Properties

Label 1.36.a.a.1.2
Level $1$
Weight $36$
Character 1.1
Self dual yes
Analytic conductor $7.760$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 36 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(7.75951306336\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\mathbb{Q}[x]/(x^{3} - \cdots)\)
Defining polynomial: \(x^{3} - 12422194 x - 2645665785\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{12}\cdot 3^{3}\cdot 5\cdot 7 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-3412.77\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-26808.0 q^{2} +3.95729e8 q^{3} -3.36411e10 q^{4} +8.21401e11 q^{5} -1.06087e13 q^{6} +6.06942e14 q^{7} +1.82297e15 q^{8} +1.06570e17 q^{9} +O(q^{10})\) \(q-26808.0 q^{2} +3.95729e8 q^{3} -3.36411e10 q^{4} +8.21401e11 q^{5} -1.06087e13 q^{6} +6.06942e14 q^{7} +1.82297e15 q^{8} +1.06570e17 q^{9} -2.20201e16 q^{10} +1.23316e18 q^{11} -1.33127e19 q^{12} -8.46079e17 q^{13} -1.62709e19 q^{14} +3.25052e20 q^{15} +1.10703e21 q^{16} -3.92226e21 q^{17} -2.85692e21 q^{18} -3.52757e20 q^{19} -2.76328e22 q^{20} +2.40184e23 q^{21} -3.30584e22 q^{22} -8.58137e23 q^{23} +7.21400e23 q^{24} -2.23568e24 q^{25} +2.26817e22 q^{26} +2.23738e25 q^{27} -2.04182e25 q^{28} -1.38664e25 q^{29} -8.71400e24 q^{30} -3.33324e25 q^{31} -9.23139e25 q^{32} +4.87995e26 q^{33} +1.05148e26 q^{34} +4.98543e26 q^{35} -3.58512e27 q^{36} +1.99674e27 q^{37} +9.45671e24 q^{38} -3.34818e26 q^{39} +1.49739e27 q^{40} +2.10955e28 q^{41} -6.43887e27 q^{42} -4.57475e28 q^{43} -4.14847e28 q^{44} +8.75365e28 q^{45} +2.30049e28 q^{46} -1.72608e29 q^{47} +4.38083e29 q^{48} -1.04400e28 q^{49} +5.99342e28 q^{50} -1.55215e30 q^{51} +2.84630e28 q^{52} +1.81145e30 q^{53} -5.99797e29 q^{54} +1.01292e30 q^{55} +1.10643e30 q^{56} -1.39596e29 q^{57} +3.71730e29 q^{58} -5.02395e30 q^{59} -1.09351e31 q^{60} -3.25742e29 q^{61} +8.93574e29 q^{62} +6.46817e31 q^{63} -3.55625e31 q^{64} -6.94970e29 q^{65} -1.30822e31 q^{66} -4.01253e31 q^{67} +1.31949e32 q^{68} -3.39589e32 q^{69} -1.33649e31 q^{70} +3.85444e32 q^{71} +1.94273e32 q^{72} +9.93637e31 q^{73} -5.35285e31 q^{74} -8.84724e32 q^{75} +1.18671e31 q^{76} +7.48454e32 q^{77} +8.97580e30 q^{78} -2.62804e33 q^{79} +9.09314e32 q^{80} +3.52211e33 q^{81} -5.65527e32 q^{82} +6.17326e33 q^{83} -8.08006e33 q^{84} -3.22175e33 q^{85} +1.22640e33 q^{86} -5.48733e33 q^{87} +2.24800e33 q^{88} +6.75031e33 q^{89} -2.34668e33 q^{90} -5.13521e32 q^{91} +2.88686e34 q^{92} -1.31906e34 q^{93} +4.62727e33 q^{94} -2.89755e32 q^{95} -3.65313e34 q^{96} -8.10218e34 q^{97} +2.79875e32 q^{98} +1.31417e35 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 139656q^{2} - 104875308q^{3} + 34841262144q^{4} + 892652054010q^{5} - 4786530564384q^{6} + 878422149346056q^{7} + 22336009925337600q^{8} + 150091978876243551q^{9} + O(q^{10}) \) \( 3q + 139656q^{2} - 104875308q^{3} + 34841262144q^{4} + 892652054010q^{5} - 4786530564384q^{6} + 878422149346056q^{7} + 22336009925337600q^{8} + 150091978876243551q^{9} + 1019870812729298160q^{10} - 1157945428549987044q^{11} - 22548891526776486144q^{12} - 62139610550998650558q^{13} + \)\(13\!\cdots\!28\)\(q^{14} + \)\(70\!\cdots\!20\)\(q^{15} + \)\(21\!\cdots\!48\)\(q^{16} - \)\(39\!\cdots\!94\)\(q^{17} - \)\(23\!\cdots\!08\)\(q^{18} - \)\(32\!\cdots\!40\)\(q^{19} + \)\(14\!\cdots\!80\)\(q^{20} + \)\(22\!\cdots\!76\)\(q^{21} + \)\(22\!\cdots\!12\)\(q^{22} - \)\(51\!\cdots\!08\)\(q^{23} - \)\(37\!\cdots\!20\)\(q^{24} + \)\(64\!\cdots\!25\)\(q^{25} + \)\(42\!\cdots\!36\)\(q^{26} + \)\(27\!\cdots\!00\)\(q^{27} + \)\(10\!\cdots\!08\)\(q^{28} - \)\(38\!\cdots\!10\)\(q^{29} - \)\(23\!\cdots\!80\)\(q^{30} + \)\(10\!\cdots\!56\)\(q^{31} - \)\(92\!\cdots\!44\)\(q^{32} + \)\(11\!\cdots\!84\)\(q^{33} - \)\(55\!\cdots\!12\)\(q^{34} + \)\(15\!\cdots\!60\)\(q^{35} - \)\(60\!\cdots\!52\)\(q^{36} + \)\(24\!\cdots\!06\)\(q^{37} - \)\(12\!\cdots\!00\)\(q^{38} + \)\(18\!\cdots\!12\)\(q^{39} + \)\(16\!\cdots\!00\)\(q^{40} + \)\(23\!\cdots\!06\)\(q^{41} - \)\(33\!\cdots\!88\)\(q^{42} - \)\(47\!\cdots\!08\)\(q^{43} - \)\(80\!\cdots\!12\)\(q^{44} - \)\(11\!\cdots\!30\)\(q^{45} + \)\(31\!\cdots\!56\)\(q^{46} + \)\(16\!\cdots\!56\)\(q^{47} + \)\(44\!\cdots\!92\)\(q^{48} - \)\(59\!\cdots\!21\)\(q^{49} + \)\(37\!\cdots\!00\)\(q^{50} - \)\(18\!\cdots\!04\)\(q^{51} - \)\(51\!\cdots\!44\)\(q^{52} - \)\(16\!\cdots\!58\)\(q^{53} + \)\(44\!\cdots\!60\)\(q^{54} + \)\(30\!\cdots\!20\)\(q^{55} + \)\(56\!\cdots\!40\)\(q^{56} + \)\(40\!\cdots\!00\)\(q^{57} - \)\(23\!\cdots\!00\)\(q^{58} + \)\(43\!\cdots\!80\)\(q^{59} - \)\(40\!\cdots\!40\)\(q^{60} + \)\(23\!\cdots\!06\)\(q^{61} + \)\(29\!\cdots\!12\)\(q^{62} + \)\(45\!\cdots\!92\)\(q^{63} + \)\(93\!\cdots\!84\)\(q^{64} + \)\(75\!\cdots\!20\)\(q^{65} - \)\(75\!\cdots\!68\)\(q^{66} - \)\(18\!\cdots\!44\)\(q^{67} + \)\(21\!\cdots\!08\)\(q^{68} - \)\(32\!\cdots\!48\)\(q^{69} + \)\(22\!\cdots\!60\)\(q^{70} + \)\(34\!\cdots\!56\)\(q^{71} + \)\(31\!\cdots\!00\)\(q^{72} - \)\(28\!\cdots\!58\)\(q^{73} + \)\(21\!\cdots\!08\)\(q^{74} - \)\(15\!\cdots\!00\)\(q^{75} - \)\(27\!\cdots\!20\)\(q^{76} + \)\(69\!\cdots\!12\)\(q^{77} - \)\(22\!\cdots\!16\)\(q^{78} - \)\(42\!\cdots\!60\)\(q^{79} + \)\(68\!\cdots\!60\)\(q^{80} + \)\(18\!\cdots\!63\)\(q^{81} - \)\(40\!\cdots\!88\)\(q^{82} + \)\(14\!\cdots\!92\)\(q^{83} - \)\(13\!\cdots\!52\)\(q^{84} - \)\(87\!\cdots\!40\)\(q^{85} + \)\(14\!\cdots\!96\)\(q^{86} - \)\(78\!\cdots\!00\)\(q^{87} - \)\(18\!\cdots\!00\)\(q^{88} + \)\(30\!\cdots\!70\)\(q^{89} + \)\(28\!\cdots\!20\)\(q^{90} + \)\(10\!\cdots\!96\)\(q^{91} + \)\(83\!\cdots\!56\)\(q^{92} - \)\(40\!\cdots\!16\)\(q^{93} + \)\(19\!\cdots\!68\)\(q^{94} - \)\(84\!\cdots\!00\)\(q^{95} - \)\(32\!\cdots\!84\)\(q^{96} - \)\(10\!\cdots\!94\)\(q^{97} - \)\(13\!\cdots\!92\)\(q^{98} + \)\(30\!\cdots\!52\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −26808.0 −0.144624 −0.0723119 0.997382i \(-0.523038\pi\)
−0.0723119 + 0.997382i \(0.523038\pi\)
\(3\) 3.95729e8 1.76920 0.884598 0.466355i \(-0.154433\pi\)
0.884598 + 0.466355i \(0.154433\pi\)
\(4\) −3.36411e10 −0.979084
\(5\) 8.21401e11 0.481482 0.240741 0.970589i \(-0.422610\pi\)
0.240741 + 0.970589i \(0.422610\pi\)
\(6\) −1.06087e13 −0.255868
\(7\) 6.06942e14 0.986124 0.493062 0.869994i \(-0.335878\pi\)
0.493062 + 0.869994i \(0.335878\pi\)
\(8\) 1.82297e15 0.286223
\(9\) 1.06570e17 2.13005
\(10\) −2.20201e16 −0.0696337
\(11\) 1.23316e18 0.735607 0.367804 0.929904i \(-0.380110\pi\)
0.367804 + 0.929904i \(0.380110\pi\)
\(12\) −1.33127e19 −1.73219
\(13\) −8.46079e17 −0.0271270 −0.0135635 0.999908i \(-0.504318\pi\)
−0.0135635 + 0.999908i \(0.504318\pi\)
\(14\) −1.62709e19 −0.142617
\(15\) 3.25052e20 0.851836
\(16\) 1.10703e21 0.937689
\(17\) −3.92226e21 −1.14995 −0.574976 0.818170i \(-0.694989\pi\)
−0.574976 + 0.818170i \(0.694989\pi\)
\(18\) −2.85692e21 −0.308056
\(19\) −3.52757e20 −0.0147668 −0.00738342 0.999973i \(-0.502350\pi\)
−0.00738342 + 0.999973i \(0.502350\pi\)
\(20\) −2.76328e22 −0.471411
\(21\) 2.40184e23 1.74465
\(22\) −3.30584e22 −0.106386
\(23\) −8.58137e23 −1.26858 −0.634292 0.773093i \(-0.718708\pi\)
−0.634292 + 0.773093i \(0.718708\pi\)
\(24\) 7.21400e23 0.506384
\(25\) −2.23568e24 −0.768175
\(26\) 2.26817e22 0.00392321
\(27\) 2.23738e25 1.99928
\(28\) −2.04182e25 −0.965498
\(29\) −1.38664e25 −0.354812 −0.177406 0.984138i \(-0.556771\pi\)
−0.177406 + 0.984138i \(0.556771\pi\)
\(30\) −8.71400e24 −0.123196
\(31\) −3.33324e25 −0.265483 −0.132741 0.991151i \(-0.542378\pi\)
−0.132741 + 0.991151i \(0.542378\pi\)
\(32\) −9.23139e25 −0.421835
\(33\) 4.87995e26 1.30143
\(34\) 1.05148e26 0.166310
\(35\) 4.98543e26 0.474801
\(36\) −3.58512e27 −2.08550
\(37\) 1.99674e27 0.719102 0.359551 0.933125i \(-0.382930\pi\)
0.359551 + 0.933125i \(0.382930\pi\)
\(38\) 9.45671e24 0.00213563
\(39\) −3.34818e26 −0.0479930
\(40\) 1.49739e27 0.137811
\(41\) 2.10955e28 1.26029 0.630146 0.776476i \(-0.282995\pi\)
0.630146 + 0.776476i \(0.282995\pi\)
\(42\) −6.43887e27 −0.252317
\(43\) −4.57475e28 −1.18760 −0.593799 0.804614i \(-0.702372\pi\)
−0.593799 + 0.804614i \(0.702372\pi\)
\(44\) −4.14847e28 −0.720221
\(45\) 8.75365e28 1.02558
\(46\) 2.30049e28 0.183467
\(47\) −1.72608e29 −0.944816 −0.472408 0.881380i \(-0.656615\pi\)
−0.472408 + 0.881380i \(0.656615\pi\)
\(48\) 4.38083e29 1.65896
\(49\) −1.04400e28 −0.0275593
\(50\) 5.99342e28 0.111096
\(51\) −1.55215e30 −2.03449
\(52\) 2.84630e28 0.0265596
\(53\) 1.81145e30 1.21115 0.605577 0.795786i \(-0.292942\pi\)
0.605577 + 0.795786i \(0.292942\pi\)
\(54\) −5.99797e29 −0.289144
\(55\) 1.01292e30 0.354182
\(56\) 1.10643e30 0.282251
\(57\) −1.39596e29 −0.0261254
\(58\) 3.71730e29 0.0513143
\(59\) −5.02395e30 −0.514204 −0.257102 0.966384i \(-0.582768\pi\)
−0.257102 + 0.966384i \(0.582768\pi\)
\(60\) −1.09351e31 −0.834019
\(61\) −3.25742e29 −0.0186038 −0.00930189 0.999957i \(-0.502961\pi\)
−0.00930189 + 0.999957i \(0.502961\pi\)
\(62\) 8.93574e29 0.0383951
\(63\) 6.46817e31 2.10050
\(64\) −3.55625e31 −0.876682
\(65\) −6.94970e29 −0.0130612
\(66\) −1.30822e31 −0.188218
\(67\) −4.01253e31 −0.443720 −0.221860 0.975079i \(-0.571213\pi\)
−0.221860 + 0.975079i \(0.571213\pi\)
\(68\) 1.31949e32 1.12590
\(69\) −3.39589e32 −2.24437
\(70\) −1.33649e31 −0.0686675
\(71\) 3.85444e32 1.54504 0.772520 0.634990i \(-0.218996\pi\)
0.772520 + 0.634990i \(0.218996\pi\)
\(72\) 1.94273e32 0.609669
\(73\) 9.93637e31 0.244950 0.122475 0.992472i \(-0.460917\pi\)
0.122475 + 0.992472i \(0.460917\pi\)
\(74\) −5.35285e31 −0.103999
\(75\) −8.84724e32 −1.35905
\(76\) 1.18671e31 0.0144580
\(77\) 7.48454e32 0.725400
\(78\) 8.97580e30 0.00694093
\(79\) −2.62804e33 −1.62614 −0.813069 0.582167i \(-0.802205\pi\)
−0.813069 + 0.582167i \(0.802205\pi\)
\(80\) 9.09314e32 0.451481
\(81\) 3.52211e33 1.40707
\(82\) −5.65527e32 −0.182268
\(83\) 6.17326e33 1.60934 0.804671 0.593722i \(-0.202342\pi\)
0.804671 + 0.593722i \(0.202342\pi\)
\(84\) −8.08006e33 −1.70815
\(85\) −3.22175e33 −0.553682
\(86\) 1.22640e33 0.171755
\(87\) −5.48733e33 −0.627732
\(88\) 2.24800e33 0.210547
\(89\) 6.75031e33 0.518799 0.259399 0.965770i \(-0.416475\pi\)
0.259399 + 0.965770i \(0.416475\pi\)
\(90\) −2.34668e33 −0.148323
\(91\) −5.13521e32 −0.0267506
\(92\) 2.88686e34 1.24205
\(93\) −1.31906e34 −0.469691
\(94\) 4.62727e33 0.136643
\(95\) −2.89755e32 −0.00710997
\(96\) −3.65313e34 −0.746308
\(97\) −8.10218e34 −1.38069 −0.690346 0.723480i \(-0.742542\pi\)
−0.690346 + 0.723480i \(0.742542\pi\)
\(98\) 2.79875e32 0.00398573
\(99\) 1.31417e35 1.56688
\(100\) 7.52108e34 0.752108
\(101\) −1.08776e35 −0.913923 −0.456962 0.889486i \(-0.651062\pi\)
−0.456962 + 0.889486i \(0.651062\pi\)
\(102\) 4.16101e34 0.294236
\(103\) −2.99910e33 −0.0178788 −0.00893941 0.999960i \(-0.502846\pi\)
−0.00893941 + 0.999960i \(0.502846\pi\)
\(104\) −1.54237e33 −0.00776436
\(105\) 1.97288e35 0.840016
\(106\) −4.85615e34 −0.175162
\(107\) −3.51492e35 −1.07572 −0.537860 0.843034i \(-0.680767\pi\)
−0.537860 + 0.843034i \(0.680767\pi\)
\(108\) −7.52679e35 −1.95746
\(109\) 6.20112e35 1.37248 0.686240 0.727375i \(-0.259260\pi\)
0.686240 + 0.727375i \(0.259260\pi\)
\(110\) −2.71542e34 −0.0512231
\(111\) 7.90166e35 1.27223
\(112\) 6.71902e35 0.924678
\(113\) −7.30280e35 −0.860234 −0.430117 0.902773i \(-0.641528\pi\)
−0.430117 + 0.902773i \(0.641528\pi\)
\(114\) 3.74229e33 0.00377835
\(115\) −7.04874e35 −0.610801
\(116\) 4.66480e35 0.347391
\(117\) −9.01664e34 −0.0577819
\(118\) 1.34682e35 0.0743661
\(119\) −2.38058e36 −1.13400
\(120\) 5.92559e35 0.243815
\(121\) −1.28957e36 −0.458882
\(122\) 8.73249e33 0.00269055
\(123\) 8.34808e36 2.22970
\(124\) 1.12134e36 0.259930
\(125\) −4.22698e36 −0.851345
\(126\) −1.73399e36 −0.303781
\(127\) 5.89251e35 0.0898949 0.0449475 0.998989i \(-0.485688\pi\)
0.0449475 + 0.998989i \(0.485688\pi\)
\(128\) 4.12524e36 0.548624
\(129\) −1.81036e37 −2.10109
\(130\) 1.86308e34 0.00188896
\(131\) 2.10664e37 1.86785 0.933925 0.357468i \(-0.116360\pi\)
0.933925 + 0.357468i \(0.116360\pi\)
\(132\) −1.64167e37 −1.27421
\(133\) −2.14103e35 −0.0145619
\(134\) 1.07568e36 0.0641725
\(135\) 1.83779e37 0.962618
\(136\) −7.15014e36 −0.329142
\(137\) 2.66291e37 1.07832 0.539158 0.842204i \(-0.318742\pi\)
0.539158 + 0.842204i \(0.318742\pi\)
\(138\) 9.10372e36 0.324590
\(139\) −1.89155e37 −0.594374 −0.297187 0.954819i \(-0.596048\pi\)
−0.297187 + 0.954819i \(0.596048\pi\)
\(140\) −1.67715e37 −0.464870
\(141\) −6.83058e37 −1.67156
\(142\) −1.03330e37 −0.223449
\(143\) −1.04335e36 −0.0199548
\(144\) 1.17976e38 1.99733
\(145\) −1.13899e37 −0.170836
\(146\) −2.66374e36 −0.0354256
\(147\) −4.13140e36 −0.0487578
\(148\) −6.71723e37 −0.704061
\(149\) 6.86254e37 0.639330 0.319665 0.947531i \(-0.396430\pi\)
0.319665 + 0.947531i \(0.396430\pi\)
\(150\) 2.37177e37 0.196551
\(151\) 1.75463e38 1.29446 0.647229 0.762295i \(-0.275928\pi\)
0.647229 + 0.762295i \(0.275928\pi\)
\(152\) −6.43064e35 −0.00422660
\(153\) −4.17994e38 −2.44946
\(154\) −2.00646e37 −0.104910
\(155\) −2.73792e37 −0.127825
\(156\) 1.12636e37 0.0469892
\(157\) −1.13686e36 −0.00424096 −0.00212048 0.999998i \(-0.500675\pi\)
−0.00212048 + 0.999998i \(0.500675\pi\)
\(158\) 7.04525e37 0.235178
\(159\) 7.16845e38 2.14277
\(160\) −7.58267e37 −0.203106
\(161\) −5.20839e38 −1.25098
\(162\) −9.44207e37 −0.203495
\(163\) 7.96117e38 1.54061 0.770307 0.637673i \(-0.220103\pi\)
0.770307 + 0.637673i \(0.220103\pi\)
\(164\) −7.09674e38 −1.23393
\(165\) 4.00840e38 0.626616
\(166\) −1.65493e38 −0.232749
\(167\) −9.18990e38 −1.16352 −0.581758 0.813362i \(-0.697635\pi\)
−0.581758 + 0.813362i \(0.697635\pi\)
\(168\) 4.37848e38 0.499357
\(169\) −9.72070e38 −0.999264
\(170\) 8.63686e37 0.0800755
\(171\) −3.75932e37 −0.0314541
\(172\) 1.53899e39 1.16276
\(173\) 1.70459e39 1.16363 0.581813 0.813323i \(-0.302344\pi\)
0.581813 + 0.813323i \(0.302344\pi\)
\(174\) 1.47104e38 0.0907849
\(175\) −1.35693e39 −0.757516
\(176\) 1.36514e39 0.689771
\(177\) −1.98812e39 −0.909727
\(178\) −1.80962e38 −0.0750306
\(179\) −9.48476e38 −0.356532 −0.178266 0.983982i \(-0.557049\pi\)
−0.178266 + 0.983982i \(0.557049\pi\)
\(180\) −2.94482e39 −1.00413
\(181\) 3.12075e39 0.965791 0.482896 0.875678i \(-0.339585\pi\)
0.482896 + 0.875678i \(0.339585\pi\)
\(182\) 1.37665e37 0.00386877
\(183\) −1.28905e38 −0.0329137
\(184\) −1.56435e39 −0.363097
\(185\) 1.64012e39 0.346235
\(186\) 3.53613e38 0.0679285
\(187\) −4.83675e39 −0.845913
\(188\) 5.80670e39 0.925054
\(189\) 1.35796e40 1.97154
\(190\) 7.76775e36 0.00102827
\(191\) −3.57216e38 −0.0431367 −0.0215683 0.999767i \(-0.506866\pi\)
−0.0215683 + 0.999767i \(0.506866\pi\)
\(192\) −1.40731e40 −1.55102
\(193\) −1.46241e40 −1.47169 −0.735847 0.677148i \(-0.763216\pi\)
−0.735847 + 0.677148i \(0.763216\pi\)
\(194\) 2.17203e39 0.199681
\(195\) −2.75020e38 −0.0231078
\(196\) 3.51212e38 0.0269829
\(197\) 1.11047e40 0.780453 0.390226 0.920719i \(-0.372397\pi\)
0.390226 + 0.920719i \(0.372397\pi\)
\(198\) −3.52303e39 −0.226608
\(199\) 1.81867e40 1.07109 0.535545 0.844507i \(-0.320106\pi\)
0.535545 + 0.844507i \(0.320106\pi\)
\(200\) −4.07558e39 −0.219869
\(201\) −1.58787e40 −0.785027
\(202\) 2.91607e39 0.132175
\(203\) −8.41610e39 −0.349889
\(204\) 5.22160e40 1.99194
\(205\) 1.73278e40 0.606808
\(206\) 8.03998e37 0.00258570
\(207\) −9.14514e40 −2.70215
\(208\) −9.36633e38 −0.0254367
\(209\) −4.35004e38 −0.0108626
\(210\) −5.28889e39 −0.121486
\(211\) −6.95408e39 −0.146993 −0.0734965 0.997295i \(-0.523416\pi\)
−0.0734965 + 0.997295i \(0.523416\pi\)
\(212\) −6.09393e40 −1.18582
\(213\) 1.52531e41 2.73348
\(214\) 9.42280e39 0.155575
\(215\) −3.75770e40 −0.571807
\(216\) 4.07867e40 0.572239
\(217\) −2.02308e40 −0.261799
\(218\) −1.66240e40 −0.198493
\(219\) 3.93211e40 0.433365
\(220\) −3.40756e40 −0.346774
\(221\) 3.31854e39 0.0311948
\(222\) −2.11828e40 −0.183995
\(223\) 7.64864e40 0.614115 0.307057 0.951691i \(-0.400656\pi\)
0.307057 + 0.951691i \(0.400656\pi\)
\(224\) −5.60292e40 −0.415981
\(225\) −2.38256e41 −1.63625
\(226\) 1.95773e40 0.124410
\(227\) −1.63339e40 −0.0960808 −0.0480404 0.998845i \(-0.515298\pi\)
−0.0480404 + 0.998845i \(0.515298\pi\)
\(228\) 4.69616e39 0.0255790
\(229\) 1.58770e41 0.801026 0.400513 0.916291i \(-0.368832\pi\)
0.400513 + 0.916291i \(0.368832\pi\)
\(230\) 1.88963e40 0.0883363
\(231\) 2.96185e41 1.28337
\(232\) −2.52780e40 −0.101555
\(233\) 1.16673e41 0.434751 0.217375 0.976088i \(-0.430250\pi\)
0.217375 + 0.976088i \(0.430250\pi\)
\(234\) 2.41718e39 0.00835664
\(235\) −1.41780e41 −0.454912
\(236\) 1.69011e41 0.503449
\(237\) −1.03999e42 −2.87696
\(238\) 6.38187e40 0.164003
\(239\) 5.09777e41 1.21735 0.608677 0.793418i \(-0.291701\pi\)
0.608677 + 0.793418i \(0.291701\pi\)
\(240\) 3.59842e41 0.798757
\(241\) −7.27282e41 −1.50108 −0.750541 0.660824i \(-0.770207\pi\)
−0.750541 + 0.660824i \(0.770207\pi\)
\(242\) 3.45708e40 0.0663653
\(243\) 2.74404e41 0.490096
\(244\) 1.09583e40 0.0182147
\(245\) −8.57541e39 −0.0132693
\(246\) −2.23795e41 −0.322468
\(247\) 2.98460e38 0.000400580 0
\(248\) −6.07638e40 −0.0759872
\(249\) 2.44294e42 2.84724
\(250\) 1.13317e41 0.123125
\(251\) 4.56359e40 0.0462399 0.0231199 0.999733i \(-0.492640\pi\)
0.0231199 + 0.999733i \(0.492640\pi\)
\(252\) −2.17596e42 −2.05656
\(253\) −1.05822e42 −0.933180
\(254\) −1.57966e40 −0.0130009
\(255\) −1.27494e42 −0.979571
\(256\) 1.11133e42 0.797338
\(257\) 2.36058e41 0.158194 0.0790968 0.996867i \(-0.474796\pi\)
0.0790968 + 0.996867i \(0.474796\pi\)
\(258\) 4.85321e41 0.303868
\(259\) 1.21190e42 0.709124
\(260\) 2.33795e40 0.0127880
\(261\) −1.47774e42 −0.755768
\(262\) −5.64748e41 −0.270136
\(263\) 7.96602e41 0.356464 0.178232 0.983988i \(-0.442962\pi\)
0.178232 + 0.983988i \(0.442962\pi\)
\(264\) 8.89599e41 0.372499
\(265\) 1.48793e42 0.583149
\(266\) 5.73967e39 0.00210600
\(267\) 2.67129e42 0.917856
\(268\) 1.34986e42 0.434439
\(269\) −4.82372e42 −1.45451 −0.727256 0.686366i \(-0.759205\pi\)
−0.727256 + 0.686366i \(0.759205\pi\)
\(270\) −4.92674e41 −0.139217
\(271\) −2.22025e42 −0.588083 −0.294042 0.955793i \(-0.595000\pi\)
−0.294042 + 0.955793i \(0.595000\pi\)
\(272\) −4.34205e42 −1.07830
\(273\) −2.03215e41 −0.0473270
\(274\) −7.13873e41 −0.155950
\(275\) −2.75695e42 −0.565075
\(276\) 1.14242e43 2.19743
\(277\) 1.62622e42 0.293619 0.146809 0.989165i \(-0.453100\pi\)
0.146809 + 0.989165i \(0.453100\pi\)
\(278\) 5.07088e41 0.0859606
\(279\) −3.55222e42 −0.565492
\(280\) 9.08827e41 0.135899
\(281\) 6.29076e42 0.883777 0.441888 0.897070i \(-0.354309\pi\)
0.441888 + 0.897070i \(0.354309\pi\)
\(282\) 1.83114e42 0.241748
\(283\) 4.07259e41 0.0505368 0.0252684 0.999681i \(-0.491956\pi\)
0.0252684 + 0.999681i \(0.491956\pi\)
\(284\) −1.29667e43 −1.51272
\(285\) −1.14664e41 −0.0125789
\(286\) 2.79700e40 0.00288594
\(287\) 1.28037e43 1.24281
\(288\) −9.83787e42 −0.898530
\(289\) 3.75055e42 0.322391
\(290\) 3.05340e41 0.0247069
\(291\) −3.20627e43 −2.44271
\(292\) −3.34270e42 −0.239827
\(293\) 2.65171e43 1.79202 0.896010 0.444033i \(-0.146453\pi\)
0.896010 + 0.444033i \(0.146453\pi\)
\(294\) 1.10755e41 0.00705154
\(295\) −4.12668e42 −0.247580
\(296\) 3.63998e42 0.205823
\(297\) 2.75904e43 1.47069
\(298\) −1.83971e42 −0.0924623
\(299\) 7.26051e41 0.0344129
\(300\) 2.97631e43 1.33063
\(301\) −2.77661e43 −1.17112
\(302\) −4.70380e42 −0.187209
\(303\) −4.30459e43 −1.61691
\(304\) −3.90512e41 −0.0138467
\(305\) −2.67565e41 −0.00895739
\(306\) 1.12056e43 0.354250
\(307\) 2.04163e43 0.609615 0.304808 0.952414i \(-0.401408\pi\)
0.304808 + 0.952414i \(0.401408\pi\)
\(308\) −2.51788e43 −0.710227
\(309\) −1.18683e42 −0.0316311
\(310\) 7.33983e41 0.0184866
\(311\) 1.35407e43 0.322355 0.161178 0.986925i \(-0.448471\pi\)
0.161178 + 0.986925i \(0.448471\pi\)
\(312\) −6.10361e41 −0.0137367
\(313\) −6.11170e43 −1.30058 −0.650289 0.759687i \(-0.725352\pi\)
−0.650289 + 0.759687i \(0.725352\pi\)
\(314\) 3.04770e40 0.000613343 0
\(315\) 5.31296e43 1.01135
\(316\) 8.84100e43 1.59213
\(317\) 7.44500e43 1.26861 0.634305 0.773083i \(-0.281286\pi\)
0.634305 + 0.773083i \(0.281286\pi\)
\(318\) −1.92172e43 −0.309895
\(319\) −1.70994e43 −0.261002
\(320\) −2.92110e43 −0.422107
\(321\) −1.39095e44 −1.90316
\(322\) 1.39627e43 0.180922
\(323\) 1.38360e42 0.0169812
\(324\) −1.18488e44 −1.37764
\(325\) 1.89156e42 0.0208383
\(326\) −2.13423e43 −0.222809
\(327\) 2.45396e44 2.42819
\(328\) 3.84563e43 0.360724
\(329\) −1.04763e44 −0.931706
\(330\) −1.07457e43 −0.0906236
\(331\) 2.60186e43 0.208110 0.104055 0.994572i \(-0.466818\pi\)
0.104055 + 0.994572i \(0.466818\pi\)
\(332\) −2.07675e44 −1.57568
\(333\) 2.12792e44 1.53172
\(334\) 2.46363e43 0.168272
\(335\) −3.29590e43 −0.213643
\(336\) 2.65891e44 1.63594
\(337\) −3.62826e43 −0.211921 −0.105961 0.994370i \(-0.533792\pi\)
−0.105961 + 0.994370i \(0.533792\pi\)
\(338\) 2.60593e43 0.144517
\(339\) −2.88993e44 −1.52192
\(340\) 1.08383e44 0.542101
\(341\) −4.11040e43 −0.195291
\(342\) 1.00780e42 0.00454901
\(343\) −2.36257e44 −1.01330
\(344\) −8.33961e43 −0.339917
\(345\) −2.78939e44 −1.08063
\(346\) −4.56967e43 −0.168288
\(347\) 3.83287e44 1.34202 0.671009 0.741449i \(-0.265861\pi\)
0.671009 + 0.741449i \(0.265861\pi\)
\(348\) 1.84600e44 0.614602
\(349\) 1.99513e44 0.631723 0.315862 0.948805i \(-0.397706\pi\)
0.315862 + 0.948805i \(0.397706\pi\)
\(350\) 3.63766e43 0.109555
\(351\) −1.89300e43 −0.0542345
\(352\) −1.13837e44 −0.310305
\(353\) 2.67595e44 0.694098 0.347049 0.937847i \(-0.387184\pi\)
0.347049 + 0.937847i \(0.387184\pi\)
\(354\) 5.32976e43 0.131568
\(355\) 3.16604e44 0.743909
\(356\) −2.27088e44 −0.507947
\(357\) −9.42065e44 −2.00626
\(358\) 2.54267e43 0.0515630
\(359\) 7.93674e44 1.53281 0.766407 0.642355i \(-0.222043\pi\)
0.766407 + 0.642355i \(0.222043\pi\)
\(360\) 1.59576e44 0.293545
\(361\) −5.70534e44 −0.999782
\(362\) −8.36610e43 −0.139676
\(363\) −5.10320e44 −0.811852
\(364\) 1.72754e43 0.0261911
\(365\) 8.16175e43 0.117939
\(366\) 3.45570e42 0.00476011
\(367\) −4.95841e44 −0.651158 −0.325579 0.945515i \(-0.605559\pi\)
−0.325579 + 0.945515i \(0.605559\pi\)
\(368\) −9.49982e44 −1.18954
\(369\) 2.24814e45 2.68449
\(370\) −4.39684e43 −0.0500738
\(371\) 1.09945e45 1.19435
\(372\) 4.43745e44 0.459867
\(373\) 1.46949e44 0.145299 0.0726496 0.997358i \(-0.476855\pi\)
0.0726496 + 0.997358i \(0.476855\pi\)
\(374\) 1.29664e44 0.122339
\(375\) −1.67274e45 −1.50619
\(376\) −3.14658e44 −0.270428
\(377\) 1.17321e43 0.00962500
\(378\) −3.64042e44 −0.285131
\(379\) −7.55442e44 −0.564956 −0.282478 0.959274i \(-0.591156\pi\)
−0.282478 + 0.959274i \(0.591156\pi\)
\(380\) 9.74766e42 0.00696125
\(381\) 2.33184e44 0.159042
\(382\) 9.57624e42 0.00623859
\(383\) −5.97753e44 −0.372000 −0.186000 0.982550i \(-0.559552\pi\)
−0.186000 + 0.982550i \(0.559552\pi\)
\(384\) 1.63248e45 0.970622
\(385\) 6.14781e44 0.349267
\(386\) 3.92044e44 0.212842
\(387\) −4.87530e45 −2.52964
\(388\) 2.72566e45 1.35181
\(389\) −2.41609e45 −1.14550 −0.572750 0.819730i \(-0.694123\pi\)
−0.572750 + 0.819730i \(0.694123\pi\)
\(390\) 7.37273e42 0.00334193
\(391\) 3.36583e45 1.45881
\(392\) −1.90317e43 −0.00788810
\(393\) 8.33657e45 3.30459
\(394\) −2.97694e44 −0.112872
\(395\) −2.15867e45 −0.782957
\(396\) −4.42101e45 −1.53411
\(397\) −1.25639e45 −0.417148 −0.208574 0.978007i \(-0.566882\pi\)
−0.208574 + 0.978007i \(0.566882\pi\)
\(398\) −4.87550e44 −0.154905
\(399\) −8.47267e43 −0.0257629
\(400\) −2.47496e45 −0.720310
\(401\) −3.77150e45 −1.05072 −0.525361 0.850880i \(-0.676070\pi\)
−0.525361 + 0.850880i \(0.676070\pi\)
\(402\) 4.25677e44 0.113534
\(403\) 2.82018e43 0.00720176
\(404\) 3.65935e45 0.894807
\(405\) 2.89306e45 0.677478
\(406\) 2.25619e44 0.0506022
\(407\) 2.46229e45 0.528977
\(408\) −2.82952e45 −0.582317
\(409\) −5.28767e45 −1.04257 −0.521286 0.853382i \(-0.674548\pi\)
−0.521286 + 0.853382i \(0.674548\pi\)
\(410\) −4.64525e44 −0.0877589
\(411\) 1.05379e46 1.90775
\(412\) 1.00893e44 0.0175049
\(413\) −3.04925e45 −0.507069
\(414\) 2.45163e45 0.390795
\(415\) 5.07072e45 0.774869
\(416\) 7.81048e43 0.0114431
\(417\) −7.48542e45 −1.05156
\(418\) 1.16616e43 0.00157099
\(419\) 3.73280e45 0.482270 0.241135 0.970492i \(-0.422480\pi\)
0.241135 + 0.970492i \(0.422480\pi\)
\(420\) −6.63697e45 −0.822446
\(421\) −1.18084e45 −0.140364 −0.0701819 0.997534i \(-0.522358\pi\)
−0.0701819 + 0.997534i \(0.522358\pi\)
\(422\) 1.86425e44 0.0212587
\(423\) −1.83947e46 −2.01251
\(424\) 3.30222e45 0.346660
\(425\) 8.76893e45 0.883365
\(426\) −4.08906e45 −0.395326
\(427\) −1.97706e44 −0.0183456
\(428\) 1.18246e46 1.05322
\(429\) −4.12882e44 −0.0353040
\(430\) 1.00736e45 0.0826968
\(431\) 5.00269e45 0.394322 0.197161 0.980371i \(-0.436828\pi\)
0.197161 + 0.980371i \(0.436828\pi\)
\(432\) 2.47684e46 1.87471
\(433\) −1.22691e46 −0.891817 −0.445909 0.895079i \(-0.647119\pi\)
−0.445909 + 0.895079i \(0.647119\pi\)
\(434\) 5.42348e44 0.0378624
\(435\) −4.50730e45 −0.302242
\(436\) −2.08612e46 −1.34377
\(437\) 3.02714e44 0.0187330
\(438\) −1.05412e45 −0.0626748
\(439\) 1.91016e46 1.09129 0.545645 0.838016i \(-0.316285\pi\)
0.545645 + 0.838016i \(0.316285\pi\)
\(440\) 1.84651e45 0.101375
\(441\) −1.11259e45 −0.0587027
\(442\) −8.89634e43 −0.00451151
\(443\) −1.54265e46 −0.751973 −0.375987 0.926625i \(-0.622696\pi\)
−0.375987 + 0.926625i \(0.622696\pi\)
\(444\) −2.65820e46 −1.24562
\(445\) 5.54471e45 0.249792
\(446\) −2.05045e45 −0.0888155
\(447\) 2.71570e46 1.13110
\(448\) −2.15843e46 −0.864517
\(449\) −3.71387e46 −1.43059 −0.715296 0.698822i \(-0.753708\pi\)
−0.715296 + 0.698822i \(0.753708\pi\)
\(450\) 6.38718e45 0.236641
\(451\) 2.60140e46 0.927080
\(452\) 2.45674e46 0.842241
\(453\) 6.94356e46 2.29015
\(454\) 4.37878e44 0.0138956
\(455\) −4.21806e44 −0.0128799
\(456\) −2.54479e44 −0.00747768
\(457\) −1.10776e46 −0.313266 −0.156633 0.987657i \(-0.550064\pi\)
−0.156633 + 0.987657i \(0.550064\pi\)
\(458\) −4.25630e45 −0.115847
\(459\) −8.77558e46 −2.29908
\(460\) 2.37127e46 0.598025
\(461\) −3.91769e46 −0.951183 −0.475592 0.879666i \(-0.657766\pi\)
−0.475592 + 0.879666i \(0.657766\pi\)
\(462\) −7.94013e45 −0.185606
\(463\) 5.50481e46 1.23901 0.619505 0.784992i \(-0.287333\pi\)
0.619505 + 0.784992i \(0.287333\pi\)
\(464\) −1.53505e46 −0.332704
\(465\) −1.08348e46 −0.226148
\(466\) −3.12776e45 −0.0628753
\(467\) 2.96872e46 0.574808 0.287404 0.957809i \(-0.407208\pi\)
0.287404 + 0.957809i \(0.407208\pi\)
\(468\) 3.03329e45 0.0565734
\(469\) −2.43537e46 −0.437563
\(470\) 3.80084e45 0.0657911
\(471\) −4.49889e44 −0.00750308
\(472\) −9.15849e45 −0.147177
\(473\) −5.64137e46 −0.873605
\(474\) 2.78801e46 0.416076
\(475\) 7.88652e44 0.0113435
\(476\) 8.00854e46 1.11028
\(477\) 1.93046e47 2.57982
\(478\) −1.36661e46 −0.176058
\(479\) −7.25716e46 −0.901354 −0.450677 0.892687i \(-0.648817\pi\)
−0.450677 + 0.892687i \(0.648817\pi\)
\(480\) −3.00068e46 −0.359334
\(481\) −1.68940e45 −0.0195071
\(482\) 1.94970e46 0.217092
\(483\) −2.06111e47 −2.21323
\(484\) 4.33825e46 0.449284
\(485\) −6.65514e46 −0.664778
\(486\) −7.35623e45 −0.0708795
\(487\) −1.32479e47 −1.23137 −0.615686 0.787992i \(-0.711121\pi\)
−0.615686 + 0.787992i \(0.711121\pi\)
\(488\) −5.93816e44 −0.00532482
\(489\) 3.15046e47 2.72565
\(490\) 2.29890e44 0.00191906
\(491\) 5.04170e46 0.406117 0.203058 0.979167i \(-0.434912\pi\)
0.203058 + 0.979167i \(0.434912\pi\)
\(492\) −2.80838e47 −2.18307
\(493\) 5.43876e46 0.408017
\(494\) −8.00112e42 −5.79334e−5 0
\(495\) 1.07946e47 0.754425
\(496\) −3.68999e46 −0.248941
\(497\) 2.33942e47 1.52360
\(498\) −6.54903e46 −0.411778
\(499\) 3.13288e46 0.190189 0.0950944 0.995468i \(-0.469685\pi\)
0.0950944 + 0.995468i \(0.469685\pi\)
\(500\) 1.42200e47 0.833538
\(501\) −3.63671e47 −2.05849
\(502\) −1.22341e45 −0.00668738
\(503\) 2.79560e47 1.47582 0.737912 0.674897i \(-0.235812\pi\)
0.737912 + 0.674897i \(0.235812\pi\)
\(504\) 1.17913e47 0.601209
\(505\) −8.93488e46 −0.440038
\(506\) 2.83687e46 0.134960
\(507\) −3.84676e47 −1.76789
\(508\) −1.98230e46 −0.0880147
\(509\) −2.02483e47 −0.868614 −0.434307 0.900765i \(-0.643007\pi\)
−0.434307 + 0.900765i \(0.643007\pi\)
\(510\) 3.41785e46 0.141669
\(511\) 6.03080e46 0.241551
\(512\) −1.71535e47 −0.663938
\(513\) −7.89251e45 −0.0295231
\(514\) −6.32824e45 −0.0228785
\(515\) −2.46346e45 −0.00860833
\(516\) 6.09024e47 2.05714
\(517\) −2.12852e47 −0.695014
\(518\) −3.24887e46 −0.102556
\(519\) 6.74556e47 2.05868
\(520\) −1.26691e45 −0.00373840
\(521\) −7.62521e46 −0.217566 −0.108783 0.994066i \(-0.534695\pi\)
−0.108783 + 0.994066i \(0.534695\pi\)
\(522\) 3.96152e46 0.109302
\(523\) 2.14532e47 0.572417 0.286208 0.958167i \(-0.407605\pi\)
0.286208 + 0.958167i \(0.407605\pi\)
\(524\) −7.08696e47 −1.82878
\(525\) −5.36976e47 −1.34019
\(526\) −2.13553e46 −0.0515532
\(527\) 1.30738e47 0.305293
\(528\) 5.40225e47 1.22034
\(529\) 2.78811e47 0.609307
\(530\) −3.98884e46 −0.0843372
\(531\) −5.35401e47 −1.09528
\(532\) 7.20265e45 0.0142574
\(533\) −1.78484e46 −0.0341880
\(534\) −7.16121e46 −0.132744
\(535\) −2.88716e47 −0.517940
\(536\) −7.31470e46 −0.127003
\(537\) −3.75339e47 −0.630774
\(538\) 1.29314e47 0.210357
\(539\) −1.28741e46 −0.0202728
\(540\) −6.18251e47 −0.942484
\(541\) 1.23166e48 1.81777 0.908884 0.417049i \(-0.136936\pi\)
0.908884 + 0.417049i \(0.136936\pi\)
\(542\) 5.95204e46 0.0850508
\(543\) 1.23497e48 1.70867
\(544\) 3.62079e47 0.485090
\(545\) 5.09360e47 0.660825
\(546\) 5.44779e45 0.00684461
\(547\) −7.20961e47 −0.877271 −0.438635 0.898665i \(-0.644538\pi\)
−0.438635 + 0.898665i \(0.644538\pi\)
\(548\) −8.95831e47 −1.05576
\(549\) −3.47142e46 −0.0396270
\(550\) 7.39082e46 0.0817233
\(551\) 4.89146e45 0.00523945
\(552\) −6.19060e47 −0.642390
\(553\) −1.59507e48 −1.60357
\(554\) −4.35958e46 −0.0424642
\(555\) 6.49043e47 0.612557
\(556\) 6.36339e47 0.581942
\(557\) 5.88528e47 0.521556 0.260778 0.965399i \(-0.416021\pi\)
0.260778 + 0.965399i \(0.416021\pi\)
\(558\) 9.52280e46 0.0817836
\(559\) 3.87060e46 0.0322160
\(560\) 5.51901e47 0.445216
\(561\) −1.91404e48 −1.49659
\(562\) −1.68643e47 −0.127815
\(563\) −1.44205e48 −1.05946 −0.529730 0.848166i \(-0.677707\pi\)
−0.529730 + 0.848166i \(0.677707\pi\)
\(564\) 2.29788e48 1.63660
\(565\) −5.99852e47 −0.414187
\(566\) −1.09178e46 −0.00730882
\(567\) 2.13772e48 1.38754
\(568\) 7.02651e47 0.442225
\(569\) 1.87904e48 1.14676 0.573379 0.819290i \(-0.305632\pi\)
0.573379 + 0.819290i \(0.305632\pi\)
\(570\) 3.07392e45 0.00181921
\(571\) −1.57690e48 −0.905050 −0.452525 0.891752i \(-0.649477\pi\)
−0.452525 + 0.891752i \(0.649477\pi\)
\(572\) 3.50993e46 0.0195375
\(573\) −1.41361e47 −0.0763172
\(574\) −3.43242e47 −0.179739
\(575\) 1.91852e48 0.974495
\(576\) −3.78988e48 −1.86738
\(577\) −7.02869e47 −0.335968 −0.167984 0.985790i \(-0.553726\pi\)
−0.167984 + 0.985790i \(0.553726\pi\)
\(578\) −1.00545e47 −0.0466254
\(579\) −5.78720e48 −2.60371
\(580\) 3.83167e47 0.167263
\(581\) 3.74681e48 1.58701
\(582\) 8.59536e47 0.353274
\(583\) 2.23381e48 0.890934
\(584\) 1.81137e47 0.0701103
\(585\) −7.40628e46 −0.0278210
\(586\) −7.10871e47 −0.259169
\(587\) −1.10752e48 −0.391908 −0.195954 0.980613i \(-0.562780\pi\)
−0.195954 + 0.980613i \(0.562780\pi\)
\(588\) 1.38985e47 0.0477380
\(589\) 1.17582e46 0.00392034
\(590\) 1.10628e47 0.0358059
\(591\) 4.39444e48 1.38077
\(592\) 2.21044e48 0.674294
\(593\) −2.15841e48 −0.639258 −0.319629 0.947543i \(-0.603558\pi\)
−0.319629 + 0.947543i \(0.603558\pi\)
\(594\) −7.39643e47 −0.212696
\(595\) −1.95541e48 −0.545999
\(596\) −2.30863e48 −0.625958
\(597\) 7.19701e48 1.89497
\(598\) −1.94640e46 −0.00497692
\(599\) −5.67895e48 −1.41026 −0.705129 0.709079i \(-0.749111\pi\)
−0.705129 + 0.709079i \(0.749111\pi\)
\(600\) −1.61282e48 −0.388991
\(601\) 6.99029e48 1.63754 0.818770 0.574122i \(-0.194656\pi\)
0.818770 + 0.574122i \(0.194656\pi\)
\(602\) 7.44353e47 0.169371
\(603\) −4.27614e48 −0.945147
\(604\) −5.90275e48 −1.26738
\(605\) −1.05925e48 −0.220944
\(606\) 1.15397e48 0.233843
\(607\) −4.92572e48 −0.969768 −0.484884 0.874578i \(-0.661138\pi\)
−0.484884 + 0.874578i \(0.661138\pi\)
\(608\) 3.25643e46 0.00622916
\(609\) −3.33049e48 −0.619022
\(610\) 7.17287e45 0.00129545
\(611\) 1.46040e47 0.0256300
\(612\) 1.40618e49 2.39823
\(613\) 3.59765e48 0.596295 0.298148 0.954520i \(-0.403631\pi\)
0.298148 + 0.954520i \(0.403631\pi\)
\(614\) −5.47321e47 −0.0881649
\(615\) 6.85712e48 1.07356
\(616\) 1.36441e48 0.207626
\(617\) −3.73363e48 −0.552257 −0.276128 0.961121i \(-0.589051\pi\)
−0.276128 + 0.961121i \(0.589051\pi\)
\(618\) 3.18165e46 0.00457461
\(619\) 2.84346e48 0.397430 0.198715 0.980057i \(-0.436323\pi\)
0.198715 + 0.980057i \(0.436323\pi\)
\(620\) 9.21067e47 0.125152
\(621\) −1.91998e49 −2.53626
\(622\) −3.62999e47 −0.0466202
\(623\) 4.09705e48 0.511600
\(624\) −3.70653e47 −0.0450025
\(625\) 3.03465e48 0.358268
\(626\) 1.63843e48 0.188094
\(627\) −1.72144e47 −0.0192180
\(628\) 3.82453e46 0.00415225
\(629\) −7.83171e48 −0.826933
\(630\) −1.42430e48 −0.146265
\(631\) 8.72640e48 0.871608 0.435804 0.900041i \(-0.356464\pi\)
0.435804 + 0.900041i \(0.356464\pi\)
\(632\) −4.79082e48 −0.465438
\(633\) −2.75193e48 −0.260059
\(634\) −1.99586e48 −0.183471
\(635\) 4.84011e47 0.0432828
\(636\) −2.41154e49 −2.09795
\(637\) 8.83305e45 0.000747602 0
\(638\) 4.58401e47 0.0377471
\(639\) 4.10766e49 3.29101
\(640\) 3.38848e48 0.264153
\(641\) 1.94871e49 1.47820 0.739098 0.673598i \(-0.235252\pi\)
0.739098 + 0.673598i \(0.235252\pi\)
\(642\) 3.72887e48 0.275242
\(643\) −2.20357e49 −1.58283 −0.791417 0.611277i \(-0.790656\pi\)
−0.791417 + 0.611277i \(0.790656\pi\)
\(644\) 1.75216e49 1.22482
\(645\) −1.48703e49 −1.01164
\(646\) −3.70916e46 −0.00245588
\(647\) −1.15002e49 −0.741106 −0.370553 0.928811i \(-0.620832\pi\)
−0.370553 + 0.928811i \(0.620832\pi\)
\(648\) 6.42069e48 0.402734
\(649\) −6.19531e48 −0.378252
\(650\) −5.07091e46 −0.00301371
\(651\) −8.00592e48 −0.463174
\(652\) −2.67822e49 −1.50839
\(653\) −3.36604e48 −0.184560 −0.0922801 0.995733i \(-0.529416\pi\)
−0.0922801 + 0.995733i \(0.529416\pi\)
\(654\) −6.57858e48 −0.351173
\(655\) 1.73039e49 0.899337
\(656\) 2.33533e49 1.18176
\(657\) 1.05892e49 0.521757
\(658\) 2.80848e48 0.134747
\(659\) −1.07733e49 −0.503334 −0.251667 0.967814i \(-0.580979\pi\)
−0.251667 + 0.967814i \(0.580979\pi\)
\(660\) −1.34847e49 −0.613510
\(661\) −1.67936e49 −0.744079 −0.372040 0.928217i \(-0.621341\pi\)
−0.372040 + 0.928217i \(0.621341\pi\)
\(662\) −6.97506e47 −0.0300977
\(663\) 1.31324e48 0.0551897
\(664\) 1.12536e49 0.460630
\(665\) −1.75864e47 −0.00701131
\(666\) −5.70452e48 −0.221524
\(667\) 1.18993e49 0.450109
\(668\) 3.09158e49 1.13918
\(669\) 3.02679e49 1.08649
\(670\) 8.83564e47 0.0308979
\(671\) −4.01690e47 −0.0136851
\(672\) −2.21724e49 −0.735952
\(673\) 2.60356e49 0.841984 0.420992 0.907064i \(-0.361682\pi\)
0.420992 + 0.907064i \(0.361682\pi\)
\(674\) 9.72664e47 0.0306489
\(675\) −5.00207e49 −1.53580
\(676\) 3.27015e49 0.978363
\(677\) −5.14137e49 −1.49891 −0.749457 0.662053i \(-0.769685\pi\)
−0.749457 + 0.662053i \(0.769685\pi\)
\(678\) 7.74732e48 0.220106
\(679\) −4.91756e49 −1.36153
\(680\) −5.87313e48 −0.158476
\(681\) −6.46378e48 −0.169986
\(682\) 1.10192e48 0.0282437
\(683\) 3.66408e47 0.00915382 0.00457691 0.999990i \(-0.498543\pi\)
0.00457691 + 0.999990i \(0.498543\pi\)
\(684\) 1.26468e48 0.0307962
\(685\) 2.18732e49 0.519190
\(686\) 6.33359e48 0.146547
\(687\) 6.28298e49 1.41717
\(688\) −5.06437e49 −1.11360
\(689\) −1.53263e48 −0.0328550
\(690\) 7.47780e48 0.156284
\(691\) 8.07844e49 1.64612 0.823060 0.567954i \(-0.192265\pi\)
0.823060 + 0.567954i \(0.192265\pi\)
\(692\) −5.73443e49 −1.13929
\(693\) 7.97626e49 1.54514
\(694\) −1.02752e49 −0.194088
\(695\) −1.55372e49 −0.286180
\(696\) −1.00032e49 −0.179671
\(697\) −8.27418e49 −1.44928
\(698\) −5.34856e48 −0.0913622
\(699\) 4.61707e49 0.769159
\(700\) 4.56486e49 0.741672
\(701\) 1.36918e49 0.216968 0.108484 0.994098i \(-0.465400\pi\)
0.108484 + 0.994098i \(0.465400\pi\)
\(702\) 5.07476e47 0.00784360
\(703\) −7.04362e47 −0.0106189
\(704\) −4.38540e49 −0.644894
\(705\) −5.61065e49 −0.804828
\(706\) −7.17369e48 −0.100383
\(707\) −6.60208e49 −0.901242
\(708\) 6.68826e49 0.890699
\(709\) 9.81931e49 1.27577 0.637884 0.770132i \(-0.279810\pi\)
0.637884 + 0.770132i \(0.279810\pi\)
\(710\) −8.48752e48 −0.107587
\(711\) −2.80069e50 −3.46376
\(712\) 1.23056e49 0.148492
\(713\) 2.86037e49 0.336787
\(714\) 2.52549e49 0.290153
\(715\) −8.57006e47 −0.00960789
\(716\) 3.19077e49 0.349075
\(717\) 2.01733e50 2.15374
\(718\) −2.12768e49 −0.221681
\(719\) 1.63037e50 1.65780 0.828899 0.559398i \(-0.188968\pi\)
0.828899 + 0.559398i \(0.188968\pi\)
\(720\) 9.69054e49 0.961677
\(721\) −1.82028e48 −0.0176307
\(722\) 1.52949e49 0.144592
\(723\) −2.87806e50 −2.65571
\(724\) −1.04985e50 −0.945591
\(725\) 3.10009e49 0.272558
\(726\) 1.36807e49 0.117413
\(727\) 3.34890e49 0.280576 0.140288 0.990111i \(-0.455197\pi\)
0.140288 + 0.990111i \(0.455197\pi\)
\(728\) −9.36131e47 −0.00765663
\(729\) −6.76269e49 −0.539993
\(730\) −2.18800e48 −0.0170568
\(731\) 1.79433e50 1.36568
\(732\) 4.33652e48 0.0322253
\(733\) −2.00965e50 −1.45814 −0.729071 0.684438i \(-0.760048\pi\)
−0.729071 + 0.684438i \(0.760048\pi\)
\(734\) 1.32925e49 0.0941729
\(735\) −3.39354e48 −0.0234760
\(736\) 7.92179e49 0.535133
\(737\) −4.94807e49 −0.326404
\(738\) −6.02681e49 −0.388241
\(739\) −1.06372e50 −0.669190 −0.334595 0.942362i \(-0.608599\pi\)
−0.334595 + 0.942362i \(0.608599\pi\)
\(740\) −5.51754e49 −0.338993
\(741\) 1.18109e47 0.000708704 0
\(742\) −2.94740e49 −0.172731
\(743\) 7.25015e49 0.414995 0.207498 0.978236i \(-0.433468\pi\)
0.207498 + 0.978236i \(0.433468\pi\)
\(744\) −2.40460e49 −0.134436
\(745\) 5.63690e49 0.307826
\(746\) −3.93942e48 −0.0210137
\(747\) 6.57883e50 3.42798
\(748\) 1.62714e50 0.828220
\(749\) −2.13335e50 −1.06079
\(750\) 4.48428e49 0.217832
\(751\) −4.51226e49 −0.214139 −0.107069 0.994252i \(-0.534147\pi\)
−0.107069 + 0.994252i \(0.534147\pi\)
\(752\) −1.91081e50 −0.885944
\(753\) 1.80595e49 0.0818074
\(754\) −3.14513e47 −0.00139200
\(755\) 1.44125e50 0.623259
\(756\) −4.56832e50 −1.93030
\(757\) −1.21415e50 −0.501296 −0.250648 0.968078i \(-0.580644\pi\)
−0.250648 + 0.968078i \(0.580644\pi\)
\(758\) 2.02519e49 0.0817061
\(759\) −4.18767e50 −1.65098
\(760\) −5.28213e47 −0.00203503
\(761\) 3.14799e50 1.18523 0.592614 0.805486i \(-0.298096\pi\)
0.592614 + 0.805486i \(0.298096\pi\)
\(762\) −6.25119e48 −0.0230012
\(763\) 3.76372e50 1.35344
\(764\) 1.20171e49 0.0422344
\(765\) −3.43341e50 −1.17937
\(766\) 1.60246e49 0.0538000
\(767\) 4.25066e48 0.0139488
\(768\) 4.39784e50 1.41065
\(769\) −5.16540e50 −1.61954 −0.809772 0.586744i \(-0.800409\pi\)
−0.809772 + 0.586744i \(0.800409\pi\)
\(770\) −1.64811e49 −0.0505123
\(771\) 9.34149e49 0.279875
\(772\) 4.91972e50 1.44091
\(773\) −4.51959e50 −1.29407 −0.647035 0.762460i \(-0.723991\pi\)
−0.647035 + 0.762460i \(0.723991\pi\)
\(774\) 1.30697e50 0.365846
\(775\) 7.45206e49 0.203937
\(776\) −1.47700e50 −0.395185
\(777\) 4.79585e50 1.25458
\(778\) 6.47705e49 0.165666
\(779\) −7.44157e48 −0.0186105
\(780\) 9.25195e48 0.0226244
\(781\) 4.75312e50 1.13654
\(782\) −9.02313e49 −0.210979
\(783\) −3.10244e50 −0.709369
\(784\) −1.15574e49 −0.0258421
\(785\) −9.33820e47 −0.00204195
\(786\) −2.23487e50 −0.477923
\(787\) −7.76649e50 −1.62430 −0.812151 0.583447i \(-0.801704\pi\)
−0.812151 + 0.583447i \(0.801704\pi\)
\(788\) −3.73573e50 −0.764129
\(789\) 3.15238e50 0.630655
\(790\) 5.78697e49 0.113234
\(791\) −4.43237e50 −0.848297
\(792\) 2.39569e50 0.448477
\(793\) 2.75603e47 0.000504665 0
\(794\) 3.36813e49 0.0603295
\(795\) 5.88817e50 1.03171
\(796\) −6.11821e50 −1.04869
\(797\) −7.96535e49 −0.133562 −0.0667812 0.997768i \(-0.521273\pi\)
−0.0667812 + 0.997768i \(0.521273\pi\)
\(798\) 2.27135e48 0.00372593
\(799\) 6.77011e50 1.08649
\(800\) 2.06385e50 0.324043
\(801\) 7.19379e50 1.10507
\(802\) 1.01106e50 0.151959
\(803\) 1.22531e50 0.180187
\(804\) 5.34178e50 0.768608
\(805\) −4.27818e50 −0.602325
\(806\) −7.56034e47 −0.00104155
\(807\) −1.90889e51 −2.57332
\(808\) −1.98295e50 −0.261585
\(809\) 8.80158e50 1.13622 0.568109 0.822954i \(-0.307675\pi\)
0.568109 + 0.822954i \(0.307675\pi\)
\(810\) −7.75573e49 −0.0979794
\(811\) 1.29798e51 1.60473 0.802364 0.596835i \(-0.203575\pi\)
0.802364 + 0.596835i \(0.203575\pi\)
\(812\) 2.83126e50 0.342571
\(813\) −8.78616e50 −1.04043
\(814\) −6.60090e49 −0.0765026
\(815\) 6.53931e50 0.741778
\(816\) −1.71827e51 −1.90772
\(817\) 1.61377e49 0.0175370
\(818\) 1.41752e50 0.150781
\(819\) −5.47258e49 −0.0569802
\(820\) −5.82927e50 −0.594116
\(821\) 8.37740e50 0.835804 0.417902 0.908492i \(-0.362766\pi\)
0.417902 + 0.908492i \(0.362766\pi\)
\(822\) −2.82500e50 −0.275906
\(823\) −1.79490e51 −1.71610 −0.858051 0.513564i \(-0.828325\pi\)
−0.858051 + 0.513564i \(0.828325\pi\)
\(824\) −5.46725e48 −0.00511732
\(825\) −1.09100e51 −0.999728
\(826\) 8.17442e49 0.0733342
\(827\) 6.78828e50 0.596230 0.298115 0.954530i \(-0.403642\pi\)
0.298115 + 0.954530i \(0.403642\pi\)
\(828\) 3.07652e51 2.64563
\(829\) 1.62563e51 1.36873 0.684363 0.729141i \(-0.260080\pi\)
0.684363 + 0.729141i \(0.260080\pi\)
\(830\) −1.35936e50 −0.112064
\(831\) 6.43543e50 0.519469
\(832\) 3.00886e49 0.0237818
\(833\) 4.09483e49 0.0316919
\(834\) 2.00669e50 0.152081
\(835\) −7.54860e50 −0.560213
\(836\) 1.46340e49 0.0106354
\(837\) −7.45772e50 −0.530775
\(838\) −1.00069e50 −0.0697476
\(839\) −2.62276e51 −1.79029 −0.895147 0.445771i \(-0.852930\pi\)
−0.895147 + 0.445771i \(0.852930\pi\)
\(840\) 3.59649e50 0.240431
\(841\) −1.33504e51 −0.874108
\(842\) 3.16560e49 0.0202999
\(843\) 2.48944e51 1.56357
\(844\) 2.33943e50 0.143918
\(845\) −7.98459e50 −0.481128
\(846\) 4.93127e50 0.291056
\(847\) −7.82695e50 −0.452515
\(848\) 2.00533e51 1.13569
\(849\) 1.61164e50 0.0894094
\(850\) −2.35077e50 −0.127756
\(851\) −1.71347e51 −0.912242
\(852\) −5.13131e51 −2.67630
\(853\) 2.63497e51 1.34638 0.673191 0.739469i \(-0.264923\pi\)
0.673191 + 0.739469i \(0.264923\pi\)
\(854\) 5.30011e48 0.00265321
\(855\) −3.08791e49 −0.0151446
\(856\) −6.40758e50 −0.307895
\(857\) 1.21045e51 0.569880 0.284940 0.958545i \(-0.408026\pi\)
0.284940 + 0.958545i \(0.408026\pi\)
\(858\) 1.10686e49 0.00510579
\(859\) 1.22181e51 0.552234 0.276117 0.961124i \(-0.410952\pi\)
0.276117 + 0.961124i \(0.410952\pi\)
\(860\) 1.26413e51 0.559847
\(861\) 5.06680e51 2.19876
\(862\) −1.34112e50 −0.0570283
\(863\) −1.06383e51 −0.443284 −0.221642 0.975128i \(-0.571142\pi\)
−0.221642 + 0.975128i \(0.571142\pi\)
\(864\) −2.06541e51 −0.843366
\(865\) 1.40015e51 0.560265
\(866\) 3.28911e50 0.128978
\(867\) 1.48420e51 0.570373
\(868\) 6.80586e50 0.256323
\(869\) −3.24078e51 −1.19620
\(870\) 1.20832e50 0.0437113
\(871\) 3.39491e49 0.0120368
\(872\) 1.13044e51 0.392835
\(873\) −8.63448e51 −2.94094
\(874\) −8.11515e48 −0.00270923
\(875\) −2.56553e51 −0.839531
\(876\) −1.32280e51 −0.424301
\(877\) 2.07831e51 0.653459 0.326729 0.945118i \(-0.394053\pi\)
0.326729 + 0.945118i \(0.394053\pi\)
\(878\) −5.12075e50 −0.157826
\(879\) 1.04936e52 3.17043
\(880\) 1.12133e51 0.332112
\(881\) −5.23747e51 −1.52070 −0.760350 0.649514i \(-0.774973\pi\)
−0.760350 + 0.649514i \(0.774973\pi\)
\(882\) 2.98262e49 0.00848981
\(883\) −2.39426e51 −0.668126 −0.334063 0.942551i \(-0.608420\pi\)
−0.334063 + 0.942551i \(0.608420\pi\)
\(884\) −1.11639e50 −0.0305423
\(885\) −1.63305e51 −0.438017
\(886\) 4.13554e50 0.108753
\(887\) 4.11591e51 1.06121 0.530606 0.847618i \(-0.321964\pi\)
0.530606 + 0.847618i \(0.321964\pi\)
\(888\) 1.44045e51 0.364141
\(889\) 3.57641e50 0.0886476
\(890\) −1.48643e50 −0.0361259
\(891\) 4.34331e51 1.03505
\(892\) −2.57309e51 −0.601270
\(893\) 6.08885e49 0.0139519
\(894\) −7.28026e50 −0.163584
\(895\) −7.79079e50 −0.171664
\(896\) 2.50378e51 0.541011
\(897\) 2.87319e50 0.0608832
\(898\) 9.95614e50 0.206898
\(899\) 4.62200e50 0.0941966
\(900\) 8.01520e51 1.60203
\(901\) −7.10499e51 −1.39277
\(902\) −6.97383e50 −0.134078
\(903\) −1.09878e52 −2.07194
\(904\) −1.33127e51 −0.246218
\(905\) 2.56338e51 0.465011
\(906\) −1.86143e51 −0.331210
\(907\) 1.27732e51 0.222932 0.111466 0.993768i \(-0.464445\pi\)
0.111466 + 0.993768i \(0.464445\pi\)
\(908\) 5.49489e50 0.0940712
\(909\) −1.15922e52 −1.94670
\(910\) 1.13078e49 0.00186274
\(911\) 4.62833e51 0.747915 0.373958 0.927446i \(-0.378001\pi\)
0.373958 + 0.927446i \(0.378001\pi\)
\(912\) −1.54537e50 −0.0244975
\(913\) 7.61259e51 1.18384
\(914\) 2.96970e50 0.0453058
\(915\) −1.05883e50 −0.0158474
\(916\) −5.34118e51 −0.784272
\(917\) 1.27861e52 1.84193
\(918\) 2.35256e51 0.332501
\(919\) 3.73013e50 0.0517253 0.0258626 0.999666i \(-0.491767\pi\)
0.0258626 + 0.999666i \(0.491767\pi\)
\(920\) −1.28496e51 −0.174825
\(921\) 8.07933e51 1.07853
\(922\) 1.05026e51 0.137564
\(923\) −3.26116e50 −0.0419123
\(924\) −9.96398e51 −1.25653
\(925\) −4.46407e51 −0.552396
\(926\) −1.47573e51 −0.179190
\(927\) −3.19613e50 −0.0380828
\(928\) 1.28006e51 0.149672
\(929\) 3.82307e51 0.438669 0.219334 0.975650i \(-0.429611\pi\)
0.219334 + 0.975650i \(0.429611\pi\)
\(930\) 2.90458e50 0.0327063
\(931\) 3.68277e48 0.000406964 0
\(932\) −3.92499e51 −0.425658
\(933\) 5.35845e51 0.570309
\(934\) −7.95853e50 −0.0831310
\(935\) −3.97291e51 −0.407292
\(936\) −1.64370e50 −0.0165385
\(937\) 1.21639e52 1.20124 0.600619 0.799536i \(-0.294921\pi\)
0.600619 + 0.799536i \(0.294921\pi\)
\(938\) 6.52875e50 0.0632820
\(939\) −2.41858e52 −2.30098
\(940\) 4.76963e51 0.445397
\(941\) −1.11091e52 −1.01827 −0.509133 0.860688i \(-0.670034\pi\)
−0.509133 + 0.860688i \(0.670034\pi\)
\(942\) 1.20606e49 0.00108512
\(943\) −1.81028e52 −1.59879
\(944\) −5.56166e51 −0.482163
\(945\) 1.11543e52 0.949261
\(946\) 1.51234e51 0.126344
\(947\) 3.07714e51 0.252362 0.126181 0.992007i \(-0.459728\pi\)
0.126181 + 0.992007i \(0.459728\pi\)
\(948\) 3.49864e52 2.81678
\(949\) −8.40695e49 −0.00664477
\(950\) −2.11422e49 −0.00164054
\(951\) 2.94620e52 2.24442
\(952\) −4.33972e51 −0.324575
\(953\) 4.41309e50 0.0324053 0.0162027 0.999869i \(-0.494842\pi\)
0.0162027 + 0.999869i \(0.494842\pi\)
\(954\) −5.17519e51 −0.373104
\(955\) −2.93417e50 −0.0207695
\(956\) −1.71494e52 −1.19189
\(957\) −6.76673e51 −0.461764
\(958\) 1.94550e51 0.130357
\(959\) 1.61623e52 1.06335
\(960\) −1.15596e52 −0.746789
\(961\) −1.46527e52 −0.929519
\(962\) 4.52893e49 0.00282119
\(963\) −3.74584e52 −2.29134
\(964\) 2.44665e52 1.46969
\(965\) −1.20123e52 −0.708594
\(966\) 5.52543e51 0.320086
\(967\) 2.95259e52 1.67973 0.839866 0.542795i \(-0.182634\pi\)
0.839866 + 0.542795i \(0.182634\pi\)
\(968\) −2.35084e51 −0.131342
\(969\) 5.47532e50 0.0300430
\(970\) 1.78411e51 0.0961427
\(971\) −8.31094e51 −0.439859 −0.219930 0.975516i \(-0.570583\pi\)
−0.219930 + 0.975516i \(0.570583\pi\)
\(972\) −9.23125e51 −0.479845
\(973\) −1.14806e52 −0.586126
\(974\) 3.55149e51 0.178086
\(975\) 7.48546e50 0.0368670
\(976\) −3.60605e50 −0.0174446
\(977\) −2.16398e52 −1.02825 −0.514125 0.857715i \(-0.671883\pi\)
−0.514125 + 0.857715i \(0.671883\pi\)
\(978\) −8.44577e51 −0.394193
\(979\) 8.32419e51 0.381632
\(980\) 2.88486e50 0.0129918
\(981\) 6.60851e52 2.92345
\(982\) −1.35158e51 −0.0587341
\(983\) 1.17980e51 0.0503643 0.0251822 0.999683i \(-0.491983\pi\)
0.0251822 + 0.999683i \(0.491983\pi\)
\(984\) 1.52183e52 0.638192
\(985\) 9.12139e51 0.375774
\(986\) −1.45802e51 −0.0590090
\(987\) −4.14577e52 −1.64837
\(988\) −1.00405e49 −0.000392202 0
\(989\) 3.92576e52 1.50657
\(990\) −2.89382e51 −0.109108
\(991\) −1.92041e52 −0.711387 −0.355694 0.934603i \(-0.615755\pi\)
−0.355694 + 0.934603i \(0.615755\pi\)
\(992\) 3.07704e51 0.111990
\(993\) 1.02963e52 0.368188
\(994\) −6.27152e51 −0.220349
\(995\) 1.49386e52 0.515710
\(996\) −8.21830e52 −2.78769
\(997\) −4.51709e52 −1.50554 −0.752772 0.658281i \(-0.771284\pi\)
−0.752772 + 0.658281i \(0.771284\pi\)
\(998\) −8.39864e50 −0.0275058
\(999\) 4.46746e52 1.43769
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1.36.a.a.1.2 3
3.2 odd 2 9.36.a.b.1.2 3
4.3 odd 2 16.36.a.d.1.1 3
5.2 odd 4 25.36.b.a.24.3 6
5.3 odd 4 25.36.b.a.24.4 6
5.4 even 2 25.36.a.a.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.36.a.a.1.2 3 1.1 even 1 trivial
9.36.a.b.1.2 3 3.2 odd 2
16.36.a.d.1.1 3 4.3 odd 2
25.36.a.a.1.2 3 5.4 even 2
25.36.b.a.24.3 6 5.2 odd 4
25.36.b.a.24.4 6 5.3 odd 4