Properties

Label 3.36.a.a.1.2
Level $3$
Weight $36$
Character 3.1
Self dual yes
Analytic conductor $23.279$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 36 \)
Character orbit: \([\chi]\) \(=\) 3.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(23.2785391901\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{2196841}) \)
Defining polynomial: \(x^{2} - x - 549210\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2^{4}\cdot 3\cdot 7 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-740.587\) of defining polynomial
Character \(\chi\) \(=\) 3.1

$q$-expansion

\(f(q)\) \(=\) \(q+218549. q^{2} +1.29140e8 q^{3} +1.34041e10 q^{4} -9.68425e11 q^{5} +2.82235e13 q^{6} -5.65365e14 q^{7} -4.57985e15 q^{8} +1.66772e16 q^{9} +O(q^{10})\) \(q+218549. q^{2} +1.29140e8 q^{3} +1.34041e10 q^{4} -9.68425e11 q^{5} +2.82235e13 q^{6} -5.65365e14 q^{7} -4.57985e15 q^{8} +1.66772e16 q^{9} -2.11649e17 q^{10} -1.62372e18 q^{11} +1.73100e18 q^{12} -2.52538e19 q^{13} -1.23560e20 q^{14} -1.25063e20 q^{15} -1.46148e21 q^{16} +4.37227e21 q^{17} +3.64479e21 q^{18} +1.72036e22 q^{19} -1.29808e22 q^{20} -7.30113e22 q^{21} -3.54863e23 q^{22} -5.13356e23 q^{23} -5.91442e23 q^{24} -1.97254e24 q^{25} -5.51920e24 q^{26} +2.15369e24 q^{27} -7.57819e24 q^{28} -3.39397e25 q^{29} -2.73323e25 q^{30} -9.89761e25 q^{31} -1.62044e26 q^{32} -2.09687e26 q^{33} +9.55557e26 q^{34} +5.47514e26 q^{35} +2.23542e26 q^{36} +4.58147e27 q^{37} +3.75982e27 q^{38} -3.26128e27 q^{39} +4.43524e27 q^{40} -2.87989e28 q^{41} -1.59566e28 q^{42} +6.85354e28 q^{43} -2.17644e28 q^{44} -1.61506e28 q^{45} -1.12194e29 q^{46} -4.79363e26 q^{47} -1.88736e29 q^{48} -5.91811e28 q^{49} -4.31096e29 q^{50} +5.64636e29 q^{51} -3.38503e29 q^{52} +2.32896e30 q^{53} +4.70688e29 q^{54} +1.57245e30 q^{55} +2.58929e30 q^{56} +2.22167e30 q^{57} -7.41751e30 q^{58} +5.75836e30 q^{59} -1.67635e30 q^{60} -2.67580e31 q^{61} -2.16312e31 q^{62} -9.42870e30 q^{63} +1.48016e31 q^{64} +2.44564e31 q^{65} -4.58270e31 q^{66} +7.66448e31 q^{67} +5.86062e31 q^{68} -6.62949e31 q^{69} +1.19659e32 q^{70} -5.08152e31 q^{71} -7.63790e31 q^{72} -2.74698e32 q^{73} +1.00128e33 q^{74} -2.54734e32 q^{75} +2.30597e32 q^{76} +9.17994e32 q^{77} -7.12750e32 q^{78} -2.13670e33 q^{79} +1.41534e33 q^{80} +2.78128e32 q^{81} -6.29399e33 q^{82} -2.22116e33 q^{83} -9.78648e32 q^{84} -4.23422e33 q^{85} +1.49784e34 q^{86} -4.38298e33 q^{87} +7.43639e33 q^{88} +2.07592e34 q^{89} -3.52970e33 q^{90} +1.42776e34 q^{91} -6.88105e33 q^{92} -1.27818e34 q^{93} -1.04765e32 q^{94} -1.66604e34 q^{95} -2.09263e34 q^{96} +1.55170e34 q^{97} -1.29340e34 q^{98} -2.70791e34 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 60912q^{2} + 258280326q^{3} + 57142939904q^{4} - 1333779496740q^{5} - 7866185608656q^{6} - 1201512782952944q^{7} - 7200956480385024q^{8} + 33354363399333138q^{9} + O(q^{10}) \) \( 2q - 60912q^{2} + 258280326q^{3} + 57142939904q^{4} - 1333779496740q^{5} - 7866185608656q^{6} - 1201512782952944q^{7} - 7200956480385024q^{8} + 33354363399333138q^{9} - 109546268366103840q^{10} - 1474443852221320632q^{11} + 7379448573501764352q^{12} + 30005213658205678828q^{13} + 54218555116626208896q^{14} - \)\(17\!\cdots\!20\)\(q^{15} - \)\(22\!\cdots\!20\)\(q^{16} + \)\(61\!\cdots\!32\)\(q^{17} - \)\(10\!\cdots\!28\)\(q^{18} - \)\(16\!\cdots\!64\)\(q^{19} - \)\(28\!\cdots\!20\)\(q^{20} - \)\(15\!\cdots\!72\)\(q^{21} - \)\(39\!\cdots\!16\)\(q^{22} + \)\(49\!\cdots\!72\)\(q^{23} - \)\(92\!\cdots\!12\)\(q^{24} - \)\(47\!\cdots\!50\)\(q^{25} - \)\(20\!\cdots\!56\)\(q^{26} + \)\(43\!\cdots\!94\)\(q^{27} - \)\(35\!\cdots\!72\)\(q^{28} - \)\(78\!\cdots\!48\)\(q^{29} - \)\(14\!\cdots\!20\)\(q^{30} - \)\(12\!\cdots\!48\)\(q^{31} + \)\(14\!\cdots\!76\)\(q^{32} - \)\(19\!\cdots\!16\)\(q^{33} + \)\(44\!\cdots\!88\)\(q^{34} + \)\(77\!\cdots\!60\)\(q^{35} + \)\(95\!\cdots\!76\)\(q^{36} + \)\(16\!\cdots\!16\)\(q^{37} + \)\(13\!\cdots\!12\)\(q^{38} + \)\(38\!\cdots\!64\)\(q^{39} + \)\(53\!\cdots\!00\)\(q^{40} - \)\(32\!\cdots\!88\)\(q^{41} + \)\(70\!\cdots\!48\)\(q^{42} + \)\(10\!\cdots\!20\)\(q^{43} - \)\(15\!\cdots\!68\)\(q^{44} - \)\(22\!\cdots\!60\)\(q^{45} - \)\(39\!\cdots\!48\)\(q^{46} - \)\(52\!\cdots\!20\)\(q^{47} - \)\(28\!\cdots\!60\)\(q^{48} - \)\(33\!\cdots\!50\)\(q^{49} + \)\(34\!\cdots\!00\)\(q^{50} + \)\(79\!\cdots\!16\)\(q^{51} + \)\(20\!\cdots\!12\)\(q^{52} - \)\(31\!\cdots\!68\)\(q^{53} - \)\(13\!\cdots\!64\)\(q^{54} + \)\(15\!\cdots\!20\)\(q^{55} + \)\(42\!\cdots\!20\)\(q^{56} - \)\(20\!\cdots\!32\)\(q^{57} + \)\(51\!\cdots\!24\)\(q^{58} + \)\(82\!\cdots\!64\)\(q^{59} - \)\(37\!\cdots\!60\)\(q^{60} - \)\(40\!\cdots\!40\)\(q^{61} - \)\(15\!\cdots\!68\)\(q^{62} - \)\(20\!\cdots\!36\)\(q^{63} - \)\(44\!\cdots\!64\)\(q^{64} + \)\(42\!\cdots\!20\)\(q^{65} - \)\(51\!\cdots\!08\)\(q^{66} + \)\(96\!\cdots\!12\)\(q^{67} + \)\(13\!\cdots\!04\)\(q^{68} + \)\(63\!\cdots\!36\)\(q^{69} + \)\(54\!\cdots\!60\)\(q^{70} + \)\(44\!\cdots\!24\)\(q^{71} - \)\(12\!\cdots\!56\)\(q^{72} - \)\(13\!\cdots\!08\)\(q^{73} + \)\(18\!\cdots\!76\)\(q^{74} - \)\(61\!\cdots\!50\)\(q^{75} - \)\(12\!\cdots\!64\)\(q^{76} + \)\(82\!\cdots\!12\)\(q^{77} - \)\(27\!\cdots\!28\)\(q^{78} - \)\(10\!\cdots\!80\)\(q^{79} + \)\(16\!\cdots\!60\)\(q^{80} + \)\(55\!\cdots\!22\)\(q^{81} - \)\(51\!\cdots\!48\)\(q^{82} - \)\(55\!\cdots\!44\)\(q^{83} - \)\(45\!\cdots\!36\)\(q^{84} - \)\(48\!\cdots\!40\)\(q^{85} + \)\(31\!\cdots\!88\)\(q^{86} - \)\(10\!\cdots\!24\)\(q^{87} + \)\(70\!\cdots\!36\)\(q^{88} + \)\(24\!\cdots\!36\)\(q^{89} - \)\(18\!\cdots\!60\)\(q^{90} - \)\(20\!\cdots\!28\)\(q^{91} + \)\(37\!\cdots\!36\)\(q^{92} - \)\(15\!\cdots\!24\)\(q^{93} + \)\(14\!\cdots\!04\)\(q^{94} - \)\(45\!\cdots\!00\)\(q^{95} + \)\(18\!\cdots\!88\)\(q^{96} + \)\(83\!\cdots\!52\)\(q^{97} - \)\(20\!\cdots\!08\)\(q^{98} - \)\(24\!\cdots\!08\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 218549. 1.17903 0.589515 0.807758i \(-0.299319\pi\)
0.589515 + 0.807758i \(0.299319\pi\)
\(3\) 1.29140e8 0.577350
\(4\) 1.34041e10 0.390109
\(5\) −9.68425e11 −0.567664 −0.283832 0.958874i \(-0.591606\pi\)
−0.283832 + 0.958874i \(0.591606\pi\)
\(6\) 2.82235e13 0.680713
\(7\) −5.65365e14 −0.918572 −0.459286 0.888288i \(-0.651895\pi\)
−0.459286 + 0.888288i \(0.651895\pi\)
\(8\) −4.57985e15 −0.719079
\(9\) 1.66772e16 0.333333
\(10\) −2.11649e17 −0.669292
\(11\) −1.62372e18 −0.968588 −0.484294 0.874905i \(-0.660923\pi\)
−0.484294 + 0.874905i \(0.660923\pi\)
\(12\) 1.73100e18 0.225230
\(13\) −2.52538e19 −0.809688 −0.404844 0.914386i \(-0.632674\pi\)
−0.404844 + 0.914386i \(0.632674\pi\)
\(14\) −1.23560e20 −1.08302
\(15\) −1.25063e20 −0.327741
\(16\) −1.46148e21 −1.23792
\(17\) 4.37227e21 1.28189 0.640946 0.767586i \(-0.278542\pi\)
0.640946 + 0.767586i \(0.278542\pi\)
\(18\) 3.64479e21 0.393010
\(19\) 1.72036e22 0.720162 0.360081 0.932921i \(-0.382749\pi\)
0.360081 + 0.932921i \(0.382749\pi\)
\(20\) −1.29808e22 −0.221451
\(21\) −7.30113e22 −0.530338
\(22\) −3.54863e23 −1.14199
\(23\) −5.13356e23 −0.758895 −0.379447 0.925213i \(-0.623886\pi\)
−0.379447 + 0.925213i \(0.623886\pi\)
\(24\) −5.91442e23 −0.415160
\(25\) −1.97254e24 −0.677758
\(26\) −5.51920e24 −0.954646
\(27\) 2.15369e24 0.192450
\(28\) −7.57819e24 −0.358344
\(29\) −3.39397e25 −0.868447 −0.434224 0.900805i \(-0.642977\pi\)
−0.434224 + 0.900805i \(0.642977\pi\)
\(30\) −2.73323e25 −0.386416
\(31\) −9.89761e25 −0.788317 −0.394158 0.919043i \(-0.628964\pi\)
−0.394158 + 0.919043i \(0.628964\pi\)
\(32\) −1.62044e26 −0.740470
\(33\) −2.09687e26 −0.559215
\(34\) 9.55557e26 1.51139
\(35\) 5.47514e26 0.521440
\(36\) 2.23542e26 0.130036
\(37\) 4.58147e27 1.64996 0.824982 0.565160i \(-0.191185\pi\)
0.824982 + 0.565160i \(0.191185\pi\)
\(38\) 3.75982e27 0.849092
\(39\) −3.26128e27 −0.467474
\(40\) 4.43524e27 0.408195
\(41\) −2.87989e28 −1.72052 −0.860259 0.509858i \(-0.829698\pi\)
−0.860259 + 0.509858i \(0.829698\pi\)
\(42\) −1.59566e28 −0.625284
\(43\) 6.85354e28 1.77917 0.889583 0.456773i \(-0.150995\pi\)
0.889583 + 0.456773i \(0.150995\pi\)
\(44\) −2.17644e28 −0.377855
\(45\) −1.61506e28 −0.189221
\(46\) −1.12194e29 −0.894759
\(47\) −4.79363e26 −0.00262393 −0.00131197 0.999999i \(-0.500418\pi\)
−0.00131197 + 0.999999i \(0.500418\pi\)
\(48\) −1.88736e29 −0.714716
\(49\) −5.91811e28 −0.156225
\(50\) −4.31096e29 −0.799096
\(51\) 5.64636e29 0.740100
\(52\) −3.38503e29 −0.315867
\(53\) 2.32896e30 1.55717 0.778583 0.627541i \(-0.215939\pi\)
0.778583 + 0.627541i \(0.215939\pi\)
\(54\) 4.70688e29 0.226904
\(55\) 1.57245e30 0.549832
\(56\) 2.58929e30 0.660526
\(57\) 2.22167e30 0.415786
\(58\) −7.41751e30 −1.02392
\(59\) 5.75836e30 0.589371 0.294685 0.955594i \(-0.404785\pi\)
0.294685 + 0.955594i \(0.404785\pi\)
\(60\) −1.67635e30 −0.127855
\(61\) −2.67580e31 −1.52820 −0.764102 0.645095i \(-0.776818\pi\)
−0.764102 + 0.645095i \(0.776818\pi\)
\(62\) −2.16312e31 −0.929448
\(63\) −9.42870e30 −0.306191
\(64\) 1.48016e31 0.364889
\(65\) 2.44564e31 0.459630
\(66\) −4.58270e31 −0.659330
\(67\) 7.66448e31 0.847566 0.423783 0.905764i \(-0.360702\pi\)
0.423783 + 0.905764i \(0.360702\pi\)
\(68\) 5.86062e31 0.500078
\(69\) −6.62949e31 −0.438148
\(70\) 1.19659e32 0.614793
\(71\) −5.08152e31 −0.203691 −0.101846 0.994800i \(-0.532475\pi\)
−0.101846 + 0.994800i \(0.532475\pi\)
\(72\) −7.63790e31 −0.239693
\(73\) −2.74698e32 −0.677181 −0.338590 0.940934i \(-0.609950\pi\)
−0.338590 + 0.940934i \(0.609950\pi\)
\(74\) 1.00128e33 1.94535
\(75\) −2.54734e32 −0.391304
\(76\) 2.30597e32 0.280942
\(77\) 9.17994e32 0.889718
\(78\) −7.12750e32 −0.551165
\(79\) −2.13670e33 −1.32212 −0.661059 0.750334i \(-0.729893\pi\)
−0.661059 + 0.750334i \(0.729893\pi\)
\(80\) 1.41534e33 0.702724
\(81\) 2.78128e32 0.111111
\(82\) −6.29399e33 −2.02854
\(83\) −2.22116e33 −0.579046 −0.289523 0.957171i \(-0.593497\pi\)
−0.289523 + 0.957171i \(0.593497\pi\)
\(84\) −9.78648e32 −0.206890
\(85\) −4.23422e33 −0.727683
\(86\) 1.49784e34 2.09769
\(87\) −4.38298e33 −0.501398
\(88\) 7.43639e33 0.696491
\(89\) 2.07592e34 1.59545 0.797727 0.603018i \(-0.206035\pi\)
0.797727 + 0.603018i \(0.206035\pi\)
\(90\) −3.52970e33 −0.223097
\(91\) 1.42776e34 0.743757
\(92\) −6.88105e33 −0.296052
\(93\) −1.27818e34 −0.455135
\(94\) −1.04765e32 −0.00309369
\(95\) −1.66604e34 −0.408810
\(96\) −2.09263e34 −0.427510
\(97\) 1.55170e34 0.264426 0.132213 0.991221i \(-0.457792\pi\)
0.132213 + 0.991221i \(0.457792\pi\)
\(98\) −1.29340e34 −0.184194
\(99\) −2.70791e34 −0.322863
\(100\) −2.64400e34 −0.264400
\(101\) −1.03897e35 −0.872929 −0.436464 0.899722i \(-0.643770\pi\)
−0.436464 + 0.899722i \(0.643770\pi\)
\(102\) 1.23401e35 0.872600
\(103\) −1.94833e35 −1.16148 −0.580740 0.814089i \(-0.697237\pi\)
−0.580740 + 0.814089i \(0.697237\pi\)
\(104\) 1.15659e35 0.582229
\(105\) 7.07060e34 0.301053
\(106\) 5.08993e35 1.83594
\(107\) −3.61557e35 −1.10652 −0.553262 0.833007i \(-0.686617\pi\)
−0.553262 + 0.833007i \(0.686617\pi\)
\(108\) 2.88682e34 0.0750766
\(109\) −7.33560e35 −1.62357 −0.811786 0.583954i \(-0.801505\pi\)
−0.811786 + 0.583954i \(0.801505\pi\)
\(110\) 3.43658e35 0.648268
\(111\) 5.91651e35 0.952607
\(112\) 8.26271e35 1.13712
\(113\) −5.95677e35 −0.701678 −0.350839 0.936436i \(-0.614104\pi\)
−0.350839 + 0.936436i \(0.614104\pi\)
\(114\) 4.85544e35 0.490223
\(115\) 4.97147e35 0.430797
\(116\) −4.54930e35 −0.338790
\(117\) −4.21162e35 −0.269896
\(118\) 1.25849e36 0.694885
\(119\) −2.47193e36 −1.17751
\(120\) 5.72768e35 0.235671
\(121\) −1.73778e35 −0.0618372
\(122\) −5.84794e36 −1.80180
\(123\) −3.71910e36 −0.993341
\(124\) −1.32668e36 −0.307530
\(125\) 4.72874e36 0.952402
\(126\) −2.06063e36 −0.361008
\(127\) 1.88168e36 0.287065 0.143533 0.989646i \(-0.454154\pi\)
0.143533 + 0.989646i \(0.454154\pi\)
\(128\) 8.80267e36 1.17068
\(129\) 8.85067e36 1.02720
\(130\) 5.34493e36 0.541918
\(131\) 6.22324e36 0.551784 0.275892 0.961189i \(-0.411027\pi\)
0.275892 + 0.961189i \(0.411027\pi\)
\(132\) −2.81066e36 −0.218155
\(133\) −9.72629e36 −0.661521
\(134\) 1.67507e37 0.999305
\(135\) −2.08569e36 −0.109247
\(136\) −2.00244e37 −0.921781
\(137\) 6.91179e36 0.279886 0.139943 0.990160i \(-0.455308\pi\)
0.139943 + 0.990160i \(0.455308\pi\)
\(138\) −1.44887e37 −0.516589
\(139\) −4.10165e37 −1.28884 −0.644421 0.764671i \(-0.722901\pi\)
−0.644421 + 0.764671i \(0.722901\pi\)
\(140\) 7.33891e36 0.203419
\(141\) −6.19051e34 −0.00151493
\(142\) −1.11056e37 −0.240158
\(143\) 4.10051e37 0.784254
\(144\) −2.43734e37 −0.412641
\(145\) 3.28681e37 0.492986
\(146\) −6.00350e37 −0.798416
\(147\) −7.64266e36 −0.0901968
\(148\) 6.14102e37 0.643666
\(149\) 3.38483e37 0.315339 0.157670 0.987492i \(-0.449602\pi\)
0.157670 + 0.987492i \(0.449602\pi\)
\(150\) −5.56718e37 −0.461359
\(151\) −4.14774e37 −0.305995 −0.152998 0.988227i \(-0.548893\pi\)
−0.152998 + 0.988227i \(0.548893\pi\)
\(152\) −7.87897e37 −0.517853
\(153\) 7.29172e37 0.427297
\(154\) 2.00627e38 1.04900
\(155\) 9.58510e37 0.447499
\(156\) −4.37144e37 −0.182366
\(157\) 2.79097e38 1.04115 0.520573 0.853817i \(-0.325718\pi\)
0.520573 + 0.853817i \(0.325718\pi\)
\(158\) −4.66975e38 −1.55881
\(159\) 3.00763e38 0.899031
\(160\) 1.56927e38 0.420338
\(161\) 2.90234e38 0.697099
\(162\) 6.07848e37 0.131003
\(163\) −9.06631e38 −1.75448 −0.877238 0.480056i \(-0.840616\pi\)
−0.877238 + 0.480056i \(0.840616\pi\)
\(164\) −3.86023e38 −0.671190
\(165\) 2.03067e38 0.317446
\(166\) −4.85433e38 −0.682712
\(167\) −2.20471e38 −0.279134 −0.139567 0.990213i \(-0.544571\pi\)
−0.139567 + 0.990213i \(0.544571\pi\)
\(168\) 3.34381e38 0.381355
\(169\) −3.35033e38 −0.344405
\(170\) −9.25386e38 −0.857959
\(171\) 2.86907e38 0.240054
\(172\) 9.18652e38 0.694070
\(173\) −1.20919e39 −0.825442 −0.412721 0.910858i \(-0.635421\pi\)
−0.412721 + 0.910858i \(0.635421\pi\)
\(174\) −9.57898e38 −0.591163
\(175\) 1.11520e39 0.622570
\(176\) 2.37304e39 1.19904
\(177\) 7.43635e38 0.340273
\(178\) 4.53690e39 1.88109
\(179\) 2.04025e39 0.766930 0.383465 0.923555i \(-0.374731\pi\)
0.383465 + 0.923555i \(0.374731\pi\)
\(180\) −2.16484e38 −0.0738170
\(181\) −4.15321e39 −1.28531 −0.642656 0.766155i \(-0.722168\pi\)
−0.642656 + 0.766155i \(0.722168\pi\)
\(182\) 3.12036e39 0.876911
\(183\) −3.45553e39 −0.882309
\(184\) 2.35109e39 0.545705
\(185\) −4.43681e39 −0.936624
\(186\) −2.79345e39 −0.536617
\(187\) −7.09935e39 −1.24162
\(188\) −6.42542e36 −0.00102362
\(189\) −1.21762e39 −0.176779
\(190\) −3.64111e39 −0.481998
\(191\) 6.52044e39 0.787396 0.393698 0.919240i \(-0.371196\pi\)
0.393698 + 0.919240i \(0.371196\pi\)
\(192\) 1.91149e39 0.210669
\(193\) −1.97397e39 −0.198649 −0.0993246 0.995055i \(-0.531668\pi\)
−0.0993246 + 0.995055i \(0.531668\pi\)
\(194\) 3.39124e39 0.311765
\(195\) 3.15830e39 0.265368
\(196\) −7.93267e38 −0.0609450
\(197\) 6.10473e39 0.429050 0.214525 0.976719i \(-0.431180\pi\)
0.214525 + 0.976719i \(0.431180\pi\)
\(198\) −5.91811e39 −0.380664
\(199\) −8.83517e39 −0.520338 −0.260169 0.965563i \(-0.583778\pi\)
−0.260169 + 0.965563i \(0.583778\pi\)
\(200\) 9.03392e39 0.487361
\(201\) 9.89792e39 0.489343
\(202\) −2.27066e40 −1.02921
\(203\) 1.91883e40 0.797732
\(204\) 7.56842e39 0.288720
\(205\) 2.78896e40 0.976675
\(206\) −4.25807e40 −1.36942
\(207\) −8.56133e39 −0.252965
\(208\) 3.69080e40 1.00233
\(209\) −2.79337e40 −0.697540
\(210\) 1.54527e40 0.354951
\(211\) 7.88511e40 1.66673 0.833364 0.552724i \(-0.186412\pi\)
0.833364 + 0.552724i \(0.186412\pi\)
\(212\) 3.12176e40 0.607465
\(213\) −6.56228e39 −0.117601
\(214\) −7.90181e40 −1.30462
\(215\) −6.63714e40 −1.00997
\(216\) −9.86359e39 −0.138387
\(217\) 5.59576e40 0.724126
\(218\) −1.60319e41 −1.91424
\(219\) −3.54745e40 −0.390971
\(220\) 2.10772e40 0.214495
\(221\) −1.10416e41 −1.03793
\(222\) 1.29305e41 1.12315
\(223\) −2.84802e40 −0.228670 −0.114335 0.993442i \(-0.536474\pi\)
−0.114335 + 0.993442i \(0.536474\pi\)
\(224\) 9.16138e40 0.680175
\(225\) −3.28963e40 −0.225919
\(226\) −1.30185e41 −0.827299
\(227\) 2.11879e41 1.24634 0.623168 0.782088i \(-0.285845\pi\)
0.623168 + 0.782088i \(0.285845\pi\)
\(228\) 2.97794e40 0.162202
\(229\) 2.44651e40 0.123432 0.0617159 0.998094i \(-0.480343\pi\)
0.0617159 + 0.998094i \(0.480343\pi\)
\(230\) 1.08651e41 0.507922
\(231\) 1.18550e41 0.513679
\(232\) 1.55439e41 0.624482
\(233\) 3.49375e41 1.30186 0.650929 0.759139i \(-0.274380\pi\)
0.650929 + 0.759139i \(0.274380\pi\)
\(234\) −9.20446e40 −0.318215
\(235\) 4.64228e38 0.00148951
\(236\) 7.71854e40 0.229919
\(237\) −2.75934e41 −0.763325
\(238\) −5.40239e41 −1.38832
\(239\) −3.32939e41 −0.795063 −0.397531 0.917589i \(-0.630133\pi\)
−0.397531 + 0.917589i \(0.630133\pi\)
\(240\) 1.82777e41 0.405718
\(241\) 6.93771e40 0.143192 0.0715959 0.997434i \(-0.477191\pi\)
0.0715959 + 0.997434i \(0.477191\pi\)
\(242\) −3.79790e40 −0.0729078
\(243\) 3.59175e40 0.0641500
\(244\) −3.58666e41 −0.596167
\(245\) 5.73125e40 0.0886835
\(246\) −8.12807e41 −1.17118
\(247\) −4.34455e41 −0.583106
\(248\) 4.53296e41 0.566862
\(249\) −2.86841e41 −0.334313
\(250\) 1.03346e42 1.12291
\(251\) 3.37146e40 0.0341608 0.0170804 0.999854i \(-0.494563\pi\)
0.0170804 + 0.999854i \(0.494563\pi\)
\(252\) −1.26383e41 −0.119448
\(253\) 8.33546e41 0.735056
\(254\) 4.11240e41 0.338458
\(255\) −5.46808e41 −0.420128
\(256\) 1.41524e42 1.01538
\(257\) −2.45764e41 −0.164698 −0.0823489 0.996604i \(-0.526242\pi\)
−0.0823489 + 0.996604i \(0.526242\pi\)
\(258\) 1.93431e42 1.21110
\(259\) −2.59020e42 −1.51561
\(260\) 3.27815e41 0.179306
\(261\) −5.66019e41 −0.289482
\(262\) 1.36009e42 0.650569
\(263\) −1.00792e42 −0.451026 −0.225513 0.974240i \(-0.572406\pi\)
−0.225513 + 0.974240i \(0.572406\pi\)
\(264\) 9.60337e41 0.402119
\(265\) −2.25543e42 −0.883947
\(266\) −2.12567e42 −0.779952
\(267\) 2.68084e42 0.921136
\(268\) 1.02735e42 0.330644
\(269\) 3.53460e42 1.06580 0.532900 0.846178i \(-0.321102\pi\)
0.532900 + 0.846178i \(0.321102\pi\)
\(270\) −4.55826e41 −0.128805
\(271\) 2.05300e40 0.00543785 0.00271893 0.999996i \(-0.499135\pi\)
0.00271893 + 0.999996i \(0.499135\pi\)
\(272\) −6.39000e42 −1.58688
\(273\) 1.84381e42 0.429408
\(274\) 1.51057e42 0.329993
\(275\) 3.20285e42 0.656468
\(276\) −8.88620e41 −0.170926
\(277\) −3.99065e42 −0.720522 −0.360261 0.932851i \(-0.617312\pi\)
−0.360261 + 0.932851i \(0.617312\pi\)
\(278\) −8.96412e42 −1.51958
\(279\) −1.65064e42 −0.262772
\(280\) −2.50753e42 −0.374956
\(281\) −6.62219e42 −0.930338 −0.465169 0.885222i \(-0.654006\pi\)
−0.465169 + 0.885222i \(0.654006\pi\)
\(282\) −1.35293e40 −0.00178614
\(283\) 9.02584e42 1.12002 0.560009 0.828487i \(-0.310798\pi\)
0.560009 + 0.828487i \(0.310798\pi\)
\(284\) −6.81130e41 −0.0794619
\(285\) −2.15152e42 −0.236026
\(286\) 8.96163e42 0.924658
\(287\) 1.62819e43 1.58042
\(288\) −2.70243e42 −0.246823
\(289\) 7.48323e42 0.643246
\(290\) 7.18330e42 0.581245
\(291\) 2.00387e42 0.152666
\(292\) −3.68206e42 −0.264175
\(293\) 1.83072e43 1.23719 0.618597 0.785708i \(-0.287701\pi\)
0.618597 + 0.785708i \(0.287701\pi\)
\(294\) −1.67030e42 −0.106345
\(295\) −5.57654e42 −0.334564
\(296\) −2.09824e43 −1.18645
\(297\) −3.49700e42 −0.186405
\(298\) 7.39753e42 0.371794
\(299\) 1.29642e43 0.614468
\(300\) −3.41446e42 −0.152651
\(301\) −3.87475e43 −1.63429
\(302\) −9.06486e42 −0.360778
\(303\) −1.34173e43 −0.503986
\(304\) −2.51427e43 −0.891506
\(305\) 2.59131e43 0.867506
\(306\) 1.59360e43 0.503796
\(307\) −5.94182e43 −1.77418 −0.887091 0.461595i \(-0.847277\pi\)
−0.887091 + 0.461595i \(0.847277\pi\)
\(308\) 1.23049e43 0.347087
\(309\) −2.51608e43 −0.670580
\(310\) 2.09482e43 0.527614
\(311\) 9.43273e42 0.224559 0.112280 0.993677i \(-0.464185\pi\)
0.112280 + 0.993677i \(0.464185\pi\)
\(312\) 1.49362e43 0.336150
\(313\) 5.95209e43 1.26661 0.633306 0.773902i \(-0.281697\pi\)
0.633306 + 0.773902i \(0.281697\pi\)
\(314\) 6.09965e43 1.22754
\(315\) 9.13099e42 0.173813
\(316\) −2.86405e43 −0.515770
\(317\) −1.09193e44 −1.86062 −0.930311 0.366772i \(-0.880463\pi\)
−0.930311 + 0.366772i \(0.880463\pi\)
\(318\) 6.57315e43 1.05998
\(319\) 5.51086e43 0.841168
\(320\) −1.43343e43 −0.207134
\(321\) −4.66916e43 −0.638852
\(322\) 6.34303e43 0.821901
\(323\) 7.52186e43 0.923169
\(324\) 3.72805e42 0.0433455
\(325\) 4.98140e43 0.548773
\(326\) −1.98144e44 −2.06858
\(327\) −9.47320e43 −0.937370
\(328\) 1.31895e44 1.23719
\(329\) 2.71015e41 0.00241027
\(330\) 4.43801e43 0.374278
\(331\) −6.64486e43 −0.531491 −0.265746 0.964043i \(-0.585618\pi\)
−0.265746 + 0.964043i \(0.585618\pi\)
\(332\) −2.97726e43 −0.225891
\(333\) 7.64059e43 0.549988
\(334\) −4.81837e43 −0.329107
\(335\) −7.42248e43 −0.481132
\(336\) 1.06705e44 0.656518
\(337\) −1.32087e44 −0.771504 −0.385752 0.922602i \(-0.626058\pi\)
−0.385752 + 0.922602i \(0.626058\pi\)
\(338\) −7.32211e43 −0.406064
\(339\) −7.69258e43 −0.405114
\(340\) −5.67557e43 −0.283876
\(341\) 1.60709e44 0.763554
\(342\) 6.27033e43 0.283031
\(343\) 2.47630e44 1.06208
\(344\) −3.13882e44 −1.27936
\(345\) 6.42016e43 0.248721
\(346\) −2.64267e44 −0.973220
\(347\) 1.51937e44 0.531983 0.265991 0.963975i \(-0.414301\pi\)
0.265991 + 0.963975i \(0.414301\pi\)
\(348\) −5.87498e43 −0.195600
\(349\) −4.35219e44 −1.37804 −0.689022 0.724741i \(-0.741960\pi\)
−0.689022 + 0.724741i \(0.741960\pi\)
\(350\) 2.43727e44 0.734028
\(351\) −5.43889e43 −0.155825
\(352\) 2.63113e44 0.717210
\(353\) 3.37356e44 0.875045 0.437523 0.899207i \(-0.355856\pi\)
0.437523 + 0.899207i \(0.355856\pi\)
\(354\) 1.62521e44 0.401192
\(355\) 4.92107e43 0.115628
\(356\) 2.78257e44 0.622402
\(357\) −3.19226e44 −0.679836
\(358\) 4.45896e44 0.904233
\(359\) 8.65151e44 1.67086 0.835428 0.549600i \(-0.185220\pi\)
0.835428 + 0.549600i \(0.185220\pi\)
\(360\) 7.39673e43 0.136065
\(361\) −2.74696e44 −0.481367
\(362\) −9.07681e44 −1.51542
\(363\) −2.24417e43 −0.0357017
\(364\) 1.91378e44 0.290147
\(365\) 2.66024e44 0.384411
\(366\) −7.55204e44 −1.04027
\(367\) 2.11463e44 0.277701 0.138851 0.990313i \(-0.455659\pi\)
0.138851 + 0.990313i \(0.455659\pi\)
\(368\) 7.50261e44 0.939454
\(369\) −4.80285e44 −0.573506
\(370\) −9.69661e44 −1.10431
\(371\) −1.31671e45 −1.43037
\(372\) −1.71328e44 −0.177552
\(373\) −8.06525e44 −0.797468 −0.398734 0.917067i \(-0.630550\pi\)
−0.398734 + 0.917067i \(0.630550\pi\)
\(374\) −1.55156e45 −1.46391
\(375\) 6.10670e44 0.549870
\(376\) 2.19541e42 0.00188681
\(377\) 8.57107e44 0.703172
\(378\) −2.66111e44 −0.208428
\(379\) 1.62962e45 1.21871 0.609356 0.792897i \(-0.291428\pi\)
0.609356 + 0.792897i \(0.291428\pi\)
\(380\) −2.23316e44 −0.159480
\(381\) 2.43000e44 0.165737
\(382\) 1.42504e45 0.928362
\(383\) 3.08699e45 1.92113 0.960565 0.278055i \(-0.0896896\pi\)
0.960565 + 0.278055i \(0.0896896\pi\)
\(384\) 1.13678e45 0.675895
\(385\) −8.89009e44 −0.505060
\(386\) −4.31409e44 −0.234213
\(387\) 1.14298e45 0.593056
\(388\) 2.07991e44 0.103155
\(389\) −2.76724e45 −1.31199 −0.655993 0.754767i \(-0.727750\pi\)
−0.655993 + 0.754767i \(0.727750\pi\)
\(390\) 6.90245e44 0.312876
\(391\) −2.24453e45 −0.972821
\(392\) 2.71040e44 0.112338
\(393\) 8.03671e44 0.318573
\(394\) 1.33418e45 0.505862
\(395\) 2.06924e45 0.750518
\(396\) −3.62969e44 −0.125952
\(397\) −3.58547e45 −1.19045 −0.595226 0.803558i \(-0.702938\pi\)
−0.595226 + 0.803558i \(0.702938\pi\)
\(398\) −1.93092e45 −0.613494
\(399\) −1.25605e45 −0.381929
\(400\) 2.88283e45 0.839013
\(401\) −4.26941e45 −1.18944 −0.594718 0.803934i \(-0.702736\pi\)
−0.594718 + 0.803934i \(0.702736\pi\)
\(402\) 2.16318e45 0.576949
\(403\) 2.49952e45 0.638291
\(404\) −1.39264e45 −0.340538
\(405\) −2.69347e44 −0.0630737
\(406\) 4.19360e45 0.940549
\(407\) −7.43902e45 −1.59813
\(408\) −2.58595e45 −0.532190
\(409\) −8.56530e43 −0.0168883 −0.00844413 0.999964i \(-0.502688\pi\)
−0.00844413 + 0.999964i \(0.502688\pi\)
\(410\) 6.09526e45 1.15153
\(411\) 8.92590e44 0.161592
\(412\) −2.61156e45 −0.453104
\(413\) −3.25557e45 −0.541379
\(414\) −1.87107e45 −0.298253
\(415\) 2.15103e45 0.328704
\(416\) 4.09221e45 0.599550
\(417\) −5.29688e45 −0.744113
\(418\) −6.10490e45 −0.822420
\(419\) 5.67787e45 0.733567 0.366783 0.930306i \(-0.380459\pi\)
0.366783 + 0.930306i \(0.380459\pi\)
\(420\) 9.47748e44 0.117444
\(421\) 4.40748e45 0.523907 0.261953 0.965081i \(-0.415633\pi\)
0.261953 + 0.965081i \(0.415633\pi\)
\(422\) 1.72329e46 1.96512
\(423\) −7.99443e42 −0.000874644 0
\(424\) −1.06663e46 −1.11973
\(425\) −8.62447e45 −0.868812
\(426\) −1.43418e45 −0.138655
\(427\) 1.51280e46 1.40377
\(428\) −4.84633e45 −0.431666
\(429\) 5.29540e45 0.452789
\(430\) −1.45054e46 −1.19078
\(431\) 2.36863e46 1.86700 0.933500 0.358578i \(-0.116738\pi\)
0.933500 + 0.358578i \(0.116738\pi\)
\(432\) −3.14759e45 −0.238239
\(433\) 6.19663e45 0.450420 0.225210 0.974310i \(-0.427693\pi\)
0.225210 + 0.974310i \(0.427693\pi\)
\(434\) 1.22295e46 0.853765
\(435\) 4.24459e45 0.284626
\(436\) −9.83268e45 −0.633371
\(437\) −8.83155e45 −0.546527
\(438\) −7.75292e45 −0.460966
\(439\) −4.03275e45 −0.230394 −0.115197 0.993343i \(-0.536750\pi\)
−0.115197 + 0.993343i \(0.536750\pi\)
\(440\) −7.20159e45 −0.395373
\(441\) −9.86974e44 −0.0520751
\(442\) −2.41314e46 −1.22375
\(443\) 9.72231e44 0.0473919 0.0236959 0.999719i \(-0.492457\pi\)
0.0236959 + 0.999719i \(0.492457\pi\)
\(444\) 7.93053e45 0.371621
\(445\) −2.01037e46 −0.905681
\(446\) −6.22433e45 −0.269608
\(447\) 4.37118e45 0.182061
\(448\) −8.36833e45 −0.335177
\(449\) −3.45806e46 −1.33205 −0.666027 0.745928i \(-0.732006\pi\)
−0.666027 + 0.745928i \(0.732006\pi\)
\(450\) −7.18947e45 −0.266365
\(451\) 4.67614e46 1.66647
\(452\) −7.98448e45 −0.273731
\(453\) −5.35640e45 −0.176667
\(454\) 4.63060e46 1.46947
\(455\) −1.38268e46 −0.422204
\(456\) −1.01749e46 −0.298983
\(457\) 3.54182e46 1.00160 0.500799 0.865564i \(-0.333040\pi\)
0.500799 + 0.865564i \(0.333040\pi\)
\(458\) 5.34684e45 0.145530
\(459\) 9.41654e45 0.246700
\(460\) 6.66379e45 0.168058
\(461\) 7.06935e45 0.171638 0.0858189 0.996311i \(-0.472649\pi\)
0.0858189 + 0.996311i \(0.472649\pi\)
\(462\) 2.59090e46 0.605642
\(463\) −6.22902e44 −0.0140201 −0.00701007 0.999975i \(-0.502231\pi\)
−0.00701007 + 0.999975i \(0.502231\pi\)
\(464\) 4.96023e46 1.07507
\(465\) 1.23782e46 0.258363
\(466\) 7.63557e46 1.53493
\(467\) −6.28266e46 −1.21646 −0.608231 0.793760i \(-0.708120\pi\)
−0.608231 + 0.793760i \(0.708120\pi\)
\(468\) −5.64528e45 −0.105289
\(469\) −4.33323e46 −0.778551
\(470\) 1.01457e44 0.00175618
\(471\) 3.60427e46 0.601106
\(472\) −2.63724e46 −0.423804
\(473\) −1.11282e47 −1.72328
\(474\) −6.03052e46 −0.899982
\(475\) −3.39346e46 −0.488095
\(476\) −3.31339e46 −0.459358
\(477\) 3.88406e46 0.519056
\(478\) −7.27636e46 −0.937402
\(479\) 1.10146e47 1.36804 0.684020 0.729463i \(-0.260230\pi\)
0.684020 + 0.729463i \(0.260230\pi\)
\(480\) 2.02656e46 0.242682
\(481\) −1.15699e47 −1.33596
\(482\) 1.51623e46 0.168827
\(483\) 3.74808e46 0.402471
\(484\) −2.32932e45 −0.0241233
\(485\) −1.50271e46 −0.150105
\(486\) 7.84975e45 0.0756347
\(487\) 8.13246e46 0.755901 0.377951 0.925826i \(-0.376629\pi\)
0.377951 + 0.925826i \(0.376629\pi\)
\(488\) 1.22548e47 1.09890
\(489\) −1.17082e47 −1.01295
\(490\) 1.25256e46 0.104560
\(491\) 1.83224e47 1.47590 0.737950 0.674855i \(-0.235794\pi\)
0.737950 + 0.674855i \(0.235794\pi\)
\(492\) −4.98510e46 −0.387512
\(493\) −1.48394e47 −1.11326
\(494\) −9.49498e46 −0.687499
\(495\) 2.62241e46 0.183277
\(496\) 1.44652e47 0.975876
\(497\) 2.87291e46 0.187105
\(498\) −6.26889e46 −0.394164
\(499\) 9.12339e45 0.0553856 0.0276928 0.999616i \(-0.491184\pi\)
0.0276928 + 0.999616i \(0.491184\pi\)
\(500\) 6.33843e46 0.371541
\(501\) −2.84716e46 −0.161158
\(502\) 7.36830e45 0.0402766
\(503\) −1.87342e47 −0.989001 −0.494500 0.869177i \(-0.664649\pi\)
−0.494500 + 0.869177i \(0.664649\pi\)
\(504\) 4.31820e46 0.220175
\(505\) 1.00616e47 0.495530
\(506\) 1.82171e47 0.866653
\(507\) −4.32662e46 −0.198842
\(508\) 2.52221e46 0.111987
\(509\) 1.22247e47 0.524418 0.262209 0.965011i \(-0.415549\pi\)
0.262209 + 0.965011i \(0.415549\pi\)
\(510\) −1.19504e47 −0.495343
\(511\) 1.55304e47 0.622039
\(512\) 6.84151e45 0.0264806
\(513\) 3.70512e46 0.138595
\(514\) −5.37115e46 −0.194184
\(515\) 1.88681e47 0.659329
\(516\) 1.18635e47 0.400721
\(517\) 7.78352e44 0.00254151
\(518\) −5.66086e47 −1.78695
\(519\) −1.56154e47 −0.476569
\(520\) −1.12007e47 −0.330510
\(521\) −6.28279e46 −0.179264 −0.0896318 0.995975i \(-0.528569\pi\)
−0.0896318 + 0.995975i \(0.528569\pi\)
\(522\) −1.23703e47 −0.341308
\(523\) −2.46925e47 −0.658849 −0.329425 0.944182i \(-0.606855\pi\)
−0.329425 + 0.944182i \(0.606855\pi\)
\(524\) 8.34167e46 0.215256
\(525\) 1.44017e47 0.359441
\(526\) −2.20281e47 −0.531773
\(527\) −4.32751e47 −1.01054
\(528\) 3.06455e47 0.692265
\(529\) −1.94053e47 −0.424079
\(530\) −4.92922e47 −1.04220
\(531\) 9.60332e46 0.196457
\(532\) −1.30372e47 −0.258065
\(533\) 7.27282e47 1.39308
\(534\) 5.85896e47 1.08605
\(535\) 3.50141e47 0.628133
\(536\) −3.51022e47 −0.609467
\(537\) 2.63478e47 0.442787
\(538\) 7.72485e47 1.25661
\(539\) 9.60935e46 0.151318
\(540\) −2.79567e46 −0.0426182
\(541\) 1.20408e47 0.177706 0.0888529 0.996045i \(-0.471680\pi\)
0.0888529 + 0.996045i \(0.471680\pi\)
\(542\) 4.48683e45 0.00641139
\(543\) −5.36346e47 −0.742075
\(544\) −7.08499e47 −0.949202
\(545\) 7.10398e47 0.921643
\(546\) 4.02964e47 0.506285
\(547\) 8.44104e47 1.02711 0.513556 0.858056i \(-0.328328\pi\)
0.513556 + 0.858056i \(0.328328\pi\)
\(548\) 9.26461e46 0.109186
\(549\) −4.46248e47 −0.509402
\(550\) 6.99980e47 0.773995
\(551\) −5.83884e47 −0.625423
\(552\) 3.03621e47 0.315063
\(553\) 1.20802e48 1.21446
\(554\) −8.72153e47 −0.849517
\(555\) −5.72970e47 −0.540760
\(556\) −5.49787e47 −0.502789
\(557\) −1.28303e48 −1.13703 −0.568514 0.822674i \(-0.692481\pi\)
−0.568514 + 0.822674i \(0.692481\pi\)
\(558\) −3.60747e47 −0.309816
\(559\) −1.73078e48 −1.44057
\(560\) −8.00182e47 −0.645503
\(561\) −9.16811e47 −0.716852
\(562\) −1.44727e48 −1.09690
\(563\) 2.05838e48 1.51227 0.756133 0.654418i \(-0.227086\pi\)
0.756133 + 0.654418i \(0.227086\pi\)
\(564\) −8.29779e44 −0.000590987 0
\(565\) 5.76868e47 0.398317
\(566\) 1.97259e48 1.32053
\(567\) −1.57244e47 −0.102064
\(568\) 2.32726e47 0.146470
\(569\) −4.38677e47 −0.267720 −0.133860 0.991000i \(-0.542737\pi\)
−0.133860 + 0.991000i \(0.542737\pi\)
\(570\) −4.70213e47 −0.278282
\(571\) −2.36363e48 −1.35658 −0.678292 0.734792i \(-0.737280\pi\)
−0.678292 + 0.734792i \(0.737280\pi\)
\(572\) 5.49634e47 0.305945
\(573\) 8.42051e47 0.454603
\(574\) 3.55840e48 1.86336
\(575\) 1.01261e48 0.514347
\(576\) 2.46850e47 0.121630
\(577\) −1.45741e48 −0.696632 −0.348316 0.937377i \(-0.613246\pi\)
−0.348316 + 0.937377i \(0.613246\pi\)
\(578\) 1.63546e48 0.758406
\(579\) −2.54918e47 −0.114690
\(580\) 4.40566e47 0.192318
\(581\) 1.25577e48 0.531896
\(582\) 4.37945e47 0.179998
\(583\) −3.78159e48 −1.50825
\(584\) 1.25807e48 0.486946
\(585\) 4.07864e47 0.153210
\(586\) 4.00102e48 1.45869
\(587\) −2.31218e48 −0.818190 −0.409095 0.912492i \(-0.634156\pi\)
−0.409095 + 0.912492i \(0.634156\pi\)
\(588\) −1.02443e47 −0.0351866
\(589\) −1.70274e48 −0.567716
\(590\) −1.21875e48 −0.394461
\(591\) 7.88366e47 0.247712
\(592\) −6.69573e48 −2.04253
\(593\) 4.31701e48 1.27857 0.639287 0.768968i \(-0.279230\pi\)
0.639287 + 0.768968i \(0.279230\pi\)
\(594\) −7.64266e47 −0.219777
\(595\) 2.39388e48 0.668429
\(596\) 4.53705e47 0.123017
\(597\) −1.14097e48 −0.300418
\(598\) 2.83331e48 0.724476
\(599\) −2.66626e48 −0.662114 −0.331057 0.943611i \(-0.607405\pi\)
−0.331057 + 0.943611i \(0.607405\pi\)
\(600\) 1.16664e48 0.281378
\(601\) 7.51112e48 1.75955 0.879775 0.475391i \(-0.157693\pi\)
0.879775 + 0.475391i \(0.157693\pi\)
\(602\) −8.46824e48 −1.92688
\(603\) 1.27822e48 0.282522
\(604\) −5.55966e47 −0.119372
\(605\) 1.68291e47 0.0351027
\(606\) −2.93234e48 −0.594214
\(607\) −4.81557e48 −0.948081 −0.474040 0.880503i \(-0.657205\pi\)
−0.474040 + 0.880503i \(0.657205\pi\)
\(608\) −2.78773e48 −0.533258
\(609\) 2.47799e48 0.460571
\(610\) 5.66329e48 1.02281
\(611\) 1.21057e46 0.00212457
\(612\) 9.77387e47 0.166693
\(613\) 1.36361e48 0.226012 0.113006 0.993594i \(-0.463952\pi\)
0.113006 + 0.993594i \(0.463952\pi\)
\(614\) −1.29858e49 −2.09181
\(615\) 3.60167e48 0.563884
\(616\) −4.20428e48 −0.639777
\(617\) 1.76559e48 0.261156 0.130578 0.991438i \(-0.458317\pi\)
0.130578 + 0.991438i \(0.458317\pi\)
\(618\) −5.49887e48 −0.790634
\(619\) 7.44879e48 1.04112 0.520559 0.853826i \(-0.325724\pi\)
0.520559 + 0.853826i \(0.325724\pi\)
\(620\) 1.28479e48 0.174573
\(621\) −1.10561e48 −0.146049
\(622\) 2.06152e48 0.264762
\(623\) −1.17365e49 −1.46554
\(624\) 4.76630e48 0.578697
\(625\) 1.16140e48 0.137114
\(626\) 1.30083e49 1.49337
\(627\) −3.60737e48 −0.402725
\(628\) 3.74104e48 0.406161
\(629\) 2.00314e49 2.11507
\(630\) 1.99557e48 0.204931
\(631\) 4.61699e48 0.461153 0.230576 0.973054i \(-0.425939\pi\)
0.230576 + 0.973054i \(0.425939\pi\)
\(632\) 9.78578e48 0.950706
\(633\) 1.01828e49 0.962286
\(634\) −2.38641e49 −2.19373
\(635\) −1.82227e48 −0.162956
\(636\) 4.03144e48 0.350720
\(637\) 1.49455e48 0.126494
\(638\) 1.20440e49 0.991761
\(639\) −8.47454e47 −0.0678971
\(640\) −8.52472e48 −0.664555
\(641\) −2.29073e49 −1.73763 −0.868816 0.495134i \(-0.835119\pi\)
−0.868816 + 0.495134i \(0.835119\pi\)
\(642\) −1.02044e49 −0.753225
\(643\) −1.75961e49 −1.26394 −0.631969 0.774994i \(-0.717753\pi\)
−0.631969 + 0.774994i \(0.717753\pi\)
\(644\) 3.89031e48 0.271945
\(645\) −8.57121e48 −0.583105
\(646\) 1.64390e49 1.08844
\(647\) −1.34530e49 −0.866950 −0.433475 0.901166i \(-0.642713\pi\)
−0.433475 + 0.901166i \(0.642713\pi\)
\(648\) −1.27379e48 −0.0798976
\(649\) −9.34996e48 −0.570857
\(650\) 1.08868e49 0.647019
\(651\) 7.22638e48 0.418074
\(652\) −1.21525e49 −0.684438
\(653\) −1.55134e49 −0.850601 −0.425300 0.905052i \(-0.639832\pi\)
−0.425300 + 0.905052i \(0.639832\pi\)
\(654\) −2.07036e49 −1.10519
\(655\) −6.02675e48 −0.313228
\(656\) 4.20892e49 2.12987
\(657\) −4.58118e48 −0.225727
\(658\) 5.92302e46 0.00284178
\(659\) −1.67026e46 −0.000780348 0 −0.000390174 1.00000i \(-0.500124\pi\)
−0.000390174 1.00000i \(0.500124\pi\)
\(660\) 2.72192e48 0.123839
\(661\) 3.86727e49 1.71348 0.856740 0.515748i \(-0.172486\pi\)
0.856740 + 0.515748i \(0.172486\pi\)
\(662\) −1.45223e49 −0.626644
\(663\) −1.42592e49 −0.599250
\(664\) 1.01726e49 0.416380
\(665\) 9.41918e48 0.375521
\(666\) 1.66985e49 0.648451
\(667\) 1.74232e49 0.659060
\(668\) −2.95520e48 −0.108893
\(669\) −3.67794e48 −0.132022
\(670\) −1.62218e49 −0.567269
\(671\) 4.34475e49 1.48020
\(672\) 1.18310e49 0.392699
\(673\) 1.92251e49 0.621734 0.310867 0.950453i \(-0.399381\pi\)
0.310867 + 0.950453i \(0.399381\pi\)
\(674\) −2.88676e49 −0.909626
\(675\) −4.24824e48 −0.130435
\(676\) −4.49080e48 −0.134356
\(677\) −2.27583e49 −0.663495 −0.331747 0.943368i \(-0.607638\pi\)
−0.331747 + 0.943368i \(0.607638\pi\)
\(678\) −1.68121e49 −0.477641
\(679\) −8.77279e48 −0.242894
\(680\) 1.93921e49 0.523261
\(681\) 2.73621e49 0.719573
\(682\) 3.51229e49 0.900253
\(683\) −7.47926e49 −1.86851 −0.934257 0.356599i \(-0.883936\pi\)
−0.934257 + 0.356599i \(0.883936\pi\)
\(684\) 3.84572e48 0.0936473
\(685\) −6.69355e48 −0.158881
\(686\) 5.41193e49 1.25222
\(687\) 3.15943e48 0.0712634
\(688\) −1.00163e50 −2.20247
\(689\) −5.88151e49 −1.26082
\(690\) 1.40312e49 0.293249
\(691\) 5.04033e49 1.02705 0.513527 0.858073i \(-0.328339\pi\)
0.513527 + 0.858073i \(0.328339\pi\)
\(692\) −1.62080e49 −0.322013
\(693\) 1.53096e49 0.296573
\(694\) 3.32057e49 0.627223
\(695\) 3.97214e49 0.731628
\(696\) 2.00734e49 0.360545
\(697\) −1.25917e50 −2.20552
\(698\) −9.51168e49 −1.62475
\(699\) 4.51184e49 0.751628
\(700\) 1.49482e49 0.242870
\(701\) 3.72125e48 0.0589690 0.0294845 0.999565i \(-0.490613\pi\)
0.0294845 + 0.999565i \(0.490613\pi\)
\(702\) −1.18867e49 −0.183722
\(703\) 7.88175e49 1.18824
\(704\) −2.40337e49 −0.353427
\(705\) 5.99504e46 0.000859969 0
\(706\) 7.37288e49 1.03170
\(707\) 5.87397e49 0.801848
\(708\) 9.96773e48 0.132744
\(709\) −5.15574e49 −0.669857 −0.334928 0.942244i \(-0.608712\pi\)
−0.334928 + 0.942244i \(0.608712\pi\)
\(710\) 1.07550e49 0.136329
\(711\) −3.56342e49 −0.440706
\(712\) −9.50738e49 −1.14726
\(713\) 5.08100e49 0.598249
\(714\) −6.97665e49 −0.801546
\(715\) −3.97103e49 −0.445193
\(716\) 2.73477e49 0.299187
\(717\) −4.29958e49 −0.459030
\(718\) 1.89078e50 1.96999
\(719\) −3.36048e49 −0.341700 −0.170850 0.985297i \(-0.554651\pi\)
−0.170850 + 0.985297i \(0.554651\pi\)
\(720\) 2.36038e49 0.234241
\(721\) 1.10152e50 1.06690
\(722\) −6.00346e49 −0.567546
\(723\) 8.95937e48 0.0826718
\(724\) −5.56699e49 −0.501412
\(725\) 6.69473e49 0.588597
\(726\) −4.90461e48 −0.0420934
\(727\) 1.31541e50 1.10207 0.551033 0.834484i \(-0.314234\pi\)
0.551033 + 0.834484i \(0.314234\pi\)
\(728\) −6.53893e49 −0.534820
\(729\) 4.63840e48 0.0370370
\(730\) 5.81394e49 0.453232
\(731\) 2.99655e50 2.28070
\(732\) −4.63182e49 −0.344197
\(733\) −2.25359e50 −1.63514 −0.817570 0.575829i \(-0.804680\pi\)
−0.817570 + 0.575829i \(0.804680\pi\)
\(734\) 4.62151e49 0.327418
\(735\) 7.40134e48 0.0512014
\(736\) 8.31861e49 0.561939
\(737\) −1.24450e50 −0.820943
\(738\) −1.04966e50 −0.676180
\(739\) −1.93424e50 −1.21684 −0.608419 0.793616i \(-0.708196\pi\)
−0.608419 + 0.793616i \(0.708196\pi\)
\(740\) −5.94712e49 −0.365386
\(741\) −5.61056e49 −0.336657
\(742\) −2.87767e50 −1.68645
\(743\) 8.43115e49 0.482595 0.241297 0.970451i \(-0.422427\pi\)
0.241297 + 0.970451i \(0.422427\pi\)
\(744\) 5.85387e49 0.327278
\(745\) −3.27796e49 −0.179006
\(746\) −1.76266e50 −0.940238
\(747\) −3.70427e49 −0.193015
\(748\) −9.51601e49 −0.484370
\(749\) 2.04412e50 1.01642
\(750\) 1.33462e50 0.648312
\(751\) −2.50076e50 −1.18679 −0.593394 0.804912i \(-0.702212\pi\)
−0.593394 + 0.804912i \(0.702212\pi\)
\(752\) 7.00581e47 0.00324823
\(753\) 4.35391e48 0.0197227
\(754\) 1.87320e50 0.829060
\(755\) 4.01678e49 0.173702
\(756\) −1.63211e49 −0.0689633
\(757\) −8.14773e49 −0.336402 −0.168201 0.985753i \(-0.553796\pi\)
−0.168201 + 0.985753i \(0.553796\pi\)
\(758\) 3.56153e50 1.43690
\(759\) 1.07644e50 0.424385
\(760\) 7.63019e49 0.293966
\(761\) −3.09181e50 −1.16408 −0.582038 0.813161i \(-0.697745\pi\)
−0.582038 + 0.813161i \(0.697745\pi\)
\(762\) 5.31076e49 0.195409
\(763\) 4.14729e50 1.49137
\(764\) 8.74004e49 0.307171
\(765\) −7.06149e49 −0.242561
\(766\) 6.74660e50 2.26507
\(767\) −1.45420e50 −0.477206
\(768\) 1.82764e50 0.586231
\(769\) −9.48513e49 −0.297394 −0.148697 0.988883i \(-0.547508\pi\)
−0.148697 + 0.988883i \(0.547508\pi\)
\(770\) −1.94292e50 −0.595481
\(771\) −3.17380e49 −0.0950884
\(772\) −2.64592e49 −0.0774950
\(773\) 1.05155e50 0.301086 0.150543 0.988603i \(-0.451898\pi\)
0.150543 + 0.988603i \(0.451898\pi\)
\(774\) 2.49797e50 0.699230
\(775\) 1.95234e50 0.534288
\(776\) −7.10657e49 −0.190143
\(777\) −3.34499e50 −0.875038
\(778\) −6.04779e50 −1.54687
\(779\) −4.95444e50 −1.23905
\(780\) 4.23341e49 0.103522
\(781\) 8.25096e49 0.197293
\(782\) −4.90541e50 −1.14698
\(783\) −7.30958e49 −0.167133
\(784\) 8.64922e49 0.193395
\(785\) −2.70285e50 −0.591021
\(786\) 1.75642e50 0.375606
\(787\) −1.75648e50 −0.367354 −0.183677 0.982987i \(-0.558800\pi\)
−0.183677 + 0.982987i \(0.558800\pi\)
\(788\) 8.18282e49 0.167376
\(789\) −1.30163e50 −0.260400
\(790\) 4.52230e50 0.884882
\(791\) 3.36775e50 0.644542
\(792\) 1.24018e50 0.232164
\(793\) 6.75741e50 1.23737
\(794\) −7.83602e50 −1.40358
\(795\) −2.91266e50 −0.510347
\(796\) −1.18427e50 −0.202989
\(797\) 5.53388e49 0.0927917 0.0463959 0.998923i \(-0.485226\pi\)
0.0463959 + 0.998923i \(0.485226\pi\)
\(798\) −2.74510e50 −0.450305
\(799\) −2.09591e48 −0.00336359
\(800\) 3.19637e50 0.501859
\(801\) 3.46204e50 0.531818
\(802\) −9.33077e50 −1.40238
\(803\) 4.46032e50 0.655909
\(804\) 1.32672e50 0.190897
\(805\) −2.81069e50 −0.395718
\(806\) 5.46269e50 0.752563
\(807\) 4.56459e50 0.615340
\(808\) 4.75832e50 0.627704
\(809\) 4.98563e50 0.643607 0.321803 0.946807i \(-0.395711\pi\)
0.321803 + 0.946807i \(0.395711\pi\)
\(810\) −5.88655e49 −0.0743658
\(811\) −1.07303e51 −1.32662 −0.663309 0.748346i \(-0.730848\pi\)
−0.663309 + 0.748346i \(0.730848\pi\)
\(812\) 2.57202e50 0.311203
\(813\) 2.65125e48 0.00313955
\(814\) −1.62579e51 −1.88425
\(815\) 8.78004e50 0.995952
\(816\) −8.25206e50 −0.916188
\(817\) 1.17905e51 1.28129
\(818\) −1.87194e49 −0.0199117
\(819\) 2.38110e50 0.247919
\(820\) 3.73834e50 0.381010
\(821\) −2.21488e50 −0.220976 −0.110488 0.993877i \(-0.535241\pi\)
−0.110488 + 0.993877i \(0.535241\pi\)
\(822\) 1.95075e50 0.190522
\(823\) 1.24351e51 1.18892 0.594459 0.804126i \(-0.297366\pi\)
0.594459 + 0.804126i \(0.297366\pi\)
\(824\) 8.92306e50 0.835195
\(825\) 4.13616e50 0.379012
\(826\) −7.11504e50 −0.638302
\(827\) 1.45573e49 0.0127860 0.00639299 0.999980i \(-0.497965\pi\)
0.00639299 + 0.999980i \(0.497965\pi\)
\(828\) −1.14757e50 −0.0986840
\(829\) −9.35859e50 −0.787964 −0.393982 0.919118i \(-0.628903\pi\)
−0.393982 + 0.919118i \(0.628903\pi\)
\(830\) 4.70106e50 0.387551
\(831\) −5.15353e50 −0.415994
\(832\) −3.73797e50 −0.295446
\(833\) −2.58756e50 −0.200264
\(834\) −1.15763e51 −0.877331
\(835\) 2.13510e50 0.158454
\(836\) −3.74426e50 −0.272117
\(837\) −2.13164e50 −0.151712
\(838\) 1.24089e51 0.864897
\(839\) −7.95070e50 −0.542714 −0.271357 0.962479i \(-0.587472\pi\)
−0.271357 + 0.962479i \(0.587472\pi\)
\(840\) −3.23823e50 −0.216481
\(841\) −3.75414e50 −0.245799
\(842\) 9.63252e50 0.617701
\(843\) −8.55190e50 −0.537131
\(844\) 1.05692e51 0.650206
\(845\) 3.24454e50 0.195506
\(846\) −1.74718e48 −0.00103123
\(847\) 9.82478e49 0.0568019
\(848\) −3.40374e51 −1.92765
\(849\) 1.16560e51 0.646642
\(850\) −1.88487e51 −1.02435
\(851\) −2.35192e51 −1.25215
\(852\) −8.79612e49 −0.0458773
\(853\) −2.54840e50 −0.130214 −0.0651072 0.997878i \(-0.520739\pi\)
−0.0651072 + 0.997878i \(0.520739\pi\)
\(854\) 3.30622e51 1.65508
\(855\) −2.77848e50 −0.136270
\(856\) 1.65588e51 0.795678
\(857\) −2.64469e51 −1.24512 −0.622558 0.782573i \(-0.713907\pi\)
−0.622558 + 0.782573i \(0.713907\pi\)
\(858\) 1.15731e51 0.533852
\(859\) −1.92463e51 −0.869894 −0.434947 0.900456i \(-0.643233\pi\)
−0.434947 + 0.900456i \(0.643233\pi\)
\(860\) −8.89646e50 −0.393998
\(861\) 2.10265e51 0.912456
\(862\) 5.17661e51 2.20125
\(863\) −1.08280e51 −0.451190 −0.225595 0.974221i \(-0.572433\pi\)
−0.225595 + 0.974221i \(0.572433\pi\)
\(864\) −3.48992e50 −0.142503
\(865\) 1.17101e51 0.468573
\(866\) 1.35427e51 0.531058
\(867\) 9.66386e50 0.371378
\(868\) 7.50059e50 0.282488
\(869\) 3.46941e51 1.28059
\(870\) 9.27653e50 0.335582
\(871\) −1.93557e51 −0.686264
\(872\) 3.35959e51 1.16748
\(873\) 2.58780e50 0.0881419
\(874\) −1.93013e51 −0.644371
\(875\) −2.67347e51 −0.874850
\(876\) −4.75502e50 −0.152521
\(877\) 1.72464e51 0.542258 0.271129 0.962543i \(-0.412603\pi\)
0.271129 + 0.962543i \(0.412603\pi\)
\(878\) −8.81354e50 −0.271642
\(879\) 2.36419e51 0.714295
\(880\) −2.29811e51 −0.680650
\(881\) 8.76279e50 0.254428 0.127214 0.991875i \(-0.459397\pi\)
0.127214 + 0.991875i \(0.459397\pi\)
\(882\) −2.15702e50 −0.0613981
\(883\) −2.14016e51 −0.597221 −0.298610 0.954375i \(-0.596523\pi\)
−0.298610 + 0.954375i \(0.596523\pi\)
\(884\) −1.48003e51 −0.404907
\(885\) −7.20155e50 −0.193161
\(886\) 2.12480e50 0.0558764
\(887\) −3.78615e51 −0.976189 −0.488095 0.872791i \(-0.662308\pi\)
−0.488095 + 0.872791i \(0.662308\pi\)
\(888\) −2.70967e51 −0.684999
\(889\) −1.06384e51 −0.263690
\(890\) −4.39365e51 −1.06782
\(891\) −4.51603e50 −0.107621
\(892\) −3.81751e50 −0.0892061
\(893\) −8.24675e48 −0.00188965
\(894\) 9.55318e50 0.214655
\(895\) −1.97583e51 −0.435358
\(896\) −4.97672e51 −1.07536
\(897\) 1.67420e51 0.354763
\(898\) −7.55757e51 −1.57053
\(899\) 3.35922e51 0.684612
\(900\) −4.40944e50 −0.0881333
\(901\) 1.01829e52 1.99612
\(902\) 1.02197e52 1.96482
\(903\) −5.00386e51 −0.943559
\(904\) 2.72811e51 0.504562
\(905\) 4.02207e51 0.729625
\(906\) −1.17064e51 −0.208295
\(907\) 5.56638e51 0.971506 0.485753 0.874096i \(-0.338545\pi\)
0.485753 + 0.874096i \(0.338545\pi\)
\(908\) 2.84004e51 0.486208
\(909\) −1.73271e51 −0.290976
\(910\) −3.02184e51 −0.497790
\(911\) −4.53769e51 −0.733268 −0.366634 0.930365i \(-0.619490\pi\)
−0.366634 + 0.930365i \(0.619490\pi\)
\(912\) −3.24693e51 −0.514711
\(913\) 3.60654e51 0.560857
\(914\) 7.74063e51 1.18091
\(915\) 3.34642e51 0.500855
\(916\) 3.27932e50 0.0481519
\(917\) −3.51840e51 −0.506853
\(918\) 2.05798e51 0.290867
\(919\) −9.66145e50 −0.133974 −0.0669870 0.997754i \(-0.521339\pi\)
−0.0669870 + 0.997754i \(0.521339\pi\)
\(920\) −2.27686e51 −0.309777
\(921\) −7.67328e51 −1.02432
\(922\) 1.54500e51 0.202366
\(923\) 1.28328e51 0.164926
\(924\) 1.58905e51 0.200391
\(925\) −9.03710e51 −1.11828
\(926\) −1.36135e50 −0.0165302
\(927\) −3.24927e51 −0.387160
\(928\) 5.49972e51 0.643059
\(929\) 1.12588e52 1.29187 0.645935 0.763392i \(-0.276468\pi\)
0.645935 + 0.763392i \(0.276468\pi\)
\(930\) 2.70525e51 0.304618
\(931\) −1.01812e51 −0.112508
\(932\) 4.68305e51 0.507867
\(933\) 1.21814e51 0.129649
\(934\) −1.37307e52 −1.43424
\(935\) 6.87519e51 0.704825
\(936\) 1.92886e51 0.194076
\(937\) −9.93521e51 −0.981147 −0.490574 0.871400i \(-0.663213\pi\)
−0.490574 + 0.871400i \(0.663213\pi\)
\(938\) −9.47024e51 −0.917934
\(939\) 7.68654e51 0.731279
\(940\) 6.22254e48 0.000581072 0
\(941\) −7.86741e51 −0.721129 −0.360565 0.932734i \(-0.617416\pi\)
−0.360565 + 0.932734i \(0.617416\pi\)
\(942\) 7.87710e51 0.708721
\(943\) 1.47841e52 1.30569
\(944\) −8.41574e51 −0.729596
\(945\) 1.17918e51 0.100351
\(946\) −2.43206e52 −2.03180
\(947\) 1.76717e52 1.44928 0.724641 0.689127i \(-0.242006\pi\)
0.724641 + 0.689127i \(0.242006\pi\)
\(948\) −3.69864e51 −0.297780
\(949\) 6.93715e51 0.548305
\(950\) −7.41639e51 −0.575479
\(951\) −1.41012e52 −1.07423
\(952\) 1.13211e52 0.846722
\(953\) −2.15077e52 −1.57931 −0.789656 0.613550i \(-0.789741\pi\)
−0.789656 + 0.613550i \(0.789741\pi\)
\(954\) 8.48858e51 0.611982
\(955\) −6.31456e51 −0.446976
\(956\) −4.46273e51 −0.310162
\(957\) 7.11674e51 0.485648
\(958\) 2.40724e52 1.61296
\(959\) −3.90769e51 −0.257095
\(960\) −1.85113e51 −0.119589
\(961\) −5.96747e51 −0.378557
\(962\) −2.52860e52 −1.57513
\(963\) −6.02976e51 −0.368841
\(964\) 9.29935e50 0.0558605
\(965\) 1.91164e51 0.112766
\(966\) 8.19140e51 0.474524
\(967\) 5.62647e51 0.320091 0.160045 0.987110i \(-0.448836\pi\)
0.160045 + 0.987110i \(0.448836\pi\)
\(968\) 7.95875e50 0.0444658
\(969\) 9.71375e51 0.532992
\(970\) −3.28416e51 −0.176978
\(971\) 3.42787e51 0.181421 0.0907104 0.995877i \(-0.471086\pi\)
0.0907104 + 0.995877i \(0.471086\pi\)
\(972\) 4.81441e50 0.0250255
\(973\) 2.31893e52 1.18389
\(974\) 1.77734e52 0.891230
\(975\) 6.43299e51 0.316834
\(976\) 3.91064e52 1.89180
\(977\) 1.18458e52 0.562872 0.281436 0.959580i \(-0.409189\pi\)
0.281436 + 0.959580i \(0.409189\pi\)
\(978\) −2.55883e52 −1.19429
\(979\) −3.37070e52 −1.54534
\(980\) 7.68220e50 0.0345963
\(981\) −1.22337e52 −0.541191
\(982\) 4.00436e52 1.74013
\(983\) 2.75159e52 1.17462 0.587311 0.809362i \(-0.300187\pi\)
0.587311 + 0.809362i \(0.300187\pi\)
\(984\) 1.70329e52 0.714291
\(985\) −5.91197e51 −0.243556
\(986\) −3.24314e52 −1.31256
\(987\) 3.49990e49 0.00139157
\(988\) −5.82346e51 −0.227475
\(989\) −3.51830e52 −1.35020
\(990\) 5.73125e51 0.216089
\(991\) −3.30440e52 −1.22406 −0.612031 0.790834i \(-0.709647\pi\)
−0.612031 + 0.790834i \(0.709647\pi\)
\(992\) 1.60384e52 0.583725
\(993\) −8.58119e51 −0.306857
\(994\) 6.27873e51 0.220602
\(995\) 8.55620e51 0.295377
\(996\) −3.84483e51 −0.130418
\(997\) −4.71253e52 −1.57068 −0.785342 0.619062i \(-0.787513\pi\)
−0.785342 + 0.619062i \(0.787513\pi\)
\(998\) 1.99391e51 0.0653012
\(999\) 9.86707e51 0.317536
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 3.36.a.a.1.2 2
3.2 odd 2 9.36.a.a.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.36.a.a.1.2 2 1.1 even 1 trivial
9.36.a.a.1.1 2 3.2 odd 2