Properties

Label 1.106.a.a.1.6
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 1.6
Root \(3.47548e13\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.85781e15 q^{2} -1.61266e25 q^{3} -2.56821e31 q^{4} +9.75211e36 q^{5} -6.22135e40 q^{6} -2.29314e44 q^{7} -2.55568e47 q^{8} +1.34832e50 q^{9} +O(q^{10})\) \(q+3.85781e15 q^{2} -1.61266e25 q^{3} -2.56821e31 q^{4} +9.75211e36 q^{5} -6.22135e40 q^{6} -2.29314e44 q^{7} -2.55568e47 q^{8} +1.34832e50 q^{9} +3.76218e52 q^{10} +1.09890e54 q^{11} +4.14166e56 q^{12} -1.87317e58 q^{13} -8.84652e59 q^{14} -1.57269e62 q^{15} +5.58564e61 q^{16} +5.30626e64 q^{17} +5.20155e65 q^{18} +1.09214e67 q^{19} -2.50455e68 q^{20} +3.69807e69 q^{21} +4.23934e69 q^{22} -8.50723e70 q^{23} +4.12146e72 q^{24} +7.04517e73 q^{25} -7.22635e73 q^{26} -1.54734e74 q^{27} +5.88928e75 q^{28} -5.56149e76 q^{29} -6.06713e77 q^{30} +1.17118e78 q^{31} +1.05826e79 q^{32} -1.77215e79 q^{33} +2.04706e80 q^{34} -2.23630e81 q^{35} -3.46276e81 q^{36} -2.00039e82 q^{37} +4.21327e82 q^{38} +3.02080e83 q^{39} -2.49233e84 q^{40} -1.54764e84 q^{41} +1.42665e85 q^{42} +5.42589e84 q^{43} -2.82220e85 q^{44} +1.31489e87 q^{45} -3.28193e86 q^{46} -1.19813e88 q^{47} -9.00775e86 q^{48} -1.77677e87 q^{49} +2.71789e89 q^{50} -8.55722e89 q^{51} +4.81070e89 q^{52} +1.16973e90 q^{53} -5.96936e89 q^{54} +1.07166e91 q^{55} +5.86054e91 q^{56} -1.76126e92 q^{57} -2.14552e92 q^{58} -1.35533e93 q^{59} +4.03899e93 q^{60} +9.28542e92 q^{61} +4.51820e93 q^{62} -3.09188e94 q^{63} +3.85597e94 q^{64} -1.82674e95 q^{65} -6.83664e94 q^{66} -5.61369e94 q^{67} -1.36276e96 q^{68} +1.37193e96 q^{69} -8.62722e96 q^{70} -1.67163e97 q^{71} -3.44587e97 q^{72} +8.53517e97 q^{73} -7.71713e97 q^{74} -1.13615e99 q^{75} -2.80485e98 q^{76} -2.51993e98 q^{77} +1.16537e99 q^{78} -4.40194e99 q^{79} +5.44717e98 q^{80} -1.43905e100 q^{81} -5.97051e99 q^{82} -2.96634e99 q^{83} -9.49742e100 q^{84} +5.17473e101 q^{85} +2.09321e100 q^{86} +8.96882e101 q^{87} -2.80844e101 q^{88} +2.97381e101 q^{89} +5.07261e102 q^{90} +4.29545e102 q^{91} +2.18484e102 q^{92} -1.88872e103 q^{93} -4.62216e103 q^{94} +1.06507e104 q^{95} -1.70661e104 q^{96} -1.35845e104 q^{97} -6.85446e102 q^{98} +1.48166e104 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 9175032489175920q^{2} - \)\(35\!\cdots\!80\)\(q^{3} + \)\(12\!\cdots\!76\)\(q^{4} + \)\(74\!\cdots\!00\)\(q^{5} - \)\(13\!\cdots\!64\)\(q^{6} + \)\(70\!\cdots\!00\)\(q^{7} - \)\(70\!\cdots\!60\)\(q^{8} + \)\(31\!\cdots\!84\)\(q^{9} + O(q^{10}) \) \( 8q - 9175032489175920q^{2} - \)\(35\!\cdots\!80\)\(q^{3} + \)\(12\!\cdots\!76\)\(q^{4} + \)\(74\!\cdots\!00\)\(q^{5} - \)\(13\!\cdots\!64\)\(q^{6} + \)\(70\!\cdots\!00\)\(q^{7} - \)\(70\!\cdots\!60\)\(q^{8} + \)\(31\!\cdots\!84\)\(q^{9} + \)\(44\!\cdots\!00\)\(q^{10} - \)\(91\!\cdots\!84\)\(q^{11} + \)\(15\!\cdots\!60\)\(q^{12} + \)\(40\!\cdots\!40\)\(q^{13} - \)\(16\!\cdots\!28\)\(q^{14} - \)\(85\!\cdots\!00\)\(q^{15} + \)\(88\!\cdots\!48\)\(q^{16} - \)\(47\!\cdots\!60\)\(q^{17} - \)\(26\!\cdots\!80\)\(q^{18} - \)\(18\!\cdots\!20\)\(q^{19} - \)\(43\!\cdots\!00\)\(q^{20} + \)\(34\!\cdots\!56\)\(q^{21} + \)\(61\!\cdots\!60\)\(q^{22} + \)\(35\!\cdots\!60\)\(q^{23} - \)\(85\!\cdots\!60\)\(q^{24} + \)\(36\!\cdots\!00\)\(q^{25} - \)\(17\!\cdots\!24\)\(q^{26} + \)\(41\!\cdots\!40\)\(q^{27} - \)\(10\!\cdots\!60\)\(q^{28} - \)\(13\!\cdots\!80\)\(q^{29} + \)\(36\!\cdots\!00\)\(q^{30} + \)\(21\!\cdots\!16\)\(q^{31} + \)\(10\!\cdots\!80\)\(q^{32} - \)\(11\!\cdots\!60\)\(q^{33} + \)\(62\!\cdots\!52\)\(q^{34} - \)\(18\!\cdots\!00\)\(q^{35} + \)\(16\!\cdots\!48\)\(q^{36} - \)\(23\!\cdots\!80\)\(q^{37} + \)\(81\!\cdots\!60\)\(q^{38} + \)\(97\!\cdots\!48\)\(q^{39} + \)\(16\!\cdots\!00\)\(q^{40} - \)\(91\!\cdots\!84\)\(q^{41} - \)\(99\!\cdots\!60\)\(q^{42} + \)\(30\!\cdots\!00\)\(q^{43} - \)\(61\!\cdots\!48\)\(q^{44} - \)\(72\!\cdots\!00\)\(q^{45} - \)\(19\!\cdots\!84\)\(q^{46} - \)\(19\!\cdots\!40\)\(q^{47} + \)\(47\!\cdots\!60\)\(q^{48} + \)\(90\!\cdots\!56\)\(q^{49} + \)\(12\!\cdots\!00\)\(q^{50} - \)\(10\!\cdots\!04\)\(q^{51} + \)\(26\!\cdots\!00\)\(q^{52} - \)\(50\!\cdots\!80\)\(q^{53} - \)\(33\!\cdots\!20\)\(q^{54} + \)\(18\!\cdots\!00\)\(q^{55} + \)\(77\!\cdots\!80\)\(q^{56} - \)\(17\!\cdots\!20\)\(q^{57} + \)\(52\!\cdots\!40\)\(q^{58} - \)\(80\!\cdots\!60\)\(q^{59} - \)\(49\!\cdots\!00\)\(q^{60} + \)\(93\!\cdots\!16\)\(q^{61} - \)\(24\!\cdots\!40\)\(q^{62} - \)\(69\!\cdots\!20\)\(q^{63} - \)\(97\!\cdots\!04\)\(q^{64} - \)\(36\!\cdots\!00\)\(q^{65} + \)\(15\!\cdots\!72\)\(q^{66} - \)\(11\!\cdots\!60\)\(q^{67} - \)\(97\!\cdots\!80\)\(q^{68} - \)\(15\!\cdots\!32\)\(q^{69} - \)\(42\!\cdots\!00\)\(q^{70} - \)\(50\!\cdots\!84\)\(q^{71} - \)\(31\!\cdots\!80\)\(q^{72} - \)\(30\!\cdots\!40\)\(q^{73} - \)\(92\!\cdots\!88\)\(q^{74} - \)\(20\!\cdots\!00\)\(q^{75} - \)\(31\!\cdots\!40\)\(q^{76} - \)\(59\!\cdots\!00\)\(q^{77} - \)\(21\!\cdots\!00\)\(q^{78} - \)\(15\!\cdots\!80\)\(q^{79} - \)\(36\!\cdots\!00\)\(q^{80} - \)\(16\!\cdots\!72\)\(q^{81} + \)\(40\!\cdots\!60\)\(q^{82} - \)\(27\!\cdots\!20\)\(q^{83} + \)\(24\!\cdots\!32\)\(q^{84} + \)\(11\!\cdots\!00\)\(q^{85} + \)\(20\!\cdots\!96\)\(q^{86} + \)\(24\!\cdots\!20\)\(q^{87} + \)\(65\!\cdots\!80\)\(q^{88} + \)\(45\!\cdots\!60\)\(q^{89} + \)\(27\!\cdots\!00\)\(q^{90} + \)\(27\!\cdots\!96\)\(q^{91} + \)\(11\!\cdots\!40\)\(q^{92} - \)\(18\!\cdots\!60\)\(q^{93} - \)\(14\!\cdots\!08\)\(q^{94} - \)\(19\!\cdots\!00\)\(q^{95} - \)\(72\!\cdots\!64\)\(q^{96} - \)\(76\!\cdots\!40\)\(q^{97} - \)\(13\!\cdots\!40\)\(q^{98} - \)\(25\!\cdots\!32\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.85781e15 0.605712 0.302856 0.953036i \(-0.402060\pi\)
0.302856 + 0.953036i \(0.402060\pi\)
\(3\) −1.61266e25 −1.44105 −0.720523 0.693431i \(-0.756098\pi\)
−0.720523 + 0.693431i \(0.756098\pi\)
\(4\) −2.56821e31 −0.633113
\(5\) 9.75211e36 1.96414 0.982072 0.188508i \(-0.0603651\pi\)
0.982072 + 0.188508i \(0.0603651\pi\)
\(6\) −6.22135e40 −0.872859
\(7\) −2.29314e44 −0.983522 −0.491761 0.870730i \(-0.663647\pi\)
−0.491761 + 0.870730i \(0.663647\pi\)
\(8\) −2.55568e47 −0.989196
\(9\) 1.34832e50 1.07661
\(10\) 3.76218e52 1.18971
\(11\) 1.09890e54 0.233261 0.116630 0.993175i \(-0.462791\pi\)
0.116630 + 0.993175i \(0.462791\pi\)
\(12\) 4.14166e56 0.912345
\(13\) −1.87317e58 −0.617379 −0.308689 0.951163i \(-0.599890\pi\)
−0.308689 + 0.951163i \(0.599890\pi\)
\(14\) −8.84652e59 −0.595731
\(15\) −1.57269e62 −2.83042
\(16\) 5.58564e61 0.0339448
\(17\) 5.30626e64 1.33727 0.668637 0.743589i \(-0.266878\pi\)
0.668637 + 0.743589i \(0.266878\pi\)
\(18\) 5.20155e65 0.652118
\(19\) 1.09214e67 0.801151 0.400576 0.916264i \(-0.368810\pi\)
0.400576 + 0.916264i \(0.368810\pi\)
\(20\) −2.50455e68 −1.24352
\(21\) 3.69807e69 1.41730
\(22\) 4.23934e69 0.141289
\(23\) −8.50723e70 −0.274838 −0.137419 0.990513i \(-0.543881\pi\)
−0.137419 + 0.990513i \(0.543881\pi\)
\(24\) 4.12146e72 1.42548
\(25\) 7.04517e73 2.85786
\(26\) −7.22635e73 −0.373954
\(27\) −1.54734e74 −0.110405
\(28\) 5.88928e75 0.622681
\(29\) −5.56149e76 −0.931744 −0.465872 0.884852i \(-0.654259\pi\)
−0.465872 + 0.884852i \(0.654259\pi\)
\(30\) −6.06713e77 −1.71442
\(31\) 1.17118e78 0.591747 0.295873 0.955227i \(-0.404389\pi\)
0.295873 + 0.955227i \(0.404389\pi\)
\(32\) 1.05826e79 1.00976
\(33\) −1.77215e79 −0.336140
\(34\) 2.04706e80 0.810003
\(35\) −2.23630e81 −1.93178
\(36\) −3.46276e81 −0.681619
\(37\) −2.00039e82 −0.934382 −0.467191 0.884157i \(-0.654734\pi\)
−0.467191 + 0.884157i \(0.654734\pi\)
\(38\) 4.21327e82 0.485267
\(39\) 3.02080e83 0.889672
\(40\) −2.49233e84 −1.94292
\(41\) −1.54764e84 −0.330003 −0.165002 0.986293i \(-0.552763\pi\)
−0.165002 + 0.986293i \(0.552763\pi\)
\(42\) 1.42665e85 0.858476
\(43\) 5.42589e84 0.0949243 0.0474621 0.998873i \(-0.484887\pi\)
0.0474621 + 0.998873i \(0.484887\pi\)
\(44\) −2.82220e85 −0.147680
\(45\) 1.31489e87 2.11463
\(46\) −3.28193e86 −0.166473
\(47\) −1.19813e88 −1.96502 −0.982509 0.186217i \(-0.940377\pi\)
−0.982509 + 0.186217i \(0.940377\pi\)
\(48\) −9.00775e86 −0.0489161
\(49\) −1.77677e87 −0.0326842
\(50\) 2.71789e89 1.73104
\(51\) −8.55722e89 −1.92707
\(52\) 4.81070e89 0.390871
\(53\) 1.16973e90 0.349624 0.174812 0.984602i \(-0.444068\pi\)
0.174812 + 0.984602i \(0.444068\pi\)
\(54\) −5.96936e89 −0.0668737
\(55\) 1.07166e91 0.458158
\(56\) 5.86054e91 0.972896
\(57\) −1.76126e92 −1.15450
\(58\) −2.14552e92 −0.564369
\(59\) −1.35533e93 −1.45317 −0.726583 0.687078i \(-0.758893\pi\)
−0.726583 + 0.687078i \(0.758893\pi\)
\(60\) 4.03899e93 1.79198
\(61\) 9.28542e92 0.172976 0.0864879 0.996253i \(-0.472436\pi\)
0.0864879 + 0.996253i \(0.472436\pi\)
\(62\) 4.51820e93 0.358428
\(63\) −3.09188e94 −1.05887
\(64\) 3.85597e94 0.577677
\(65\) −1.82674e95 −1.21262
\(66\) −6.83664e94 −0.203604
\(67\) −5.61369e94 −0.0759139 −0.0379569 0.999279i \(-0.512085\pi\)
−0.0379569 + 0.999279i \(0.512085\pi\)
\(68\) −1.36276e96 −0.846646
\(69\) 1.37193e96 0.396054
\(70\) −8.62722e96 −1.17010
\(71\) −1.67163e97 −1.07665 −0.538327 0.842736i \(-0.680943\pi\)
−0.538327 + 0.842736i \(0.680943\pi\)
\(72\) −3.44587e97 −1.06498
\(73\) 8.53517e97 1.27868 0.639340 0.768924i \(-0.279208\pi\)
0.639340 + 0.768924i \(0.279208\pi\)
\(74\) −7.71713e97 −0.565966
\(75\) −1.13615e99 −4.11831
\(76\) −2.80485e98 −0.507219
\(77\) −2.51993e98 −0.229417
\(78\) 1.16537e99 0.538885
\(79\) −4.40194e99 −1.04285 −0.521425 0.853297i \(-0.674599\pi\)
−0.521425 + 0.853297i \(0.674599\pi\)
\(80\) 5.44717e98 0.0666725
\(81\) −1.43905e100 −0.917516
\(82\) −5.97051e99 −0.199887
\(83\) −2.96634e99 −0.0525559 −0.0262779 0.999655i \(-0.508365\pi\)
−0.0262779 + 0.999655i \(0.508365\pi\)
\(84\) −9.49742e100 −0.897312
\(85\) 5.17473e101 2.62660
\(86\) 2.09321e100 0.0574968
\(87\) 8.96882e101 1.34269
\(88\) −2.80844e101 −0.230741
\(89\) 2.97381e101 0.135001 0.0675006 0.997719i \(-0.478498\pi\)
0.0675006 + 0.997719i \(0.478498\pi\)
\(90\) 5.07261e102 1.28085
\(91\) 4.29545e102 0.607206
\(92\) 2.18484e102 0.174003
\(93\) −1.88872e103 −0.852735
\(94\) −4.62216e103 −1.19023
\(95\) 1.06507e104 1.57358
\(96\) −1.70661e104 −1.45511
\(97\) −1.35845e104 −0.672245 −0.336122 0.941818i \(-0.609116\pi\)
−0.336122 + 0.941818i \(0.609116\pi\)
\(98\) −6.85446e102 −0.0197972
\(99\) 1.48166e104 0.251132
\(100\) −1.80935e105 −1.80935
\(101\) 2.13987e104 0.126916 0.0634579 0.997985i \(-0.479787\pi\)
0.0634579 + 0.997985i \(0.479787\pi\)
\(102\) −3.30121e105 −1.16725
\(103\) 2.64790e105 0.560980 0.280490 0.959857i \(-0.409503\pi\)
0.280490 + 0.959857i \(0.409503\pi\)
\(104\) 4.78723e105 0.610709
\(105\) 3.60640e106 2.78378
\(106\) 4.51258e105 0.211771
\(107\) −3.56766e106 −1.02267 −0.511334 0.859382i \(-0.670849\pi\)
−0.511334 + 0.859382i \(0.670849\pi\)
\(108\) 3.97391e105 0.0698989
\(109\) 1.04589e106 0.113395 0.0566976 0.998391i \(-0.481943\pi\)
0.0566976 + 0.998391i \(0.481943\pi\)
\(110\) 4.13425e106 0.277512
\(111\) 3.22596e107 1.34649
\(112\) −1.28087e106 −0.0333855
\(113\) −8.97870e107 −1.46756 −0.733778 0.679389i \(-0.762245\pi\)
−0.733778 + 0.679389i \(0.762245\pi\)
\(114\) −6.79459e107 −0.699292
\(115\) −8.29634e107 −0.539821
\(116\) 1.42831e108 0.589899
\(117\) −2.52563e108 −0.664679
\(118\) −5.22862e108 −0.880201
\(119\) −1.21680e109 −1.31524
\(120\) 4.01929e109 2.79984
\(121\) −2.09862e109 −0.945589
\(122\) 3.58214e108 0.104773
\(123\) 2.49583e109 0.475550
\(124\) −3.00785e109 −0.374643
\(125\) 4.46644e110 3.64910
\(126\) −1.19279e110 −0.641373
\(127\) −2.54759e110 −0.904554 −0.452277 0.891878i \(-0.649388\pi\)
−0.452277 + 0.891878i \(0.649388\pi\)
\(128\) −2.80524e110 −0.659851
\(129\) −8.75014e109 −0.136790
\(130\) −7.04721e110 −0.734499
\(131\) 5.81963e110 0.405651 0.202825 0.979215i \(-0.434988\pi\)
0.202825 + 0.979215i \(0.434988\pi\)
\(132\) 4.55127e110 0.212814
\(133\) −2.50444e111 −0.787950
\(134\) −2.16566e110 −0.0459819
\(135\) −1.50899e111 −0.216852
\(136\) −1.35611e112 −1.32283
\(137\) 1.10293e112 0.732348 0.366174 0.930546i \(-0.380668\pi\)
0.366174 + 0.930546i \(0.380668\pi\)
\(138\) 5.29265e111 0.239895
\(139\) −2.42594e112 −0.752666 −0.376333 0.926484i \(-0.622815\pi\)
−0.376333 + 0.926484i \(0.622815\pi\)
\(140\) 5.74328e112 1.22303
\(141\) 1.93218e113 2.83168
\(142\) −6.44882e112 −0.652142
\(143\) −2.05843e112 −0.144010
\(144\) 7.53121e111 0.0365455
\(145\) −5.42363e113 −1.83008
\(146\) 3.29271e113 0.774512
\(147\) 2.86534e112 0.0470995
\(148\) 5.13742e113 0.591569
\(149\) −6.88442e113 −0.556658 −0.278329 0.960486i \(-0.589781\pi\)
−0.278329 + 0.960486i \(0.589781\pi\)
\(150\) −4.38305e114 −2.49451
\(151\) 1.52326e114 0.611622 0.305811 0.952092i \(-0.401072\pi\)
0.305811 + 0.952092i \(0.401072\pi\)
\(152\) −2.79116e114 −0.792496
\(153\) 7.15453e114 1.43973
\(154\) −9.72143e113 −0.138961
\(155\) 1.14215e115 1.16228
\(156\) −7.75805e114 −0.563263
\(157\) 1.53277e115 0.795693 0.397846 0.917452i \(-0.369758\pi\)
0.397846 + 0.917452i \(0.369758\pi\)
\(158\) −1.69818e115 −0.631666
\(159\) −1.88637e115 −0.503824
\(160\) 1.03202e116 1.98331
\(161\) 1.95083e115 0.270309
\(162\) −5.55160e115 −0.555750
\(163\) −4.71155e115 −0.341440 −0.170720 0.985320i \(-0.554609\pi\)
−0.170720 + 0.985320i \(0.554609\pi\)
\(164\) 3.97467e115 0.208929
\(165\) −1.72822e116 −0.660226
\(166\) −1.14436e115 −0.0318337
\(167\) −5.58290e116 −1.13304 −0.566520 0.824048i \(-0.691711\pi\)
−0.566520 + 0.824048i \(0.691711\pi\)
\(168\) −9.45109e116 −1.40199
\(169\) −5.69682e116 −0.618843
\(170\) 1.99631e117 1.59096
\(171\) 1.47255e117 0.862531
\(172\) −1.39348e116 −0.0600978
\(173\) 5.19513e117 1.65263 0.826316 0.563207i \(-0.190433\pi\)
0.826316 + 0.563207i \(0.190433\pi\)
\(174\) 3.46000e117 0.813281
\(175\) −1.61556e118 −2.81077
\(176\) 6.13805e115 0.00791800
\(177\) 2.18570e118 2.09408
\(178\) 1.14724e117 0.0817719
\(179\) 5.93619e117 0.315300 0.157650 0.987495i \(-0.449608\pi\)
0.157650 + 0.987495i \(0.449608\pi\)
\(180\) −3.37692e118 −1.33880
\(181\) −1.51713e118 −0.449673 −0.224837 0.974396i \(-0.572185\pi\)
−0.224837 + 0.974396i \(0.572185\pi\)
\(182\) 1.65711e118 0.367792
\(183\) −1.49743e118 −0.249266
\(184\) 2.17418e118 0.271869
\(185\) −1.95080e119 −1.83526
\(186\) −7.28634e118 −0.516512
\(187\) 5.83105e118 0.311934
\(188\) 3.07705e119 1.24408
\(189\) 3.54828e118 0.108586
\(190\) 4.10883e119 0.953134
\(191\) −1.97568e119 −0.347908 −0.173954 0.984754i \(-0.555654\pi\)
−0.173954 + 0.984754i \(0.555654\pi\)
\(192\) −6.21839e119 −0.832460
\(193\) 1.10407e120 1.12523 0.562613 0.826721i \(-0.309796\pi\)
0.562613 + 0.826721i \(0.309796\pi\)
\(194\) −5.24064e119 −0.407187
\(195\) 2.94591e120 1.74744
\(196\) 4.56313e118 0.0206928
\(197\) −9.83716e119 −0.341502 −0.170751 0.985314i \(-0.554619\pi\)
−0.170751 + 0.985314i \(0.554619\pi\)
\(198\) 5.71598e119 0.152114
\(199\) −4.76500e120 −0.973367 −0.486684 0.873578i \(-0.661794\pi\)
−0.486684 + 0.873578i \(0.661794\pi\)
\(200\) −1.80052e121 −2.82698
\(201\) 9.05299e119 0.109395
\(202\) 8.25522e119 0.0768744
\(203\) 1.27533e121 0.916391
\(204\) 2.19767e121 1.22006
\(205\) −1.50928e121 −0.648174
\(206\) 1.02151e121 0.339792
\(207\) −1.14704e121 −0.295895
\(208\) −1.04629e120 −0.0209568
\(209\) 1.20015e121 0.186877
\(210\) 1.39128e122 1.68617
\(211\) −1.39237e122 −1.31500 −0.657499 0.753455i \(-0.728386\pi\)
−0.657499 + 0.753455i \(0.728386\pi\)
\(212\) −3.00410e121 −0.221351
\(213\) 2.69577e122 1.55151
\(214\) −1.37634e122 −0.619443
\(215\) 5.29139e121 0.186445
\(216\) 3.95452e121 0.109212
\(217\) −2.68569e122 −0.581996
\(218\) 4.03485e121 0.0686849
\(219\) −1.37644e123 −1.84264
\(220\) −2.75224e122 −0.290066
\(221\) −9.93955e122 −0.825605
\(222\) 1.24451e123 0.815584
\(223\) 1.74645e123 0.903965 0.451983 0.892027i \(-0.350717\pi\)
0.451983 + 0.892027i \(0.350717\pi\)
\(224\) −2.42673e123 −0.993118
\(225\) 9.49912e123 3.07681
\(226\) −3.46381e123 −0.888917
\(227\) −5.34039e123 −1.08696 −0.543482 0.839421i \(-0.682894\pi\)
−0.543482 + 0.839421i \(0.682894\pi\)
\(228\) 4.52328e123 0.730927
\(229\) 5.63117e123 0.723162 0.361581 0.932341i \(-0.382237\pi\)
0.361581 + 0.932341i \(0.382237\pi\)
\(230\) −3.20057e123 −0.326976
\(231\) 4.06380e123 0.330601
\(232\) 1.42134e124 0.921678
\(233\) 5.69834e122 0.0294824 0.0147412 0.999891i \(-0.495308\pi\)
0.0147412 + 0.999891i \(0.495308\pi\)
\(234\) −9.74341e123 −0.402604
\(235\) −1.16843e125 −3.85958
\(236\) 3.48078e124 0.920019
\(237\) 7.09885e124 1.50279
\(238\) −4.69420e124 −0.796656
\(239\) −4.34877e124 −0.592211 −0.296105 0.955155i \(-0.595688\pi\)
−0.296105 + 0.955155i \(0.595688\pi\)
\(240\) −8.78446e123 −0.0960782
\(241\) 1.14521e125 1.00691 0.503455 0.864021i \(-0.332062\pi\)
0.503455 + 0.864021i \(0.332062\pi\)
\(242\) −8.09609e124 −0.572755
\(243\) 2.51449e125 1.43259
\(244\) −2.38469e124 −0.109513
\(245\) −1.73273e124 −0.0641965
\(246\) 9.62843e124 0.288046
\(247\) −2.04577e125 −0.494614
\(248\) −2.99317e125 −0.585354
\(249\) 4.78371e124 0.0757355
\(250\) 1.72307e126 2.21031
\(251\) −2.90548e125 −0.302237 −0.151119 0.988516i \(-0.548288\pi\)
−0.151119 + 0.988516i \(0.548288\pi\)
\(252\) 7.94061e125 0.670387
\(253\) −9.34858e124 −0.0641089
\(254\) −9.82813e125 −0.547899
\(255\) −8.34509e126 −3.78505
\(256\) −2.64637e126 −0.977357
\(257\) 5.72367e126 1.72261 0.861303 0.508092i \(-0.169649\pi\)
0.861303 + 0.508092i \(0.169649\pi\)
\(258\) −3.37564e125 −0.0828555
\(259\) 4.58718e126 0.918985
\(260\) 4.69145e126 0.767726
\(261\) −7.49866e126 −1.00313
\(262\) 2.24510e126 0.245708
\(263\) 1.04359e127 0.935090 0.467545 0.883969i \(-0.345139\pi\)
0.467545 + 0.883969i \(0.345139\pi\)
\(264\) 4.52906e126 0.332508
\(265\) 1.14073e127 0.686711
\(266\) −9.66164e126 −0.477271
\(267\) −4.79575e126 −0.194543
\(268\) 1.44171e126 0.0480621
\(269\) 2.31236e127 0.633960 0.316980 0.948432i \(-0.397331\pi\)
0.316980 + 0.948432i \(0.397331\pi\)
\(270\) −5.82139e126 −0.131350
\(271\) −6.16932e127 −1.14644 −0.573218 0.819403i \(-0.694305\pi\)
−0.573218 + 0.819403i \(0.694305\pi\)
\(272\) 2.96389e126 0.0453935
\(273\) −6.92712e127 −0.875012
\(274\) 4.25489e127 0.443592
\(275\) 7.74193e127 0.666627
\(276\) −3.52341e127 −0.250747
\(277\) −3.05677e128 −1.79918 −0.899592 0.436732i \(-0.856136\pi\)
−0.899592 + 0.436732i \(0.856136\pi\)
\(278\) −9.35881e127 −0.455899
\(279\) 1.57913e128 0.637083
\(280\) 5.71527e128 1.91091
\(281\) −6.05535e128 −1.67903 −0.839513 0.543340i \(-0.817159\pi\)
−0.839513 + 0.543340i \(0.817159\pi\)
\(282\) 7.45399e128 1.71518
\(283\) 4.58881e128 0.876824 0.438412 0.898774i \(-0.355541\pi\)
0.438412 + 0.898774i \(0.355541\pi\)
\(284\) 4.29309e128 0.681643
\(285\) −1.71760e129 −2.26760
\(286\) −7.94102e127 −0.0872288
\(287\) 3.54897e128 0.324566
\(288\) 1.42686e129 1.08712
\(289\) 1.24117e129 0.788303
\(290\) −2.09233e129 −1.10850
\(291\) 2.19072e129 0.968736
\(292\) −2.19201e129 −0.809549
\(293\) −2.26596e129 −0.699361 −0.349681 0.936869i \(-0.613710\pi\)
−0.349681 + 0.936869i \(0.613710\pi\)
\(294\) 1.10539e128 0.0285287
\(295\) −1.32174e130 −2.85423
\(296\) 5.11236e129 0.924287
\(297\) −1.70038e128 −0.0257532
\(298\) −2.65588e129 −0.337175
\(299\) 1.59355e129 0.169679
\(300\) 2.91787e130 2.60735
\(301\) −1.24423e129 −0.0933601
\(302\) 5.87644e129 0.370467
\(303\) −3.45089e129 −0.182891
\(304\) 6.10030e128 0.0271949
\(305\) 9.05524e129 0.339749
\(306\) 2.76008e130 0.872061
\(307\) −6.45251e130 −1.71777 −0.858883 0.512171i \(-0.828841\pi\)
−0.858883 + 0.512171i \(0.828841\pi\)
\(308\) 6.47172e129 0.145247
\(309\) −4.27017e130 −0.808398
\(310\) 4.40620e130 0.704004
\(311\) −2.67741e130 −0.361239 −0.180620 0.983553i \(-0.557810\pi\)
−0.180620 + 0.983553i \(0.557810\pi\)
\(312\) −7.72020e130 −0.880060
\(313\) 1.88529e131 1.81678 0.908388 0.418129i \(-0.137314\pi\)
0.908388 + 0.418129i \(0.137314\pi\)
\(314\) 5.91314e130 0.481961
\(315\) −3.01524e131 −2.07978
\(316\) 1.13051e131 0.660241
\(317\) −3.65781e131 −1.80971 −0.904857 0.425715i \(-0.860023\pi\)
−0.904857 + 0.425715i \(0.860023\pi\)
\(318\) −7.27728e130 −0.305172
\(319\) −6.11152e130 −0.217339
\(320\) 3.76038e131 1.13464
\(321\) 5.75343e131 1.47371
\(322\) 7.52593e130 0.163730
\(323\) 5.79519e131 1.07136
\(324\) 3.69579e131 0.580891
\(325\) −1.31968e132 −1.76438
\(326\) −1.81763e131 −0.206815
\(327\) −1.68667e131 −0.163408
\(328\) 3.95528e131 0.326438
\(329\) 2.74748e132 1.93264
\(330\) −6.66716e131 −0.399907
\(331\) −2.35018e132 −1.20263 −0.601313 0.799014i \(-0.705355\pi\)
−0.601313 + 0.799014i \(0.705355\pi\)
\(332\) 7.61819e130 0.0332738
\(333\) −2.69716e132 −1.00597
\(334\) −2.15378e132 −0.686296
\(335\) −5.47453e131 −0.149106
\(336\) 2.06561e131 0.0481100
\(337\) −7.74707e131 −0.154372 −0.0771858 0.997017i \(-0.524593\pi\)
−0.0771858 + 0.997017i \(0.524593\pi\)
\(338\) −2.19773e132 −0.374841
\(339\) 1.44796e133 2.11482
\(340\) −1.32898e133 −1.66293
\(341\) 1.28701e132 0.138031
\(342\) 5.68083e132 0.522446
\(343\) 1.28734e133 1.01567
\(344\) −1.38669e132 −0.0938987
\(345\) 1.33792e133 0.777907
\(346\) 2.00418e133 1.00102
\(347\) 1.77869e133 0.763490 0.381745 0.924268i \(-0.375323\pi\)
0.381745 + 0.924268i \(0.375323\pi\)
\(348\) −2.30338e133 −0.850072
\(349\) −4.31176e133 −1.36873 −0.684367 0.729137i \(-0.739921\pi\)
−0.684367 + 0.729137i \(0.739921\pi\)
\(350\) −6.23252e133 −1.70252
\(351\) 2.89844e132 0.0681618
\(352\) 1.16292e133 0.235537
\(353\) 2.59573e133 0.452989 0.226494 0.974012i \(-0.427274\pi\)
0.226494 + 0.974012i \(0.427274\pi\)
\(354\) 8.43201e133 1.26841
\(355\) −1.63019e134 −2.11470
\(356\) −7.63737e132 −0.0854710
\(357\) 1.96229e134 1.89532
\(358\) 2.29007e133 0.190981
\(359\) −5.41344e133 −0.389955 −0.194977 0.980808i \(-0.562463\pi\)
−0.194977 + 0.980808i \(0.562463\pi\)
\(360\) −3.36045e134 −2.09178
\(361\) −6.65581e133 −0.358156
\(362\) −5.85279e133 −0.272372
\(363\) 3.38437e134 1.36264
\(364\) −1.10316e134 −0.384430
\(365\) 8.32359e134 2.51151
\(366\) −5.77679e133 −0.150983
\(367\) 4.27460e134 0.968115 0.484058 0.875036i \(-0.339163\pi\)
0.484058 + 0.875036i \(0.339163\pi\)
\(368\) −4.75183e132 −0.00932933
\(369\) −2.08671e134 −0.355286
\(370\) −7.52583e134 −1.11164
\(371\) −2.68235e134 −0.343863
\(372\) 4.85064e134 0.539877
\(373\) 9.25400e134 0.894573 0.447287 0.894391i \(-0.352390\pi\)
0.447287 + 0.894391i \(0.352390\pi\)
\(374\) 2.24951e134 0.188942
\(375\) −7.20287e135 −5.25853
\(376\) 3.06204e135 1.94379
\(377\) 1.04176e135 0.575239
\(378\) 1.36886e134 0.0657718
\(379\) 6.72747e134 0.281380 0.140690 0.990054i \(-0.455068\pi\)
0.140690 + 0.990054i \(0.455068\pi\)
\(380\) −2.73532e135 −0.996251
\(381\) 4.10841e135 1.30350
\(382\) −7.62179e134 −0.210732
\(383\) −2.11776e135 −0.510437 −0.255218 0.966883i \(-0.582147\pi\)
−0.255218 + 0.966883i \(0.582147\pi\)
\(384\) 4.52390e135 0.950876
\(385\) −2.45747e135 −0.450608
\(386\) 4.25931e135 0.681563
\(387\) 7.31582e134 0.102197
\(388\) 3.48879e135 0.425607
\(389\) 2.05445e135 0.218949 0.109474 0.993990i \(-0.465083\pi\)
0.109474 + 0.993990i \(0.465083\pi\)
\(390\) 1.13648e136 1.05845
\(391\) −4.51416e135 −0.367534
\(392\) 4.54087e134 0.0323311
\(393\) −9.38511e135 −0.584562
\(394\) −3.79499e135 −0.206852
\(395\) −4.29282e136 −2.04831
\(396\) −3.80523e135 −0.158995
\(397\) 5.61029e135 0.205345 0.102672 0.994715i \(-0.467261\pi\)
0.102672 + 0.994715i \(0.467261\pi\)
\(398\) −1.83825e136 −0.589580
\(399\) 4.03881e136 1.13547
\(400\) 3.93517e135 0.0970095
\(401\) 3.23792e136 0.700142 0.350071 0.936723i \(-0.386157\pi\)
0.350071 + 0.936723i \(0.386157\pi\)
\(402\) 3.49247e135 0.0662621
\(403\) −2.19383e136 −0.365332
\(404\) −5.49564e135 −0.0803520
\(405\) −1.40338e137 −1.80213
\(406\) 4.91998e136 0.555069
\(407\) −2.19823e136 −0.217955
\(408\) 2.18695e137 1.90625
\(409\) 1.96494e137 1.50617 0.753087 0.657921i \(-0.228564\pi\)
0.753087 + 0.657921i \(0.228564\pi\)
\(410\) −5.82251e136 −0.392607
\(411\) −1.77865e137 −1.05535
\(412\) −6.80037e136 −0.355164
\(413\) 3.10797e137 1.42922
\(414\) −4.42508e136 −0.179227
\(415\) −2.89281e136 −0.103227
\(416\) −1.98230e137 −0.623403
\(417\) 3.91222e137 1.08463
\(418\) 4.62996e136 0.113194
\(419\) −5.84636e137 −1.26081 −0.630405 0.776267i \(-0.717111\pi\)
−0.630405 + 0.776267i \(0.717111\pi\)
\(420\) −9.26199e137 −1.76245
\(421\) 1.86699e137 0.313568 0.156784 0.987633i \(-0.449887\pi\)
0.156784 + 0.987633i \(0.449887\pi\)
\(422\) −5.37150e137 −0.796511
\(423\) −1.61546e138 −2.11557
\(424\) −2.98945e137 −0.345846
\(425\) 3.73835e138 3.82174
\(426\) 1.03998e138 0.939767
\(427\) −2.12928e137 −0.170125
\(428\) 9.16250e137 0.647465
\(429\) 3.31955e137 0.207526
\(430\) 2.04132e137 0.112932
\(431\) −1.43316e138 −0.701842 −0.350921 0.936405i \(-0.614131\pi\)
−0.350921 + 0.936405i \(0.614131\pi\)
\(432\) −8.64290e135 −0.00374768
\(433\) −3.38800e138 −1.30115 −0.650577 0.759441i \(-0.725473\pi\)
−0.650577 + 0.759441i \(0.725473\pi\)
\(434\) −1.03609e138 −0.352522
\(435\) 8.74649e138 2.63723
\(436\) −2.68607e137 −0.0717920
\(437\) −9.29109e137 −0.220187
\(438\) −5.31003e138 −1.11611
\(439\) 4.59945e138 0.857668 0.428834 0.903383i \(-0.358925\pi\)
0.428834 + 0.903383i \(0.358925\pi\)
\(440\) −2.73882e138 −0.453208
\(441\) −2.39565e137 −0.0351883
\(442\) −3.83449e138 −0.500079
\(443\) −9.97115e138 −1.15491 −0.577457 0.816421i \(-0.695955\pi\)
−0.577457 + 0.816421i \(0.695955\pi\)
\(444\) −8.28494e138 −0.852478
\(445\) 2.90009e138 0.265162
\(446\) 6.73749e138 0.547543
\(447\) 1.11023e139 0.802170
\(448\) −8.84230e138 −0.568158
\(449\) −1.45874e139 −0.833767 −0.416884 0.908960i \(-0.636878\pi\)
−0.416884 + 0.908960i \(0.636878\pi\)
\(450\) 3.66458e139 1.86366
\(451\) −1.70070e138 −0.0769768
\(452\) 2.30592e139 0.929129
\(453\) −2.45650e139 −0.881376
\(454\) −2.06022e139 −0.658388
\(455\) 4.18897e139 1.19264
\(456\) 4.50121e139 1.14202
\(457\) −6.69538e139 −1.51417 −0.757085 0.653317i \(-0.773377\pi\)
−0.757085 + 0.653317i \(0.773377\pi\)
\(458\) 2.17240e139 0.438028
\(459\) −8.21062e138 −0.147642
\(460\) 2.13067e139 0.341768
\(461\) −3.68396e138 −0.0527250 −0.0263625 0.999652i \(-0.508392\pi\)
−0.0263625 + 0.999652i \(0.508392\pi\)
\(462\) 1.56774e139 0.200249
\(463\) 9.52994e136 0.00108665 0.000543323 1.00000i \(-0.499827\pi\)
0.000543323 1.00000i \(0.499827\pi\)
\(464\) −3.10645e138 −0.0316279
\(465\) −1.84190e140 −1.67489
\(466\) 2.19831e138 0.0178578
\(467\) 7.58015e138 0.0550226 0.0275113 0.999621i \(-0.491242\pi\)
0.0275113 + 0.999621i \(0.491242\pi\)
\(468\) 6.48635e139 0.420817
\(469\) 1.28730e139 0.0746630
\(470\) −4.50758e140 −2.33779
\(471\) −2.47184e140 −1.14663
\(472\) 3.46380e140 1.43747
\(473\) 5.96251e138 0.0221421
\(474\) 2.73860e140 0.910261
\(475\) 7.69432e140 2.28958
\(476\) 3.12501e140 0.832695
\(477\) 1.57716e140 0.376410
\(478\) −1.67767e140 −0.358709
\(479\) 3.21066e140 0.615148 0.307574 0.951524i \(-0.400483\pi\)
0.307574 + 0.951524i \(0.400483\pi\)
\(480\) −1.66431e141 −2.85804
\(481\) 3.74708e140 0.576868
\(482\) 4.41801e140 0.609898
\(483\) −3.14603e140 −0.389528
\(484\) 5.38971e140 0.598665
\(485\) −1.32477e141 −1.32039
\(486\) 9.70044e140 0.867736
\(487\) −1.74855e141 −1.40413 −0.702064 0.712114i \(-0.747738\pi\)
−0.702064 + 0.712114i \(0.747738\pi\)
\(488\) −2.37306e140 −0.171107
\(489\) 7.59815e140 0.492031
\(490\) −6.68454e139 −0.0388846
\(491\) 1.62859e141 0.851205 0.425603 0.904910i \(-0.360062\pi\)
0.425603 + 0.904910i \(0.360062\pi\)
\(492\) −6.40981e140 −0.301077
\(493\) −2.95108e141 −1.24600
\(494\) −7.89219e140 −0.299594
\(495\) 1.44493e141 0.493259
\(496\) 6.54180e139 0.0200867
\(497\) 3.83328e141 1.05891
\(498\) 1.84547e140 0.0458739
\(499\) 9.87635e140 0.220962 0.110481 0.993878i \(-0.464761\pi\)
0.110481 + 0.993878i \(0.464761\pi\)
\(500\) −1.14708e142 −2.31029
\(501\) 9.00334e141 1.63276
\(502\) −1.12088e141 −0.183069
\(503\) 6.48833e141 0.954583 0.477291 0.878745i \(-0.341619\pi\)
0.477291 + 0.878745i \(0.341619\pi\)
\(504\) 7.90187e141 1.04743
\(505\) 2.08682e141 0.249281
\(506\) −3.60651e140 −0.0388315
\(507\) 9.18706e141 0.891782
\(508\) 6.54275e141 0.572685
\(509\) −1.90504e142 −1.50390 −0.751952 0.659218i \(-0.770888\pi\)
−0.751952 + 0.659218i \(0.770888\pi\)
\(510\) −3.21938e142 −2.29265
\(511\) −1.95724e142 −1.25761
\(512\) 1.17017e141 0.0678541
\(513\) −1.68992e141 −0.0884513
\(514\) 2.20809e142 1.04340
\(515\) 2.58226e142 1.10185
\(516\) 2.24722e141 0.0866037
\(517\) −1.31662e142 −0.458361
\(518\) 1.76965e142 0.556640
\(519\) −8.37800e142 −2.38152
\(520\) 4.66856e142 1.19952
\(521\) 2.44040e141 0.0566865 0.0283433 0.999598i \(-0.490977\pi\)
0.0283433 + 0.999598i \(0.490977\pi\)
\(522\) −2.89284e142 −0.607607
\(523\) −6.77418e142 −1.28682 −0.643410 0.765522i \(-0.722481\pi\)
−0.643410 + 0.765522i \(0.722481\pi\)
\(524\) −1.49460e142 −0.256823
\(525\) 2.60535e143 4.05045
\(526\) 4.02598e142 0.566396
\(527\) 6.21461e142 0.791328
\(528\) −9.89861e140 −0.0114102
\(529\) −8.85753e142 −0.924464
\(530\) 4.40072e142 0.415949
\(531\) −1.82742e143 −1.56450
\(532\) 6.43192e142 0.498861
\(533\) 2.89900e142 0.203737
\(534\) −1.85011e142 −0.117837
\(535\) −3.47922e143 −2.00867
\(536\) 1.43468e142 0.0750937
\(537\) −9.57308e142 −0.454362
\(538\) 8.92067e142 0.383997
\(539\) −1.95249e141 −0.00762394
\(540\) 3.87540e142 0.137292
\(541\) −5.98871e142 −0.192521 −0.0962603 0.995356i \(-0.530688\pi\)
−0.0962603 + 0.995356i \(0.530688\pi\)
\(542\) −2.38001e143 −0.694410
\(543\) 2.44662e143 0.648000
\(544\) 5.61539e143 1.35032
\(545\) 1.01996e143 0.222725
\(546\) −2.67235e143 −0.530005
\(547\) 1.51335e143 0.272649 0.136324 0.990664i \(-0.456471\pi\)
0.136324 + 0.990664i \(0.456471\pi\)
\(548\) −2.83255e143 −0.463659
\(549\) 1.25197e143 0.186228
\(550\) 2.98669e143 0.403784
\(551\) −6.07393e143 −0.746468
\(552\) −3.50622e143 −0.391775
\(553\) 1.00943e144 1.02567
\(554\) −1.17925e144 −1.08979
\(555\) 3.14599e144 2.64469
\(556\) 6.23032e143 0.476523
\(557\) −1.80980e144 −1.25960 −0.629800 0.776757i \(-0.716863\pi\)
−0.629800 + 0.776757i \(0.716863\pi\)
\(558\) 6.09197e143 0.385889
\(559\) −1.01636e143 −0.0586042
\(560\) −1.24911e143 −0.0655739
\(561\) −9.40352e143 −0.449511
\(562\) −2.33604e144 −1.01701
\(563\) 3.46251e144 1.37309 0.686546 0.727086i \(-0.259126\pi\)
0.686546 + 0.727086i \(0.259126\pi\)
\(564\) −4.96225e144 −1.79277
\(565\) −8.75612e144 −2.88249
\(566\) 1.77028e144 0.531103
\(567\) 3.29996e144 0.902397
\(568\) 4.27215e144 1.06502
\(569\) 2.15493e144 0.489823 0.244912 0.969545i \(-0.421241\pi\)
0.244912 + 0.969545i \(0.421241\pi\)
\(570\) −6.62616e144 −1.37351
\(571\) 8.75199e144 1.65467 0.827334 0.561710i \(-0.189856\pi\)
0.827334 + 0.561710i \(0.189856\pi\)
\(572\) 5.28648e143 0.0911748
\(573\) 3.18610e144 0.501351
\(574\) 1.36912e144 0.196593
\(575\) −5.99348e144 −0.785448
\(576\) 5.19907e144 0.621936
\(577\) 6.97485e144 0.761737 0.380868 0.924629i \(-0.375625\pi\)
0.380868 + 0.924629i \(0.375625\pi\)
\(578\) 4.78818e144 0.477484
\(579\) −1.78050e145 −1.62150
\(580\) 1.39290e145 1.15865
\(581\) 6.80225e143 0.0516899
\(582\) 8.45140e144 0.586775
\(583\) 1.28541e144 0.0815535
\(584\) −2.18132e145 −1.26487
\(585\) −2.46302e145 −1.30553
\(586\) −8.74164e144 −0.423612
\(587\) 2.14596e145 0.950872 0.475436 0.879750i \(-0.342290\pi\)
0.475436 + 0.879750i \(0.342290\pi\)
\(588\) −7.35879e143 −0.0298193
\(589\) 1.27910e145 0.474079
\(590\) −5.09901e145 −1.72884
\(591\) 1.58640e145 0.492120
\(592\) −1.11735e144 −0.0317174
\(593\) 2.86896e145 0.745338 0.372669 0.927964i \(-0.378443\pi\)
0.372669 + 0.927964i \(0.378443\pi\)
\(594\) −6.55973e143 −0.0155990
\(595\) −1.18664e146 −2.58332
\(596\) 1.76807e145 0.352427
\(597\) 7.68435e145 1.40267
\(598\) 6.14762e144 0.102777
\(599\) −4.36997e145 −0.669221 −0.334611 0.942356i \(-0.608605\pi\)
−0.334611 + 0.942356i \(0.608605\pi\)
\(600\) 2.90363e146 4.07381
\(601\) −2.07766e145 −0.267094 −0.133547 0.991042i \(-0.542637\pi\)
−0.133547 + 0.991042i \(0.542637\pi\)
\(602\) −4.80002e144 −0.0565494
\(603\) −7.56903e144 −0.0817300
\(604\) −3.91205e145 −0.387226
\(605\) −2.04660e146 −1.85727
\(606\) −1.33129e145 −0.110780
\(607\) 1.34388e145 0.102555 0.0512773 0.998684i \(-0.483671\pi\)
0.0512773 + 0.998684i \(0.483671\pi\)
\(608\) 1.15576e146 0.808968
\(609\) −2.05668e146 −1.32056
\(610\) 3.49334e145 0.205790
\(611\) 2.24430e146 1.21316
\(612\) −1.83743e146 −0.911511
\(613\) 3.61034e146 1.64389 0.821946 0.569565i \(-0.192888\pi\)
0.821946 + 0.569565i \(0.192888\pi\)
\(614\) −2.48926e146 −1.04047
\(615\) 2.43396e146 0.934049
\(616\) 6.44015e145 0.226939
\(617\) −4.17702e146 −1.35175 −0.675873 0.737018i \(-0.736233\pi\)
−0.675873 + 0.737018i \(0.736233\pi\)
\(618\) −1.64735e146 −0.489657
\(619\) −6.25468e146 −1.70784 −0.853918 0.520408i \(-0.825780\pi\)
−0.853918 + 0.520408i \(0.825780\pi\)
\(620\) −2.93328e146 −0.735852
\(621\) 1.31636e145 0.0303435
\(622\) −1.03290e146 −0.218807
\(623\) −6.81937e145 −0.132777
\(624\) 1.68731e145 0.0301997
\(625\) 2.61895e147 4.30950
\(626\) 7.27311e146 1.10044
\(627\) −1.93544e146 −0.269299
\(628\) −3.93648e146 −0.503763
\(629\) −1.06146e147 −1.24952
\(630\) −1.16322e147 −1.25975
\(631\) 1.39055e147 1.38562 0.692810 0.721120i \(-0.256372\pi\)
0.692810 + 0.721120i \(0.256372\pi\)
\(632\) 1.12500e147 1.03158
\(633\) 2.24542e147 1.89497
\(634\) −1.41111e147 −1.09617
\(635\) −2.48444e147 −1.77667
\(636\) 4.84461e146 0.318977
\(637\) 3.32820e145 0.0201785
\(638\) −2.35771e146 −0.131645
\(639\) −2.25388e147 −1.15914
\(640\) −2.73569e147 −1.29604
\(641\) −2.86145e147 −1.24893 −0.624467 0.781051i \(-0.714684\pi\)
−0.624467 + 0.781051i \(0.714684\pi\)
\(642\) 2.21957e147 0.892645
\(643\) 4.77165e147 1.76845 0.884225 0.467062i \(-0.154687\pi\)
0.884225 + 0.467062i \(0.154687\pi\)
\(644\) −5.01014e146 −0.171136
\(645\) −8.53323e146 −0.268676
\(646\) 2.23567e147 0.648935
\(647\) −2.58902e147 −0.692883 −0.346442 0.938071i \(-0.612610\pi\)
−0.346442 + 0.938071i \(0.612610\pi\)
\(648\) 3.67776e147 0.907603
\(649\) −1.48937e147 −0.338967
\(650\) −5.09108e147 −1.06871
\(651\) 4.33112e147 0.838683
\(652\) 1.21003e147 0.216170
\(653\) −2.82440e147 −0.465569 −0.232785 0.972528i \(-0.574784\pi\)
−0.232785 + 0.972528i \(0.574784\pi\)
\(654\) −6.50685e146 −0.0989781
\(655\) 5.67537e147 0.796756
\(656\) −8.64457e145 −0.0112019
\(657\) 1.15081e148 1.37665
\(658\) 1.05993e148 1.17062
\(659\) −1.00022e148 −1.02003 −0.510014 0.860166i \(-0.670360\pi\)
−0.510014 + 0.860166i \(0.670360\pi\)
\(660\) 4.43844e147 0.417998
\(661\) −1.30786e148 −1.13759 −0.568793 0.822481i \(-0.692589\pi\)
−0.568793 + 0.822481i \(0.692589\pi\)
\(662\) −9.06653e147 −0.728445
\(663\) 1.60292e148 1.18974
\(664\) 7.58103e146 0.0519881
\(665\) −2.44235e148 −1.54765
\(666\) −1.04051e148 −0.609327
\(667\) 4.73129e147 0.256079
\(668\) 1.43381e148 0.717342
\(669\) −2.81644e148 −1.30266
\(670\) −2.11197e147 −0.0903151
\(671\) 1.02037e147 0.0403485
\(672\) 3.91350e148 1.43113
\(673\) −2.79605e148 −0.945701 −0.472851 0.881143i \(-0.656775\pi\)
−0.472851 + 0.881143i \(0.656775\pi\)
\(674\) −2.98867e147 −0.0935048
\(675\) −1.09013e148 −0.315522
\(676\) 1.46306e148 0.391798
\(677\) −2.29011e148 −0.567480 −0.283740 0.958901i \(-0.591575\pi\)
−0.283740 + 0.958901i \(0.591575\pi\)
\(678\) 5.58596e148 1.28097
\(679\) 3.11512e148 0.661168
\(680\) −1.32250e149 −2.59822
\(681\) 8.61225e148 1.56637
\(682\) 4.96505e147 0.0836072
\(683\) 5.95955e148 0.929238 0.464619 0.885511i \(-0.346191\pi\)
0.464619 + 0.885511i \(0.346191\pi\)
\(684\) −3.78182e148 −0.546080
\(685\) 1.07559e149 1.43844
\(686\) 4.96631e148 0.615202
\(687\) −9.08119e148 −1.04211
\(688\) 3.03071e146 0.00322219
\(689\) −2.19110e148 −0.215850
\(690\) 5.16145e148 0.471188
\(691\) 1.11983e149 0.947446 0.473723 0.880674i \(-0.342910\pi\)
0.473723 + 0.880674i \(0.342910\pi\)
\(692\) −1.33422e149 −1.04630
\(693\) −3.39767e148 −0.246994
\(694\) 6.86186e148 0.462455
\(695\) −2.36580e149 −1.47834
\(696\) −2.29214e149 −1.32818
\(697\) −8.21220e148 −0.441305
\(698\) −1.66339e149 −0.829059
\(699\) −9.18950e147 −0.0424854
\(700\) 4.14909e149 1.77953
\(701\) −3.90688e149 −1.55466 −0.777328 0.629095i \(-0.783426\pi\)
−0.777328 + 0.629095i \(0.783426\pi\)
\(702\) 1.11816e148 0.0412864
\(703\) −2.18471e149 −0.748581
\(704\) 4.23732e148 0.134749
\(705\) 1.88428e150 5.56183
\(706\) 1.00138e149 0.274381
\(707\) −4.90703e148 −0.124824
\(708\) −5.61333e149 −1.32579
\(709\) 2.40986e149 0.528524 0.264262 0.964451i \(-0.414872\pi\)
0.264262 + 0.964451i \(0.414872\pi\)
\(710\) −6.28896e149 −1.28090
\(711\) −5.93521e149 −1.12275
\(712\) −7.60011e148 −0.133543
\(713\) −9.96352e148 −0.162634
\(714\) 7.57016e149 1.14802
\(715\) −2.00740e149 −0.282857
\(716\) −1.52454e149 −0.199620
\(717\) 7.01310e149 0.853403
\(718\) −2.08840e149 −0.236200
\(719\) 1.40303e150 1.47503 0.737513 0.675333i \(-0.236000\pi\)
0.737513 + 0.675333i \(0.236000\pi\)
\(720\) 7.34451e148 0.0717806
\(721\) −6.07202e149 −0.551736
\(722\) −2.56769e149 −0.216940
\(723\) −1.84684e150 −1.45100
\(724\) 3.89630e149 0.284694
\(725\) −3.91817e150 −2.66279
\(726\) 1.30563e150 0.825366
\(727\) 1.97966e150 1.16422 0.582109 0.813111i \(-0.302228\pi\)
0.582109 + 0.813111i \(0.302228\pi\)
\(728\) −1.09778e150 −0.600646
\(729\) −2.25281e150 −1.14691
\(730\) 3.21108e150 1.52125
\(731\) 2.87912e149 0.126940
\(732\) 3.84571e149 0.157814
\(733\) −1.03662e150 −0.395970 −0.197985 0.980205i \(-0.563440\pi\)
−0.197985 + 0.980205i \(0.563440\pi\)
\(734\) 1.64906e150 0.586399
\(735\) 2.79431e149 0.0925101
\(736\) −9.00282e149 −0.277520
\(737\) −6.16888e148 −0.0177077
\(738\) −8.05015e149 −0.215201
\(739\) 4.27280e150 1.06385 0.531924 0.846792i \(-0.321469\pi\)
0.531924 + 0.846792i \(0.321469\pi\)
\(740\) 5.01007e150 1.16193
\(741\) 3.29914e150 0.712762
\(742\) −1.03480e150 −0.208282
\(743\) −6.15028e150 −1.15341 −0.576703 0.816954i \(-0.695661\pi\)
−0.576703 + 0.816954i \(0.695661\pi\)
\(744\) 4.82698e150 0.843522
\(745\) −6.71376e150 −1.09336
\(746\) 3.57002e150 0.541854
\(747\) −3.99957e149 −0.0565824
\(748\) −1.49754e150 −0.197489
\(749\) 8.18115e150 1.00582
\(750\) −2.77873e151 −3.18515
\(751\) 7.08228e149 0.0756966 0.0378483 0.999283i \(-0.487950\pi\)
0.0378483 + 0.999283i \(0.487950\pi\)
\(752\) −6.69232e149 −0.0667022
\(753\) 4.68557e150 0.435538
\(754\) 4.01893e150 0.348429
\(755\) 1.48550e151 1.20131
\(756\) −9.11274e149 −0.0687472
\(757\) −2.59698e151 −1.82782 −0.913911 0.405914i \(-0.866953\pi\)
−0.913911 + 0.405914i \(0.866953\pi\)
\(758\) 2.59533e150 0.170435
\(759\) 1.50761e150 0.0923839
\(760\) −2.72197e151 −1.55658
\(761\) −4.79193e150 −0.255750 −0.127875 0.991790i \(-0.540816\pi\)
−0.127875 + 0.991790i \(0.540816\pi\)
\(762\) 1.58495e151 0.789548
\(763\) −2.39838e150 −0.111527
\(764\) 5.07396e150 0.220265
\(765\) 6.97717e151 2.82783
\(766\) −8.16994e150 −0.309178
\(767\) 2.53877e151 0.897155
\(768\) 4.26771e151 1.40842
\(769\) 2.80525e151 0.864648 0.432324 0.901718i \(-0.357694\pi\)
0.432324 + 0.901718i \(0.357694\pi\)
\(770\) −9.48044e150 −0.272939
\(771\) −9.23036e151 −2.48235
\(772\) −2.83550e151 −0.712395
\(773\) −5.28505e151 −1.24058 −0.620291 0.784371i \(-0.712986\pi\)
−0.620291 + 0.784371i \(0.712986\pi\)
\(774\) 2.82231e150 0.0619019
\(775\) 8.25118e151 1.69113
\(776\) 3.47177e151 0.664982
\(777\) −7.39758e151 −1.32430
\(778\) 7.92569e150 0.132620
\(779\) −1.69024e151 −0.264383
\(780\) −7.56573e151 −1.10633
\(781\) −1.83695e151 −0.251141
\(782\) −1.74148e151 −0.222620
\(783\) 8.60555e150 0.102869
\(784\) −9.92441e148 −0.00110946
\(785\) 1.49477e152 1.56285
\(786\) −3.62060e151 −0.354076
\(787\) 8.59116e151 0.785920 0.392960 0.919555i \(-0.371451\pi\)
0.392960 + 0.919555i \(0.371451\pi\)
\(788\) 2.52639e151 0.216209
\(789\) −1.68296e152 −1.34751
\(790\) −1.65609e152 −1.24068
\(791\) 2.05894e152 1.44337
\(792\) −3.78666e151 −0.248419
\(793\) −1.73932e151 −0.106792
\(794\) 2.16434e151 0.124380
\(795\) −1.83961e152 −0.989583
\(796\) 1.22375e152 0.616251
\(797\) 2.78075e152 1.31099 0.655497 0.755198i \(-0.272459\pi\)
0.655497 + 0.755198i \(0.272459\pi\)
\(798\) 1.55810e152 0.687770
\(799\) −6.35759e152 −2.62777
\(800\) 7.45559e152 2.88574
\(801\) 4.00964e151 0.145344
\(802\) 1.24913e152 0.424084
\(803\) 9.37929e151 0.298266
\(804\) −2.32500e151 −0.0692596
\(805\) 1.90247e152 0.530926
\(806\) −8.46338e151 −0.221286
\(807\) −3.72907e152 −0.913565
\(808\) −5.46883e151 −0.125545
\(809\) −8.78756e152 −1.89048 −0.945238 0.326383i \(-0.894170\pi\)
−0.945238 + 0.326383i \(0.894170\pi\)
\(810\) −5.41398e152 −1.09157
\(811\) −2.90293e152 −0.548583 −0.274291 0.961647i \(-0.588443\pi\)
−0.274291 + 0.961647i \(0.588443\pi\)
\(812\) −3.27532e152 −0.580179
\(813\) 9.94904e152 1.65207
\(814\) −8.48034e151 −0.132018
\(815\) −4.59476e152 −0.670638
\(816\) −4.77975e151 −0.0654142
\(817\) 5.92584e151 0.0760487
\(818\) 7.58036e152 0.912308
\(819\) 5.79163e152 0.653727
\(820\) 3.87614e152 0.410367
\(821\) 1.45710e153 1.44701 0.723507 0.690318i \(-0.242529\pi\)
0.723507 + 0.690318i \(0.242529\pi\)
\(822\) −6.86170e152 −0.639236
\(823\) −1.16445e153 −1.01772 −0.508861 0.860849i \(-0.669933\pi\)
−0.508861 + 0.860849i \(0.669933\pi\)
\(824\) −6.76719e152 −0.554919
\(825\) −1.24851e153 −0.960640
\(826\) 1.19900e153 0.865697
\(827\) 1.68034e153 1.13856 0.569282 0.822142i \(-0.307221\pi\)
0.569282 + 0.822142i \(0.307221\pi\)
\(828\) 2.94585e152 0.187335
\(829\) −5.29417e152 −0.315999 −0.157999 0.987439i \(-0.550504\pi\)
−0.157999 + 0.987439i \(0.550504\pi\)
\(830\) −1.11599e152 −0.0625260
\(831\) 4.92955e153 2.59271
\(832\) −7.22290e152 −0.356646
\(833\) −9.42803e151 −0.0437077
\(834\) 1.50926e153 0.656972
\(835\) −5.44450e153 −2.22545
\(836\) −3.08224e152 −0.118314
\(837\) −1.81222e152 −0.0653319
\(838\) −2.25542e153 −0.763688
\(839\) 9.42582e152 0.299789 0.149895 0.988702i \(-0.452107\pi\)
0.149895 + 0.988702i \(0.452107\pi\)
\(840\) −9.21680e153 −2.75371
\(841\) −4.69765e152 −0.131853
\(842\) 7.20249e152 0.189932
\(843\) 9.76524e153 2.41955
\(844\) 3.57590e153 0.832543
\(845\) −5.55560e153 −1.21550
\(846\) −6.23214e153 −1.28142
\(847\) 4.81245e153 0.930008
\(848\) 6.53366e151 0.0118679
\(849\) −7.40021e153 −1.26354
\(850\) 1.44219e154 2.31488
\(851\) 1.70178e153 0.256804
\(852\) −6.92331e153 −0.982280
\(853\) −5.92490e153 −0.790418 −0.395209 0.918591i \(-0.629328\pi\)
−0.395209 + 0.918591i \(0.629328\pi\)
\(854\) −8.21436e152 −0.103047
\(855\) 1.43605e154 1.69414
\(856\) 9.11780e153 1.01162
\(857\) 5.88114e153 0.613718 0.306859 0.951755i \(-0.400722\pi\)
0.306859 + 0.951755i \(0.400722\pi\)
\(858\) 1.28062e153 0.125701
\(859\) −9.47543e153 −0.874898 −0.437449 0.899243i \(-0.644118\pi\)
−0.437449 + 0.899243i \(0.644118\pi\)
\(860\) −1.35894e153 −0.118041
\(861\) −5.72329e153 −0.467714
\(862\) −5.52888e153 −0.425114
\(863\) −1.91728e154 −1.38713 −0.693567 0.720392i \(-0.743962\pi\)
−0.693567 + 0.720392i \(0.743962\pi\)
\(864\) −1.63749e153 −0.111482
\(865\) 5.06635e154 3.24601
\(866\) −1.30703e154 −0.788124
\(867\) −2.00158e154 −1.13598
\(868\) 6.89742e153 0.368469
\(869\) −4.83728e153 −0.243256
\(870\) 3.37423e154 1.59740
\(871\) 1.05154e153 0.0468676
\(872\) −2.67296e153 −0.112170
\(873\) −1.83162e154 −0.723749
\(874\) −3.58433e153 −0.133370
\(875\) −1.02422e155 −3.58897
\(876\) 3.53498e154 1.16660
\(877\) −5.33567e154 −1.65848 −0.829240 0.558893i \(-0.811226\pi\)
−0.829240 + 0.558893i \(0.811226\pi\)
\(878\) 1.77438e154 0.519500
\(879\) 3.65423e154 1.00781
\(880\) 5.98589e152 0.0155521
\(881\) −2.42473e154 −0.593510 −0.296755 0.954954i \(-0.595904\pi\)
−0.296755 + 0.954954i \(0.595904\pi\)
\(882\) −9.24198e152 −0.0213140
\(883\) 1.13732e154 0.247142 0.123571 0.992336i \(-0.460565\pi\)
0.123571 + 0.992336i \(0.460565\pi\)
\(884\) 2.55269e154 0.522701
\(885\) 2.13151e155 4.11307
\(886\) −3.84668e154 −0.699546
\(887\) 3.65900e154 0.627152 0.313576 0.949563i \(-0.398473\pi\)
0.313576 + 0.949563i \(0.398473\pi\)
\(888\) −8.24452e154 −1.33194
\(889\) 5.84199e154 0.889649
\(890\) 1.11880e154 0.160612
\(891\) −1.58137e154 −0.214020
\(892\) −4.48526e154 −0.572312
\(893\) −1.30853e155 −1.57428
\(894\) 4.28304e154 0.485884
\(895\) 5.78904e154 0.619294
\(896\) 6.43281e154 0.648978
\(897\) −2.56986e154 −0.244516
\(898\) −5.62754e154 −0.505023
\(899\) −6.51353e154 −0.551356
\(900\) −2.43957e155 −1.94797
\(901\) 6.20687e154 0.467543
\(902\) −6.56099e153 −0.0466258
\(903\) 2.00653e154 0.134536
\(904\) 2.29467e155 1.45170
\(905\) −1.47952e155 −0.883222
\(906\) −9.47672e154 −0.533860
\(907\) −1.41609e155 −0.752852 −0.376426 0.926447i \(-0.622847\pi\)
−0.376426 + 0.926447i \(0.622847\pi\)
\(908\) 1.37152e155 0.688171
\(909\) 2.88522e154 0.136639
\(910\) 1.61603e155 0.722396
\(911\) 1.60586e155 0.677632 0.338816 0.940853i \(-0.389974\pi\)
0.338816 + 0.940853i \(0.389974\pi\)
\(912\) −9.83774e153 −0.0391892
\(913\) −3.25971e153 −0.0122592
\(914\) −2.58295e155 −0.917151
\(915\) −1.46031e155 −0.489594
\(916\) −1.44620e155 −0.457843
\(917\) −1.33452e155 −0.398967
\(918\) −3.16750e154 −0.0894285
\(919\) 7.22092e155 1.92543 0.962716 0.270514i \(-0.0871936\pi\)
0.962716 + 0.270514i \(0.0871936\pi\)
\(920\) 2.12028e155 0.533989
\(921\) 1.04057e156 2.47538
\(922\) −1.42120e154 −0.0319362
\(923\) 3.13125e155 0.664703
\(924\) −1.04367e155 −0.209308
\(925\) −1.40931e156 −2.67033
\(926\) 3.67647e152 0.000658194 0
\(927\) 3.57021e155 0.603959
\(928\) −5.88548e155 −0.940835
\(929\) −2.41990e155 −0.365572 −0.182786 0.983153i \(-0.558512\pi\)
−0.182786 + 0.983153i \(0.558512\pi\)
\(930\) −7.10572e155 −1.01450
\(931\) −1.94049e154 −0.0261850
\(932\) −1.46345e154 −0.0186657
\(933\) 4.31777e155 0.520563
\(934\) 2.92428e154 0.0333279
\(935\) 5.68650e155 0.612682
\(936\) 6.45471e155 0.657498
\(937\) −9.71475e155 −0.935628 −0.467814 0.883827i \(-0.654958\pi\)
−0.467814 + 0.883827i \(0.654958\pi\)
\(938\) 4.96616e154 0.0452243
\(939\) −3.04034e156 −2.61806
\(940\) 3.00077e156 2.44355
\(941\) 4.90410e155 0.377663 0.188832 0.982010i \(-0.439530\pi\)
0.188832 + 0.982010i \(0.439530\pi\)
\(942\) −9.53590e155 −0.694528
\(943\) 1.31662e155 0.0906974
\(944\) −7.57040e154 −0.0493275
\(945\) 3.46032e155 0.213278
\(946\) 2.30022e154 0.0134117
\(947\) −1.95961e156 −1.08093 −0.540464 0.841367i \(-0.681751\pi\)
−0.540464 + 0.841367i \(0.681751\pi\)
\(948\) −1.82313e156 −0.951438
\(949\) −1.59878e156 −0.789430
\(950\) 2.96832e156 1.38683
\(951\) 5.89882e156 2.60788
\(952\) 3.10976e156 1.30103
\(953\) 5.58969e155 0.221315 0.110657 0.993859i \(-0.464704\pi\)
0.110657 + 0.993859i \(0.464704\pi\)
\(954\) 6.08439e155 0.227996
\(955\) −1.92670e156 −0.683341
\(956\) 1.11686e156 0.374936
\(957\) 9.85583e155 0.313196
\(958\) 1.23861e156 0.372603
\(959\) −2.52917e156 −0.720280
\(960\) −6.06424e156 −1.63507
\(961\) −2.54555e156 −0.649836
\(962\) 1.44555e156 0.349416
\(963\) −4.81033e156 −1.10102
\(964\) −2.94114e156 −0.637488
\(965\) 1.07670e157 2.21010
\(966\) −1.21368e156 −0.235942
\(967\) −9.52983e156 −1.75467 −0.877335 0.479879i \(-0.840681\pi\)
−0.877335 + 0.479879i \(0.840681\pi\)
\(968\) 5.36341e156 0.935373
\(969\) −9.34569e156 −1.54388
\(970\) −5.11073e156 −0.799773
\(971\) 6.33625e156 0.939340 0.469670 0.882842i \(-0.344373\pi\)
0.469670 + 0.882842i \(0.344373\pi\)
\(972\) −6.45775e156 −0.906990
\(973\) 5.56302e156 0.740264
\(974\) −6.74556e156 −0.850497
\(975\) 2.12820e157 2.54256
\(976\) 5.18650e154 0.00587163
\(977\) 3.04048e156 0.326195 0.163098 0.986610i \(-0.447851\pi\)
0.163098 + 0.986610i \(0.447851\pi\)
\(978\) 2.93122e156 0.298029
\(979\) 3.26792e155 0.0314905
\(980\) 4.45001e155 0.0406436
\(981\) 1.41019e156 0.122083
\(982\) 6.28280e156 0.515585
\(983\) 2.40548e157 1.87129 0.935646 0.352939i \(-0.114818\pi\)
0.935646 + 0.352939i \(0.114818\pi\)
\(984\) −6.37854e156 −0.470412
\(985\) −9.59330e156 −0.670758
\(986\) −1.13847e157 −0.754716
\(987\) −4.43077e157 −2.78502
\(988\) 5.25396e156 0.313147
\(989\) −4.61593e155 −0.0260888
\(990\) 5.57428e156 0.298773
\(991\) 1.87572e157 0.953455 0.476728 0.879051i \(-0.341823\pi\)
0.476728 + 0.879051i \(0.341823\pi\)
\(992\) 1.23941e157 0.597520
\(993\) 3.79004e157 1.73304
\(994\) 1.47881e157 0.641396
\(995\) −4.64688e157 −1.91183
\(996\) −1.22856e156 −0.0479491
\(997\) 1.53697e157 0.569076 0.284538 0.958665i \(-0.408160\pi\)
0.284538 + 0.958665i \(0.408160\pi\)
\(998\) 3.81011e156 0.133839
\(999\) 3.09529e156 0.103161
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.1.6 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.106.a.a.1.6 8 1.1 even 1 trivial