Properties

Label 3.44.a.a.1.1
Level $3$
Weight $44$
Character 3.1
Self dual yes
Analytic conductor $35.133$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 44 \)
Character orbit: \([\chi]\) \(=\) 3.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(35.1331186037\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: \(\mathbb{Q}[x]/(x^{3} - \cdots)\)
Defining polynomial: \(x^{3} - x^{2} - 908401710 x + 974756489742\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{13}\cdot 3^{5}\cdot 5\cdot 11 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(29588.6\) of defining polynomial
Character \(\chi\) \(=\) 3.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.22147e6 q^{2} +1.04604e10 q^{3} -7.30411e12 q^{4} -8.84097e14 q^{5} -1.27770e16 q^{6} +1.48034e18 q^{7} +1.96659e19 q^{8} +1.09419e20 q^{9} +O(q^{10})\) \(q-1.22147e6 q^{2} +1.04604e10 q^{3} -7.30411e12 q^{4} -8.84097e14 q^{5} -1.27770e16 q^{6} +1.48034e18 q^{7} +1.96659e19 q^{8} +1.09419e20 q^{9} +1.07990e21 q^{10} +1.46320e21 q^{11} -7.64035e22 q^{12} -4.36401e23 q^{13} -1.80819e24 q^{14} -9.24796e24 q^{15} +4.02263e25 q^{16} +3.51740e26 q^{17} -1.33652e26 q^{18} -1.50013e27 q^{19} +6.45753e27 q^{20} +1.54849e28 q^{21} -1.78725e27 q^{22} -1.10333e29 q^{23} +2.05712e29 q^{24} -3.55242e29 q^{25} +5.33051e29 q^{26} +1.14456e30 q^{27} -1.08126e31 q^{28} -3.00258e31 q^{29} +1.12961e31 q^{30} +1.83651e32 q^{31} -2.22118e32 q^{32} +1.53056e31 q^{33} -4.29639e32 q^{34} -1.30876e33 q^{35} -7.99208e32 q^{36} -9.66835e33 q^{37} +1.83236e33 q^{38} -4.56491e33 q^{39} -1.73866e34 q^{40} -5.73635e34 q^{41} -1.89143e34 q^{42} -1.24932e35 q^{43} -1.06874e34 q^{44} -9.67370e34 q^{45} +1.34768e35 q^{46} -6.52473e35 q^{47} +4.20781e35 q^{48} +7.59027e33 q^{49} +4.33917e35 q^{50} +3.67932e36 q^{51} +3.18752e36 q^{52} +2.03194e37 q^{53} -1.39805e36 q^{54} -1.29361e36 q^{55} +2.91122e37 q^{56} -1.56919e37 q^{57} +3.66756e37 q^{58} -7.05565e37 q^{59} +6.75481e37 q^{60} -4.16411e38 q^{61} -2.24324e38 q^{62} +1.61977e38 q^{63} -8.25234e37 q^{64} +3.85821e38 q^{65} -1.86953e37 q^{66} -1.46698e39 q^{67} -2.56914e39 q^{68} -1.15412e39 q^{69} +1.59861e39 q^{70} +6.58697e39 q^{71} +2.15182e39 q^{72} +8.76849e39 q^{73} +1.18096e40 q^{74} -3.71595e39 q^{75} +1.09571e40 q^{76} +2.16603e39 q^{77} +5.57590e39 q^{78} -3.63007e39 q^{79} -3.55639e40 q^{80} +1.19725e40 q^{81} +7.00677e40 q^{82} -2.43814e41 q^{83} -1.13103e41 q^{84} -3.10972e41 q^{85} +1.52600e41 q^{86} -3.14080e41 q^{87} +2.87752e40 q^{88} +6.12259e41 q^{89} +1.18161e41 q^{90} -6.46022e41 q^{91} +8.05884e41 q^{92} +1.92106e42 q^{93} +7.96976e41 q^{94} +1.32626e42 q^{95} -2.32344e42 q^{96} +8.54423e41 q^{97} -9.27128e39 q^{98} +1.60102e41 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 4857024q^{2} + 31381059609q^{3} - 1781058029568q^{4} - 507753321105270q^{5} + 50806186555447872q^{6} - 1633169303707089288q^{7} + 11196260694472851456q^{8} + 328256967394537077627q^{9} + O(q^{10}) \) \( 3q + 4857024q^{2} + 31381059609q^{3} - 1781058029568q^{4} - 507753321105270q^{5} + 50806186555447872q^{6} - 1633169303707089288q^{7} + 11196260694472851456q^{8} + \)\(32\!\cdots\!27\)\(q^{9} - \)\(22\!\cdots\!20\)\(q^{10} - \)\(27\!\cdots\!20\)\(q^{11} - \)\(18\!\cdots\!04\)\(q^{12} - \)\(99\!\cdots\!50\)\(q^{13} - \)\(94\!\cdots\!28\)\(q^{14} - \)\(53\!\cdots\!10\)\(q^{15} + \)\(23\!\cdots\!36\)\(q^{16} - \)\(16\!\cdots\!82\)\(q^{17} + \)\(53\!\cdots\!16\)\(q^{18} - \)\(32\!\cdots\!64\)\(q^{19} - \)\(19\!\cdots\!60\)\(q^{20} - \)\(17\!\cdots\!64\)\(q^{21} - \)\(17\!\cdots\!24\)\(q^{22} + \)\(11\!\cdots\!04\)\(q^{23} + \)\(11\!\cdots\!68\)\(q^{24} + \)\(18\!\cdots\!25\)\(q^{25} + \)\(17\!\cdots\!36\)\(q^{26} + \)\(34\!\cdots\!81\)\(q^{27} - \)\(84\!\cdots\!44\)\(q^{28} - \)\(28\!\cdots\!58\)\(q^{29} - \)\(23\!\cdots\!60\)\(q^{30} - \)\(56\!\cdots\!36\)\(q^{31} - \)\(29\!\cdots\!88\)\(q^{32} - \)\(29\!\cdots\!60\)\(q^{33} - \)\(17\!\cdots\!76\)\(q^{34} - \)\(36\!\cdots\!20\)\(q^{35} - \)\(19\!\cdots\!12\)\(q^{36} - \)\(77\!\cdots\!78\)\(q^{37} - \)\(11\!\cdots\!08\)\(q^{38} - \)\(10\!\cdots\!50\)\(q^{39} - \)\(75\!\cdots\!00\)\(q^{40} - \)\(15\!\cdots\!66\)\(q^{41} - \)\(99\!\cdots\!84\)\(q^{42} - \)\(50\!\cdots\!88\)\(q^{43} - \)\(58\!\cdots\!72\)\(q^{44} - \)\(55\!\cdots\!30\)\(q^{45} + \)\(12\!\cdots\!64\)\(q^{46} + \)\(51\!\cdots\!36\)\(q^{47} + \)\(24\!\cdots\!08\)\(q^{48} + \)\(11\!\cdots\!03\)\(q^{49} + \)\(53\!\cdots\!00\)\(q^{50} - \)\(16\!\cdots\!46\)\(q^{51} + \)\(19\!\cdots\!08\)\(q^{52} + \)\(31\!\cdots\!34\)\(q^{53} + \)\(55\!\cdots\!48\)\(q^{54} + \)\(72\!\cdots\!60\)\(q^{55} + \)\(64\!\cdots\!20\)\(q^{56} - \)\(33\!\cdots\!92\)\(q^{57} + \)\(16\!\cdots\!64\)\(q^{58} - \)\(17\!\cdots\!76\)\(q^{59} - \)\(20\!\cdots\!80\)\(q^{60} - \)\(12\!\cdots\!18\)\(q^{61} - \)\(68\!\cdots\!56\)\(q^{62} - \)\(17\!\cdots\!92\)\(q^{63} - \)\(97\!\cdots\!36\)\(q^{64} - \)\(25\!\cdots\!40\)\(q^{65} - \)\(18\!\cdots\!72\)\(q^{66} + \)\(12\!\cdots\!48\)\(q^{67} - \)\(27\!\cdots\!68\)\(q^{68} + \)\(12\!\cdots\!12\)\(q^{69} + \)\(18\!\cdots\!80\)\(q^{70} + \)\(22\!\cdots\!16\)\(q^{71} + \)\(12\!\cdots\!04\)\(q^{72} + \)\(31\!\cdots\!54\)\(q^{73} + \)\(12\!\cdots\!32\)\(q^{74} + \)\(19\!\cdots\!75\)\(q^{75} - \)\(45\!\cdots\!04\)\(q^{76} + \)\(15\!\cdots\!44\)\(q^{77} + \)\(18\!\cdots\!08\)\(q^{78} - \)\(43\!\cdots\!80\)\(q^{79} + \)\(51\!\cdots\!80\)\(q^{80} + \)\(35\!\cdots\!43\)\(q^{81} - \)\(20\!\cdots\!96\)\(q^{82} + \)\(89\!\cdots\!68\)\(q^{83} - \)\(88\!\cdots\!32\)\(q^{84} - \)\(60\!\cdots\!20\)\(q^{85} - \)\(10\!\cdots\!20\)\(q^{86} - \)\(29\!\cdots\!74\)\(q^{87} - \)\(86\!\cdots\!84\)\(q^{88} + \)\(65\!\cdots\!06\)\(q^{89} - \)\(25\!\cdots\!80\)\(q^{90} + \)\(13\!\cdots\!24\)\(q^{91} + \)\(37\!\cdots\!72\)\(q^{92} - \)\(59\!\cdots\!08\)\(q^{93} + \)\(78\!\cdots\!20\)\(q^{94} + \)\(93\!\cdots\!00\)\(q^{95} - \)\(30\!\cdots\!64\)\(q^{96} + \)\(61\!\cdots\!78\)\(q^{97} - \)\(20\!\cdots\!60\)\(q^{98} - \)\(30\!\cdots\!80\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22147e6 −0.411849 −0.205924 0.978568i \(-0.566020\pi\)
−0.205924 + 0.978568i \(0.566020\pi\)
\(3\) 1.04604e10 0.577350
\(4\) −7.30411e12 −0.830381
\(5\) −8.84097e14 −0.829172 −0.414586 0.910010i \(-0.636074\pi\)
−0.414586 + 0.910010i \(0.636074\pi\)
\(6\) −1.27770e16 −0.237781
\(7\) 1.48034e18 1.00174 0.500868 0.865524i \(-0.333014\pi\)
0.500868 + 0.865524i \(0.333014\pi\)
\(8\) 1.96659e19 0.753840
\(9\) 1.09419e20 0.333333
\(10\) 1.07990e21 0.341493
\(11\) 1.46320e21 0.0596158 0.0298079 0.999556i \(-0.490510\pi\)
0.0298079 + 0.999556i \(0.490510\pi\)
\(12\) −7.64035e22 −0.479420
\(13\) −4.36401e23 −0.489896 −0.244948 0.969536i \(-0.578771\pi\)
−0.244948 + 0.969536i \(0.578771\pi\)
\(14\) −1.80819e24 −0.412564
\(15\) −9.24796e24 −0.478723
\(16\) 4.02263e25 0.519913
\(17\) 3.51740e26 1.23472 0.617362 0.786680i \(-0.288202\pi\)
0.617362 + 0.786680i \(0.288202\pi\)
\(18\) −1.33652e26 −0.137283
\(19\) −1.50013e27 −0.481865 −0.240933 0.970542i \(-0.577453\pi\)
−0.240933 + 0.970542i \(0.577453\pi\)
\(20\) 6.45753e27 0.688528
\(21\) 1.54849e28 0.578353
\(22\) −1.78725e27 −0.0245527
\(23\) −1.10333e29 −0.582850 −0.291425 0.956594i \(-0.594129\pi\)
−0.291425 + 0.956594i \(0.594129\pi\)
\(24\) 2.05712e29 0.435230
\(25\) −3.55242e29 −0.312474
\(26\) 5.33051e29 0.201763
\(27\) 1.14456e30 0.192450
\(28\) −1.08126e31 −0.831822
\(29\) −3.00258e31 −1.08627 −0.543135 0.839646i \(-0.682763\pi\)
−0.543135 + 0.839646i \(0.682763\pi\)
\(30\) 1.12961e31 0.197161
\(31\) 1.83651e32 1.58386 0.791931 0.610611i \(-0.209076\pi\)
0.791931 + 0.610611i \(0.209076\pi\)
\(32\) −2.22118e32 −0.967965
\(33\) 1.53056e31 0.0344192
\(34\) −4.29639e32 −0.508519
\(35\) −1.30876e33 −0.830612
\(36\) −7.99208e32 −0.276794
\(37\) −9.66835e33 −1.85787 −0.928935 0.370243i \(-0.879274\pi\)
−0.928935 + 0.370243i \(0.879274\pi\)
\(38\) 1.83236e33 0.198456
\(39\) −4.56491e33 −0.282841
\(40\) −1.73866e34 −0.625063
\(41\) −5.73635e34 −1.21278 −0.606391 0.795167i \(-0.707383\pi\)
−0.606391 + 0.795167i \(0.707383\pi\)
\(42\) −1.89143e34 −0.238194
\(43\) −1.24932e35 −0.948638 −0.474319 0.880353i \(-0.657306\pi\)
−0.474319 + 0.880353i \(0.657306\pi\)
\(44\) −1.06874e34 −0.0495038
\(45\) −9.67370e34 −0.276391
\(46\) 1.34768e35 0.240046
\(47\) −6.52473e35 −0.731912 −0.365956 0.930632i \(-0.619258\pi\)
−0.365956 + 0.930632i \(0.619258\pi\)
\(48\) 4.20781e35 0.300172
\(49\) 7.59027e33 0.00347569
\(50\) 4.33917e35 0.128692
\(51\) 3.67932e36 0.712868
\(52\) 3.18752e36 0.406800
\(53\) 2.03194e37 1.72179 0.860895 0.508783i \(-0.169904\pi\)
0.860895 + 0.508783i \(0.169904\pi\)
\(54\) −1.39805e36 −0.0792603
\(55\) −1.29361e36 −0.0494317
\(56\) 2.91122e37 0.755149
\(57\) −1.56919e37 −0.278205
\(58\) 3.66756e37 0.447379
\(59\) −7.05565e37 −0.595963 −0.297981 0.954572i \(-0.596313\pi\)
−0.297981 + 0.954572i \(0.596313\pi\)
\(60\) 6.75481e37 0.397522
\(61\) −4.16411e38 −1.71763 −0.858816 0.512284i \(-0.828800\pi\)
−0.858816 + 0.512284i \(0.828800\pi\)
\(62\) −2.24324e38 −0.652311
\(63\) 1.61977e38 0.333912
\(64\) −8.25234e37 −0.121257
\(65\) 3.85821e38 0.406208
\(66\) −1.86953e37 −0.0141755
\(67\) −1.46698e39 −0.805038 −0.402519 0.915412i \(-0.631865\pi\)
−0.402519 + 0.915412i \(0.631865\pi\)
\(68\) −2.56914e39 −1.02529
\(69\) −1.15412e39 −0.336509
\(70\) 1.59861e39 0.342086
\(71\) 6.58697e39 1.03904 0.519519 0.854459i \(-0.326111\pi\)
0.519519 + 0.854459i \(0.326111\pi\)
\(72\) 2.15182e39 0.251280
\(73\) 8.76849e39 0.761173 0.380587 0.924745i \(-0.375722\pi\)
0.380587 + 0.924745i \(0.375722\pi\)
\(74\) 1.18096e40 0.765161
\(75\) −3.71595e39 −0.180407
\(76\) 1.09571e40 0.400132
\(77\) 2.16603e39 0.0597193
\(78\) 5.57590e39 0.116488
\(79\) −3.63007e39 −0.0576676 −0.0288338 0.999584i \(-0.509179\pi\)
−0.0288338 + 0.999584i \(0.509179\pi\)
\(80\) −3.55639e40 −0.431097
\(81\) 1.19725e40 0.111111
\(82\) 7.00677e40 0.499482
\(83\) −2.43814e41 −1.33930 −0.669652 0.742675i \(-0.733557\pi\)
−0.669652 + 0.742675i \(0.733557\pi\)
\(84\) −1.13103e41 −0.480253
\(85\) −3.10972e41 −1.02380
\(86\) 1.52600e41 0.390695
\(87\) −3.14080e41 −0.627158
\(88\) 2.87752e40 0.0449407
\(89\) 6.12259e41 0.749981 0.374991 0.927029i \(-0.377646\pi\)
0.374991 + 0.927029i \(0.377646\pi\)
\(90\) 1.18161e41 0.113831
\(91\) −6.46022e41 −0.490746
\(92\) 8.05884e41 0.483988
\(93\) 1.92106e42 0.914443
\(94\) 7.96976e41 0.301437
\(95\) 1.32626e42 0.399549
\(96\) −2.32344e42 −0.558855
\(97\) 8.54423e41 0.164468 0.0822338 0.996613i \(-0.473795\pi\)
0.0822338 + 0.996613i \(0.473795\pi\)
\(98\) −9.27128e39 −0.00143146
\(99\) 1.60102e41 0.0198719
\(100\) 2.59472e42 0.259472
\(101\) 1.68908e43 1.36377 0.681885 0.731459i \(-0.261160\pi\)
0.681885 + 0.731459i \(0.261160\pi\)
\(102\) −4.49418e42 −0.293594
\(103\) −2.32882e43 −1.23349 −0.616744 0.787164i \(-0.711549\pi\)
−0.616744 + 0.787164i \(0.711549\pi\)
\(104\) −8.58222e42 −0.369303
\(105\) −1.36901e43 −0.479554
\(106\) −2.48196e43 −0.709117
\(107\) 2.29289e43 0.535343 0.267671 0.963510i \(-0.413746\pi\)
0.267671 + 0.963510i \(0.413746\pi\)
\(108\) −8.36000e42 −0.159807
\(109\) −4.44751e43 −0.697344 −0.348672 0.937245i \(-0.613367\pi\)
−0.348672 + 0.937245i \(0.613367\pi\)
\(110\) 1.58011e42 0.0203584
\(111\) −1.01134e44 −1.07264
\(112\) 5.95486e43 0.520815
\(113\) 1.44503e44 1.04397 0.521987 0.852954i \(-0.325191\pi\)
0.521987 + 0.852954i \(0.325191\pi\)
\(114\) 1.91671e43 0.114578
\(115\) 9.75450e43 0.483283
\(116\) 2.19312e44 0.902017
\(117\) −4.77506e43 −0.163299
\(118\) 8.61827e43 0.245446
\(119\) 5.20694e44 1.23687
\(120\) −1.81870e44 −0.360880
\(121\) −6.00260e44 −0.996446
\(122\) 5.08633e44 0.707405
\(123\) −6.00042e44 −0.700200
\(124\) −1.34141e45 −1.31521
\(125\) 1.31917e45 1.08827
\(126\) −1.97850e44 −0.137521
\(127\) −1.35712e45 −0.795860 −0.397930 0.917416i \(-0.630271\pi\)
−0.397930 + 0.917416i \(0.630271\pi\)
\(128\) 2.05457e45 1.01790
\(129\) −1.30683e45 −0.547696
\(130\) −4.71268e44 −0.167296
\(131\) −4.22352e45 −1.27157 −0.635787 0.771864i \(-0.719324\pi\)
−0.635787 + 0.771864i \(0.719324\pi\)
\(132\) −1.11794e44 −0.0285810
\(133\) −2.22070e45 −0.482702
\(134\) 1.79187e45 0.331554
\(135\) −1.01190e45 −0.159574
\(136\) 6.91728e45 0.930784
\(137\) 1.16008e46 1.33350 0.666751 0.745280i \(-0.267684\pi\)
0.666751 + 0.745280i \(0.267684\pi\)
\(138\) 1.40973e45 0.138591
\(139\) −3.54561e45 −0.298451 −0.149225 0.988803i \(-0.547678\pi\)
−0.149225 + 0.988803i \(0.547678\pi\)
\(140\) 9.55934e45 0.689724
\(141\) −6.82510e45 −0.422569
\(142\) −8.04579e45 −0.427926
\(143\) −6.38542e44 −0.0292055
\(144\) 4.40152e45 0.173304
\(145\) 2.65457e46 0.900704
\(146\) −1.07104e46 −0.313488
\(147\) 7.93969e43 0.00200669
\(148\) 7.06186e46 1.54274
\(149\) −7.81974e46 −1.47804 −0.739022 0.673681i \(-0.764712\pi\)
−0.739022 + 0.673681i \(0.764712\pi\)
\(150\) 4.53892e45 0.0743003
\(151\) −1.13420e47 −1.60947 −0.804736 0.593633i \(-0.797693\pi\)
−0.804736 + 0.593633i \(0.797693\pi\)
\(152\) −2.95014e46 −0.363249
\(153\) 3.84870e46 0.411574
\(154\) −2.64574e45 −0.0245953
\(155\) −1.62365e47 −1.31329
\(156\) 3.33426e46 0.234866
\(157\) −6.59354e46 −0.404833 −0.202417 0.979300i \(-0.564879\pi\)
−0.202417 + 0.979300i \(0.564879\pi\)
\(158\) 4.43402e45 0.0237503
\(159\) 2.12548e47 0.994076
\(160\) 1.96374e47 0.802610
\(161\) −1.63330e47 −0.583862
\(162\) −1.46241e46 −0.0457610
\(163\) 3.98621e47 1.09276 0.546382 0.837536i \(-0.316005\pi\)
0.546382 + 0.837536i \(0.316005\pi\)
\(164\) 4.18989e47 1.00707
\(165\) −1.35316e46 −0.0285394
\(166\) 2.97811e47 0.551590
\(167\) −5.79083e47 −0.942619 −0.471310 0.881968i \(-0.656219\pi\)
−0.471310 + 0.881968i \(0.656219\pi\)
\(168\) 3.04524e47 0.435985
\(169\) −6.03086e47 −0.760002
\(170\) 3.79843e47 0.421650
\(171\) −1.64142e47 −0.160622
\(172\) 9.12513e47 0.787730
\(173\) −2.23477e48 −1.70311 −0.851554 0.524267i \(-0.824340\pi\)
−0.851554 + 0.524267i \(0.824340\pi\)
\(174\) 3.83640e47 0.258294
\(175\) −5.25878e47 −0.313016
\(176\) 5.88591e46 0.0309950
\(177\) −7.38046e47 −0.344079
\(178\) −7.47856e47 −0.308879
\(179\) 1.61027e47 0.0589603 0.0294801 0.999565i \(-0.490615\pi\)
0.0294801 + 0.999565i \(0.490615\pi\)
\(180\) 7.06577e47 0.229509
\(181\) −7.92049e47 −0.228383 −0.114191 0.993459i \(-0.536428\pi\)
−0.114191 + 0.993459i \(0.536428\pi\)
\(182\) 7.89096e47 0.202113
\(183\) −4.35580e48 −0.991676
\(184\) −2.16980e48 −0.439376
\(185\) 8.54775e48 1.54049
\(186\) −2.34651e48 −0.376612
\(187\) 5.14666e47 0.0736090
\(188\) 4.76573e48 0.607765
\(189\) 1.69434e48 0.192784
\(190\) −1.61998e48 −0.164554
\(191\) 9.55527e48 0.867013 0.433507 0.901150i \(-0.357276\pi\)
0.433507 + 0.901150i \(0.357276\pi\)
\(192\) −8.63224e47 −0.0700079
\(193\) 2.03467e48 0.147574 0.0737872 0.997274i \(-0.476491\pi\)
0.0737872 + 0.997274i \(0.476491\pi\)
\(194\) −1.04365e48 −0.0677358
\(195\) 4.03582e48 0.234524
\(196\) −5.54401e46 −0.00288615
\(197\) 2.76148e49 1.28860 0.644300 0.764773i \(-0.277149\pi\)
0.644300 + 0.764773i \(0.277149\pi\)
\(198\) −1.95560e47 −0.00818422
\(199\) −3.48688e49 −1.30947 −0.654735 0.755858i \(-0.727220\pi\)
−0.654735 + 0.755858i \(0.727220\pi\)
\(200\) −6.98615e48 −0.235555
\(201\) −1.53451e49 −0.464789
\(202\) −2.06316e49 −0.561667
\(203\) −4.44484e49 −1.08816
\(204\) −2.68742e49 −0.591952
\(205\) 5.07148e49 1.00560
\(206\) 2.84458e49 0.508011
\(207\) −1.20725e49 −0.194283
\(208\) −1.75548e49 −0.254703
\(209\) −2.19499e48 −0.0287268
\(210\) 1.67221e49 0.197504
\(211\) 1.86123e49 0.198484 0.0992422 0.995063i \(-0.468358\pi\)
0.0992422 + 0.995063i \(0.468358\pi\)
\(212\) −1.48415e50 −1.42974
\(213\) 6.89021e49 0.599889
\(214\) −2.80069e49 −0.220480
\(215\) 1.10452e50 0.786584
\(216\) 2.25088e49 0.145077
\(217\) 2.71866e50 1.58661
\(218\) 5.43249e49 0.287200
\(219\) 9.17215e49 0.439463
\(220\) 9.44867e48 0.0410471
\(221\) −1.53500e50 −0.604886
\(222\) 1.23533e50 0.441766
\(223\) 2.85176e50 0.925889 0.462945 0.886387i \(-0.346793\pi\)
0.462945 + 0.886387i \(0.346793\pi\)
\(224\) −3.28810e50 −0.969646
\(225\) −3.88702e49 −0.104158
\(226\) −1.76506e50 −0.429959
\(227\) −6.18346e50 −1.36986 −0.684929 0.728609i \(-0.740167\pi\)
−0.684929 + 0.728609i \(0.740167\pi\)
\(228\) 1.14615e50 0.231016
\(229\) −3.54720e50 −0.650762 −0.325381 0.945583i \(-0.605493\pi\)
−0.325381 + 0.945583i \(0.605493\pi\)
\(230\) −1.19148e50 −0.199040
\(231\) 2.26575e49 0.0344789
\(232\) −5.90484e50 −0.818873
\(233\) 8.36113e50 1.05709 0.528546 0.848905i \(-0.322738\pi\)
0.528546 + 0.848905i \(0.322738\pi\)
\(234\) 5.83258e49 0.0672543
\(235\) 5.76849e50 0.606881
\(236\) 5.15352e50 0.494876
\(237\) −3.79718e49 −0.0332944
\(238\) −6.36012e50 −0.509402
\(239\) −1.78108e51 −1.30355 −0.651775 0.758412i \(-0.725976\pi\)
−0.651775 + 0.758412i \(0.725976\pi\)
\(240\) −3.72011e50 −0.248894
\(241\) −2.31617e50 −0.141711 −0.0708557 0.997487i \(-0.522573\pi\)
−0.0708557 + 0.997487i \(0.522573\pi\)
\(242\) 7.33199e50 0.410385
\(243\) 1.25237e50 0.0641500
\(244\) 3.04151e51 1.42629
\(245\) −6.71053e48 −0.00288195
\(246\) 7.32933e50 0.288376
\(247\) 6.54657e50 0.236064
\(248\) 3.61166e51 1.19398
\(249\) −2.55038e51 −0.773247
\(250\) −1.61133e51 −0.448201
\(251\) 3.21256e51 0.820100 0.410050 0.912063i \(-0.365511\pi\)
0.410050 + 0.912063i \(0.365511\pi\)
\(252\) −1.18310e51 −0.277274
\(253\) −1.61439e50 −0.0347471
\(254\) 1.65767e51 0.327774
\(255\) −3.25288e51 −0.591090
\(256\) −1.78371e51 −0.297966
\(257\) 6.07157e51 0.932693 0.466347 0.884602i \(-0.345570\pi\)
0.466347 + 0.884602i \(0.345570\pi\)
\(258\) 1.59625e51 0.225568
\(259\) −1.43124e52 −1.86110
\(260\) −2.81807e51 −0.337307
\(261\) −3.28539e51 −0.362090
\(262\) 5.15890e51 0.523696
\(263\) −6.37529e51 −0.596281 −0.298141 0.954522i \(-0.596366\pi\)
−0.298141 + 0.954522i \(0.596366\pi\)
\(264\) 3.00998e50 0.0259465
\(265\) −1.79643e52 −1.42766
\(266\) 2.71251e51 0.198800
\(267\) 6.40445e51 0.433002
\(268\) 1.07150e52 0.668488
\(269\) −1.13773e52 −0.655186 −0.327593 0.944819i \(-0.606237\pi\)
−0.327593 + 0.944819i \(0.606237\pi\)
\(270\) 1.23601e51 0.0657204
\(271\) 3.06013e52 1.50280 0.751399 0.659848i \(-0.229379\pi\)
0.751399 + 0.659848i \(0.229379\pi\)
\(272\) 1.41492e52 0.641948
\(273\) −6.75761e51 −0.283333
\(274\) −1.41700e52 −0.549201
\(275\) −5.19790e50 −0.0186284
\(276\) 8.42983e51 0.279430
\(277\) 3.79780e52 1.16471 0.582354 0.812936i \(-0.302132\pi\)
0.582354 + 0.812936i \(0.302132\pi\)
\(278\) 4.33085e51 0.122917
\(279\) 2.00949e52 0.527954
\(280\) −2.57380e52 −0.626148
\(281\) 1.86684e51 0.0420651 0.0210325 0.999779i \(-0.493305\pi\)
0.0210325 + 0.999779i \(0.493305\pi\)
\(282\) 8.33665e51 0.174035
\(283\) 2.48229e52 0.480224 0.240112 0.970745i \(-0.422816\pi\)
0.240112 + 0.970745i \(0.422816\pi\)
\(284\) −4.81119e52 −0.862797
\(285\) 1.38731e52 0.230680
\(286\) 7.79960e50 0.0120282
\(287\) −8.49174e52 −1.21489
\(288\) −2.43040e52 −0.322655
\(289\) 4.25680e52 0.524541
\(290\) −3.24248e52 −0.370954
\(291\) 8.93756e51 0.0949555
\(292\) −6.40460e52 −0.632063
\(293\) −2.43606e52 −0.223374 −0.111687 0.993743i \(-0.535625\pi\)
−0.111687 + 0.993743i \(0.535625\pi\)
\(294\) −9.69809e49 −0.000826454 0
\(295\) 6.23788e52 0.494156
\(296\) −1.90137e53 −1.40054
\(297\) 1.67472e51 0.0114731
\(298\) 9.55157e52 0.608731
\(299\) 4.81494e52 0.285536
\(300\) 2.71417e52 0.149806
\(301\) −1.84941e53 −0.950285
\(302\) 1.38538e53 0.662859
\(303\) 1.76684e53 0.787373
\(304\) −6.03445e52 −0.250528
\(305\) 3.68147e53 1.42421
\(306\) −4.70107e52 −0.169506
\(307\) −2.77366e51 −0.00932348 −0.00466174 0.999989i \(-0.501484\pi\)
−0.00466174 + 0.999989i \(0.501484\pi\)
\(308\) −1.58209e52 −0.0495897
\(309\) −2.43602e53 −0.712155
\(310\) 1.98324e53 0.540878
\(311\) 4.97151e53 1.26514 0.632572 0.774501i \(-0.281999\pi\)
0.632572 + 0.774501i \(0.281999\pi\)
\(312\) −8.97730e52 −0.213217
\(313\) −4.32278e53 −0.958429 −0.479215 0.877698i \(-0.659078\pi\)
−0.479215 + 0.877698i \(0.659078\pi\)
\(314\) 8.05381e52 0.166730
\(315\) −1.43204e53 −0.276871
\(316\) 2.65144e52 0.0478861
\(317\) 2.29417e53 0.387125 0.193563 0.981088i \(-0.437996\pi\)
0.193563 + 0.981088i \(0.437996\pi\)
\(318\) −2.59621e53 −0.409409
\(319\) −4.39337e52 −0.0647588
\(320\) 7.29587e52 0.100543
\(321\) 2.39844e53 0.309080
\(322\) 1.99503e53 0.240463
\(323\) −5.27654e53 −0.594970
\(324\) −8.74485e52 −0.0922645
\(325\) 1.55028e53 0.153080
\(326\) −4.86903e53 −0.450053
\(327\) −4.65225e53 −0.402612
\(328\) −1.12810e54 −0.914243
\(329\) −9.65882e53 −0.733183
\(330\) 1.65285e52 0.0117539
\(331\) −1.97700e54 −1.31736 −0.658681 0.752422i \(-0.728885\pi\)
−0.658681 + 0.752422i \(0.728885\pi\)
\(332\) 1.78084e54 1.11213
\(333\) −1.05790e54 −0.619290
\(334\) 7.07332e53 0.388217
\(335\) 1.29695e54 0.667515
\(336\) 6.22899e53 0.300693
\(337\) 3.64300e54 1.64974 0.824872 0.565319i \(-0.191247\pi\)
0.824872 + 0.565319i \(0.191247\pi\)
\(338\) 7.36651e53 0.313006
\(339\) 1.51155e54 0.602738
\(340\) 2.27137e54 0.850142
\(341\) 2.68718e53 0.0944231
\(342\) 2.00495e53 0.0661519
\(343\) −3.22155e54 −0.998255
\(344\) −2.45689e54 −0.715121
\(345\) 1.02036e54 0.279024
\(346\) 2.72971e54 0.701423
\(347\) −4.88799e54 −1.18045 −0.590224 0.807240i \(-0.700961\pi\)
−0.590224 + 0.807240i \(0.700961\pi\)
\(348\) 2.29408e54 0.520780
\(349\) 2.09870e54 0.447923 0.223962 0.974598i \(-0.428101\pi\)
0.223962 + 0.974598i \(0.428101\pi\)
\(350\) 6.42344e53 0.128915
\(351\) −4.99488e53 −0.0942805
\(352\) −3.25004e53 −0.0577060
\(353\) −4.91912e54 −0.821734 −0.410867 0.911695i \(-0.634774\pi\)
−0.410867 + 0.911695i \(0.634774\pi\)
\(354\) 9.01501e53 0.141709
\(355\) −5.82352e54 −0.861541
\(356\) −4.47201e54 −0.622770
\(357\) 5.44664e54 0.714106
\(358\) −1.96690e53 −0.0242827
\(359\) −8.13508e53 −0.0945869 −0.0472935 0.998881i \(-0.515060\pi\)
−0.0472935 + 0.998881i \(0.515060\pi\)
\(360\) −1.90242e54 −0.208354
\(361\) −7.44143e54 −0.767806
\(362\) 9.67464e53 0.0940591
\(363\) −6.27893e54 −0.575298
\(364\) 4.71861e54 0.407506
\(365\) −7.75219e54 −0.631143
\(366\) 5.32048e54 0.408420
\(367\) 1.94351e55 1.40691 0.703455 0.710740i \(-0.251640\pi\)
0.703455 + 0.710740i \(0.251640\pi\)
\(368\) −4.43829e54 −0.303031
\(369\) −6.27665e54 −0.404260
\(370\) −1.04408e55 −0.634450
\(371\) 3.00796e55 1.72478
\(372\) −1.40316e55 −0.759335
\(373\) 2.61183e55 1.33415 0.667075 0.744991i \(-0.267546\pi\)
0.667075 + 0.744991i \(0.267546\pi\)
\(374\) −6.28648e53 −0.0303158
\(375\) 1.37990e55 0.628311
\(376\) −1.28315e55 −0.551744
\(377\) 1.31033e55 0.532159
\(378\) −2.06958e54 −0.0793980
\(379\) −1.70034e55 −0.616302 −0.308151 0.951337i \(-0.599710\pi\)
−0.308151 + 0.951337i \(0.599710\pi\)
\(380\) −9.68712e54 −0.331778
\(381\) −1.41959e55 −0.459490
\(382\) −1.16715e55 −0.357078
\(383\) 6.50840e55 1.88235 0.941175 0.337919i \(-0.109723\pi\)
0.941175 + 0.337919i \(0.109723\pi\)
\(384\) 2.14916e55 0.587688
\(385\) −1.91498e54 −0.0495175
\(386\) −2.48528e54 −0.0607783
\(387\) −1.36699e55 −0.316213
\(388\) −6.24079e54 −0.136571
\(389\) −3.77716e55 −0.782075 −0.391038 0.920375i \(-0.627884\pi\)
−0.391038 + 0.920375i \(0.627884\pi\)
\(390\) −4.92963e54 −0.0965885
\(391\) −3.88085e55 −0.719659
\(392\) 1.49269e53 0.00262012
\(393\) −4.41795e55 −0.734144
\(394\) −3.37306e55 −0.530708
\(395\) 3.20933e54 0.0478164
\(396\) −1.16940e54 −0.0165013
\(397\) 1.25028e55 0.167114 0.0835569 0.996503i \(-0.473372\pi\)
0.0835569 + 0.996503i \(0.473372\pi\)
\(398\) 4.25912e55 0.539304
\(399\) −2.32293e55 −0.278688
\(400\) −1.42901e55 −0.162459
\(401\) 1.06687e56 1.14949 0.574746 0.818332i \(-0.305101\pi\)
0.574746 + 0.818332i \(0.305101\pi\)
\(402\) 1.87436e55 0.191423
\(403\) −8.01455e55 −0.775927
\(404\) −1.23372e56 −1.13245
\(405\) −1.05849e55 −0.0921302
\(406\) 5.42923e55 0.448155
\(407\) −1.41467e55 −0.110758
\(408\) 7.23572e55 0.537388
\(409\) 1.13698e56 0.801124 0.400562 0.916270i \(-0.368815\pi\)
0.400562 + 0.916270i \(0.368815\pi\)
\(410\) −6.19466e55 −0.414157
\(411\) 1.21348e56 0.769898
\(412\) 1.70099e56 1.02426
\(413\) −1.04448e56 −0.596997
\(414\) 1.47462e55 0.0800154
\(415\) 2.15555e56 1.11051
\(416\) 9.69326e55 0.474202
\(417\) −3.70883e55 −0.172311
\(418\) 2.68111e54 0.0118311
\(419\) −2.17540e56 −0.911881 −0.455940 0.890010i \(-0.650697\pi\)
−0.455940 + 0.890010i \(0.650697\pi\)
\(420\) 9.99941e55 0.398212
\(421\) −1.38105e56 −0.522572 −0.261286 0.965261i \(-0.584147\pi\)
−0.261286 + 0.965261i \(0.584147\pi\)
\(422\) −2.27343e55 −0.0817456
\(423\) −7.13930e55 −0.243971
\(424\) 3.99600e56 1.29795
\(425\) −1.24953e56 −0.385819
\(426\) −8.41618e55 −0.247063
\(427\) −6.16429e56 −1.72062
\(428\) −1.67475e56 −0.444538
\(429\) −6.67938e54 −0.0168618
\(430\) −1.34913e56 −0.323954
\(431\) −1.40065e56 −0.319940 −0.159970 0.987122i \(-0.551140\pi\)
−0.159970 + 0.987122i \(0.551140\pi\)
\(432\) 4.60415e55 0.100057
\(433\) −3.59607e56 −0.743599 −0.371800 0.928313i \(-0.621259\pi\)
−0.371800 + 0.928313i \(0.621259\pi\)
\(434\) −3.32076e56 −0.653444
\(435\) 2.77677e56 0.520022
\(436\) 3.24851e56 0.579061
\(437\) 1.65514e56 0.280855
\(438\) −1.12035e56 −0.180992
\(439\) 2.54990e56 0.392225 0.196112 0.980581i \(-0.437168\pi\)
0.196112 + 0.980581i \(0.437168\pi\)
\(440\) −2.54400e55 −0.0372636
\(441\) 8.30520e53 0.00115856
\(442\) 1.87495e56 0.249121
\(443\) 1.35904e57 1.72010 0.860049 0.510211i \(-0.170433\pi\)
0.860049 + 0.510211i \(0.170433\pi\)
\(444\) 7.38696e56 0.890701
\(445\) −5.41296e56 −0.621863
\(446\) −3.48334e56 −0.381326
\(447\) −8.17972e56 −0.853349
\(448\) −1.22163e56 −0.121468
\(449\) 1.61899e57 1.53443 0.767216 0.641388i \(-0.221641\pi\)
0.767216 + 0.641388i \(0.221641\pi\)
\(450\) 4.74787e55 0.0428973
\(451\) −8.39342e55 −0.0723009
\(452\) −1.05546e57 −0.866895
\(453\) −1.18641e57 −0.929229
\(454\) 7.55291e56 0.564175
\(455\) 5.71145e56 0.406913
\(456\) −3.08595e56 −0.209722
\(457\) 9.28707e56 0.602116 0.301058 0.953606i \(-0.402660\pi\)
0.301058 + 0.953606i \(0.402660\pi\)
\(458\) 4.33279e56 0.268016
\(459\) 4.02588e56 0.237623
\(460\) −7.12479e56 −0.401309
\(461\) 2.44925e57 1.31663 0.658313 0.752744i \(-0.271270\pi\)
0.658313 + 0.752744i \(0.271270\pi\)
\(462\) −2.76754e55 −0.0142001
\(463\) −1.26241e57 −0.618315 −0.309157 0.951011i \(-0.600047\pi\)
−0.309157 + 0.951011i \(0.600047\pi\)
\(464\) −1.20783e57 −0.564765
\(465\) −1.69840e57 −0.758230
\(466\) −1.02129e57 −0.435362
\(467\) 2.72382e56 0.110883 0.0554415 0.998462i \(-0.482343\pi\)
0.0554415 + 0.998462i \(0.482343\pi\)
\(468\) 3.48775e56 0.135600
\(469\) −2.17163e57 −0.806436
\(470\) −7.04604e56 −0.249943
\(471\) −6.89707e56 −0.233730
\(472\) −1.38756e57 −0.449260
\(473\) −1.82800e56 −0.0565537
\(474\) 4.63814e55 0.0137123
\(475\) 5.32908e56 0.150570
\(476\) −3.80320e57 −1.02707
\(477\) 2.22333e57 0.573930
\(478\) 2.17553e57 0.536866
\(479\) 6.71590e56 0.158449 0.0792247 0.996857i \(-0.474756\pi\)
0.0792247 + 0.996857i \(0.474756\pi\)
\(480\) 2.05414e57 0.463387
\(481\) 4.21928e57 0.910162
\(482\) 2.82913e56 0.0583636
\(483\) −1.70849e57 −0.337093
\(484\) 4.38436e57 0.827429
\(485\) −7.55392e56 −0.136372
\(486\) −1.52973e56 −0.0264201
\(487\) 6.52355e56 0.107798 0.0538991 0.998546i \(-0.482835\pi\)
0.0538991 + 0.998546i \(0.482835\pi\)
\(488\) −8.18909e57 −1.29482
\(489\) 4.16971e57 0.630907
\(490\) 8.19671e54 0.00118693
\(491\) 9.15403e57 1.26870 0.634352 0.773045i \(-0.281267\pi\)
0.634352 + 0.773045i \(0.281267\pi\)
\(492\) 4.38277e57 0.581432
\(493\) −1.05613e58 −1.34124
\(494\) −7.99644e56 −0.0972226
\(495\) −1.41546e56 −0.0164772
\(496\) 7.38760e57 0.823469
\(497\) 9.75096e57 1.04084
\(498\) 3.11521e57 0.318461
\(499\) 8.05141e57 0.788334 0.394167 0.919039i \(-0.371033\pi\)
0.394167 + 0.919039i \(0.371033\pi\)
\(500\) −9.63535e57 −0.903675
\(501\) −6.05741e57 −0.544221
\(502\) −3.92405e57 −0.337757
\(503\) −1.27336e58 −1.05012 −0.525059 0.851066i \(-0.675957\pi\)
−0.525059 + 0.851066i \(0.675957\pi\)
\(504\) 3.18543e57 0.251716
\(505\) −1.49331e58 −1.13080
\(506\) 1.97193e56 0.0143105
\(507\) −6.30849e57 −0.438787
\(508\) 9.91251e57 0.660867
\(509\) −2.89502e58 −1.85021 −0.925103 0.379717i \(-0.876021\pi\)
−0.925103 + 0.379717i \(0.876021\pi\)
\(510\) 3.97329e57 0.243440
\(511\) 1.29803e58 0.762495
\(512\) −1.58935e58 −0.895188
\(513\) −1.71699e57 −0.0927350
\(514\) −7.41624e57 −0.384128
\(515\) 2.05890e58 1.02277
\(516\) 9.54521e57 0.454796
\(517\) −9.54699e56 −0.0436335
\(518\) 1.74822e58 0.766490
\(519\) −2.33765e58 −0.983290
\(520\) 7.58751e57 0.306216
\(521\) −4.03859e57 −0.156393 −0.0781967 0.996938i \(-0.524916\pi\)
−0.0781967 + 0.996938i \(0.524916\pi\)
\(522\) 4.01301e57 0.149126
\(523\) −1.88422e58 −0.671963 −0.335981 0.941869i \(-0.609068\pi\)
−0.335981 + 0.941869i \(0.609068\pi\)
\(524\) 3.08490e58 1.05589
\(525\) −5.50087e57 −0.180720
\(526\) 7.78722e57 0.245578
\(527\) 6.45974e58 1.95563
\(528\) 6.15687e56 0.0178950
\(529\) −2.36608e58 −0.660286
\(530\) 2.19429e58 0.587980
\(531\) −7.72023e57 −0.198654
\(532\) 1.62202e58 0.400826
\(533\) 2.50335e58 0.594136
\(534\) −7.82284e57 −0.178331
\(535\) −2.02714e58 −0.443891
\(536\) −2.88495e58 −0.606870
\(537\) 1.68440e57 0.0340407
\(538\) 1.38970e58 0.269837
\(539\) 1.11061e55 0.000207206 0
\(540\) 7.39104e57 0.132507
\(541\) −2.61000e58 −0.449675 −0.224838 0.974396i \(-0.572185\pi\)
−0.224838 + 0.974396i \(0.572185\pi\)
\(542\) −3.73786e58 −0.618926
\(543\) −8.28512e57 −0.131857
\(544\) −7.81278e58 −1.19517
\(545\) 3.93202e58 0.578218
\(546\) 8.25422e57 0.116690
\(547\) 4.86896e58 0.661772 0.330886 0.943671i \(-0.392652\pi\)
0.330886 + 0.943671i \(0.392652\pi\)
\(548\) −8.47331e58 −1.10731
\(549\) −4.55632e58 −0.572544
\(550\) 6.34907e56 0.00767207
\(551\) 4.50425e58 0.523436
\(552\) −2.26969e58 −0.253674
\(553\) −5.37373e57 −0.0577678
\(554\) −4.63889e58 −0.479683
\(555\) 8.94125e58 0.889404
\(556\) 2.58975e58 0.247828
\(557\) 1.92712e58 0.177428 0.0887138 0.996057i \(-0.471724\pi\)
0.0887138 + 0.996057i \(0.471724\pi\)
\(558\) −2.45453e58 −0.217437
\(559\) 5.45203e58 0.464734
\(560\) −5.26467e58 −0.431845
\(561\) 5.38358e57 0.0424981
\(562\) −2.28029e57 −0.0173244
\(563\) −1.21276e59 −0.886841 −0.443420 0.896314i \(-0.646235\pi\)
−0.443420 + 0.896314i \(0.646235\pi\)
\(564\) 4.98513e58 0.350893
\(565\) −1.27754e59 −0.865633
\(566\) −3.03204e58 −0.197780
\(567\) 1.77234e58 0.111304
\(568\) 1.29539e59 0.783268
\(569\) 1.02783e59 0.598420 0.299210 0.954187i \(-0.403277\pi\)
0.299210 + 0.954187i \(0.403277\pi\)
\(570\) −1.69456e58 −0.0950052
\(571\) 2.10956e59 1.13898 0.569488 0.821999i \(-0.307141\pi\)
0.569488 + 0.821999i \(0.307141\pi\)
\(572\) 4.66398e57 0.0242517
\(573\) 9.99515e58 0.500570
\(574\) 1.03724e59 0.500350
\(575\) 3.91949e58 0.182125
\(576\) −9.02963e57 −0.0404191
\(577\) 2.50403e59 1.07984 0.539921 0.841716i \(-0.318454\pi\)
0.539921 + 0.841716i \(0.318454\pi\)
\(578\) −5.19955e58 −0.216032
\(579\) 2.12833e58 0.0852021
\(580\) −1.93893e59 −0.747927
\(581\) −3.60927e59 −1.34163
\(582\) −1.09170e58 −0.0391073
\(583\) 2.97314e58 0.102646
\(584\) 1.72440e59 0.573803
\(585\) 4.22161e58 0.135403
\(586\) 2.97557e58 0.0919965
\(587\) −1.76752e59 −0.526800 −0.263400 0.964687i \(-0.584844\pi\)
−0.263400 + 0.964687i \(0.584844\pi\)
\(588\) −5.79923e56 −0.00166632
\(589\) −2.75500e59 −0.763208
\(590\) −7.61938e58 −0.203517
\(591\) 2.88861e59 0.743973
\(592\) −3.88922e59 −0.965930
\(593\) −6.37698e59 −1.52735 −0.763676 0.645600i \(-0.776607\pi\)
−0.763676 + 0.645600i \(0.776607\pi\)
\(594\) −2.04562e57 −0.00472516
\(595\) −4.60344e59 −1.02558
\(596\) 5.71162e59 1.22734
\(597\) −3.64740e59 −0.756023
\(598\) −5.88131e58 −0.117598
\(599\) 5.75228e59 1.10959 0.554796 0.831986i \(-0.312796\pi\)
0.554796 + 0.831986i \(0.312796\pi\)
\(600\) −7.30776e58 −0.135998
\(601\) −3.64629e59 −0.654711 −0.327355 0.944901i \(-0.606157\pi\)
−0.327355 + 0.944901i \(0.606157\pi\)
\(602\) 2.25900e59 0.391374
\(603\) −1.60516e59 −0.268346
\(604\) 8.28428e59 1.33647
\(605\) 5.30688e59 0.826225
\(606\) −2.15814e59 −0.324279
\(607\) 5.14767e59 0.746542 0.373271 0.927722i \(-0.378236\pi\)
0.373271 + 0.927722i \(0.378236\pi\)
\(608\) 3.33206e59 0.466429
\(609\) −4.64946e59 −0.628247
\(610\) −4.49681e59 −0.586560
\(611\) 2.84740e59 0.358560
\(612\) −2.81113e59 −0.341763
\(613\) −1.37174e59 −0.161017 −0.0805083 0.996754i \(-0.525654\pi\)
−0.0805083 + 0.996754i \(0.525654\pi\)
\(614\) 3.38794e57 0.00383986
\(615\) 5.30495e59 0.580586
\(616\) 4.25970e58 0.0450188
\(617\) −7.62052e59 −0.777774 −0.388887 0.921285i \(-0.627140\pi\)
−0.388887 + 0.921285i \(0.627140\pi\)
\(618\) 2.97553e59 0.293300
\(619\) 1.72119e60 1.63862 0.819311 0.573349i \(-0.194356\pi\)
0.819311 + 0.573349i \(0.194356\pi\)
\(620\) 1.18593e60 1.09053
\(621\) −1.26283e59 −0.112170
\(622\) −6.07255e59 −0.521048
\(623\) 9.06352e59 0.751283
\(624\) −1.83629e59 −0.147053
\(625\) −7.62410e59 −0.589886
\(626\) 5.28015e59 0.394728
\(627\) −2.29603e58 −0.0165854
\(628\) 4.81599e59 0.336166
\(629\) −3.40074e60 −2.29395
\(630\) 1.74919e59 0.114029
\(631\) −2.19924e60 −1.38561 −0.692807 0.721123i \(-0.743626\pi\)
−0.692807 + 0.721123i \(0.743626\pi\)
\(632\) −7.13885e58 −0.0434722
\(633\) 1.94691e59 0.114595
\(634\) −2.80226e59 −0.159437
\(635\) 1.19982e60 0.659905
\(636\) −1.55248e60 −0.825461
\(637\) −3.31240e57 −0.00170273
\(638\) 5.36637e58 0.0266708
\(639\) 7.20740e59 0.346346
\(640\) −1.81644e60 −0.844018
\(641\) −3.07540e60 −1.38183 −0.690914 0.722937i \(-0.742791\pi\)
−0.690914 + 0.722937i \(0.742791\pi\)
\(642\) −2.92963e59 −0.127294
\(643\) 3.88562e60 1.63277 0.816385 0.577508i \(-0.195975\pi\)
0.816385 + 0.577508i \(0.195975\pi\)
\(644\) 1.19298e60 0.484828
\(645\) 1.15536e60 0.454134
\(646\) 6.44514e59 0.245038
\(647\) 3.66567e59 0.134807 0.0674034 0.997726i \(-0.478529\pi\)
0.0674034 + 0.997726i \(0.478529\pi\)
\(648\) 2.35450e59 0.0837600
\(649\) −1.03238e59 −0.0355288
\(650\) −1.89362e59 −0.0630456
\(651\) 2.84381e60 0.916030
\(652\) −2.91157e60 −0.907410
\(653\) −2.33400e60 −0.703829 −0.351915 0.936032i \(-0.614469\pi\)
−0.351915 + 0.936032i \(0.614469\pi\)
\(654\) 5.68258e59 0.165815
\(655\) 3.73400e60 1.05435
\(656\) −2.30752e60 −0.630540
\(657\) 9.59439e59 0.253724
\(658\) 1.17980e60 0.301960
\(659\) −3.08702e60 −0.764721 −0.382360 0.924013i \(-0.624889\pi\)
−0.382360 + 0.924013i \(0.624889\pi\)
\(660\) 9.88364e58 0.0236986
\(661\) 5.93115e60 1.37660 0.688300 0.725426i \(-0.258357\pi\)
0.688300 + 0.725426i \(0.258357\pi\)
\(662\) 2.41485e60 0.542554
\(663\) −1.60566e60 −0.349231
\(664\) −4.79482e60 −1.00962
\(665\) 1.96331e60 0.400243
\(666\) 1.29219e60 0.255054
\(667\) 3.31284e60 0.633132
\(668\) 4.22968e60 0.782733
\(669\) 2.98305e60 0.534562
\(670\) −1.58419e60 −0.274915
\(671\) −6.09292e59 −0.102398
\(672\) −3.43947e60 −0.559825
\(673\) −3.82992e60 −0.603763 −0.301881 0.953346i \(-0.597615\pi\)
−0.301881 + 0.953346i \(0.597615\pi\)
\(674\) −4.44982e60 −0.679445
\(675\) −4.06596e59 −0.0601356
\(676\) 4.40500e60 0.631091
\(677\) −3.89712e60 −0.540863 −0.270432 0.962739i \(-0.587166\pi\)
−0.270432 + 0.962739i \(0.587166\pi\)
\(678\) −1.84631e60 −0.248237
\(679\) 1.26484e60 0.164753
\(680\) −6.11554e60 −0.771780
\(681\) −6.46812e60 −0.790888
\(682\) −3.28231e59 −0.0388880
\(683\) 1.22609e61 1.40759 0.703797 0.710401i \(-0.251486\pi\)
0.703797 + 0.710401i \(0.251486\pi\)
\(684\) 1.19891e60 0.133377
\(685\) −1.02562e61 −1.10570
\(686\) 3.93503e60 0.411130
\(687\) −3.71049e60 −0.375718
\(688\) −5.02553e60 −0.493209
\(689\) −8.86742e60 −0.843498
\(690\) −1.24633e60 −0.114916
\(691\) −5.01752e60 −0.448447 −0.224223 0.974538i \(-0.571985\pi\)
−0.224223 + 0.974538i \(0.571985\pi\)
\(692\) 1.63230e61 1.41423
\(693\) 2.37005e59 0.0199064
\(694\) 5.97053e60 0.486166
\(695\) 3.13466e60 0.247467
\(696\) −6.17667e60 −0.472777
\(697\) −2.01770e61 −1.49745
\(698\) −2.56350e60 −0.184477
\(699\) 8.74603e60 0.610312
\(700\) 3.84107e60 0.259923
\(701\) 1.42916e61 0.937874 0.468937 0.883232i \(-0.344637\pi\)
0.468937 + 0.883232i \(0.344637\pi\)
\(702\) 6.10109e59 0.0388293
\(703\) 1.45038e61 0.895243
\(704\) −1.20748e59 −0.00722884
\(705\) 6.03405e60 0.350383
\(706\) 6.00855e60 0.338430
\(707\) 2.50041e61 1.36614
\(708\) 5.39077e60 0.285717
\(709\) 4.09729e59 0.0210670 0.0105335 0.999945i \(-0.496647\pi\)
0.0105335 + 0.999945i \(0.496647\pi\)
\(710\) 7.11325e60 0.354825
\(711\) −3.97198e59 −0.0192225
\(712\) 1.20406e61 0.565366
\(713\) −2.02628e61 −0.923154
\(714\) −6.65291e60 −0.294103
\(715\) 5.64533e59 0.0242164
\(716\) −1.17616e60 −0.0489595
\(717\) −1.86307e61 −0.752606
\(718\) 9.93675e59 0.0389555
\(719\) −2.67487e61 −1.01773 −0.508864 0.860847i \(-0.669934\pi\)
−0.508864 + 0.860847i \(0.669934\pi\)
\(720\) −3.89137e60 −0.143699
\(721\) −3.44744e61 −1.23563
\(722\) 9.08948e60 0.316220
\(723\) −2.42280e60 −0.0818171
\(724\) 5.78521e60 0.189644
\(725\) 1.06664e61 0.339431
\(726\) 7.66952e60 0.236936
\(727\) −2.69955e60 −0.0809659 −0.0404829 0.999180i \(-0.512890\pi\)
−0.0404829 + 0.999180i \(0.512890\pi\)
\(728\) −1.27046e61 −0.369944
\(729\) 1.31002e60 0.0370370
\(730\) 9.46907e60 0.259936
\(731\) −4.39434e61 −1.17130
\(732\) 3.18152e61 0.823468
\(733\) −2.80157e61 −0.704151 −0.352075 0.935972i \(-0.614524\pi\)
−0.352075 + 0.935972i \(0.614524\pi\)
\(734\) −2.37394e61 −0.579434
\(735\) −7.01945e58 −0.00166389
\(736\) 2.45070e61 0.564179
\(737\) −2.14649e60 −0.0479929
\(738\) 7.66674e60 0.166494
\(739\) 5.72171e61 1.20690 0.603449 0.797402i \(-0.293793\pi\)
0.603449 + 0.797402i \(0.293793\pi\)
\(740\) −6.24337e61 −1.27920
\(741\) 6.84794e60 0.136291
\(742\) −3.67414e61 −0.710348
\(743\) −2.53630e60 −0.0476366 −0.0238183 0.999716i \(-0.507582\pi\)
−0.0238183 + 0.999716i \(0.507582\pi\)
\(744\) 3.77793e61 0.689343
\(745\) 6.91340e61 1.22555
\(746\) −3.19027e61 −0.549468
\(747\) −2.66778e61 −0.446435
\(748\) −3.75917e60 −0.0611234
\(749\) 3.39425e61 0.536272
\(750\) −1.68550e61 −0.258769
\(751\) 6.37711e61 0.951405 0.475703 0.879606i \(-0.342194\pi\)
0.475703 + 0.879606i \(0.342194\pi\)
\(752\) −2.62466e61 −0.380530
\(753\) 3.36046e61 0.473485
\(754\) −1.60053e61 −0.219169
\(755\) 1.00274e62 1.33453
\(756\) −1.23756e61 −0.160084
\(757\) −2.56176e61 −0.322090 −0.161045 0.986947i \(-0.551486\pi\)
−0.161045 + 0.986947i \(0.551486\pi\)
\(758\) 2.07692e61 0.253823
\(759\) −1.68871e60 −0.0200612
\(760\) 2.60820e61 0.301196
\(761\) 1.22342e62 1.37342 0.686712 0.726929i \(-0.259053\pi\)
0.686712 + 0.726929i \(0.259053\pi\)
\(762\) 1.73399e61 0.189240
\(763\) −6.58382e61 −0.698554
\(764\) −6.97927e61 −0.719951
\(765\) −3.40262e61 −0.341266
\(766\) −7.94981e61 −0.775244
\(767\) 3.07909e61 0.291960
\(768\) −1.86583e61 −0.172031
\(769\) −5.11370e61 −0.458479 −0.229239 0.973370i \(-0.573624\pi\)
−0.229239 + 0.973370i \(0.573624\pi\)
\(770\) 2.33909e60 0.0203937
\(771\) 6.35108e61 0.538491
\(772\) −1.48614e61 −0.122543
\(773\) −1.07353e62 −0.860903 −0.430452 0.902614i \(-0.641646\pi\)
−0.430452 + 0.902614i \(0.641646\pi\)
\(774\) 1.66973e61 0.130232
\(775\) −6.52405e61 −0.494915
\(776\) 1.68030e61 0.123982
\(777\) −1.49713e62 −1.07450
\(778\) 4.61368e61 0.322097
\(779\) 8.60525e61 0.584397
\(780\) −2.94781e61 −0.194744
\(781\) 9.63806e60 0.0619430
\(782\) 4.74034e61 0.296391
\(783\) −3.43664e61 −0.209053
\(784\) 3.05328e59 0.00180706
\(785\) 5.82932e61 0.335676
\(786\) 5.39639e61 0.302356
\(787\) −1.80931e62 −0.986406 −0.493203 0.869914i \(-0.664174\pi\)
−0.493203 + 0.869914i \(0.664174\pi\)
\(788\) −2.01701e62 −1.07003
\(789\) −6.66878e61 −0.344263
\(790\) −3.92010e60 −0.0196931
\(791\) 2.13913e62 1.04579
\(792\) 3.14855e60 0.0149802
\(793\) 1.81722e62 0.841461
\(794\) −1.52718e61 −0.0688256
\(795\) −1.87913e62 −0.824260
\(796\) 2.54685e62 1.08736
\(797\) 8.36111e61 0.347464 0.173732 0.984793i \(-0.444417\pi\)
0.173732 + 0.984793i \(0.444417\pi\)
\(798\) 2.83739e61 0.114777
\(799\) −2.29501e62 −0.903708
\(800\) 7.89057e61 0.302464
\(801\) 6.69928e61 0.249994
\(802\) −1.30314e62 −0.473417
\(803\) 1.28301e61 0.0453779
\(804\) 1.12083e62 0.385952
\(805\) 1.44400e62 0.484122
\(806\) 9.78953e61 0.319564
\(807\) −1.19010e62 −0.378272
\(808\) 3.32173e62 1.02806
\(809\) 1.30597e62 0.393585 0.196793 0.980445i \(-0.436947\pi\)
0.196793 + 0.980445i \(0.436947\pi\)
\(810\) 1.29291e61 0.0379437
\(811\) −2.29199e61 −0.0655036 −0.0327518 0.999464i \(-0.510427\pi\)
−0.0327518 + 0.999464i \(0.510427\pi\)
\(812\) 3.24656e62 0.903583
\(813\) 3.20101e62 0.867641
\(814\) 1.72798e61 0.0456157
\(815\) −3.52419e62 −0.906089
\(816\) 1.48005e62 0.370629
\(817\) 1.87413e62 0.457116
\(818\) −1.38878e62 −0.329942
\(819\) −7.06870e61 −0.163582
\(820\) −3.70427e62 −0.835034
\(821\) −3.14859e62 −0.691414 −0.345707 0.938343i \(-0.612361\pi\)
−0.345707 + 0.938343i \(0.612361\pi\)
\(822\) −1.48223e62 −0.317082
\(823\) −8.04910e62 −1.67745 −0.838727 0.544552i \(-0.816700\pi\)
−0.838727 + 0.544552i \(0.816700\pi\)
\(824\) −4.57983e62 −0.929853
\(825\) −5.43718e60 −0.0107551
\(826\) 1.27580e62 0.245873
\(827\) −7.55224e62 −1.41810 −0.709050 0.705158i \(-0.750876\pi\)
−0.709050 + 0.705158i \(0.750876\pi\)
\(828\) 8.81790e61 0.161329
\(829\) 4.48039e62 0.798718 0.399359 0.916795i \(-0.369233\pi\)
0.399359 + 0.916795i \(0.369233\pi\)
\(830\) −2.63294e62 −0.457363
\(831\) 3.97263e62 0.672444
\(832\) 3.60133e61 0.0594034
\(833\) 2.66980e60 0.00429152
\(834\) 4.53023e61 0.0709659
\(835\) 5.11965e62 0.781593
\(836\) 1.60324e61 0.0238541
\(837\) 2.10200e62 0.304814
\(838\) 2.65719e62 0.375557
\(839\) −9.00857e62 −1.24100 −0.620502 0.784205i \(-0.713071\pi\)
−0.620502 + 0.784205i \(0.713071\pi\)
\(840\) −2.69229e62 −0.361507
\(841\) 1.37512e62 0.179981
\(842\) 1.68692e62 0.215220
\(843\) 1.95278e61 0.0242863
\(844\) −1.35946e62 −0.164818
\(845\) 5.33186e62 0.630172
\(846\) 8.72043e61 0.100479
\(847\) −8.88588e62 −0.998176
\(848\) 8.17375e62 0.895180
\(849\) 2.59656e62 0.277257
\(850\) 1.52626e62 0.158899
\(851\) 1.06674e63 1.08286
\(852\) −5.03268e62 −0.498136
\(853\) 3.94807e62 0.381048 0.190524 0.981682i \(-0.438981\pi\)
0.190524 + 0.981682i \(0.438981\pi\)
\(854\) 7.52949e62 0.708633
\(855\) 1.45118e62 0.133183
\(856\) 4.50917e62 0.403563
\(857\) 9.25891e62 0.808113 0.404056 0.914734i \(-0.367600\pi\)
0.404056 + 0.914734i \(0.367600\pi\)
\(858\) 8.15865e60 0.00694451
\(859\) −1.13513e62 −0.0942309 −0.0471155 0.998889i \(-0.515003\pi\)
−0.0471155 + 0.998889i \(0.515003\pi\)
\(860\) −8.06750e62 −0.653164
\(861\) −8.88266e62 −0.701415
\(862\) 1.71085e62 0.131767
\(863\) −1.90326e63 −1.42977 −0.714885 0.699242i \(-0.753521\pi\)
−0.714885 + 0.699242i \(0.753521\pi\)
\(864\) −2.54228e62 −0.186285
\(865\) 1.97576e63 1.41217
\(866\) 4.39249e62 0.306250
\(867\) 4.45276e62 0.302844
\(868\) −1.98574e63 −1.31749
\(869\) −5.31151e60 −0.00343790
\(870\) −3.39175e62 −0.214170
\(871\) 6.40192e62 0.394385
\(872\) −8.74642e62 −0.525686
\(873\) 9.34901e61 0.0548226
\(874\) −2.02170e62 −0.115670
\(875\) 1.95282e63 1.09016
\(876\) −6.69944e62 −0.364922
\(877\) −3.05610e63 −1.62434 −0.812170 0.583421i \(-0.801714\pi\)
−0.812170 + 0.583421i \(0.801714\pi\)
\(878\) −3.11462e62 −0.161537
\(879\) −2.54820e62 −0.128965
\(880\) −5.20371e61 −0.0257002
\(881\) 1.33139e63 0.641687 0.320843 0.947132i \(-0.396034\pi\)
0.320843 + 0.947132i \(0.396034\pi\)
\(882\) −1.01445e60 −0.000477153 0
\(883\) 3.18228e62 0.146077 0.0730387 0.997329i \(-0.476730\pi\)
0.0730387 + 0.997329i \(0.476730\pi\)
\(884\) 1.12118e63 0.502285
\(885\) 6.52504e62 0.285301
\(886\) −1.66003e63 −0.708421
\(887\) 1.09631e62 0.0456641 0.0228320 0.999739i \(-0.492732\pi\)
0.0228320 + 0.999739i \(0.492732\pi\)
\(888\) −1.98890e63 −0.808600
\(889\) −2.00899e63 −0.797242
\(890\) 6.61177e62 0.256114
\(891\) 1.75182e61 0.00662397
\(892\) −2.08296e63 −0.768840
\(893\) 9.78793e62 0.352683
\(894\) 9.99128e62 0.351451
\(895\) −1.42364e62 −0.0488882
\(896\) 3.04147e63 1.01967
\(897\) 5.03660e62 0.164854
\(898\) −1.97755e63 −0.631954
\(899\) −5.51427e63 −1.72050
\(900\) 2.83912e62 0.0864908
\(901\) 7.14715e63 2.12593
\(902\) 1.02523e62 0.0297770
\(903\) −1.93455e63 −0.548647
\(904\) 2.84178e63 0.786989
\(905\) 7.00248e62 0.189368
\(906\) 1.44916e63 0.382702
\(907\) 5.74551e63 1.48174 0.740870 0.671648i \(-0.234413\pi\)
0.740870 + 0.671648i \(0.234413\pi\)
\(908\) 4.51647e63 1.13750
\(909\) 1.84818e63 0.454590
\(910\) −6.97637e62 −0.167587
\(911\) −5.00178e63 −1.17349 −0.586745 0.809772i \(-0.699591\pi\)
−0.586745 + 0.809772i \(0.699591\pi\)
\(912\) −6.31225e62 −0.144642
\(913\) −3.56748e62 −0.0798436
\(914\) −1.13439e63 −0.247981
\(915\) 3.85095e63 0.822270
\(916\) 2.59091e63 0.540380
\(917\) −6.25224e63 −1.27378
\(918\) −4.91749e62 −0.0978646
\(919\) −4.87365e63 −0.947482 −0.473741 0.880664i \(-0.657097\pi\)
−0.473741 + 0.880664i \(0.657097\pi\)
\(920\) 1.91831e63 0.364318
\(921\) −2.90135e61 −0.00538292
\(922\) −2.99168e63 −0.542251
\(923\) −2.87456e63 −0.509020
\(924\) −1.65493e62 −0.0286306
\(925\) 3.43460e63 0.580536
\(926\) 1.54200e63 0.254652
\(927\) −2.54817e63 −0.411163
\(928\) 6.66928e63 1.05147
\(929\) −7.28764e63 −1.12266 −0.561331 0.827591i \(-0.689711\pi\)
−0.561331 + 0.827591i \(0.689711\pi\)
\(930\) 2.07454e63 0.312276
\(931\) −1.13864e61 −0.00167482
\(932\) −6.10705e63 −0.877788
\(933\) 5.20038e63 0.730432
\(934\) −3.32706e62 −0.0456670
\(935\) −4.55014e62 −0.0610345
\(936\) −9.39058e62 −0.123101
\(937\) −1.27714e64 −1.63621 −0.818103 0.575072i \(-0.804974\pi\)
−0.818103 + 0.575072i \(0.804974\pi\)
\(938\) 2.65258e63 0.332130
\(939\) −4.52178e63 −0.553349
\(940\) −4.21337e63 −0.503942
\(941\) 2.91347e63 0.340592 0.170296 0.985393i \(-0.445528\pi\)
0.170296 + 0.985393i \(0.445528\pi\)
\(942\) 8.42457e62 0.0962616
\(943\) 6.32908e63 0.706870
\(944\) −2.83823e63 −0.309848
\(945\) −1.49796e63 −0.159851
\(946\) 2.23284e62 0.0232916
\(947\) −7.13938e63 −0.728008 −0.364004 0.931397i \(-0.618591\pi\)
−0.364004 + 0.931397i \(0.618591\pi\)
\(948\) 2.77350e62 0.0276470
\(949\) −3.82658e63 −0.372895
\(950\) −6.50931e62 −0.0620122
\(951\) 2.39978e63 0.223507
\(952\) 1.02399e64 0.932400
\(953\) 1.57816e64 1.40493 0.702466 0.711718i \(-0.252083\pi\)
0.702466 + 0.711718i \(0.252083\pi\)
\(954\) −2.71573e63 −0.236372
\(955\) −8.44779e63 −0.718903
\(956\) 1.30092e64 1.08244
\(957\) −4.59563e62 −0.0373885
\(958\) −8.20326e62 −0.0652572
\(959\) 1.71730e64 1.33582
\(960\) 7.63174e62 0.0580486
\(961\) 2.02830e64 1.50862
\(962\) −5.15372e63 −0.374849
\(963\) 2.50886e63 0.178448
\(964\) 1.69176e63 0.117674
\(965\) −1.79884e63 −0.122365
\(966\) 2.08687e63 0.138831
\(967\) −1.41648e64 −0.921597 −0.460799 0.887505i \(-0.652437\pi\)
−0.460799 + 0.887505i \(0.652437\pi\)
\(968\) −1.18046e64 −0.751161
\(969\) −5.51945e63 −0.343506
\(970\) 9.22689e62 0.0561646
\(971\) 3.18091e64 1.89382 0.946908 0.321505i \(-0.104189\pi\)
0.946908 + 0.321505i \(0.104189\pi\)
\(972\) −9.14742e62 −0.0532689
\(973\) −5.24870e63 −0.298969
\(974\) −7.96832e62 −0.0443965
\(975\) 1.62165e63 0.0883806
\(976\) −1.67507e64 −0.893019
\(977\) −2.23211e64 −1.16408 −0.582039 0.813161i \(-0.697745\pi\)
−0.582039 + 0.813161i \(0.697745\pi\)
\(978\) −5.09318e63 −0.259838
\(979\) 8.95858e62 0.0447107
\(980\) 4.90144e61 0.00239311
\(981\) −4.86642e63 −0.232448
\(982\) −1.11814e64 −0.522514
\(983\) 9.61367e63 0.439530 0.219765 0.975553i \(-0.429471\pi\)
0.219765 + 0.975553i \(0.429471\pi\)
\(984\) −1.18004e64 −0.527838
\(985\) −2.44141e64 −1.06847
\(986\) 1.29003e64 0.552389
\(987\) −1.01035e64 −0.423303
\(988\) −4.78168e63 −0.196023
\(989\) 1.37841e64 0.552914
\(990\) 1.72894e62 0.00678613
\(991\) 5.07104e64 1.94766 0.973830 0.227278i \(-0.0729825\pi\)
0.973830 + 0.227278i \(0.0729825\pi\)
\(992\) −4.07923e64 −1.53312
\(993\) −2.06801e64 −0.760580
\(994\) −1.19105e64 −0.428669
\(995\) 3.08274e64 1.08578
\(996\) 1.86282e64 0.642090
\(997\) 5.61838e63 0.189524 0.0947622 0.995500i \(-0.469791\pi\)
0.0947622 + 0.995500i \(0.469791\pi\)
\(998\) −9.83455e63 −0.324674
\(999\) −1.10660e64 −0.357547
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 3.44.a.a.1.1 3
3.2 odd 2 9.44.a.a.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.44.a.a.1.1 3 1.1 even 1 trivial
9.44.a.a.1.3 3 3.2 odd 2