Properties

Label 21.38.g.a.17.1
Level $21$
Weight $38$
Character 21.17
Analytic conductor $182.099$
Analytic rank $0$
Dimension $2$
CM discriminant -3
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 38 \)
Character orbit: \([\chi]\) \(=\) 21.g (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(182.099480062\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{6}]$

Embedding invariants

Embedding label 17.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 21.17
Dual form 21.38.g.a.5.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-5.81131e8 - 3.35516e8i) q^{3} +(-6.87195e10 + 1.19026e11i) q^{4} +(2.94136e15 - 3.14809e15i) q^{7} +(2.25142e17 + 3.89957e17i) q^{9} +O(q^{10})\) \(q+(-5.81131e8 - 3.35516e8i) q^{3} +(-6.87195e10 + 1.19026e11i) q^{4} +(2.94136e15 - 3.14809e15i) q^{7} +(2.25142e17 + 3.89957e17i) q^{9} +(7.98700e19 - 4.61130e19i) q^{12} +3.52663e20i q^{13} +(-9.44473e21 - 1.63588e22i) q^{16} +(7.84496e23 - 4.52929e23i) q^{19} +(-2.76555e24 + 8.42580e23i) q^{21} +(3.63798e25 - 6.30116e25i) q^{25} -3.02155e26i q^{27} +(1.72575e26 + 5.66433e26i) q^{28} +(6.74022e27 + 3.89147e27i) q^{31} -6.18865e28 q^{36} +(-9.92707e27 - 1.71942e28i) q^{37} +(1.18324e29 - 2.04943e29i) q^{39} -3.12847e30 q^{43} +1.26754e31i q^{48} +(-1.25889e30 - 1.85194e31i) q^{49} +(-4.19760e31 - 2.42348e31i) q^{52} -6.07860e32 q^{57} +(-1.77999e33 + 1.02768e33i) q^{61} +(1.88985e33 + 4.38238e32i) q^{63} +2.59615e33 q^{64} +(-5.13785e33 + 8.89901e33i) q^{67} +(5.10751e34 + 2.94882e34i) q^{73} +(-4.22828e34 + 2.44120e34i) q^{75} +1.24500e35i q^{76} +(-1.11822e35 - 1.93681e35i) q^{79} +(-1.01378e35 + 1.75591e35i) q^{81} +(8.97587e34 - 3.87073e35i) q^{84} +(1.11022e36 + 1.03731e36i) q^{91} +(-2.61130e36 - 4.52290e36i) q^{93} -6.37793e36i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 1162261467q^{3} - 137438953472q^{4} + 5882725491086809q^{7} + 450283905890997363q^{9} + O(q^{10}) \) \( 2q - 1162261467q^{3} - 137438953472q^{4} + 5882725491086809q^{7} + 450283905890997363q^{9} + \)\(15\!\cdots\!24\)\(q^{12} - \)\(18\!\cdots\!84\)\(q^{16} + \)\(15\!\cdots\!11\)\(q^{19} - \)\(55\!\cdots\!86\)\(q^{21} + \)\(72\!\cdots\!25\)\(q^{25} + \)\(34\!\cdots\!32\)\(q^{28} + \)\(13\!\cdots\!55\)\(q^{31} - \)\(12\!\cdots\!72\)\(q^{36} - \)\(19\!\cdots\!09\)\(q^{37} + \)\(23\!\cdots\!63\)\(q^{39} - \)\(62\!\cdots\!30\)\(q^{43} - \)\(25\!\cdots\!33\)\(q^{49} - \)\(83\!\cdots\!24\)\(q^{52} - \)\(12\!\cdots\!58\)\(q^{57} - \)\(35\!\cdots\!48\)\(q^{61} + \)\(37\!\cdots\!95\)\(q^{63} + \)\(51\!\cdots\!96\)\(q^{64} - \)\(10\!\cdots\!39\)\(q^{67} + \)\(10\!\cdots\!77\)\(q^{73} - \)\(84\!\cdots\!75\)\(q^{75} - \)\(22\!\cdots\!67\)\(q^{79} - \)\(20\!\cdots\!69\)\(q^{81} + \)\(17\!\cdots\!24\)\(q^{84} + \)\(22\!\cdots\!69\)\(q^{91} - \)\(52\!\cdots\!95\)\(q^{93} + O(q^{100}) \)

Character values

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

\(n\) \(8\) \(10\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(3\) −5.81131e8 3.35516e8i −0.866025 0.500000i
\(4\) −6.87195e10 + 1.19026e11i −0.500000 + 0.866025i
\(5\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(6\) 0 0
\(7\) 2.94136e15 3.14809e15i 0.682708 0.730692i
\(8\) 0 0
\(9\) 2.25142e17 + 3.89957e17i 0.500000 + 0.866025i
\(10\) 0 0
\(11\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(12\) 7.98700e19 4.61130e19i 0.866025 0.500000i
\(13\) 3.52663e20i 0.869777i 0.900484 + 0.434889i \(0.143212\pi\)
−0.900484 + 0.434889i \(0.856788\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −9.44473e21 1.63588e22i −0.500000 0.866025i
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) 0 0
\(19\) 7.84496e23 4.52929e23i 1.72842 0.997904i 0.831851 0.555000i \(-0.187282\pi\)
0.896569 0.442904i \(-0.146052\pi\)
\(20\) 0 0
\(21\) −2.76555e24 + 8.42580e23i −0.956588 + 0.291444i
\(22\) 0 0
\(23\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(24\) 0 0
\(25\) 3.63798e25 6.30116e25i 0.500000 0.866025i
\(26\) 0 0
\(27\) 3.02155e26i 1.00000i
\(28\) 1.72575e26 + 5.66433e26i 0.291444 + 0.956588i
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 6.74022e27 + 3.89147e27i 1.73174 + 0.999820i 0.875348 + 0.483493i \(0.160632\pi\)
0.856392 + 0.516327i \(0.172701\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −6.18865e28 −1.00000
\(37\) −9.92707e27 1.71942e28i −0.0966250 0.167359i 0.813661 0.581340i \(-0.197471\pi\)
−0.910286 + 0.413981i \(0.864138\pi\)
\(38\) 0 0
\(39\) 1.18324e29 2.04943e29i 0.434889 0.753249i
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) −3.12847e30 −1.88871 −0.944355 0.328927i \(-0.893313\pi\)
−0.944355 + 0.328927i \(0.893313\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 1.26754e31i 1.00000i
\(49\) −1.25889e30 1.85194e31i −0.0678202 0.997698i
\(50\) 0 0
\(51\) 0 0
\(52\) −4.19760e31 2.42348e31i −0.753249 0.434889i
\(53\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −6.07860e32 −1.99581
\(58\) 0 0
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 0 0
\(61\) −1.77999e33 + 1.02768e33i −1.66654 + 0.962178i −0.697060 + 0.717012i \(0.745509\pi\)
−0.969481 + 0.245166i \(0.921158\pi\)
\(62\) 0 0
\(63\) 1.88985e33 + 4.38238e32i 0.974151 + 0.225897i
\(64\) 2.59615e33 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) −5.13785e33 + 8.89901e33i −0.848003 + 1.46878i 0.0349851 + 0.999388i \(0.488862\pi\)
−0.882988 + 0.469396i \(0.844472\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 5.10751e34 + 2.94882e34i 1.72479 + 0.995807i 0.908132 + 0.418684i \(0.137509\pi\)
0.816657 + 0.577123i \(0.195825\pi\)
\(74\) 0 0
\(75\) −4.22828e34 + 2.44120e34i −0.866025 + 0.500000i
\(76\) 1.24500e35i 1.99581i
\(77\) 0 0
\(78\) 0 0
\(79\) −1.11822e35 1.93681e35i −0.875842 1.51700i −0.855863 0.517202i \(-0.826974\pi\)
−0.0199782 0.999800i \(-0.506360\pi\)
\(80\) 0 0
\(81\) −1.01378e35 + 1.75591e35i −0.500000 + 0.866025i
\(82\) 0 0
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 8.97587e34 3.87073e35i 0.225897 0.974151i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(90\) 0 0
\(91\) 1.11022e36 + 1.03731e36i 0.635539 + 0.593804i
\(92\) 0 0
\(93\) −2.61130e36 4.52290e36i −0.999820 1.73174i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 6.37793e36i 1.12048i −0.828332 0.560238i \(-0.810710\pi\)
0.828332 0.560238i \(-0.189290\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 5.00000e36 + 8.66025e36i 0.500000 + 0.866025i
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) 0 0
\(103\) 2.68000e37 1.54730e37i 1.55112 0.895540i 0.553070 0.833135i \(-0.313456\pi\)
0.998051 0.0624056i \(-0.0198772\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(108\) 3.59642e37 + 2.07639e37i 0.866025 + 0.500000i
\(109\) −2.93868e37 + 5.08993e37i −0.596707 + 1.03353i 0.396596 + 0.917993i \(0.370191\pi\)
−0.993304 + 0.115534i \(0.963142\pi\)
\(110\) 0 0
\(111\) 1.33228e37i 0.193250i
\(112\) −7.92793e37 1.83841e37i −0.974151 0.225897i
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.37524e38 + 7.93993e37i −0.753249 + 0.434889i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −1.70020e38 2.94483e38i −0.500000 0.866025i
\(122\) 0 0
\(123\) 0 0
\(124\) −9.26368e38 + 5.34839e38i −1.73174 + 0.999820i
\(125\) 0 0
\(126\) 0 0
\(127\) 9.33146e38 1.12094 0.560468 0.828176i \(-0.310621\pi\)
0.560468 + 0.828176i \(0.310621\pi\)
\(128\) 0 0
\(129\) 1.81805e39 + 1.04965e39i 1.63567 + 0.944355i
\(130\) 0 0
\(131\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(132\) 0 0
\(133\) 8.81624e38 3.80190e39i 0.450846 1.94422i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(138\) 0 0
\(139\) 1.37950e39i 0.311851i −0.987769 0.155925i \(-0.950164\pi\)
0.987769 0.155925i \(-0.0498360\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 4.25281e39 7.36609e39i 0.500000 0.866025i
\(145\) 0 0
\(146\) 0 0
\(147\) −5.48197e39 + 1.11846e40i −0.440115 + 0.897942i
\(148\) 2.72873e39 0.193250
\(149\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(150\) 0 0
\(151\) 4.75071e39 8.22847e39i 0.232105 0.402018i −0.726322 0.687354i \(-0.758772\pi\)
0.958427 + 0.285336i \(0.0921053\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 1.62623e40 + 2.81672e40i 0.434889 + 0.753249i
\(157\) −7.27708e40 4.20142e40i −1.72907 0.998281i −0.893844 0.448378i \(-0.852002\pi\)
−0.835229 0.549902i \(-0.814665\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 5.89716e40 + 1.02142e41i 0.700120 + 1.21264i 0.968424 + 0.249309i \(0.0802036\pi\)
−0.268304 + 0.963334i \(0.586463\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) 4.00295e40 0.243487
\(170\) 0 0
\(171\) 3.53246e41 + 2.03947e41i 1.72842 + 0.997904i
\(172\) 2.14987e41 3.72368e41i 0.944355 1.63567i
\(173\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(174\) 0 0
\(175\) −9.13605e40 2.99867e41i −0.291444 0.956588i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(180\) 0 0
\(181\) 1.11293e42i 1.90289i −0.307823 0.951444i \(-0.599601\pi\)
0.307823 0.951444i \(-0.400399\pi\)
\(182\) 0 0
\(183\) 1.37921e42 1.92436
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −9.51212e41 8.88747e41i −0.730692 0.682708i
\(190\) 0 0
\(191\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(192\) −1.50870e42 8.71049e41i −0.866025 0.500000i
\(193\) 1.03691e42 1.79597e42i 0.540666 0.936461i −0.458200 0.888849i \(-0.651506\pi\)
0.998866 0.0476117i \(-0.0151610\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 2.29079e42 + 1.12280e42i 0.897942 + 0.440115i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 5.77964e42 + 3.33688e42i 1.71048 + 0.987549i 0.933899 + 0.357538i \(0.116384\pi\)
0.776586 + 0.630011i \(0.216950\pi\)
\(200\) 0 0
\(201\) 5.97152e42 3.44766e42i 1.46878 0.848003i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 5.76913e42 3.33081e42i 0.753249 0.434889i
\(209\) 0 0
\(210\) 0 0
\(211\) 7.97186e42 0.798609 0.399304 0.916818i \(-0.369252\pi\)
0.399304 + 0.916818i \(0.369252\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 3.20761e43 9.77263e42i 1.91283 0.582782i
\(218\) 0 0
\(219\) −1.97875e43 3.42730e43i −0.995807 1.72479i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 3.05912e43i 1.10143i −0.834693 0.550715i \(-0.814355\pi\)
0.834693 0.550715i \(-0.185645\pi\)
\(224\) 0 0
\(225\) 3.27625e43 1.00000
\(226\) 0 0
\(227\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(228\) 4.17718e43 7.23509e43i 0.997904 1.72842i
\(229\) 5.53910e43 3.19800e43i 1.22035 0.704567i 0.255354 0.966848i \(-0.417808\pi\)
0.964992 + 0.262281i \(0.0844747\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 1.50072e44i 1.75168i
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) −5.91597e42 3.41559e42i −0.0506653 0.0292516i 0.474453 0.880281i \(-0.342646\pi\)
−0.525119 + 0.851029i \(0.675979\pi\)
\(242\) 0 0
\(243\) 1.17828e44 6.80277e43i 0.866025 0.500000i
\(244\) 2.82486e44i 1.92436i
\(245\) 0 0
\(246\) 0 0
\(247\) 1.59731e44 + 2.76663e44i 0.867954 + 1.50334i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) −1.82031e44 + 1.94825e44i −0.682708 + 0.730692i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −1.78406e44 + 3.09008e44i −0.500000 + 0.866025i
\(257\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(258\) 0 0
\(259\) −8.33281e43 1.93230e43i −0.188255 0.0436545i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −7.06140e44 1.22307e45i −0.848003 1.46878i
\(269\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(270\) 0 0
\(271\) −1.76690e45 + 1.02012e45i −1.72695 + 0.997055i −0.825127 + 0.564947i \(0.808897\pi\)
−0.901822 + 0.432108i \(0.857770\pi\)
\(272\) 0 0
\(273\) −2.97147e44 9.75308e44i −0.253491 0.832019i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 5.15841e44 8.93463e44i 0.336233 0.582372i −0.647488 0.762076i \(-0.724180\pi\)
0.983721 + 0.179703i \(0.0575138\pi\)
\(278\) 0 0
\(279\) 3.50453e45i 1.99964i
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 3.91834e44 + 2.26226e44i 0.171812 + 0.0991957i 0.583440 0.812156i \(-0.301706\pi\)
−0.411628 + 0.911352i \(0.635040\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 1.68105e45 + 2.91166e45i 0.500000 + 0.866025i
\(290\) 0 0
\(291\) −2.13990e45 + 3.70641e45i −0.560238 + 0.970361i
\(292\) −7.01970e45 + 4.05283e45i −1.72479 + 0.995807i
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 6.71032e45i 1.00000i
\(301\) −9.20196e45 + 9.84872e45i −1.28944 + 1.38006i
\(302\) 0 0
\(303\) 0 0
\(304\) −1.48187e46 8.55559e45i −1.72842 0.997904i
\(305\) 0 0
\(306\) 0 0
\(307\) 1.98787e46i 1.93343i 0.255859 + 0.966714i \(0.417642\pi\)
−0.255859 + 0.966714i \(0.582358\pi\)
\(308\) 0 0
\(309\) −2.07657e46 −1.79108
\(310\) 0 0
\(311\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(312\) 0 0
\(313\) 1.87985e46 1.08533e46i 1.27807 0.737892i 0.301574 0.953443i \(-0.402488\pi\)
0.976493 + 0.215551i \(0.0691547\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 3.07374e46 1.75168
\(317\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −1.39333e46 2.41331e46i −0.500000 0.866025i
\(325\) 2.22219e46 + 1.28298e46i 0.753249 + 0.434889i
\(326\) 0 0
\(327\) 3.41551e46 1.97194e46i 1.03353 0.596707i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −3.51969e46 6.09628e46i −0.850524 1.47315i −0.880737 0.473607i \(-0.842952\pi\)
0.0302129 0.999543i \(-0.490381\pi\)
\(332\) 0 0
\(333\) 4.47000e45 7.74227e45i 0.0966250 0.167359i
\(334\) 0 0
\(335\) 0 0
\(336\) 3.99035e46 + 3.72831e46i 0.730692 + 0.682708i
\(337\) 1.08707e47 1.88410 0.942048 0.335479i \(-0.108898\pi\)
0.942048 + 0.335479i \(0.108898\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −6.20036e46 5.05091e46i −0.775311 0.631580i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(348\) 0 0
\(349\) 1.62094e46i 0.147061i 0.997293 + 0.0735305i \(0.0234266\pi\)
−0.997293 + 0.0735305i \(0.976573\pi\)
\(350\) 0 0
\(351\) 1.06559e47 0.869777
\(352\) 0 0
\(353\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(360\) 0 0
\(361\) 3.07286e47 5.32234e47i 1.49162 2.58357i
\(362\) 0 0
\(363\) 2.28177e47i 1.00000i
\(364\) −1.99760e47 + 6.08609e46i −0.832019 + 0.253491i
\(365\) 0 0
\(366\) 0 0
\(367\) −9.83590e46 5.67876e46i −0.351959 0.203204i 0.313589 0.949559i \(-0.398469\pi\)
−0.665548 + 0.746355i \(0.731802\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 7.17788e47 1.99964
\(373\) 5.04704e46 + 8.74173e46i 0.133790 + 0.231731i 0.925135 0.379639i \(-0.123952\pi\)
−0.791345 + 0.611370i \(0.790619\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 6.68943e47 1.31997 0.659985 0.751279i \(-0.270563\pi\)
0.659985 + 0.751279i \(0.270563\pi\)
\(380\) 0 0
\(381\) −5.42280e47 3.13086e47i −0.970759 0.560468i
\(382\) 0 0
\(383\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −7.04350e47 1.21997e48i −0.944355 1.63567i
\(388\) 7.59137e47 + 4.38288e47i 0.970361 + 0.560238i
\(389\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −8.15997e47 + 4.71116e47i −0.682440 + 0.394007i −0.800774 0.598967i \(-0.795578\pi\)
0.118334 + 0.992974i \(0.462245\pi\)
\(398\) 0 0
\(399\) −1.78794e48 + 1.91360e48i −1.36255 + 1.45832i
\(400\) −1.37439e48 −1.00000
\(401\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(402\) 0 0
\(403\) −1.37238e48 + 2.37703e48i −0.869621 + 1.50623i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −3.55113e48 2.05025e48i −1.71193 0.988382i −0.931959 0.362564i \(-0.881901\pi\)
−0.779969 0.625818i \(-0.784765\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 4.25318e48i 1.79108i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −4.62843e47 + 8.01668e47i −0.155925 + 0.270071i
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) 6.10362e48 1.72333 0.861666 0.507477i \(-0.169422\pi\)
0.861666 + 0.507477i \(0.169422\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −2.00037e48 + 8.62636e48i −0.434705 + 1.87461i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) −4.94288e48 + 2.85377e48i −0.866025 + 0.500000i
\(433\) 8.86530e48i 1.48822i −0.668057 0.744110i \(-0.732874\pi\)
0.668057 0.744110i \(-0.267126\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −4.03888e48 6.99555e48i −0.596707 1.03353i
\(437\) 0 0
\(438\) 0 0
\(439\) −4.83459e48 + 2.79125e48i −0.629167 + 0.363250i −0.780429 0.625244i \(-0.784999\pi\)
0.151263 + 0.988494i \(0.451666\pi\)
\(440\) 0 0
\(441\) 6.93834e48 4.66040e48i 0.830121 0.557583i
\(442\) 0 0
\(443\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(444\) −1.58575e48 9.15534e47i −0.167359 0.0966250i
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 7.63621e48 8.17292e48i 0.682708 0.730692i
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −5.52156e48 + 3.18788e48i −0.402018 + 0.232105i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −5.65146e48 9.78862e48i −0.349713 0.605720i 0.636486 0.771288i \(-0.280387\pi\)
−0.986198 + 0.165569i \(0.947054\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 3.71811e49 1.80748 0.903741 0.428079i \(-0.140810\pi\)
0.903741 + 0.428079i \(0.140810\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(468\) 2.18251e49i 0.869777i
\(469\) 1.29027e49 + 4.23496e49i 0.494290 + 1.62238i
\(470\) 0 0
\(471\) 2.81929e49 + 4.88315e49i 0.998281 + 1.72907i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 6.59099e49i 1.99581i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(480\) 0 0
\(481\) 6.06376e48 3.50091e48i 0.145565 0.0840422i
\(482\) 0 0
\(483\) 0 0
\(484\) 4.67347e49 1.00000
\(485\) 0 0
\(486\) 0 0
\(487\) 1.49323e49 2.58636e49i 0.284998 0.493631i −0.687611 0.726080i \(-0.741340\pi\)
0.972609 + 0.232449i \(0.0746737\pi\)
\(488\) 0 0
\(489\) 7.91437e49i 1.40024i
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 1.47015e50i 1.99964i
\(497\) 0 0
\(498\) 0 0
\(499\) 6.04884e49 + 1.04769e50i 0.735889 + 1.27460i 0.954332 + 0.298747i \(0.0965688\pi\)
−0.218443 + 0.975850i \(0.570098\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −2.32624e49 1.34306e49i −0.210866 0.121744i
\(508\) −6.41253e49 + 1.11068e50i −0.560468 + 0.970759i
\(509\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(510\) 0 0
\(511\) 2.43062e50 7.40536e49i 1.90515 0.580443i
\(512\) 0 0
\(513\) −1.36855e50 2.37039e50i −0.997904 1.72842i
\(514\) 0 0
\(515\) 0 0
\(516\) −2.49871e50 + 1.44263e50i −1.63567 + 0.944355i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(522\) 0 0
\(523\) −2.30288e50 + 1.32957e50i −1.17487 + 0.678311i −0.954822 0.297178i \(-0.903954\pi\)
−0.220047 + 0.975489i \(0.570621\pi\)
\(524\) 0 0
\(525\) −4.75178e49 + 2.04915e50i −0.225897 + 0.974151i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −1.21032e50 + 2.09633e50i −0.500000 + 0.866025i
\(530\) 0 0
\(531\) 0 0
\(532\) 3.91938e50 + 3.66200e50i 1.45832 + 1.36255i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 8.30237e49 + 1.43801e50i 0.226492 + 0.392295i 0.956766 0.290859i \(-0.0939410\pi\)
−0.730274 + 0.683154i \(0.760608\pi\)
\(542\) 0 0
\(543\) −3.73405e50 + 6.46756e50i −0.951444 + 1.64795i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −2.27774e50 −0.506686 −0.253343 0.967377i \(-0.581530\pi\)
−0.253343 + 0.967377i \(0.581530\pi\)
\(548\) 0 0
\(549\) −8.01502e50 4.62747e50i −1.66654 0.962178i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −9.38635e50 2.17661e50i −1.70640 0.395699i
\(554\) 0 0
\(555\) 0 0
\(556\) 1.64195e50 + 9.47983e49i 0.270071 + 0.155925i
\(557\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(558\) 0 0
\(559\) 1.10330e51i 1.64276i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 2.54590e50 + 8.35625e50i 0.291444 + 0.956588i
\(568\) 0 0
\(569\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(570\) 0 0
\(571\) 8.27588e50 1.43343e51i 0.831853 1.44081i −0.0647150 0.997904i \(-0.520614\pi\)
0.896568 0.442907i \(-0.146053\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 5.84502e50 + 1.01239e51i 0.500000 + 0.866025i
\(577\) 7.23872e50 + 4.17928e50i 0.599666 + 0.346217i 0.768910 0.639357i \(-0.220799\pi\)
−0.169244 + 0.985574i \(0.554133\pi\)
\(578\) 0 0
\(579\) −1.20516e51 + 6.95797e50i −0.936461 + 0.540666i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) −9.54531e50 1.42109e51i −0.557583 0.830121i
\(589\) 7.05023e51 3.99090
\(590\) 0 0
\(591\) 0 0
\(592\) −1.87517e50 + 3.24789e50i −0.0966250 + 0.167359i
\(593\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −2.23915e51 3.87833e51i −0.987549 1.71048i
\(598\) 0 0
\(599\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(600\) 0 0
\(601\) 4.95401e51i 1.93099i 0.260428 + 0.965493i \(0.416136\pi\)
−0.260428 + 0.965493i \(0.583864\pi\)
\(602\) 0 0
\(603\) −4.62698e51 −1.69601
\(604\) 6.52932e50 + 1.13091e51i 0.232105 + 0.402018i
\(605\) 0 0
\(606\) 0 0
\(607\) 3.70756e51 2.14056e51i 1.20253 0.694283i 0.241416 0.970422i \(-0.422388\pi\)
0.961118 + 0.276138i \(0.0890548\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 3.49869e51 6.05991e51i 0.945991 1.63850i 0.192237 0.981349i \(-0.438426\pi\)
0.753754 0.657156i \(-0.228241\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 1.44378e51 + 8.33567e50i 0.326005 + 0.188219i 0.654066 0.756437i \(-0.273062\pi\)
−0.328061 + 0.944657i \(0.606395\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) −4.47016e51 −0.869777
\(625\) −2.64698e51 4.58470e51i −0.500000 0.866025i
\(626\) 0 0
\(627\) 0 0
\(628\) 1.00015e52 5.77439e51i 1.72907 0.998281i
\(629\) 0 0
\(630\) 0 0
\(631\) 1.23496e52 1.95483 0.977417 0.211318i \(-0.0677756\pi\)
0.977417 + 0.211318i \(0.0677756\pi\)
\(632\) 0 0
\(633\) −4.63269e51 2.67469e51i −0.691615 0.399304i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 6.53110e51 4.43963e50i 0.867775 0.0589885i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(642\) 0 0
\(643\) 7.15200e51i 0.798959i 0.916742 + 0.399479i \(0.130809\pi\)
−0.916742 + 0.399479i \(0.869191\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −2.19193e52 5.08288e51i −1.94795 0.451712i
\(652\) −1.62100e52 −1.40024
\(653\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 2.65561e52i 1.99161i
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 2.37929e52 + 1.37369e52i 1.59485 + 0.920789i 0.992457 + 0.122592i \(0.0391207\pi\)
0.602397 + 0.798197i \(0.294213\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −1.02638e52 + 1.77775e52i −0.550715 + 0.953866i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −3.71216e52 −1.78381 −0.891903 0.452227i \(-0.850630\pi\)
−0.891903 + 0.452227i \(0.850630\pi\)
\(674\) 0 0
\(675\) −1.90393e52 1.09923e52i −0.866025 0.500000i
\(676\) −2.75081e51 + 4.76454e51i −0.121744 + 0.210866i
\(677\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(678\) 0 0
\(679\) −2.00783e52 1.87598e52i −0.818722 0.764958i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(684\) −4.85498e52 + 2.80302e52i −1.72842 + 0.997904i
\(685\) 0 0
\(686\) 0 0
\(687\) −4.29192e52 −1.40913
\(688\) 2.95476e52 + 5.11779e52i 0.944355 + 1.63567i
\(689\) 0 0
\(690\) 0 0
\(691\) 5.37229e52 3.10169e52i 1.58422 0.914650i 0.589987 0.807413i \(-0.299133\pi\)
0.994233 0.107237i \(-0.0342005\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 4.19701e52 + 9.73247e51i 0.974151 + 0.225897i
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) −1.55755e52 8.99252e51i −0.334017 0.192845i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 2.68621e51 + 4.65264e51i 0.0492248 + 0.0852598i 0.889588 0.456764i \(-0.150992\pi\)
−0.840363 + 0.542024i \(0.817658\pi\)
\(710\) 0 0
\(711\) 5.03516e52 8.72115e52i 0.875842 1.51700i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(720\) 0 0
\(721\) 3.01181e52 1.29880e53i 0.404599 1.74478i
\(722\) 0 0
\(723\) 2.29197e51 + 3.96981e51i 0.0292516 + 0.0506653i
\(724\) 1.32467e53 + 7.64798e52i 1.64795 + 0.951444i
\(725\) 0 0
\(726\) 0 0
\(727\) 3.95008e52i 0.455218i 0.973753 + 0.227609i \(0.0730909\pi\)
−0.973753 + 0.227609i \(0.926909\pi\)
\(728\) 0 0
\(729\) −9.12976e52 −1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) −9.47786e52 + 1.64161e53i −0.962178 + 1.66654i
\(733\) −1.47204e52 + 8.49885e51i −0.145713 + 0.0841272i −0.571084 0.820892i \(-0.693477\pi\)
0.425371 + 0.905019i \(0.360144\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 5.28868e52 9.16026e52i 0.450220 0.779805i −0.548179 0.836361i \(-0.684679\pi\)
0.998399 + 0.0565563i \(0.0180121\pi\)
\(740\) 0 0
\(741\) 2.14370e53i 1.73591i
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −2.30559e52 3.99340e52i −0.145695 0.252350i 0.783937 0.620840i \(-0.213208\pi\)
−0.929632 + 0.368490i \(0.879875\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 1.71150e53 5.21444e52i 0.956588 0.291444i
\(757\) 2.19345e53 1.19634 0.598169 0.801370i \(-0.295895\pi\)
0.598169 + 0.801370i \(0.295895\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(762\) 0 0
\(763\) 7.37989e52 + 2.42226e53i 0.347813 + 1.14161i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 2.07354e53 1.19716e53i 0.866025 0.500000i
\(769\) 3.55605e53i 1.44988i −0.688814 0.724938i \(-0.741868\pi\)
0.688814 0.724938i \(-0.258132\pi\)
\(770\) 0 0
\(771\) 0 0