Properties

Label 21.22.c.b.20.9
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 20.9
Character \(\chi\) \(=\) 21.20
Dual form 21.22.c.b.20.10

$q$-expansion

\(f(q)\) \(=\) \(q-1925.57i q^{2} +(78349.6 - 65739.6i) q^{3} -1.61068e6 q^{4} +2.77549e7 q^{5} +(-1.26586e8 - 1.50868e8i) q^{6} +(7.43581e8 + 7.50540e7i) q^{7} -9.36744e8i q^{8} +(1.81697e9 - 1.03013e10i) q^{9} +O(q^{10})\) \(q-1925.57i q^{2} +(78349.6 - 65739.6i) q^{3} -1.61068e6 q^{4} +2.77549e7 q^{5} +(-1.26586e8 - 1.50868e8i) q^{6} +(7.43581e8 + 7.50540e7i) q^{7} -9.36744e8i q^{8} +(1.81697e9 - 1.03013e10i) q^{9} -5.34441e10i q^{10} +5.61106e10i q^{11} +(-1.26196e11 + 1.05885e11i) q^{12} +3.86369e11i q^{13} +(1.44522e11 - 1.43182e12i) q^{14} +(2.17459e12 - 1.82460e12i) q^{15} -5.18160e12 q^{16} +1.33419e13 q^{17} +(-1.98360e13 - 3.49870e12i) q^{18} +3.04856e13i q^{19} -4.47042e13 q^{20} +(6.31933e13 - 4.30023e13i) q^{21} +1.08045e14 q^{22} -2.80800e14i q^{23} +(-6.15811e13 - 7.33935e13i) q^{24} +2.93499e14 q^{25} +7.43981e14 q^{26} +(-5.34847e14 - 9.26553e14i) q^{27} +(-1.19767e15 - 1.20888e14i) q^{28} -2.28112e15i q^{29} +(-3.51340e15 - 4.18733e15i) q^{30} -3.90771e15i q^{31} +8.01305e15i q^{32} +(3.68869e15 + 4.39624e15i) q^{33} -2.56909e16i q^{34} +(2.06380e16 + 2.08312e15i) q^{35} +(-2.92655e15 + 1.65921e16i) q^{36} +3.61922e16 q^{37} +5.87023e16 q^{38} +(2.53997e16 + 3.02718e16i) q^{39} -2.59993e16i q^{40} +7.43654e16 q^{41} +(-8.28040e16 - 1.21683e17i) q^{42} -1.37569e17 q^{43} -9.03760e16i q^{44} +(5.04298e16 - 2.85913e17i) q^{45} -5.40700e17 q^{46} -1.27732e17 q^{47} +(-4.05976e17 + 3.40636e17i) q^{48} +(5.47280e17 + 1.11617e17i) q^{49} -5.65154e17i q^{50} +(1.04534e18 - 8.77094e17i) q^{51} -6.22315e17i q^{52} +1.55747e18i q^{53} +(-1.78414e18 + 1.02989e18i) q^{54} +1.55734e18i q^{55} +(7.03063e16 - 6.96545e17i) q^{56} +(2.00411e18 + 2.38854e18i) q^{57} -4.39246e18 q^{58} -6.38773e18 q^{59} +(-3.50256e18 + 2.93884e18i) q^{60} -1.92216e18i q^{61} -7.52457e18 q^{62} +(2.12422e18 - 7.52351e18i) q^{63} +4.56311e18 q^{64} +1.07236e19i q^{65} +(8.46528e18 - 7.10283e18i) q^{66} +2.86226e18 q^{67} -2.14896e19 q^{68} +(-1.84597e19 - 2.20006e19i) q^{69} +(4.01120e18 - 3.97400e19i) q^{70} +2.30678e19i q^{71} +(-9.64971e18 - 1.70203e18i) q^{72} -1.86483e19i q^{73} -6.96907e19i q^{74} +(2.29955e19 - 1.92945e19i) q^{75} -4.91025e19i q^{76} +(-4.21132e18 + 4.17227e19i) q^{77} +(5.82906e19 - 4.89090e19i) q^{78} -1.57015e20 q^{79} -1.43815e20 q^{80} +(-1.02816e20 - 3.74344e19i) q^{81} -1.43196e20i q^{82} +1.76885e20 q^{83} +(-1.01784e20 + 6.92627e19i) q^{84} +3.70305e20 q^{85} +2.64898e20i q^{86} +(-1.49960e20 - 1.78725e20i) q^{87} +5.25612e19 q^{88} -3.24298e20 q^{89} +(-5.50546e20 - 9.71062e19i) q^{90} +(-2.89985e19 + 2.87296e20i) q^{91} +4.52278e20i q^{92} +(-2.56891e20 - 3.06167e20i) q^{93} +2.45958e20i q^{94} +8.46127e20i q^{95} +(5.26775e20 + 6.27820e20i) q^{96} +2.37119e20i q^{97} +(2.14927e20 - 1.05383e21i) q^{98} +(5.78014e20 + 1.01951e20i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1925.57i 1.32967i −0.746989 0.664837i \(-0.768501\pi\)
0.746989 0.664837i \(-0.231499\pi\)
\(3\) 78349.6 65739.6i 0.766061 0.642767i
\(4\) −1.61068e6 −0.768030
\(5\) 2.77549e7 1.27103 0.635514 0.772089i \(-0.280788\pi\)
0.635514 + 0.772089i \(0.280788\pi\)
\(6\) −1.26586e8 1.50868e8i −0.854670 1.01861i
\(7\) 7.43581e8 + 7.50540e7i 0.994945 + 0.100426i
\(8\) 9.36744e8i 0.308444i
\(9\) 1.81697e9 1.03013e10i 0.173700 0.984799i
\(10\) 5.34441e10i 1.69005i
\(11\) 5.61106e10i 0.652261i 0.945325 + 0.326131i \(0.105745\pi\)
−0.945325 + 0.326131i \(0.894255\pi\)
\(12\) −1.26196e11 + 1.05885e11i −0.588359 + 0.493665i
\(13\) 3.86369e11i 0.777314i 0.921382 + 0.388657i \(0.127061\pi\)
−0.921382 + 0.388657i \(0.872939\pi\)
\(14\) 1.44522e11 1.43182e12i 0.133533 1.32295i
\(15\) 2.17459e12 1.82460e12i 0.973686 0.816975i
\(16\) −5.18160e12 −1.17816
\(17\) 1.33419e13 1.60511 0.802556 0.596576i \(-0.203473\pi\)
0.802556 + 0.596576i \(0.203473\pi\)
\(18\) −1.98360e13 3.49870e12i −1.30946 0.230965i
\(19\) 3.04856e13i 1.14073i 0.821392 + 0.570365i \(0.193198\pi\)
−0.821392 + 0.570365i \(0.806802\pi\)
\(20\) −4.47042e13 −0.976188
\(21\) 6.31933e13 4.30023e13i 0.826739 0.562586i
\(22\) 1.08045e14 0.867294
\(23\) 2.80800e14i 1.41337i −0.707530 0.706683i \(-0.750191\pi\)
0.707530 0.706683i \(-0.249809\pi\)
\(24\) −6.15811e13 7.33935e13i −0.198258 0.236287i
\(25\) 2.93499e14 0.615513
\(26\) 7.43981e14 1.03357
\(27\) −5.34847e14 9.26553e14i −0.499931 0.866065i
\(28\) −1.19767e15 1.20888e14i −0.764148 0.0771299i
\(29\) 2.28112e15i 1.00686i −0.864036 0.503430i \(-0.832071\pi\)
0.864036 0.503430i \(-0.167929\pi\)
\(30\) −3.51340e15 4.18733e15i −1.08631 1.29468i
\(31\) 3.90771e15i 0.856297i −0.903708 0.428148i \(-0.859166\pi\)
0.903708 0.428148i \(-0.140834\pi\)
\(32\) 8.01305e15i 1.25812i
\(33\) 3.68869e15 + 4.39624e15i 0.419252 + 0.499672i
\(34\) 2.56909e16i 2.13428i
\(35\) 2.06380e16 + 2.08312e15i 1.26460 + 0.127644i
\(36\) −2.92655e15 + 1.65921e16i −0.133407 + 0.756355i
\(37\) 3.61922e16 1.23736 0.618681 0.785642i \(-0.287667\pi\)
0.618681 + 0.785642i \(0.287667\pi\)
\(38\) 5.87023e16 1.51680
\(39\) 2.53997e16 + 3.02718e16i 0.499632 + 0.595471i
\(40\) 2.59993e16i 0.392041i
\(41\) 7.43654e16 0.865248 0.432624 0.901574i \(-0.357588\pi\)
0.432624 + 0.901574i \(0.357588\pi\)
\(42\) −8.28040e16 1.21683e17i −0.748055 1.09929i
\(43\) −1.37569e17 −0.970735 −0.485367 0.874310i \(-0.661314\pi\)
−0.485367 + 0.874310i \(0.661314\pi\)
\(44\) 9.03760e16i 0.500956i
\(45\) 5.04298e16 2.85913e17i 0.220778 1.25171i
\(46\) −5.40700e17 −1.87931
\(47\) −1.27732e17 −0.354220 −0.177110 0.984191i \(-0.556675\pi\)
−0.177110 + 0.984191i \(0.556675\pi\)
\(48\) −4.05976e17 + 3.40636e17i −0.902543 + 0.757283i
\(49\) 5.47280e17 + 1.11617e17i 0.979829 + 0.199836i
\(50\) 5.65154e17i 0.818430i
\(51\) 1.04534e18 8.77094e17i 1.22961 1.03171i
\(52\) 6.22315e17i 0.597001i
\(53\) 1.55747e18i 1.22327i 0.791139 + 0.611636i \(0.209488\pi\)
−0.791139 + 0.611636i \(0.790512\pi\)
\(54\) −1.78414e18 + 1.02989e18i −1.15158 + 0.664745i
\(55\) 1.55734e18i 0.829042i
\(56\) 7.03063e16 6.96545e17i 0.0309756 0.306884i
\(57\) 2.00411e18 + 2.38854e18i 0.733224 + 0.873869i
\(58\) −4.39246e18 −1.33879
\(59\) −6.38773e18 −1.62705 −0.813524 0.581531i \(-0.802454\pi\)
−0.813524 + 0.581531i \(0.802454\pi\)
\(60\) −3.50256e18 + 2.93884e18i −0.747820 + 0.627462i
\(61\) 1.92216e18i 0.345006i −0.985009 0.172503i \(-0.944815\pi\)
0.985009 0.172503i \(-0.0551854\pi\)
\(62\) −7.52457e18 −1.13859
\(63\) 2.12422e18 7.52351e18i 0.271721 0.962376i
\(64\) 4.56311e18 0.494733
\(65\) 1.07236e19i 0.987988i
\(66\) 8.46528e18 7.10283e18i 0.664400 0.557468i
\(67\) 2.86226e18 0.191833 0.0959165 0.995389i \(-0.469422\pi\)
0.0959165 + 0.995389i \(0.469422\pi\)
\(68\) −2.14896e19 −1.23278
\(69\) −1.84597e19 2.20006e19i −0.908465 1.08273i
\(70\) 4.01120e18 3.97400e19i 0.169724 1.68151i
\(71\) 2.30678e19i 0.840995i 0.907294 + 0.420498i \(0.138145\pi\)
−0.907294 + 0.420498i \(0.861855\pi\)
\(72\) −9.64971e18 1.70203e18i −0.303755 0.0535767i
\(73\) 1.86483e19i 0.507866i −0.967222 0.253933i \(-0.918276\pi\)
0.967222 0.253933i \(-0.0817243\pi\)
\(74\) 6.96907e19i 1.64529i
\(75\) 2.29955e19 1.92945e19i 0.471520 0.395631i
\(76\) 4.91025e19i 0.876115i
\(77\) −4.21132e18 + 4.17227e19i −0.0655037 + 0.648964i
\(78\) 5.82906e19 4.89090e19i 0.791781 0.664348i
\(79\) −1.57015e20 −1.86576 −0.932879 0.360190i \(-0.882712\pi\)
−0.932879 + 0.360190i \(0.882712\pi\)
\(80\) −1.43815e20 −1.49747
\(81\) −1.02816e20 3.74344e19i −0.939656 0.342120i
\(82\) 1.43196e20i 1.15050i
\(83\) 1.76885e20 1.25133 0.625665 0.780092i \(-0.284828\pi\)
0.625665 + 0.780092i \(0.284828\pi\)
\(84\) −1.01784e20 + 6.92627e19i −0.634961 + 0.432083i
\(85\) 3.70305e20 2.04014
\(86\) 2.64898e20i 1.29076i
\(87\) −1.49960e20 1.78725e20i −0.647177 0.771317i
\(88\) 5.25612e19 0.201186
\(89\) −3.24298e20 −1.10242 −0.551212 0.834365i \(-0.685835\pi\)
−0.551212 + 0.834365i \(0.685835\pi\)
\(90\) −5.50546e20 9.71062e19i −1.66436 0.293562i
\(91\) −2.89985e19 + 2.87296e20i −0.0780622 + 0.773385i
\(92\) 4.52278e20i 1.08551i
\(93\) −2.56891e20 3.06167e20i −0.550399 0.655976i
\(94\) 2.45958e20i 0.470997i
\(95\) 8.46127e20i 1.44990i
\(96\) 5.26775e20 + 6.27820e20i 0.808681 + 0.963800i
\(97\) 2.37119e20i 0.326485i 0.986586 + 0.163243i \(0.0521954\pi\)
−0.986586 + 0.163243i \(0.947805\pi\)
\(98\) 2.14927e20 1.05383e21i 0.265716 1.30285i
\(99\) 5.78014e20 + 1.01951e20i 0.642346 + 0.113298i
\(100\) −4.72732e20 −0.472732
\(101\) 4.39518e20 0.395916 0.197958 0.980211i \(-0.436569\pi\)
0.197958 + 0.980211i \(0.436569\pi\)
\(102\) −1.68891e21 2.01287e21i −1.37184 1.63499i
\(103\) 4.97085e20i 0.364452i 0.983257 + 0.182226i \(0.0583302\pi\)
−0.983257 + 0.182226i \(0.941670\pi\)
\(104\) 3.61928e20 0.239758
\(105\) 1.75393e21 1.19352e21i 1.05081 0.715062i
\(106\) 2.99902e21 1.62655
\(107\) 9.87407e20i 0.485251i 0.970120 + 0.242626i \(0.0780087\pi\)
−0.970120 + 0.242626i \(0.921991\pi\)
\(108\) 8.61466e20 + 1.49238e21i 0.383962 + 0.665164i
\(109\) −3.08434e21 −1.24791 −0.623956 0.781459i \(-0.714476\pi\)
−0.623956 + 0.781459i \(0.714476\pi\)
\(110\) 2.99878e21 1.10235
\(111\) 2.83564e21 2.37926e21i 0.947895 0.795336i
\(112\) −3.85294e21 3.88900e20i −1.17220 0.118317i
\(113\) 6.50283e21i 1.80210i 0.433715 + 0.901050i \(0.357203\pi\)
−0.433715 + 0.901050i \(0.642797\pi\)
\(114\) 4.59930e21 3.85907e21i 1.16196 0.974948i
\(115\) 7.79358e21i 1.79643i
\(116\) 3.67415e21i 0.773299i
\(117\) 3.98012e21 + 7.02019e20i 0.765498 + 0.135020i
\(118\) 1.23000e22i 2.16344i
\(119\) 9.92082e21 + 1.00137e21i 1.59700 + 0.161194i
\(120\) −1.70918e21 2.03703e21i −0.251991 0.300327i
\(121\) 4.25185e21 0.574556
\(122\) −3.70126e21 −0.458745
\(123\) 5.82650e21 4.88875e21i 0.662833 0.556153i
\(124\) 6.29405e21i 0.657662i
\(125\) −5.08853e21 −0.488694
\(126\) −1.44871e22 4.09034e21i −1.27965 0.361300i
\(127\) −5.07003e21 −0.412165 −0.206083 0.978535i \(-0.566072\pi\)
−0.206083 + 0.978535i \(0.566072\pi\)
\(128\) 8.01800e21i 0.600290i
\(129\) −1.07784e22 + 9.04370e21i −0.743642 + 0.623956i
\(130\) 2.06491e22 1.31370
\(131\) 1.15331e22 0.677013 0.338507 0.940964i \(-0.390078\pi\)
0.338507 + 0.940964i \(0.390078\pi\)
\(132\) −5.94128e21 7.08092e21i −0.321998 0.383763i
\(133\) −2.28807e21 + 2.26685e22i −0.114558 + 1.13496i
\(134\) 5.51148e21i 0.255075i
\(135\) −1.48447e22 2.57164e22i −0.635427 1.10079i
\(136\) 1.24980e22i 0.495087i
\(137\) 5.50329e21i 0.201863i 0.994893 + 0.100932i \(0.0321823\pi\)
−0.994893 + 0.100932i \(0.967818\pi\)
\(138\) −4.23637e22 + 3.55454e22i −1.43967 + 1.20796i
\(139\) 3.09790e22i 0.975915i −0.872867 0.487958i \(-0.837742\pi\)
0.872867 0.487958i \(-0.162258\pi\)
\(140\) −3.32412e22 3.35523e21i −0.971253 0.0980343i
\(141\) −1.00078e22 + 8.39707e21i −0.271354 + 0.227681i
\(142\) 4.44187e22 1.11825
\(143\) −2.16794e22 −0.507012
\(144\) −9.41479e21 + 5.33774e22i −0.204647 + 1.16025i
\(145\) 6.33123e22i 1.27975i
\(146\) −3.59086e22 −0.675296
\(147\) 5.02168e22 2.72328e22i 0.879057 0.476716i
\(148\) −5.82939e22 −0.950332
\(149\) 2.26280e22i 0.343709i −0.985122 0.171854i \(-0.945024\pi\)
0.985122 0.171854i \(-0.0549759\pi\)
\(150\) −3.71530e22 4.42796e22i −0.526060 0.626968i
\(151\) −9.09150e21 −0.120054 −0.0600271 0.998197i \(-0.519119\pi\)
−0.0600271 + 0.998197i \(0.519119\pi\)
\(152\) 2.85572e22 0.351851
\(153\) 2.42419e22 1.37440e23i 0.278809 1.58071i
\(154\) 8.03402e22 + 8.10920e21i 0.862909 + 0.0870985i
\(155\) 1.08458e23i 1.08838i
\(156\) −4.09107e22 4.87581e22i −0.383733 0.457340i
\(157\) 1.65613e23i 1.45261i −0.687373 0.726304i \(-0.741236\pi\)
0.687373 0.726304i \(-0.258764\pi\)
\(158\) 3.02343e23i 2.48085i
\(159\) 1.02387e23 + 1.22027e23i 0.786280 + 0.937102i
\(160\) 2.22402e23i 1.59911i
\(161\) 2.10751e22 2.08797e23i 0.141938 1.40622i
\(162\) −7.20826e22 + 1.97980e23i −0.454907 + 1.24944i
\(163\) −1.13381e23 −0.670763 −0.335381 0.942082i \(-0.608865\pi\)
−0.335381 + 0.942082i \(0.608865\pi\)
\(164\) −1.19779e23 −0.664537
\(165\) 1.02379e23 + 1.22017e23i 0.532881 + 0.635097i
\(166\) 3.40606e23i 1.66386i
\(167\) −5.03836e22 −0.231082 −0.115541 0.993303i \(-0.536860\pi\)
−0.115541 + 0.993303i \(0.536860\pi\)
\(168\) −4.02821e22 5.91959e22i −0.173526 0.255002i
\(169\) 9.77838e22 0.395782
\(170\) 7.13049e23i 2.71272i
\(171\) 3.14043e23 + 5.53914e22i 1.12339 + 0.198145i
\(172\) 2.21579e23 0.745554
\(173\) −2.90415e23 −0.919465 −0.459732 0.888057i \(-0.652055\pi\)
−0.459732 + 0.888057i \(0.652055\pi\)
\(174\) −3.44147e23 + 2.88759e23i −1.02560 + 0.860533i
\(175\) 2.18240e23 + 2.20283e22i 0.612401 + 0.0618132i
\(176\) 2.90743e23i 0.768468i
\(177\) −5.00476e23 + 4.19927e23i −1.24642 + 1.04581i
\(178\) 6.24459e23i 1.46586i
\(179\) 1.65216e23i 0.365676i 0.983143 + 0.182838i \(0.0585283\pi\)
−0.983143 + 0.182838i \(0.941472\pi\)
\(180\) −8.12261e22 + 4.60513e23i −0.169564 + 0.961349i
\(181\) 5.22379e23i 1.02887i 0.857529 + 0.514436i \(0.171999\pi\)
−0.857529 + 0.514436i \(0.828001\pi\)
\(182\) 5.53210e23 + 5.58387e22i 1.02835 + 0.103797i
\(183\) −1.26362e23 1.50600e23i −0.221758 0.264296i
\(184\) −2.63037e23 −0.435944
\(185\) 1.00451e24 1.57272
\(186\) −5.89547e23 + 4.94662e23i −0.872233 + 0.731851i
\(187\) 7.48624e23i 1.04695i
\(188\) 2.05736e23 0.272052
\(189\) −3.28161e23 7.29109e23i −0.410429 0.911893i
\(190\) 1.62928e24 1.92789
\(191\) 7.34429e23i 0.822431i 0.911538 + 0.411215i \(0.134896\pi\)
−0.911538 + 0.411215i \(0.865104\pi\)
\(192\) 3.57518e23 2.99977e23i 0.378996 0.317998i
\(193\) 1.04432e24 1.04829 0.524147 0.851628i \(-0.324384\pi\)
0.524147 + 0.851628i \(0.324384\pi\)
\(194\) 4.56591e23 0.434119
\(195\) 7.04967e23 + 8.40193e23i 0.635047 + 0.756860i
\(196\) −8.81491e23 1.79780e23i −0.752539 0.153480i
\(197\) 8.01223e23i 0.648423i 0.945985 + 0.324211i \(0.105099\pi\)
−0.945985 + 0.324211i \(0.894901\pi\)
\(198\) 1.96314e23 1.11301e24i 0.150649 0.854110i
\(199\) 1.31900e24i 0.960039i −0.877258 0.480019i \(-0.840630\pi\)
0.877258 0.480019i \(-0.159370\pi\)
\(200\) 2.74934e23i 0.189851i
\(201\) 2.24257e23 1.88164e23i 0.146956 0.123304i
\(202\) 8.46325e23i 0.526438i
\(203\) 1.71207e23 1.69620e24i 0.101114 1.00177i
\(204\) −1.68370e24 + 1.41271e24i −0.944382 + 0.792388i
\(205\) 2.06401e24 1.09975
\(206\) 9.57174e23 0.484602
\(207\) −2.89262e24 5.10204e23i −1.39188 0.245502i
\(208\) 2.00201e24i 0.915800i
\(209\) −1.71057e24 −0.744053
\(210\) −2.29822e24 3.37731e24i −0.950799 1.39723i
\(211\) 6.91056e23 0.271987 0.135993 0.990710i \(-0.456577\pi\)
0.135993 + 0.990710i \(0.456577\pi\)
\(212\) 2.50858e24i 0.939511i
\(213\) 1.51647e24 + 1.80735e24i 0.540564 + 0.644254i
\(214\) 1.90132e24 0.645226
\(215\) −3.81821e24 −1.23383
\(216\) −8.67942e23 + 5.01015e23i −0.267132 + 0.154201i
\(217\) 2.93289e23 2.90570e24i 0.0859941 0.851968i
\(218\) 5.93912e24i 1.65932i
\(219\) −1.22593e24 1.46109e24i −0.326440 0.389057i
\(220\) 2.50838e24i 0.636730i
\(221\) 5.15491e24i 1.24768i
\(222\) −4.58144e24 5.46024e24i −1.05754 1.26039i
\(223\) 6.92689e24i 1.52524i 0.646849 + 0.762618i \(0.276086\pi\)
−0.646849 + 0.762618i \(0.723914\pi\)
\(224\) −6.01412e23 + 5.95835e24i −0.126348 + 1.25176i
\(225\) 5.33278e23 3.02344e24i 0.106915 0.606156i
\(226\) 1.25217e25 2.39620
\(227\) −1.03328e24 −0.188776 −0.0943882 0.995535i \(-0.530089\pi\)
−0.0943882 + 0.995535i \(0.530089\pi\)
\(228\) −3.22798e24 3.84716e24i −0.563138 0.671158i
\(229\) 9.83603e24i 1.63888i 0.573164 + 0.819441i \(0.305716\pi\)
−0.573164 + 0.819441i \(0.694284\pi\)
\(230\) −1.50071e25 −2.38866
\(231\) 2.41288e24 + 3.54581e24i 0.366953 + 0.539250i
\(232\) −2.13682e24 −0.310560
\(233\) 5.26607e24i 0.731559i 0.930702 + 0.365779i \(0.119198\pi\)
−0.930702 + 0.365779i \(0.880802\pi\)
\(234\) 1.35179e24 7.66400e24i 0.179532 1.01786i
\(235\) −3.54520e24 −0.450224
\(236\) 1.02886e25 1.24962
\(237\) −1.23020e25 + 1.03221e25i −1.42929 + 1.19925i
\(238\) 1.92820e24 1.91033e25i 0.214336 2.12349i
\(239\) 7.97115e24i 0.847897i −0.905686 0.423948i \(-0.860644\pi\)
0.905686 0.423948i \(-0.139356\pi\)
\(240\) −1.12678e25 + 9.45434e24i −1.14716 + 0.962527i
\(241\) 1.14952e25i 1.12031i −0.828388 0.560154i \(-0.810742\pi\)
0.828388 0.560154i \(-0.189258\pi\)
\(242\) 8.18725e24i 0.763971i
\(243\) −1.05165e25 + 3.82613e24i −0.939738 + 0.341896i
\(244\) 3.09598e24i 0.264975i
\(245\) 1.51897e25 + 3.09793e24i 1.24539 + 0.253997i
\(246\) −9.41365e24 1.12194e25i −0.739502 0.881351i
\(247\) −1.17787e25 −0.886705
\(248\) −3.66052e24 −0.264119
\(249\) 1.38589e25 1.16284e25i 0.958596 0.804315i
\(250\) 9.79834e24i 0.649804i
\(251\) 1.98280e24 0.126097 0.0630485 0.998010i \(-0.479918\pi\)
0.0630485 + 0.998010i \(0.479918\pi\)
\(252\) −3.42143e24 + 1.21179e25i −0.208690 + 0.739134i
\(253\) 1.57558e25 0.921884
\(254\) 9.76271e24i 0.548045i
\(255\) 2.90132e25 2.43437e25i 1.56288 1.31134i
\(256\) 2.50088e25 1.29292
\(257\) 2.28306e25 1.13297 0.566487 0.824070i \(-0.308302\pi\)
0.566487 + 0.824070i \(0.308302\pi\)
\(258\) 1.74143e25 + 2.07547e25i 0.829658 + 0.988801i
\(259\) 2.69118e25 + 2.71637e24i 1.23111 + 0.124263i
\(260\) 1.72723e25i 0.758805i
\(261\) −2.34986e25 4.14472e24i −0.991554 0.174892i
\(262\) 2.22078e25i 0.900207i
\(263\) 2.78372e25i 1.08415i −0.840329 0.542076i \(-0.817638\pi\)
0.840329 0.542076i \(-0.182362\pi\)
\(264\) 4.11815e24 3.45535e24i 0.154121 0.129316i
\(265\) 4.32275e25i 1.55481i
\(266\) 4.36499e25 + 4.40584e24i 1.50913 + 0.152325i
\(267\) −2.54086e25 + 2.13192e25i −0.844525 + 0.708602i
\(268\) −4.61017e24 −0.147334
\(269\) 2.33332e25 0.717091 0.358546 0.933512i \(-0.383273\pi\)
0.358546 + 0.933512i \(0.383273\pi\)
\(270\) −4.95188e25 + 2.85845e25i −1.46369 + 0.844910i
\(271\) 2.60440e25i 0.740508i 0.928931 + 0.370254i \(0.120729\pi\)
−0.928931 + 0.370254i \(0.879271\pi\)
\(272\) −6.91326e25 −1.89108
\(273\) 1.66147e25 + 2.44159e25i 0.437306 + 0.642636i
\(274\) 1.05970e25 0.268412
\(275\) 1.64684e25i 0.401475i
\(276\) 2.97326e25 + 3.54358e25i 0.697729 + 0.831566i
\(277\) −1.05713e25 −0.238830 −0.119415 0.992844i \(-0.538102\pi\)
−0.119415 + 0.992844i \(0.538102\pi\)
\(278\) −5.96523e25 −1.29765
\(279\) −4.02546e25 7.10017e24i −0.843280 0.148739i
\(280\) 1.95135e24 1.93326e25i 0.0393709 0.390059i
\(281\) 4.52746e25i 0.879909i −0.898020 0.439955i \(-0.854995\pi\)
0.898020 0.439955i \(-0.145005\pi\)
\(282\) 1.61692e25 + 1.92707e25i 0.302742 + 0.360813i
\(283\) 8.01307e24i 0.144558i −0.997384 0.0722789i \(-0.976973\pi\)
0.997384 0.0722789i \(-0.0230272\pi\)
\(284\) 3.71548e25i 0.645910i
\(285\) 5.56240e25 + 6.62937e25i 0.931948 + 1.11071i
\(286\) 4.17452e25i 0.674160i
\(287\) 5.52967e25 + 5.58142e24i 0.860874 + 0.0868930i
\(288\) 8.25452e25 + 1.45594e25i 1.23900 + 0.218536i
\(289\) 1.08916e26 1.57639
\(290\) −1.21912e26 −1.70165
\(291\) 1.55881e25 + 1.85782e25i 0.209854 + 0.250108i
\(292\) 3.00364e25i 0.390057i
\(293\) 6.16639e24 0.0772540 0.0386270 0.999254i \(-0.487702\pi\)
0.0386270 + 0.999254i \(0.487702\pi\)
\(294\) −5.24386e25 9.66961e25i −0.633876 1.16886i
\(295\) −1.77291e26 −2.06802
\(296\) 3.39028e25i 0.381656i
\(297\) 5.19894e25 3.00106e25i 0.564900 0.326086i
\(298\) −4.35719e25 −0.457020
\(299\) 1.08492e26 1.09863
\(300\) −3.70384e25 + 3.10772e25i −0.362142 + 0.303857i
\(301\) −1.02293e26 1.03251e25i −0.965827 0.0974866i
\(302\) 1.75063e25i 0.159633i
\(303\) 3.44361e25 2.88938e25i 0.303296 0.254482i
\(304\) 1.57964e26i 1.34396i
\(305\) 5.33494e25i 0.438512i
\(306\) −2.64651e26 4.66795e25i −2.10183 0.370724i
\(307\) 7.64771e25i 0.586919i 0.955971 + 0.293460i \(0.0948066\pi\)
−0.955971 + 0.293460i \(0.905193\pi\)
\(308\) 6.78308e24 6.72019e25i 0.0503088 0.498424i
\(309\) 3.26782e25 + 3.89464e25i 0.234258 + 0.279192i
\(310\) −2.08844e26 −1.44719
\(311\) 1.67333e26 1.12098 0.560488 0.828162i \(-0.310613\pi\)
0.560488 + 0.828162i \(0.310613\pi\)
\(312\) 2.83569e25 2.37930e25i 0.183669 0.154108i
\(313\) 3.15921e26i 1.97862i −0.145814 0.989312i \(-0.546580\pi\)
0.145814 0.989312i \(-0.453420\pi\)
\(314\) −3.18900e26 −1.93150
\(315\) 5.89575e25 2.08815e26i 0.345365 1.22321i
\(316\) 2.52900e26 1.43296
\(317\) 1.06857e26i 0.585706i 0.956157 + 0.292853i \(0.0946047\pi\)
−0.956157 + 0.292853i \(0.905395\pi\)
\(318\) 2.34972e26 1.97154e26i 1.24604 1.04549i
\(319\) 1.27995e26 0.656735
\(320\) 1.26649e26 0.628820
\(321\) 6.49118e25 + 7.73630e25i 0.311904 + 0.371732i
\(322\) −4.02055e26 4.05817e25i −1.86981 0.188731i
\(323\) 4.06738e26i 1.83100i
\(324\) 1.65604e26 + 6.02947e25i 0.721685 + 0.262758i
\(325\) 1.13399e26i 0.478447i
\(326\) 2.18323e26i 0.891895i
\(327\) −2.41657e26 + 2.02763e26i −0.955977 + 0.802117i
\(328\) 6.96613e25i 0.266880i
\(329\) −9.49794e25 9.58682e24i −0.352430 0.0355728i
\(330\) 2.34953e26 1.97139e26i 0.844472 0.708558i
\(331\) 4.53313e26 1.57835 0.789177 0.614166i \(-0.210507\pi\)
0.789177 + 0.614166i \(0.210507\pi\)
\(332\) −2.84905e26 −0.961060
\(333\) 6.57600e25 3.72828e26i 0.214930 1.21855i
\(334\) 9.70173e25i 0.307264i
\(335\) 7.94417e25 0.243825
\(336\) −3.27442e26 + 2.22821e26i −0.974031 + 0.662816i
\(337\) −6.68212e26 −1.92664 −0.963320 0.268357i \(-0.913519\pi\)
−0.963320 + 0.268357i \(0.913519\pi\)
\(338\) 1.88290e26i 0.526261i
\(339\) 4.27494e26 + 5.09494e26i 1.15833 + 1.38052i
\(340\) −5.96441e26 −1.56689
\(341\) 2.19264e26 0.558529
\(342\) 1.06660e26 6.04713e26i 0.263468 1.49374i
\(343\) 3.98569e26 + 1.24072e26i 0.954807 + 0.297225i
\(344\) 1.28866e26i 0.299417i
\(345\) −5.12347e26 6.10624e26i −1.15469 1.37617i
\(346\) 5.59215e26i 1.22259i
\(347\) 4.27377e26i 0.906466i 0.891392 + 0.453233i \(0.149729\pi\)
−0.891392 + 0.453233i \(0.850271\pi\)
\(348\) 2.41537e26 + 2.87868e26i 0.497051 + 0.592395i
\(349\) 4.85429e26i 0.969301i 0.874708 + 0.484650i \(0.161053\pi\)
−0.874708 + 0.484650i \(0.838947\pi\)
\(350\) 4.24171e25 4.20238e26i 0.0821913 0.814293i
\(351\) 3.57991e26 2.06648e26i 0.673205 0.388604i
\(352\) −4.49617e26 −0.820625
\(353\) −7.81307e26 −1.38416 −0.692082 0.721819i \(-0.743306\pi\)
−0.692082 + 0.721819i \(0.743306\pi\)
\(354\) 8.08599e26 + 9.63703e26i 1.39059 + 1.65733i
\(355\) 6.40245e26i 1.06893i
\(356\) 5.22339e26 0.846696
\(357\) 8.43122e26 5.73734e26i 1.32701 0.903013i
\(358\) 3.18136e26 0.486229
\(359\) 2.80022e26i 0.415624i −0.978169 0.207812i \(-0.933366\pi\)
0.978169 0.207812i \(-0.0666343\pi\)
\(360\) −2.67827e26 4.72398e25i −0.386081 0.0680976i
\(361\) −2.15165e26 −0.301263
\(362\) 1.00588e27 1.36806
\(363\) 3.33131e26 2.79515e26i 0.440145 0.369306i
\(364\) 4.67072e25 4.62742e26i 0.0599542 0.593983i
\(365\) 5.17582e26i 0.645512i
\(366\) −2.89992e26 + 2.43319e26i −0.351427 + 0.294866i
\(367\) 6.09104e26i 0.717295i 0.933473 + 0.358647i \(0.116762\pi\)
−0.933473 + 0.358647i \(0.883238\pi\)
\(368\) 1.45499e27i 1.66517i
\(369\) 1.35119e26 7.66064e26i 0.150294 0.852095i
\(370\) 1.93426e27i 2.09121i
\(371\) −1.16894e26 + 1.15811e27i −0.122848 + 1.21709i
\(372\) 4.13768e26 + 4.93136e26i 0.422724 + 0.503809i
\(373\) −7.50786e26 −0.745716 −0.372858 0.927888i \(-0.621622\pi\)
−0.372858 + 0.927888i \(0.621622\pi\)
\(374\) 1.44153e27 1.39210
\(375\) −3.98684e26 + 3.34518e26i −0.374370 + 0.314117i
\(376\) 1.19652e26i 0.109257i
\(377\) 8.81353e26 0.782647
\(378\) −1.40395e27 + 6.31897e26i −1.21252 + 0.545736i
\(379\) −1.75903e27 −1.47761 −0.738806 0.673918i \(-0.764610\pi\)
−0.738806 + 0.673918i \(0.764610\pi\)
\(380\) 1.36284e27i 1.11357i
\(381\) −3.97235e26 + 3.33302e26i −0.315744 + 0.264926i
\(382\) 1.41420e27 1.09356
\(383\) 7.73461e26 0.581904 0.290952 0.956738i \(-0.406028\pi\)
0.290952 + 0.956738i \(0.406028\pi\)
\(384\) 5.27100e26 + 6.28207e26i 0.385847 + 0.459859i
\(385\) −1.16885e26 + 1.15801e27i −0.0832570 + 0.824851i
\(386\) 2.01092e27i 1.39389i
\(387\) −2.49957e26 + 1.41714e27i −0.168617 + 0.955978i
\(388\) 3.81923e26i 0.250751i
\(389\) 2.54238e27i 1.62469i −0.583179 0.812344i \(-0.698191\pi\)
0.583179 0.812344i \(-0.301809\pi\)
\(390\) 1.61785e27 1.35747e27i 1.00638 0.844404i
\(391\) 3.74642e27i 2.26861i
\(392\) 1.04557e26 5.12661e26i 0.0616381 0.302222i
\(393\) 9.03613e26 7.58181e26i 0.518634 0.435162i
\(394\) 1.54281e27 0.862190
\(395\) −4.35793e27 −2.37143
\(396\) −9.30994e26 1.64210e26i −0.493341 0.0870163i
\(397\) 2.81779e27i 1.45415i 0.686560 + 0.727073i \(0.259120\pi\)
−0.686560 + 0.727073i \(0.740880\pi\)
\(398\) −2.53984e27 −1.27654
\(399\) 1.31095e27 + 1.92649e27i 0.641758 + 0.943085i
\(400\) −1.52080e27 −0.725172
\(401\) 2.77530e27i 1.28912i 0.764553 + 0.644560i \(0.222960\pi\)
−0.764553 + 0.644560i \(0.777040\pi\)
\(402\) −3.62323e26 4.31822e26i −0.163954 0.195403i
\(403\) 1.50982e27 0.665612
\(404\) −7.07922e26 −0.304075
\(405\) −2.85366e27 1.03899e27i −1.19433 0.434844i
\(406\) −3.26615e27 3.29672e26i −1.33203 0.134449i
\(407\) 2.03076e27i 0.807083i
\(408\) −8.21612e26 9.79212e26i −0.318226 0.379267i
\(409\) 5.91345e26i 0.223227i −0.993752 0.111613i \(-0.964398\pi\)
0.993752 0.111613i \(-0.0356018\pi\)
\(410\) 3.97440e27i 1.46231i
\(411\) 3.61784e26 + 4.31181e26i 0.129751 + 0.154639i
\(412\) 8.00644e26i 0.279910i
\(413\) −4.74979e27 4.79425e26i −1.61882 0.163397i
\(414\) −9.82434e26 + 5.56994e27i −0.326437 + 1.85075i
\(415\) 4.90944e27 1.59048
\(416\) −3.09599e27 −0.977957
\(417\) −2.03655e27 2.42719e27i −0.627287 0.747611i
\(418\) 3.29382e27i 0.989348i
\(419\) 2.24733e27 0.658294 0.329147 0.944279i \(-0.393239\pi\)
0.329147 + 0.944279i \(0.393239\pi\)
\(420\) −2.82501e27 + 1.92238e27i −0.807053 + 0.549190i
\(421\) 2.26692e27 0.631647 0.315823 0.948818i \(-0.397719\pi\)
0.315823 + 0.948818i \(0.397719\pi\)
\(422\) 1.33068e27i 0.361653i
\(423\) −2.32085e26 + 1.31581e27i −0.0615282 + 0.348836i
\(424\) 1.45895e27 0.377311
\(425\) 3.91585e27 0.987967
\(426\) 3.48019e27 2.92007e27i 0.856647 0.718774i
\(427\) 1.44266e26 1.42928e27i 0.0346474 0.343262i
\(428\) 1.59039e27i 0.372688i
\(429\) −1.69857e27 + 1.42519e27i −0.388402 + 0.325891i
\(430\) 7.35223e27i 1.64059i
\(431\) 5.14323e27i 1.12002i 0.828487 + 0.560008i \(0.189202\pi\)
−0.828487 + 0.560008i \(0.810798\pi\)
\(432\) 2.77137e27 + 4.80103e27i 0.588999 + 1.02036i
\(433\) 9.09697e27i 1.88701i −0.331361 0.943504i \(-0.607508\pi\)
0.331361 0.943504i \(-0.392492\pi\)
\(434\) −5.59513e27 5.64749e26i −1.13284 0.114344i
\(435\) −4.16213e27 4.96049e27i −0.822580 0.980365i
\(436\) 4.96787e27 0.958435
\(437\) 8.56037e27 1.61227
\(438\) −2.81343e27 + 2.36062e27i −0.517318 + 0.434058i
\(439\) 9.97832e27i 1.79135i −0.444712 0.895674i \(-0.646694\pi\)
0.444712 0.895674i \(-0.353306\pi\)
\(440\) 1.45883e27 0.255713
\(441\) 2.14420e27 5.43491e27i 0.366995 0.930223i
\(442\) 9.92615e27 1.65900
\(443\) 4.96044e27i 0.809619i 0.914401 + 0.404809i \(0.132662\pi\)
−0.914401 + 0.404809i \(0.867338\pi\)
\(444\) −4.56731e27 + 3.83222e27i −0.728013 + 0.610842i
\(445\) −9.00086e27 −1.40121
\(446\) 1.33382e28 2.02807
\(447\) −1.48756e27 1.77290e27i −0.220925 0.263302i
\(448\) 3.39304e27 + 3.42480e26i 0.492232 + 0.0496839i
\(449\) 2.45297e26i 0.0347621i 0.999849 + 0.0173811i \(0.00553284\pi\)
−0.999849 + 0.0173811i \(0.994467\pi\)
\(450\) −5.82184e27 1.02687e27i −0.805989 0.142162i
\(451\) 4.17269e27i 0.564368i
\(452\) 1.04740e28i 1.38407i
\(453\) −7.12316e26 + 5.97672e26i −0.0919690 + 0.0771670i
\(454\) 1.98966e27i 0.251011i
\(455\) −8.04852e26 + 7.97389e27i −0.0992193 + 0.982994i
\(456\) 2.23745e27 1.87734e27i 0.269539 0.226158i
\(457\) 6.64451e27 0.782245 0.391122 0.920339i \(-0.372087\pi\)
0.391122 + 0.920339i \(0.372087\pi\)
\(458\) 1.89400e28 2.17918
\(459\) −7.13590e27 1.23620e28i −0.802446 1.39013i
\(460\) 1.25529e28i 1.37971i
\(461\) −3.34150e27 −0.358989 −0.179495 0.983759i \(-0.557446\pi\)
−0.179495 + 0.983759i \(0.557446\pi\)
\(462\) 6.82772e27 4.64618e27i 0.717026 0.487927i
\(463\) −6.64484e27 −0.682157 −0.341079 0.940035i \(-0.610792\pi\)
−0.341079 + 0.940035i \(0.610792\pi\)
\(464\) 1.18199e28i 1.18624i
\(465\) −7.12999e27 8.49765e27i −0.699573 0.833764i
\(466\) 1.01402e28 0.972734
\(467\) −8.33818e27 −0.782067 −0.391034 0.920376i \(-0.627882\pi\)
−0.391034 + 0.920376i \(0.627882\pi\)
\(468\) −6.41068e27 1.13073e27i −0.587926 0.103699i
\(469\) 2.12832e27 + 2.14824e26i 0.190863 + 0.0192649i
\(470\) 6.82654e27i 0.598651i
\(471\) −1.08873e28 1.29757e28i −0.933690 1.11279i
\(472\) 5.98366e27i 0.501853i
\(473\) 7.71905e27i 0.633172i
\(474\) 1.98759e28 + 2.36884e28i 1.59461 + 1.90048i
\(475\) 8.94751e27i 0.702133i
\(476\) −1.59792e28 1.61288e27i −1.22654 0.123802i
\(477\) 1.60440e28 + 2.82987e27i 1.20468 + 0.212483i
\(478\) −1.53490e28 −1.12743
\(479\) 1.41307e28 1.01541 0.507705 0.861531i \(-0.330494\pi\)
0.507705 + 0.861531i \(0.330494\pi\)
\(480\) 1.46206e28 + 1.74251e28i 1.02786 + 1.22502i
\(481\) 1.39835e28i 0.961819i
\(482\) −2.21348e28 −1.48964
\(483\) −1.20750e28 1.77447e28i −0.795140 1.16848i
\(484\) −6.84836e27 −0.441276
\(485\) 6.58123e27i 0.414972i
\(486\) 7.36749e27 + 2.02503e28i 0.454610 + 1.24954i
\(487\) 1.06815e28 0.645030 0.322515 0.946564i \(-0.395472\pi\)
0.322515 + 0.946564i \(0.395472\pi\)
\(488\) −1.80057e27 −0.106415
\(489\) −8.88333e27 + 7.45360e27i −0.513846 + 0.431144i
\(490\) 5.96530e27 2.92489e28i 0.337733 1.65596i
\(491\) 2.41648e27i 0.133914i 0.997756 + 0.0669571i \(0.0213291\pi\)
−0.997756 + 0.0669571i \(0.978671\pi\)
\(492\) −9.38461e27 + 7.87420e27i −0.509076 + 0.427143i
\(493\) 3.04346e28i 1.61612i
\(494\) 2.26807e28i 1.17903i
\(495\) 1.60427e28 + 2.82964e27i 0.816439 + 0.144005i
\(496\) 2.02482e28i 1.00885i
\(497\) −1.73133e27 + 1.71528e28i −0.0844574 + 0.836744i
\(498\) −2.23913e28 2.66863e28i −1.06948 1.27462i
\(499\) −1.64695e27 −0.0770237 −0.0385119 0.999258i \(-0.512262\pi\)
−0.0385119 + 0.999258i \(0.512262\pi\)
\(500\) 8.19598e27 0.375332
\(501\) −3.94754e27 + 3.31220e27i −0.177023 + 0.148532i
\(502\) 3.81802e27i 0.167668i
\(503\) −3.37523e28 −1.45158 −0.725788 0.687919i \(-0.758525\pi\)
−0.725788 + 0.687919i \(0.758525\pi\)
\(504\) −7.04760e27 1.98985e27i −0.296839 0.0838107i
\(505\) 1.21988e28 0.503220
\(506\) 3.03390e28i 1.22580i
\(507\) 7.66132e27 6.42827e27i 0.303194 0.254396i
\(508\) 8.16618e27 0.316555
\(509\) −8.01174e27 −0.304222 −0.152111 0.988363i \(-0.548607\pi\)
−0.152111 + 0.988363i \(0.548607\pi\)
\(510\) −4.68755e28 5.58671e28i −1.74365 2.07811i
\(511\) 1.39963e27 1.38665e28i 0.0510027 0.505298i
\(512\) 3.13412e28i 1.11887i
\(513\) 2.82466e28 1.63052e28i 0.987946 0.570286i
\(514\) 4.39620e28i 1.50649i
\(515\) 1.37966e28i 0.463228i
\(516\) 1.73606e28 1.45665e28i 0.571140 0.479218i
\(517\) 7.16713e27i 0.231044i
\(518\) 5.23056e27 5.18207e28i 0.165229 1.63697i
\(519\) −2.27539e28 + 1.90918e28i −0.704367 + 0.591002i
\(520\) 1.00453e28 0.304739
\(521\) −9.08908e26 −0.0270224 −0.0135112 0.999909i \(-0.504301\pi\)
−0.0135112 + 0.999909i \(0.504301\pi\)
\(522\) −7.98095e27 + 4.52482e28i −0.232549 + 1.31844i
\(523\) 3.59245e28i 1.02594i 0.858406 + 0.512972i \(0.171455\pi\)
−0.858406 + 0.512972i \(0.828545\pi\)
\(524\) −1.85761e28 −0.519967
\(525\) 1.85472e28 1.26211e28i 0.508868 0.346279i
\(526\) −5.36026e28 −1.44157
\(527\) 5.21364e28i 1.37445i
\(528\) −1.91133e28 2.27796e28i −0.493946 0.588693i
\(529\) −3.93770e28 −0.997603
\(530\) 8.32377e28 2.06739
\(531\) −1.16063e28 + 6.58022e28i −0.282619 + 1.60231i
\(532\) 3.68534e27 3.65117e28i 0.0879843 0.871686i
\(533\) 2.87325e28i 0.672570i
\(534\) 4.10517e28 + 4.89261e28i 0.942210 + 1.12294i
\(535\) 2.74054e28i 0.616768i
\(536\) 2.68120e27i 0.0591696i
\(537\) 1.08612e28 + 1.29446e28i 0.235044 + 0.280130i
\(538\) 4.49297e28i 0.953497i
\(539\) −6.26292e27 + 3.07082e28i −0.130345 + 0.639105i
\(540\) 2.39099e28 + 4.14208e28i 0.488027 + 0.845443i
\(541\) −1.75217e28 −0.350756 −0.175378 0.984501i \(-0.556115\pi\)
−0.175378 + 0.984501i \(0.556115\pi\)
\(542\) 5.01496e28 0.984634
\(543\) 3.43410e28 + 4.09282e28i 0.661325 + 0.788179i
\(544\) 1.06910e29i 2.01943i
\(545\) −8.56057e28 −1.58613
\(546\) 4.70146e28 3.19929e28i 0.854496 0.581474i
\(547\) 3.46969e28 0.618620 0.309310 0.950961i \(-0.399902\pi\)
0.309310 + 0.950961i \(0.399902\pi\)
\(548\) 8.86403e27i 0.155037i
\(549\) −1.98008e28 3.49250e27i −0.339761 0.0599276i
\(550\) 3.17111e28 0.533830
\(551\) 6.95414e28 1.14855
\(552\) −2.06089e28 + 1.72920e28i −0.333960 + 0.280210i
\(553\) −1.16753e29 1.17846e28i −1.85633 0.187370i
\(554\) 2.03557e28i 0.317566i
\(555\) 7.87031e28 6.60362e28i 1.20480 1.01089i
\(556\) 4.98972e28i 0.749533i
\(557\) 4.15528e28i 0.612520i −0.951948 0.306260i \(-0.900922\pi\)
0.951948 0.306260i \(-0.0990777\pi\)
\(558\) −1.36719e28 + 7.75132e28i −0.197774 + 1.12129i
\(559\) 5.31522e28i 0.754566i
\(560\) −1.06938e29 1.07939e28i −1.48990 0.150385i
\(561\) 4.92142e28 + 5.86544e28i 0.672947 + 0.802030i
\(562\) −8.71794e28 −1.16999
\(563\) −5.10572e27 −0.0672542 −0.0336271 0.999434i \(-0.510706\pi\)
−0.0336271 + 0.999434i \(0.510706\pi\)
\(564\) 1.61193e28 1.35250e28i 0.208409 0.174866i
\(565\) 1.80486e29i 2.29052i
\(566\) −1.54298e28 −0.192215
\(567\) −7.36426e28 3.55523e28i −0.900549 0.434756i
\(568\) 2.16086e28 0.259400
\(569\) 7.65351e28i 0.901949i 0.892537 + 0.450974i \(0.148923\pi\)
−0.892537 + 0.450974i \(0.851077\pi\)
\(570\) 1.27653e29 1.07108e29i 1.47688 1.23919i
\(571\) −8.22289e28 −0.933997 −0.466999 0.884258i \(-0.654665\pi\)
−0.466999 + 0.884258i \(0.654665\pi\)
\(572\) 3.49184e28 0.389401
\(573\) 4.82810e28 + 5.75422e28i 0.528632 + 0.630033i
\(574\) 1.07474e28 1.06478e29i 0.115539 1.14468i
\(575\) 8.24145e28i 0.869944i
\(576\) 8.29102e27 4.70061e28i 0.0859353 0.487213i
\(577\) 8.74909e28i 0.890465i 0.895415 + 0.445233i \(0.146879\pi\)
−0.895415 + 0.445233i \(0.853121\pi\)
\(578\) 2.09725e29i 2.09608i
\(579\) 8.18223e28 6.86534e28i 0.803058 0.673809i
\(580\) 1.01976e29i 0.982885i
\(581\) 1.31529e29 + 1.32760e28i 1.24500 + 0.125666i
\(582\) 3.57737e28 3.00161e28i 0.332562 0.279037i
\(583\) −8.73905e28 −0.797893
\(584\) −1.74687e28 −0.156648
\(585\) 1.10468e29 + 1.94845e28i 0.972970 + 0.171614i
\(586\) 1.18738e28i 0.102723i
\(587\) −5.04337e28 −0.428569 −0.214285 0.976771i \(-0.568742\pi\)
−0.214285 + 0.976771i \(0.568742\pi\)
\(588\) −8.08831e28 + 4.38632e28i −0.675143 + 0.366132i
\(589\) 1.19129e29 0.976803
\(590\) 3.41387e29i 2.74980i
\(591\) 5.26721e28 + 6.27755e28i 0.416785 + 0.496732i
\(592\) −1.87534e29 −1.45781
\(593\) 1.97856e29 1.51104 0.755518 0.655128i \(-0.227385\pi\)
0.755518 + 0.655128i \(0.227385\pi\)
\(594\) −5.77875e28 1.00109e29i −0.433587 0.751133i
\(595\) 2.75352e29 + 2.77929e28i 2.02983 + 0.204883i
\(596\) 3.64464e28i 0.263979i
\(597\) −8.67108e28 1.03343e29i −0.617082 0.735449i
\(598\) 2.08910e29i 1.46082i
\(599\) 1.49836e28i 0.102952i 0.998674 + 0.0514761i \(0.0163926\pi\)
−0.998674 + 0.0514761i \(0.983607\pi\)
\(600\) −1.80740e28 2.15409e28i −0.122030 0.145437i
\(601\) 1.76300e29i 1.16969i −0.811147 0.584843i \(-0.801156\pi\)
0.811147 0.584843i \(-0.198844\pi\)
\(602\) −1.98817e28 + 1.96973e29i −0.129625 + 1.28423i
\(603\) 5.20062e27 2.94851e28i 0.0333214 0.188917i
\(604\) 1.46435e28 0.0922054
\(605\) 1.18010e29 0.730276
\(606\) −5.56370e28 6.63092e28i −0.338377 0.403284i
\(607\) 2.80398e29i 1.67607i −0.545613 0.838037i \(-0.683703\pi\)
0.545613 0.838037i \(-0.316297\pi\)
\(608\) −2.44283e29 −1.43518
\(609\) −9.80933e28 1.44151e29i −0.566445 0.832410i
\(610\) −1.02728e29 −0.583078
\(611\) 4.93518e28i 0.275341i
\(612\) −3.90458e28 + 2.21371e29i −0.214133 + 1.21404i
\(613\) 5.20652e28 0.280680 0.140340 0.990103i \(-0.455180\pi\)
0.140340 + 0.990103i \(0.455180\pi\)
\(614\) 1.47262e29 0.780411
\(615\) 1.61714e29 1.35687e29i 0.842480 0.706886i
\(616\) 3.90835e28 + 3.94493e27i 0.200169 + 0.0202042i
\(617\) 1.37863e28i 0.0694150i −0.999398 0.0347075i \(-0.988950\pi\)
0.999398 0.0347075i \(-0.0110500\pi\)
\(618\) 7.49942e28 6.29242e28i 0.371235 0.311486i
\(619\) 3.20993e29i 1.56223i 0.624390 + 0.781113i \(0.285348\pi\)
−0.624390 + 0.781113i \(0.714652\pi\)
\(620\) 1.74691e29i 0.835907i
\(621\) −2.60176e29 + 1.50185e29i −1.22407 + 0.706586i
\(622\) 3.22211e29i 1.49053i
\(623\) −2.41142e29 2.43398e28i −1.09685 0.110712i
\(624\) −1.31611e29 1.56857e29i −0.588647 0.701559i
\(625\) −2.81183e29 −1.23666
\(626\) −6.08329e29 −2.63092
\(627\) −1.34022e29 + 1.12452e29i −0.569990 + 0.478253i
\(628\) 2.66749e29i 1.11565i
\(629\) 4.82874e29 1.98611
\(630\) −4.02088e29 1.13527e29i −1.62647 0.459223i
\(631\) −7.58492e28 −0.301747 −0.150873 0.988553i \(-0.548209\pi\)
−0.150873 + 0.988553i \(0.548209\pi\)
\(632\) 1.47082e29i 0.575481i
\(633\) 5.41440e28 4.54297e28i 0.208358 0.174824i
\(634\) 2.05760e29 0.778798
\(635\) −1.40718e29 −0.523874
\(636\) −1.64913e29 1.96546e29i −0.603887 0.719723i
\(637\) −4.31255e28 + 2.11452e29i −0.155335 + 0.761635i
\(638\) 2.46463e29i 0.873243i
\(639\) 2.37629e29 + 4.19134e28i 0.828211 + 0.146081i
\(640\) 2.22539e29i 0.762985i
\(641\) 2.72204e29i 0.918089i −0.888413 0.459045i \(-0.848192\pi\)
0.888413 0.459045i \(-0.151808\pi\)
\(642\) 1.48968e29 1.24992e29i 0.494282 0.414730i
\(643\) 3.19978e28i 0.104449i −0.998635 0.0522246i \(-0.983369\pi\)
0.998635 0.0522246i \(-0.0166312\pi\)
\(644\) −3.39452e28 + 3.36305e29i −0.109013 + 1.08002i
\(645\) −2.99155e29 + 2.51007e29i −0.945190 + 0.793066i
\(646\) 7.83203e29 2.43463
\(647\) −1.36569e29 −0.417693 −0.208846 0.977948i \(-0.566971\pi\)
−0.208846 + 0.977948i \(0.566971\pi\)
\(648\) −3.50664e28 + 9.63125e28i −0.105525 + 0.289831i
\(649\) 3.58419e29i 1.06126i
\(650\) 2.18358e29 0.636178
\(651\) −1.68040e29 2.46941e29i −0.481740 0.707934i
\(652\) 1.82620e29 0.515166
\(653\) 3.54552e29i 0.984220i −0.870533 0.492110i \(-0.836226\pi\)
0.870533 0.492110i \(-0.163774\pi\)
\(654\) 3.90435e29 + 4.65328e29i 1.06655 + 1.27114i
\(655\) 3.20100e29 0.860503
\(656\) −3.85332e29 −1.01940
\(657\) −1.92102e29 3.38833e28i −0.500146 0.0882165i
\(658\) −1.84601e28 + 1.82890e29i −0.0473002 + 0.468616i
\(659\) 1.19685e28i 0.0301816i 0.999886 + 0.0150908i \(0.00480374\pi\)
−0.999886 + 0.0150908i \(0.995196\pi\)
\(660\) −1.64900e29 1.96530e29i −0.409269 0.487774i
\(661\) 9.19128e28i 0.224523i −0.993679 0.112261i \(-0.964191\pi\)
0.993679 0.112261i \(-0.0358094\pi\)
\(662\) 8.72887e29i 2.09869i
\(663\) 3.38882e29 + 4.03885e29i 0.801966 + 0.955797i
\(664\) 1.65696e29i 0.385965i
\(665\) −6.35052e28 + 6.29164e29i −0.145607 + 1.44257i
\(666\) −7.17907e29 1.26626e29i −1.62028 0.285787i
\(667\) −6.40538e29 −1.42306
\(668\) 8.11517e28 0.177478
\(669\) 4.55371e29 + 5.42719e29i 0.980372 + 1.16842i
\(670\) 1.52971e29i 0.324208i
\(671\) 1.07853e29 0.225034
\(672\) 3.44579e29 + 5.06371e29i 0.707802 + 1.04014i
\(673\) −1.38103e29 −0.279282 −0.139641 0.990202i \(-0.544595\pi\)
−0.139641 + 0.990202i \(0.544595\pi\)
\(674\) 1.28669e30i 2.56180i
\(675\) −1.56977e29 2.71942e29i −0.307714 0.533074i
\(676\) −1.57498e29 −0.303973
\(677\) 8.51714e29 1.61850 0.809250 0.587464i \(-0.199874\pi\)
0.809250 + 0.587464i \(0.199874\pi\)
\(678\) 9.81068e29 8.23170e29i 1.83564 1.54020i
\(679\) −1.77968e28 + 1.76317e29i −0.0327875 + 0.324835i
\(680\) 3.46881e29i 0.629269i
\(681\) −8.09573e28 + 6.79276e28i −0.144614 + 0.121339i
\(682\) 4.22208e29i 0.742661i
\(683\) 9.04924e29i 1.56745i −0.621106 0.783727i \(-0.713316\pi\)
0.621106 0.783727i \(-0.286684\pi\)
\(684\) −5.05822e29 8.92176e28i −0.862797 0.152181i
\(685\) 1.52744e29i 0.256574i
\(686\) 2.38910e29 7.67474e29i 0.395213 1.26958i
\(687\) 6.46617e29 + 7.70649e29i 1.05342 + 1.25548i
\(688\) 7.12826e29 1.14368
\(689\) −6.01758e29 −0.950867
\(690\) −1.17580e30 + 9.86561e29i −1.82986 + 1.53535i
\(691\) 4.48765e29i 0.687859i −0.938995 0.343930i \(-0.888242\pi\)
0.938995 0.343930i \(-0.111758\pi\)
\(692\) 4.67765e29 0.706177
\(693\) 4.22148e29 + 1.19191e29i 0.627720 + 0.177233i
\(694\) 8.22945e29 1.20530
\(695\) 8.59820e29i 1.24042i
\(696\) −1.67419e29 + 1.40474e29i −0.237908 + 0.199618i
\(697\) 9.92180e29 1.38882
\(698\) 9.34728e29 1.28885
\(699\) 3.46189e29 + 4.12594e29i 0.470222 + 0.560419i
\(700\) −3.51515e29 3.54804e28i −0.470342 0.0474744i
\(701\) 1.27363e29i 0.167882i 0.996471 + 0.0839411i \(0.0267507\pi\)
−0.996471 + 0.0839411i \(0.973249\pi\)
\(702\) −3.97916e29 6.89337e29i −0.516716 0.895142i
\(703\) 1.10334e30i 1.41150i
\(704\) 2.56039e29i 0.322695i
\(705\) −2.77765e29 + 2.33060e29i −0.344899 + 0.289389i
\(706\) 1.50446e30i 1.84048i
\(707\) 3.26818e29 + 3.29876e28i 0.393914 + 0.0397601i
\(708\) 8.06105e29 6.76366e29i 0.957288 0.803217i
\(709\) 4.06778e29 0.475962 0.237981 0.971270i \(-0.423514\pi\)
0.237981 + 0.971270i \(0.423514\pi\)
\(710\) 1.23284e30 1.42133
\(711\) −2.85290e29 + 1.61746e30i −0.324083 + 1.83740i
\(712\) 3.03784e29i 0.340036i
\(713\) −1.09728e30 −1.21026
\(714\) −1.10477e30 1.62349e30i −1.20071 1.76449i
\(715\) −6.01709e29 −0.644426
\(716\) 2.66110e29i 0.280850i
\(717\) −5.24020e29 6.24536e29i −0.545000 0.649541i
\(718\) −5.39203e29 −0.552645
\(719\) −1.44590e30 −1.46044 −0.730221 0.683211i \(-0.760583\pi\)
−0.730221 + 0.683211i \(0.760583\pi\)
\(720\) −2.61307e29 + 1.48149e30i −0.260112 + 1.47471i
\(721\) −3.73082e28 + 3.69623e29i −0.0366003 + 0.362609i
\(722\) 4.14316e29i 0.400582i
\(723\) −7.55690e29 9.00644e29i −0.720098 0.858225i
\(724\) 8.41384e29i 0.790205i
\(725\) 6.69507e29i 0.619735i
\(726\) −5.38227e29 6.41468e29i −0.491056 0.585249i
\(727\) 1.70184e30i 1.53040i −0.643790 0.765202i \(-0.722639\pi\)
0.643790 0.765202i \(-0.277361\pi\)
\(728\) 2.69123e29 + 2.71642e28i 0.238546 + 0.0240778i
\(729\) −5.72438e29 + 9.91128e29i −0.500137 + 0.865946i
\(730\) −9.96642e29 −0.858320
\(731\) −1.83543e30 −1.55814
\(732\) 2.03528e29 + 2.42569e29i 0.170317 + 0.202987i
\(733\) 7.82447e29i 0.645451i 0.946493 + 0.322726i \(0.104599\pi\)
−0.946493 + 0.322726i \(0.895401\pi\)
\(734\) 1.17287e30 0.953767
\(735\) 1.39376e30 7.55843e29i 1.11731 0.605919i
\(736\) 2.25006e30 1.77819
\(737\) 1.60603e29i 0.125125i
\(738\) −1.47511e30 2.60182e29i −1.13301 0.199842i
\(739\) −1.72597e30 −1.30697 −0.653486 0.756939i \(-0.726694\pi\)
−0.653486 + 0.756939i \(0.726694\pi\)
\(740\) −1.61794e30 −1.20790
\(741\) −9.22856e29 + 7.74327e29i −0.679271 + 0.569945i
\(742\) 2.23002e30 + 2.25089e29i 1.61833 + 0.163347i
\(743\) 1.66446e30i 1.19094i 0.803377 + 0.595470i \(0.203034\pi\)
−0.803377 + 0.595470i \(0.796966\pi\)
\(744\) −2.86800e29 + 2.40641e29i −0.202332 + 0.169767i
\(745\) 6.28039e29i 0.436864i
\(746\) 1.44569e30i 0.991559i
\(747\) 3.21395e29 1.82216e30i 0.217357 1.23231i
\(748\) 1.20579e30i 0.804091i
\(749\) −7.41089e28 + 7.34217e29i −0.0487316 + 0.482798i
\(750\) 6.44139e29 + 7.67696e29i 0.417673 + 0.497790i
\(751\) 1.15511e30 0.738590 0.369295 0.929312i \(-0.379599\pi\)
0.369295 + 0.929312i \(0.379599\pi\)
\(752\) 6.61858e29 0.417328
\(753\) 1.55352e29 1.30348e29i 0.0965980 0.0810510i
\(754\) 1.69711e30i 1.04066i
\(755\) −2.52334e29 −0.152592
\(756\) 5.28561e29 + 1.17436e30i 0.315222 + 0.700361i
\(757\) −1.75730e30 −1.03357 −0.516783 0.856116i \(-0.672871\pi\)
−0.516783 + 0.856116i \(0.672871\pi\)
\(758\) 3.38713e30i 1.96474i
\(759\) 1.23446e30 1.03578e30i 0.706219 0.592557i
\(760\) 7.92604e29 0.447212
\(761\) −2.62418e30