Properties

Label 21.22.c.b.20.45
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 20.45
Character \(\chi\) \(=\) 21.20
Dual form 21.22.c.b.20.46

$q$-expansion

\(f(q)\) \(=\) \(q-367.125i q^{2} +(91325.3 + 46043.9i) q^{3} +1.96237e6 q^{4} +3.23352e7 q^{5} +(1.69039e7 - 3.35278e7i) q^{6} +(-4.79207e8 + 5.73504e8i) q^{7} -1.49035e9i q^{8} +(6.22027e9 + 8.40995e9i) q^{9} +O(q^{10})\) \(q-367.125i q^{2} +(91325.3 + 46043.9i) q^{3} +1.96237e6 q^{4} +3.23352e7 q^{5} +(1.69039e7 - 3.35278e7i) q^{6} +(-4.79207e8 + 5.73504e8i) q^{7} -1.49035e9i q^{8} +(6.22027e9 + 8.40995e9i) q^{9} -1.18711e10i q^{10} -1.31196e11i q^{11} +(1.79214e11 + 9.03553e10i) q^{12} +6.69122e11i q^{13} +(2.10547e11 + 1.75929e11i) q^{14} +(2.95302e12 + 1.48884e12i) q^{15} +3.56825e12 q^{16} +9.54655e12 q^{17} +(3.08750e12 - 2.28361e12i) q^{18} +1.11389e13i q^{19} +6.34537e13 q^{20} +(-7.01701e13 + 3.03108e13i) q^{21} -4.81652e13 q^{22} -2.12594e14i q^{23} +(6.86216e13 - 1.36107e14i) q^{24} +5.68730e14 q^{25} +2.45651e14 q^{26} +(1.80841e14 + 1.05445e15i) q^{27} +(-9.40382e14 + 1.12543e15i) q^{28} -1.26875e15i q^{29} +(5.46590e14 - 1.08413e15i) q^{30} +5.66433e15i q^{31} -4.43548e15i q^{32} +(6.04077e15 - 1.19815e16i) q^{33} -3.50477e15i q^{34} +(-1.54953e16 + 1.85444e16i) q^{35} +(1.22065e16 + 1.65034e16i) q^{36} -4.08103e16 q^{37} +4.08938e15 q^{38} +(-3.08090e16 + 6.11077e16i) q^{39} -4.81909e16i q^{40} -2.27791e16 q^{41} +(1.11279e16 + 2.57612e16i) q^{42} +1.15256e17 q^{43} -2.57455e17i q^{44} +(2.01134e17 + 2.71938e17i) q^{45} -7.80486e16 q^{46} -1.81071e17 q^{47} +(3.25871e17 + 1.64296e17i) q^{48} +(-9.92673e16 - 5.49654e17i) q^{49} -2.08795e17i q^{50} +(8.71841e17 + 4.39560e17i) q^{51} +1.31307e18i q^{52} +7.35468e17i q^{53} +(3.87113e17 - 6.63911e16i) q^{54} -4.24225e18i q^{55} +(8.54722e17 + 7.14187e17i) q^{56} +(-5.12881e17 + 1.01727e18i) q^{57} -4.65790e17 q^{58} +2.94154e18 q^{59} +(5.79493e18 + 2.92166e18i) q^{60} -1.08357e18i q^{61} +2.07951e18 q^{62} +(-7.80393e18 - 4.62759e17i) q^{63} +5.85478e18 q^{64} +2.16362e19i q^{65} +(-4.39870e18 - 2.21772e18i) q^{66} -6.78306e18 q^{67} +1.87339e19 q^{68} +(9.78867e18 - 1.94152e19i) q^{69} +(6.80810e18 + 5.68869e18i) q^{70} +2.06767e19i q^{71} +(1.25338e19 - 9.27038e18i) q^{72} -4.03443e19i q^{73} +1.49825e19i q^{74} +(5.19394e19 + 2.61866e19i) q^{75} +2.18587e19i q^{76} +(7.52413e19 + 6.28700e19i) q^{77} +(2.24342e19 + 1.13107e19i) q^{78} +9.41640e19 q^{79} +1.15380e20 q^{80} +(-3.20355e19 + 1.04624e20i) q^{81} +8.36275e18i q^{82} +2.74031e19 q^{83} +(-1.37700e20 + 5.94811e19i) q^{84} +3.08690e20 q^{85} -4.23135e19i q^{86} +(5.84183e19 - 1.15869e20i) q^{87} -1.95528e20 q^{88} -4.43565e20 q^{89} +(9.98350e19 - 7.38412e19i) q^{90} +(-3.83744e20 - 3.20648e20i) q^{91} -4.17189e20i q^{92} +(-2.60808e20 + 5.17296e20i) q^{93} +6.64757e19i q^{94} +3.60180e20i q^{95} +(2.04227e20 - 4.05072e20i) q^{96} +8.62831e20i q^{97} +(-2.01792e20 + 3.64435e19i) q^{98} +(1.10335e21 - 8.16073e20i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 367.125i 0.253512i −0.991934 0.126756i \(-0.959543\pi\)
0.991934 0.126756i \(-0.0404565\pi\)
\(3\) 91325.3 + 46043.9i 0.892931 + 0.450193i
\(4\) 1.96237e6 0.935732
\(5\) 3.23352e7 1.48078 0.740391 0.672177i \(-0.234641\pi\)
0.740391 + 0.672177i \(0.234641\pi\)
\(6\) 1.69039e7 3.35278e7i 0.114129 0.226369i
\(7\) −4.79207e8 + 5.73504e8i −0.641200 + 0.767374i
\(8\) 1.49035e9i 0.490731i
\(9\) 6.22027e9 + 8.40995e9i 0.594652 + 0.803983i
\(10\) 1.18711e10i 0.375396i
\(11\) 1.31196e11i 1.52510i −0.646932 0.762548i \(-0.723948\pi\)
0.646932 0.762548i \(-0.276052\pi\)
\(12\) 1.79214e11 + 9.03553e10i 0.835544 + 0.421260i
\(13\) 6.69122e11i 1.34617i 0.739565 + 0.673085i \(0.235031\pi\)
−0.739565 + 0.673085i \(0.764969\pi\)
\(14\) 2.10547e11 + 1.75929e11i 0.194538 + 0.162552i
\(15\) 2.95302e12 + 1.48884e12i 1.32224 + 0.666638i
\(16\) 3.56825e12 0.811325
\(17\) 9.54655e12 1.14850 0.574252 0.818679i \(-0.305293\pi\)
0.574252 + 0.818679i \(0.305293\pi\)
\(18\) 3.08750e12 2.28361e12i 0.203819 0.150751i
\(19\) 1.11389e13i 0.416803i 0.978043 + 0.208402i \(0.0668261\pi\)
−0.978043 + 0.208402i \(0.933174\pi\)
\(20\) 6.34537e13 1.38561
\(21\) −7.01701e13 + 3.03108e13i −0.918014 + 0.396548i
\(22\) −4.81652e13 −0.386630
\(23\) 2.12594e14i 1.07006i −0.844832 0.535031i \(-0.820300\pi\)
0.844832 0.535031i \(-0.179700\pi\)
\(24\) 6.86216e13 1.36107e14i 0.220924 0.438189i
\(25\) 5.68730e14 1.19271
\(26\) 2.45651e14 0.341270
\(27\) 1.80841e14 + 1.05445e15i 0.169035 + 0.985610i
\(28\) −9.40382e14 + 1.12543e15i −0.599991 + 0.718056i
\(29\) 1.26875e15i 0.560012i −0.959998 0.280006i \(-0.909663\pi\)
0.959998 0.280006i \(-0.0903365\pi\)
\(30\) 5.46590e14 1.08413e15i 0.169001 0.335203i
\(31\) 5.66433e15i 1.24123i 0.784117 + 0.620613i \(0.213116\pi\)
−0.784117 + 0.620613i \(0.786884\pi\)
\(32\) 4.43548e15i 0.696412i
\(33\) 6.04077e15 1.19815e16i 0.686588 1.36180i
\(34\) 3.50477e15i 0.291160i
\(35\) −1.54953e16 + 1.85444e16i −0.949477 + 1.13631i
\(36\) 1.22065e16 + 1.65034e16i 0.556435 + 0.752313i
\(37\) −4.08103e16 −1.39525 −0.697624 0.716464i \(-0.745759\pi\)
−0.697624 + 0.716464i \(0.745759\pi\)
\(38\) 4.08938e15 0.105665
\(39\) −3.08090e16 + 6.11077e16i −0.606037 + 1.20204i
\(40\) 4.81909e16i 0.726666i
\(41\) −2.27791e16 −0.265036 −0.132518 0.991181i \(-0.542306\pi\)
−0.132518 + 0.991181i \(0.542306\pi\)
\(42\) 1.11279e16 + 2.57612e16i 0.100530 + 0.232728i
\(43\) 1.15256e17 0.813292 0.406646 0.913586i \(-0.366698\pi\)
0.406646 + 0.913586i \(0.366698\pi\)
\(44\) 2.57455e17i 1.42708i
\(45\) 2.01134e17 + 2.71938e17i 0.880549 + 1.19052i
\(46\) −7.80486e16 −0.271274
\(47\) −1.81071e17 −0.502136 −0.251068 0.967969i \(-0.580782\pi\)
−0.251068 + 0.967969i \(0.580782\pi\)
\(48\) 3.25871e17 + 1.64296e17i 0.724458 + 0.365253i
\(49\) −9.92673e16 5.49654e17i −0.177725 0.984080i
\(50\) 2.08795e17i 0.302367i
\(51\) 8.71841e17 + 4.39560e17i 1.02554 + 0.517049i
\(52\) 1.31307e18i 1.25965i
\(53\) 7.35468e17i 0.577653i 0.957381 + 0.288826i \(0.0932650\pi\)
−0.957381 + 0.288826i \(0.906735\pi\)
\(54\) 3.87113e17 6.63911e16i 0.249864 0.0428524i
\(55\) 4.24225e18i 2.25833i
\(56\) 8.54722e17 + 7.14187e17i 0.376574 + 0.314657i
\(57\) −5.12881e17 + 1.01727e18i −0.187642 + 0.372177i
\(58\) −4.65790e17 −0.141970
\(59\) 2.94154e18 0.749254 0.374627 0.927176i \(-0.377771\pi\)
0.374627 + 0.927176i \(0.377771\pi\)
\(60\) 5.79493e18 + 2.92166e18i 1.23726 + 0.623794i
\(61\) 1.08357e18i 0.194488i −0.995261 0.0972441i \(-0.968997\pi\)
0.995261 0.0972441i \(-0.0310028\pi\)
\(62\) 2.07951e18 0.314666
\(63\) −7.80393e18 4.62759e17i −0.998246 0.0591941i
\(64\) 5.85478e18 0.634776
\(65\) 2.16362e19i 1.99338i
\(66\) −4.39870e18 2.21772e18i −0.345234 0.174058i
\(67\) −6.78306e18 −0.454611 −0.227306 0.973823i \(-0.572992\pi\)
−0.227306 + 0.973823i \(0.572992\pi\)
\(68\) 1.87339e19 1.07469
\(69\) 9.78867e18 1.94152e19i 0.481735 0.955492i
\(70\) 6.80810e18 + 5.68869e18i 0.288069 + 0.240704i
\(71\) 2.06767e19i 0.753822i 0.926250 + 0.376911i \(0.123014\pi\)
−0.926250 + 0.376911i \(0.876986\pi\)
\(72\) 1.25338e19 9.27038e18i 0.394540 0.291814i
\(73\) 4.03443e19i 1.09873i −0.835582 0.549366i \(-0.814869\pi\)
0.835582 0.549366i \(-0.185131\pi\)
\(74\) 1.49825e19i 0.353712i
\(75\) 5.19394e19 + 2.61866e19i 1.06501 + 0.536952i
\(76\) 2.18587e19i 0.390016i
\(77\) 7.52413e19 + 6.28700e19i 1.17032 + 0.977891i
\(78\) 2.24342e19 + 1.13107e19i 0.304731 + 0.153638i
\(79\) 9.41640e19 1.11892 0.559462 0.828856i \(-0.311008\pi\)
0.559462 + 0.828856i \(0.311008\pi\)
\(80\) 1.15380e20 1.20140
\(81\) −3.20355e19 + 1.04624e20i −0.292778 + 0.956180i
\(82\) 8.36275e18i 0.0671899i
\(83\) 2.74031e19 0.193856 0.0969281 0.995291i \(-0.469098\pi\)
0.0969281 + 0.995291i \(0.469098\pi\)
\(84\) −1.37700e20 + 5.94811e19i −0.859015 + 0.371062i
\(85\) 3.08690e20 1.70068
\(86\) 4.23135e19i 0.206179i
\(87\) 5.84183e19 1.15869e20i 0.252114 0.500052i
\(88\) −1.95528e20 −0.748412
\(89\) −4.43565e20 −1.50786 −0.753932 0.656953i \(-0.771845\pi\)
−0.753932 + 0.656953i \(0.771845\pi\)
\(90\) 9.98350e19 7.38412e19i 0.301812 0.223230i
\(91\) −3.83744e20 3.20648e20i −1.03302 0.863165i
\(92\) 4.17189e20i 1.00129i
\(93\) −2.60808e20 + 5.17296e20i −0.558791 + 1.10833i
\(94\) 6.64757e19i 0.127298i
\(95\) 3.60180e20i 0.617195i
\(96\) 2.04227e20 4.05072e20i 0.313520 0.621848i
\(97\) 8.62831e20i 1.18802i 0.804459 + 0.594008i \(0.202455\pi\)
−0.804459 + 0.594008i \(0.797545\pi\)
\(98\) −2.01792e20 + 3.64435e19i −0.249476 + 0.0450553i
\(99\) 1.10335e21 8.16073e20i 1.22615 0.906901i
\(100\) 1.11606e21 1.11606
\(101\) 5.09810e20 0.459234 0.229617 0.973281i \(-0.426253\pi\)
0.229617 + 0.973281i \(0.426253\pi\)
\(102\) 1.61373e20 3.20074e20i 0.131078 0.259985i
\(103\) 1.30498e20i 0.0956782i −0.998855 0.0478391i \(-0.984767\pi\)
0.998855 0.0478391i \(-0.0152335\pi\)
\(104\) 9.97226e20 0.660608
\(105\) −2.26897e21 + 9.80108e20i −1.35938 + 0.587200i
\(106\) 2.70008e20 0.146442
\(107\) 2.46662e21i 1.21220i −0.795390 0.606098i \(-0.792734\pi\)
0.795390 0.606098i \(-0.207266\pi\)
\(108\) 3.54877e20 + 2.06922e21i 0.158172 + 0.922266i
\(109\) −4.07891e21 −1.65031 −0.825155 0.564907i \(-0.808912\pi\)
−0.825155 + 0.564907i \(0.808912\pi\)
\(110\) −1.55743e21 −0.572514
\(111\) −3.72701e21 1.87906e21i −1.24586 0.628131i
\(112\) −1.70993e21 + 2.04640e21i −0.520222 + 0.622590i
\(113\) 1.83094e21i 0.507401i −0.967283 0.253701i \(-0.918352\pi\)
0.967283 0.253701i \(-0.0816478\pi\)
\(114\) 3.73464e20 + 1.88291e20i 0.0943513 + 0.0475695i
\(115\) 6.87428e21i 1.58453i
\(116\) 2.48976e21i 0.524021i
\(117\) −5.62728e21 + 4.16212e21i −1.08230 + 0.800503i
\(118\) 1.07991e21i 0.189945i
\(119\) −4.57477e21 + 5.47498e21i −0.736421 + 0.881332i
\(120\) 2.21890e21 4.40104e21i 0.327140 0.648862i
\(121\) −9.81210e21 −1.32591
\(122\) −3.97805e20 −0.0493051
\(123\) −2.08030e21 1.04884e21i −0.236659 0.119318i
\(124\) 1.11155e22i 1.16145i
\(125\) 2.97138e21 0.285366
\(126\) −1.69890e20 + 2.86502e21i −0.0150064 + 0.253068i
\(127\) 1.75513e22 1.42683 0.713413 0.700744i \(-0.247148\pi\)
0.713413 + 0.700744i \(0.247148\pi\)
\(128\) 1.14513e22i 0.857336i
\(129\) 1.05258e22 + 5.30686e21i 0.726213 + 0.366139i
\(130\) 7.94319e21 0.505347
\(131\) −3.21780e21 −0.188891 −0.0944453 0.995530i \(-0.530108\pi\)
−0.0944453 + 0.995530i \(0.530108\pi\)
\(132\) 1.18542e22 2.35122e22i 0.642462 1.27428i
\(133\) −6.38823e21 5.33786e21i −0.319844 0.267254i
\(134\) 2.49023e21i 0.115249i
\(135\) 5.84753e21 + 3.40958e22i 0.250304 + 1.45947i
\(136\) 1.42277e22i 0.563607i
\(137\) 3.65830e22i 1.34188i −0.741512 0.670940i \(-0.765891\pi\)
0.741512 0.670940i \(-0.234109\pi\)
\(138\) −7.12781e21 3.59366e21i −0.242229 0.122126i
\(139\) 4.00599e22i 1.26198i 0.775789 + 0.630992i \(0.217352\pi\)
−0.775789 + 0.630992i \(0.782648\pi\)
\(140\) −3.04075e22 + 3.63910e22i −0.888456 + 1.06328i
\(141\) −1.65364e22 8.33722e21i −0.448373 0.226058i
\(142\) 7.59093e21 0.191103
\(143\) 8.77860e22 2.05304
\(144\) 2.21955e22 + 3.00088e22i 0.482456 + 0.652292i
\(145\) 4.10254e22i 0.829256i
\(146\) −1.48114e22 −0.278542
\(147\) 1.62426e22 5.47680e22i 0.284331 0.958726i
\(148\) −8.00849e22 −1.30558
\(149\) 5.70779e22i 0.866986i 0.901157 + 0.433493i \(0.142719\pi\)
−0.901157 + 0.433493i \(0.857281\pi\)
\(150\) 9.61373e21 1.90683e22i 0.136124 0.269993i
\(151\) 1.37183e23 1.81151 0.905755 0.423801i \(-0.139304\pi\)
0.905755 + 0.423801i \(0.139304\pi\)
\(152\) 1.66009e22 0.204538
\(153\) 5.93821e22 + 8.02860e22i 0.682960 + 0.923378i
\(154\) 2.30811e22 2.76229e22i 0.247907 0.296690i
\(155\) 1.83157e23i 1.83798i
\(156\) −6.04587e22 + 1.19916e23i −0.567088 + 1.12478i
\(157\) 8.48354e22i 0.744099i −0.928213 0.372050i \(-0.878655\pi\)
0.928213 0.372050i \(-0.121345\pi\)
\(158\) 3.45699e22i 0.283661i
\(159\) −3.38638e22 + 6.71668e22i −0.260055 + 0.515804i
\(160\) 1.43422e23i 1.03123i
\(161\) 1.21924e23 + 1.01877e23i 0.821138 + 0.686124i
\(162\) 3.84102e22 + 1.17610e22i 0.242403 + 0.0742228i
\(163\) −2.44238e23 −1.44492 −0.722461 0.691412i \(-0.756989\pi\)
−0.722461 + 0.691412i \(0.756989\pi\)
\(164\) −4.47010e22 −0.248003
\(165\) 1.95330e23 3.87425e23i 1.01669 2.01654i
\(166\) 1.00604e22i 0.0491449i
\(167\) 4.94570e22 0.226832 0.113416 0.993548i \(-0.463821\pi\)
0.113416 + 0.993548i \(0.463821\pi\)
\(168\) 4.51738e22 + 1.04578e23i 0.194598 + 0.450498i
\(169\) −2.00659e23 −0.812174
\(170\) 1.13328e23i 0.431144i
\(171\) −9.36780e22 + 6.92872e22i −0.335103 + 0.247853i
\(172\) 2.26176e23 0.761023
\(173\) −1.35934e23 −0.430371 −0.215185 0.976573i \(-0.569036\pi\)
−0.215185 + 0.976573i \(0.569036\pi\)
\(174\) −4.25384e22 2.14468e22i −0.126769 0.0639139i
\(175\) −2.72539e23 + 3.26169e23i −0.764768 + 0.915257i
\(176\) 4.68139e23i 1.23735i
\(177\) 2.68637e23 + 1.35440e23i 0.669032 + 0.337309i
\(178\) 1.62844e23i 0.382262i
\(179\) 5.09904e23i 1.12858i −0.825578 0.564289i \(-0.809150\pi\)
0.825578 0.564289i \(-0.190850\pi\)
\(180\) 3.94699e23 + 5.33643e23i 0.823958 + 1.11401i
\(181\) 2.55697e23i 0.503617i −0.967777 0.251809i \(-0.918975\pi\)
0.967777 0.251809i \(-0.0810253\pi\)
\(182\) −1.17718e23 + 1.40882e23i −0.218823 + 0.261882i
\(183\) 4.98918e22 9.89573e22i 0.0875573 0.173665i
\(184\) −3.16840e23 −0.525113
\(185\) −1.31961e24 −2.06606
\(186\) 1.89912e23 + 9.57490e22i 0.280975 + 0.141660i
\(187\) 1.25247e24i 1.75158i
\(188\) −3.55329e23 −0.469865
\(189\) −6.91389e23 4.01585e23i −0.864717 0.502260i
\(190\) 1.32231e23 0.156466
\(191\) 9.41669e23i 1.05450i 0.849709 + 0.527252i \(0.176778\pi\)
−0.849709 + 0.527252i \(0.823222\pi\)
\(192\) 5.34690e23 + 2.69577e23i 0.566812 + 0.285772i
\(193\) −1.22581e24 −1.23047 −0.615236 0.788343i \(-0.710939\pi\)
−0.615236 + 0.788343i \(0.710939\pi\)
\(194\) 3.16767e23 0.301176
\(195\) −9.96216e23 + 1.97593e24i −0.897408 + 1.77995i
\(196\) −1.94799e23 1.07863e24i −0.166302 0.920835i
\(197\) 1.96576e24i 1.59087i −0.606040 0.795434i \(-0.707243\pi\)
0.606040 0.795434i \(-0.292757\pi\)
\(198\) −2.99601e23 4.05067e23i −0.229910 0.310844i
\(199\) 9.29643e23i 0.676642i 0.941031 + 0.338321i \(0.109859\pi\)
−0.941031 + 0.338321i \(0.890141\pi\)
\(200\) 8.47608e23i 0.585302i
\(201\) −6.19465e23 3.12319e23i −0.405937 0.204663i
\(202\) 1.87164e23i 0.116421i
\(203\) 7.27634e23 + 6.07994e23i 0.429739 + 0.359080i
\(204\) 1.71088e24 + 8.62581e23i 0.959626 + 0.483819i
\(205\) −7.36566e23 −0.392461
\(206\) −4.79090e22 −0.0242556
\(207\) 1.78791e24 1.32239e24i 0.860312 0.636314i
\(208\) 2.38759e24i 1.09218i
\(209\) 1.46138e24 0.635665
\(210\) 3.59822e23 + 8.32993e23i 0.148862 + 0.344619i
\(211\) 2.16585e24 0.852436 0.426218 0.904621i \(-0.359846\pi\)
0.426218 + 0.904621i \(0.359846\pi\)
\(212\) 1.44326e24i 0.540528i
\(213\) −9.52036e23 + 1.88831e24i −0.339366 + 0.673111i
\(214\) −9.05557e23 −0.307306
\(215\) 3.72684e24 1.20431
\(216\) 1.57150e24 2.69516e23i 0.483670 0.0829508i
\(217\) −3.24851e24 2.71438e24i −0.952483 0.795874i
\(218\) 1.49747e24i 0.418373i
\(219\) 1.85761e24 3.68445e24i 0.494642 0.981093i
\(220\) 8.32487e24i 2.11319i
\(221\) 6.38780e24i 1.54608i
\(222\) −6.89851e23 + 1.36828e24i −0.159239 + 0.315840i
\(223\) 1.09956e24i 0.242113i −0.992646 0.121056i \(-0.961372\pi\)
0.992646 0.121056i \(-0.0386282\pi\)
\(224\) 2.54377e24 + 2.12551e24i 0.534408 + 0.446540i
\(225\) 3.53765e24 + 4.78299e24i 0.709249 + 0.958922i
\(226\) −6.72185e23 −0.128632
\(227\) −3.04133e24 −0.555638 −0.277819 0.960633i \(-0.589612\pi\)
−0.277819 + 0.960633i \(0.589612\pi\)
\(228\) −1.00646e24 + 1.99626e24i −0.175583 + 0.348257i
\(229\) 9.05432e24i 1.50863i −0.656511 0.754316i \(-0.727969\pi\)
0.656511 0.754316i \(-0.272031\pi\)
\(230\) −2.52372e24 −0.401697
\(231\) 3.97666e24 + 9.20602e24i 0.604773 + 1.40006i
\(232\) −1.89089e24 −0.274816
\(233\) 8.39062e23i 0.116562i 0.998300 + 0.0582810i \(0.0185619\pi\)
−0.998300 + 0.0582810i \(0.981438\pi\)
\(234\) 1.52802e24 + 2.06591e24i 0.202937 + 0.274376i
\(235\) −5.85498e24 −0.743554
\(236\) 5.77240e24 0.701100
\(237\) 8.59956e24 + 4.33568e24i 0.999122 + 0.503732i
\(238\) 2.01000e24 + 1.67951e24i 0.223428 + 0.186692i
\(239\) 1.16933e25i 1.24383i −0.783087 0.621913i \(-0.786356\pi\)
0.783087 0.621913i \(-0.213644\pi\)
\(240\) 1.05371e25 + 5.31255e24i 1.07276 + 0.540860i
\(241\) 5.54789e24i 0.540691i −0.962763 0.270345i \(-0.912862\pi\)
0.962763 0.270345i \(-0.0871379\pi\)
\(242\) 3.60226e24i 0.336135i
\(243\) −7.74297e24 + 8.07980e24i −0.691897 + 0.721996i
\(244\) 2.12637e24i 0.181989i
\(245\) −3.20983e24 1.77732e25i −0.263171 1.45721i
\(246\) −3.85054e23 + 7.63731e23i −0.0302484 + 0.0599959i
\(247\) −7.45331e24 −0.561088
\(248\) 8.44184e24 0.609108
\(249\) 2.50260e24 + 1.26175e24i 0.173100 + 0.0872728i
\(250\) 1.09087e24i 0.0723438i
\(251\) −8.18893e24 −0.520779 −0.260389 0.965504i \(-0.583851\pi\)
−0.260389 + 0.965504i \(0.583851\pi\)
\(252\) −1.53142e25 9.08104e23i −0.934091 0.0553898i
\(253\) −2.78915e25 −1.63195
\(254\) 6.44353e24i 0.361718i
\(255\) 2.81912e25 + 1.42133e25i 1.51859 + 0.765636i
\(256\) 8.07430e24 0.417432
\(257\) −1.49657e25 −0.742674 −0.371337 0.928498i \(-0.621100\pi\)
−0.371337 + 0.928498i \(0.621100\pi\)
\(258\) 1.94828e24 3.86429e24i 0.0928205 0.184104i
\(259\) 1.95566e25 2.34048e25i 0.894633 1.07068i
\(260\) 4.24583e25i 1.86527i
\(261\) 1.06701e25 7.89197e24i 0.450241 0.333012i
\(262\) 1.18133e24i 0.0478860i
\(263\) 1.45078e25i 0.565024i −0.959264 0.282512i \(-0.908832\pi\)
0.959264 0.282512i \(-0.0911678\pi\)
\(264\) −1.78566e25 9.00287e24i −0.668280 0.336930i
\(265\) 2.37815e25i 0.855377i
\(266\) −1.95966e24 + 2.34528e24i −0.0677522 + 0.0810843i
\(267\) −4.05087e25 2.04235e25i −1.34642 0.678830i
\(268\) −1.33109e25 −0.425394
\(269\) −5.57484e25 −1.71330 −0.856650 0.515897i \(-0.827459\pi\)
−0.856650 + 0.515897i \(0.827459\pi\)
\(270\) 1.25174e25 2.14677e24i 0.369994 0.0634551i
\(271\) 5.26405e25i 1.49673i 0.663290 + 0.748363i \(0.269160\pi\)
−0.663290 + 0.748363i \(0.730840\pi\)
\(272\) 3.40644e25 0.931810
\(273\) −2.02816e25 4.69523e25i −0.533821 1.23580i
\(274\) −1.34305e25 −0.340183
\(275\) 7.46150e25i 1.81900i
\(276\) 1.92090e25 3.80999e25i 0.450775 0.894084i
\(277\) −4.98204e25 −1.12556 −0.562781 0.826606i \(-0.690269\pi\)
−0.562781 + 0.826606i \(0.690269\pi\)
\(278\) 1.47070e25 0.319928
\(279\) −4.76367e25 + 3.52336e25i −0.997924 + 0.738097i
\(280\) 2.76376e25 + 2.30934e25i 0.557624 + 0.465938i
\(281\) 2.53148e25i 0.491992i 0.969271 + 0.245996i \(0.0791150\pi\)
−0.969271 + 0.245996i \(0.920885\pi\)
\(282\) −3.06080e24 + 6.07091e24i −0.0573085 + 0.113668i
\(283\) 5.18238e25i 0.934913i −0.884016 0.467457i \(-0.845170\pi\)
0.884016 0.467457i \(-0.154830\pi\)
\(284\) 4.05754e25i 0.705375i
\(285\) −1.65841e25 + 3.28936e25i −0.277857 + 0.551112i
\(286\) 3.22284e25i 0.520470i
\(287\) 1.09159e25 1.30639e25i 0.169941 0.203382i
\(288\) 3.73022e25 2.75899e25i 0.559904 0.414123i
\(289\) 2.20446e25 0.319062
\(290\) −1.50614e25 −0.210226
\(291\) −3.97281e25 + 7.87983e25i −0.534837 + 1.06082i
\(292\) 7.91705e25i 1.02812i
\(293\) −5.26755e25 −0.659932 −0.329966 0.943993i \(-0.607037\pi\)
−0.329966 + 0.943993i \(0.607037\pi\)
\(294\) −2.01067e25 5.96306e24i −0.243049 0.0720812i
\(295\) 9.51154e25 1.10948
\(296\) 6.08216e25i 0.684692i
\(297\) 1.38339e26 2.37256e25i 1.50315 0.257795i
\(298\) 2.09547e25 0.219792
\(299\) 1.42251e26 1.44049
\(300\) 1.01924e26 + 5.13878e25i 0.996564 + 0.502443i
\(301\) −5.52317e25 + 6.61000e25i −0.521483 + 0.624099i
\(302\) 5.03631e25i 0.459240i
\(303\) 4.65586e25 + 2.34737e25i 0.410064 + 0.206744i
\(304\) 3.97465e25i 0.338163i
\(305\) 3.50375e25i 0.287995i
\(306\) 2.94750e25 2.18006e25i 0.234087 0.173139i
\(307\) 3.81010e25i 0.292404i 0.989255 + 0.146202i \(0.0467050\pi\)
−0.989255 + 0.146202i \(0.953295\pi\)
\(308\) 1.47651e26 + 1.23374e26i 1.09510 + 0.915044i
\(309\) 6.00864e24 1.19178e25i 0.0430737 0.0854340i
\(310\) 6.72416e25 0.465951
\(311\) −2.86439e26 −1.91888 −0.959440 0.281914i \(-0.909031\pi\)
−0.959440 + 0.281914i \(0.909031\pi\)
\(312\) 9.10720e25 + 4.59162e25i 0.589877 + 0.297401i
\(313\) 7.04402e25i 0.441169i −0.975368 0.220585i \(-0.929204\pi\)
0.975368 0.220585i \(-0.0707965\pi\)
\(314\) −3.11452e25 −0.188638
\(315\) −2.52342e26 1.49634e25i −1.47818 0.0876536i
\(316\) 1.84785e26 1.04701
\(317\) 1.14082e25i 0.0625307i 0.999511 + 0.0312653i \(0.00995369\pi\)
−0.999511 + 0.0312653i \(0.990046\pi\)
\(318\) 2.46586e25 + 1.24322e25i 0.130763 + 0.0659272i
\(319\) −1.66455e26 −0.854072
\(320\) 1.89316e26 0.939965
\(321\) 1.13573e26 2.25265e26i 0.545723 1.08241i
\(322\) 3.74014e25 4.47611e25i 0.173941 0.208168i
\(323\) 1.06338e26i 0.478700i
\(324\) −6.28656e25 + 2.05312e26i −0.273962 + 0.894728i
\(325\) 3.80550e26i 1.60560i
\(326\) 8.96659e25i 0.366305i
\(327\) −3.72507e26 1.87809e26i −1.47361 0.742958i
\(328\) 3.39488e25i 0.130062i
\(329\) 8.67705e25 1.03845e26i 0.321970 0.385326i
\(330\) −1.42233e26 7.17104e25i −0.511216 0.257742i
\(331\) −2.67563e26 −0.931605 −0.465802 0.884889i \(-0.654234\pi\)
−0.465802 + 0.884889i \(0.654234\pi\)
\(332\) 5.37751e25 0.181397
\(333\) −2.53851e26 3.43212e26i −0.829686 1.12176i
\(334\) 1.81569e25i 0.0575047i
\(335\) −2.19332e26 −0.673180
\(336\) −2.50384e26 + 1.08157e26i −0.744808 + 0.321729i
\(337\) 5.06422e26 1.46015 0.730076 0.683366i \(-0.239485\pi\)
0.730076 + 0.683366i \(0.239485\pi\)
\(338\) 7.36670e25i 0.205896i
\(339\) 8.43039e25 1.67212e26i 0.228429 0.453074i
\(340\) 6.05764e26 1.59138
\(341\) 7.43136e26 1.89299
\(342\) 2.54370e25 + 3.43915e25i 0.0628337 + 0.0849526i
\(343\) 3.62798e26 + 2.06468e26i 0.869114 + 0.494611i
\(344\) 1.71773e26i 0.399108i
\(345\) 3.16519e26 6.27796e26i 0.713344 1.41487i
\(346\) 4.99046e25i 0.109104i
\(347\) 5.76925e26i 1.22366i −0.790991 0.611828i \(-0.790434\pi\)
0.790991 0.611828i \(-0.209566\pi\)
\(348\) 1.14638e26 2.27378e26i 0.235911 0.467915i
\(349\) 7.69223e26i 1.53598i 0.640463 + 0.767989i \(0.278742\pi\)
−0.640463 + 0.767989i \(0.721258\pi\)
\(350\) 1.19745e26 + 1.00056e26i 0.232029 + 0.193878i
\(351\) −7.05553e26 + 1.21005e26i −1.32680 + 0.227550i
\(352\) −5.81917e26 −1.06209
\(353\) −7.28618e26 −1.29082 −0.645410 0.763837i \(-0.723313\pi\)
−0.645410 + 0.763837i \(0.723313\pi\)
\(354\) 4.97234e25 9.86233e25i 0.0855119 0.169608i
\(355\) 6.68586e26i 1.11625i
\(356\) −8.70439e26 −1.41096
\(357\) −6.69882e26 + 2.89364e26i −1.05434 + 0.455437i
\(358\) −1.87198e26 −0.286108
\(359\) 8.02107e26i 1.19053i 0.803529 + 0.595265i \(0.202953\pi\)
−0.803529 + 0.595265i \(0.797047\pi\)
\(360\) 4.05283e26 2.99760e26i 0.584227 0.432113i
\(361\) 5.90133e26 0.826275
\(362\) −9.38726e25 −0.127673
\(363\) −8.96093e26 4.51788e26i −1.18395 0.596918i
\(364\) −7.53048e26 6.29230e26i −0.966625 0.807690i
\(365\) 1.30454e27i 1.62698i
\(366\) −3.63297e25 1.83165e25i −0.0440261 0.0221968i
\(367\) 1.07712e27i 1.26844i −0.773153 0.634219i \(-0.781322\pi\)
0.773153 0.634219i \(-0.218678\pi\)
\(368\) 7.58588e26i 0.868169i
\(369\) −1.41692e26 1.91571e26i −0.157604 0.213085i
\(370\) 4.84461e26i 0.523770i
\(371\) −4.21793e26 3.52441e26i −0.443276 0.370391i
\(372\) −5.11802e26 + 1.01513e27i −0.522879 + 1.03710i
\(373\) −3.65727e26 −0.363258 −0.181629 0.983367i \(-0.558137\pi\)
−0.181629 + 0.983367i \(0.558137\pi\)
\(374\) −4.59812e26 −0.444046
\(375\) 2.71362e26 + 1.36814e26i 0.254813 + 0.128470i
\(376\) 2.69860e26i 0.246414i
\(377\) 8.48949e26 0.753872
\(378\) −1.47432e26 + 2.53826e26i −0.127329 + 0.219216i
\(379\) −1.04194e27 −0.875250 −0.437625 0.899158i \(-0.644180\pi\)
−0.437625 + 0.899158i \(0.644180\pi\)
\(380\) 7.06808e26i 0.577529i
\(381\) 1.60288e27 + 8.08132e26i 1.27406 + 0.642347i
\(382\) 3.45710e26 0.267329
\(383\) −2.53492e26 −0.190711 −0.0953557 0.995443i \(-0.530399\pi\)
−0.0953557 + 0.995443i \(0.530399\pi\)
\(384\) 5.27264e26 1.04580e27i 0.385967 0.765542i
\(385\) 2.43295e27 + 2.03291e27i 1.73298 + 1.44804i
\(386\) 4.50025e26i 0.311939i
\(387\) 7.16926e26 + 9.69301e26i 0.483625 + 0.653873i
\(388\) 1.69319e27i 1.11166i
\(389\) 1.49463e27i 0.955132i 0.878596 + 0.477566i \(0.158481\pi\)
−0.878596 + 0.477566i \(0.841519\pi\)
\(390\) 7.25414e26 + 3.65735e26i 0.451240 + 0.227504i
\(391\) 2.02954e27i 1.22897i
\(392\) −8.19177e26 + 1.47943e26i −0.482919 + 0.0872150i
\(393\) −2.93866e26 1.48160e26i −0.168666 0.0850373i
\(394\) −7.21678e26 −0.403304
\(395\) 3.04482e27 1.65688
\(396\) 2.16518e27 1.60144e27i 1.14735 0.848616i
\(397\) 3.24066e27i 1.67237i −0.548446 0.836186i \(-0.684780\pi\)
0.548446 0.836186i \(-0.315220\pi\)
\(398\) 3.41295e26 0.171537
\(399\) −3.37631e26 7.81621e26i −0.165282 0.382631i
\(400\) 2.02937e27 0.967679
\(401\) 2.32859e27i 1.08163i −0.841142 0.540814i \(-0.818116\pi\)
0.841142 0.540814i \(-0.181884\pi\)
\(402\) −1.14660e26 + 2.27421e26i −0.0518845 + 0.102910i
\(403\) −3.79012e27 −1.67090
\(404\) 1.00044e27 0.429720
\(405\) −1.03588e27 + 3.38305e27i −0.433541 + 1.41589i
\(406\) 2.23210e26 2.67132e26i 0.0910311 0.108944i
\(407\) 5.35414e27i 2.12788i
\(408\) 6.55099e26 1.29935e27i 0.253732 0.503262i
\(409\) 2.01191e27i 0.759476i −0.925094 0.379738i \(-0.876014\pi\)
0.925094 0.379738i \(-0.123986\pi\)
\(410\) 2.70412e26i 0.0994935i
\(411\) 1.68443e27 3.34095e27i 0.604105 1.19821i
\(412\) 2.56085e26i 0.0895291i
\(413\) −1.40961e27 + 1.68699e27i −0.480422 + 0.574957i
\(414\) −4.85483e26 6.56384e26i −0.161313 0.218100i
\(415\) 8.86086e26 0.287059
\(416\) 2.96788e27 0.937489
\(417\) −1.84451e27 + 3.65848e27i −0.568137 + 1.12686i
\(418\) 5.36510e26i 0.161149i
\(419\) −4.70631e27 −1.37858 −0.689292 0.724483i \(-0.742078\pi\)
−0.689292 + 0.724483i \(0.742078\pi\)
\(420\) −4.45255e27 + 1.92334e27i −1.27201 + 0.549462i
\(421\) 2.99709e27 0.835099 0.417550 0.908654i \(-0.362889\pi\)
0.417550 + 0.908654i \(0.362889\pi\)
\(422\) 7.95135e26i 0.216103i
\(423\) −1.12631e27 1.52280e27i −0.298596 0.403709i
\(424\) 1.09610e27 0.283472
\(425\) 5.42941e27 1.36984
\(426\) 6.93244e26 + 3.49516e26i 0.170642 + 0.0860333i
\(427\) 6.21431e26 + 5.19254e26i 0.149245 + 0.124706i
\(428\) 4.84043e27i 1.13429i
\(429\) 8.01708e27 + 4.04201e27i 1.83322 + 0.924264i
\(430\) 1.36822e27i 0.305306i
\(431\) 7.88872e27i 1.71789i 0.512068 + 0.858945i \(0.328879\pi\)
−0.512068 + 0.858945i \(0.671121\pi\)
\(432\) 6.45285e26 + 3.76253e27i 0.137142 + 0.799650i
\(433\) 1.12507e27i 0.233377i −0.993169 0.116689i \(-0.962772\pi\)
0.993169 0.116689i \(-0.0372279\pi\)
\(434\) −9.96518e26 + 1.19261e27i −0.201764 + 0.241466i
\(435\) 1.88897e27 3.74665e27i 0.373325 0.740468i
\(436\) −8.00433e27 −1.54425
\(437\) 2.36807e27 0.446006
\(438\) −1.35265e27 6.81974e26i −0.248719 0.125398i
\(439\) 2.62451e26i 0.0471163i 0.999722 + 0.0235582i \(0.00749949\pi\)
−0.999722 + 0.0235582i \(0.992501\pi\)
\(440\) −6.32244e27 −1.10823
\(441\) 4.00509e27 4.25383e27i 0.685500 0.728073i
\(442\) 2.34512e27 0.391950
\(443\) 8.58094e27i 1.40054i −0.713878 0.700270i \(-0.753063\pi\)
0.713878 0.700270i \(-0.246937\pi\)
\(444\) −7.31378e27 3.68742e27i −1.16579 0.587762i
\(445\) −1.43428e28 −2.23282
\(446\) −4.03676e26 −0.0613786
\(447\) −2.62809e27 + 5.21266e27i −0.390312 + 0.774159i
\(448\) −2.80565e27 + 3.35774e27i −0.407019 + 0.487111i
\(449\) 4.40140e27i 0.623741i −0.950125 0.311871i \(-0.899044\pi\)
0.950125 0.311871i \(-0.100956\pi\)
\(450\) 1.75595e27 1.29876e27i 0.243098 0.179803i
\(451\) 2.98852e27i 0.404205i
\(452\) 3.59299e27i 0.474791i
\(453\) 1.25282e28 + 6.31642e27i 1.61755 + 0.815530i
\(454\) 1.11655e27i 0.140861i
\(455\) −1.24084e28 1.03682e28i −1.52967 1.27816i
\(456\) 1.51609e27 + 7.64372e26i 0.182639 + 0.0920819i
\(457\) 3.77890e27 0.444883 0.222441 0.974946i \(-0.428597\pi\)
0.222441 + 0.974946i \(0.428597\pi\)
\(458\) −3.32406e27 −0.382456
\(459\) 1.72641e27 + 1.00663e28i 0.194138 + 1.13198i
\(460\) 1.34899e28i 1.48269i
\(461\) −3.80104e27 −0.408359 −0.204180 0.978933i \(-0.565453\pi\)
−0.204180 + 0.978933i \(0.565453\pi\)
\(462\) 3.37976e27 1.45993e27i 0.354932 0.153317i
\(463\) −4.97281e27 −0.510507 −0.255253 0.966874i \(-0.582159\pi\)
−0.255253 + 0.966874i \(0.582159\pi\)
\(464\) 4.52722e27i 0.454352i
\(465\) −8.43328e27 + 1.67269e28i −0.827448 + 1.64119i
\(466\) 3.08040e26 0.0295499
\(467\) 1.65815e28 1.55523 0.777617 0.628738i \(-0.216428\pi\)
0.777617 + 0.628738i \(0.216428\pi\)
\(468\) −1.10428e28 + 8.16762e27i −1.01274 + 0.749056i
\(469\) 3.25049e27 3.89011e27i 0.291497 0.348857i
\(470\) 2.14951e27i 0.188500i
\(471\) 3.90615e27 7.74762e27i 0.334988 0.664429i
\(472\) 4.38393e27i 0.367682i
\(473\) 1.51212e28i 1.24035i
\(474\) 1.59174e27 3.15711e27i 0.127702 0.253290i
\(475\) 6.33505e27i 0.497127i
\(476\) −8.97740e27 + 1.07439e28i −0.689093 + 0.824690i
\(477\) −6.18524e27 + 4.57481e27i −0.464423 + 0.343502i
\(478\) −4.29290e27 −0.315325
\(479\) 1.67048e28 1.20038 0.600188 0.799859i \(-0.295092\pi\)
0.600188 + 0.799859i \(0.295092\pi\)
\(480\) 6.60373e27 1.30981e28i 0.464255 0.920821i
\(481\) 2.73070e28i 1.87824i
\(482\) −2.03677e27 −0.137072
\(483\) 6.44391e27 + 1.49177e28i 0.424331 + 0.982332i
\(484\) −1.92550e28 −1.24070
\(485\) 2.78998e28i 1.75919i
\(486\) 2.96630e27 + 2.84263e27i 0.183035 + 0.175404i
\(487\) 1.69052e28 1.02086 0.510429 0.859920i \(-0.329487\pi\)
0.510429 + 0.859920i \(0.329487\pi\)
\(488\) −1.61490e27 −0.0954415
\(489\) −2.23051e28 1.12457e28i −1.29021 0.650494i
\(490\) −6.52498e27 + 1.17841e27i −0.369420 + 0.0667171i
\(491\) 2.73101e28i 1.51345i 0.653734 + 0.756725i \(0.273202\pi\)
−0.653734 + 0.756725i \(0.726798\pi\)
\(492\) −4.08233e27 2.05821e27i −0.221449 0.111649i
\(493\) 1.21122e28i 0.643176i
\(494\) 2.73629e27i 0.142243i
\(495\) 3.56771e28 2.63879e28i 1.81566 1.34292i
\(496\) 2.02117e28i 1.00704i
\(497\) −1.18582e28 9.90842e27i −0.578463 0.483351i
\(498\) 4.63218e26 9.18765e26i 0.0221247 0.0438830i
\(499\) −1.99149e28 −0.931372 −0.465686 0.884950i \(-0.654192\pi\)
−0.465686 + 0.884950i \(0.654192\pi\)
\(500\) 5.83095e27 0.267026
\(501\) 4.51668e27 + 2.27719e27i 0.202546 + 0.102118i
\(502\) 3.00636e27i 0.132024i
\(503\) 1.58196e27 0.0680350 0.0340175 0.999421i \(-0.489170\pi\)
0.0340175 + 0.999421i \(0.489170\pi\)
\(504\) −6.89673e26 + 1.16306e28i −0.0290484 + 0.489871i
\(505\) 1.64848e28 0.680025
\(506\) 1.02396e28i 0.413718i
\(507\) −1.83253e28 9.23915e27i −0.725216 0.365635i
\(508\) 3.44422e28 1.33513
\(509\) 3.99452e28 1.51680 0.758400 0.651789i \(-0.225981\pi\)
0.758400 + 0.651789i \(0.225981\pi\)
\(510\) 5.21805e27 1.03497e28i 0.194098 0.384982i
\(511\) 2.31376e28 + 1.93333e28i 0.843138 + 0.704508i
\(512\) 2.69794e28i 0.963159i
\(513\) −1.17454e28 + 2.01438e27i −0.410806 + 0.0704544i
\(514\) 5.49426e27i 0.188277i
\(515\) 4.21968e27i 0.141678i
\(516\) 2.06556e28 + 1.04140e28i 0.679541 + 0.342607i
\(517\) 2.37558e28i 0.765806i
\(518\) −8.59249e27 7.17969e27i −0.271429 0.226800i
\(519\) −1.24142e28 6.25891e27i −0.384291 0.193750i
\(520\) 3.22456e28 0.978216
\(521\) 4.15617e28 1.23565 0.617827 0.786314i \(-0.288013\pi\)
0.617827 + 0.786314i \(0.288013\pi\)
\(522\) −2.89734e27 3.91727e27i −0.0844226 0.114141i
\(523\) 4.59294e28i 1.31167i 0.754906 + 0.655833i \(0.227682\pi\)
−0.754906 + 0.655833i \(0.772318\pi\)
\(524\) −6.31451e27 −0.176751
\(525\) −3.99078e28 + 1.72387e28i −1.09493 + 0.472968i
\(526\) −5.32618e27 −0.143240
\(527\) 5.40748e28i 1.42555i
\(528\) 2.15550e28 4.27529e28i 0.557046 1.10487i
\(529\) −5.72469e27 −0.145033
\(530\) 8.73078e27 0.216849
\(531\) 1.82972e28 + 2.47382e28i 0.445545 + 0.602387i
\(532\) −1.25361e28 1.04749e28i −0.299288 0.250078i
\(533\) 1.52420e28i 0.356784i
\(534\) −7.49796e27 + 1.48717e28i −0.172092 + 0.341333i
\(535\) 7.97588e28i 1.79500i
\(536\) 1.01091e28i 0.223092i
\(537\) 2.34780e28 4.65671e28i 0.508078 1.00774i
\(538\) 2.04666e28i 0.434342i
\(539\) −7.21123e28 + 1.30235e28i −1.50082 + 0.271047i
\(540\) 1.14750e28 + 6.69086e28i 0.234217 + 1.36568i
\(541\) 1.45892e28 0.292052 0.146026 0.989281i \(-0.453352\pi\)
0.146026 + 0.989281i \(0.453352\pi\)
\(542\) 1.93256e28 0.379438
\(543\) 1.17733e28 2.33516e28i 0.226725 0.449695i
\(544\) 4.23436e28i 0.799832i
\(545\) −1.31892e29 −2.44375
\(546\) −1.72374e28 + 7.44589e27i −0.313291 + 0.135330i
\(547\) 2.78371e28 0.496314 0.248157 0.968720i \(-0.420175\pi\)
0.248157 + 0.968720i \(0.420175\pi\)
\(548\) 7.17895e28i 1.25564i
\(549\) 9.11276e27 6.74009e27i 0.156365 0.115653i
\(550\) −2.73930e28 −0.461139
\(551\) 1.41326e28 0.233415
\(552\) −2.89355e28 1.45886e28i −0.468890 0.236402i
\(553\) −4.51241e28 + 5.40034e28i −0.717454 + 0.858633i
\(554\) 1.82903e28i 0.285344i
\(555\) −1.20514e29 6.07600e28i −1.84485 0.930125i
\(556\) 7.86123e28i 1.18088i
\(557\) 8.40041e28i 1.23829i −0.785278 0.619143i \(-0.787480\pi\)
0.785278 0.619143i \(-0.212520\pi\)
\(558\) 1.29351e28 + 1.74886e28i 0.187116 + 0.252986i
\(559\) 7.71206e28i 1.09483i
\(560\) −5.52909e28 + 6.61709e28i −0.770335 + 0.921919i
\(561\) 5.76685e28 1.14382e29i 0.788549 1.56404i
\(562\) 9.29368e27 0.124726
\(563\) 4.44784e28 0.585883 0.292941 0.956130i \(-0.405366\pi\)
0.292941 + 0.956130i \(0.405366\pi\)
\(564\) −3.24505e28 1.63607e28i −0.419557 0.211530i
\(565\) 5.92040e28i 0.751350i
\(566\) −1.90258e28 −0.237012
\(567\) −4.46508e28 6.85092e28i −0.546018 0.837773i
\(568\) 3.08156e28 0.369924
\(569\) 3.84484e27i 0.0453106i −0.999743 0.0226553i \(-0.992788\pi\)
0.999743 0.0226553i \(-0.00721202\pi\)
\(570\) 1.20760e28 + 6.08844e27i 0.139714 + 0.0704401i
\(571\) 7.58051e28 0.861032 0.430516 0.902583i \(-0.358332\pi\)
0.430516 + 0.902583i \(0.358332\pi\)
\(572\) 1.72269e29 1.92109
\(573\) −4.33581e28 + 8.59982e28i −0.474731 + 0.941599i
\(574\) −4.79607e27 4.00749e27i −0.0515597 0.0430822i
\(575\) 1.20909e29i 1.27628i
\(576\) 3.64183e28 + 4.92384e28i 0.377471 + 0.510350i
\(577\) 1.48691e29i 1.51334i 0.653795 + 0.756672i \(0.273176\pi\)
−0.653795 + 0.756672i \(0.726824\pi\)
\(578\) 8.09311e27i 0.0808860i
\(579\) −1.11947e29 5.64411e28i −1.09873 0.553950i
\(580\) 8.05070e28i 0.775961i
\(581\) −1.31318e28 + 1.57158e28i −0.124301 + 0.148760i
\(582\) 2.89288e28 + 1.45852e28i 0.268930 + 0.135588i
\(583\) 9.64903e28 0.880975
\(584\) −6.01272e28 −0.539183
\(585\) −1.81959e29 + 1.34583e29i −1.60265 + 1.18537i
\(586\) 1.93385e28i 0.167301i
\(587\) −9.38445e27 −0.0797460 −0.0398730 0.999205i \(-0.512695\pi\)
−0.0398730 + 0.999205i \(0.512695\pi\)
\(588\) 3.18740e28 1.07475e29i 0.266057 0.897111i
\(589\) −6.30946e28 −0.517347
\(590\) 3.49192e28i 0.281267i
\(591\) 9.05111e28 1.79523e29i 0.716198 1.42054i
\(592\) −1.45621e29 −1.13200
\(593\) 1.65099e29 1.26087 0.630436 0.776241i \(-0.282876\pi\)
0.630436 + 0.776241i \(0.282876\pi\)
\(594\) −8.71024e27 5.07877e28i −0.0653541 0.381066i
\(595\) −1.47926e29 + 1.77035e29i −1.09048 + 1.30506i
\(596\) 1.12008e29i 0.811267i
\(597\) −4.28044e28 + 8.48999e28i −0.304620 + 0.604194i
\(598\) 5.22240e28i 0.365181i
\(599\) 1.09948e29i 0.755452i 0.925917 + 0.377726i \(0.123294\pi\)
−0.925917 + 0.377726i \(0.876706\pi\)
\(600\) 3.90272e28 7.74080e28i 0.263499 0.522634i
\(601\) 1.93693e28i 0.128508i −0.997934 0.0642541i \(-0.979533\pi\)
0.997934 0.0642541i \(-0.0204668\pi\)
\(602\) 2.42669e28 + 2.02769e28i 0.158217 + 0.132202i
\(603\) −4.21924e28 5.70452e28i −0.270335 0.365500i
\(604\) 2.69203e29 1.69509
\(605\) −3.17277e29 −1.96339
\(606\) 8.61776e27 1.70928e28i 0.0524121 0.103956i
\(607\) 1.36592e28i 0.0816474i 0.999166 + 0.0408237i \(0.0129982\pi\)
−0.999166 + 0.0408237i \(0.987002\pi\)
\(608\) 4.94066e28 0.290267
\(609\) 3.84569e28 + 8.90284e28i 0.222072 + 0.514099i
\(610\) −1.28631e28 −0.0730101
\(611\) 1.21159e29i 0.675961i
\(612\) 1.16530e29 + 1.57551e29i 0.639067 + 0.864034i
\(613\) 1.87515e29 1.01089 0.505443 0.862860i \(-0.331329\pi\)
0.505443 + 0.862860i \(0.331329\pi\)
\(614\) 1.39878e28 0.0741280
\(615\) −6.72671e28 3.39144e28i −0.350440 0.176683i
\(616\) 9.36983e28 1.12136e29i 0.479882 0.574312i
\(617\) 7.21390e28i 0.363225i 0.983370 + 0.181613i \(0.0581317\pi\)
−0.983370 + 0.181613i \(0.941868\pi\)
\(618\) −4.37531e27 2.20592e27i −0.0216586 0.0109197i
\(619\) 9.03568e28i 0.439753i −0.975528 0.219877i \(-0.929434\pi\)
0.975528 0.219877i \(-0.0705655\pi\)
\(620\) 3.59423e29i 1.71986i
\(621\) 2.24169e29 3.84457e28i 1.05466 0.180878i
\(622\) 1.05159e29i 0.486459i
\(623\) 2.12559e29 2.54386e29i 0.966843 1.15709i
\(624\) −1.09934e29 + 2.18048e29i −0.491693 + 0.975243i
\(625\) −1.75111e29 −0.770148
\(626\) −2.58603e28 −0.111842
\(627\) 1.33461e29 + 6.72878e28i 0.567605 + 0.286172i
\(628\) 1.66479e29i 0.696277i
\(629\) −3.89597e29 −1.60245
\(630\) −5.49344e27 + 9.26410e28i −0.0222212 + 0.374738i
\(631\) −1.32905e29 −0.528729 −0.264364 0.964423i \(-0.585162\pi\)
−0.264364 + 0.964423i \(0.585162\pi\)
\(632\) 1.40337e29i 0.549091i
\(633\) 1.97796e29 + 9.97240e28i 0.761166 + 0.383761i
\(634\) 4.18822e27 0.0158523
\(635\) 5.67526e29 2.11282
\(636\) −6.64534e28 + 1.31806e29i −0.243342 + 0.482654i
\(637\) 3.67785e29 6.64219e28i 1.32474 0.239247i
\(638\) 6.11097e28i 0.216518i
\(639\) −1.73890e29 + 1.28615e29i −0.606060 + 0.448261i
\(640\) 3.70281e29i 1.26953i
\(641\) 4.35352e29i 1.46836i −0.678957 0.734178i \(-0.737568\pi\)
0.678957 0.734178i \(-0.262432\pi\)
\(642\) −8.27003e28 4.16954e28i −0.274403 0.138347i
\(643\) 2.05844e29i 0.671927i 0.941875 + 0.335964i \(0.109062\pi\)
−0.941875 + 0.335964i \(0.890938\pi\)
\(644\) 2.39259e29 + 1.99920e29i 0.768364 + 0.642028i
\(645\) 3.40355e29 + 1.71598e29i 1.07536 + 0.542171i
\(646\) 3.90395e28 0.121356
\(647\) 2.25180e28 0.0688709 0.0344354 0.999407i \(-0.489037\pi\)
0.0344354 + 0.999407i \(0.489037\pi\)
\(648\) 1.55927e29 + 4.77442e28i 0.469228 + 0.143676i
\(649\) 3.85918e29i 1.14268i
\(650\) 1.39709e29 0.407038
\(651\) −1.71691e29 3.97466e29i −0.492205 1.13946i
\(652\) −4.79286e29 −1.35206
\(653\) 4.78474e29i 1.32822i 0.747635 + 0.664110i \(0.231189\pi\)
−0.747635 + 0.664110i \(0.768811\pi\)
\(654\) −6.89492e28 + 1.36757e29i −0.188349 + 0.373579i
\(655\) −1.04048e29 −0.279706
\(656\) −8.12813e28 −0.215031
\(657\) 3.39293e29 2.50952e29i 0.883363 0.653363i
\(658\) −3.81240e28 3.18556e28i −0.0976848 0.0816233i
\(659\) 2.97678e29i 0.750672i 0.926889 + 0.375336i \(0.122473\pi\)
−0.926889 + 0.375336i \(0.877527\pi\)
\(660\) 3.83310e29 7.60271e29i 0.951345 1.88694i
\(661\) 5.59125e29i 1.36582i 0.730503 + 0.682910i \(0.239286\pi\)
−0.730503 + 0.682910i \(0.760714\pi\)
\(662\) 9.82289e28i 0.236173i
\(663\) −2.94119e29 + 5.83368e29i −0.696036 + 1.38054i
\(664\) 4.08403e28i 0.0951313i
\(665\) −2.06565e29 1.72601e29i −0.473619 0.395745i
\(666\) −1.26002e29 + 9.31949e28i −0.284379 + 0.210336i
\(667\) −2.69729e29 −0.599248
\(668\) 9.70530e28 0.212254
\(669\) 5.06281e28 1.00418e29i 0.108998 0.216190i
\(670\) 8.05221e28i 0.170659i
\(671\) −1.42160e29 −0.296613
\(672\) 1.34443e29 + 3.11238e29i 0.276161 + 0.639316i
\(673\) −2.43237e29 −0.491893 −0.245947 0.969283i \(-0.579099\pi\)
−0.245947 + 0.969283i \(0.579099\pi\)
\(674\) 1.85920e29i 0.370166i
\(675\) 1.02850e29 + 5.99696e29i 0.201610 + 1.17555i
\(676\) −3.93768e29 −0.759977
\(677\) −9.11748e29 −1.73258 −0.866291 0.499540i \(-0.833502\pi\)
−0.866291 + 0.499540i \(0.833502\pi\)
\(678\) −6.13875e28 3.09500e28i −0.114860 0.0579094i
\(679\) −4.94837e29 4.13475e29i −0.911652 0.761756i
\(680\) 4.60056e29i 0.834579i
\(681\) −2.77751e29 1.40035e29i −0.496147 0.250145i
\(682\) 2.72824e29i 0.479895i
\(683\) 1.45654e29i 0.252293i −0.992012 0.126146i \(-0.959739\pi\)
0.992012 0.126146i \(-0.0402609\pi\)
\(684\) −1.83831e29 + 1.35967e29i −0.313566 + 0.231924i
\(685\) 1.18292e30i 1.98703i
\(686\) 7.57994e28 1.33192e29i 0.125390 0.220331i
\(687\) 4.16896e29 8.26889e29i 0.679176 1.34710i
\(688\) 4.11263e29 0.659844
\(689\) −4.92117e29 −0.777619
\(690\) −2.30479e29 1.16202e29i −0.358688 0.180841i
\(691\) 2.38869e29i 0.366135i 0.983100 + 0.183067i \(0.0586026\pi\)
−0.983100 + 0.183067i \(0.941397\pi\)
\(692\) −2.66752e29 −0.402711
\(693\) −6.07120e28 + 1.02384e30i −0.0902767 + 1.52242i
\(694\) −2.11803e29 −0.310212
\(695\) 1.29534e30i 1.86872i
\(696\) −1.72686e29 8.70638e28i −0.245391 0.123720i
\(697\) −2.17461e29 −0.304395
\(698\) 2.82401e29 0.389389
\(699\) −3.86337e28 + 7.66276e28i −0.0524754 + 0.104082i
\(700\) −5.34824e29 + 6.40064e29i −0.715618 + 0.856435i
\(701\) 1.08484e30i 1.42996i −0.699143 0.714981i \(-0.746435\pi\)
0.699143 0.714981i \(-0.253565\pi\)
\(702\) 4.44238e28 + 2.59026e29i 0.0576867 + 0.336360i
\(703\) 4.54583e29i 0.581544i
\(704\) 7.68123e29i 0.968094i
\(705\) −5.34707e29 2.69586e29i −0.663943 0.334743i
\(706\) 2.67494e29i 0.327238i
\(707\) −2.44305e29 + 2.92378e29i −0.294461 + 0.352404i
\(708\) 5.27166e29 + 2.65784e29i 0.626034 + 0.315631i
\(709\) −8.41126e29 −0.984182 −0.492091 0.870544i \(-0.663767\pi\)
−0.492091 + 0.870544i \(0.663767\pi\)
\(710\) 2.45454e29 0.282982
\(711\) 5.85726e29 + 7.91915e29i 0.665370 + 0.899596i
\(712\) 6.61067e29i 0.739956i
\(713\) 1.20420e30 1.32819
\(714\) 1.06233e29 + 2.45930e29i 0.115459 + 0.267289i
\(715\) 2.83858e30 3.04010
\(716\) 1.00062e30i 1.05605i
\(717\) 5.38406e29 1.06789e30i 0.559962 1.11065i
\(718\) 2.94473e29 0.301814
\(719\) −4.13198e29 −0.417354 −0.208677 0.977985i \(-0.566916\pi\)
−0.208677 + 0.977985i \(0.566916\pi\)
\(720\) 7.17695e29 + 9.70341e29i 0.714412 + 0.965902i
\(721\) 7.48411e28 + 6.25355e28i 0.0734209 + 0.0613489i
\(722\) 2.16653e29i 0.209471i
\(723\) 2.55447e29 5.06663e29i 0.243416 0.482800i
\(724\) 5.01772e29i 0.471250i
\(725\) 7.21577e29i 0.667934i
\(726\) −1.65862e29 + 3.28978e29i −0.151326 + 0.300146i
\(727\) 3.45036e29i 0.310279i 0.987893 + 0.155140i \(0.0495828\pi\)
−0.987893 + 0.155140i \(0.950417\pi\)
\(728\) −4.77878e29 + 5.71913e29i −0.423582 + 0.506933i
\(729\) −1.07915e30 + 3.81374e29i −0.942854 + 0.333205i
\(730\) −4.78930e29 −0.412460
\(731\) 1.10030e30 0.934069
\(732\) 9.79062e28 1.94191e29i 0.0819302 0.162503i
\(733\) 5.24361e28i 0.0432553i 0.999766 + 0.0216276i \(0.00688482\pi\)
−0.999766 + 0.0216276i \(0.993115\pi\)
\(734\) −3.95437e29 −0.321565
\(735\) 5.25208e29 1.77094e30i 0.421032 1.41966i
\(736\) −9.42958e29 −0.745204
\(737\) 8.89909e29i 0.693325i
\(738\) −7.03303e28 + 5.20186e28i −0.0540195 + 0.0399546i
\(739\) 3.97690e29 0.301147 0.150573 0.988599i \(-0.451888\pi\)
0.150573 + 0.988599i \(0.451888\pi\)
\(740\) −2.58956e30 −1.93327
\(741\) −6.80676e29 3.43180e29i −0.501013 0.252598i
\(742\) −1.29390e29 + 1.54851e29i −0.0938986 + 0.112376i
\(743\) 1.67451e30i 1.19814i 0.800698 + 0.599068i \(0.204462\pi\)
−0.800698 + 0.599068i \(0.795538\pi\)
\(744\) 7.70953e29 + 3.88695e29i 0.543891 + 0.274216i
\(745\) 1.84563e30i 1.28382i
\(746\) 1.34268e29i 0.0920902i
\(747\) 1.70455e29 + 2.30459e29i 0.115277 + 0.155857i
\(748\) 2.45781e30i 1.63901i
\(749\) 1.41462e30 + 1.18202e30i 0.930207 + 0.777260i
\(750\) 5.02278e28 9.96237e28i 0.0325687 0.0645981i
\(751\) 6.70899e28 0.0428981 0.0214490 0.999770i \(-0.493172\pi\)
0.0214490 + 0.999770i \(0.493172\pi\)
\(752\) −6.46106e29 −0.407396
\(753\) −7.47856e29 3.77050e29i −0.465019 0.234451i
\(754\) 3.11670e29i 0.191116i
\(755\) 4.43583e30 2.68245
\(756\) −1.35676e30 7.88059e29i −0.809143 0.469981i
\(757\) 3.15591e29 0.185617 0.0928084 0.995684i \(-0.470416\pi\)
0.0928084 + 0.995684i \(0.470416\pi\)
\(758\) 3.82523e29i 0.221886i
\(759\) −2.54720e30 1.28423e30i −1.45722 0.734692i
\(760\) 5.36795e29 0.302877
\(761\) −1.60120e30