Properties

Label 1.40.a.a.1.3
Level $1$
Weight $40$
Character 1.1
Self dual yes
Analytic conductor $9.634$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 40 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(9.63395513897\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\mathbb{Q}[x]/(x^{3} - \cdots)\)
Defining polynomial: \(x^{3} - 175630027 x - 142249227846\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{10}\cdot 3^{5}\cdot 5\cdot 13 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-12827.3\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.10652e6 q^{2} +2.98790e9 q^{3} +6.74631e11 q^{4} +2.54496e13 q^{5} +3.30617e15 q^{6} -5.05826e16 q^{7} +1.38177e17 q^{8} +4.87501e18 q^{9} +O(q^{10})\) \(q+1.10652e6 q^{2} +2.98790e9 q^{3} +6.74631e11 q^{4} +2.54496e13 q^{5} +3.30617e15 q^{6} -5.05826e16 q^{7} +1.38177e17 q^{8} +4.87501e18 q^{9} +2.81604e19 q^{10} +7.53597e19 q^{11} +2.01573e21 q^{12} +3.07373e21 q^{13} -5.59707e22 q^{14} +7.60408e22 q^{15} -2.17987e23 q^{16} -4.56106e23 q^{17} +5.39430e24 q^{18} -1.63031e24 q^{19} +1.71691e25 q^{20} -1.51136e26 q^{21} +8.33870e25 q^{22} +2.17009e26 q^{23} +4.12858e26 q^{24} -1.17131e27 q^{25} +3.40114e27 q^{26} +2.45742e27 q^{27} -3.41246e28 q^{28} -6.88782e27 q^{29} +8.41407e28 q^{30} +1.62636e29 q^{31} -3.17170e29 q^{32} +2.25168e29 q^{33} -5.04690e29 q^{34} -1.28730e30 q^{35} +3.28883e30 q^{36} -1.23773e30 q^{37} -1.80397e30 q^{38} +9.18399e30 q^{39} +3.51653e30 q^{40} +1.60595e31 q^{41} -1.67235e32 q^{42} +1.28211e32 q^{43} +5.08400e31 q^{44} +1.24067e32 q^{45} +2.40125e32 q^{46} -6.09258e32 q^{47} -6.51324e32 q^{48} +1.64906e33 q^{49} -1.29608e33 q^{50} -1.36280e33 q^{51} +2.07363e33 q^{52} +1.51248e33 q^{53} +2.71918e33 q^{54} +1.91787e33 q^{55} -6.98933e33 q^{56} -4.87122e33 q^{57} -7.62152e33 q^{58} -4.73479e34 q^{59} +5.12995e34 q^{60} +7.02166e34 q^{61} +1.79960e35 q^{62} -2.46591e35 q^{63} -2.31116e35 q^{64} +7.82250e34 q^{65} +2.49152e35 q^{66} -9.34963e34 q^{67} -3.07703e35 q^{68} +6.48402e35 q^{69} -1.42443e36 q^{70} +2.40247e36 q^{71} +6.73613e35 q^{72} -7.72964e35 q^{73} -1.36958e36 q^{74} -3.49976e36 q^{75} -1.09986e36 q^{76} -3.81189e36 q^{77} +1.01623e37 q^{78} +1.44777e37 q^{79} -5.54767e36 q^{80} -1.24137e37 q^{81} +1.77702e37 q^{82} +1.12684e37 q^{83} -1.01961e38 q^{84} -1.16077e37 q^{85} +1.41868e38 q^{86} -2.05802e37 q^{87} +1.04129e37 q^{88} -1.09111e38 q^{89} +1.37282e38 q^{90} -1.55477e38 q^{91} +1.46401e38 q^{92} +4.85940e38 q^{93} -6.74156e38 q^{94} -4.14907e37 q^{95} -9.47674e38 q^{96} +7.84026e37 q^{97} +1.82471e39 q^{98} +3.67379e38 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 548856q^{2} + 1109442852q^{3} + 272078981184q^{4} + 17426916500490q^{5} + 1529727847867296q^{6} - 17996297718635544q^{7} + 255044243806133760q^{8} + 8305879902078677391q^{9} + O(q^{10}) \) \( 3q + 548856q^{2} + 1109442852q^{3} + 272078981184q^{4} + 17426916500490q^{5} + 1529727847867296q^{6} - 17996297718635544q^{7} + 255044243806133760q^{8} + 8305879902078677391q^{9} + 90373081165367671440q^{10} + \)\(66\!\cdots\!76\)\(q^{11} + \)\(36\!\cdots\!96\)\(q^{12} + \)\(31\!\cdots\!62\)\(q^{13} - \)\(63\!\cdots\!72\)\(q^{14} - \)\(17\!\cdots\!20\)\(q^{15} - \)\(35\!\cdots\!72\)\(q^{16} + \)\(89\!\cdots\!06\)\(q^{17} + \)\(87\!\cdots\!72\)\(q^{18} + \)\(92\!\cdots\!80\)\(q^{19} - \)\(14\!\cdots\!80\)\(q^{20} - \)\(19\!\cdots\!44\)\(q^{21} - \)\(12\!\cdots\!48\)\(q^{22} + \)\(30\!\cdots\!72\)\(q^{23} + \)\(16\!\cdots\!40\)\(q^{24} + \)\(18\!\cdots\!25\)\(q^{25} + \)\(28\!\cdots\!96\)\(q^{26} - \)\(11\!\cdots\!60\)\(q^{27} - \)\(41\!\cdots\!12\)\(q^{28} - \)\(24\!\cdots\!30\)\(q^{29} + \)\(10\!\cdots\!80\)\(q^{30} + \)\(30\!\cdots\!16\)\(q^{31} - \)\(56\!\cdots\!64\)\(q^{32} - \)\(15\!\cdots\!16\)\(q^{33} - \)\(16\!\cdots\!12\)\(q^{34} - \)\(11\!\cdots\!60\)\(q^{35} + \)\(18\!\cdots\!48\)\(q^{36} + \)\(75\!\cdots\!06\)\(q^{37} + \)\(24\!\cdots\!40\)\(q^{38} + \)\(22\!\cdots\!92\)\(q^{39} - \)\(32\!\cdots\!00\)\(q^{40} + \)\(23\!\cdots\!86\)\(q^{41} - \)\(19\!\cdots\!28\)\(q^{42} + \)\(16\!\cdots\!92\)\(q^{43} - \)\(45\!\cdots\!72\)\(q^{44} + \)\(58\!\cdots\!30\)\(q^{45} - \)\(24\!\cdots\!04\)\(q^{46} + \)\(20\!\cdots\!56\)\(q^{47} - \)\(17\!\cdots\!28\)\(q^{48} + \)\(36\!\cdots\!79\)\(q^{49} - \)\(26\!\cdots\!00\)\(q^{50} + \)\(78\!\cdots\!76\)\(q^{51} + \)\(37\!\cdots\!76\)\(q^{52} + \)\(58\!\cdots\!02\)\(q^{53} + \)\(79\!\cdots\!80\)\(q^{54} - \)\(49\!\cdots\!20\)\(q^{55} - \)\(62\!\cdots\!80\)\(q^{56} - \)\(46\!\cdots\!20\)\(q^{57} + \)\(25\!\cdots\!60\)\(q^{58} - \)\(56\!\cdots\!60\)\(q^{59} + \)\(12\!\cdots\!40\)\(q^{60} + \)\(39\!\cdots\!26\)\(q^{61} + \)\(26\!\cdots\!32\)\(q^{62} - \)\(17\!\cdots\!28\)\(q^{63} - \)\(16\!\cdots\!76\)\(q^{64} - \)\(26\!\cdots\!20\)\(q^{65} - \)\(28\!\cdots\!68\)\(q^{66} - \)\(14\!\cdots\!44\)\(q^{67} - \)\(13\!\cdots\!12\)\(q^{68} + \)\(15\!\cdots\!92\)\(q^{69} - \)\(48\!\cdots\!60\)\(q^{70} + \)\(38\!\cdots\!96\)\(q^{71} - \)\(16\!\cdots\!80\)\(q^{72} - \)\(18\!\cdots\!78\)\(q^{73} - \)\(50\!\cdots\!92\)\(q^{74} - \)\(43\!\cdots\!00\)\(q^{75} - \)\(73\!\cdots\!60\)\(q^{76} + \)\(56\!\cdots\!52\)\(q^{77} + \)\(93\!\cdots\!44\)\(q^{78} + \)\(13\!\cdots\!20\)\(q^{79} + \)\(26\!\cdots\!40\)\(q^{80} - \)\(18\!\cdots\!37\)\(q^{81} + \)\(50\!\cdots\!72\)\(q^{82} - \)\(20\!\cdots\!68\)\(q^{83} - \)\(72\!\cdots\!32\)\(q^{84} - \)\(10\!\cdots\!60\)\(q^{85} + \)\(17\!\cdots\!96\)\(q^{86} - \)\(73\!\cdots\!80\)\(q^{87} + \)\(69\!\cdots\!20\)\(q^{88} + \)\(20\!\cdots\!10\)\(q^{89} + \)\(93\!\cdots\!80\)\(q^{90} - \)\(16\!\cdots\!44\)\(q^{91} + \)\(26\!\cdots\!56\)\(q^{92} - \)\(16\!\cdots\!56\)\(q^{93} - \)\(11\!\cdots\!32\)\(q^{94} + \)\(72\!\cdots\!00\)\(q^{95} - \)\(14\!\cdots\!24\)\(q^{96} + \)\(17\!\cdots\!06\)\(q^{97} + \)\(22\!\cdots\!08\)\(q^{98} + \)\(10\!\cdots\!72\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.10652e6 1.49236 0.746181 0.665743i \(-0.231885\pi\)
0.746181 + 0.665743i \(0.231885\pi\)
\(3\) 2.98790e9 1.48423 0.742116 0.670271i \(-0.233822\pi\)
0.742116 + 0.670271i \(0.233822\pi\)
\(4\) 6.74631e11 1.22715
\(5\) 2.54496e13 0.596713 0.298356 0.954455i \(-0.403562\pi\)
0.298356 + 0.954455i \(0.403562\pi\)
\(6\) 3.30617e15 2.21501
\(7\) −5.05826e16 −1.67722 −0.838609 0.544734i \(-0.816631\pi\)
−0.838609 + 0.544734i \(0.816631\pi\)
\(8\) 1.38177e17 0.338984
\(9\) 4.87501e18 1.20295
\(10\) 2.81604e19 0.890511
\(11\) 7.53597e19 0.371520 0.185760 0.982595i \(-0.440525\pi\)
0.185760 + 0.982595i \(0.440525\pi\)
\(12\) 2.01573e21 1.82137
\(13\) 3.07373e21 0.583136 0.291568 0.956550i \(-0.405823\pi\)
0.291568 + 0.956550i \(0.405823\pi\)
\(14\) −5.59707e22 −2.50302
\(15\) 7.60408e22 0.885660
\(16\) −2.17987e23 −0.721258
\(17\) −4.56106e23 −0.462713 −0.231357 0.972869i \(-0.574316\pi\)
−0.231357 + 0.972869i \(0.574316\pi\)
\(18\) 5.39430e24 1.79523
\(19\) −1.63031e24 −0.189050 −0.0945248 0.995523i \(-0.530133\pi\)
−0.0945248 + 0.995523i \(0.530133\pi\)
\(20\) 1.71691e25 0.732253
\(21\) −1.51136e26 −2.48938
\(22\) 8.33870e25 0.554442
\(23\) 2.17009e26 0.606436 0.303218 0.952921i \(-0.401939\pi\)
0.303218 + 0.952921i \(0.401939\pi\)
\(24\) 4.12858e26 0.503132
\(25\) −1.17131e27 −0.643934
\(26\) 3.40114e27 0.870250
\(27\) 2.45742e27 0.301222
\(28\) −3.41246e28 −2.05819
\(29\) −6.88782e27 −0.209566 −0.104783 0.994495i \(-0.533415\pi\)
−0.104783 + 0.994495i \(0.533415\pi\)
\(30\) 8.41407e28 1.32173
\(31\) 1.62636e29 1.34792 0.673959 0.738769i \(-0.264593\pi\)
0.673959 + 0.738769i \(0.264593\pi\)
\(32\) −3.17170e29 −1.41536
\(33\) 2.25168e29 0.551422
\(34\) −5.04690e29 −0.690536
\(35\) −1.28730e30 −1.00082
\(36\) 3.28883e30 1.47619
\(37\) −1.23773e30 −0.325606 −0.162803 0.986659i \(-0.552054\pi\)
−0.162803 + 0.986659i \(0.552054\pi\)
\(38\) −1.80397e30 −0.282130
\(39\) 9.18399e30 0.865509
\(40\) 3.51653e30 0.202276
\(41\) 1.60595e31 0.570751 0.285375 0.958416i \(-0.407882\pi\)
0.285375 + 0.958416i \(0.407882\pi\)
\(42\) −1.67235e32 −3.71506
\(43\) 1.28211e32 1.80007 0.900036 0.435815i \(-0.143540\pi\)
0.900036 + 0.435815i \(0.143540\pi\)
\(44\) 5.08400e31 0.455909
\(45\) 1.24067e32 0.717814
\(46\) 2.40125e32 0.905022
\(47\) −6.09258e32 −1.50971 −0.754854 0.655893i \(-0.772292\pi\)
−0.754854 + 0.655893i \(0.772292\pi\)
\(48\) −6.51324e32 −1.07052
\(49\) 1.64906e33 1.81306
\(50\) −1.29608e33 −0.960983
\(51\) −1.36280e33 −0.686774
\(52\) 2.07363e33 0.715593
\(53\) 1.51248e33 0.360006 0.180003 0.983666i \(-0.442389\pi\)
0.180003 + 0.983666i \(0.442389\pi\)
\(54\) 2.71918e33 0.449532
\(55\) 1.91787e33 0.221690
\(56\) −6.98933e33 −0.568551
\(57\) −4.87122e33 −0.280594
\(58\) −7.62152e33 −0.312749
\(59\) −4.73479e34 −1.39215 −0.696076 0.717969i \(-0.745072\pi\)
−0.696076 + 0.717969i \(0.745072\pi\)
\(60\) 5.12995e34 1.08683
\(61\) 7.02166e34 1.07772 0.538862 0.842394i \(-0.318854\pi\)
0.538862 + 0.842394i \(0.318854\pi\)
\(62\) 1.79960e35 2.01158
\(63\) −2.46591e35 −2.01760
\(64\) −2.31116e35 −1.39098
\(65\) 7.82250e34 0.347964
\(66\) 2.49152e35 0.822921
\(67\) −9.34963e34 −0.230322 −0.115161 0.993347i \(-0.536738\pi\)
−0.115161 + 0.993347i \(0.536738\pi\)
\(68\) −3.07703e35 −0.567817
\(69\) 6.48402e35 0.900092
\(70\) −1.42443e36 −1.49358
\(71\) 2.40247e36 1.91038 0.955190 0.295994i \(-0.0956509\pi\)
0.955190 + 0.295994i \(0.0956509\pi\)
\(72\) 6.73613e35 0.407781
\(73\) −7.72964e35 −0.357572 −0.178786 0.983888i \(-0.557217\pi\)
−0.178786 + 0.983888i \(0.557217\pi\)
\(74\) −1.36958e36 −0.485923
\(75\) −3.49976e36 −0.955748
\(76\) −1.09986e36 −0.231991
\(77\) −3.81189e36 −0.623119
\(78\) 1.01623e37 1.29165
\(79\) 1.44777e37 1.43540 0.717699 0.696353i \(-0.245195\pi\)
0.717699 + 0.696353i \(0.245195\pi\)
\(80\) −5.54767e36 −0.430384
\(81\) −1.24137e37 −0.755865
\(82\) 1.77702e37 0.851767
\(83\) 1.12684e37 0.426423 0.213212 0.977006i \(-0.431608\pi\)
0.213212 + 0.977006i \(0.431608\pi\)
\(84\) −1.01961e38 −3.05483
\(85\) −1.16077e37 −0.276107
\(86\) 1.41868e38 2.68636
\(87\) −2.05802e37 −0.311045
\(88\) 1.04129e37 0.125939
\(89\) −1.09111e38 −1.05868 −0.529338 0.848411i \(-0.677560\pi\)
−0.529338 + 0.848411i \(0.677560\pi\)
\(90\) 1.37282e38 1.07124
\(91\) −1.55477e38 −0.978045
\(92\) 1.46401e38 0.744185
\(93\) 4.85940e38 2.00062
\(94\) −6.74156e38 −2.25303
\(95\) −4.14907e37 −0.112808
\(96\) −9.47674e38 −2.10073
\(97\) 7.84026e37 0.141998 0.0709989 0.997476i \(-0.477381\pi\)
0.0709989 + 0.997476i \(0.477381\pi\)
\(98\) 1.82471e39 2.70574
\(99\) 3.67379e38 0.446919
\(100\) −7.90201e38 −0.790201
\(101\) 1.53402e39 1.26347 0.631734 0.775185i \(-0.282344\pi\)
0.631734 + 0.775185i \(0.282344\pi\)
\(102\) −1.50797e39 −1.02492
\(103\) −1.10618e39 −0.621586 −0.310793 0.950478i \(-0.600595\pi\)
−0.310793 + 0.950478i \(0.600595\pi\)
\(104\) 4.24717e38 0.197674
\(105\) −3.84634e39 −1.48545
\(106\) 1.67359e39 0.537260
\(107\) 2.25314e39 0.602288 0.301144 0.953579i \(-0.402631\pi\)
0.301144 + 0.953579i \(0.402631\pi\)
\(108\) 1.65785e39 0.369643
\(109\) −3.29726e38 −0.0614239 −0.0307119 0.999528i \(-0.509777\pi\)
−0.0307119 + 0.999528i \(0.509777\pi\)
\(110\) 2.12216e39 0.330843
\(111\) −3.69822e39 −0.483276
\(112\) 1.10263e40 1.20971
\(113\) −9.62984e39 −0.888361 −0.444181 0.895937i \(-0.646505\pi\)
−0.444181 + 0.895937i \(0.646505\pi\)
\(114\) −5.39010e39 −0.418747
\(115\) 5.52278e39 0.361868
\(116\) −4.64674e39 −0.257168
\(117\) 1.49844e40 0.701482
\(118\) −5.23914e40 −2.07759
\(119\) 2.30710e40 0.776070
\(120\) 1.05071e40 0.300225
\(121\) −3.54657e40 −0.861973
\(122\) 7.76961e40 1.60836
\(123\) 4.79842e40 0.847127
\(124\) 1.09719e41 1.65409
\(125\) −7.61018e40 −0.980956
\(126\) −2.72858e41 −3.01100
\(127\) −7.59694e40 −0.718565 −0.359282 0.933229i \(-0.616978\pi\)
−0.359282 + 0.933229i \(0.616978\pi\)
\(128\) −8.13679e40 −0.660479
\(129\) 3.83082e41 2.67173
\(130\) 8.65575e40 0.519289
\(131\) −2.08014e41 −1.07474 −0.537368 0.843348i \(-0.680581\pi\)
−0.537368 + 0.843348i \(0.680581\pi\)
\(132\) 1.51905e41 0.676675
\(133\) 8.24654e40 0.317077
\(134\) −1.03456e41 −0.343724
\(135\) 6.25403e40 0.179743
\(136\) −6.30232e40 −0.156853
\(137\) −3.53926e41 −0.763592 −0.381796 0.924247i \(-0.624694\pi\)
−0.381796 + 0.924247i \(0.624694\pi\)
\(138\) 7.17470e41 1.34326
\(139\) −5.01395e39 −0.00815438 −0.00407719 0.999992i \(-0.501298\pi\)
−0.00407719 + 0.999992i \(0.501298\pi\)
\(140\) −8.68455e41 −1.22815
\(141\) −1.82040e42 −2.24076
\(142\) 2.65838e42 2.85098
\(143\) 2.31635e41 0.216646
\(144\) −1.06269e42 −0.867636
\(145\) −1.75292e41 −0.125051
\(146\) −8.55300e41 −0.533627
\(147\) 4.92722e42 2.69100
\(148\) −8.35012e41 −0.399567
\(149\) 1.36965e42 0.574749 0.287374 0.957818i \(-0.407218\pi\)
0.287374 + 0.957818i \(0.407218\pi\)
\(150\) −3.87255e42 −1.42632
\(151\) −2.28466e42 −0.739214 −0.369607 0.929188i \(-0.620508\pi\)
−0.369607 + 0.929188i \(0.620508\pi\)
\(152\) −2.25271e41 −0.0640848
\(153\) −2.22352e42 −0.556620
\(154\) −4.21793e42 −0.929920
\(155\) 4.13901e42 0.804319
\(156\) 6.19580e42 1.06211
\(157\) −3.22622e42 −0.488260 −0.244130 0.969743i \(-0.578502\pi\)
−0.244130 + 0.969743i \(0.578502\pi\)
\(158\) 1.60199e43 2.14213
\(159\) 4.51914e42 0.534333
\(160\) −8.07185e42 −0.844565
\(161\) −1.09769e43 −1.01712
\(162\) −1.37360e43 −1.12802
\(163\) −4.44788e42 −0.323963 −0.161981 0.986794i \(-0.551788\pi\)
−0.161981 + 0.986794i \(0.551788\pi\)
\(164\) 1.08342e43 0.700395
\(165\) 5.73041e42 0.329040
\(166\) 1.24688e43 0.636378
\(167\) 4.33425e42 0.196762 0.0983812 0.995149i \(-0.468634\pi\)
0.0983812 + 0.995149i \(0.468634\pi\)
\(168\) −2.08834e43 −0.843862
\(169\) −1.83360e43 −0.659953
\(170\) −1.28441e43 −0.412051
\(171\) −7.94779e42 −0.227417
\(172\) 8.64950e43 2.20895
\(173\) 2.21391e43 0.504965 0.252482 0.967601i \(-0.418753\pi\)
0.252482 + 0.967601i \(0.418753\pi\)
\(174\) −2.27724e43 −0.464192
\(175\) 5.92479e43 1.08002
\(176\) −1.64274e43 −0.267962
\(177\) −1.41471e44 −2.06628
\(178\) −1.20733e44 −1.57993
\(179\) 1.32994e44 1.56026 0.780130 0.625618i \(-0.215153\pi\)
0.780130 + 0.625618i \(0.215153\pi\)
\(180\) 8.36993e43 0.880863
\(181\) −1.07254e44 −1.01317 −0.506584 0.862191i \(-0.669092\pi\)
−0.506584 + 0.862191i \(0.669092\pi\)
\(182\) −1.72038e44 −1.45960
\(183\) 2.09800e44 1.59959
\(184\) 2.99856e43 0.205572
\(185\) −3.14997e43 −0.194293
\(186\) 5.37703e44 2.98566
\(187\) −3.43720e43 −0.171907
\(188\) −4.11024e44 −1.85263
\(189\) −1.24303e44 −0.505214
\(190\) −4.59103e43 −0.168351
\(191\) 2.71109e44 0.897414 0.448707 0.893679i \(-0.351885\pi\)
0.448707 + 0.893679i \(0.351885\pi\)
\(192\) −6.90551e44 −2.06453
\(193\) −8.26925e43 −0.223408 −0.111704 0.993742i \(-0.535631\pi\)
−0.111704 + 0.993742i \(0.535631\pi\)
\(194\) 8.67541e43 0.211912
\(195\) 2.33729e44 0.516460
\(196\) 1.11250e45 2.22489
\(197\) −5.36056e44 −0.970776 −0.485388 0.874299i \(-0.661322\pi\)
−0.485388 + 0.874299i \(0.661322\pi\)
\(198\) 4.06513e44 0.666965
\(199\) −1.00046e45 −1.48787 −0.743935 0.668252i \(-0.767043\pi\)
−0.743935 + 0.668252i \(0.767043\pi\)
\(200\) −1.61848e44 −0.218284
\(201\) −2.79358e44 −0.341852
\(202\) 1.69742e45 1.88555
\(203\) 3.48404e44 0.351488
\(204\) −9.19387e44 −0.842772
\(205\) 4.08707e44 0.340574
\(206\) −1.22401e45 −0.927631
\(207\) 1.05792e45 0.729511
\(208\) −6.70032e44 −0.420592
\(209\) −1.22860e44 −0.0702356
\(210\) −4.25605e45 −2.21682
\(211\) −1.34673e45 −0.639402 −0.319701 0.947518i \(-0.603582\pi\)
−0.319701 + 0.947518i \(0.603582\pi\)
\(212\) 1.02037e45 0.441780
\(213\) 7.17834e45 2.83545
\(214\) 2.49314e45 0.898832
\(215\) 3.26291e45 1.07413
\(216\) 3.39558e44 0.102109
\(217\) −8.22655e45 −2.26075
\(218\) −3.64849e44 −0.0916667
\(219\) −2.30954e45 −0.530720
\(220\) 1.29385e45 0.272047
\(221\) −1.40194e45 −0.269825
\(222\) −4.09216e45 −0.721223
\(223\) −4.53007e45 −0.731409 −0.365705 0.930731i \(-0.619172\pi\)
−0.365705 + 0.930731i \(0.619172\pi\)
\(224\) 1.60433e46 2.37387
\(225\) −5.71015e45 −0.774619
\(226\) −1.06556e46 −1.32576
\(227\) 1.08195e46 1.23510 0.617550 0.786532i \(-0.288125\pi\)
0.617550 + 0.786532i \(0.288125\pi\)
\(228\) −3.28627e45 −0.344329
\(229\) 1.83988e46 1.77010 0.885051 0.465494i \(-0.154123\pi\)
0.885051 + 0.465494i \(0.154123\pi\)
\(230\) 6.11107e45 0.540038
\(231\) −1.13896e46 −0.924854
\(232\) −9.51736e44 −0.0710397
\(233\) −1.58389e46 −1.08714 −0.543570 0.839364i \(-0.682928\pi\)
−0.543570 + 0.839364i \(0.682928\pi\)
\(234\) 1.65806e46 1.04687
\(235\) −1.55053e46 −0.900861
\(236\) −3.19423e46 −1.70837
\(237\) 4.32581e46 2.13047
\(238\) 2.55285e46 1.15818
\(239\) −2.86406e46 −1.19736 −0.598678 0.800990i \(-0.704307\pi\)
−0.598678 + 0.800990i \(0.704307\pi\)
\(240\) −1.65759e46 −0.638790
\(241\) 1.94777e46 0.692159 0.346080 0.938205i \(-0.387513\pi\)
0.346080 + 0.938205i \(0.387513\pi\)
\(242\) −3.92435e46 −1.28638
\(243\) −4.70498e46 −1.42310
\(244\) 4.73703e46 1.32253
\(245\) 4.19677e46 1.08187
\(246\) 5.30955e46 1.26422
\(247\) −5.01113e45 −0.110242
\(248\) 2.24725e46 0.456923
\(249\) 3.36690e46 0.632911
\(250\) −8.42081e46 −1.46394
\(251\) 6.63788e46 1.06756 0.533779 0.845624i \(-0.320771\pi\)
0.533779 + 0.845624i \(0.320771\pi\)
\(252\) −1.66358e47 −2.47590
\(253\) 1.63537e46 0.225303
\(254\) −8.40616e46 −1.07236
\(255\) −3.46827e46 −0.409807
\(256\) 3.70220e46 0.405303
\(257\) −1.60889e47 −1.63241 −0.816206 0.577761i \(-0.803927\pi\)
−0.816206 + 0.577761i \(0.803927\pi\)
\(258\) 4.23888e47 3.98719
\(259\) 6.26077e46 0.546113
\(260\) 5.27730e46 0.427003
\(261\) −3.35782e46 −0.252097
\(262\) −2.30171e47 −1.60390
\(263\) 3.82398e46 0.247388 0.123694 0.992320i \(-0.460526\pi\)
0.123694 + 0.992320i \(0.460526\pi\)
\(264\) 3.11129e46 0.186923
\(265\) 3.84919e46 0.214820
\(266\) 9.12497e46 0.473194
\(267\) −3.26013e47 −1.57132
\(268\) −6.30755e46 −0.282639
\(269\) 7.76998e46 0.323780 0.161890 0.986809i \(-0.448241\pi\)
0.161890 + 0.986809i \(0.448241\pi\)
\(270\) 6.92020e46 0.268241
\(271\) 2.35011e47 0.847591 0.423796 0.905758i \(-0.360697\pi\)
0.423796 + 0.905758i \(0.360697\pi\)
\(272\) 9.94252e46 0.333736
\(273\) −4.64550e47 −1.45165
\(274\) −3.91626e47 −1.13956
\(275\) −8.82695e46 −0.239234
\(276\) 4.37432e47 1.10454
\(277\) 4.19090e47 0.986170 0.493085 0.869981i \(-0.335869\pi\)
0.493085 + 0.869981i \(0.335869\pi\)
\(278\) −5.54803e45 −0.0121693
\(279\) 7.92852e47 1.62147
\(280\) −1.77875e47 −0.339261
\(281\) 2.30674e46 0.0410417 0.0205209 0.999789i \(-0.493468\pi\)
0.0205209 + 0.999789i \(0.493468\pi\)
\(282\) −2.01431e48 −3.34402
\(283\) 6.25956e47 0.969858 0.484929 0.874554i \(-0.338846\pi\)
0.484929 + 0.874554i \(0.338846\pi\)
\(284\) 1.62078e48 2.34431
\(285\) −1.23970e47 −0.167434
\(286\) 2.56309e47 0.323315
\(287\) −8.12331e47 −0.957273
\(288\) −1.54621e48 −1.70261
\(289\) −7.63613e47 −0.785897
\(290\) −1.93964e47 −0.186621
\(291\) 2.34259e47 0.210758
\(292\) −5.21465e47 −0.438793
\(293\) 4.49093e47 0.353523 0.176762 0.984254i \(-0.443438\pi\)
0.176762 + 0.984254i \(0.443438\pi\)
\(294\) 5.45207e48 4.01595
\(295\) −1.20498e48 −0.830714
\(296\) −1.71026e47 −0.110376
\(297\) 1.85190e47 0.111910
\(298\) 1.51555e48 0.857733
\(299\) 6.67026e47 0.353634
\(300\) −2.36105e48 −1.17284
\(301\) −6.48524e48 −3.01911
\(302\) −2.52802e48 −1.10318
\(303\) 4.58350e48 1.87528
\(304\) 3.55387e47 0.136354
\(305\) 1.78698e48 0.643092
\(306\) −2.46037e48 −0.830678
\(307\) 5.77022e48 1.82808 0.914038 0.405628i \(-0.132947\pi\)
0.914038 + 0.405628i \(0.132947\pi\)
\(308\) −2.57162e48 −0.764659
\(309\) −3.30517e48 −0.922578
\(310\) 4.57990e48 1.20034
\(311\) −3.50073e48 −0.861651 −0.430826 0.902435i \(-0.641778\pi\)
−0.430826 + 0.902435i \(0.641778\pi\)
\(312\) 1.26901e48 0.293394
\(313\) 4.32088e48 0.938551 0.469276 0.883052i \(-0.344515\pi\)
0.469276 + 0.883052i \(0.344515\pi\)
\(314\) −3.56988e48 −0.728661
\(315\) −6.27563e48 −1.20393
\(316\) 9.76713e48 1.76144
\(317\) −3.38834e47 −0.0574554 −0.0287277 0.999587i \(-0.509146\pi\)
−0.0287277 + 0.999587i \(0.509146\pi\)
\(318\) 5.00052e48 0.797419
\(319\) −5.19065e47 −0.0778580
\(320\) −5.88179e48 −0.830014
\(321\) 6.73216e48 0.893936
\(322\) −1.21461e49 −1.51792
\(323\) 7.43595e47 0.0874757
\(324\) −8.37468e48 −0.927556
\(325\) −3.60028e48 −0.375501
\(326\) −4.92167e48 −0.483470
\(327\) −9.85191e47 −0.0911673
\(328\) 2.21905e48 0.193476
\(329\) 3.08178e49 2.53211
\(330\) 6.34082e48 0.491047
\(331\) −1.23716e49 −0.903189 −0.451595 0.892223i \(-0.649145\pi\)
−0.451595 + 0.892223i \(0.649145\pi\)
\(332\) 7.60203e48 0.523284
\(333\) −6.03396e48 −0.391688
\(334\) 4.79593e48 0.293641
\(335\) −2.37944e48 −0.137436
\(336\) 3.29457e49 1.79549
\(337\) −1.65140e49 −0.849316 −0.424658 0.905354i \(-0.639606\pi\)
−0.424658 + 0.905354i \(0.639606\pi\)
\(338\) −2.02891e49 −0.984889
\(339\) −2.87730e49 −1.31853
\(340\) −7.83091e48 −0.338823
\(341\) 1.22562e49 0.500778
\(342\) −8.79439e48 −0.339388
\(343\) −3.74064e49 −1.36368
\(344\) 1.77157e49 0.610197
\(345\) 1.65015e49 0.537096
\(346\) 2.44974e49 0.753591
\(347\) 3.18063e49 0.924885 0.462443 0.886649i \(-0.346973\pi\)
0.462443 + 0.886649i \(0.346973\pi\)
\(348\) −1.38840e49 −0.381698
\(349\) 1.04623e49 0.271976 0.135988 0.990711i \(-0.456579\pi\)
0.135988 + 0.990711i \(0.456579\pi\)
\(350\) 6.55590e49 1.61178
\(351\) 7.55343e48 0.175653
\(352\) −2.39019e49 −0.525835
\(353\) −3.28850e49 −0.684527 −0.342263 0.939604i \(-0.611194\pi\)
−0.342263 + 0.939604i \(0.611194\pi\)
\(354\) −1.56540e50 −3.08363
\(355\) 6.11417e49 1.13995
\(356\) −7.36096e49 −1.29915
\(357\) 6.89340e49 1.15187
\(358\) 1.47160e50 2.32847
\(359\) 4.88065e49 0.731367 0.365684 0.930739i \(-0.380835\pi\)
0.365684 + 0.930739i \(0.380835\pi\)
\(360\) 1.71431e49 0.243328
\(361\) −7.17108e49 −0.964260
\(362\) −1.18679e50 −1.51201
\(363\) −1.05968e50 −1.27937
\(364\) −1.04890e50 −1.20020
\(365\) −1.96716e49 −0.213368
\(366\) 2.32148e50 2.38718
\(367\) 7.14273e49 0.696428 0.348214 0.937415i \(-0.386788\pi\)
0.348214 + 0.937415i \(0.386788\pi\)
\(368\) −4.73051e49 −0.437397
\(369\) 7.82902e49 0.686583
\(370\) −3.48551e49 −0.289956
\(371\) −7.65051e49 −0.603809
\(372\) 3.27830e50 2.45506
\(373\) 1.05915e50 0.752724 0.376362 0.926473i \(-0.377175\pi\)
0.376362 + 0.926473i \(0.377175\pi\)
\(374\) −3.80333e49 −0.256548
\(375\) −2.27385e50 −1.45597
\(376\) −8.41852e49 −0.511767
\(377\) −2.11713e49 −0.122206
\(378\) −1.37543e50 −0.753962
\(379\) −1.87195e50 −0.974605 −0.487302 0.873233i \(-0.662019\pi\)
−0.487302 + 0.873233i \(0.662019\pi\)
\(380\) −2.79909e49 −0.138432
\(381\) −2.26989e50 −1.06652
\(382\) 2.99987e50 1.33927
\(383\) 3.66531e50 1.55502 0.777508 0.628873i \(-0.216484\pi\)
0.777508 + 0.628873i \(0.216484\pi\)
\(384\) −2.43120e50 −0.980305
\(385\) −9.70109e49 −0.371823
\(386\) −9.15009e49 −0.333406
\(387\) 6.25030e50 2.16539
\(388\) 5.28928e49 0.174252
\(389\) −4.12272e49 −0.129171 −0.0645857 0.997912i \(-0.520573\pi\)
−0.0645857 + 0.997912i \(0.520573\pi\)
\(390\) 2.58625e50 0.770746
\(391\) −9.89791e49 −0.280606
\(392\) 2.27861e50 0.614598
\(393\) −6.21525e50 −1.59516
\(394\) −5.93157e50 −1.44875
\(395\) 3.68452e50 0.856520
\(396\) 2.47845e50 0.548435
\(397\) 4.25670e50 0.896723 0.448361 0.893852i \(-0.352008\pi\)
0.448361 + 0.893852i \(0.352008\pi\)
\(398\) −1.10703e51 −2.22044
\(399\) 2.46399e50 0.470616
\(400\) 2.55330e50 0.464443
\(401\) −6.90511e50 −1.19634 −0.598171 0.801368i \(-0.704106\pi\)
−0.598171 + 0.801368i \(0.704106\pi\)
\(402\) −3.09115e50 −0.510167
\(403\) 4.99898e50 0.786019
\(404\) 1.03490e51 1.55046
\(405\) −3.15924e50 −0.451034
\(406\) 3.85516e50 0.524548
\(407\) −9.32751e49 −0.120969
\(408\) −1.88307e50 −0.232806
\(409\) −5.24800e50 −0.618571 −0.309286 0.950969i \(-0.600090\pi\)
−0.309286 + 0.950969i \(0.600090\pi\)
\(410\) 4.52243e50 0.508260
\(411\) −1.05750e51 −1.13335
\(412\) −7.46265e50 −0.762776
\(413\) 2.39498e51 2.33494
\(414\) 1.17061e51 1.08869
\(415\) 2.86777e50 0.254452
\(416\) −9.74895e50 −0.825349
\(417\) −1.49812e49 −0.0121030
\(418\) −1.35947e50 −0.104817
\(419\) 1.54729e51 1.13867 0.569334 0.822106i \(-0.307201\pi\)
0.569334 + 0.822106i \(0.307201\pi\)
\(420\) −2.59486e51 −1.82286
\(421\) −1.69195e51 −1.13472 −0.567359 0.823471i \(-0.692035\pi\)
−0.567359 + 0.823471i \(0.692035\pi\)
\(422\) −1.49019e51 −0.954220
\(423\) −2.97014e51 −1.81610
\(424\) 2.08989e50 0.122037
\(425\) 5.34241e50 0.297957
\(426\) 7.94298e51 4.23152
\(427\) −3.55174e51 −1.80758
\(428\) 1.52004e51 0.739096
\(429\) 6.92103e50 0.321554
\(430\) 3.61048e51 1.60299
\(431\) 2.11949e51 0.899341 0.449670 0.893195i \(-0.351541\pi\)
0.449670 + 0.893195i \(0.351541\pi\)
\(432\) −5.35686e50 −0.217259
\(433\) 1.57391e51 0.610193 0.305097 0.952321i \(-0.401311\pi\)
0.305097 + 0.952321i \(0.401311\pi\)
\(434\) −9.10284e51 −3.37386
\(435\) −5.23756e50 −0.185604
\(436\) −2.22444e50 −0.0753761
\(437\) −3.53792e50 −0.114646
\(438\) −2.55555e51 −0.792027
\(439\) 7.36309e50 0.218274 0.109137 0.994027i \(-0.465191\pi\)
0.109137 + 0.994027i \(0.465191\pi\)
\(440\) 2.65005e50 0.0751496
\(441\) 8.03916e51 2.18101
\(442\) −1.55128e51 −0.402676
\(443\) −3.79349e51 −0.942251 −0.471125 0.882066i \(-0.656152\pi\)
−0.471125 + 0.882066i \(0.656152\pi\)
\(444\) −2.49494e51 −0.593050
\(445\) −2.77683e51 −0.631726
\(446\) −5.01262e51 −1.09153
\(447\) 4.09239e51 0.853061
\(448\) 1.16904e52 2.33297
\(449\) 7.69430e51 1.47016 0.735081 0.677979i \(-0.237144\pi\)
0.735081 + 0.677979i \(0.237144\pi\)
\(450\) −6.31839e51 −1.15601
\(451\) 1.21024e51 0.212045
\(452\) −6.49659e51 −1.09015
\(453\) −6.82633e51 −1.09717
\(454\) 1.19720e52 1.84322
\(455\) −3.95682e51 −0.583612
\(456\) −6.73088e50 −0.0951168
\(457\) −9.48171e51 −1.28387 −0.641935 0.766759i \(-0.721868\pi\)
−0.641935 + 0.766759i \(0.721868\pi\)
\(458\) 2.03587e52 2.64163
\(459\) −1.12084e51 −0.139379
\(460\) 3.72584e51 0.444065
\(461\) −1.00315e52 −1.14604 −0.573018 0.819543i \(-0.694227\pi\)
−0.573018 + 0.819543i \(0.694227\pi\)
\(462\) −1.26028e52 −1.38022
\(463\) −6.38266e51 −0.670151 −0.335075 0.942191i \(-0.608762\pi\)
−0.335075 + 0.942191i \(0.608762\pi\)
\(464\) 1.50146e51 0.151151
\(465\) 1.23670e52 1.19380
\(466\) −1.75261e52 −1.62241
\(467\) 8.44728e51 0.749960 0.374980 0.927033i \(-0.377650\pi\)
0.374980 + 0.927033i \(0.377650\pi\)
\(468\) 1.01090e52 0.860821
\(469\) 4.72929e51 0.386300
\(470\) −1.71570e52 −1.34441
\(471\) −9.63964e51 −0.724692
\(472\) −6.54237e51 −0.471918
\(473\) 9.66194e51 0.668762
\(474\) 4.78659e52 3.17943
\(475\) 1.90960e51 0.121735
\(476\) 1.55644e52 0.952352
\(477\) 7.37335e51 0.433069
\(478\) −3.16914e52 −1.78689
\(479\) 3.34415e51 0.181027 0.0905134 0.995895i \(-0.471149\pi\)
0.0905134 + 0.995895i \(0.471149\pi\)
\(480\) −2.41179e52 −1.25353
\(481\) −3.80445e51 −0.189873
\(482\) 2.15525e52 1.03295
\(483\) −3.27978e52 −1.50965
\(484\) −2.39262e52 −1.05777
\(485\) 1.99531e51 0.0847319
\(486\) −5.20616e52 −2.12378
\(487\) 3.02586e52 1.18586 0.592931 0.805254i \(-0.297971\pi\)
0.592931 + 0.805254i \(0.297971\pi\)
\(488\) 9.70229e51 0.365332
\(489\) −1.32898e52 −0.480836
\(490\) 4.64381e52 1.61455
\(491\) 5.39058e52 1.80114 0.900568 0.434715i \(-0.143151\pi\)
0.900568 + 0.434715i \(0.143151\pi\)
\(492\) 3.23716e52 1.03955
\(493\) 3.14158e51 0.0969690
\(494\) −5.54492e51 −0.164520
\(495\) 9.34964e51 0.266682
\(496\) −3.54525e52 −0.972197
\(497\) −1.21523e53 −3.20412
\(498\) 3.72554e52 0.944533
\(499\) 4.77343e52 1.16378 0.581888 0.813269i \(-0.302314\pi\)
0.581888 + 0.813269i \(0.302314\pi\)
\(500\) −5.13406e52 −1.20378
\(501\) 1.29503e52 0.292041
\(502\) 7.34494e52 1.59318
\(503\) 4.55769e51 0.0950974 0.0475487 0.998869i \(-0.484859\pi\)
0.0475487 + 0.998869i \(0.484859\pi\)
\(504\) −3.40731e52 −0.683937
\(505\) 3.90401e52 0.753927
\(506\) 1.80957e52 0.336234
\(507\) −5.47861e52 −0.979524
\(508\) −5.12513e52 −0.881784
\(509\) −4.13304e52 −0.684341 −0.342170 0.939638i \(-0.611162\pi\)
−0.342170 + 0.939638i \(0.611162\pi\)
\(510\) −3.83771e52 −0.611580
\(511\) 3.90985e52 0.599726
\(512\) 8.56980e52 1.26534
\(513\) −4.00636e51 −0.0569458
\(514\) −1.78027e53 −2.43615
\(515\) −2.81519e52 −0.370908
\(516\) 2.58439e53 3.27860
\(517\) −4.59135e52 −0.560886
\(518\) 6.92767e52 0.814998
\(519\) 6.61495e52 0.749486
\(520\) 1.08089e52 0.117955
\(521\) −4.81863e52 −0.506510 −0.253255 0.967400i \(-0.581501\pi\)
−0.253255 + 0.967400i \(0.581501\pi\)
\(522\) −3.71550e52 −0.376220
\(523\) 1.41580e52 0.138108 0.0690541 0.997613i \(-0.478002\pi\)
0.0690541 + 0.997613i \(0.478002\pi\)
\(524\) −1.40333e53 −1.31886
\(525\) 1.77027e53 1.60300
\(526\) 4.23131e52 0.369193
\(527\) −7.41792e52 −0.623699
\(528\) −4.90836e52 −0.397718
\(529\) −8.09589e52 −0.632236
\(530\) 4.25921e52 0.320590
\(531\) −2.30821e53 −1.67468
\(532\) 5.56337e52 0.389100
\(533\) 4.93625e52 0.332825
\(534\) −3.60740e53 −2.34498
\(535\) 5.73414e52 0.359393
\(536\) −1.29190e52 −0.0780756
\(537\) 3.97372e53 2.31579
\(538\) 8.59763e52 0.483197
\(539\) 1.24272e53 0.673587
\(540\) 4.21916e52 0.220570
\(541\) 1.61080e53 0.812258 0.406129 0.913816i \(-0.366878\pi\)
0.406129 + 0.913816i \(0.366878\pi\)
\(542\) 2.60044e53 1.26491
\(543\) −3.20465e53 −1.50378
\(544\) 1.44663e53 0.654907
\(545\) −8.39139e51 −0.0366524
\(546\) −5.14034e53 −2.16638
\(547\) −2.03359e52 −0.0827010 −0.0413505 0.999145i \(-0.513166\pi\)
−0.0413505 + 0.999145i \(0.513166\pi\)
\(548\) −2.38769e53 −0.937039
\(549\) 3.42307e53 1.29645
\(550\) −9.76720e52 −0.357024
\(551\) 1.12293e52 0.0396184
\(552\) 8.95940e52 0.305117
\(553\) −7.32322e53 −2.40747
\(554\) 4.63731e53 1.47172
\(555\) −9.41182e52 −0.288377
\(556\) −3.38256e51 −0.0100066
\(557\) −4.33061e53 −1.23701 −0.618505 0.785781i \(-0.712261\pi\)
−0.618505 + 0.785781i \(0.712261\pi\)
\(558\) 8.77306e53 2.41983
\(559\) 3.94085e53 1.04969
\(560\) 2.80616e53 0.721847
\(561\) −1.02700e53 −0.255150
\(562\) 2.55246e52 0.0612491
\(563\) −6.67730e53 −1.54770 −0.773851 0.633368i \(-0.781672\pi\)
−0.773851 + 0.633368i \(0.781672\pi\)
\(564\) −1.22810e54 −2.74974
\(565\) −2.45075e53 −0.530096
\(566\) 6.92632e53 1.44738
\(567\) 6.27918e53 1.26775
\(568\) 3.31965e53 0.647589
\(569\) 9.32793e53 1.75831 0.879156 0.476534i \(-0.158107\pi\)
0.879156 + 0.476534i \(0.158107\pi\)
\(570\) −1.37176e53 −0.249872
\(571\) −2.47736e53 −0.436099 −0.218049 0.975938i \(-0.569969\pi\)
−0.218049 + 0.975938i \(0.569969\pi\)
\(572\) 1.56268e53 0.265857
\(573\) 8.10046e53 1.33197
\(574\) −8.98860e53 −1.42860
\(575\) −2.54185e53 −0.390505
\(576\) −1.12669e54 −1.67327
\(577\) 4.60066e53 0.660528 0.330264 0.943889i \(-0.392862\pi\)
0.330264 + 0.943889i \(0.392862\pi\)
\(578\) −8.44953e53 −1.17284
\(579\) −2.47077e53 −0.331590
\(580\) −1.18257e53 −0.153456
\(581\) −5.69987e53 −0.715204
\(582\) 2.59213e53 0.314527
\(583\) 1.13980e53 0.133749
\(584\) −1.06806e53 −0.121211
\(585\) 3.81348e53 0.418583
\(586\) 4.96930e53 0.527585
\(587\) 1.03979e54 1.06783 0.533916 0.845537i \(-0.320720\pi\)
0.533916 + 0.845537i \(0.320720\pi\)
\(588\) 3.32405e54 3.30225
\(589\) −2.65147e53 −0.254823
\(590\) −1.33334e54 −1.23973
\(591\) −1.60168e54 −1.44086
\(592\) 2.69809e53 0.234846
\(593\) −4.68001e53 −0.394167 −0.197084 0.980387i \(-0.563147\pi\)
−0.197084 + 0.980387i \(0.563147\pi\)
\(594\) 2.04917e53 0.167010
\(595\) 5.87147e53 0.463091
\(596\) 9.24009e53 0.705301
\(597\) −2.98928e54 −2.20835
\(598\) 7.38078e53 0.527751
\(599\) 1.95085e54 1.35021 0.675106 0.737721i \(-0.264098\pi\)
0.675106 + 0.737721i \(0.264098\pi\)
\(600\) −4.83585e53 −0.323984
\(601\) 2.02439e54 1.31293 0.656467 0.754355i \(-0.272050\pi\)
0.656467 + 0.754355i \(0.272050\pi\)
\(602\) −7.17605e54 −4.50561
\(603\) −4.55796e53 −0.277066
\(604\) −1.54130e54 −0.907124
\(605\) −9.02586e53 −0.514350
\(606\) 5.07174e54 2.79860
\(607\) 2.12357e54 1.13472 0.567359 0.823471i \(-0.307965\pi\)
0.567359 + 0.823471i \(0.307965\pi\)
\(608\) 5.17087e53 0.267574
\(609\) 1.04100e54 0.521690
\(610\) 1.97733e54 0.959726
\(611\) −1.87269e54 −0.880364
\(612\) −1.50006e54 −0.683054
\(613\) −3.14022e54 −1.38510 −0.692549 0.721371i \(-0.743512\pi\)
−0.692549 + 0.721371i \(0.743512\pi\)
\(614\) 6.38487e54 2.72815
\(615\) 1.22118e54 0.505492
\(616\) −5.26714e53 −0.211228
\(617\) −2.88947e54 −1.12268 −0.561341 0.827585i \(-0.689714\pi\)
−0.561341 + 0.827585i \(0.689714\pi\)
\(618\) −3.65723e54 −1.37682
\(619\) −8.69334e53 −0.317116 −0.158558 0.987350i \(-0.550685\pi\)
−0.158558 + 0.987350i \(0.550685\pi\)
\(620\) 2.79230e54 0.987017
\(621\) 5.33282e53 0.182672
\(622\) −3.87363e54 −1.28590
\(623\) 5.51912e54 1.77563
\(624\) −2.00199e54 −0.624256
\(625\) 1.93843e53 0.0585853
\(626\) 4.78114e54 1.40066
\(627\) −3.67093e53 −0.104246
\(628\) −2.17651e54 −0.599166
\(629\) 5.64537e53 0.150662
\(630\) −6.94411e54 −1.79670
\(631\) −2.40764e54 −0.603976 −0.301988 0.953312i \(-0.597650\pi\)
−0.301988 + 0.953312i \(0.597650\pi\)
\(632\) 2.00048e54 0.486578
\(633\) −4.02391e54 −0.949022
\(634\) −3.74926e53 −0.0857443
\(635\) −1.93339e54 −0.428777
\(636\) 3.04875e54 0.655705
\(637\) 5.06874e54 1.05726
\(638\) −5.74355e53 −0.116192
\(639\) 1.17121e55 2.29809
\(640\) −2.07078e54 −0.394116
\(641\) −2.69211e53 −0.0497005 −0.0248503 0.999691i \(-0.507911\pi\)
−0.0248503 + 0.999691i \(0.507911\pi\)
\(642\) 7.44927e54 1.33408
\(643\) −3.09318e54 −0.537393 −0.268696 0.963225i \(-0.586593\pi\)
−0.268696 + 0.963225i \(0.586593\pi\)
\(644\) −7.40534e54 −1.24816
\(645\) 9.74926e54 1.59425
\(646\) 8.22803e53 0.130545
\(647\) −1.66944e54 −0.257003 −0.128501 0.991709i \(-0.541017\pi\)
−0.128501 + 0.991709i \(0.541017\pi\)
\(648\) −1.71529e54 −0.256226
\(649\) −3.56812e54 −0.517212
\(650\) −3.98379e54 −0.560384
\(651\) −2.45801e55 −3.35548
\(652\) −3.00068e54 −0.397549
\(653\) 1.05739e55 1.35965 0.679824 0.733375i \(-0.262056\pi\)
0.679824 + 0.733375i \(0.262056\pi\)
\(654\) −1.09013e54 −0.136055
\(655\) −5.29386e54 −0.641309
\(656\) −3.50076e54 −0.411659
\(657\) −3.76821e54 −0.430140
\(658\) 3.41006e55 3.77882
\(659\) 3.28150e54 0.353026 0.176513 0.984298i \(-0.443518\pi\)
0.176513 + 0.984298i \(0.443518\pi\)
\(660\) 3.86591e54 0.403781
\(661\) 1.10445e55 1.12000 0.560001 0.828492i \(-0.310801\pi\)
0.560001 + 0.828492i \(0.310801\pi\)
\(662\) −1.36894e55 −1.34789
\(663\) −4.18887e54 −0.400482
\(664\) 1.55703e54 0.144551
\(665\) 2.09871e54 0.189204
\(666\) −6.67670e54 −0.584540
\(667\) −1.49472e54 −0.127088
\(668\) 2.92402e54 0.241456
\(669\) −1.35354e55 −1.08558
\(670\) −2.63290e54 −0.205105
\(671\) 5.29150e54 0.400396
\(672\) 4.79358e55 3.52338
\(673\) −1.32277e55 −0.944478 −0.472239 0.881471i \(-0.656554\pi\)
−0.472239 + 0.881471i \(0.656554\pi\)
\(674\) −1.82731e55 −1.26749
\(675\) −2.87840e54 −0.193967
\(676\) −1.23700e55 −0.809858
\(677\) 1.10632e54 0.0703723 0.0351861 0.999381i \(-0.488798\pi\)
0.0351861 + 0.999381i \(0.488798\pi\)
\(678\) −3.18379e55 −1.96773
\(679\) −3.96581e54 −0.238161
\(680\) −1.60391e54 −0.0935959
\(681\) 3.23276e55 1.83318
\(682\) 1.35617e55 0.747342
\(683\) 1.00248e55 0.536873 0.268437 0.963297i \(-0.413493\pi\)
0.268437 + 0.963297i \(0.413493\pi\)
\(684\) −5.36182e54 −0.279073
\(685\) −9.00726e54 −0.455645
\(686\) −4.13910e55 −2.03510
\(687\) 5.49739e55 2.62724
\(688\) −2.79483e55 −1.29832
\(689\) 4.64895e54 0.209933
\(690\) 1.82593e55 0.801542
\(691\) −1.51432e55 −0.646242 −0.323121 0.946358i \(-0.604732\pi\)
−0.323121 + 0.946358i \(0.604732\pi\)
\(692\) 1.49357e55 0.619666
\(693\) −1.85830e55 −0.749580
\(694\) 3.51943e55 1.38026
\(695\) −1.27603e53 −0.00486582
\(696\) −2.84370e54 −0.105439
\(697\) −7.32483e54 −0.264094
\(698\) 1.15767e55 0.405886
\(699\) −4.73252e55 −1.61357
\(700\) 3.99704e55 1.32534
\(701\) 4.82172e55 1.55489 0.777447 0.628948i \(-0.216514\pi\)
0.777447 + 0.628948i \(0.216514\pi\)
\(702\) 8.35803e54 0.262138
\(703\) 2.01789e54 0.0615557
\(704\) −1.74168e55 −0.516775
\(705\) −4.63285e55 −1.33709
\(706\) −3.63879e55 −1.02156
\(707\) −7.75947e55 −2.11911
\(708\) −9.54406e55 −2.53562
\(709\) 6.05445e53 0.0156485 0.00782426 0.999969i \(-0.497509\pi\)
0.00782426 + 0.999969i \(0.497509\pi\)
\(710\) 6.76545e55 1.70121
\(711\) 7.05791e55 1.72671
\(712\) −1.50766e55 −0.358875
\(713\) 3.52934e55 0.817425
\(714\) 7.62768e55 1.71901
\(715\) 5.89501e54 0.129276
\(716\) 8.97216e55 1.91467
\(717\) −8.55754e55 −1.77716
\(718\) 5.40053e55 1.09147
\(719\) −7.05056e54 −0.138679 −0.0693394 0.997593i \(-0.522089\pi\)
−0.0693394 + 0.997593i \(0.522089\pi\)
\(720\) −2.70450e55 −0.517729
\(721\) 5.59536e55 1.04253
\(722\) −7.93495e55 −1.43903
\(723\) 5.81976e55 1.02733
\(724\) −7.23568e55 −1.24330
\(725\) 8.06777e54 0.134947
\(726\) −1.17256e56 −1.90928
\(727\) 7.92077e55 1.25559 0.627793 0.778380i \(-0.283958\pi\)
0.627793 + 0.778380i \(0.283958\pi\)
\(728\) −2.14833e55 −0.331542
\(729\) −9.02730e55 −1.35635
\(730\) −2.17670e55 −0.318422
\(731\) −5.84777e55 −0.832917
\(732\) 1.41538e56 1.96294
\(733\) −6.30225e55 −0.851076 −0.425538 0.904941i \(-0.639915\pi\)
−0.425538 + 0.904941i \(0.639915\pi\)
\(734\) 7.90358e55 1.03932
\(735\) 1.25396e56 1.60575
\(736\) −6.88288e55 −0.858327
\(737\) −7.04586e54 −0.0855692
\(738\) 8.66297e55 1.02463
\(739\) −1.14548e56 −1.31954 −0.659768 0.751469i \(-0.729345\pi\)
−0.659768 + 0.751469i \(0.729345\pi\)
\(740\) −2.12507e55 −0.238426
\(741\) −1.49728e55 −0.163624
\(742\) −8.46545e55 −0.901101
\(743\) 3.14628e55 0.326224 0.163112 0.986608i \(-0.447847\pi\)
0.163112 + 0.986608i \(0.447847\pi\)
\(744\) 6.71456e55 0.678180
\(745\) 3.48570e55 0.342960
\(746\) 1.17197e56 1.12334
\(747\) 5.49338e55 0.512965
\(748\) −2.31884e55 −0.210955
\(749\) −1.13970e56 −1.01017
\(750\) −2.51606e56 −2.17283
\(751\) 1.74710e56 1.47007 0.735036 0.678028i \(-0.237165\pi\)
0.735036 + 0.678028i \(0.237165\pi\)
\(752\) 1.32810e56 1.08889
\(753\) 1.98333e56 1.58451
\(754\) −2.34264e55 −0.182375
\(755\) −5.81435e55 −0.441098
\(756\) −8.38584e55 −0.619971
\(757\) 2.77438e55 0.199893 0.0999463 0.994993i \(-0.468133\pi\)
0.0999463 + 0.994993i \(0.468133\pi\)
\(758\) −2.07134e56 −1.45446
\(759\) 4.88634e55 0.334402
\(760\) −5.73305e54 −0.0382402
\(761\) −2.40584e56 −1.56411 −0.782053 0.623212i \(-0.785827\pi\)
−0.782053 + 0.623212i \(0.785827\pi\)
\(762\) −2.51168e56 −1.59163
\(763\) 1.66784e55 0.103021
\(764\) 1.82898e56 1.10126
\(765\) −5.65876e55 −0.332142
\(766\) 4.05574e56 2.32065
\(767\) −1.45534e56 −0.811813
\(768\) 1.10618e56 0.601565
\(769\) 3.04973e56 1.61695 0.808477 0.588528i \(-0.200292\pi\)
0.808477 + 0.588528i \(0.200292\pi\)
\(770\) −1.07345e56 −0.554895
\(771\) −4.80720e56 −2.42288
\(772\) −5.57869e55 −0.274154
\(773\) 4.36657e55 0.209238 0.104619 0.994512i \(-0.466638\pi\)
0.104619 + 0.994512i \(0.466638\pi\)
\(774\) 6.91608e56 3.23155
\(775\) −1.90497e56 −0.867970
\(776\) 1.08334e55 0.0481351
\(777\) 1.87066e56 0.810559
\(778\) −4.56187e55 −0.192771
\(779\) −2.61820e55 −0.107900
\(780\) 1.57680e56 0.633772
\(781\) 1.81049e56 0.709744
\(782\) −1.09522e56 −0.418766
\(783\) −1.69263e55 −0.0631258
\(784\) −3.59473e56 −1.30768
\(785\) −8.21060e55 −0.291351
\(786\) −6.87730e56 −2.38056
\(787\) −4.86747e56 −1.64360 −0.821800 0.569777i \(-0.807030\pi\)
−0.821800 + 0.569777i \(0.807030\pi\)
\(788\) −3.61640e56 −1.19128
\(789\) 1.14257e56 0.367182
\(790\) 4.07700e56 1.27824
\(791\) 4.87102e56 1.48997
\(792\) 5.07632e55 0.151499
\(793\) 2.15827e56 0.628460
\(794\) 4.71012e56 1.33824
\(795\) 1.15010e56 0.318843
\(796\) −6.74942e56 −1.82583
\(797\) 5.82796e56 1.53844 0.769218 0.638986i \(-0.220646\pi\)
0.769218 + 0.638986i \(0.220646\pi\)
\(798\) 2.72645e56 0.702330
\(799\) 2.77886e56 0.698561
\(800\) 3.71505e56 0.911401
\(801\) −5.31917e56 −1.27353
\(802\) −7.64064e56 −1.78538
\(803\) −5.82503e55 −0.132845
\(804\) −1.88463e56 −0.419502
\(805\) −2.79357e56 −0.606931
\(806\) 5.53147e56 1.17303
\(807\) 2.32159e56 0.480565
\(808\) 2.11966e56 0.428296
\(809\) −7.85718e56 −1.54978 −0.774891 0.632095i \(-0.782195\pi\)
−0.774891 + 0.632095i \(0.782195\pi\)
\(810\) −3.49576e56 −0.673106
\(811\) 4.57812e56 0.860558 0.430279 0.902696i \(-0.358415\pi\)
0.430279 + 0.902696i \(0.358415\pi\)
\(812\) 2.35044e56 0.431327
\(813\) 7.02189e56 1.25802
\(814\) −1.03211e56 −0.180530
\(815\) −1.13197e56 −0.193312
\(816\) 2.97073e56 0.495342
\(817\) −2.09024e56 −0.340303
\(818\) −5.80702e56 −0.923132
\(819\) −7.57952e56 −1.17654
\(820\) 2.75726e56 0.417934
\(821\) 5.79486e56 0.857731 0.428866 0.903368i \(-0.358913\pi\)
0.428866 + 0.903368i \(0.358913\pi\)
\(822\) −1.17014e57 −1.69137
\(823\) −1.26890e57 −1.79114 −0.895572 0.444916i \(-0.853233\pi\)
−0.895572 + 0.444916i \(0.853233\pi\)
\(824\) −1.52849e56 −0.210708
\(825\) −2.63741e56 −0.355079
\(826\) 2.65009e57 3.48458
\(827\) 3.04410e56 0.390932 0.195466 0.980710i \(-0.437378\pi\)
0.195466 + 0.980710i \(0.437378\pi\)
\(828\) 7.13706e56 0.895216
\(829\) −4.36698e56 −0.535017 −0.267509 0.963555i \(-0.586200\pi\)
−0.267509 + 0.963555i \(0.586200\pi\)
\(830\) 3.17324e56 0.379735
\(831\) 1.25220e57 1.46371
\(832\) −7.10386e56 −0.811129
\(833\) −7.52144e56 −0.838926
\(834\) −1.65770e55 −0.0180621
\(835\) 1.10305e56 0.117411
\(836\) −8.28850e55 −0.0861894
\(837\) 3.99665e56 0.406022
\(838\) 1.71210e57 1.69931
\(839\) 1.05819e56 0.102614 0.0513070 0.998683i \(-0.483661\pi\)
0.0513070 + 0.998683i \(0.483661\pi\)
\(840\) −5.31475e56 −0.503543
\(841\) −1.03280e57 −0.956082
\(842\) −1.87218e57 −1.69341
\(843\) 6.89232e55 0.0609155
\(844\) −9.08549e56 −0.784640
\(845\) −4.66642e56 −0.393802
\(846\) −3.28652e57 −2.71028
\(847\) 1.79395e57 1.44572
\(848\) −3.29701e56 −0.259658
\(849\) 1.87029e57 1.43949
\(850\) 5.91149e56 0.444660
\(851\) −2.68599e56 −0.197459
\(852\) 4.84273e57 3.47951
\(853\) −1.08758e57 −0.763756 −0.381878 0.924213i \(-0.624723\pi\)
−0.381878 + 0.924213i \(0.624723\pi\)
\(854\) −3.93007e57 −2.69756
\(855\) −2.02268e56 −0.135702
\(856\) 3.11331e56 0.204166
\(857\) 1.97964e57 1.26900 0.634498 0.772925i \(-0.281207\pi\)
0.634498 + 0.772925i \(0.281207\pi\)
\(858\) 7.65826e56 0.479875
\(859\) 5.66557e56 0.347038 0.173519 0.984831i \(-0.444486\pi\)
0.173519 + 0.984831i \(0.444486\pi\)
\(860\) 2.20126e57 1.31811
\(861\) −2.42717e57 −1.42082
\(862\) 2.34526e57 1.34214
\(863\) −5.59601e56 −0.313089 −0.156545 0.987671i \(-0.550036\pi\)
−0.156545 + 0.987671i \(0.550036\pi\)
\(864\) −7.79421e56 −0.426338
\(865\) 5.63431e56 0.301319
\(866\) 1.74157e57 0.910629
\(867\) −2.28160e57 −1.16645
\(868\) −5.54988e57 −2.77427
\(869\) 1.09104e57 0.533279
\(870\) −5.79546e56 −0.276989
\(871\) −2.87382e56 −0.134309
\(872\) −4.55605e55 −0.0208217
\(873\) 3.82214e56 0.170816
\(874\) −3.91478e56 −0.171094
\(875\) 3.84943e57 1.64528
\(876\) −1.55809e57 −0.651271
\(877\) −3.51912e57 −1.43861 −0.719304 0.694695i \(-0.755539\pi\)
−0.719304 + 0.694695i \(0.755539\pi\)
\(878\) 8.14740e56 0.325744
\(879\) 1.34185e57 0.524711
\(880\) −4.18071e56 −0.159896
\(881\) −2.67197e57 −0.999542 −0.499771 0.866158i \(-0.666583\pi\)
−0.499771 + 0.866158i \(0.666583\pi\)
\(882\) 8.89550e57 3.25486
\(883\) 3.97981e57 1.42439 0.712194 0.701982i \(-0.247701\pi\)
0.712194 + 0.701982i \(0.247701\pi\)
\(884\) −9.45795e56 −0.331114
\(885\) −3.60037e57 −1.23297
\(886\) −4.19757e57 −1.40618
\(887\) −2.01262e57 −0.659555 −0.329778 0.944059i \(-0.606974\pi\)
−0.329778 + 0.944059i \(0.606974\pi\)
\(888\) −5.11008e56 −0.163823
\(889\) 3.84273e57 1.20519
\(890\) −3.07261e57 −0.942764
\(891\) −9.35494e56 −0.280819
\(892\) −3.05613e57 −0.897546
\(893\) 9.93280e56 0.285409
\(894\) 4.52831e57 1.27308
\(895\) 3.38463e57 0.931026
\(896\) 4.11580e57 1.10777
\(897\) 1.99301e57 0.524876
\(898\) 8.51389e57 2.19401
\(899\) −1.12021e57 −0.282478
\(900\) −3.85224e57 −0.950571
\(901\) −6.89851e56 −0.166580
\(902\) 1.33915e57 0.316448
\(903\) −1.93773e58 −4.48107
\(904\) −1.33062e57 −0.301141
\(905\) −2.72957e57 −0.604570
\(906\) −7.55347e57 −1.63737
\(907\) −1.92035e57 −0.407416 −0.203708 0.979032i \(-0.565299\pi\)
−0.203708 + 0.979032i \(0.565299\pi\)
\(908\) 7.29915e57 1.51565
\(909\) 7.47836e57 1.51989
\(910\) −4.37830e57 −0.870961
\(911\) 5.42803e57 1.05690 0.528450 0.848964i \(-0.322773\pi\)
0.528450 + 0.848964i \(0.322773\pi\)
\(912\) 1.06186e57 0.202380
\(913\) 8.49186e56 0.158425
\(914\) −1.04917e58 −1.91600
\(915\) 5.33933e57 0.954498
\(916\) 1.24124e58 2.17217
\(917\) 1.05219e58 1.80257
\(918\) −1.24024e57 −0.208004
\(919\) −1.06801e58 −1.75357 −0.876785 0.480883i \(-0.840316\pi\)
−0.876785 + 0.480883i \(0.840316\pi\)
\(920\) 7.63119e56 0.122668
\(921\) 1.72409e58 2.71329
\(922\) −1.11001e58 −1.71030
\(923\) 7.38452e57 1.11401
\(924\) −7.68375e57 −1.13493
\(925\) 1.44977e57 0.209669
\(926\) −7.06255e57 −1.00011
\(927\) −5.39265e57 −0.747735
\(928\) 2.18461e57 0.296612
\(929\) −9.61260e57 −1.27801 −0.639005 0.769202i \(-0.720654\pi\)
−0.639005 + 0.769202i \(0.720654\pi\)
\(930\) 1.36843e58 1.78158
\(931\) −2.68848e57 −0.342758
\(932\) −1.06854e58 −1.33408
\(933\) −1.04599e58 −1.27889
\(934\) 9.34709e57 1.11921
\(935\) −8.74753e56 −0.102579
\(936\) 2.07050e57 0.237791
\(937\) −6.32461e57 −0.711396 −0.355698 0.934601i \(-0.615757\pi\)
−0.355698 + 0.934601i \(0.615757\pi\)
\(938\) 5.23305e57 0.576500
\(939\) 1.29104e58 1.39303
\(940\) −1.04604e58 −1.10549
\(941\) 4.44546e57 0.460171 0.230085 0.973170i \(-0.426099\pi\)
0.230085 + 0.973170i \(0.426099\pi\)
\(942\) −1.06665e58 −1.08150
\(943\) 3.48505e57 0.346124
\(944\) 1.03212e58 1.00410
\(945\) −3.16345e57 −0.301467
\(946\) 1.06911e58 0.998036
\(947\) −2.02681e58 −1.85348 −0.926739 0.375705i \(-0.877401\pi\)
−0.926739 + 0.375705i \(0.877401\pi\)
\(948\) 2.91832e58 2.61439
\(949\) −2.37588e57 −0.208513
\(950\) 2.11301e57 0.181673
\(951\) −1.01240e57 −0.0852772
\(952\) 3.18788e57 0.263076
\(953\) −2.18717e58 −1.76837 −0.884183 0.467141i \(-0.845284\pi\)
−0.884183 + 0.467141i \(0.845284\pi\)
\(954\) 8.15876e57 0.646295
\(955\) 6.89959e57 0.535498
\(956\) −1.93218e58 −1.46933
\(957\) −1.55091e57 −0.115559
\(958\) 3.70037e57 0.270158
\(959\) 1.79025e58 1.28071
\(960\) −1.75742e58 −1.23193
\(961\) 1.18923e58 0.816882
\(962\) −4.20970e57 −0.283359
\(963\) 1.09841e58 0.724521
\(964\) 1.31403e58 0.849381
\(965\) −2.10449e57 −0.133310
\(966\) −3.62915e58 −2.25295
\(967\) −8.40382e57 −0.511282 −0.255641 0.966772i \(-0.582287\pi\)
−0.255641 + 0.966772i \(0.582287\pi\)
\(968\) −4.90053e57 −0.292195
\(969\) 2.22179e57 0.129834
\(970\) 2.20785e57 0.126451
\(971\) 2.19465e58 1.23194 0.615972 0.787768i \(-0.288763\pi\)
0.615972 + 0.787768i \(0.288763\pi\)
\(972\) −3.17413e58 −1.74635
\(973\) 2.53618e56 0.0136767
\(974\) 3.34817e58 1.76974
\(975\) −1.07573e58 −0.557331
\(976\) −1.53063e58 −0.777318
\(977\) 4.53213e57 0.225610 0.112805 0.993617i \(-0.464016\pi\)
0.112805 + 0.993617i \(0.464016\pi\)
\(978\) −1.47055e58 −0.717581
\(979\) −8.22257e57 −0.393319
\(980\) 2.83127e58 1.32762
\(981\) −1.60742e57 −0.0738897
\(982\) 5.96479e58 2.68795
\(983\) −3.96363e58 −1.75105 −0.875527 0.483169i \(-0.839486\pi\)
−0.875527 + 0.483169i \(0.839486\pi\)
\(984\) 6.63030e57 0.287163
\(985\) −1.36424e58 −0.579274
\(986\) 3.47622e57 0.144713
\(987\) 9.20807e58 3.75824
\(988\) −3.38066e57 −0.135282
\(989\) 2.78229e58 1.09163
\(990\) 1.03456e58 0.397986
\(991\) −1.58403e58 −0.597486 −0.298743 0.954334i \(-0.596567\pi\)
−0.298743 + 0.954334i \(0.596567\pi\)
\(992\) −5.15833e58 −1.90779
\(993\) −3.69650e58 −1.34054
\(994\) −1.34468e59 −4.78171
\(995\) −2.54613e58 −0.887831
\(996\) 2.27141e58 0.776675
\(997\) 6.66270e57 0.223406 0.111703 0.993742i \(-0.464369\pi\)
0.111703 + 0.993742i \(0.464369\pi\)
\(998\) 5.28189e58 1.73678
\(999\) −3.04163e57 −0.0980797
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 1.40.a.a.1.3 3
3.2 odd 2 9.40.a.b.1.1 3
4.3 odd 2 16.40.a.c.1.1 3
5.2 odd 4 25.40.b.a.24.6 6
5.3 odd 4 25.40.b.a.24.1 6
5.4 even 2 25.40.a.a.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.40.a.a.1.3 3 1.1 even 1 trivial
9.40.a.b.1.1 3 3.2 odd 2
16.40.a.c.1.1 3 4.3 odd 2
25.40.a.a.1.1 3 5.4 even 2
25.40.b.a.24.1 6 5.3 odd 4
25.40.b.a.24.6 6 5.2 odd 4