Properties

Label 3.39.b.a.2.12
Level 3
Weight 39
Character 3.2
Analytic conductor 27.439
Analytic rank 0
Dimension 12
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 39 \)
Character orbit: \([\chi]\) \(=\) 3.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(27.4390407101\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 17353504902 x^{10} + 111006258614054318328 x^{8} + 323765701965839203118204176384 x^{6} + 420150309279704216298413492838082805760 x^{4} + 190068212511425710374530430459662273636990976000 x^{2} + 27342285412416035125187079526375866471795145886924800000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{75}\cdot 3^{91}\cdot 5^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2.12
Root \(81459.4i\) of defining polynomial
Character \(\chi\) \(=\) 3.2
Dual form 3.39.b.a.2.1

$q$-expansion

\(f(q)\) \(=\) \(q+977513. i q^{2} +(-4.43499e8 + 1.07432e9i) q^{3} -6.80653e11 q^{4} -1.94075e13i q^{5} +(-1.05016e15 - 4.33526e14i) q^{6} -1.85443e15 q^{7} -3.96650e17i q^{8} +(-9.57469e17 - 9.52919e17i) q^{9} +O(q^{10})\) \(q+977513. i q^{2} +(-4.43499e8 + 1.07432e9i) q^{3} -6.80653e11 q^{4} -1.94075e13i q^{5} +(-1.05016e15 - 4.33526e14i) q^{6} -1.85443e15 q^{7} -3.96650e17i q^{8} +(-9.57469e17 - 9.52919e17i) q^{9} +1.89711e19 q^{10} +1.00331e20i q^{11} +(3.01869e20 - 7.31238e20i) q^{12} +5.34879e20 q^{13} -1.81273e21i q^{14} +(2.08499e22 + 8.60722e21i) q^{15} +2.00634e23 q^{16} -2.93124e23i q^{17} +(9.31490e23 - 9.35938e23i) q^{18} -2.13221e24 q^{19} +1.32098e25i q^{20} +(8.22439e23 - 1.99225e24i) q^{21} -9.80751e25 q^{22} -6.81549e25i q^{23} +(4.26128e26 + 1.75914e26i) q^{24} -1.28546e25 q^{25} +5.22851e26i q^{26} +(1.44837e27 - 6.06008e26i) q^{27} +1.26222e27 q^{28} +4.43183e27i q^{29} +(-8.41367e27 + 2.03810e28i) q^{30} +9.20206e27 q^{31} +8.70919e28i q^{32} +(-1.07788e29 - 4.44969e28i) q^{33} +2.86533e29 q^{34} +3.59900e28i q^{35} +(6.51704e29 + 6.48607e29i) q^{36} -1.71160e29 q^{37} -2.08426e30i q^{38} +(-2.37219e29 + 5.74631e29i) q^{39} -7.69800e30 q^{40} +3.25222e30i q^{41} +(1.94745e30 + 8.03944e29i) q^{42} +9.05664e30 q^{43} -6.82908e31i q^{44} +(-1.84938e31 + 1.85821e31i) q^{45} +6.66223e31 q^{46} -4.90800e31i q^{47} +(-8.89810e31 + 2.15545e32i) q^{48} -1.26496e32 q^{49} -1.25655e31i q^{50} +(3.14909e32 + 1.30000e32i) q^{51} -3.64067e32 q^{52} -3.19951e32i q^{53} +(5.92380e32 + 1.41580e33i) q^{54} +1.94718e33 q^{55} +7.35561e32i q^{56} +(9.45632e32 - 2.29067e33i) q^{57} -4.33217e33 q^{58} -2.55619e33i q^{59} +(-1.41915e34 - 5.85853e33i) q^{60} +1.24839e34 q^{61} +8.99513e33i q^{62} +(1.77556e33 + 1.76712e33i) q^{63} -2.99835e34 q^{64} -1.03807e34i q^{65} +(4.34962e34 - 1.05364e35i) q^{66} +4.69883e34 q^{67} +1.99516e35i q^{68} +(7.32201e34 + 3.02266e34i) q^{69} -3.51806e34 q^{70} -1.03720e35i q^{71} +(-3.77975e35 + 3.79780e35i) q^{72} -1.12163e35 q^{73} -1.67311e35i q^{74} +(5.70100e33 - 1.38099e34i) q^{75} +1.45129e36 q^{76} -1.86058e35i q^{77} +(-5.61709e35 - 2.31884e35i) q^{78} +5.18105e34 q^{79} -3.89381e36i q^{80} +(8.69280e33 + 1.82478e36i) q^{81} -3.17908e36 q^{82} -1.87566e35i q^{83} +(-5.59795e35 + 1.35603e36i) q^{84} -5.68882e36 q^{85} +8.85298e36i q^{86} +(-4.76120e36 - 1.96551e36i) q^{87} +3.97964e37 q^{88} -4.77590e36i q^{89} +(-1.81642e37 - 1.80779e37i) q^{90} -9.91898e35 q^{91} +4.63898e37i q^{92} +(-4.08111e36 + 9.88595e36i) q^{93} +4.79763e37 q^{94} +4.13809e37i q^{95} +(-9.35644e37 - 3.86252e37i) q^{96} -7.67399e37 q^{97} -1.23651e38i q^{98} +(9.56076e37 - 9.60641e37i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 114742404q^{3} - 1699274528448q^{4} - 483611204680128q^{6} + 8107872236538648q^{7} - 424319151461513940q^{9} + O(q^{10}) \) \( 12q - 114742404q^{3} - 1699274528448q^{4} - 483611204680128q^{6} + 8107872236538648q^{7} - 424319151461513940q^{9} + 8521437485093339520q^{10} - 2862564534392665536q^{12} + \)\(10\!\cdots\!52\)\(q^{13} + \)\(63\!\cdots\!80\)\(q^{15} + \)\(67\!\cdots\!56\)\(q^{16} + \)\(14\!\cdots\!20\)\(q^{18} - \)\(46\!\cdots\!60\)\(q^{19} + \)\(33\!\cdots\!52\)\(q^{21} - \)\(13\!\cdots\!60\)\(q^{22} + \)\(78\!\cdots\!84\)\(q^{24} - \)\(12\!\cdots\!20\)\(q^{25} + \)\(35\!\cdots\!04\)\(q^{27} - \)\(77\!\cdots\!68\)\(q^{28} - \)\(31\!\cdots\!40\)\(q^{30} + \)\(62\!\cdots\!84\)\(q^{31} - \)\(20\!\cdots\!40\)\(q^{33} + \)\(27\!\cdots\!04\)\(q^{34} + \)\(52\!\cdots\!44\)\(q^{36} - \)\(10\!\cdots\!52\)\(q^{37} + \)\(37\!\cdots\!68\)\(q^{39} - \)\(86\!\cdots\!40\)\(q^{40} + \)\(37\!\cdots\!80\)\(q^{42} + \)\(10\!\cdots\!92\)\(q^{43} - \)\(61\!\cdots\!20\)\(q^{45} + \)\(13\!\cdots\!64\)\(q^{46} - \)\(16\!\cdots\!64\)\(q^{48} - \)\(74\!\cdots\!52\)\(q^{49} + \)\(71\!\cdots\!72\)\(q^{51} - \)\(99\!\cdots\!32\)\(q^{52} + \)\(12\!\cdots\!12\)\(q^{54} - \)\(14\!\cdots\!40\)\(q^{55} - \)\(19\!\cdots\!12\)\(q^{57} + \)\(54\!\cdots\!20\)\(q^{58} - \)\(21\!\cdots\!80\)\(q^{60} + \)\(19\!\cdots\!24\)\(q^{61} - \)\(68\!\cdots\!88\)\(q^{63} - \)\(33\!\cdots\!44\)\(q^{64} + \)\(29\!\cdots\!20\)\(q^{66} - \)\(12\!\cdots\!52\)\(q^{67} + \)\(14\!\cdots\!32\)\(q^{69} + \)\(13\!\cdots\!80\)\(q^{70} - \)\(84\!\cdots\!40\)\(q^{72} + \)\(90\!\cdots\!72\)\(q^{73} - \)\(19\!\cdots\!60\)\(q^{75} + \)\(37\!\cdots\!48\)\(q^{76} - \)\(47\!\cdots\!80\)\(q^{78} + \)\(33\!\cdots\!20\)\(q^{79} - \)\(38\!\cdots\!88\)\(q^{81} + \)\(97\!\cdots\!60\)\(q^{82} - \)\(23\!\cdots\!52\)\(q^{84} + \)\(16\!\cdots\!60\)\(q^{85} - \)\(46\!\cdots\!20\)\(q^{87} + \)\(11\!\cdots\!20\)\(q^{88} - \)\(16\!\cdots\!20\)\(q^{90} + \)\(12\!\cdots\!24\)\(q^{91} - \)\(17\!\cdots\!28\)\(q^{93} + \)\(32\!\cdots\!64\)\(q^{94} - \)\(45\!\cdots\!24\)\(q^{96} + \)\(24\!\cdots\!28\)\(q^{97} - \)\(34\!\cdots\!40\)\(q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 977513.i 1.86446i 0.361870 + 0.932229i \(0.382138\pi\)
−0.361870 + 0.932229i \(0.617862\pi\)
\(3\) −4.43499e8 + 1.07432e9i −0.381583 + 0.924335i
\(4\) −6.80653e11 −2.47620
\(5\) 1.94075e13i 1.01751i −0.860910 0.508757i \(-0.830105\pi\)
0.860910 0.508757i \(-0.169895\pi\)
\(6\) −1.05016e15 4.33526e14i −1.72338 0.711445i
\(7\) −1.85443e15 −0.162685 −0.0813426 0.996686i \(-0.525921\pi\)
−0.0813426 + 0.996686i \(0.525921\pi\)
\(8\) 3.96650e17i 2.75231i
\(9\) −9.57469e17 9.52919e17i −0.708789 0.705421i
\(10\) 1.89711e19 1.89711
\(11\) 1.00331e20i 1.64050i 0.572007 + 0.820249i \(0.306165\pi\)
−0.572007 + 0.820249i \(0.693835\pi\)
\(12\) 3.01869e20 7.31238e20i 0.944876 2.28884i
\(13\) 5.34879e20 0.365875 0.182937 0.983125i \(-0.441439\pi\)
0.182937 + 0.983125i \(0.441439\pi\)
\(14\) 1.81273e21i 0.303320i
\(15\) 2.08499e22 + 8.60722e21i 0.940523 + 0.388266i
\(16\) 2.00634e23 2.65537
\(17\) 2.93124e23i 1.22609i −0.790048 0.613045i \(-0.789944\pi\)
0.790048 0.613045i \(-0.210056\pi\)
\(18\) 9.31490e23 9.35938e23i 1.31523 1.32151i
\(19\) −2.13221e24 −1.07773 −0.538866 0.842391i \(-0.681147\pi\)
−0.538866 + 0.842391i \(0.681147\pi\)
\(20\) 1.32098e25i 2.51957i
\(21\) 8.22439e23 1.99225e24i 0.0620779 0.150376i
\(22\) −9.80751e25 −3.05864
\(23\) 6.81549e25i 0.913416i −0.889617 0.456708i \(-0.849029\pi\)
0.889617 0.456708i \(-0.150971\pi\)
\(24\) 4.26128e26 + 1.75914e26i 2.54406 + 1.05024i
\(25\) −1.28546e25 −0.0353344
\(26\) 5.22851e26i 0.682157i
\(27\) 1.44837e27 6.06008e26i 0.922506 0.385982i
\(28\) 1.26222e27 0.402841
\(29\) 4.43183e27i 0.726141i 0.931762 + 0.363071i \(0.118272\pi\)
−0.931762 + 0.363071i \(0.881728\pi\)
\(30\) −8.41367e27 + 2.03810e28i −0.723905 + 1.75357i
\(31\) 9.20206e27 0.424632 0.212316 0.977201i \(-0.431899\pi\)
0.212316 + 0.977201i \(0.431899\pi\)
\(32\) 8.70919e28i 2.19851i
\(33\) −1.07788e29 4.44969e28i −1.51637 0.625986i
\(34\) 2.86533e29 2.28599
\(35\) 3.59900e28i 0.165535i
\(36\) 6.51704e29 + 6.48607e29i 1.75510 + 1.74676i
\(37\) −1.71160e29 −0.273886 −0.136943 0.990579i \(-0.543728\pi\)
−0.136943 + 0.990579i \(0.543728\pi\)
\(38\) 2.08426e30i 2.00939i
\(39\) −2.37219e29 + 5.74631e29i −0.139611 + 0.338190i
\(40\) −7.69800e30 −2.80052
\(41\) 3.25222e30i 0.740093i 0.929013 + 0.370046i \(0.120658\pi\)
−0.929013 + 0.370046i \(0.879342\pi\)
\(42\) 1.94745e30 + 8.03944e29i 0.280369 + 0.115742i
\(43\) 9.05664e30 0.833809 0.416904 0.908950i \(-0.363115\pi\)
0.416904 + 0.908950i \(0.363115\pi\)
\(44\) 6.82908e31i 4.06220i
\(45\) −1.84938e31 + 1.85821e31i −0.717775 + 0.721203i
\(46\) 6.66223e31 1.70302
\(47\) 4.90800e31i 0.833769i −0.908960 0.416884i \(-0.863122\pi\)
0.908960 0.416884i \(-0.136878\pi\)
\(48\) −8.89810e31 + 2.15545e32i −1.01324 + 2.45445i
\(49\) −1.26496e32 −0.973534
\(50\) 1.25655e31i 0.0658795i
\(51\) 3.14909e32 + 1.30000e32i 1.13332 + 0.467855i
\(52\) −3.64067e32 −0.905979
\(53\) 3.19951e32i 0.554425i −0.960809 0.277212i \(-0.910589\pi\)
0.960809 0.277212i \(-0.0894105\pi\)
\(54\) 5.92380e32 + 1.41580e33i 0.719647 + 1.71997i
\(55\) 1.94718e33 1.66923
\(56\) 7.35561e32i 0.447761i
\(57\) 9.45632e32 2.29067e33i 0.411244 0.996186i
\(58\) −4.33217e33 −1.35386
\(59\) 2.55619e33i 0.577304i −0.957434 0.288652i \(-0.906793\pi\)
0.957434 0.288652i \(-0.0932071\pi\)
\(60\) −1.41915e34 5.85853e33i −2.32892 0.961424i
\(61\) 1.24839e34 1.49653 0.748263 0.663403i \(-0.230888\pi\)
0.748263 + 0.663403i \(0.230888\pi\)
\(62\) 8.99513e33i 0.791709i
\(63\) 1.77556e33 + 1.76712e33i 0.115310 + 0.114762i
\(64\) −2.99835e34 −1.44366
\(65\) 1.03807e34i 0.372282i
\(66\) 4.34962e34 1.05364e35i 1.16712 2.82720i
\(67\) 4.69883e34 0.947476 0.473738 0.880666i \(-0.342904\pi\)
0.473738 + 0.880666i \(0.342904\pi\)
\(68\) 1.99516e35i 3.03605i
\(69\) 7.32201e34 + 3.02266e34i 0.844302 + 0.348544i
\(70\) −3.51806e34 −0.308632
\(71\) 1.03720e35i 0.694949i −0.937689 0.347475i \(-0.887039\pi\)
0.937689 0.347475i \(-0.112961\pi\)
\(72\) −3.77975e35 + 3.79780e35i −1.94154 + 1.95081i
\(73\) −1.12163e35 −0.443317 −0.221659 0.975124i \(-0.571147\pi\)
−0.221659 + 0.975124i \(0.571147\pi\)
\(74\) 1.67311e35i 0.510649i
\(75\) 5.70100e33 1.38099e34i 0.0134830 0.0326608i
\(76\) 1.45129e36 2.66868
\(77\) 1.86058e35i 0.266885i
\(78\) −5.61709e35 2.31884e35i −0.630542 0.260300i
\(79\) 5.18105e34 0.0456565 0.0228283 0.999739i \(-0.492733\pi\)
0.0228283 + 0.999739i \(0.492733\pi\)
\(80\) 3.89381e36i 2.70187i
\(81\) 8.69280e33 + 1.82478e36i 0.00476370 + 0.999989i
\(82\) −3.17908e36 −1.37987
\(83\) 1.87566e35i 0.0646652i −0.999477 0.0323326i \(-0.989706\pi\)
0.999477 0.0323326i \(-0.0102936\pi\)
\(84\) −5.59795e35 + 1.35603e36i −0.153717 + 0.372360i
\(85\) −5.68882e36 −1.24756
\(86\) 8.85298e36i 1.55460i
\(87\) −4.76120e36 1.96551e36i −0.671197 0.277083i
\(88\) 3.97964e37 4.51516
\(89\) 4.77590e36i 0.437164i −0.975819 0.218582i \(-0.929857\pi\)
0.975819 0.218582i \(-0.0701432\pi\)
\(90\) −1.81642e37 1.80779e37i −1.34465 1.33826i
\(91\) −9.91898e35 −0.0595224
\(92\) 4.63898e37i 2.26180i
\(93\) −4.08111e36 + 9.88595e36i −0.162032 + 0.392502i
\(94\) 4.79763e37 1.55453
\(95\) 4.13809e37i 1.09661i
\(96\) −9.35644e37 3.86252e37i −2.03216 0.838913i
\(97\) −7.67399e37 −1.36886 −0.684428 0.729080i \(-0.739948\pi\)
−0.684428 + 0.729080i \(0.739948\pi\)
\(98\) 1.23651e38i 1.81511i
\(99\) 9.56076e37 9.60641e37i 1.15724 1.16277i
\(100\) 8.74951e36 0.0874951
\(101\) 4.54349e37i 0.376083i −0.982161 0.188041i \(-0.939786\pi\)
0.982161 0.188041i \(-0.0602139\pi\)
\(102\) −1.27077e38 + 3.07828e38i −0.872296 + 2.11302i
\(103\) 2.67470e38 1.52535 0.762673 0.646785i \(-0.223887\pi\)
0.762673 + 0.646785i \(0.223887\pi\)
\(104\) 2.12160e38i 1.00700i
\(105\) −3.86647e37 1.59615e37i −0.153009 0.0631651i
\(106\) 3.12756e38 1.03370
\(107\) 5.88759e38i 1.62797i −0.580887 0.813984i \(-0.697294\pi\)
0.580887 0.813984i \(-0.302706\pi\)
\(108\) −9.85840e38 + 4.12481e38i −2.28431 + 0.955768i
\(109\) 3.21551e38 0.625383 0.312691 0.949855i \(-0.398769\pi\)
0.312691 + 0.949855i \(0.398769\pi\)
\(110\) 1.90340e39i 3.11221i
\(111\) 7.59094e37 1.83881e38i 0.104510 0.253163i
\(112\) −3.72062e38 −0.431989
\(113\) 8.86717e37i 0.0869550i −0.999054 0.0434775i \(-0.986156\pi\)
0.999054 0.0434775i \(-0.0138437\pi\)
\(114\) 2.23916e39 + 9.24367e38i 1.85735 + 0.766748i
\(115\) −1.32272e39 −0.929413
\(116\) 3.01654e39i 1.79807i
\(117\) −5.12130e38 5.09696e38i −0.259328 0.258095i
\(118\) 2.49871e39 1.07636
\(119\) 5.43579e38i 0.199467i
\(120\) 3.41406e39 8.27010e39i 1.06863 2.58861i
\(121\) −6.32594e39 −1.69123
\(122\) 1.22032e40i 2.79021i
\(123\) −3.49392e39 1.44236e39i −0.684094 0.282407i
\(124\) −6.26341e39 −1.05147
\(125\) 6.81094e39i 0.981561i
\(126\) −1.72738e39 + 1.73563e39i −0.213968 + 0.214990i
\(127\) 3.29072e39 0.350768 0.175384 0.984500i \(-0.443883\pi\)
0.175384 + 0.984500i \(0.443883\pi\)
\(128\) 5.36966e39i 0.493125i
\(129\) −4.01661e39 + 9.72972e39i −0.318167 + 0.770718i
\(130\) 1.01473e40 0.694105
\(131\) 1.52248e40i 0.900322i −0.892947 0.450161i \(-0.851367\pi\)
0.892947 0.450161i \(-0.148633\pi\)
\(132\) 7.33661e40 + 3.02869e40i 3.75483 + 1.55007i
\(133\) 3.95404e39 0.175331
\(134\) 4.59316e40i 1.76653i
\(135\) −1.17611e40 2.81094e40i −0.392742 0.938663i
\(136\) −1.16268e41 −3.37458
\(137\) 7.34845e40i 1.85569i −0.372969 0.927844i \(-0.621660\pi\)
0.372969 0.927844i \(-0.378340\pi\)
\(138\) −2.95469e40 + 7.15736e40i −0.649845 + 1.57416i
\(139\) 6.07971e38 0.0116574 0.00582870 0.999983i \(-0.498145\pi\)
0.00582870 + 0.999983i \(0.498145\pi\)
\(140\) 2.44967e40i 0.409897i
\(141\) 5.27276e40 + 2.17669e40i 0.770681 + 0.318152i
\(142\) 1.01387e41 1.29570
\(143\) 5.36652e40i 0.600216i
\(144\) −1.92101e41 1.91188e41i −1.88210 1.87315i
\(145\) 8.60109e40 0.738859
\(146\) 1.09641e41i 0.826546i
\(147\) 5.61008e40 1.35897e41i 0.371484 0.899871i
\(148\) 1.16501e41 0.678197
\(149\) 1.48174e40i 0.0758983i 0.999280 + 0.0379491i \(0.0120825\pi\)
−0.999280 + 0.0379491i \(0.987918\pi\)
\(150\) 1.34994e40 + 5.57280e39i 0.0608947 + 0.0251385i
\(151\) −1.38443e41 −0.550438 −0.275219 0.961382i \(-0.588750\pi\)
−0.275219 + 0.961382i \(0.588750\pi\)
\(152\) 8.45740e41i 2.96626i
\(153\) −2.79324e41 + 2.80658e41i −0.864910 + 0.869040i
\(154\) 1.81874e41 0.497595
\(155\) 1.78589e41i 0.432069i
\(156\) 1.61463e41 3.91124e41i 0.345706 0.837427i
\(157\) −7.44067e41 −1.41097 −0.705486 0.708723i \(-0.749271\pi\)
−0.705486 + 0.708723i \(0.749271\pi\)
\(158\) 5.06454e40i 0.0851247i
\(159\) 3.43730e41 + 1.41898e41i 0.512474 + 0.211559i
\(160\) 1.69024e42 2.23701
\(161\) 1.26389e41i 0.148599i
\(162\) −1.78374e42 + 8.49732e39i −1.86444 + 0.00888171i
\(163\) 1.76036e42 1.63695 0.818477 0.574539i \(-0.194819\pi\)
0.818477 + 0.574539i \(0.194819\pi\)
\(164\) 2.21363e42i 1.83262i
\(165\) −8.63574e41 + 2.09190e42i −0.636949 + 1.54293i
\(166\) 1.83348e41 0.120566
\(167\) 1.17329e42i 0.688321i −0.938911 0.344161i \(-0.888164\pi\)
0.938911 0.344161i \(-0.111836\pi\)
\(168\) −7.90226e41 3.26220e41i −0.413881 0.170858i
\(169\) −1.85111e42 −0.866136
\(170\) 5.56090e42i 2.32603i
\(171\) 2.04152e42 + 2.03182e42i 0.763885 + 0.760255i
\(172\) −6.16443e42 −2.06468
\(173\) 3.20663e42i 0.961995i 0.876722 + 0.480998i \(0.159725\pi\)
−0.876722 + 0.480998i \(0.840275\pi\)
\(174\) 1.92131e42 4.65413e42i 0.516609 1.25142i
\(175\) 2.38380e40 0.00574839
\(176\) 2.01299e43i 4.35612i
\(177\) 2.74616e42 + 1.13367e42i 0.533622 + 0.220289i
\(178\) 4.66850e42 0.815074
\(179\) 1.08485e43i 1.70280i −0.524520 0.851398i \(-0.675755\pi\)
0.524520 0.851398i \(-0.324245\pi\)
\(180\) 1.25879e43 1.26480e43i 1.77736 1.78584i
\(181\) 7.21699e42 0.917199 0.458599 0.888643i \(-0.348351\pi\)
0.458599 + 0.888643i \(0.348351\pi\)
\(182\) 9.69592e41i 0.110977i
\(183\) −5.53661e42 + 1.34117e43i −0.571048 + 1.38329i
\(184\) −2.70337e43 −2.51400
\(185\) 3.32180e42i 0.278683i
\(186\) −9.66364e42 3.98933e42i −0.731804 0.302102i
\(187\) 2.94096e43 2.01140
\(188\) 3.34065e43i 2.06458i
\(189\) −2.68591e42 + 1.12380e42i −0.150078 + 0.0627936i
\(190\) −4.04504e43 −2.04458
\(191\) 2.14694e43i 0.982168i −0.871112 0.491084i \(-0.836601\pi\)
0.871112 0.491084i \(-0.163399\pi\)
\(192\) 1.32977e43 3.22119e43i 0.550874 1.33442i
\(193\) −3.76780e43 −1.41416 −0.707081 0.707133i \(-0.749988\pi\)
−0.707081 + 0.707133i \(0.749988\pi\)
\(194\) 7.50142e43i 2.55218i
\(195\) 1.11522e43 + 4.60383e42i 0.344113 + 0.142057i
\(196\) 8.60998e43 2.41066
\(197\) 2.57608e43i 0.654789i −0.944888 0.327395i \(-0.893829\pi\)
0.944888 0.327395i \(-0.106171\pi\)
\(198\) 9.39039e43 + 9.34576e43i 2.16793 + 2.15763i
\(199\) −9.03602e43 −1.89570 −0.947848 0.318722i \(-0.896746\pi\)
−0.947848 + 0.318722i \(0.896746\pi\)
\(200\) 5.09877e42i 0.0972514i
\(201\) −2.08393e43 + 5.04804e43i −0.361541 + 0.875785i
\(202\) 4.44131e43 0.701190
\(203\) 8.21853e42i 0.118132i
\(204\) −2.14344e44 8.84852e43i −2.80632 1.15850i
\(205\) 6.31175e43 0.753055
\(206\) 2.61456e44i 2.84394i
\(207\) −6.49461e43 + 6.52562e43i −0.644342 + 0.647419i
\(208\) 1.07315e44 0.971532
\(209\) 2.13927e44i 1.76802i
\(210\) 1.56026e43 3.77952e43i 0.117769 0.285279i
\(211\) −7.21399e43 −0.497518 −0.248759 0.968565i \(-0.580023\pi\)
−0.248759 + 0.968565i \(0.580023\pi\)
\(212\) 2.17776e44i 1.37287i
\(213\) 1.11428e44 + 4.59996e43i 0.642366 + 0.265181i
\(214\) 5.75519e44 3.03528
\(215\) 1.75767e44i 0.848412i
\(216\) −2.40373e44 5.74498e44i −1.06234 2.53903i
\(217\) −1.70646e43 −0.0690814
\(218\) 3.14320e44i 1.16600i
\(219\) 4.97441e43 1.20499e44i 0.169162 0.409773i
\(220\) −1.32536e45 −4.13335
\(221\) 1.56786e44i 0.448595i
\(222\) 1.79746e44 + 7.42024e43i 0.472011 + 0.194855i
\(223\) 5.48150e44 1.32162 0.660811 0.750552i \(-0.270213\pi\)
0.660811 + 0.750552i \(0.270213\pi\)
\(224\) 1.61506e44i 0.357665i
\(225\) 1.23079e43 + 1.22494e43i 0.0250447 + 0.0249256i
\(226\) 8.66777e43 0.162124
\(227\) 2.52600e44i 0.434452i 0.976121 + 0.217226i \(0.0697008\pi\)
−0.976121 + 0.217226i \(0.930299\pi\)
\(228\) −6.43647e44 + 1.55915e45i −1.01832 + 2.46676i
\(229\) 6.92899e43 0.100878 0.0504389 0.998727i \(-0.483938\pi\)
0.0504389 + 0.998727i \(0.483938\pi\)
\(230\) 1.29297e45i 1.73285i
\(231\) 1.99885e44 + 8.25164e43i 0.246691 + 0.101839i
\(232\) 1.75789e45 1.99857
\(233\) 4.70136e44i 0.492563i −0.969198 0.246281i \(-0.920791\pi\)
0.969198 0.246281i \(-0.0792087\pi\)
\(234\) 4.98235e44 5.00614e44i 0.481208 0.483506i
\(235\) −9.52522e44 −0.848371
\(236\) 1.73988e45i 1.42952i
\(237\) −2.29779e43 + 5.56610e43i −0.0174218 + 0.0422019i
\(238\) −5.31356e44 −0.371897
\(239\) 2.79152e45i 1.80418i 0.431545 + 0.902092i \(0.357969\pi\)
−0.431545 + 0.902092i \(0.642031\pi\)
\(240\) 4.18319e45 + 1.72690e45i 2.49744 + 1.03099i
\(241\) −6.40166e44 −0.353158 −0.176579 0.984286i \(-0.556503\pi\)
−0.176579 + 0.984286i \(0.556503\pi\)
\(242\) 6.18369e45i 3.15323i
\(243\) −1.96425e45 7.99949e44i −0.926142 0.377175i
\(244\) −8.49721e45 −3.70570
\(245\) 2.45497e45i 0.990584i
\(246\) 1.40992e45 3.41535e45i 0.526535 1.27546i
\(247\) −1.14047e45 −0.394315
\(248\) 3.65000e45i 1.16872i
\(249\) 2.01506e44 + 8.31854e43i 0.0597723 + 0.0246751i
\(250\) 6.65778e45 1.83008
\(251\) 6.44255e45i 1.64156i 0.571243 + 0.820781i \(0.306461\pi\)
−0.571243 + 0.820781i \(0.693539\pi\)
\(252\) −1.20854e45 1.20280e45i −0.285529 0.284173i
\(253\) 6.83807e45 1.49846
\(254\) 3.21672e45i 0.653991i
\(255\) 2.52299e45 6.11161e45i 0.476049 1.15317i
\(256\) −2.99290e45 −0.524244
\(257\) 3.63646e44i 0.0591492i −0.999563 0.0295746i \(-0.990585\pi\)
0.999563 0.0295746i \(-0.00941527\pi\)
\(258\) −9.51092e45 3.92629e45i −1.43697 0.593209i
\(259\) 3.17405e44 0.0445572
\(260\) 7.06565e45i 0.921846i
\(261\) 4.22317e45 4.24334e45i 0.512235 0.514681i
\(262\) 1.48825e46 1.67861
\(263\) 9.58317e45i 1.00543i −0.864454 0.502713i \(-0.832335\pi\)
0.864454 0.502713i \(-0.167665\pi\)
\(264\) −1.76497e46 + 4.27540e46i −1.72291 + 4.17352i
\(265\) −6.20947e45 −0.564135
\(266\) 3.86512e45i 0.326898i
\(267\) 5.13083e45 + 2.11811e45i 0.404086 + 0.166814i
\(268\) −3.19827e46 −2.34614
\(269\) 9.07840e45i 0.620463i 0.950661 + 0.310231i \(0.100407\pi\)
−0.950661 + 0.310231i \(0.899593\pi\)
\(270\) 2.74773e46 1.14966e46i 1.75010 0.732250i
\(271\) 1.17965e46 0.700383 0.350192 0.936678i \(-0.386116\pi\)
0.350192 + 0.936678i \(0.386116\pi\)
\(272\) 5.88107e46i 3.25572i
\(273\) 4.39906e44 1.06561e45i 0.0227127 0.0550186i
\(274\) 7.18320e46 3.45985
\(275\) 1.28972e45i 0.0579660i
\(276\) −4.98375e46 2.05739e46i −2.09066 0.863064i
\(277\) −3.13591e46 −1.22814 −0.614071 0.789251i \(-0.710469\pi\)
−0.614071 + 0.789251i \(0.710469\pi\)
\(278\) 5.94299e44i 0.0217347i
\(279\) −8.81069e45 8.76882e45i −0.300975 0.299544i
\(280\) 1.42754e46 0.455603
\(281\) 2.23453e45i 0.0666447i 0.999445 + 0.0333224i \(0.0106088\pi\)
−0.999445 + 0.0333224i \(0.989391\pi\)
\(282\) −2.12775e46 + 5.15419e46i −0.593180 + 1.43690i
\(283\) −1.42833e45 −0.0372295 −0.0186147 0.999827i \(-0.505926\pi\)
−0.0186147 + 0.999827i \(0.505926\pi\)
\(284\) 7.05972e46i 1.72083i
\(285\) −4.44563e46 1.83524e46i −1.01363 0.418447i
\(286\) −5.24584e46 −1.11908
\(287\) 6.03102e45i 0.120402i
\(288\) 8.29915e46 8.33877e46i 1.55087 1.55828i
\(289\) −2.87663e46 −0.503298
\(290\) 8.40767e46i 1.37757i
\(291\) 3.40341e46 8.24431e46i 0.522332 1.26528i
\(292\) 7.63439e46 1.09774
\(293\) 8.13702e45i 0.109643i −0.998496 0.0548214i \(-0.982541\pi\)
0.998496 0.0548214i \(-0.0174590\pi\)
\(294\) 1.32841e47 + 5.48392e46i 1.67777 + 0.692615i
\(295\) −4.96093e46 −0.587415
\(296\) 6.78907e46i 0.753820i
\(297\) 6.08016e46 + 1.45317e47i 0.633202 + 1.51337i
\(298\) −1.44842e46 −0.141509
\(299\) 3.64547e46i 0.334195i
\(300\) −3.88040e45 + 9.39976e45i −0.0333866 + 0.0808748i
\(301\) −1.67949e46 −0.135648
\(302\) 1.35330e47i 1.02627i
\(303\) 4.88115e46 + 2.01503e46i 0.347626 + 0.143507i
\(304\) −4.27793e47 −2.86178
\(305\) 2.42282e47i 1.52274i
\(306\) −2.74346e47 2.73042e47i −1.62029 1.61259i
\(307\) 1.21487e47 0.674375 0.337188 0.941437i \(-0.390524\pi\)
0.337188 + 0.941437i \(0.390524\pi\)
\(308\) 1.26641e47i 0.660860i
\(309\) −1.18623e47 + 2.87348e47i −0.582046 + 1.40993i
\(310\) 1.74573e47 0.805575
\(311\) 2.51496e47i 1.09165i 0.837899 + 0.545825i \(0.183784\pi\)
−0.837899 + 0.545825i \(0.816216\pi\)
\(312\) 2.27927e47 + 9.40927e46i 0.930806 + 0.384254i
\(313\) 3.84707e47 1.47838 0.739192 0.673495i \(-0.235208\pi\)
0.739192 + 0.673495i \(0.235208\pi\)
\(314\) 7.27335e47i 2.63070i
\(315\) 3.42955e46 3.44593e46i 0.116771 0.117329i
\(316\) −3.52650e46 −0.113055
\(317\) 5.94628e47i 1.79523i −0.440784 0.897613i \(-0.645299\pi\)
0.440784 0.897613i \(-0.354701\pi\)
\(318\) −1.38707e47 + 3.36000e47i −0.394443 + 0.955485i
\(319\) −4.44651e47 −1.19123
\(320\) 5.81907e47i 1.46894i
\(321\) 6.32515e47 + 2.61114e47i 1.50479 + 0.621205i
\(322\) −1.23547e47 −0.277057
\(323\) 6.25002e47i 1.32140i
\(324\) −5.91678e45 1.24204e48i −0.0117959 2.47617i
\(325\) −6.87565e45 −0.0129280
\(326\) 1.72077e48i 3.05203i
\(327\) −1.42607e47 + 3.45448e47i −0.238635 + 0.578063i
\(328\) 1.28999e48 2.03697
\(329\) 9.10156e46i 0.135642i
\(330\) −2.04485e48 8.44155e47i −2.87672 1.18756i
\(331\) −5.89042e47 −0.782374 −0.391187 0.920311i \(-0.627935\pi\)
−0.391187 + 0.920311i \(0.627935\pi\)
\(332\) 1.27667e47i 0.160124i
\(333\) 1.63881e47 + 1.63102e47i 0.194128 + 0.193205i
\(334\) 1.14690e48 1.28335
\(335\) 9.11927e47i 0.964070i
\(336\) 1.65009e47 3.99713e47i 0.164840 0.399303i
\(337\) −1.54032e48 −1.45426 −0.727132 0.686498i \(-0.759147\pi\)
−0.727132 + 0.686498i \(0.759147\pi\)
\(338\) 1.80949e48i 1.61487i
\(339\) 9.52617e46 + 3.93258e46i 0.0803755 + 0.0331806i
\(340\) 3.87211e48 3.08922
\(341\) 9.23255e47i 0.696608i
\(342\) −1.98613e48 + 1.99561e48i −1.41746 + 1.42423i
\(343\) 4.75533e47 0.321065
\(344\) 3.59232e48i 2.29490i
\(345\) 5.86625e47 1.42102e48i 0.354648 0.859089i
\(346\) −3.13452e48 −1.79360
\(347\) 1.35408e48i 0.733473i 0.930325 + 0.366736i \(0.119525\pi\)
−0.930325 + 0.366736i \(0.880475\pi\)
\(348\) 3.24072e48 + 1.33783e48i 1.66202 + 0.686113i
\(349\) 2.81170e47 0.136548 0.0682740 0.997667i \(-0.478251\pi\)
0.0682740 + 0.997667i \(0.478251\pi\)
\(350\) 2.33019e46i 0.0107176i
\(351\) 7.74706e47 3.24141e47i 0.337522 0.141221i
\(352\) −8.73804e48 −3.60665
\(353\) 1.03153e47i 0.0403425i −0.999797 0.0201712i \(-0.993579\pi\)
0.999797 0.0201712i \(-0.00642114\pi\)
\(354\) −1.10817e48 + 2.68441e48i −0.410720 + 0.994916i
\(355\) −2.01295e48 −0.707121
\(356\) 3.25073e48i 1.08251i
\(357\) −5.83978e47 2.41077e47i −0.184374 0.0761131i
\(358\) 1.06046e49 3.17479
\(359\) 4.39348e48i 1.24742i −0.781654 0.623712i \(-0.785624\pi\)
0.781654 0.623712i \(-0.214376\pi\)
\(360\) 7.37059e48 + 7.33557e48i 1.98497 + 1.97554i
\(361\) 6.32167e47 0.161508
\(362\) 7.05470e48i 1.71008i
\(363\) 2.80555e48 6.79608e48i 0.645345 1.56326i
\(364\) 6.75138e47 0.147389
\(365\) 2.17680e48i 0.451081i
\(366\) −1.31101e49 5.41210e48i −2.57909 1.06470i
\(367\) 2.89773e48 0.541257 0.270628 0.962684i \(-0.412769\pi\)
0.270628 + 0.962684i \(0.412769\pi\)
\(368\) 1.36742e49i 2.42545i
\(369\) 3.09910e48 3.11390e48i 0.522077 0.524570i
\(370\) −3.24710e48 −0.519593
\(371\) 5.93328e47i 0.0901967i
\(372\) 2.77782e48 6.72890e48i 0.401225 0.971914i
\(373\) −9.95641e48 −1.36658 −0.683290 0.730147i \(-0.739452\pi\)
−0.683290 + 0.730147i \(0.739452\pi\)
\(374\) 2.87482e49i 3.75017i
\(375\) 7.31712e48 + 3.02065e48i 0.907290 + 0.374547i
\(376\) −1.94676e49 −2.29479
\(377\) 2.37049e48i 0.265677i
\(378\) −1.09853e48 2.62551e48i −0.117076 0.279814i
\(379\) −6.31988e48 −0.640566 −0.320283 0.947322i \(-0.603778\pi\)
−0.320283 + 0.947322i \(0.603778\pi\)
\(380\) 2.81660e49i 2.71542i
\(381\) −1.45943e48 + 3.53528e48i −0.133847 + 0.324227i
\(382\) 2.09866e49 1.83121
\(383\) 4.72786e48i 0.392544i 0.980549 + 0.196272i \(0.0628835\pi\)
−0.980549 + 0.196272i \(0.937116\pi\)
\(384\) 5.76873e48 + 2.38144e48i 0.455813 + 0.188168i
\(385\) −3.61092e48 −0.271559
\(386\) 3.68307e49i 2.63664i
\(387\) −8.67145e48 8.63024e48i −0.590994 0.588186i
\(388\) 5.22332e49 3.38956
\(389\) 2.31399e49i 1.42994i 0.699153 + 0.714972i \(0.253561\pi\)
−0.699153 + 0.714972i \(0.746439\pi\)
\(390\) −4.50030e48 + 1.09014e49i −0.264858 + 0.641585i
\(391\) −1.99779e49 −1.11993
\(392\) 5.01746e49i 2.67947i
\(393\) 1.63563e49 + 6.75220e48i 0.832199 + 0.343547i
\(394\) 2.51815e49 1.22083
\(395\) 1.00551e48i 0.0464562i
\(396\) −6.50756e49 + 6.53863e49i −2.86556 + 2.87924i
\(397\) −9.52386e48 −0.399755 −0.199877 0.979821i \(-0.564054\pi\)
−0.199877 + 0.979821i \(0.564054\pi\)
\(398\) 8.83282e49i 3.53444i
\(399\) −1.75361e48 + 4.24789e48i −0.0669034 + 0.162065i
\(400\) −2.57907e48 −0.0938259
\(401\) 1.71356e48i 0.0594506i 0.999558 + 0.0297253i \(0.00946325\pi\)
−0.999558 + 0.0297253i \(0.990537\pi\)
\(402\) −4.93452e49 2.03706e49i −1.63286 0.674077i
\(403\) 4.92199e48 0.155362
\(404\) 3.09254e49i 0.931256i
\(405\) 3.54145e49 1.68706e47i 1.01750 0.00484713i
\(406\) 8.03371e48 0.220253
\(407\) 1.71727e49i 0.449310i
\(408\) 5.15647e49 1.24909e50i 1.28768 3.11925i
\(409\) 5.80638e49 1.38408 0.692042 0.721857i \(-0.256711\pi\)
0.692042 + 0.721857i \(0.256711\pi\)
\(410\) 6.16982e49i 1.40404i
\(411\) 7.89457e49 + 3.25903e49i 1.71528 + 0.708099i
\(412\) −1.82054e50 −3.77706
\(413\) 4.74028e48i 0.0939189i
\(414\) −6.37888e49 6.34856e49i −1.20708 1.20135i
\(415\) −3.64020e48 −0.0657978
\(416\) 4.65836e49i 0.804378i
\(417\) −2.69635e47 + 6.53155e47i −0.00444826 + 0.0107753i
\(418\) 2.09117e50 3.29639
\(419\) 8.20553e49i 1.23606i −0.786154 0.618031i \(-0.787931\pi\)
0.786154 0.618031i \(-0.212069\pi\)
\(420\) 2.63172e49 + 1.08642e49i 0.378882 + 0.156410i
\(421\) −1.10651e50 −1.52263 −0.761315 0.648382i \(-0.775446\pi\)
−0.761315 + 0.648382i \(0.775446\pi\)
\(422\) 7.05176e49i 0.927601i
\(423\) −4.67693e49 + 4.69926e49i −0.588157 + 0.590966i
\(424\) −1.26909e50 −1.52595
\(425\) 3.76799e48i 0.0433232i
\(426\) −4.49652e49 + 1.08922e50i −0.494418 + 1.19766i
\(427\) −2.31506e49 −0.243463
\(428\) 4.00741e50i 4.03118i
\(429\) −5.76535e49 2.38004e49i −0.554801 0.229032i
\(430\) 1.71815e50 1.58183
\(431\) 1.46867e50i 1.29377i −0.762587 0.646885i \(-0.776071\pi\)
0.762587 0.646885i \(-0.223929\pi\)
\(432\) 2.90593e50 1.21586e50i 2.44959 1.02492i
\(433\) 1.20647e50 0.973296 0.486648 0.873598i \(-0.338219\pi\)
0.486648 + 0.873598i \(0.338219\pi\)
\(434\) 1.66809e49i 0.128799i
\(435\) −3.81458e49 + 9.24031e49i −0.281936 + 0.682953i
\(436\) −2.18864e50 −1.54857
\(437\) 1.45320e50i 0.984418i
\(438\) 1.17789e50 + 4.86255e49i 0.764005 + 0.315396i
\(439\) −2.49606e50 −1.55035 −0.775175 0.631746i \(-0.782338\pi\)
−0.775175 + 0.631746i \(0.782338\pi\)
\(440\) 7.72351e50i 4.59424i
\(441\) 1.21116e50 + 1.20540e50i 0.690030 + 0.686751i
\(442\) 1.53261e50 0.836387
\(443\) 1.99617e50i 1.04358i −0.853074 0.521790i \(-0.825264\pi\)
0.853074 0.521790i \(-0.174736\pi\)
\(444\) −5.16680e49 + 1.25159e50i −0.258788 + 0.626881i
\(445\) −9.26884e49 −0.444821
\(446\) 5.35824e50i 2.46411i
\(447\) −1.59186e49 6.57149e48i −0.0701554 0.0289615i
\(448\) 5.56025e49 0.234861
\(449\) 2.63311e50i 1.06608i −0.846090 0.533039i \(-0.821050\pi\)
0.846090 0.533039i \(-0.178950\pi\)
\(450\) −1.19739e49 + 1.20311e49i −0.0464728 + 0.0466947i
\(451\) −3.26299e50 −1.21412
\(452\) 6.03547e49i 0.215318i
\(453\) 6.13993e49 1.48732e50i 0.210038 0.508789i
\(454\) −2.46919e50 −0.810016
\(455\) 1.92503e49i 0.0605649i
\(456\) −9.08595e50 3.75085e50i −2.74181 1.13187i
\(457\) 3.95099e50 1.14366 0.571832 0.820371i \(-0.306233\pi\)
0.571832 + 0.820371i \(0.306233\pi\)
\(458\) 6.77317e49i 0.188082i
\(459\) −1.77636e50 4.24554e50i −0.473249 1.13108i
\(460\) 9.00313e50 2.30141
\(461\) 5.51810e50i 1.35354i 0.736193 + 0.676771i \(0.236621\pi\)
−0.736193 + 0.676771i \(0.763379\pi\)
\(462\) −8.06608e49 + 1.95390e50i −0.189874 + 0.459944i
\(463\) 7.87996e50 1.78027 0.890133 0.455700i \(-0.150611\pi\)
0.890133 + 0.455700i \(0.150611\pi\)
\(464\) 8.89175e50i 1.92817i
\(465\) 1.91862e50 + 7.92042e49i 0.399377 + 0.164870i
\(466\) 4.59564e50 0.918362
\(467\) 2.60117e49i 0.0499054i 0.999689 + 0.0249527i \(0.00794351\pi\)
−0.999689 + 0.0249527i \(0.992056\pi\)
\(468\) 3.48583e50 + 3.46926e50i 0.642148 + 0.639096i
\(469\) −8.71366e49 −0.154140
\(470\) 9.31103e50i 1.58175i
\(471\) 3.29993e50 7.99365e50i 0.538403 1.30421i
\(472\) −1.01391e51 −1.58892
\(473\) 9.08665e50i 1.36786i
\(474\) −5.44093e49 2.24612e49i −0.0786837 0.0324821i
\(475\) 2.74087e49 0.0380811
\(476\) 3.69989e50i 0.493920i
\(477\) −3.04888e50 + 3.06343e50i −0.391102 + 0.392970i
\(478\) −2.72875e51 −3.36382
\(479\) 3.83296e50i 0.454108i −0.973882 0.227054i \(-0.927091\pi\)
0.973882 0.227054i \(-0.0729095\pi\)
\(480\) −7.49619e50 + 1.81585e51i −0.853605 + 2.06775i
\(481\) −9.15501e49 −0.100208
\(482\) 6.25770e50i 0.658448i
\(483\) −1.35782e50 5.60533e49i −0.137355 0.0567029i
\(484\) 4.30577e51 4.18783
\(485\) 1.48933e51i 1.39283i
\(486\) 7.81960e50 1.92008e51i 0.703227 1.72675i
\(487\) −5.23031e50 −0.452353 −0.226176 0.974086i \(-0.572623\pi\)
−0.226176 + 0.974086i \(0.572623\pi\)
\(488\) 4.95175e51i 4.11891i
\(489\) −7.80717e50 + 1.89119e51i −0.624634 + 1.51309i
\(490\) −2.39977e51 −1.84690
\(491\) 2.96080e50i 0.219210i −0.993975 0.109605i \(-0.965041\pi\)
0.993975 0.109605i \(-0.0349586\pi\)
\(492\) 2.37814e51 + 9.81743e50i 1.69395 + 0.699296i
\(493\) 1.29908e51 0.890315
\(494\) 1.11483e51i 0.735183i
\(495\) −1.86437e51 1.85551e51i −1.18313 1.17751i
\(496\) 1.84625e51 1.12755
\(497\) 1.92341e50i 0.113058i
\(498\) −8.13148e49 + 1.96974e50i −0.0460057 + 0.111443i
\(499\) 5.15637e50 0.280823 0.140412 0.990093i \(-0.455157\pi\)
0.140412 + 0.990093i \(0.455157\pi\)
\(500\) 4.63589e51i 2.43054i
\(501\) 1.26048e51 + 5.20352e50i 0.636239 + 0.262652i
\(502\) −6.29767e51 −3.06062
\(503\) 1.33918e51i 0.626682i 0.949641 + 0.313341i \(0.101448\pi\)
−0.949641 + 0.313341i \(0.898552\pi\)
\(504\) 7.00929e50 7.04276e50i 0.315860 0.317368i
\(505\) −8.81779e50 −0.382669
\(506\) 6.68430e51i 2.79381i
\(507\) 8.20968e50 1.98869e51i 0.330503 0.800599i
\(508\) −2.23983e51 −0.868571
\(509\) 7.06657e50i 0.263980i 0.991251 + 0.131990i \(0.0421367\pi\)
−0.991251 + 0.131990i \(0.957863\pi\)
\(510\) 5.97417e51 + 2.46625e51i 2.15003 + 0.887573i
\(511\) 2.07998e50 0.0721212
\(512\) 4.40160e51i 1.47056i
\(513\) −3.08824e51 + 1.29214e51i −0.994216 + 0.415985i
\(514\) 3.55468e50 0.110281
\(515\) 5.19094e51i 1.55206i
\(516\) 2.73392e51 6.62256e51i 0.787846 1.90845i
\(517\) 4.92426e51 1.36780
\(518\) 3.10267e50i 0.0830751i
\(519\) −3.44494e51 1.42214e51i −0.889206 0.367081i
\(520\) −4.11750e51 −1.02464
\(521\) 3.23363e50i 0.0775843i −0.999247 0.0387922i \(-0.987649\pi\)
0.999247 0.0387922i \(-0.0123510\pi\)
\(522\) 4.14792e51 + 4.12820e51i 0.959600 + 0.955040i
\(523\) 3.56990e51 0.796386 0.398193 0.917302i \(-0.369637\pi\)
0.398193 + 0.917302i \(0.369637\pi\)
\(524\) 1.03628e52i 2.22938i
\(525\) −1.05721e49 + 2.56096e49i −0.00219349 + 0.00531344i
\(526\) 9.36767e51 1.87457
\(527\) 2.69735e51i 0.520638i
\(528\) −2.16259e52 8.92758e51i −4.02652 1.66222i
\(529\) 9.22374e50 0.165672
\(530\) 6.06983e51i 1.05180i
\(531\) −2.43584e51 + 2.44747e51i −0.407242 + 0.409187i
\(532\) −2.69133e51 −0.434155
\(533\) 1.73954e51i 0.270781i
\(534\) −2.07047e51 + 5.01545e51i −0.311018 + 0.753401i
\(535\) −1.14264e52 −1.65648
\(536\) 1.86379e52i 2.60775i
\(537\) 1.16548e52 + 4.81131e51i 1.57395 + 0.649758i
\(538\) −8.87425e51 −1.15683
\(539\) 1.26915e52i 1.59708i
\(540\) 8.00524e51 + 1.91327e52i 0.972507 + 2.32432i
\(541\) 1.47773e52 1.73319 0.866594 0.499014i \(-0.166304\pi\)
0.866594 + 0.499014i \(0.166304\pi\)
\(542\) 1.15312e52i 1.30583i
\(543\) −3.20073e51 + 7.75335e51i −0.349987 + 0.847799i
\(544\) 2.55288e52 2.69557
\(545\) 6.24051e51i 0.636336i
\(546\) 1.04165e51 + 4.30013e50i 0.102580 + 0.0423469i
\(547\) −1.26863e52 −1.20663 −0.603317 0.797501i \(-0.706155\pi\)
−0.603317 + 0.797501i \(0.706155\pi\)
\(548\) 5.00174e52i 4.59505i
\(549\) −1.19530e52 1.18962e52i −1.06072 1.05568i
\(550\) 1.26072e51 0.108075
\(551\) 9.44958e51i 0.782586i
\(552\) 1.19894e52 2.90428e52i 0.959301 2.32378i
\(553\) −9.60791e49 −0.00742765
\(554\) 3.06539e52i 2.28982i
\(555\) −3.56867e51 1.47321e51i −0.257596 0.106341i
\(556\) −4.13817e50 −0.0288661
\(557\) 2.59652e52i 1.75042i 0.483740 + 0.875212i \(0.339278\pi\)
−0.483740 + 0.875212i \(0.660722\pi\)
\(558\) 8.57163e51 8.61256e51i 0.558488 0.561154i
\(559\) 4.84421e51 0.305069
\(560\) 7.22081e51i 0.439555i
\(561\) −1.30431e52 + 3.15952e52i −0.767515 + 1.85921i
\(562\) −2.18428e51 −0.124256
\(563\) 3.13079e51i 0.172184i 0.996287 + 0.0860922i \(0.0274380\pi\)
−0.996287 + 0.0860922i \(0.972562\pi\)
\(564\) −3.58892e52 1.48157e52i −1.90836 0.787808i
\(565\) −1.72090e51 −0.0884779
\(566\) 1.39621e51i 0.0694127i
\(567\) −1.61202e49 3.38393e51i −0.000774984 0.162683i
\(568\) −4.11405e52 −1.91272
\(569\) 1.09157e52i 0.490816i 0.969420 + 0.245408i \(0.0789218\pi\)
−0.969420 + 0.245408i \(0.921078\pi\)
\(570\) 1.79397e52 4.34566e52i 0.780176 1.88988i
\(571\) 2.15960e52 0.908422 0.454211 0.890894i \(-0.349921\pi\)
0.454211 + 0.890894i \(0.349921\pi\)
\(572\) 3.65273e52i 1.48626i
\(573\) 2.30650e52 + 9.52165e51i 0.907852 + 0.374778i
\(574\) 5.89539e51 0.224485
\(575\) 8.76104e50i 0.0322750i
\(576\) 2.87083e52 + 2.85719e52i 1.02325 + 1.01838i
\(577\) −2.05789e52 −0.709713 −0.354856 0.934921i \(-0.615470\pi\)
−0.354856 + 0.934921i \(0.615470\pi\)
\(578\) 2.81195e52i 0.938378i
\(579\) 1.67102e52 4.04782e52i 0.539620 1.30716i
\(580\) −5.85436e52 −1.82956
\(581\) 3.47829e50i 0.0105201i
\(582\) 8.05891e52 + 3.32687e52i 2.35906 + 0.973866i
\(583\) 3.21011e52 0.909532
\(584\) 4.44894e52i 1.22015i
\(585\) −9.89195e51 + 9.93919e51i −0.262616 + 0.263870i
\(586\) 7.95404e51 0.204424
\(587\) 4.30984e51i 0.107235i −0.998562 0.0536176i \(-0.982925\pi\)
0.998562 0.0536176i \(-0.0170752\pi\)
\(588\) −3.81852e52 + 9.24986e52i −0.919868 + 2.22826i
\(589\) −1.96207e52 −0.457640
\(590\) 4.84937e52i 1.09521i
\(591\) 2.76753e52 + 1.14249e52i 0.605244 + 0.249856i
\(592\) −3.43406e52 −0.727269
\(593\) 4.71208e52i 0.966437i 0.875500 + 0.483218i \(0.160532\pi\)
−0.875500 + 0.483218i \(0.839468\pi\)
\(594\) −1.42050e53 + 5.94343e52i −2.82161 + 1.18058i
\(595\) 1.05495e52 0.202960
\(596\) 1.00855e52i 0.187939i
\(597\) 4.00747e52 9.70756e52i 0.723365 1.75226i
\(598\) 3.56349e52 0.623093
\(599\) 2.00006e52i 0.338793i −0.985548 0.169396i \(-0.945818\pi\)
0.985548 0.169396i \(-0.0541818\pi\)
\(600\) −5.47771e51 2.26130e51i −0.0898928 0.0371095i
\(601\) 5.78120e52 0.919185 0.459592 0.888130i \(-0.347996\pi\)
0.459592 + 0.888130i \(0.347996\pi\)
\(602\) 1.64172e52i 0.252911i
\(603\) −4.49898e52 4.47760e52i −0.671561 0.668369i
\(604\) 9.42315e52 1.36300
\(605\) 1.22771e53i 1.72085i
\(606\) −1.96972e52 + 4.77139e52i −0.267562 + 0.648134i
\(607\) −1.31976e53 −1.73744 −0.868721 0.495301i \(-0.835058\pi\)
−0.868721 + 0.495301i \(0.835058\pi\)
\(608\) 1.85698e53i 2.36940i
\(609\) 8.82932e51 + 3.64491e51i 0.109194 + 0.0450773i
\(610\) 2.36834e53 2.83907
\(611\) 2.62519e52i 0.305055i
\(612\) 1.90122e53 1.91030e53i 2.14169 2.15192i
\(613\) −5.15273e52 −0.562715 −0.281357 0.959603i \(-0.590785\pi\)
−0.281357 + 0.959603i \(0.590785\pi\)
\(614\) 1.18755e53i 1.25734i
\(615\) −2.79926e52 + 6.78083e52i −0.287353 + 0.696075i
\(616\) −7.37998e52 −0.734550
\(617\) 1.13864e53i 1.09893i −0.835517 0.549465i \(-0.814832\pi\)
0.835517 0.549465i \(-0.185168\pi\)
\(618\) −2.80887e53 1.15955e53i −2.62875 1.08520i
\(619\) −6.36249e52 −0.577437 −0.288718 0.957414i \(-0.593229\pi\)
−0.288718 + 0.957414i \(0.593229\pi\)
\(620\) 1.21557e53i 1.06989i
\(621\) −4.13024e52 9.87139e52i −0.352562 0.842632i
\(622\) −2.45840e53 −2.03534
\(623\) 8.85658e51i 0.0711202i
\(624\) −4.75941e52 + 1.15290e53i −0.370720 + 0.898020i
\(625\) −1.36860e53 −1.03409
\(626\) 3.76056e53i 2.75638i
\(627\) 2.29826e53 + 9.48765e52i 1.63424 + 0.674645i
\(628\) 5.06451e53 3.49385
\(629\) 5.01713e52i 0.335809i
\(630\) 3.36844e52 + 3.35243e52i 0.218755 + 0.217715i
\(631\) −1.55428e53 −0.979427 −0.489713 0.871883i \(-0.662899\pi\)
−0.489713 + 0.871883i \(0.662899\pi\)
\(632\) 2.05506e52i 0.125661i
\(633\) 3.19940e52 7.75012e52i 0.189844 0.459873i
\(634\) 5.81256e53 3.34712
\(635\) 6.38647e52i 0.356911i
\(636\) −2.33961e53 9.65834e52i −1.26899 0.523862i
\(637\) −6.76600e52 −0.356191
\(638\) 4.34652e53i 2.22100i
\(639\) −9.88365e52 + 9.93085e52i −0.490232 + 0.492572i
\(640\) −1.04212e53 −0.501762
\(641\) 3.62328e53i 1.69356i −0.531947 0.846778i \(-0.678539\pi\)
0.531947 0.846778i \(-0.321461\pi\)
\(642\) −2.55242e53 + 6.18291e53i −1.15821 + 2.80561i
\(643\) 4.40218e53 1.93937 0.969683 0.244367i \(-0.0785801\pi\)
0.969683 + 0.244367i \(0.0785801\pi\)
\(644\) 8.60268e52i 0.367962i
\(645\) 1.88830e53 + 7.79525e52i 0.784217 + 0.323739i
\(646\) −6.10948e53 −2.46369
\(647\) 3.53960e53i 1.38603i 0.720923 + 0.693015i \(0.243718\pi\)
−0.720923 + 0.693015i \(0.756282\pi\)
\(648\) 7.23799e53 3.44800e51i 2.75228 0.0131112i
\(649\) 2.56466e53 0.947066
\(650\) 6.72104e51i 0.0241036i
\(651\) 7.56814e51 1.83328e52i 0.0263603 0.0638543i
\(652\) −1.19819e54 −4.05343
\(653\) 4.16045e53i 1.36707i −0.729919 0.683534i \(-0.760442\pi\)
0.729919 0.683534i \(-0.239558\pi\)
\(654\) −3.37680e53 1.39401e53i −1.07777 0.444926i
\(655\) −2.95476e53 −0.916090
\(656\) 6.52505e53i 1.96522i
\(657\) 1.07392e53 + 1.06882e53i 0.314218 + 0.312725i
\(658\) −8.89689e52 −0.252898
\(659\) 1.42734e53i 0.394189i −0.980384 0.197095i \(-0.936849\pi\)
0.980384 0.197095i \(-0.0631506\pi\)
\(660\) 5.87794e53 1.42385e54i 1.57721 3.82059i
\(661\) 7.90981e51 0.0206224 0.0103112 0.999947i \(-0.496718\pi\)
0.0103112 + 0.999947i \(0.496718\pi\)
\(662\) 5.75796e53i 1.45870i
\(663\) 1.68438e53 + 6.95346e52i 0.414652 + 0.171176i
\(664\) −7.43981e52 −0.177979
\(665\) 7.67381e52i 0.178402i
\(666\) −1.59434e53 + 1.60195e53i −0.360222 + 0.361942i
\(667\) 3.02051e53 0.663269
\(668\) 7.98601e53i 1.70442i
\(669\) −2.43104e53 + 5.88888e53i −0.504308 + 1.22162i
\(670\) 8.91420e53 1.79747
\(671\) 1.25253e54i 2.45505i
\(672\) 1.73509e53 + 7.16277e52i 0.330602 + 0.136479i
\(673\) −3.96213e53 −0.733910 −0.366955 0.930239i \(-0.619600\pi\)
−0.366955 + 0.930239i \(0.619600\pi\)
\(674\) 1.50568e54i 2.71141i
\(675\) −1.86183e52 + 7.78998e51i −0.0325962 + 0.0136384i
\(676\) 1.25997e54 2.14473
\(677\) 4.33082e53i 0.716779i −0.933572 0.358390i \(-0.883326\pi\)
0.933572 0.358390i \(-0.116674\pi\)
\(678\) −3.84415e52 + 9.31195e52i −0.0618637 + 0.149857i
\(679\) 1.42309e53 0.222693
\(680\) 2.25647e54i 3.43369i
\(681\) −2.71372e53 1.12028e53i −0.401579 0.165779i
\(682\) −9.02493e53 −1.29880
\(683\) 2.18362e53i 0.305621i 0.988255 + 0.152811i \(0.0488325\pi\)
−0.988255 + 0.152811i \(0.951168\pi\)
\(684\) −1.38957e54 1.38296e54i −1.89153 1.88254i
\(685\) −1.42615e54 −1.88819
\(686\) 4.64840e53i 0.598612i
\(687\) −3.07300e52 + 7.44394e52i −0.0384932 + 0.0932448i
\(688\) 1.81707e54 2.21407
\(689\) 1.71135e53i 0.202850i
\(690\) 1.38907e54 + 5.73433e53i 1.60173 + 0.661226i
\(691\) −8.19021e52 −0.0918782 −0.0459391 0.998944i \(-0.514628\pi\)
−0.0459391 + 0.998944i \(0.514628\pi\)
\(692\) 2.18260e54i 2.38209i
\(693\) −1.77298e53 + 1.78144e53i −0.188266 + 0.189165i
\(694\) −1.32363e54 −1.36753
\(695\) 1.17992e52i 0.0118616i
\(696\) −7.79620e53 + 1.88853e54i −0.762619 + 1.84735i
\(697\) 9.53304e53 0.907421
\(698\) 2.74847e53i 0.254588i
\(699\) 5.05076e53 + 2.08505e53i 0.455293 + 0.187953i
\(700\) −1.62254e52 −0.0142342
\(701\) 1.27469e54i 1.08834i −0.838976 0.544169i \(-0.816845\pi\)
0.838976 0.544169i \(-0.183155\pi\)
\(702\) 3.16852e53 + 7.57285e53i 0.263300 + 0.629295i
\(703\) 3.64949e53 0.295176
\(704\) 3.00829e54i 2.36831i
\(705\) 4.22443e53 1.02331e54i 0.323724 0.784179i
\(706\) 1.00833e53 0.0752168
\(707\) 8.42559e52i 0.0611831i
\(708\) −1.86918e54 7.71634e53i −1.32136 0.545481i
\(709\) 2.05256e54 1.41260 0.706298 0.707914i \(-0.250364\pi\)
0.706298 + 0.707914i \(0.250364\pi\)
\(710\) 1.96768e54i 1.31840i
\(711\) −4.96069e52 4.93712e52i −0.0323609 0.0322071i
\(712\) −1.89436e54 −1.20321
\(713\) 6.27166e53i 0.387866i
\(714\) 2.35656e53 5.70845e53i 0.141910 0.343758i
\(715\) 1.04151e54 0.610728
\(716\) 7.38407e54i 4.21647i
\(717\) −2.99898e54 1.23804e54i −1.66767 0.688445i
\(718\) 4.29468e54 2.32577
\(719\) 1.72629e54i 0.910469i 0.890371 + 0.455235i \(0.150445\pi\)
−0.890371 + 0.455235i \(0.849555\pi\)
\(720\) −3.71048e54 + 3.72820e54i −1.90596 + 1.91506i
\(721\) −4.96005e53 −0.248151
\(722\) 6.17951e53i 0.301125i
\(723\) 2.83913e53 6.87742e53i 0.134759 0.326436i
\(724\) −4.91227e54 −2.27117
\(725\) 5.69693e52i 0.0256578i
\(726\) 6.64325e54 + 2.74246e54i 2.91464 + 1.20322i
\(727\) −1.24366e53 −0.0531555 −0.0265778 0.999647i \(-0.508461\pi\)
−0.0265778 + 0.999647i \(0.508461\pi\)
\(728\) 3.93436e53i 0.163824i
\(729\) 1.73054e54 1.75545e54i 0.702036 0.712141i
\(730\) −2.12785e54 −0.841022
\(731\) 2.65472e54i 1.02233i
\(732\) 3.76851e54 9.12871e54i 1.41403 3.42530i
\(733\) −4.38973e54 −1.60495 −0.802476 0.596685i \(-0.796484\pi\)
−0.802476 + 0.596685i \(0.796484\pi\)
\(734\) 2.83257e54i 1.00915i
\(735\) −2.63742e54 1.08878e54i −0.915631 0.377990i
\(736\) 5.93574e54 2.00815
\(737\) 4.71440e54i 1.55433i
\(738\) 3.04387e54 + 3.02941e54i 0.978038 + 0.973390i
\(739\) 4.48590e54 1.40477 0.702384 0.711798i \(-0.252119\pi\)
0.702384 + 0.711798i \(0.252119\pi\)
\(740\) 2.26099e54i 0.690075i
\(741\) 5.05799e53 1.22523e54i 0.150464 0.364479i
\(742\) −5.79986e53 −0.168168
\(743\) 3.32855e54i 0.940736i 0.882470 + 0.470368i \(0.155879\pi\)
−0.882470 + 0.470368i \(0.844121\pi\)
\(744\) 3.92126e54 + 1.61877e54i 1.08029 + 0.445964i
\(745\) 2.87569e53 0.0772275
\(746\) 9.73252e54i 2.54793i
\(747\) −1.78735e53 + 1.79589e53i −0.0456162 + 0.0458340i
\(748\) −2.00177e55 −4.98063
\(749\) 1.09181e54i 0.264846i
\(750\) −2.95272e54 + 7.15258e54i −0.698326 + 1.69160i
\(751\) −1.83280e54 −0.422627 −0.211313 0.977418i \(-0.567774\pi\)
−0.211313 + 0.977418i \(0.567774\pi\)
\(752\) 9.84712e54i 2.21396i
\(753\) −6.92135e54 2.85727e54i −1.51735 0.626392i
\(754\) −2.31719e54 −0.495343
\(755\) 2.68683e54i 0.560078i
\(756\) 1.82817e54 7.64918e53i 0.371624 0.155489i
\(757\) 7.97431e54 1.58078 0.790390 0.612604i \(-0.209878\pi\)
0.790390 + 0.612604i \(0.209878\pi\)
\(