Properties

Label 1.90.a.a.1.2
Level 1
Weight 90
Character 1.1
Self dual yes
Analytic conductor 50.162
Analytic rank 1
Dimension 7
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 90 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(50.1624291928\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: multiple of \( 2^{83}\cdot 3^{29}\cdot 5^{9}\cdot 7^{5}\cdot 11^{2}\cdot 13^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(5.71170e11\) of \(x^{7} - 3 x^{6} - 1400531600527934473811256 x^{5} + 92429106535860966322690362643440028 x^{4} + 486502004825754823566786579226467181483733375376 x^{3} - 41390338158988484679355574715314473323669246141474080139600 x^{2} - 47785461930919140795588898989186212855196409324706742802409577734342400 x + 5612439960923763868733925256800794059272997589318959539312206365735127554315560000\)
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.19029e13 q^{2} +3.23465e21 q^{3} +3.98828e26 q^{4} +1.00222e30 q^{5} -1.03195e35 q^{6} +1.60489e37 q^{7} +7.02319e39 q^{8} +7.55364e42 q^{9} +O(q^{10})\) \(q-3.19029e13 q^{2} +3.23465e21 q^{3} +3.98828e26 q^{4} +1.00222e30 q^{5} -1.03195e35 q^{6} +1.60489e37 q^{7} +7.02319e39 q^{8} +7.55364e42 q^{9} -3.19739e43 q^{10} -3.40556e46 q^{11} +1.29007e48 q^{12} -5.21527e49 q^{13} -5.12007e50 q^{14} +3.24184e51 q^{15} -4.70923e53 q^{16} -3.62126e53 q^{17} -2.40983e56 q^{18} -5.12451e56 q^{19} +3.99715e56 q^{20} +5.19126e58 q^{21} +1.08647e60 q^{22} -4.07651e60 q^{23} +2.27176e61 q^{24} -1.60554e62 q^{25} +1.66382e63 q^{26} +1.50227e64 q^{27} +6.40074e63 q^{28} -1.51052e64 q^{29} -1.03424e65 q^{30} -6.54829e65 q^{31} +1.06767e67 q^{32} -1.10158e68 q^{33} +1.15529e67 q^{34} +1.60846e67 q^{35} +3.01260e69 q^{36} +3.74749e69 q^{37} +1.63487e70 q^{38} -1.68696e71 q^{39} +7.03881e69 q^{40} +4.56036e71 q^{41} -1.65616e72 q^{42} +6.44841e72 q^{43} -1.35823e73 q^{44} +7.57044e72 q^{45} +1.30053e74 q^{46} -3.14673e74 q^{47} -1.52327e75 q^{48} -1.37822e75 q^{49} +5.12215e75 q^{50} -1.17135e75 q^{51} -2.07999e76 q^{52} -1.60814e76 q^{53} -4.79270e77 q^{54} -3.41313e76 q^{55} +1.12714e77 q^{56} -1.65760e78 q^{57} +4.81900e77 q^{58} -3.75851e78 q^{59} +1.29294e78 q^{60} -8.19597e78 q^{61} +2.08910e79 q^{62} +1.21228e80 q^{63} -4.91303e79 q^{64} -5.22687e79 q^{65} +3.51436e81 q^{66} -2.77246e80 q^{67} -1.44426e80 q^{68} -1.31861e82 q^{69} -5.13146e80 q^{70} -2.48739e82 q^{71} +5.30507e82 q^{72} +1.94198e82 q^{73} -1.19556e83 q^{74} -5.19337e83 q^{75} -2.04380e83 q^{76} -5.46555e83 q^{77} +5.38189e84 q^{78} -3.70591e84 q^{79} -4.71970e83 q^{80} +2.66174e85 q^{81} -1.45489e85 q^{82} -1.07302e85 q^{83} +2.07042e85 q^{84} -3.62931e83 q^{85} -2.05723e86 q^{86} -4.88600e85 q^{87} -2.39179e86 q^{88} +7.67903e86 q^{89} -2.41519e86 q^{90} -8.36993e86 q^{91} -1.62582e87 q^{92} -2.11814e87 q^{93} +1.00390e88 q^{94} -5.13591e86 q^{95} +3.45353e88 q^{96} +1.74718e88 q^{97} +4.39691e88 q^{98} -2.57244e89 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 31407330351408q^{2} - \)\(13\!\cdots\!64\)\(q^{3} + \)\(22\!\cdots\!04\)\(q^{4} + \)\(10\!\cdots\!50\)\(q^{5} - \)\(47\!\cdots\!76\)\(q^{6} + \)\(38\!\cdots\!92\)\(q^{7} - \)\(17\!\cdots\!20\)\(q^{8} + \)\(56\!\cdots\!71\)\(q^{9} + O(q^{10}) \) \( 7q - 31407330351408q^{2} - \)\(13\!\cdots\!64\)\(q^{3} + \)\(22\!\cdots\!04\)\(q^{4} + \)\(10\!\cdots\!50\)\(q^{5} - \)\(47\!\cdots\!76\)\(q^{6} + \)\(38\!\cdots\!92\)\(q^{7} - \)\(17\!\cdots\!20\)\(q^{8} + \)\(56\!\cdots\!71\)\(q^{9} - \)\(33\!\cdots\!00\)\(q^{10} - \)\(33\!\cdots\!56\)\(q^{11} - \)\(10\!\cdots\!28\)\(q^{12} - \)\(10\!\cdots\!34\)\(q^{13} - \)\(33\!\cdots\!32\)\(q^{14} - \)\(39\!\cdots\!00\)\(q^{15} + \)\(11\!\cdots\!32\)\(q^{16} + \)\(83\!\cdots\!42\)\(q^{17} - \)\(14\!\cdots\!04\)\(q^{18} + \)\(56\!\cdots\!80\)\(q^{19} + \)\(17\!\cdots\!00\)\(q^{20} - \)\(90\!\cdots\!36\)\(q^{21} - \)\(57\!\cdots\!36\)\(q^{22} - \)\(11\!\cdots\!04\)\(q^{23} + \)\(10\!\cdots\!40\)\(q^{24} - \)\(21\!\cdots\!75\)\(q^{25} + \)\(25\!\cdots\!24\)\(q^{26} + \)\(11\!\cdots\!80\)\(q^{27} + \)\(42\!\cdots\!84\)\(q^{28} - \)\(14\!\cdots\!30\)\(q^{29} + \)\(68\!\cdots\!00\)\(q^{30} + \)\(68\!\cdots\!04\)\(q^{31} - \)\(18\!\cdots\!48\)\(q^{32} - \)\(86\!\cdots\!88\)\(q^{33} + \)\(31\!\cdots\!28\)\(q^{34} + \)\(33\!\cdots\!00\)\(q^{35} - \)\(16\!\cdots\!88\)\(q^{36} - \)\(54\!\cdots\!58\)\(q^{37} + \)\(45\!\cdots\!20\)\(q^{38} - \)\(52\!\cdots\!48\)\(q^{39} - \)\(36\!\cdots\!00\)\(q^{40} - \)\(65\!\cdots\!66\)\(q^{41} + \)\(11\!\cdots\!04\)\(q^{42} + \)\(32\!\cdots\!56\)\(q^{43} - \)\(15\!\cdots\!32\)\(q^{44} - \)\(47\!\cdots\!50\)\(q^{45} - \)\(56\!\cdots\!76\)\(q^{46} - \)\(58\!\cdots\!08\)\(q^{47} - \)\(38\!\cdots\!04\)\(q^{48} - \)\(30\!\cdots\!01\)\(q^{49} - \)\(11\!\cdots\!00\)\(q^{50} - \)\(44\!\cdots\!56\)\(q^{51} - \)\(19\!\cdots\!68\)\(q^{52} - \)\(18\!\cdots\!14\)\(q^{53} - \)\(10\!\cdots\!20\)\(q^{54} - \)\(12\!\cdots\!00\)\(q^{55} - \)\(58\!\cdots\!20\)\(q^{56} - \)\(66\!\cdots\!40\)\(q^{57} - \)\(30\!\cdots\!20\)\(q^{58} - \)\(90\!\cdots\!60\)\(q^{59} - \)\(28\!\cdots\!00\)\(q^{60} + \)\(87\!\cdots\!94\)\(q^{61} + \)\(16\!\cdots\!24\)\(q^{62} + \)\(60\!\cdots\!96\)\(q^{63} + \)\(14\!\cdots\!44\)\(q^{64} + \)\(13\!\cdots\!00\)\(q^{65} + \)\(57\!\cdots\!08\)\(q^{66} + \)\(58\!\cdots\!92\)\(q^{67} + \)\(33\!\cdots\!84\)\(q^{68} - \)\(59\!\cdots\!48\)\(q^{69} - \)\(48\!\cdots\!00\)\(q^{70} - \)\(54\!\cdots\!76\)\(q^{71} - \)\(19\!\cdots\!60\)\(q^{72} - \)\(19\!\cdots\!54\)\(q^{73} - \)\(96\!\cdots\!52\)\(q^{74} - \)\(44\!\cdots\!00\)\(q^{75} - \)\(62\!\cdots\!40\)\(q^{76} + \)\(13\!\cdots\!64\)\(q^{77} + \)\(51\!\cdots\!92\)\(q^{78} + \)\(26\!\cdots\!20\)\(q^{79} + \)\(27\!\cdots\!00\)\(q^{80} + \)\(48\!\cdots\!47\)\(q^{81} + \)\(63\!\cdots\!04\)\(q^{82} - \)\(35\!\cdots\!24\)\(q^{83} - \)\(91\!\cdots\!92\)\(q^{84} - \)\(14\!\cdots\!00\)\(q^{85} - \)\(24\!\cdots\!76\)\(q^{86} - \)\(41\!\cdots\!60\)\(q^{87} - \)\(18\!\cdots\!40\)\(q^{88} - \)\(16\!\cdots\!90\)\(q^{89} - \)\(15\!\cdots\!00\)\(q^{90} - \)\(30\!\cdots\!36\)\(q^{91} + \)\(72\!\cdots\!92\)\(q^{92} + \)\(87\!\cdots\!92\)\(q^{93} + \)\(22\!\cdots\!08\)\(q^{94} + \)\(22\!\cdots\!00\)\(q^{95} + \)\(84\!\cdots\!44\)\(q^{96} + \)\(71\!\cdots\!42\)\(q^{97} - \)\(17\!\cdots\!56\)\(q^{98} - \)\(19\!\cdots\!68\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.19029e13 −1.28232 −0.641159 0.767408i \(-0.721546\pi\)
−0.641159 + 0.767408i \(0.721546\pi\)
\(3\) 3.23465e21 1.89641 0.948203 0.317664i \(-0.102898\pi\)
0.948203 + 0.317664i \(0.102898\pi\)
\(4\) 3.98828e26 0.644341
\(5\) 1.00222e30 0.0788496 0.0394248 0.999223i \(-0.487447\pi\)
0.0394248 + 0.999223i \(0.487447\pi\)
\(6\) −1.03195e35 −2.43180
\(7\) 1.60489e37 0.396810 0.198405 0.980120i \(-0.436424\pi\)
0.198405 + 0.980120i \(0.436424\pi\)
\(8\) 7.02319e39 0.456068
\(9\) 7.55364e42 2.59636
\(10\) −3.19739e43 −0.101110
\(11\) −3.40556e46 −1.54958 −0.774790 0.632219i \(-0.782144\pi\)
−0.774790 + 0.632219i \(0.782144\pi\)
\(12\) 1.29007e48 1.22193
\(13\) −5.21527e49 −1.40216 −0.701080 0.713083i \(-0.747298\pi\)
−0.701080 + 0.713083i \(0.747298\pi\)
\(14\) −5.12007e50 −0.508837
\(15\) 3.24184e51 0.149531
\(16\) −4.70923e53 −1.22917
\(17\) −3.62126e53 −0.0636623 −0.0318311 0.999493i \(-0.510134\pi\)
−0.0318311 + 0.999493i \(0.510134\pi\)
\(18\) −2.40983e56 −3.32936
\(19\) −5.12451e56 −0.638436 −0.319218 0.947681i \(-0.603420\pi\)
−0.319218 + 0.947681i \(0.603420\pi\)
\(20\) 3.99715e56 0.0508060
\(21\) 5.19126e58 0.752513
\(22\) 1.08647e60 1.98705
\(23\) −4.07651e60 −1.03134 −0.515668 0.856789i \(-0.672456\pi\)
−0.515668 + 0.856789i \(0.672456\pi\)
\(24\) 2.27176e61 0.864891
\(25\) −1.60554e62 −0.993783
\(26\) 1.66382e63 1.79802
\(27\) 1.50227e64 3.02734
\(28\) 6.40074e63 0.255681
\(29\) −1.51052e64 −0.126595 −0.0632973 0.997995i \(-0.520162\pi\)
−0.0632973 + 0.997995i \(0.520162\pi\)
\(30\) −1.03424e65 −0.191746
\(31\) −6.54829e65 −0.282184 −0.141092 0.989996i \(-0.545061\pi\)
−0.141092 + 0.989996i \(0.545061\pi\)
\(32\) 1.06767e67 1.12011
\(33\) −1.10158e68 −2.93863
\(34\) 1.15529e67 0.0816353
\(35\) 1.60846e67 0.0312883
\(36\) 3.01260e69 1.67294
\(37\) 3.74749e69 0.614842 0.307421 0.951574i \(-0.400534\pi\)
0.307421 + 0.951574i \(0.400534\pi\)
\(38\) 1.63487e70 0.818678
\(39\) −1.68696e71 −2.65906
\(40\) 7.03881e69 0.0359608
\(41\) 4.56036e71 0.776457 0.388228 0.921563i \(-0.373087\pi\)
0.388228 + 0.921563i \(0.373087\pi\)
\(42\) −1.65616e72 −0.964961
\(43\) 6.44841e72 1.31858 0.659290 0.751889i \(-0.270857\pi\)
0.659290 + 0.751889i \(0.270857\pi\)
\(44\) −1.35823e73 −0.998457
\(45\) 7.57044e72 0.204722
\(46\) 1.30053e74 1.32250
\(47\) −3.14673e74 −1.22886 −0.614432 0.788969i \(-0.710615\pi\)
−0.614432 + 0.788969i \(0.710615\pi\)
\(48\) −1.52327e75 −2.33100
\(49\) −1.37822e75 −0.842542
\(50\) 5.12215e75 1.27435
\(51\) −1.17135e75 −0.120730
\(52\) −2.07999e76 −0.903468
\(53\) −1.60814e76 −0.299260 −0.149630 0.988742i \(-0.547808\pi\)
−0.149630 + 0.988742i \(0.547808\pi\)
\(54\) −4.79270e77 −3.88202
\(55\) −3.41313e76 −0.122184
\(56\) 1.12714e77 0.180972
\(57\) −1.65760e78 −1.21073
\(58\) 4.81900e77 0.162335
\(59\) −3.75851e78 −0.591700 −0.295850 0.955234i \(-0.595603\pi\)
−0.295850 + 0.955234i \(0.595603\pi\)
\(60\) 1.29294e78 0.0963489
\(61\) −8.19597e78 −0.292700 −0.146350 0.989233i \(-0.546753\pi\)
−0.146350 + 0.989233i \(0.546753\pi\)
\(62\) 2.08910e79 0.361850
\(63\) 1.21228e80 1.03026
\(64\) −4.91303e79 −0.207176
\(65\) −5.22687e79 −0.110560
\(66\) 3.51436e81 3.76826
\(67\) −2.77246e80 −0.152243 −0.0761214 0.997099i \(-0.524254\pi\)
−0.0761214 + 0.997099i \(0.524254\pi\)
\(68\) −1.44426e80 −0.0410202
\(69\) −1.31861e82 −1.95583
\(70\) −5.13146e80 −0.0401216
\(71\) −2.48739e82 −1.03454 −0.517271 0.855822i \(-0.673052\pi\)
−0.517271 + 0.855822i \(0.673052\pi\)
\(72\) 5.30507e82 1.18412
\(73\) 1.94198e82 0.234627 0.117313 0.993095i \(-0.462572\pi\)
0.117313 + 0.993095i \(0.462572\pi\)
\(74\) −1.19556e83 −0.788423
\(75\) −5.19337e83 −1.88462
\(76\) −2.04380e83 −0.411370
\(77\) −5.46555e83 −0.614888
\(78\) 5.38189e84 3.40977
\(79\) −3.70591e84 −1.33196 −0.665978 0.745972i \(-0.731985\pi\)
−0.665978 + 0.745972i \(0.731985\pi\)
\(80\) −4.71970e83 −0.0969192
\(81\) 2.66174e85 3.14472
\(82\) −1.45489e85 −0.995665
\(83\) −1.07302e85 −0.428185 −0.214093 0.976813i \(-0.568679\pi\)
−0.214093 + 0.976813i \(0.568679\pi\)
\(84\) 2.07042e85 0.484875
\(85\) −3.62931e83 −0.00501975
\(86\) −2.05723e86 −1.69084
\(87\) −4.88600e85 −0.240075
\(88\) −2.39179e86 −0.706714
\(89\) 7.67903e86 1.37231 0.686153 0.727457i \(-0.259298\pi\)
0.686153 + 0.727457i \(0.259298\pi\)
\(90\) −2.41519e86 −0.262519
\(91\) −8.36993e86 −0.556391
\(92\) −1.62582e87 −0.664531
\(93\) −2.11814e87 −0.535136
\(94\) 1.00390e88 1.57580
\(95\) −5.13591e86 −0.0503404
\(96\) 3.45353e88 2.12419
\(97\) 1.74718e88 0.677635 0.338818 0.940852i \(-0.389973\pi\)
0.338818 + 0.940852i \(0.389973\pi\)
\(98\) 4.39691e88 1.08041
\(99\) −2.57244e89 −4.02326
\(100\) −6.40335e88 −0.640335
\(101\) 1.19479e89 0.767343 0.383671 0.923470i \(-0.374660\pi\)
0.383671 + 0.923470i \(0.374660\pi\)
\(102\) 3.73695e88 0.154814
\(103\) −1.38153e88 −0.0370769 −0.0185385 0.999828i \(-0.505901\pi\)
−0.0185385 + 0.999828i \(0.505901\pi\)
\(104\) −3.66278e89 −0.639481
\(105\) 5.20280e88 0.0593353
\(106\) 5.13045e89 0.383747
\(107\) −1.99720e90 −0.983656 −0.491828 0.870692i \(-0.663671\pi\)
−0.491828 + 0.870692i \(0.663671\pi\)
\(108\) 5.99148e90 1.95064
\(109\) −1.48917e90 −0.321711 −0.160855 0.986978i \(-0.551425\pi\)
−0.160855 + 0.986978i \(0.551425\pi\)
\(110\) 1.08889e90 0.156678
\(111\) 1.21218e91 1.16599
\(112\) −7.55779e90 −0.487745
\(113\) −2.72847e91 −1.18557 −0.592787 0.805359i \(-0.701973\pi\)
−0.592787 + 0.805359i \(0.701973\pi\)
\(114\) 5.28823e91 1.55255
\(115\) −4.08558e90 −0.0813204
\(116\) −6.02436e90 −0.0815700
\(117\) −3.93943e92 −3.64051
\(118\) 1.19908e92 0.758747
\(119\) −5.81172e90 −0.0252618
\(120\) 2.27681e91 0.0681963
\(121\) 6.76780e92 1.40120
\(122\) 2.61476e92 0.375335
\(123\) 1.47512e93 1.47248
\(124\) −2.61164e92 −0.181823
\(125\) −3.22829e92 −0.157209
\(126\) −3.86752e93 −1.32112
\(127\) −8.97792e92 −0.215730 −0.107865 0.994166i \(-0.534401\pi\)
−0.107865 + 0.994166i \(0.534401\pi\)
\(128\) −5.04114e93 −0.854447
\(129\) 2.08583e94 2.50056
\(130\) 1.66752e93 0.141773
\(131\) −1.51084e94 −0.913370 −0.456685 0.889628i \(-0.650963\pi\)
−0.456685 + 0.889628i \(0.650963\pi\)
\(132\) −4.39340e94 −1.89348
\(133\) −8.22428e93 −0.253338
\(134\) 8.84496e93 0.195224
\(135\) 1.50562e94 0.238705
\(136\) −2.54328e93 −0.0290344
\(137\) 4.03766e94 0.332709 0.166355 0.986066i \(-0.446800\pi\)
0.166355 + 0.986066i \(0.446800\pi\)
\(138\) 4.20675e95 2.50800
\(139\) −2.42776e94 −0.104965 −0.0524827 0.998622i \(-0.516713\pi\)
−0.0524827 + 0.998622i \(0.516713\pi\)
\(140\) 6.41498e93 0.0201603
\(141\) −1.01786e96 −2.33043
\(142\) 7.93551e95 1.32661
\(143\) 1.77609e96 2.17276
\(144\) −3.55718e96 −3.19135
\(145\) −1.51388e94 −0.00998193
\(146\) −6.19548e95 −0.300866
\(147\) −4.45804e96 −1.59780
\(148\) 1.49460e96 0.396168
\(149\) 4.62119e96 0.907746 0.453873 0.891066i \(-0.350042\pi\)
0.453873 + 0.891066i \(0.350042\pi\)
\(150\) 1.65684e97 2.41668
\(151\) −9.15258e96 −0.993275 −0.496638 0.867958i \(-0.665432\pi\)
−0.496638 + 0.867958i \(0.665432\pi\)
\(152\) −3.59904e96 −0.291170
\(153\) −2.73537e96 −0.165290
\(154\) 1.74367e97 0.788483
\(155\) −6.56286e95 −0.0222501
\(156\) −6.72805e97 −1.71334
\(157\) 5.65103e97 1.08291 0.541456 0.840729i \(-0.317873\pi\)
0.541456 + 0.840729i \(0.317873\pi\)
\(158\) 1.18230e98 1.70799
\(159\) −5.20178e97 −0.567519
\(160\) 1.07004e97 0.0883205
\(161\) −6.54235e97 −0.409244
\(162\) −8.49172e98 −4.03253
\(163\) 3.56675e98 1.28802 0.644012 0.765015i \(-0.277269\pi\)
0.644012 + 0.765015i \(0.277269\pi\)
\(164\) 1.81880e98 0.500303
\(165\) −1.10403e98 −0.231710
\(166\) 3.42324e98 0.549070
\(167\) 1.30174e99 1.59824 0.799121 0.601170i \(-0.205298\pi\)
0.799121 + 0.601170i \(0.205298\pi\)
\(168\) 3.64592e98 0.343197
\(169\) 1.33647e99 0.966051
\(170\) 1.15786e97 0.00643691
\(171\) −3.87087e99 −1.65761
\(172\) 2.57180e99 0.849614
\(173\) −6.61614e99 −1.68870 −0.844351 0.535791i \(-0.820014\pi\)
−0.844351 + 0.535791i \(0.820014\pi\)
\(174\) 1.55878e99 0.307852
\(175\) −2.57672e99 −0.394343
\(176\) 1.60375e100 1.90469
\(177\) −1.21575e100 −1.12210
\(178\) −2.44984e100 −1.75973
\(179\) −1.26918e99 −0.0710497 −0.0355249 0.999369i \(-0.511310\pi\)
−0.0355249 + 0.999369i \(0.511310\pi\)
\(180\) 3.01930e99 0.131911
\(181\) 5.28698e100 1.80514 0.902571 0.430541i \(-0.141677\pi\)
0.902571 + 0.430541i \(0.141677\pi\)
\(182\) 2.67025e100 0.713470
\(183\) −2.65111e100 −0.555078
\(184\) −2.86301e100 −0.470360
\(185\) 3.75582e99 0.0484801
\(186\) 6.75750e100 0.686215
\(187\) 1.23324e100 0.0986498
\(188\) −1.25500e101 −0.791808
\(189\) 2.41098e101 1.20128
\(190\) 1.63851e100 0.0645524
\(191\) −2.70845e100 −0.0844764 −0.0422382 0.999108i \(-0.513449\pi\)
−0.0422382 + 0.999108i \(0.513449\pi\)
\(192\) −1.58919e101 −0.392891
\(193\) −7.69721e101 −1.51019 −0.755097 0.655613i \(-0.772410\pi\)
−0.755097 + 0.655613i \(0.772410\pi\)
\(194\) −5.57403e101 −0.868944
\(195\) −1.69071e101 −0.209666
\(196\) −5.49670e101 −0.542884
\(197\) −1.82807e102 −1.43961 −0.719805 0.694176i \(-0.755769\pi\)
−0.719805 + 0.694176i \(0.755769\pi\)
\(198\) 8.20683e102 5.15910
\(199\) 1.85967e102 0.934273 0.467137 0.884185i \(-0.345286\pi\)
0.467137 + 0.884185i \(0.345286\pi\)
\(200\) −1.12760e102 −0.453233
\(201\) −8.96794e101 −0.288714
\(202\) −3.81172e102 −0.983978
\(203\) −2.42421e101 −0.0502340
\(204\) −4.67166e101 −0.0777910
\(205\) 4.57050e101 0.0612233
\(206\) 4.40749e101 0.0475444
\(207\) −3.07925e103 −2.67772
\(208\) 2.45599e103 1.72349
\(209\) 1.74518e103 0.989307
\(210\) −1.65985e102 −0.0760868
\(211\) −1.52726e103 −0.566688 −0.283344 0.959018i \(-0.591444\pi\)
−0.283344 + 0.959018i \(0.591444\pi\)
\(212\) −6.41372e102 −0.192825
\(213\) −8.04584e103 −1.96191
\(214\) 6.37165e103 1.26136
\(215\) 6.46275e102 0.103969
\(216\) 1.05508e104 1.38068
\(217\) −1.05093e103 −0.111973
\(218\) 4.75089e103 0.412535
\(219\) 6.28162e103 0.444947
\(220\) −1.36125e103 −0.0787279
\(221\) 1.88858e103 0.0892647
\(222\) −3.86721e104 −1.49517
\(223\) 3.56431e104 1.12826 0.564130 0.825686i \(-0.309212\pi\)
0.564130 + 0.825686i \(0.309212\pi\)
\(224\) 1.71349e104 0.444472
\(225\) −1.21277e105 −2.58022
\(226\) 8.70463e104 1.52028
\(227\) −1.20998e105 −1.73631 −0.868154 0.496294i \(-0.834694\pi\)
−0.868154 + 0.496294i \(0.834694\pi\)
\(228\) −6.61097e104 −0.780125
\(229\) 1.82845e105 1.77584 0.887922 0.459994i \(-0.152148\pi\)
0.887922 + 0.459994i \(0.152148\pi\)
\(230\) 1.30342e104 0.104279
\(231\) −1.76791e105 −1.16608
\(232\) −1.06087e104 −0.0577358
\(233\) 4.63528e104 0.208323 0.104162 0.994560i \(-0.466784\pi\)
0.104162 + 0.994560i \(0.466784\pi\)
\(234\) 1.25679e106 4.66829
\(235\) −3.15372e104 −0.0968955
\(236\) −1.49900e105 −0.381256
\(237\) −1.19873e106 −2.52593
\(238\) 1.85411e104 0.0323937
\(239\) −9.19408e105 −1.33291 −0.666456 0.745544i \(-0.732190\pi\)
−0.666456 + 0.745544i \(0.732190\pi\)
\(240\) −1.52666e105 −0.183798
\(241\) 9.93847e105 0.994400 0.497200 0.867636i \(-0.334362\pi\)
0.497200 + 0.867636i \(0.334362\pi\)
\(242\) −2.15913e106 −1.79678
\(243\) 4.23918e106 2.93632
\(244\) −3.26878e105 −0.188599
\(245\) −1.38128e105 −0.0664341
\(246\) −4.70605e106 −1.88819
\(247\) 2.67257e106 0.895189
\(248\) −4.59899e105 −0.128695
\(249\) −3.47084e106 −0.812013
\(250\) 1.02992e106 0.201592
\(251\) 6.45749e105 0.105824 0.0529119 0.998599i \(-0.483150\pi\)
0.0529119 + 0.998599i \(0.483150\pi\)
\(252\) 4.83489e106 0.663839
\(253\) 1.38828e107 1.59814
\(254\) 2.86422e106 0.276634
\(255\) −1.17395e105 −0.00951948
\(256\) 1.91237e107 1.30285
\(257\) −1.37257e107 −0.786159 −0.393079 0.919504i \(-0.628590\pi\)
−0.393079 + 0.919504i \(0.628590\pi\)
\(258\) −6.65443e107 −3.20652
\(259\) 6.01431e106 0.243975
\(260\) −2.08462e106 −0.0712381
\(261\) −1.14099e107 −0.328685
\(262\) 4.82003e107 1.17123
\(263\) −1.85087e107 −0.379616 −0.189808 0.981821i \(-0.560787\pi\)
−0.189808 + 0.981821i \(0.560787\pi\)
\(264\) −7.73660e107 −1.34022
\(265\) −1.61172e106 −0.0235965
\(266\) 2.62379e107 0.324860
\(267\) 2.48390e108 2.60245
\(268\) −1.10573e107 −0.0980962
\(269\) −7.26822e107 −0.546326 −0.273163 0.961968i \(-0.588070\pi\)
−0.273163 + 0.961968i \(0.588070\pi\)
\(270\) −4.80336e107 −0.306096
\(271\) 2.62902e108 1.42122 0.710610 0.703586i \(-0.248419\pi\)
0.710610 + 0.703586i \(0.248419\pi\)
\(272\) 1.70533e107 0.0782515
\(273\) −2.70738e108 −1.05514
\(274\) −1.28813e108 −0.426639
\(275\) 5.46777e108 1.53995
\(276\) −5.25897e108 −1.26022
\(277\) −6.85250e108 −1.39797 −0.698987 0.715134i \(-0.746366\pi\)
−0.698987 + 0.715134i \(0.746366\pi\)
\(278\) 7.74525e107 0.134599
\(279\) −4.94634e108 −0.732651
\(280\) 1.12965e107 0.0142696
\(281\) −2.51845e108 −0.271457 −0.135729 0.990746i \(-0.543338\pi\)
−0.135729 + 0.990746i \(0.543338\pi\)
\(282\) 3.24726e109 2.98835
\(283\) 1.20621e108 0.0948254 0.0474127 0.998875i \(-0.484902\pi\)
0.0474127 + 0.998875i \(0.484902\pi\)
\(284\) −9.92041e108 −0.666597
\(285\) −1.66129e108 −0.0954659
\(286\) −5.66625e109 −2.78617
\(287\) 7.31887e108 0.308106
\(288\) 8.06478e109 2.90822
\(289\) −3.22248e109 −0.995947
\(290\) 4.82971e107 0.0128000
\(291\) 5.65152e109 1.28507
\(292\) 7.74514e108 0.151179
\(293\) −5.59855e109 −0.938570 −0.469285 0.883047i \(-0.655488\pi\)
−0.469285 + 0.883047i \(0.655488\pi\)
\(294\) 1.42225e110 2.04889
\(295\) −3.76687e108 −0.0466553
\(296\) 2.63193e109 0.280410
\(297\) −5.11608e110 −4.69111
\(298\) −1.47429e110 −1.16402
\(299\) 2.12601e110 1.44610
\(300\) −2.07126e110 −1.21433
\(301\) 1.03490e110 0.523225
\(302\) 2.91994e110 1.27370
\(303\) 3.86472e110 1.45519
\(304\) 2.41325e110 0.784744
\(305\) −8.21420e108 −0.0230793
\(306\) 8.72662e109 0.211955
\(307\) −2.89040e110 −0.607157 −0.303578 0.952806i \(-0.598181\pi\)
−0.303578 + 0.952806i \(0.598181\pi\)
\(308\) −2.17981e110 −0.396198
\(309\) −4.46876e109 −0.0703129
\(310\) 2.09374e109 0.0285317
\(311\) 1.10485e111 1.30456 0.652282 0.757977i \(-0.273812\pi\)
0.652282 + 0.757977i \(0.273812\pi\)
\(312\) −1.18478e111 −1.21272
\(313\) 7.78951e110 0.691492 0.345746 0.938328i \(-0.387626\pi\)
0.345746 + 0.938328i \(0.387626\pi\)
\(314\) −1.80285e111 −1.38864
\(315\) 1.21497e110 0.0812356
\(316\) −1.47802e111 −0.858233
\(317\) 3.26678e110 0.164810 0.0824049 0.996599i \(-0.473740\pi\)
0.0824049 + 0.996599i \(0.473740\pi\)
\(318\) 1.65952e111 0.727740
\(319\) 5.14416e110 0.196168
\(320\) −4.92395e109 −0.0163358
\(321\) −6.46024e111 −1.86541
\(322\) 2.08720e111 0.524781
\(323\) 1.85572e110 0.0406443
\(324\) 1.06157e112 2.02627
\(325\) 8.37333e111 1.39344
\(326\) −1.13790e112 −1.65166
\(327\) −4.81695e111 −0.610094
\(328\) 3.20283e111 0.354117
\(329\) −5.05015e111 −0.487626
\(330\) 3.52218e111 0.297126
\(331\) 1.61579e112 1.19135 0.595675 0.803226i \(-0.296885\pi\)
0.595675 + 0.803226i \(0.296885\pi\)
\(332\) −4.27949e111 −0.275897
\(333\) 2.83072e112 1.59635
\(334\) −4.15295e112 −2.04946
\(335\) −2.77863e110 −0.0120043
\(336\) −2.44468e112 −0.924963
\(337\) 3.52838e112 1.16962 0.584810 0.811170i \(-0.301169\pi\)
0.584810 + 0.811170i \(0.301169\pi\)
\(338\) −4.26373e112 −1.23879
\(339\) −8.82566e112 −2.24833
\(340\) −1.44747e110 −0.00323443
\(341\) 2.23006e112 0.437267
\(342\) 1.23492e113 2.12558
\(343\) −4.83713e112 −0.731139
\(344\) 4.52884e112 0.601363
\(345\) −1.32154e112 −0.154217
\(346\) 2.11074e113 2.16545
\(347\) 1.07241e113 0.967612 0.483806 0.875175i \(-0.339254\pi\)
0.483806 + 0.875175i \(0.339254\pi\)
\(348\) −1.94867e112 −0.154690
\(349\) 5.96829e112 0.416983 0.208491 0.978024i \(-0.433145\pi\)
0.208491 + 0.978024i \(0.433145\pi\)
\(350\) 8.22049e112 0.505673
\(351\) −7.83476e113 −4.24482
\(352\) −3.63600e113 −1.73570
\(353\) 1.30915e113 0.550827 0.275414 0.961326i \(-0.411185\pi\)
0.275414 + 0.961326i \(0.411185\pi\)
\(354\) 3.87859e113 1.43889
\(355\) −2.49292e112 −0.0815732
\(356\) 3.06261e113 0.884233
\(357\) −1.87989e112 −0.0479067
\(358\) 4.04905e112 0.0911084
\(359\) −4.82670e112 −0.0959284 −0.0479642 0.998849i \(-0.515273\pi\)
−0.0479642 + 0.998849i \(0.515273\pi\)
\(360\) 5.31686e112 0.0933672
\(361\) −3.81668e113 −0.592400
\(362\) −1.68670e114 −2.31477
\(363\) 2.18915e114 2.65724
\(364\) −3.33816e113 −0.358505
\(365\) 1.94630e112 0.0185002
\(366\) 8.45782e113 0.711787
\(367\) −2.20853e114 −1.64613 −0.823063 0.567950i \(-0.807737\pi\)
−0.823063 + 0.567950i \(0.807737\pi\)
\(368\) 1.91972e114 1.26768
\(369\) 3.44473e114 2.01596
\(370\) −1.19822e113 −0.0621669
\(371\) −2.58089e113 −0.118749
\(372\) −8.44774e113 −0.344810
\(373\) −2.99699e114 −1.08553 −0.542765 0.839884i \(-0.682623\pi\)
−0.542765 + 0.839884i \(0.682623\pi\)
\(374\) −3.93440e113 −0.126500
\(375\) −1.04424e114 −0.298132
\(376\) −2.21001e114 −0.560447
\(377\) 7.87775e113 0.177506
\(378\) −7.69175e114 −1.54042
\(379\) 1.07738e115 1.91834 0.959170 0.282829i \(-0.0912727\pi\)
0.959170 + 0.282829i \(0.0912727\pi\)
\(380\) −2.04834e113 −0.0324364
\(381\) −2.90404e114 −0.409111
\(382\) 8.64074e113 0.108326
\(383\) −7.15115e114 −0.798051 −0.399025 0.916940i \(-0.630651\pi\)
−0.399025 + 0.916940i \(0.630651\pi\)
\(384\) −1.63063e115 −1.62038
\(385\) −5.47770e113 −0.0484837
\(386\) 2.45563e115 1.93655
\(387\) 4.87090e115 3.42350
\(388\) 6.96825e114 0.436628
\(389\) −2.74793e115 −1.53549 −0.767747 0.640753i \(-0.778622\pi\)
−0.767747 + 0.640753i \(0.778622\pi\)
\(390\) 5.39386e114 0.268859
\(391\) 1.47621e114 0.0656572
\(392\) −9.67947e114 −0.384257
\(393\) −4.88705e115 −1.73212
\(394\) 5.83207e115 1.84604
\(395\) −3.71415e114 −0.105024
\(396\) −1.02596e116 −2.59235
\(397\) 7.31767e114 0.165270 0.0826352 0.996580i \(-0.473666\pi\)
0.0826352 + 0.996580i \(0.473666\pi\)
\(398\) −5.93289e115 −1.19804
\(399\) −2.66027e115 −0.480431
\(400\) 7.56087e115 1.22152
\(401\) 6.87201e115 0.993480 0.496740 0.867899i \(-0.334530\pi\)
0.496740 + 0.867899i \(0.334530\pi\)
\(402\) 2.86104e115 0.370224
\(403\) 3.41511e115 0.395667
\(404\) 4.76514e115 0.494430
\(405\) 2.66765e115 0.247960
\(406\) 7.73396e114 0.0644159
\(407\) −1.27623e116 −0.952746
\(408\) −8.22661e114 −0.0550610
\(409\) −1.57330e116 −0.944328 −0.472164 0.881511i \(-0.656527\pi\)
−0.472164 + 0.881511i \(0.656527\pi\)
\(410\) −1.45812e115 −0.0785078
\(411\) 1.30604e116 0.630952
\(412\) −5.50992e114 −0.0238902
\(413\) −6.03200e115 −0.234792
\(414\) 9.82371e116 3.43368
\(415\) −1.07540e115 −0.0337622
\(416\) −5.56817e116 −1.57058
\(417\) −7.85294e115 −0.199057
\(418\) −5.56764e116 −1.26861
\(419\) 2.45919e116 0.503811 0.251906 0.967752i \(-0.418943\pi\)
0.251906 + 0.967752i \(0.418943\pi\)
\(420\) 2.07502e115 0.0382322
\(421\) −5.39311e116 −0.893893 −0.446947 0.894561i \(-0.647489\pi\)
−0.446947 + 0.894561i \(0.647489\pi\)
\(422\) 4.87241e116 0.726675
\(423\) −2.37692e117 −3.19057
\(424\) −1.12943e116 −0.136483
\(425\) 5.81408e115 0.0632665
\(426\) 2.56686e117 2.51579
\(427\) −1.31536e116 −0.116146
\(428\) −7.96538e116 −0.633809
\(429\) 5.74503e117 4.12043
\(430\) −2.06181e116 −0.133322
\(431\) 2.12129e116 0.123698 0.0618489 0.998086i \(-0.480300\pi\)
0.0618489 + 0.998086i \(0.480300\pi\)
\(432\) −7.07455e117 −3.72111
\(433\) 3.26732e117 1.55053 0.775265 0.631636i \(-0.217616\pi\)
0.775265 + 0.631636i \(0.217616\pi\)
\(434\) 3.35277e116 0.143586
\(435\) −4.89686e115 −0.0189298
\(436\) −5.93922e116 −0.207291
\(437\) 2.08901e117 0.658441
\(438\) −2.00402e117 −0.570564
\(439\) 2.12142e117 0.545702 0.272851 0.962056i \(-0.412033\pi\)
0.272851 + 0.962056i \(0.412033\pi\)
\(440\) −2.39711e116 −0.0557241
\(441\) −1.04105e118 −2.18754
\(442\) −6.02513e116 −0.114466
\(443\) −4.42831e117 −0.760802 −0.380401 0.924822i \(-0.624214\pi\)
−0.380401 + 0.924822i \(0.624214\pi\)
\(444\) 4.83451e117 0.751295
\(445\) 7.69611e116 0.108206
\(446\) −1.13712e118 −1.44679
\(447\) 1.49479e118 1.72146
\(448\) −7.88487e116 −0.0822097
\(449\) 4.39818e117 0.415251 0.207626 0.978208i \(-0.433426\pi\)
0.207626 + 0.978208i \(0.433426\pi\)
\(450\) 3.86909e118 3.30866
\(451\) −1.55306e118 −1.20318
\(452\) −1.08819e118 −0.763914
\(453\) −2.96054e118 −1.88365
\(454\) 3.86019e118 2.22650
\(455\) −8.38854e116 −0.0438712
\(456\) −1.16416e118 −0.552178
\(457\) 2.74806e118 1.18238 0.591188 0.806533i \(-0.298659\pi\)
0.591188 + 0.806533i \(0.298659\pi\)
\(458\) −5.83330e118 −2.27720
\(459\) −5.44012e117 −0.192728
\(460\) −1.62944e117 −0.0523980
\(461\) −2.01568e118 −0.588477 −0.294239 0.955732i \(-0.595066\pi\)
−0.294239 + 0.955732i \(0.595066\pi\)
\(462\) 5.64016e118 1.49528
\(463\) 6.20126e118 1.49323 0.746613 0.665258i \(-0.231679\pi\)
0.746613 + 0.665258i \(0.231679\pi\)
\(464\) 7.11337e117 0.155606
\(465\) −2.12285e117 −0.0421953
\(466\) −1.47879e118 −0.267137
\(467\) −1.14327e119 −1.87735 −0.938676 0.344800i \(-0.887947\pi\)
−0.938676 + 0.344800i \(0.887947\pi\)
\(468\) −1.57115e119 −2.34573
\(469\) −4.44949e117 −0.0604114
\(470\) 1.00613e118 0.124251
\(471\) 1.82791e119 2.05364
\(472\) −2.63967e118 −0.269856
\(473\) −2.19604e119 −2.04324
\(474\) 3.82431e119 3.23905
\(475\) 8.22762e118 0.634467
\(476\) −2.31787e117 −0.0162772
\(477\) −1.21473e119 −0.776986
\(478\) 2.93318e119 1.70922
\(479\) 1.95218e119 1.03655 0.518273 0.855215i \(-0.326575\pi\)
0.518273 + 0.855215i \(0.326575\pi\)
\(480\) 3.46121e118 0.167492
\(481\) −1.95442e119 −0.862107
\(482\) −3.17066e119 −1.27514
\(483\) −2.11622e119 −0.776093
\(484\) 2.69919e119 0.902847
\(485\) 1.75107e118 0.0534313
\(486\) −1.35242e120 −3.76529
\(487\) −2.36047e119 −0.599736 −0.299868 0.953981i \(-0.596943\pi\)
−0.299868 + 0.953981i \(0.596943\pi\)
\(488\) −5.75619e118 −0.133491
\(489\) 1.15372e120 2.44262
\(490\) 4.40669e118 0.0851897
\(491\) 4.48321e119 0.791522 0.395761 0.918354i \(-0.370481\pi\)
0.395761 + 0.918354i \(0.370481\pi\)
\(492\) 5.88317e119 0.948777
\(493\) 5.46997e117 0.00805930
\(494\) −8.52628e119 −1.14792
\(495\) −2.57816e119 −0.317233
\(496\) 3.08374e119 0.346851
\(497\) −3.99199e119 −0.410516
\(498\) 1.10730e120 1.04126
\(499\) −9.47256e119 −0.814692 −0.407346 0.913274i \(-0.633546\pi\)
−0.407346 + 0.913274i \(0.633546\pi\)
\(500\) −1.28753e119 −0.101296
\(501\) 4.21069e120 3.03092
\(502\) −2.06013e119 −0.135700
\(503\) −3.20241e120 −1.93064 −0.965321 0.261065i \(-0.915926\pi\)
−0.965321 + 0.261065i \(0.915926\pi\)
\(504\) 8.51405e119 0.469869
\(505\) 1.19744e119 0.0605047
\(506\) −4.42902e120 −2.04932
\(507\) 4.32301e120 1.83203
\(508\) −3.58064e119 −0.139003
\(509\) −1.53283e120 −0.545196 −0.272598 0.962128i \(-0.587883\pi\)
−0.272598 + 0.962128i \(0.587883\pi\)
\(510\) 3.74526e118 0.0122070
\(511\) 3.11666e119 0.0931021
\(512\) −2.98072e120 −0.816221
\(513\) −7.69842e120 −1.93276
\(514\) 4.37890e120 1.00811
\(515\) −1.38460e118 −0.00292350
\(516\) 8.31888e120 1.61121
\(517\) 1.07164e121 1.90422
\(518\) −1.91874e120 −0.312854
\(519\) −2.14009e121 −3.20246
\(520\) −3.67093e119 −0.0504228
\(521\) 2.75020e120 0.346805 0.173403 0.984851i \(-0.444524\pi\)
0.173403 + 0.984851i \(0.444524\pi\)
\(522\) 3.64010e120 0.421478
\(523\) 1.45893e121 1.55135 0.775674 0.631134i \(-0.217410\pi\)
0.775674 + 0.631134i \(0.217410\pi\)
\(524\) −6.02566e120 −0.588522
\(525\) −8.33478e120 −0.747834
\(526\) 5.90481e120 0.486789
\(527\) 2.37130e119 0.0179645
\(528\) 5.18759e121 3.61207
\(529\) 9.94471e119 0.0636524
\(530\) 5.14186e119 0.0302583
\(531\) −2.83904e121 −1.53626
\(532\) −3.28007e120 −0.163236
\(533\) −2.37835e121 −1.08872
\(534\) −7.92436e121 −3.33717
\(535\) −2.00164e120 −0.0775609
\(536\) −1.94715e120 −0.0694331
\(537\) −4.10534e120 −0.134739
\(538\) 2.31878e121 0.700564
\(539\) 4.69359e121 1.30559
\(540\) 6.00481e120 0.153807
\(541\) −5.02723e120 −0.118591 −0.0592953 0.998240i \(-0.518885\pi\)
−0.0592953 + 0.998240i \(0.518885\pi\)
\(542\) −8.38736e121 −1.82246
\(543\) 1.71015e122 3.42328
\(544\) −3.86630e120 −0.0713090
\(545\) −1.49248e120 −0.0253668
\(546\) 8.63734e121 1.35303
\(547\) 1.81478e121 0.262053 0.131026 0.991379i \(-0.458173\pi\)
0.131026 + 0.991379i \(0.458173\pi\)
\(548\) 1.61033e121 0.214378
\(549\) −6.19094e121 −0.759954
\(550\) −1.74438e122 −1.97470
\(551\) 7.74067e120 0.0808225
\(552\) −9.26084e121 −0.891993
\(553\) −5.94758e121 −0.528533
\(554\) 2.18615e122 1.79265
\(555\) 1.21488e121 0.0919379
\(556\) −9.68256e120 −0.0676335
\(557\) 4.76949e121 0.307550 0.153775 0.988106i \(-0.450857\pi\)
0.153775 + 0.988106i \(0.450857\pi\)
\(558\) 1.57803e122 0.939492
\(559\) −3.36302e122 −1.84886
\(560\) −7.57460e120 −0.0384585
\(561\) 3.98910e121 0.187080
\(562\) 8.03458e121 0.348095
\(563\) −6.41763e121 −0.256892 −0.128446 0.991716i \(-0.540999\pi\)
−0.128446 + 0.991716i \(0.540999\pi\)
\(564\) −4.05949e122 −1.50159
\(565\) −2.73454e121 −0.0934821
\(566\) −3.84815e121 −0.121596
\(567\) 4.27179e122 1.24785
\(568\) −1.74694e122 −0.471822
\(569\) 3.36684e122 0.840867 0.420433 0.907323i \(-0.361878\pi\)
0.420433 + 0.907323i \(0.361878\pi\)
\(570\) 5.29999e121 0.122418
\(571\) −2.53729e122 −0.542080 −0.271040 0.962568i \(-0.587368\pi\)
−0.271040 + 0.962568i \(0.587368\pi\)
\(572\) 7.08354e122 1.40000
\(573\) −8.76087e121 −0.160202
\(574\) −2.33493e122 −0.395090
\(575\) 6.54501e122 1.02492
\(576\) −3.71112e122 −0.537904
\(577\) 1.10107e123 1.47737 0.738687 0.674049i \(-0.235446\pi\)
0.738687 + 0.674049i \(0.235446\pi\)
\(578\) 1.02807e123 1.27712
\(579\) −2.48978e123 −2.86394
\(580\) −6.03776e120 −0.00643176
\(581\) −1.72207e122 −0.169908
\(582\) −1.80300e123 −1.64787
\(583\) 5.47663e122 0.463727
\(584\) 1.36389e122 0.107006
\(585\) −3.94819e122 −0.287053
\(586\) 1.78610e123 1.20355
\(587\) 3.13449e122 0.195781 0.0978905 0.995197i \(-0.468790\pi\)
0.0978905 + 0.995197i \(0.468790\pi\)
\(588\) −1.77799e123 −1.02953
\(589\) 3.35568e122 0.180157
\(590\) 1.20174e122 0.0598269
\(591\) −5.91315e123 −2.73009
\(592\) −1.76478e123 −0.755743
\(593\) −3.85499e123 −1.53140 −0.765702 0.643196i \(-0.777608\pi\)
−0.765702 + 0.643196i \(0.777608\pi\)
\(594\) 1.63218e124 6.01550
\(595\) −5.82464e120 −0.00199188
\(596\) 1.84306e123 0.584898
\(597\) 6.01538e123 1.77176
\(598\) −6.78259e123 −1.85436
\(599\) 6.84145e123 1.73642 0.868210 0.496198i \(-0.165271\pi\)
0.868210 + 0.496198i \(0.165271\pi\)
\(600\) −3.64740e123 −0.859514
\(601\) 5.81715e122 0.127291 0.0636453 0.997973i \(-0.479727\pi\)
0.0636453 + 0.997973i \(0.479727\pi\)
\(602\) −3.30163e123 −0.670941
\(603\) −2.09422e123 −0.395277
\(604\) −3.65030e123 −0.640008
\(605\) 6.78285e122 0.110484
\(606\) −1.23296e124 −1.86602
\(607\) 7.22901e122 0.101667 0.0508337 0.998707i \(-0.483812\pi\)
0.0508337 + 0.998707i \(0.483812\pi\)
\(608\) −5.47128e123 −0.715121
\(609\) −7.84149e122 −0.0952640
\(610\) 2.62057e122 0.0295950
\(611\) 1.64110e124 1.72306
\(612\) −1.09094e123 −0.106503
\(613\) −1.46296e123 −0.132814 −0.0664068 0.997793i \(-0.521154\pi\)
−0.0664068 + 0.997793i \(0.521154\pi\)
\(614\) 9.22124e123 0.778569
\(615\) 1.47840e123 0.116104
\(616\) −3.83856e123 −0.280431
\(617\) 8.13622e123 0.553010 0.276505 0.961013i \(-0.410824\pi\)
0.276505 + 0.961013i \(0.410824\pi\)
\(618\) 1.42567e123 0.0901636
\(619\) 4.24524e123 0.249844 0.124922 0.992167i \(-0.460132\pi\)
0.124922 + 0.992167i \(0.460132\pi\)
\(620\) −2.61745e122 −0.0143367
\(621\) −6.12404e124 −3.12221
\(622\) −3.52479e124 −1.67287
\(623\) 1.23240e124 0.544545
\(624\) 7.94426e124 3.26843
\(625\) 2.56154e124 0.981387
\(626\) −2.48508e124 −0.886712
\(627\) 5.64505e124 1.87613
\(628\) 2.25379e124 0.697765
\(629\) −1.35706e123 −0.0391422
\(630\) −3.87612e123 −0.104170
\(631\) −4.16093e124 −1.04204 −0.521019 0.853545i \(-0.674448\pi\)
−0.521019 + 0.853545i \(0.674448\pi\)
\(632\) −2.60273e124 −0.607463
\(633\) −4.94016e124 −1.07467
\(634\) −1.04220e124 −0.211339
\(635\) −8.99788e122 −0.0170102
\(636\) −2.07461e124 −0.365675
\(637\) 7.18776e124 1.18138
\(638\) −1.64114e124 −0.251550
\(639\) −1.87889e125 −2.68604
\(640\) −5.05235e123 −0.0673728
\(641\) −5.88543e124 −0.732144 −0.366072 0.930587i \(-0.619298\pi\)
−0.366072 + 0.930587i \(0.619298\pi\)
\(642\) 2.06101e125 2.39205
\(643\) 1.22279e124 0.132423 0.0662116 0.997806i \(-0.478909\pi\)
0.0662116 + 0.997806i \(0.478909\pi\)
\(644\) −2.60927e124 −0.263693
\(645\) 2.09047e124 0.197168
\(646\) −5.92028e123 −0.0521189
\(647\) 1.38772e125 1.14041 0.570204 0.821503i \(-0.306864\pi\)
0.570204 + 0.821503i \(0.306864\pi\)
\(648\) 1.86939e125 1.43421
\(649\) 1.27998e125 0.916885
\(650\) −2.67134e125 −1.78684
\(651\) −3.39939e124 −0.212347
\(652\) 1.42252e125 0.829926
\(653\) −1.57716e125 −0.859487 −0.429743 0.902951i \(-0.641396\pi\)
−0.429743 + 0.902951i \(0.641396\pi\)
\(654\) 1.53675e125 0.782335
\(655\) −1.51420e124 −0.0720189
\(656\) −2.14758e125 −0.954394
\(657\) 1.46690e125 0.609174
\(658\) 1.61115e125 0.625291
\(659\) −3.75748e125 −1.36300 −0.681500 0.731818i \(-0.738672\pi\)
−0.681500 + 0.731818i \(0.738672\pi\)
\(660\) −4.40317e124 −0.149300
\(661\) 1.24288e125 0.393970 0.196985 0.980406i \(-0.436885\pi\)
0.196985 + 0.980406i \(0.436885\pi\)
\(662\) −5.15485e125 −1.52769
\(663\) 6.10890e124 0.169282
\(664\) −7.53601e124 −0.195282
\(665\) −8.24257e123 −0.0199756
\(666\) −9.03082e125 −2.04703
\(667\) 6.15764e124 0.130561
\(668\) 5.19172e125 1.02981
\(669\) 1.15293e126 2.13964
\(670\) 8.86463e123 0.0153933
\(671\) 2.79119e125 0.453562
\(672\) 5.54254e125 0.842900
\(673\) 9.59713e125 1.36606 0.683032 0.730389i \(-0.260661\pi\)
0.683032 + 0.730389i \(0.260661\pi\)
\(674\) −1.12566e126 −1.49983
\(675\) −2.41197e126 −3.00852
\(676\) 5.33020e125 0.622466
\(677\) 4.24330e125 0.463989 0.231994 0.972717i \(-0.425475\pi\)
0.231994 + 0.972717i \(0.425475\pi\)
\(678\) 2.81564e126 2.88308
\(679\) 2.80404e125 0.268892
\(680\) −2.54893e123 −0.00228935
\(681\) −3.91386e126 −3.29275
\(682\) −7.11454e125 −0.560715
\(683\) 1.36159e126 1.00536 0.502682 0.864471i \(-0.332347\pi\)
0.502682 + 0.864471i \(0.332347\pi\)
\(684\) −1.54381e126 −1.06806
\(685\) 4.04664e124 0.0262340
\(686\) 1.54319e126 0.937553
\(687\) 5.91441e126 3.36772
\(688\) −3.03670e126 −1.62075
\(689\) 8.38690e125 0.419610
\(690\) 4.21610e125 0.197755
\(691\) −6.63422e125 −0.291754 −0.145877 0.989303i \(-0.546600\pi\)
−0.145877 + 0.989303i \(0.546600\pi\)
\(692\) −2.63870e126 −1.08810
\(693\) −4.12848e126 −1.59647
\(694\) −3.42132e126 −1.24079
\(695\) −2.43315e124 −0.00827648
\(696\) −3.43153e125 −0.109491
\(697\) −1.65142e125 −0.0494310
\(698\) −1.90406e126 −0.534705
\(699\) 1.49935e126 0.395065
\(700\) −1.02767e126 −0.254091
\(701\) 1.31009e126 0.303984 0.151992 0.988382i \(-0.451431\pi\)
0.151992 + 0.988382i \(0.451431\pi\)
\(702\) 2.49952e127 5.44321
\(703\) −1.92040e126 −0.392537
\(704\) 1.67316e126 0.321036
\(705\) −1.02012e126 −0.183753
\(706\) −4.17658e126 −0.706336
\(707\) 1.91750e126 0.304489
\(708\) −4.84873e126 −0.723017
\(709\) 5.61717e126 0.786611 0.393305 0.919408i \(-0.371332\pi\)
0.393305 + 0.919408i \(0.371332\pi\)
\(710\) 7.95316e125 0.104603
\(711\) −2.79931e127 −3.45823
\(712\) 5.39313e126 0.625866
\(713\) 2.66942e126 0.291027
\(714\) 5.99739e125 0.0614316
\(715\) 1.78004e126 0.171321
\(716\) −5.06183e125 −0.0457802
\(717\) −2.97396e127 −2.52774
\(718\) 1.53986e126 0.123011
\(719\) 1.05953e127 0.795569 0.397784 0.917479i \(-0.369779\pi\)
0.397784 + 0.917479i \(0.369779\pi\)
\(720\) −3.56509e126 −0.251637
\(721\) −2.21720e125 −0.0147125
\(722\) 1.21763e127 0.759645
\(723\) 3.21475e127 1.88579
\(724\) 2.10860e127 1.16313
\(725\) 2.42520e126 0.125807
\(726\) −6.98402e127 −3.40742
\(727\) −1.34692e127 −0.618104 −0.309052 0.951045i \(-0.600012\pi\)
−0.309052 + 0.951045i \(0.600012\pi\)
\(728\) −5.87836e126 −0.253752
\(729\) 5.96843e127 2.42374
\(730\) −6.20926e125 −0.0237232
\(731\) −2.33513e126 −0.0839438
\(732\) −1.05734e127 −0.357660
\(733\) 3.56447e127 1.13467 0.567333 0.823489i \(-0.307975\pi\)
0.567333 + 0.823489i \(0.307975\pi\)
\(734\) 7.04586e127 2.11086
\(735\) −4.46796e126 −0.125986
\(736\) −4.35236e127 −1.15521
\(737\) 9.44177e126 0.235912
\(738\) −1.09897e128 −2.58510
\(739\) −2.93556e127 −0.650150 −0.325075 0.945688i \(-0.605390\pi\)
−0.325075 + 0.945688i \(0.605390\pi\)
\(740\) 1.49793e126 0.0312377
\(741\) 8.64483e127 1.69764
\(742\) 8.23381e126 0.152274
\(743\) −6.01913e127 −1.04841 −0.524206 0.851592i \(-0.675638\pi\)
−0.524206 + 0.851592i \(0.675638\pi\)
\(744\) −1.48761e127 −0.244059
\(745\) 4.63146e126 0.0715754
\(746\) 9.56128e127 1.39200
\(747\) −8.10519e127 −1.11172
\(748\) 4.91850e126 0.0635640
\(749\) −3.20528e127 −0.390324
\(750\) 3.33143e127 0.382300
\(751\) −1.76278e128 −1.90643 −0.953217 0.302287i \(-0.902250\pi\)
−0.953217 + 0.302287i \(0.902250\pi\)
\(752\) 1.48186e128 1.51048
\(753\) 2.08877e127 0.200685
\(754\) −2.51324e127 −0.227619
\(755\) −9.17294e126 −0.0783194
\(756\) 9.61567e127 0.774033
\(757\) −1.57049e127 −0.119198 −0.0595988 0.998222i \(-0.518982\pi\)
−0.0595988 + 0.998222i \(0.518982\pi\)
\(758\) −3.43717e128 −2.45992
\(759\) 4.49060e128 3.03071
\(760\) −3.60705e126 −0.0229587
\(761\) −6.19247e127 −0.371746 −0.185873 0.982574i \(-0.559511\pi\)
−0.185873 + 0.982574i \(0.559511\pi\)
\(762\) 9.26475e127 0.524611
\(763\) −2.38996e127 −0.127658
\(764\) −1.08020e127 −0.0544316
\(765\) −2.74145e126 −0.0130331
\(766\) 2.28143e128 1.02336
\(767\) 1.96016e128 0.829657
\(768\) 6.18586e128 2.47073
\(769\) −5.08598e128 −1.91714 −0.958568 0.284864i \(-0.908051\pi\)
−0.958568 + 0.284864i \(0.908051\pi\)
\(770\) 1.74755e127 0.0621715
\(771\) −4.43978e128 −1.49088
\(772\) −3.06986e128 −0.973080
\(773\) −1.07698e128 −0.322270 −0.161135 0.986932i \(-0.551515\pi\)
−0.161135 + 0.986932i \(0.551515\pi\)
\(774\) −1.55396e129 −4.39002
\(775\) 1.05136e128 0.280430
\(776\) 1.22708e128 0.309048
\(777\) 1.94542e128 0.462677
\(778\) 8.76670e128 1.96899
\(779\) −2.33696e128 −0.495718
\(780\) −6.74301e127 −0.135096
\(781\) 8.47096e128 1.60310
\(782\) −4.70954e127 −0.0841934
\(783\) −2.26921e128 −0.383245
\(784\) 6.49033e128 1.03562
\(785\) 5.66360e127 0.0853872
\(786\) 1.55911e129 2.22113
\(787\) 4.48703e128 0.604065 0.302032 0.953298i \(-0.402335\pi\)
0.302032 + 0.953298i \(0.402335\pi\)
\(788\) −7.29083e128 −0.927599
\(789\) −5.98691e128 −0.719906
\(790\) 1.18492e128 0.134674
\(791\) −4.37890e128 −0.470448
\(792\) −1.80667e129 −1.83488
\(793\) 4.27442e128 0.410412
\(794\) −2.33455e128 −0.211929
\(795\) −5.21335e127 −0.0447486
\(796\) 7.41687e128 0.601990
\(797\) −1.23563e129 −0.948402 −0.474201 0.880417i \(-0.657263\pi\)
−0.474201 + 0.880417i \(0.657263\pi\)
\(798\) 8.48703e128 0.616066
\(799\) 1.13951e128 0.0782323
\(800\) −1.71419e129 −1.11315
\(801\) 5.80046e129 3.56300
\(802\) −2.19237e129 −1.27396
\(803\) −6.61352e128 −0.363572
\(804\) −3.57666e128 −0.186030
\(805\) −6.55690e127 −0.0322687
\(806\) −1.08952e129 −0.507372
\(807\) −2.35102e129 −1.03606
\(808\) 8.39122e128 0.349961
\(809\) −4.09545e129 −1.61656 −0.808281 0.588797i \(-0.799602\pi\)
−0.808281 + 0.588797i \(0.799602\pi\)
\(810\) −8.51060e128 −0.317963
\(811\) −5.08524e128 −0.179839 −0.0899195 0.995949i \(-0.528661\pi\)
−0.0899195 + 0.995949i \(0.528661\pi\)
\(812\) −9.66844e127 −0.0323678
\(813\) 8.50397e129 2.69521
\(814\) 4.07155e129 1.22172
\(815\) 3.57468e128 0.101560
\(816\) 5.51615e128 0.148397
\(817\) −3.30449e129 −0.841828
\(818\) 5.01927e129 1.21093
\(819\) −6.32234e129 −1.44459
\(820\) 1.82284e128 0.0394487
\(821\) 7.00375e129 1.43569 0.717844 0.696204i \(-0.245129\pi\)
0.717844 + 0.696204i \(0.245129\pi\)
\(822\) −4.16666e129 −0.809081
\(823\) −1.04462e130 −1.92162 −0.960808 0.277214i \(-0.910589\pi\)
−0.960808 + 0.277214i \(0.910589\pi\)
\(824\) −9.70275e127 −0.0169096
\(825\) 1.76863e130 2.92036
\(826\) 1.92438e129 0.301078
\(827\) 5.36964e129 0.796068 0.398034 0.917371i \(-0.369693\pi\)
0.398034 + 0.917371i \(0.369693\pi\)
\(828\) −1.22809e130 −1.72536
\(829\) −8.74341e128 −0.116414 −0.0582069 0.998305i \(-0.518538\pi\)
−0.0582069 + 0.998305i \(0.518538\pi\)
\(830\) 3.43085e128 0.0432939
\(831\) −2.21654e130 −2.65113
\(832\) 2.56228e129 0.290494
\(833\) 4.99087e128 0.0536381
\(834\) 2.50532e129 0.255255
\(835\) 1.30464e129 0.126021
\(836\) 6.96027e129 0.637451
\(837\) −9.83733e129 −0.854269
\(838\) −7.84554e129 −0.646047
\(839\) 1.06592e129 0.0832369 0.0416185 0.999134i \(-0.486749\pi\)
0.0416185 + 0.999134i \(0.486749\pi\)
\(840\) 3.65403e128 0.0270610
\(841\) −1.40089e130 −0.983974
\(842\) 1.72056e130 1.14626
\(843\) −8.14629e129 −0.514793
\(844\) −6.09114e129 −0.365140
\(845\) 1.33944e129 0.0761728
\(846\) 7.58308e130 4.09133
\(847\) 1.08616e130 0.556008
\(848\) 7.57312e129 0.367840
\(849\) 3.90165e129 0.179828
\(850\) −1.85486e129 −0.0811278
\(851\) −1.52767e130 −0.634108
\(852\) −3.20890e130 −1.26414
\(853\) 1.93219e130 0.722467 0.361233 0.932475i \(-0.382356\pi\)
0.361233 + 0.932475i \(0.382356\pi\)
\(854\) 4.19639e129 0.148936
\(855\) −3.87948e129 −0.130702
\(856\) −1.40267e130 −0.448614
\(857\) 7.26166e129 0.220490 0.110245 0.993904i \(-0.464836\pi\)
0.110245 + 0.993904i \(0.464836\pi\)
\(858\) −1.83283e131 −5.28371
\(859\) 3.54047e130 0.969091 0.484545 0.874766i \(-0.338985\pi\)
0.484545 + 0.874766i \(0.338985\pi\)
\(860\) 2.57752e129 0.0669918
\(861\) 2.36740e130 0.584294
\(862\) −6.76755e129 −0.158620
\(863\) 3.76103e130 0.837195 0.418598 0.908172i \(-0.362522\pi\)
0.418598 + 0.908172i \(0.362522\pi\)
\(864\) 1.60393e131 3.39097
\(865\) −6.63085e129 −0.133153
\(866\) −1.04237e131 −1.98827
\(867\) −1.04236e131 −1.88872
\(868\) −4.19139e129 −0.0721491
\(869\) 1.26207e131 2.06397
\(870\) 1.56224e129 0.0242740
\(871\) 1.44591e130 0.213469
\(872\) −1.04587e130 −0.146722
\(873\) 1.31976e131 1.75938
\(874\) −6.66456e130 −0.844332
\(875\) −5.18105e129 −0.0623821
\(876\) 2.50528e130 0.286698
\(877\) −1.55152e131 −1.68762 −0.843811 0.536641i \(-0.819693\pi\)
−0.843811 + 0.536641i \(0.819693\pi\)
\(878\) −6.76796e130 −0.699764
\(879\) −1.81094e131 −1.77991
\(880\) 1.60732e130 0.150184
\(881\) 9.08036e130 0.806631 0.403316 0.915061i \(-0.367858\pi\)
0.403316 + 0.915061i \(0.367858\pi\)
\(882\) 3.32127e131 2.80512
\(883\) 1.55010e131 1.24482 0.622411 0.782690i \(-0.286153\pi\)
0.622411 + 0.782690i \(0.286153\pi\)
\(884\) 7.53219e129 0.0575169
\(885\) −1.21845e130 −0.0884774
\(886\) 1.41276e131 0.975591
\(887\) −6.55371e130 −0.430414 −0.215207 0.976568i \(-0.569043\pi\)
−0.215207 + 0.976568i \(0.569043\pi\)
\(888\) 8.51338e130 0.531772
\(889\) −1.44086e130 −0.0856037
\(890\) −2.45528e130 −0.138754
\(891\) −9.06469e131 −4.87299
\(892\) 1.42155e131 0.726984
\(893\) 1.61254e131 0.784551
\(894\) −4.76883e131 −2.20745
\(895\) −1.27200e129 −0.00560224
\(896\) −8.09048e130 −0.339053
\(897\) 6.87690e131 2.74239
\(898\) −1.40315e131 −0.532484
\(899\) 9.89131e129 0.0357230
\(900\) −4.83686e131 −1.66254
\(901\) 5.82350e129 0.0190516
\(902\) 4.95471e131 1.54286
\(903\) 3.34753e131 0.992248
\(904\) −1.91626e131 −0.540703
\(905\) 5.29874e130 0.142335
\(906\) 9.44499e131 2.41544
\(907\) −5.61057e131 −1.36610 −0.683051 0.730371i \(-0.739347\pi\)
−0.683051 + 0.730371i \(0.739347\pi\)
\(908\) −4.82573e131 −1.11877
\(909\) 9.02499e131 1.99230
\(910\) 2.67619e130 0.0562568
\(911\) −7.85678e131 −1.57281 −0.786406 0.617710i \(-0.788060\pi\)
−0.786406 + 0.617710i \(0.788060\pi\)
\(912\) 7.80602e131 1.48819
\(913\) 3.65422e131 0.663507
\(914\) −8.76713e131 −1.51618
\(915\) −2.65701e130 −0.0437677
\(916\) 7.29238e131 1.14425
\(917\) −2.42474e131 −0.362434
\(918\) 1.73556e131 0.247138
\(919\) −1.20827e132 −1.63917 −0.819587 0.572955i \(-0.805797\pi\)
−0.819587 + 0.572955i \(0.805797\pi\)
\(920\) −2.86938e130 −0.0370877
\(921\) −9.34945e131 −1.15142
\(922\) 6.43060e131 0.754615
\(923\) 1.29724e132 1.45059
\(924\) −7.05092e131 −0.751352
\(925\) −6.01675e131 −0.611019
\(926\) −1.97838e132 −1.91479
\(927\) −1.04356e131 −0.0962650
\(928\) −1.61273e131 −0.141800
\(929\) −8.48290e131 −0.710960 −0.355480 0.934684i \(-0.615683\pi\)
−0.355480 + 0.934684i \(0.615683\pi\)
\(930\) 6.77253e130 0.0541078
\(931\) 7.06268e131 0.537909
\(932\) 1.84868e131 0.134231
\(933\) 3.57380e132 2.47398
\(934\) 3.64735e132 2.40736
\(935\) 1.23598e130 0.00777849
\(936\) −2.76673e132 −1.66032
\(937\) 1.06062e132 0.606941 0.303470 0.952841i \(-0.401855\pi\)
0.303470 + 0.952841i \(0.401855\pi\)
\(938\) 1.41952e131 0.0774667
\(939\) 2.51963e132 1.31135
\(940\) −1.25779e131 −0.0624337
\(941\) −2.79020e132 −1.32098 −0.660492 0.750833i \(-0.729652\pi\)
−0.660492 + 0.750833i \(0.729652\pi\)
\(942\) −5.83158e132 −2.63342
\(943\) −1.85903e132 −0.800787
\(944\) 1.76997e132 0.727297
\(945\) 2.41635e131 0.0947204
\(946\) 7.00602e132 2.62009
\(947\) 1.84501e132 0.658302 0.329151 0.944277i \(-0.393238\pi\)
0.329151 + 0.944277i \(0.393238\pi\)
\(948\) −4.78088e132 −1.62756
\(949\) −1.01279e132 −0.328984
\(950\) −2.62485e132 −0.813588
\(951\) 1.05669e132 0.312547
\(952\) −4.08168e130 −0.0115211
\(953\) 3.12272e132 0.841199 0.420599 0.907246i \(-0.361820\pi\)
0.420599 + 0.907246i \(0.361820\pi\)
\(954\) 3.87536e132 0.996344
\(955\) −2.71447e130 −0.00666093
\(956\) −3.66685e132 −0.858850
\(957\) 1.66395e132 0.372015
\(958\) −6.22802e132 −1.32918
\(959\) 6.48000e131 0.132022
\(960\) −1.59273e131 −0.0309793
\(961\) −4.95626e132 −0.920372
\(962\) 6.23516e132 1.10550
\(963\) −1.50861e133 −2.55392
\(964\) 3.96374e132 0.640732
\(965\) −7.71432e131 −0.119078
\(966\) 6.75137e132 0.995198
\(967\) −9.50210e132 −1.33765 −0.668823 0.743421i \(-0.733202\pi\)
−0.668823 + 0.743421i \(0.733202\pi\)
\(968\) 4.75316e132 0.639041
\(969\) 6.00259e131 0.0770781
\(970\) −5.58642e131 −0.0685159
\(971\) 8.78389e132 1.02904 0.514518 0.857479i \(-0.327971\pi\)
0.514518 + 0.857479i \(0.327971\pi\)
\(972\) 1.69070e133 1.89199
\(973\) −3.89628e131 −0.0416513
\(974\) 7.53060e132 0.769053
\(975\) 2.70848e133 2.64253
\(976\) 3.85967e132 0.359777
\(977\) 1.26615e133 1.12765 0.563827 0.825893i \(-0.309328\pi\)
0.563827 + 0.825893i \(0.309328\pi\)
\(978\) −3.68070e133 −3.13221
\(979\) −2.61514e133 −2.12650
\(980\) −5.50893e131 −0.0428062
\(981\) −1.12487e133 −0.835276
\(982\) −1.43028e133 −1.01498
\(983\) 3.88384e132 0.263408 0.131704 0.991289i \(-0.457955\pi\)
0.131704 + 0.991289i \(0.457955\pi\)
\(984\) 1.03600e133 0.671551
\(985\) −1.83213e132 −0.113513
\(986\) −1.74508e131 −0.0103346
\(987\) −1.63355e133 −0.924737
\(988\) 1.06589e133 0.576807
\(989\) −2.62870e133 −1.35990
\(990\) 8.22508e132 0.406793
\(991\) −2.30184e133 −1.08842 −0.544211 0.838948i \(-0.683171\pi\)
−0.544211 + 0.838948i \(0.683171\pi\)
\(992\) −6.99140e132 −0.316078
\(993\) 5.22652e133 2.25928
\(994\) 1.27356e133 0.526412
\(995\) 1.86380e132 0.0736671
\(996\) −1.38426e133 −0.523213
\(997\) −3.12858e132 −0.113087 −0.0565435 0.998400i \(-0.518008\pi\)
−0.0565435 + 0.998400i \(0.518008\pi\)
\(998\) 3.02203e133 1.04469
\(999\) 5.62976e133 1.86134
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 1.90.a.a.1.2 7
3.2 odd 2 9.90.a.b.1.6 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.90.a.a.1.2 7 1.1 even 1 trivial
9.90.a.b.1.6 7 3.2 odd 2