Properties

Label 1.90.a.a.1.5
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 1.5
Root \(-4.68207e11\) 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

\(f(q)\) \(=\) \(q+1.79872e13 q^{2} -3.11193e21 q^{3} -2.95431e26 q^{4} -4.75717e30 q^{5} -5.59749e34 q^{6} +3.90338e37 q^{7} -1.64475e40 q^{8} +6.77478e42 q^{9} +O(q^{10})\) \(q+1.79872e13 q^{2} -3.11193e21 q^{3} -2.95431e26 q^{4} -4.75717e30 q^{5} -5.59749e34 q^{6} +3.90338e37 q^{7} -1.64475e40 q^{8} +6.77478e42 q^{9} -8.55680e43 q^{10} -2.01197e45 q^{11} +9.19360e47 q^{12} -1.05046e49 q^{13} +7.02109e50 q^{14} +1.48040e52 q^{15} -1.12982e53 q^{16} +1.05148e55 q^{17} +1.21859e56 q^{18} +1.08050e57 q^{19} +1.40541e57 q^{20} -1.21471e59 q^{21} -3.61897e58 q^{22} -5.03802e60 q^{23} +5.11835e61 q^{24} -1.38928e62 q^{25} -1.88949e62 q^{26} -1.20290e64 q^{27} -1.15318e64 q^{28} +1.12164e65 q^{29} +2.66282e65 q^{30} -3.18722e66 q^{31} +8.14829e66 q^{32} +6.26111e66 q^{33} +1.89132e68 q^{34} -1.85690e68 q^{35} -2.00148e69 q^{36} -6.99627e69 q^{37} +1.94351e70 q^{38} +3.26897e70 q^{39} +7.82435e70 q^{40} -7.38883e70 q^{41} -2.18491e72 q^{42} +4.97212e72 q^{43} +5.94398e71 q^{44} -3.22288e73 q^{45} -9.06197e73 q^{46} +5.91267e73 q^{47} +3.51590e74 q^{48} -1.12142e74 q^{49} -2.49893e75 q^{50} -3.27213e76 q^{51} +3.10339e75 q^{52} +2.39386e76 q^{53} -2.16369e77 q^{54} +9.57127e75 q^{55} -6.42009e77 q^{56} -3.36243e78 q^{57} +2.01752e78 q^{58} -1.72292e78 q^{59} -4.37355e78 q^{60} +1.90453e79 q^{61} -5.73291e79 q^{62} +2.64446e80 q^{63} +2.16497e80 q^{64} +4.99723e79 q^{65} +1.12620e80 q^{66} +7.04228e80 q^{67} -3.10640e81 q^{68} +1.56779e82 q^{69} -3.34005e81 q^{70} -1.27373e82 q^{71} -1.11428e83 q^{72} -3.75786e82 q^{73} -1.25843e83 q^{74} +4.32334e83 q^{75} -3.19212e83 q^{76} -7.85349e82 q^{77} +5.87995e83 q^{78} +3.21546e83 q^{79} +5.37472e83 q^{80} +1.77235e85 q^{81} -1.32904e84 q^{82} -2.22227e85 q^{83} +3.58862e85 q^{84} -5.00207e85 q^{85} +8.94344e85 q^{86} -3.49047e86 q^{87} +3.30919e85 q^{88} -5.54352e86 q^{89} -5.79705e86 q^{90} -4.10036e86 q^{91} +1.48839e87 q^{92} +9.91840e87 q^{93} +1.06352e87 q^{94} -5.14011e87 q^{95} -2.53569e88 q^{96} +4.88818e88 q^{97} -2.01713e87 q^{98} -1.36307e88 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 31407330351408q^{2} - \)\(13\!\cdots\!64\)\(q^{3} + \)\(22\!\cdots\!04\)\(q^{4} + \)\(10\!\cdots\!50\)\(q^{5} - \)\(47\!\cdots\!76\)\(q^{6} + \)\(38\!\cdots\!92\)\(q^{7} - \)\(17\!\cdots\!20\)\(q^{8} + \)\(56\!\cdots\!71\)\(q^{9} + O(q^{10}) \) \( 7q - 31407330351408q^{2} - \)\(13\!\cdots\!64\)\(q^{3} + \)\(22\!\cdots\!04\)\(q^{4} + \)\(10\!\cdots\!50\)\(q^{5} - \)\(47\!\cdots\!76\)\(q^{6} + \)\(38\!\cdots\!92\)\(q^{7} - \)\(17\!\cdots\!20\)\(q^{8} + \)\(56\!\cdots\!71\)\(q^{9} - \)\(33\!\cdots\!00\)\(q^{10} - \)\(33\!\cdots\!56\)\(q^{11} - \)\(10\!\cdots\!28\)\(q^{12} - \)\(10\!\cdots\!34\)\(q^{13} - \)\(33\!\cdots\!32\)\(q^{14} - \)\(39\!\cdots\!00\)\(q^{15} + \)\(11\!\cdots\!32\)\(q^{16} + \)\(83\!\cdots\!42\)\(q^{17} - \)\(14\!\cdots\!04\)\(q^{18} + \)\(56\!\cdots\!80\)\(q^{19} + \)\(17\!\cdots\!00\)\(q^{20} - \)\(90\!\cdots\!36\)\(q^{21} - \)\(57\!\cdots\!36\)\(q^{22} - \)\(11\!\cdots\!04\)\(q^{23} + \)\(10\!\cdots\!40\)\(q^{24} - \)\(21\!\cdots\!75\)\(q^{25} + \)\(25\!\cdots\!24\)\(q^{26} + \)\(11\!\cdots\!80\)\(q^{27} + \)\(42\!\cdots\!84\)\(q^{28} - \)\(14\!\cdots\!30\)\(q^{29} + \)\(68\!\cdots\!00\)\(q^{30} + \)\(68\!\cdots\!04\)\(q^{31} - \)\(18\!\cdots\!48\)\(q^{32} - \)\(86\!\cdots\!88\)\(q^{33} + \)\(31\!\cdots\!28\)\(q^{34} + \)\(33\!\cdots\!00\)\(q^{35} - \)\(16\!\cdots\!88\)\(q^{36} - \)\(54\!\cdots\!58\)\(q^{37} + \)\(45\!\cdots\!20\)\(q^{38} - \)\(52\!\cdots\!48\)\(q^{39} - \)\(36\!\cdots\!00\)\(q^{40} - \)\(65\!\cdots\!66\)\(q^{41} + \)\(11\!\cdots\!04\)\(q^{42} + \)\(32\!\cdots\!56\)\(q^{43} - \)\(15\!\cdots\!32\)\(q^{44} - \)\(47\!\cdots\!50\)\(q^{45} - \)\(56\!\cdots\!76\)\(q^{46} - \)\(58\!\cdots\!08\)\(q^{47} - \)\(38\!\cdots\!04\)\(q^{48} - \)\(30\!\cdots\!01\)\(q^{49} - \)\(11\!\cdots\!00\)\(q^{50} - \)\(44\!\cdots\!56\)\(q^{51} - \)\(19\!\cdots\!68\)\(q^{52} - \)\(18\!\cdots\!14\)\(q^{53} - \)\(10\!\cdots\!20\)\(q^{54} - \)\(12\!\cdots\!00\)\(q^{55} - \)\(58\!\cdots\!20\)\(q^{56} - \)\(66\!\cdots\!40\)\(q^{57} - \)\(30\!\cdots\!20\)\(q^{58} - \)\(90\!\cdots\!60\)\(q^{59} - \)\(28\!\cdots\!00\)\(q^{60} + \)\(87\!\cdots\!94\)\(q^{61} + \)\(16\!\cdots\!24\)\(q^{62} + \)\(60\!\cdots\!96\)\(q^{63} + \)\(14\!\cdots\!44\)\(q^{64} + \)\(13\!\cdots\!00\)\(q^{65} + \)\(57\!\cdots\!08\)\(q^{66} + \)\(58\!\cdots\!92\)\(q^{67} + \)\(33\!\cdots\!84\)\(q^{68} - \)\(59\!\cdots\!48\)\(q^{69} - \)\(48\!\cdots\!00\)\(q^{70} - \)\(54\!\cdots\!76\)\(q^{71} - \)\(19\!\cdots\!60\)\(q^{72} - \)\(19\!\cdots\!54\)\(q^{73} - \)\(96\!\cdots\!52\)\(q^{74} - \)\(44\!\cdots\!00\)\(q^{75} - \)\(62\!\cdots\!40\)\(q^{76} + \)\(13\!\cdots\!64\)\(q^{77} + \)\(51\!\cdots\!92\)\(q^{78} + \)\(26\!\cdots\!20\)\(q^{79} + \)\(27\!\cdots\!00\)\(q^{80} + \)\(48\!\cdots\!47\)\(q^{81} + \)\(63\!\cdots\!04\)\(q^{82} - \)\(35\!\cdots\!24\)\(q^{83} - \)\(91\!\cdots\!92\)\(q^{84} - \)\(14\!\cdots\!00\)\(q^{85} - \)\(24\!\cdots\!76\)\(q^{86} - \)\(41\!\cdots\!60\)\(q^{87} - \)\(18\!\cdots\!40\)\(q^{88} - \)\(16\!\cdots\!90\)\(q^{89} - \)\(15\!\cdots\!00\)\(q^{90} - \)\(30\!\cdots\!36\)\(q^{91} + \)\(72\!\cdots\!92\)\(q^{92} + \)\(87\!\cdots\!92\)\(q^{93} + \)\(22\!\cdots\!08\)\(q^{94} + \)\(22\!\cdots\!00\)\(q^{95} + \)\(84\!\cdots\!44\)\(q^{96} + \)\(71\!\cdots\!42\)\(q^{97} - \)\(17\!\cdots\!56\)\(q^{98} - \)\(19\!\cdots\!68\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.79872e13 0.722984 0.361492 0.932375i \(-0.382268\pi\)
0.361492 + 0.932375i \(0.382268\pi\)
\(3\) −3.11193e21 −1.82446 −0.912229 0.409680i \(-0.865640\pi\)
−0.912229 + 0.409680i \(0.865640\pi\)
\(4\) −2.95431e26 −0.477294
\(5\) −4.75717e30 −0.374268 −0.187134 0.982334i \(-0.559920\pi\)
−0.187134 + 0.982334i \(0.559920\pi\)
\(6\) −5.59749e34 −1.31905
\(7\) 3.90338e37 0.965114 0.482557 0.875865i \(-0.339708\pi\)
0.482557 + 0.875865i \(0.339708\pi\)
\(8\) −1.64475e40 −1.06806
\(9\) 6.77478e42 2.32865
\(10\) −8.55680e43 −0.270590
\(11\) −2.01197e45 −0.0915476 −0.0457738 0.998952i \(-0.514575\pi\)
−0.0457738 + 0.998952i \(0.514575\pi\)
\(12\) 9.19360e47 0.870804
\(13\) −1.05046e49 −0.282424 −0.141212 0.989979i \(-0.545100\pi\)
−0.141212 + 0.989979i \(0.545100\pi\)
\(14\) 7.02109e50 0.697761
\(15\) 1.48040e52 0.682837
\(16\) −1.12982e53 −0.294895
\(17\) 1.05148e55 1.84852 0.924260 0.381763i \(-0.124683\pi\)
0.924260 + 0.381763i \(0.124683\pi\)
\(18\) 1.21859e56 1.68357
\(19\) 1.08050e57 1.34613 0.673067 0.739581i \(-0.264976\pi\)
0.673067 + 0.739581i \(0.264976\pi\)
\(20\) 1.40541e57 0.178636
\(21\) −1.21471e59 −1.76081
\(22\) −3.61897e58 −0.0661874
\(23\) −5.03802e60 −1.27459 −0.637295 0.770620i \(-0.719947\pi\)
−0.637295 + 0.770620i \(0.719947\pi\)
\(24\) 5.11835e61 1.94863
\(25\) −1.38928e62 −0.859923
\(26\) −1.88949e62 −0.204188
\(27\) −1.20290e64 −2.42406
\(28\) −1.15318e64 −0.460643
\(29\) 1.12164e65 0.940032 0.470016 0.882658i \(-0.344248\pi\)
0.470016 + 0.882658i \(0.344248\pi\)
\(30\) 2.66282e65 0.493680
\(31\) −3.18722e66 −1.37346 −0.686731 0.726912i \(-0.740955\pi\)
−0.686731 + 0.726912i \(0.740955\pi\)
\(32\) 8.14829e66 0.854855
\(33\) 6.26111e66 0.167025
\(34\) 1.89132e68 1.33645
\(35\) −1.85690e68 −0.361211
\(36\) −2.00148e69 −1.11145
\(37\) −6.99627e69 −1.14786 −0.573931 0.818904i \(-0.694582\pi\)
−0.573931 + 0.818904i \(0.694582\pi\)
\(38\) 1.94351e70 0.973233
\(39\) 3.26897e70 0.515271
\(40\) 7.82435e70 0.399741
\(41\) −7.38883e70 −0.125804 −0.0629020 0.998020i \(-0.520036\pi\)
−0.0629020 + 0.998020i \(0.520036\pi\)
\(42\) −2.18491e72 −1.27304
\(43\) 4.97212e72 1.01671 0.508353 0.861149i \(-0.330255\pi\)
0.508353 + 0.861149i \(0.330255\pi\)
\(44\) 5.94398e71 0.0436952
\(45\) −3.22288e73 −0.871539
\(46\) −9.06197e73 −0.921508
\(47\) 5.91267e73 0.230903 0.115451 0.993313i \(-0.463169\pi\)
0.115451 + 0.993313i \(0.463169\pi\)
\(48\) 3.51590e74 0.538025
\(49\) −1.12142e74 −0.0685558
\(50\) −2.49893e75 −0.621711
\(51\) −3.27213e76 −3.37255
\(52\) 3.10339e75 0.134799
\(53\) 2.39386e76 0.445475 0.222738 0.974878i \(-0.428501\pi\)
0.222738 + 0.974878i \(0.428501\pi\)
\(54\) −2.16369e77 −1.75256
\(55\) 9.57127e75 0.0342634
\(56\) −6.42009e77 −1.03080
\(57\) −3.36243e78 −2.45597
\(58\) 2.01752e78 0.679628
\(59\) −1.72292e78 −0.271239 −0.135619 0.990761i \(-0.543302\pi\)
−0.135619 + 0.990761i \(0.543302\pi\)
\(60\) −4.37355e78 −0.325914
\(61\) 1.90453e79 0.680158 0.340079 0.940397i \(-0.389546\pi\)
0.340079 + 0.940397i \(0.389546\pi\)
\(62\) −5.73291e79 −0.992990
\(63\) 2.64446e80 2.24741
\(64\) 2.16497e80 0.912942
\(65\) 4.99723e79 0.105702
\(66\) 1.12620e80 0.120756
\(67\) 7.04228e80 0.386709 0.193355 0.981129i \(-0.438063\pi\)
0.193355 + 0.981129i \(0.438063\pi\)
\(68\) −3.10640e81 −0.882289
\(69\) 1.56779e82 2.32544
\(70\) −3.34005e81 −0.261150
\(71\) −1.27373e82 −0.529762 −0.264881 0.964281i \(-0.585333\pi\)
−0.264881 + 0.964281i \(0.585333\pi\)
\(72\) −1.11428e83 −2.48714
\(73\) −3.75786e82 −0.454018 −0.227009 0.973893i \(-0.572895\pi\)
−0.227009 + 0.973893i \(0.572895\pi\)
\(74\) −1.25843e83 −0.829886
\(75\) 4.32334e83 1.56889
\(76\) −3.19212e83 −0.642503
\(77\) −7.85349e82 −0.0883538
\(78\) 5.87995e83 0.372532
\(79\) 3.21546e83 0.115568 0.0577840 0.998329i \(-0.481597\pi\)
0.0577840 + 0.998329i \(0.481597\pi\)
\(80\) 5.37472e83 0.110370
\(81\) 1.77235e85 2.09395
\(82\) −1.32904e84 −0.0909542
\(83\) −2.22227e85 −0.886793 −0.443396 0.896326i \(-0.646227\pi\)
−0.443396 + 0.896326i \(0.646227\pi\)
\(84\) 3.58862e85 0.840425
\(85\) −5.00207e85 −0.691843
\(86\) 8.94344e85 0.735062
\(87\) −3.49047e86 −1.71505
\(88\) 3.30919e85 0.0977783
\(89\) −5.54352e86 −0.990672 −0.495336 0.868701i \(-0.664955\pi\)
−0.495336 + 0.868701i \(0.664955\pi\)
\(90\) −5.79705e86 −0.630109
\(91\) −4.10036e86 −0.272571
\(92\) 1.48839e87 0.608355
\(93\) 9.91840e87 2.50582
\(94\) 1.06352e87 0.166939
\(95\) −5.14011e87 −0.503816
\(96\) −2.53569e88 −1.55965
\(97\) 4.88818e88 1.89585 0.947927 0.318488i \(-0.103175\pi\)
0.947927 + 0.318488i \(0.103175\pi\)
\(98\) −2.01713e87 −0.0495647
\(99\) −1.36307e88 −0.213182
\(100\) 4.10437e88 0.410437
\(101\) 6.30836e88 0.405150 0.202575 0.979267i \(-0.435069\pi\)
0.202575 + 0.979267i \(0.435069\pi\)
\(102\) −5.88565e89 −2.43830
\(103\) −3.95925e89 −1.06257 −0.531284 0.847194i \(-0.678290\pi\)
−0.531284 + 0.847194i \(0.678290\pi\)
\(104\) 1.72775e89 0.301646
\(105\) 5.77855e89 0.659015
\(106\) 4.30589e89 0.322071
\(107\) 5.08196e88 0.0250296 0.0125148 0.999922i \(-0.496016\pi\)
0.0125148 + 0.999922i \(0.496016\pi\)
\(108\) 3.55375e90 1.15699
\(109\) −3.00179e90 −0.648487 −0.324244 0.945974i \(-0.605110\pi\)
−0.324244 + 0.945974i \(0.605110\pi\)
\(110\) 1.72160e89 0.0247719
\(111\) 2.17719e91 2.09423
\(112\) −4.41010e90 −0.284608
\(113\) −1.01787e91 −0.442284 −0.221142 0.975242i \(-0.570978\pi\)
−0.221142 + 0.975242i \(0.570978\pi\)
\(114\) −6.04807e91 −1.77562
\(115\) 2.39667e91 0.477039
\(116\) −3.31367e91 −0.448672
\(117\) −7.11666e91 −0.657666
\(118\) −3.09906e91 −0.196101
\(119\) 4.10433e92 1.78403
\(120\) −2.43488e92 −0.729311
\(121\) −4.78954e92 −0.991619
\(122\) 3.42571e92 0.491743
\(123\) 2.29935e92 0.229524
\(124\) 9.41603e92 0.655546
\(125\) 1.42947e93 0.696110
\(126\) 4.75664e93 1.62484
\(127\) −3.42465e93 −0.822908 −0.411454 0.911431i \(-0.634979\pi\)
−0.411454 + 0.911431i \(0.634979\pi\)
\(128\) −1.14937e93 −0.194813
\(129\) −1.54729e94 −1.85494
\(130\) 8.98861e92 0.0764211
\(131\) −2.21360e94 −1.33821 −0.669107 0.743166i \(-0.733323\pi\)
−0.669107 + 0.743166i \(0.733323\pi\)
\(132\) −1.84973e93 −0.0797200
\(133\) 4.21760e94 1.29917
\(134\) 1.26671e94 0.279585
\(135\) 5.72242e94 0.907250
\(136\) −1.72942e95 −1.97433
\(137\) 1.50357e93 0.0123896 0.00619482 0.999981i \(-0.498028\pi\)
0.00619482 + 0.999981i \(0.498028\pi\)
\(138\) 2.82002e95 1.68125
\(139\) 1.85854e95 0.803550 0.401775 0.915738i \(-0.368393\pi\)
0.401775 + 0.915738i \(0.368393\pi\)
\(140\) 5.48587e94 0.172404
\(141\) −1.83998e95 −0.421272
\(142\) −2.29108e95 −0.383009
\(143\) 2.11350e94 0.0258552
\(144\) −7.65425e95 −0.686708
\(145\) −5.33583e95 −0.351824
\(146\) −6.75933e95 −0.328248
\(147\) 3.48979e95 0.125077
\(148\) 2.06691e96 0.547868
\(149\) −6.69346e96 −1.31481 −0.657403 0.753539i \(-0.728345\pi\)
−0.657403 + 0.753539i \(0.728345\pi\)
\(150\) 7.77648e96 1.13428
\(151\) −8.94714e96 −0.970980 −0.485490 0.874242i \(-0.661359\pi\)
−0.485490 + 0.874242i \(0.661359\pi\)
\(152\) −1.77715e97 −1.43775
\(153\) 7.12356e97 4.30455
\(154\) −1.41262e96 −0.0638784
\(155\) 1.51621e97 0.514043
\(156\) −9.65754e96 −0.245936
\(157\) −7.99466e97 −1.53202 −0.766012 0.642826i \(-0.777762\pi\)
−0.766012 + 0.642826i \(0.777762\pi\)
\(158\) 5.78371e96 0.0835538
\(159\) −7.44954e97 −0.812751
\(160\) −3.87628e97 −0.319945
\(161\) −1.96653e98 −1.23012
\(162\) 3.18797e98 1.51389
\(163\) 8.25331e97 0.298044 0.149022 0.988834i \(-0.452388\pi\)
0.149022 + 0.988834i \(0.452388\pi\)
\(164\) 2.18289e97 0.0600455
\(165\) −2.97851e97 −0.0625121
\(166\) −3.99724e98 −0.641137
\(167\) −2.58266e98 −0.317091 −0.158546 0.987352i \(-0.550680\pi\)
−0.158546 + 0.987352i \(0.550680\pi\)
\(168\) 1.99789e99 1.88065
\(169\) −1.27309e99 −0.920237
\(170\) −8.99732e98 −0.500191
\(171\) 7.32014e99 3.13467
\(172\) −1.46892e99 −0.485268
\(173\) −2.87467e99 −0.733730 −0.366865 0.930274i \(-0.619569\pi\)
−0.366865 + 0.930274i \(0.619569\pi\)
\(174\) −6.27837e99 −1.23995
\(175\) −5.42290e99 −0.829924
\(176\) 2.27315e98 0.0269970
\(177\) 5.36162e99 0.494864
\(178\) −9.97123e99 −0.716240
\(179\) −7.10087e99 −0.397513 −0.198757 0.980049i \(-0.563690\pi\)
−0.198757 + 0.980049i \(0.563690\pi\)
\(180\) 9.52138e99 0.415981
\(181\) 3.14165e100 1.07266 0.536329 0.844009i \(-0.319811\pi\)
0.536329 + 0.844009i \(0.319811\pi\)
\(182\) −7.37540e99 −0.197065
\(183\) −5.92676e100 −1.24092
\(184\) 8.28628e100 1.36134
\(185\) 3.32824e100 0.429608
\(186\) 1.78404e101 1.81167
\(187\) −2.11555e100 −0.169228
\(188\) −1.74679e100 −0.110209
\(189\) −4.69540e101 −2.33950
\(190\) −9.24561e100 −0.364250
\(191\) 1.75148e101 0.546285 0.273142 0.961974i \(-0.411937\pi\)
0.273142 + 0.961974i \(0.411937\pi\)
\(192\) −6.73724e101 −1.66562
\(193\) 3.08614e101 0.605502 0.302751 0.953070i \(-0.402095\pi\)
0.302751 + 0.953070i \(0.402095\pi\)
\(194\) 8.79246e101 1.37067
\(195\) −1.55510e101 −0.192850
\(196\) 3.31303e100 0.0327213
\(197\) −6.10297e101 −0.480612 −0.240306 0.970697i \(-0.577248\pi\)
−0.240306 + 0.970697i \(0.577248\pi\)
\(198\) −2.45177e101 −0.154127
\(199\) 9.92591e100 0.0498665 0.0249332 0.999689i \(-0.492063\pi\)
0.0249332 + 0.999689i \(0.492063\pi\)
\(200\) 2.28502e102 0.918450
\(201\) −2.19151e102 −0.705535
\(202\) 1.13470e102 0.292917
\(203\) 4.37819e102 0.907238
\(204\) 9.66690e102 1.60970
\(205\) 3.51499e101 0.0470844
\(206\) −7.12158e102 −0.768219
\(207\) −3.41315e103 −2.96807
\(208\) 1.18683e102 0.0832856
\(209\) −2.17393e102 −0.123235
\(210\) 1.03940e103 0.476457
\(211\) −8.33167e102 −0.309145 −0.154573 0.987981i \(-0.549400\pi\)
−0.154573 + 0.987981i \(0.549400\pi\)
\(212\) −7.07222e102 −0.212623
\(213\) 3.96376e103 0.966529
\(214\) 9.14103e101 0.0180960
\(215\) −2.36532e103 −0.380521
\(216\) 1.97848e104 2.58904
\(217\) −1.24409e104 −1.32555
\(218\) −5.39938e103 −0.468846
\(219\) 1.16942e104 0.828337
\(220\) −2.82765e102 −0.0163537
\(221\) −1.10454e104 −0.522067
\(222\) 3.91615e104 1.51409
\(223\) −5.60785e104 −1.77513 −0.887564 0.460684i \(-0.847604\pi\)
−0.887564 + 0.460684i \(0.847604\pi\)
\(224\) 3.18059e104 0.825032
\(225\) −9.41208e104 −2.00246
\(226\) −1.83086e104 −0.319764
\(227\) −4.37425e104 −0.627701 −0.313851 0.949472i \(-0.601619\pi\)
−0.313851 + 0.949472i \(0.601619\pi\)
\(228\) 9.93367e104 1.17222
\(229\) 6.98125e104 0.678038 0.339019 0.940779i \(-0.389905\pi\)
0.339019 + 0.940779i \(0.389905\pi\)
\(230\) 4.31093e104 0.344891
\(231\) 2.44395e104 0.161198
\(232\) −1.84482e105 −1.00401
\(233\) 2.70074e105 1.21379 0.606897 0.794781i \(-0.292414\pi\)
0.606897 + 0.794781i \(0.292414\pi\)
\(234\) −1.28009e105 −0.475482
\(235\) −2.81276e104 −0.0864196
\(236\) 5.09005e104 0.129461
\(237\) −1.00063e105 −0.210849
\(238\) 7.38254e105 1.28983
\(239\) 8.33363e105 1.20817 0.604084 0.796920i \(-0.293539\pi\)
0.604084 + 0.796920i \(0.293539\pi\)
\(240\) −1.67257e105 −0.201366
\(241\) −1.56610e106 −1.56697 −0.783487 0.621408i \(-0.786561\pi\)
−0.783487 + 0.621408i \(0.786561\pi\)
\(242\) −8.61504e105 −0.716924
\(243\) −2.01580e106 −1.39627
\(244\) −5.62657e105 −0.324636
\(245\) 5.33480e104 0.0256583
\(246\) 4.13589e105 0.165942
\(247\) −1.13502e106 −0.380181
\(248\) 5.24218e106 1.46694
\(249\) 6.91555e106 1.61792
\(250\) 2.57121e106 0.503276
\(251\) −1.03640e106 −0.169843 −0.0849217 0.996388i \(-0.527064\pi\)
−0.0849217 + 0.996388i \(0.527064\pi\)
\(252\) −7.81255e106 −1.07268
\(253\) 1.01363e106 0.116686
\(254\) −6.15999e106 −0.594949
\(255\) 1.55661e107 1.26224
\(256\) −1.54679e107 −1.05379
\(257\) 2.59608e107 1.48694 0.743471 0.668768i \(-0.233178\pi\)
0.743471 + 0.668768i \(0.233178\pi\)
\(258\) −2.78314e107 −1.34109
\(259\) −2.73091e107 −1.10782
\(260\) −1.47634e106 −0.0504512
\(261\) 7.59887e107 2.18900
\(262\) −3.98164e107 −0.967508
\(263\) −9.18230e107 −1.88331 −0.941653 0.336586i \(-0.890728\pi\)
−0.941653 + 0.336586i \(0.890728\pi\)
\(264\) −1.02980e107 −0.178392
\(265\) −1.13880e107 −0.166727
\(266\) 7.58627e107 0.939281
\(267\) 1.72510e108 1.80744
\(268\) −2.08051e107 −0.184574
\(269\) −4.34307e107 −0.326453 −0.163227 0.986589i \(-0.552190\pi\)
−0.163227 + 0.986589i \(0.552190\pi\)
\(270\) 1.02930e108 0.655927
\(271\) −2.01852e107 −0.109119 −0.0545595 0.998511i \(-0.517375\pi\)
−0.0545595 + 0.998511i \(0.517375\pi\)
\(272\) −1.18798e108 −0.545120
\(273\) 1.27600e108 0.497295
\(274\) 2.70450e106 0.00895751
\(275\) 2.79519e107 0.0787239
\(276\) −4.63175e108 −1.10992
\(277\) 6.30470e108 1.28622 0.643109 0.765774i \(-0.277644\pi\)
0.643109 + 0.765774i \(0.277644\pi\)
\(278\) 3.34299e108 0.580954
\(279\) −2.15927e109 −3.19831
\(280\) 3.05414e108 0.385795
\(281\) 2.21025e108 0.238238 0.119119 0.992880i \(-0.461993\pi\)
0.119119 + 0.992880i \(0.461993\pi\)
\(282\) −3.30961e108 −0.304573
\(283\) −5.73795e108 −0.451087 −0.225544 0.974233i \(-0.572416\pi\)
−0.225544 + 0.974233i \(0.572416\pi\)
\(284\) 3.76299e108 0.252853
\(285\) 1.59956e109 0.919190
\(286\) 3.80159e107 0.0186929
\(287\) −2.88414e108 −0.121415
\(288\) 5.52029e109 1.99066
\(289\) 7.82052e109 2.41703
\(290\) −9.59766e108 −0.254363
\(291\) −1.52117e110 −3.45891
\(292\) 1.11019e109 0.216700
\(293\) −8.06470e109 −1.35201 −0.676004 0.736898i \(-0.736290\pi\)
−0.676004 + 0.736898i \(0.736290\pi\)
\(294\) 6.27715e108 0.0904288
\(295\) 8.19624e108 0.101516
\(296\) 1.15071e110 1.22599
\(297\) 2.42021e109 0.221917
\(298\) −1.20397e110 −0.950584
\(299\) 5.29225e109 0.359975
\(300\) −1.27725e110 −0.748824
\(301\) 1.94081e110 0.981236
\(302\) −1.60934e110 −0.702002
\(303\) −1.96312e110 −0.739178
\(304\) −1.22076e110 −0.396969
\(305\) −9.06015e109 −0.254562
\(306\) 1.28133e111 3.11212
\(307\) −5.28891e110 −1.11099 −0.555493 0.831521i \(-0.687471\pi\)
−0.555493 + 0.831521i \(0.687471\pi\)
\(308\) 2.32016e109 0.0421708
\(309\) 1.23209e111 1.93861
\(310\) 2.72724e110 0.371645
\(311\) −1.09333e111 −1.29097 −0.645484 0.763773i \(-0.723344\pi\)
−0.645484 + 0.763773i \(0.723344\pi\)
\(312\) −5.37664e110 −0.550340
\(313\) 4.11236e110 0.365063 0.182531 0.983200i \(-0.441571\pi\)
0.182531 + 0.983200i \(0.441571\pi\)
\(314\) −1.43802e111 −1.10763
\(315\) −1.25801e111 −0.841134
\(316\) −9.49947e109 −0.0551600
\(317\) 1.98612e111 1.00200 0.501000 0.865447i \(-0.332966\pi\)
0.501000 + 0.865447i \(0.332966\pi\)
\(318\) −1.33996e111 −0.587605
\(319\) −2.25671e110 −0.0860577
\(320\) −1.02991e111 −0.341685
\(321\) −1.58147e110 −0.0456654
\(322\) −3.53724e111 −0.889360
\(323\) 1.13612e112 2.48836
\(324\) −5.23608e111 −0.999432
\(325\) 1.45939e111 0.242863
\(326\) 1.48454e111 0.215481
\(327\) 9.34137e111 1.18314
\(328\) 1.21528e111 0.134366
\(329\) 2.30794e111 0.222847
\(330\) −5.35751e110 −0.0451952
\(331\) 6.49334e110 0.0478765 0.0239383 0.999713i \(-0.492379\pi\)
0.0239383 + 0.999713i \(0.492379\pi\)
\(332\) 6.56528e111 0.423261
\(333\) −4.73982e112 −2.67297
\(334\) −4.64548e111 −0.229252
\(335\) −3.35013e111 −0.144733
\(336\) 1.37239e112 0.519255
\(337\) −1.31744e112 −0.436718 −0.218359 0.975869i \(-0.570070\pi\)
−0.218359 + 0.975869i \(0.570070\pi\)
\(338\) −2.28992e112 −0.665316
\(339\) 3.16754e112 0.806929
\(340\) 1.47777e112 0.330213
\(341\) 6.41259e111 0.125737
\(342\) 1.31669e113 2.26632
\(343\) −6.82282e112 −1.03128
\(344\) −8.17789e112 −1.08590
\(345\) −7.45826e112 −0.870338
\(346\) −5.17072e112 −0.530475
\(347\) 1.51622e113 1.36805 0.684023 0.729461i \(-0.260229\pi\)
0.684023 + 0.729461i \(0.260229\pi\)
\(348\) 1.03119e113 0.818584
\(349\) 1.52478e113 1.06531 0.532653 0.846334i \(-0.321195\pi\)
0.532653 + 0.846334i \(0.321195\pi\)
\(350\) −9.75427e112 −0.600021
\(351\) 1.26361e113 0.684614
\(352\) −1.63941e112 −0.0782600
\(353\) −2.78663e113 −1.17248 −0.586239 0.810138i \(-0.699392\pi\)
−0.586239 + 0.810138i \(0.699392\pi\)
\(354\) 9.64405e112 0.357778
\(355\) 6.05934e112 0.198273
\(356\) 1.63773e113 0.472842
\(357\) −1.27724e114 −3.25489
\(358\) −1.27725e113 −0.287396
\(359\) −5.91157e113 −1.17490 −0.587448 0.809262i \(-0.699867\pi\)
−0.587448 + 0.809262i \(0.699867\pi\)
\(360\) 5.30083e113 0.930856
\(361\) 5.23201e113 0.812078
\(362\) 5.65094e113 0.775514
\(363\) 1.49047e114 1.80917
\(364\) 1.21137e113 0.130097
\(365\) 1.78768e113 0.169925
\(366\) −1.06606e114 −0.897165
\(367\) −2.85230e113 −0.212596 −0.106298 0.994334i \(-0.533900\pi\)
−0.106298 + 0.994334i \(0.533900\pi\)
\(368\) 5.69203e113 0.375871
\(369\) −5.00577e113 −0.292953
\(370\) 5.98657e113 0.310600
\(371\) 9.34417e113 0.429934
\(372\) −2.93020e114 −1.19602
\(373\) 4.52146e114 1.63770 0.818852 0.574005i \(-0.194611\pi\)
0.818852 + 0.574005i \(0.194611\pi\)
\(374\) −3.80528e113 −0.122349
\(375\) −4.44840e114 −1.27002
\(376\) −9.72487e113 −0.246618
\(377\) −1.17824e114 −0.265488
\(378\) −8.44570e114 −1.69142
\(379\) 9.92623e113 0.176742 0.0883709 0.996088i \(-0.471834\pi\)
0.0883709 + 0.996088i \(0.471834\pi\)
\(380\) 1.51855e114 0.240468
\(381\) 1.06573e115 1.50136
\(382\) 3.15041e114 0.394955
\(383\) −1.05705e115 −1.17964 −0.589821 0.807534i \(-0.700802\pi\)
−0.589821 + 0.807534i \(0.700802\pi\)
\(384\) 3.57677e114 0.355428
\(385\) 3.73604e113 0.0330680
\(386\) 5.55110e114 0.437768
\(387\) 3.36850e115 2.36755
\(388\) −1.44412e115 −0.904881
\(389\) −2.17710e114 −0.121653 −0.0608263 0.998148i \(-0.519374\pi\)
−0.0608263 + 0.998148i \(0.519374\pi\)
\(390\) −2.79719e114 −0.139427
\(391\) −5.29738e115 −2.35611
\(392\) 1.84446e114 0.0732217
\(393\) 6.88856e115 2.44152
\(394\) −1.09775e115 −0.347475
\(395\) −1.52965e114 −0.0432535
\(396\) 4.02692e114 0.101751
\(397\) 4.00607e113 0.00904776 0.00452388 0.999990i \(-0.498560\pi\)
0.00452388 + 0.999990i \(0.498560\pi\)
\(398\) 1.78539e114 0.0360526
\(399\) −1.31249e116 −2.37029
\(400\) 1.56963e115 0.253587
\(401\) 6.23287e114 0.0901080 0.0450540 0.998985i \(-0.485654\pi\)
0.0450540 + 0.998985i \(0.485654\pi\)
\(402\) −3.94191e115 −0.510091
\(403\) 3.34806e115 0.387899
\(404\) −1.86368e115 −0.193376
\(405\) −8.43138e115 −0.783700
\(406\) 7.87514e115 0.655918
\(407\) 1.40763e115 0.105084
\(408\) 5.38184e116 3.60208
\(409\) −6.55225e115 −0.393281 −0.196641 0.980476i \(-0.563003\pi\)
−0.196641 + 0.980476i \(0.563003\pi\)
\(410\) 6.32248e114 0.0340413
\(411\) −4.67901e114 −0.0226044
\(412\) 1.16969e116 0.507158
\(413\) −6.72523e115 −0.261776
\(414\) −6.13929e116 −2.14587
\(415\) 1.05717e116 0.331898
\(416\) −8.55948e115 −0.241432
\(417\) −5.78364e116 −1.46604
\(418\) −3.91029e115 −0.0890972
\(419\) 3.38221e116 0.692909 0.346454 0.938067i \(-0.387386\pi\)
0.346454 + 0.938067i \(0.387386\pi\)
\(420\) −1.70716e116 −0.314544
\(421\) 7.60301e116 1.26018 0.630090 0.776522i \(-0.283018\pi\)
0.630090 + 0.776522i \(0.283018\pi\)
\(422\) −1.49863e116 −0.223507
\(423\) 4.00571e116 0.537691
\(424\) −3.93731e116 −0.475794
\(425\) −1.46080e117 −1.58959
\(426\) 7.12969e116 0.698785
\(427\) 7.43410e116 0.656430
\(428\) −1.50137e115 −0.0119465
\(429\) −6.57706e115 −0.0471718
\(430\) −4.25454e116 −0.275110
\(431\) 1.02975e117 0.600470 0.300235 0.953865i \(-0.402935\pi\)
0.300235 + 0.953865i \(0.402935\pi\)
\(432\) 1.35906e117 0.714845
\(433\) 2.72587e117 1.29358 0.646791 0.762668i \(-0.276111\pi\)
0.646791 + 0.762668i \(0.276111\pi\)
\(434\) −2.23777e117 −0.958348
\(435\) 1.66047e117 0.641889
\(436\) 8.86823e116 0.309519
\(437\) −5.44356e117 −1.71577
\(438\) 2.10346e117 0.598874
\(439\) −5.39464e117 −1.38769 −0.693843 0.720126i \(-0.744084\pi\)
−0.693843 + 0.720126i \(0.744084\pi\)
\(440\) −1.57424e116 −0.0365953
\(441\) −7.59740e116 −0.159642
\(442\) −1.98676e117 −0.377446
\(443\) 5.69469e117 0.978372 0.489186 0.872179i \(-0.337294\pi\)
0.489186 + 0.872179i \(0.337294\pi\)
\(444\) −6.43209e117 −0.999563
\(445\) 2.63714e117 0.370777
\(446\) −1.00869e118 −1.28339
\(447\) 2.08296e118 2.39881
\(448\) 8.45071e117 0.881093
\(449\) −1.50535e118 −1.42126 −0.710631 0.703565i \(-0.751590\pi\)
−0.710631 + 0.703565i \(0.751590\pi\)
\(450\) −1.69297e118 −1.44774
\(451\) 1.48661e116 0.0115170
\(452\) 3.00710e117 0.211100
\(453\) 2.78429e118 1.77151
\(454\) −7.86805e117 −0.453818
\(455\) 1.95061e117 0.102015
\(456\) 5.53036e118 2.62312
\(457\) 2.94233e118 1.26596 0.632980 0.774168i \(-0.281831\pi\)
0.632980 + 0.774168i \(0.281831\pi\)
\(458\) 1.25573e118 0.490211
\(459\) −1.26483e119 −4.48093
\(460\) −7.08050e117 −0.227688
\(461\) 1.09403e117 0.0319402 0.0159701 0.999872i \(-0.494916\pi\)
0.0159701 + 0.999872i \(0.494916\pi\)
\(462\) 4.39598e117 0.116543
\(463\) −1.51518e118 −0.364847 −0.182423 0.983220i \(-0.558394\pi\)
−0.182423 + 0.983220i \(0.558394\pi\)
\(464\) −1.26725e118 −0.277211
\(465\) −4.71835e118 −0.937850
\(466\) 4.85788e118 0.877553
\(467\) −8.24498e118 −1.35391 −0.676953 0.736026i \(-0.736700\pi\)
−0.676953 + 0.736026i \(0.736700\pi\)
\(468\) 2.10248e118 0.313900
\(469\) 2.74887e118 0.373219
\(470\) −5.05936e117 −0.0624799
\(471\) 2.48788e119 2.79511
\(472\) 2.83378e118 0.289699
\(473\) −1.00038e118 −0.0930770
\(474\) −1.79985e118 −0.152440
\(475\) −1.50111e119 −1.15757
\(476\) −1.21255e119 −0.851509
\(477\) 1.62179e119 1.03735
\(478\) 1.49899e119 0.873487
\(479\) −3.05065e119 −1.61980 −0.809900 0.586567i \(-0.800479\pi\)
−0.809900 + 0.586567i \(0.800479\pi\)
\(480\) 1.20627e119 0.583727
\(481\) 7.34932e118 0.324184
\(482\) −2.81698e119 −1.13290
\(483\) 6.11970e119 2.24431
\(484\) 1.41498e119 0.473294
\(485\) −2.32539e119 −0.709558
\(486\) −3.62586e119 −1.00948
\(487\) −1.88865e118 −0.0479857 −0.0239929 0.999712i \(-0.507638\pi\)
−0.0239929 + 0.999712i \(0.507638\pi\)
\(488\) −3.13247e119 −0.726449
\(489\) −2.56837e119 −0.543768
\(490\) 9.59580e117 0.0185505
\(491\) −7.35262e119 −1.29812 −0.649061 0.760736i \(-0.724838\pi\)
−0.649061 + 0.760736i \(0.724838\pi\)
\(492\) −6.79300e118 −0.109551
\(493\) 1.17938e120 1.73767
\(494\) −2.04159e119 −0.274865
\(495\) 6.48433e118 0.0797873
\(496\) 3.60097e119 0.405028
\(497\) −4.97186e119 −0.511281
\(498\) 1.24391e120 1.16973
\(499\) 1.88248e120 1.61903 0.809515 0.587099i \(-0.199730\pi\)
0.809515 + 0.587099i \(0.199730\pi\)
\(500\) −4.22308e119 −0.332250
\(501\) 8.03706e119 0.578520
\(502\) −1.86420e119 −0.122794
\(503\) −2.65462e119 −0.160039 −0.0800197 0.996793i \(-0.525498\pi\)
−0.0800197 + 0.996793i \(0.525498\pi\)
\(504\) −4.34947e120 −2.40037
\(505\) −3.00099e119 −0.151635
\(506\) 1.82324e119 0.0843619
\(507\) 3.96176e120 1.67893
\(508\) 1.01175e120 0.392769
\(509\) −3.57212e120 −1.27053 −0.635265 0.772294i \(-0.719109\pi\)
−0.635265 + 0.772294i \(0.719109\pi\)
\(510\) 2.79990e120 0.912578
\(511\) −1.46684e120 −0.438179
\(512\) −2.07082e120 −0.567059
\(513\) −1.29974e121 −3.26311
\(514\) 4.66962e120 1.07503
\(515\) 1.88348e120 0.397685
\(516\) 4.57117e120 0.885351
\(517\) −1.18961e119 −0.0211386
\(518\) −4.91214e120 −0.800934
\(519\) 8.94577e120 1.33866
\(520\) −8.21919e119 −0.112896
\(521\) 9.79424e119 0.123507 0.0617535 0.998091i \(-0.480331\pi\)
0.0617535 + 0.998091i \(0.480331\pi\)
\(522\) 1.36682e121 1.58261
\(523\) 1.44190e120 0.153324 0.0766618 0.997057i \(-0.475574\pi\)
0.0766618 + 0.997057i \(0.475574\pi\)
\(524\) 6.53965e120 0.638722
\(525\) 1.68757e121 1.51416
\(526\) −1.65164e121 −1.36160
\(527\) −3.35130e121 −2.53887
\(528\) −7.07390e119 −0.0492549
\(529\) 9.75813e120 0.624582
\(530\) −2.04838e120 −0.120541
\(531\) −1.16724e121 −0.631620
\(532\) −1.24601e121 −0.620088
\(533\) 7.76170e119 0.0355301
\(534\) 3.10298e121 1.30675
\(535\) −2.41757e119 −0.00936778
\(536\) −1.15828e121 −0.413029
\(537\) 2.20974e121 0.725247
\(538\) −7.81197e120 −0.236020
\(539\) 2.25627e119 0.00627612
\(540\) −1.69058e121 −0.433025
\(541\) −3.32756e121 −0.784960 −0.392480 0.919761i \(-0.628383\pi\)
−0.392480 + 0.919761i \(0.628383\pi\)
\(542\) −3.63076e120 −0.0788913
\(543\) −9.77659e121 −1.95702
\(544\) 8.56777e121 1.58022
\(545\) 1.42800e121 0.242708
\(546\) 2.29517e121 0.359536
\(547\) 8.03429e121 1.16014 0.580072 0.814565i \(-0.303025\pi\)
0.580072 + 0.814565i \(0.303025\pi\)
\(548\) −4.44201e119 −0.00591351
\(549\) 1.29028e122 1.58385
\(550\) 5.02776e120 0.0569161
\(551\) 1.21193e122 1.26541
\(552\) −2.57863e122 −2.48371
\(553\) 1.25512e121 0.111536
\(554\) 1.13404e122 0.929915
\(555\) −1.03573e122 −0.783803
\(556\) −5.49070e121 −0.383530
\(557\) 4.95449e121 0.319479 0.159740 0.987159i \(-0.448935\pi\)
0.159740 + 0.987159i \(0.448935\pi\)
\(558\) −3.88392e122 −2.31232
\(559\) −5.22303e121 −0.287142
\(560\) 2.09796e121 0.106520
\(561\) 6.58344e121 0.308749
\(562\) 3.97562e121 0.172242
\(563\) −1.54057e122 −0.616679 −0.308340 0.951276i \(-0.599773\pi\)
−0.308340 + 0.951276i \(0.599773\pi\)
\(564\) 5.43588e121 0.201071
\(565\) 4.84217e121 0.165533
\(566\) −1.03210e122 −0.326129
\(567\) 6.91817e122 2.02090
\(568\) 2.09497e122 0.565818
\(569\) −5.08576e121 −0.127017 −0.0635083 0.997981i \(-0.520229\pi\)
−0.0635083 + 0.997981i \(0.520229\pi\)
\(570\) 2.87717e122 0.664560
\(571\) −6.07440e122 −1.29777 −0.648883 0.760888i \(-0.724764\pi\)
−0.648883 + 0.760888i \(0.724764\pi\)
\(572\) −6.24394e120 −0.0123406
\(573\) −5.45047e122 −0.996674
\(574\) −5.18777e121 −0.0877811
\(575\) 6.99922e122 1.09605
\(576\) 1.46672e123 2.12592
\(577\) −9.97444e122 −1.33834 −0.669168 0.743111i \(-0.733349\pi\)
−0.669168 + 0.743111i \(0.733349\pi\)
\(578\) 1.40669e123 1.74747
\(579\) −9.60385e122 −1.10471
\(580\) 1.57637e122 0.167924
\(581\) −8.67438e122 −0.855856
\(582\) −2.73615e123 −2.50073
\(583\) −4.81638e121 −0.0407822
\(584\) 6.18074e122 0.484919
\(585\) 3.38551e122 0.246144
\(586\) −1.45061e123 −0.977479
\(587\) 3.03625e123 1.89645 0.948226 0.317595i \(-0.102875\pi\)
0.948226 + 0.317595i \(0.102875\pi\)
\(588\) −1.03099e122 −0.0596986
\(589\) −3.44378e123 −1.84886
\(590\) 1.47427e122 0.0733945
\(591\) 1.89920e123 0.876856
\(592\) 7.90449e122 0.338499
\(593\) 3.31837e123 1.31823 0.659114 0.752043i \(-0.270931\pi\)
0.659114 + 0.752043i \(0.270931\pi\)
\(594\) 4.35328e122 0.160442
\(595\) −1.95250e123 −0.667707
\(596\) 1.97746e123 0.627550
\(597\) −3.08887e122 −0.0909793
\(598\) 9.51927e122 0.260256
\(599\) −4.88132e123 −1.23892 −0.619460 0.785028i \(-0.712648\pi\)
−0.619460 + 0.785028i \(0.712648\pi\)
\(600\) −7.11082e123 −1.67567
\(601\) 6.45254e123 1.41194 0.705970 0.708241i \(-0.250511\pi\)
0.705970 + 0.708241i \(0.250511\pi\)
\(602\) 3.49097e123 0.709418
\(603\) 4.77100e123 0.900510
\(604\) 2.64326e123 0.463443
\(605\) 2.27846e123 0.371132
\(606\) −3.53110e123 −0.534414
\(607\) −3.71680e123 −0.522724 −0.261362 0.965241i \(-0.584172\pi\)
−0.261362 + 0.965241i \(0.584172\pi\)
\(608\) 8.80421e123 1.15075
\(609\) −1.36246e124 −1.65522
\(610\) −1.62967e123 −0.184044
\(611\) −6.21104e122 −0.0652125
\(612\) −2.10452e124 −2.05454
\(613\) −2.51871e123 −0.228658 −0.114329 0.993443i \(-0.536472\pi\)
−0.114329 + 0.993443i \(0.536472\pi\)
\(614\) −9.51327e123 −0.803225
\(615\) −1.09384e123 −0.0859036
\(616\) 1.29170e123 0.0943672
\(617\) 1.46315e124 0.994484 0.497242 0.867612i \(-0.334346\pi\)
0.497242 + 0.867612i \(0.334346\pi\)
\(618\) 2.21619e124 1.40158
\(619\) 7.24631e123 0.426465 0.213232 0.977002i \(-0.431601\pi\)
0.213232 + 0.977002i \(0.431601\pi\)
\(620\) −4.47936e123 −0.245350
\(621\) 6.06025e124 3.08969
\(622\) −1.96660e124 −0.933350
\(623\) −2.16385e124 −0.956111
\(624\) −3.69333e123 −0.151951
\(625\) 1.56448e124 0.599391
\(626\) 7.39697e123 0.263935
\(627\) 6.76511e123 0.224838
\(628\) 2.36187e124 0.731227
\(629\) −7.35644e124 −2.12185
\(630\) −2.26281e124 −0.608126
\(631\) −4.53146e124 −1.13483 −0.567416 0.823431i \(-0.692057\pi\)
−0.567416 + 0.823431i \(0.692057\pi\)
\(632\) −5.28863e123 −0.123434
\(633\) 2.59276e124 0.564023
\(634\) 3.57247e124 0.724430
\(635\) 1.62916e124 0.307988
\(636\) 2.20082e124 0.387921
\(637\) 1.17801e123 0.0193618
\(638\) −4.05918e123 −0.0622183
\(639\) −8.62925e124 −1.23363
\(640\) 5.46777e123 0.0729124
\(641\) −7.56055e124 −0.940526 −0.470263 0.882526i \(-0.655841\pi\)
−0.470263 + 0.882526i \(0.655841\pi\)
\(642\) −2.84462e123 −0.0330154
\(643\) −4.06237e124 −0.439937 −0.219969 0.975507i \(-0.570596\pi\)
−0.219969 + 0.975507i \(0.570596\pi\)
\(644\) 5.80974e124 0.587132
\(645\) 7.36071e124 0.694244
\(646\) 2.04356e125 1.79904
\(647\) 7.70585e124 0.633257 0.316629 0.948550i \(-0.397449\pi\)
0.316629 + 0.948550i \(0.397449\pi\)
\(648\) −2.91508e125 −2.23647
\(649\) 3.46647e123 0.0248313
\(650\) 2.62503e124 0.175586
\(651\) 3.87153e125 2.41840
\(652\) −2.43828e124 −0.142255
\(653\) −2.83307e125 −1.54391 −0.771954 0.635678i \(-0.780721\pi\)
−0.771954 + 0.635678i \(0.780721\pi\)
\(654\) 1.68025e125 0.855390
\(655\) 1.05304e125 0.500851
\(656\) 8.34801e123 0.0370990
\(657\) −2.54587e125 −1.05725
\(658\) 4.15134e124 0.161115
\(659\) −3.52918e125 −1.28018 −0.640092 0.768298i \(-0.721104\pi\)
−0.640092 + 0.768298i \(0.721104\pi\)
\(660\) 8.79945e123 0.0298367
\(661\) −1.91190e125 −0.606037 −0.303019 0.952985i \(-0.597994\pi\)
−0.303019 + 0.952985i \(0.597994\pi\)
\(662\) 1.16797e124 0.0346139
\(663\) 3.43726e125 0.952489
\(664\) 3.65508e125 0.947148
\(665\) −2.00638e125 −0.486239
\(666\) −8.52561e125 −1.93251
\(667\) −5.65084e125 −1.19816
\(668\) 7.62998e124 0.151346
\(669\) 1.74512e126 3.23865
\(670\) −6.02594e124 −0.104640
\(671\) −3.83185e124 −0.0622668
\(672\) −9.89778e125 −1.50524
\(673\) −6.51200e125 −0.926924 −0.463462 0.886117i \(-0.653393\pi\)
−0.463462 + 0.886117i \(0.653393\pi\)
\(674\) −2.36971e125 −0.315740
\(675\) 1.67117e126 2.08451
\(676\) 3.76109e125 0.439224
\(677\) −7.27595e125 −0.795599 −0.397799 0.917472i \(-0.630226\pi\)
−0.397799 + 0.917472i \(0.630226\pi\)
\(678\) 5.69751e125 0.583396
\(679\) 1.90804e126 1.82971
\(680\) 8.22715e125 0.738930
\(681\) 1.36124e126 1.14521
\(682\) 1.15344e125 0.0909059
\(683\) −2.25576e126 −1.66560 −0.832802 0.553571i \(-0.813265\pi\)
−0.832802 + 0.553571i \(0.813265\pi\)
\(684\) −2.16260e126 −1.49616
\(685\) −7.15274e123 −0.00463705
\(686\) −1.22723e126 −0.745597
\(687\) −2.17252e126 −1.23705
\(688\) −5.61757e125 −0.299822
\(689\) −2.51467e125 −0.125813
\(690\) −1.34153e126 −0.629240
\(691\) 9.57630e125 0.421138 0.210569 0.977579i \(-0.432468\pi\)
0.210569 + 0.977579i \(0.432468\pi\)
\(692\) 8.49267e125 0.350205
\(693\) −5.32057e125 −0.205745
\(694\) 2.72725e126 0.989075
\(695\) −8.84137e125 −0.300743
\(696\) 5.74095e126 1.83178
\(697\) −7.76921e125 −0.232551
\(698\) 2.74264e126 0.770199
\(699\) −8.40452e126 −2.21452
\(700\) 1.60209e126 0.396118
\(701\) 7.40940e126 1.71922 0.859610 0.510951i \(-0.170707\pi\)
0.859610 + 0.510951i \(0.170707\pi\)
\(702\) 2.27287e126 0.494964
\(703\) −7.55945e126 −1.54518
\(704\) −4.35586e125 −0.0835777
\(705\) 8.75310e125 0.157669
\(706\) −5.01237e126 −0.847683
\(707\) 2.46239e126 0.391015
\(708\) −1.58399e126 −0.236196
\(709\) 5.85411e126 0.819792 0.409896 0.912132i \(-0.365565\pi\)
0.409896 + 0.912132i \(0.365565\pi\)
\(710\) 1.08991e126 0.143348
\(711\) 2.17841e126 0.269117
\(712\) 9.11770e126 1.05810
\(713\) 1.60573e127 1.75060
\(714\) −2.29739e127 −2.35323
\(715\) −1.00543e125 −0.00967680
\(716\) 2.09782e126 0.189731
\(717\) −2.59337e127 −2.20425
\(718\) −1.06332e127 −0.849431
\(719\) −8.16889e126 −0.613377 −0.306689 0.951810i \(-0.599221\pi\)
−0.306689 + 0.951810i \(0.599221\pi\)
\(720\) 3.64126e126 0.257013
\(721\) −1.54545e127 −1.02550
\(722\) 9.41091e126 0.587119
\(723\) 4.87360e127 2.85888
\(724\) −9.28141e126 −0.511974
\(725\) −1.55827e127 −0.808356
\(726\) 2.68094e127 1.30800
\(727\) −3.60710e127 −1.65530 −0.827651 0.561243i \(-0.810323\pi\)
−0.827651 + 0.561243i \(0.810323\pi\)
\(728\) 6.74407e126 0.291122
\(729\) 1.11669e127 0.453478
\(730\) 3.21553e126 0.122853
\(731\) 5.22809e127 1.87940
\(732\) 1.75095e127 0.592284
\(733\) −1.35200e127 −0.430377 −0.215188 0.976573i \(-0.569037\pi\)
−0.215188 + 0.976573i \(0.569037\pi\)
\(734\) −5.13048e126 −0.153703
\(735\) −1.66015e126 −0.0468124
\(736\) −4.10512e127 −1.08959
\(737\) −1.41689e126 −0.0354023
\(738\) −9.00398e126 −0.211800
\(739\) 2.74269e127 0.607434 0.303717 0.952762i \(-0.401772\pi\)
0.303717 + 0.952762i \(0.401772\pi\)
\(740\) −9.83265e126 −0.205050
\(741\) 3.53211e127 0.693624
\(742\) 1.68075e127 0.310835
\(743\) −3.00345e126 −0.0523139 −0.0261570 0.999658i \(-0.508327\pi\)
−0.0261570 + 0.999658i \(0.508327\pi\)
\(744\) −1.63133e128 −2.67637
\(745\) 3.18419e127 0.492091
\(746\) 8.13283e127 1.18403
\(747\) −1.50554e128 −2.06503
\(748\) 6.24998e126 0.0807714
\(749\) 1.98369e126 0.0241564
\(750\) −8.00141e127 −0.918207
\(751\) 7.58766e127 0.820599 0.410299 0.911951i \(-0.365424\pi\)
0.410299 + 0.911951i \(0.365424\pi\)
\(752\) −6.68022e126 −0.0680922
\(753\) 3.22522e127 0.309872
\(754\) −2.11933e127 −0.191943
\(755\) 4.25630e127 0.363407
\(756\) 1.38717e128 1.11663
\(757\) 1.94772e128 1.47829 0.739145 0.673546i \(-0.235230\pi\)
0.739145 + 0.673546i \(0.235230\pi\)
\(758\) 1.78545e127 0.127782
\(759\) −3.15436e127 −0.212888
\(760\) 8.45419e127 0.538105
\(761\) −9.33020e127 −0.560111 −0.280055 0.959984i \(-0.590353\pi\)
−0.280055 + 0.959984i \(0.590353\pi\)
\(762\) 1.91695e128 1.08546
\(763\) −1.17171e128 −0.625864
\(764\) −5.17440e127 −0.260739
\(765\) −3.38879e128 −1.61106
\(766\) −1.90134e128 −0.852861
\(767\) 1.80987e127 0.0766043
\(768\) 4.81351e128 1.92259
\(769\) 1.54824e127 0.0583602 0.0291801 0.999574i \(-0.490710\pi\)
0.0291801 + 0.999574i \(0.490710\pi\)
\(770\) 6.72008e126 0.0239077
\(771\) −8.07882e128 −2.71286
\(772\) −9.11742e127 −0.289003
\(773\) −5.49356e127 −0.164387 −0.0821933 0.996616i \(-0.526192\pi\)
−0.0821933 + 0.996616i \(0.526192\pi\)
\(774\) 6.05899e128 1.71170
\(775\) 4.42794e128 1.18107
\(776\) −8.03983e128 −2.02489
\(777\) 8.49840e128 2.02117
\(778\) −3.91599e127 −0.0879528
\(779\) −7.98361e127 −0.169349
\(780\) 4.59425e127 0.0920460
\(781\) 2.56271e127 0.0484985
\(782\) −9.52849e128 −1.70343
\(783\) −1.34923e129 −2.27870
\(784\) 1.26700e127 0.0202168
\(785\) 3.80319e128 0.573388
\(786\) 1.23906e129 1.76518
\(787\) −3.53123e128 −0.475391 −0.237695 0.971340i \(-0.576392\pi\)
−0.237695 + 0.971340i \(0.576392\pi\)
\(788\) 1.80301e128 0.229393
\(789\) 2.85747e129 3.43601
\(790\) −2.75141e127 −0.0312716
\(791\) −3.97313e128 −0.426854
\(792\) 2.24190e128 0.227691
\(793\) −2.00064e128 −0.192093
\(794\) 7.20579e126 0.00654138
\(795\) 3.54387e128 0.304187
\(796\) −2.93242e127 −0.0238010
\(797\) −7.97738e127 −0.0612301 −0.0306151 0.999531i \(-0.509747\pi\)
−0.0306151 + 0.999531i \(0.509747\pi\)
\(798\) −2.36079e129 −1.71368
\(799\) 6.21706e128 0.426828
\(800\) −1.13203e129 −0.735110
\(801\) −3.75561e129 −2.30693
\(802\) 1.12112e128 0.0651466
\(803\) 7.56070e127 0.0415643
\(804\) 6.47440e128 0.336748
\(805\) 9.35511e128 0.460397
\(806\) 6.02221e128 0.280444
\(807\) 1.35153e129 0.595600
\(808\) −1.03757e129 −0.432724
\(809\) 1.78703e129 0.705379 0.352690 0.935740i \(-0.385267\pi\)
0.352690 + 0.935740i \(0.385267\pi\)
\(810\) −1.51657e129 −0.566603
\(811\) 1.09543e129 0.387396 0.193698 0.981061i \(-0.437952\pi\)
0.193698 + 0.981061i \(0.437952\pi\)
\(812\) −1.29345e129 −0.433020
\(813\) 6.28151e128 0.199083
\(814\) 2.53193e128 0.0759740
\(815\) −3.92624e128 −0.111548
\(816\) 3.69691e129 0.994549
\(817\) 5.37236e129 1.36862
\(818\) −1.17857e129 −0.284336
\(819\) −2.77791e129 −0.634723
\(820\) −1.03844e128 −0.0224731
\(821\) −3.64821e129 −0.747840 −0.373920 0.927461i \(-0.621987\pi\)
−0.373920 + 0.927461i \(0.621987\pi\)
\(822\) −8.41622e127 −0.0163426
\(823\) 3.97364e129 0.730964 0.365482 0.930818i \(-0.380904\pi\)
0.365482 + 0.930818i \(0.380904\pi\)
\(824\) 6.51198e129 1.13489
\(825\) −8.69844e128 −0.143628
\(826\) −1.20968e129 −0.189260
\(827\) −5.47831e129 −0.812178 −0.406089 0.913834i \(-0.633108\pi\)
−0.406089 + 0.913834i \(0.633108\pi\)
\(828\) 1.00835e130 1.41664
\(829\) −1.19299e130 −1.58840 −0.794199 0.607658i \(-0.792109\pi\)
−0.794199 + 0.607658i \(0.792109\pi\)
\(830\) 1.90155e129 0.239957
\(831\) −1.96198e130 −2.34665
\(832\) −2.27422e129 −0.257837
\(833\) −1.17916e129 −0.126727
\(834\) −1.04031e130 −1.05993
\(835\) 1.22861e129 0.118677
\(836\) 6.42246e128 0.0588196
\(837\) 3.83392e130 3.32936
\(838\) 6.08364e129 0.500962
\(839\) −9.99439e129 −0.780457 −0.390228 0.920718i \(-0.627604\pi\)
−0.390228 + 0.920718i \(0.627604\pi\)
\(840\) −9.50428e129 −0.703868
\(841\) −1.65633e129 −0.116339
\(842\) 1.36757e130 0.911089
\(843\) −6.87814e129 −0.434655
\(844\) 2.46143e129 0.147553
\(845\) 6.05628e129 0.344415
\(846\) 7.20514e129 0.388742
\(847\) −1.86954e130 −0.957025
\(848\) −2.70462e129 −0.131369
\(849\) 1.78561e130 0.822990
\(850\) −2.62757e130 −1.14924
\(851\) 3.52473e130 1.46305
\(852\) −1.17102e130 −0.461319
\(853\) 1.76906e130 0.661470 0.330735 0.943724i \(-0.392703\pi\)
0.330735 + 0.943724i \(0.392703\pi\)
\(854\) 1.33719e130 0.474588
\(855\) −3.48231e130 −1.17321
\(856\) −8.35856e128 −0.0267331
\(857\) 4.47933e130 1.36009 0.680044 0.733171i \(-0.261961\pi\)
0.680044 + 0.733171i \(0.261961\pi\)
\(858\) −1.18303e129 −0.0341045
\(859\) −4.95328e130 −1.35580 −0.677902 0.735152i \(-0.737111\pi\)
−0.677902 + 0.735152i \(0.737111\pi\)
\(860\) 6.98789e129 0.181620
\(861\) 8.97525e129 0.221517
\(862\) 1.85222e130 0.434130
\(863\) 2.69455e129 0.0599798 0.0299899 0.999550i \(-0.490452\pi\)
0.0299899 + 0.999550i \(0.490452\pi\)
\(864\) −9.80162e130 −2.07222
\(865\) 1.36753e130 0.274612
\(866\) 4.90307e130 0.935238
\(867\) −2.43369e131 −4.40977
\(868\) 3.67544e130 0.632676
\(869\) −6.46941e128 −0.0105800
\(870\) 2.98672e130 0.464075
\(871\) −7.39766e129 −0.109216
\(872\) 4.93720e130 0.692623
\(873\) 3.31164e131 4.41478
\(874\) −9.79144e130 −1.24047
\(875\) 5.57975e130 0.671826
\(876\) −3.45483e130 −0.395361
\(877\) 2.89651e130 0.315060 0.157530 0.987514i \(-0.449647\pi\)
0.157530 + 0.987514i \(0.449647\pi\)
\(878\) −9.70344e130 −1.00327
\(879\) 2.50968e131 2.46668
\(880\) −1.08138e129 −0.0101041
\(881\) −1.34623e131 −1.19589 −0.597944 0.801538i \(-0.704015\pi\)
−0.597944 + 0.801538i \(0.704015\pi\)
\(882\) −1.36656e130 −0.115419
\(883\) −8.82317e130 −0.708554 −0.354277 0.935140i \(-0.615273\pi\)
−0.354277 + 0.935140i \(0.615273\pi\)
\(884\) 3.26316e130 0.249180
\(885\) −2.55061e130 −0.185212
\(886\) 1.02431e131 0.707347
\(887\) −8.56098e130 −0.562241 −0.281120 0.959673i \(-0.590706\pi\)
−0.281120 + 0.959673i \(0.590706\pi\)
\(888\) −3.58093e131 −2.23676
\(889\) −1.33677e131 −0.794199
\(890\) 4.74348e130 0.268066
\(891\) −3.56592e130 −0.191696
\(892\) 1.65673e131 0.847259
\(893\) 6.38863e130 0.310826
\(894\) 3.74666e131 1.73430
\(895\) 3.37800e130 0.148777
\(896\) −4.48645e130 −0.188017
\(897\) −1.64691e131 −0.656759
\(898\) −2.70769e131 −1.02755
\(899\) −3.57491e131 −1.29110
\(900\) 2.78062e131 0.955762
\(901\) 2.51710e131 0.823470
\(902\) 2.67400e129 0.00832664
\(903\) −6.03966e131 −1.79022
\(904\) 1.67414e131 0.472386
\(905\) −1.49453e131 −0.401462
\(906\) 5.00815e131 1.28077
\(907\) 5.43134e131 1.32246 0.661230 0.750184i \(-0.270035\pi\)
0.661230 + 0.750184i \(0.270035\pi\)
\(908\) 1.29229e131 0.299598
\(909\) 4.27378e131 0.943451
\(910\) 3.50860e130 0.0737550
\(911\) −6.55369e131 −1.31195 −0.655976 0.754782i \(-0.727743\pi\)
−0.655976 + 0.754782i \(0.727743\pi\)
\(912\) 3.79893e131 0.724253
\(913\) 4.47114e130 0.0811837
\(914\) 5.29242e131 0.915269
\(915\) 2.81946e131 0.464437
\(916\) −2.06248e131 −0.323624
\(917\) −8.64052e131 −1.29153
\(918\) −2.27508e132 −3.23964
\(919\) 3.69672e131 0.501506 0.250753 0.968051i \(-0.419322\pi\)
0.250753 + 0.968051i \(0.419322\pi\)
\(920\) −3.94192e131 −0.509506
\(921\) 1.64587e132 2.02695
\(922\) 1.96785e130 0.0230922
\(923\) 1.33801e131 0.149618
\(924\) −7.22019e130 −0.0769389
\(925\) 9.71978e131 0.987073
\(926\) −2.72539e131 −0.263778
\(927\) −2.68231e132 −2.47435
\(928\) 9.13946e131 0.803592
\(929\) 2.08057e131 0.174375 0.0871873 0.996192i \(-0.472212\pi\)
0.0871873 + 0.996192i \(0.472212\pi\)
\(930\) −8.48698e131 −0.678050
\(931\) −1.21170e131 −0.0922853
\(932\) −7.97883e131 −0.579337
\(933\) 3.40238e132 2.35532
\(934\) −1.48304e132 −0.978852
\(935\) 1.00640e131 0.0633366
\(936\) 1.17051e132 0.702427
\(937\) −1.38597e132 −0.793124 −0.396562 0.918008i \(-0.629797\pi\)
−0.396562 + 0.918008i \(0.629797\pi\)
\(938\) 4.94445e131 0.269831
\(939\) −1.27974e132 −0.666042
\(940\) 8.30975e130 0.0412476
\(941\) 1.36215e132 0.644890 0.322445 0.946588i \(-0.395495\pi\)
0.322445 + 0.946588i \(0.395495\pi\)
\(942\) 4.47500e132 2.02082
\(943\) 3.72250e131 0.160349
\(944\) 1.94659e131 0.0799871
\(945\) 2.23368e132 0.875599
\(946\) −1.79939e131 −0.0672931
\(947\) 1.23478e130 0.00440572 0.00220286 0.999998i \(-0.499299\pi\)
0.00220286 + 0.999998i \(0.499299\pi\)
\(948\) 2.95617e131 0.100637
\(949\) 3.94749e131 0.128226
\(950\) −2.70008e132 −0.836906
\(951\) −6.18066e132 −1.82811
\(952\) −6.75060e132 −1.90545
\(953\) −2.21160e130 −0.00595762 −0.00297881 0.999996i \(-0.500948\pi\)
−0.00297881 + 0.999996i \(0.500948\pi\)
\(954\) 2.91715e132 0.749990
\(955\) −8.33206e131 −0.204457
\(956\) −2.46201e132 −0.576652
\(957\) 7.02271e131 0.157009
\(958\) −5.48726e132 −1.17109
\(959\) 5.86901e130 0.0119574
\(960\) 3.20501e132 0.623390
\(961\) 4.77330e132 0.886396
\(962\) 1.32194e132 0.234380
\(963\) 3.44292e131 0.0582851
\(964\) 4.62675e132 0.747908
\(965\) −1.46813e132 −0.226620
\(966\) 1.10076e133 1.62260
\(967\) 1.28780e133 1.81288 0.906440 0.422334i \(-0.138789\pi\)
0.906440 + 0.422334i \(0.138789\pi\)
\(968\) 7.87760e132 1.05911
\(969\) −3.53553e133 −4.53990
\(970\) −4.18272e132 −0.512999
\(971\) 1.86631e132 0.218639 0.109320 0.994007i \(-0.465133\pi\)
0.109320 + 0.994007i \(0.465133\pi\)
\(972\) 5.95530e132 0.666431
\(973\) 7.25459e132 0.775517
\(974\) −3.39715e131 −0.0346929
\(975\) −4.54151e132 −0.443093
\(976\) −2.15176e132 −0.200575
\(977\) 1.65586e133 1.47474 0.737370 0.675489i \(-0.236067\pi\)
0.737370 + 0.675489i \(0.236067\pi\)
\(978\) −4.61978e132 −0.393136
\(979\) 1.11534e132 0.0906937
\(980\) −1.57606e131 −0.0122465
\(981\) −2.03365e133 −1.51010
\(982\) −1.32253e133 −0.938522
\(983\) 2.57060e133 1.74342 0.871711 0.490021i \(-0.163011\pi\)
0.871711 + 0.490021i \(0.163011\pi\)
\(984\) −3.78186e132 −0.245145
\(985\) 2.90329e132 0.179878
\(986\) 2.12138e133 1.25631
\(987\) −7.18215e132 −0.406576
\(988\) 3.35321e132 0.181458
\(989\) −2.50496e133 −1.29588
\(990\) 1.16635e132 0.0576849
\(991\) −2.75768e133 −1.30397 −0.651984 0.758233i \(-0.726063\pi\)
−0.651984 + 0.758233i \(0.726063\pi\)
\(992\) −2.59704e133 −1.17411
\(993\) −2.02068e132 −0.0873487
\(994\) −8.94297e132 −0.369648
\(995\) −4.72192e131 −0.0186634
\(996\) −2.04307e133 −0.772222
\(997\) 3.36932e133 1.21789 0.608945 0.793213i \(-0.291593\pi\)
0.608945 + 0.793213i \(0.291593\pi\)
\(998\) 3.38604e133 1.17053
\(999\) 8.41585e133 2.78249
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.1.5 7
3.2 odd 2 9.90.a.b.1.3 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.90.a.a.1.5 7 1.1 even 1 trivial
9.90.a.b.1.3 7 3.2 odd 2