Properties

Label 21.22.c.b.20.21
Level $21$
Weight $22$
Character 21.20
Analytic conductor $58.690$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $4$

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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 20.21
Character \(\chi\) \(=\) 21.20
Dual form 21.22.c.b.20.22

$q$-expansion

\(f(q)\) \(=\) \(q-687.640i q^{2} +(-100506. + 18946.7i) q^{3} +1.62430e6 q^{4} +6.28469e6 q^{5} +(1.30285e7 + 6.91116e7i) q^{6} +(4.61336e8 + 5.87975e8i) q^{7} -2.55902e9i q^{8} +(9.74240e9 - 3.80851e9i) q^{9} +O(q^{10})\) \(q-687.640i q^{2} +(-100506. + 18946.7i) q^{3} +1.62430e6 q^{4} +6.28469e6 q^{5} +(1.30285e7 + 6.91116e7i) q^{6} +(4.61336e8 + 5.87975e8i) q^{7} -2.55902e9i q^{8} +(9.74240e9 - 3.80851e9i) q^{9} -4.32160e9i q^{10} -6.92257e10i q^{11} +(-1.63252e11 + 3.07752e10i) q^{12} -2.42034e11i q^{13} +(4.04315e11 - 3.17233e11i) q^{14} +(-6.31646e11 + 1.19074e11i) q^{15} +1.64673e12 q^{16} +6.97114e12 q^{17} +(-2.61888e12 - 6.69926e12i) q^{18} +3.12105e13i q^{19} +1.02082e13 q^{20} +(-5.75071e13 - 5.03540e13i) q^{21} -4.76024e13 q^{22} -5.39902e13i q^{23} +(4.84851e13 + 2.57196e14i) q^{24} -4.37340e14 q^{25} -1.66432e14 q^{26} +(-9.07007e14 + 5.67363e14i) q^{27} +(7.49350e14 + 9.55050e14i) q^{28} +2.80226e15i q^{29} +(8.18802e13 + 4.34345e14i) q^{30} -2.80728e15i q^{31} -6.49901e15i q^{32} +(1.31160e15 + 6.95757e15i) q^{33} -4.79363e15i q^{34} +(2.89936e15 + 3.69524e15i) q^{35} +(1.58246e16 - 6.18617e15i) q^{36} +3.19164e16 q^{37} +2.14616e16 q^{38} +(4.58575e15 + 2.43257e16i) q^{39} -1.60826e16i q^{40} -1.94702e16 q^{41} +(-3.46254e16 + 3.95442e16i) q^{42} +9.38339e16 q^{43} -1.12444e17i q^{44} +(6.12279e16 - 2.39353e16i) q^{45} -3.71258e16 q^{46} -3.19152e16 q^{47} +(-1.65505e17 + 3.12001e16i) q^{48} +(-1.32883e17 + 5.42509e17i) q^{49} +3.00732e17i q^{50} +(-7.00638e17 + 1.32080e17i) q^{51} -3.93136e17i q^{52} -1.47276e18i q^{53} +(3.90141e17 + 6.23694e17i) q^{54} -4.35062e17i q^{55} +(1.50464e18 - 1.18057e18i) q^{56} +(-5.91336e17 - 3.13683e18i) q^{57} +1.92695e18 q^{58} +5.35304e18 q^{59} +(-1.02599e18 + 1.93413e17i) q^{60} -9.25237e18i q^{61} -1.93040e18 q^{62} +(6.73383e18 + 3.97128e18i) q^{63} -1.01554e18 q^{64} -1.52111e18i q^{65} +(4.78430e18 - 9.01909e17i) q^{66} +8.77935e18 q^{67} +1.13232e19 q^{68} +(1.02294e18 + 5.42632e18i) q^{69} +(2.54099e18 - 1.99371e18i) q^{70} -4.46340e19i q^{71} +(-9.74605e18 - 2.49310e19i) q^{72} +4.34206e19i q^{73} -2.19470e19i q^{74} +(4.39551e19 - 8.28616e18i) q^{75} +5.06953e19i q^{76} +(4.07030e19 - 3.19363e19i) q^{77} +(1.67273e19 - 3.15334e18i) q^{78} +6.43691e18 q^{79} +1.03492e19 q^{80} +(8.04096e19 - 7.42079e19i) q^{81} +1.33885e19i q^{82} +2.21180e20 q^{83} +(-9.34090e19 - 8.17901e19i) q^{84} +4.38114e19 q^{85} -6.45239e19i q^{86} +(-5.30937e19 - 2.81643e20i) q^{87} -1.77150e20 q^{88} +6.58942e19 q^{89} +(-1.64588e19 - 4.21028e19i) q^{90} +(1.42310e20 - 1.11659e20i) q^{91} -8.76965e19i q^{92} +(5.31888e19 + 2.82148e20i) q^{93} +2.19462e19i q^{94} +1.96148e20i q^{95} +(1.23135e20 + 6.53187e20i) q^{96} -4.64245e20i q^{97} +(3.73050e20 + 9.13759e19i) q^{98} +(-2.63647e20 - 6.74424e20i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 687.640i 0.474839i −0.971407 0.237419i \(-0.923698\pi\)
0.971407 0.237419i \(-0.0763015\pi\)
\(3\) −100506. + 18946.7i −0.982691 + 0.185251i
\(4\) 1.62430e6 0.774528
\(5\) 6.28469e6 0.287805 0.143903 0.989592i \(-0.454035\pi\)
0.143903 + 0.989592i \(0.454035\pi\)
\(6\) 1.30285e7 + 6.91116e7i 0.0879645 + 0.466620i
\(7\) 4.61336e8 + 5.87975e8i 0.617289 + 0.786737i
\(8\) 2.55902e9i 0.842615i
\(9\) 9.74240e9 3.80851e9i 0.931364 0.364090i
\(10\) 4.32160e9i 0.136661i
\(11\) 6.92257e10i 0.804719i −0.915482 0.402360i \(-0.868190\pi\)
0.915482 0.402360i \(-0.131810\pi\)
\(12\) −1.63252e11 + 3.07752e10i −0.761122 + 0.143482i
\(13\) 2.42034e11i 0.486934i −0.969909 0.243467i \(-0.921715\pi\)
0.969909 0.243467i \(-0.0782848\pi\)
\(14\) 4.04315e11 3.17233e11i 0.373573 0.293112i
\(15\) −6.31646e11 + 1.19074e11i −0.282824 + 0.0533163i
\(16\) 1.64673e12 0.374422
\(17\) 6.97114e12 0.838668 0.419334 0.907832i \(-0.362264\pi\)
0.419334 + 0.907832i \(0.362264\pi\)
\(18\) −2.61888e12 6.69926e12i −0.172884 0.442248i
\(19\) 3.12105e13i 1.16785i 0.811807 + 0.583925i \(0.198484\pi\)
−0.811807 + 0.583925i \(0.801516\pi\)
\(20\) 1.02082e13 0.222913
\(21\) −5.75071e13 5.03540e13i −0.752348 0.658766i
\(22\) −4.76024e13 −0.382112
\(23\) 5.39902e13i 0.271752i −0.990726 0.135876i \(-0.956615\pi\)
0.990726 0.135876i \(-0.0433849\pi\)
\(24\) 4.84851e13 + 2.57196e14i 0.156095 + 0.828030i
\(25\) −4.37340e14 −0.917168
\(26\) −1.66432e14 −0.231215
\(27\) −9.07007e14 + 5.67363e14i −0.847795 + 0.530324i
\(28\) 7.49350e14 + 9.55050e14i 0.478107 + 0.609350i
\(29\) 2.80226e15i 1.23689i 0.785830 + 0.618443i \(0.212236\pi\)
−0.785830 + 0.618443i \(0.787764\pi\)
\(30\) 8.18802e13 + 4.34345e14i 0.0253166 + 0.134296i
\(31\) 2.80728e15i 0.615160i −0.951522 0.307580i \(-0.900481\pi\)
0.951522 0.307580i \(-0.0995192\pi\)
\(32\) 6.49901e15i 1.02040i
\(33\) 1.31160e15 + 6.95757e15i 0.149075 + 0.790790i
\(34\) 4.79363e15i 0.398232i
\(35\) 2.89936e15 + 3.69524e15i 0.177659 + 0.226427i
\(36\) 1.58246e16 6.18617e15i 0.721368 0.281998i
\(37\) 3.19164e16 1.09118 0.545590 0.838053i \(-0.316306\pi\)
0.545590 + 0.838053i \(0.316306\pi\)
\(38\) 2.14616e16 0.554541
\(39\) 4.58575e15 + 2.43257e16i 0.0902052 + 0.478506i
\(40\) 1.60826e16i 0.242509i
\(41\) −1.94702e16 −0.226537 −0.113269 0.993564i \(-0.536132\pi\)
−0.113269 + 0.993564i \(0.536132\pi\)
\(42\) −3.46254e16 + 3.95442e16i −0.312807 + 0.357244i
\(43\) 9.38339e16 0.662126 0.331063 0.943609i \(-0.392593\pi\)
0.331063 + 0.943609i \(0.392593\pi\)
\(44\) 1.12444e17i 0.623278i
\(45\) 6.12279e16 2.39353e16i 0.268051 0.104787i
\(46\) −3.71258e16 −0.129038
\(47\) −3.19152e16 −0.0885055 −0.0442528 0.999020i \(-0.514091\pi\)
−0.0442528 + 0.999020i \(0.514091\pi\)
\(48\) −1.65505e17 + 3.12001e16i −0.367942 + 0.0693622i
\(49\) −1.32883e17 + 5.42509e17i −0.237910 + 0.971287i
\(50\) 3.00732e17i 0.435507i
\(51\) −7.00638e17 + 1.32080e17i −0.824151 + 0.155364i
\(52\) 3.93136e17i 0.377144i
\(53\) 1.47276e18i 1.15674i −0.815774 0.578370i \(-0.803689\pi\)
0.815774 0.578370i \(-0.196311\pi\)
\(54\) 3.90141e17 + 6.23694e17i 0.251818 + 0.402566i
\(55\) 4.35062e17i 0.231602i
\(56\) 1.50464e18 1.18057e18i 0.662916 0.520136i
\(57\) −5.91336e17 3.13683e18i −0.216346 1.14764i
\(58\) 1.92695e18 0.587321
\(59\) 5.35304e18 1.36350 0.681749 0.731586i \(-0.261220\pi\)
0.681749 + 0.731586i \(0.261220\pi\)
\(60\) −1.02599e18 + 1.93413e17i −0.219055 + 0.0412950i
\(61\) 9.25237e18i 1.66069i −0.557247 0.830347i \(-0.688142\pi\)
0.557247 0.830347i \(-0.311858\pi\)
\(62\) −1.93040e18 −0.292102
\(63\) 6.73383e18 + 3.97128e18i 0.861363 + 0.507990i
\(64\) −1.01554e18 −0.110105
\(65\) 1.52111e18i 0.140142i
\(66\) 4.78430e18 9.01909e17i 0.375498 0.0707867i
\(67\) 8.77935e18 0.588406 0.294203 0.955743i \(-0.404946\pi\)
0.294203 + 0.955743i \(0.404946\pi\)
\(68\) 1.13232e19 0.649572
\(69\) 1.02294e18 + 5.42632e18i 0.0503424 + 0.267048i
\(70\) 2.54099e18 1.99371e18i 0.107516 0.0843593i
\(71\) 4.46340e19i 1.62724i −0.581394 0.813622i \(-0.697492\pi\)
0.581394 0.813622i \(-0.302508\pi\)
\(72\) −9.74605e18 2.49310e19i −0.306787 0.784781i
\(73\) 4.34206e19i 1.18251i 0.806484 + 0.591257i \(0.201368\pi\)
−0.806484 + 0.591257i \(0.798632\pi\)
\(74\) 2.19470e19i 0.518134i
\(75\) 4.39551e19 8.28616e18i 0.901293 0.169907i
\(76\) 5.06953e19i 0.904534i
\(77\) 4.07030e19 3.19363e19i 0.633102 0.496744i
\(78\) 1.67273e19 3.15334e18i 0.227213 0.0428329i
\(79\) 6.43691e18 0.0764879 0.0382439 0.999268i \(-0.487824\pi\)
0.0382439 + 0.999268i \(0.487824\pi\)
\(80\) 1.03492e19 0.107761
\(81\) 8.04096e19 7.42079e19i 0.734878 0.678200i
\(82\) 1.33885e19i 0.107569i
\(83\) 2.21180e20 1.56468 0.782341 0.622850i \(-0.214025\pi\)
0.782341 + 0.622850i \(0.214025\pi\)
\(84\) −9.34090e19 8.17901e19i −0.582715 0.510233i
\(85\) 4.38114e19 0.241373
\(86\) 6.45239e19i 0.314403i
\(87\) −5.30937e19 2.81643e20i −0.229135 1.21548i
\(88\) −1.77150e20 −0.678068
\(89\) 6.58942e19 0.224002 0.112001 0.993708i \(-0.464274\pi\)
0.112001 + 0.993708i \(0.464274\pi\)
\(90\) −1.64588e19 4.21028e19i −0.0497569 0.127281i
\(91\) 1.42310e20 1.11659e20i 0.383089 0.300579i
\(92\) 8.76965e19i 0.210480i
\(93\) 5.31888e19 + 2.82148e20i 0.113959 + 0.604513i
\(94\) 2.19462e19i 0.0420258i
\(95\) 1.96148e20i 0.336114i
\(96\) 1.23135e20 + 6.53187e20i 0.189031 + 1.00274i
\(97\) 4.64245e20i 0.639211i −0.947551 0.319605i \(-0.896450\pi\)
0.947551 0.319605i \(-0.103550\pi\)
\(98\) 3.73050e20 + 9.13759e19i 0.461205 + 0.112969i
\(99\) −2.63647e20 6.74424e20i −0.292990 0.749486i
\(100\) −7.10373e20 −0.710373
\(101\) −8.74981e20 −0.788178 −0.394089 0.919072i \(-0.628940\pi\)
−0.394089 + 0.919072i \(0.628940\pi\)
\(102\) 9.08236e19 + 4.81787e20i 0.0737729 + 0.391339i
\(103\) 3.36089e20i 0.246413i 0.992381 + 0.123206i \(0.0393177\pi\)
−0.992381 + 0.123206i \(0.960682\pi\)
\(104\) −6.19369e20 −0.410298
\(105\) −3.61414e20 3.16459e20i −0.216530 0.189596i
\(106\) −1.01273e21 −0.549265
\(107\) 1.57535e21i 0.774188i 0.922040 + 0.387094i \(0.126521\pi\)
−0.922040 + 0.387094i \(0.873479\pi\)
\(108\) −1.47325e21 + 9.21569e20i −0.656641 + 0.410751i
\(109\) 2.80464e21 1.13475 0.567374 0.823460i \(-0.307959\pi\)
0.567374 + 0.823460i \(0.307959\pi\)
\(110\) −2.99166e20 −0.109974
\(111\) −3.20778e21 + 6.04712e20i −1.07229 + 0.202142i
\(112\) 7.59695e20 + 9.68234e20i 0.231127 + 0.294572i
\(113\) 5.14750e21i 1.42650i 0.700908 + 0.713252i \(0.252779\pi\)
−0.700908 + 0.713252i \(0.747221\pi\)
\(114\) −2.15701e21 + 4.06626e20i −0.544942 + 0.102729i
\(115\) 3.39312e20i 0.0782117i
\(116\) 4.55172e21i 0.958003i
\(117\) −9.21786e20 2.35799e21i −0.177288 0.453513i
\(118\) 3.68096e21i 0.647442i
\(119\) 3.21604e21 + 4.09885e21i 0.517700 + 0.659811i
\(120\) 3.04714e20 + 1.61640e21i 0.0449251 + 0.238311i
\(121\) 2.60805e21 0.352427
\(122\) −6.36230e21 −0.788562
\(123\) 1.95686e21 3.68897e20i 0.222616 0.0419663i
\(124\) 4.55988e21i 0.476459i
\(125\) −5.74532e21 −0.551771
\(126\) 2.73081e21 4.63045e21i 0.241213 0.409008i
\(127\) −2.26715e20 −0.0184307 −0.00921534 0.999958i \(-0.502933\pi\)
−0.00921534 + 0.999958i \(0.502933\pi\)
\(128\) 1.29311e22i 0.968123i
\(129\) −9.43083e21 + 1.77785e21i −0.650666 + 0.122660i
\(130\) −1.04597e21 −0.0665450
\(131\) 2.10295e22 1.23447 0.617234 0.786780i \(-0.288253\pi\)
0.617234 + 0.786780i \(0.288253\pi\)
\(132\) 2.13044e21 + 1.13012e22i 0.115463 + 0.612489i
\(133\) −1.83510e22 + 1.43985e22i −0.918791 + 0.720901i
\(134\) 6.03703e21i 0.279398i
\(135\) −5.70025e21 + 3.56570e21i −0.244000 + 0.152630i
\(136\) 1.78393e22i 0.706674i
\(137\) 3.53810e21i 0.129779i −0.997892 0.0648895i \(-0.979331\pi\)
0.997892 0.0648895i \(-0.0206695\pi\)
\(138\) 3.73135e21 7.03413e20i 0.126805 0.0239045i
\(139\) 6.64239e21i 0.209252i 0.994512 + 0.104626i \(0.0333645\pi\)
−0.994512 + 0.104626i \(0.966636\pi\)
\(140\) 4.70943e21 + 6.00219e21i 0.137602 + 0.175374i
\(141\) 3.20766e21 6.04689e20i 0.0869736 0.0163958i
\(142\) −3.06921e22 −0.772679
\(143\) −1.67550e22 −0.391845
\(144\) 1.60431e22 6.27157e21i 0.348723 0.136323i
\(145\) 1.76113e22i 0.355982i
\(146\) 2.98577e22 0.561503
\(147\) 3.07676e21 5.70428e22i 0.0538594 0.998549i
\(148\) 5.18420e22 0.845149
\(149\) 9.63864e22i 1.46406i −0.681271 0.732031i \(-0.738572\pi\)
0.681271 0.732031i \(-0.261428\pi\)
\(150\) −5.69789e21 3.02253e22i −0.0806782 0.427969i
\(151\) 1.48220e23 1.95727 0.978633 0.205617i \(-0.0659201\pi\)
0.978633 + 0.205617i \(0.0659201\pi\)
\(152\) 7.98682e22 0.984048
\(153\) 6.79156e22 2.65496e22i 0.781105 0.305350i
\(154\) −2.19607e22 2.79890e22i −0.235873 0.300621i
\(155\) 1.76429e22i 0.177046i
\(156\) 7.44864e21 + 3.95124e22i 0.0698665 + 0.370617i
\(157\) 4.52599e22i 0.396979i 0.980103 + 0.198490i \(0.0636036\pi\)
−0.980103 + 0.198490i \(0.936396\pi\)
\(158\) 4.42627e21i 0.0363194i
\(159\) 2.79040e22 + 1.48021e23i 0.214288 + 1.13672i
\(160\) 4.08443e22i 0.293678i
\(161\) 3.17449e22 2.49077e22i 0.213797 0.167749i
\(162\) −5.10283e22 5.52928e22i −0.322035 0.348948i
\(163\) −1.01747e23 −0.601938 −0.300969 0.953634i \(-0.597310\pi\)
−0.300969 + 0.953634i \(0.597310\pi\)
\(164\) −3.16255e22 −0.175460
\(165\) 8.24301e21 + 4.37262e22i 0.0429046 + 0.227594i
\(166\) 1.52092e23i 0.742972i
\(167\) −1.17221e23 −0.537630 −0.268815 0.963192i \(-0.586632\pi\)
−0.268815 + 0.963192i \(0.586632\pi\)
\(168\) −1.28857e23 + 1.47162e23i −0.555086 + 0.633939i
\(169\) 1.88484e23 0.762895
\(170\) 3.01265e22i 0.114613i
\(171\) 1.18865e23 + 3.04065e23i 0.425202 + 1.08769i
\(172\) 1.52415e23 0.512836
\(173\) −4.68987e23 −1.48483 −0.742415 0.669940i \(-0.766320\pi\)
−0.742415 + 0.669940i \(0.766320\pi\)
\(174\) −1.93669e23 + 3.65093e22i −0.577155 + 0.108802i
\(175\) −2.01761e23 2.57145e23i −0.566157 0.721570i
\(176\) 1.13996e23i 0.301305i
\(177\) −5.38011e23 + 1.01423e23i −1.33990 + 0.252590i
\(178\) 4.53115e22i 0.106365i
\(179\) 6.57802e23i 1.45592i 0.685619 + 0.727961i \(0.259532\pi\)
−0.685619 + 0.727961i \(0.740468\pi\)
\(180\) 9.94527e22 3.88781e22i 0.207613 0.0811604i
\(181\) 5.16324e23i 1.01695i −0.861078 0.508473i \(-0.830210\pi\)
0.861078 0.508473i \(-0.169790\pi\)
\(182\) −7.67811e22 9.78578e22i −0.142727 0.181906i
\(183\) 1.75302e23 + 9.29915e23i 0.307646 + 1.63195i
\(184\) −1.38162e23 −0.228982
\(185\) 2.00585e23 0.314047
\(186\) 1.94016e23 3.65748e22i 0.287046 0.0541123i
\(187\) 4.82582e23i 0.674892i
\(188\) −5.18400e22 −0.0685500
\(189\) −7.52030e23 2.71552e23i −0.940560 0.339629i
\(190\) 1.34879e23 0.159600
\(191\) 4.71277e23i 0.527747i 0.964557 + 0.263874i \(0.0850002\pi\)
−0.964557 + 0.263874i \(0.915000\pi\)
\(192\) 1.02068e23 1.92412e22i 0.108199 0.0203971i
\(193\) 1.57401e24 1.58000 0.789999 0.613108i \(-0.210081\pi\)
0.789999 + 0.613108i \(0.210081\pi\)
\(194\) −3.19233e23 −0.303522
\(195\) 2.88200e22 + 1.52880e23i 0.0259615 + 0.137717i
\(196\) −2.15843e23 + 8.81198e23i −0.184268 + 0.752289i
\(197\) 6.17191e23i 0.499487i −0.968312 0.249744i \(-0.919654\pi\)
0.968312 0.249744i \(-0.0803463\pi\)
\(198\) −4.63761e23 + 1.81294e23i −0.355885 + 0.139123i
\(199\) 1.18071e24i 0.859380i −0.902977 0.429690i \(-0.858623\pi\)
0.902977 0.429690i \(-0.141377\pi\)
\(200\) 1.11916e24i 0.772819i
\(201\) −8.82374e23 + 1.66340e23i −0.578221 + 0.109003i
\(202\) 6.01672e23i 0.374257i
\(203\) −1.64766e24 + 1.29279e24i −0.973104 + 0.763516i
\(204\) −1.13805e24 + 2.14538e23i −0.638329 + 0.120334i
\(205\) −1.22364e23 −0.0651987
\(206\) 2.31108e23 0.117006
\(207\) −2.05622e23 5.25994e23i −0.0989421 0.253100i
\(208\) 3.98563e23i 0.182319i
\(209\) 2.16057e24 0.939792
\(210\) −2.17610e23 + 2.48523e23i −0.0900276 + 0.102817i
\(211\) 3.65042e23 0.143674 0.0718368 0.997416i \(-0.477114\pi\)
0.0718368 + 0.997416i \(0.477114\pi\)
\(212\) 2.39221e24i 0.895928i
\(213\) 8.45668e23 + 4.48596e24i 0.301449 + 1.59908i
\(214\) 1.08327e24 0.367614
\(215\) 5.89717e23 0.190563
\(216\) 1.45189e24 + 2.32105e24i 0.446859 + 0.714364i
\(217\) 1.65061e24 1.29510e24i 0.483969 0.379732i
\(218\) 1.92858e24i 0.538822i
\(219\) −8.22679e23 4.36401e24i −0.219062 1.16205i
\(220\) 7.06673e23i 0.179383i
\(221\) 1.68725e24i 0.408376i
\(222\) 4.15824e23 + 2.20580e24i 0.0959850 + 0.509166i
\(223\) 8.80006e24i 1.93769i −0.247666 0.968846i \(-0.579663\pi\)
0.247666 0.968846i \(-0.420337\pi\)
\(224\) 3.82126e24 2.99823e24i 0.802790 0.629884i
\(225\) −4.26074e24 + 1.66561e24i −0.854217 + 0.333931i
\(226\) 3.53963e24 0.677359
\(227\) 3.39805e24 0.620810 0.310405 0.950604i \(-0.399535\pi\)
0.310405 + 0.950604i \(0.399535\pi\)
\(228\) −9.60510e23 5.09516e24i −0.167566 0.888877i
\(229\) 6.08362e24i 1.01365i −0.862048 0.506827i \(-0.830818\pi\)
0.862048 0.506827i \(-0.169182\pi\)
\(230\) −2.33324e23 −0.0371379
\(231\) −3.48579e24 + 3.98097e24i −0.530121 + 0.605429i
\(232\) 7.17105e24 1.04222
\(233\) 5.19101e24i 0.721132i 0.932734 + 0.360566i \(0.117416\pi\)
−0.932734 + 0.360566i \(0.882584\pi\)
\(234\) −1.62145e24 + 6.33857e23i −0.215346 + 0.0841831i
\(235\) −2.00577e23 −0.0254724
\(236\) 8.69496e24 1.05607
\(237\) −6.46945e23 + 1.21958e23i −0.0751640 + 0.0141695i
\(238\) 2.81854e24 2.21148e24i 0.313304 0.245824i
\(239\) 2.28072e24i 0.242602i −0.992616 0.121301i \(-0.961293\pi\)
0.992616 0.121301i \(-0.0387066\pi\)
\(240\) −1.04015e24 + 1.96083e23i −0.105896 + 0.0199628i
\(241\) 1.01334e25i 0.987586i 0.869579 + 0.493793i \(0.164390\pi\)
−0.869579 + 0.493793i \(0.835610\pi\)
\(242\) 1.79340e24i 0.167346i
\(243\) −6.67561e24 + 8.98181e24i −0.596520 + 0.802598i
\(244\) 1.50287e25i 1.28625i
\(245\) −8.35131e23 + 3.40950e24i −0.0684716 + 0.279542i
\(246\) −2.53668e23 1.34562e24i −0.0199272 0.105707i
\(247\) 7.55398e24 0.568667
\(248\) −7.18390e24 −0.518343
\(249\) −2.22298e25 + 4.19064e24i −1.53760 + 0.289859i
\(250\) 3.95071e24i 0.262002i
\(251\) −9.11602e24 −0.579737 −0.289869 0.957066i \(-0.593612\pi\)
−0.289869 + 0.957066i \(0.593612\pi\)
\(252\) 1.09378e25 + 6.45057e24i 0.667150 + 0.393453i
\(253\) −3.73751e24 −0.218684
\(254\) 1.55898e23i 0.00875160i
\(255\) −4.40329e24 + 8.30083e23i −0.237195 + 0.0447147i
\(256\) −1.10217e25 −0.569807
\(257\) −1.05919e25 −0.525623 −0.262812 0.964847i \(-0.584650\pi\)
−0.262812 + 0.964847i \(0.584650\pi\)
\(258\) 1.22252e24 + 6.48501e24i 0.0582436 + 0.308961i
\(259\) 1.47242e25 + 1.87661e25i 0.673572 + 0.858471i
\(260\) 2.47074e24i 0.108544i
\(261\) 1.06724e25 + 2.73007e25i 0.450337 + 1.15199i
\(262\) 1.44607e25i 0.586173i
\(263\) 1.05737e25i 0.411804i 0.978573 + 0.205902i \(0.0660128\pi\)
−0.978573 + 0.205902i \(0.933987\pi\)
\(264\) 1.78046e25 3.35642e24i 0.666331 0.125613i
\(265\) 9.25585e24i 0.332916i
\(266\) 9.90100e24 + 1.26189e25i 0.342312 + 0.436278i
\(267\) −6.62274e24 + 1.24848e24i −0.220125 + 0.0414967i
\(268\) 1.42603e25 0.455737
\(269\) −6.26136e25 −1.92429 −0.962143 0.272546i \(-0.912134\pi\)
−0.962143 + 0.272546i \(0.912134\pi\)
\(270\) 2.45192e24 + 3.91972e24i 0.0724746 + 0.115861i
\(271\) 4.94248e25i 1.40529i −0.711538 0.702647i \(-0.752001\pi\)
0.711538 0.702647i \(-0.247999\pi\)
\(272\) 1.14796e25 0.314016
\(273\) −1.21874e25 + 1.39186e25i −0.320776 + 0.366344i
\(274\) −2.43294e24 −0.0616241
\(275\) 3.02752e25i 0.738063i
\(276\) 1.66156e24 + 8.81399e24i 0.0389916 + 0.206837i
\(277\) −3.75420e25 −0.848163 −0.424082 0.905624i \(-0.639403\pi\)
−0.424082 + 0.905624i \(0.639403\pi\)
\(278\) 4.56757e24 0.0993608
\(279\) −1.06916e25 2.73497e25i −0.223974 0.572938i
\(280\) 9.45620e24 7.41951e24i 0.190791 0.149698i
\(281\) 7.95440e25i 1.54594i 0.634446 + 0.772968i \(0.281228\pi\)
−0.634446 + 0.772968i \(0.718772\pi\)
\(282\) −4.15808e23 2.20571e24i −0.00778534 0.0412984i
\(283\) 8.41458e24i 0.151801i 0.997115 + 0.0759006i \(0.0241832\pi\)
−0.997115 + 0.0759006i \(0.975817\pi\)
\(284\) 7.24991e25i 1.26035i
\(285\) −3.71636e24 1.97140e25i −0.0622655 0.330296i
\(286\) 1.15214e25i 0.186063i
\(287\) −8.98231e24 1.14480e25i −0.139839 0.178225i
\(288\) −2.47515e25 6.33159e25i −0.371519 0.950368i
\(289\) −2.04952e25 −0.296637
\(290\) 1.21103e25 0.169034
\(291\) 8.79593e24 + 4.66592e25i 0.118415 + 0.628147i
\(292\) 7.05283e25i 0.915890i
\(293\) 2.40398e25 0.301177 0.150588 0.988597i \(-0.451883\pi\)
0.150588 + 0.988597i \(0.451883\pi\)
\(294\) −3.92249e25 2.11570e24i −0.474149 0.0255745i
\(295\) 3.36422e25 0.392422
\(296\) 8.16748e25i 0.919443i
\(297\) 3.92761e25 + 6.27882e25i 0.426762 + 0.682237i
\(298\) −6.62791e25 −0.695194
\(299\) −1.30675e25 −0.132325
\(300\) 7.13964e25 1.34592e25i 0.698077 0.131597i
\(301\) 4.32890e25 + 5.51720e25i 0.408723 + 0.520919i
\(302\) 1.01922e26i 0.929385i
\(303\) 8.79405e25 1.65780e25i 0.774536 0.146011i
\(304\) 5.13951e25i 0.437269i
\(305\) 5.81483e25i 0.477956i
\(306\) −1.82566e25 4.67014e25i −0.144992 0.370899i
\(307\) 6.48510e25i 0.497695i −0.968543 0.248848i \(-0.919948\pi\)
0.968543 0.248848i \(-0.0800518\pi\)
\(308\) 6.61140e25 5.18743e25i 0.490355 0.384742i
\(309\) −6.36778e24 3.37788e25i −0.0456482 0.242147i
\(310\) −1.21320e25 −0.0840685
\(311\) 6.92031e25 0.463598 0.231799 0.972764i \(-0.425539\pi\)
0.231799 + 0.972764i \(0.425539\pi\)
\(312\) 6.22501e25 1.17350e25i 0.403196 0.0760082i
\(313\) 3.85686e25i 0.241556i 0.992680 + 0.120778i \(0.0385390\pi\)
−0.992680 + 0.120778i \(0.961461\pi\)
\(314\) 3.11225e25 0.188501
\(315\) 4.23200e25 + 2.49583e25i 0.247905 + 0.146202i
\(316\) 1.04555e25 0.0592420
\(317\) 1.86982e25i 0.102489i −0.998686 0.0512444i \(-0.983681\pi\)
0.998686 0.0512444i \(-0.0163188\pi\)
\(318\) 1.01785e26 1.91879e25i 0.539758 0.101752i
\(319\) 1.93989e26 0.995346
\(320\) −6.38236e24 −0.0316889
\(321\) −2.98477e25 1.58331e26i −0.143419 0.760788i
\(322\) −1.71275e25 2.18291e25i −0.0796539 0.101519i
\(323\) 2.17572e26i 0.979439i
\(324\) 1.30610e26 1.20536e26i 0.569183 0.525285i
\(325\) 1.05851e26i 0.446601i
\(326\) 6.99653e25i 0.285823i
\(327\) −2.81882e26 + 5.31388e25i −1.11511 + 0.210214i
\(328\) 4.98246e25i 0.190884i
\(329\) −1.47237e25 1.87654e25i −0.0546335 0.0696306i
\(330\) 3.00679e25 5.66822e24i 0.108070 0.0203728i
\(331\) −5.29120e26 −1.84230 −0.921149 0.389210i \(-0.872748\pi\)
−0.921149 + 0.389210i \(0.872748\pi\)
\(332\) 3.59264e26 1.21189
\(333\) 3.10942e26 1.21554e26i 1.01628 0.397287i
\(334\) 8.06060e25i 0.255287i
\(335\) 5.51755e25 0.169346
\(336\) −9.46985e25 8.29192e25i −0.281696 0.246657i
\(337\) −2.44499e26 −0.704959 −0.352479 0.935820i \(-0.614661\pi\)
−0.352479 + 0.935820i \(0.614661\pi\)
\(338\) 1.29609e26i 0.362252i
\(339\) −9.75284e25 5.17353e26i −0.264262 1.40181i
\(340\) 7.11630e25 0.186950
\(341\) −1.94336e26 −0.495031
\(342\) 2.09087e26 8.17365e25i 0.516479 0.201902i
\(343\) −3.80285e26 + 1.72147e26i −0.911006 + 0.412392i
\(344\) 2.40123e26i 0.557917i
\(345\) 6.42885e24 + 3.41027e25i 0.0144888 + 0.0768579i
\(346\) 3.22494e26i 0.705055i
\(347\) 5.87259e26i 1.24558i 0.782391 + 0.622788i \(0.214000\pi\)
−0.782391 + 0.622788i \(0.786000\pi\)
\(348\) −8.62403e25 4.57474e26i −0.177471 0.941421i
\(349\) 9.24854e26i 1.84674i 0.383909 + 0.923371i \(0.374578\pi\)
−0.383909 + 0.923371i \(0.625422\pi\)
\(350\) −1.76823e26 + 1.38739e26i −0.342629 + 0.268833i
\(351\) 1.37321e26 + 2.19526e26i 0.258233 + 0.412821i
\(352\) −4.49899e26 −0.821139
\(353\) −9.28342e26 −1.64465 −0.822326 0.569017i \(-0.807324\pi\)
−0.822326 + 0.569017i \(0.807324\pi\)
\(354\) 6.97423e25 + 3.69958e26i 0.119939 + 0.636235i
\(355\) 2.80511e26i 0.468330i
\(356\) 1.07032e26 0.173496
\(357\) −4.00890e26 3.51024e26i −0.630970 0.552486i
\(358\) 4.52331e26 0.691328
\(359\) 9.86718e26i 1.46454i 0.681014 + 0.732270i \(0.261539\pi\)
−0.681014 + 0.732270i \(0.738461\pi\)
\(360\) −6.12509e25 1.56684e26i −0.0882950 0.225864i
\(361\) −2.59883e26 −0.363876
\(362\) −3.55045e26 −0.482885
\(363\) −2.62124e26 + 4.94140e25i −0.346327 + 0.0652876i
\(364\) 2.31154e26 1.81368e26i 0.296713 0.232807i
\(365\) 2.72885e26i 0.340333i
\(366\) 6.39446e26 1.20545e26i 0.774913 0.146082i
\(367\) 2.46775e26i 0.290608i −0.989387 0.145304i \(-0.953584\pi\)
0.989387 0.145304i \(-0.0464161\pi\)
\(368\) 8.89072e25i 0.101750i
\(369\) −1.89686e26 + 7.41524e25i −0.210989 + 0.0824799i
\(370\) 1.37930e26i 0.149122i
\(371\) 8.65947e26 6.79439e26i 0.910050 0.714043i
\(372\) 8.63948e25 + 4.58293e26i 0.0882647 + 0.468212i
\(373\) −9.39882e26 −0.933535 −0.466768 0.884380i \(-0.654582\pi\)
−0.466768 + 0.884380i \(0.654582\pi\)
\(374\) −3.31843e26 −0.320465
\(375\) 5.77437e26 1.08855e26i 0.542221 0.102216i
\(376\) 8.16717e25i 0.0745760i
\(377\) 6.78241e26 0.602282
\(378\) −1.86730e26 + 5.17126e26i −0.161269 + 0.446614i
\(379\) 1.36756e27 1.14877 0.574387 0.818584i \(-0.305240\pi\)
0.574387 + 0.818584i \(0.305240\pi\)
\(380\) 3.18604e26i 0.260330i
\(381\) 2.27861e25 4.29551e24i 0.0181117 0.00341431i
\(382\) 3.24069e26 0.250595
\(383\) −6.34635e26 −0.477460 −0.238730 0.971086i \(-0.576731\pi\)
−0.238730 + 0.971086i \(0.576731\pi\)
\(384\) 2.45002e26 + 1.29965e27i 0.179346 + 0.951365i
\(385\) 2.55806e26 2.00710e26i 0.182210 0.142966i
\(386\) 1.08235e27i 0.750244i
\(387\) 9.14167e26 3.57367e26i 0.616681 0.241073i
\(388\) 7.54075e26i 0.495087i
\(389\) 7.80106e25i 0.0498520i −0.999689 0.0249260i \(-0.992065\pi\)
0.999689 0.0249260i \(-0.00793502\pi\)
\(390\) 1.05126e26 1.98178e25i 0.0653932 0.0123275i
\(391\) 3.76373e26i 0.227910i
\(392\) 1.38829e27 + 3.40051e26i 0.818421 + 0.200466i
\(393\) −2.11358e27 + 3.98440e26i −1.21310 + 0.228687i
\(394\) −4.24405e26 −0.237176
\(395\) 4.04539e25 0.0220136
\(396\) −4.28242e26 1.09547e27i −0.226929 0.580498i
\(397\) 2.38734e27i 1.23201i 0.787742 + 0.616005i \(0.211250\pi\)
−0.787742 + 0.616005i \(0.788750\pi\)
\(398\) −8.11902e26 −0.408067
\(399\) 1.57157e27 1.79482e27i 0.769340 0.878630i
\(400\) −7.20179e26 −0.343408
\(401\) 4.27170e27i 1.98420i −0.125460 0.992099i \(-0.540041\pi\)
0.125460 0.992099i \(-0.459959\pi\)
\(402\) 1.14382e26 + 6.06755e26i 0.0517588 + 0.274562i
\(403\) −6.79457e26 −0.299543
\(404\) −1.42124e27 −0.610466
\(405\) 5.05349e26 4.66374e26i 0.211502 0.195189i
\(406\) 8.88970e26 + 1.13300e27i 0.362547 + 0.462067i
\(407\) 2.20944e27i 0.878093i
\(408\) 3.37996e26 + 1.79295e27i 0.130912 + 0.694442i
\(409\) 2.55709e27i 0.965276i −0.875820 0.482638i \(-0.839679\pi\)
0.875820 0.482638i \(-0.160321\pi\)
\(410\) 8.41424e25i 0.0309588i
\(411\) 6.70355e25 + 3.55599e26i 0.0240417 + 0.127533i
\(412\) 5.45910e26i 0.190854i
\(413\) 2.46955e27 + 3.14745e27i 0.841672 + 1.07271i
\(414\) −3.61695e26 + 1.41394e26i −0.120182 + 0.0469815i
\(415\) 1.39005e27 0.450324
\(416\) −1.57298e27 −0.496870
\(417\) −1.25852e26 6.67597e26i −0.0387641 0.205630i
\(418\) 1.48569e27i 0.446249i
\(419\) 5.10810e27 1.49628 0.748139 0.663542i \(-0.230948\pi\)
0.748139 + 0.663542i \(0.230948\pi\)
\(420\) −5.87046e26 5.14025e26i −0.167708 0.146848i
\(421\) 1.00536e27 0.280129 0.140065 0.990142i \(-0.455269\pi\)
0.140065 + 0.990142i \(0.455269\pi\)
\(422\) 2.51017e26i 0.0682217i
\(423\) −3.10931e26 + 1.21549e26i −0.0824309 + 0.0322239i
\(424\) −3.76883e27 −0.974687
\(425\) −3.04876e27 −0.769199
\(426\) 3.08473e27 5.81515e26i 0.759304 0.143140i
\(427\) 5.44016e27 4.26845e27i 1.30653 1.02513i
\(428\) 2.55884e27i 0.599630i
\(429\) 1.68397e27 3.17452e26i 0.385063 0.0725899i
\(430\) 4.05513e26i 0.0904869i
\(431\) 5.86068e27i 1.27625i −0.769932 0.638126i \(-0.779710\pi\)
0.769932 0.638126i \(-0.220290\pi\)
\(432\) −1.49359e27 + 9.34291e26i −0.317433 + 0.198565i
\(433\) 5.82855e27i 1.20903i 0.796593 + 0.604516i \(0.206633\pi\)
−0.796593 + 0.604516i \(0.793367\pi\)
\(434\) −8.90563e26 1.13503e27i −0.180311 0.229807i
\(435\) −3.33677e26 1.77004e27i −0.0659462 0.349821i
\(436\) 4.55559e27 0.878894
\(437\) 1.68506e27 0.317366
\(438\) −3.00087e27 + 5.65707e26i −0.551784 + 0.104019i
\(439\) 1.00121e28i 1.79742i −0.438545 0.898709i \(-0.644506\pi\)
0.438545 0.898709i \(-0.355494\pi\)
\(440\) −1.11333e27 −0.195152
\(441\) 7.71544e26 + 5.79142e27i 0.132055 + 0.991242i
\(442\) −1.16022e27 −0.193913
\(443\) 7.11611e27i 1.16146i 0.814097 + 0.580729i \(0.197233\pi\)
−0.814097 + 0.580729i \(0.802767\pi\)
\(444\) −5.21041e27 + 9.82236e26i −0.830521 + 0.156565i
\(445\) 4.14125e26 0.0644690
\(446\) −6.05127e27 −0.920091
\(447\) 1.82621e27 + 9.68737e27i 0.271220 + 1.43872i
\(448\) −4.68506e26 5.97113e26i −0.0679667 0.0866239i
\(449\) 4.62514e27i 0.655448i 0.944774 + 0.327724i \(0.106282\pi\)
−0.944774 + 0.327724i \(0.893718\pi\)
\(450\) 1.14534e27 + 2.92985e27i 0.158564 + 0.405615i
\(451\) 1.34784e27i 0.182299i
\(452\) 8.36111e27i 1.10487i
\(453\) −1.48970e28 + 2.80829e27i −1.92339 + 0.362586i
\(454\) 2.33664e27i 0.294785i
\(455\) 8.94372e26 7.01741e26i 0.110255 0.0865082i
\(456\) −8.02720e27 + 1.51324e27i −0.967015 + 0.182296i
\(457\) −5.65110e27 −0.665293 −0.332647 0.943052i \(-0.607942\pi\)
−0.332647 + 0.943052i \(0.607942\pi\)
\(458\) −4.18334e27 −0.481322
\(459\) −6.32287e27 + 3.95516e27i −0.711018 + 0.444766i
\(460\) 5.51145e26i 0.0605772i
\(461\) 1.27891e28 1.37398 0.686990 0.726666i \(-0.258931\pi\)
0.686990 + 0.726666i \(0.258931\pi\)
\(462\) 2.73747e27 + 2.39697e27i 0.287481 + 0.251722i
\(463\) 8.88393e27 0.912021 0.456010 0.889974i \(-0.349278\pi\)
0.456010 + 0.889974i \(0.349278\pi\)
\(464\) 4.61456e27i 0.463118i
\(465\) 3.34275e26 + 1.77321e27i 0.0327981 + 0.173982i
\(466\) 3.56955e27 0.342421
\(467\) −2.02160e28 −1.89613 −0.948066 0.318072i \(-0.896965\pi\)
−0.948066 + 0.318072i \(0.896965\pi\)
\(468\) −1.49726e27 3.83009e27i −0.137314 0.351259i
\(469\) 4.05023e27 + 5.16204e27i 0.363216 + 0.462920i
\(470\) 1.37925e26i 0.0120953i
\(471\) −8.57528e26 4.54888e27i −0.0735409 0.390108i
\(472\) 1.36985e28i 1.14890i
\(473\) 6.49572e27i 0.532826i
\(474\) 8.38634e25 + 4.44865e26i 0.00672822 + 0.0356908i
\(475\) 1.36496e28i 1.07112i
\(476\) 5.22382e27 + 6.65778e27i 0.400973 + 0.511042i
\(477\) −5.60902e27 1.43482e28i −0.421157 1.07735i
\(478\) −1.56832e27 −0.115197
\(479\) 1.43805e28 1.03336 0.516680 0.856179i \(-0.327168\pi\)
0.516680 + 0.856179i \(0.327168\pi\)
\(480\) 7.73865e26 + 4.10508e27i 0.0544042 + 0.288595i
\(481\) 7.72485e27i 0.531333i
\(482\) 6.96811e27 0.468944
\(483\) −2.71862e27 + 3.10482e27i −0.179021 + 0.204452i
\(484\) 4.23626e27 0.272965
\(485\) 2.91764e27i 0.183968i
\(486\) 6.17625e27 + 4.59042e27i 0.381105 + 0.283251i
\(487\) 8.25040e26 0.0498219 0.0249110 0.999690i \(-0.492070\pi\)
0.0249110 + 0.999690i \(0.492070\pi\)
\(488\) −2.36770e28 −1.39932
\(489\) 1.02261e28 1.92777e27i 0.591519 0.111510i
\(490\) 2.34451e27 + 5.74269e26i 0.132737 + 0.0325130i
\(491\) 4.28429e27i 0.237423i 0.992929 + 0.118712i \(0.0378764\pi\)
−0.992929 + 0.118712i \(0.962124\pi\)
\(492\) 3.17854e27 5.99200e26i 0.172423 0.0325041i
\(493\) 1.95349e28i 1.03734i
\(494\) 5.19442e27i 0.270025i
\(495\) −1.65694e27 4.23855e27i −0.0843240 0.215706i
\(496\) 4.62283e27i 0.230330i
\(497\) 2.62437e28 2.05913e28i 1.28021 1.00448i
\(498\) 2.88165e27 + 1.52861e28i 0.137636 + 0.730112i
\(499\) 6.11301e26 0.0285890 0.0142945 0.999898i \(-0.495450\pi\)
0.0142945 + 0.999898i \(0.495450\pi\)
\(500\) −9.33214e27 −0.427362
\(501\) 1.17814e28 2.22096e27i 0.528324 0.0995966i
\(502\) 6.26854e27i 0.275282i
\(503\) 3.59743e28 1.54713 0.773567 0.633714i \(-0.218470\pi\)
0.773567 + 0.633714i \(0.218470\pi\)
\(504\) 1.01626e28 1.72320e28i 0.428040 0.725797i
\(505\) −5.49899e27 −0.226842
\(506\) 2.57006e27i 0.103840i
\(507\) −1.89437e28 + 3.57116e27i −0.749690 + 0.141327i
\(508\) −3.68254e26 −0.0142751
\(509\) −3.19042e28 −1.21146 −0.605732 0.795669i \(-0.707120\pi\)
−0.605732 + 0.795669i \(0.707120\pi\)
\(510\) 5.70798e26 + 3.02788e27i 0.0212322 + 0.112629i
\(511\) −2.55302e28 + 2.00315e28i −0.930327 + 0.729952i
\(512\) 1.95395e28i 0.697556i
\(513\) −1.77077e28 2.83081e28i −0.619339 0.990098i
\(514\) 7.28339e27i 0.249586i
\(515\) 2.11221e27i 0.0709188i
\(516\) −1.53185e28 + 2.88776e27i −0.503959 + 0.0950035i
\(517\) 2.20935e27i 0.0712221i
\(518\) 1.29043e28 1.01249e28i 0.407635 0.319838i
\(519\) 4.71358e28 8.88577e27i 1.45913 0.275067i
\(520\) −3.89254e27 −0.118086
\(521\) −2.39651e28 −0.712496 −0.356248 0.934391i \(-0.615944\pi\)
−0.356248 + 0.934391i \(0.615944\pi\)
\(522\) 1.87731e28 7.33879e27i 0.547010 0.213838i
\(523\) 9.11876e27i 0.260416i 0.991487 + 0.130208i \(0.0415645\pi\)
−0.991487 + 0.130208i \(0.958435\pi\)
\(524\) 3.41583e28 0.956130
\(525\) 2.51501e28 + 2.20218e28i 0.690030 + 0.604199i
\(526\) 7.27087e27 0.195540
\(527\) 1.95700e28i 0.515915i
\(528\) 2.15985e27 + 1.14572e28i 0.0558171 + 0.296090i
\(529\) 3.65566e28 0.926151
\(530\) −6.36469e27 −0.158081
\(531\) 5.21515e28 2.03871e28i 1.26991 0.496435i
\(532\) −2.98075e28 + 2.33876e28i −0.711630 + 0.558358i
\(533\) 4.71244e27i 0.110309i
\(534\) 8.58505e26 + 4.55406e27i 0.0197042 + 0.104524i
\(535\) 9.90056e27i 0.222815i
\(536\) 2.24665e28i 0.495799i
\(537\) −1.24632e28 6.61127e28i −0.269711 1.43072i
\(538\) 4.30556e28i 0.913725i
\(539\) 3.75555e28 + 9.19895e27i 0.781613 + 0.191450i
\(540\) −9.25894e27 + 5.79178e27i −0.188985 + 0.118216i
\(541\) −3.18902e28 −0.638389 −0.319194 0.947689i \(-0.603412\pi\)
−0.319194 + 0.947689i \(0.603412\pi\)
\(542\) −3.39865e28 −0.667288
\(543\) 9.78266e27 + 5.18935e28i 0.188390 + 0.999343i
\(544\) 4.53055e28i 0.855780i
\(545\) 1.76263e28 0.326586
\(546\) 9.57102e27 + 8.38051e27i 0.173954 + 0.152317i
\(547\) −4.10267e28 −0.731475 −0.365738 0.930718i \(-0.619183\pi\)
−0.365738 + 0.930718i \(0.619183\pi\)
\(548\) 5.74695e27i 0.100517i
\(549\) −3.52377e28 9.01402e28i −0.604641 1.54671i
\(550\) 2.08184e28 0.350461
\(551\) −8.74599e28 −1.44450
\(552\) 1.38861e28 2.61772e27i 0.225019 0.0424193i
\(553\) 2.96958e27 + 3.78474e27i 0.0472151 + 0.0601758i
\(554\) 2.58153e28i 0.402741i
\(555\) −2.01599e28 + 3.80043e27i −0.308611 + 0.0581776i
\(556\) 1.07893e28i 0.162071i
\(557\) 4.59822e28i 0.677813i 0.940820 + 0.338906i \(0.110057\pi\)
−0.940820 + 0.338906i \(0.889943\pi\)
\(558\) −1.88067e28 + 7.35194e27i −0.272053 + 0.106351i
\(559\) 2.27110e28i 0.322412i
\(560\) 4.77445e27 + 6.08505e27i 0.0665195 + 0.0847793i
\(561\) 9.14335e27 + 4.85022e28i 0.125025 + 0.663210i
\(562\) 5.46976e28 0.734070
\(563\) −1.17978e29 −1.55405 −0.777023 0.629472i \(-0.783271\pi\)
−0.777023 + 0.629472i \(0.783271\pi\)
\(564\) 5.21021e27 9.82199e26i 0.0673635 0.0126990i
\(565\) 3.23505e28i 0.410555i
\(566\) 5.78620e27 0.0720810
\(567\) 8.07283e28 + 1.30440e28i 0.987196 + 0.159510i
\(568\) −1.14219e29 −1.37114
\(569\) 6.38010e28i 0.751881i 0.926644 + 0.375940i \(0.122680\pi\)
−0.926644 + 0.375940i \(0.877320\pi\)
\(570\) −1.35561e28 + 2.55552e27i −0.156837 + 0.0295661i
\(571\) −8.11711e28 −0.921982 −0.460991 0.887405i \(-0.652506\pi\)
−0.460991 + 0.887405i \(0.652506\pi\)
\(572\) −2.72151e28 −0.303495
\(573\) −8.92916e27 4.73660e28i −0.0977658 0.518613i
\(574\) −7.87209e27 + 6.17659e27i −0.0846283 + 0.0664009i
\(575\) 2.36121e28i 0.249242i
\(576\) −9.89381e27 + 3.86770e27i −0.102548 + 0.0400882i
\(577\) 2.97701e28i 0.302994i 0.988458 + 0.151497i \(0.0484095\pi\)
−0.988458 + 0.151497i \(0.951591\pi\)
\(578\) 1.40933e28i 0.140854i
\(579\) −1.58197e29 + 2.98224e28i −1.55265 + 0.292697i
\(580\) 2.86062e28i 0.275718i
\(581\) 1.02038e29 + 1.30048e29i 0.965861 + 1.23099i
\(582\) 3.20847e28 6.04843e27i 0.298268 0.0562278i
\(583\) −1.01953e29 −0.930851
\(584\) 1.11114e29 0.996403
\(585\) −5.79314e27 1.48192e28i −0.0510244 0.130523i
\(586\) 1.65307e28i 0.143010i
\(587\) 1.40022e28 0.118986 0.0594932 0.998229i \(-0.481052\pi\)
0.0594932 + 0.998229i \(0.481052\pi\)
\(588\) 4.99759e27 9.26549e28i 0.0417156 0.773404i
\(589\) 8.76166e28 0.718416
\(590\) 2.31337e28i 0.186337i
\(591\) 1.16938e28 + 6.20311e28i 0.0925306 + 0.490842i
\(592\) 5.25576e28 0.408562
\(593\) −1.86937e29 −1.42765 −0.713824 0.700325i \(-0.753038\pi\)
−0.713824 + 0.700325i \(0.753038\pi\)
\(594\) 4.31756e28 2.70078e28i 0.323952 0.202643i
\(595\) 2.02118e28 + 2.57600e28i 0.148997 + 0.189897i
\(596\) 1.56561e29i 1.13396i
\(597\) 2.23706e28 + 1.18668e29i 0.159201 + 0.844505i
\(598\) 8.98570e27i 0.0628332i
\(599\) 3.47967e28i 0.239087i −0.992829 0.119544i \(-0.961857\pi\)
0.992829 0.119544i \(-0.0381432\pi\)
\(600\) −2.12045e28 1.12482e29i −0.143166 0.759443i
\(601\) 9.77592e28i 0.648598i 0.945955 + 0.324299i \(0.105128\pi\)
−0.945955 + 0.324299i \(0.894872\pi\)
\(602\) 3.79385e28 2.97672e28i 0.247353 0.194078i
\(603\) 8.55319e28 3.34362e28i 0.548020 0.214232i
\(604\) 2.40755e29 1.51596
\(605\) 1.63908e28 0.101430
\(606\) −1.13997e28 6.04714e28i −0.0693317 0.367779i
\(607\) 6.18499e28i 0.369707i 0.982766 + 0.184854i \(0.0591811\pi\)
−0.982766 + 0.184854i \(0.940819\pi\)
\(608\) 2.02837e29 1.19168
\(609\) 1.41105e29 1.61150e29i 0.814818 0.930569i
\(610\) −3.99851e28 −0.226952
\(611\) 7.72456e27i 0.0430964i
\(612\) 1.10315e29 4.31246e28i 0.604988 0.236502i
\(613\) −2.24650e29 −1.21107 −0.605537 0.795817i \(-0.707042\pi\)
−0.605537 + 0.795817i \(0.707042\pi\)
\(614\) −4.45941e28 −0.236325
\(615\) 1.22983e28 2.31840e27i 0.0640701 0.0120781i
\(616\) −8.17258e28 1.04160e29i −0.418564 0.533461i
\(617\) 5.06622e27i 0.0255088i −0.999919 0.0127544i \(-0.995940\pi\)
0.999919 0.0127544i \(-0.00405996\pi\)
\(618\) −2.32276e28 + 4.37874e27i −0.114981 + 0.0216755i
\(619\) 3.95071e28i 0.192275i −0.995368 0.0961376i \(-0.969351\pi\)
0.995368 0.0961376i \(-0.0306489\pi\)
\(620\) 2.86574e28i 0.137127i
\(621\) 3.06320e28 + 4.89695e28i 0.144117 + 0.230390i
\(622\) 4.75868e28i 0.220134i
\(623\) 3.03994e28 + 3.87442e28i 0.138274 + 0.176231i
\(624\) 7.55147e27 + 4.00578e28i 0.0337749 + 0.179163i
\(625\) 1.72432e29 0.758366
\(626\) 2.65213e28 0.114700
\(627\) −2.17149e29 + 4.09357e28i −0.923525 + 0.174098i
\(628\) 7.35159e28i 0.307471i
\(629\) 2.22494e29 0.915137
\(630\) 1.71623e28 2.91009e28i 0.0694224 0.117715i
\(631\) −1.04298e29 −0.414922 −0.207461 0.978243i \(-0.566520\pi\)
−0.207461 + 0.978243i \(0.566520\pi\)
\(632\) 1.64722e28i 0.0644498i
\(633\) −3.66887e28 + 6.91635e27i −0.141187 + 0.0266157i
\(634\) −1.28576e28 −0.0486657
\(635\) −1.42483e27 −0.00530445
\(636\) 4.53246e28 + 2.40431e29i 0.165972 + 0.880421i
\(637\) 1.31305e29 + 3.21622e28i 0.472953 + 0.115846i
\(638\) 1.33394e29i 0.472629i
\(639\) −1.69989e29 4.34842e29i −0.592463 1.51556i
\(640\) 8.12679e28i 0.278631i
\(641\) 5.90673e29i 1.99222i −0.0881055 0.996111i \(-0.528081\pi\)
0.0881055 0.996111i \(-0.471919\pi\)
\(642\) −1.08875e29 + 2.05244e28i −0.361251 + 0.0681010i
\(643\) 3.63466e29i 1.18645i 0.805038 + 0.593224i \(0.202145\pi\)
−0.805038 + 0.593224i \(0.797855\pi\)
\(644\) 5.15634e28 4.04576e28i 0.165592 0.129927i
\(645\) −5.92698e28 + 1.11732e28i −0.187265 + 0.0353021i
\(646\) 1.49611e29 0.465075
\(647\) 1.11731e29 0.341728 0.170864 0.985295i \(-0.445344\pi\)
0.170864 + 0.985295i \(0.445344\pi\)
\(648\) −1.89900e29 2.05770e29i −0.571461 0.619219i
\(649\) 3.70568e29i 1.09723i
\(650\) 7.27873e28 0.212063
\(651\) −1.41358e29 + 1.61439e29i −0.405247 + 0.462815i
\(652\) −1.65268e29 −0.466218
\(653\) 1.74296e29i 0.483836i 0.970297 + 0.241918i \(0.0777765\pi\)
−0.970297 + 0.241918i \(0.922223\pi\)
\(654\) 3.65404e28 + 1.93834e29i 0.0998175 + 0.529496i
\(655\) 1.32164e29 0.355286
\(656\) −3.20621e28 −0.0848207
\(657\) 1.65368e29 + 4.23021e29i 0.430541 + 1.10135i
\(658\) −1.29038e28 + 1.01246e28i −0.0330633 + 0.0259421i
\(659\) 3.51653e29i 0.886783i 0.896328 + 0.443391i \(0.146225\pi\)
−0.896328 + 0.443391i \(0.853775\pi\)
\(660\) 1.33891e28 + 7.10246e28i 0.0332309 + 0.176278i
\(661\) 7.04382e29i 1.72065i −0.509744 0.860326i \(-0.670260\pi\)
0.509744 0.860326i \(-0.329740\pi\)
\(662\) 3.63844e29i 0.874794i
\(663\) 3.19679e28 + 1.69578e29i 0.0756522 + 0.401308i
\(664\) 5.66005e29i 1.31842i
\(665\) −1.15330e29 + 9.04902e28i −0.264433 + 0.207479i
\(666\) −8.35853e28 2.13816e29i −0.188647 0.482571i
\(667\) 1.51295e29 0.336126
\(668\) −1.90403e29 −0.416409
\(669\) 1.66732e29 + 8.84455e29i 0.358960 + 1.90415i
\(670\) 3.79409e28i 0.0804121i
\(671\) −6.40502e29 −1.33639
\(672\) −3.27251e29 + 3.73739e29i −0.672208 + 0.767700i
\(673\) 4.00984e29 0.810902 0.405451 0.914117i \(-0.367114\pi\)
0.405451 + 0.914117i \(0.367114\pi\)
\(674\) 1.68128e29i 0.334742i
\(675\) 3.96670e29 2.48130e29i 0.777571 0.486396i
\(676\) 3.06156e29 0.590884
\(677\) −2.14790e29 −0.408162 −0.204081 0.978954i \(-0.565421\pi\)
−0.204081 + 0.978954i \(0.565421\pi\)
\(678\) −3.55753e29 + 6.70644e28i −0.665635 + 0.125482i
\(679\) 2.72965e29 2.14173e29i 0.502891 0.394578i
\(680\) 1.12114e29i 0.203384i
\(681\) −3.41523e29 + 6.43820e28i −0.610064 + 0.115006i
\(682\) 1.33633e29i 0.235060i
\(683\) 5.53628e28i 0.0958961i −0.998850 0.0479480i \(-0.984732\pi\)
0.998850 0.0479480i \(-0.0152682\pi\)
\(684\) 1.93073e29 + 4.93893e29i 0.329331 + 0.842450i
\(685\) 2.22359e28i 0.0373511i
\(686\) 1.18375e29 + 2.61499e29i 0.195820 + 0.432581i
\(687\) 1.15265e29 + 6.11438e29i 0.187781 + 0.996108i
\(688\) 1.54519e29 0.247915
\(689\) −3.56458e29 −0.563257
\(690\) 2.34504e28 4.42073e27i 0.0364951 0.00687985i
\(691\) 2.55853e29i 0.392168i −0.980587 0.196084i \(-0.937178\pi\)
0.980587 0.196084i \(-0.0628225\pi\)
\(692\) −7.61777e29 −1.15004
\(693\) 2.74915e29 4.66154e29i 0.408789 0.693155i
\(694\) 4.03822e29 0.591447
\(695\) 4.17453e28i 0.0602237i
\(696\) −7.20730e29 + 1.35868e29i −1.02418 + 0.193072i
\(697\) −1.35729e29 −0.189990
\(698\) 6.35966e29 0.876904
\(699\) −9.83527e28 5.21726e29i −0.133591 0.708650i
\(700\) −3.27721e29 4.17681e29i −0.438505 0.558876i
\(701\) 1.49094e29i 0.196527i 0.995160 + 0.0982633i \(0.0313287\pi\)
−0.995160 + 0.0982633i \(0.968671\pi\)
\(702\) 1.50955e29 9.44273e28i 0.196023 0.122619i
\(703\) 9.96126e29i 1.27433i
\(704\) 7.03016e28i 0.0886038i
\(705\) 2.01591e28 3.80028e27i 0.0250315 0.00471879i
\(706\) 6.38365e29i 0.780944i
\(707\) −4.03661e29 5.14467e29i −0.486533 0.620089i
\(708\) −8.73893e29 + 1.64741e29i −1.03779 + 0.195638i
\(709\) −1.33414e30 −1.56104 −0.780521 0.625130i \(-0.785046\pi\)
−0.780521 + 0.625130i \(0.785046\pi\)
\(710\) −1.92890e29 −0.222381
\(711\) 6.27109e28 2.45150e28i 0.0712381 0.0278484i
\(712\) 1.68625e29i 0.188747i
\(713\) −1.51566e29 −0.167171
\(714\) −2.41378e29 + 2.75668e29i −0.262341 + 0.299609i
\(715\) −1.05300e29 −0.112775
\(716\) 1.06847e30i 1.12765i
\(717\) 4.32122e28 + 2.29225e29i 0.0449423 + 0.238403i
\(718\) 6.78507e29 0.695421
\(719\) 1.71233e30 1.72955 0.864775 0.502159i \(-0.167461\pi\)
0.864775 + 0.502159i \(0.167461\pi\)
\(720\) 1.00826e29 3.94149e28i 0.100364 0.0392346i
\(721\) −1.97612e29 + 1.55050e29i −0.193862 + 0.152108i
\(722\) 1.78706e29i 0.172782i
\(723\) −1.91994e29 1.01846e30i −0.182952 0.970492i
\(724\) 8.38668e29i 0.787653i
\(725\) 1.22554e30i 1.13443i
\(726\) 3.39791e28 + 1.80247e29i 0.0310011 + 0.164450i
\(727\) 1.15281e30i 1.03668i −0.855174 0.518341i \(-0.826550\pi\)
0.855174 0.518341i \(-0.173450\pi\)
\(728\) −2.85737e29 3.64174e29i −0.253272 0.322797i
\(729\) 5.00760e29 1.02920e30i 0.437513 0.899212i
\(730\) 1.87647e29 0.161603
\(731\) 6.54129e29 0.555304
\(732\) 2.84744e29 + 1.51046e30i 0.238280 + 1.26399i
\(733\) 1.96769e30i 1.62317i 0.584233 + 0.811586i \(0.301395\pi\)
−0.584233 + 0.811586i \(0.698605\pi\)
\(734\) −1.69692e29 −0.137992
\(735\) 1.93365e28 3.58497e29i 0.0155010 0.287388i
\(736\) −3.50883e29 −0.277297
\(737\) 6.07757e29i 0.473501i
\(738\) 5.09901e28 + 1.30436e29i 0.0391646 + 0.100186i
\(739\) 1.29711e30 0.982226 0.491113 0.871096i \(-0.336590\pi\)
0.491113 + 0.871096i \(0.336590\pi\)
\(740\) 3.25811e29 0.243238
\(741\) −7.59217e29 + 1.43123e29i −0.558824 + 0.105346i
\(742\) −4.67209e29 5.95460e29i −0.339055 0.432127i
\(743\) 1.12719e30i 0.806521i −0.915085 0.403260i \(-0.867877\pi\)
0.915085 0.403260i \(-0.132123\pi\)
\(744\) 7.22022e29 1.36111e29i 0.509371 0.0960237i
\(745\) 6.05758e29i 0.421365i
\(746\) 6.46300e29i 0.443279i
\(747\) 2.15483e30 8.42366e29i 1.45729 0.569685i
\(748\) 7.83860e29i 0.522723i
\(749\) −9.26264e29 + 7.26765e29i −0.609082 + 0.477897i
\(750\) −7.48530e28 3.97068e29i −0.0485362 0.257467i
\(751\) −2.62935e30 −1.68124 −0.840618 0.541629i \(-0.817808\pi\)
−0.840618 + 0.541629i \(0.817808\pi\)
\(752\) −5.25557e28 −0.0331384
\(753\) 9.16211e29 1.72719e29i 0.569703 0.107397i
\(754\) 4.66386e29i 0.285987i
\(755\) 9.31518e29 0.563311
\(756\) −1.22153e30 4.41083e29i −0.728490 0.263052i
\(757\) 1.02765e30 0.604422 0.302211 0.953241i \(-0.402275\pi\)
0.302211 + 0.953241i \(0.402275\pi\)
\(758\) 9.40389e29i 0.545483i
\(759\) 3.75641e29 7.08137e28i 0.214899 0.0405115i
\(760\) 5.01947e29 0.283214
\(761\) 2.20358e30