Properties

Label 3.39.b.a.2.6
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 2.6
Root \(-18089.7i\) of defining polynomial
Character \(\chi\) \(=\) 3.2
Dual form 3.39.b.a.2.7

$q$-expansion

\(f(q)\) \(=\) \(q-217076. i q^{2} +(7.82134e8 - 8.59720e8i) q^{3} +2.27756e11 q^{4} +1.16100e13i q^{5} +(-1.86625e14 - 1.69783e14i) q^{6} -8.59590e15 q^{7} -1.09110e17i q^{8} +(-1.27385e17 - 1.34483e18i) q^{9} +O(q^{10})\) \(q-217076. i q^{2} +(7.82134e8 - 8.59720e8i) q^{3} +2.27756e11 q^{4} +1.16100e13i q^{5} +(-1.86625e14 - 1.69783e14i) q^{6} -8.59590e15 q^{7} -1.09110e17i q^{8} +(-1.27385e17 - 1.34483e18i) q^{9} +2.52026e18 q^{10} -3.26530e19i q^{11} +(1.78136e20 - 1.95806e20i) q^{12} -6.39572e20 q^{13} +1.86596e21i q^{14} +(9.98136e21 + 9.08058e21i) q^{15} +3.89199e22 q^{16} -3.38515e23i q^{17} +(-2.91931e23 + 2.76523e22i) q^{18} +9.26108e23 q^{19} +2.64425e24i q^{20} +(-6.72314e24 + 7.39006e24i) q^{21} -7.08819e24 q^{22} -5.58717e25i q^{23} +(-9.38039e25 - 8.53384e25i) q^{24} +2.29005e26 q^{25} +1.38836e26i q^{26} +(-1.25581e27 - 9.42323e26i) q^{27} -1.95777e27 q^{28} -8.27744e27i q^{29} +(1.97118e27 - 2.16671e27i) q^{30} -3.97870e28 q^{31} -3.84405e28i q^{32} +(-2.80725e28 - 2.55390e28i) q^{33} -7.34836e28 q^{34} -9.97985e28i q^{35} +(-2.90127e28 - 3.06293e29i) q^{36} +2.19564e28 q^{37} -2.01036e29i q^{38} +(-5.00231e29 + 5.49853e29i) q^{39} +1.26677e30 q^{40} +8.17751e30i q^{41} +(1.60421e30 + 1.45943e30i) q^{42} +1.17242e31 q^{43} -7.43692e30i q^{44} +(1.56135e31 - 1.47894e30i) q^{45} -1.21284e31 q^{46} +8.05102e31i q^{47} +(3.04406e31 - 3.34603e31i) q^{48} -5.60454e31 q^{49} -4.97116e31i q^{50} +(-2.91028e32 - 2.64764e32i) q^{51} -1.45666e32 q^{52} -7.18608e32i q^{53} +(-2.04556e32 + 2.72607e32i) q^{54} +3.79102e32 q^{55} +9.37896e32i q^{56} +(7.24340e32 - 7.96194e32i) q^{57} -1.79683e33 q^{58} +4.73793e32i q^{59} +(2.27331e33 + 2.06816e33i) q^{60} +8.08012e33 q^{61} +8.63680e33i q^{62} +(1.09499e33 + 1.15600e34i) q^{63} +2.35373e33 q^{64} -7.42544e33i q^{65} +(-5.54391e33 + 6.09386e33i) q^{66} +1.06941e34 q^{67} -7.70989e34i q^{68} +(-4.80341e34 - 4.36992e34i) q^{69} -2.16639e34 q^{70} +1.81258e34i q^{71} +(-1.46734e35 + 1.38990e34i) q^{72} -1.52047e35 q^{73} -4.76621e33i q^{74} +(1.79113e35 - 1.96881e35i) q^{75} +2.10927e35 q^{76} +2.80682e35i q^{77} +(1.19360e35 + 1.08588e35i) q^{78} +1.40993e36 q^{79} +4.51861e35i q^{80} +(-1.79235e36 + 3.42624e35i) q^{81} +1.77514e36 q^{82} +2.75195e36i q^{83} +(-1.53123e36 + 1.68313e36i) q^{84} +3.93017e36 q^{85} -2.54504e36i q^{86} +(-7.11628e36 - 6.47406e36i) q^{87} -3.56276e36 q^{88} -1.01319e37i q^{89} +(-3.21043e35 - 3.38932e36i) q^{90} +5.49770e36 q^{91} -1.27251e37i q^{92} +(-3.11187e37 + 3.42056e37i) q^{93} +1.74768e37 q^{94} +1.07521e37i q^{95} +(-3.30480e37 - 3.00656e37i) q^{96} +8.94455e37 q^{97} +1.21661e37i q^{98} +(-4.39128e37 + 4.15951e36i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 217076.i 0.414040i −0.978337 0.207020i \(-0.933624\pi\)
0.978337 0.207020i \(-0.0663765\pi\)
\(3\) 7.82134e8 8.59720e8i 0.672941 0.739696i
\(4\) 2.27756e11 0.828571
\(5\) 1.16100e13i 0.608699i 0.952560 + 0.304350i \(0.0984391\pi\)
−0.952560 + 0.304350i \(0.901561\pi\)
\(6\) −1.86625e14 1.69783e14i −0.306263 0.278624i
\(7\) −8.59590e15 −0.754099 −0.377050 0.926193i \(-0.623061\pi\)
−0.377050 + 0.926193i \(0.623061\pi\)
\(8\) 1.09110e17i 0.757101i
\(9\) −1.27385e17 1.34483e18i −0.0942999 0.995544i
\(10\) 2.52026e18 0.252026
\(11\) 3.26530e19i 0.533903i −0.963710 0.266952i \(-0.913984\pi\)
0.963710 0.266952i \(-0.0860164\pi\)
\(12\) 1.78136e20 1.95806e20i 0.557580 0.612891i
\(13\) −6.39572e20 −0.437488 −0.218744 0.975782i \(-0.570196\pi\)
−0.218744 + 0.975782i \(0.570196\pi\)
\(14\) 1.86596e21i 0.312227i
\(15\) 9.98136e21 + 9.08058e21i 0.450252 + 0.409619i
\(16\) 3.89199e22 0.515101
\(17\) 3.38515e23i 1.41595i −0.706236 0.707977i \(-0.749608\pi\)
0.706236 0.707977i \(-0.250392\pi\)
\(18\) −2.91931e23 + 2.76523e22i −0.412195 + 0.0390439i
\(19\) 9.26108e23 0.468105 0.234053 0.972224i \(-0.424801\pi\)
0.234053 + 0.972224i \(0.424801\pi\)
\(20\) 2.64425e24i 0.504350i
\(21\) −6.72314e24 + 7.39006e24i −0.507464 + 0.557804i
\(22\) −7.08819e24 −0.221057
\(23\) 5.58717e25i 0.748796i −0.927268 0.374398i \(-0.877849\pi\)
0.927268 0.374398i \(-0.122151\pi\)
\(24\) −9.38039e25 8.53384e25i −0.560025 0.509485i
\(25\) 2.29005e26 0.629485
\(26\) 1.38836e26i 0.181137i
\(27\) −1.25581e27 9.42323e26i −0.799858 0.600189i
\(28\) −1.95777e27 −0.624825
\(29\) 8.27744e27i 1.35623i −0.734955 0.678116i \(-0.762797\pi\)
0.734955 0.678116i \(-0.237203\pi\)
\(30\) 1.97118e27 2.16671e27i 0.169598 0.186422i
\(31\) −3.97870e28 −1.83598 −0.917991 0.396600i \(-0.870190\pi\)
−0.917991 + 0.396600i \(0.870190\pi\)
\(32\) 3.84405e28i 0.970373i
\(33\) −2.80725e28 2.55390e28i −0.394926 0.359285i
\(34\) −7.34836e28 −0.586261
\(35\) 9.97985e28i 0.459019i
\(36\) −2.90127e28 3.06293e29i −0.0781342 0.824879i
\(37\) 2.19564e28 0.0351341 0.0175670 0.999846i \(-0.494408\pi\)
0.0175670 + 0.999846i \(0.494408\pi\)
\(38\) 2.01036e29i 0.193814i
\(39\) −5.00231e29 + 5.49853e29i −0.294404 + 0.323608i
\(40\) 1.26677e30 0.460847
\(41\) 8.17751e30i 1.86092i 0.366392 + 0.930461i \(0.380593\pi\)
−0.366392 + 0.930461i \(0.619407\pi\)
\(42\) 1.60421e30 + 1.45943e30i 0.230953 + 0.210110i
\(43\) 1.17242e31 1.07940 0.539698 0.841858i \(-0.318538\pi\)
0.539698 + 0.841858i \(0.318538\pi\)
\(44\) 7.43692e30i 0.442377i
\(45\) 1.56135e31 1.47894e30i 0.605987 0.0574003i
\(46\) −1.21284e31 −0.310031
\(47\) 8.05102e31i 1.36770i 0.729622 + 0.683851i \(0.239696\pi\)
−0.729622 + 0.683851i \(0.760304\pi\)
\(48\) 3.04406e31 3.34603e31i 0.346633 0.381018i
\(49\) −5.60454e31 −0.431335
\(50\) 4.97116e31i 0.260632i
\(51\) −2.91028e32 2.64764e32i −1.04737 0.952853i
\(52\) −1.45666e32 −0.362490
\(53\) 7.18608e32i 1.24523i −0.782527 0.622617i \(-0.786070\pi\)
0.782527 0.622617i \(-0.213930\pi\)
\(54\) −2.04556e32 + 2.72607e32i −0.248502 + 0.331173i
\(55\) 3.79102e32 0.324986
\(56\) 9.37896e32i 0.570929i
\(57\) 7.24340e32 7.96194e32i 0.315007 0.346255i
\(58\) −1.79683e33 −0.561534
\(59\) 4.73793e32i 0.107004i 0.998568 + 0.0535020i \(0.0170384\pi\)
−0.998568 + 0.0535020i \(0.982962\pi\)
\(60\) 2.27331e33 + 2.06816e33i 0.373066 + 0.339398i
\(61\) 8.08012e33 0.968615 0.484307 0.874898i \(-0.339072\pi\)
0.484307 + 0.874898i \(0.339072\pi\)
\(62\) 8.63680e33i 0.760170i
\(63\) 1.09499e33 + 1.15600e34i 0.0711115 + 0.750739i
\(64\) 2.35373e33 0.113328
\(65\) 7.42544e33i 0.266298i
\(66\) −5.54391e33 + 6.09386e33i −0.148758 + 0.163515i
\(67\) 1.06941e34 0.215636 0.107818 0.994171i \(-0.465614\pi\)
0.107818 + 0.994171i \(0.465614\pi\)
\(68\) 7.70989e34i 1.17322i
\(69\) −4.80341e34 4.36992e34i −0.553881 0.503896i
\(70\) −2.16639e34 −0.190052
\(71\) 1.81258e34i 0.121448i 0.998155 + 0.0607238i \(0.0193409\pi\)
−0.998155 + 0.0607238i \(0.980659\pi\)
\(72\) −1.46734e35 + 1.38990e34i −0.753727 + 0.0713946i
\(73\) −1.52047e35 −0.600959 −0.300479 0.953788i \(-0.597147\pi\)
−0.300479 + 0.953788i \(0.597147\pi\)
\(74\) 4.76621e33i 0.0145469i
\(75\) 1.79113e35 1.96881e35i 0.423607 0.465628i
\(76\) 2.10927e35 0.387858
\(77\) 2.80682e35i 0.402616i
\(78\) 1.19360e35 + 1.08588e35i 0.133987 + 0.121895i
\(79\) 1.40993e36 1.24246 0.621232 0.783627i \(-0.286633\pi\)
0.621232 + 0.783627i \(0.286633\pi\)
\(80\) 4.51861e35i 0.313542i
\(81\) −1.79235e36 + 3.42624e35i −0.982215 + 0.187759i
\(82\) 1.77514e36 0.770495
\(83\) 2.75195e36i 0.948761i 0.880320 + 0.474380i \(0.157328\pi\)
−0.880320 + 0.474380i \(0.842672\pi\)
\(84\) −1.53123e36 + 1.68313e36i −0.420470 + 0.462180i
\(85\) 3.93017e36 0.861889
\(86\) 2.54504e36i 0.446913i
\(87\) −7.11628e36 6.47406e36i −1.00320 0.912665i
\(88\) −3.56276e36 −0.404219
\(89\) 1.01319e37i 0.927432i −0.885984 0.463716i \(-0.846516\pi\)
0.885984 0.463716i \(-0.153484\pi\)
\(90\) −3.21043e35 3.38932e36i −0.0237660 0.250903i
\(91\) 5.49770e36 0.329909
\(92\) 1.27251e37i 0.620430i
\(93\) −3.11187e37 + 3.42056e37i −1.23551 + 1.35807i
\(94\) 1.74768e37 0.566283
\(95\) 1.07521e37i 0.284935i
\(96\) −3.30480e37 3.00656e37i −0.717781 0.653004i
\(97\) 8.94455e37 1.59550 0.797748 0.602991i \(-0.206025\pi\)
0.797748 + 0.602991i \(0.206025\pi\)
\(98\) 1.21661e37i 0.178590i
\(99\) −4.39128e37 + 4.15951e36i −0.531524 + 0.0503470i
\(100\) 5.21573e37 0.521573
\(101\) 1.21156e38i 1.00286i 0.865199 + 0.501429i \(0.167192\pi\)
−0.865199 + 0.501429i \(0.832808\pi\)
\(102\) −5.74740e37 + 6.31753e37i −0.394519 + 0.433655i
\(103\) 2.96491e38 1.69084 0.845422 0.534099i \(-0.179349\pi\)
0.845422 + 0.534099i \(0.179349\pi\)
\(104\) 6.97836e37i 0.331222i
\(105\) −8.57987e37 7.80558e37i −0.339535 0.308893i
\(106\) −1.55993e38 −0.515576
\(107\) 3.96227e38i 1.09560i −0.836609 0.547800i \(-0.815465\pi\)
0.836609 0.547800i \(-0.184535\pi\)
\(108\) −2.86018e38 2.14620e38i −0.662739 0.497299i
\(109\) −2.13957e38 −0.416124 −0.208062 0.978116i \(-0.566716\pi\)
−0.208062 + 0.978116i \(0.566716\pi\)
\(110\) 8.22940e37i 0.134557i
\(111\) 1.71729e37 1.88764e37i 0.0236432 0.0259885i
\(112\) −3.34552e38 −0.388437
\(113\) 6.47368e38i 0.634835i 0.948286 + 0.317417i \(0.102816\pi\)
−0.948286 + 0.317417i \(0.897184\pi\)
\(114\) −1.72835e38 1.57237e38i −0.143363 0.130426i
\(115\) 6.48672e38 0.455791
\(116\) 1.88524e39i 1.12373i
\(117\) 8.14721e37 + 8.60117e38i 0.0412551 + 0.435538i
\(118\) 1.02849e38 0.0443039
\(119\) 2.90984e39i 1.06777i
\(120\) 9.90780e38 1.08906e39i 0.310123 0.340886i
\(121\) 2.67421e39 0.714947
\(122\) 1.75400e39i 0.401045i
\(123\) 7.03037e39 + 6.39591e39i 1.37652 + 1.25229i
\(124\) −9.06171e39 −1.52124
\(125\) 6.88245e39i 0.991866i
\(126\) 2.50941e39 2.37696e38i 0.310836 0.0294430i
\(127\) −1.00465e40 −1.07088 −0.535442 0.844572i \(-0.679855\pi\)
−0.535442 + 0.844572i \(0.679855\pi\)
\(128\) 1.10774e40i 1.01730i
\(129\) 9.16986e39 1.00795e40i 0.726371 0.798425i
\(130\) −1.61189e39 −0.110258
\(131\) 6.17005e39i 0.364866i −0.983218 0.182433i \(-0.941603\pi\)
0.983218 0.182433i \(-0.0583973\pi\)
\(132\) −6.39367e39 5.81667e39i −0.327224 0.297694i
\(133\) −7.96073e39 −0.352998
\(134\) 2.32143e39i 0.0892819i
\(135\) 1.09404e40 1.45800e40i 0.365335 0.486873i
\(136\) −3.69353e40 −1.07202
\(137\) 3.72731e40i 0.941249i 0.882333 + 0.470625i \(0.155971\pi\)
−0.882333 + 0.470625i \(0.844029\pi\)
\(138\) −9.48605e39 + 1.04270e40i −0.208633 + 0.229329i
\(139\) 2.18885e40 0.419696 0.209848 0.977734i \(-0.432703\pi\)
0.209848 + 0.977734i \(0.432703\pi\)
\(140\) 2.27297e40i 0.380330i
\(141\) 6.92162e40 + 6.29697e40i 1.01168 + 0.920383i
\(142\) 3.93468e39 0.0502841
\(143\) 2.08840e40i 0.233576i
\(144\) −4.95783e39 5.23408e40i −0.0485740 0.512806i
\(145\) 9.61012e40 0.825537
\(146\) 3.30059e40i 0.248821i
\(147\) −4.38350e40 + 4.81833e40i −0.290263 + 0.319056i
\(148\) 5.00070e39 0.0291111
\(149\) 4.85956e40i 0.248919i 0.992225 + 0.124459i \(0.0397197\pi\)
−0.992225 + 0.124459i \(0.960280\pi\)
\(150\) −4.27381e40 3.88811e40i −0.192788 0.175390i
\(151\) 1.04870e41 0.416956 0.208478 0.978027i \(-0.433149\pi\)
0.208478 + 0.978027i \(0.433149\pi\)
\(152\) 1.01047e41i 0.354403i
\(153\) −4.55246e41 + 4.31219e40i −1.40964 + 0.133524i
\(154\) 6.09294e40 0.166699
\(155\) 4.61927e41i 1.11756i
\(156\) −1.13931e41 + 1.25232e41i −0.243934 + 0.268132i
\(157\) −4.20278e40 −0.0796972 −0.0398486 0.999206i \(-0.512688\pi\)
−0.0398486 + 0.999206i \(0.512688\pi\)
\(158\) 3.06063e41i 0.514429i
\(159\) −6.17802e41 5.62048e41i −0.921094 0.837969i
\(160\) 4.46294e41 0.590665
\(161\) 4.80268e41i 0.564666i
\(162\) 7.43754e40 + 3.89076e41i 0.0777399 + 0.406676i
\(163\) 8.86187e41 0.824064 0.412032 0.911169i \(-0.364819\pi\)
0.412032 + 0.911169i \(0.364819\pi\)
\(164\) 1.86248e42i 1.54191i
\(165\) 2.96509e41 3.25922e41i 0.218697 0.240391i
\(166\) 5.97382e41 0.392825
\(167\) 6.53848e41i 0.383587i −0.981435 0.191793i \(-0.938570\pi\)
0.981435 0.191793i \(-0.0614304\pi\)
\(168\) 8.06328e41 + 7.33560e41i 0.422314 + 0.384202i
\(169\) −1.72816e42 −0.808604
\(170\) 8.53145e41i 0.356856i
\(171\) −1.17973e41 1.24546e42i −0.0441423 0.466019i
\(172\) 2.67025e42 0.894357
\(173\) 3.86083e42i 1.15826i 0.815237 + 0.579128i \(0.196607\pi\)
−0.815237 + 0.579128i \(0.803393\pi\)
\(174\) −1.40536e42 + 1.54477e42i −0.377879 + 0.415364i
\(175\) −1.96851e42 −0.474694
\(176\) 1.27085e42i 0.275014i
\(177\) 4.07329e41 + 3.70569e41i 0.0791504 + 0.0720074i
\(178\) −2.19940e42 −0.383994
\(179\) 1.20565e43i 1.89240i −0.323579 0.946201i \(-0.604886\pi\)
0.323579 0.946201i \(-0.395114\pi\)
\(180\) 3.55607e42 3.36838e41i 0.502103 0.0475602i
\(181\) −9.88749e42 −1.25659 −0.628294 0.777976i \(-0.716247\pi\)
−0.628294 + 0.777976i \(0.716247\pi\)
\(182\) 1.19342e42i 0.136595i
\(183\) 6.31974e42 6.94664e42i 0.651821 0.716480i
\(184\) −6.09615e42 −0.566914
\(185\) 2.54914e41i 0.0213861i
\(186\) 7.42523e42 + 6.75513e42i 0.562295 + 0.511550i
\(187\) −1.10536e43 −0.755982
\(188\) 1.83367e43i 1.13324i
\(189\) 1.07948e43 + 8.10011e42i 0.603172 + 0.452602i
\(190\) 2.33403e42 0.117974
\(191\) 1.45692e43i 0.666502i 0.942838 + 0.333251i \(0.108146\pi\)
−0.942838 + 0.333251i \(0.891854\pi\)
\(192\) 1.84093e42 2.02355e42i 0.0762630 0.0838282i
\(193\) 3.23505e43 1.21421 0.607103 0.794623i \(-0.292331\pi\)
0.607103 + 0.794623i \(0.292331\pi\)
\(194\) 1.94165e43i 0.660599i
\(195\) −6.38380e42 5.80769e42i −0.196980 0.179203i
\(196\) −1.27647e43 −0.357391
\(197\) 9.62900e42i 0.244750i 0.992484 + 0.122375i \(0.0390511\pi\)
−0.992484 + 0.122375i \(0.960949\pi\)
\(198\) 9.02931e41 + 9.53243e42i 0.0208457 + 0.220072i
\(199\) 1.10540e43 0.231904 0.115952 0.993255i \(-0.463008\pi\)
0.115952 + 0.993255i \(0.463008\pi\)
\(200\) 2.49867e43i 0.476584i
\(201\) 8.36419e42 9.19390e42i 0.145110 0.159505i
\(202\) 2.63001e43 0.415223
\(203\) 7.11520e43i 1.02273i
\(204\) −6.62834e43 6.03016e43i −0.867824 0.789507i
\(205\) −9.49410e43 −1.13274
\(206\) 6.43610e43i 0.700077i
\(207\) −7.51381e43 + 7.11724e42i −0.745459 + 0.0706114i
\(208\) −2.48921e43 −0.225350
\(209\) 3.02402e43i 0.249923i
\(210\) −1.69440e43 + 1.86249e43i −0.127894 + 0.140581i
\(211\) 2.65656e44 1.83212 0.916058 0.401045i \(-0.131353\pi\)
0.916058 + 0.401045i \(0.131353\pi\)
\(212\) 1.63667e44i 1.03176i
\(213\) 1.55831e43 + 1.41768e43i 0.0898342 + 0.0817271i
\(214\) −8.60114e43 −0.453622
\(215\) 1.36118e44i 0.657028i
\(216\) −1.02817e44 + 1.37021e44i −0.454404 + 0.605573i
\(217\) 3.42005e44 1.38451
\(218\) 4.64449e43i 0.172292i
\(219\) −1.18921e44 + 1.30718e44i −0.404410 + 0.444527i
\(220\) 8.63427e43 0.269274
\(221\) 2.16505e44i 0.619462i
\(222\) −4.09761e42 3.72782e42i −0.0107603 0.00978922i
\(223\) 9.47786e43 0.228517 0.114258 0.993451i \(-0.463551\pi\)
0.114258 + 0.993451i \(0.463551\pi\)
\(224\) 3.30430e44i 0.731758i
\(225\) −2.91719e43 3.07974e44i −0.0593605 0.626680i
\(226\) 1.40528e44 0.262847
\(227\) 5.00665e44i 0.861105i −0.902566 0.430553i \(-0.858319\pi\)
0.902566 0.430553i \(-0.141681\pi\)
\(228\) 1.64973e44 1.81338e44i 0.261006 0.286897i
\(229\) −7.07940e44 −1.03068 −0.515338 0.856987i \(-0.672334\pi\)
−0.515338 + 0.856987i \(0.672334\pi\)
\(230\) 1.40811e44i 0.188716i
\(231\) 2.41308e44 + 2.19531e44i 0.297813 + 0.270937i
\(232\) −9.03149e44 −1.02680
\(233\) 5.35452e44i 0.560994i −0.959855 0.280497i \(-0.909501\pi\)
0.959855 0.280497i \(-0.0904993\pi\)
\(234\) 1.86711e44 1.76856e43i 0.180330 0.0170812i
\(235\) −9.34724e44 −0.832519
\(236\) 1.07909e44i 0.0886604i
\(237\) 1.10276e45 1.21215e45i 0.836105 0.919045i
\(238\) 6.31657e44 0.442099
\(239\) 8.20152e44i 0.530071i 0.964239 + 0.265036i \(0.0853837\pi\)
−0.964239 + 0.265036i \(0.914616\pi\)
\(240\) 3.88474e44 + 3.53416e44i 0.231925 + 0.210995i
\(241\) −1.70773e45 −0.942094 −0.471047 0.882108i \(-0.656124\pi\)
−0.471047 + 0.882108i \(0.656124\pi\)
\(242\) 5.80508e44i 0.296017i
\(243\) −1.10729e45 + 1.80889e45i −0.522088 + 0.852892i
\(244\) 1.84030e45 0.802566
\(245\) 6.50687e44i 0.262553i
\(246\) 1.38840e45 1.52613e45i 0.518498 0.569932i
\(247\) −5.92313e44 −0.204790
\(248\) 4.34115e45i 1.39002i
\(249\) 2.36591e45 + 2.15239e45i 0.701794 + 0.638460i
\(250\) 1.49402e45 0.410672
\(251\) 1.10103e45i 0.280544i −0.990113 0.140272i \(-0.955202\pi\)
0.990113 0.140272i \(-0.0447976\pi\)
\(252\) 2.49391e44 + 2.63287e45i 0.0589209 + 0.622040i
\(253\) −1.82438e45 −0.399784
\(254\) 2.18084e45i 0.443388i
\(255\) 3.07392e45 3.37884e45i 0.580001 0.637536i
\(256\) −1.75764e45 −0.307873
\(257\) 1.01754e46i 1.65509i −0.561400 0.827544i \(-0.689737\pi\)
0.561400 0.827544i \(-0.310263\pi\)
\(258\) −2.18802e45 1.99056e45i −0.330580 0.300746i
\(259\) −1.88735e44 −0.0264946
\(260\) 1.69119e45i 0.220647i
\(261\) −1.11318e46 + 1.05442e45i −1.35019 + 0.127893i
\(262\) −1.33937e45 −0.151069
\(263\) 1.50075e45i 0.157452i −0.996896 0.0787262i \(-0.974915\pi\)
0.996896 0.0787262i \(-0.0250853\pi\)
\(264\) −2.78656e45 + 3.06298e45i −0.272015 + 0.298999i
\(265\) 8.34305e45 0.757972
\(266\) 1.72808e45i 0.146155i
\(267\) −8.71063e45 7.92453e45i −0.686018 0.624108i
\(268\) 2.43564e45 0.178670
\(269\) 2.53416e46i 1.73197i 0.500067 + 0.865987i \(0.333309\pi\)
−0.500067 + 0.865987i \(0.666691\pi\)
\(270\) −3.16497e45 2.37490e45i −0.201585 0.151263i
\(271\) 1.10594e46 0.656621 0.328311 0.944570i \(-0.393521\pi\)
0.328311 + 0.944570i \(0.393521\pi\)
\(272\) 1.31750e46i 0.729359i
\(273\) 4.29993e45 4.72648e45i 0.222009 0.244032i
\(274\) 8.09110e45 0.389715
\(275\) 7.47772e45i 0.336084i
\(276\) −1.09400e46 9.95274e45i −0.458930 0.417513i
\(277\) 3.23361e46 1.26640 0.633201 0.773987i \(-0.281741\pi\)
0.633201 + 0.773987i \(0.281741\pi\)
\(278\) 4.75147e45i 0.173771i
\(279\) 5.06827e45 + 5.35068e46i 0.173133 + 1.82780i
\(280\) −1.08890e46 −0.347524
\(281\) 5.22440e46i 1.55818i 0.626914 + 0.779088i \(0.284318\pi\)
−0.626914 + 0.779088i \(0.715682\pi\)
\(282\) 1.36692e46 1.50252e46i 0.381075 0.418877i
\(283\) −1.78433e46 −0.465087 −0.232543 0.972586i \(-0.574705\pi\)
−0.232543 + 0.972586i \(0.574705\pi\)
\(284\) 4.12826e45i 0.100628i
\(285\) 9.24382e45 + 8.40960e45i 0.210765 + 0.191745i
\(286\) 4.53341e45 0.0967098
\(287\) 7.02931e46i 1.40332i
\(288\) −5.16960e46 + 4.89675e45i −0.966049 + 0.0915062i
\(289\) −5.74370e46 −1.00492
\(290\) 2.08613e46i 0.341805i
\(291\) 6.99584e46 7.68981e46i 1.07367 1.18018i
\(292\) −3.46297e46 −0.497937
\(293\) 2.83698e46i 0.382271i −0.981564 0.191135i \(-0.938783\pi\)
0.981564 0.191135i \(-0.0612170\pi\)
\(294\) 1.04594e46 + 9.51552e45i 0.132102 + 0.120180i
\(295\) −5.50074e45 −0.0651332
\(296\) 2.39566e45i 0.0266001i
\(297\) −3.07697e46 + 4.10060e46i −0.320443 + 0.427047i
\(298\) 1.05489e46 0.103062
\(299\) 3.57340e46i 0.327589i
\(300\) 4.07940e46 4.48407e46i 0.350988 0.385806i
\(301\) −1.00780e47 −0.813972
\(302\) 2.27648e46i 0.172636i
\(303\) 1.04160e47 + 9.47604e46i 0.741811 + 0.674865i
\(304\) 3.60441e46 0.241121
\(305\) 9.38103e46i 0.589595i
\(306\) 9.36073e45 + 9.88231e46i 0.0552844 + 0.583648i
\(307\) −7.42296e46 −0.412048 −0.206024 0.978547i \(-0.566052\pi\)
−0.206024 + 0.978547i \(0.566052\pi\)
\(308\) 6.39270e46i 0.333596i
\(309\) 2.31895e47 2.54899e47i 1.13784 1.25071i
\(310\) −1.00273e47 −0.462715
\(311\) 1.65900e47i 0.720111i 0.932931 + 0.360056i \(0.117242\pi\)
−0.932931 + 0.360056i \(0.882758\pi\)
\(312\) 5.99943e46 + 5.45801e46i 0.245004 + 0.222893i
\(313\) 1.39272e47 0.535208 0.267604 0.963529i \(-0.413768\pi\)
0.267604 + 0.963529i \(0.413768\pi\)
\(314\) 9.12323e45i 0.0329978i
\(315\) −1.34212e47 + 1.27129e46i −0.456974 + 0.0432855i
\(316\) 3.21120e47 1.02947
\(317\) 1.64475e47i 0.496562i −0.968688 0.248281i \(-0.920134\pi\)
0.968688 0.248281i \(-0.0798656\pi\)
\(318\) −1.22007e47 + 1.34110e47i −0.346952 + 0.381369i
\(319\) −2.70283e47 −0.724097
\(320\) 2.73268e46i 0.0689826i
\(321\) −3.40644e47 3.09902e47i −0.810411 0.737275i
\(322\) 1.04255e47 0.233794
\(323\) 3.13502e47i 0.662815i
\(324\) −4.08217e47 + 7.80345e46i −0.813835 + 0.155572i
\(325\) −1.46466e47 −0.275392
\(326\) 1.92370e47i 0.341195i
\(327\) −1.67343e47 + 1.83943e47i −0.280027 + 0.307805i
\(328\) 8.92247e47 1.40891
\(329\) 6.92057e47i 1.03138i
\(330\) −7.07498e46 6.43649e46i −0.0995315 0.0905491i
\(331\) −5.39840e47 −0.717023 −0.358511 0.933525i \(-0.616716\pi\)
−0.358511 + 0.933525i \(0.616716\pi\)
\(332\) 6.26773e47i 0.786116i
\(333\) −2.79692e45 2.95277e46i −0.00331314 0.0349775i
\(334\) −1.41935e47 −0.158820
\(335\) 1.24158e47i 0.131257i
\(336\) −2.61664e47 + 2.87621e47i −0.261396 + 0.287325i
\(337\) 5.79296e47 0.546931 0.273465 0.961882i \(-0.411830\pi\)
0.273465 + 0.961882i \(0.411830\pi\)
\(338\) 3.75142e47i 0.334794i
\(339\) 5.56555e47 + 5.06328e47i 0.469585 + 0.427206i
\(340\) 8.95119e47 0.714137
\(341\) 1.29916e48i 0.980237i
\(342\) −2.70360e47 + 2.56090e46i −0.192950 + 0.0182767i
\(343\) 1.59867e48 1.07937
\(344\) 1.27922e48i 0.817213i
\(345\) 5.07348e47 5.57676e47i 0.306721 0.337147i
\(346\) 8.38093e47 0.479564
\(347\) 1.23811e48i 0.670654i 0.942102 + 0.335327i \(0.108847\pi\)
−0.942102 + 0.335327i \(0.891153\pi\)
\(348\) −1.62077e48 1.47451e48i −0.831222 0.756207i
\(349\) −3.02513e48 −1.46913 −0.734566 0.678537i \(-0.762614\pi\)
−0.734566 + 0.678537i \(0.762614\pi\)
\(350\) 4.27316e47i 0.196542i
\(351\) 8.03182e47 + 6.02684e47i 0.349928 + 0.262575i
\(352\) −1.25520e48 −0.518085
\(353\) 1.78026e47i 0.0696249i −0.999394 0.0348125i \(-0.988917\pi\)
0.999394 0.0348125i \(-0.0110834\pi\)
\(354\) 8.04417e46 8.84214e46i 0.0298139 0.0327714i
\(355\) −2.10441e47 −0.0739250
\(356\) 2.30761e48i 0.768444i
\(357\) 2.50165e48 + 2.27589e48i 0.789824 + 0.718546i
\(358\) −2.61718e48 −0.783530
\(359\) 2.59770e48i 0.737555i −0.929518 0.368777i \(-0.879776\pi\)
0.929518 0.368777i \(-0.120224\pi\)
\(360\) −1.61367e47 1.70359e48i −0.0434578 0.458793i
\(361\) −3.05647e48 −0.780878
\(362\) 2.14634e48i 0.520278i
\(363\) 2.09159e48 2.29908e48i 0.481118 0.528844i
\(364\) 1.25213e48 0.273353
\(365\) 1.76527e48i 0.365803i
\(366\) −1.50795e48 1.37186e48i −0.296651 0.269880i
\(367\) −3.22556e48 −0.602491 −0.301245 0.953547i \(-0.597402\pi\)
−0.301245 + 0.953547i \(0.597402\pi\)
\(368\) 2.17452e48i 0.385705i
\(369\) 1.09974e49 1.04169e48i 1.85263 0.175485i
\(370\) 5.53358e46 0.00885469
\(371\) 6.17708e48i 0.939029i
\(372\) −7.08747e48 + 7.79054e48i −1.02371 + 1.12526i
\(373\) −3.04854e48 −0.418431 −0.209216 0.977870i \(-0.567091\pi\)
−0.209216 + 0.977870i \(0.567091\pi\)
\(374\) 2.39946e48i 0.313007i
\(375\) 5.91698e48 + 5.38300e48i 0.733679 + 0.667468i
\(376\) 8.78444e48 1.03549
\(377\) 5.29402e48i 0.593335i
\(378\) 1.75834e48 2.34330e48i 0.187395 0.249737i
\(379\) 2.53209e48 0.256646 0.128323 0.991732i \(-0.459041\pi\)
0.128323 + 0.991732i \(0.459041\pi\)
\(380\) 2.44886e48i 0.236089i
\(381\) −7.85767e48 + 8.63714e48i −0.720642 + 0.792128i
\(382\) 3.16262e48 0.275958
\(383\) 1.59490e49i 1.32421i −0.749413 0.662103i \(-0.769664\pi\)
0.749413 0.662103i \(-0.230336\pi\)
\(384\) −9.52344e48 8.66398e48i −0.752489 0.684580i
\(385\) −3.25872e48 −0.245072
\(386\) 7.02253e48i 0.502730i
\(387\) −1.49349e48 1.57670e49i −0.101787 1.07459i
\(388\) 2.03717e49 1.32198
\(389\) 3.60823e48i 0.222973i 0.993766 + 0.111487i \(0.0355612\pi\)
−0.993766 + 0.111487i \(0.964439\pi\)
\(390\) −1.26071e48 + 1.38577e48i −0.0741972 + 0.0815575i
\(391\) −1.89134e49 −1.06026
\(392\) 6.11510e48i 0.326564i
\(393\) −5.30451e48 4.82580e48i −0.269890 0.245534i
\(394\) 2.09023e48 0.101336
\(395\) 1.63693e49i 0.756286i
\(396\) −1.00014e49 + 9.47354e47i −0.440405 + 0.0417161i
\(397\) −1.50901e49 −0.633391 −0.316695 0.948527i \(-0.602573\pi\)
−0.316695 + 0.948527i \(0.602573\pi\)
\(398\) 2.39955e48i 0.0960177i
\(399\) −6.22636e48 + 6.84400e48i −0.237547 + 0.261111i
\(400\) 8.91288e48 0.324249
\(401\) 4.28089e49i 1.48522i −0.669724 0.742610i \(-0.733587\pi\)
0.669724 0.742610i \(-0.266413\pi\)
\(402\) −1.99578e48 1.81567e48i −0.0660415 0.0600815i
\(403\) 2.54466e49 0.803220
\(404\) 2.75941e49i 0.830940i
\(405\) −3.97786e48 2.08092e49i −0.114289 0.597873i
\(406\) 1.54454e49 0.423452
\(407\) 7.16944e47i 0.0187582i
\(408\) −2.88884e49 + 3.17540e49i −0.721406 + 0.792969i
\(409\) 1.75084e49 0.417353 0.208676 0.977985i \(-0.433084\pi\)
0.208676 + 0.977985i \(0.433084\pi\)
\(410\) 2.06094e49i 0.469000i
\(411\) 3.20444e49 + 2.91525e49i 0.696238 + 0.633406i
\(412\) 6.75275e49 1.40098
\(413\) 4.07267e48i 0.0806916i
\(414\) 1.54498e48 + 1.63107e49i 0.0292359 + 0.308650i
\(415\) −3.19502e49 −0.577510
\(416\) 2.45854e49i 0.424526i
\(417\) 1.71197e49 1.88180e49i 0.282431 0.310447i
\(418\) −6.56443e48 −0.103478
\(419\) 2.94106e49i 0.443034i 0.975156 + 0.221517i \(0.0711009\pi\)
−0.975156 + 0.221517i \(0.928899\pi\)
\(420\) −1.95412e49 1.77777e49i −0.281329 0.255940i
\(421\) −9.87880e49 −1.35939 −0.679695 0.733495i \(-0.737888\pi\)
−0.679695 + 0.733495i \(0.737888\pi\)
\(422\) 5.76676e49i 0.758569i
\(423\) 1.08273e50 1.02558e49i 1.36161 0.128974i
\(424\) −7.84072e49 −0.942767
\(425\) 7.75219e49i 0.891322i
\(426\) 3.07745e48 3.38272e48i 0.0338383 0.0371950i
\(427\) −6.94559e49 −0.730432
\(428\) 9.02430e49i 0.907783i
\(429\) 1.79544e49 + 1.63341e49i 0.172775 + 0.157183i
\(430\) 2.95479e49 0.272036
\(431\) 1.98622e50i 1.74968i 0.484413 + 0.874840i \(0.339033\pi\)
−0.484413 + 0.874840i \(0.660967\pi\)
\(432\) −4.88761e49 3.66752e49i −0.412008 0.309158i
\(433\) −8.49777e49 −0.685544 −0.342772 0.939419i \(-0.611366\pi\)
−0.342772 + 0.939419i \(0.611366\pi\)
\(434\) 7.42410e49i 0.573243i
\(435\) 7.51640e49 8.26201e49i 0.555538 0.610646i
\(436\) −4.87299e49 −0.344788
\(437\) 5.17433e49i 0.350515i
\(438\) 2.83758e49 + 2.58150e49i 0.184052 + 0.167442i
\(439\) 5.61434e49 0.348717 0.174358 0.984682i \(-0.444215\pi\)
0.174358 + 0.984682i \(0.444215\pi\)
\(440\) 4.13637e49i 0.246048i
\(441\) 7.13935e48 + 7.53716e49i 0.0406748 + 0.429412i
\(442\) 4.69981e49 0.256482
\(443\) 2.44317e50i 1.27727i 0.769511 + 0.638634i \(0.220500\pi\)
−0.769511 + 0.638634i \(0.779500\pi\)
\(444\) 3.91122e48 4.29921e48i 0.0195901 0.0215334i
\(445\) 1.17632e50 0.564527
\(446\) 2.05742e49i 0.0946150i
\(447\) 4.17786e49 + 3.80082e49i 0.184124 + 0.167508i
\(448\) −2.02324e49 −0.0854605
\(449\) 1.96170e49i 0.0794242i 0.999211 + 0.0397121i \(0.0126441\pi\)
−0.999211 + 0.0397121i \(0.987356\pi\)
\(450\) −6.68538e49 + 6.33253e48i −0.259471 + 0.0245776i
\(451\) 2.67021e50 0.993552
\(452\) 1.47442e50i 0.526006i
\(453\) 8.20226e49 9.01591e49i 0.280587 0.308421i
\(454\) −1.08682e50 −0.356532
\(455\) 6.38283e49i 0.200815i
\(456\) −8.68725e49 7.90326e49i −0.262150 0.238492i
\(457\) −1.68065e50 −0.486486 −0.243243 0.969965i \(-0.578211\pi\)
−0.243243 + 0.969965i \(0.578211\pi\)
\(458\) 1.53677e50i 0.426741i
\(459\) −3.18991e50 + 4.25111e50i −0.849840 + 1.13256i
\(460\) 1.47739e50 0.377655
\(461\) 4.39671e50i 1.07848i −0.842154 0.539238i \(-0.818712\pi\)
0.842154 0.539238i \(-0.181288\pi\)
\(462\) 4.76549e49 5.23822e49i 0.112179 0.123307i
\(463\) 3.58690e50 0.810365 0.405183 0.914236i \(-0.367208\pi\)
0.405183 + 0.914236i \(0.367208\pi\)
\(464\) 3.22157e50i 0.698597i
\(465\) −3.97128e50 3.61289e50i −0.826655 0.752053i
\(466\) −1.16234e50 −0.232274
\(467\) 7.02904e50i 1.34858i −0.738468 0.674288i \(-0.764451\pi\)
0.738468 0.674288i \(-0.235549\pi\)
\(468\) 1.85557e49 + 1.95897e50i 0.0341828 + 0.360874i
\(469\) −9.19251e49 −0.162611
\(470\) 2.02906e50i 0.344696i
\(471\) −3.28714e49 + 3.61321e49i −0.0536316 + 0.0589517i
\(472\) 5.16954e49 0.0810129
\(473\) 3.82829e50i 0.576293i
\(474\) −2.63128e50 2.39382e50i −0.380521 0.346181i
\(475\) 2.12084e50 0.294665
\(476\) 6.62734e50i 0.884723i
\(477\) −9.66407e50 + 9.15401e49i −1.23968 + 0.117425i
\(478\) 1.78035e50 0.219471
\(479\) 1.03282e51i 1.22363i 0.790999 + 0.611817i \(0.209561\pi\)
−0.790999 + 0.611817i \(0.790439\pi\)
\(480\) 3.49062e50 3.83688e50i 0.397483 0.436913i
\(481\) −1.40427e49 −0.0153707
\(482\) 3.70707e50i 0.390065i
\(483\) 4.12896e50 + 3.75634e50i 0.417681 + 0.379987i
\(484\) 6.09068e50 0.592385
\(485\) 1.03846e51i 0.971177i
\(486\) 3.92667e50 + 2.40367e50i 0.353131 + 0.216165i
\(487\) 9.70405e50 0.839272 0.419636 0.907692i \(-0.362158\pi\)
0.419636 + 0.907692i \(0.362158\pi\)
\(488\) 8.81620e50i 0.733339i
\(489\) 6.93117e50 7.61873e50i 0.554547 0.609557i
\(490\) −1.41249e50 −0.108707
\(491\) 1.32882e51i 0.983823i −0.870645 0.491911i \(-0.836298\pi\)
0.870645 0.491911i \(-0.163702\pi\)
\(492\) 1.60121e51 + 1.45671e51i 1.14054 + 1.03761i
\(493\) −2.80204e51 −1.92036
\(494\) 1.28577e50i 0.0847913i
\(495\) −4.82920e49 5.09829e50i −0.0306462 0.323538i
\(496\) −1.54851e51 −0.945717
\(497\) 1.55808e50i 0.0915835i
\(498\) 4.67233e50 5.13582e50i 0.264348 0.290571i
\(499\) 1.14247e51 0.622205 0.311102 0.950376i \(-0.399302\pi\)
0.311102 + 0.950376i \(0.399302\pi\)
\(500\) 1.56752e51i 0.821832i
\(501\) −5.62126e50 5.11397e50i −0.283738 0.258131i
\(502\) −2.39008e50 −0.116156
\(503\) 6.96254e49i 0.0325819i 0.999867 + 0.0162909i \(0.00518579\pi\)
−0.999867 + 0.0162909i \(0.994814\pi\)
\(504\) 1.26131e51 1.19474e50i 0.568385 0.0538386i
\(505\) −1.40663e51 −0.610439
\(506\) 3.96030e50i 0.165527i
\(507\) −1.35165e51 + 1.48573e51i −0.544143 + 0.598121i
\(508\) −2.28814e51 −0.887303
\(509\) 4.65910e51i 1.74046i −0.492644 0.870231i \(-0.663970\pi\)
0.492644 0.870231i \(-0.336030\pi\)
\(510\) −7.33466e50 6.67274e50i −0.263965 0.240143i
\(511\) 1.30698e51 0.453183
\(512\) 2.66338e51i 0.889824i
\(513\) −1.16302e51 8.72693e50i −0.374418 0.280952i
\(514\) −2.20883e51 −0.685272
\(515\) 3.44226e51i 1.02922i
\(516\) 2.08849e51 2.29566e51i 0.601850 0.661552i
\(517\) 2.62890e51 0.730220
\(518\) 4.09699e49i 0.0109698i
\(519\) 3.31923e51 + 3.01968e51i 0.856757 + 0.779438i
\(520\) −8.10188e50 −0.201615
\(521\) 4.37767e50i 0.105033i −0.998620 0.0525166i \(-0.983276\pi\)
0.998620 0.0525166i \(-0.0167242\pi\)
\(522\) 2.28890e50 + 2.41644e51i 0.0529526 + 0.559032i
\(523\) 4.43924e51 0.990322 0.495161 0.868801i \(-0.335109\pi\)
0.495161 + 0.868801i \(0.335109\pi\)
\(524\) 1.40526e51i 0.302318i
\(525\) −1.53964e51 + 1.69237e51i −0.319442 + 0.351130i
\(526\) −3.25777e50 −0.0651916
\(527\) 1.34685e52i 2.59967i
\(528\) −1.09258e51 9.93978e50i −0.203427 0.185068i
\(529\) 2.44582e51 0.439305
\(530\) 1.81108e51i 0.313831i
\(531\) 6.37172e50 6.03542e49i 0.106527 0.0100905i
\(532\) −1.81310e51 −0.292484
\(533\) 5.23011e51i 0.814130i
\(534\) −1.72023e51 + 1.89087e51i −0.258405 + 0.284039i
\(535\) 4.60020e51 0.666891
\(536\) 1.16683e51i 0.163258i
\(537\) −1.03652e52 9.42979e51i −1.39980 1.27348i
\(538\) 5.50106e51 0.717106
\(539\) 1.83005e51i 0.230291i
\(540\) 2.49174e51 3.32068e51i 0.302706 0.403409i
\(541\) 4.03992e51 0.473832 0.236916 0.971530i \(-0.423863\pi\)
0.236916 + 0.971530i \(0.423863\pi\)
\(542\) 2.40073e51i 0.271867i
\(543\) −7.73334e51 + 8.50047e51i −0.845610 + 0.929493i
\(544\) −1.30127e52 −1.37400
\(545\) 2.48404e51i 0.253294i
\(546\) −1.02601e51 9.33413e50i −0.101039 0.0919208i
\(547\) 1.41630e52 1.34709 0.673544 0.739147i \(-0.264771\pi\)
0.673544 + 0.739147i \(0.264771\pi\)
\(548\) 8.48917e51i 0.779892i
\(549\) −1.02929e51 1.08664e52i −0.0913403 0.964299i
\(550\) −1.62323e51 −0.139152
\(551\) 7.66580e51i 0.634859i
\(552\) −4.76801e51 + 5.24098e51i −0.381500 + 0.419344i
\(553\) −1.21196e52 −0.936940
\(554\) 7.01939e51i 0.524341i
\(555\) 2.19155e50 + 1.99377e50i 0.0158192 + 0.0143916i
\(556\) 4.98523e51 0.347748
\(557\) 1.20730e52i 0.813892i −0.913452 0.406946i \(-0.866594\pi\)
0.913452 0.406946i \(-0.133406\pi\)
\(558\) 1.16150e52 1.10020e51i 0.756782 0.0716840i
\(559\) −7.49845e51 −0.472223
\(560\) 3.88415e51i 0.236441i
\(561\) −8.64536e51 + 9.50296e51i −0.508731 + 0.559197i
\(562\) 1.13409e52 0.645147
\(563\) 2.27823e52i 1.25296i 0.779436 + 0.626482i \(0.215506\pi\)
−0.779436 + 0.626482i \(0.784494\pi\)
\(564\) 1.57644e52 + 1.43417e52i 0.838251 + 0.762603i
\(565\) −7.51595e51 −0.386423
\(566\) 3.87336e51i 0.192564i
\(567\) 1.54068e52 2.94516e51i 0.740687 0.141589i
\(568\) 1.97770e51 0.0919481
\(569\) 1.55143e52i 0.697587i 0.937200 + 0.348793i \(0.113409\pi\)
−0.937200 + 0.348793i \(0.886591\pi\)
\(570\) 1.82552e51 2.00661e51i 0.0793899 0.0872652i
\(571\) −2.97040e51 −0.124948 −0.0624740 0.998047i \(-0.519899\pi\)
−0.0624740 + 0.998047i \(0.519899\pi\)
\(572\) 4.75645e51i 0.193534i
\(573\) 1.25254e52 + 1.13951e52i 0.493009 + 0.448517i
\(574\) −1.52589e52 −0.581030
\(575\) 1.27949e52i 0.471356i
\(576\) −2.99830e50 3.16537e51i −0.0106868 0.112823i
\(577\) −8.21294e51 −0.283242 −0.141621 0.989921i \(-0.545231\pi\)
−0.141621 + 0.989921i \(0.545231\pi\)
\(578\) 1.24682e52i 0.416078i
\(579\) 2.53024e52 2.78124e52i 0.817090 0.898144i
\(580\) 2.18876e52 0.684016
\(581\) 2.36555e52i 0.715460i
\(582\) −1.66927e52 1.51863e52i −0.488642 0.444544i
\(583\) −2.34647e52 −0.664834
\(584\) 1.65899e52i 0.454987i
\(585\) −9.98597e51 + 9.45892e50i −0.265112 + 0.0251119i
\(586\) −6.15840e51 −0.158275
\(587\) 3.58770e52i 0.892673i −0.894865 0.446337i \(-0.852728\pi\)
0.894865 0.446337i \(-0.147272\pi\)
\(588\) −9.98367e51 + 1.09740e52i −0.240503 + 0.264361i
\(589\) −3.68470e52 −0.859433
\(590\) 1.19408e51i 0.0269677i
\(591\) 8.27825e51 + 7.53117e51i 0.181041 + 0.164703i
\(592\) 8.54543e50 0.0180976
\(593\) 4.28826e52i 0.879513i −0.898117 0.439756i \(-0.855065\pi\)
0.898117 0.439756i \(-0.144935\pi\)
\(594\) 8.90143e51 + 6.67937e51i 0.176814 + 0.132676i
\(595\) −3.37833e52 −0.649950
\(596\) 1.10679e52i 0.206247i
\(597\) 8.64567e51 9.50330e51i 0.156058 0.171539i
\(598\) 7.75700e51 0.135635
\(599\) 6.18793e52i 1.04818i 0.851663 + 0.524090i \(0.175595\pi\)
−0.851663 + 0.524090i \(0.824405\pi\)
\(600\) −2.14816e52 1.95430e52i −0.352527 0.320713i
\(601\) −2.85517e52 −0.453960 −0.226980 0.973899i \(-0.572885\pi\)
−0.226980 + 0.973899i \(0.572885\pi\)
\(602\) 2.18769e52i 0.337017i
\(603\) −1.36227e51 1.43817e52i −0.0203345 0.214675i
\(604\) 2.38848e52 0.345478
\(605\) 3.10477e52i 0.435188i
\(606\) 2.05702e52 2.26107e52i 0.279421 0.307139i
\(607\) 1.49174e53 1.96385 0.981927 0.189262i \(-0.0606094\pi\)
0.981927 + 0.189262i \(0.0606094\pi\)
\(608\) 3.56000e52i 0.454237i
\(609\) 6.11708e52 + 5.56504e52i 0.756512 + 0.688240i
\(610\) 2.03640e52 0.244116
\(611\) 5.14921e52i 0.598353i
\(612\) −1.03685e53 + 9.82126e51i −1.16799 + 0.110634i
\(613\) 5.96551e52 0.651476 0.325738 0.945460i \(-0.394387\pi\)
0.325738 + 0.945460i \(0.394387\pi\)
\(614\) 1.61135e52i 0.170604i
\(615\) −7.42566e52 + 8.16227e52i −0.762268 + 0.837884i
\(616\) 3.06252e52 0.304821
\(617\) 9.54719e52i 0.921420i 0.887551 + 0.460710i \(0.152405\pi\)
−0.887551 + 0.460710i \(0.847595\pi\)
\(618\) −5.53325e52 5.03389e52i −0.517844 0.471111i
\(619\) 4.48839e52 0.407350 0.203675 0.979039i \(-0.434711\pi\)
0.203675 + 0.979039i \(0.434711\pi\)
\(620\) 1.05207e53i 0.925979i
\(621\) −5.26492e52 + 7.01644e52i −0.449419 + 0.598930i
\(622\) 3.60130e52 0.298155
\(623\) 8.70931e52i 0.699376i
\(624\) −1.94690e52 + 2.14002e52i −0.151648 + 0.166691i
\(625\) 3.40633e51 0.0257375
\(626\) 3.02327e52i 0.221598i
\(627\) −2.59981e52 2.36519e52i −0.184867 0.168183i
\(628\) −9.57208e51 −0.0660348
\(629\) 7.43259e51i 0.0497482i
\(630\) 2.75966e51 + 2.91343e52i 0.0179219 + 0.189205i
\(631\) −2.42722e53 −1.52951 −0.764755 0.644321i \(-0.777140\pi\)
−0.764755 + 0.644321i \(0.777140\pi\)
\(632\) 1.53837e53i 0.940670i
\(633\) 2.07779e53 2.28390e53i 1.23291 1.35521i
\(634\) −3.57035e52 −0.205596
\(635\) 1.16639e53i 0.651846i
\(636\) −1.40708e53 1.28010e53i −0.763192 0.694317i
\(637\) 3.58451e52 0.188704
\(638\) 5.86721e52i 0.299805i
\(639\) 2.43762e52 2.30896e51i 0.120906 0.0114525i
\(640\) 1.28608e53 0.619227
\(641\) 6.15370e52i 0.287630i −0.989605 0.143815i \(-0.954063\pi\)
0.989605 0.143815i \(-0.0459370\pi\)
\(642\) −6.72724e52 + 7.39457e52i −0.305261 + 0.335542i
\(643\) −2.28770e53 −1.00784 −0.503919 0.863751i \(-0.668109\pi\)
−0.503919 + 0.863751i \(0.668109\pi\)
\(644\) 1.09384e53i 0.467866i
\(645\) 1.17023e53 + 1.06462e53i 0.486001 + 0.442141i
\(646\) −6.80538e52 −0.274432
\(647\) 3.20559e53i 1.25524i 0.778520 + 0.627620i \(0.215971\pi\)
−0.778520 + 0.627620i \(0.784029\pi\)
\(648\) 3.73836e52 + 1.95563e53i 0.142153 + 0.743636i
\(649\) 1.54708e52 0.0571298
\(650\) 3.17942e52i 0.114023i
\(651\) 2.67493e53 2.94028e53i 0.931696 1.02412i
\(652\) 2.01834e53 0.682796
\(653\) 1.70418e52i 0.0559969i −0.999608 0.0279984i \(-0.991087\pi\)
0.999608 0.0279984i \(-0.00891335\pi\)
\(654\) 3.99296e52 + 3.63261e52i 0.127443 + 0.115942i
\(655\) 7.16343e52 0.222094
\(656\) 3.18268e53i 0.958563i
\(657\) 1.93686e52 + 2.04478e53i 0.0566704 + 0.598281i
\(658\) −1.50229e53 −0.427033
\(659\) 4.17454e53i 1.15288i −0.817138 0.576442i \(-0.804441\pi\)
0.817138 0.576442i \(-0.195559\pi\)
\(660\) 6.75316e52 7.42306e52i 0.181206 0.199181i
\(661\) −3.32313e53 −0.866401 −0.433201 0.901298i \(-0.642616\pi\)
−0.433201 + 0.901298i \(0.642616\pi\)
\(662\) 1.17186e53i 0.296876i
\(663\) 1.86134e53 + 1.69336e53i 0.458214 + 0.416862i
\(664\) 3.00265e53 0.718308
\(665\) 9.24242e52i 0.214869i
\(666\) −6.40976e51 + 6.07145e50i −0.0144821 + 0.00137177i
\(667\) −4.62475e53 −1.01554
\(668\) 1.48918e53i 0.317829i
\(669\) 7.41295e52 8.14830e52i 0.153778 0.169033i
\(670\) 2.69518e52 0.0543458
\(671\) 2.63841e53i 0.517147i
\(672\) 2.84077e53 + 2.58441e53i 0.541278 + 0.492430i
\(673\) 4.02945e53 0.746380 0.373190 0.927755i \(-0.378264\pi\)
0.373190 + 0.927755i \(0.378264\pi\)
\(674\) 1.25751e53i 0.226451i
\(675\) −2.87588e53 2.15797e53i −0.503499 0.377810i
\(676\) −3.93598e53 −0.669986
\(677\) 1.02881e54i 1.70275i 0.524560 + 0.851374i \(0.324230\pi\)
−0.524560 + 0.851374i \(0.675770\pi\)
\(678\) 1.09912e53 1.20815e53i 0.176880 0.194427i
\(679\) −7.68864e53 −1.20316
\(680\) 4.28820e53i 0.652537i
\(681\) −4.30432e53 3.91587e53i −0.636956 0.579473i
\(682\) 2.82018e53 0.405857
\(683\) 1.37499e54i 1.92445i −0.272261 0.962223i \(-0.587771\pi\)
0.272261 0.962223i \(-0.412229\pi\)
\(684\) −2.68689e52 2.83661e53i −0.0365750 0.386130i
\(685\) −4.32741e53 −0.572938
\(686\) 3.47032e53i 0.446901i
\(687\) −5.53703e53 + 6.08630e53i −0.693584 + 0.762386i
\(688\) 4.56304e53 0.555999
\(689\) 4.59602e53i 0.544774i
\(690\) −1.21058e53 1.10133e53i −0.139592 0.126995i
\(691\) 4.56403e53 0.511995 0.255998 0.966677i \(-0.417596\pi\)
0.255998 + 0.966677i \(0.417596\pi\)
\(692\) 8.79326e53i 0.959697i
\(693\) 3.77470e53 3.57548e52i 0.400822 0.0379667i
\(694\) 2.68764e53 0.277677
\(695\) 2.54126e53i 0.255468i
\(696\) −7.06384e53 + 7.76456e53i −0.690979 + 0.759523i
\(697\) 2.76821e54 2.63498
\(698\) 6.56684e53i 0.608279i
\(699\) −4.60339e53 4.18795e53i −0.414965 0.377516i
\(700\) −4.48339e53 −0.393318
\(701\) 7.40728e53i 0.632435i 0.948687 + 0.316218i \(0.102413\pi\)
−0.948687 + 0.316218i \(0.897587\pi\)
\(702\) 1.30828e53 1.74352e53i 0.108717 0.144884i
\(703\) 2.03340e52 0.0164464
\(704\) 7.68564e52i 0.0605061i
\(705\) −7.31079e53 + 8.03601e53i −0.560236 + 0.615811i
\(706\) −3.86453e52 −0.0288275
\(707\) 1.04145e54i 0.756255i
\(708\) 9.27716e52 + 8.43993e52i 0.0655818 + 0.0596633i
\(709\) 2.08847e54 1.43731 0.718653 0.695369i \(-0.244759\pi\)
0.718653 + 0.695369i \(0.244759\pi\)
\(710\) 4.56817e52i 0.0306079i
\(711\) −1.79605e53 1.89612e54i −0.117164 1.23693i
\(712\) −1.10549e54 −0.702160
\(713\) 2.22297e54i 1.37478i
\(714\) 4.94041e53 5.43048e53i 0.297507 0.327019i
\(715\) −2.42463e53 −0.142178
\(716\) 2.74594e54i 1.56799i
\(717\) 7.05101e53 + 6.41468e53i 0.392091 + 0.356707i
\(718\) −5.63898e53 −0.305377
\(719\) 1.00454e54i 0.529809i 0.964275 + 0.264904i \(0.0853404\pi\)
−0.964275 + 0.264904i \(0.914660\pi\)
\(720\) 6.07677e53 5.75604e52i 0.312144 0.0295670i
\(721\) −2.54860e54 −1.27506
\(722\) 6.63486e53i 0.323314i
\(723\) −1.33567e54 + 1.46817e54i −0.633974 + 0.696863i
\(724\) −2.25193e54 −1.04117
\(725\) 1.89558e54i 0.853728i
\(726\) −4.99074e53 4.54035e53i −0.218962 0.199202i
\(727\) 9.26127e53 0.395837 0.197919 0.980218i \(-0.436582\pi\)
0.197919 + 0.980218i \(0.436582\pi\)
\(728\) 5.99852e53i 0.249775i
\(729\) 6.89090e53 + 2.36676e54i 0.279546 + 0.960132i
\(730\) −3.83198e53 −0.151457
\(731\) 3.96881e54i 1.52838i
\(732\) 1.43936e54 1.58214e54i 0.540080 0.593655i
\(733\) 1.72136e54 0.629355 0.314678 0.949199i \(-0.398104\pi\)
0.314678 + 0.949199i \(0.398104\pi\)
\(734\) 7.00193e53i 0.249455i
\(735\) −5.59409e53 5.08925e53i −0.194209 0.176683i
\(736\) −2.14774e54 −0.726611
\(737\) 3.49194e53i 0.115129i
\(738\) −2.26127e53 2.38727e54i −0.0726577 0.767062i
\(739\) 1.06435e54 0.333303 0.166652 0.986016i \(-0.446704\pi\)
0.166652 + 0.986016i \(0.446704\pi\)
\(740\) 5.80582e52i 0.0177199i
\(741\) −4.63268e53 + 5.09223e53i −0.137812 + 0.151482i
\(742\) 1.34090e54 0.388795
\(743\) 4.26412e54i 1.20515i 0.798061 + 0.602577i \(0.205859\pi\)
−0.798061 + 0.602577i \(0.794141\pi\)
\(744\) 3.73217e54 + 3.39536e54i 1.02820 + 0.935405i
\(745\) −5.64195e53 −0.151517
\(746\) 6.61765e53i 0.173247i
\(747\) 3.70091e54 3.50558e53i 0.944533 0.0894681i
\(748\) −2.51751e54 −0.626385
\(749\) 3.40593e54i 0.826191i
\(750\) 1.16852e54 1.28444e54i 0.276358 0.303772i
\(751\) −1.53622e54 −0.354237 −0.177119 0.984190i \(-0.556678\pi\)
−0.177119 + 0.984190i \(0.556678\pi\)
\(752\) 3.13345e54i 0.704505i
\(753\) −9.46582e53 8.61156e53i −0.207517 0.188789i
\(754\) 1.14920e54 0.245664
\(755\) 1.21755e54i 0.253801i
\(756\) 2.45858e54 + 1.84485e54i 0.499771 + 0.375013i
\(757\) −3.98519e54 −0.790000 −0.395000 0.918681i \(-0.629255\pi\)
−0.395000 + 0.918681i \(0.629255\pi\)