Properties

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

Related objects

Downloads

Learn more about

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 1.1
Root \(9.08809e11\) 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

\(f(q)\) \(=\) \(q-4.81096e13 q^{2} -1.58991e21 q^{3} +1.69556e27 q^{4} +1.07790e31 q^{5} +7.64900e34 q^{6} +5.70296e37 q^{7} -5.17945e40 q^{8} -3.81503e41 q^{9} +O(q^{10})\) \(q-4.81096e13 q^{2} -1.58991e21 q^{3} +1.69556e27 q^{4} +1.07790e31 q^{5} +7.64900e34 q^{6} +5.70296e37 q^{7} -5.17945e40 q^{8} -3.81503e41 q^{9} -5.18572e44 q^{10} +1.25806e46 q^{11} -2.69579e48 q^{12} -3.04674e49 q^{13} -2.74367e51 q^{14} -1.71376e52 q^{15} +1.44231e54 q^{16} -1.44307e54 q^{17} +1.83540e55 q^{18} -2.63820e56 q^{19} +1.82764e58 q^{20} -9.06721e58 q^{21} -6.05246e59 q^{22} +1.82853e60 q^{23} +8.23486e61 q^{24} -4.53723e61 q^{25} +1.46577e63 q^{26} +5.23212e63 q^{27} +9.66973e64 q^{28} -1.87067e65 q^{29} +8.24484e65 q^{30} +9.55617e65 q^{31} -3.73296e67 q^{32} -2.00020e67 q^{33} +6.94257e67 q^{34} +6.14721e68 q^{35} -6.46863e68 q^{36} +6.40520e69 q^{37} +1.26923e70 q^{38} +4.84404e70 q^{39} -5.58291e71 q^{40} -1.04557e72 q^{41} +4.36220e72 q^{42} -3.49195e72 q^{43} +2.13312e73 q^{44} -4.11221e72 q^{45} -8.79700e73 q^{46} +6.29528e72 q^{47} -2.29314e75 q^{48} +1.61660e75 q^{49} +2.18284e75 q^{50} +2.29436e75 q^{51} -5.16593e76 q^{52} +6.67038e75 q^{53} -2.51715e77 q^{54} +1.35606e77 q^{55} -2.95382e78 q^{56} +4.19451e77 q^{57} +8.99970e78 q^{58} -1.69313e78 q^{59} -2.90579e79 q^{60} +1.46459e79 q^{61} -4.59743e79 q^{62} -2.17570e79 q^{63} +9.03167e80 q^{64} -3.28407e80 q^{65} +9.62288e80 q^{66} +2.58895e81 q^{67} -2.44682e81 q^{68} -2.90720e81 q^{69} -2.95740e82 q^{70} +2.08753e82 q^{71} +1.97597e82 q^{72} +2.80058e82 q^{73} -3.08152e83 q^{74} +7.21380e82 q^{75} -4.47324e83 q^{76} +7.17466e83 q^{77} -2.33045e84 q^{78} +1.45733e84 q^{79} +1.55466e85 q^{80} -7.20869e84 q^{81} +5.03020e85 q^{82} -3.27919e85 q^{83} -1.53740e86 q^{84} -1.55549e85 q^{85} +1.67996e86 q^{86} +2.97419e86 q^{87} -6.51604e86 q^{88} -3.07472e86 q^{89} +1.97837e86 q^{90} -1.73754e87 q^{91} +3.10039e87 q^{92} -1.51935e87 q^{93} -3.02863e86 q^{94} -2.84371e87 q^{95} +5.93508e88 q^{96} +1.70392e88 q^{97} -7.77738e88 q^{98} -4.79953e87 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 31407330351408q^{2} - \)\(13\!\cdots\!64\)\(q^{3} + \)\(22\!\cdots\!04\)\(q^{4} + \)\(10\!\cdots\!50\)\(q^{5} - \)\(47\!\cdots\!76\)\(q^{6} + \)\(38\!\cdots\!92\)\(q^{7} - \)\(17\!\cdots\!20\)\(q^{8} + \)\(56\!\cdots\!71\)\(q^{9} + O(q^{10}) \) \( 7q - 31407330351408q^{2} - \)\(13\!\cdots\!64\)\(q^{3} + \)\(22\!\cdots\!04\)\(q^{4} + \)\(10\!\cdots\!50\)\(q^{5} - \)\(47\!\cdots\!76\)\(q^{6} + \)\(38\!\cdots\!92\)\(q^{7} - \)\(17\!\cdots\!20\)\(q^{8} + \)\(56\!\cdots\!71\)\(q^{9} - \)\(33\!\cdots\!00\)\(q^{10} - \)\(33\!\cdots\!56\)\(q^{11} - \)\(10\!\cdots\!28\)\(q^{12} - \)\(10\!\cdots\!34\)\(q^{13} - \)\(33\!\cdots\!32\)\(q^{14} - \)\(39\!\cdots\!00\)\(q^{15} + \)\(11\!\cdots\!32\)\(q^{16} + \)\(83\!\cdots\!42\)\(q^{17} - \)\(14\!\cdots\!04\)\(q^{18} + \)\(56\!\cdots\!80\)\(q^{19} + \)\(17\!\cdots\!00\)\(q^{20} - \)\(90\!\cdots\!36\)\(q^{21} - \)\(57\!\cdots\!36\)\(q^{22} - \)\(11\!\cdots\!04\)\(q^{23} + \)\(10\!\cdots\!40\)\(q^{24} - \)\(21\!\cdots\!75\)\(q^{25} + \)\(25\!\cdots\!24\)\(q^{26} + \)\(11\!\cdots\!80\)\(q^{27} + \)\(42\!\cdots\!84\)\(q^{28} - \)\(14\!\cdots\!30\)\(q^{29} + \)\(68\!\cdots\!00\)\(q^{30} + \)\(68\!\cdots\!04\)\(q^{31} - \)\(18\!\cdots\!48\)\(q^{32} - \)\(86\!\cdots\!88\)\(q^{33} + \)\(31\!\cdots\!28\)\(q^{34} + \)\(33\!\cdots\!00\)\(q^{35} - \)\(16\!\cdots\!88\)\(q^{36} - \)\(54\!\cdots\!58\)\(q^{37} + \)\(45\!\cdots\!20\)\(q^{38} - \)\(52\!\cdots\!48\)\(q^{39} - \)\(36\!\cdots\!00\)\(q^{40} - \)\(65\!\cdots\!66\)\(q^{41} + \)\(11\!\cdots\!04\)\(q^{42} + \)\(32\!\cdots\!56\)\(q^{43} - \)\(15\!\cdots\!32\)\(q^{44} - \)\(47\!\cdots\!50\)\(q^{45} - \)\(56\!\cdots\!76\)\(q^{46} - \)\(58\!\cdots\!08\)\(q^{47} - \)\(38\!\cdots\!04\)\(q^{48} - \)\(30\!\cdots\!01\)\(q^{49} - \)\(11\!\cdots\!00\)\(q^{50} - \)\(44\!\cdots\!56\)\(q^{51} - \)\(19\!\cdots\!68\)\(q^{52} - \)\(18\!\cdots\!14\)\(q^{53} - \)\(10\!\cdots\!20\)\(q^{54} - \)\(12\!\cdots\!00\)\(q^{55} - \)\(58\!\cdots\!20\)\(q^{56} - \)\(66\!\cdots\!40\)\(q^{57} - \)\(30\!\cdots\!20\)\(q^{58} - \)\(90\!\cdots\!60\)\(q^{59} - \)\(28\!\cdots\!00\)\(q^{60} + \)\(87\!\cdots\!94\)\(q^{61} + \)\(16\!\cdots\!24\)\(q^{62} + \)\(60\!\cdots\!96\)\(q^{63} + \)\(14\!\cdots\!44\)\(q^{64} + \)\(13\!\cdots\!00\)\(q^{65} + \)\(57\!\cdots\!08\)\(q^{66} + \)\(58\!\cdots\!92\)\(q^{67} + \)\(33\!\cdots\!84\)\(q^{68} - \)\(59\!\cdots\!48\)\(q^{69} - \)\(48\!\cdots\!00\)\(q^{70} - \)\(54\!\cdots\!76\)\(q^{71} - \)\(19\!\cdots\!60\)\(q^{72} - \)\(19\!\cdots\!54\)\(q^{73} - \)\(96\!\cdots\!52\)\(q^{74} - \)\(44\!\cdots\!00\)\(q^{75} - \)\(62\!\cdots\!40\)\(q^{76} + \)\(13\!\cdots\!64\)\(q^{77} + \)\(51\!\cdots\!92\)\(q^{78} + \)\(26\!\cdots\!20\)\(q^{79} + \)\(27\!\cdots\!00\)\(q^{80} + \)\(48\!\cdots\!47\)\(q^{81} + \)\(63\!\cdots\!04\)\(q^{82} - \)\(35\!\cdots\!24\)\(q^{83} - \)\(91\!\cdots\!92\)\(q^{84} - \)\(14\!\cdots\!00\)\(q^{85} - \)\(24\!\cdots\!76\)\(q^{86} - \)\(41\!\cdots\!60\)\(q^{87} - \)\(18\!\cdots\!40\)\(q^{88} - \)\(16\!\cdots\!90\)\(q^{89} - \)\(15\!\cdots\!00\)\(q^{90} - \)\(30\!\cdots\!36\)\(q^{91} + \)\(72\!\cdots\!92\)\(q^{92} + \)\(87\!\cdots\!92\)\(q^{93} + \)\(22\!\cdots\!08\)\(q^{94} + \)\(22\!\cdots\!00\)\(q^{95} + \)\(84\!\cdots\!44\)\(q^{96} + \)\(71\!\cdots\!42\)\(q^{97} - \)\(17\!\cdots\!56\)\(q^{98} - \)\(19\!\cdots\!68\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.81096e13 −1.93373 −0.966867 0.255279i \(-0.917833\pi\)
−0.966867 + 0.255279i \(0.917833\pi\)
\(3\) −1.58991e21 −0.932131 −0.466066 0.884750i \(-0.654329\pi\)
−0.466066 + 0.884750i \(0.654329\pi\)
\(4\) 1.69556e27 2.73933
\(5\) 1.07790e31 0.848032 0.424016 0.905655i \(-0.360620\pi\)
0.424016 + 0.905655i \(0.360620\pi\)
\(6\) 7.64900e34 1.80249
\(7\) 5.70296e37 1.41006 0.705030 0.709177i \(-0.250933\pi\)
0.705030 + 0.709177i \(0.250933\pi\)
\(8\) −5.17945e40 −3.36340
\(9\) −3.81503e41 −0.131131
\(10\) −5.18572e44 −1.63987
\(11\) 1.25806e46 0.572435 0.286217 0.958165i \(-0.407602\pi\)
0.286217 + 0.958165i \(0.407602\pi\)
\(12\) −2.69579e48 −2.55341
\(13\) −3.04674e49 −0.819136 −0.409568 0.912280i \(-0.634320\pi\)
−0.409568 + 0.912280i \(0.634320\pi\)
\(14\) −2.74367e51 −2.72668
\(15\) −1.71376e52 −0.790477
\(16\) 1.44231e54 3.76460
\(17\) −1.44307e54 −0.253695 −0.126847 0.991922i \(-0.540486\pi\)
−0.126847 + 0.991922i \(0.540486\pi\)
\(18\) 1.83540e55 0.253573
\(19\) −2.63820e56 −0.328680 −0.164340 0.986404i \(-0.552549\pi\)
−0.164340 + 0.986404i \(0.552549\pi\)
\(20\) 1.82764e58 2.32304
\(21\) −9.06721e58 −1.31436
\(22\) −6.05246e59 −1.10694
\(23\) 1.82853e60 0.462609 0.231304 0.972881i \(-0.425701\pi\)
0.231304 + 0.972881i \(0.425701\pi\)
\(24\) 8.23486e61 3.13513
\(25\) −4.53723e61 −0.280841
\(26\) 1.46577e63 1.58399
\(27\) 5.23212e63 1.05436
\(28\) 9.66973e64 3.86262
\(29\) −1.87067e65 −1.56778 −0.783890 0.620899i \(-0.786768\pi\)
−0.783890 + 0.620899i \(0.786768\pi\)
\(30\) 8.24484e65 1.52857
\(31\) 9.55617e65 0.411802 0.205901 0.978573i \(-0.433988\pi\)
0.205901 + 0.978573i \(0.433988\pi\)
\(32\) −3.73296e67 −3.91633
\(33\) −2.00020e67 −0.533584
\(34\) 6.94257e67 0.490579
\(35\) 6.14721e68 1.19578
\(36\) −6.46863e68 −0.359212
\(37\) 6.40520e69 1.05089 0.525443 0.850829i \(-0.323899\pi\)
0.525443 + 0.850829i \(0.323899\pi\)
\(38\) 1.26923e70 0.635580
\(39\) 4.84404e70 0.763542
\(40\) −5.58291e71 −2.85227
\(41\) −1.04557e72 −1.78021 −0.890106 0.455754i \(-0.849370\pi\)
−0.890106 + 0.455754i \(0.849370\pi\)
\(42\) 4.36220e72 2.54163
\(43\) −3.49195e72 −0.714039 −0.357019 0.934097i \(-0.616207\pi\)
−0.357019 + 0.934097i \(0.616207\pi\)
\(44\) 2.13312e73 1.56809
\(45\) −4.11221e72 −0.111204
\(46\) −8.79700e73 −0.894563
\(47\) 6.29528e72 0.0245845 0.0122922 0.999924i \(-0.496087\pi\)
0.0122922 + 0.999924i \(0.496087\pi\)
\(48\) −2.29314e75 −3.50910
\(49\) 1.61660e75 0.988271
\(50\) 2.18284e75 0.543072
\(51\) 2.29436e75 0.236477
\(52\) −5.16593e76 −2.24388
\(53\) 6.67038e75 0.124129 0.0620647 0.998072i \(-0.480231\pi\)
0.0620647 + 0.998072i \(0.480231\pi\)
\(54\) −2.51715e77 −2.03886
\(55\) 1.35606e77 0.485443
\(56\) −2.95382e78 −4.74260
\(57\) 4.19451e77 0.306373
\(58\) 8.99970e78 3.03167
\(59\) −1.69313e78 −0.266549 −0.133274 0.991079i \(-0.542549\pi\)
−0.133274 + 0.991079i \(0.542549\pi\)
\(60\) −2.90579e79 −2.16538
\(61\) 1.46459e79 0.523044 0.261522 0.965197i \(-0.415776\pi\)
0.261522 + 0.965197i \(0.415776\pi\)
\(62\) −4.59743e79 −0.796316
\(63\) −2.17570e79 −0.184903
\(64\) 9.03167e80 3.80855
\(65\) −3.28407e80 −0.694653
\(66\) 9.62288e80 1.03181
\(67\) 2.58895e81 1.42166 0.710828 0.703366i \(-0.248321\pi\)
0.710828 + 0.703366i \(0.248321\pi\)
\(68\) −2.44682e81 −0.694954
\(69\) −2.90720e81 −0.431212
\(70\) −2.95740e82 −2.31232
\(71\) 2.08753e82 0.868234 0.434117 0.900856i \(-0.357060\pi\)
0.434117 + 0.900856i \(0.357060\pi\)
\(72\) 1.97597e82 0.441047
\(73\) 2.80058e82 0.338361 0.169181 0.985585i \(-0.445888\pi\)
0.169181 + 0.985585i \(0.445888\pi\)
\(74\) −3.08152e83 −2.03214
\(75\) 7.21380e82 0.261781
\(76\) −4.47324e83 −0.900362
\(77\) 7.17466e83 0.807168
\(78\) −2.33045e84 −1.47649
\(79\) 1.45733e84 0.523783 0.261892 0.965097i \(-0.415654\pi\)
0.261892 + 0.965097i \(0.415654\pi\)
\(80\) 1.55466e85 3.19250
\(81\) −7.20869e84 −0.851673
\(82\) 5.03020e85 3.44246
\(83\) −3.27919e85 −1.30855 −0.654276 0.756256i \(-0.727027\pi\)
−0.654276 + 0.756256i \(0.727027\pi\)
\(84\) −1.53740e86 −3.60047
\(85\) −1.55549e85 −0.215141
\(86\) 1.67996e86 1.38076
\(87\) 2.97419e86 1.46138
\(88\) −6.51604e86 −1.92533
\(89\) −3.07472e86 −0.549478 −0.274739 0.961519i \(-0.588591\pi\)
−0.274739 + 0.961519i \(0.588591\pi\)
\(90\) 1.97837e86 0.215038
\(91\) −1.73754e87 −1.15503
\(92\) 3.10039e87 1.26724
\(93\) −1.51935e87 −0.383854
\(94\) −3.02863e86 −0.0475398
\(95\) −2.84371e87 −0.278731
\(96\) 5.93508e88 3.65053
\(97\) 1.70392e88 0.660856 0.330428 0.943831i \(-0.392807\pi\)
0.330428 + 0.943831i \(0.392807\pi\)
\(98\) −7.77738e88 −1.91105
\(99\) −4.79953e87 −0.0750641
\(100\) −7.69317e88 −0.769317
\(101\) −1.94636e89 −1.25003 −0.625016 0.780612i \(-0.714908\pi\)
−0.625016 + 0.780612i \(0.714908\pi\)
\(102\) −1.10381e89 −0.457284
\(103\) −2.49750e89 −0.670270 −0.335135 0.942170i \(-0.608782\pi\)
−0.335135 + 0.942170i \(0.608782\pi\)
\(104\) 1.57804e90 2.75508
\(105\) −9.77352e89 −1.11462
\(106\) −3.20909e89 −0.240033
\(107\) −1.15673e90 −0.569708 −0.284854 0.958571i \(-0.591945\pi\)
−0.284854 + 0.958571i \(0.591945\pi\)
\(108\) 8.87139e90 2.88825
\(109\) −7.89198e90 −1.70493 −0.852466 0.522783i \(-0.824894\pi\)
−0.852466 + 0.522783i \(0.824894\pi\)
\(110\) −6.52394e90 −0.938718
\(111\) −1.01837e91 −0.979564
\(112\) 8.22543e91 5.30831
\(113\) −2.57271e91 −1.11789 −0.558946 0.829204i \(-0.688794\pi\)
−0.558946 + 0.829204i \(0.688794\pi\)
\(114\) −2.01796e91 −0.592444
\(115\) 1.97097e91 0.392307
\(116\) −3.17183e92 −4.29467
\(117\) 1.16234e91 0.107414
\(118\) 8.14559e91 0.515434
\(119\) −8.22980e91 −0.357725
\(120\) 8.87634e92 2.65869
\(121\) −3.24731e92 −0.672318
\(122\) −7.04609e92 −1.01143
\(123\) 1.66236e93 1.65939
\(124\) 1.62031e93 1.12806
\(125\) −2.23051e93 −1.08619
\(126\) 1.04672e93 0.357554
\(127\) 2.77892e93 0.667744 0.333872 0.942618i \(-0.391645\pi\)
0.333872 + 0.942618i \(0.391645\pi\)
\(128\) −2.03451e94 −3.44839
\(129\) 5.55189e93 0.665578
\(130\) 1.57995e94 1.34328
\(131\) 2.61791e94 1.58264 0.791318 0.611404i \(-0.209395\pi\)
0.791318 + 0.611404i \(0.209395\pi\)
\(132\) −3.39147e94 −1.46166
\(133\) −1.50456e94 −0.463458
\(134\) −1.24553e95 −2.74910
\(135\) 5.63969e94 0.894134
\(136\) 7.47433e94 0.853278
\(137\) 1.28376e95 1.05784 0.528920 0.848672i \(-0.322597\pi\)
0.528920 + 0.848672i \(0.322597\pi\)
\(138\) 1.39864e95 0.833850
\(139\) −3.19520e95 −1.38146 −0.690732 0.723111i \(-0.742712\pi\)
−0.690732 + 0.723111i \(0.742712\pi\)
\(140\) 1.04230e96 3.27563
\(141\) −1.00089e94 −0.0229159
\(142\) −1.00430e96 −1.67893
\(143\) −3.83297e95 −0.468902
\(144\) −5.50245e95 −0.493657
\(145\) −2.01639e96 −1.32953
\(146\) −1.34735e96 −0.654301
\(147\) −2.57024e96 −0.921198
\(148\) 1.08604e97 2.87873
\(149\) 5.65429e96 1.11068 0.555340 0.831624i \(-0.312588\pi\)
0.555340 + 0.831624i \(0.312588\pi\)
\(150\) −3.47053e96 −0.506215
\(151\) −1.22003e97 −1.32402 −0.662011 0.749495i \(-0.730297\pi\)
−0.662011 + 0.749495i \(0.730297\pi\)
\(152\) 1.36644e97 1.10548
\(153\) 5.50538e95 0.0332674
\(154\) −3.45170e97 −1.56085
\(155\) 1.03006e97 0.349221
\(156\) 8.21338e97 2.09159
\(157\) 5.80043e97 1.11154 0.555771 0.831335i \(-0.312423\pi\)
0.555771 + 0.831335i \(0.312423\pi\)
\(158\) −7.01114e97 −1.01286
\(159\) −1.06053e97 −0.115705
\(160\) −4.02375e98 −3.32118
\(161\) 1.04281e98 0.652307
\(162\) 3.46807e98 1.64691
\(163\) 4.97994e98 1.79835 0.899177 0.437584i \(-0.144166\pi\)
0.899177 + 0.437584i \(0.144166\pi\)
\(164\) −1.77283e99 −4.87659
\(165\) −2.15601e98 −0.452497
\(166\) 1.57760e99 2.53039
\(167\) −1.16618e99 −1.43180 −0.715900 0.698202i \(-0.753984\pi\)
−0.715900 + 0.698202i \(0.753984\pi\)
\(168\) 4.69631e99 4.42073
\(169\) −4.55173e98 −0.329017
\(170\) 7.48338e98 0.416027
\(171\) 1.00648e98 0.0431002
\(172\) −5.92082e99 −1.95599
\(173\) 1.56484e99 0.399410 0.199705 0.979856i \(-0.436002\pi\)
0.199705 + 0.979856i \(0.436002\pi\)
\(174\) −1.43087e100 −2.82592
\(175\) −2.58757e99 −0.396003
\(176\) 1.81451e100 2.15499
\(177\) 2.69193e99 0.248458
\(178\) 1.47924e100 1.06254
\(179\) −3.09061e100 −1.73015 −0.865077 0.501639i \(-0.832730\pi\)
−0.865077 + 0.501639i \(0.832730\pi\)
\(180\) −6.97252e99 −0.304623
\(181\) −9.98755e99 −0.341006 −0.170503 0.985357i \(-0.554539\pi\)
−0.170503 + 0.985357i \(0.554539\pi\)
\(182\) 8.35925e100 2.23352
\(183\) −2.32857e100 −0.487546
\(184\) −9.47078e100 −1.55594
\(185\) 6.90415e100 0.891186
\(186\) 7.30951e100 0.742271
\(187\) −1.81547e100 −0.145224
\(188\) 1.06740e100 0.0673449
\(189\) 2.98386e101 1.48672
\(190\) 1.36810e101 0.538992
\(191\) −8.28952e100 −0.258550 −0.129275 0.991609i \(-0.541265\pi\)
−0.129275 + 0.991609i \(0.541265\pi\)
\(192\) −1.43596e102 −3.55007
\(193\) −2.59064e101 −0.508284 −0.254142 0.967167i \(-0.581793\pi\)
−0.254142 + 0.967167i \(0.581793\pi\)
\(194\) −8.19749e101 −1.27792
\(195\) 5.22138e101 0.647508
\(196\) 2.74104e102 2.70720
\(197\) −1.12650e102 −0.887121 −0.443560 0.896244i \(-0.646285\pi\)
−0.443560 + 0.896244i \(0.646285\pi\)
\(198\) 2.30903e101 0.145154
\(199\) 2.12882e102 1.06949 0.534745 0.845013i \(-0.320408\pi\)
0.534745 + 0.845013i \(0.320408\pi\)
\(200\) 2.35004e102 0.944582
\(201\) −4.11620e102 −1.32517
\(202\) 9.36385e102 2.41723
\(203\) −1.06683e103 −2.21067
\(204\) 3.89023e102 0.647788
\(205\) −1.12702e103 −1.50968
\(206\) 1.20154e103 1.29612
\(207\) −6.97591e101 −0.0606625
\(208\) −4.39433e103 −3.08372
\(209\) −3.31901e102 −0.188148
\(210\) 4.70200e103 2.15538
\(211\) 2.09663e103 0.777950 0.388975 0.921248i \(-0.372829\pi\)
0.388975 + 0.921248i \(0.372829\pi\)
\(212\) 1.13101e103 0.340031
\(213\) −3.31899e103 −0.809308
\(214\) 5.56496e103 1.10166
\(215\) −3.76396e103 −0.605528
\(216\) −2.70995e104 −3.54625
\(217\) 5.44985e103 0.580666
\(218\) 3.79680e104 3.29688
\(219\) −4.45267e103 −0.315397
\(220\) 2.29928e104 1.32979
\(221\) 4.39667e103 0.207811
\(222\) 4.89934e104 1.89422
\(223\) −3.38231e104 −1.07065 −0.535325 0.844646i \(-0.679811\pi\)
−0.535325 + 0.844646i \(0.679811\pi\)
\(224\) −2.12889e105 −5.52226
\(225\) 1.73097e103 0.0368271
\(226\) 1.23772e105 2.16171
\(227\) −3.05939e104 −0.439020 −0.219510 0.975610i \(-0.570446\pi\)
−0.219510 + 0.975610i \(0.570446\pi\)
\(228\) 7.11205e104 0.839256
\(229\) −1.51461e105 −1.47103 −0.735514 0.677509i \(-0.763059\pi\)
−0.735514 + 0.677509i \(0.763059\pi\)
\(230\) −9.48226e104 −0.758618
\(231\) −1.14071e105 −0.752386
\(232\) 9.68901e105 5.27308
\(233\) −8.75172e104 −0.393328 −0.196664 0.980471i \(-0.563011\pi\)
−0.196664 + 0.980471i \(0.563011\pi\)
\(234\) −5.59197e104 −0.207711
\(235\) 6.78567e103 0.0208484
\(236\) −2.87081e105 −0.730165
\(237\) −2.31702e105 −0.488235
\(238\) 3.95932e105 0.691746
\(239\) −2.25016e105 −0.326217 −0.163109 0.986608i \(-0.552152\pi\)
−0.163109 + 0.986608i \(0.552152\pi\)
\(240\) −2.47177e106 −2.97583
\(241\) 7.69108e105 0.769536 0.384768 0.923013i \(-0.374281\pi\)
0.384768 + 0.923013i \(0.374281\pi\)
\(242\) 1.56227e106 1.30009
\(243\) −3.76074e105 −0.260492
\(244\) 2.48331e106 1.43279
\(245\) 1.74253e106 0.838086
\(246\) −7.99757e106 −3.20882
\(247\) 8.03791e105 0.269233
\(248\) −4.94957e106 −1.38506
\(249\) 5.21362e106 1.21974
\(250\) 1.07309e107 2.10041
\(251\) 2.20478e105 0.0361314 0.0180657 0.999837i \(-0.494249\pi\)
0.0180657 + 0.999837i \(0.494249\pi\)
\(252\) −3.68903e106 −0.506511
\(253\) 2.30040e106 0.264813
\(254\) −1.33693e107 −1.29124
\(255\) 2.47309e106 0.200540
\(256\) 4.19761e107 2.85972
\(257\) −9.37238e106 −0.536816 −0.268408 0.963305i \(-0.586498\pi\)
−0.268408 + 0.963305i \(0.586498\pi\)
\(258\) −2.67099e107 −1.28705
\(259\) 3.65286e107 1.48181
\(260\) −5.56835e107 −1.90288
\(261\) 7.13665e106 0.205585
\(262\) −1.25946e108 −3.06040
\(263\) −6.07350e107 −1.24569 −0.622843 0.782347i \(-0.714022\pi\)
−0.622843 + 0.782347i \(0.714022\pi\)
\(264\) 1.03599e108 1.79466
\(265\) 7.18999e106 0.105266
\(266\) 7.23837e107 0.896206
\(267\) 4.88853e107 0.512186
\(268\) 4.38972e108 3.89438
\(269\) −3.10570e107 −0.233444 −0.116722 0.993165i \(-0.537239\pi\)
−0.116722 + 0.993165i \(0.537239\pi\)
\(270\) −2.71323e108 −1.72902
\(271\) −3.28545e107 −0.177607 −0.0888037 0.996049i \(-0.528304\pi\)
−0.0888037 + 0.996049i \(0.528304\pi\)
\(272\) −2.08136e108 −0.955059
\(273\) 2.76254e108 1.07664
\(274\) −6.17614e108 −2.04558
\(275\) −5.70810e107 −0.160763
\(276\) −4.92935e108 −1.18123
\(277\) 8.23734e108 1.68050 0.840248 0.542203i \(-0.182410\pi\)
0.840248 + 0.542203i \(0.182410\pi\)
\(278\) 1.53720e109 2.67139
\(279\) −3.64571e107 −0.0540001
\(280\) −3.18391e109 −4.02188
\(281\) 7.73806e108 0.834067 0.417034 0.908891i \(-0.363070\pi\)
0.417034 + 0.908891i \(0.363070\pi\)
\(282\) 4.81526e107 0.0443133
\(283\) −1.50030e109 −1.17946 −0.589728 0.807602i \(-0.700765\pi\)
−0.589728 + 0.807602i \(0.700765\pi\)
\(284\) 3.53954e109 2.37838
\(285\) 4.52125e108 0.259814
\(286\) 1.84403e109 0.906732
\(287\) −5.96285e109 −2.51021
\(288\) 1.42414e109 0.513554
\(289\) −3.02735e109 −0.935639
\(290\) 9.70076e109 2.57096
\(291\) −2.70908e109 −0.616005
\(292\) 4.74856e109 0.926883
\(293\) −2.42775e108 −0.0407001 −0.0203500 0.999793i \(-0.506478\pi\)
−0.0203500 + 0.999793i \(0.506478\pi\)
\(294\) 1.23653e110 1.78135
\(295\) −1.82502e109 −0.226042
\(296\) −3.31754e110 −3.53456
\(297\) 6.58231e109 0.603554
\(298\) −2.72025e110 −2.14776
\(299\) −5.57106e109 −0.378939
\(300\) 1.22315e110 0.717104
\(301\) −1.99145e110 −1.00684
\(302\) 5.86949e110 2.56031
\(303\) 3.09454e110 1.16519
\(304\) −3.80510e110 −1.23735
\(305\) 1.57868e110 0.443559
\(306\) −2.64861e109 −0.0643302
\(307\) −2.66215e107 −0.000559209 0 −0.000279604 1.00000i \(-0.500089\pi\)
−0.000279604 1.00000i \(0.500089\pi\)
\(308\) 1.21651e111 2.21110
\(309\) 3.97081e110 0.624780
\(310\) −4.95556e110 −0.675302
\(311\) −5.79663e110 −0.684444 −0.342222 0.939619i \(-0.611179\pi\)
−0.342222 + 0.939619i \(0.611179\pi\)
\(312\) −2.50894e111 −2.56810
\(313\) 1.83417e111 1.62823 0.814117 0.580701i \(-0.197221\pi\)
0.814117 + 0.580701i \(0.197221\pi\)
\(314\) −2.79057e111 −2.14943
\(315\) −2.34518e110 −0.156804
\(316\) 2.47099e111 1.43481
\(317\) −1.33808e111 −0.675062 −0.337531 0.941314i \(-0.609592\pi\)
−0.337531 + 0.941314i \(0.609592\pi\)
\(318\) 5.10217e110 0.223742
\(319\) −2.35341e111 −0.897452
\(320\) 9.73522e111 3.22977
\(321\) 1.83909e111 0.531043
\(322\) −5.01689e111 −1.26139
\(323\) 3.80712e110 0.0833844
\(324\) −1.22228e112 −2.33301
\(325\) 1.38238e111 0.230047
\(326\) −2.39583e112 −3.47754
\(327\) 1.25475e112 1.58922
\(328\) 5.41548e112 5.98757
\(329\) 3.59018e110 0.0346656
\(330\) 1.03725e112 0.875009
\(331\) −1.40461e112 −1.03564 −0.517821 0.855489i \(-0.673257\pi\)
−0.517821 + 0.855489i \(0.673257\pi\)
\(332\) −5.56007e112 −3.58456
\(333\) −2.44360e111 −0.137804
\(334\) 5.61044e112 2.76872
\(335\) 2.79062e112 1.20561
\(336\) −1.30777e113 −4.94804
\(337\) −1.78572e112 −0.591949 −0.295974 0.955196i \(-0.595644\pi\)
−0.295974 + 0.955196i \(0.595644\pi\)
\(338\) 2.18982e112 0.636232
\(339\) 4.09038e112 1.04202
\(340\) −2.63743e112 −0.589344
\(341\) 1.20222e112 0.235730
\(342\) −4.84215e111 −0.0833444
\(343\) −1.09418e111 −0.0165386
\(344\) 1.80864e113 2.40160
\(345\) −3.13367e112 −0.365682
\(346\) −7.52838e112 −0.772352
\(347\) −1.99873e112 −0.180340 −0.0901700 0.995926i \(-0.528741\pi\)
−0.0901700 + 0.995926i \(0.528741\pi\)
\(348\) 5.04293e113 4.00320
\(349\) −2.76100e113 −1.92901 −0.964504 0.264067i \(-0.914936\pi\)
−0.964504 + 0.264067i \(0.914936\pi\)
\(350\) 1.24487e113 0.765765
\(351\) −1.59409e113 −0.863666
\(352\) −4.69628e113 −2.24184
\(353\) −1.57593e113 −0.663075 −0.331537 0.943442i \(-0.607567\pi\)
−0.331537 + 0.943442i \(0.607567\pi\)
\(354\) −1.29508e113 −0.480453
\(355\) 2.25015e113 0.736291
\(356\) −5.21338e113 −1.50520
\(357\) 1.30847e113 0.333447
\(358\) 1.48688e114 3.34566
\(359\) −4.80149e113 −0.954274 −0.477137 0.878829i \(-0.658325\pi\)
−0.477137 + 0.878829i \(0.658325\pi\)
\(360\) 2.12990e113 0.374022
\(361\) −5.74673e113 −0.891970
\(362\) 4.80497e113 0.659416
\(363\) 5.16294e113 0.626689
\(364\) −2.94611e114 −3.16401
\(365\) 3.01874e113 0.286941
\(366\) 1.12027e114 0.942785
\(367\) 1.15953e114 0.864255 0.432128 0.901812i \(-0.357763\pi\)
0.432128 + 0.901812i \(0.357763\pi\)
\(368\) 2.63731e114 1.74154
\(369\) 3.98888e113 0.233442
\(370\) −3.32156e114 −1.72332
\(371\) 3.80409e113 0.175030
\(372\) −2.57615e114 −1.05150
\(373\) 2.55903e114 0.926900 0.463450 0.886123i \(-0.346611\pi\)
0.463450 + 0.886123i \(0.346611\pi\)
\(374\) 8.73416e113 0.280824
\(375\) 3.54631e114 1.01248
\(376\) −3.26061e113 −0.0826874
\(377\) 5.69943e114 1.28423
\(378\) −1.43552e115 −2.87491
\(379\) −9.87836e114 −1.75890 −0.879448 0.475995i \(-0.842088\pi\)
−0.879448 + 0.475995i \(0.842088\pi\)
\(380\) −4.82170e114 −0.763536
\(381\) −4.41823e114 −0.622425
\(382\) 3.98805e114 0.499967
\(383\) −9.67896e114 −1.08015 −0.540074 0.841617i \(-0.681604\pi\)
−0.540074 + 0.841617i \(0.681604\pi\)
\(384\) 3.23469e115 3.21435
\(385\) 7.73355e114 0.684504
\(386\) 1.24635e115 0.982887
\(387\) 1.33219e114 0.0936328
\(388\) 2.88910e115 1.81030
\(389\) 1.42694e115 0.797352 0.398676 0.917092i \(-0.369470\pi\)
0.398676 + 0.917092i \(0.369470\pi\)
\(390\) −2.51199e115 −1.25211
\(391\) −2.63871e114 −0.117362
\(392\) −8.37307e115 −3.32395
\(393\) −4.16224e115 −1.47523
\(394\) 5.41953e115 1.71546
\(395\) 1.57085e115 0.444185
\(396\) −8.13791e114 −0.205625
\(397\) 5.95174e115 1.34421 0.672104 0.740456i \(-0.265391\pi\)
0.672104 + 0.740456i \(0.265391\pi\)
\(398\) −1.02417e116 −2.06811
\(399\) 2.39211e115 0.432004
\(400\) −6.54409e115 −1.05725
\(401\) 4.18136e115 0.604495 0.302248 0.953229i \(-0.402263\pi\)
0.302248 + 0.953229i \(0.402263\pi\)
\(402\) 1.98028e116 2.56253
\(403\) −2.91151e115 −0.337322
\(404\) −3.30017e116 −3.42425
\(405\) −7.77023e115 −0.722246
\(406\) 5.13249e116 4.27484
\(407\) 8.05811e115 0.601564
\(408\) −1.18835e116 −0.795367
\(409\) −2.79410e116 −1.67709 −0.838543 0.544836i \(-0.816592\pi\)
−0.838543 + 0.544836i \(0.816592\pi\)
\(410\) 5.42204e116 2.91932
\(411\) −2.04107e116 −0.986045
\(412\) −4.23468e116 −1.83609
\(413\) −9.65587e115 −0.375850
\(414\) 3.35608e115 0.117305
\(415\) −3.53463e116 −1.10969
\(416\) 1.13733e117 3.20801
\(417\) 5.08009e116 1.28771
\(418\) 1.59676e116 0.363828
\(419\) −7.53082e115 −0.154283 −0.0771415 0.997020i \(-0.524579\pi\)
−0.0771415 + 0.997020i \(0.524579\pi\)
\(420\) −1.65716e117 −3.05331
\(421\) −1.74478e116 −0.289193 −0.144596 0.989491i \(-0.546188\pi\)
−0.144596 + 0.989491i \(0.546188\pi\)
\(422\) −1.00868e117 −1.50435
\(423\) −2.40167e114 −0.00322379
\(424\) −3.45489e116 −0.417497
\(425\) 6.54757e115 0.0712480
\(426\) 1.59675e117 1.56499
\(427\) 8.35251e116 0.737524
\(428\) −1.96130e117 −1.56062
\(429\) 6.09408e116 0.437078
\(430\) 1.81083e117 1.17093
\(431\) 6.52772e116 0.380648 0.190324 0.981721i \(-0.439046\pi\)
0.190324 + 0.981721i \(0.439046\pi\)
\(432\) 7.54632e117 3.96925
\(433\) −1.58060e117 −0.750083 −0.375042 0.927008i \(-0.622372\pi\)
−0.375042 + 0.927008i \(0.622372\pi\)
\(434\) −2.62190e117 −1.12285
\(435\) 3.20588e117 1.23930
\(436\) −1.33813e118 −4.67037
\(437\) −4.82404e116 −0.152050
\(438\) 2.14216e117 0.609894
\(439\) 6.33463e117 1.62948 0.814742 0.579823i \(-0.196878\pi\)
0.814742 + 0.579823i \(0.196878\pi\)
\(440\) −7.02363e117 −1.63274
\(441\) −6.16737e116 −0.129593
\(442\) −2.11522e117 −0.401850
\(443\) 4.84950e117 0.833165 0.416583 0.909098i \(-0.363228\pi\)
0.416583 + 0.909098i \(0.363228\pi\)
\(444\) −1.72671e118 −2.68335
\(445\) −3.31424e117 −0.465975
\(446\) 1.62722e118 2.07035
\(447\) −8.98981e117 −1.03530
\(448\) 5.15073e118 5.37028
\(449\) −2.82363e117 −0.266591 −0.133296 0.991076i \(-0.542556\pi\)
−0.133296 + 0.991076i \(0.542556\pi\)
\(450\) −8.32762e116 −0.0712138
\(451\) −1.31539e118 −1.01906
\(452\) −4.36219e118 −3.06228
\(453\) 1.93973e118 1.23416
\(454\) 1.47186e118 0.848948
\(455\) −1.87289e118 −0.979503
\(456\) −2.17252e118 −1.03045
\(457\) −1.85598e118 −0.798552 −0.399276 0.916831i \(-0.630738\pi\)
−0.399276 + 0.916831i \(0.630738\pi\)
\(458\) 7.28671e118 2.84458
\(459\) −7.55034e117 −0.267487
\(460\) 3.34191e118 1.07466
\(461\) 1.46775e118 0.428510 0.214255 0.976778i \(-0.431268\pi\)
0.214255 + 0.976778i \(0.431268\pi\)
\(462\) 5.48789e118 1.45492
\(463\) 2.77498e118 0.668198 0.334099 0.942538i \(-0.391568\pi\)
0.334099 + 0.942538i \(0.391568\pi\)
\(464\) −2.69808e119 −5.90206
\(465\) −1.63770e118 −0.325520
\(466\) 4.21042e118 0.760592
\(467\) −6.20631e118 −1.01914 −0.509568 0.860430i \(-0.670195\pi\)
−0.509568 + 0.860430i \(0.670195\pi\)
\(468\) 1.97082e118 0.294243
\(469\) 1.47647e119 2.00462
\(470\) −3.26456e117 −0.0403153
\(471\) −9.22218e118 −1.03610
\(472\) 8.76949e118 0.896510
\(473\) −4.39307e118 −0.408741
\(474\) 1.11471e119 0.944116
\(475\) 1.19701e118 0.0923068
\(476\) −1.39541e119 −0.979927
\(477\) −2.54477e117 −0.0162772
\(478\) 1.08254e119 0.630817
\(479\) 2.47010e119 1.31155 0.655774 0.754958i \(-0.272343\pi\)
0.655774 + 0.754958i \(0.272343\pi\)
\(480\) 6.39741e119 3.09577
\(481\) −1.95150e119 −0.860819
\(482\) −3.70015e119 −1.48808
\(483\) −1.65797e119 −0.608035
\(484\) −5.50602e119 −1.84170
\(485\) 1.83665e119 0.560427
\(486\) 1.80928e119 0.503722
\(487\) −3.27475e119 −0.832031 −0.416015 0.909358i \(-0.636574\pi\)
−0.416015 + 0.909358i \(0.636574\pi\)
\(488\) −7.58577e119 −1.75921
\(489\) −7.91766e119 −1.67630
\(490\) −8.38322e119 −1.62064
\(491\) 7.69474e119 1.35852 0.679262 0.733896i \(-0.262300\pi\)
0.679262 + 0.733896i \(0.262300\pi\)
\(492\) 2.81864e120 4.54562
\(493\) 2.69951e119 0.397738
\(494\) −3.86701e119 −0.520626
\(495\) −5.17340e118 −0.0636568
\(496\) 1.37829e120 1.55027
\(497\) 1.19051e120 1.22426
\(498\) −2.50825e120 −2.35866
\(499\) 6.79740e119 0.584613 0.292306 0.956325i \(-0.405577\pi\)
0.292306 + 0.956325i \(0.405577\pi\)
\(500\) −3.78196e120 −2.97545
\(501\) 1.85412e120 1.33463
\(502\) −1.06071e119 −0.0698686
\(503\) 9.48767e119 0.571985 0.285992 0.958232i \(-0.407677\pi\)
0.285992 + 0.958232i \(0.407677\pi\)
\(504\) 1.12689e120 0.621904
\(505\) −2.09797e120 −1.06007
\(506\) −1.10671e120 −0.512079
\(507\) 7.23685e119 0.306687
\(508\) 4.71183e120 1.82917
\(509\) −1.57324e120 −0.559569 −0.279784 0.960063i \(-0.590263\pi\)
−0.279784 + 0.960063i \(0.590263\pi\)
\(510\) −1.18979e120 −0.387791
\(511\) 1.59716e120 0.477110
\(512\) −7.60153e120 −2.08155
\(513\) −1.38034e120 −0.346548
\(514\) 4.50901e120 1.03806
\(515\) −2.69206e120 −0.568411
\(516\) 9.41358e120 1.82324
\(517\) 7.91983e118 0.0140730
\(518\) −1.75738e121 −2.86544
\(519\) −2.48796e120 −0.372302
\(520\) 1.70097e121 2.33640
\(521\) −1.40305e121 −1.76927 −0.884637 0.466280i \(-0.845594\pi\)
−0.884637 + 0.466280i \(0.845594\pi\)
\(522\) −3.43341e120 −0.397547
\(523\) −7.70708e120 −0.819530 −0.409765 0.912191i \(-0.634389\pi\)
−0.409765 + 0.912191i \(0.634389\pi\)
\(524\) 4.43882e121 4.33536
\(525\) 4.11400e120 0.369127
\(526\) 2.92194e121 2.40882
\(527\) −1.37903e120 −0.104472
\(528\) −2.88490e121 −2.00873
\(529\) −1.22799e121 −0.785993
\(530\) −3.45908e120 −0.203556
\(531\) 6.45936e119 0.0349529
\(532\) −2.55107e121 −1.26957
\(533\) 3.18558e121 1.45823
\(534\) −2.35185e121 −0.990431
\(535\) −1.24683e121 −0.483131
\(536\) −1.34093e122 −4.78160
\(537\) 4.91380e121 1.61273
\(538\) 1.49414e121 0.451419
\(539\) 2.03377e121 0.565721
\(540\) 9.56245e121 2.44933
\(541\) 1.41172e121 0.333019 0.166510 0.986040i \(-0.446750\pi\)
0.166510 + 0.986040i \(0.446750\pi\)
\(542\) 1.58061e121 0.343445
\(543\) 1.58793e121 0.317863
\(544\) 5.38694e121 0.993553
\(545\) −8.50675e121 −1.44584
\(546\) −1.32905e122 −2.08194
\(547\) −2.47148e121 −0.356879 −0.178440 0.983951i \(-0.557105\pi\)
−0.178440 + 0.983951i \(0.557105\pi\)
\(548\) 2.17670e122 2.89777
\(549\) −5.58746e120 −0.0685875
\(550\) 2.74614e121 0.310874
\(551\) 4.93520e121 0.515298
\(552\) 1.50577e122 1.45034
\(553\) 8.31108e121 0.738566
\(554\) −3.96295e122 −3.24963
\(555\) −1.09770e122 −0.830702
\(556\) −5.41767e122 −3.78429
\(557\) 9.31061e121 0.600374 0.300187 0.953880i \(-0.402951\pi\)
0.300187 + 0.953880i \(0.402951\pi\)
\(558\) 1.75394e121 0.104422
\(559\) 1.06391e122 0.584894
\(560\) 8.86617e122 4.50162
\(561\) 2.88644e121 0.135368
\(562\) −3.72275e122 −1.61286
\(563\) 3.11201e121 0.124571 0.0622855 0.998058i \(-0.480161\pi\)
0.0622855 + 0.998058i \(0.480161\pi\)
\(564\) −1.69708e121 −0.0627743
\(565\) −2.77312e122 −0.948009
\(566\) 7.21788e122 2.28075
\(567\) −4.11109e122 −1.20091
\(568\) −1.08123e123 −2.92022
\(569\) 2.71930e122 0.679142 0.339571 0.940580i \(-0.389718\pi\)
0.339571 + 0.940580i \(0.389718\pi\)
\(570\) −2.17516e122 −0.502411
\(571\) 2.89172e122 0.617801 0.308901 0.951094i \(-0.400039\pi\)
0.308901 + 0.951094i \(0.400039\pi\)
\(572\) −6.49904e122 −1.28448
\(573\) 1.31796e122 0.241003
\(574\) 2.86870e123 4.85407
\(575\) −8.29648e121 −0.129920
\(576\) −3.44561e122 −0.499420
\(577\) 3.49596e122 0.469075 0.234538 0.972107i \(-0.424642\pi\)
0.234538 + 0.972107i \(0.424642\pi\)
\(578\) 1.45644e123 1.80928
\(579\) 4.11889e122 0.473788
\(580\) −3.41891e123 −3.64202
\(581\) −1.87011e123 −1.84514
\(582\) 1.30333e123 1.19119
\(583\) 8.39173e121 0.0710560
\(584\) −1.45054e123 −1.13804
\(585\) 1.25288e122 0.0910908
\(586\) 1.16798e122 0.0787031
\(587\) −5.88136e121 −0.0367352 −0.0183676 0.999831i \(-0.505847\pi\)
−0.0183676 + 0.999831i \(0.505847\pi\)
\(588\) −4.35801e123 −2.52347
\(589\) −2.52111e122 −0.135351
\(590\) 8.78012e122 0.437105
\(591\) 1.79103e123 0.826913
\(592\) 9.23827e123 3.95617
\(593\) −3.21670e123 −1.27784 −0.638920 0.769273i \(-0.720618\pi\)
−0.638920 + 0.769273i \(0.720618\pi\)
\(594\) −3.16672e123 −1.16711
\(595\) −8.87088e122 −0.303363
\(596\) 9.58720e123 3.04252
\(597\) −3.38463e123 −0.996905
\(598\) 2.68021e123 0.732768
\(599\) −3.33166e122 −0.0845603 −0.0422802 0.999106i \(-0.513462\pi\)
−0.0422802 + 0.999106i \(0.513462\pi\)
\(600\) −3.73635e123 −0.880474
\(601\) 3.45390e123 0.755781 0.377890 0.925850i \(-0.376650\pi\)
0.377890 + 0.925850i \(0.376650\pi\)
\(602\) 9.58077e123 1.94696
\(603\) −9.87691e122 −0.186424
\(604\) −2.06863e124 −3.62693
\(605\) −3.50027e123 −0.570148
\(606\) −1.48877e124 −2.25318
\(607\) 8.57587e122 0.120609 0.0603047 0.998180i \(-0.480793\pi\)
0.0603047 + 0.998180i \(0.480793\pi\)
\(608\) 9.84831e123 1.28722
\(609\) 1.69617e124 2.06063
\(610\) −7.59496e123 −0.857725
\(611\) −1.91801e122 −0.0201380
\(612\) 9.33471e122 0.0911303
\(613\) 7.99900e123 0.726180 0.363090 0.931754i \(-0.381722\pi\)
0.363090 + 0.931754i \(0.381722\pi\)
\(614\) 1.28075e121 0.00108136
\(615\) 1.79186e124 1.40722
\(616\) −3.71607e124 −2.71483
\(617\) 2.42228e124 1.64640 0.823199 0.567752i \(-0.192187\pi\)
0.823199 + 0.567752i \(0.192187\pi\)
\(618\) −1.91034e124 −1.20816
\(619\) −3.19334e124 −1.87936 −0.939682 0.342050i \(-0.888879\pi\)
−0.939682 + 0.342050i \(0.888879\pi\)
\(620\) 1.74653e124 0.956633
\(621\) 9.56710e123 0.487758
\(622\) 2.78873e124 1.32353
\(623\) −1.75350e124 −0.774798
\(624\) 6.98660e124 2.87443
\(625\) −1.67123e124 −0.640287
\(626\) −8.82412e124 −3.14857
\(627\) 5.27693e123 0.175378
\(628\) 9.83500e124 3.04488
\(629\) −9.24318e123 −0.266605
\(630\) 1.12826e124 0.303217
\(631\) −1.27838e124 −0.320151 −0.160076 0.987105i \(-0.551174\pi\)
−0.160076 + 0.987105i \(0.551174\pi\)
\(632\) −7.54815e124 −1.76169
\(633\) −3.33345e124 −0.725151
\(634\) 6.43743e124 1.30539
\(635\) 2.99539e124 0.566269
\(636\) −1.79820e124 −0.316954
\(637\) −4.92534e124 −0.809528
\(638\) 1.13221e125 1.73543
\(639\) −7.96400e123 −0.113853
\(640\) −2.19299e125 −2.92435
\(641\) −1.15177e125 −1.43279 −0.716393 0.697697i \(-0.754208\pi\)
−0.716393 + 0.697697i \(0.754208\pi\)
\(642\) −8.84780e124 −1.02690
\(643\) 1.29646e123 0.0140401 0.00702004 0.999975i \(-0.497765\pi\)
0.00702004 + 0.999975i \(0.497765\pi\)
\(644\) 1.76814e125 1.78688
\(645\) 5.98437e124 0.564431
\(646\) −1.83159e124 −0.161243
\(647\) 4.09400e124 0.336440 0.168220 0.985750i \(-0.446198\pi\)
0.168220 + 0.985750i \(0.446198\pi\)
\(648\) 3.73370e125 2.86452
\(649\) −2.13006e124 −0.152582
\(650\) −6.65055e124 −0.444850
\(651\) −8.66478e124 −0.541257
\(652\) 8.44380e125 4.92629
\(653\) 2.61194e125 1.42340 0.711698 0.702485i \(-0.247926\pi\)
0.711698 + 0.702485i \(0.247926\pi\)
\(654\) −6.03657e125 −3.07313
\(655\) 2.82183e125 1.34213
\(656\) −1.50803e126 −6.70178
\(657\) −1.06843e124 −0.0443698
\(658\) −1.72722e124 −0.0670340
\(659\) −4.17300e124 −0.151373 −0.0756864 0.997132i \(-0.524115\pi\)
−0.0756864 + 0.997132i \(0.524115\pi\)
\(660\) −3.65565e125 −1.23954
\(661\) −1.80404e125 −0.571850 −0.285925 0.958252i \(-0.592301\pi\)
−0.285925 + 0.958252i \(0.592301\pi\)
\(662\) 6.75752e125 2.00266
\(663\) −6.99031e124 −0.193707
\(664\) 1.69844e126 4.40119
\(665\) −1.62176e125 −0.393028
\(666\) 1.17561e125 0.266477
\(667\) −3.42057e125 −0.725269
\(668\) −1.97733e126 −3.92217
\(669\) 5.37758e125 0.997986
\(670\) −1.34256e126 −2.33133
\(671\) 1.84254e125 0.299409
\(672\) 3.38475e126 5.14748
\(673\) −4.58978e125 −0.653313 −0.326656 0.945143i \(-0.605922\pi\)
−0.326656 + 0.945143i \(0.605922\pi\)
\(674\) 8.59105e125 1.14467
\(675\) −2.37393e125 −0.296109
\(676\) −7.71775e125 −0.901286
\(677\) −4.89209e125 −0.534932 −0.267466 0.963567i \(-0.586186\pi\)
−0.267466 + 0.963567i \(0.586186\pi\)
\(678\) −1.96786e126 −2.01499
\(679\) 9.71739e125 0.931847
\(680\) 8.05656e125 0.723607
\(681\) 4.86416e125 0.409224
\(682\) −5.78384e125 −0.455839
\(683\) 2.01226e124 0.0148581 0.00742905 0.999972i \(-0.497635\pi\)
0.00742905 + 0.999972i \(0.497635\pi\)
\(684\) 1.70656e125 0.118066
\(685\) 1.38377e126 0.897082
\(686\) 5.26404e124 0.0319813
\(687\) 2.40809e126 1.37119
\(688\) −5.03646e126 −2.68807
\(689\) −2.03229e125 −0.101679
\(690\) 1.50760e126 0.707132
\(691\) −2.29357e126 −1.00865 −0.504324 0.863515i \(-0.668258\pi\)
−0.504324 + 0.863515i \(0.668258\pi\)
\(692\) 2.65329e126 1.09411
\(693\) −2.73715e125 −0.105845
\(694\) 9.61580e125 0.348730
\(695\) −3.44410e126 −1.17153
\(696\) −1.54047e127 −4.91520
\(697\) 1.50884e126 0.451631
\(698\) 1.32830e127 3.73019
\(699\) 1.39145e126 0.366634
\(700\) −4.38738e126 −1.08478
\(701\) 2.57316e126 0.597057 0.298528 0.954401i \(-0.403504\pi\)
0.298528 + 0.954401i \(0.403504\pi\)
\(702\) 7.66910e126 1.67010
\(703\) −1.68982e126 −0.345405
\(704\) 1.13624e127 2.18015
\(705\) −1.07886e125 −0.0194335
\(706\) 7.58173e126 1.28221
\(707\) −1.11000e127 −1.76262
\(708\) 4.56434e126 0.680609
\(709\) −6.78467e126 −0.950104 −0.475052 0.879958i \(-0.657571\pi\)
−0.475052 + 0.879958i \(0.657571\pi\)
\(710\) −1.08254e127 −1.42379
\(711\) −5.55975e125 −0.0686844
\(712\) 1.59253e127 1.84812
\(713\) 1.74738e126 0.190503
\(714\) −6.29497e126 −0.644798
\(715\) −4.13155e126 −0.397644
\(716\) −5.24033e127 −4.73946
\(717\) 3.57755e126 0.304077
\(718\) 2.30998e127 1.84531
\(719\) 1.13360e127 0.851182 0.425591 0.904916i \(-0.360066\pi\)
0.425591 + 0.904916i \(0.360066\pi\)
\(720\) −5.93108e126 −0.418637
\(721\) −1.42432e127 −0.945121
\(722\) 2.76473e127 1.72483
\(723\) −1.22281e127 −0.717309
\(724\) −1.69345e127 −0.934129
\(725\) 8.48765e126 0.440297
\(726\) −2.48387e127 −1.21185
\(727\) 3.79015e127 1.73930 0.869651 0.493666i \(-0.164344\pi\)
0.869651 + 0.493666i \(0.164344\pi\)
\(728\) 8.99951e127 3.88483
\(729\) 2.69516e127 1.09449
\(730\) −1.45230e127 −0.554868
\(731\) 5.03914e126 0.181148
\(732\) −3.94824e127 −1.33555
\(733\) −1.80508e127 −0.574606 −0.287303 0.957840i \(-0.592759\pi\)
−0.287303 + 0.957840i \(0.592759\pi\)
\(734\) −5.57845e127 −1.67124
\(735\) −2.77046e127 −0.781206
\(736\) −6.82584e127 −1.81173
\(737\) 3.25704e127 0.813805
\(738\) −1.91904e127 −0.451414
\(739\) 4.14460e127 0.917921 0.458960 0.888457i \(-0.348222\pi\)
0.458960 + 0.888457i \(0.348222\pi\)
\(740\) 1.17064e128 2.44125
\(741\) −1.27796e127 −0.250961
\(742\) −1.83013e127 −0.338461
\(743\) −3.30910e126 −0.0576379 −0.0288189 0.999585i \(-0.509175\pi\)
−0.0288189 + 0.999585i \(0.509175\pi\)
\(744\) 7.86937e127 1.29105
\(745\) 6.09474e127 0.941892
\(746\) −1.23114e128 −1.79238
\(747\) 1.25102e127 0.171592
\(748\) −3.07825e127 −0.397816
\(749\) −6.59677e127 −0.803323
\(750\) −1.70611e128 −1.95786
\(751\) 6.11801e127 0.661657 0.330829 0.943691i \(-0.392672\pi\)
0.330829 + 0.943691i \(0.392672\pi\)
\(752\) 9.07973e126 0.0925506
\(753\) −3.50541e126 −0.0336793
\(754\) −2.74197e128 −2.48335
\(755\) −1.31506e128 −1.12281
\(756\) 5.05932e128 4.07260
\(757\) −1.17540e128 −0.892110 −0.446055 0.895005i \(-0.647171\pi\)
−0.446055 + 0.895005i \(0.647171\pi\)
\(758\) 4.75244e128 3.40124
\(759\) −3.65743e127 −0.246841
\(760\) 1.47289e128 0.937485
\(761\) −3.45209e127 −0.207236 −0.103618 0.994617i \(-0.533042\pi\)
−0.103618 + 0.994617i \(0.533042\pi\)
\(762\) 2.12559e128 1.20361
\(763\) −4.50077e128 −2.40406
\(764\) −1.40554e128 −0.708254
\(765\) 5.93423e126 0.0282118
\(766\) 4.65651e128 2.08872
\(767\) 5.15853e127 0.218339
\(768\) −6.67383e128 −2.66564
\(769\) 4.31920e128 1.62810 0.814050 0.580794i \(-0.197258\pi\)
0.814050 + 0.580794i \(0.197258\pi\)
\(770\) −3.72058e128 −1.32365
\(771\) 1.49013e128 0.500383
\(772\) −4.39259e128 −1.39236
\(773\) 5.58575e128 1.67145 0.835727 0.549145i \(-0.185047\pi\)
0.835727 + 0.549145i \(0.185047\pi\)
\(774\) −6.40911e127 −0.181061
\(775\) −4.33586e127 −0.115651
\(776\) −8.82536e128 −2.22272
\(777\) −5.80773e128 −1.38125
\(778\) −6.86497e128 −1.54187
\(779\) 2.75843e128 0.585120
\(780\) 8.85318e128 1.77374
\(781\) 2.62624e128 0.497007
\(782\) 1.26947e128 0.226946
\(783\) −9.78755e128 −1.65301
\(784\) 2.33163e129 3.72044
\(785\) 6.25228e128 0.942624
\(786\) 2.00244e129 2.85269
\(787\) −2.16044e128 −0.290849 −0.145424 0.989369i \(-0.546455\pi\)
−0.145424 + 0.989369i \(0.546455\pi\)
\(788\) −1.91005e129 −2.43012
\(789\) 9.65633e128 1.16114
\(790\) −7.55729e128 −0.858936
\(791\) −1.46721e129 −1.57630
\(792\) 2.48589e128 0.252471
\(793\) −4.46222e128 −0.428444
\(794\) −2.86336e129 −2.59934
\(795\) −1.14314e128 −0.0981215
\(796\) 3.60955e129 2.92969
\(797\) 5.79107e128 0.444492 0.222246 0.974991i \(-0.428661\pi\)
0.222246 + 0.974991i \(0.428661\pi\)
\(798\) −1.15084e129 −0.835381
\(799\) −9.08456e126 −0.00623695
\(800\) 1.69373e129 1.09987
\(801\) 1.17302e128 0.0720538
\(802\) −2.01164e129 −1.16893
\(803\) 3.52329e128 0.193690
\(804\) −6.97927e129 −3.63008
\(805\) 1.12404e129 0.553177
\(806\) 1.40072e129 0.652291
\(807\) 4.93779e128 0.217601
\(808\) 1.00810e130 4.20436
\(809\) −1.68676e129 −0.665799 −0.332899 0.942962i \(-0.608027\pi\)
−0.332899 + 0.942962i \(0.608027\pi\)
\(810\) 3.73823e129 1.39663
\(811\) 1.55157e129 0.548712 0.274356 0.961628i \(-0.411535\pi\)
0.274356 + 0.961628i \(0.411535\pi\)
\(812\) −1.80888e130 −6.05574
\(813\) 5.22357e128 0.165553
\(814\) −3.87672e129 −1.16327
\(815\) 5.36786e129 1.52506
\(816\) 3.30917e129 0.890241
\(817\) 9.21247e128 0.234690
\(818\) 1.34423e130 3.24304
\(819\) 6.62878e128 0.151461
\(820\) −1.91093e130 −4.13550
\(821\) 3.14500e129 0.644689 0.322345 0.946622i \(-0.395529\pi\)
0.322345 + 0.946622i \(0.395529\pi\)
\(822\) 9.81951e129 1.90675
\(823\) −9.23589e129 −1.69897 −0.849486 0.527612i \(-0.823088\pi\)
−0.849486 + 0.527612i \(0.823088\pi\)
\(824\) 1.29357e130 2.25439
\(825\) 9.07538e128 0.149852
\(826\) 4.64540e129 0.726794
\(827\) −3.35499e129 −0.497389 −0.248694 0.968582i \(-0.580001\pi\)
−0.248694 + 0.968582i \(0.580001\pi\)
\(828\) −1.18281e129 −0.166175
\(829\) 4.80463e129 0.639711 0.319855 0.947466i \(-0.396366\pi\)
0.319855 + 0.947466i \(0.396366\pi\)
\(830\) 1.70050e130 2.14586
\(831\) −1.30966e130 −1.56644
\(832\) −2.75171e130 −3.11972
\(833\) −2.33287e129 −0.250719
\(834\) −2.44401e130 −2.49008
\(835\) −1.25702e130 −1.21421
\(836\) −5.62759e129 −0.515399
\(837\) 4.99990e129 0.434189
\(838\) 3.62305e129 0.298342
\(839\) −1.24765e130 −0.974282 −0.487141 0.873323i \(-0.661960\pi\)
−0.487141 + 0.873323i \(0.661960\pi\)
\(840\) 5.06214e130 3.74892
\(841\) 2.07568e130 1.45794
\(842\) 8.39407e129 0.559222
\(843\) −1.23028e130 −0.777460
\(844\) 3.55496e130 2.13106
\(845\) −4.90630e129 −0.279017
\(846\) 1.15543e128 0.00623396
\(847\) −1.85193e130 −0.948010
\(848\) 9.62074e129 0.467297
\(849\) 2.38534e130 1.09941
\(850\) −3.15001e129 −0.137775
\(851\) 1.17121e130 0.486150
\(852\) −5.62756e130 −2.21696
\(853\) −3.16115e130 −1.18199 −0.590993 0.806676i \(-0.701264\pi\)
−0.590993 + 0.806676i \(0.701264\pi\)
\(854\) −4.01836e130 −1.42618
\(855\) 1.08489e129 0.0365504
\(856\) 5.99120e130 1.91616
\(857\) 4.85246e130 1.47338 0.736692 0.676229i \(-0.236387\pi\)
0.736692 + 0.676229i \(0.236387\pi\)
\(858\) −2.93184e130 −0.845193
\(859\) 1.53494e129 0.0420141 0.0210070 0.999779i \(-0.493313\pi\)
0.0210070 + 0.999779i \(0.493313\pi\)
\(860\) −6.38204e130 −1.65874
\(861\) 9.48040e130 2.33984
\(862\) −3.14046e130 −0.736072
\(863\) −2.23394e130 −0.497269 −0.248634 0.968597i \(-0.579982\pi\)
−0.248634 + 0.968597i \(0.579982\pi\)
\(864\) −1.95313e131 −4.12923
\(865\) 1.68674e130 0.338712
\(866\) 7.60418e130 1.45046
\(867\) 4.81321e130 0.872138
\(868\) 9.24056e130 1.59064
\(869\) 1.83340e130 0.299832
\(870\) −1.54233e131 −2.39647
\(871\) −7.88784e130 −1.16453
\(872\) 4.08761e131 5.73437
\(873\) −6.50051e129 −0.0866589
\(874\) 2.32083e130 0.294025
\(875\) −1.27205e131 −1.53160
\(876\) −7.54979e130 −0.863977
\(877\) −9.11800e129 −0.0991785 −0.0495892 0.998770i \(-0.515791\pi\)
−0.0495892 + 0.998770i \(0.515791\pi\)
\(878\) −3.04757e131 −3.15099
\(879\) 3.85991e129 0.0379378
\(880\) 1.95585e131 1.82750
\(881\) 1.41911e131 1.26063 0.630314 0.776340i \(-0.282926\pi\)
0.630314 + 0.776340i \(0.282926\pi\)
\(882\) 2.96709e130 0.250599
\(883\) −6.40533e130 −0.514388 −0.257194 0.966360i \(-0.582798\pi\)
−0.257194 + 0.966360i \(0.582798\pi\)
\(884\) 7.45483e130 0.569262
\(885\) 2.90163e130 0.210701
\(886\) −2.33307e131 −1.61112
\(887\) −1.13778e131 −0.747235 −0.373617 0.927583i \(-0.621883\pi\)
−0.373617 + 0.927583i \(0.621883\pi\)
\(888\) 5.27459e131 3.29467
\(889\) 1.58481e131 0.941560
\(890\) 1.59447e131 0.901072
\(891\) −9.06895e130 −0.487527
\(892\) −5.73492e131 −2.93286
\(893\) −1.66082e129 −0.00808041
\(894\) 4.32496e131 2.00199
\(895\) −3.33136e131 −1.46723
\(896\) −1.16027e132 −4.86244
\(897\) 8.85749e130 0.353221
\(898\) 1.35844e131 0.515517
\(899\) −1.78764e131 −0.645615
\(900\) 2.93497e130 0.100882
\(901\) −9.62586e129 −0.0314910
\(902\) 6.32828e131 1.97058
\(903\) 3.16622e131 0.938505
\(904\) 1.33252e132 3.75992
\(905\) −1.07656e131 −0.289184
\(906\) −9.33198e131 −2.38654
\(907\) −2.07157e131 −0.504401 −0.252201 0.967675i \(-0.581154\pi\)
−0.252201 + 0.967675i \(0.581154\pi\)
\(908\) −5.18739e131 −1.20262
\(909\) 7.42541e130 0.163918
\(910\) 9.01042e131 1.89410
\(911\) 7.32060e131 1.46548 0.732738 0.680511i \(-0.238242\pi\)
0.732738 + 0.680511i \(0.238242\pi\)
\(912\) 6.04977e131 1.15337
\(913\) −4.12541e131 −0.749061
\(914\) 8.92906e131 1.54419
\(915\) −2.50996e131 −0.413455
\(916\) −2.56811e132 −4.02963
\(917\) 1.49298e132 2.23161
\(918\) 3.63244e131 0.517248
\(919\) −9.54003e131 −1.29422 −0.647112 0.762395i \(-0.724023\pi\)
−0.647112 + 0.762395i \(0.724023\pi\)
\(920\) −1.02085e132 −1.31949
\(921\) 4.23258e128 0.000521256 0
\(922\) −7.06128e131 −0.828624
\(923\) −6.36016e131 −0.711201
\(924\) −1.93414e132 −2.06103
\(925\) −2.90619e131 −0.295132
\(926\) −1.33503e132 −1.29212
\(927\) 9.52806e130 0.0878934
\(928\) 6.98312e132 6.13995
\(929\) −6.90699e130 −0.0578882 −0.0289441 0.999581i \(-0.509214\pi\)
−0.0289441 + 0.999581i \(0.509214\pi\)
\(930\) 7.87891e131 0.629470
\(931\) −4.26491e131 −0.324825
\(932\) −1.48391e132 −1.07746
\(933\) 9.21612e131 0.637992
\(934\) 2.98583e132 1.97074
\(935\) −1.95689e131 −0.123154
\(936\) −6.02027e131 −0.361278
\(937\) 9.96476e131 0.570237 0.285118 0.958492i \(-0.407967\pi\)
0.285118 + 0.958492i \(0.407967\pi\)
\(938\) −7.10322e132 −3.87640
\(939\) −2.91617e132 −1.51773
\(940\) 1.15055e131 0.0571107
\(941\) 3.96538e132 1.87736 0.938678 0.344795i \(-0.112052\pi\)
0.938678 + 0.344795i \(0.112052\pi\)
\(942\) 4.43675e132 2.00355
\(943\) −1.91186e132 −0.823542
\(944\) −2.44202e132 −1.00345
\(945\) 3.21629e132 1.26078
\(946\) 2.11349e132 0.790396
\(947\) 7.97066e131 0.284394 0.142197 0.989838i \(-0.454583\pi\)
0.142197 + 0.989838i \(0.454583\pi\)
\(948\) −3.92865e132 −1.33744
\(949\) −8.53263e131 −0.277164
\(950\) −5.75879e131 −0.178497
\(951\) 2.12742e132 0.629246
\(952\) 4.26258e132 1.20317
\(953\) −1.94714e132 −0.524521 −0.262260 0.964997i \(-0.584468\pi\)
−0.262260 + 0.964997i \(0.584468\pi\)
\(954\) 1.22428e131 0.0314759
\(955\) −8.93526e131 −0.219259
\(956\) −3.81529e132 −0.893616
\(957\) 3.74171e132 0.836543
\(958\) −1.18835e133 −2.53618
\(959\) 7.32126e132 1.49162
\(960\) −1.54781e133 −3.01057
\(961\) −4.47186e132 −0.830419
\(962\) 9.38857e132 1.66459
\(963\) 4.41295e131 0.0747066
\(964\) 1.30407e133 2.10801
\(965\) −2.79244e132 −0.431041
\(966\) 7.97642e132 1.17578
\(967\) −1.33124e133 −1.87403 −0.937017 0.349283i \(-0.886425\pi\)
−0.937017 + 0.349283i \(0.886425\pi\)
\(968\) 1.68193e133 2.26128
\(969\) −6.05299e131 −0.0777252
\(970\) −8.83605e132 −1.08372
\(971\) 2.41972e132 0.283471 0.141735 0.989905i \(-0.454732\pi\)
0.141735 + 0.989905i \(0.454732\pi\)
\(972\) −6.37657e132 −0.713572
\(973\) −1.82221e133 −1.94795
\(974\) 1.57547e133 1.60893
\(975\) −2.19785e132 −0.214434
\(976\) 2.11239e133 1.96905
\(977\) −3.12470e132 −0.278292 −0.139146 0.990272i \(-0.544436\pi\)
−0.139146 + 0.990272i \(0.544436\pi\)
\(978\) 3.80915e133 3.24152
\(979\) −3.86818e132 −0.314540
\(980\) 2.95456e133 2.29579
\(981\) 3.01082e132 0.223570
\(982\) −3.70191e133 −2.62703
\(983\) 6.48939e132 0.440121 0.220061 0.975486i \(-0.429374\pi\)
0.220061 + 0.975486i \(0.429374\pi\)
\(984\) −8.61013e133 −5.58120
\(985\) −1.21425e133 −0.752307
\(986\) −1.29872e133 −0.769120
\(987\) −5.70806e131 −0.0323129
\(988\) 1.36288e133 0.737519
\(989\) −6.38514e132 −0.330321
\(990\) 2.48890e132 0.123095
\(991\) 3.49977e133 1.65486 0.827432 0.561566i \(-0.189801\pi\)
0.827432 + 0.561566i \(0.189801\pi\)
\(992\) −3.56728e133 −1.61275
\(993\) 2.23320e133 0.965355
\(994\) −5.72751e133 −2.36740
\(995\) 2.29465e133 0.906962
\(996\) 8.84002e133 3.34128
\(997\) 2.65956e133 0.961336 0.480668 0.876903i \(-0.340394\pi\)
0.480668 + 0.876903i \(0.340394\pi\)
\(998\) −3.27020e133 −1.13049
\(999\) 3.35128e133 1.10802
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.1.1 7
3.2 odd 2 9.90.a.b.1.7 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.90.a.a.1.1 7 1.1 even 1 trivial
9.90.a.b.1.7 7 3.2 odd 2