785\) 1.30666e152 1.36617
\(786\) 4.09544e152 4.00513
\(787\) 1.02568e152 0.938289 0.469145 0.883121i \(-0.344562\pi\)
0.469145 + 0.883121i \(0.344562\pi\)
\(788\) −2.97115e152 −2.54271
\(789\) −2.95931e152 −2.36945
\(790\) −1.61647e152 −1.21100
\(791\) 2.85599e150 0.0200213
\(792\) 6.93155e152 4.54735
\(793\) 9.46693e151 0.581255
\(794\) 5.65902e152 3.25211
\(795\) 1.22682e152 0.659945
\(796\) −1.96202e152 −0.988025
\(797\) 6.06121e151 0.285757 0.142879 0.989740i \(-0.454364\pi\)
0.142879 + 0.989740i \(0.454364\pi\)
\(798\) 2.01028e151 0.0887371
\(799\) −1.12758e152 −0.466061
\(800\) 1.02195e152 0.395552
\(801\) −9.31437e152 −3.37634
\(802\) −2.28751e152 −0.776621
\(803\) −1.42627e152 −0.453560
\(804\) 1.55575e152 0.463444
\(805\) −3.24010e150 −0.00904222
\(806\) −7.26987e152 −1.90080
\(807\) 8.16953e152 2.00141
\(808\) −5.63223e152 −1.29296
\(809\) 2.40237e152 0.516823 0.258412 0.966035i \(-0.416801\pi\)
0.258412 + 0.966035i \(0.416801\pi\)
\(810\) 1.20543e153 2.43040
\(811\) 8.16006e152 1.54205 0.771025 0.636805i \(-0.219744\pi\)
0.771025 + 0.636805i \(0.219744\pi\)
\(812\) 7.78764e151 0.137948
\(813\) −4.21680e152 −0.700211
\(814\) −1.02159e152 −0.159037
\(815\) −8.00278e152 −1.16806
\(816\) −3.44603e153 −4.71612
\(817\) −1.94213e152 −0.249241
\(818\) 2.12250e153 2.55446
\(819\) −1.79723e152 −0.202861
\(820\) 2.01990e153 2.13847
\(821\) 9.67277e152 0.960583 0.480292 0.877109i \(-0.340531\pi\)
0.480292 + 0.877109i \(0.340531\pi\)
\(822\) −3.83421e153 −3.57195
\(823\) 6.39371e152 0.558807 0.279403 0.960174i \(-0.409863\pi\)
0.279403 + 0.960174i \(0.409863\pi\)
\(824\) 4.48355e153 3.67658
\(825\) 7.08754e152 0.545335
\(826\) 2.94309e152 0.212496
\(827\) −1.35582e153 −0.918675 −0.459338 0.888262i \(-0.651913\pi\)
−0.459338 + 0.888262i \(0.651913\pi\)
\(828\) −1.37501e153 −0.874409
\(829\) −1.59964e151 −0.00954791 −0.00477396 0.999989i \(-0.501520\pi\)
−0.00477396 + 0.999989i \(0.501520\pi\)
\(830\) −2.26910e153 −1.27132
\(831\) −3.78187e153 −1.98909
\(832\) 5.08520e152 0.251092
\(833\) 2.95092e153 1.36803
\(834\) 6.58031e153 2.86437
\(835\) 2.73758e153 1.11899
\(836\) −2.25787e153 −0.866701
\(837\) 4.37045e153 1.57558
\(838\) −5.42359e153 −1.83644
\(839\) −2.91785e153 −0.928025 −0.464012 0.885829i \(-0.653591\pi\)
−0.464012 + 0.885829i \(0.653591\pi\)
\(840\) −7.21730e152 −0.215631
\(841\) −3.86438e152 −0.108465
\(842\) −1.23018e154 −3.24402
\(843\) 3.03422e153 0.751795
\(844\) 1.07389e154 2.50023
\(845\) −3.93801e153 −0.861588
\(846\) −6.58736e153 −1.35446
\(847\) 6.89439e151 0.0133235
\(848\) −4.80001e153 −0.871887
\(849\) −1.81285e153 −0.309533
\(850\) −5.30531e153 −0.851564
\(851\) 1.13766e152 0.0171676
\(852\) 2.70179e154 3.83330
\(853\) −1.89242e153 −0.252460 −0.126230 0.992001i \(-0.540288\pi\)
−0.126230 + 0.992001i \(0.540288\pi\)
\(854\) 3.74440e152 0.0469726
\(855\) −6.47269e153 −0.763597
\(856\) −6.68566e153 −0.741774
\(857\) 1.69723e154 1.77111 0.885557 0.464531i \(-0.153777\pi\)
0.885557 + 0.464531i \(0.153777\pi\)
\(858\) 4.22136e154 4.14352
\(859\) −1.63155e154 −1.50646 −0.753232 0.657755i \(-0.771506\pi\)
−0.753232 + 0.657755i \(0.771506\pi\)
\(860\) 1.24205e154 1.07888
\(861\) 1.62349e153 0.132673
\(862\) −2.56706e154 −1.97381
\(863\) −1.13157e153 −0.0818682 −0.0409341 0.999162i \(-0.513033\pi\)
−0.0409341 + 0.999162i \(0.513033\pi\)
\(864\) −3.65918e154 −2.49122
\(865\) 1.34152e154 0.859512
\(866\) −2.96296e154 −1.78664
\(867\) 2.79754e154 1.58772
\(868\) −1.99873e153 −0.106775
\(869\) 1.45924e154 0.733819
\(870\) −5.24374e154 −2.48245
\(871\) 3.65896e153 0.163081
\(872\) 3.64297e154 1.52876
\(873\) −9.42656e154 −3.72482
\(874\) 3.61724e153 0.134595
\(875\) −1.99077e153 −0.0697587
\(876\) 6.30221e154 2.07983
\(877\) 1.22909e154 0.382038 0.191019 0.981586i \(-0.438821\pi\)
0.191019 + 0.981586i \(0.438821\pi\)
\(878\) 1.37290e154 0.401955
\(879\) 1.39475e154 0.384663
\(880\) 5.32813e154 1.38431
\(881\) −7.81284e153 −0.191238 −0.0956189 0.995418i \(-0.530483\pi\)
−0.0956189 + 0.995418i \(0.530483\pi\)
\(882\) 1.72393e155 3.97575
\(883\) 1.14392e154 0.248575 0.124288 0.992246i \(-0.460335\pi\)
0.124288 + 0.992246i \(0.460335\pi\)
\(884\) −2.19645e155 −4.49756
\(885\) −1.37750e155 −2.65810
\(886\) 1.67696e154 0.304966
\(887\) 8.81345e154 1.51062 0.755311 0.655367i \(-0.227486\pi\)
0.755311 + 0.655367i \(0.227486\pi\)
\(888\) 2.53411e154 0.409398
\(889\) −1.05051e153 −0.0159977
\(890\) −1.56706e155 −2.24963
\(891\) −1.08818e155 −1.47273
\(892\) 6.69664e154 0.854481
\(893\) 1.20458e154 0.144922
\(894\) 4.56519e155 5.17892
\(895\) 7.76812e154 0.831010
\(896\) −5.32876e153 −0.0537596
\(897\) −4.70094e154 −0.447282
\(898\) 1.58868e154 0.142570
\(899\) −8.15222e154 −0.690068
\(900\) −2.15441e155 −1.72027
\(901\) 8.29007e154 0.624463
\(902\) −2.62324e155 −1.86421
\(903\) 9.98294e153 0.0669348
\(904\) 1.14470e155 0.724187
\(905\) 1.58165e155 0.944193
\(906\) −9.23303e155 −5.20132
\(907\) 2.85448e155 1.51756 0.758778 0.651349i \(-0.225797\pi\)
0.758778 + 0.651349i \(0.225797\pi\)
\(908\) −2.41107e155 −1.20977
\(909\) 2.59640e155 1.22961
\(910\) −3.02368e154 −0.135165
\(911\) 3.07697e155 1.29840 0.649199 0.760619i \(-0.275104\pi\)
0.649199 + 0.760619i \(0.275104\pi\)
\(912\) 3.68133e155 1.46648
\(913\) 2.04840e155 0.770368
\(914\) −3.90675e155 −1.38720
\(915\) −1.75255e155 −0.587576
\(916\) −3.53664e155 −1.11964
\(917\) 2.64816e154 0.0791689
\(918\) 1.89962e156 5.36323
\(919\) −6.63998e155 −1.77053 −0.885263 0.465092i \(-0.846021\pi\)
−0.885263 + 0.465092i \(0.846021\pi\)
\(920\) −1.29866e155 −0.327065
\(921\) 8.27839e154 0.196932
\(922\) −3.03557e155 −0.682130
\(923\) 6.35432e155 1.34890
\(924\) 1.16059e155 0.232756
\(925\) 1.78251e154 0.0337746
\(926\) −2.06729e155 −0.370104
\(927\) −2.06687e156 −3.49645
\(928\) 6.82548e155 1.09110
\(929\) 1.50933e155 0.228014 0.114007 0.993480i \(-0.463631\pi\)
0.114007 + 0.993480i \(0.463631\pi\)
\(930\) 1.34583e156 1.92147
\(931\) −3.15242e155 −0.425388
\(932\) 2.30450e156 2.93929
\(933\) −7.06327e155 −0.851568
\(934\) −1.47001e156 −1.67537
\(935\) −9.20219e155 −0.991474
\(936\) −7.20344e156 −7.33767
\(937\) 1.05238e156 1.01355 0.506773 0.862079i \(-0.330838\pi\)
0.506773 + 0.862079i \(0.330838\pi\)
\(938\) 1.44721e154 0.0131790
\(939\) 2.78980e156 2.40231
\(940\) −7.70366e155 −0.627314
\(941\) −2.16414e156 −1.66660 −0.833298 0.552825i \(-0.813550\pi\)
−0.833298 + 0.552825i \(0.813550\pi\)
\(942\) 7.49828e156 5.46121
\(943\) 2.92126e155 0.201236
\(944\) 5.38955e156 3.51174
\(945\) 1.81776e155 0.112038
\(946\) −1.61305e156 −0.940508
\(947\) 1.62005e156 0.893625 0.446813 0.894628i \(-0.352559\pi\)
0.446813 + 0.894628i \(0.352559\pi\)
\(948\) −6.44792e156 −3.36498
\(949\) 1.48221e156 0.731870
\(950\) 5.66758e155 0.264794
\(951\) −4.28230e156 −1.89322
\(952\) −4.87698e155 −0.204038
\(953\) −1.07207e156 −0.424470 −0.212235 0.977219i \(-0.568074\pi\)
−0.212235 + 0.977219i \(0.568074\pi\)
\(954\) 4.84307e156 1.81481
\(955\) −2.16117e156 −0.766500
\(956\) −6.85023e155 −0.229967
\(957\) 4.73371e156 1.50427
\(958\) −2.51929e156 −0.757861
\(959\) −2.47925e155 −0.0706062
\(960\) −9.41391e155 −0.253823
\(961\) −1.82492e156 −0.465871
\(962\) 1.06167e156 0.256623
\(963\) 3.08202e156 0.705432
\(964\) −3.87855e156 −0.840669
\(965\) 4.95507e156 1.01711
\(966\) −1.85934e155 −0.0361459
\(967\) 1.63853e156 0.301692 0.150846 0.988557i \(-0.451800\pi\)
0.150846 + 0.988557i \(0.451800\pi\)
\(968\) 2.76333e156 0.481921
\(969\) −6.35801e156 −1.05032
\(970\) −1.58594e157 −2.48182
\(971\) 1.42295e156 0.210951 0.105475 0.994422i \(-0.466364\pi\)
0.105475 + 0.994422i \(0.466364\pi\)
\(972\) 1.30882e157 1.83824
\(973\) 4.25491e155 0.0566196
\(974\) 7.64251e156 0.963587
\(975\) −7.36555e156 −0.879959
\(976\) 6.85696e156 0.776276
\(977\) −1.83385e157 −1.96743 −0.983715 0.179733i \(-0.942477\pi\)
−0.983715 + 0.179733i \(0.942477\pi\)
\(978\) −4.59241e157 −4.66928
\(979\) 1.41464e157 1.36319
\(980\) 2.01607e157 1.84135
\(981\) −1.67937e157 −1.45386
\(982\) 1.58569e157 1.30127
\(983\) 2.13639e157 1.66196 0.830980 0.556303i \(-0.187780\pi\)
0.830980 + 0.556303i \(0.187780\pi\)
\(984\) 6.50707e157 4.79891
\(985\) 1.29361e157 0.904484
\(986\) −3.54337e157 −2.34898
\(987\) −6.19178e155 −0.0389193
\(988\) 2.34643e157 1.39852
\(989\) 1.79630e156 0.101525
\(990\) −5.37593e157 −2.88142
\(991\) 1.35147e157 0.686973 0.343487 0.939158i \(-0.388392\pi\)
0.343487 + 0.939158i \(0.388392\pi\)
\(992\) −1.75179e157 −0.844537
\(993\) 3.70401e157 1.69370
\(994\) 2.51329e156 0.109008
\(995\) 8.54247e156 0.351457
\(996\) −9.05120e157 −3.53257
\(997\) −4.76047e156 −0.176260 −0.0881301 0.996109i \(-0.528089\pi\)
−0.0881301 + 0.996109i \(0.528089\pi\)
\(998\) −3.72743e157 −1.30935
\(999\) −6.38244e156 −0.212715
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1.106.a.a.1.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.106.a.a.1.1 8 1.1 even 1 trivial