Properties

Label 3.44.a.a.1.3
Level 3
Weight 44
Character 3.1
Self dual yes
Analytic conductor 35.133
Analytic rank 1
Dimension 3
CM no
Inner twists 1

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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 1.3
Root \(-30662.1\) of defining polynomial
Character \(\chi\) \(=\) 3.1

$q$-expansion

\(f(q)\) \(=\) \(q+4.56260e6 q^{2} +1.04604e10 q^{3} +1.20212e13 q^{4} -1.29230e15 q^{5} +4.77264e16 q^{6} -9.66721e17 q^{7} +1.47149e19 q^{8} +1.09419e20 q^{9} +O(q^{10})\) \(q+4.56260e6 q^{2} +1.04604e10 q^{3} +1.20212e13 q^{4} -1.29230e15 q^{5} +4.77264e16 q^{6} -9.66721e17 q^{7} +1.47149e19 q^{8} +1.09419e20 q^{9} -5.89624e21 q^{10} -4.14867e22 q^{11} +1.25746e23 q^{12} +6.85476e23 q^{13} -4.41076e24 q^{14} -1.35179e25 q^{15} -3.86016e25 q^{16} -1.87770e26 q^{17} +4.99235e26 q^{18} -3.67577e27 q^{19} -1.55350e28 q^{20} -1.01122e28 q^{21} -1.89287e29 q^{22} +2.38175e29 q^{23} +1.53923e29 q^{24} +5.33166e29 q^{25} +3.12755e30 q^{26} +1.14456e30 q^{27} -1.16211e31 q^{28} +4.15139e31 q^{29} -6.16767e31 q^{30} -3.15649e31 q^{31} -3.05557e32 q^{32} -4.33966e32 q^{33} -8.56717e32 q^{34} +1.24929e33 q^{35} +1.31535e33 q^{36} -6.10581e32 q^{37} -1.67711e34 q^{38} +7.17033e33 q^{39} -1.90160e34 q^{40} -4.47211e34 q^{41} -4.61381e34 q^{42} -2.07163e35 q^{43} -4.98720e35 q^{44} -1.41402e35 q^{45} +1.08670e36 q^{46} +1.73685e36 q^{47} -4.03787e35 q^{48} -1.24926e36 q^{49} +2.43262e36 q^{50} -1.96414e36 q^{51} +8.24025e36 q^{52} -1.34883e37 q^{53} +5.22217e36 q^{54} +5.36132e37 q^{55} -1.42252e37 q^{56} -3.84499e37 q^{57} +1.89411e38 q^{58} -7.90833e37 q^{59} -1.62501e38 q^{60} +1.04129e38 q^{61} -1.44018e38 q^{62} -1.05778e38 q^{63} -1.05459e39 q^{64} -8.85840e38 q^{65} -1.98001e39 q^{66} +2.71441e39 q^{67} -2.25722e39 q^{68} +2.49140e39 q^{69} +5.70002e39 q^{70} +6.41305e39 q^{71} +1.61008e39 q^{72} +4.03967e39 q^{73} -2.78583e39 q^{74} +5.57711e39 q^{75} -4.41872e40 q^{76} +4.01061e40 q^{77} +3.27153e40 q^{78} -6.03727e40 q^{79} +4.98848e40 q^{80} +1.19725e40 q^{81} -2.04044e41 q^{82} +2.83283e41 q^{83} -1.21561e41 q^{84} +2.42654e41 q^{85} -9.45200e41 q^{86} +4.34250e41 q^{87} -6.10471e41 q^{88} -7.96312e41 q^{89} -6.45160e41 q^{90} -6.62665e41 q^{91} +2.86315e42 q^{92} -3.30180e41 q^{93} +7.92454e42 q^{94} +4.75019e42 q^{95} -3.19623e42 q^{96} -2.28074e41 q^{97} -5.69989e42 q^{98} -4.53944e42 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 4857024q^{2} + 31381059609q^{3} - 1781058029568q^{4} - 507753321105270q^{5} + 50806186555447872q^{6} - 1633169303707089288q^{7} + 11196260694472851456q^{8} + 328256967394537077627q^{9} + O(q^{10}) \) \( 3q + 4857024q^{2} + 31381059609q^{3} - 1781058029568q^{4} - 507753321105270q^{5} + 50806186555447872q^{6} - 1633169303707089288q^{7} + 11196260694472851456q^{8} + \)\(32\!\cdots\!27\)\(q^{9} - \)\(22\!\cdots\!20\)\(q^{10} - \)\(27\!\cdots\!20\)\(q^{11} - \)\(18\!\cdots\!04\)\(q^{12} - \)\(99\!\cdots\!50\)\(q^{13} - \)\(94\!\cdots\!28\)\(q^{14} - \)\(53\!\cdots\!10\)\(q^{15} + \)\(23\!\cdots\!36\)\(q^{16} - \)\(16\!\cdots\!82\)\(q^{17} + \)\(53\!\cdots\!16\)\(q^{18} - \)\(32\!\cdots\!64\)\(q^{19} - \)\(19\!\cdots\!60\)\(q^{20} - \)\(17\!\cdots\!64\)\(q^{21} - \)\(17\!\cdots\!24\)\(q^{22} + \)\(11\!\cdots\!04\)\(q^{23} + \)\(11\!\cdots\!68\)\(q^{24} + \)\(18\!\cdots\!25\)\(q^{25} + \)\(17\!\cdots\!36\)\(q^{26} + \)\(34\!\cdots\!81\)\(q^{27} - \)\(84\!\cdots\!44\)\(q^{28} - \)\(28\!\cdots\!58\)\(q^{29} - \)\(23\!\cdots\!60\)\(q^{30} - \)\(56\!\cdots\!36\)\(q^{31} - \)\(29\!\cdots\!88\)\(q^{32} - \)\(29\!\cdots\!60\)\(q^{33} - \)\(17\!\cdots\!76\)\(q^{34} - \)\(36\!\cdots\!20\)\(q^{35} - \)\(19\!\cdots\!12\)\(q^{36} - \)\(77\!\cdots\!78\)\(q^{37} - \)\(11\!\cdots\!08\)\(q^{38} - \)\(10\!\cdots\!50\)\(q^{39} - \)\(75\!\cdots\!00\)\(q^{40} - \)\(15\!\cdots\!66\)\(q^{41} - \)\(99\!\cdots\!84\)\(q^{42} - \)\(50\!\cdots\!88\)\(q^{43} - \)\(58\!\cdots\!72\)\(q^{44} - \)\(55\!\cdots\!30\)\(q^{45} + \)\(12\!\cdots\!64\)\(q^{46} + \)\(51\!\cdots\!36\)\(q^{47} + \)\(24\!\cdots\!08\)\(q^{48} + \)\(11\!\cdots\!03\)\(q^{49} + \)\(53\!\cdots\!00\)\(q^{50} - \)\(16\!\cdots\!46\)\(q^{51} + \)\(19\!\cdots\!08\)\(q^{52} + \)\(31\!\cdots\!34\)\(q^{53} + \)\(55\!\cdots\!48\)\(q^{54} + \)\(72\!\cdots\!60\)\(q^{55} + \)\(64\!\cdots\!20\)\(q^{56} - \)\(33\!\cdots\!92\)\(q^{57} + \)\(16\!\cdots\!64\)\(q^{58} - \)\(17\!\cdots\!76\)\(q^{59} - \)\(20\!\cdots\!80\)\(q^{60} - \)\(12\!\cdots\!18\)\(q^{61} - \)\(68\!\cdots\!56\)\(q^{62} - \)\(17\!\cdots\!92\)\(q^{63} - \)\(97\!\cdots\!36\)\(q^{64} - \)\(25\!\cdots\!40\)\(q^{65} - \)\(18\!\cdots\!72\)\(q^{66} + \)\(12\!\cdots\!48\)\(q^{67} - \)\(27\!\cdots\!68\)\(q^{68} + \)\(12\!\cdots\!12\)\(q^{69} + \)\(18\!\cdots\!80\)\(q^{70} + \)\(22\!\cdots\!16\)\(q^{71} + \)\(12\!\cdots\!04\)\(q^{72} + \)\(31\!\cdots\!54\)\(q^{73} + \)\(12\!\cdots\!32\)\(q^{74} + \)\(19\!\cdots\!75\)\(q^{75} - \)\(45\!\cdots\!04\)\(q^{76} + \)\(15\!\cdots\!44\)\(q^{77} + \)\(18\!\cdots\!08\)\(q^{78} - \)\(43\!\cdots\!80\)\(q^{79} + \)\(51\!\cdots\!80\)\(q^{80} + \)\(35\!\cdots\!43\)\(q^{81} - \)\(20\!\cdots\!96\)\(q^{82} + \)\(89\!\cdots\!68\)\(q^{83} - \)\(88\!\cdots\!32\)\(q^{84} - \)\(60\!\cdots\!20\)\(q^{85} - \)\(10\!\cdots\!20\)\(q^{86} - \)\(29\!\cdots\!74\)\(q^{87} - \)\(86\!\cdots\!84\)\(q^{88} + \)\(65\!\cdots\!06\)\(q^{89} - \)\(25\!\cdots\!80\)\(q^{90} + \)\(13\!\cdots\!24\)\(q^{91} + \)\(37\!\cdots\!72\)\(q^{92} - \)\(59\!\cdots\!08\)\(q^{93} + \)\(78\!\cdots\!20\)\(q^{94} + \)\(93\!\cdots\!00\)\(q^{95} - \)\(30\!\cdots\!64\)\(q^{96} + \)\(61\!\cdots\!78\)\(q^{97} - \)\(20\!\cdots\!60\)\(q^{98} - \)\(30\!\cdots\!80\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.56260e6 1.53839 0.769196 0.639013i \(-0.220657\pi\)
0.769196 + 0.639013i \(0.220657\pi\)
\(3\) 1.04604e10 0.577350
\(4\) 1.20212e13 1.36665
\(5\) −1.29230e15 −1.21201 −0.606007 0.795459i \(-0.707230\pi\)
−0.606007 + 0.795459i \(0.707230\pi\)
\(6\) 4.77264e16 0.888191
\(7\) −9.66721e17 −0.654174 −0.327087 0.944994i \(-0.606067\pi\)
−0.327087 + 0.944994i \(0.606067\pi\)
\(8\) 1.47149e19 0.564055
\(9\) 1.09419e20 0.333333
\(10\) −5.89624e21 −1.86455
\(11\) −4.14867e22 −1.69031 −0.845155 0.534521i \(-0.820492\pi\)
−0.845155 + 0.534521i \(0.820492\pi\)
\(12\) 1.25746e23 0.789037
\(13\) 6.85476e23 0.769503 0.384752 0.923020i \(-0.374287\pi\)
0.384752 + 0.923020i \(0.374287\pi\)
\(14\) −4.41076e24 −1.00638
\(15\) −1.35179e25 −0.699757
\(16\) −3.86016e25 −0.498914
\(17\) −1.87770e26 −0.659134 −0.329567 0.944132i \(-0.606903\pi\)
−0.329567 + 0.944132i \(0.606903\pi\)
\(18\) 4.99235e26 0.512798
\(19\) −3.67577e27 −1.18072 −0.590359 0.807141i \(-0.701014\pi\)
−0.590359 + 0.807141i \(0.701014\pi\)
\(20\) −1.55350e28 −1.65640
\(21\) −1.01122e28 −0.377688
\(22\) −1.89287e29 −2.60036
\(23\) 2.38175e29 1.25820 0.629098 0.777326i \(-0.283424\pi\)
0.629098 + 0.777326i \(0.283424\pi\)
\(24\) 1.53923e29 0.325657
\(25\) 5.33166e29 0.468978
\(26\) 3.12755e30 1.18380
\(27\) 1.14456e30 0.192450
\(28\) −1.16211e31 −0.894028
\(29\) 4.15139e31 1.50188 0.750942 0.660368i \(-0.229600\pi\)
0.750942 + 0.660368i \(0.229600\pi\)
\(30\) −6.16767e31 −1.07650
\(31\) −3.15649e31 −0.272225 −0.136112 0.990693i \(-0.543461\pi\)
−0.136112 + 0.990693i \(0.543461\pi\)
\(32\) −3.05557e32 −1.33158
\(33\) −4.33966e32 −0.975901
\(34\) −8.56717e32 −1.01401
\(35\) 1.24929e33 0.792868
\(36\) 1.31535e33 0.455551
\(37\) −6.10581e32 −0.117329 −0.0586646 0.998278i \(-0.518684\pi\)
−0.0586646 + 0.998278i \(0.518684\pi\)
\(38\) −1.67711e34 −1.81641
\(39\) 7.17033e33 0.444273
\(40\) −1.90160e34 −0.683642
\(41\) −4.47211e34 −0.945496 −0.472748 0.881198i \(-0.656738\pi\)
−0.472748 + 0.881198i \(0.656738\pi\)
\(42\) −4.61381e34 −0.581032
\(43\) −2.07163e35 −1.57304 −0.786520 0.617565i \(-0.788119\pi\)
−0.786520 + 0.617565i \(0.788119\pi\)
\(44\) −4.98720e35 −2.31007
\(45\) −1.41402e35 −0.404005
\(46\) 1.08670e36 1.93560
\(47\) 1.73685e36 1.94831 0.974155 0.225883i \(-0.0725266\pi\)
0.974155 + 0.225883i \(0.0725266\pi\)
\(48\) −4.03787e35 −0.288048
\(49\) −1.24926e36 −0.572056
\(50\) 2.43262e36 0.721472
\(51\) −1.96414e36 −0.380551
\(52\) 8.24025e36 1.05164
\(53\) −1.34883e37 −1.14294 −0.571472 0.820622i \(-0.693627\pi\)
−0.571472 + 0.820622i \(0.693627\pi\)
\(54\) 5.22217e36 0.296064
\(55\) 5.36132e37 2.04868
\(56\) −1.42252e37 −0.368990
\(57\) −3.84499e37 −0.681687
\(58\) 1.89411e38 2.31049
\(59\) −7.90833e37 −0.667985 −0.333992 0.942576i \(-0.608396\pi\)
−0.333992 + 0.942576i \(0.608396\pi\)
\(60\) −1.62501e38 −0.956324
\(61\) 1.04129e38 0.429517 0.214759 0.976667i \(-0.431103\pi\)
0.214759 + 0.976667i \(0.431103\pi\)
\(62\) −1.44018e38 −0.418789
\(63\) −1.05778e38 −0.218058
\(64\) −1.05459e39 −1.54958
\(65\) −8.85840e38 −0.932649
\(66\) −1.98001e39 −1.50132
\(67\) 2.71441e39 1.48959 0.744796 0.667292i \(-0.232547\pi\)
0.744796 + 0.667292i \(0.232547\pi\)
\(68\) −2.25722e39 −0.900806
\(69\) 2.49140e39 0.726420
\(70\) 5.70002e39 1.21974
\(71\) 6.41305e39 1.01160 0.505801 0.862650i \(-0.331197\pi\)
0.505801 + 0.862650i \(0.331197\pi\)
\(72\) 1.61008e39 0.188018
\(73\) 4.03967e39 0.350675 0.175337 0.984508i \(-0.443898\pi\)
0.175337 + 0.984508i \(0.443898\pi\)
\(74\) −2.78583e39 −0.180498
\(75\) 5.57711e39 0.270765
\(76\) −4.41872e40 −1.61363
\(77\) 4.01061e40 1.10576
\(78\) 3.27153e40 0.683466
\(79\) −6.03727e40 −0.959087 −0.479543 0.877518i \(-0.659198\pi\)
−0.479543 + 0.877518i \(0.659198\pi\)
\(80\) 4.98848e40 0.604691
\(81\) 1.19725e40 0.111111
\(82\) −2.04044e41 −1.45454
\(83\) 2.83283e41 1.55612 0.778058 0.628193i \(-0.216205\pi\)
0.778058 + 0.628193i \(0.216205\pi\)
\(84\) −1.21561e41 −0.516168
\(85\) 2.42654e41 0.798879
\(86\) −9.45200e41 −2.41995
\(87\) 4.34250e41 0.867113
\(88\) −6.10471e41 −0.953427
\(89\) −7.96312e41 −0.975434 −0.487717 0.873002i \(-0.662170\pi\)
−0.487717 + 0.873002i \(0.662170\pi\)
\(90\) −6.45160e41 −0.621518
\(91\) −6.62665e41 −0.503389
\(92\) 2.86315e42 1.71952
\(93\) −3.30180e41 −0.157169
\(94\) 7.92454e42 2.99726
\(95\) 4.75019e42 1.43105
\(96\) −3.19623e42 −0.768789
\(97\) −2.28074e41 −0.0439018 −0.0219509 0.999759i \(-0.506988\pi\)
−0.0219509 + 0.999759i \(0.506988\pi\)
\(98\) −5.69989e42 −0.880047
\(99\) −4.53944e42 −0.563437
\(100\) 6.40930e42 0.640930
\(101\) −1.22069e41 −0.00985585 −0.00492793 0.999988i \(-0.501569\pi\)
−0.00492793 + 0.999988i \(0.501569\pi\)
\(102\) −8.96156e42 −0.585437
\(103\) −1.54032e43 −0.815851 −0.407926 0.913015i \(-0.633748\pi\)
−0.407926 + 0.913015i \(0.633748\pi\)
\(104\) 1.00867e43 0.434042
\(105\) 1.30680e43 0.457763
\(106\) −6.15415e43 −1.75830
\(107\) −3.88129e43 −0.906201 −0.453100 0.891459i \(-0.649682\pi\)
−0.453100 + 0.891459i \(0.649682\pi\)
\(108\) 1.37590e43 0.263012
\(109\) −6.58075e43 −1.03182 −0.515912 0.856642i \(-0.672547\pi\)
−0.515912 + 0.856642i \(0.672547\pi\)
\(110\) 2.44616e44 3.15167
\(111\) −6.38689e42 −0.0677400
\(112\) 3.73170e43 0.326377
\(113\) 1.24527e43 0.0899655 0.0449828 0.998988i \(-0.485677\pi\)
0.0449828 + 0.998988i \(0.485677\pi\)
\(114\) −1.75431e44 −1.04870
\(115\) −3.07794e44 −1.52495
\(116\) 4.99046e44 2.05255
\(117\) 7.50041e43 0.256501
\(118\) −3.60825e44 −1.02762
\(119\) 1.81521e44 0.431188
\(120\) −1.98914e44 −0.394701
\(121\) 1.11875e45 1.85715
\(122\) 4.75099e44 0.660767
\(123\) −4.67799e44 −0.545882
\(124\) −3.79448e44 −0.372037
\(125\) 7.80163e44 0.643606
\(126\) −4.82621e44 −0.335459
\(127\) 5.22881e44 0.306636 0.153318 0.988177i \(-0.451004\pi\)
0.153318 + 0.988177i \(0.451004\pi\)
\(128\) −2.12396e45 −1.05228
\(129\) −2.16699e45 −0.908195
\(130\) −4.04173e45 −1.43478
\(131\) −1.97998e45 −0.596112 −0.298056 0.954548i \(-0.596338\pi\)
−0.298056 + 0.954548i \(0.596338\pi\)
\(132\) −5.21679e45 −1.33372
\(133\) 3.55345e45 0.772395
\(134\) 1.23848e46 2.29158
\(135\) −1.47911e45 −0.233252
\(136\) −2.76300e45 −0.371787
\(137\) 7.04963e45 0.810352 0.405176 0.914239i \(-0.367210\pi\)
0.405176 + 0.914239i \(0.367210\pi\)
\(138\) 1.13673e46 1.11752
\(139\) −1.36482e46 −1.14884 −0.574419 0.818562i \(-0.694772\pi\)
−0.574419 + 0.818562i \(0.694772\pi\)
\(140\) 1.50180e46 1.08357
\(141\) 1.81680e46 1.12486
\(142\) 2.92601e46 1.55624
\(143\) −2.84382e46 −1.30070
\(144\) −4.22375e45 −0.166305
\(145\) −5.36483e46 −1.82030
\(146\) 1.84314e46 0.539475
\(147\) −1.30677e46 −0.330277
\(148\) −7.33991e45 −0.160348
\(149\) −6.34924e46 −1.20010 −0.600049 0.799963i \(-0.704852\pi\)
−0.600049 + 0.799963i \(0.704852\pi\)
\(150\) 2.54461e46 0.416542
\(151\) 7.57341e45 0.107470 0.0537350 0.998555i \(-0.482887\pi\)
0.0537350 + 0.998555i \(0.482887\pi\)
\(152\) −5.40884e46 −0.665989
\(153\) −2.05456e46 −0.219711
\(154\) 1.82988e47 1.70109
\(155\) 4.07913e46 0.329940
\(156\) 8.61959e46 0.607166
\(157\) −1.59997e47 −0.982358 −0.491179 0.871059i \(-0.663434\pi\)
−0.491179 + 0.871059i \(0.663434\pi\)
\(158\) −2.75456e47 −1.47545
\(159\) −1.41092e47 −0.659879
\(160\) 3.94871e47 1.61389
\(161\) −2.30249e47 −0.823080
\(162\) 5.46258e46 0.170933
\(163\) 2.01881e47 0.553430 0.276715 0.960952i \(-0.410754\pi\)
0.276715 + 0.960952i \(0.410754\pi\)
\(164\) −5.37601e47 −1.29216
\(165\) 5.60813e47 1.18281
\(166\) 1.29251e48 2.39392
\(167\) −2.04593e47 −0.333033 −0.166517 0.986039i \(-0.553252\pi\)
−0.166517 + 0.986039i \(0.553252\pi\)
\(168\) −1.48800e47 −0.213036
\(169\) −3.23653e47 −0.407865
\(170\) 1.10713e48 1.22899
\(171\) −4.02199e47 −0.393572
\(172\) −2.49034e48 −2.14980
\(173\) 3.51004e47 0.267498 0.133749 0.991015i \(-0.457298\pi\)
0.133749 + 0.991015i \(0.457298\pi\)
\(174\) 1.98131e48 1.33396
\(175\) −5.15423e47 −0.306793
\(176\) 1.60146e48 0.843320
\(177\) −8.27239e47 −0.385661
\(178\) −3.63325e48 −1.50060
\(179\) −2.04481e48 −0.748708 −0.374354 0.927286i \(-0.622136\pi\)
−0.374354 + 0.927286i \(0.622136\pi\)
\(180\) −1.69982e48 −0.552134
\(181\) −3.20223e48 −0.923345 −0.461672 0.887051i \(-0.652750\pi\)
−0.461672 + 0.887051i \(0.652750\pi\)
\(182\) −3.02347e48 −0.774410
\(183\) 1.08923e48 0.247982
\(184\) 3.50472e48 0.709692
\(185\) 7.89053e47 0.142205
\(186\) −1.50648e48 −0.241788
\(187\) 7.78995e48 1.11414
\(188\) 2.08790e49 2.66266
\(189\) −1.10647e48 −0.125896
\(190\) 2.16732e49 2.20151
\(191\) −3.02200e48 −0.274206 −0.137103 0.990557i \(-0.543779\pi\)
−0.137103 + 0.990557i \(0.543779\pi\)
\(192\) −1.10314e49 −0.894650
\(193\) −1.79481e49 −1.30178 −0.650888 0.759174i \(-0.725603\pi\)
−0.650888 + 0.759174i \(0.725603\pi\)
\(194\) −1.04061e48 −0.0675383
\(195\) −9.26620e48 −0.538465
\(196\) −1.50177e49 −0.781802
\(197\) 2.54943e49 1.18965 0.594825 0.803855i \(-0.297221\pi\)
0.594825 + 0.803855i \(0.297221\pi\)
\(198\) −2.07116e49 −0.866787
\(199\) −2.22144e49 −0.834244 −0.417122 0.908851i \(-0.636961\pi\)
−0.417122 + 0.908851i \(0.636961\pi\)
\(200\) 7.84546e48 0.264529
\(201\) 2.83937e49 0.860016
\(202\) −5.56950e47 −0.0151622
\(203\) −4.01323e49 −0.982494
\(204\) −2.36113e49 −0.520081
\(205\) 5.77930e49 1.14595
\(206\) −7.02786e49 −1.25510
\(207\) 2.60609e49 0.419399
\(208\) −2.64605e49 −0.383916
\(209\) 1.52496e50 1.99578
\(210\) 5.96242e49 0.704219
\(211\) −1.11346e50 −1.18741 −0.593706 0.804682i \(-0.702336\pi\)
−0.593706 + 0.804682i \(0.702336\pi\)
\(212\) −1.62145e50 −1.56201
\(213\) 6.70827e49 0.584049
\(214\) −1.77087e50 −1.39409
\(215\) 2.67716e50 1.90655
\(216\) 1.68420e49 0.108552
\(217\) 3.05145e49 0.178083
\(218\) −3.00253e50 −1.58735
\(219\) 4.22564e49 0.202462
\(220\) 6.44495e50 2.79983
\(221\) −1.28712e50 −0.507206
\(222\) −2.91408e49 −0.104211
\(223\) 8.11200e49 0.263374 0.131687 0.991291i \(-0.457961\pi\)
0.131687 + 0.991291i \(0.457961\pi\)
\(224\) 2.95388e50 0.871086
\(225\) 5.83385e49 0.156326
\(226\) 5.68165e49 0.138402
\(227\) −3.50053e50 −0.775492 −0.387746 0.921766i \(-0.626746\pi\)
−0.387746 + 0.921766i \(0.626746\pi\)
\(228\) −4.62213e50 −0.931630
\(229\) 5.91349e50 1.08488 0.542439 0.840095i \(-0.317501\pi\)
0.542439 + 0.840095i \(0.317501\pi\)
\(230\) −1.40434e51 −2.34597
\(231\) 4.19524e50 0.638409
\(232\) 6.10870e50 0.847144
\(233\) −9.65662e50 −1.22088 −0.610440 0.792063i \(-0.709007\pi\)
−0.610440 + 0.792063i \(0.709007\pi\)
\(234\) 3.42214e50 0.394599
\(235\) −2.24453e51 −2.36138
\(236\) −9.50676e50 −0.912902
\(237\) −6.31520e50 −0.553729
\(238\) 8.28207e50 0.663337
\(239\) 2.10427e51 1.54009 0.770047 0.637987i \(-0.220233\pi\)
0.770047 + 0.637987i \(0.220233\pi\)
\(240\) 5.21813e50 0.349119
\(241\) −1.35652e51 −0.829965 −0.414982 0.909829i \(-0.636212\pi\)
−0.414982 + 0.909829i \(0.636212\pi\)
\(242\) 5.10440e51 2.85702
\(243\) 1.25237e50 0.0641500
\(244\) 1.25176e51 0.587001
\(245\) 1.61442e51 0.693340
\(246\) −2.13438e51 −0.839781
\(247\) −2.51965e51 −0.908566
\(248\) −4.64473e50 −0.153550
\(249\) 2.96324e51 0.898424
\(250\) 3.55957e51 0.990119
\(251\) 1.64213e51 0.419201 0.209601 0.977787i \(-0.432784\pi\)
0.209601 + 0.977787i \(0.432784\pi\)
\(252\) −1.27157e51 −0.298009
\(253\) −9.88112e51 −2.12674
\(254\) 2.38570e51 0.471727
\(255\) 2.53825e51 0.461233
\(256\) −4.14504e50 −0.0692420
\(257\) −6.10196e50 −0.0937362 −0.0468681 0.998901i \(-0.514924\pi\)
−0.0468681 + 0.998901i \(0.514924\pi\)
\(258\) −9.88712e51 −1.39716
\(259\) 5.90262e50 0.0767537
\(260\) −1.06489e52 −1.27461
\(261\) 4.54241e51 0.500628
\(262\) −9.03384e51 −0.917054
\(263\) 2.81731e51 0.263504 0.131752 0.991283i \(-0.457940\pi\)
0.131752 + 0.991283i \(0.457940\pi\)
\(264\) −6.38574e51 −0.550462
\(265\) 1.74309e52 1.38526
\(266\) 1.62129e52 1.18825
\(267\) −8.32970e51 −0.563167
\(268\) 3.26305e52 2.03575
\(269\) −6.28193e51 −0.361759 −0.180880 0.983505i \(-0.557894\pi\)
−0.180880 + 0.983505i \(0.557894\pi\)
\(270\) −6.74860e51 −0.358833
\(271\) −3.10633e52 −1.52549 −0.762743 0.646702i \(-0.776148\pi\)
−0.762743 + 0.646702i \(0.776148\pi\)
\(272\) 7.24821e51 0.328851
\(273\) −6.93171e51 −0.290632
\(274\) 3.21646e52 1.24664
\(275\) −2.21193e52 −0.792718
\(276\) 2.99496e52 0.992763
\(277\) −3.49544e52 −1.07198 −0.535991 0.844224i \(-0.680062\pi\)
−0.535991 + 0.844224i \(0.680062\pi\)
\(278\) −6.22714e52 −1.76736
\(279\) −3.45380e51 −0.0907416
\(280\) 1.83831e52 0.447221
\(281\) 2.62712e52 0.591962 0.295981 0.955194i \(-0.404353\pi\)
0.295981 + 0.955194i \(0.404353\pi\)
\(282\) 8.28935e52 1.73047
\(283\) 7.08487e52 1.37064 0.685320 0.728242i \(-0.259662\pi\)
0.685320 + 0.728242i \(0.259662\pi\)
\(284\) 7.70925e52 1.38251
\(285\) 4.96887e52 0.826215
\(286\) −1.29752e53 −2.00099
\(287\) 4.32328e52 0.618519
\(288\) −3.34337e52 −0.443860
\(289\) −4.58954e52 −0.565543
\(290\) −2.44776e53 −2.80034
\(291\) −2.38573e51 −0.0253467
\(292\) 4.85617e52 0.479250
\(293\) −9.78673e52 −0.897395 −0.448698 0.893684i \(-0.648112\pi\)
−0.448698 + 0.893684i \(0.648112\pi\)
\(294\) −5.96229e52 −0.508095
\(295\) 1.02199e53 0.809607
\(296\) −8.98461e51 −0.0661801
\(297\) −4.74841e52 −0.325300
\(298\) −2.89690e53 −1.84622
\(299\) 1.63264e53 0.968186
\(300\) 6.70435e52 0.370041
\(301\) 2.00269e53 1.02904
\(302\) 3.45544e52 0.165331
\(303\) −1.27688e51 −0.00569028
\(304\) 1.41891e53 0.589077
\(305\) −1.34566e53 −0.520581
\(306\) −9.37411e52 −0.338002
\(307\) 3.49196e53 1.17380 0.586899 0.809660i \(-0.300348\pi\)
0.586899 + 0.809660i \(0.300348\pi\)
\(308\) 4.82123e53 1.51119
\(309\) −1.61123e53 −0.471032
\(310\) 1.86114e53 0.507578
\(311\) 1.85544e53 0.472170 0.236085 0.971732i \(-0.424136\pi\)
0.236085 + 0.971732i \(0.424136\pi\)
\(312\) 1.05510e53 0.250594
\(313\) 7.17292e53 1.59035 0.795175 0.606380i \(-0.207379\pi\)
0.795175 + 0.606380i \(0.207379\pi\)
\(314\) −7.30002e53 −1.51125
\(315\) 1.36696e53 0.264289
\(316\) −7.25752e53 −1.31074
\(317\) −7.25321e52 −0.122393 −0.0611964 0.998126i \(-0.519492\pi\)
−0.0611964 + 0.998126i \(0.519492\pi\)
\(318\) −6.43746e53 −1.01515
\(319\) −1.72227e54 −2.53865
\(320\) 1.36284e54 1.87811
\(321\) −4.05996e53 −0.523195
\(322\) −1.05053e54 −1.26622
\(323\) 6.90198e53 0.778251
\(324\) 1.43924e53 0.151850
\(325\) 3.65473e53 0.360880
\(326\) 9.21103e53 0.851393
\(327\) −6.88370e53 −0.595724
\(328\) −6.58064e53 −0.533311
\(329\) −1.67905e54 −1.27453
\(330\) 2.55876e54 1.81962
\(331\) −6.34311e53 −0.422669 −0.211334 0.977414i \(-0.567781\pi\)
−0.211334 + 0.977414i \(0.567781\pi\)
\(332\) 3.40540e54 2.12667
\(333\) −6.68091e52 −0.0391097
\(334\) −9.33477e53 −0.512336
\(335\) −3.50783e54 −1.80541
\(336\) 3.90349e53 0.188434
\(337\) 2.65467e54 1.20218 0.601088 0.799183i \(-0.294734\pi\)
0.601088 + 0.799183i \(0.294734\pi\)
\(338\) −1.47670e54 −0.627456
\(339\) 1.30259e53 0.0519416
\(340\) 2.91700e54 1.09179
\(341\) 1.30952e54 0.460145
\(342\) −1.83507e54 −0.605469
\(343\) 3.31883e54 1.02840
\(344\) −3.04837e54 −0.887280
\(345\) −3.21963e54 −0.880431
\(346\) 1.60149e54 0.411518
\(347\) −3.14107e54 −0.758567 −0.379284 0.925280i \(-0.623830\pi\)
−0.379284 + 0.925280i \(0.623830\pi\)
\(348\) 5.22020e54 1.18504
\(349\) −1.66164e54 −0.354643 −0.177321 0.984153i \(-0.556743\pi\)
−0.177321 + 0.984153i \(0.556743\pi\)
\(350\) −2.35167e54 −0.471969
\(351\) 7.84570e53 0.148091
\(352\) 1.26766e55 2.25079
\(353\) 6.16284e54 1.02950 0.514748 0.857342i \(-0.327886\pi\)
0.514748 + 0.857342i \(0.327886\pi\)
\(354\) −3.77436e54 −0.593298
\(355\) −8.28757e54 −1.22608
\(356\) −9.57262e54 −1.33308
\(357\) 1.89877e54 0.248947
\(358\) −9.32964e54 −1.15181
\(359\) 5.63280e54 0.654929 0.327464 0.944864i \(-0.393806\pi\)
0.327464 + 0.944864i \(0.393806\pi\)
\(360\) −2.08071e54 −0.227881
\(361\) 3.81948e54 0.394094
\(362\) −1.46105e55 −1.42047
\(363\) 1.17025e55 1.07223
\(364\) −7.96602e54 −0.687958
\(365\) −5.22046e54 −0.425023
\(366\) 4.96971e54 0.381494
\(367\) −6.57731e54 −0.476132 −0.238066 0.971249i \(-0.576514\pi\)
−0.238066 + 0.971249i \(0.576514\pi\)
\(368\) −9.19396e54 −0.627732
\(369\) −4.89334e54 −0.315165
\(370\) 3.60013e54 0.218767
\(371\) 1.30394e55 0.747685
\(372\) −3.96916e54 −0.214795
\(373\) −1.12137e55 −0.572807 −0.286404 0.958109i \(-0.592460\pi\)
−0.286404 + 0.958109i \(0.592460\pi\)
\(374\) 3.55424e55 1.71399
\(375\) 8.16078e54 0.371586
\(376\) 2.55575e55 1.09895
\(377\) 2.84568e55 1.15570
\(378\) −5.04838e54 −0.193677
\(379\) 3.17152e54 0.114954 0.0574771 0.998347i \(-0.481694\pi\)
0.0574771 + 0.998347i \(0.481694\pi\)
\(380\) 5.71030e55 1.95574
\(381\) 5.46952e54 0.177036
\(382\) −1.37882e55 −0.421837
\(383\) 2.67653e55 0.774102 0.387051 0.922058i \(-0.373494\pi\)
0.387051 + 0.922058i \(0.373494\pi\)
\(384\) −2.22174e55 −0.607535
\(385\) −5.18290e55 −1.34019
\(386\) −8.18899e55 −2.00264
\(387\) −2.26675e55 −0.524346
\(388\) −2.74172e54 −0.0599985
\(389\) −4.96399e55 −1.02781 −0.513907 0.857846i \(-0.671802\pi\)
−0.513907 + 0.857846i \(0.671802\pi\)
\(390\) −4.22779e55 −0.828371
\(391\) −4.47221e55 −0.829320
\(392\) −1.83827e55 −0.322671
\(393\) −2.07113e55 −0.344165
\(394\) 1.16320e56 1.83015
\(395\) 7.80195e55 1.16243
\(396\) −5.45695e55 −0.770022
\(397\) 1.17506e56 1.57060 0.785300 0.619116i \(-0.212509\pi\)
0.785300 + 0.619116i \(0.212509\pi\)
\(398\) −1.01355e56 −1.28339
\(399\) 3.71703e55 0.445942
\(400\) −2.05811e55 −0.233980
\(401\) −1.22312e54 −0.0131785 −0.00658926 0.999978i \(-0.502097\pi\)
−0.00658926 + 0.999978i \(0.502097\pi\)
\(402\) 1.29549e56 1.32304
\(403\) −2.16370e55 −0.209478
\(404\) −1.46741e54 −0.0134695
\(405\) −1.54721e55 −0.134668
\(406\) −1.83108e56 −1.51146
\(407\) 2.53310e55 0.198323
\(408\) −2.89020e55 −0.214652
\(409\) 1.58299e56 1.11539 0.557696 0.830045i \(-0.311686\pi\)
0.557696 + 0.830045i \(0.311686\pi\)
\(410\) 2.63686e56 1.76293
\(411\) 7.37416e55 0.467857
\(412\) −1.85165e56 −1.11498
\(413\) 7.64515e55 0.436978
\(414\) 1.18905e56 0.645200
\(415\) −3.66086e56 −1.88603
\(416\) −2.09452e56 −1.02466
\(417\) −1.42765e56 −0.663282
\(418\) 6.95776e56 3.07029
\(419\) 8.93668e55 0.374606 0.187303 0.982302i \(-0.440025\pi\)
0.187303 + 0.982302i \(0.440025\pi\)
\(420\) 1.57093e56 0.625602
\(421\) −2.19258e56 −0.829641 −0.414821 0.909903i \(-0.636156\pi\)
−0.414821 + 0.909903i \(0.636156\pi\)
\(422\) −5.08027e56 −1.82671
\(423\) 1.90044e56 0.649436
\(424\) −1.98478e56 −0.644683
\(425\) −1.00112e56 −0.309119
\(426\) 3.06071e56 0.898497
\(427\) −1.00664e56 −0.280979
\(428\) −4.66577e56 −1.23846
\(429\) −2.97473e56 −0.750959
\(430\) 1.22148e57 2.93302
\(431\) 3.47761e55 0.0794364 0.0397182 0.999211i \(-0.487354\pi\)
0.0397182 + 0.999211i \(0.487354\pi\)
\(432\) −4.41819e55 −0.0960161
\(433\) 2.55606e56 0.528545 0.264272 0.964448i \(-0.414868\pi\)
0.264272 + 0.964448i \(0.414868\pi\)
\(434\) 1.39225e56 0.273961
\(435\) −5.61180e56 −1.05095
\(436\) −7.91085e56 −1.41014
\(437\) −8.75478e56 −1.48557
\(438\) 1.92799e56 0.311466
\(439\) −6.27063e56 −0.964548 −0.482274 0.876020i \(-0.660189\pi\)
−0.482274 + 0.876020i \(0.660189\pi\)
\(440\) 7.88911e56 1.15557
\(441\) −1.36693e56 −0.190685
\(442\) −5.87259e56 −0.780281
\(443\) −2.70311e55 −0.0342124 −0.0171062 0.999854i \(-0.505445\pi\)
−0.0171062 + 0.999854i \(0.505445\pi\)
\(444\) −7.67781e55 −0.0925771
\(445\) 1.02907e57 1.18224
\(446\) 3.70118e56 0.405173
\(447\) −6.64152e56 −0.692877
\(448\) 1.01949e57 1.01370
\(449\) 1.72989e57 1.63954 0.819768 0.572696i \(-0.194102\pi\)
0.819768 + 0.572696i \(0.194102\pi\)
\(450\) 2.66175e56 0.240491
\(451\) 1.85533e57 1.59818
\(452\) 1.49696e56 0.122952
\(453\) 7.92205e55 0.0620478
\(454\) −1.59715e57 −1.19301
\(455\) 8.56360e56 0.610115
\(456\) −5.65784e56 −0.384509
\(457\) −9.95087e56 −0.645153 −0.322577 0.946543i \(-0.604549\pi\)
−0.322577 + 0.946543i \(0.604549\pi\)
\(458\) 2.69809e57 1.66897
\(459\) −2.14914e56 −0.126850
\(460\) −3.70005e57 −2.08408
\(461\) −1.80262e57 −0.969025 −0.484512 0.874784i \(-0.661003\pi\)
−0.484512 + 0.874784i \(0.661003\pi\)
\(462\) 1.91412e57 0.982124
\(463\) 2.20081e57 1.07793 0.538965 0.842328i \(-0.318815\pi\)
0.538965 + 0.842328i \(0.318815\pi\)
\(464\) −1.60250e57 −0.749311
\(465\) 4.26691e56 0.190491
\(466\) −4.40593e57 −1.87819
\(467\) 3.37955e57 1.37577 0.687885 0.725820i \(-0.258539\pi\)
0.687885 + 0.725820i \(0.258539\pi\)
\(468\) 9.01640e56 0.350548
\(469\) −2.62408e57 −0.974453
\(470\) −1.02409e58 −3.63273
\(471\) −1.67363e57 −0.567164
\(472\) −1.16370e57 −0.376780
\(473\) 8.59450e57 2.65893
\(474\) −2.88137e57 −0.851853
\(475\) −1.95980e57 −0.553730
\(476\) 2.18210e57 0.589284
\(477\) −1.47587e57 −0.380981
\(478\) 9.60095e57 2.36927
\(479\) 1.37561e57 0.324551 0.162275 0.986746i \(-0.448117\pi\)
0.162275 + 0.986746i \(0.448117\pi\)
\(480\) 4.13049e57 0.931783
\(481\) −4.18539e56 −0.0902852
\(482\) −6.18925e57 −1.27681
\(483\) −2.40849e57 −0.475205
\(484\) 1.34487e58 2.53808
\(485\) 2.94739e56 0.0532096
\(486\) 5.71405e56 0.0986879
\(487\) 4.03185e57 0.666242 0.333121 0.942884i \(-0.391898\pi\)
0.333121 + 0.942884i \(0.391898\pi\)
\(488\) 1.53224e57 0.242271
\(489\) 2.11175e57 0.319523
\(490\) 7.36596e57 1.06663
\(491\) −1.20430e58 −1.66910 −0.834552 0.550929i \(-0.814274\pi\)
−0.834552 + 0.550929i \(0.814274\pi\)
\(492\) −5.62350e57 −0.746031
\(493\) −7.79504e57 −0.989942
\(494\) −1.14962e58 −1.39773
\(495\) 5.86630e57 0.682893
\(496\) 1.21846e57 0.135817
\(497\) −6.19963e57 −0.661764
\(498\) 1.35201e58 1.38213
\(499\) −1.80912e58 −1.77135 −0.885675 0.464305i \(-0.846304\pi\)
−0.885675 + 0.464305i \(0.846304\pi\)
\(500\) 9.37850e57 0.879586
\(501\) −2.14012e57 −0.192277
\(502\) 7.49238e57 0.644896
\(503\) 1.83848e58 1.51617 0.758084 0.652157i \(-0.226136\pi\)
0.758084 + 0.652157i \(0.226136\pi\)
\(504\) −1.55650e57 −0.122997
\(505\) 1.57749e56 0.0119454
\(506\) −4.50836e58 −3.27177
\(507\) −3.38553e57 −0.235481
\(508\) 6.28566e57 0.419065
\(509\) 2.58706e58 1.65338 0.826691 0.562656i \(-0.190220\pi\)
0.826691 + 0.562656i \(0.190220\pi\)
\(510\) 1.15810e58 0.709558
\(511\) −3.90523e57 −0.229402
\(512\) 1.67913e58 0.945760
\(513\) −4.20714e57 −0.227229
\(514\) −2.78408e57 −0.144203
\(515\) 1.99055e58 0.988823
\(516\) −2.60499e58 −1.24119
\(517\) −7.20561e58 −3.29325
\(518\) 2.69313e57 0.118077
\(519\) 3.67163e57 0.154440
\(520\) −1.30350e58 −0.526065
\(521\) −1.15962e58 −0.449059 −0.224530 0.974467i \(-0.572085\pi\)
−0.224530 + 0.974467i \(0.572085\pi\)
\(522\) 2.07252e58 0.770162
\(523\) 4.11381e58 1.46709 0.733547 0.679639i \(-0.237863\pi\)
0.733547 + 0.679639i \(0.237863\pi\)
\(524\) −2.38017e58 −0.814677
\(525\) −5.39151e57 −0.177127
\(526\) 1.28543e58 0.405372
\(527\) 5.92693e57 0.179433
\(528\) 1.67518e58 0.486891
\(529\) 2.08934e58 0.583059
\(530\) 7.95300e58 2.13108
\(531\) −8.65321e57 −0.222662
\(532\) 4.27167e58 1.05559
\(533\) −3.06553e58 −0.727562
\(534\) −3.80051e58 −0.866372
\(535\) 5.01578e58 1.09833
\(536\) 3.99422e58 0.840211
\(537\) −2.13894e58 −0.432267
\(538\) −2.86619e58 −0.556527
\(539\) 5.18279e58 0.966952
\(540\) −1.77807e58 −0.318775
\(541\) −7.75327e58 −1.33581 −0.667903 0.744248i \(-0.732808\pi\)
−0.667903 + 0.744248i \(0.732808\pi\)
\(542\) −1.41729e59 −2.34680
\(543\) −3.34965e58 −0.533093
\(544\) 5.73743e58 0.877690
\(545\) 8.50429e58 1.25059
\(546\) −3.16266e58 −0.447106
\(547\) 2.55610e58 0.347416 0.173708 0.984797i \(-0.444425\pi\)
0.173708 + 0.984797i \(0.444425\pi\)
\(548\) 8.47449e58 1.10747
\(549\) 1.13937e58 0.143172
\(550\) −1.00922e59 −1.21951
\(551\) −1.52595e59 −1.77330
\(552\) 3.66606e58 0.409741
\(553\) 5.83636e58 0.627410
\(554\) −1.59483e59 −1.64913
\(555\) 8.25377e57 0.0821019
\(556\) −1.64068e59 −1.57006
\(557\) 5.65846e58 0.520969 0.260484 0.965478i \(-0.416118\pi\)
0.260484 + 0.965478i \(0.416118\pi\)
\(558\) −1.57583e58 −0.139596
\(559\) −1.42005e59 −1.21046
\(560\) −4.82247e58 −0.395573
\(561\) 8.14856e58 0.643249
\(562\) 1.19865e59 0.910670
\(563\) 1.84272e59 1.34750 0.673751 0.738958i \(-0.264682\pi\)
0.673751 + 0.738958i \(0.264682\pi\)
\(564\) 2.18402e59 1.53729
\(565\) −1.60926e58 −0.109039
\(566\) 3.23254e59 2.10858
\(567\) −1.15741e58 −0.0726860
\(568\) 9.43670e58 0.570599
\(569\) −2.36928e59 −1.37944 −0.689719 0.724077i \(-0.742266\pi\)
−0.689719 + 0.724077i \(0.742266\pi\)
\(570\) 2.26709e59 1.27104
\(571\) 2.07972e59 1.12287 0.561433 0.827522i \(-0.310250\pi\)
0.561433 + 0.827522i \(0.310250\pi\)
\(572\) −3.41861e59 −1.77760
\(573\) −3.16112e58 −0.158313
\(574\) 1.97254e59 0.951525
\(575\) 1.26987e59 0.590066
\(576\) −1.15392e59 −0.516527
\(577\) 2.08396e59 0.898688 0.449344 0.893359i \(-0.351658\pi\)
0.449344 + 0.893359i \(0.351658\pi\)
\(578\) −2.09402e59 −0.870027
\(579\) −1.87743e59 −0.751581
\(580\) −6.44917e59 −2.48772
\(581\) −2.73856e59 −1.01797
\(582\) −1.08851e58 −0.0389932
\(583\) 5.59584e59 1.93193
\(584\) 5.94431e58 0.197800
\(585\) −9.69277e58 −0.310883
\(586\) −4.46529e59 −1.38055
\(587\) 2.73977e58 0.0816574 0.0408287 0.999166i \(-0.487000\pi\)
0.0408287 + 0.999166i \(0.487000\pi\)
\(588\) −1.57090e59 −0.451373
\(589\) 1.16025e59 0.321421
\(590\) 4.66294e59 1.24549
\(591\) 2.66679e59 0.686845
\(592\) 2.35694e58 0.0585372
\(593\) 2.35256e58 0.0563462 0.0281731 0.999603i \(-0.491031\pi\)
0.0281731 + 0.999603i \(0.491031\pi\)
\(594\) −2.16651e59 −0.500440
\(595\) −2.34579e59 −0.522606
\(596\) −7.63254e59 −1.64012
\(597\) −2.32370e59 −0.481651
\(598\) 7.44906e59 1.48945
\(599\) −1.14383e59 −0.220641 −0.110320 0.993896i \(-0.535188\pi\)
−0.110320 + 0.993896i \(0.535188\pi\)
\(600\) 8.20663e58 0.152726
\(601\) 1.46354e59 0.262787 0.131393 0.991330i \(-0.458055\pi\)
0.131393 + 0.991330i \(0.458055\pi\)
\(602\) 9.13745e59 1.58307
\(603\) 2.97008e59 0.496531
\(604\) 9.10414e58 0.146874
\(605\) −1.44576e60 −2.25089
\(606\) −5.82589e57 −0.00875389
\(607\) −5.45219e59 −0.790705 −0.395352 0.918530i \(-0.629378\pi\)
−0.395352 + 0.918530i \(0.629378\pi\)
\(608\) 1.12316e60 1.57222
\(609\) −4.19798e59 −0.567243
\(610\) −6.13970e59 −0.800858
\(611\) 1.19057e60 1.49923
\(612\) −2.46982e59 −0.300269
\(613\) −1.00661e60 −1.18158 −0.590790 0.806826i \(-0.701184\pi\)
−0.590790 + 0.806826i \(0.701184\pi\)
\(614\) 1.59324e60 1.80576
\(615\) 6.04535e59 0.661617
\(616\) 5.90155e59 0.623708
\(617\) −1.26792e60 −1.29408 −0.647038 0.762458i \(-0.723992\pi\)
−0.647038 + 0.762458i \(0.723992\pi\)
\(618\) −7.35139e59 −0.724632
\(619\) −8.28879e59 −0.789119 −0.394559 0.918870i \(-0.629103\pi\)
−0.394559 + 0.918870i \(0.629103\pi\)
\(620\) 4.90360e59 0.450914
\(621\) 2.72606e59 0.242140
\(622\) 8.46562e59 0.726382
\(623\) 7.69811e59 0.638104
\(624\) −2.76786e59 −0.221654
\(625\) −1.61434e60 −1.24904
\(626\) 3.27271e60 2.44658
\(627\) 1.59516e60 1.15226
\(628\) −1.92336e60 −1.34254
\(629\) 1.14649e59 0.0773356
\(630\) 6.23690e59 0.406581
\(631\) 2.76062e60 1.73930 0.869650 0.493668i \(-0.164344\pi\)
0.869650 + 0.493668i \(0.164344\pi\)
\(632\) −8.88375e59 −0.540977
\(633\) −1.16472e60 −0.685553
\(634\) −3.30935e59 −0.188288
\(635\) −6.75719e59 −0.371647
\(636\) −1.69610e60 −0.901825
\(637\) −8.56341e59 −0.440199
\(638\) −7.85805e60 −3.90544
\(639\) 7.01709e59 0.337201
\(640\) 2.74479e60 1.27538
\(641\) −2.57952e60 −1.15902 −0.579510 0.814965i \(-0.696756\pi\)
−0.579510 + 0.814965i \(0.696756\pi\)
\(642\) −1.85240e60 −0.804880
\(643\) −9.94946e59 −0.418084 −0.209042 0.977907i \(-0.567035\pi\)
−0.209042 + 0.977907i \(0.567035\pi\)
\(644\) −2.76787e60 −1.12486
\(645\) 2.80040e60 1.10074
\(646\) 3.14910e60 1.19726
\(647\) −9.07848e59 −0.333865 −0.166933 0.985968i \(-0.553386\pi\)
−0.166933 + 0.985968i \(0.553386\pi\)
\(648\) 1.76174e59 0.0626727
\(649\) 3.28091e60 1.12910
\(650\) 1.66751e60 0.555175
\(651\) 3.19192e59 0.102816
\(652\) 2.42686e60 0.756346
\(653\) 3.98516e60 1.20175 0.600873 0.799344i \(-0.294820\pi\)
0.600873 + 0.799344i \(0.294820\pi\)
\(654\) −3.14075e60 −0.916457
\(655\) 2.55872e60 0.722496
\(656\) 1.72631e60 0.471722
\(657\) 4.42017e59 0.116892
\(658\) −7.66082e60 −1.96073
\(659\) 7.30688e60 1.81007 0.905035 0.425337i \(-0.139844\pi\)
0.905035 + 0.425337i \(0.139844\pi\)
\(660\) 6.74165e60 1.61648
\(661\) 6.34402e59 0.147243 0.0736213 0.997286i \(-0.476544\pi\)
0.0736213 + 0.997286i \(0.476544\pi\)
\(662\) −2.89410e60 −0.650231
\(663\) −1.34637e60 −0.292835
\(664\) 4.16847e60 0.877734
\(665\) −4.59211e60 −0.936153
\(666\) −3.04823e59 −0.0601661
\(667\) 9.88758e60 1.88966
\(668\) −2.45946e60 −0.455140
\(669\) 8.48544e59 0.152059
\(670\) −1.60048e61 −2.77742
\(671\) −4.31998e60 −0.726018
\(672\) 3.08987e60 0.502922
\(673\) −1.08068e61 −1.70363 −0.851814 0.523845i \(-0.824497\pi\)
−0.851814 + 0.523845i \(0.824497\pi\)
\(674\) 1.21122e61 1.84942
\(675\) 6.10241e59 0.0902548
\(676\) −3.89070e60 −0.557409
\(677\) −7.78512e60 −1.08046 −0.540230 0.841517i \(-0.681663\pi\)
−0.540230 + 0.841517i \(0.681663\pi\)
\(678\) 5.94321e59 0.0799066
\(679\) 2.20484e59 0.0287194
\(680\) 3.57062e60 0.450612
\(681\) −3.66167e60 −0.447731
\(682\) 5.97483e60 0.707883
\(683\) −1.04731e61 −1.20235 −0.601174 0.799118i \(-0.705300\pi\)
−0.601174 + 0.799118i \(0.705300\pi\)
\(684\) −4.83491e60 −0.537877
\(685\) −9.11022e60 −0.982158
\(686\) 1.51425e61 1.58208
\(687\) 6.18572e60 0.626355
\(688\) 7.99682e60 0.784812
\(689\) −9.24589e60 −0.879499
\(690\) −1.46899e61 −1.35445
\(691\) 9.34628e60 0.835335 0.417668 0.908600i \(-0.362848\pi\)
0.417668 + 0.908600i \(0.362848\pi\)
\(692\) 4.21949e60 0.365577
\(693\) 4.38837e60 0.368586
\(694\) −1.43314e61 −1.16697
\(695\) 1.76376e61 1.39241
\(696\) 6.38992e60 0.489099
\(697\) 8.39727e60 0.623208
\(698\) −7.58141e60 −0.545580
\(699\) −1.01012e61 −0.704875
\(700\) −6.19600e60 −0.419280
\(701\) 1.17846e61 0.773356 0.386678 0.922215i \(-0.373623\pi\)
0.386678 + 0.922215i \(0.373623\pi\)
\(702\) 3.57968e60 0.227822
\(703\) 2.24436e60 0.138533
\(704\) 4.37515e61 2.61927
\(705\) −2.34785e61 −1.36334
\(706\) 2.81185e61 1.58377
\(707\) 1.18006e59 0.00644745
\(708\) −9.94440e60 −0.527064
\(709\) −2.12559e61 −1.09291 −0.546457 0.837487i \(-0.684024\pi\)
−0.546457 + 0.837487i \(0.684024\pi\)
\(710\) −3.78128e61 −1.88619
\(711\) −6.60592e60 −0.319696
\(712\) −1.17176e61 −0.550198
\(713\) −7.51798e60 −0.342512
\(714\) 8.66333e60 0.382978
\(715\) 3.67506e61 1.57647
\(716\) −2.45810e61 −1.02322
\(717\) 2.20114e61 0.889173
\(718\) 2.57002e61 1.00754
\(719\) −2.58349e61 −0.982960 −0.491480 0.870889i \(-0.663544\pi\)
−0.491480 + 0.870889i \(0.663544\pi\)
\(720\) 5.45835e60 0.201564
\(721\) 1.48906e61 0.533709
\(722\) 1.74267e61 0.606271
\(723\) −1.41897e61 −0.479180
\(724\) −3.84947e61 −1.26189
\(725\) 2.21338e61 0.704350
\(726\) 5.33938e61 1.64950
\(727\) −7.14277e59 −0.0214228 −0.0107114 0.999943i \(-0.503410\pi\)
−0.0107114 + 0.999943i \(0.503410\pi\)
\(728\) −9.75101e60 −0.283939
\(729\) 1.31002e60 0.0370370
\(730\) −2.38188e61 −0.653852
\(731\) 3.88988e61 1.03684
\(732\) 1.30938e61 0.338905
\(733\) −5.72283e61 −1.43839 −0.719193 0.694811i \(-0.755488\pi\)
−0.719193 + 0.694811i \(0.755488\pi\)
\(734\) −3.00096e61 −0.732479
\(735\) 1.68874e61 0.400300
\(736\) −7.27761e61 −1.67539
\(737\) −1.12612e62 −2.51787
\(738\) −2.23263e61 −0.484848
\(739\) −5.83871e61 −1.23158 −0.615788 0.787912i \(-0.711162\pi\)
−0.615788 + 0.787912i \(0.711162\pi\)
\(740\) 9.48536e60 0.194344
\(741\) −2.63565e61 −0.524561
\(742\) 5.94935e61 1.15023
\(743\) 9.77520e61 1.83597 0.917987 0.396611i \(-0.129814\pi\)
0.917987 + 0.396611i \(0.129814\pi\)
\(744\) −4.85855e60 −0.0886520
\(745\) 8.20510e61 1.45454
\(746\) −5.11635e61 −0.881202
\(747\) 3.09966e61 0.518705
\(748\) 9.36445e61 1.52264
\(749\) 3.75212e61 0.592813
\(750\) 3.72344e61 0.571645
\(751\) −2.27440e61 −0.339319 −0.169659 0.985503i \(-0.554267\pi\)
−0.169659 + 0.985503i \(0.554267\pi\)
\(752\) −6.70452e61 −0.972040
\(753\) 1.71773e61 0.242026
\(754\) 1.29837e62 1.77793
\(755\) −9.78710e60 −0.130255
\(756\) −1.33011e61 −0.172056
\(757\) −2.28350e61 −0.287104 −0.143552 0.989643i \(-0.545852\pi\)
−0.143552 + 0.989643i \(0.545852\pi\)
\(758\) 1.44704e61 0.176845
\(759\) −1.03360e62 −1.22788
\(760\) 6.98984e61 0.807188
\(761\) 8.53778e61 0.958462 0.479231 0.877689i \(-0.340916\pi\)
0.479231 + 0.877689i \(0.340916\pi\)
\(762\) 2.49552e61 0.272351
\(763\) 6.36175e61 0.674993
\(764\) −3.63281e61 −0.374745
\(765\) 2.65510e61 0.266293
\(766\) 1.22119e62 1.19087
\(767\) −5.42097e61 −0.514016
\(768\) −4.33586e60 −0.0399769
\(769\) −1.13257e62 −1.01542 −0.507712 0.861527i \(-0.669509\pi\)
−0.507712 + 0.861527i \(0.669509\pi\)
\(770\) −2.36475e62 −2.06174
\(771\) −6.38287e60 −0.0541186
\(772\) −2.15758e62 −1.77907
\(773\) 2.18119e62 1.74918 0.874588 0.484866i \(-0.161132\pi\)
0.874588 + 0.484866i \(0.161132\pi\)
\(774\) −1.03423e62 −0.806651
\(775\) −1.68293e61 −0.127667
\(776\) −3.35607e60 −0.0247630
\(777\) 6.17434e60 0.0443138
\(778\) −2.26487e62 −1.58118
\(779\) 1.64385e62 1.11636
\(780\) −1.11391e62 −0.735894
\(781\) −2.66056e62 −1.70992
\(782\) −2.04049e62 −1.27582
\(783\) 4.75152e61 0.289038
\(784\) 4.82236e61 0.285407
\(785\) 2.06764e62 1.19063
\(786\) −9.44972e61 −0.529461
\(787\) 3.94168e61 0.214894 0.107447 0.994211i \(-0.465732\pi\)
0.107447 + 0.994211i \(0.465732\pi\)
\(788\) 3.06472e62 1.62584
\(789\) 2.94701e61 0.152134
\(790\) 3.55972e62 1.78827
\(791\) −1.20383e61 −0.0588531
\(792\) −6.67971e61 −0.317809
\(793\) 7.13781e61 0.330515
\(794\) 5.36134e62 2.41620
\(795\) 1.82333e62 0.799783
\(796\) −2.67043e62 −1.14012
\(797\) −1.85308e62 −0.770087 −0.385043 0.922898i \(-0.625814\pi\)
−0.385043 + 0.922898i \(0.625814\pi\)
\(798\) 1.69593e62 0.686034
\(799\) −3.26127e62 −1.28420
\(800\) −1.62913e62 −0.624482
\(801\) −8.71316e61 −0.325145
\(802\) −5.58062e60 −0.0202737
\(803\) −1.67593e62 −0.592749
\(804\) 3.41326e62 1.17534
\(805\) 2.97551e62 0.997584
\(806\) −9.87209e61 −0.322259
\(807\) −6.57113e61 −0.208862
\(808\) −1.79622e60 −0.00555924
\(809\) 2.89492e62 0.872455 0.436228 0.899836i \(-0.356314\pi\)
0.436228 + 0.899836i \(0.356314\pi\)
\(810\) −7.05928e61 −0.207173
\(811\) −3.86441e62 −1.10442 −0.552211 0.833704i \(-0.686216\pi\)
−0.552211 + 0.833704i \(0.686216\pi\)
\(812\) −4.82439e62 −1.34273
\(813\) −3.24933e62 −0.880740
\(814\) 1.15575e62 0.305098
\(815\) −2.60891e62 −0.670765
\(816\) 7.58189e61 0.189862
\(817\) 7.61482e62 1.85732
\(818\) 7.22255e62 1.71591
\(819\) −7.25081e61 −0.167796
\(820\) 6.94741e62 1.56612
\(821\) −7.00271e62 −1.53776 −0.768880 0.639394i \(-0.779185\pi\)
−0.768880 + 0.639394i \(0.779185\pi\)
\(822\) 3.36453e62 0.719748
\(823\) −6.16948e62 −1.28574 −0.642868 0.765977i \(-0.722256\pi\)
−0.642868 + 0.765977i \(0.722256\pi\)
\(824\) −2.26656e62 −0.460185
\(825\) −2.31376e62 −0.457676
\(826\) 3.48817e62 0.672244
\(827\) −1.18524e62 −0.222555 −0.111277 0.993789i \(-0.535494\pi\)
−0.111277 + 0.993789i \(0.535494\pi\)
\(828\) 3.13283e62 0.573172
\(829\) 5.09313e62 0.907951 0.453976 0.891014i \(-0.350005\pi\)
0.453976 + 0.891014i \(0.350005\pi\)
\(830\) −1.67030e63 −2.90146
\(831\) −3.65636e62 −0.618909
\(832\) −7.22896e62 −1.19241
\(833\) 2.34574e62 0.377061
\(834\) −6.51381e62 −1.02039
\(835\) 2.64396e62 0.403641
\(836\) 1.83318e63 2.72754
\(837\) −3.61280e61 −0.0523897
\(838\) 4.07745e62 0.576291
\(839\) −1.03721e63 −1.42884 −0.714422 0.699715i \(-0.753310\pi\)
−0.714422 + 0.699715i \(0.753310\pi\)
\(840\) 1.92294e62 0.258203
\(841\) 9.59365e62 1.25565
\(842\) −1.00039e63 −1.27631
\(843\) 2.74806e62 0.341769
\(844\) −1.33851e63 −1.62278
\(845\) 4.18257e62 0.494338
\(846\) 8.67095e62 0.999088
\(847\) −1.08152e63 −1.21490
\(848\) 5.20669e62 0.570231
\(849\) 7.41102e62 0.791340
\(850\) −4.56773e62 −0.475547
\(851\) −1.45425e62 −0.147623
\(852\) 8.06415e62 0.798192
\(853\) 6.46285e62 0.623764 0.311882 0.950121i \(-0.399041\pi\)
0.311882 + 0.950121i \(0.399041\pi\)
\(854\) −4.59289e62 −0.432256
\(855\) 5.19761e62 0.477015
\(856\) −5.71126e62 −0.511147
\(857\) −3.89227e62 −0.339715 −0.169858 0.985469i \(-0.554331\pi\)
−0.169858 + 0.985469i \(0.554331\pi\)
\(858\) −1.35725e63 −1.15527
\(859\) 5.04634e62 0.418913 0.209456 0.977818i \(-0.432831\pi\)
0.209456 + 0.977818i \(0.432831\pi\)
\(860\) 3.21827e63 2.60558
\(861\) 4.52231e62 0.357102
\(862\) 1.58669e62 0.122204
\(863\) 9.68552e62 0.727597 0.363799 0.931478i \(-0.381480\pi\)
0.363799 + 0.931478i \(0.381480\pi\)
\(864\) −3.49729e62 −0.256263
\(865\) −4.53602e62 −0.324212
\(866\) 1.16623e63 0.813109
\(867\) −4.80082e62 −0.326516
\(868\) 3.66820e62 0.243377
\(869\) 2.50466e63 1.62115
\(870\) −2.56044e63 −1.61678
\(871\) 1.86066e63 1.14625
\(872\) −9.68348e62 −0.582005
\(873\) −2.49556e61 −0.0146339
\(874\) −3.99445e63 −2.28540
\(875\) −7.54200e62 −0.421031
\(876\) 5.07972e62 0.276695
\(877\) −6.26532e61 −0.0333006 −0.0166503 0.999861i \(-0.505300\pi\)
−0.0166503 + 0.999861i \(0.505300\pi\)
\(878\) −2.86104e63 −1.48385
\(879\) −1.02373e63 −0.518111
\(880\) −2.06956e63 −1.02212
\(881\) −3.44233e61 −0.0165909 −0.00829546 0.999966i \(-0.502641\pi\)
−0.00829546 + 0.999966i \(0.502641\pi\)
\(882\) −6.23676e62 −0.293349
\(883\) 3.56652e62 0.163715 0.0818576 0.996644i \(-0.473915\pi\)
0.0818576 + 0.996644i \(0.473915\pi\)
\(884\) −1.54727e63 −0.693173
\(885\) 1.06904e63 0.467427
\(886\) −1.23332e62 −0.0526321
\(887\) −1.11406e63 −0.464035 −0.232017 0.972712i \(-0.574533\pi\)
−0.232017 + 0.972712i \(0.574533\pi\)
\(888\) −9.39822e61 −0.0382091
\(889\) −5.05481e62 −0.200593
\(890\) 4.69524e63 1.81875
\(891\) −4.96700e62 −0.187812
\(892\) 9.75159e62 0.359941
\(893\) −6.38425e63 −2.30040
\(894\) −3.03026e63 −1.06592
\(895\) 2.64250e63 0.907445
\(896\) 2.05328e63 0.688375
\(897\) 1.70780e63 0.558983
\(898\) 7.89277e63 2.52225
\(899\) −1.31038e63 −0.408850
\(900\) 7.01299e62 0.213643
\(901\) 2.53269e63 0.753353
\(902\) 8.46513e63 2.45863
\(903\) 2.09488e63 0.594118
\(904\) 1.83239e62 0.0507455
\(905\) 4.13824e63 1.11911
\(906\) 3.61451e62 0.0954539
\(907\) −4.75180e63 −1.22547 −0.612734 0.790289i \(-0.709930\pi\)
−0.612734 + 0.790289i \(0.709930\pi\)
\(908\) −4.20805e63 −1.05983
\(909\) −1.33566e61 −0.00328528
\(910\) 3.90723e63 0.938596
\(911\) −4.95250e63 −1.16193 −0.580964 0.813929i \(-0.697324\pi\)
−0.580964 + 0.813929i \(0.697324\pi\)
\(912\) 1.48423e63 0.340104
\(913\) −1.17525e64 −2.63032
\(914\) −4.54018e63 −0.992499
\(915\) −1.40761e63 −0.300558
\(916\) 7.10873e63 1.48265
\(917\) 1.91409e63 0.389961
\(918\) −9.80565e62 −0.195146
\(919\) −2.19827e63 −0.427364 −0.213682 0.976903i \(-0.568546\pi\)
−0.213682 + 0.976903i \(0.568546\pi\)
\(920\) −4.52914e63 −0.860156
\(921\) 3.65271e63 0.677693
\(922\) −8.22464e63 −1.49074
\(923\) 4.39599e63 0.778431
\(924\) 5.04318e63 0.872483
\(925\) −3.25541e62 −0.0550248
\(926\) 1.00414e64 1.65828
\(927\) −1.68540e63 −0.271950
\(928\) −1.26848e64 −1.99988
\(929\) −8.33744e62 −0.128438 −0.0642192 0.997936i \(-0.520456\pi\)
−0.0642192 + 0.997936i \(0.520456\pi\)
\(930\) 1.94682e63 0.293050
\(931\) 4.59201e63 0.675437
\(932\) −1.16084e64 −1.66852
\(933\) 1.94085e63 0.272607
\(934\) 1.54195e64 2.11647
\(935\) −1.00669e64 −1.35035
\(936\) 1.10367e63 0.144681
\(937\) 1.31192e64 1.68077 0.840383 0.541993i \(-0.182330\pi\)
0.840383 + 0.541993i \(0.182330\pi\)
\(938\) −1.19726e64 −1.49909
\(939\) 7.50313e63 0.918189
\(940\) −2.69819e64 −3.22718
\(941\) 1.09648e64 1.28181 0.640905 0.767620i \(-0.278559\pi\)
0.640905 + 0.767620i \(0.278559\pi\)
\(942\) −7.63608e63 −0.872522
\(943\) −1.06515e64 −1.18962
\(944\) 3.05274e63 0.333267
\(945\) 1.42989e63 0.152588
\(946\) 3.92132e64 4.09047
\(947\) 4.97351e62 0.0507152 0.0253576 0.999678i \(-0.491928\pi\)
0.0253576 + 0.999678i \(0.491928\pi\)
\(948\) −7.59162e63 −0.756755
\(949\) 2.76910e63 0.269845
\(950\) −8.94176e63 −0.851855
\(951\) −7.58711e62 −0.0706635
\(952\) 2.67105e63 0.243214
\(953\) −1.25621e64 −1.11832 −0.559160 0.829060i \(-0.688876\pi\)
−0.559160 + 0.829060i \(0.688876\pi\)
\(954\) −6.73381e63 −0.586099
\(955\) 3.90533e63 0.332342
\(956\) 2.52959e64 2.10477
\(957\) −1.80156e64 −1.46569
\(958\) 6.27636e63 0.499286
\(959\) −6.81502e63 −0.530112
\(960\) 1.42558e64 1.08433
\(961\) −1.24484e64 −0.925894
\(962\) −1.90962e63 −0.138894
\(963\) −4.24686e63 −0.302067
\(964\) −1.63070e64 −1.13427
\(965\) 2.31943e64 1.57777
\(966\) −1.09890e64 −0.731052
\(967\) −1.92657e63 −0.125347 −0.0626737 0.998034i \(-0.519963\pi\)
−0.0626737 + 0.998034i \(0.519963\pi\)
\(968\) 1.64622e64 1.04753
\(969\) 7.21971e63 0.449323
\(970\) 1.34478e63 0.0818573
\(971\) 1.82399e64 1.08595 0.542973 0.839750i \(-0.317299\pi\)
0.542973 + 0.839750i \(0.317299\pi\)
\(972\) 1.50550e63 0.0876708
\(973\) 1.31940e64 0.751540
\(974\) 1.83957e64 1.02494
\(975\) 3.82298e63 0.208354
\(976\) −4.01956e63 −0.214292
\(977\) −2.86004e64 −1.49155 −0.745776 0.666197i \(-0.767921\pi\)
−0.745776 + 0.666197i \(0.767921\pi\)
\(978\) 9.63507e63 0.491552
\(979\) 3.30364e64 1.64879
\(980\) 1.94073e64 0.947554
\(981\) −7.20059e63 −0.343941
\(982\) −5.49475e64 −2.56774
\(983\) 2.49132e64 1.13901 0.569507 0.821986i \(-0.307134\pi\)
0.569507 + 0.821986i \(0.307134\pi\)
\(984\) −6.88359e63 −0.307907
\(985\) −3.29462e64 −1.44187
\(986\) −3.55656e64 −1.52292
\(987\) −1.75634e64 −0.735852
\(988\) −3.02893e64 −1.24169
\(989\) −4.93411e64 −1.97919
\(990\) 2.67656e64 1.05056
\(991\) 2.27461e63 0.0873620 0.0436810 0.999046i \(-0.486091\pi\)
0.0436810 + 0.999046i \(0.486091\pi\)
\(992\) 9.64487e63 0.362490
\(993\) −6.63512e63 −0.244028
\(994\) −2.82864e64 −1.01805
\(995\) 2.87076e64 1.01111
\(996\) 3.56217e64 1.22783
\(997\) 3.04681e64 1.02778 0.513890 0.857856i \(-0.328204\pi\)
0.513890 + 0.857856i \(0.328204\pi\)
\(998\) −8.25426e64 −2.72503
\(999\) −6.98847e62 −0.0225800
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.1.3 3
3.2 odd 2 9.44.a.a.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.44.a.a.1.3 3 1.1 even 1 trivial
9.44.a.a.1.1 3 3.2 odd 2