Properties

Label 21.30.g.a.17.1
Level $21$
Weight $30$
Character 21.17
Analytic conductor $111.884$
Analytic rank $0$
Dimension $2$
CM discriminant -3
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 30 \)
Character orbit: \([\chi]\) \(=\) 21.g (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(111.883889004\)
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 21.30.g.a.5.1

$q$-expansion

\(f(q)\) \(=\) \(q+(7.17445e6 + 4.14217e6i) q^{3} +(-2.68435e8 + 4.64944e8i) q^{4} +(-1.24856e12 + 1.28880e12i) q^{7} +(3.43152e13 + 5.94357e13i) q^{9} +O(q^{10})\) \(q+(7.17445e6 + 4.14217e6i) q^{3} +(-2.68435e8 + 4.64944e8i) q^{4} +(-1.24856e12 + 1.28880e12i) q^{7} +(3.43152e13 + 5.94357e13i) q^{9} +(-3.85176e15 + 2.22381e15i) q^{12} -1.93779e16i q^{13} +(-1.44115e17 - 2.49615e17i) q^{16} +(-1.96231e18 + 1.13294e18i) q^{19} +(-1.42962e19 + 4.07465e18i) q^{21} +(9.31323e19 - 1.61310e20i) q^{25} +5.68558e20i q^{27} +(-2.64060e20 - 9.26470e20i) q^{28} +(-4.74078e21 - 2.73709e21i) q^{31} -3.68457e22 q^{36} +(-3.75709e22 - 6.50747e22i) q^{37} +(8.02665e22 - 1.39026e23i) q^{39} +9.11042e23 q^{43} -2.38780e24i q^{48} +(-1.02088e23 - 3.21829e24i) q^{49} +(9.00963e24 + 5.20171e24i) q^{52} -1.87713e25 q^{57} +(-9.20660e25 + 5.31543e25i) q^{61} +(-1.19445e26 - 2.99838e25i) q^{63} +1.54743e26 q^{64} +(-1.75561e26 + 3.04081e26i) q^{67} +(1.71067e27 + 9.87658e26i) q^{73} +(1.33635e27 - 7.71540e26i) q^{75} -1.21648e27i q^{76} +(-3.19532e27 - 5.53446e27i) q^{79} +(-2.35506e27 + 4.07909e27i) q^{81} +(1.94312e27 - 7.74070e27i) q^{84} +(2.49742e28 + 2.41945e28i) q^{91} +(-2.26750e28 - 3.92742e28i) q^{93} +7.63732e28i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 14348907q^{3} - 536870912q^{4} - 2497125299549q^{7} + 68630377364883q^{9} + O(q^{10}) \) \( 2q + 14348907q^{3} - 536870912q^{4} - 2497125299549q^{7} + 68630377364883q^{9} - 7703510787293184q^{12} - 288230376151711744q^{16} - 3924610471000543239q^{19} - 28592346676653918486q^{21} + \)\(18\!\cdots\!25\)\(q^{25} - \)\(52\!\cdots\!52\)\(q^{28} - \)\(94\!\cdots\!35\)\(q^{31} - \)\(73\!\cdots\!92\)\(q^{36} - \)\(75\!\cdots\!61\)\(q^{37} + \)\(16\!\cdots\!73\)\(q^{39} + \)\(18\!\cdots\!90\)\(q^{43} - \)\(20\!\cdots\!13\)\(q^{49} + \)\(18\!\cdots\!04\)\(q^{52} - \)\(37\!\cdots\!82\)\(q^{57} - \)\(18\!\cdots\!08\)\(q^{61} - \)\(23\!\cdots\!35\)\(q^{63} + \)\(30\!\cdots\!56\)\(q^{64} - \)\(35\!\cdots\!81\)\(q^{67} + \)\(34\!\cdots\!93\)\(q^{73} + \)\(26\!\cdots\!75\)\(q^{75} - \)\(63\!\cdots\!97\)\(q^{79} - \)\(47\!\cdots\!89\)\(q^{81} + \)\(38\!\cdots\!84\)\(q^{84} + \)\(49\!\cdots\!99\)\(q^{91} - \)\(45\!\cdots\!15\)\(q^{93} + O(q^{100}) \)

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 \(0.333333\pi\)
\(3\) 7.17445e6 + 4.14217e6i 0.866025 + 0.500000i
\(4\) −2.68435e8 + 4.64944e8i −0.500000 + 0.866025i
\(5\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(6\) 0 0
\(7\) −1.24856e12 + 1.28880e12i −0.695807 + 0.718229i
\(8\) 0 0
\(9\) 3.43152e13 + 5.94357e13i 0.500000 + 0.866025i
\(10\) 0 0
\(11\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(12\) −3.85176e15 + 2.22381e15i −0.866025 + 0.500000i
\(13\) 1.93779e16i 1.36498i −0.730893 0.682492i \(-0.760896\pi\)
0.730893 0.682492i \(-0.239104\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −1.44115e17 2.49615e17i −0.500000 0.866025i
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) 0 0
\(19\) −1.96231e18 + 1.13294e18i −0.563429 + 0.325296i −0.754521 0.656276i \(-0.772131\pi\)
0.191092 + 0.981572i \(0.438797\pi\)
\(20\) 0 0
\(21\) −1.42962e19 + 4.07465e18i −0.961701 + 0.274101i
\(22\) 0 0
\(23\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(24\) 0 0
\(25\) 9.31323e19 1.61310e20i 0.500000 0.866025i
\(26\) 0 0
\(27\) 5.68558e20i 1.00000i
\(28\) −2.64060e20 9.26470e20i −0.274101 0.961701i
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) −4.74078e21 2.73709e21i −1.12488 0.649448i −0.182236 0.983255i \(-0.558333\pi\)
−0.942642 + 0.333807i \(0.891667\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −3.68457e22 −1.00000
\(37\) −3.75709e22 6.50747e22i −0.685372 1.18710i −0.973320 0.229453i \(-0.926306\pi\)
0.287947 0.957646i \(-0.407027\pi\)
\(38\) 0 0
\(39\) 8.02665e22 1.39026e23i 0.682492 1.18211i
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 9.11042e23 1.88038 0.940191 0.340649i \(-0.110647\pi\)
0.940191 + 0.340649i \(0.110647\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 2.38780e24i 1.00000i
\(49\) −1.02088e23 3.21829e24i −0.0317054 0.999497i
\(50\) 0 0
\(51\) 0 0
\(52\) 9.00963e24 + 5.20171e24i 1.18211 + 0.682492i
\(53\) 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
\(57\) −1.87713e25 −0.650592
\(58\) 0 0
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 0 0
\(61\) −9.20660e25 + 5.31543e25i −1.19348 + 0.689058i −0.959095 0.283085i \(-0.908642\pi\)
−0.234389 + 0.972143i \(0.575309\pi\)
\(62\) 0 0
\(63\) −1.19445e26 2.99838e25i −0.969908 0.243472i
\(64\) 1.54743e26 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) −1.75561e26 + 3.04081e26i −0.583908 + 1.01136i 0.411103 + 0.911589i \(0.365144\pi\)
−0.995011 + 0.0997693i \(0.968190\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 1.71067e27 + 9.87658e26i 1.64054 + 0.947164i 0.980643 + 0.195805i \(0.0627320\pi\)
0.659894 + 0.751359i \(0.270601\pi\)
\(74\) 0 0
\(75\) 1.33635e27 7.71540e26i 0.866025 0.500000i
\(76\) 1.21648e27i 0.650592i
\(77\) 0 0
\(78\) 0 0
\(79\) −3.19532e27 5.53446e27i −0.974814 1.68843i −0.680549 0.732703i \(-0.738259\pi\)
−0.294265 0.955724i \(-0.595075\pi\)
\(80\) 0 0
\(81\) −2.35506e27 + 4.07909e27i −0.500000 + 0.866025i
\(82\) 0 0
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 1.94312e27 7.74070e27i 0.243472 0.969908i
\(85\) 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
\(91\) 2.49742e28 + 2.41945e28i 0.980371 + 0.949766i
\(92\) 0 0
\(93\) −2.26750e28 3.92742e28i −0.649448 1.12488i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 7.63732e28i 1.18782i 0.804531 + 0.593911i \(0.202417\pi\)
−0.804531 + 0.593911i \(0.797583\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 5.00000e28 + 8.66025e28i 0.500000 + 0.866025i
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) 0 0
\(103\) 1.87902e29 1.08485e29i 1.22403 0.706693i 0.258254 0.966077i \(-0.416853\pi\)
0.965774 + 0.259384i \(0.0835196\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(108\) −2.64347e29 1.52621e29i −0.866025 0.500000i
\(109\) 2.21424e29 3.83517e29i 0.634658 1.09926i −0.351929 0.936027i \(-0.614474\pi\)
0.986587 0.163233i \(-0.0521924\pi\)
\(110\) 0 0
\(111\) 6.22500e29i 1.37074i
\(112\) 5.01640e29 + 1.25925e29i 0.969908 + 0.243472i
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1.15174e30 6.64956e29i 1.18211 0.682492i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −7.93155e29 1.37378e30i −0.500000 0.866025i
\(122\) 0 0
\(123\) 0 0
\(124\) 2.54519e30 1.46946e30i 1.12488 0.649448i
\(125\) 0 0
\(126\) 0 0
\(127\) 4.62357e30 1.44485 0.722427 0.691447i \(-0.243027\pi\)
0.722427 + 0.691447i \(0.243027\pi\)
\(128\) 0 0
\(129\) 6.53623e30 + 3.77369e30i 1.62846 + 0.940191i
\(130\) 0 0
\(131\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(132\) 0 0
\(133\) 9.89935e29 3.94356e30i 0.158401 0.631014i
\(134\) 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
\(139\) 1.83699e31i 1.55021i −0.631831 0.775107i \(-0.717696\pi\)
0.631831 0.775107i \(-0.282304\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 9.89068e30 1.71312e31i 0.500000 0.866025i
\(145\) 0 0
\(146\) 0 0
\(147\) 1.25983e31 2.35123e31i 0.472291 0.881443i
\(148\) 4.03414e31 1.37074
\(149\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(150\) 0 0
\(151\) 3.93538e31 6.81629e31i 0.999589 1.73134i 0.474964 0.880005i \(-0.342461\pi\)
0.524625 0.851334i \(-0.324206\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 4.30928e31 + 7.46389e31i 0.682492 + 1.18211i
\(157\) 1.05949e31 + 6.11698e30i 0.152951 + 0.0883065i 0.574522 0.818489i \(-0.305188\pi\)
−0.421571 + 0.906795i \(0.638521\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −2.17537e31 3.76785e31i −0.182311 0.315772i 0.760356 0.649506i \(-0.225024\pi\)
−0.942667 + 0.333734i \(0.891691\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) −1.73964e32 −0.863182
\(170\) 0 0
\(171\) −1.34674e32 7.77539e31i −0.563429 0.325296i
\(172\) −2.44556e32 + 4.23583e32i −0.940191 + 1.62846i
\(173\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(174\) 0 0
\(175\) 9.16141e31 + 3.21434e32i 0.274101 + 0.961701i
\(176\) 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
\(181\) 2.39694e32i 0.439863i −0.975515 0.219931i \(-0.929417\pi\)
0.975515 0.219931i \(-0.0705833\pi\)
\(182\) 0 0
\(183\) −8.80697e32 −1.37812
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −7.32755e32 7.09880e32i −0.718229 0.695807i
\(190\) 0 0
\(191\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(192\) 1.11019e33 + 6.40970e32i 0.866025 + 0.500000i
\(193\) −1.19349e33 + 2.06719e33i −0.863453 + 1.49554i 0.00512254 + 0.999987i \(0.498369\pi\)
−0.868575 + 0.495557i \(0.834964\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 1.52373e33 + 8.16437e32i 0.881443 + 0.472291i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) −1.54923e33 8.94450e32i −0.719030 0.415132i 0.0953657 0.995442i \(-0.469598\pi\)
−0.814395 + 0.580310i \(0.802931\pi\)
\(200\) 0 0
\(201\) −2.51911e33 + 1.45441e33i −1.01136 + 0.583908i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −4.83701e33 + 2.79265e33i −1.18211 + 0.682492i
\(209\) 0 0
\(210\) 0 0
\(211\) −9.41087e33 −1.86868 −0.934338 0.356388i \(-0.884008\pi\)
−0.934338 + 0.356388i \(0.884008\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 9.44671e33 2.69247e33i 1.24915 0.356029i
\(218\) 0 0
\(219\) 8.18210e33 + 1.41718e34i 0.947164 + 1.64054i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 1.73361e34i 1.54359i −0.635872 0.771794i \(-0.719359\pi\)
0.635872 0.771794i \(-0.280641\pi\)
\(224\) 0 0
\(225\) 1.27834e34 1.00000
\(226\) 0 0
\(227\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(228\) 5.03888e33 8.72760e33i 0.325296 0.563429i
\(229\) 2.52851e34 1.45984e34i 1.53197 0.884484i 0.532700 0.846304i \(-0.321177\pi\)
0.999271 0.0381794i \(-0.0121558\pi\)
\(230\) 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
\(237\) 5.29423e34i 1.94963i
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 3.24242e34 + 1.87201e34i 0.936747 + 0.540831i 0.888939 0.458025i \(-0.151443\pi\)
0.0478081 + 0.998857i \(0.484776\pi\)
\(242\) 0 0
\(243\) −3.37926e34 + 1.95102e34i −0.866025 + 0.500000i
\(244\) 5.70740e34i 1.37812i
\(245\) 0 0
\(246\) 0 0
\(247\) 2.19539e34 + 3.80253e34i 0.444024 + 0.769072i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 4.60041e34 4.74866e34i 0.695807 0.718229i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −4.15384e34 + 7.19466e34i −0.500000 + 0.866025i
\(257\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(258\) 0 0
\(259\) 1.30778e35 + 3.28286e34i 1.32950 + 0.333738i
\(260\) 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
\(268\) −9.42538e34 1.63252e35i −0.583908 1.01136i
\(269\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(270\) 0 0
\(271\) −1.14928e35 + 6.63536e34i −0.605857 + 0.349792i −0.771342 0.636420i \(-0.780414\pi\)
0.165485 + 0.986212i \(0.447081\pi\)
\(272\) 0 0
\(273\) 7.89581e34 + 2.77030e35i 0.374144 + 1.31271i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −4.76431e34 + 8.25203e34i −0.182828 + 0.316668i −0.942843 0.333238i \(-0.891859\pi\)
0.760014 + 0.649906i \(0.225192\pi\)
\(278\) 0 0
\(279\) 3.75695e35i 1.29890i
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) −6.02910e35 3.48090e35i −1.69570 0.979013i −0.949750 0.313010i \(-0.898663\pi\)
−0.745950 0.666002i \(-0.768004\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 2.40984e35 + 4.17397e35i 0.500000 + 0.866025i
\(290\) 0 0
\(291\) −3.16351e35 + 5.47936e35i −0.593911 + 1.02868i
\(292\) −9.18411e35 + 5.30245e35i −1.64054 + 0.947164i
\(293\) 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
\(300\) 8.28435e35i 1.00000i
\(301\) −1.13749e36 + 1.17415e36i −1.30838 + 1.35054i
\(302\) 0 0
\(303\) 0 0
\(304\) 5.65596e35 + 3.26547e35i 0.563429 + 0.325296i
\(305\) 0 0
\(306\) 0 0
\(307\) 2.29328e36i 1.98130i −0.136412 0.990652i \(-0.543557\pi\)
0.136412 0.990652i \(-0.456443\pi\)
\(308\) 0 0
\(309\) 1.79746e36 1.41339
\(310\) 0 0
\(311\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(312\) 0 0
\(313\) −2.40350e36 + 1.38766e36i −1.56838 + 0.905506i −0.572025 + 0.820236i \(0.693842\pi\)
−0.996358 + 0.0852700i \(0.972825\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 3.43095e36 1.94963
\(317\) 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
\(324\) −1.26437e36 2.18995e36i −0.500000 0.866025i
\(325\) −3.12584e36 1.80471e36i −1.18211 0.682492i
\(326\) 0 0
\(327\) 3.17719e36 1.83435e36i 1.09926 0.634658i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −2.46610e36 4.27141e36i −0.715327 1.23898i −0.962833 0.270097i \(-0.912944\pi\)
0.247506 0.968886i \(-0.420389\pi\)
\(332\) 0 0
\(333\) 2.57850e36 4.46610e36i 0.685372 1.18710i
\(334\) 0 0
\(335\) 0 0
\(336\) 3.07739e36 + 2.98132e36i 0.718229 + 0.695807i
\(337\) 6.54162e36 1.46235 0.731176 0.682189i \(-0.238972\pi\)
0.731176 + 0.682189i \(0.238972\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 4.27518e36 + 3.88666e36i 0.739929 + 0.672685i
\(344\) 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
\(349\) 2.11165e36i 0.284219i 0.989851 + 0.142109i \(0.0453884\pi\)
−0.989851 + 0.142109i \(0.954612\pi\)
\(350\) 0 0
\(351\) 1.10174e37 1.36498
\(352\) 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
\(361\) −3.49782e36 + 6.05840e36i −0.288365 + 0.499463i
\(362\) 0 0
\(363\) 1.31415e37i 1.00000i
\(364\) −1.79530e37 + 5.11692e36i −1.31271 + 0.374144i
\(365\) 0 0
\(366\) 0 0
\(367\) −1.07606e37 6.21261e36i −0.698517 0.403289i 0.108278 0.994121i \(-0.465466\pi\)
−0.806795 + 0.590832i \(0.798800\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 2.43471e37 1.29890
\(373\) −9.84732e36 1.70561e37i −0.505289 0.875187i −0.999981 0.00611850i \(-0.998052\pi\)
0.494692 0.869068i \(-0.335281\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −4.76969e37 −1.94188 −0.970939 0.239329i \(-0.923073\pi\)
−0.970939 + 0.239329i \(0.923073\pi\)
\(380\) 0 0
\(381\) 3.31716e37 + 1.91516e37i 1.25128 + 0.722427i
\(382\) 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
\(387\) 3.12626e37 + 5.41484e37i 0.940191 + 1.62846i
\(388\) −3.55093e37 2.05013e37i −1.02868 0.593911i
\(389\) 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
\(397\) −7.91562e37 + 4.57009e37i −1.64446 + 0.949428i −0.665237 + 0.746633i \(0.731669\pi\)
−0.979221 + 0.202795i \(0.934997\pi\)
\(398\) 0 0
\(399\) 2.34371e37 2.41924e37i 0.452686 0.467274i
\(400\) −5.36871e37 −1.00000
\(401\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(402\) 0 0
\(403\) −5.30390e37 + 9.18662e37i −0.886487 + 1.53544i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 4.18314e37 + 2.41514e37i 0.564306 + 0.325802i 0.754872 0.655872i \(-0.227699\pi\)
−0.190566 + 0.981674i \(0.561032\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 1.16485e38i 1.41339i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 7.60912e37 1.31794e38i 0.775107 1.34252i
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) −2.21956e38 −1.96869 −0.984344 0.176258i \(-0.943601\pi\)
−0.984344 + 0.176258i \(0.943601\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 4.64450e37 1.85021e38i 0.335533 1.33665i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) 1.41920e38 8.19378e37i 0.866025 0.500000i
\(433\) 2.59179e38i 1.52942i −0.644376 0.764709i \(-0.722883\pi\)
0.644376 0.764709i \(-0.277117\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1.18876e38 + 2.05899e38i 0.634658 + 1.09926i
\(437\) 0 0
\(438\) 0 0
\(439\) 2.57263e38 1.48531e38i 1.24349 0.717928i 0.273686 0.961819i \(-0.411757\pi\)
0.969803 + 0.243891i \(0.0784239\pi\)
\(440\) 0 0
\(441\) 1.87778e38 1.16504e38i 0.849737 0.527206i
\(442\) 0 0
\(443\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(444\) 2.89428e38 + 1.67101e38i 1.18710 + 0.685372i
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −1.93206e38 + 1.99432e38i −0.695807 + 0.718229i
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 5.64685e38 3.26021e38i 1.73134 0.999589i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −1.72451e38 2.98694e38i −0.465459 0.806199i 0.533763 0.845634i \(-0.320777\pi\)
−0.999222 + 0.0394353i \(0.987444\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) −5.37446e38 −1.20063 −0.600317 0.799762i \(-0.704959\pi\)
−0.600317 + 0.799762i \(0.704959\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(468\) 7.13991e38i 1.36498i
\(469\) −1.72700e38 6.05928e38i −0.320100 1.12309i
\(470\) 0 0
\(471\) 5.06752e37 + 8.77720e37i 0.0883065 + 0.152951i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 4.22052e38i 0.650592i
\(476\) 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
\(481\) −1.26101e39 + 7.28044e38i −1.62037 + 0.935522i
\(482\) 0 0
\(483\) 0 0
\(484\) 8.51643e38 1.00000
\(485\) 0 0
\(486\) 0 0
\(487\) 9.15738e38 1.58610e39i 0.983108 1.70279i 0.333049 0.942909i \(-0.391922\pi\)
0.650059 0.759884i \(-0.274744\pi\)
\(488\) 0 0
\(489\) 3.60430e38i 0.364622i
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 1.57782e39i 1.29890i
\(497\) 0 0
\(498\) 0 0
\(499\) 1.53440e38 + 2.65765e38i 0.115739 + 0.200466i 0.918075 0.396407i \(-0.129743\pi\)
−0.802336 + 0.596873i \(0.796410\pi\)
\(500\) 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
\(507\) −1.24810e39 7.20590e38i −0.747538 0.431591i
\(508\) −1.24113e39 + 2.14970e39i −0.722427 + 1.25128i
\(509\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(510\) 0 0
\(511\) −3.40877e39 + 9.71558e38i −1.82178 + 0.519237i
\(512\) 0 0
\(513\) −6.44140e38 1.11568e39i −0.325296 0.563429i
\(514\) 0 0
\(515\) 0 0
\(516\) −3.50911e39 + 2.02599e39i −1.62846 + 0.940191i
\(517\) 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
\(523\) 4.49490e39 2.59513e39i 1.71572 0.990570i 0.789357 0.613934i \(-0.210414\pi\)
0.926361 0.376636i \(-0.122919\pi\)
\(524\) 0 0
\(525\) −6.74154e38 + 2.68559e39i −0.243472 + 0.969908i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −1.54553e39 + 2.67694e39i −0.500000 + 0.866025i
\(530\) 0 0
\(531\) 0 0
\(532\) 1.56780e39 + 1.51885e39i 0.467274 + 0.452686i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −2.65732e39 4.60262e39i −0.620990 1.07559i −0.989302 0.145883i \(-0.953398\pi\)
0.368312 0.929702i \(-0.379936\pi\)
\(542\) 0 0
\(543\) 9.92852e38 1.71967e39i 0.219931 0.380932i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 9.99595e39 1.99071 0.995355 0.0962743i \(-0.0306926\pi\)
0.995355 + 0.0962743i \(0.0306926\pi\)
\(548\) 0 0
\(549\) −6.31852e39 3.64800e39i −1.19348 0.689058i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 1.11223e40 + 2.79200e39i 1.89096 + 0.474680i
\(554\) 0 0
\(555\) 0 0
\(556\) 8.54096e39 + 4.93112e39i 1.34252 + 0.775107i
\(557\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(558\) 0 0
\(559\) 1.76541e40i 2.56669i
\(560\) 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
\(567\) −2.31667e39 8.12820e39i −0.274101 0.961701i
\(568\) 0 0
\(569\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(570\) 0 0
\(571\) 9.34796e39 1.61911e40i 0.998834 1.73003i 0.457603 0.889157i \(-0.348708\pi\)
0.541231 0.840874i \(-0.317959\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 5.31002e39 + 9.19722e39i 0.500000 + 0.866025i
\(577\) −2.01974e39 1.16610e39i −0.185458 0.107074i 0.404396 0.914584i \(-0.367482\pi\)
−0.589855 + 0.807509i \(0.700815\pi\)
\(578\) 0 0
\(579\) −1.71253e40 + 9.88730e39i −1.49554 + 0.863453i
\(580\) 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 \(0.5\pi\)
\(588\) 7.55008e39 + 1.21690e40i 0.527206 + 0.849737i
\(589\) 1.24038e40 0.845052
\(590\) 0 0
\(591\) 0 0
\(592\) −1.08291e40 + 1.87565e40i −0.685372 + 1.18710i
\(593\) 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
\(597\) −7.40993e39 1.28344e40i −0.415132 0.719030i
\(598\) 0 0
\(599\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(600\) 0 0
\(601\) 3.36080e40i 1.70908i −0.519385 0.854540i \(-0.673839\pi\)
0.519385 0.854540i \(-0.326161\pi\)
\(602\) 0 0
\(603\) −2.40977e40 −1.16782
\(604\) 2.11279e40 + 3.65947e40i 0.999589 + 1.73134i
\(605\) 0 0
\(606\) 0 0
\(607\) 3.05609e39 1.76443e39i 0.134564 0.0776907i −0.431207 0.902253i \(-0.641912\pi\)
0.565771 + 0.824562i \(0.308579\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −9.86435e39 + 1.70856e40i −0.376610 + 0.652308i −0.990567 0.137032i \(-0.956244\pi\)
0.613957 + 0.789340i \(0.289577\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 4.88869e40 + 2.82248e40i 1.62061 + 0.935658i 0.986758 + 0.162201i \(0.0518593\pi\)
0.633849 + 0.773457i \(0.281474\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) −4.62705e40 −1.36498
\(625\) −1.73472e40 3.00463e40i −0.500000 0.866025i
\(626\) 0 0
\(627\) 0 0
\(628\) −5.68811e39 + 3.28403e39i −0.152951 + 0.0883065i
\(629\) 0 0
\(630\) 0 0
\(631\) −3.60894e40 −0.905636 −0.452818 0.891603i \(-0.649581\pi\)
−0.452818 + 0.891603i \(0.649581\pi\)
\(632\) 0 0
\(633\) −6.75178e40 3.89814e40i −1.61832 0.934338i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −6.23636e40 + 1.97826e39i −1.36430 + 0.0432774i
\(638\) 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
\(643\) 6.72150e40i 1.28353i 0.766900 + 0.641767i \(0.221798\pi\)
−0.766900 + 0.641767i \(0.778202\pi\)
\(644\) 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
\(651\) 7.89277e40 + 1.98129e40i 1.25981 + 0.316245i
\(652\) 2.33579e40 0.364622
\(653\) 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
\(657\) 1.35567e41i 1.89433i
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 6.40088e40 + 3.69555e40i 0.819065 + 0.472888i 0.850094 0.526631i \(-0.176545\pi\)
−0.0310288 + 0.999518i \(0.509878\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 7.18092e40 1.24377e41i 0.771794 1.33679i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −1.74264e41 −1.71786 −0.858932 0.512089i \(-0.828872\pi\)
−0.858932 + 0.512089i \(0.828872\pi\)
\(674\) 0 0
\(675\) 9.17139e40 + 5.29511e40i 0.866025 + 0.500000i
\(676\) 4.66982e40 8.08836e40i 0.431591 0.747538i
\(677\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(678\) 0 0
\(679\) −9.84296e40 9.53568e40i −0.853128 0.826494i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(684\) 7.23024e40 4.17438e40i 0.563429 0.325296i
\(685\) 0 0
\(686\) 0 0
\(687\) 2.41876e41 1.76897
\(688\) −1.31295e41 2.27410e41i −0.940191 1.62846i
\(689\) 0 0
\(690\) 0 0
\(691\) 2.50166e41 1.44433e41i 1.68188 0.971036i 0.721475 0.692441i \(-0.243464\pi\)
0.960409 0.278595i \(-0.0898688\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −1.74041e41 4.36889e40i −0.969908 0.243472i
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 1.47451e41 + 8.51309e40i 0.772317 + 0.445898i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 4.63119e40 + 8.02145e40i 0.214448 + 0.371435i 0.953102 0.302650i \(-0.0978715\pi\)
−0.738654 + 0.674085i \(0.764538\pi\)
\(710\) 0 0
\(711\) 2.19296e41 3.79832e41i 0.974814 1.68843i
\(712\) 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
\(721\) −9.47919e40 + 3.77618e41i −0.344120 + 1.37085i
\(722\) 0 0
\(723\) 1.55084e41 + 2.68613e41i 0.540831 + 0.936747i
\(724\) 1.11444e41 + 6.43423e40i 0.380932 + 0.219931i
\(725\) 0 0
\(726\) 0 0
\(727\) 4.63965e40i 0.149361i −0.997208 0.0746804i \(-0.976206\pi\)
0.997208 0.0746804i \(-0.0237937\pi\)
\(728\) 0 0
\(729\) −3.23258e41 −1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 2.36410e41 4.09475e41i 0.689058 1.19348i
\(733\) −4.94052e41 + 2.85241e41i −1.41177 + 0.815087i −0.995555 0.0941784i \(-0.969978\pi\)
−0.416217 + 0.909265i \(0.636644\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −3.82697e41 + 6.62851e41i −0.971652 + 1.68295i −0.281085 + 0.959683i \(0.590694\pi\)
−0.690568 + 0.723268i \(0.742639\pi\)
\(740\) 0 0
\(741\) 3.63748e41i 0.888048i
\(742\) 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
\(751\) −2.90692e41 5.03494e41i −0.584325 1.01208i −0.994959 0.100281i \(-0.968026\pi\)
0.410634 0.911800i \(-0.365307\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 5.26752e41 1.50133e41i 0.961701 0.274101i
\(757\) −1.10661e42 −1.98201 −0.991004 0.133833i \(-0.957271\pi\)
−0.991004 + 0.133833i \(0.957271\pi\)
\(758\) 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
\(763\) 2.17814e41 + 7.64215e41i 0.347921 + 1.22070i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −5.96030e41 + 3.44118e41i −0.866025 + 0.500000i
\(769\) 1.40269e42i 2.00000i −0.00120402 0.999999i \(-0.500383\pi\)
0.00120402 0.999999i \(-0.499617\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −6.40751e41 1.10981e42i −0.863453 1.49554i
\(773\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(774\) 0 0