Properties

Label 5.34.a.b.1.4
Level 5
Weight 34
Character 5.1
Self dual yes
Analytic conductor 34.491
Analytic rank 0
Dimension 6
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 5 \)
Weight: \( k \) \(=\) \( 34 \)
Character orbit: \([\chi]\) \(=\) 5.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(34.4914144405\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
Defining polynomial: \(x^{6} - x^{5} - 9680197848 x^{4} + 8052423720422 x^{3} + 24239866893261762265 x^{2} - 69081627028404093368325 x - 10572274201725134136583265250\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{21}\cdot 3^{5}\cdot 5^{6}\cdot 7\cdot 11^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(25925.6\) of defining polynomial
Character \(\chi\) \(=\) 5.1

$q$-expansion

\(f(q)\) \(=\) \(q+76409.2 q^{2} +7.43191e7 q^{3} -2.75157e9 q^{4} +1.52588e11 q^{5} +5.67866e12 q^{6} +1.36987e14 q^{7} -8.66595e14 q^{8} -3.57381e13 q^{9} +O(q^{10})\) \(q+76409.2 q^{2} +7.43191e7 q^{3} -2.75157e9 q^{4} +1.52588e11 q^{5} +5.67866e12 q^{6} +1.36987e14 q^{7} -8.66595e14 q^{8} -3.57381e13 q^{9} +1.16591e16 q^{10} +3.84389e16 q^{11} -2.04494e17 q^{12} +2.57012e18 q^{13} +1.04671e19 q^{14} +1.13402e19 q^{15} -4.25800e19 q^{16} +1.44621e20 q^{17} -2.73072e18 q^{18} -2.79512e20 q^{19} -4.19856e20 q^{20} +1.01808e22 q^{21} +2.93708e21 q^{22} +3.71118e22 q^{23} -6.44045e22 q^{24} +2.32831e22 q^{25} +1.96381e23 q^{26} -4.15800e23 q^{27} -3.76930e23 q^{28} -1.90470e24 q^{29} +8.66495e23 q^{30} +5.88152e24 q^{31} +4.19049e24 q^{32} +2.85674e24 q^{33} +1.10503e25 q^{34} +2.09026e25 q^{35} +9.83358e22 q^{36} +1.05655e26 q^{37} -2.13573e25 q^{38} +1.91009e26 q^{39} -1.32232e26 q^{40} -2.64164e25 q^{41} +7.77905e26 q^{42} +1.20441e27 q^{43} -1.05767e26 q^{44} -5.45320e24 q^{45} +2.83569e27 q^{46} -3.53827e27 q^{47} -3.16451e27 q^{48} +1.10345e28 q^{49} +1.77904e27 q^{50} +1.07481e28 q^{51} -7.07187e27 q^{52} -3.25098e28 q^{53} -3.17710e28 q^{54} +5.86531e27 q^{55} -1.18713e29 q^{56} -2.07731e28 q^{57} -1.45537e29 q^{58} +3.41770e28 q^{59} -3.12033e28 q^{60} -6.01152e28 q^{61} +4.49402e29 q^{62} -4.89566e27 q^{63} +6.85952e29 q^{64} +3.92169e29 q^{65} +2.18281e29 q^{66} -2.17962e30 q^{67} -3.97934e29 q^{68} +2.75812e30 q^{69} +1.59715e30 q^{70} +9.20055e29 q^{71} +3.09704e28 q^{72} -4.72873e30 q^{73} +8.07302e30 q^{74} +1.73038e30 q^{75} +7.69097e29 q^{76} +5.26564e30 q^{77} +1.45948e31 q^{78} -2.14123e31 q^{79} -6.49720e30 q^{80} -3.07032e31 q^{81} -2.01845e30 q^{82} -6.60838e31 q^{83} -2.80131e31 q^{84} +2.20674e31 q^{85} +9.20283e31 q^{86} -1.41556e32 q^{87} -3.33109e31 q^{88} -6.08523e31 q^{89} -4.16674e29 q^{90} +3.52074e32 q^{91} -1.02116e32 q^{92} +4.37109e32 q^{93} -2.70356e32 q^{94} -4.26502e31 q^{95} +3.11433e32 q^{96} +6.12049e30 q^{97} +8.43141e32 q^{98} -1.37373e30 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 147350q^{2} + 26513900q^{3} + 29520645652q^{4} + 915527343750q^{5} + 6615759249352q^{6} + 19113832847500q^{7} + 3069820115785800q^{8} + 13602102583345438q^{9} + O(q^{10}) \) \( 6q + 147350q^{2} + 26513900q^{3} + 29520645652q^{4} + 915527343750q^{5} + 6615759249352q^{6} + 19113832847500q^{7} + 3069820115785800q^{8} + 13602102583345438q^{9} + 22483825683593750q^{10} + 150760896555890192q^{11} + 466351581756413200q^{12} - 1403095636752804700q^{13} - 7086110008989891456q^{14} + 4045700073242187500q^{15} + 64511520005858668816q^{16} + \)\(13\!\cdots\!00\)\(q^{17} + \)\(67\!\cdots\!50\)\(q^{18} + \)\(17\!\cdots\!00\)\(q^{19} + \)\(45\!\cdots\!00\)\(q^{20} - \)\(10\!\cdots\!28\)\(q^{21} + \)\(24\!\cdots\!00\)\(q^{22} + \)\(68\!\cdots\!00\)\(q^{23} + \)\(21\!\cdots\!00\)\(q^{24} + \)\(13\!\cdots\!50\)\(q^{25} - \)\(36\!\cdots\!88\)\(q^{26} - \)\(34\!\cdots\!00\)\(q^{27} - \)\(17\!\cdots\!00\)\(q^{28} + \)\(13\!\cdots\!00\)\(q^{29} + \)\(10\!\cdots\!00\)\(q^{30} + \)\(10\!\cdots\!52\)\(q^{31} + \)\(26\!\cdots\!00\)\(q^{32} + \)\(34\!\cdots\!00\)\(q^{33} + \)\(88\!\cdots\!24\)\(q^{34} + \)\(29\!\cdots\!00\)\(q^{35} + \)\(16\!\cdots\!96\)\(q^{36} + \)\(27\!\cdots\!00\)\(q^{37} + \)\(83\!\cdots\!00\)\(q^{38} + \)\(57\!\cdots\!56\)\(q^{39} + \)\(46\!\cdots\!00\)\(q^{40} + \)\(44\!\cdots\!32\)\(q^{41} + \)\(14\!\cdots\!00\)\(q^{42} + \)\(22\!\cdots\!00\)\(q^{43} + \)\(71\!\cdots\!64\)\(q^{44} + \)\(20\!\cdots\!50\)\(q^{45} + \)\(34\!\cdots\!72\)\(q^{46} + \)\(38\!\cdots\!00\)\(q^{47} + \)\(24\!\cdots\!00\)\(q^{48} - \)\(71\!\cdots\!58\)\(q^{49} + \)\(34\!\cdots\!50\)\(q^{50} - \)\(54\!\cdots\!88\)\(q^{51} - \)\(90\!\cdots\!00\)\(q^{52} + \)\(47\!\cdots\!00\)\(q^{53} - \)\(18\!\cdots\!00\)\(q^{54} + \)\(23\!\cdots\!00\)\(q^{55} - \)\(39\!\cdots\!00\)\(q^{56} - \)\(24\!\cdots\!00\)\(q^{57} - \)\(44\!\cdots\!00\)\(q^{58} - \)\(17\!\cdots\!00\)\(q^{59} + \)\(71\!\cdots\!00\)\(q^{60} - \)\(28\!\cdots\!08\)\(q^{61} + \)\(34\!\cdots\!00\)\(q^{62} - \)\(55\!\cdots\!00\)\(q^{63} + \)\(19\!\cdots\!72\)\(q^{64} - \)\(21\!\cdots\!00\)\(q^{65} + \)\(50\!\cdots\!64\)\(q^{66} + \)\(33\!\cdots\!00\)\(q^{67} + \)\(38\!\cdots\!00\)\(q^{68} + \)\(31\!\cdots\!36\)\(q^{69} - \)\(10\!\cdots\!00\)\(q^{70} + \)\(84\!\cdots\!72\)\(q^{71} + \)\(87\!\cdots\!00\)\(q^{72} - \)\(17\!\cdots\!00\)\(q^{73} + \)\(20\!\cdots\!84\)\(q^{74} + \)\(61\!\cdots\!00\)\(q^{75} + \)\(29\!\cdots\!00\)\(q^{76} - \)\(11\!\cdots\!00\)\(q^{77} - \)\(57\!\cdots\!00\)\(q^{78} - \)\(22\!\cdots\!00\)\(q^{79} + \)\(98\!\cdots\!00\)\(q^{80} - \)\(13\!\cdots\!74\)\(q^{81} - \)\(15\!\cdots\!00\)\(q^{82} - \)\(47\!\cdots\!00\)\(q^{83} - \)\(23\!\cdots\!76\)\(q^{84} + \)\(20\!\cdots\!00\)\(q^{85} - \)\(12\!\cdots\!08\)\(q^{86} - \)\(17\!\cdots\!00\)\(q^{87} + \)\(49\!\cdots\!00\)\(q^{88} - \)\(33\!\cdots\!00\)\(q^{89} + \)\(10\!\cdots\!50\)\(q^{90} + \)\(19\!\cdots\!32\)\(q^{91} - \)\(41\!\cdots\!00\)\(q^{92} + \)\(21\!\cdots\!00\)\(q^{93} + \)\(14\!\cdots\!64\)\(q^{94} + \)\(26\!\cdots\!00\)\(q^{95} + \)\(31\!\cdots\!72\)\(q^{96} + \)\(25\!\cdots\!00\)\(q^{97} + \)\(69\!\cdots\!50\)\(q^{98} + \)\(16\!\cdots\!16\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 76409.2 0.824424 0.412212 0.911088i \(-0.364756\pi\)
0.412212 + 0.911088i \(0.364756\pi\)
\(3\) 7.43191e7 0.996780 0.498390 0.866953i \(-0.333925\pi\)
0.498390 + 0.866953i \(0.333925\pi\)
\(4\) −2.75157e9 −0.320325
\(5\) 1.52588e11 0.447214
\(6\) 5.67866e12 0.821770
\(7\) 1.36987e14 1.55798 0.778992 0.627034i \(-0.215731\pi\)
0.778992 + 0.627034i \(0.215731\pi\)
\(8\) −8.66595e14 −1.08851
\(9\) −3.57381e13 −0.00642880
\(10\) 1.16591e16 0.368694
\(11\) 3.84389e16 0.252227 0.126113 0.992016i \(-0.459750\pi\)
0.126113 + 0.992016i \(0.459750\pi\)
\(12\) −2.04494e17 −0.319294
\(13\) 2.57012e18 1.07124 0.535622 0.844458i \(-0.320077\pi\)
0.535622 + 0.844458i \(0.320077\pi\)
\(14\) 1.04671e19 1.28444
\(15\) 1.13402e19 0.445774
\(16\) −4.25800e19 −0.577067
\(17\) 1.44621e20 0.720814 0.360407 0.932795i \(-0.382638\pi\)
0.360407 + 0.932795i \(0.382638\pi\)
\(18\) −2.73072e18 −0.00530005
\(19\) −2.79512e20 −0.222314 −0.111157 0.993803i \(-0.535456\pi\)
−0.111157 + 0.993803i \(0.535456\pi\)
\(20\) −4.19856e20 −0.143254
\(21\) 1.01808e22 1.55297
\(22\) 2.93708e21 0.207942
\(23\) 3.71118e22 1.26184 0.630918 0.775849i \(-0.282678\pi\)
0.630918 + 0.775849i \(0.282678\pi\)
\(24\) −6.44045e22 −1.08500
\(25\) 2.32831e22 0.200000
\(26\) 1.96381e23 0.883159
\(27\) −4.15800e23 −1.00319
\(28\) −3.76930e23 −0.499061
\(29\) −1.90470e24 −1.41339 −0.706693 0.707520i \(-0.749814\pi\)
−0.706693 + 0.707520i \(0.749814\pi\)
\(30\) 8.66495e23 0.367507
\(31\) 5.88152e24 1.45218 0.726092 0.687597i \(-0.241334\pi\)
0.726092 + 0.687597i \(0.241334\pi\)
\(32\) 4.19049e24 0.612760
\(33\) 2.85674e24 0.251415
\(34\) 1.10503e25 0.594256
\(35\) 2.09026e25 0.696751
\(36\) 9.83358e22 0.00205930
\(37\) 1.05655e26 1.40787 0.703934 0.710265i \(-0.251425\pi\)
0.703934 + 0.710265i \(0.251425\pi\)
\(38\) −2.13573e25 −0.183281
\(39\) 1.91009e26 1.06779
\(40\) −1.32232e26 −0.486795
\(41\) −2.64164e25 −0.0647052 −0.0323526 0.999477i \(-0.510300\pi\)
−0.0323526 + 0.999477i \(0.510300\pi\)
\(42\) 7.77905e26 1.28030
\(43\) 1.20441e27 1.34446 0.672228 0.740344i \(-0.265338\pi\)
0.672228 + 0.740344i \(0.265338\pi\)
\(44\) −1.05767e26 −0.0807946
\(45\) −5.45320e24 −0.00287505
\(46\) 2.83569e27 1.04029
\(47\) −3.53827e27 −0.910282 −0.455141 0.890419i \(-0.650411\pi\)
−0.455141 + 0.890419i \(0.650411\pi\)
\(48\) −3.16451e27 −0.575209
\(49\) 1.10345e28 1.42731
\(50\) 1.77904e27 0.164885
\(51\) 1.07481e28 0.718493
\(52\) −7.07187e27 −0.343146
\(53\) −3.25098e28 −1.15203 −0.576014 0.817440i \(-0.695392\pi\)
−0.576014 + 0.817440i \(0.695392\pi\)
\(54\) −3.17710e28 −0.827053
\(55\) 5.86531e27 0.112799
\(56\) −1.18713e29 −1.69588
\(57\) −2.07731e28 −0.221598
\(58\) −1.45537e29 −1.16523
\(59\) 3.41770e28 0.206384 0.103192 0.994661i \(-0.467094\pi\)
0.103192 + 0.994661i \(0.467094\pi\)
\(60\) −3.12033e28 −0.142792
\(61\) −6.01152e28 −0.209431 −0.104716 0.994502i \(-0.533393\pi\)
−0.104716 + 0.994502i \(0.533393\pi\)
\(62\) 4.49402e29 1.19722
\(63\) −4.89566e27 −0.0100160
\(64\) 6.85952e29 1.08224
\(65\) 3.92169e29 0.479075
\(66\) 2.18281e29 0.207272
\(67\) −2.17962e30 −1.61490 −0.807451 0.589934i \(-0.799154\pi\)
−0.807451 + 0.589934i \(0.799154\pi\)
\(68\) −3.97934e29 −0.230895
\(69\) 2.75812e30 1.25777
\(70\) 1.59715e30 0.574419
\(71\) 9.20055e29 0.261849 0.130924 0.991392i \(-0.458205\pi\)
0.130924 + 0.991392i \(0.458205\pi\)
\(72\) 3.09704e28 0.00699779
\(73\) −4.72873e30 −0.850977 −0.425488 0.904964i \(-0.639898\pi\)
−0.425488 + 0.904964i \(0.639898\pi\)
\(74\) 8.07302e30 1.16068
\(75\) 1.73038e30 0.199356
\(76\) 7.69097e29 0.0712126
\(77\) 5.26564e30 0.392965
\(78\) 1.45948e31 0.880316
\(79\) −2.14123e31 −1.04668 −0.523342 0.852122i \(-0.675315\pi\)
−0.523342 + 0.852122i \(0.675315\pi\)
\(80\) −6.49720e30 −0.258072
\(81\) −3.07032e31 −0.993530
\(82\) −2.01845e30 −0.0533445
\(83\) −6.60838e31 −1.42990 −0.714951 0.699174i \(-0.753551\pi\)
−0.714951 + 0.699174i \(0.753551\pi\)
\(84\) −2.80131e31 −0.497454
\(85\) 2.20674e31 0.322358
\(86\) 9.20283e31 1.10840
\(87\) −1.41556e32 −1.40884
\(88\) −3.33109e31 −0.274551
\(89\) −6.08523e31 −0.416238 −0.208119 0.978104i \(-0.566734\pi\)
−0.208119 + 0.978104i \(0.566734\pi\)
\(90\) −4.16674e29 −0.00237026
\(91\) 3.52074e32 1.66898
\(92\) −1.02116e32 −0.404198
\(93\) 4.37109e32 1.44751
\(94\) −2.70356e32 −0.750458
\(95\) −4.26502e31 −0.0994217
\(96\) 3.11433e32 0.610787
\(97\) 6.12049e30 0.0101170 0.00505851 0.999987i \(-0.498390\pi\)
0.00505851 + 0.999987i \(0.498390\pi\)
\(98\) 8.43141e32 1.17671
\(99\) −1.37373e30 −0.00162152
\(100\) −6.40650e31 −0.0640650
\(101\) 1.27681e33 1.08349 0.541743 0.840544i \(-0.317765\pi\)
0.541743 + 0.840544i \(0.317765\pi\)
\(102\) 8.21251e32 0.592343
\(103\) −1.91249e33 −1.17432 −0.587158 0.809473i \(-0.699753\pi\)
−0.587158 + 0.809473i \(0.699753\pi\)
\(104\) −2.22725e33 −1.16606
\(105\) 1.55346e33 0.694508
\(106\) −2.48405e33 −0.949759
\(107\) −5.25843e33 −1.72196 −0.860981 0.508638i \(-0.830149\pi\)
−0.860981 + 0.508638i \(0.830149\pi\)
\(108\) 1.14410e33 0.321346
\(109\) 1.63289e33 0.393930 0.196965 0.980411i \(-0.436891\pi\)
0.196965 + 0.980411i \(0.436891\pi\)
\(110\) 4.48163e32 0.0929945
\(111\) 7.85219e33 1.40334
\(112\) −5.83293e33 −0.899061
\(113\) −1.10961e34 −1.47699 −0.738495 0.674259i \(-0.764463\pi\)
−0.738495 + 0.674259i \(0.764463\pi\)
\(114\) −1.58725e33 −0.182691
\(115\) 5.66282e33 0.564311
\(116\) 5.24093e33 0.452743
\(117\) −9.18512e31 −0.00688681
\(118\) 2.61144e33 0.170148
\(119\) 1.98112e34 1.12302
\(120\) −9.82735e33 −0.485228
\(121\) −2.17476e34 −0.936382
\(122\) −4.59335e33 −0.172660
\(123\) −1.96324e33 −0.0644969
\(124\) −1.61834e34 −0.465171
\(125\) 3.55271e33 0.0894427
\(126\) −3.74074e32 −0.00825740
\(127\) 9.92625e34 1.92320 0.961599 0.274458i \(-0.0884985\pi\)
0.961599 + 0.274458i \(0.0884985\pi\)
\(128\) 1.64170e34 0.279466
\(129\) 8.95110e34 1.34013
\(130\) 2.99653e34 0.394961
\(131\) 5.93400e34 0.689241 0.344621 0.938742i \(-0.388008\pi\)
0.344621 + 0.938742i \(0.388008\pi\)
\(132\) −7.86052e33 −0.0805344
\(133\) −3.82896e34 −0.346361
\(134\) −1.66543e35 −1.33136
\(135\) −6.34461e34 −0.448640
\(136\) −1.25328e35 −0.784611
\(137\) −7.72864e34 −0.428759 −0.214380 0.976750i \(-0.568773\pi\)
−0.214380 + 0.976750i \(0.568773\pi\)
\(138\) 2.10746e35 1.03694
\(139\) −3.33723e35 −1.45761 −0.728806 0.684720i \(-0.759925\pi\)
−0.728806 + 0.684720i \(0.759925\pi\)
\(140\) −5.75150e34 −0.223187
\(141\) −2.62961e35 −0.907351
\(142\) 7.03006e34 0.215875
\(143\) 9.87926e34 0.270196
\(144\) 1.52173e33 0.00370985
\(145\) −2.90635e35 −0.632085
\(146\) −3.61319e35 −0.701566
\(147\) 8.20077e35 1.42272
\(148\) −2.90717e35 −0.450975
\(149\) 9.18769e35 1.27536 0.637680 0.770301i \(-0.279894\pi\)
0.637680 + 0.770301i \(0.279894\pi\)
\(150\) 1.32217e35 0.164354
\(151\) −1.06733e33 −0.00118899 −0.000594497 1.00000i \(-0.500189\pi\)
−0.000594497 1.00000i \(0.500189\pi\)
\(152\) 2.42224e35 0.241990
\(153\) −5.16846e33 −0.00463397
\(154\) 4.02343e35 0.323970
\(155\) 8.97449e35 0.649437
\(156\) −5.25575e35 −0.342041
\(157\) 2.04504e36 1.19773 0.598863 0.800851i \(-0.295619\pi\)
0.598863 + 0.800851i \(0.295619\pi\)
\(158\) −1.63610e36 −0.862912
\(159\) −2.41610e36 −1.14832
\(160\) 6.39418e35 0.274034
\(161\) 5.08385e36 1.96592
\(162\) −2.34601e36 −0.819090
\(163\) 8.53783e35 0.269310 0.134655 0.990893i \(-0.457007\pi\)
0.134655 + 0.990893i \(0.457007\pi\)
\(164\) 7.26865e34 0.0207267
\(165\) 4.35904e35 0.112436
\(166\) −5.04941e36 −1.17885
\(167\) 2.30718e36 0.487819 0.243910 0.969798i \(-0.421570\pi\)
0.243910 + 0.969798i \(0.421570\pi\)
\(168\) −8.82261e36 −1.69042
\(169\) 8.49393e35 0.147563
\(170\) 1.68615e36 0.265759
\(171\) 9.98922e33 0.00142921
\(172\) −3.31403e36 −0.430663
\(173\) 7.44289e36 0.878984 0.439492 0.898247i \(-0.355158\pi\)
0.439492 + 0.898247i \(0.355158\pi\)
\(174\) −1.08162e37 −1.16148
\(175\) 3.18949e36 0.311597
\(176\) −1.63673e36 −0.145552
\(177\) 2.54000e36 0.205719
\(178\) −4.64967e36 −0.343157
\(179\) −1.14363e37 −0.769506 −0.384753 0.923020i \(-0.625713\pi\)
−0.384753 + 0.923020i \(0.625713\pi\)
\(180\) 1.50049e34 0.000920949 0
\(181\) 9.37075e36 0.524902 0.262451 0.964945i \(-0.415469\pi\)
0.262451 + 0.964945i \(0.415469\pi\)
\(182\) 2.69017e37 1.37595
\(183\) −4.46770e36 −0.208757
\(184\) −3.21609e37 −1.37352
\(185\) 1.61217e37 0.629618
\(186\) 3.33992e37 1.19336
\(187\) 5.55906e36 0.181809
\(188\) 9.73579e36 0.291586
\(189\) −5.69594e37 −1.56295
\(190\) −3.25886e36 −0.0819656
\(191\) 1.69883e37 0.391831 0.195915 0.980621i \(-0.437232\pi\)
0.195915 + 0.980621i \(0.437232\pi\)
\(192\) 5.09793e37 1.07876
\(193\) 7.50799e36 0.145824 0.0729119 0.997338i \(-0.476771\pi\)
0.0729119 + 0.997338i \(0.476771\pi\)
\(194\) 4.67662e35 0.00834072
\(195\) 2.91457e37 0.477532
\(196\) −3.03623e37 −0.457204
\(197\) 1.41045e38 1.95284 0.976418 0.215886i \(-0.0692641\pi\)
0.976418 + 0.215886i \(0.0692641\pi\)
\(198\) −1.04966e35 −0.00133682
\(199\) 1.95572e37 0.229208 0.114604 0.993411i \(-0.463440\pi\)
0.114604 + 0.993411i \(0.463440\pi\)
\(200\) −2.01770e37 −0.217702
\(201\) −1.61987e38 −1.60970
\(202\) 9.75600e37 0.893252
\(203\) −2.60921e38 −2.20203
\(204\) −2.95741e37 −0.230151
\(205\) −4.03082e36 −0.0289371
\(206\) −1.46132e38 −0.968134
\(207\) −1.32631e36 −0.00811209
\(208\) −1.09436e38 −0.618179
\(209\) −1.07441e37 −0.0560735
\(210\) 1.18699e38 0.572569
\(211\) −2.65891e38 −1.18589 −0.592944 0.805244i \(-0.702034\pi\)
−0.592944 + 0.805244i \(0.702034\pi\)
\(212\) 8.94530e37 0.369023
\(213\) 6.83776e37 0.261006
\(214\) −4.01792e38 −1.41963
\(215\) 1.83779e38 0.601259
\(216\) 3.60330e38 1.09198
\(217\) 8.05694e38 2.26248
\(218\) 1.24768e38 0.324765
\(219\) −3.51435e38 −0.848237
\(220\) −1.61388e37 −0.0361324
\(221\) 3.71693e38 0.772167
\(222\) 5.99979e38 1.15694
\(223\) −2.18179e38 −0.390645 −0.195323 0.980739i \(-0.562575\pi\)
−0.195323 + 0.980739i \(0.562575\pi\)
\(224\) 5.74044e38 0.954670
\(225\) −8.32092e35 −0.00128576
\(226\) −8.47847e38 −1.21767
\(227\) −5.43077e38 −0.725161 −0.362581 0.931952i \(-0.618104\pi\)
−0.362581 + 0.931952i \(0.618104\pi\)
\(228\) 5.71586e37 0.0709833
\(229\) −1.10600e39 −1.27782 −0.638908 0.769284i \(-0.720613\pi\)
−0.638908 + 0.769284i \(0.720613\pi\)
\(230\) 4.32691e38 0.465231
\(231\) 3.91337e38 0.391700
\(232\) 1.65061e39 1.53848
\(233\) −5.67177e38 −0.492431 −0.246216 0.969215i \(-0.579187\pi\)
−0.246216 + 0.969215i \(0.579187\pi\)
\(234\) −7.01827e36 −0.00567765
\(235\) −5.39897e38 −0.407091
\(236\) −9.40404e37 −0.0661099
\(237\) −1.59134e39 −1.04332
\(238\) 1.51376e39 0.925842
\(239\) −2.69103e39 −1.53587 −0.767933 0.640530i \(-0.778715\pi\)
−0.767933 + 0.640530i \(0.778715\pi\)
\(240\) −4.82866e38 −0.257241
\(241\) 3.85216e39 1.91612 0.958061 0.286565i \(-0.0925134\pi\)
0.958061 + 0.286565i \(0.0925134\pi\)
\(242\) −1.66172e39 −0.771976
\(243\) 2.96249e37 0.0128574
\(244\) 1.65411e38 0.0670861
\(245\) 1.68374e39 0.638314
\(246\) −1.50009e38 −0.0531728
\(247\) −7.18380e38 −0.238152
\(248\) −5.09690e39 −1.58071
\(249\) −4.91128e39 −1.42530
\(250\) 2.71460e38 0.0737387
\(251\) 1.40214e37 0.00356594 0.00178297 0.999998i \(-0.499432\pi\)
0.00178297 + 0.999998i \(0.499432\pi\)
\(252\) 1.34708e37 0.00320836
\(253\) 1.42654e39 0.318269
\(254\) 7.58457e39 1.58553
\(255\) 1.64003e39 0.321320
\(256\) −4.63787e39 −0.851843
\(257\) −3.74219e39 −0.644510 −0.322255 0.946653i \(-0.604441\pi\)
−0.322255 + 0.946653i \(0.604441\pi\)
\(258\) 6.83946e39 1.10483
\(259\) 1.44734e40 2.19344
\(260\) −1.07908e39 −0.153460
\(261\) 6.80705e37 0.00908637
\(262\) 4.53412e39 0.568227
\(263\) −8.59682e39 −1.01174 −0.505869 0.862610i \(-0.668828\pi\)
−0.505869 + 0.862610i \(0.668828\pi\)
\(264\) −2.47564e39 −0.273667
\(265\) −4.96060e39 −0.515202
\(266\) −2.92568e39 −0.285548
\(267\) −4.52248e39 −0.414898
\(268\) 5.99737e39 0.517293
\(269\) 2.20144e40 1.78564 0.892820 0.450414i \(-0.148724\pi\)
0.892820 + 0.450414i \(0.148724\pi\)
\(270\) −4.84786e39 −0.369869
\(271\) 4.26536e39 0.306170 0.153085 0.988213i \(-0.451079\pi\)
0.153085 + 0.988213i \(0.451079\pi\)
\(272\) −6.15795e39 −0.415958
\(273\) 2.61658e40 1.66361
\(274\) −5.90539e39 −0.353480
\(275\) 8.94975e38 0.0504454
\(276\) −7.58915e39 −0.402896
\(277\) −2.32580e40 −1.16321 −0.581603 0.813473i \(-0.697574\pi\)
−0.581603 + 0.813473i \(0.697574\pi\)
\(278\) −2.54995e40 −1.20169
\(279\) −2.10194e38 −0.00933580
\(280\) −1.81141e40 −0.758419
\(281\) −3.04347e39 −0.120147 −0.0600737 0.998194i \(-0.519134\pi\)
−0.0600737 + 0.998194i \(0.519134\pi\)
\(282\) −2.00926e40 −0.748042
\(283\) 1.78513e40 0.626893 0.313447 0.949606i \(-0.398516\pi\)
0.313447 + 0.949606i \(0.398516\pi\)
\(284\) −2.53160e39 −0.0838768
\(285\) −3.16972e39 −0.0991016
\(286\) 7.54866e39 0.222756
\(287\) −3.61871e39 −0.100810
\(288\) −1.49760e38 −0.00393931
\(289\) −1.93394e40 −0.480427
\(290\) −2.22072e40 −0.521106
\(291\) 4.54869e38 0.0100844
\(292\) 1.30114e40 0.272589
\(293\) 5.63289e39 0.111536 0.0557681 0.998444i \(-0.482239\pi\)
0.0557681 + 0.998444i \(0.482239\pi\)
\(294\) 6.26614e40 1.17292
\(295\) 5.21499e39 0.0922976
\(296\) −9.15602e40 −1.53248
\(297\) −1.59829e40 −0.253031
\(298\) 7.02024e40 1.05144
\(299\) 9.53819e40 1.35174
\(300\) −4.76125e39 −0.0638587
\(301\) 1.64990e41 2.09464
\(302\) −8.15540e37 −0.000980236 0
\(303\) 9.48913e40 1.08000
\(304\) 1.19016e40 0.128290
\(305\) −9.17284e39 −0.0936605
\(306\) −3.94918e38 −0.00382035
\(307\) −1.51598e41 −1.38966 −0.694832 0.719173i \(-0.744521\pi\)
−0.694832 + 0.719173i \(0.744521\pi\)
\(308\) −1.44888e40 −0.125877
\(309\) −1.42134e41 −1.17053
\(310\) 6.85734e40 0.535411
\(311\) 1.38324e41 1.02412 0.512062 0.858949i \(-0.328882\pi\)
0.512062 + 0.858949i \(0.328882\pi\)
\(312\) −1.65527e41 −1.16230
\(313\) −2.31070e41 −1.53908 −0.769540 0.638598i \(-0.779515\pi\)
−0.769540 + 0.638598i \(0.779515\pi\)
\(314\) 1.56260e41 0.987434
\(315\) −7.47019e38 −0.00447927
\(316\) 5.89174e40 0.335279
\(317\) −1.18117e41 −0.638022 −0.319011 0.947751i \(-0.603351\pi\)
−0.319011 + 0.947751i \(0.603351\pi\)
\(318\) −1.84612e41 −0.946701
\(319\) −7.32147e40 −0.356494
\(320\) 1.04668e41 0.483993
\(321\) −3.90801e41 −1.71642
\(322\) 3.88453e41 1.62075
\(323\) −4.04232e40 −0.160247
\(324\) 8.44820e40 0.318252
\(325\) 5.98403e40 0.214249
\(326\) 6.52369e40 0.222026
\(327\) 1.21355e41 0.392662
\(328\) 2.28923e40 0.0704321
\(329\) −4.84698e41 −1.41820
\(330\) 3.33071e40 0.0926951
\(331\) 2.42794e41 0.642801 0.321400 0.946943i \(-0.395847\pi\)
0.321400 + 0.946943i \(0.395847\pi\)
\(332\) 1.81834e41 0.458033
\(333\) −3.77591e39 −0.00905090
\(334\) 1.76290e41 0.402170
\(335\) −3.32583e41 −0.722206
\(336\) −4.33498e41 −0.896166
\(337\) 5.79957e41 1.14157 0.570785 0.821100i \(-0.306639\pi\)
0.570785 + 0.821100i \(0.306639\pi\)
\(338\) 6.49015e40 0.121655
\(339\) −8.24654e41 −1.47223
\(340\) −6.07199e40 −0.103259
\(341\) 2.26079e41 0.366280
\(342\) 7.63268e38 0.00117827
\(343\) 4.52545e41 0.665747
\(344\) −1.04374e42 −1.46345
\(345\) 4.20855e41 0.562494
\(346\) 5.68705e41 0.724656
\(347\) 1.00536e42 1.22148 0.610739 0.791832i \(-0.290872\pi\)
0.610739 + 0.791832i \(0.290872\pi\)
\(348\) 3.89501e41 0.451285
\(349\) 1.46484e42 1.61872 0.809360 0.587313i \(-0.199814\pi\)
0.809360 + 0.587313i \(0.199814\pi\)
\(350\) 2.43706e41 0.256888
\(351\) −1.06866e42 −1.07466
\(352\) 1.61078e41 0.154554
\(353\) −7.67079e40 −0.0702356 −0.0351178 0.999383i \(-0.511181\pi\)
−0.0351178 + 0.999383i \(0.511181\pi\)
\(354\) 1.94079e41 0.169600
\(355\) 1.40389e41 0.117102
\(356\) 1.67439e41 0.133331
\(357\) 1.47235e42 1.11940
\(358\) −8.73842e41 −0.634399
\(359\) −2.27621e42 −1.57817 −0.789084 0.614285i \(-0.789445\pi\)
−0.789084 + 0.614285i \(0.789445\pi\)
\(360\) 4.72571e39 0.00312951
\(361\) −1.50264e42 −0.950577
\(362\) 7.16012e41 0.432742
\(363\) −1.61626e42 −0.933367
\(364\) −9.68757e41 −0.534616
\(365\) −7.21548e41 −0.380568
\(366\) −3.41373e41 −0.172104
\(367\) 2.44390e42 1.17786 0.588929 0.808185i \(-0.299550\pi\)
0.588929 + 0.808185i \(0.299550\pi\)
\(368\) −1.58022e42 −0.728165
\(369\) 9.44070e38 0.000415977 0
\(370\) 1.23184e42 0.519072
\(371\) −4.45343e42 −1.79484
\(372\) −1.20274e42 −0.463673
\(373\) 2.18298e42 0.805108 0.402554 0.915396i \(-0.368123\pi\)
0.402554 + 0.915396i \(0.368123\pi\)
\(374\) 4.24763e41 0.149887
\(375\) 2.64034e41 0.0891548
\(376\) 3.06625e42 0.990849
\(377\) −4.89532e42 −1.51408
\(378\) −4.35222e42 −1.28853
\(379\) 3.29619e42 0.934254 0.467127 0.884190i \(-0.345289\pi\)
0.467127 + 0.884190i \(0.345289\pi\)
\(380\) 1.17355e41 0.0318472
\(381\) 7.37710e42 1.91701
\(382\) 1.29806e42 0.323035
\(383\) 2.10779e42 0.502399 0.251199 0.967935i \(-0.419175\pi\)
0.251199 + 0.967935i \(0.419175\pi\)
\(384\) 1.22009e42 0.278566
\(385\) 8.03473e41 0.175739
\(386\) 5.73680e41 0.120221
\(387\) −4.30434e40 −0.00864323
\(388\) −1.68410e40 −0.00324073
\(389\) −4.71038e42 −0.868735 −0.434368 0.900736i \(-0.643028\pi\)
−0.434368 + 0.900736i \(0.643028\pi\)
\(390\) 2.22700e42 0.393689
\(391\) 5.36714e42 0.909550
\(392\) −9.56249e42 −1.55364
\(393\) 4.41009e42 0.687022
\(394\) 1.07772e43 1.60997
\(395\) −3.26726e42 −0.468092
\(396\) 3.77992e39 0.000519412 0
\(397\) 4.19658e42 0.553162 0.276581 0.960991i \(-0.410799\pi\)
0.276581 + 0.960991i \(0.410799\pi\)
\(398\) 1.49435e42 0.188965
\(399\) −2.84565e42 −0.345246
\(400\) −9.91394e41 −0.115413
\(401\) 5.75416e42 0.642835 0.321418 0.946938i \(-0.395841\pi\)
0.321418 + 0.946938i \(0.395841\pi\)
\(402\) −1.23773e43 −1.32708
\(403\) 1.51162e43 1.55564
\(404\) −3.51323e42 −0.347068
\(405\) −4.68494e42 −0.444320
\(406\) −1.99367e43 −1.81541
\(407\) 4.06126e42 0.355102
\(408\) −9.31423e42 −0.782085
\(409\) −1.41308e43 −1.13954 −0.569772 0.821803i \(-0.692968\pi\)
−0.569772 + 0.821803i \(0.692968\pi\)
\(410\) −3.07991e41 −0.0238564
\(411\) −5.74385e42 −0.427379
\(412\) 5.26235e42 0.376162
\(413\) 4.68182e42 0.321543
\(414\) −1.01342e41 −0.00668780
\(415\) −1.00836e43 −0.639472
\(416\) 1.07701e43 0.656415
\(417\) −2.48020e43 −1.45292
\(418\) −8.20950e41 −0.0462283
\(419\) 2.86224e43 1.54944 0.774720 0.632305i \(-0.217891\pi\)
0.774720 + 0.632305i \(0.217891\pi\)
\(420\) −4.27446e42 −0.222468
\(421\) 1.34194e43 0.671549 0.335774 0.941942i \(-0.391002\pi\)
0.335774 + 0.941942i \(0.391002\pi\)
\(422\) −2.03165e43 −0.977674
\(423\) 1.26451e41 0.00585202
\(424\) 2.81729e43 1.25399
\(425\) 3.36721e42 0.144163
\(426\) 5.22468e42 0.215180
\(427\) −8.23502e42 −0.326291
\(428\) 1.44689e43 0.551587
\(429\) 7.34217e42 0.269327
\(430\) 1.40424e43 0.495692
\(431\) −4.00130e43 −1.35933 −0.679667 0.733521i \(-0.737876\pi\)
−0.679667 + 0.733521i \(0.737876\pi\)
\(432\) 1.77048e43 0.578907
\(433\) −1.03509e43 −0.325783 −0.162891 0.986644i \(-0.552082\pi\)
−0.162891 + 0.986644i \(0.552082\pi\)
\(434\) 6.15625e43 1.86524
\(435\) −2.15997e43 −0.630050
\(436\) −4.49300e42 −0.126186
\(437\) −1.03732e43 −0.280524
\(438\) −2.68529e43 −0.699307
\(439\) 3.15434e42 0.0791122 0.0395561 0.999217i \(-0.487406\pi\)
0.0395561 + 0.999217i \(0.487406\pi\)
\(440\) −5.08285e42 −0.122783
\(441\) −3.94353e41 −0.00917591
\(442\) 2.84007e43 0.636593
\(443\) −1.66215e43 −0.358929 −0.179464 0.983764i \(-0.557436\pi\)
−0.179464 + 0.983764i \(0.557436\pi\)
\(444\) −2.16058e43 −0.449523
\(445\) −9.28532e42 −0.186147
\(446\) −1.66709e43 −0.322057
\(447\) 6.82821e43 1.27125
\(448\) 9.39667e43 1.68611
\(449\) −2.11347e43 −0.365537 −0.182768 0.983156i \(-0.558506\pi\)
−0.182768 + 0.983156i \(0.558506\pi\)
\(450\) −6.35795e40 −0.00106001
\(451\) −1.01542e42 −0.0163204
\(452\) 3.05318e43 0.473117
\(453\) −7.93231e40 −0.00118517
\(454\) −4.14961e43 −0.597840
\(455\) 5.37223e43 0.746391
\(456\) 1.80018e43 0.241211
\(457\) −1.42828e44 −1.84585 −0.922924 0.384981i \(-0.874208\pi\)
−0.922924 + 0.384981i \(0.874208\pi\)
\(458\) −8.45082e43 −1.05346
\(459\) −6.01333e43 −0.723112
\(460\) −1.55816e43 −0.180763
\(461\) 3.53458e43 0.395615 0.197807 0.980241i \(-0.436618\pi\)
0.197807 + 0.980241i \(0.436618\pi\)
\(462\) 2.99018e43 0.322927
\(463\) −3.07914e43 −0.320880 −0.160440 0.987046i \(-0.551291\pi\)
−0.160440 + 0.987046i \(0.551291\pi\)
\(464\) 8.11024e43 0.815618
\(465\) 6.66976e43 0.647346
\(466\) −4.33375e43 −0.405972
\(467\) −3.68923e43 −0.333586 −0.166793 0.985992i \(-0.553341\pi\)
−0.166793 + 0.985992i \(0.553341\pi\)
\(468\) 2.52735e41 0.00220602
\(469\) −2.98580e44 −2.51599
\(470\) −4.12531e43 −0.335615
\(471\) 1.51985e44 1.19387
\(472\) −2.96176e43 −0.224650
\(473\) 4.62963e43 0.339108
\(474\) −1.21593e44 −0.860134
\(475\) −6.50790e42 −0.0444627
\(476\) −5.45119e43 −0.359730
\(477\) 1.16184e42 0.00740615
\(478\) −2.05619e44 −1.26620
\(479\) −3.09046e43 −0.183860 −0.0919300 0.995765i \(-0.529304\pi\)
−0.0919300 + 0.995765i \(0.529304\pi\)
\(480\) 4.75209e43 0.273152
\(481\) 2.71546e44 1.50817
\(482\) 2.94340e44 1.57970
\(483\) 3.77827e44 1.95959
\(484\) 5.98401e43 0.299946
\(485\) 9.33913e41 0.00452447
\(486\) 2.26361e42 0.0105999
\(487\) 4.31638e44 1.95385 0.976926 0.213578i \(-0.0685118\pi\)
0.976926 + 0.213578i \(0.0685118\pi\)
\(488\) 5.20955e43 0.227968
\(489\) 6.34524e43 0.268443
\(490\) 1.28653e44 0.526241
\(491\) −2.93145e44 −1.15941 −0.579706 0.814826i \(-0.696832\pi\)
−0.579706 + 0.814826i \(0.696832\pi\)
\(492\) 5.40199e42 0.0206600
\(493\) −2.75460e44 −1.01879
\(494\) −5.48908e43 −0.196338
\(495\) −2.09615e41 −0.000725164 0
\(496\) −2.50435e44 −0.838008
\(497\) 1.26036e44 0.407956
\(498\) −3.75267e44 −1.17505
\(499\) −9.00632e42 −0.0272828 −0.0136414 0.999907i \(-0.504342\pi\)
−0.0136414 + 0.999907i \(0.504342\pi\)
\(500\) −9.77554e42 −0.0286507
\(501\) 1.71467e44 0.486249
\(502\) 1.07136e42 0.00293985
\(503\) −3.10986e44 −0.825789 −0.412895 0.910779i \(-0.635482\pi\)
−0.412895 + 0.910779i \(0.635482\pi\)
\(504\) 4.24256e42 0.0109024
\(505\) 1.94826e44 0.484550
\(506\) 1.09001e44 0.262389
\(507\) 6.31261e43 0.147088
\(508\) −2.73128e44 −0.616048
\(509\) 7.95788e43 0.173762 0.0868808 0.996219i \(-0.472310\pi\)
0.0868808 + 0.996219i \(0.472310\pi\)
\(510\) 1.25313e44 0.264904
\(511\) −6.47777e44 −1.32581
\(512\) −4.95397e44 −0.981745
\(513\) 1.16221e44 0.223023
\(514\) −2.85938e44 −0.531350
\(515\) −2.91823e44 −0.525170
\(516\) −2.46296e44 −0.429276
\(517\) −1.36007e44 −0.229598
\(518\) 1.10590e45 1.80832
\(519\) 5.53149e44 0.876154
\(520\) −3.39852e44 −0.521477
\(521\) 1.27119e44 0.188968 0.0944841 0.995526i \(-0.469880\pi\)
0.0944841 + 0.995526i \(0.469880\pi\)
\(522\) 5.20121e42 0.00749102
\(523\) −1.19591e44 −0.166887 −0.0834434 0.996513i \(-0.526592\pi\)
−0.0834434 + 0.996513i \(0.526592\pi\)
\(524\) −1.63278e44 −0.220781
\(525\) 2.37040e44 0.310594
\(526\) −6.56876e44 −0.834101
\(527\) 8.50590e44 1.04675
\(528\) −1.21640e44 −0.145083
\(529\) 5.12284e44 0.592233
\(530\) −3.79036e44 −0.424745
\(531\) −1.22142e42 −0.00132680
\(532\) 1.05357e44 0.110948
\(533\) −6.78932e43 −0.0693151
\(534\) −3.45559e44 −0.342052
\(535\) −8.02372e44 −0.770085
\(536\) 1.88885e45 1.75783
\(537\) −8.49938e44 −0.767029
\(538\) 1.68210e45 1.47212
\(539\) 4.24156e44 0.360007
\(540\) 1.74576e44 0.143710
\(541\) −1.24548e45 −0.994451 −0.497225 0.867621i \(-0.665648\pi\)
−0.497225 + 0.867621i \(0.665648\pi\)
\(542\) 3.25913e44 0.252414
\(543\) 6.96426e44 0.523212
\(544\) 6.06031e44 0.441686
\(545\) 2.49159e44 0.176171
\(546\) 1.99931e45 1.37152
\(547\) −9.41755e44 −0.626826 −0.313413 0.949617i \(-0.601472\pi\)
−0.313413 + 0.949617i \(0.601472\pi\)
\(548\) 2.12659e44 0.137342
\(549\) 2.14840e42 0.00134639
\(550\) 6.83843e43 0.0415884
\(551\) 5.32388e44 0.314215
\(552\) −2.39017e45 −1.36910
\(553\) −2.93321e45 −1.63072
\(554\) −1.77713e45 −0.958975
\(555\) 1.19815e45 0.627591
\(556\) 9.18263e44 0.466910
\(557\) −2.81038e45 −1.38725 −0.693624 0.720338i \(-0.743987\pi\)
−0.693624 + 0.720338i \(0.743987\pi\)
\(558\) −1.60608e43 −0.00769666
\(559\) 3.09549e45 1.44024
\(560\) −8.90034e44 −0.402072
\(561\) 4.13144e44 0.181223
\(562\) −2.32549e44 −0.0990524
\(563\) 2.48634e45 1.02842 0.514212 0.857663i \(-0.328084\pi\)
0.514212 + 0.857663i \(0.328084\pi\)
\(564\) 7.23555e44 0.290647
\(565\) −1.69314e45 −0.660530
\(566\) 1.36400e45 0.516826
\(567\) −4.20595e45 −1.54790
\(568\) −7.97315e44 −0.285025
\(569\) 1.50472e45 0.522521 0.261261 0.965268i \(-0.415862\pi\)
0.261261 + 0.965268i \(0.415862\pi\)
\(570\) −2.42196e44 −0.0817017
\(571\) −2.28889e45 −0.750117 −0.375059 0.927001i \(-0.622377\pi\)
−0.375059 + 0.927001i \(0.622377\pi\)
\(572\) −2.71835e44 −0.0865507
\(573\) 1.26255e45 0.390569
\(574\) −2.76503e44 −0.0831099
\(575\) 8.64077e44 0.252367
\(576\) −2.45146e43 −0.00695751
\(577\) 1.59455e45 0.439781 0.219891 0.975525i \(-0.429430\pi\)
0.219891 + 0.975525i \(0.429430\pi\)
\(578\) −1.47771e45 −0.396076
\(579\) 5.57987e44 0.145354
\(580\) 7.99702e44 0.202473
\(581\) −9.05264e45 −2.22776
\(582\) 3.47562e43 0.00831386
\(583\) −1.24964e45 −0.290572
\(584\) 4.09790e45 0.926295
\(585\) −1.40154e43 −0.00307987
\(586\) 4.30405e44 0.0919531
\(587\) 5.55956e45 1.15481 0.577407 0.816457i \(-0.304065\pi\)
0.577407 + 0.816457i \(0.304065\pi\)
\(588\) −2.25650e45 −0.455732
\(589\) −1.64396e45 −0.322841
\(590\) 3.98473e44 0.0760924
\(591\) 1.04824e46 1.94655
\(592\) −4.49880e45 −0.812434
\(593\) −1.33454e45 −0.234384 −0.117192 0.993109i \(-0.537389\pi\)
−0.117192 + 0.993109i \(0.537389\pi\)
\(594\) −1.22124e45 −0.208605
\(595\) 3.02295e45 0.502228
\(596\) −2.52806e45 −0.408530
\(597\) 1.45347e45 0.228470
\(598\) 7.28806e45 1.11440
\(599\) 2.61382e45 0.388806 0.194403 0.980922i \(-0.437723\pi\)
0.194403 + 0.980922i \(0.437723\pi\)
\(600\) −1.49954e45 −0.217001
\(601\) 1.12433e45 0.158295 0.0791474 0.996863i \(-0.474780\pi\)
0.0791474 + 0.996863i \(0.474780\pi\)
\(602\) 1.26067e46 1.72687
\(603\) 7.78954e43 0.0103819
\(604\) 2.93684e42 0.000380865 0
\(605\) −3.31842e45 −0.418763
\(606\) 7.25056e45 0.890376
\(607\) 1.38809e46 1.65884 0.829418 0.558628i \(-0.188672\pi\)
0.829418 + 0.558628i \(0.188672\pi\)
\(608\) −1.17129e45 −0.136225
\(609\) −1.93914e46 −2.19494
\(610\) −7.00890e44 −0.0772160
\(611\) −9.09378e45 −0.975134
\(612\) 1.42214e43 0.00148437
\(613\) 1.28344e46 1.30400 0.652001 0.758218i \(-0.273930\pi\)
0.652001 + 0.758218i \(0.273930\pi\)
\(614\) −1.15835e46 −1.14567
\(615\) −2.99566e44 −0.0288439
\(616\) −4.56318e45 −0.427746
\(617\) −1.41494e46 −1.29131 −0.645657 0.763628i \(-0.723416\pi\)
−0.645657 + 0.763628i \(0.723416\pi\)
\(618\) −1.08604e46 −0.965017
\(619\) 3.49373e45 0.302269 0.151134 0.988513i \(-0.451707\pi\)
0.151134 + 0.988513i \(0.451707\pi\)
\(620\) −2.46939e45 −0.208031
\(621\) −1.54311e46 −1.26586
\(622\) 1.05693e46 0.844312
\(623\) −8.33600e45 −0.648492
\(624\) −8.13317e45 −0.616189
\(625\) 5.42101e44 0.0400000
\(626\) −1.76558e46 −1.26885
\(627\) −7.98494e44 −0.0558929
\(628\) −5.62707e45 −0.383662
\(629\) 1.52799e46 1.01481
\(630\) −5.70791e43 −0.00369282
\(631\) 2.21383e46 1.39528 0.697638 0.716451i \(-0.254234\pi\)
0.697638 + 0.716451i \(0.254234\pi\)
\(632\) 1.85558e46 1.13932
\(633\) −1.97608e46 −1.18207
\(634\) −9.02525e45 −0.526001
\(635\) 1.51463e46 0.860080
\(636\) 6.64807e45 0.367835
\(637\) 2.83601e46 1.52900
\(638\) −5.59428e45 −0.293902
\(639\) −3.28810e43 −0.00168337
\(640\) 2.50503e45 0.124981
\(641\) −4.90058e45 −0.238281 −0.119141 0.992877i \(-0.538014\pi\)
−0.119141 + 0.992877i \(0.538014\pi\)
\(642\) −2.98608e46 −1.41506
\(643\) 2.98051e46 1.37661 0.688303 0.725423i \(-0.258356\pi\)
0.688303 + 0.725423i \(0.258356\pi\)
\(644\) −1.39886e46 −0.629734
\(645\) 1.36583e46 0.599323
\(646\) −3.08871e45 −0.132111
\(647\) −3.18321e45 −0.132723 −0.0663613 0.997796i \(-0.521139\pi\)
−0.0663613 + 0.997796i \(0.521139\pi\)
\(648\) 2.66073e46 1.08146
\(649\) 1.31372e45 0.0520555
\(650\) 4.57235e45 0.176632
\(651\) 5.98785e46 2.25520
\(652\) −2.34924e45 −0.0862666
\(653\) −4.44872e46 −1.59282 −0.796411 0.604756i \(-0.793271\pi\)
−0.796411 + 0.604756i \(0.793271\pi\)
\(654\) 9.27261e45 0.323720
\(655\) 9.05457e45 0.308238
\(656\) 1.12481e45 0.0373392
\(657\) 1.68996e44 0.00547076
\(658\) −3.70354e46 −1.16920
\(659\) −3.64438e46 −1.12206 −0.561028 0.827797i \(-0.689594\pi\)
−0.561028 + 0.827797i \(0.689594\pi\)
\(660\) −1.19942e45 −0.0360161
\(661\) −2.16411e46 −0.633804 −0.316902 0.948458i \(-0.602643\pi\)
−0.316902 + 0.948458i \(0.602643\pi\)
\(662\) 1.85517e46 0.529940
\(663\) 2.76238e46 0.769681
\(664\) 5.72679e46 1.55646
\(665\) −5.84253e45 −0.154897
\(666\) −2.88514e44 −0.00746178
\(667\) −7.06871e46 −1.78346
\(668\) −6.34836e45 −0.156261
\(669\) −1.62148e46 −0.389387
\(670\) −2.54124e46 −0.595404
\(671\) −2.31076e45 −0.0528242
\(672\) 4.26624e46 0.951596
\(673\) 5.34875e46 1.16414 0.582068 0.813140i \(-0.302244\pi\)
0.582068 + 0.813140i \(0.302244\pi\)
\(674\) 4.43140e46 0.941137
\(675\) −9.68110e45 −0.200638
\(676\) −2.33717e45 −0.0472682
\(677\) −3.90814e46 −0.771359 −0.385679 0.922633i \(-0.626033\pi\)
−0.385679 + 0.922633i \(0.626033\pi\)
\(678\) −6.30112e46 −1.21375
\(679\) 8.38430e44 0.0157622
\(680\) −1.91235e46 −0.350889
\(681\) −4.03610e46 −0.722826
\(682\) 1.72745e46 0.301970
\(683\) 9.82421e46 1.67632 0.838158 0.545427i \(-0.183632\pi\)
0.838158 + 0.545427i \(0.183632\pi\)
\(684\) −2.74860e43 −0.000457811 0
\(685\) −1.17930e46 −0.191747
\(686\) 3.45786e46 0.548858
\(687\) −8.21966e46 −1.27370
\(688\) −5.12840e46 −0.775841
\(689\) −8.35542e46 −1.23410
\(690\) 3.21572e46 0.463733
\(691\) −7.20065e46 −1.01387 −0.506937 0.861983i \(-0.669222\pi\)
−0.506937 + 0.861983i \(0.669222\pi\)
\(692\) −2.04796e46 −0.281560
\(693\) −1.88184e44 −0.00252629
\(694\) 7.68188e46 1.00702
\(695\) −5.09221e46 −0.651864
\(696\) 1.22672e47 1.53353
\(697\) −3.82035e45 −0.0466404
\(698\) 1.11927e47 1.33451
\(699\) −4.21520e46 −0.490846
\(700\) −8.77609e45 −0.0998122
\(701\) −3.78749e46 −0.420731 −0.210366 0.977623i \(-0.567465\pi\)
−0.210366 + 0.977623i \(0.567465\pi\)
\(702\) −8.16552e46 −0.885975
\(703\) −2.95319e46 −0.312988
\(704\) 2.63672e46 0.272970
\(705\) −4.01246e46 −0.405780
\(706\) −5.86119e45 −0.0579039
\(707\) 1.74907e47 1.68805
\(708\) −6.98899e45 −0.0658970
\(709\) 8.09313e46 0.745510 0.372755 0.927930i \(-0.378413\pi\)
0.372755 + 0.927930i \(0.378413\pi\)
\(710\) 1.07270e46 0.0965421
\(711\) 7.65234e44 0.00672892
\(712\) 5.27343e46 0.453078
\(713\) 2.18274e47 1.83242
\(714\) 1.12501e47 0.922861
\(715\) 1.50746e46 0.120836
\(716\) 3.14679e46 0.246492
\(717\) −1.99995e47 −1.53092
\(718\) −1.73923e47 −1.30108
\(719\) 1.77184e47 1.29538 0.647692 0.761902i \(-0.275734\pi\)
0.647692 + 0.761902i \(0.275734\pi\)
\(720\) 2.32197e44 0.00165909
\(721\) −2.61987e47 −1.82956
\(722\) −1.14816e47 −0.783678
\(723\) 2.86289e47 1.90995
\(724\) −2.57843e46 −0.168139
\(725\) −4.43474e46 −0.282677
\(726\) −1.23497e47 −0.769490
\(727\) 1.73206e47 1.05498 0.527490 0.849561i \(-0.323133\pi\)
0.527490 + 0.849561i \(0.323133\pi\)
\(728\) −3.05106e47 −1.81670
\(729\) 1.72883e47 1.00635
\(730\) −5.51329e46 −0.313750
\(731\) 1.74183e47 0.969102
\(732\) 1.22932e46 0.0668701
\(733\) −2.26618e47 −1.20525 −0.602626 0.798024i \(-0.705879\pi\)
−0.602626 + 0.798024i \(0.705879\pi\)
\(734\) 1.86736e47 0.971054
\(735\) 1.25134e47 0.636259
\(736\) 1.55517e47 0.773203
\(737\) −8.37821e46 −0.407322
\(738\) 7.21356e43 0.000342941 0
\(739\) 3.80934e46 0.177099 0.0885496 0.996072i \(-0.471777\pi\)
0.0885496 + 0.996072i \(0.471777\pi\)
\(740\) −4.43599e46 −0.201682
\(741\) −5.33893e46 −0.237385
\(742\) −3.40283e47 −1.47971
\(743\) −1.22091e47 −0.519238 −0.259619 0.965711i \(-0.583597\pi\)
−0.259619 + 0.965711i \(0.583597\pi\)
\(744\) −3.78797e47 −1.57563
\(745\) 1.40193e47 0.570359
\(746\) 1.66800e47 0.663750
\(747\) 2.36171e45 0.00919255
\(748\) −1.52961e46 −0.0582378
\(749\) −7.20338e47 −2.68279
\(750\) 2.01747e46 0.0735013
\(751\) −2.36534e46 −0.0843014 −0.0421507 0.999111i \(-0.513421\pi\)
−0.0421507 + 0.999111i \(0.513421\pi\)
\(752\) 1.50660e47 0.525294
\(753\) 1.04206e45 0.00355446
\(754\) −3.74048e47 −1.24824
\(755\) −1.62862e44 −0.000531735 0
\(756\) 1.56728e47 0.500652
\(757\) −1.36056e47 −0.425243 −0.212621 0.977135i \(-0.568200\pi\)
−0.212621 + 0.977135i \(0.568200\pi\)
\(758\) 2.51859e47 0.770222
\(759\) 1.06019e47 0.317245
\(760\) 3.69604e46 0.108221
\(761\) 2.10711e47 0.603727 0.301863 0.953351i \(-0.402391\pi\)
0.301863 + 0.953351i \(0.402391\pi\)
\(762\) 5.63678e47 1.58043
\(763\) 2.23685e47 0.613737
\(764\) −4.67444e46 −0.125513
\(765\) −7.88645e44 −0.00207237
\(766\) 1.61055e47 0.414189
\(767\) 8.78390e46 0.221087
\(768\) −3.44682e47 −0.849100
\(769\) 3.42055e47 0.824728 0.412364 0.911019i \(-0.364703\pi\)
0.412364 + 0.911019i \(0.364703\pi\)
\(770\) 6.13927e46 0.144884
\(771\) −2.78116e47 −0.642435
\(772\) −2.06588e46 −0.0467110
\(773\) 2.59138e47 0.573549 0.286774 0.957998i \(-0.407417\pi\)
0.286774 + 0.957998i \(0.407417\pi\)
\(774\) −3.28892e45 −0.00712569
\(775\) 1.36940e47 0.290437
\(776\) −5.30399e45 −0.0110125
\(777\) 1.07565e48 2.18637
\(778\) −3.59916e47 −0.716206
\(779\) 7.38369e45 0.0143849
\(780\) −8.01963e46 −0.152966
\(781\) 3.53659e46 0.0660454
\(782\) 4.10099e47 0.749855
\(783\) 7.91977e47 1.41789
\(784\) −4.69851e47 −0.823655
\(785\) 3.12048e47 0.535639
\(786\) 3.36972e47 0.566398
\(787\) −3.31448e47 −0.545546 −0.272773 0.962078i \(-0.587941\pi\)
−0.272773 + 0.962078i \(0.587941\pi\)
\(788\) −3.88096e47 −0.625542
\(789\) −6.38908e47 −1.00848
\(790\) −2.49648e47 −0.385906
\(791\) −1.52003e48 −2.30113
\(792\) 1.19047e45 0.00176503
\(793\) −1.54503e47 −0.224352
\(794\) 3.20658e47 0.456040
\(795\) −3.68667e47 −0.513543
\(796\) −5.38129e46 −0.0734211
\(797\) −1.21980e48 −1.63015 −0.815076 0.579354i \(-0.803305\pi\)
−0.815076 + 0.579354i \(0.803305\pi\)
\(798\) −2.17434e47 −0.284629
\(799\) −5.11707e47 −0.656144
\(800\) 9.75675e46 0.122552
\(801\) 2.17474e45 0.00267591
\(802\) 4.39671e47 0.529969
\(803\) −1.81767e47 −0.214639
\(804\) 4.45719e47 0.515628
\(805\) 7.75735e47 0.879187
\(806\) 1.15502e48 1.28251
\(807\) 1.63609e48 1.77989
\(808\) −1.10648e48 −1.17938
\(809\) −2.89096e47 −0.301920 −0.150960 0.988540i \(-0.548236\pi\)
−0.150960 + 0.988540i \(0.548236\pi\)
\(810\) −3.57972e47 −0.366308
\(811\) −8.79228e47 −0.881571 −0.440786 0.897612i \(-0.645300\pi\)
−0.440786 + 0.897612i \(0.645300\pi\)
\(812\) 7.17941e47 0.705366
\(813\) 3.16998e47 0.305184
\(814\) 3.10318e47 0.292755
\(815\) 1.30277e47 0.120439
\(816\) −4.57653e47 −0.414619
\(817\) −3.36648e47 −0.298891
\(818\) −1.07972e48 −0.939467
\(819\) −1.25825e46 −0.0107295
\(820\) 1.10911e46 0.00926926
\(821\) −6.16314e47 −0.504824 −0.252412 0.967620i \(-0.581224\pi\)
−0.252412 + 0.967620i \(0.581224\pi\)
\(822\) −4.38883e47 −0.352342
\(823\) −1.89117e47 −0.148810 −0.0744052 0.997228i \(-0.523706\pi\)
−0.0744052 + 0.997228i \(0.523706\pi\)
\(824\) 1.65735e48 1.27825
\(825\) 6.65137e46 0.0502830
\(826\) 3.57734e47 0.265087
\(827\) −9.51973e47 −0.691486 −0.345743 0.938329i \(-0.612373\pi\)
−0.345743 + 0.938329i \(0.612373\pi\)
\(828\) 3.64942e45 0.00259851
\(829\) 2.56276e48 1.78878 0.894392 0.447284i \(-0.147609\pi\)
0.894392 + 0.447284i \(0.147609\pi\)
\(830\) −7.70479e47 −0.527196
\(831\) −1.72851e48 −1.15946
\(832\) 1.76298e48 1.15934
\(833\) 1.59582e48 1.02883
\(834\) −1.89510e48 −1.19782
\(835\) 3.52047e47 0.218159
\(836\) 2.95632e46 0.0179617
\(837\) −2.44554e48 −1.45682
\(838\) 2.18701e48 1.27740
\(839\) −5.48536e47 −0.314147 −0.157073 0.987587i \(-0.550206\pi\)
−0.157073 + 0.987587i \(0.550206\pi\)
\(840\) −1.34622e48 −0.755978
\(841\) 1.81182e48 0.997659
\(842\) 1.02536e48 0.553641
\(843\) −2.26188e47 −0.119761
\(844\) 7.31618e47 0.379869
\(845\) 1.29607e47 0.0659923
\(846\) 9.66201e45 0.00482454
\(847\) −2.97915e48 −1.45887
\(848\) 1.38427e48 0.664797
\(849\) 1.32669e48 0.624875
\(850\) 2.57286e47 0.118851
\(851\) 3.92105e48 1.77650
\(852\) −1.88146e47 −0.0836067
\(853\) 6.63073e47 0.289003 0.144501 0.989505i \(-0.453842\pi\)
0.144501 + 0.989505i \(0.453842\pi\)
\(854\) −6.29231e47 −0.269002
\(855\) 1.52423e45 0.000639162 0
\(856\) 4.55693e48 1.87437
\(857\) −3.61344e48 −1.45793 −0.728966 0.684550i \(-0.759999\pi\)
−0.728966 + 0.684550i \(0.759999\pi\)
\(858\) 5.61009e47 0.222039
\(859\) −2.95644e47 −0.114784 −0.0573921 0.998352i \(-0.518279\pi\)
−0.0573921 + 0.998352i \(0.518279\pi\)
\(860\) −5.05681e47 −0.192598
\(861\) −2.68939e47 −0.100485
\(862\) −3.05736e48 −1.12067
\(863\) 1.94226e48 0.698440 0.349220 0.937041i \(-0.386447\pi\)
0.349220 + 0.937041i \(0.386447\pi\)
\(864\) −1.74241e48 −0.614713
\(865\) 1.13570e48 0.393094
\(866\) −7.90904e47 −0.268583
\(867\) −1.43728e48 −0.478881
\(868\) −2.21692e48 −0.724729
\(869\) −8.23064e47 −0.264002
\(870\) −1.65042e48 −0.519429
\(871\) −5.60188e48 −1.72995
\(872\) −1.41505e48 −0.428796
\(873\) −2.18735e44 −6.50403e−5 0
\(874\) −7.92608e47 −0.231270
\(875\) 4.86677e47 0.139350
\(876\) 9.66998e47 0.271711
\(877\) 3.36176e48 0.926985 0.463493 0.886101i \(-0.346596\pi\)
0.463493 + 0.886101i \(0.346596\pi\)
\(878\) 2.41020e47 0.0652220
\(879\) 4.18631e47 0.111177
\(880\) −2.49745e47 −0.0650928
\(881\) 2.89868e47 0.0741477 0.0370738 0.999313i \(-0.488196\pi\)
0.0370738 + 0.999313i \(0.488196\pi\)
\(882\) −3.01322e46 −0.00756484
\(883\) −2.27915e48 −0.561592 −0.280796 0.959767i \(-0.590598\pi\)
−0.280796 + 0.959767i \(0.590598\pi\)
\(884\) −1.02274e48 −0.247344
\(885\) 3.87573e47 0.0920005
\(886\) −1.27003e48 −0.295910
\(887\) −3.67815e48 −0.841180 −0.420590 0.907251i \(-0.638177\pi\)
−0.420590 + 0.907251i \(0.638177\pi\)
\(888\) −6.80467e48 −1.52754
\(889\) 1.35977e49 2.99631
\(890\) −7.09484e47 −0.153464
\(891\) −1.18020e48 −0.250595
\(892\) 6.00334e47 0.125133
\(893\) 9.88988e47 0.202368
\(894\) 5.21738e48 1.04805
\(895\) −1.74505e48 −0.344134
\(896\) 2.24892e48 0.435403
\(897\) 7.08870e48 1.34738
\(898\) −1.61488e48 −0.301357
\(899\) −1.12026e49 −2.05250
\(900\) 2.28956e45 0.000411861 0
\(901\) −4.70159e48 −0.830397
\(902\) −7.75870e46 −0.0134549
\(903\) 1.22619e49 2.08790
\(904\) 9.61586e48 1.60771
\(905\) 1.42986e48 0.234743
\(906\) −6.06102e45 −0.000977080 0
\(907\) −1.60568e48 −0.254178 −0.127089 0.991891i \(-0.540563\pi\)
−0.127089 + 0.991891i \(0.540563\pi\)
\(908\) 1.49431e48 0.232287
\(909\) −4.56307e46 −0.00696551
\(910\) 4.10487e48 0.615342
\(911\) 7.70098e48 1.13369 0.566843 0.823826i \(-0.308165\pi\)
0.566843 + 0.823826i \(0.308165\pi\)
\(912\) 8.84518e47 0.127877
\(913\) −2.54019e48 −0.360660
\(914\) −1.09134e49 −1.52176
\(915\) −6.81717e47 −0.0933590
\(916\) 3.04322e48 0.409316
\(917\) 8.12883e48 1.07383
\(918\) −4.59474e48 −0.596151
\(919\) 5.42603e48 0.691474 0.345737 0.938331i \(-0.387629\pi\)
0.345737 + 0.938331i \(0.387629\pi\)
\(920\) −4.90737e48 −0.614256
\(921\) −1.12666e49 −1.38519
\(922\) 2.70074e48 0.326154
\(923\) 2.36465e48 0.280504
\(924\) −1.07679e48 −0.125471
\(925\) 2.45997e48 0.281574
\(926\) −2.35275e48 −0.264542
\(927\) 6.83487e46 0.00754944
\(928\) −7.98165e48 −0.866066
\(929\) −7.82524e48 −0.834139 −0.417070 0.908875i \(-0.636943\pi\)
−0.417070 + 0.908875i \(0.636943\pi\)
\(930\) 5.09631e48 0.533688
\(931\) −3.08429e48 −0.317311
\(932\) 1.56063e48 0.157738
\(933\) 1.02801e49 1.02083
\(934\) −2.81891e48 −0.275016
\(935\) 8.48245e47 0.0813073
\(936\) 7.95978e46 0.00749634
\(937\) 1.34653e49 1.24599 0.622994 0.782227i \(-0.285916\pi\)
0.622994 + 0.782227i \(0.285916\pi\)
\(938\) −2.28143e49 −2.07424
\(939\) −1.71729e49 −1.53413
\(940\) 1.48556e48 0.130401
\(941\) −1.57761e49 −1.36073 −0.680365 0.732874i \(-0.738179\pi\)
−0.680365 + 0.732874i \(0.738179\pi\)
\(942\) 1.16131e49 0.984255
\(943\) −9.80360e47 −0.0816474
\(944\) −1.45526e48 −0.119097
\(945\) −8.69131e48 −0.698973
\(946\) 3.53747e48 0.279569
\(947\) 7.45162e48 0.578730 0.289365 0.957219i \(-0.406556\pi\)
0.289365 + 0.957219i \(0.406556\pi\)
\(948\) 4.37869e48 0.334200
\(949\) −1.21534e49 −0.911604
\(950\) −4.97263e47 −0.0366561
\(951\) −8.77837e48 −0.635968
\(952\) −1.71683e49 −1.22241
\(953\) 2.12970e49 1.49034 0.745171 0.666874i \(-0.232368\pi\)
0.745171 + 0.666874i \(0.232368\pi\)
\(954\) 8.87751e46 0.00610581
\(955\) 2.59220e48 0.175232
\(956\) 7.40456e48 0.491976
\(957\) −5.44125e48 −0.355346
\(958\) −2.36140e48 −0.151579
\(959\) −1.05873e49 −0.668000
\(960\) 7.77882e48 0.482435
\(961\) 1.81888e49 1.10884
\(962\) 2.07486e49 1.24337
\(963\) 1.87926e47 0.0110701
\(964\) −1.05995e49 −0.613781
\(965\) 1.14563e48 0.0652144
\(966\) 2.88695e49 1.61553
\(967\) 7.81881e47 0.0430134 0.0215067 0.999769i \(-0.493154\pi\)
0.0215067 + 0.999769i \(0.493154\pi\)
\(968\) 1.88464e49 1.01926
\(969\) −3.00422e48 −0.159731
\(970\) 7.13595e46 0.00373008
\(971\) 2.07870e49 1.06825 0.534127 0.845404i \(-0.320640\pi\)
0.534127 + 0.845404i \(0.320640\pi\)
\(972\) −8.15149e46 −0.00411854
\(973\) −4.57159e49 −2.27094
\(974\) 3.29811e49 1.61080
\(975\) 4.44727e48 0.213559
\(976\) 2.55971e48 0.120856
\(977\) −1.16244e49 −0.539647 −0.269824 0.962910i \(-0.586965\pi\)
−0.269824 + 0.962910i \(0.586965\pi\)
\(978\) 4.84834e48 0.221311
\(979\) −2.33909e48 −0.104986
\(980\) −4.63292e48 −0.204468
\(981\) −5.83563e46 −0.00253250
\(982\) −2.23990e49 −0.955846
\(983\) −2.37943e49 −0.998482 −0.499241 0.866463i \(-0.666388\pi\)
−0.499241 + 0.866463i \(0.666388\pi\)
\(984\) 1.70133e48 0.0702054
\(985\) 2.15218e49 0.873335
\(986\) −2.10476e49 −0.839913
\(987\) −3.60223e49 −1.41364
\(988\) 1.97667e48 0.0762861
\(989\) 4.46980e49 1.69648
\(990\) −1.60165e46 −0.000597842 0
\(991\) −3.80696e49 −1.39754 −0.698768 0.715348i \(-0.746268\pi\)
−0.698768 + 0.715348i \(0.746268\pi\)
\(992\) 2.46465e49 0.889840
\(993\) 1.80442e49 0.640731
\(994\) 9.63030e48 0.336329
\(995\) 2.98419e48 0.102505
\(996\) 1.35137e49 0.456559
\(997\) 6.76901e48 0.224934 0.112467 0.993655i \(-0.464125\pi\)
0.112467 + 0.993655i \(0.464125\pi\)
\(998\) −6.88166e47 −0.0224926
\(999\) −4.39314e49 −1.41236
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 5.34.a.b.1.4 6
5.2 odd 4 25.34.b.c.24.8 12
5.3 odd 4 25.34.b.c.24.5 12
5.4 even 2 25.34.a.c.1.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5.34.a.b.1.4 6 1.1 even 1 trivial
25.34.a.c.1.3 6 5.4 even 2
25.34.b.c.24.5 12 5.3 odd 4
25.34.b.c.24.8 12 5.2 odd 4