Properties

Label 21.22.c.b.20.19
Level $21$
Weight $22$
Character 21.20
Analytic conductor $58.690$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 22 \)
Character orbit: \([\chi]\) \(=\) 21.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(58.6902423003\)
Analytic rank: \(0\)
Dimension: \(52\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 20.19
Character \(\chi\) \(=\) 21.20
Dual form 21.22.c.b.20.20

$q$-expansion

\(f(q)\) \(=\) \(q-1077.74i q^{2} +(64855.1 - 79083.3i) q^{3} +935630. q^{4} -7.14030e6 q^{5} +(-8.52312e7 - 6.98969e7i) q^{6} +(-3.76236e8 + 6.45749e8i) q^{7} -3.26855e9i q^{8} +(-2.04799e9 - 1.02579e10i) q^{9} +O(q^{10})\) \(q-1077.74i q^{2} +(64855.1 - 79083.3i) q^{3} +935630. q^{4} -7.14030e6 q^{5} +(-8.52312e7 - 6.98969e7i) q^{6} +(-3.76236e8 + 6.45749e8i) q^{7} -3.26855e9i q^{8} +(-2.04799e9 - 1.02579e10i) q^{9} +7.69538e9i q^{10} -6.21657e8i q^{11} +(6.06803e10 - 7.39927e10i) q^{12} -3.37753e11i q^{13} +(6.95949e11 + 4.05485e11i) q^{14} +(-4.63085e11 + 5.64679e11i) q^{15} -1.56049e12 q^{16} -6.87345e12 q^{17} +(-1.10554e13 + 2.20720e12i) q^{18} +1.17334e13i q^{19} -6.68068e12 q^{20} +(2.66672e13 + 7.16341e13i) q^{21} -6.69984e11 q^{22} +8.43774e13i q^{23} +(-2.58488e14 - 2.11982e14i) q^{24} -4.25853e14 q^{25} -3.64010e14 q^{26} +(-9.44052e14 - 5.03316e14i) q^{27} +(-3.52018e14 + 6.04182e14i) q^{28} -6.05365e14i q^{29} +(6.08576e14 + 4.99085e14i) q^{30} +1.22561e15i q^{31} -5.17285e15i q^{32} +(-4.91627e13 - 4.03176e13i) q^{33} +7.40779e15i q^{34} +(2.68644e15 - 4.61084e15i) q^{35} +(-1.91616e15 - 9.59760e15i) q^{36} -3.62083e16 q^{37} +1.26456e16 q^{38} +(-2.67107e16 - 2.19050e16i) q^{39} +2.33384e16i q^{40} -1.58503e16 q^{41} +(7.72029e16 - 2.87402e16i) q^{42} -2.84588e16 q^{43} -5.81640e14i q^{44} +(1.46233e16 + 7.32446e16i) q^{45} +9.09368e16 q^{46} -2.36994e17 q^{47} +(-1.01205e17 + 1.23408e17i) q^{48} +(-2.75438e17 - 4.85909e17i) q^{49} +4.58959e17i q^{50} +(-4.45778e17 + 5.43575e17i) q^{51} -3.16012e17i q^{52} +6.88418e17i q^{53} +(-5.42443e17 + 1.01744e18i) q^{54} +4.43881e15i q^{55} +(2.11066e18 + 1.22975e18i) q^{56} +(9.27917e17 + 7.60972e17i) q^{57} -6.52426e17 q^{58} +4.19426e18 q^{59} +(-4.33276e17 + 5.28330e17i) q^{60} +5.56709e18i q^{61} +1.32089e18 q^{62} +(7.39457e18 + 2.53691e18i) q^{63} -8.84756e18 q^{64} +2.41166e18i q^{65} +(-4.34519e16 + 5.29845e16i) q^{66} -1.57639e19 q^{67} -6.43100e18 q^{68} +(6.67284e18 + 5.47230e18i) q^{69} +(-4.96929e18 - 2.89528e18i) q^{70} +7.43701e18i q^{71} +(-3.35285e19 + 6.69396e18i) q^{72} +4.27354e19i q^{73} +3.90231e19i q^{74} +(-2.76187e19 + 3.36779e19i) q^{75} +1.09781e19i q^{76} +(4.01434e17 + 2.33890e17i) q^{77} +(-2.36079e19 + 2.87871e19i) q^{78} -1.56226e20 q^{79} +1.11423e19 q^{80} +(-1.01030e20 + 4.20162e19i) q^{81} +1.70825e19i q^{82} +1.29172e20 q^{83} +(2.49506e19 + 6.70230e19i) q^{84} +4.90785e19 q^{85} +3.06712e19i q^{86} +(-4.78743e19 - 3.92610e19i) q^{87} -2.03191e18 q^{88} +4.94133e20 q^{89} +(7.89385e19 - 1.57601e19i) q^{90} +(2.18104e20 + 1.27075e20i) q^{91} +7.89460e19i q^{92} +(9.69253e19 + 7.94870e19i) q^{93} +2.55418e20i q^{94} -8.37801e19i q^{95} +(-4.09086e20 - 3.35485e20i) q^{96} -5.62341e19i q^{97} +(-5.23683e20 + 2.96851e20i) q^{98} +(-6.37690e18 + 1.27315e18i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q - 58720260q^{4} + 1422287188q^{7} + 10150644696q^{9} + O(q^{10}) \) \( 52q - 58720260q^{4} + 1422287188q^{7} + 10150644696q^{9} - 687153165468q^{15} + 36241782390404q^{16} + 36759093002772q^{18} + 79412641656180q^{21} + 228880341648112q^{22} + 4502168959229812q^{25} - 328465100861772q^{28} - 2422487119598196q^{30} + 94669723666911312q^{36} - 111253244635261912q^{37} - 198389110134084780q^{39} - 125754675449474820q^{42} + 808208758088766656q^{43} - 1124214920076830456q^{46} + 760563680048831596q^{49} + 4341973540932052200q^{51} - 13080454499124088812q^{57} - 10814528487339424568q^{58} + 13643758017961015644q^{60} - 38182310822257441896q^{63} - 30480555033993680900q^{64} - 25547251957658589040q^{67} + 73727169165159410040q^{70} + 39846964674222889428q^{72} + 45848199464273536260q^{78} + 199210197493083963080q^{79} + 235499606962845306588q^{81} - 373919224753720758924q^{84} - 570842672309470848672q^{85} - 1060053674241923431168q^{88} - 923077800435233893128q^{91} - 2832166256981601869904q^{93} + 1525182290356701596928q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1077.74i 0.744216i −0.928189 0.372108i \(-0.878635\pi\)
0.928189 0.372108i \(-0.121365\pi\)
\(3\) 64855.1 79083.3i 0.634119 0.773235i
\(4\) 935630. 0.446143
\(5\) −7.14030e6 −0.326988 −0.163494 0.986544i \(-0.552276\pi\)
−0.163494 + 0.986544i \(0.552276\pi\)
\(6\) −8.52312e7 6.98969e7i −0.575454 0.471921i
\(7\) −3.76236e8 + 6.45749e8i −0.503421 + 0.864041i
\(8\) 3.26855e9i 1.07624i
\(9\) −2.04799e9 1.02579e10i −0.195786 0.980647i
\(10\) 7.69538e9i 0.243349i
\(11\) 6.21657e8i 0.00722649i −0.999993 0.00361324i \(-0.998850\pi\)
0.999993 0.00361324i \(-0.00115013\pi\)
\(12\) 6.06803e10 7.39927e10i 0.282908 0.344974i
\(13\) 3.37753e11i 0.679508i −0.940514 0.339754i \(-0.889656\pi\)
0.940514 0.339754i \(-0.110344\pi\)
\(14\) 6.95949e11 + 4.05485e11i 0.643033 + 0.374654i
\(15\) −4.63085e11 + 5.64679e11i −0.207349 + 0.252838i
\(16\) −1.56049e12 −0.354813
\(17\) −6.87345e12 −0.826915 −0.413458 0.910523i \(-0.635679\pi\)
−0.413458 + 0.910523i \(0.635679\pi\)
\(18\) −1.10554e13 + 2.20720e12i −0.729813 + 0.145707i
\(19\) 1.17334e13i 0.439048i 0.975607 + 0.219524i \(0.0704504\pi\)
−0.975607 + 0.219524i \(0.929550\pi\)
\(20\) −6.68068e12 −0.145883
\(21\) 2.66672e13 + 7.16341e13i 0.348878 + 0.937168i
\(22\) −6.69984e11 −0.00537807
\(23\) 8.43774e13i 0.424701i 0.977194 + 0.212351i \(0.0681119\pi\)
−0.977194 + 0.212351i \(0.931888\pi\)
\(24\) −2.58488e14 2.11982e14i −0.832189 0.682466i
\(25\) −4.25853e14 −0.893079
\(26\) −3.64010e14 −0.505700
\(27\) −9.44052e14 5.03316e14i −0.882422 0.470458i
\(28\) −3.52018e14 + 6.04182e14i −0.224598 + 0.385486i
\(29\) 6.05365e14i 0.267201i −0.991035 0.133601i \(-0.957346\pi\)
0.991035 0.133601i \(-0.0426539\pi\)
\(30\) 6.08576e14 + 4.99085e14i 0.188166 + 0.154312i
\(31\) 1.22561e15i 0.268568i 0.990943 + 0.134284i \(0.0428734\pi\)
−0.990943 + 0.134284i \(0.957127\pi\)
\(32\) 5.17285e15i 0.812185i
\(33\) −4.91627e13 4.03176e13i −0.00558778 0.00458245i
\(34\) 7.40779e15i 0.615403i
\(35\) 2.68644e15 4.61084e15i 0.164612 0.282531i
\(36\) −1.91616e15 9.59760e15i −0.0873485 0.437509i
\(37\) −3.62083e16 −1.23791 −0.618957 0.785425i \(-0.712444\pi\)
−0.618957 + 0.785425i \(0.712444\pi\)
\(38\) 1.26456e16 0.326746
\(39\) −2.67107e16 2.19050e16i −0.525420 0.430889i
\(40\) 2.33384e16i 0.351918i
\(41\) −1.58503e16 −0.184420 −0.0922100 0.995740i \(-0.529393\pi\)
−0.0922100 + 0.995740i \(0.529393\pi\)
\(42\) 7.72029e16 2.87402e16i 0.697455 0.259641i
\(43\) −2.84588e16 −0.200816 −0.100408 0.994946i \(-0.532015\pi\)
−0.100408 + 0.994946i \(0.532015\pi\)
\(44\) 5.81640e14i 0.00322405i
\(45\) 1.46233e16 + 7.32446e16i 0.0640196 + 0.320659i
\(46\) 9.09368e16 0.316069
\(47\) −2.36994e17 −0.657219 −0.328609 0.944466i \(-0.606580\pi\)
−0.328609 + 0.944466i \(0.606580\pi\)
\(48\) −1.01205e17 + 1.23408e17i −0.224994 + 0.274354i
\(49\) −2.75438e17 4.85909e17i −0.493134 0.869953i
\(50\) 4.58959e17i 0.664643i
\(51\) −4.45778e17 + 5.43575e17i −0.524363 + 0.639400i
\(52\) 3.16012e17i 0.303158i
\(53\) 6.88418e17i 0.540699i 0.962762 + 0.270350i \(0.0871393\pi\)
−0.962762 + 0.270350i \(0.912861\pi\)
\(54\) −5.42443e17 + 1.01744e18i −0.350122 + 0.656713i
\(55\) 4.43881e15i 0.00236297i
\(56\) 2.11066e18 + 1.22975e18i 0.929918 + 0.541803i
\(57\) 9.27917e17 + 7.60972e17i 0.339487 + 0.278408i
\(58\) −6.52426e17 −0.198855
\(59\) 4.19426e18 1.06834 0.534170 0.845377i \(-0.320624\pi\)
0.534170 + 0.845377i \(0.320624\pi\)
\(60\) −4.33276e17 + 5.28330e17i −0.0925074 + 0.112802i
\(61\) 5.56709e18i 0.999229i 0.866248 + 0.499615i \(0.166525\pi\)
−0.866248 + 0.499615i \(0.833475\pi\)
\(62\) 1.32089e18 0.199873
\(63\) 7.39457e18 + 2.53691e18i 0.945882 + 0.324511i
\(64\) −8.84756e18 −0.959254
\(65\) 2.41166e18i 0.222191i
\(66\) −4.34519e16 + 5.29845e16i −0.00341033 + 0.00415851i
\(67\) −1.57639e19 −1.05652 −0.528261 0.849082i \(-0.677156\pi\)
−0.528261 + 0.849082i \(0.677156\pi\)
\(68\) −6.43100e18 −0.368922
\(69\) 6.67284e18 + 5.47230e18i 0.328394 + 0.269311i
\(70\) −4.96929e18 2.89528e18i −0.210264 0.122507i
\(71\) 7.43701e18i 0.271135i 0.990768 + 0.135567i \(0.0432857\pi\)
−0.990768 + 0.135567i \(0.956714\pi\)
\(72\) −3.35285e19 + 6.69396e18i −1.05541 + 0.210713i
\(73\) 4.27354e19i 1.16385i 0.813242 + 0.581926i \(0.197701\pi\)
−0.813242 + 0.581926i \(0.802299\pi\)
\(74\) 3.90231e19i 0.921275i
\(75\) −2.76187e19 + 3.36779e19i −0.566318 + 0.690560i
\(76\) 1.09781e19i 0.195878i
\(77\) 4.01434e17 + 2.33890e17i 0.00624398 + 0.00363797i
\(78\) −2.36079e19 + 2.87871e19i −0.320674 + 0.391026i
\(79\) −1.56226e20 −1.85639 −0.928196 0.372092i \(-0.878641\pi\)
−0.928196 + 0.372092i \(0.878641\pi\)
\(80\) 1.11423e19 0.116020
\(81\) −1.01030e20 + 4.20162e19i −0.923336 + 0.383994i
\(82\) 1.70825e19i 0.137248i
\(83\) 1.29172e20 0.913793 0.456897 0.889520i \(-0.348961\pi\)
0.456897 + 0.889520i \(0.348961\pi\)
\(84\) 2.49506e19 + 6.70230e19i 0.155650 + 0.418111i
\(85\) 4.90785e19 0.270391
\(86\) 3.06712e19i 0.149450i
\(87\) −4.78743e19 3.92610e19i −0.206609 0.169437i
\(88\) −2.03191e18 −0.00777745
\(89\) 4.94133e20 1.67977 0.839883 0.542767i \(-0.182623\pi\)
0.839883 + 0.542767i \(0.182623\pi\)
\(90\) 7.89385e19 1.57601e19i 0.238640 0.0476444i
\(91\) 2.18104e20 + 1.27075e20i 0.587123 + 0.342079i
\(92\) 7.89460e19i 0.189478i
\(93\) 9.69253e19 + 7.94870e19i 0.207666 + 0.170304i
\(94\) 2.55418e20i 0.489112i
\(95\) 8.37801e19i 0.143563i
\(96\) −4.09086e20 3.35485e20i −0.628010 0.515022i
\(97\) 5.62341e19i 0.0774277i −0.999250 0.0387139i \(-0.987674\pi\)
0.999250 0.0387139i \(-0.0123261\pi\)
\(98\) −5.23683e20 + 2.96851e20i −0.647433 + 0.366998i
\(99\) −6.37690e18 + 1.27315e18i −0.00708663 + 0.00141485i
\(100\) −3.98441e20 −0.398441
\(101\) 7.78423e20 0.701199 0.350599 0.936526i \(-0.385978\pi\)
0.350599 + 0.936526i \(0.385978\pi\)
\(102\) 5.85832e20 + 4.80433e20i 0.475852 + 0.390239i
\(103\) 1.44000e21i 1.05578i −0.849314 0.527888i \(-0.822984\pi\)
0.849314 0.527888i \(-0.177016\pi\)
\(104\) −1.10396e21 −0.731315
\(105\) −1.90411e20 5.11489e20i −0.114079 0.306442i
\(106\) 7.41936e20 0.402397
\(107\) 2.60763e21i 1.28149i −0.767752 0.640747i \(-0.778625\pi\)
0.767752 0.640747i \(-0.221375\pi\)
\(108\) −8.83283e20 4.70917e20i −0.393687 0.209892i
\(109\) 1.47050e21 0.594957 0.297479 0.954728i \(-0.403854\pi\)
0.297479 + 0.954728i \(0.403854\pi\)
\(110\) 4.78389e18 0.00175856
\(111\) −2.34829e21 + 2.86347e21i −0.784985 + 0.957199i
\(112\) 5.87112e20 1.00768e21i 0.178621 0.306573i
\(113\) 6.05155e21i 1.67704i −0.544873 0.838519i \(-0.683422\pi\)
0.544873 0.838519i \(-0.316578\pi\)
\(114\) 8.20129e20 1.00005e21i 0.207196 0.252652i
\(115\) 6.02480e20i 0.138872i
\(116\) 5.66397e20i 0.119210i
\(117\) −3.46464e21 + 6.91716e20i −0.666357 + 0.133038i
\(118\) 4.52032e21i 0.795076i
\(119\) 2.58604e21 4.43852e21i 0.416287 0.714489i
\(120\) 1.84568e21 + 1.51361e21i 0.272115 + 0.223158i
\(121\) 7.39986e21 0.999948
\(122\) 5.99987e21 0.743642
\(123\) −1.02798e21 + 1.25350e21i −0.116944 + 0.142600i
\(124\) 1.14672e21i 0.119820i
\(125\) 6.44548e21 0.619014
\(126\) 2.73413e21 7.96942e21i 0.241506 0.703940i
\(127\) −7.21609e21 −0.586628 −0.293314 0.956016i \(-0.594758\pi\)
−0.293314 + 0.956016i \(0.594758\pi\)
\(128\) 1.31288e21i 0.0982926i
\(129\) −1.84570e21 + 2.25062e21i −0.127341 + 0.155278i
\(130\) 2.59914e21 0.165358
\(131\) −1.65885e22 −0.973778 −0.486889 0.873464i \(-0.661868\pi\)
−0.486889 + 0.873464i \(0.661868\pi\)
\(132\) −4.59980e19 3.77223e19i −0.00249295 0.00204443i
\(133\) −7.57684e21 4.41454e21i −0.379355 0.221026i
\(134\) 1.69894e22i 0.786281i
\(135\) 6.74082e21 + 3.59383e21i 0.288541 + 0.153834i
\(136\) 2.24662e22i 0.889961i
\(137\) 4.04119e22i 1.48232i 0.671327 + 0.741161i \(0.265725\pi\)
−0.671327 + 0.741161i \(0.734275\pi\)
\(138\) 5.89771e21 7.19159e21i 0.200426 0.244396i
\(139\) 7.25523e21i 0.228558i −0.993449 0.114279i \(-0.963544\pi\)
0.993449 0.114279i \(-0.0364557\pi\)
\(140\) 2.51351e21 4.31404e21i 0.0734407 0.126049i
\(141\) −1.53703e22 + 1.87423e22i −0.416755 + 0.508185i
\(142\) 8.01515e21 0.201783
\(143\) −2.09967e20 −0.00491046
\(144\) 3.19586e21 + 1.60073e22i 0.0694675 + 0.347947i
\(145\) 4.32249e21i 0.0873715i
\(146\) 4.60576e22 0.866157
\(147\) −5.62908e22 9.73108e21i −0.985385 0.170345i
\(148\) −3.38776e22 −0.552286
\(149\) 5.74877e22i 0.873210i −0.899653 0.436605i \(-0.856181\pi\)
0.899653 0.436605i \(-0.143819\pi\)
\(150\) 3.62960e22 + 2.97658e22i 0.513926 + 0.421463i
\(151\) −1.09733e23 −1.44903 −0.724515 0.689259i \(-0.757936\pi\)
−0.724515 + 0.689259i \(0.757936\pi\)
\(152\) 3.83512e22 0.472522
\(153\) 1.40768e22 + 7.05072e22i 0.161898 + 0.810912i
\(154\) 2.52072e20 4.32642e20i 0.00270743 0.00464687i
\(155\) 8.75122e21i 0.0878184i
\(156\) −2.49913e22 2.04950e22i −0.234412 0.192238i
\(157\) 7.99062e21i 0.0700865i −0.999386 0.0350432i \(-0.988843\pi\)
0.999386 0.0350432i \(-0.0111569\pi\)
\(158\) 1.68371e23i 1.38156i
\(159\) 5.44424e22 + 4.46474e22i 0.418088 + 0.342868i
\(160\) 3.69357e22i 0.265574i
\(161\) −5.44866e22 3.17458e22i −0.366959 0.213804i
\(162\) 4.52825e22 + 1.08885e23i 0.285774 + 0.687161i
\(163\) −1.71233e23 −1.01302 −0.506510 0.862234i \(-0.669065\pi\)
−0.506510 + 0.862234i \(0.669065\pi\)
\(164\) −1.48300e22 −0.0822777
\(165\) 3.51036e20 + 2.87880e20i 0.00182713 + 0.00149841i
\(166\) 1.39214e23i 0.680059i
\(167\) −3.54755e23 −1.62707 −0.813533 0.581519i \(-0.802459\pi\)
−0.813533 + 0.581519i \(0.802459\pi\)
\(168\) 2.34140e23 8.71629e22i 1.00862 0.375478i
\(169\) 1.32987e23 0.538269
\(170\) 5.28938e22i 0.201229i
\(171\) 1.20360e23 2.40299e22i 0.430551 0.0859594i
\(172\) −2.66269e22 −0.0895926
\(173\) −1.34777e23 −0.426709 −0.213354 0.976975i \(-0.568439\pi\)
−0.213354 + 0.976975i \(0.568439\pi\)
\(174\) −4.23131e22 + 5.15960e22i −0.126098 + 0.153762i
\(175\) 1.60222e23 2.74994e23i 0.449595 0.771657i
\(176\) 9.70087e20i 0.00256406i
\(177\) 2.72019e23 3.31696e23i 0.677455 0.826079i
\(178\) 5.32547e23i 1.25011i
\(179\) 6.29190e23i 1.39260i 0.717753 + 0.696298i \(0.245171\pi\)
−0.717753 + 0.696298i \(0.754829\pi\)
\(180\) 1.36820e22 + 6.85298e22i 0.0285619 + 0.143060i
\(181\) 8.74990e22i 0.172337i −0.996281 0.0861684i \(-0.972538\pi\)
0.996281 0.0861684i \(-0.0274623\pi\)
\(182\) 1.36954e23 2.35059e23i 0.254580 0.436946i
\(183\) 4.40264e23 + 3.61054e23i 0.772639 + 0.633630i
\(184\) 2.75792e23 0.457082
\(185\) 2.58538e23 0.404783
\(186\) 8.56663e22 1.04460e23i 0.126743 0.154549i
\(187\) 4.27293e21i 0.00597569i
\(188\) −2.21739e23 −0.293213
\(189\) 6.80203e23 4.20255e23i 0.850725 0.525611i
\(190\) −9.02931e22 −0.106842
\(191\) 1.61611e24i 1.80976i −0.425668 0.904879i \(-0.639961\pi\)
0.425668 0.904879i \(-0.360039\pi\)
\(192\) −5.73809e23 + 6.99694e23i −0.608281 + 0.741729i
\(193\) 1.92008e23 0.192738 0.0963691 0.995346i \(-0.469277\pi\)
0.0963691 + 0.995346i \(0.469277\pi\)
\(194\) −6.06057e22 −0.0576229
\(195\) 1.90722e23 + 1.56408e23i 0.171806 + 0.140895i
\(196\) −2.57708e23 4.54631e23i −0.220008 0.388123i
\(197\) 1.23814e24i 1.00202i −0.865443 0.501008i \(-0.832963\pi\)
0.865443 0.501008i \(-0.167037\pi\)
\(198\) 1.37212e21 + 6.87263e21i 0.00105295 + 0.00527398i
\(199\) 1.90069e24i 1.38342i −0.722176 0.691710i \(-0.756858\pi\)
0.722176 0.691710i \(-0.243142\pi\)
\(200\) 1.39192e24i 0.961169i
\(201\) −1.02237e24 + 1.24666e24i −0.669961 + 0.816941i
\(202\) 8.38937e23i 0.521843i
\(203\) 3.90914e23 + 2.27760e23i 0.230873 + 0.134515i
\(204\) −4.17083e23 + 5.08585e23i −0.233941 + 0.285264i
\(205\) 1.13176e23 0.0603031
\(206\) −1.55195e24 −0.785725
\(207\) 8.65535e23 1.72804e23i 0.416482 0.0831506i
\(208\) 5.27060e23i 0.241099i
\(209\) 7.29415e21 0.00317277
\(210\) −5.51252e23 + 2.05214e23i −0.228059 + 0.0848993i
\(211\) −2.81290e24 −1.10710 −0.553552 0.832815i \(-0.686728\pi\)
−0.553552 + 0.832815i \(0.686728\pi\)
\(212\) 6.44105e23i 0.241229i
\(213\) 5.88143e23 + 4.82328e23i 0.209651 + 0.171932i
\(214\) −2.81035e24 −0.953708
\(215\) 2.03204e23 0.0656643
\(216\) −1.64511e24 + 3.08568e24i −0.506327 + 0.949700i
\(217\) −7.91436e23 4.61119e23i −0.232054 0.135203i
\(218\) 1.58481e24i 0.442777i
\(219\) 3.37966e24 + 2.77161e24i 0.899931 + 0.738021i
\(220\) 4.15309e21i 0.00105422i
\(221\) 2.32153e24i 0.561896i
\(222\) 3.08608e24 + 2.53085e24i 0.712362 + 0.584198i
\(223\) 2.45705e23i 0.0541021i 0.999634 + 0.0270510i \(0.00861166\pi\)
−0.999634 + 0.0270510i \(0.991388\pi\)
\(224\) 3.34036e24 + 1.94621e24i 0.701761 + 0.408871i
\(225\) 8.72143e23 + 4.36836e24i 0.174852 + 0.875795i
\(226\) −6.52199e24 −1.24808
\(227\) 1.08437e25 1.98109 0.990545 0.137190i \(-0.0438070\pi\)
0.990545 + 0.137190i \(0.0438070\pi\)
\(228\) 8.68187e23 + 7.11988e23i 0.151460 + 0.124210i
\(229\) 7.03610e24i 1.17236i −0.810183 0.586178i \(-0.800632\pi\)
0.810183 0.586178i \(-0.199368\pi\)
\(230\) −6.49316e23 −0.103351
\(231\) 4.45318e22 1.65778e22i 0.00677243 0.00252117i
\(232\) −1.97866e24 −0.287573
\(233\) 3.24912e24i 0.451366i 0.974201 + 0.225683i \(0.0724613\pi\)
−0.974201 + 0.225683i \(0.927539\pi\)
\(234\) 7.45489e23 + 3.73398e24i 0.0990091 + 0.495913i
\(235\) 1.69221e24 0.214902
\(236\) 3.92428e24 0.476633
\(237\) −1.01321e25 + 1.23549e25i −1.17717 + 1.43543i
\(238\) −4.78357e24 2.78708e24i −0.531734 0.309807i
\(239\) 1.00716e24i 0.107132i −0.998564 0.0535662i \(-0.982941\pi\)
0.998564 0.0535662i \(-0.0170588\pi\)
\(240\) 7.22637e23 8.81173e23i 0.0735703 0.0897105i
\(241\) 1.65145e25i 1.60949i −0.593623 0.804743i \(-0.702303\pi\)
0.593623 0.804743i \(-0.297697\pi\)
\(242\) 7.97513e24i 0.744177i
\(243\) −3.22956e24 + 1.07148e25i −0.288587 + 0.957454i
\(244\) 5.20874e24i 0.445799i
\(245\) 1.96671e24 + 3.46953e24i 0.161249 + 0.284464i
\(246\) 1.35094e24 + 1.10789e24i 0.106125 + 0.0870318i
\(247\) 3.96300e24 0.298336
\(248\) 4.00596e24 0.289044
\(249\) 8.37745e24 1.02153e25i 0.579454 0.706577i
\(250\) 6.94655e24i 0.460680i
\(251\) −2.59270e25 −1.64884 −0.824418 0.565981i \(-0.808498\pi\)
−0.824418 + 0.565981i \(0.808498\pi\)
\(252\) 6.91857e24 + 2.37361e24i 0.421999 + 0.144778i
\(253\) 5.24537e22 0.00306910
\(254\) 7.77707e24i 0.436578i
\(255\) 3.18299e24 3.88129e24i 0.171460 0.209076i
\(256\) −1.99696e25 −1.03240
\(257\) −2.85855e25 −1.41856 −0.709279 0.704927i \(-0.750980\pi\)
−0.709279 + 0.704927i \(0.750980\pi\)
\(258\) 2.42558e24 + 1.98918e24i 0.115560 + 0.0947693i
\(259\) 1.36229e25 2.33815e25i 0.623192 1.06961i
\(260\) 2.25642e24i 0.0991288i
\(261\) −6.20978e24 + 1.23978e24i −0.262030 + 0.0523142i
\(262\) 1.78781e25i 0.724701i
\(263\) 4.87018e25i 1.89675i −0.317153 0.948374i \(-0.602727\pi\)
0.317153 0.948374i \(-0.397273\pi\)
\(264\) −1.31780e23 + 1.60691e23i −0.00493183 + 0.00601380i
\(265\) 4.91551e24i 0.176802i
\(266\) −4.75772e24 + 8.16586e24i −0.164491 + 0.282322i
\(267\) 3.20471e25 3.90777e25i 1.06517 1.29886i
\(268\) −1.47492e25 −0.471360
\(269\) 1.71594e25 0.527355 0.263678 0.964611i \(-0.415064\pi\)
0.263678 + 0.964611i \(0.415064\pi\)
\(270\) 3.87321e24 7.26484e24i 0.114486 0.214737i
\(271\) 5.72937e24i 0.162903i 0.996677 + 0.0814515i \(0.0259556\pi\)
−0.996677 + 0.0814515i \(0.974044\pi\)
\(272\) 1.07259e25 0.293401
\(273\) 2.41947e25 9.00692e24i 0.636813 0.237066i
\(274\) 4.35535e25 1.10317
\(275\) 2.64734e23i 0.00645383i
\(276\) 6.24331e24 + 5.12005e24i 0.146511 + 0.120151i
\(277\) 6.39436e25 1.44464 0.722320 0.691559i \(-0.243076\pi\)
0.722320 + 0.691559i \(0.243076\pi\)
\(278\) −7.81925e24 −0.170096
\(279\) 1.25722e25 2.51004e24i 0.263370 0.0525819i
\(280\) −1.50708e25 8.78076e24i −0.304072 0.177163i
\(281\) 5.72925e24i 0.111348i 0.998449 + 0.0556739i \(0.0177307\pi\)
−0.998449 + 0.0556739i \(0.982269\pi\)
\(282\) 2.01993e25 + 1.65651e25i 0.378199 + 0.310155i
\(283\) 5.34411e25i 0.964090i −0.876147 0.482045i \(-0.839894\pi\)
0.876147 0.482045i \(-0.160106\pi\)
\(284\) 6.95828e24i 0.120965i
\(285\) −6.62561e24 5.43357e24i −0.111008 0.0910361i
\(286\) 2.26289e23i 0.00365444i
\(287\) 5.96348e24 1.02353e25i 0.0928409 0.159347i
\(288\) −5.30626e25 + 1.05939e25i −0.796466 + 0.159014i
\(289\) −2.18476e25 −0.316211
\(290\) 4.65851e24 0.0650232
\(291\) −4.44718e24 3.64707e24i −0.0598699 0.0490984i
\(292\) 3.99845e25i 0.519244i
\(293\) −1.11333e26 −1.39480 −0.697402 0.716680i \(-0.745661\pi\)
−0.697402 + 0.716680i \(0.745661\pi\)
\(294\) −1.04876e25 + 6.06669e25i −0.126773 + 0.733339i
\(295\) −2.99483e25 −0.349334
\(296\) 1.18349e26i 1.33230i
\(297\) −3.12890e23 + 5.86876e23i −0.00339976 + 0.00637682i
\(298\) −6.19567e25 −0.649857
\(299\) 2.84987e25 0.288588
\(300\) −2.58409e25 + 3.15100e25i −0.252659 + 0.308089i
\(301\) 1.07072e25 1.83773e25i 0.101095 0.173513i
\(302\) 1.18263e26i 1.07839i
\(303\) 5.04847e25 6.15602e25i 0.444643 0.542192i
\(304\) 1.83098e25i 0.155780i
\(305\) 3.97507e25i 0.326736i
\(306\) 7.59884e25 1.51711e25i 0.603493 0.120487i
\(307\) 2.15589e26i 1.65452i 0.561817 + 0.827261i \(0.310102\pi\)
−0.561817 + 0.827261i \(0.689898\pi\)
\(308\) 3.75594e23 + 2.18834e23i 0.00278571 + 0.00162305i
\(309\) −1.13880e26 9.33914e25i −0.816364 0.669488i
\(310\) −9.43154e24 −0.0653559
\(311\) 1.36821e26 0.916576 0.458288 0.888804i \(-0.348463\pi\)
0.458288 + 0.888804i \(0.348463\pi\)
\(312\) −7.15976e25 + 8.73051e25i −0.463741 + 0.565479i
\(313\) 1.05616e26i 0.661474i 0.943723 + 0.330737i \(0.107297\pi\)
−0.943723 + 0.330737i \(0.892703\pi\)
\(314\) −8.61181e24 −0.0521595
\(315\) −5.27994e25 1.81143e25i −0.309292 0.106111i
\(316\) −1.46170e26 −0.828216
\(317\) 1.49928e26i 0.821790i −0.911683 0.410895i \(-0.865216\pi\)
0.911683 0.410895i \(-0.134784\pi\)
\(318\) 4.81183e25 5.86747e25i 0.255168 0.311148i
\(319\) −3.76329e23 −0.00193093
\(320\) 6.31742e25 0.313664
\(321\) −2.06220e26 1.69118e26i −0.990897 0.812620i
\(322\) −3.42137e25 + 5.87224e25i −0.159116 + 0.273097i
\(323\) 8.06490e25i 0.363055i
\(324\) −9.45271e25 + 3.93116e25i −0.411940 + 0.171316i
\(325\) 1.43833e26i 0.606854i
\(326\) 1.84545e26i 0.753905i
\(327\) 9.53692e25 1.16292e26i 0.377274 0.460042i
\(328\) 5.18076e25i 0.198481i
\(329\) 8.91658e25 1.53039e26i 0.330858 0.567864i
\(330\) 3.10259e23 3.78326e23i 0.00111514 0.00135978i
\(331\) 1.65667e26 0.576822 0.288411 0.957507i \(-0.406873\pi\)
0.288411 + 0.957507i \(0.406873\pi\)
\(332\) 1.20857e26 0.407682
\(333\) 7.41543e25 + 3.71422e26i 0.242366 + 1.21396i
\(334\) 3.82333e26i 1.21089i
\(335\) 1.12559e26 0.345470
\(336\) −4.16137e25 1.11784e26i −0.123787 0.332520i
\(337\) 3.84946e26 1.10991 0.554953 0.831882i \(-0.312736\pi\)
0.554953 + 0.831882i \(0.312736\pi\)
\(338\) 1.43326e26i 0.400588i
\(339\) −4.78576e26 3.92474e26i −1.29674 1.06344i
\(340\) 4.59193e25 0.120633
\(341\) 7.61908e23 0.00194080
\(342\) −2.58980e25 1.29717e26i −0.0639723 0.320423i
\(343\) 4.17405e26 + 4.95254e24i 0.999930 + 0.0118642i
\(344\) 9.30190e25i 0.216126i
\(345\) −4.76461e25 3.90739e25i −0.107381 0.0880615i
\(346\) 1.45254e26i 0.317563i
\(347\) 2.57009e26i 0.545116i 0.962139 + 0.272558i \(0.0878697\pi\)
−0.962139 + 0.272558i \(0.912130\pi\)
\(348\) −4.47926e25 3.67337e25i −0.0921773 0.0755933i
\(349\) 6.70849e26i 1.33955i −0.742565 0.669773i \(-0.766391\pi\)
0.742565 0.669773i \(-0.233609\pi\)
\(350\) −2.96372e26 1.72677e26i −0.574279 0.334596i
\(351\) −1.69997e26 + 3.18857e26i −0.319680 + 0.599613i
\(352\) −3.21573e24 −0.00586924
\(353\) −5.19858e26 −0.920980 −0.460490 0.887665i \(-0.652326\pi\)
−0.460490 + 0.887665i \(0.652326\pi\)
\(354\) −3.57482e26 2.93166e26i −0.614781 0.504173i
\(355\) 5.31024e25i 0.0886578i
\(356\) 4.62326e26 0.749416
\(357\) −1.83295e26 4.92374e26i −0.288493 0.774959i
\(358\) 6.78103e26 1.03639
\(359\) 6.53139e26i 0.969424i −0.874674 0.484712i \(-0.838924\pi\)
0.874674 0.484712i \(-0.161076\pi\)
\(360\) 2.39403e26 4.77969e25i 0.345107 0.0689006i
\(361\) 5.76536e26 0.807237
\(362\) −9.43011e25 −0.128256
\(363\) 4.79919e26 5.85206e26i 0.634086 0.773195i
\(364\) 2.04065e26 + 1.18895e26i 0.261941 + 0.152616i
\(365\) 3.05144e26i 0.380565i
\(366\) 3.89122e26 4.74490e26i 0.471558 0.575010i
\(367\) 1.07354e27i 1.26423i 0.774874 + 0.632115i \(0.217813\pi\)
−0.774874 + 0.632115i \(0.782187\pi\)
\(368\) 1.31670e26i 0.150690i
\(369\) 3.24613e25 + 1.62591e26i 0.0361069 + 0.180851i
\(370\) 2.78637e26i 0.301246i
\(371\) −4.44546e26 2.59008e26i −0.467187 0.272199i
\(372\) 9.06862e25 + 7.43704e25i 0.0926489 + 0.0759800i
\(373\) −2.84476e26 −0.282555 −0.141278 0.989970i \(-0.545121\pi\)
−0.141278 + 0.989970i \(0.545121\pi\)
\(374\) 4.60510e24 0.00444721
\(375\) 4.18022e26 5.09730e26i 0.392528 0.478643i
\(376\) 7.74626e26i 0.707326i
\(377\) −2.04464e26 −0.181565
\(378\) −4.52926e26 7.33081e26i −0.391168 0.633123i
\(379\) −1.97170e26 −0.165626 −0.0828129 0.996565i \(-0.526390\pi\)
−0.0828129 + 0.996565i \(0.526390\pi\)
\(380\) 7.83871e25i 0.0640497i
\(381\) −4.68000e26 + 5.70673e26i −0.371992 + 0.453602i
\(382\) −1.74175e27 −1.34685
\(383\) 1.51088e27 1.13669 0.568347 0.822789i \(-0.307583\pi\)
0.568347 + 0.822789i \(0.307583\pi\)
\(384\) −1.03827e26 8.51471e25i −0.0760034 0.0623292i
\(385\) −2.86636e24 1.67004e24i −0.00204171 0.00118957i
\(386\) 2.06935e26i 0.143439i
\(387\) 5.82834e25 + 2.91928e26i 0.0393169 + 0.196929i
\(388\) 5.26143e25i 0.0345438i
\(389\) 1.62998e27i 1.04163i 0.853671 + 0.520813i \(0.174371\pi\)
−0.853671 + 0.520813i \(0.825629\pi\)
\(390\) 1.68568e26 2.05549e26i 0.104857 0.127861i
\(391\) 5.79964e26i 0.351192i
\(392\) −1.58822e27 + 9.00283e26i −0.936280 + 0.530732i
\(393\) −1.07585e27 + 1.31188e27i −0.617491 + 0.752959i
\(394\) −1.33439e27 −0.745715
\(395\) 1.11550e27 0.607017
\(396\) −5.96641e24 + 1.19119e24i −0.00316165 + 0.000631223i
\(397\) 2.20610e26i 0.113848i −0.998379 0.0569239i \(-0.981871\pi\)
0.998379 0.0569239i \(-0.0181292\pi\)
\(398\) −2.04845e27 −1.02956
\(399\) −8.40513e26 + 3.12897e26i −0.411461 + 0.153174i
\(400\) 6.64538e26 0.316876
\(401\) 1.71853e27i 0.798256i 0.916895 + 0.399128i \(0.130687\pi\)
−0.916895 + 0.399128i \(0.869313\pi\)
\(402\) 1.34358e27 + 1.10185e27i 0.607980 + 0.498596i
\(403\) 4.13954e26 0.182494
\(404\) 7.28315e26 0.312835
\(405\) 7.21388e26 3.00008e26i 0.301919 0.125561i
\(406\) 2.45466e26 4.21303e26i 0.100108 0.171819i
\(407\) 2.25091e25i 0.00894577i
\(408\) 1.77670e27 + 1.45705e27i 0.688150 + 0.564341i
\(409\) 1.01469e27i 0.383037i 0.981489 + 0.191518i \(0.0613411\pi\)
−0.981489 + 0.191518i \(0.938659\pi\)
\(410\) 1.21974e26i 0.0448785i
\(411\) 3.19590e27 + 2.62091e27i 1.14618 + 0.939969i
\(412\) 1.34731e27i 0.471027i
\(413\) −1.57803e27 + 2.70844e27i −0.537825 + 0.923090i
\(414\) −1.86238e26 9.32822e26i −0.0618820 0.309952i
\(415\) −9.22326e26 −0.298799
\(416\) −1.74715e27 −0.551886
\(417\) −5.73768e26 4.70539e26i −0.176729 0.144933i
\(418\) 7.86120e24i 0.00236123i
\(419\) 3.27068e27 0.958056 0.479028 0.877800i \(-0.340989\pi\)
0.479028 + 0.877800i \(0.340989\pi\)
\(420\) −1.78155e26 4.78564e26i −0.0508955 0.136717i
\(421\) −4.01568e27 −1.11892 −0.559458 0.828859i \(-0.688991\pi\)
−0.559458 + 0.828859i \(0.688991\pi\)
\(422\) 3.03157e27i 0.823924i
\(423\) 4.85361e26 + 2.43106e27i 0.128674 + 0.644499i
\(424\) 2.25013e27 0.581923
\(425\) 2.92708e27 0.738501
\(426\) 5.19823e26 6.33865e26i 0.127954 0.156026i
\(427\) −3.59494e27 2.09454e27i −0.863375 0.503033i
\(428\) 2.43978e27i 0.571730i
\(429\) −1.36174e25 + 1.66049e25i −0.00311381 + 0.00379694i
\(430\) 2.19001e26i 0.0488684i
\(431\) 6.37440e27i 1.38812i −0.719916 0.694061i \(-0.755820\pi\)
0.719916 0.694061i \(-0.244180\pi\)
\(432\) 1.47318e27 + 7.85417e26i 0.313095 + 0.166925i
\(433\) 6.23955e27i 1.29429i −0.762369 0.647143i \(-0.775964\pi\)
0.762369 0.647143i \(-0.224036\pi\)
\(434\) −4.96966e26 + 8.52962e26i −0.100620 + 0.172698i
\(435\) 3.41837e26 + 2.80335e26i 0.0675587 + 0.0554039i
\(436\) 1.37584e27 0.265436
\(437\) −9.90035e26 −0.186464
\(438\) 2.98707e27 3.64239e27i 0.549247 0.669743i
\(439\) 8.26648e27i 1.48403i 0.670383 + 0.742015i \(0.266130\pi\)
−0.670383 + 0.742015i \(0.733870\pi\)
\(440\) 1.45085e25 0.00254313
\(441\) −4.42031e27 + 3.82056e27i −0.756568 + 0.653915i
\(442\) 2.50201e27 0.418172
\(443\) 1.94582e27i 0.317587i −0.987312 0.158794i \(-0.949240\pi\)
0.987312 0.158794i \(-0.0507604\pi\)
\(444\) −2.19713e27 + 2.67915e27i −0.350215 + 0.427047i
\(445\) −3.52826e27 −0.549263
\(446\) 2.64806e26 0.0402636
\(447\) −4.54632e27 3.72837e27i −0.675197 0.553719i
\(448\) 3.32877e27 5.71330e27i 0.482909 0.828835i
\(449\) 1.69203e27i 0.239785i −0.992787 0.119893i \(-0.961745\pi\)
0.992787 0.119893i \(-0.0382550\pi\)
\(450\) 4.70796e27 9.39943e26i 0.651780 0.130128i
\(451\) 9.85347e24i 0.00133271i
\(452\) 5.66201e27i 0.748198i
\(453\) −7.11671e27 + 8.67801e27i −0.918858 + 1.12044i
\(454\) 1.16866e28i 1.47436i
\(455\) −1.55733e27 9.07354e26i −0.191982 0.111855i
\(456\) 2.48727e27 3.03294e27i 0.299635 0.365370i
\(457\) −7.92917e27 −0.933486 −0.466743 0.884393i \(-0.654573\pi\)
−0.466743 + 0.884393i \(0.654573\pi\)
\(458\) −7.58308e27 −0.872485
\(459\) 6.48890e27 + 3.45952e27i 0.729689 + 0.389029i
\(460\) 5.63698e26i 0.0619568i
\(461\) −5.88926e27 −0.632705 −0.316352 0.948642i \(-0.602458\pi\)
−0.316352 + 0.948642i \(0.602458\pi\)
\(462\) −1.78666e25 4.79937e25i −0.00187629 0.00504015i
\(463\) 2.89487e27 0.297186 0.148593 0.988898i \(-0.452526\pi\)
0.148593 + 0.988898i \(0.452526\pi\)
\(464\) 9.44664e26i 0.0948066i
\(465\) −6.92076e26 5.67561e26i −0.0679043 0.0556874i
\(466\) 3.50170e27 0.335913
\(467\) 1.50197e28 1.40875 0.704374 0.709829i \(-0.251228\pi\)
0.704374 + 0.709829i \(0.251228\pi\)
\(468\) −3.24162e27 + 6.47190e26i −0.297291 + 0.0593540i
\(469\) 5.93096e27 1.01795e28i 0.531876 0.912879i
\(470\) 1.82376e27i 0.159934i
\(471\) −6.31925e26 5.18233e26i −0.0541934 0.0444432i
\(472\) 1.37092e28i 1.14979i
\(473\) 1.76916e25i 0.00145119i
\(474\) 1.33154e28 + 1.09197e28i 1.06827 + 0.876071i
\(475\) 4.99671e27i 0.392104i
\(476\) 2.41958e27 4.15282e27i 0.185723 0.318764i
\(477\) 7.06173e27 1.40987e27i 0.530235 0.105861i
\(478\) −1.08546e27 −0.0797297
\(479\) 2.05235e28 1.47478 0.737391 0.675467i \(-0.236058\pi\)
0.737391 + 0.675467i \(0.236058\pi\)
\(480\) 2.92100e27 + 2.39547e27i 0.205351 + 0.168406i
\(481\) 1.22295e28i 0.841172i
\(482\) −1.77984e28 −1.19780
\(483\) −6.04430e27 + 2.25010e27i −0.398017 + 0.148169i
\(484\) 6.92353e27 0.446120
\(485\) 4.01528e26i 0.0253179i
\(486\) 1.15478e28 + 3.48062e27i 0.712552 + 0.214771i
\(487\) −1.39386e28 −0.841712 −0.420856 0.907127i \(-0.638270\pi\)
−0.420856 + 0.907127i \(0.638270\pi\)
\(488\) 1.81963e28 1.07541
\(489\) −1.11053e28 + 1.35417e28i −0.642375 + 0.783302i
\(490\) 3.73925e27 2.11960e27i 0.211703 0.120004i
\(491\) 2.14939e28i 1.19113i 0.803308 + 0.595564i \(0.203071\pi\)
−0.803308 + 0.595564i \(0.796929\pi\)
\(492\) −9.61804e26 + 1.17281e27i −0.0521739 + 0.0636200i
\(493\) 4.16095e27i 0.220953i
\(494\) 4.27108e27i 0.222027i
\(495\) 4.55330e25 9.09065e24i 0.00231724 0.000462637i
\(496\) 1.91255e27i 0.0952916i
\(497\) −4.80244e27 2.79807e27i −0.234272 0.136495i
\(498\) −1.10095e28 9.02871e27i −0.525846 0.431239i
\(499\) −4.87093e27 −0.227801 −0.113901 0.993492i \(-0.536335\pi\)
−0.113901 + 0.993492i \(0.536335\pi\)
\(500\) 6.03058e27 0.276169
\(501\) −2.30076e28 + 2.80552e28i −1.03175 + 1.25811i
\(502\) 2.79425e28i 1.22709i
\(503\) −3.80145e28 −1.63488 −0.817439 0.576015i \(-0.804607\pi\)
−0.817439 + 0.576015i \(0.804607\pi\)
\(504\) 8.29202e27 2.41695e28i 0.349253 1.01800i
\(505\) −5.55817e27 −0.229283
\(506\) 5.65315e25i 0.00228407i
\(507\) 8.62489e27 1.05171e28i 0.341327 0.416209i
\(508\) −6.75159e27 −0.261720
\(509\) 3.14244e28 1.19325 0.596623 0.802521i \(-0.296509\pi\)
0.596623 + 0.802521i \(0.296509\pi\)
\(510\) −4.18302e27 3.43043e27i −0.155598 0.127603i
\(511\) −2.75963e28 1.60786e28i −1.00562 0.585908i
\(512\) 1.87687e28i 0.670039i
\(513\) 5.90561e27 1.10770e28i 0.206554 0.387425i
\(514\) 3.08077e28i 1.05571i
\(515\) 1.02820e28i 0.345226i
\(516\) −1.72689e27 + 2.10574e27i −0.0568124 + 0.0692761i
\(517\) 1.47329e26i 0.00474938i
\(518\) −2.51992e28 1.46819e28i −0.796019 0.463789i
\(519\) −8.74097e27 + 1.06586e28i −0.270584 + 0.329946i
\(520\) 7.88263e27 0.239131
\(521\) 1.29490e28 0.384982 0.192491 0.981299i \(-0.438343\pi\)
0.192491 + 0.981299i \(0.438343\pi\)
\(522\) 1.33616e27 + 6.69252e27i 0.0389331 + 0.195007i
\(523\) 5.98374e28i 1.70885i 0.519571 + 0.854427i \(0.326092\pi\)
−0.519571 + 0.854427i \(0.673908\pi\)
\(524\) −1.55207e28 −0.434444
\(525\) −1.13563e28 3.05056e28i −0.311576 0.836965i
\(526\) −5.24879e28 −1.41159
\(527\) 8.42417e27i 0.222083i
\(528\) 7.67177e25 + 6.29150e25i 0.00198262 + 0.00162592i
\(529\) 3.23520e28 0.819629
\(530\) −5.29764e27 −0.131579
\(531\) −8.58981e27 4.30244e28i −0.209166 1.04766i
\(532\) −7.08912e27 4.13037e27i −0.169247 0.0986091i
\(533\) 5.35351e27i 0.125315i
\(534\) −4.21156e28 3.45384e28i −0.966629 0.792718i
\(535\) 1.86193e28i 0.419033i
\(536\) 5.15251e28i 1.13707i
\(537\) 4.97584e28 + 4.08062e28i 1.07680 + 0.883071i
\(538\) 1.84934e28i 0.392466i
\(539\) −3.02068e26 + 1.71228e26i −0.00628671 + 0.00356363i
\(540\) 6.30691e27 + 3.36249e27i 0.128731 + 0.0686320i
\(541\) 7.37106e28 1.47557 0.737783 0.675038i \(-0.235873\pi\)
0.737783 + 0.675038i \(0.235873\pi\)
\(542\) 6.17476e27 0.121235
\(543\) −6.91971e27 5.67475e27i −0.133257 0.109282i
\(544\) 3.55553e28i 0.671608i
\(545\) −1.04998e28 −0.194544
\(546\) −9.70711e27 2.60756e28i −0.176428 0.473926i
\(547\) 6.40075e28 1.14121 0.570603 0.821226i \(-0.306709\pi\)
0.570603 + 0.821226i \(0.306709\pi\)
\(548\) 3.78105e28i 0.661328i
\(549\) 5.71067e28 1.14013e28i 0.979891 0.195635i
\(550\) 2.85315e26 0.00480304
\(551\) 7.10300e27 0.117314
\(552\) 1.78865e28 2.18105e28i 0.289844 0.353432i
\(553\) 5.87780e28 1.00883e29i 0.934547 1.60400i
\(554\) 6.89145e28i 1.07512i
\(555\) 1.67675e28 2.04461e28i 0.256680 0.312992i
\(556\) 6.78821e27i 0.101969i
\(557\) 2.96472e28i 0.437023i −0.975834 0.218512i \(-0.929880\pi\)
0.975834 0.218512i \(-0.0701202\pi\)
\(558\) −2.70517e27 1.35495e28i −0.0391322 0.196004i
\(559\) 9.61206e27i 0.136456i
\(560\) −4.19215e27 + 7.19516e27i −0.0584067 + 0.100246i
\(561\) 3.37917e26 + 2.77121e26i 0.00462062 + 0.00378930i
\(562\) 6.17464e27 0.0828668
\(563\) −2.39088e28 −0.314934 −0.157467 0.987524i \(-0.550333\pi\)
−0.157467 + 0.987524i \(0.550333\pi\)
\(564\) −1.43809e28 + 1.75358e28i −0.185932 + 0.226723i
\(565\) 4.32099e28i 0.548371i
\(566\) −5.75955e28 −0.717491
\(567\) 1.08794e28 8.10484e28i 0.133040 0.991111i
\(568\) 2.43082e28 0.291807
\(569\) 9.30524e28i 1.09660i −0.836281 0.548300i \(-0.815275\pi\)
0.836281 0.548300i \(-0.184725\pi\)
\(570\) −5.85597e27 + 7.14068e27i −0.0677505 + 0.0826140i
\(571\) 3.32995e28 0.378232 0.189116 0.981955i \(-0.439438\pi\)
0.189116 + 0.981955i \(0.439438\pi\)
\(572\) −1.96451e26 −0.00219077
\(573\) −1.27807e29 1.04813e29i −1.39937 1.14760i
\(574\) −1.10310e28 6.42707e27i −0.118588 0.0690937i
\(575\) 3.59324e28i 0.379292i
\(576\) 1.81197e28 + 9.07574e28i 0.187808 + 0.940689i
\(577\) 5.75601e28i 0.585835i 0.956138 + 0.292917i \(0.0946261\pi\)
−0.956138 + 0.292917i \(0.905374\pi\)
\(578\) 2.35460e28i 0.235329i
\(579\) 1.24527e28 1.51846e28i 0.122219 0.149032i
\(580\) 4.04425e27i 0.0389802i
\(581\) −4.85991e28 + 8.34126e28i −0.460023 + 0.789555i
\(582\) −3.93059e27 + 4.79290e27i −0.0365398 + 0.0445561i
\(583\) 4.27960e26 0.00390736
\(584\) 1.39683e29 1.25259
\(585\) 2.47386e28 4.93906e27i 0.217891 0.0435018i
\(586\) 1.19988e29i 1.03804i
\(587\) −1.17507e29 −0.998540 −0.499270 0.866447i \(-0.666398\pi\)
−0.499270 + 0.866447i \(0.666398\pi\)
\(588\) −5.26674e28 9.10469e27i −0.439622 0.0759982i
\(589\) −1.43806e28 −0.117914
\(590\) 3.22765e28i 0.259980i
\(591\) −9.79162e28 8.02996e28i −0.774793 0.635397i
\(592\) 5.65026e28 0.439228
\(593\) 1.36983e29 1.04614 0.523072 0.852289i \(-0.324786\pi\)
0.523072 + 0.852289i \(0.324786\pi\)
\(594\) 6.32500e26 + 3.37213e26i 0.00474573 + 0.00253016i
\(595\) −1.84651e28 + 3.16924e28i −0.136121 + 0.233629i
\(596\) 5.37872e28i 0.389577i
\(597\) −1.50313e29 1.23269e29i −1.06971 0.877252i
\(598\) 3.07142e28i 0.214772i
\(599\) 2.40682e29i 1.65372i −0.562410 0.826859i \(-0.690126\pi\)
0.562410 0.826859i \(-0.309874\pi\)
\(600\) 1.10078e29 + 9.02732e28i 0.743210 + 0.609496i
\(601\) 3.96548e28i 0.263096i −0.991310 0.131548i \(-0.958005\pi\)
0.991310 0.131548i \(-0.0419947\pi\)
\(602\) −1.98059e28 1.15396e28i −0.129131 0.0752364i
\(603\) 3.22844e28 + 1.61705e29i 0.206852 + 1.03608i
\(604\) −1.02669e29 −0.646475
\(605\) −5.28372e28 −0.326971
\(606\) −6.63459e28 5.44093e28i −0.403507 0.330911i
\(607\) 1.06491e29i 0.636546i 0.947999 + 0.318273i \(0.103103\pi\)
−0.947999 + 0.318273i \(0.896897\pi\)
\(608\) 6.06951e28 0.356588
\(609\) 4.33648e28 1.61434e28i 0.250412 0.0932207i
\(610\) −4.28409e28 −0.243162
\(611\) 8.00455e28i 0.446585i
\(612\) 1.31706e28 + 6.59687e28i 0.0722298 + 0.361783i
\(613\) −6.00070e28 −0.323494 −0.161747 0.986832i \(-0.551713\pi\)
−0.161747 + 0.986832i \(0.551713\pi\)
\(614\) 2.32348e29 1.23132
\(615\) 7.34005e27 8.95035e27i 0.0382393 0.0466285i
\(616\) 7.64480e26 1.31211e27i 0.00391533 0.00672004i
\(617\) 4.47628e28i 0.225384i −0.993630 0.112692i \(-0.964053\pi\)
0.993630 0.112692i \(-0.0359473\pi\)
\(618\) −1.00652e29 + 1.22733e29i −0.498243 + 0.607551i
\(619\) 9.07018e28i 0.441432i 0.975338 + 0.220716i \(0.0708394\pi\)
−0.975338 + 0.220716i \(0.929161\pi\)
\(620\) 8.18790e27i 0.0391796i
\(621\) 4.24685e28 7.96566e28i 0.199804 0.374766i
\(622\) 1.47457e29i 0.682130i
\(623\) −1.85911e29 + 3.19086e29i −0.845630 + 1.45139i
\(624\) 4.16816e28 + 3.41825e28i 0.186426 + 0.152885i
\(625\) 1.57040e29 0.690669
\(626\) 1.13826e29 0.492280
\(627\) 4.73063e26 5.76846e26i 0.00201192 0.00245330i
\(628\) 7.47626e27i 0.0312686i
\(629\) 2.48876e29 1.02365
\(630\) −1.95225e28 + 5.69040e28i −0.0789696 + 0.230180i
\(631\) −6.30668e28 −0.250895 −0.125448 0.992100i \(-0.540037\pi\)
−0.125448 + 0.992100i \(0.540037\pi\)
\(632\) 5.10633e29i 1.99793i
\(633\) −1.82431e29 + 2.22453e29i −0.702036 + 0.856052i
\(634\) −1.61583e29 −0.611589
\(635\) 5.15251e28 0.191820
\(636\) 5.09379e28 + 4.17735e28i 0.186527 + 0.152968i
\(637\) −1.64117e29 + 9.30302e28i −0.591140 + 0.335089i
\(638\) 4.05585e26i 0.00143703i
\(639\) 7.62881e28 1.52309e28i 0.265888 0.0530844i
\(640\) 9.37437e27i 0.0321405i
\(641\) 2.58094e29i 0.870501i −0.900309 0.435250i \(-0.856660\pi\)
0.900309 0.435250i \(-0.143340\pi\)
\(642\) −1.82265e29 + 2.22252e29i −0.604765 + 0.737441i
\(643\) 3.31180e29i 1.08106i −0.841325 0.540529i \(-0.818224\pi\)
0.841325 0.540529i \(-0.181776\pi\)
\(644\) −5.09793e28 2.97023e28i −0.163716 0.0953870i
\(645\) 1.31788e28 1.60701e28i 0.0416390 0.0507740i
\(646\) −8.69187e28 −0.270191
\(647\) −2.95666e29 −0.904287 −0.452143 0.891945i \(-0.649340\pi\)
−0.452143 + 0.891945i \(0.649340\pi\)
\(648\) 1.37332e29 + 3.30223e29i 0.413270 + 0.993733i
\(649\) 2.60739e27i 0.00772035i
\(650\) 1.55015e29 0.451631
\(651\) −8.77955e28 + 3.26835e28i −0.251693 + 0.0936976i
\(652\) −1.60211e29 −0.451951
\(653\) 4.60468e28i 0.127824i 0.997956 + 0.0639118i \(0.0203576\pi\)
−0.997956 + 0.0639118i \(0.979642\pi\)
\(654\) −1.25332e29 1.02783e29i −0.342371 0.280773i
\(655\) 1.18447e29 0.318413
\(656\) 2.47342e28 0.0654347
\(657\) 4.38376e29 8.75217e28i 1.14133 0.227866i
\(658\) −1.64936e29 9.60975e28i −0.422613 0.246229i
\(659\) 5.55268e28i 0.140025i 0.997546 + 0.0700126i \(0.0223039\pi\)
−0.997546 + 0.0700126i \(0.977696\pi\)
\(660\) 3.28440e26 + 2.69349e26i 0.000815163 + 0.000668503i
\(661\) 3.21572e28i 0.0785530i −0.999228 0.0392765i \(-0.987495\pi\)
0.999228 0.0392765i \(-0.0125053\pi\)
\(662\) 1.78546e29i 0.429280i
\(663\) 1.83594e29 + 1.50563e29i 0.434478 + 0.356309i
\(664\) 4.22204e29i 0.983463i
\(665\) 5.41009e28 + 3.15211e28i 0.124044 + 0.0722727i
\(666\) 4.00296e29 7.99190e28i 0.903445 0.180373i
\(667\) 5.10791e28 0.113481
\(668\) −3.31919e29 −0.725904
\(669\) 1.94312e28 + 1.59352e28i 0.0418336 + 0.0343071i
\(670\) 1.21309e29i 0.257104i
\(671\) 3.46082e27 0.00722092
\(672\) 3.70552e29 1.37945e29i 0.761153 0.283354i
\(673\) −1.37267e29 −0.277592 −0.138796 0.990321i \(-0.544323\pi\)
−0.138796 + 0.990321i \(0.544323\pi\)
\(674\) 4.14872e29i 0.826010i
\(675\) 4.02028e29 + 2.14339e29i 0.788073 + 0.420156i
\(676\) 1.24427e29 0.240145
\(677\) −6.52328e29 −1.23961 −0.619805 0.784756i \(-0.712788\pi\)
−0.619805 + 0.784756i \(0.712788\pi\)
\(678\) −4.22984e29 + 5.15781e29i −0.791430 + 0.965058i
\(679\) 3.63131e28 + 2.11573e28i 0.0669008 + 0.0389788i
\(680\) 1.60415e29i 0.291006i
\(681\) 7.03266e29 8.57552e29i 1.25625 1.53185i
\(682\) 8.21139e26i 0.00144438i
\(683\) 3.61830e29i 0.626740i −0.949631 0.313370i \(-0.898542\pi\)
0.949631 0.313370i \(-0.101458\pi\)
\(684\) 1.12613e29 2.24831e28i 0.192087 0.0383502i
\(685\) 2.88553e29i 0.484701i
\(686\) 5.33755e27 4.49854e29i 0.00882955 0.744163i
\(687\) −5.56438e29 4.56327e29i −0.906506 0.743413i
\(688\) 4.44096e28 0.0712522
\(689\) 2.32516e29 0.367409
\(690\) −4.21114e28 + 5.13501e28i −0.0655367 + 0.0799145i
\(691\) 6.57444e29i 1.00772i −0.863786 0.503859i \(-0.831913\pi\)
0.863786 0.503859i \(-0.168087\pi\)
\(692\) −1.26101e29 −0.190373
\(693\) 1.57709e27 4.59688e27i 0.00234508 0.00683541i
\(694\) 2.76989e29 0.405684
\(695\) 5.18045e28i 0.0747356i
\(696\) −1.28326e29 + 1.56479e29i −0.182356 + 0.222362i
\(697\) 1.08947e29 0.152500
\(698\) −7.23001e29 −0.996912
\(699\) 2.56951e29 + 2.10722e29i 0.349012 + 0.286220i
\(700\) 1.49908e29 2.57293e29i 0.200584 0.344269i
\(701\) 8.98314e29i 1.18410i 0.805901 + 0.592051i \(0.201682\pi\)
−0.805901 + 0.592051i \(0.798318\pi\)
\(702\) 3.43645e29 + 1.83212e29i 0.446241 + 0.237911i
\(703\) 4.24847e29i 0.543503i
\(704\) 5.50014e27i 0.00693204i
\(705\) 1.09748e29 1.33825e29i 0.136274 0.166170i
\(706\) 5.60271e29i 0.685408i
\(707\) −2.92871e29 + 5.02666e29i −0.352998 + 0.605864i
\(708\) 2.54509e29 3.10345e29i 0.302242 0.368549i
\(709\) −2.07195e29 −0.242435 −0.121217 0.992626i \(-0.538680\pi\)
−0.121217 + 0.992626i \(0.538680\pi\)
\(710\) −5.72306e28 −0.0659805
\(711\) 3.19950e29 + 1.60256e30i 0.363455 + 1.82046i
\(712\) 1.61510e30i 1.80784i
\(713\) −1.03414e29 −0.114061
\(714\) −5.30651e29 + 1.97545e29i −0.576736 + 0.214701i
\(715\) 1.49922e27 0.00160566
\(716\) 5.88689e29i 0.621297i
\(717\) −7.96497e28 6.53195e28i −0.0828386 0.0679347i
\(718\) −7.03914e29 −0.721461
\(719\) 4.91706e29 0.496651 0.248326 0.968677i \(-0.420120\pi\)
0.248326 + 0.968677i \(0.420120\pi\)
\(720\) −2.28194e28 1.14297e29i −0.0227150 0.113774i
\(721\) 9.29879e29 + 5.41781e29i 0.912234 + 0.531500i
\(722\) 6.21356e29i 0.600759i
\(723\) −1.30602e30 1.07105e30i −1.24451 1.02061i
\(724\) 8.18666e28i 0.0768868i
\(725\) 2.57797e29i 0.238632i
\(726\) −6.30699e29 5.17227e29i −0.575424 0.471897i
\(727\) 1.76811e30i 1.59000i 0.606609 + 0.795001i \(0.292529\pi\)
−0.606609 + 0.795001i \(0.707471\pi\)
\(728\) 4.15351e29 7.12883e29i 0.368159 0.631886i
\(729\) 6.37908e29 + 9.50313e29i 0.557338 + 0.830286i
\(730\) −3.28865e29 −0.283223
\(731\) 1.95610e29 0.166058
\(732\) 4.11924e29 + 3.37813e29i 0.344708 + 0.282690i
\(733\) 3.09927e29i 0.255663i 0.991796 + 0.127832i \(0.0408017\pi\)
−0.991796 + 0.127832i \(0.959198\pi\)
\(734\) 1.15700e30 0.940860
\(735\) 4.01933e29 + 6.94828e28i 0.322209 + 0.0557007i
\(736\) 4.36471e29 0.344936
\(737\) 9.79974e27i 0.00763495i
\(738\) 1.75231e29 3.49849e28i 0.134592 0.0268713i
\(739\) −1.92783e29 −0.145983 −0.0729915 0.997333i \(-0.523255\pi\)
−0.0729915 + 0.997333i \(0.523255\pi\)
\(740\) 2.41896e29 0.180591
\(741\) 2.57021e29 3.13407e29i 0.189181 0.230684i
\(742\) −2.79143e29 + 4.79104e29i −0.202575 + 0.347688i
\(743\) 8.09967e29i 0.579542i 0.957096 + 0.289771i \(0.0935791\pi\)
−0.957096 + 0.289771i \(0.906421\pi\)
\(744\) 2.59807e29 3.16805e29i 0.183289 0.223499i
\(745\) 4.10479e29i 0.285529i
\(746\) 3.06591e29i 0.210282i
\(747\) −2.64543e29 1.32503e30i −0.178908 0.896108i
\(748\) 3.99788e27i 0.00266601i
\(749\) 1.68388e30 + 9.81086e29i 1.10726 + 0.645131i
\(750\) −5.49356e29 4.50519e29i −0.356214 0.292126i
\(751\) −9.79340e29 −0.626201 −0.313101 0.949720i \(-0.601368\pi\)
−0.313101 + 0.949720i \(0.601368\pi\)
\(752\) 3.69826e29 0.233190
\(753\) −1.68150e30 + 2.05039e30i −1.04556 + 1.27494i
\(754\) 2.20359e29i 0.135124i
\(755\) 7.83523e29 0.473815
\(756\) 6.36418e29 3.93203e29i 0.379545 0.234498i
\(757\) −1.72229e30 −1.01298 −0.506489 0.862246i \(-0.669057\pi\)
−0.506489 + 0.862246i \(0.669057\pi\)
\(758\) 2.12497e29i 0.123261i
\(759\) 3.40189e27 4.14822e27i 0.00194617 0.00237314i
\(760\) −2.73839e29 −0.154509