Properties

Label 3.44.a.a.1.2
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 1.2
Root \(1074.41\) of defining polynomial
Character \(\chi\) \(=\) 3.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.51590e6 q^{2} +1.04604e10 q^{3} -6.49815e12 q^{4} +1.66864e15 q^{5} +1.58568e16 q^{6} -2.14679e18 q^{7} -2.31845e19 q^{8} +1.09419e20 q^{9} +O(q^{10})\) \(q+1.51590e6 q^{2} +1.04604e10 q^{3} -6.49815e12 q^{4} +1.66864e15 q^{5} +1.58568e16 q^{6} -2.14679e18 q^{7} -2.31845e19 q^{8} +1.09419e20 q^{9} +2.52949e21 q^{10} +1.22726e22 q^{11} -6.79729e22 q^{12} -1.24386e24 q^{13} -3.25431e24 q^{14} +1.74546e25 q^{15} +2.20130e25 q^{16} -3.24488e26 q^{17} +1.65868e26 q^{18} +1.94876e27 q^{19} -1.08431e28 q^{20} -2.24562e28 q^{21} +1.86039e28 q^{22} -1.30622e28 q^{23} -2.42518e29 q^{24} +1.64750e30 q^{25} -1.88557e30 q^{26} +1.14456e30 q^{27} +1.39501e31 q^{28} -3.97297e31 q^{29} +2.64593e31 q^{30} -2.09034e32 q^{31} +2.37302e32 q^{32} +1.28375e32 q^{33} -4.91890e32 q^{34} -3.58222e33 q^{35} -7.11021e32 q^{36} +2.50717e33 q^{37} +2.95412e33 q^{38} -1.30112e34 q^{39} -3.86866e34 q^{40} -4.85378e34 q^{41} -3.40412e34 q^{42} -1.71176e35 q^{43} -7.97490e34 q^{44} +1.82581e35 q^{45} -1.98009e34 q^{46} -5.66784e35 q^{47} +2.30264e35 q^{48} +2.42488e36 q^{49} +2.49743e36 q^{50} -3.39426e36 q^{51} +8.08280e36 q^{52} -3.68350e36 q^{53} +1.73504e36 q^{54} +2.04785e37 q^{55} +4.97722e37 q^{56} +2.03848e37 q^{57} -6.02261e37 q^{58} -2.83712e37 q^{59} -1.13422e38 q^{60} +1.88748e38 q^{61} -3.16873e38 q^{62} -2.34899e38 q^{63} +1.66097e38 q^{64} -2.07556e39 q^{65} +1.94604e38 q^{66} +4.53449e37 q^{67} +2.10857e39 q^{68} -1.36635e38 q^{69} -5.43027e39 q^{70} +9.40045e39 q^{71} -2.53682e39 q^{72} +1.85053e40 q^{73} +3.80061e39 q^{74} +1.72334e40 q^{75} -1.26634e40 q^{76} -2.63466e40 q^{77} -1.97237e40 q^{78} +2.01772e40 q^{79} +3.67319e40 q^{80} +1.19725e40 q^{81} -7.35784e40 q^{82} +5.04418e40 q^{83} +1.45923e41 q^{84} -5.41454e41 q^{85} -2.59485e41 q^{86} -4.15586e41 q^{87} -2.84533e41 q^{88} +2.49342e41 q^{89} +2.76774e41 q^{90} +2.67031e42 q^{91} +8.48798e40 q^{92} -2.18657e42 q^{93} -8.59186e41 q^{94} +3.25179e42 q^{95} +2.48227e42 q^{96} +5.50446e42 q^{97} +3.67587e42 q^{98} +1.34285e42 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 4857024q^{2} + 31381059609q^{3} - 1781058029568q^{4} - 507753321105270q^{5} + 50806186555447872q^{6} - 1633169303707089288q^{7} + 11196260694472851456q^{8} + 328256967394537077627q^{9} + O(q^{10}) \) \( 3q + 4857024q^{2} + 31381059609q^{3} - 1781058029568q^{4} - 507753321105270q^{5} + 50806186555447872q^{6} - 1633169303707089288q^{7} + 11196260694472851456q^{8} + \)\(32\!\cdots\!27\)\(q^{9} - \)\(22\!\cdots\!20\)\(q^{10} - \)\(27\!\cdots\!20\)\(q^{11} - \)\(18\!\cdots\!04\)\(q^{12} - \)\(99\!\cdots\!50\)\(q^{13} - \)\(94\!\cdots\!28\)\(q^{14} - \)\(53\!\cdots\!10\)\(q^{15} + \)\(23\!\cdots\!36\)\(q^{16} - \)\(16\!\cdots\!82\)\(q^{17} + \)\(53\!\cdots\!16\)\(q^{18} - \)\(32\!\cdots\!64\)\(q^{19} - \)\(19\!\cdots\!60\)\(q^{20} - \)\(17\!\cdots\!64\)\(q^{21} - \)\(17\!\cdots\!24\)\(q^{22} + \)\(11\!\cdots\!04\)\(q^{23} + \)\(11\!\cdots\!68\)\(q^{24} + \)\(18\!\cdots\!25\)\(q^{25} + \)\(17\!\cdots\!36\)\(q^{26} + \)\(34\!\cdots\!81\)\(q^{27} - \)\(84\!\cdots\!44\)\(q^{28} - \)\(28\!\cdots\!58\)\(q^{29} - \)\(23\!\cdots\!60\)\(q^{30} - \)\(56\!\cdots\!36\)\(q^{31} - \)\(29\!\cdots\!88\)\(q^{32} - \)\(29\!\cdots\!60\)\(q^{33} - \)\(17\!\cdots\!76\)\(q^{34} - \)\(36\!\cdots\!20\)\(q^{35} - \)\(19\!\cdots\!12\)\(q^{36} - \)\(77\!\cdots\!78\)\(q^{37} - \)\(11\!\cdots\!08\)\(q^{38} - \)\(10\!\cdots\!50\)\(q^{39} - \)\(75\!\cdots\!00\)\(q^{40} - \)\(15\!\cdots\!66\)\(q^{41} - \)\(99\!\cdots\!84\)\(q^{42} - \)\(50\!\cdots\!88\)\(q^{43} - \)\(58\!\cdots\!72\)\(q^{44} - \)\(55\!\cdots\!30\)\(q^{45} + \)\(12\!\cdots\!64\)\(q^{46} + \)\(51\!\cdots\!36\)\(q^{47} + \)\(24\!\cdots\!08\)\(q^{48} + \)\(11\!\cdots\!03\)\(q^{49} + \)\(53\!\cdots\!00\)\(q^{50} - \)\(16\!\cdots\!46\)\(q^{51} + \)\(19\!\cdots\!08\)\(q^{52} + \)\(31\!\cdots\!34\)\(q^{53} + \)\(55\!\cdots\!48\)\(q^{54} + \)\(72\!\cdots\!60\)\(q^{55} + \)\(64\!\cdots\!20\)\(q^{56} - \)\(33\!\cdots\!92\)\(q^{57} + \)\(16\!\cdots\!64\)\(q^{58} - \)\(17\!\cdots\!76\)\(q^{59} - \)\(20\!\cdots\!80\)\(q^{60} - \)\(12\!\cdots\!18\)\(q^{61} - \)\(68\!\cdots\!56\)\(q^{62} - \)\(17\!\cdots\!92\)\(q^{63} - \)\(97\!\cdots\!36\)\(q^{64} - \)\(25\!\cdots\!40\)\(q^{65} - \)\(18\!\cdots\!72\)\(q^{66} + \)\(12\!\cdots\!48\)\(q^{67} - \)\(27\!\cdots\!68\)\(q^{68} + \)\(12\!\cdots\!12\)\(q^{69} + \)\(18\!\cdots\!80\)\(q^{70} + \)\(22\!\cdots\!16\)\(q^{71} + \)\(12\!\cdots\!04\)\(q^{72} + \)\(31\!\cdots\!54\)\(q^{73} + \)\(12\!\cdots\!32\)\(q^{74} + \)\(19\!\cdots\!75\)\(q^{75} - \)\(45\!\cdots\!04\)\(q^{76} + \)\(15\!\cdots\!44\)\(q^{77} + \)\(18\!\cdots\!08\)\(q^{78} - \)\(43\!\cdots\!80\)\(q^{79} + \)\(51\!\cdots\!80\)\(q^{80} + \)\(35\!\cdots\!43\)\(q^{81} - \)\(20\!\cdots\!96\)\(q^{82} + \)\(89\!\cdots\!68\)\(q^{83} - \)\(88\!\cdots\!32\)\(q^{84} - \)\(60\!\cdots\!20\)\(q^{85} - \)\(10\!\cdots\!20\)\(q^{86} - \)\(29\!\cdots\!74\)\(q^{87} - \)\(86\!\cdots\!84\)\(q^{88} + \)\(65\!\cdots\!06\)\(q^{89} - \)\(25\!\cdots\!80\)\(q^{90} + \)\(13\!\cdots\!24\)\(q^{91} + \)\(37\!\cdots\!72\)\(q^{92} - \)\(59\!\cdots\!08\)\(q^{93} + \)\(78\!\cdots\!20\)\(q^{94} + \)\(93\!\cdots\!00\)\(q^{95} - \)\(30\!\cdots\!64\)\(q^{96} + \)\(61\!\cdots\!78\)\(q^{97} - \)\(20\!\cdots\!60\)\(q^{98} - \)\(30\!\cdots\!80\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.51590e6 0.511122 0.255561 0.966793i \(-0.417740\pi\)
0.255561 + 0.966793i \(0.417740\pi\)
\(3\) 1.04604e10 0.577350
\(4\) −6.49815e12 −0.738754
\(5\) 1.66864e15 1.56498 0.782488 0.622665i \(-0.213950\pi\)
0.782488 + 0.622665i \(0.213950\pi\)
\(6\) 1.58568e16 0.295097
\(7\) −2.14679e18 −1.45272 −0.726359 0.687316i \(-0.758789\pi\)
−0.726359 + 0.687316i \(0.758789\pi\)
\(8\) −2.31845e19 −0.888716
\(9\) 1.09419e20 0.333333
\(10\) 2.52949e21 0.799894
\(11\) 1.22726e22 0.500026 0.250013 0.968242i \(-0.419565\pi\)
0.250013 + 0.968242i \(0.419565\pi\)
\(12\) −6.79729e22 −0.426520
\(13\) −1.24386e24 −1.39634 −0.698168 0.715934i \(-0.746001\pi\)
−0.698168 + 0.715934i \(0.746001\pi\)
\(14\) −3.25431e24 −0.742516
\(15\) 1.74546e25 0.903540
\(16\) 2.20130e25 0.284512
\(17\) −3.24488e26 −1.13906 −0.569530 0.821971i \(-0.692875\pi\)
−0.569530 + 0.821971i \(0.692875\pi\)
\(18\) 1.65868e26 0.170374
\(19\) 1.94876e27 0.625975 0.312987 0.949757i \(-0.398670\pi\)
0.312987 + 0.949757i \(0.398670\pi\)
\(20\) −1.08431e28 −1.15613
\(21\) −2.24562e28 −0.838727
\(22\) 1.86039e28 0.255574
\(23\) −1.30622e28 −0.0690027 −0.0345014 0.999405i \(-0.510984\pi\)
−0.0345014 + 0.999405i \(0.510984\pi\)
\(24\) −2.42518e29 −0.513100
\(25\) 1.64750e30 1.44915
\(26\) −1.88557e30 −0.713698
\(27\) 1.14456e30 0.192450
\(28\) 1.39501e31 1.07320
\(29\) −3.97297e31 −1.43733 −0.718667 0.695354i \(-0.755248\pi\)
−0.718667 + 0.695354i \(0.755248\pi\)
\(30\) 2.64593e31 0.461819
\(31\) −2.09034e32 −1.80277 −0.901384 0.433021i \(-0.857448\pi\)
−0.901384 + 0.433021i \(0.857448\pi\)
\(32\) 2.37302e32 1.03414
\(33\) 1.28375e32 0.288690
\(34\) −4.91890e32 −0.582199
\(35\) −3.58222e33 −2.27347
\(36\) −7.11021e32 −0.246251
\(37\) 2.50717e33 0.481778 0.240889 0.970553i \(-0.422561\pi\)
0.240889 + 0.970553i \(0.422561\pi\)
\(38\) 2.95412e33 0.319950
\(39\) −1.30112e34 −0.806175
\(40\) −3.86866e34 −1.39082
\(41\) −4.85378e34 −1.02619 −0.513095 0.858332i \(-0.671501\pi\)
−0.513095 + 0.858332i \(0.671501\pi\)
\(42\) −3.40412e34 −0.428692
\(43\) −1.71176e35 −1.29978 −0.649890 0.760028i \(-0.725185\pi\)
−0.649890 + 0.760028i \(0.725185\pi\)
\(44\) −7.97490e34 −0.369396
\(45\) 1.82581e35 0.521659
\(46\) −1.98009e34 −0.0352688
\(47\) −5.66784e35 −0.635790 −0.317895 0.948126i \(-0.602976\pi\)
−0.317895 + 0.948126i \(0.602976\pi\)
\(48\) 2.30264e35 0.164263
\(49\) 2.42488e36 1.11039
\(50\) 2.49743e36 0.740694
\(51\) −3.39426e36 −0.657636
\(52\) 8.08280e36 1.03155
\(53\) −3.68350e36 −0.312126 −0.156063 0.987747i \(-0.549880\pi\)
−0.156063 + 0.987747i \(0.549880\pi\)
\(54\) 1.73504e36 0.0983655
\(55\) 2.04785e37 0.782529
\(56\) 4.97722e37 1.29105
\(57\) 2.03848e37 0.361407
\(58\) −6.02261e37 −0.734654
\(59\) −2.83712e37 −0.239640 −0.119820 0.992796i \(-0.538232\pi\)
−0.119820 + 0.992796i \(0.538232\pi\)
\(60\) −1.13422e38 −0.667494
\(61\) 1.88748e38 0.778558 0.389279 0.921120i \(-0.372724\pi\)
0.389279 + 0.921120i \(0.372724\pi\)
\(62\) −3.16873e38 −0.921435
\(63\) −2.34899e38 −0.484239
\(64\) 1.66097e38 0.244058
\(65\) −2.07556e39 −2.18523
\(66\) 1.94604e38 0.147556
\(67\) 4.53449e37 0.0248840 0.0124420 0.999923i \(-0.496039\pi\)
0.0124420 + 0.999923i \(0.496039\pi\)
\(68\) 2.10857e39 0.841485
\(69\) −1.36635e38 −0.0398387
\(70\) −5.43027e39 −1.16202
\(71\) 9.40045e39 1.48284 0.741420 0.671042i \(-0.234153\pi\)
0.741420 + 0.671042i \(0.234153\pi\)
\(72\) −2.53682e39 −0.296239
\(73\) 1.85053e40 1.60641 0.803204 0.595704i \(-0.203127\pi\)
0.803204 + 0.595704i \(0.203127\pi\)
\(74\) 3.80061e39 0.246247
\(75\) 1.72334e40 0.836669
\(76\) −1.26634e40 −0.462441
\(77\) −2.63466e40 −0.726396
\(78\) −1.97237e40 −0.412054
\(79\) 2.01772e40 0.320537 0.160269 0.987073i \(-0.448764\pi\)
0.160269 + 0.987073i \(0.448764\pi\)
\(80\) 3.67319e40 0.445254
\(81\) 1.19725e40 0.111111
\(82\) −7.35784e40 −0.524508
\(83\) 5.04418e40 0.277084 0.138542 0.990357i \(-0.455758\pi\)
0.138542 + 0.990357i \(0.455758\pi\)
\(84\) 1.45923e41 0.619613
\(85\) −5.41454e41 −1.78260
\(86\) −2.59485e41 −0.664347
\(87\) −4.15586e41 −0.829846
\(88\) −2.84533e41 −0.444381
\(89\) 2.49342e41 0.305429 0.152714 0.988270i \(-0.451199\pi\)
0.152714 + 0.988270i \(0.451199\pi\)
\(90\) 2.76774e41 0.266631
\(91\) 2.67031e42 2.02848
\(92\) 8.48798e40 0.0509761
\(93\) −2.18657e42 −1.04083
\(94\) −8.59186e41 −0.324966
\(95\) 3.25179e42 0.979636
\(96\) 2.48227e42 0.597059
\(97\) 5.50446e42 1.05955 0.529776 0.848138i \(-0.322276\pi\)
0.529776 + 0.848138i \(0.322276\pi\)
\(98\) 3.67587e42 0.567544
\(99\) 1.34285e42 0.166675
\(100\) −1.07057e43 −1.07057
\(101\) −1.04274e43 −0.841908 −0.420954 0.907082i \(-0.638305\pi\)
−0.420954 + 0.907082i \(0.638305\pi\)
\(102\) −5.14534e42 −0.336133
\(103\) −9.43707e42 −0.499847 −0.249923 0.968266i \(-0.580405\pi\)
−0.249923 + 0.968266i \(0.580405\pi\)
\(104\) 2.88383e43 1.24095
\(105\) −3.74713e43 −1.31259
\(106\) −5.58381e42 −0.159535
\(107\) 8.75396e42 0.204387 0.102194 0.994765i \(-0.467414\pi\)
0.102194 + 0.994765i \(0.467414\pi\)
\(108\) −7.43753e42 −0.142173
\(109\) −7.27594e43 −1.14083 −0.570413 0.821358i \(-0.693217\pi\)
−0.570413 + 0.821358i \(0.693217\pi\)
\(110\) 3.10433e43 0.399968
\(111\) 2.62259e43 0.278154
\(112\) −4.72573e43 −0.413315
\(113\) 1.39067e44 1.00471 0.502353 0.864663i \(-0.332468\pi\)
0.502353 + 0.864663i \(0.332468\pi\)
\(114\) 3.09012e43 0.184723
\(115\) −2.17961e43 −0.107988
\(116\) 2.58169e44 1.06184
\(117\) −1.36102e44 −0.465445
\(118\) −4.30078e43 −0.122485
\(119\) 6.96606e44 1.65473
\(120\) −4.04676e44 −0.802990
\(121\) −4.51785e44 −0.749974
\(122\) 2.86122e44 0.397938
\(123\) −5.07723e44 −0.592471
\(124\) 1.35833e45 1.33180
\(125\) 8.52054e44 0.702913
\(126\) −3.56083e44 −0.247505
\(127\) −2.19819e45 −1.28910 −0.644549 0.764563i \(-0.722955\pi\)
−0.644549 + 0.764563i \(0.722955\pi\)
\(128\) −1.83555e45 −0.909393
\(129\) −1.79056e45 −0.750429
\(130\) −3.14633e45 −1.11692
\(131\) 5.04143e45 1.51782 0.758911 0.651194i \(-0.225732\pi\)
0.758911 + 0.651194i \(0.225732\pi\)
\(132\) −8.34202e44 −0.213271
\(133\) −4.18358e45 −0.909364
\(134\) 6.87382e43 0.0127188
\(135\) 1.90986e45 0.301180
\(136\) 7.52308e45 1.01230
\(137\) −1.07968e45 −0.124109 −0.0620547 0.998073i \(-0.519765\pi\)
−0.0620547 + 0.998073i \(0.519765\pi\)
\(138\) −2.07124e44 −0.0203625
\(139\) 9.70997e45 0.817334 0.408667 0.912684i \(-0.365994\pi\)
0.408667 + 0.912684i \(0.365994\pi\)
\(140\) 2.32778e46 1.67953
\(141\) −5.92876e45 −0.367073
\(142\) 1.42501e46 0.757912
\(143\) −1.52654e46 −0.698204
\(144\) 2.40864e45 0.0948373
\(145\) −6.62946e46 −2.24940
\(146\) 2.80522e46 0.821071
\(147\) 2.53651e46 0.641083
\(148\) −1.62920e46 −0.355915
\(149\) −5.51076e46 −1.04161 −0.520807 0.853675i \(-0.674369\pi\)
−0.520807 + 0.853675i \(0.674369\pi\)
\(150\) 2.61240e46 0.427640
\(151\) 9.44853e46 1.34079 0.670393 0.742006i \(-0.266125\pi\)
0.670393 + 0.742006i \(0.266125\pi\)
\(152\) −4.51811e46 −0.556314
\(153\) −3.55051e46 −0.379687
\(154\) −3.99387e46 −0.371277
\(155\) −3.48802e47 −2.82129
\(156\) 8.45490e46 0.595565
\(157\) 1.63045e47 1.00107 0.500535 0.865717i \(-0.333137\pi\)
0.500535 + 0.865717i \(0.333137\pi\)
\(158\) 3.05866e46 0.163834
\(159\) −3.85308e46 −0.180206
\(160\) 3.95973e47 1.61840
\(161\) 2.80417e46 0.100241
\(162\) 1.81491e46 0.0567913
\(163\) −4.14610e47 −1.13660 −0.568298 0.822823i \(-0.692398\pi\)
−0.568298 + 0.822823i \(0.692398\pi\)
\(164\) 3.15406e47 0.758102
\(165\) 2.14212e47 0.451793
\(166\) 7.64646e46 0.141624
\(167\) −4.03729e47 −0.657183 −0.328591 0.944472i \(-0.606574\pi\)
−0.328591 + 0.944472i \(0.606574\pi\)
\(168\) 5.20635e47 0.745390
\(169\) 7.53661e47 0.949756
\(170\) −8.20788e47 −0.911127
\(171\) 2.13232e47 0.208658
\(172\) 1.11233e48 0.960219
\(173\) 6.36250e46 0.0484882 0.0242441 0.999706i \(-0.492282\pi\)
0.0242441 + 0.999706i \(0.492282\pi\)
\(174\) −6.29986e47 −0.424152
\(175\) −3.53682e48 −2.10521
\(176\) 2.70156e47 0.142263
\(177\) −2.96773e47 −0.138356
\(178\) 3.77976e47 0.156111
\(179\) −2.31263e48 −0.846771 −0.423386 0.905950i \(-0.639158\pi\)
−0.423386 + 0.905950i \(0.639158\pi\)
\(180\) −1.18644e48 −0.385378
\(181\) −2.60454e48 −0.751002 −0.375501 0.926822i \(-0.622529\pi\)
−0.375501 + 0.926822i \(0.622529\pi\)
\(182\) 4.04791e48 1.03680
\(183\) 1.97437e48 0.449500
\(184\) 3.02839e47 0.0613238
\(185\) 4.18357e48 0.753971
\(186\) −3.31461e48 −0.531991
\(187\) −3.98230e48 −0.569559
\(188\) 3.68305e48 0.469692
\(189\) −2.45713e48 −0.279576
\(190\) 4.92937e48 0.500714
\(191\) 2.03787e49 1.84909 0.924546 0.381069i \(-0.124444\pi\)
0.924546 + 0.381069i \(0.124444\pi\)
\(192\) 1.73744e48 0.140907
\(193\) 1.75587e49 1.27353 0.636766 0.771057i \(-0.280272\pi\)
0.636766 + 0.771057i \(0.280272\pi\)
\(194\) 8.34419e48 0.541561
\(195\) −2.17111e49 −1.26165
\(196\) −1.57572e49 −0.820304
\(197\) −2.71813e49 −1.26837 −0.634186 0.773180i \(-0.718665\pi\)
−0.634186 + 0.773180i \(0.718665\pi\)
\(198\) 2.03562e48 0.0851914
\(199\) 5.71271e48 0.214536 0.107268 0.994230i \(-0.465790\pi\)
0.107268 + 0.994230i \(0.465790\pi\)
\(200\) −3.81964e49 −1.28788
\(201\) 4.74324e47 0.0143668
\(202\) −1.58068e49 −0.430318
\(203\) 8.52911e49 2.08804
\(204\) 2.20564e49 0.485832
\(205\) −8.09923e49 −1.60596
\(206\) −1.43056e49 −0.255483
\(207\) −1.42925e48 −0.0230009
\(208\) −2.73812e49 −0.397274
\(209\) 2.39163e49 0.313004
\(210\) −5.68026e49 −0.670893
\(211\) 5.09193e49 0.543013 0.271506 0.962437i \(-0.412478\pi\)
0.271506 + 0.962437i \(0.412478\pi\)
\(212\) 2.39360e49 0.230584
\(213\) 9.83320e49 0.856118
\(214\) 1.32701e49 0.104467
\(215\) −2.85631e50 −2.03413
\(216\) −2.65361e49 −0.171033
\(217\) 4.48751e50 2.61891
\(218\) −1.10296e50 −0.583101
\(219\) 1.93572e50 0.927460
\(220\) −1.33072e50 −0.578097
\(221\) 4.03618e50 1.59051
\(222\) 3.97557e49 0.142171
\(223\) −4.92392e49 −0.159866 −0.0799330 0.996800i \(-0.525471\pi\)
−0.0799330 + 0.996800i \(0.525471\pi\)
\(224\) −5.09438e50 −1.50231
\(225\) 1.80267e50 0.483051
\(226\) 2.10812e50 0.513527
\(227\) −1.42699e50 −0.316129 −0.158064 0.987429i \(-0.550525\pi\)
−0.158064 + 0.987429i \(0.550525\pi\)
\(228\) −1.32463e50 −0.266991
\(229\) −6.15509e50 −1.12920 −0.564600 0.825364i \(-0.690970\pi\)
−0.564600 + 0.825364i \(0.690970\pi\)
\(230\) −3.30406e49 −0.0551949
\(231\) −2.75595e50 −0.419385
\(232\) 9.21112e50 1.27738
\(233\) −1.20973e51 −1.52946 −0.764728 0.644353i \(-0.777127\pi\)
−0.764728 + 0.644353i \(0.777127\pi\)
\(234\) −2.06317e50 −0.237899
\(235\) −9.45759e50 −0.994996
\(236\) 1.84360e50 0.177035
\(237\) 2.11061e50 0.185062
\(238\) 1.05598e51 0.845770
\(239\) 3.57664e50 0.261770 0.130885 0.991398i \(-0.458218\pi\)
0.130885 + 0.991398i \(0.458218\pi\)
\(240\) 3.84228e50 0.257068
\(241\) 3.74733e50 0.229274 0.114637 0.993407i \(-0.463429\pi\)
0.114637 + 0.993407i \(0.463429\pi\)
\(242\) −6.84859e50 −0.383328
\(243\) 1.25237e50 0.0641500
\(244\) −1.22651e51 −0.575163
\(245\) 4.04626e51 1.73773
\(246\) −7.69656e50 −0.302825
\(247\) −2.42399e51 −0.874071
\(248\) 4.84634e51 1.60215
\(249\) 5.27639e50 0.159975
\(250\) 1.29163e51 0.359275
\(251\) 3.17420e51 0.810305 0.405153 0.914249i \(-0.367218\pi\)
0.405153 + 0.914249i \(0.367218\pi\)
\(252\) 1.52641e51 0.357734
\(253\) −1.60306e50 −0.0345032
\(254\) −3.33224e51 −0.658887
\(255\) −5.66380e51 −1.02919
\(256\) −4.24351e51 −0.708869
\(257\) −9.53789e51 −1.46518 −0.732589 0.680671i \(-0.761688\pi\)
−0.732589 + 0.680671i \(0.761688\pi\)
\(258\) −2.71430e51 −0.383561
\(259\) −5.38236e51 −0.699887
\(260\) 1.34873e52 1.61435
\(261\) −4.34718e51 −0.479112
\(262\) 7.64229e51 0.775793
\(263\) 7.09426e51 0.663527 0.331763 0.943363i \(-0.392356\pi\)
0.331763 + 0.943363i \(0.392356\pi\)
\(264\) −2.97632e51 −0.256563
\(265\) −6.14645e51 −0.488470
\(266\) −6.34188e51 −0.464796
\(267\) 2.60820e51 0.176339
\(268\) −2.94658e50 −0.0183832
\(269\) −1.76915e52 −1.01881 −0.509403 0.860528i \(-0.670134\pi\)
−0.509403 + 0.860528i \(0.670134\pi\)
\(270\) 2.89515e51 0.153940
\(271\) 1.52807e52 0.750418 0.375209 0.926940i \(-0.377571\pi\)
0.375209 + 0.926940i \(0.377571\pi\)
\(272\) −7.14296e51 −0.324076
\(273\) 2.79324e52 1.17114
\(274\) −1.63669e51 −0.0634351
\(275\) 2.02190e52 0.724614
\(276\) 8.87873e50 0.0294310
\(277\) −1.23660e52 −0.379239 −0.189620 0.981858i \(-0.560725\pi\)
−0.189620 + 0.981858i \(0.560725\pi\)
\(278\) 1.47193e52 0.417758
\(279\) −2.28723e52 −0.600923
\(280\) 8.30519e52 2.02047
\(281\) −3.60004e52 −0.811188 −0.405594 0.914053i \(-0.632935\pi\)
−0.405594 + 0.914053i \(0.632935\pi\)
\(282\) −8.98739e51 −0.187619
\(283\) −1.88793e52 −0.365239 −0.182620 0.983184i \(-0.558458\pi\)
−0.182620 + 0.983184i \(0.558458\pi\)
\(284\) −6.10855e52 −1.09545
\(285\) 3.40149e52 0.565593
\(286\) −2.31407e52 −0.356868
\(287\) 1.04200e53 1.49076
\(288\) 2.59654e52 0.344712
\(289\) 2.41395e52 0.297457
\(290\) −1.00496e53 −1.14972
\(291\) 5.75786e52 0.611733
\(292\) −1.20251e53 −1.18674
\(293\) −2.00854e53 −1.84173 −0.920867 0.389877i \(-0.872517\pi\)
−0.920867 + 0.389877i \(0.872517\pi\)
\(294\) 3.84509e52 0.327672
\(295\) −4.73414e52 −0.375031
\(296\) −5.81274e52 −0.428163
\(297\) 1.40467e52 0.0962300
\(298\) −8.35374e52 −0.532392
\(299\) 1.62475e52 0.0963510
\(300\) −1.11985e53 −0.618092
\(301\) 3.67478e53 1.88821
\(302\) 1.43230e53 0.685306
\(303\) −1.09074e53 −0.486076
\(304\) 4.28982e52 0.178097
\(305\) 3.14953e53 1.21842
\(306\) −5.38221e52 −0.194066
\(307\) 4.77984e53 1.60671 0.803357 0.595498i \(-0.203045\pi\)
0.803357 + 0.595498i \(0.203045\pi\)
\(308\) 1.71204e53 0.536628
\(309\) −9.87151e52 −0.288587
\(310\) −5.28748e53 −1.44202
\(311\) −1.77470e53 −0.451625 −0.225812 0.974171i \(-0.572504\pi\)
−0.225812 + 0.974171i \(0.572504\pi\)
\(312\) 3.01659e53 0.716461
\(313\) −1.55554e53 −0.344888 −0.172444 0.985019i \(-0.555166\pi\)
−0.172444 + 0.985019i \(0.555166\pi\)
\(314\) 2.47159e53 0.511669
\(315\) −3.91963e53 −0.757823
\(316\) −1.31114e53 −0.236798
\(317\) 6.62322e53 1.11762 0.558811 0.829295i \(-0.311258\pi\)
0.558811 + 0.829295i \(0.311258\pi\)
\(318\) −5.84086e52 −0.0921073
\(319\) −4.87585e53 −0.718705
\(320\) 2.77157e53 0.381945
\(321\) 9.15695e52 0.118003
\(322\) 4.25083e52 0.0512356
\(323\) −6.32350e53 −0.713023
\(324\) −7.77992e52 −0.0820838
\(325\) −2.04926e54 −2.02350
\(326\) −6.28505e53 −0.580939
\(327\) −7.61089e53 −0.658656
\(328\) 1.12533e54 0.911991
\(329\) 1.21676e54 0.923623
\(330\) 3.24724e53 0.230922
\(331\) 1.05656e54 0.704035 0.352018 0.935993i \(-0.385496\pi\)
0.352018 + 0.935993i \(0.385496\pi\)
\(332\) −3.27779e53 −0.204697
\(333\) 2.74332e53 0.160593
\(334\) −6.12012e53 −0.335901
\(335\) 7.56644e52 0.0389429
\(336\) −4.94328e53 −0.238628
\(337\) −4.32819e53 −0.196003 −0.0980017 0.995186i \(-0.531245\pi\)
−0.0980017 + 0.995186i \(0.531245\pi\)
\(338\) 1.14247e54 0.485441
\(339\) 1.45469e54 0.580067
\(340\) 3.51845e54 1.31690
\(341\) −2.56538e54 −0.901431
\(342\) 3.23237e53 0.106650
\(343\) −5.17520e53 −0.160363
\(344\) 3.96862e54 1.15514
\(345\) −2.27994e53 −0.0623467
\(346\) 9.64489e52 0.0247834
\(347\) −1.96230e54 −0.473893 −0.236947 0.971523i \(-0.576147\pi\)
−0.236947 + 0.971523i \(0.576147\pi\)
\(348\) 2.70054e54 0.613052
\(349\) −1.61567e54 −0.344830 −0.172415 0.985024i \(-0.555157\pi\)
−0.172415 + 0.985024i \(0.555157\pi\)
\(350\) −5.36146e54 −1.07602
\(351\) −1.42368e54 −0.268725
\(352\) 2.91231e54 0.517095
\(353\) −9.00279e54 −1.50391 −0.751954 0.659216i \(-0.770888\pi\)
−0.751954 + 0.659216i \(0.770888\pi\)
\(354\) −4.49877e53 −0.0707170
\(355\) 1.56860e55 2.32061
\(356\) −1.62026e54 −0.225637
\(357\) 7.28675e54 0.955360
\(358\) −3.50571e54 −0.432803
\(359\) −1.30294e55 −1.51493 −0.757465 0.652875i \(-0.773563\pi\)
−0.757465 + 0.652875i \(0.773563\pi\)
\(360\) −4.23305e54 −0.463607
\(361\) −5.89413e54 −0.608156
\(362\) −3.94821e54 −0.383854
\(363\) −4.72583e54 −0.432998
\(364\) −1.73521e55 −1.49855
\(365\) 3.08788e55 2.51399
\(366\) 2.99294e54 0.229750
\(367\) −1.38069e55 −0.999485 −0.499742 0.866174i \(-0.666572\pi\)
−0.499742 + 0.866174i \(0.666572\pi\)
\(368\) −2.87538e53 −0.0196321
\(369\) −5.31096e54 −0.342063
\(370\) 6.34185e54 0.385371
\(371\) 7.90770e54 0.453431
\(372\) 1.42086e55 0.768916
\(373\) 3.06603e54 0.156616 0.0783080 0.996929i \(-0.475048\pi\)
0.0783080 + 0.996929i \(0.475048\pi\)
\(374\) −6.03675e54 −0.291114
\(375\) 8.91279e54 0.405827
\(376\) 1.31406e55 0.565036
\(377\) 4.94182e55 2.00700
\(378\) −3.72475e54 −0.142897
\(379\) 1.92415e55 0.697423 0.348711 0.937230i \(-0.386619\pi\)
0.348711 + 0.937230i \(0.386619\pi\)
\(380\) −2.11306e55 −0.723710
\(381\) −2.29939e55 −0.744261
\(382\) 3.08920e55 0.945112
\(383\) −3.08070e55 −0.890995 −0.445498 0.895283i \(-0.646973\pi\)
−0.445498 + 0.895283i \(0.646973\pi\)
\(384\) −1.92005e55 −0.525038
\(385\) −4.39630e55 −1.13679
\(386\) 2.66171e55 0.650930
\(387\) −1.87299e55 −0.433260
\(388\) −3.57688e55 −0.782748
\(389\) 6.70663e55 1.38863 0.694317 0.719669i \(-0.255706\pi\)
0.694317 + 0.719669i \(0.255706\pi\)
\(390\) −3.29118e55 −0.644855
\(391\) 4.23851e54 0.0785982
\(392\) −5.62197e55 −0.986820
\(393\) 5.27352e55 0.876315
\(394\) −4.12041e55 −0.648293
\(395\) 3.36685e55 0.501633
\(396\) −8.72605e54 −0.123132
\(397\) −1.48189e56 −1.98071 −0.990356 0.138546i \(-0.955757\pi\)
−0.990356 + 0.138546i \(0.955757\pi\)
\(398\) 8.65988e54 0.109654
\(399\) −4.37617e55 −0.525022
\(400\) 3.62664e55 0.412301
\(401\) −7.65298e55 −0.824569 −0.412284 0.911055i \(-0.635269\pi\)
−0.412284 + 0.911055i \(0.635269\pi\)
\(402\) 7.19026e53 0.00734318
\(403\) 2.60009e56 2.51727
\(404\) 6.77585e55 0.621963
\(405\) 1.99778e55 0.173886
\(406\) 1.29293e56 1.06724
\(407\) 3.07694e55 0.240901
\(408\) 7.86941e55 0.584452
\(409\) −2.46970e56 −1.74018 −0.870088 0.492897i \(-0.835938\pi\)
−0.870088 + 0.492897i \(0.835938\pi\)
\(410\) −1.22776e56 −0.820843
\(411\) −1.12939e55 −0.0716546
\(412\) 6.13235e55 0.369264
\(413\) 6.09070e55 0.348130
\(414\) −2.16659e54 −0.0117563
\(415\) 8.41693e55 0.433630
\(416\) −2.95171e56 −1.44400
\(417\) 1.01570e56 0.471888
\(418\) 3.62547e55 0.159983
\(419\) 2.28426e56 0.957512 0.478756 0.877948i \(-0.341088\pi\)
0.478756 + 0.877948i \(0.341088\pi\)
\(420\) 2.43494e56 0.969680
\(421\) 9.19655e55 0.347984 0.173992 0.984747i \(-0.444333\pi\)
0.173992 + 0.984747i \(0.444333\pi\)
\(422\) 7.71884e55 0.277546
\(423\) −6.20169e55 −0.211930
\(424\) 8.54002e55 0.277391
\(425\) −5.34592e56 −1.65067
\(426\) 1.49061e56 0.437581
\(427\) −4.05202e56 −1.13102
\(428\) −5.68846e55 −0.150992
\(429\) −1.59681e56 −0.403109
\(430\) −4.32987e56 −1.03969
\(431\) −5.33175e56 −1.21789 −0.608945 0.793212i \(-0.708407\pi\)
−0.608945 + 0.793212i \(0.708407\pi\)
\(432\) 2.51953e55 0.0547543
\(433\) 4.04326e56 0.836068 0.418034 0.908431i \(-0.362719\pi\)
0.418034 + 0.908431i \(0.362719\pi\)
\(434\) 6.80260e56 1.33858
\(435\) −6.93465e56 −1.29869
\(436\) 4.72802e56 0.842790
\(437\) −2.54551e55 −0.0431940
\(438\) 2.93436e56 0.474045
\(439\) −2.13640e56 −0.328622 −0.164311 0.986409i \(-0.552540\pi\)
−0.164311 + 0.986409i \(0.552540\pi\)
\(440\) −4.74784e56 −0.695446
\(441\) 2.65328e56 0.370129
\(442\) 6.11843e56 0.812945
\(443\) −7.02530e55 −0.0889170 −0.0444585 0.999011i \(-0.514156\pi\)
−0.0444585 + 0.999011i \(0.514156\pi\)
\(444\) −1.70420e56 −0.205488
\(445\) 4.16062e56 0.477989
\(446\) −7.46415e55 −0.0817110
\(447\) −5.76445e56 −0.601376
\(448\) −3.56575e56 −0.354547
\(449\) 1.72784e57 1.63760 0.818799 0.574080i \(-0.194640\pi\)
0.818799 + 0.574080i \(0.194640\pi\)
\(450\) 2.73267e56 0.246898
\(451\) −5.95684e56 −0.513121
\(452\) −9.03681e56 −0.742231
\(453\) 9.88349e56 0.774104
\(454\) −2.16316e56 −0.161580
\(455\) 4.45578e57 3.17453
\(456\) −4.72610e56 −0.321188
\(457\) −1.18433e57 −0.767848 −0.383924 0.923365i \(-0.625428\pi\)
−0.383924 + 0.923365i \(0.625428\pi\)
\(458\) −9.33047e56 −0.577160
\(459\) −3.71396e56 −0.219212
\(460\) 1.41634e56 0.0797764
\(461\) 1.98824e57 1.06881 0.534403 0.845230i \(-0.320536\pi\)
0.534403 + 0.845230i \(0.320536\pi\)
\(462\) −4.17773e56 −0.214357
\(463\) −1.36504e57 −0.668579 −0.334289 0.942470i \(-0.608496\pi\)
−0.334289 + 0.942470i \(0.608496\pi\)
\(464\) −8.74571e56 −0.408939
\(465\) −3.64859e57 −1.62887
\(466\) −1.83383e57 −0.781739
\(467\) −1.51882e57 −0.618290 −0.309145 0.951015i \(-0.600043\pi\)
−0.309145 + 0.951015i \(0.600043\pi\)
\(468\) 8.84412e56 0.343850
\(469\) −9.73458e55 −0.0361494
\(470\) −1.43367e57 −0.508565
\(471\) 1.70551e57 0.577968
\(472\) 6.57772e56 0.212972
\(473\) −2.10076e57 −0.649924
\(474\) 3.19946e56 0.0945894
\(475\) 3.21058e57 0.907133
\(476\) −4.52665e57 −1.22244
\(477\) −4.03045e56 −0.104042
\(478\) 5.42181e56 0.133797
\(479\) 4.05448e57 0.956582 0.478291 0.878201i \(-0.341256\pi\)
0.478291 + 0.878201i \(0.341256\pi\)
\(480\) 4.14201e57 0.934383
\(481\) −3.11857e57 −0.672724
\(482\) 5.68056e56 0.117187
\(483\) 2.93326e56 0.0578744
\(484\) 2.93577e57 0.554046
\(485\) 9.18497e57 1.65817
\(486\) 1.89846e56 0.0327885
\(487\) −7.98190e56 −0.131897 −0.0659483 0.997823i \(-0.521007\pi\)
−0.0659483 + 0.997823i \(0.521007\pi\)
\(488\) −4.37602e57 −0.691916
\(489\) −4.33696e57 −0.656214
\(490\) 6.13371e57 0.888193
\(491\) −4.53391e57 −0.628378 −0.314189 0.949360i \(-0.601733\pi\)
−0.314189 + 0.949360i \(0.601733\pi\)
\(492\) 3.29926e57 0.437690
\(493\) 1.28918e58 1.63721
\(494\) −3.67452e57 −0.446757
\(495\) 2.24074e57 0.260843
\(496\) −4.60147e57 −0.512909
\(497\) −2.01808e58 −2.15415
\(498\) 7.99847e56 0.0817666
\(499\) 2.52533e57 0.247262 0.123631 0.992328i \(-0.460546\pi\)
0.123631 + 0.992328i \(0.460546\pi\)
\(500\) −5.53677e57 −0.519280
\(501\) −4.22315e57 −0.379425
\(502\) 4.81175e57 0.414165
\(503\) 1.87361e58 1.54514 0.772568 0.634932i \(-0.218972\pi\)
0.772568 + 0.634932i \(0.218972\pi\)
\(504\) 5.44602e57 0.430351
\(505\) −1.73995e58 −1.31757
\(506\) −2.43007e56 −0.0176353
\(507\) 7.88356e57 0.548342
\(508\) 1.42842e58 0.952327
\(509\) −7.68365e57 −0.491061 −0.245531 0.969389i \(-0.578962\pi\)
−0.245531 + 0.969389i \(0.578962\pi\)
\(510\) −8.58573e57 −0.526040
\(511\) −3.97270e58 −2.33366
\(512\) 9.71293e57 0.547074
\(513\) 2.23048e57 0.120469
\(514\) −1.44585e58 −0.748885
\(515\) −1.57471e58 −0.782249
\(516\) 1.16353e58 0.554382
\(517\) −6.95589e57 −0.317911
\(518\) −8.15910e57 −0.357728
\(519\) 6.65539e56 0.0279947
\(520\) 4.81208e58 1.94205
\(521\) 4.49484e58 1.74062 0.870309 0.492507i \(-0.163919\pi\)
0.870309 + 0.492507i \(0.163919\pi\)
\(522\) −6.58988e57 −0.244885
\(523\) 1.61795e57 0.0577006 0.0288503 0.999584i \(-0.490815\pi\)
0.0288503 + 0.999584i \(0.490815\pi\)
\(524\) −3.27600e58 −1.12130
\(525\) −3.69964e58 −1.21544
\(526\) 1.07542e58 0.339143
\(527\) 6.78289e58 2.05346
\(528\) 2.82593e57 0.0821358
\(529\) −3.56635e58 −0.995239
\(530\) −9.31738e57 −0.249668
\(531\) −3.10435e57 −0.0798801
\(532\) 2.71855e58 0.671797
\(533\) 6.03744e58 1.43291
\(534\) 3.95376e57 0.0901309
\(535\) 1.46072e58 0.319861
\(536\) −1.05130e57 −0.0221148
\(537\) −2.41909e58 −0.488884
\(538\) −2.68185e58 −0.520734
\(539\) 2.97595e58 0.555223
\(540\) −1.24106e58 −0.222498
\(541\) 4.63052e58 0.797790 0.398895 0.916997i \(-0.369394\pi\)
0.398895 + 0.916997i \(0.369394\pi\)
\(542\) 2.31640e58 0.383555
\(543\) −2.72444e58 −0.433591
\(544\) −7.70017e58 −1.17794
\(545\) −1.21409e59 −1.78537
\(546\) 4.23426e58 0.598598
\(547\) −6.58436e58 −0.894924 −0.447462 0.894303i \(-0.647672\pi\)
−0.447462 + 0.894303i \(0.647672\pi\)
\(548\) 7.01595e57 0.0916863
\(549\) 2.06526e58 0.259519
\(550\) 3.06499e58 0.370366
\(551\) −7.74237e58 −0.899735
\(552\) 3.16781e57 0.0354053
\(553\) −4.33162e58 −0.465650
\(554\) −1.87455e58 −0.193837
\(555\) 4.37616e58 0.435305
\(556\) −6.30968e58 −0.603809
\(557\) −1.19339e58 −0.109874 −0.0549372 0.998490i \(-0.517496\pi\)
−0.0549372 + 0.998490i \(0.517496\pi\)
\(558\) −3.46720e58 −0.307145
\(559\) 2.12919e59 1.81493
\(560\) −7.88555e58 −0.646829
\(561\) −4.16562e58 −0.328835
\(562\) −5.45729e58 −0.414616
\(563\) 2.41291e59 1.76445 0.882227 0.470824i \(-0.156043\pi\)
0.882227 + 0.470824i \(0.156043\pi\)
\(564\) 3.85260e58 0.271177
\(565\) 2.32054e59 1.57234
\(566\) −2.86191e58 −0.186682
\(567\) −2.57024e58 −0.161413
\(568\) −2.17945e59 −1.31782
\(569\) −1.74795e59 −1.01769 −0.508846 0.860858i \(-0.669928\pi\)
−0.508846 + 0.860858i \(0.669928\pi\)
\(570\) 5.15630e58 0.289087
\(571\) 1.95279e58 0.105434 0.0527169 0.998609i \(-0.483212\pi\)
0.0527169 + 0.998609i \(0.483212\pi\)
\(572\) 9.91967e58 0.515801
\(573\) 2.13168e59 1.06757
\(574\) 1.57957e59 0.761962
\(575\) −2.15198e58 −0.0999955
\(576\) 1.81742e58 0.0813527
\(577\) −1.56433e59 −0.674603 −0.337302 0.941397i \(-0.609514\pi\)
−0.337302 + 0.941397i \(0.609514\pi\)
\(578\) 3.65929e58 0.152037
\(579\) 1.83670e59 0.735274
\(580\) 4.30792e59 1.66175
\(581\) −1.08288e59 −0.402525
\(582\) 8.72832e58 0.312670
\(583\) −4.52060e58 −0.156071
\(584\) −4.29037e59 −1.42764
\(585\) −2.27106e59 −0.728411
\(586\) −3.04474e59 −0.941351
\(587\) −2.46451e59 −0.734534 −0.367267 0.930116i \(-0.619707\pi\)
−0.367267 + 0.930116i \(0.619707\pi\)
\(588\) −1.64826e59 −0.473603
\(589\) −4.07357e59 −1.12849
\(590\) −7.17646e58 −0.191687
\(591\) −2.84326e59 −0.732295
\(592\) 5.51904e58 0.137071
\(593\) −9.08544e58 −0.217606 −0.108803 0.994063i \(-0.534702\pi\)
−0.108803 + 0.994063i \(0.534702\pi\)
\(594\) 2.12933e58 0.0491853
\(595\) 1.16239e60 2.58962
\(596\) 3.58097e59 0.769496
\(597\) 5.97570e58 0.123863
\(598\) 2.46296e58 0.0492472
\(599\) 6.01513e59 1.16029 0.580147 0.814512i \(-0.302995\pi\)
0.580147 + 0.814512i \(0.302995\pi\)
\(600\) −3.99547e59 −0.743561
\(601\) −6.18827e59 −1.11114 −0.555569 0.831470i \(-0.687500\pi\)
−0.555569 + 0.831470i \(0.687500\pi\)
\(602\) 5.57058e59 0.965108
\(603\) 4.96159e57 0.00829467
\(604\) −6.13979e59 −0.990512
\(605\) −7.53867e59 −1.17369
\(606\) −1.65345e59 −0.248444
\(607\) −9.05144e59 −1.31269 −0.656343 0.754463i \(-0.727897\pi\)
−0.656343 + 0.754463i \(0.727897\pi\)
\(608\) 4.62446e59 0.647343
\(609\) 8.92175e59 1.20553
\(610\) 4.77436e59 0.622764
\(611\) 7.05001e59 0.887777
\(612\) 2.30718e59 0.280495
\(613\) −6.99999e59 −0.821670 −0.410835 0.911710i \(-0.634763\pi\)
−0.410835 + 0.911710i \(0.634763\pi\)
\(614\) 7.24575e59 0.821227
\(615\) −8.47208e59 −0.927203
\(616\) 6.10832e59 0.645560
\(617\) −4.01412e59 −0.409693 −0.204847 0.978794i \(-0.565670\pi\)
−0.204847 + 0.978794i \(0.565670\pi\)
\(618\) −1.49642e59 −0.147503
\(619\) 9.69603e59 0.923092 0.461546 0.887116i \(-0.347295\pi\)
0.461546 + 0.887116i \(0.347295\pi\)
\(620\) 2.26657e60 2.08424
\(621\) −1.49504e58 −0.0132796
\(622\) −2.69027e59 −0.230835
\(623\) −5.35283e59 −0.443701
\(624\) −2.86417e59 −0.229366
\(625\) −4.51213e59 −0.349109
\(626\) −2.35804e59 −0.176280
\(627\) 2.50173e59 0.180713
\(628\) −1.05949e60 −0.739544
\(629\) −8.13546e59 −0.548773
\(630\) −5.94175e59 −0.387340
\(631\) 2.52059e60 1.58808 0.794039 0.607867i \(-0.207975\pi\)
0.794039 + 0.607867i \(0.207975\pi\)
\(632\) −4.67798e59 −0.284866
\(633\) 5.32634e59 0.313508
\(634\) 1.00401e60 0.571241
\(635\) −3.66800e60 −2.01741
\(636\) 2.50379e59 0.133128
\(637\) −3.01622e60 −1.55048
\(638\) −7.39128e59 −0.367346
\(639\) 1.02859e60 0.494280
\(640\) −3.06287e60 −1.42318
\(641\) 1.50472e60 0.676096 0.338048 0.941129i \(-0.390233\pi\)
0.338048 + 0.941129i \(0.390233\pi\)
\(642\) 1.38810e59 0.0603139
\(643\) 2.31363e60 0.972205 0.486102 0.873902i \(-0.338418\pi\)
0.486102 + 0.873902i \(0.338418\pi\)
\(644\) −1.82219e59 −0.0740538
\(645\) −2.98780e60 −1.17440
\(646\) −9.58577e59 −0.364442
\(647\) 3.71495e60 1.36619 0.683095 0.730330i \(-0.260634\pi\)
0.683095 + 0.730330i \(0.260634\pi\)
\(648\) −2.77577e59 −0.0987462
\(649\) −3.48187e59 −0.119826
\(650\) −3.10646e60 −1.03426
\(651\) 4.69409e60 1.51203
\(652\) 2.69420e60 0.839665
\(653\) −3.74629e60 −1.12971 −0.564856 0.825190i \(-0.691068\pi\)
−0.564856 + 0.825190i \(0.691068\pi\)
\(654\) −1.15373e60 −0.336654
\(655\) 8.41234e60 2.37536
\(656\) −1.06847e60 −0.291963
\(657\) 2.02484e60 0.535469
\(658\) 1.84449e60 0.472084
\(659\) 6.33557e59 0.156946 0.0784728 0.996916i \(-0.474996\pi\)
0.0784728 + 0.996916i \(0.474996\pi\)
\(660\) −1.39198e60 −0.333764
\(661\) −1.49755e59 −0.0347576 −0.0173788 0.999849i \(-0.505532\pi\)
−0.0173788 + 0.999849i \(0.505532\pi\)
\(662\) 1.60164e60 0.359848
\(663\) 4.22199e60 0.918282
\(664\) −1.16947e60 −0.246249
\(665\) −6.98090e60 −1.42313
\(666\) 4.15859e59 0.0820824
\(667\) 5.18955e59 0.0991800
\(668\) 2.62349e60 0.485496
\(669\) −5.15059e59 −0.0922987
\(670\) 1.14699e59 0.0199046
\(671\) 2.31642e60 0.389299
\(672\) −5.32890e60 −0.867358
\(673\) −3.41197e60 −0.537875 −0.268938 0.963158i \(-0.586673\pi\)
−0.268938 + 0.963158i \(0.586673\pi\)
\(674\) −6.56109e59 −0.100182
\(675\) 1.88566e60 0.278890
\(676\) −4.89740e60 −0.701636
\(677\) 2.74942e60 0.381579 0.190790 0.981631i \(-0.438895\pi\)
0.190790 + 0.981631i \(0.438895\pi\)
\(678\) 2.20517e60 0.296485
\(679\) −1.18169e61 −1.53923
\(680\) 1.25533e61 1.58423
\(681\) −1.49268e60 −0.182517
\(682\) −3.88885e60 −0.460741
\(683\) −8.88685e60 −1.02024 −0.510120 0.860103i \(-0.670399\pi\)
−0.510120 + 0.860103i \(0.670399\pi\)
\(684\) −1.38561e60 −0.154147
\(685\) −1.80161e60 −0.194228
\(686\) −7.84508e59 −0.0819650
\(687\) −6.43844e60 −0.651944
\(688\) −3.76810e60 −0.369803
\(689\) 4.58177e60 0.435833
\(690\) −3.45616e59 −0.0318668
\(691\) 5.07739e60 0.453798 0.226899 0.973918i \(-0.427141\pi\)
0.226899 + 0.973918i \(0.427141\pi\)
\(692\) −4.13445e59 −0.0358209
\(693\) −2.88282e60 −0.242132
\(694\) −2.97464e60 −0.242217
\(695\) 1.62025e61 1.27911
\(696\) 9.63516e60 0.737497
\(697\) 1.57499e61 1.16889
\(698\) −2.44918e60 −0.176250
\(699\) −1.26542e61 −0.883032
\(700\) 2.29828e61 1.55523
\(701\) −2.21004e61 −1.45032 −0.725158 0.688583i \(-0.758233\pi\)
−0.725158 + 0.688583i \(0.758233\pi\)
\(702\) −2.15815e60 −0.137351
\(703\) 4.88588e60 0.301581
\(704\) 2.03844e60 0.122035
\(705\) −9.89297e60 −0.574461
\(706\) −1.36473e61 −0.768680
\(707\) 2.23853e61 1.22305
\(708\) 1.92847e60 0.102211
\(709\) −5.10478e59 −0.0262472 −0.0131236 0.999914i \(-0.504177\pi\)
−0.0131236 + 0.999914i \(0.504177\pi\)
\(710\) 2.37783e61 1.18611
\(711\) 2.20777e60 0.106846
\(712\) −5.78086e60 −0.271439
\(713\) 2.73043e60 0.124396
\(714\) 1.10460e61 0.488306
\(715\) −2.54724e61 −1.09267
\(716\) 1.50278e61 0.625556
\(717\) 3.74129e60 0.151133
\(718\) −1.97512e61 −0.774315
\(719\) −7.78566e59 −0.0296227 −0.0148113 0.999890i \(-0.504715\pi\)
−0.0148113 + 0.999890i \(0.504715\pi\)
\(720\) 4.01916e60 0.148418
\(721\) 2.02594e61 0.726136
\(722\) −8.93489e60 −0.310842
\(723\) 3.91984e60 0.132372
\(724\) 1.69247e61 0.554806
\(725\) −6.54545e61 −2.08292
\(726\) −7.16387e60 −0.221315
\(727\) −2.51056e61 −0.752975 −0.376488 0.926422i \(-0.622868\pi\)
−0.376488 + 0.926422i \(0.622868\pi\)
\(728\) −6.19097e61 −1.80274
\(729\) 1.31002e60 0.0370370
\(730\) 4.68091e61 1.28496
\(731\) 5.55444e61 1.48053
\(732\) −1.28298e61 −0.332070
\(733\) −1.67859e61 −0.421900 −0.210950 0.977497i \(-0.567656\pi\)
−0.210950 + 0.977497i \(0.567656\pi\)
\(734\) −2.09299e61 −0.510859
\(735\) 4.23253e61 1.00328
\(736\) −3.09968e60 −0.0713582
\(737\) 5.56498e59 0.0124426
\(738\) −8.05087e60 −0.174836
\(739\) 1.90742e61 0.402338 0.201169 0.979557i \(-0.435526\pi\)
0.201169 + 0.979557i \(0.435526\pi\)
\(740\) −2.71854e61 −0.556999
\(741\) −2.53558e61 −0.504645
\(742\) 1.19873e61 0.231759
\(743\) −4.77233e61 −0.896336 −0.448168 0.893949i \(-0.647923\pi\)
−0.448168 + 0.893949i \(0.647923\pi\)
\(744\) 5.06944e61 0.925001
\(745\) −9.19548e61 −1.63010
\(746\) 4.64778e60 0.0800499
\(747\) 5.51929e60 0.0923614
\(748\) 2.58776e61 0.420764
\(749\) −1.87929e61 −0.296917
\(750\) 1.35109e61 0.207427
\(751\) 5.90777e61 0.881384 0.440692 0.897658i \(-0.354733\pi\)
0.440692 + 0.897658i \(0.354733\pi\)
\(752\) −1.24766e61 −0.180890
\(753\) 3.32032e61 0.467830
\(754\) 7.49129e61 1.02582
\(755\) 1.57662e62 2.09830
\(756\) 1.59668e61 0.206538
\(757\) 3.29771e61 0.414621 0.207310 0.978275i \(-0.433529\pi\)
0.207310 + 0.978275i \(0.433529\pi\)
\(758\) 2.91681e61 0.356468
\(759\) −1.67686e60 −0.0199204
\(760\) −7.53911e61 −0.870618
\(761\) 1.71303e61 0.192307 0.0961537 0.995366i \(-0.469346\pi\)
0.0961537 + 0.995366i \(0.469346\pi\)
\(762\) −3.48564e61 −0.380408
\(763\) 1.56199e62 1.65730
\(764\) −1.32424e62 −1.36603
\(765\) −5.92453e61 −0.594201
\(766\) −4.67002e61 −0.455407
\(767\) 3.52899e61 0.334618
\(768\) −4.43886e61 −0.409266
\(769\) 2.14436e61 0.192256 0.0961282 0.995369i \(-0.469354\pi\)
0.0961282 + 0.995369i \(0.469354\pi\)
\(770\) −6.66434e61 −0.581040
\(771\) −9.97697e61 −0.845921
\(772\) −1.14099e62 −0.940826
\(773\) 2.20993e62 1.77223 0.886115 0.463465i \(-0.153394\pi\)
0.886115 + 0.463465i \(0.153394\pi\)
\(774\) −2.83925e61 −0.221449
\(775\) −3.44382e62 −2.61249
\(776\) −1.27618e62 −0.941641
\(777\) −5.63014e61 −0.404080
\(778\) 1.01666e62 0.709762
\(779\) −9.45888e61 −0.642369
\(780\) 1.41082e62 0.932046
\(781\) 1.15368e62 0.741458
\(782\) 6.42514e60 0.0401733
\(783\) −4.54730e61 −0.276615
\(784\) 5.33790e61 0.315919
\(785\) 2.72063e62 1.56665
\(786\) 7.99410e61 0.447904
\(787\) −2.05060e62 −1.11796 −0.558978 0.829183i \(-0.688806\pi\)
−0.558978 + 0.829183i \(0.688806\pi\)
\(788\) 1.76628e62 0.937015
\(789\) 7.42084e61 0.383087
\(790\) 5.10380e61 0.256396
\(791\) −2.98548e62 −1.45955
\(792\) −3.11333e61 −0.148127
\(793\) −2.34776e62 −1.08713
\(794\) −2.24640e62 −1.01239
\(795\) −6.42940e61 −0.282018
\(796\) −3.71220e61 −0.158490
\(797\) 4.43887e62 1.84467 0.922336 0.386390i \(-0.126278\pi\)
0.922336 + 0.386390i \(0.126278\pi\)
\(798\) −6.63383e61 −0.268350
\(799\) 1.83914e62 0.724203
\(800\) 3.90955e62 1.49862
\(801\) 2.72827e61 0.101810
\(802\) −1.16011e62 −0.421455
\(803\) 2.27108e62 0.803246
\(804\) −3.08223e60 −0.0106135
\(805\) 4.67915e61 0.156876
\(806\) 3.94147e62 1.28663
\(807\) −1.85060e62 −0.588208
\(808\) 2.41753e62 0.748217
\(809\) −3.35142e62 −1.01003 −0.505017 0.863109i \(-0.668514\pi\)
−0.505017 + 0.863109i \(0.668514\pi\)
\(810\) 3.02843e61 0.0888771
\(811\) 3.67586e62 1.05054 0.525268 0.850937i \(-0.323965\pi\)
0.525268 + 0.850937i \(0.323965\pi\)
\(812\) −5.54235e62 −1.54255
\(813\) 1.59841e62 0.433254
\(814\) 4.66432e61 0.123130
\(815\) −6.91835e62 −1.77875
\(816\) −7.47179e61 −0.187105
\(817\) −3.33581e62 −0.813630
\(818\) −3.74381e62 −0.889442
\(819\) 2.92182e62 0.676161
\(820\) 5.26300e62 1.18641
\(821\) 1.88608e62 0.414173 0.207087 0.978323i \(-0.433602\pi\)
0.207087 + 0.978323i \(0.433602\pi\)
\(822\) −1.71204e61 −0.0366243
\(823\) −5.87682e61 −0.122475 −0.0612373 0.998123i \(-0.519505\pi\)
−0.0612373 + 0.998123i \(0.519505\pi\)
\(824\) 2.18794e62 0.444222
\(825\) 2.11498e62 0.418356
\(826\) 9.23287e61 0.177937
\(827\) −4.80326e62 −0.901920 −0.450960 0.892544i \(-0.648918\pi\)
−0.450960 + 0.892544i \(0.648918\pi\)
\(828\) 9.28747e60 0.0169920
\(829\) −3.34419e62 −0.596167 −0.298084 0.954540i \(-0.596347\pi\)
−0.298084 + 0.954540i \(0.596347\pi\)
\(830\) 1.27592e62 0.221638
\(831\) −1.29352e62 −0.218954
\(832\) −2.06602e62 −0.340787
\(833\) −7.86844e62 −1.26480
\(834\) 1.53969e62 0.241192
\(835\) −6.73679e62 −1.02848
\(836\) −1.55412e62 −0.231233
\(837\) −2.39252e62 −0.346943
\(838\) 3.46270e62 0.489406
\(839\) −4.42846e62 −0.610057 −0.305028 0.952343i \(-0.598666\pi\)
−0.305028 + 0.952343i \(0.598666\pi\)
\(840\) 8.68752e62 1.16652
\(841\) 8.14410e62 1.06593
\(842\) 1.39410e62 0.177863
\(843\) −3.76577e62 −0.468340
\(844\) −3.30881e62 −0.401153
\(845\) 1.25759e63 1.48635
\(846\) −9.40112e61 −0.108322
\(847\) 9.69886e62 1.08950
\(848\) −8.10851e61 −0.0888036
\(849\) −1.97484e62 −0.210871
\(850\) −8.10386e62 −0.843695
\(851\) −3.27490e61 −0.0332440
\(852\) −6.38976e62 −0.632461
\(853\) 1.53630e63 1.48276 0.741381 0.671084i \(-0.234171\pi\)
0.741381 + 0.671084i \(0.234171\pi\)
\(854\) −6.14244e62 −0.578091
\(855\) 3.55807e62 0.326545
\(856\) −2.02956e62 −0.181642
\(857\) 2.03104e62 0.177268 0.0886340 0.996064i \(-0.471750\pi\)
0.0886340 + 0.996064i \(0.471750\pi\)
\(858\) −2.42060e62 −0.206038
\(859\) −2.60716e62 −0.216429 −0.108214 0.994128i \(-0.534513\pi\)
−0.108214 + 0.994128i \(0.534513\pi\)
\(860\) 1.85607e63 1.50272
\(861\) 1.08997e63 0.860693
\(862\) −8.08238e62 −0.622491
\(863\) 6.40324e62 0.481025 0.240513 0.970646i \(-0.422684\pi\)
0.240513 + 0.970646i \(0.422684\pi\)
\(864\) 2.71607e62 0.199020
\(865\) 1.06167e62 0.0758829
\(866\) 6.12916e62 0.427333
\(867\) 2.52507e62 0.171737
\(868\) −2.91605e63 −1.93473
\(869\) 2.47626e62 0.160277
\(870\) −1.05122e63 −0.663789
\(871\) −5.64028e61 −0.0347464
\(872\) 1.68689e63 1.01387
\(873\) 6.02292e62 0.353184
\(874\) −3.85872e61 −0.0220774
\(875\) −1.82918e63 −1.02113
\(876\) −1.25786e63 −0.685165
\(877\) −2.92060e62 −0.155232 −0.0776158 0.996983i \(-0.524731\pi\)
−0.0776158 + 0.996983i \(0.524731\pi\)
\(878\) −3.23857e62 −0.167966
\(879\) −2.10100e63 −1.06333
\(880\) 4.50794e62 0.222639
\(881\) 1.29888e63 0.626020 0.313010 0.949750i \(-0.398663\pi\)
0.313010 + 0.949750i \(0.398663\pi\)
\(882\) 4.02210e62 0.189181
\(883\) −1.32664e63 −0.608972 −0.304486 0.952517i \(-0.598485\pi\)
−0.304486 + 0.952517i \(0.598485\pi\)
\(884\) −2.62277e63 −1.17500
\(885\) −4.95208e62 −0.216524
\(886\) −1.06496e62 −0.0454475
\(887\) −2.79044e63 −1.16229 −0.581146 0.813799i \(-0.697396\pi\)
−0.581146 + 0.813799i \(0.697396\pi\)
\(888\) −6.08034e62 −0.247200
\(889\) 4.71906e63 1.87270
\(890\) 6.30707e62 0.244311
\(891\) 1.46933e62 0.0555584
\(892\) 3.19963e62 0.118102
\(893\) −1.10453e63 −0.397988
\(894\) −8.73831e62 −0.307376
\(895\) −3.85895e63 −1.32518
\(896\) 3.94053e63 1.32109
\(897\) 1.69955e62 0.0556283
\(898\) 2.61923e63 0.837013
\(899\) 8.30484e63 2.59118
\(900\) −1.17140e63 −0.356856
\(901\) 1.19525e63 0.355530
\(902\) −9.02995e62 −0.262268
\(903\) 3.84395e63 1.09016
\(904\) −3.22421e63 −0.892898
\(905\) −4.34604e63 −1.17530
\(906\) 1.49824e63 0.395661
\(907\) −2.67600e63 −0.690127 −0.345063 0.938579i \(-0.612143\pi\)
−0.345063 + 0.938579i \(0.612143\pi\)
\(908\) 9.27278e62 0.233541
\(909\) −1.14095e63 −0.280636
\(910\) 6.75451e63 1.62257
\(911\) 4.14838e63 0.973270 0.486635 0.873605i \(-0.338224\pi\)
0.486635 + 0.873605i \(0.338224\pi\)
\(912\) 4.48731e62 0.102824
\(913\) 6.19050e62 0.138549
\(914\) −1.79533e63 −0.392464
\(915\) 3.29452e63 0.703458
\(916\) 3.99967e63 0.834202
\(917\) −1.08229e64 −2.20497
\(918\) −5.62998e62 −0.112044
\(919\) −7.22515e63 −1.40463 −0.702317 0.711864i \(-0.747851\pi\)
−0.702317 + 0.711864i \(0.747851\pi\)
\(920\) 5.05330e62 0.0959704
\(921\) 4.99988e63 0.927636
\(922\) 3.01397e63 0.546290
\(923\) −1.16929e64 −2.07054
\(924\) 1.79085e63 0.309823
\(925\) 4.13055e63 0.698169
\(926\) −2.06925e63 −0.341726
\(927\) −1.03259e63 −0.166616
\(928\) −9.42795e63 −1.48640
\(929\) 1.05329e63 0.162260 0.0811299 0.996704i \(-0.474147\pi\)
0.0811299 + 0.996704i \(0.474147\pi\)
\(930\) −5.53089e63 −0.832553
\(931\) 4.72552e63 0.695075
\(932\) 7.86103e63 1.12989
\(933\) −1.85640e63 −0.260746
\(934\) −2.30237e63 −0.316022
\(935\) −6.64502e63 −0.891347
\(936\) 3.15546e63 0.413649
\(937\) 2.35279e63 0.301427 0.150713 0.988577i \(-0.451843\pi\)
0.150713 + 0.988577i \(0.451843\pi\)
\(938\) −1.47566e62 −0.0184768
\(939\) −1.62715e63 −0.199121
\(940\) 6.14568e63 0.735058
\(941\) 1.00287e64 1.17237 0.586187 0.810176i \(-0.300628\pi\)
0.586187 + 0.810176i \(0.300628\pi\)
\(942\) 2.58537e63 0.295412
\(943\) 6.34009e62 0.0708099
\(944\) −6.24537e62 −0.0681805
\(945\) −4.10007e63 −0.437529
\(946\) −3.18454e63 −0.332191
\(947\) −7.19088e63 −0.733259 −0.366630 0.930367i \(-0.619488\pi\)
−0.366630 + 0.930367i \(0.619488\pi\)
\(948\) −1.37150e63 −0.136715
\(949\) −2.30181e64 −2.24309
\(950\) 4.86691e63 0.463656
\(951\) 6.92812e63 0.645259
\(952\) −1.61505e64 −1.47059
\(953\) −2.88072e63 −0.256450 −0.128225 0.991745i \(-0.540928\pi\)
−0.128225 + 0.991745i \(0.540928\pi\)
\(954\) −6.10975e62 −0.0531782
\(955\) 3.40047e64 2.89379
\(956\) −2.32415e63 −0.193384
\(957\) −5.10031e63 −0.414944
\(958\) 6.14618e63 0.488930
\(959\) 2.31785e63 0.180296
\(960\) 2.89916e63 0.220516
\(961\) 3.02503e64 2.24997
\(962\) −4.72743e63 −0.343844
\(963\) 9.57850e62 0.0681290
\(964\) −2.43507e63 −0.169377
\(965\) 2.92991e64 1.99305
\(966\) 4.44652e62 0.0295809
\(967\) −2.88412e64 −1.87648 −0.938240 0.345985i \(-0.887545\pi\)
−0.938240 + 0.345985i \(0.887545\pi\)
\(968\) 1.04744e64 0.666514
\(969\) −6.61460e63 −0.411664
\(970\) 1.39235e64 0.847530
\(971\) 1.06413e64 0.633550 0.316775 0.948501i \(-0.397400\pi\)
0.316775 + 0.948501i \(0.397400\pi\)
\(972\) −8.13807e62 −0.0473911
\(973\) −2.08452e64 −1.18736
\(974\) −1.20997e63 −0.0674153
\(975\) −2.14360e64 −1.16827
\(976\) 4.15492e63 0.221509
\(977\) −7.33219e63 −0.382385 −0.191192 0.981553i \(-0.561235\pi\)
−0.191192 + 0.981553i \(0.561235\pi\)
\(978\) −6.57439e63 −0.335405
\(979\) 3.06006e63 0.152722
\(980\) −2.62932e64 −1.28376
\(981\) −7.96126e63 −0.380275
\(982\) −6.87294e63 −0.321178
\(983\) 3.20351e64 1.46462 0.732311 0.680971i \(-0.238442\pi\)
0.732311 + 0.680971i \(0.238442\pi\)
\(984\) 1.17713e64 0.526538
\(985\) −4.53559e64 −1.98497
\(986\) 1.95426e64 0.836814
\(987\) 1.27278e64 0.533254
\(988\) 1.57515e64 0.645724
\(989\) 2.23592e63 0.0896884
\(990\) 3.39673e63 0.133323
\(991\) 5.41696e63 0.208052 0.104026 0.994575i \(-0.466827\pi\)
0.104026 + 0.994575i \(0.466827\pi\)
\(992\) −4.96042e64 −1.86431
\(993\) 1.10520e64 0.406475
\(994\) −3.05920e64 −1.10103
\(995\) 9.53246e63 0.335745
\(996\) −3.42868e63 −0.118182
\(997\) −2.61802e64 −0.883135 −0.441568 0.897228i \(-0.645577\pi\)
−0.441568 + 0.897228i \(0.645577\pi\)
\(998\) 3.82814e63 0.126381
\(999\) 2.86961e63 0.0927181
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.1.2 3
3.2 odd 2 9.44.a.a.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.44.a.a.1.2 3 1.1 even 1 trivial
9.44.a.a.1.2 3 3.2 odd 2