Properties

Label 3.39.b.a.2.3
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 2.3
Root \(-54008.5i\) of defining polynomial
Character \(\chi\) \(=\) 3.2
Dual form 3.39.b.a.2.10

$q$-expansion

\(f(q)\) \(=\) \(q-648102. i q^{2} +(-9.89523e8 + 6.09669e8i) q^{3} -1.45158e11 q^{4} -1.81665e13i q^{5} +(3.95128e14 + 6.41312e14i) q^{6} -1.77541e16 q^{7} -8.40715e16i q^{8} +(6.07458e17 - 1.20656e18i) q^{9} +O(q^{10})\) \(q-648102. i q^{2} +(-9.89523e8 + 6.09669e8i) q^{3} -1.45158e11 q^{4} -1.81665e13i q^{5} +(3.95128e14 + 6.41312e14i) q^{6} -1.77541e16 q^{7} -8.40715e16i q^{8} +(6.07458e17 - 1.20656e18i) q^{9} -1.17737e19 q^{10} -1.89593e19i q^{11} +(1.43638e20 - 8.84987e19i) q^{12} -1.72547e21 q^{13} +1.15065e22i q^{14} +(1.10756e22 + 1.79762e22i) q^{15} -9.43877e22 q^{16} +2.70625e23i q^{17} +(-7.81976e23 - 3.93695e23i) q^{18} +1.47413e24 q^{19} +2.63702e24i q^{20} +(1.75681e25 - 1.08241e25i) q^{21} -1.22876e25 q^{22} -7.60174e25i q^{23} +(5.12558e25 + 8.31906e25i) q^{24} +3.37762e25 q^{25} +1.11828e27i q^{26} +(1.34511e26 + 1.56427e27i) q^{27} +2.57716e27 q^{28} -5.84738e26i q^{29} +(1.16504e28 - 7.17809e27i) q^{30} +3.31299e28 q^{31} +3.80635e28i q^{32} +(1.15589e28 + 1.87607e28i) q^{33} +1.75393e29 q^{34} +3.22530e29i q^{35} +(-8.81777e28 + 1.75143e29i) q^{36} -2.91996e29 q^{37} -9.55389e29i q^{38} +(1.70739e30 - 1.05197e30i) q^{39} -1.52728e30 q^{40} +3.49689e30i q^{41} +(-7.01514e30 - 1.13859e31i) q^{42} -3.83235e30 q^{43} +2.75210e30i q^{44} +(-2.19190e31 - 1.10354e31i) q^{45} -4.92670e31 q^{46} +8.27513e31i q^{47} +(9.33988e31 - 5.75453e31i) q^{48} +1.85273e32 q^{49} -2.18904e31i q^{50} +(-1.64992e32 - 2.67790e32i) q^{51} +2.50467e32 q^{52} +1.02088e33i q^{53} +(1.01381e33 - 8.71771e31i) q^{54} -3.44424e32 q^{55} +1.49261e33i q^{56} +(-1.45869e33 + 8.98734e32i) q^{57} -3.78970e32 q^{58} -7.44815e33i q^{59} +(-1.60771e33 - 2.60939e33i) q^{60} -1.73391e33 q^{61} -2.14716e34i q^{62} +(-1.07849e34 + 2.14214e34i) q^{63} -1.27607e33 q^{64} +3.13458e34i q^{65} +(1.21588e34 - 7.49136e33i) q^{66} -4.97460e34 q^{67} -3.92835e34i q^{68} +(4.63455e34 + 7.52209e34i) q^{69} +2.09032e35 q^{70} -2.73051e34i q^{71} +(-1.01438e35 - 5.10699e34i) q^{72} +2.76394e35 q^{73} +1.89243e35i q^{74} +(-3.34223e34 + 2.05923e34i) q^{75} -2.13983e35 q^{76} +3.36605e35i q^{77} +(-6.81783e35 - 1.10657e36i) q^{78} -1.24191e36 q^{79} +1.71469e36i q^{80} +(-1.08679e36 - 1.46587e36i) q^{81} +2.26634e36 q^{82} -4.54609e36i q^{83} +(-2.55015e36 + 1.57121e36i) q^{84} +4.91631e36 q^{85} +2.48376e36i q^{86} +(3.56497e35 + 5.78611e35i) q^{87} -1.59394e36 q^{88} -1.42170e36i q^{89} +(-7.15206e36 + 1.42058e37i) q^{90} +3.06342e37 q^{91} +1.10346e37i q^{92} +(-3.27828e37 + 2.01983e37i) q^{93} +5.36313e37 q^{94} -2.67798e37i q^{95} +(-2.32062e37 - 3.76647e37i) q^{96} -3.92918e37 q^{97} -1.20076e38i q^{98} +(-2.28756e37 - 1.15170e37i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 648102.i 1.23616i −0.786117 0.618078i \(-0.787911\pi\)
0.786117 0.618078i \(-0.212089\pi\)
\(3\) −9.89523e8 + 6.09669e8i −0.851377 + 0.524554i
\(4\) −1.45158e11 −0.528083
\(5\) 1.81665e13i 0.952448i −0.879324 0.476224i \(-0.842005\pi\)
0.879324 0.476224i \(-0.157995\pi\)
\(6\) 3.95128e14 + 6.41312e14i 0.648432 + 1.05244i
\(7\) −1.77541e16 −1.55753 −0.778764 0.627317i \(-0.784153\pi\)
−0.778764 + 0.627317i \(0.784153\pi\)
\(8\) 8.40715e16i 0.583363i
\(9\) 6.07458e17 1.20656e18i 0.449685 0.893187i
\(10\) −1.17737e19 −1.17737
\(11\) 1.89593e19i 0.310000i −0.987914 0.155000i \(-0.950462\pi\)
0.987914 0.155000i \(-0.0495377\pi\)
\(12\) 1.43638e20 8.84987e19i 0.449598 0.277008i
\(13\) −1.72547e21 −1.18028 −0.590139 0.807302i \(-0.700927\pi\)
−0.590139 + 0.807302i \(0.700927\pi\)
\(14\) 1.15065e22i 1.92535i
\(15\) 1.10756e22 + 1.79762e22i 0.499611 + 0.810892i
\(16\) −9.43877e22 −1.24921
\(17\) 2.70625e23i 1.13198i 0.824412 + 0.565990i \(0.191506\pi\)
−0.824412 + 0.565990i \(0.808494\pi\)
\(18\) −7.81976e23 3.93695e23i −1.10412 0.555881i
\(19\) 1.47413e24 0.745107 0.372553 0.928011i \(-0.378482\pi\)
0.372553 + 0.928011i \(0.378482\pi\)
\(20\) 2.63702e24i 0.502972i
\(21\) 1.75681e25 1.08241e25i 1.32604 0.817008i
\(22\) −1.22876e25 −0.383208
\(23\) 7.60174e25i 1.01879i −0.860533 0.509394i \(-0.829870\pi\)
0.860533 0.509394i \(-0.170130\pi\)
\(24\) 5.12558e25 + 8.31906e25i 0.306006 + 0.496662i
\(25\) 3.37762e25 0.0928433
\(26\) 1.11828e27i 1.45901i
\(27\) 1.34511e26 + 1.56427e27i 0.0856737 + 0.996323i
\(28\) 2.57716e27 0.822504
\(29\) 5.84738e26i 0.0958074i −0.998852 0.0479037i \(-0.984746\pi\)
0.998852 0.0479037i \(-0.0152541\pi\)
\(30\) 1.16504e28 7.17809e27i 1.00239 0.617597i
\(31\) 3.31299e28 1.52879 0.764395 0.644748i \(-0.223038\pi\)
0.764395 + 0.644748i \(0.223038\pi\)
\(32\) 3.80635e28i 0.960858i
\(33\) 1.15589e28 + 1.87607e28i 0.162612 + 0.263927i
\(34\) 1.75393e29 1.39930
\(35\) 3.22530e29i 1.48346i
\(36\) −8.81777e28 + 1.75143e29i −0.237471 + 0.471677i
\(37\) −2.91996e29 −0.467244 −0.233622 0.972327i \(-0.575058\pi\)
−0.233622 + 0.972327i \(0.575058\pi\)
\(38\) 9.55389e29i 0.921068i
\(39\) 1.70739e30 1.05197e30i 1.00486 0.619120i
\(40\) −1.52728e30 −0.555623
\(41\) 3.49689e30i 0.795772i 0.917435 + 0.397886i \(0.130256\pi\)
−0.917435 + 0.397886i \(0.869744\pi\)
\(42\) −7.01514e30 1.13859e31i −1.00995 1.63920i
\(43\) −3.83235e30 −0.352829 −0.176415 0.984316i \(-0.556450\pi\)
−0.176415 + 0.984316i \(0.556450\pi\)
\(44\) 2.75210e30i 0.163706i
\(45\) −2.19190e31 1.10354e31i −0.850714 0.428302i
\(46\) −4.92670e31 −1.25938
\(47\) 8.27513e31i 1.40577i 0.711301 + 0.702887i \(0.248106\pi\)
−0.711301 + 0.702887i \(0.751894\pi\)
\(48\) 9.33988e31 5.75453e31i 1.06355 0.655279i
\(49\) 1.85273e32 1.42589
\(50\) 2.18904e31i 0.114769i
\(51\) −1.64992e32 2.67790e32i −0.593785 0.963742i
\(52\) 2.50467e32 0.623285
\(53\) 1.02088e33i 1.76902i 0.466519 + 0.884511i \(0.345508\pi\)
−0.466519 + 0.884511i \(0.654492\pi\)
\(54\) 1.01381e33 8.71771e31i 1.23161 0.105906i
\(55\) −3.44424e32 −0.295259
\(56\) 1.49261e33i 0.908604i
\(57\) −1.45869e33 + 8.98734e32i −0.634367 + 0.390849i
\(58\) −3.78970e32 −0.118433
\(59\) 7.44815e33i 1.68213i −0.540932 0.841066i \(-0.681929\pi\)
0.540932 0.841066i \(-0.318071\pi\)
\(60\) −1.60771e33 2.60939e33i −0.263836 0.428219i
\(61\) −1.73391e33 −0.207855 −0.103928 0.994585i \(-0.533141\pi\)
−0.103928 + 0.994585i \(0.533141\pi\)
\(62\) 2.14716e34i 1.88983i
\(63\) −1.07849e34 + 2.14214e34i −0.700397 + 1.39116i
\(64\) −1.27607e33 −0.0614403
\(65\) 3.13458e34i 1.12415i
\(66\) 1.21588e34 7.49136e33i 0.326255 0.201014i
\(67\) −4.97460e34 −1.00308 −0.501541 0.865134i \(-0.667233\pi\)
−0.501541 + 0.865134i \(0.667233\pi\)
\(68\) 3.92835e34i 0.597780i
\(69\) 4.63455e34 + 7.52209e34i 0.534410 + 0.867373i
\(70\) 2.09032e35 1.83379
\(71\) 2.73051e34i 0.182951i −0.995807 0.0914757i \(-0.970842\pi\)
0.995807 0.0914757i \(-0.0291584\pi\)
\(72\) −1.01438e35 5.10699e34i −0.521052 0.262330i
\(73\) 2.76394e35 1.09243 0.546216 0.837644i \(-0.316068\pi\)
0.546216 + 0.837644i \(0.316068\pi\)
\(74\) 1.89243e35i 0.577587i
\(75\) −3.34223e34 + 2.05923e34i −0.0790447 + 0.0487014i
\(76\) −2.13983e35 −0.393478
\(77\) 3.36605e35i 0.482833i
\(78\) −6.81783e35 1.10657e36i −0.765329 1.24217i
\(79\) −1.24191e36 −1.09440 −0.547200 0.837002i \(-0.684306\pi\)
−0.547200 + 0.837002i \(0.684306\pi\)
\(80\) 1.71469e36i 1.18981i
\(81\) −1.08679e36 1.46587e36i −0.595566 0.803306i
\(82\) 2.26634e36 0.983699
\(83\) 4.54609e36i 1.56731i −0.621198 0.783654i \(-0.713354\pi\)
0.621198 0.783654i \(-0.286646\pi\)
\(84\) −2.55015e36 + 1.57121e36i −0.700261 + 0.431448i
\(85\) 4.91631e36 1.07815
\(86\) 2.48376e36i 0.436152i
\(87\) 3.56497e35 + 5.78611e35i 0.0502562 + 0.0815682i
\(88\) −1.59394e36 −0.180842
\(89\) 1.42170e36i 0.130136i −0.997881 0.0650681i \(-0.979274\pi\)
0.997881 0.0650681i \(-0.0207264\pi\)
\(90\) −7.15206e36 + 1.42058e37i −0.529448 + 1.05162i
\(91\) 3.06342e37 1.83832
\(92\) 1.10346e37i 0.538005i
\(93\) −3.27828e37 + 2.01983e37i −1.30158 + 0.801934i
\(94\) 5.36313e37 1.73776
\(95\) 2.67798e37i 0.709675i
\(96\) −2.32062e37 3.76647e37i −0.504022 0.818052i
\(97\) −3.92918e37 −0.700873 −0.350436 0.936587i \(-0.613967\pi\)
−0.350436 + 0.936587i \(0.613967\pi\)
\(98\) 1.20076e38i 1.76263i
\(99\) −2.28756e37 1.15170e37i −0.276888 0.139402i
\(100\) −4.90290e36 −0.0490290
\(101\) 1.48887e38i 1.23240i 0.787591 + 0.616199i \(0.211328\pi\)
−0.787591 + 0.616199i \(0.788672\pi\)
\(102\) −1.73555e38 + 1.06932e38i −1.19134 + 0.734012i
\(103\) −2.17514e37 −0.124045 −0.0620226 0.998075i \(-0.519755\pi\)
−0.0620226 + 0.998075i \(0.519755\pi\)
\(104\) 1.45063e38i 0.688530i
\(105\) −1.96637e38 3.19150e38i −0.778158 1.26299i
\(106\) 6.61635e38 2.18679
\(107\) 1.19319e38i 0.329926i 0.986300 + 0.164963i \(0.0527504\pi\)
−0.986300 + 0.164963i \(0.947250\pi\)
\(108\) −1.95255e37 2.27067e38i −0.0452428 0.526142i
\(109\) −2.95320e38 −0.574366 −0.287183 0.957876i \(-0.592719\pi\)
−0.287183 + 0.957876i \(0.592719\pi\)
\(110\) 2.23222e38i 0.364986i
\(111\) 2.88936e38 1.78021e38i 0.397801 0.245095i
\(112\) 1.67577e39 1.94568
\(113\) 1.63304e38i 0.160143i 0.996789 + 0.0800713i \(0.0255148\pi\)
−0.996789 + 0.0800713i \(0.974485\pi\)
\(114\) 5.82472e38 + 9.45379e38i 0.483151 + 0.784176i
\(115\) −1.38097e39 −0.970342
\(116\) 8.48796e37i 0.0505943i
\(117\) −1.04815e39 + 2.08189e39i −0.530754 + 1.05421i
\(118\) −4.82716e39 −2.07938
\(119\) 4.80471e39i 1.76309i
\(120\) 1.51128e39 9.31138e38i 0.473044 0.291454i
\(121\) 3.38098e39 0.903900
\(122\) 1.12375e39i 0.256941i
\(123\) −2.13195e39 3.46025e39i −0.417426 0.677502i
\(124\) −4.80909e39 −0.807329
\(125\) 7.22253e39i 1.04088i
\(126\) 1.38833e40 + 6.98970e39i 1.71970 + 0.865801i
\(127\) −1.46772e40 −1.56449 −0.782244 0.622972i \(-0.785925\pi\)
−0.782244 + 0.622972i \(0.785925\pi\)
\(128\) 1.12898e40i 1.03681i
\(129\) 3.79220e39 2.33647e39i 0.300391 0.185078i
\(130\) 2.03153e40 1.38963
\(131\) 4.11410e39i 0.243288i 0.992574 + 0.121644i \(0.0388166\pi\)
−0.992574 + 0.121644i \(0.961183\pi\)
\(132\) −1.67787e39 2.72327e39i −0.0858726 0.139375i
\(133\) −2.61719e40 −1.16052
\(134\) 3.22405e40i 1.23997i
\(135\) 2.84173e40 2.44360e39i 0.948946 0.0815997i
\(136\) 2.27519e40 0.660355
\(137\) 5.35814e39i 0.135308i 0.997709 + 0.0676540i \(0.0215514\pi\)
−0.997709 + 0.0676540i \(0.978449\pi\)
\(138\) 4.87508e40 3.00366e40i 1.07221 0.660614i
\(139\) −5.82409e40 −1.11673 −0.558364 0.829596i \(-0.688571\pi\)
−0.558364 + 0.829596i \(0.688571\pi\)
\(140\) 4.68179e40i 0.783392i
\(141\) −5.04509e40 8.18843e40i −0.737405 1.19684i
\(142\) −1.76965e40 −0.226156
\(143\) 3.27138e40i 0.365886i
\(144\) −5.73366e40 + 1.13885e41i −0.561752 + 1.11578i
\(145\) −1.06226e40 −0.0912515
\(146\) 1.79132e41i 1.35042i
\(147\) −1.83332e41 + 1.12955e41i −1.21397 + 0.747958i
\(148\) 4.23857e40 0.246744
\(149\) 1.49060e41i 0.763522i 0.924261 + 0.381761i \(0.124682\pi\)
−0.924261 + 0.381761i \(0.875318\pi\)
\(150\) 1.33459e40 + 2.16611e40i 0.0602025 + 0.0977116i
\(151\) 2.41693e41 0.960954 0.480477 0.877007i \(-0.340464\pi\)
0.480477 + 0.877007i \(0.340464\pi\)
\(152\) 1.23933e41i 0.434668i
\(153\) 3.26527e41 + 1.64393e41i 1.01107 + 0.509035i
\(154\) 2.18155e41 0.596858
\(155\) 6.01855e41i 1.45609i
\(156\) −2.47843e41 + 1.52702e41i −0.530651 + 0.326947i
\(157\) 3.44795e41 0.653833 0.326917 0.945053i \(-0.393990\pi\)
0.326917 + 0.945053i \(0.393990\pi\)
\(158\) 8.04886e41i 1.35285i
\(159\) −6.22400e41 1.01018e42i −0.927949 1.50610i
\(160\) 6.91481e41 0.915167
\(161\) 1.34962e42i 1.58679i
\(162\) −9.50036e41 + 7.04351e41i −0.993012 + 0.736213i
\(163\) 6.29354e41 0.585235 0.292618 0.956230i \(-0.405474\pi\)
0.292618 + 0.956230i \(0.405474\pi\)
\(164\) 5.07603e41i 0.420234i
\(165\) 3.40816e41 2.09985e41i 0.251376 0.154879i
\(166\) −2.94633e42 −1.93744
\(167\) 5.94985e41i 0.349055i −0.984652 0.174527i \(-0.944160\pi\)
0.984652 0.174527i \(-0.0558397\pi\)
\(168\) −9.10000e41 1.47697e42i −0.476612 0.773564i
\(169\) 8.40044e41 0.393056
\(170\) 3.18627e42i 1.33276i
\(171\) 8.95474e41 1.77864e42i 0.335063 0.665520i
\(172\) 5.56298e41 0.186323
\(173\) 3.53109e42i 1.05933i 0.848206 + 0.529667i \(0.177683\pi\)
−0.848206 + 0.529667i \(0.822317\pi\)
\(174\) 3.74999e41 2.31046e41i 0.100831 0.0621245i
\(175\) −5.99666e41 −0.144606
\(176\) 1.78953e42i 0.387255i
\(177\) 4.54091e42 + 7.37011e42i 0.882370 + 1.43213i
\(178\) −9.21407e41 −0.160869
\(179\) 6.72765e42i 1.05598i 0.849250 + 0.527990i \(0.177054\pi\)
−0.849250 + 0.527990i \(0.822946\pi\)
\(180\) 3.18173e42 + 1.60188e42i 0.449248 + 0.226179i
\(181\) −1.74934e42 −0.222322 −0.111161 0.993802i \(-0.535457\pi\)
−0.111161 + 0.993802i \(0.535457\pi\)
\(182\) 1.98541e43i 2.27245i
\(183\) 1.71575e42 1.05711e42i 0.176963 0.109031i
\(184\) −6.39089e42 −0.594323
\(185\) 5.30454e42i 0.445026i
\(186\) 1.30906e43 + 2.12466e43i 0.991316 + 1.60895i
\(187\) 5.13087e42 0.350914
\(188\) 1.20121e43i 0.742366i
\(189\) −2.38813e42 2.77722e43i −0.133439 1.55180i
\(190\) −1.73561e43 −0.877270
\(191\) 1.98913e42i 0.0909974i −0.998964 0.0454987i \(-0.985512\pi\)
0.998964 0.0454987i \(-0.0144877\pi\)
\(192\) 1.26270e42 7.77978e41i 0.0523089 0.0322288i
\(193\) −1.36164e43 −0.511062 −0.255531 0.966801i \(-0.582250\pi\)
−0.255531 + 0.966801i \(0.582250\pi\)
\(194\) 2.54651e43i 0.866388i
\(195\) −1.91106e43 3.10174e43i −0.589680 0.957078i
\(196\) −2.68940e43 −0.752990
\(197\) 3.03925e43i 0.772516i 0.922391 + 0.386258i \(0.126233\pi\)
−0.922391 + 0.386258i \(0.873767\pi\)
\(198\) −7.46418e42 + 1.48257e43i −0.172323 + 0.342277i
\(199\) −2.53440e43 −0.531699 −0.265850 0.964015i \(-0.585652\pi\)
−0.265850 + 0.964015i \(0.585652\pi\)
\(200\) 2.83962e42i 0.0541614i
\(201\) 4.92248e43 3.03286e43i 0.854001 0.526171i
\(202\) 9.64940e43 1.52344
\(203\) 1.03815e43i 0.149223i
\(204\) 2.39500e43 + 3.88719e43i 0.313568 + 0.508936i
\(205\) 6.35263e43 0.757931
\(206\) 1.40971e43i 0.153339i
\(207\) −9.17198e43 4.61774e43i −0.909968 0.458134i
\(208\) 1.62863e44 1.47442
\(209\) 2.79486e43i 0.230983i
\(210\) −2.06842e44 + 1.27441e44i −1.56125 + 0.961925i
\(211\) 4.43284e43 0.305714 0.152857 0.988248i \(-0.451153\pi\)
0.152857 + 0.988248i \(0.451153\pi\)
\(212\) 1.48189e44i 0.934191i
\(213\) 1.66471e43 + 2.70190e43i 0.0959679 + 0.155761i
\(214\) 7.73306e43 0.407840
\(215\) 6.96204e43i 0.336051i
\(216\) 1.31510e44 1.13086e43i 0.581218 0.0499789i
\(217\) −5.88192e44 −2.38113
\(218\) 1.91397e44i 0.710006i
\(219\) −2.73498e44 + 1.68509e44i −0.930072 + 0.573040i
\(220\) 4.99961e43 0.155921
\(221\) 4.66956e44i 1.33605i
\(222\) −1.15376e44 1.87260e44i −0.302976 0.491744i
\(223\) 6.60825e44 1.59329 0.796644 0.604449i \(-0.206607\pi\)
0.796644 + 0.604449i \(0.206607\pi\)
\(224\) 6.75783e44i 1.49656i
\(225\) 2.05176e43 4.07531e43i 0.0417503 0.0829265i
\(226\) 1.05838e44 0.197961
\(227\) 4.58767e44i 0.789044i 0.918886 + 0.394522i \(0.129090\pi\)
−0.918886 + 0.394522i \(0.870910\pi\)
\(228\) 2.11741e44 1.30459e44i 0.334998 0.206401i
\(229\) −6.65426e44 −0.968781 −0.484391 0.874852i \(-0.660959\pi\)
−0.484391 + 0.874852i \(0.660959\pi\)
\(230\) 8.95009e44i 1.19950i
\(231\) −2.05218e44 3.33079e44i −0.253272 0.411073i
\(232\) −4.91597e43 −0.0558905
\(233\) 1.11955e45i 1.17295i 0.809966 + 0.586477i \(0.199486\pi\)
−0.809966 + 0.586477i \(0.800514\pi\)
\(234\) 1.34928e45 + 6.79310e44i 1.30317 + 0.656095i
\(235\) 1.50330e45 1.33893
\(236\) 1.08116e45i 0.888306i
\(237\) 1.22890e45 7.57156e44i 0.931747 0.574073i
\(238\) −3.11394e45 −2.17946
\(239\) 8.12433e43i 0.0525082i 0.999655 + 0.0262541i \(0.00835790\pi\)
−0.999655 + 0.0262541i \(0.991642\pi\)
\(240\) −1.04540e45 1.69673e45i −0.624119 1.01298i
\(241\) 3.65619e44 0.201700 0.100850 0.994902i \(-0.467844\pi\)
0.100850 + 0.994902i \(0.467844\pi\)
\(242\) 2.19122e45i 1.11736i
\(243\) 1.96910e45 + 7.87932e44i 0.928429 + 0.371509i
\(244\) 2.51692e44 0.109765
\(245\) 3.36576e45i 1.35809i
\(246\) −2.24260e45 + 1.38172e45i −0.837499 + 0.516004i
\(247\) −2.54358e45 −0.879433
\(248\) 2.78528e45i 0.891840i
\(249\) 2.77161e45 + 4.49846e45i 0.822138 + 1.33437i
\(250\) −4.68094e45 −1.28669
\(251\) 4.82587e44i 0.122963i 0.998108 + 0.0614816i \(0.0195826\pi\)
−0.998108 + 0.0614816i \(0.980417\pi\)
\(252\) 1.56551e45 3.10950e45i 0.369868 0.734650i
\(253\) −1.44124e45 −0.315824
\(254\) 9.51232e45i 1.93395i
\(255\) −4.86480e45 + 2.99733e45i −0.917914 + 0.565549i
\(256\) 6.96621e45 1.22022
\(257\) 5.66705e45i 0.921782i −0.887457 0.460891i \(-0.847530\pi\)
0.887457 0.460891i \(-0.152470\pi\)
\(258\) −1.51427e45 2.45773e45i −0.228786 0.371330i
\(259\) 5.18412e45 0.727746
\(260\) 4.55011e45i 0.593647i
\(261\) −7.05523e44 3.55204e44i −0.0855739 0.0430832i
\(262\) 2.66636e45 0.300742
\(263\) 8.90384e44i 0.0934154i −0.998909 0.0467077i \(-0.985127\pi\)
0.998909 0.0467077i \(-0.0148729\pi\)
\(264\) 1.57724e45 9.71775e44i 0.153965 0.0948617i
\(265\) 1.85458e46 1.68490
\(266\) 1.69621e46i 1.43459i
\(267\) 8.66767e44 + 1.40680e45i 0.0682635 + 0.110795i
\(268\) 7.22105e45 0.529711
\(269\) 1.57961e46i 1.07958i 0.841799 + 0.539791i \(0.181497\pi\)
−0.841799 + 0.539791i \(0.818503\pi\)
\(270\) −1.58370e45 1.84173e46i −0.100870 1.17305i
\(271\) −2.70873e46 −1.60823 −0.804117 0.594471i \(-0.797361\pi\)
−0.804117 + 0.594471i \(0.797361\pi\)
\(272\) 2.55437e46i 1.41408i
\(273\) −3.03132e46 + 1.86767e46i −1.56510 + 0.964297i
\(274\) 3.47262e45 0.167262
\(275\) 6.40374e44i 0.0287814i
\(276\) −6.72743e45 1.09189e46i −0.282213 0.458045i
\(277\) −1.83033e46 −0.716825 −0.358412 0.933563i \(-0.616682\pi\)
−0.358412 + 0.933563i \(0.616682\pi\)
\(278\) 3.77461e46i 1.38045i
\(279\) 2.01250e46 3.99733e46i 0.687475 1.36550i
\(280\) 2.71155e46 0.865398
\(281\) 4.59507e46i 1.37048i −0.728318 0.685239i \(-0.759698\pi\)
0.728318 0.685239i \(-0.240302\pi\)
\(282\) −5.30694e46 + 3.26974e46i −1.47949 + 0.911548i
\(283\) 1.92704e46 0.502283 0.251142 0.967950i \(-0.419194\pi\)
0.251142 + 0.967950i \(0.419194\pi\)
\(284\) 3.96357e45i 0.0966135i
\(285\) 1.63269e46 + 2.64993e46i 0.372263 + 0.604201i
\(286\) 2.12019e46 0.452292
\(287\) 6.20841e46i 1.23944i
\(288\) 4.59260e46 + 2.31220e46i 0.858226 + 0.432084i
\(289\) −1.60824e46 −0.281379
\(290\) 6.88455e45i 0.112801i
\(291\) 3.88801e46 2.39550e46i 0.596707 0.367646i
\(292\) −4.01209e46 −0.576895
\(293\) 2.63325e46i 0.354819i 0.984137 + 0.177410i \(0.0567718\pi\)
−0.984137 + 0.177410i \(0.943228\pi\)
\(294\) 7.32066e46 + 1.18818e47i 0.924594 + 1.50066i
\(295\) −1.35307e47 −1.60214
\(296\) 2.45485e46i 0.272573i
\(297\) 2.96575e46 2.55024e45i 0.308860 0.0265588i
\(298\) 9.66060e46 0.943833
\(299\) 1.31166e47i 1.20245i
\(300\) 4.85153e45 2.98915e45i 0.0417422 0.0257184i
\(301\) 6.80399e46 0.549541
\(302\) 1.56642e47i 1.18789i
\(303\) −9.07719e46 1.47327e47i −0.646460 1.04923i
\(304\) −1.39140e47 −0.930796
\(305\) 3.14991e46i 0.197971i
\(306\) 1.06544e47 2.11623e47i 0.629247 1.24984i
\(307\) −2.52179e46 −0.139984 −0.0699922 0.997548i \(-0.522297\pi\)
−0.0699922 + 0.997548i \(0.522297\pi\)
\(308\) 4.88611e46i 0.254976i
\(309\) 2.15235e46 1.32612e46i 0.105609 0.0650685i
\(310\) −3.90063e47 −1.79996
\(311\) 2.15421e47i 0.935064i 0.883976 + 0.467532i \(0.154857\pi\)
−0.883976 + 0.467532i \(0.845143\pi\)
\(312\) −8.84405e46 1.43543e47i −0.361172 0.586199i
\(313\) 2.41646e46 0.0928619 0.0464310 0.998922i \(-0.485215\pi\)
0.0464310 + 0.998922i \(0.485215\pi\)
\(314\) 2.23462e47i 0.808240i
\(315\) 3.89153e47 + 1.95923e47i 1.32501 + 0.667092i
\(316\) 1.80274e47 0.577935
\(317\) 2.28377e47i 0.689488i 0.938697 + 0.344744i \(0.112034\pi\)
−0.938697 + 0.344744i \(0.887966\pi\)
\(318\) −6.54703e47 + 4.03379e47i −1.86178 + 1.14709i
\(319\) −1.10862e46 −0.0297003
\(320\) 2.31817e46i 0.0585187i
\(321\) −7.27449e46 1.18068e47i −0.173064 0.280891i
\(322\) 8.74691e47 1.96152
\(323\) 3.98938e47i 0.843446i
\(324\) 1.57757e47 + 2.12784e47i 0.314509 + 0.424213i
\(325\) −5.82799e46 −0.109581
\(326\) 4.07886e47i 0.723442i
\(327\) 2.92225e47 1.80047e47i 0.489002 0.301286i
\(328\) 2.93989e47 0.464224
\(329\) 1.46917e48i 2.18953i
\(330\) −1.36092e47 2.20883e47i −0.191455 0.310741i
\(331\) 5.75118e47 0.763880 0.381940 0.924187i \(-0.375256\pi\)
0.381940 + 0.924187i \(0.375256\pi\)
\(332\) 6.59903e47i 0.827669i
\(333\) −1.77375e47 + 3.52311e47i −0.210113 + 0.417336i
\(334\) −3.85611e47 −0.431486
\(335\) 9.03710e47i 0.955383i
\(336\) −1.65821e48 + 1.02167e48i −1.65651 + 1.02062i
\(337\) 4.14070e47 0.390936 0.195468 0.980710i \(-0.437377\pi\)
0.195468 + 0.980710i \(0.437377\pi\)
\(338\) 5.44434e47i 0.485879i
\(339\) −9.95616e46 1.61593e47i −0.0840036 0.136342i
\(340\) −7.13644e47 −0.569354
\(341\) 6.28120e47i 0.473925i
\(342\) −1.15274e48 5.80359e47i −0.822686 0.414191i
\(343\) −9.82481e47 −0.663339
\(344\) 3.22191e47i 0.205828i
\(345\) 1.36650e48 8.41935e47i 0.826127 0.508997i
\(346\) 2.28851e48 1.30950
\(347\) 5.22721e47i 0.283145i −0.989928 0.141573i \(-0.954784\pi\)
0.989928 0.141573i \(-0.0452159\pi\)
\(348\) −5.17485e46 8.39903e46i −0.0265395 0.0430748i
\(349\) −3.42784e48 −1.66470 −0.832352 0.554248i \(-0.813006\pi\)
−0.832352 + 0.554248i \(0.813006\pi\)
\(350\) 3.88645e47i 0.178756i
\(351\) −2.32096e47 2.69911e48i −0.101119 1.17594i
\(352\) 7.21658e47 0.297866
\(353\) 4.00027e48i 1.56448i 0.622976 + 0.782241i \(0.285923\pi\)
−0.622976 + 0.782241i \(0.714077\pi\)
\(354\) 4.77658e48 2.94297e48i 1.77034 1.09075i
\(355\) −4.96038e47 −0.174252
\(356\) 2.06372e47i 0.0687227i
\(357\) 2.92928e48 + 4.75437e48i 0.924837 + 1.50105i
\(358\) 4.36021e48 1.30536
\(359\) 3.14520e47i 0.0893006i 0.999003 + 0.0446503i \(0.0142174\pi\)
−0.999003 + 0.0446503i \(0.985783\pi\)
\(360\) −9.27761e47 + 1.84277e48i −0.249855 + 0.496275i
\(361\) −1.74107e48 −0.444816
\(362\) 1.13375e48i 0.274825i
\(363\) −3.34555e48 + 2.06128e48i −0.769560 + 0.474145i
\(364\) −4.44681e48 −0.970784
\(365\) 5.02111e48i 1.04048i
\(366\) −6.85118e47 1.11198e48i −0.134780 0.218754i
\(367\) −3.28894e48 −0.614328 −0.307164 0.951657i \(-0.599380\pi\)
−0.307164 + 0.951657i \(0.599380\pi\)
\(368\) 7.17511e48i 1.27268i
\(369\) 4.21922e48 + 2.12421e48i 0.710773 + 0.357847i
\(370\) 3.43788e48 0.550121
\(371\) 1.81248e49i 2.75530i
\(372\) 4.75870e48 2.93195e48i 0.687341 0.423488i
\(373\) −1.07749e49 −1.47892 −0.739458 0.673203i \(-0.764918\pi\)
−0.739458 + 0.673203i \(0.764918\pi\)
\(374\) 3.32533e48i 0.433784i
\(375\) 4.40336e48 + 7.14686e48i 0.545996 + 0.886178i
\(376\) 6.95702e48 0.820077
\(377\) 1.00895e48i 0.113079i
\(378\) −1.79992e49 + 1.54775e48i −1.91827 + 0.164952i
\(379\) −9.11914e48 −0.924292 −0.462146 0.886804i \(-0.652920\pi\)
−0.462146 + 0.886804i \(0.652920\pi\)
\(380\) 3.88732e48i 0.374768i
\(381\) 1.45234e49 8.94824e48i 1.33197 0.820659i
\(382\) −1.28916e48 −0.112487
\(383\) 2.13694e47i 0.0177425i 0.999961 + 0.00887126i \(0.00282385\pi\)
−0.999961 + 0.00887126i \(0.997176\pi\)
\(384\) −6.88307e48 1.11715e49i −0.543862 0.882714i
\(385\) 6.11494e48 0.459874
\(386\) 8.82483e48i 0.631753i
\(387\) −2.32799e48 + 4.62397e48i −0.158662 + 0.315143i
\(388\) 5.70354e48 0.370119
\(389\) 2.26825e49i 1.40168i 0.713320 + 0.700838i \(0.247191\pi\)
−0.713320 + 0.700838i \(0.752809\pi\)
\(390\) −2.01024e49 + 1.23856e49i −1.18310 + 0.728936i
\(391\) 2.05722e49 1.15325
\(392\) 1.55762e49i 0.831813i
\(393\) −2.50824e48 4.07099e48i −0.127618 0.207129i
\(394\) 1.96974e49 0.954951
\(395\) 2.25612e49i 1.04236i
\(396\) 3.32059e48 + 1.67179e48i 0.146220 + 0.0736161i
\(397\) 3.46730e49 1.45537 0.727683 0.685914i \(-0.240597\pi\)
0.727683 + 0.685914i \(0.240597\pi\)
\(398\) 1.64255e49i 0.657263i
\(399\) 2.58977e49 1.59562e49i 0.988043 0.608758i
\(400\) −3.18806e48 −0.115981
\(401\) 3.68492e49i 1.27845i −0.769019 0.639226i \(-0.779255\pi\)
0.769019 0.639226i \(-0.220745\pi\)
\(402\) −1.96560e49 3.19027e49i −0.650430 1.05568i
\(403\) −5.71648e49 −1.80440
\(404\) 2.16122e49i 0.650808i
\(405\) −2.66298e49 + 1.97432e49i −0.765107 + 0.567246i
\(406\) 6.72826e48 0.184463
\(407\) 5.53604e48i 0.144846i
\(408\) −2.25135e49 + 1.38711e49i −0.562211 + 0.346392i
\(409\) 2.76423e49 0.658918 0.329459 0.944170i \(-0.393134\pi\)
0.329459 + 0.944170i \(0.393134\pi\)
\(410\) 4.11715e49i 0.936922i
\(411\) −3.26670e48 5.30200e48i −0.0709764 0.115198i
\(412\) 3.15740e48 0.0655062
\(413\) 1.32235e50i 2.61997i
\(414\) −2.99276e49 + 5.94438e49i −0.566325 + 1.12486i
\(415\) −8.25865e49 −1.49278
\(416\) 6.56775e49i 1.13408i
\(417\) 5.76307e49 3.55077e49i 0.950756 0.585784i
\(418\) −1.81135e49 −0.285531
\(419\) 1.27907e50i 1.92676i −0.268140 0.963380i \(-0.586409\pi\)
0.268140 0.963380i \(-0.413591\pi\)
\(420\) 2.85435e49 + 4.63274e49i 0.410932 + 0.666962i
\(421\) −5.39599e49 −0.742525 −0.371263 0.928528i \(-0.621075\pi\)
−0.371263 + 0.928528i \(0.621075\pi\)
\(422\) 2.87293e49i 0.377911i
\(423\) 9.98447e49 + 5.02680e49i 1.25562 + 0.632156i
\(424\) 8.58269e49 1.03198
\(425\) 9.14070e48i 0.105097i
\(426\) 1.75111e49 1.07890e49i 0.192544 0.118631i
\(427\) 3.07841e49 0.323740
\(428\) 1.73201e49i 0.174228i
\(429\) −1.99446e49 3.23710e49i −0.191927 0.311507i
\(430\) 4.51211e49 0.415412
\(431\) 9.45230e49i 0.832663i 0.909213 + 0.416332i \(0.136684\pi\)
−0.909213 + 0.416332i \(0.863316\pi\)
\(432\) −1.26962e49 1.47648e50i −0.107025 1.24462i
\(433\) −2.71832e49 −0.219296 −0.109648 0.993970i \(-0.534972\pi\)
−0.109648 + 0.993970i \(0.534972\pi\)
\(434\) 3.81208e50i 2.94346i
\(435\) 1.05113e49 6.47630e48i 0.0776895 0.0478664i
\(436\) 4.28681e49 0.303313
\(437\) 1.12060e50i 0.759106i
\(438\) 1.09211e50 + 1.77255e50i 0.708368 + 1.14971i
\(439\) −1.88917e50 −1.17340 −0.586698 0.809806i \(-0.699572\pi\)
−0.586698 + 0.809806i \(0.699572\pi\)
\(440\) 2.89563e49i 0.172243i
\(441\) 1.12546e50 2.23544e50i 0.641203 1.27359i
\(442\) −3.02635e50 −1.65157
\(443\) 1.29252e50i 0.675722i 0.941196 + 0.337861i \(0.109703\pi\)
−0.941196 + 0.337861i \(0.890297\pi\)
\(444\) −4.19416e49 + 2.58412e49i −0.210072 + 0.129431i
\(445\) −2.58273e49 −0.123948
\(446\) 4.28282e50i 1.96955i
\(447\) −9.08772e49 1.47498e50i −0.400509 0.650045i
\(448\) 2.26554e49 0.0956950
\(449\) 5.07913e49i 0.205641i −0.994700 0.102820i \(-0.967213\pi\)
0.994700 0.102820i \(-0.0327867\pi\)
\(450\) −2.64122e49 1.32975e49i −0.102510 0.0516099i
\(451\) 6.62986e49 0.246689
\(452\) 2.37050e49i 0.0845687i
\(453\) −2.39161e50 + 1.47353e50i −0.818134 + 0.504073i
\(454\) 2.97328e50 0.975382
\(455\) 5.56516e50i 1.75090i
\(456\) 7.55579e49 + 1.22634e50i 0.228007 + 0.370066i
\(457\) 3.11470e50 0.901588 0.450794 0.892628i \(-0.351141\pi\)
0.450794 + 0.892628i \(0.351141\pi\)
\(458\) 4.31264e50i 1.19757i
\(459\) −4.23331e50 + 3.64022e49i −1.12782 + 0.0969809i
\(460\) 2.00459e50 0.512422
\(461\) 4.63073e50i 1.13588i 0.823070 + 0.567939i \(0.192259\pi\)
−0.823070 + 0.567939i \(0.807741\pi\)
\(462\) −2.15869e50 + 1.33002e50i −0.508151 + 0.313084i
\(463\) −5.99101e50 −1.35351 −0.676755 0.736208i \(-0.736614\pi\)
−0.676755 + 0.736208i \(0.736614\pi\)
\(464\) 5.51921e49i 0.119684i
\(465\) 3.66932e50 + 5.95549e50i 0.763800 + 1.23968i
\(466\) 7.25583e50 1.44995
\(467\) 1.30184e50i 0.249767i 0.992171 + 0.124884i \(0.0398558\pi\)
−0.992171 + 0.124884i \(0.960144\pi\)
\(468\) 1.52148e50 3.02204e50i 0.280282 0.556710i
\(469\) 8.83195e50 1.56233
\(470\) 9.74293e50i 1.65512i
\(471\) −3.41182e50 + 2.10211e50i −0.556659 + 0.342971i
\(472\) −6.26177e50 −0.981294
\(473\) 7.26587e49i 0.109377i
\(474\) −4.90714e50 7.96453e50i −0.709644 1.15179i
\(475\) 4.97906e49 0.0691782
\(476\) 6.97444e50i 0.931059i
\(477\) 1.23176e51 + 6.20142e50i 1.58007 + 0.795503i
\(478\) 5.26539e49 0.0649084
\(479\) 4.70426e50i 0.557335i −0.960388 0.278667i \(-0.910107\pi\)
0.960388 0.278667i \(-0.0898927\pi\)
\(480\) −6.84236e50 + 4.21575e50i −0.779152 + 0.480055i
\(481\) 5.03831e50 0.551478
\(482\) 2.36959e50i 0.249333i
\(483\) −8.22822e50 1.33548e51i −0.832358 1.35096i
\(484\) −4.90778e50 −0.477335
\(485\) 7.13795e50i 0.667545i
\(486\) 5.10660e50 1.27618e51i 0.459244 1.14768i
\(487\) −2.23897e50 −0.193641 −0.0968205 0.995302i \(-0.530867\pi\)
−0.0968205 + 0.995302i \(0.530867\pi\)
\(488\) 1.45773e50i 0.121255i
\(489\) −6.22760e50 + 3.83698e50i −0.498256 + 0.306988i
\(490\) −2.18136e51 −1.67881
\(491\) 6.15519e50i 0.455715i −0.973695 0.227857i \(-0.926828\pi\)
0.973695 0.227857i \(-0.0731720\pi\)
\(492\) 3.09470e50 + 5.02285e50i 0.220436 + 0.357778i
\(493\) 1.58245e50 0.108452
\(494\) 1.64850e51i 1.08712i
\(495\) −2.09223e50 + 4.15570e50i −0.132773 + 0.263721i
\(496\) −3.12706e51 −1.90978
\(497\) 4.84778e50i 0.284952i
\(498\) 2.91546e51 1.79629e51i 1.64949 1.01629i
\(499\) 2.53731e51 1.38186 0.690929 0.722922i \(-0.257202\pi\)
0.690929 + 0.722922i \(0.257202\pi\)
\(500\) 1.04841e51i 0.549669i
\(501\) 3.62744e50 + 5.88751e50i 0.183098 + 0.297177i
\(502\) 3.12766e50 0.152002
\(503\) 2.84261e51i 1.33023i −0.746742 0.665114i \(-0.768383\pi\)
0.746742 0.665114i \(-0.231617\pi\)
\(504\) 1.80093e51 + 9.06700e50i 0.811553 + 0.408586i
\(505\) 2.70476e51 1.17379
\(506\) 9.34069e50i 0.390408i
\(507\) −8.31243e50 + 5.12149e50i −0.334639 + 0.206179i
\(508\) 2.13052e51 0.826180
\(509\) 2.96092e51i 1.10609i −0.833152 0.553043i \(-0.813466\pi\)
0.833152 0.553043i \(-0.186534\pi\)
\(510\) 1.94257e51 + 3.15289e51i 0.699108 + 1.13469i
\(511\) −4.90713e51 −1.70149
\(512\) 1.41149e51i 0.471571i
\(513\) 1.98288e50 + 2.30594e51i 0.0638360 + 0.742367i
\(514\) −3.67283e51 −1.13947
\(515\) 3.95147e50i 0.118147i
\(516\) −5.50470e50 + 3.39158e50i −0.158631 + 0.0977367i
\(517\) 1.56891e51 0.435790
\(518\) 3.35984e51i 0.899608i
\(519\) −2.15280e51 3.49409e51i −0.555678 0.901893i
\(520\) 2.63529e51 0.655789
\(521\) 7.20899e51i 1.72965i 0.502076 + 0.864824i \(0.332570\pi\)
−0.502076 + 0.864824i \(0.667430\pi\)
\(522\) −2.30208e50 + 4.57251e50i −0.0532576 + 0.105783i
\(523\) −3.95673e51 −0.882682 −0.441341 0.897339i \(-0.645497\pi\)
−0.441341 + 0.897339i \(0.645497\pi\)
\(524\) 5.97196e50i 0.128476i
\(525\) 5.93383e50 3.65598e50i 0.123114 0.0758538i
\(526\) −5.77060e50 −0.115476
\(527\) 8.96579e51i 1.73056i
\(528\) −1.09102e51 1.77078e51i −0.203137 0.329700i
\(529\) −2.11171e50 −0.0379294
\(530\) 1.20196e52i 2.08280i
\(531\) −8.98666e51 4.52444e51i −1.50246 0.756430i
\(532\) 3.79907e51 0.612853
\(533\) 6.03379e51i 0.939232i
\(534\) 9.11753e50 5.61754e50i 0.136960 0.0843843i
\(535\) 2.16760e51 0.314237
\(536\) 4.18222e51i 0.585161i
\(537\) −4.10164e51 6.65717e51i −0.553919 0.899038i
\(538\) 1.02375e52 1.33453
\(539\) 3.51265e51i 0.442026i
\(540\) −4.12501e51 + 3.54709e50i −0.501122 + 0.0430914i
\(541\) 1.36288e52 1.59848 0.799242 0.601009i \(-0.205234\pi\)
0.799242 + 0.601009i \(0.205234\pi\)
\(542\) 1.75553e52i 1.98803i
\(543\) 1.73102e51 1.06652e51i 0.189280 0.116620i
\(544\) −1.03009e52 −1.08767
\(545\) 5.36492e51i 0.547054i
\(546\) 1.21044e52 + 1.96461e52i 1.19202 + 1.93471i
\(547\) −1.37722e52 −1.30992 −0.654960 0.755664i \(-0.727314\pi\)
−0.654960 + 0.755664i \(0.727314\pi\)
\(548\) 7.77780e50i 0.0714539i
\(549\) −1.05328e51 + 2.09208e51i −0.0934693 + 0.185653i
\(550\) −4.15027e50 −0.0355783
\(551\) 8.61981e50i 0.0713867i
\(552\) 6.32393e51 3.89633e51i 0.505993 0.311755i
\(553\) 2.20490e52 1.70456
\(554\) 1.18624e52i 0.886108i
\(555\) −3.23402e51 5.24896e51i −0.233440 0.378885i
\(556\) 8.45417e51 0.589725
\(557\) 5.13700e51i 0.346307i −0.984895 0.173153i \(-0.944604\pi\)
0.984895 0.173153i \(-0.0553957\pi\)
\(558\) −2.59068e52 1.30431e52i −1.68797 0.849826i
\(559\) 6.61262e51 0.416437
\(560\) 3.04429e52i 1.85316i
\(561\) −5.07711e51 + 3.12813e51i −0.298760 + 0.184073i
\(562\) −2.97808e52 −1.69413
\(563\) 1.88646e52i 1.03750i −0.854926 0.518751i \(-0.826397\pi\)
0.854926 0.518751i \(-0.173603\pi\)
\(564\) 7.32338e51 + 1.18862e52i 0.389411 + 0.632033i
\(565\) 2.96667e51 0.152528
\(566\) 1.24892e52i 0.620901i
\(567\) 1.92950e52 + 2.60253e52i 0.927611 + 1.25117i
\(568\) −2.29558e51 −0.106727
\(569\) 1.23088e52i 0.553454i 0.960949 + 0.276727i \(0.0892498\pi\)
−0.960949 + 0.276727i \(0.910750\pi\)
\(570\) 1.71742e52 1.05815e52i 0.746887 0.460176i
\(571\) −2.12798e52 −0.895122 −0.447561 0.894253i \(-0.647707\pi\)
−0.447561 + 0.894253i \(0.647707\pi\)
\(572\) 4.74868e51i 0.193218i
\(573\) 1.21271e51 + 1.96829e51i 0.0477331 + 0.0774731i
\(574\) −4.02369e52 −1.53214
\(575\) 2.56758e51i 0.0945877i
\(576\) −7.75157e50 + 1.53965e51i −0.0276288 + 0.0548777i
\(577\) −2.50966e52 −0.865515 −0.432757 0.901510i \(-0.642459\pi\)
−0.432757 + 0.901510i \(0.642459\pi\)
\(578\) 1.04230e52i 0.347829i
\(579\) 1.34738e52 8.30151e51i 0.435107 0.268080i
\(580\) 1.54197e51 0.0481884
\(581\) 8.07117e52i 2.44112i
\(582\) −1.55253e52 2.51983e52i −0.454468 0.737623i
\(583\) 1.93552e52 0.548397
\(584\) 2.32369e52i 0.637285i
\(585\) 3.78207e52 + 1.90413e52i 1.00408 + 0.505515i
\(586\) 1.70661e52 0.438612
\(587\) 7.01707e52i 1.74595i −0.487764 0.872976i \(-0.662187\pi\)
0.487764 0.872976i \(-0.337813\pi\)
\(588\) 2.66122e52 1.63964e52i 0.641078 0.394984i
\(589\) 4.88379e52 1.13911
\(590\) 8.76926e52i 1.98050i
\(591\) −1.85294e52 3.00740e52i −0.405227 0.657702i
\(592\) 2.75608e52 0.583687
\(593\) 2.25698e52i 0.462902i 0.972847 + 0.231451i \(0.0743473\pi\)
−0.972847 + 0.231451i \(0.925653\pi\)
\(594\) −1.65282e51 1.92211e52i −0.0328309 0.381799i
\(595\) −8.72847e52 −1.67925
\(596\) 2.16373e52i 0.403203i
\(597\) 2.50784e52 1.54514e52i 0.452676 0.278905i
\(598\) 8.50089e52 1.48642
\(599\) 5.56949e52i 0.943421i 0.881753 + 0.471711i \(0.156363\pi\)
−0.881753 + 0.471711i \(0.843637\pi\)
\(600\) 1.73123e51 + 2.80986e51i 0.0284106 + 0.0461117i
\(601\) 9.90786e51 0.157531 0.0787653 0.996893i \(-0.474902\pi\)
0.0787653 + 0.996893i \(0.474902\pi\)
\(602\) 4.40968e52i 0.679319i
\(603\) −3.02186e52 + 6.00217e52i −0.451071 + 0.895940i
\(604\) −3.50838e52 −0.507464
\(605\) 6.14205e52i 0.860918i
\(606\) −9.54830e52 + 5.88294e52i −1.29702 + 0.799125i
\(607\) −5.20912e52 −0.685771 −0.342885 0.939377i \(-0.611404\pi\)
−0.342885 + 0.939377i \(0.611404\pi\)
\(608\) 5.61107e52i 0.715942i
\(609\) −6.32928e51 1.02727e52i −0.0782754 0.127045i
\(610\) 2.04147e52 0.244723
\(611\) 1.42785e53i 1.65920i
\(612\) −4.73981e52 2.38631e52i −0.533929 0.268813i
\(613\) −1.02204e53 −1.11614 −0.558070 0.829794i \(-0.688458\pi\)
−0.558070 + 0.829794i \(0.688458\pi\)
\(614\) 1.63438e52i 0.173043i
\(615\) −6.28607e52 + 3.87300e52i −0.645285 + 0.397576i
\(616\) 2.82989e52 0.281667
\(617\) 1.35383e53i 1.30661i −0.757093 0.653307i \(-0.773381\pi\)
0.757093 0.653307i \(-0.226619\pi\)
\(618\) −8.59459e51 1.39494e52i −0.0804348 0.130550i
\(619\) 2.04083e53 1.85219 0.926095 0.377291i \(-0.123144\pi\)
0.926095 + 0.377291i \(0.123144\pi\)
\(620\) 8.73643e52i 0.768939i
\(621\) 1.18912e53 1.02252e52i 1.01504 0.0872833i
\(622\) 1.39615e53 1.15589
\(623\) 2.52410e52i 0.202691i
\(624\) −1.61157e53 + 9.92929e52i −1.25528 + 0.773412i
\(625\) −1.18920e53 −0.898537
\(626\) 1.56611e52i 0.114792i
\(627\) 1.70394e52 + 2.76557e52i 0.121163 + 0.196654i
\(628\) −5.00498e52 −0.345278
\(629\) 7.90214e52i 0.528911i
\(630\) 1.26978e53 2.52211e53i 0.824630 1.63792i
\(631\) 2.03438e53 1.28196 0.640979 0.767559i \(-0.278529\pi\)
0.640979 + 0.767559i \(0.278529\pi\)
\(632\) 1.04409e53i 0.638433i
\(633\) −4.38640e52 + 2.70257e52i −0.260278 + 0.160364i
\(634\) 1.48012e53 0.852316
\(635\) 2.66633e53i 1.49009i
\(636\) 9.03466e52 + 1.46637e53i 0.490034 + 0.795349i
\(637\) −3.19684e53 −1.68295
\(638\) 7.18500e51i 0.0367142i
\(639\) −3.29454e52 1.65867e52i −0.163410 0.0822705i
\(640\) 2.05097e53 0.987505
\(641\) 6.25463e52i 0.292347i 0.989259 + 0.146174i \(0.0466958\pi\)
−0.989259 + 0.146174i \(0.953304\pi\)
\(642\) −7.65204e52 + 4.71461e52i −0.347225 + 0.213934i
\(643\) −3.09130e53 −1.36186 −0.680931 0.732347i \(-0.738425\pi\)
−0.680931 + 0.732347i \(0.738425\pi\)
\(644\) 1.95909e53i 0.837958i
\(645\) −4.24454e52 6.88910e52i −0.176277 0.286106i
\(646\) 2.58552e53 1.04263
\(647\) 3.18139e53i 1.24576i 0.782316 + 0.622881i \(0.214038\pi\)
−0.782316 + 0.622881i \(0.785962\pi\)
\(648\) −1.23238e53 + 9.13680e52i −0.468619 + 0.347431i
\(649\) −1.41212e53 −0.521461
\(650\) 3.77713e52i 0.135459i
\(651\) 5.82029e53 3.58602e53i 2.02724 1.24903i
\(652\) −9.13560e52 −0.309053
\(653\) 1.93902e53i 0.637134i −0.947900 0.318567i \(-0.896798\pi\)
0.947900 0.318567i \(-0.103202\pi\)
\(654\) −1.16689e53 1.89392e53i −0.372437 0.604483i
\(655\) 7.47388e52 0.231719
\(656\) 3.30064e53i 0.994088i
\(657\) 1.67898e53 3.33487e53i 0.491251 0.975746i
\(658\) −9.52175e53 −2.70661
\(659\) 5.59717e52i 0.154577i −0.997009 0.0772887i \(-0.975374\pi\)
0.997009 0.0772887i \(-0.0246263\pi\)
\(660\) −4.94723e52 + 3.04811e52i −0.132748 + 0.0817892i
\(661\) −1.40193e53 −0.365509 −0.182754 0.983159i \(-0.558501\pi\)
−0.182754 + 0.983159i \(0.558501\pi\)
\(662\) 3.72735e53i 0.944276i
\(663\) 2.84689e53 + 4.62064e53i 0.700832 + 1.13748i
\(664\) −3.82196e53 −0.914309
\(665\) 4.75452e53i 1.10534i
\(666\) 2.28334e53 + 1.14957e53i 0.515893 + 0.259732i
\(667\) −4.44502e52 −0.0976075
\(668\) 8.63671e52i 0.184330i
\(669\) −6.53902e53 + 4.02885e53i −1.35649 + 0.835766i
\(670\) 5.85696e53 1.18100
\(671\) 3.28738e52i 0.0644350i
\(672\) 4.12004e53 + 6.68703e53i 0.785029 + 1.27414i
\(673\) 8.08996e53 1.49851 0.749256 0.662281i \(-0.230411\pi\)
0.749256 + 0.662281i \(0.230411\pi\)
\(674\) 2.68360e53i 0.483258i
\(675\) 4.54328e51 + 5.28351e52i 0.00795423 + 0.0925020i
\(676\) −1.21939e53 −0.207566
\(677\) 6.24887e52i 0.103423i −0.998662 0.0517114i \(-0.983532\pi\)
0.998662 0.0517114i \(-0.0164676\pi\)
\(678\) −1.04729e53 + 6.45261e52i −0.168540 + 0.103842i
\(679\) 6.97591e53 1.09163
\(680\) 4.13322e53i 0.628954i
\(681\) −2.79697e53 4.53961e53i −0.413897 0.671774i
\(682\) −4.07086e53 −0.585846
\(683\) 6.52201e53i 0.912826i 0.889768 + 0.456413i \(0.150866\pi\)
−0.889768 + 0.456413i \(0.849134\pi\)
\(684\) −1.29986e53 + 2.58184e53i −0.176941 + 0.351450i
\(685\) 9.73387e52 0.128874
\(686\) 6.36748e53i 0.819991i
\(687\) 6.58454e53 4.05690e53i 0.824798 0.508179i
\(688\) 3.61727e53 0.440758
\(689\) 1.76150e54i 2.08794i
\(690\) −5.45660e53 8.85632e53i −0.629201 1.02122i
\(691\) 4.63099e53 0.519506 0.259753 0.965675i \(-0.416359\pi\)
0.259753 + 0.965675i \(0.416359\pi\)
\(692\) 5.12568e53i 0.559417i
\(693\) 4.06136e53 + 2.04474e53i 0.431261 + 0.217123i
\(694\) −3.38776e53 −0.350012
\(695\) 1.05803e54i 1.06362i
\(696\) 4.86447e52 2.99712e52i 0.0475839 0.0293176i
\(697\) −9.46347e53 −0.900798
\(698\) 2.22159e54i 2.05783i
\(699\) −6.82555e53 1.10782e54i −0.615278 0.998626i
\(700\) 8.70466e52 0.0763641
\(701\) 1.26487e54i 1.07995i 0.841682 + 0.539974i \(0.181566\pi\)
−0.841682 + 0.539974i \(0.818434\pi\)
\(702\) −1.74930e54 + 1.50422e53i −1.45364 + 0.124999i
\(703\) −4.30441e53 −0.348147
\(704\) 2.41933e52i 0.0190465i
\(705\) −1.48755e54 + 9.16517e53i −1.13993 + 0.702340i
\(706\) 2.59259e54 1.93394
\(707\) 2.64335e54i 1.91949i
\(708\) −6.59151e53 1.06983e54i −0.465965 0.756283i
\(709\) −1.36880e54 −0.942026 −0.471013 0.882126i \(-0.656111\pi\)
−0.471013 + 0.882126i \(0.656111\pi\)
\(710\) 3.21484e53i 0.215402i
\(711\) −7.54410e53 + 1.49845e54i −0.492136 + 0.977504i
\(712\) −1.19524e53 −0.0759166
\(713\) 2.51845e54i 1.55751i
\(714\) 3.08131e54 1.89847e54i 1.85554 1.14324i
\(715\) 5.94295e53 0.348487
\(716\) 9.76576e53i 0.557646i
\(717\) −4.95315e52 8.03920e52i −0.0275434 0.0447043i
\(718\) 2.03841e53 0.110389
\(719\) 3.45208e54i 1.82067i 0.413867 + 0.910337i \(0.364178\pi\)
−0.413867 + 0.910337i \(0.635822\pi\)
\(720\) 2.06889e54 + 1.04161e54i 1.06272 + 0.535039i
\(721\) 3.86176e53 0.193204
\(722\) 1.12839e54i 0.549862i
\(723\) −3.61789e53 + 2.22907e53i −0.171723 + 0.105803i
\(724\) 2.53932e53 0.117405
\(725\) 1.97502e52i 0.00889508i
\(726\) 1.33592e54 + 2.16826e54i 0.586117 + 0.951296i
\(727\) 3.73998e54 1.59851 0.799255 0.600993i \(-0.205228\pi\)
0.799255 + 0.600993i \(0.205228\pi\)
\(728\) 2.57546e54i 1.07241i
\(729\) −2.42885e54 + 4.20824e53i −0.985320 + 0.170717i
\(730\) −3.25419e54 −1.28620
\(731\) 1.03713e54i 0.399396i
\(732\) −2.49055e53 + 1.53449e53i −0.0934512 + 0.0575776i
\(733\) −7.35671e53 −0.268973 −0.134486 0.990915i \(-0.542938\pi\)
−0.134486 + 0.990915i \(0.542938\pi\)
\(734\) 2.13157e54i 0.759406i
\(735\) 2.05200e54 + 3.33050e54i 0.712391 + 1.15624i
\(736\) 2.89349e54 0.978911
\(737\) 9.43149e53i 0.310955i
\(738\) 1.37671e54 2.73449e54i 0.442355 0.878627i
\(739\) −4.27863e54 −1.33986 −0.669932 0.742423i \(-0.733677\pi\)
−0.669932 + 0.742423i \(0.733677\pi\)
\(740\) 7.69999e53i 0.235011i
\(741\) 2.51693e54 1.55074e54i 0.748729 0.461310i
\(742\) −1.17467e55 −3.40598
\(743\) 4.92310e54i 1.39140i −0.718333 0.695699i \(-0.755095\pi\)
0.718333 0.695699i \(-0.244905\pi\)
\(744\) 1.69810e54 + 2.75610e54i 0.467819 + 0.759292i
\(745\) 2.70790e54 0.727215
\(746\) 6.98320e54i 1.82817i
\(747\) −5.48514e54 2.76156e54i −1.39990 0.704795i
\(748\) −7.44789e53 −0.185312
\(749\) 2.11839e54i 0.513868i
\(750\) 4.63189e54 2.85382e54i 1.09545 0.674937i
\(751\) 5.46984e54 1.26129 0.630646 0.776070i \(-0.282790\pi\)
0.630646 + 0.776070i \(0.282790\pi\)
\(752\) 7.81071e54i 1.75611i
\(753\) −2.94219e53 4.77531e53i −0.0645009 0.104688i
\(754\) 6.53902e53 0.139784
\(755\) 4.39072e54i 0.915259i
\(756\) 3.46657e53 + 4.03137e54i 0.0704670 + 0.819480i
\(757\) −6.24062e54 −1.23710 −0.618551 0.785744i \(-0.712280\pi\)
−0.618551 + 0.785744i \(0.712280\pi\)
\(758\)