Properties

Label 21.33.h.a.11.1
Level $21$
Weight $33$
Character 21.11
Analytic conductor $136.220$
Analytic rank $0$
Dimension $2$
CM discriminant -3
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 33 \)
Character orbit: \([\chi]\) \(=\) 21.h (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(136.219975799\)
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 11.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 21.11
Dual form 21.33.h.a.2.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.15234e7 + 3.72796e7i) q^{3} +(-2.14748e9 + 3.71955e9i) q^{4} +(3.25760e13 + 6.57520e12i) q^{7} +(-9.26510e14 - 1.60476e15i) q^{9} +O(q^{10})\) \(q+(-2.15234e7 + 3.72796e7i) q^{3} +(-2.14748e9 + 3.71955e9i) q^{4} +(3.25760e13 + 6.57520e12i) q^{7} +(-9.26510e14 - 1.60476e15i) q^{9} +(-9.24421e16 - 1.60114e17i) q^{12} +1.22181e17 q^{13} +(-9.22337e18 - 1.59753e19i) q^{16} +(3.91058e18 + 6.77332e18i) q^{19} +(-9.46265e20 + 1.07290e21i) q^{21} +(-1.16415e22 + 2.01637e22i) q^{25} +7.97664e22 q^{27} +(-9.44132e22 + 1.07048e23i) q^{28} +(7.06862e23 - 1.22432e24i) q^{31} +7.95866e24 q^{36} +(1.07781e25 + 1.86682e25i) q^{37} +(-2.62975e24 + 4.55487e24i) q^{39} +2.72890e26 q^{43} +7.94072e26 q^{48} +(1.01796e27 + 4.28387e26i) q^{49} +(-2.62383e26 + 4.54460e26i) q^{52} -3.36675e26 q^{57} +(1.97705e28 + 3.42436e28i) q^{61} +(-1.96303e28 - 5.83687e28i) q^{63} +7.92282e28 q^{64} +(-2.65665e27 + 4.60145e27i) q^{67} +(-3.83758e29 + 6.64688e29i) q^{73} +(-5.01130e29 - 8.67982e29i) q^{75} -3.35916e28 q^{76} +(-1.01348e30 - 1.75540e30i) q^{79} +(-1.71684e30 + 2.97366e30i) q^{81} +(-1.95861e30 - 5.82371e30i) q^{84} +(3.98018e30 + 8.03367e29i) q^{91} +(3.04281e31 + 5.27030e31i) q^{93} +1.21183e32 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 43046721q^{3} - 4294967296q^{4} + 65151959156159q^{7} - 1853020188851841q^{9} + O(q^{10}) \) \( 2q - 43046721q^{3} - 4294967296q^{4} + 65151959156159q^{7} - 1853020188851841q^{9} - 184884258895036416q^{12} + 244362804407950078q^{13} - 18446744073709551616q^{16} + 7821153231347348161q^{19} - \)\(18\!\cdots\!06\)\(q^{21} - \)\(23\!\cdots\!25\)\(q^{25} + \)\(15\!\cdots\!22\)\(q^{27} - \)\(18\!\cdots\!56\)\(q^{28} + \)\(14\!\cdots\!13\)\(q^{31} + \)\(15\!\cdots\!72\)\(q^{36} + \)\(21\!\cdots\!61\)\(q^{37} - \)\(52\!\cdots\!19\)\(q^{39} + \)\(54\!\cdots\!54\)\(q^{43} + \)\(15\!\cdots\!72\)\(q^{48} + \)\(20\!\cdots\!79\)\(q^{49} - \)\(52\!\cdots\!44\)\(q^{52} - \)\(67\!\cdots\!62\)\(q^{57} + \)\(39\!\cdots\!26\)\(q^{61} - \)\(39\!\cdots\!93\)\(q^{63} + \)\(15\!\cdots\!72\)\(q^{64} - \)\(53\!\cdots\!59\)\(q^{67} - \)\(76\!\cdots\!79\)\(q^{73} - \)\(10\!\cdots\!25\)\(q^{75} - \)\(67\!\cdots\!12\)\(q^{76} - \)\(20\!\cdots\!39\)\(q^{79} - \)\(34\!\cdots\!81\)\(q^{81} - \)\(39\!\cdots\!68\)\(q^{84} + \)\(79\!\cdots\!01\)\(q^{91} + \)\(60\!\cdots\!73\)\(q^{93} + \)\(24\!\cdots\!28\)\(q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(8\) \(10\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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 \(0.333333\pi\)
\(3\) −2.15234e7 + 3.72796e7i −0.500000 + 0.866025i
\(4\) −2.14748e9 + 3.71955e9i −0.500000 + 0.866025i
\(5\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(6\) 0 0
\(7\) 3.25760e13 + 6.57520e12i 0.980232 + 0.197852i
\(8\) 0 0
\(9\) −9.26510e14 1.60476e15i −0.500000 0.866025i
\(10\) 0 0
\(11\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(12\) −9.24421e16 1.60114e17i −0.500000 0.866025i
\(13\) 1.22181e17 0.183616 0.0918082 0.995777i \(-0.470735\pi\)
0.0918082 + 0.995777i \(0.470735\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −9.22337e18 1.59753e19i −0.500000 0.866025i
\(17\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(18\) 0 0
\(19\) 3.91058e18 + 6.77332e18i 0.0135576 + 0.0234825i 0.872725 0.488213i \(-0.162351\pi\)
−0.859167 + 0.511695i \(0.829018\pi\)
\(20\) 0 0
\(21\) −9.46265e20 + 1.07290e21i −0.661461 + 0.749980i
\(22\) 0 0
\(23\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(24\) 0 0
\(25\) −1.16415e22 + 2.01637e22i −0.500000 + 0.866025i
\(26\) 0 0
\(27\) 7.97664e22 1.00000
\(28\) −9.44132e22 + 1.07048e23i −0.661461 + 0.749980i
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 7.06862e23 1.22432e24i 0.971734 1.68309i 0.281417 0.959585i \(-0.409195\pi\)
0.690317 0.723507i \(-0.257471\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 7.95866e24 1.00000
\(37\) 1.07781e25 + 1.86682e25i 0.873603 + 1.51313i 0.858243 + 0.513244i \(0.171556\pi\)
0.0153605 + 0.999882i \(0.495110\pi\)
\(38\) 0 0
\(39\) −2.62975e24 + 4.55487e24i −0.0918082 + 0.159016i
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 2.72890e26 1.99752 0.998762 0.0497364i \(-0.0158381\pi\)
0.998762 + 0.0497364i \(0.0158381\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(48\) 7.94072e26 1.00000
\(49\) 1.01796e27 + 4.28387e26i 0.921709 + 0.387881i
\(50\) 0 0
\(51\) 0 0
\(52\) −2.62383e26 + 4.54460e26i −0.0918082 + 0.159016i
\(53\) 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
\(57\) −3.36675e26 −0.0271152
\(58\) 0 0
\(59\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(60\) 0 0
\(61\) 1.97705e28 + 3.42436e28i 0.537949 + 0.931755i 0.999014 + 0.0443885i \(0.0141340\pi\)
−0.461066 + 0.887366i \(0.652533\pi\)
\(62\) 0 0
\(63\) −1.96303e28 5.83687e28i −0.318771 0.947832i
\(64\) 7.92282e28 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) −2.65665e27 + 4.60145e27i −0.0161115 + 0.0279060i −0.873969 0.485982i \(-0.838462\pi\)
0.857857 + 0.513888i \(0.171795\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) −3.83758e29 + 6.64688e29i −0.590054 + 1.02200i 0.404171 + 0.914684i \(0.367560\pi\)
−0.994225 + 0.107320i \(0.965773\pi\)
\(74\) 0 0
\(75\) −5.01130e29 8.67982e29i −0.500000 0.866025i
\(76\) −3.35916e28 −0.0271152
\(77\) 0 0
\(78\) 0 0
\(79\) −1.01348e30 1.75540e30i −0.440334 0.762681i 0.557380 0.830257i \(-0.311807\pi\)
−0.997714 + 0.0675768i \(0.978473\pi\)
\(80\) 0 0
\(81\) −1.71684e30 + 2.97366e30i −0.500000 + 0.866025i
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) −1.95861e30 5.82371e30i −0.318771 0.947832i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(90\) 0 0
\(91\) 3.98018e30 + 8.03367e29i 0.179987 + 0.0363289i
\(92\) 0 0
\(93\) 3.04281e31 + 5.27030e31i 0.971734 + 1.68309i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 1.21183e32 1.97285 0.986426 0.164204i \(-0.0525057\pi\)
0.986426 + 0.164204i \(0.0525057\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −5.00000e31 8.66025e31i −0.500000 0.866025i
\(101\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(102\) 0 0
\(103\) −4.30303e31 7.45307e31i −0.268151 0.464450i 0.700234 0.713914i \(-0.253079\pi\)
−0.968384 + 0.249463i \(0.919746\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(108\) −1.71297e32 + 2.96695e32i −0.500000 + 0.866025i
\(109\) −2.22684e32 + 3.85700e32i −0.560874 + 0.971462i 0.436546 + 0.899682i \(0.356202\pi\)
−0.997420 + 0.0717807i \(0.977132\pi\)
\(110\) 0 0
\(111\) −9.27923e32 −1.74721
\(112\) −1.95419e32 5.81058e32i −0.318771 0.947832i
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.13202e32 1.96072e32i −0.0918082 0.159016i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −1.05569e33 1.82851e33i −0.500000 0.866025i
\(122\) 0 0
\(123\) 0 0
\(124\) 3.03595e33 + 5.25842e33i 0.971734 + 1.68309i
\(125\) 0 0
\(126\) 0 0
\(127\) 7.15599e33 1.56247 0.781233 0.624240i \(-0.214591\pi\)
0.781233 + 0.624240i \(0.214591\pi\)
\(128\) 0 0
\(129\) −5.87351e33 + 1.01732e34i −0.998762 + 1.72991i
\(130\) 0 0
\(131\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(132\) 0 0
\(133\) 8.28550e31 + 2.46360e32i 0.00864355 + 0.0257007i
\(134\) 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
\(139\) −3.79001e34 −1.95166 −0.975829 0.218537i \(-0.929872\pi\)
−0.975829 + 0.218537i \(0.929872\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −1.70911e34 + 2.96026e34i −0.500000 + 0.866025i
\(145\) 0 0
\(146\) 0 0
\(147\) −3.78800e34 + 2.87288e34i −0.796770 + 0.604283i
\(148\) −9.25831e34 −1.74721
\(149\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(150\) 0 0
\(151\) −3.62428e34 + 6.27745e34i −0.496125 + 0.859314i −0.999990 0.00446863i \(-0.998578\pi\)
0.503865 + 0.863782i \(0.331911\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −1.12947e34 1.95630e34i −0.0918082 0.159016i
\(157\) −1.35303e35 + 2.34352e35i −0.992917 + 1.71978i −0.393565 + 0.919297i \(0.628758\pi\)
−0.599352 + 0.800485i \(0.704575\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 1.77804e35 + 3.07966e35i 0.716046 + 1.24023i 0.962555 + 0.271088i \(0.0873833\pi\)
−0.246509 + 0.969141i \(0.579283\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) −4.27851e35 −0.966285
\(170\) 0 0
\(171\) 7.24638e33 1.25511e34i 0.0135576 0.0234825i
\(172\) −5.86027e35 + 1.01503e36i −0.998762 + 1.72991i
\(173\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(174\) 0 0
\(175\) −5.11815e35 + 5.80308e35i −0.661461 + 0.749980i
\(176\) 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
\(181\) −1.42721e36 −1.07555 −0.537777 0.843087i \(-0.680736\pi\)
−0.537777 + 0.843087i \(0.680736\pi\)
\(182\) 0 0
\(183\) −1.70211e36 −1.07590
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 2.59847e36 + 5.24480e35i 0.980232 + 0.197852i
\(190\) 0 0
\(191\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(192\) −1.70526e36 + 2.95359e36i −0.500000 + 0.866025i
\(193\) 1.13971e36 1.97404e36i 0.307524 0.532647i −0.670296 0.742094i \(-0.733833\pi\)
0.977820 + 0.209447i \(0.0671663\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −3.77946e36 + 2.86640e36i −0.796770 + 0.604283i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 4.22546e36 7.31872e36i 0.698594 1.21000i −0.270360 0.962759i \(-0.587143\pi\)
0.968954 0.247241i \(-0.0795241\pi\)
\(200\) 0 0
\(201\) −1.14360e35 1.98077e35i −0.0161115 0.0279060i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −1.12692e36 1.95189e36i −0.0918082 0.159016i
\(209\) 0 0
\(210\) 0 0
\(211\) 3.03417e37 1.96571 0.982856 0.184373i \(-0.0590256\pi\)
0.982856 + 0.184373i \(0.0590256\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 3.10769e37 3.52357e37i 1.28553 1.45756i
\(218\) 0 0
\(219\) −1.65195e37 2.86126e37i −0.590054 1.02200i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 2.75399e37 0.736349 0.368175 0.929757i \(-0.379983\pi\)
0.368175 + 0.929757i \(0.379983\pi\)
\(224\) 0 0
\(225\) 4.31440e37 1.00000
\(226\) 0 0
\(227\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(228\) 7.23004e35 1.25228e36i 0.0135576 0.0234825i
\(229\) −2.14905e37 3.72226e37i −0.375732 0.650787i 0.614704 0.788758i \(-0.289275\pi\)
−0.990436 + 0.137971i \(0.955942\pi\)
\(230\) 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
\(237\) 8.72540e37 0.880668
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 9.57310e37 1.65811e38i 0.739231 1.28039i −0.213611 0.976919i \(-0.568523\pi\)
0.952842 0.303467i \(-0.0981441\pi\)
\(242\) 0 0
\(243\) −7.39044e37 1.28006e38i −0.500000 0.866025i
\(244\) −1.69828e38 −1.07590
\(245\) 0 0
\(246\) 0 0
\(247\) 4.77800e35 + 8.27573e35i 0.00248940 + 0.00431177i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 2.59261e38 + 5.23298e37i 0.980232 + 0.197852i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −1.70141e38 + 2.94693e38i −0.500000 + 0.866025i
\(257\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(258\) 0 0
\(259\) 2.28360e38 + 6.79003e38i 0.556959 + 1.65606i
\(260\) 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
\(268\) −1.14102e37 1.97631e37i −0.0161115 0.0279060i
\(269\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(270\) 0 0
\(271\) −3.66940e38 6.35560e38i −0.433598 0.751013i 0.563582 0.826060i \(-0.309423\pi\)
−0.997180 + 0.0750466i \(0.976089\pi\)
\(272\) 0 0
\(273\) −1.15616e38 + 1.31088e38i −0.121455 + 0.137709i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −9.66328e38 + 1.67373e39i −0.804356 + 1.39319i 0.112369 + 0.993667i \(0.464156\pi\)
−0.916725 + 0.399519i \(0.869177\pi\)
\(278\) 0 0
\(279\) −2.61966e39 −1.94347
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) −1.54316e39 + 2.67283e39i −0.911650 + 1.57902i −0.0999165 + 0.994996i \(0.531858\pi\)
−0.811733 + 0.584028i \(0.801476\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −1.18396e39 2.05067e39i −0.500000 0.866025i
\(290\) 0 0
\(291\) −2.60827e39 + 4.51766e39i −0.986426 + 1.70854i
\(292\) −1.64823e39 2.85481e39i −0.590054 1.02200i
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 4.30467e39 1.00000
\(301\) 8.88966e39 + 1.79431e39i 1.95804 + 0.395214i
\(302\) 0 0
\(303\) 0 0
\(304\) 7.21374e37 1.24946e38i 0.0135576 0.0234825i
\(305\) 0 0
\(306\) 0 0
\(307\) −1.43223e38 −0.0230038 −0.0115019 0.999934i \(-0.503661\pi\)
−0.0115019 + 0.999934i \(0.503661\pi\)
\(308\) 0 0
\(309\) 3.70463e39 0.536301
\(310\) 0 0
\(311\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(312\) 0 0
\(313\) −3.33486e37 5.77614e37i −0.00392978 0.00680657i 0.864054 0.503399i \(-0.167918\pi\)
−0.867984 + 0.496593i \(0.834584\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 8.70573e39 0.880668
\(317\) 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
\(324\) −7.37378e39 1.27718e40i −0.500000 0.866025i
\(325\) −1.42238e39 + 2.46363e39i −0.0918082 + 0.159016i
\(326\) 0 0
\(327\) −9.58582e39 1.66031e40i −0.560874 0.971462i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −1.32351e40 2.29238e40i −0.637498 1.10418i −0.985980 0.166863i \(-0.946636\pi\)
0.348482 0.937315i \(-0.386697\pi\)
\(332\) 0 0
\(333\) 1.99720e40 3.45926e40i 0.873603 1.51313i
\(334\) 0 0
\(335\) 0 0
\(336\) 2.58677e40 + 5.22118e39i 0.980232 + 0.197852i
\(337\) −1.85065e40 −0.668723 −0.334361 0.942445i \(-0.608521\pi\)
−0.334361 + 0.942445i \(0.608521\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 3.03444e40 + 2.06484e40i 0.826746 + 0.562576i
\(344\) 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
\(349\) 9.32145e40 1.92432 0.962159 0.272490i \(-0.0878472\pi\)
0.962159 + 0.272490i \(0.0878472\pi\)
\(350\) 0 0
\(351\) 9.74598e39 0.183616
\(352\) 0 0
\(353\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(354\) 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
\(361\) 4.15686e40 7.19990e40i 0.499632 0.865389i
\(362\) 0 0
\(363\) 9.08879e40 1.00000
\(364\) −1.15355e40 + 1.30793e40i −0.121455 + 0.137709i
\(365\) 0 0
\(366\) 0 0
\(367\) −7.21361e40 + 1.24943e41i −0.666033 + 1.15360i 0.312971 + 0.949763i \(0.398676\pi\)
−0.979004 + 0.203840i \(0.934658\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −2.61375e41 −1.94347
\(373\) 1.58690e39 + 2.74860e39i 0.0113034 + 0.0195781i 0.871622 0.490179i \(-0.163069\pi\)
−0.860318 + 0.509757i \(0.829735\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −2.75275e41 −1.51894 −0.759468 0.650545i \(-0.774541\pi\)
−0.759468 + 0.650545i \(0.774541\pi\)
\(380\) 0 0
\(381\) −1.54021e41 + 2.66772e41i −0.781233 + 1.35313i
\(382\) 0 0
\(383\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −2.52835e41 4.37923e41i −0.998762 1.72991i
\(388\) −2.60239e41 + 4.50747e41i −0.986426 + 1.70854i
\(389\) 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
\(397\) 3.69470e41 + 6.39941e41i 0.970356 + 1.68071i 0.694479 + 0.719513i \(0.255635\pi\)
0.275877 + 0.961193i \(0.411032\pi\)
\(398\) 0 0
\(399\) −1.09675e40 2.21370e39i −0.0265792 0.00536480i
\(400\) 4.29497e41 1.00000
\(401\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(402\) 0 0
\(403\) 8.63654e40 1.49589e41i 0.178426 0.309043i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −4.62140e41 + 8.00450e41i −0.753703 + 1.30545i 0.192313 + 0.981334i \(0.438401\pi\)
−0.946016 + 0.324119i \(0.894932\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 3.69627e41 0.536301
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 8.15738e41 1.41290e42i 0.975829 1.69018i
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) −1.85857e42 −1.90839 −0.954194 0.299190i \(-0.903284\pi\)
−0.954194 + 0.299190i \(0.903284\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 4.18886e41 + 1.24551e42i 0.342965 + 1.01977i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) −7.35716e41 1.27430e42i −0.500000 0.866025i
\(433\) 2.59382e42 1.69877 0.849383 0.527777i \(-0.176974\pi\)
0.849383 + 0.527777i \(0.176974\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −9.56421e41 1.65657e42i −0.560874 0.971462i
\(437\) 0 0
\(438\) 0 0
\(439\) 2.75863e41 + 4.77809e41i 0.144965 + 0.251086i 0.929360 0.369175i \(-0.120360\pi\)
−0.784395 + 0.620261i \(0.787027\pi\)
\(440\) 0 0
\(441\) −2.55692e41 2.03049e42i −0.124939 0.992164i
\(442\) 0 0
\(443\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(444\) 1.99270e42 3.45146e42i 0.873603 1.51313i
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 2.58094e42 + 5.20941e41i 0.980232 + 0.197852i
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −1.56014e42 2.70223e42i −0.496125 0.859314i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 3.52910e42 + 6.11258e42i 0.975000 + 1.68875i 0.679937 + 0.733271i \(0.262007\pi\)
0.295063 + 0.955478i \(0.404659\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 6.17477e42 1.38460 0.692301 0.721609i \(-0.256597\pi\)
0.692301 + 0.721609i \(0.256597\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(468\) 9.72400e41 0.183616
\(469\) −1.16798e41 + 1.32429e41i −0.0213143 + 0.0241667i
\(470\) 0 0
\(471\) −5.82435e42 1.00881e43i −0.992917 1.71978i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −1.82100e41 −0.0271152
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(480\) 0 0
\(481\) 1.31688e42 + 2.28091e42i 0.160408 + 0.277835i
\(482\) 0 0
\(483\) 0 0
\(484\) 9.06830e42 1.00000
\(485\) 0 0
\(486\) 0 0
\(487\) −9.14159e42 + 1.58337e43i −0.913185 + 1.58168i −0.103647 + 0.994614i \(0.533051\pi\)
−0.809538 + 0.587068i \(0.800282\pi\)
\(488\) 0 0
\(489\) −1.53078e43 −1.43209
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −2.60786e43 −1.94347
\(497\) 0 0
\(498\) 0 0
\(499\) 1.19381e43 + 2.06774e43i 0.807841 + 1.39922i 0.914356 + 0.404910i \(0.132697\pi\)
−0.106515 + 0.994311i \(0.533969\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 9.20879e42 1.59501e43i 0.483143 0.836827i
\(508\) −1.53674e43 + 2.66171e43i −0.781233 + 1.35313i
\(509\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(510\) 0 0
\(511\) −1.68717e43 + 1.91296e43i −0.780595 + 0.885057i
\(512\) 0 0
\(513\) 3.11933e41 + 5.40283e41i 0.0135576 + 0.0234825i
\(514\) 0 0
\(515\) 0 0
\(516\) −2.52265e43 4.36936e43i −0.998762 1.72991i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(522\) 0 0
\(523\) 2.89818e43 + 5.01980e43i 0.924909 + 1.60199i 0.791707 + 0.610901i \(0.209193\pi\)
0.133202 + 0.991089i \(0.457474\pi\)
\(524\) 0 0
\(525\) −1.06176e43 3.15704e43i −0.318771 0.947832i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −1.88045e43 + 3.25703e43i −0.500000 + 0.866025i
\(530\) 0 0
\(531\) 0 0
\(532\) −1.09428e42 2.20871e41i −0.0265792 0.00536480i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 4.84312e43 + 8.38854e43i 0.899434 + 1.55787i 0.828219 + 0.560405i \(0.189354\pi\)
0.0712152 + 0.997461i \(0.477312\pi\)
\(542\) 0 0
\(543\) 3.07184e43 5.32059e43i 0.537777 0.931456i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 2.05403e43 0.319750 0.159875 0.987137i \(-0.448891\pi\)
0.159875 + 0.987137i \(0.448891\pi\)
\(548\) 0 0
\(549\) 3.66352e43 6.34540e43i 0.537949 0.931755i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −2.14730e43 6.38477e43i −0.280731 0.834725i
\(554\) 0 0
\(555\) 0 0
\(556\) 8.13899e43 1.40971e44i 0.975829 1.69018i
\(557\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(558\) 0 0
\(559\) 3.33421e43 0.366778
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −7.54802e43 + 8.55812e43i −0.661461 + 0.749980i
\(568\) 0 0
\(569\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(570\) 0 0
\(571\) 1.05755e44 1.83173e44i 0.828176 1.43444i −0.0712925 0.997455i \(-0.522712\pi\)
0.899468 0.436987i \(-0.143954\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −7.34057e43 1.27142e44i −0.500000 0.866025i
\(577\) −8.34478e43 + 1.44536e44i −0.552843 + 0.957552i 0.445225 + 0.895419i \(0.353124\pi\)
−0.998068 + 0.0621333i \(0.980210\pi\)
\(578\) 0 0
\(579\) 4.90609e43 + 8.49760e43i 0.307524 + 0.532647i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) −2.55115e43 2.02591e44i −0.124939 0.992164i
\(589\) 1.10569e43 0.0526976
\(590\) 0 0
\(591\) 0 0
\(592\) 1.98821e44 3.44368e44i 0.873603 1.51313i
\(593\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 1.81892e44 + 3.15047e44i 0.698594 + 1.21000i
\(598\) 0 0
\(599\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(600\) 0 0
\(601\) 2.46883e44 0.852118 0.426059 0.904695i \(-0.359902\pi\)
0.426059 + 0.904695i \(0.359902\pi\)
\(602\) 0 0
\(603\) 9.84564e42 0.0322231
\(604\) −1.55662e44 2.69614e44i −0.496125 0.859314i
\(605\) 0 0
\(606\) 0 0
\(607\) 3.29972e44 + 5.71528e44i 0.971533 + 1.68274i 0.690932 + 0.722920i \(0.257201\pi\)
0.280601 + 0.959824i \(0.409466\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −3.87605e44 + 6.71351e44i −0.975038 + 1.68881i −0.295227 + 0.955427i \(0.595395\pi\)
−0.679811 + 0.733388i \(0.737938\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) −3.59678e44 + 6.22980e44i −0.774218 + 1.34098i 0.161016 + 0.986952i \(0.448523\pi\)
−0.935233 + 0.354032i \(0.884810\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 9.70208e43 0.183616
\(625\) −2.71051e44 4.69473e44i −0.500000 0.866025i
\(626\) 0 0
\(627\) 0 0
\(628\) −5.81122e44 1.00653e45i −0.992917 1.71978i
\(629\) 0 0
\(630\) 0 0
\(631\) −1.15848e45 −1.83408 −0.917039 0.398798i \(-0.869428\pi\)
−0.917039 + 0.398798i \(0.869428\pi\)
\(632\) 0 0
\(633\) −6.53054e44 + 1.13112e45i −0.982856 + 1.70236i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 1.24376e44 + 5.23409e43i 0.169241 + 0.0712214i
\(638\) 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
\(643\) −4.74213e44 −0.555390 −0.277695 0.960669i \(-0.589571\pi\)
−0.277695 + 0.960669i \(0.589571\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 6.44692e44 + 1.91692e45i 0.619522 + 1.84208i
\(652\) −1.52733e45 −1.43209
\(653\) 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
\(657\) 1.42222e45 1.18011
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 1.20637e45 2.08949e45i 0.908357 1.57332i 0.0920114 0.995758i \(-0.470670\pi\)
0.816346 0.577563i \(-0.195996\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −5.92750e44 + 1.02667e45i −0.368175 + 0.637697i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 3.41061e45 1.92571 0.962854 0.270022i \(-0.0870310\pi\)
0.962854 + 0.270022i \(0.0870310\pi\)
\(674\) 0 0
\(675\) −9.28604e44 + 1.60839e45i −0.500000 + 0.866025i
\(676\) 9.18803e44 1.59141e45i 0.483143 0.836827i
\(677\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(678\) 0 0
\(679\) 3.94766e45 + 7.96804e44i 1.93385 + 0.390333i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(684\) 3.11230e43 + 5.39065e43i 0.0135576 + 0.0234825i
\(685\) 0 0
\(686\) 0 0
\(687\) 1.85019e45 0.751464
\(688\) −2.51697e45 4.35951e45i −0.998762 1.72991i
\(689\) 0 0
\(690\) 0 0
\(691\) −2.06721e45 3.58052e45i −0.765132 1.32525i −0.940177 0.340688i \(-0.889340\pi\)
0.175044 0.984561i \(-0.443993\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −1.05937e45 3.14992e45i −0.318771 0.947832i
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) −8.42971e43 + 1.46007e44i −0.0236880 + 0.0410287i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −1.98784e45 3.44305e45i −0.487576 0.844507i 0.512322 0.858794i \(-0.328786\pi\)
−0.999898 + 0.0142869i \(0.995452\pi\)
\(710\) 0 0
\(711\) −1.87800e45 + 3.25279e45i −0.440334 + 0.762681i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(720\) 0 0
\(721\) −9.11700e44 2.71084e45i −0.170957 0.508323i
\(722\) 0 0
\(723\) 4.12091e45 + 7.13762e45i 0.739231 + 1.28039i
\(724\) 3.06492e45 5.30860e45i 0.537777 0.931456i
\(725\) 0 0
\(726\) 0 0
\(727\) 4.21369e45 0.692010 0.346005 0.938233i \(-0.387538\pi\)
0.346005 + 0.938233i \(0.387538\pi\)
\(728\) 0 0
\(729\) 6.36269e45 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 3.65526e45 6.33110e45i 0.537949 0.931755i
\(733\) 3.71231e45 + 6.42992e45i 0.534541 + 0.925852i 0.999185 + 0.0403548i \(0.0128488\pi\)
−0.464644 + 0.885497i \(0.653818\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −4.83528e45 + 8.37495e45i −0.611098 + 1.05845i 0.379958 + 0.925004i \(0.375938\pi\)
−0.991056 + 0.133448i \(0.957395\pi\)
\(740\) 0 0
\(741\) −4.11354e43 −0.00497880
\(742\) 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
\(751\) 3.41961e45 + 5.92294e45i 0.333994 + 0.578494i 0.983291 0.182041i \(-0.0582703\pi\)
−0.649297 + 0.760535i \(0.724937\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −7.53100e45 + 8.53883e45i −0.661461 + 0.749980i
\(757\) −2.32391e46 −1.99842 −0.999208 0.0397813i \(-0.987334\pi\)
−0.999208 + 0.0397813i \(0.987334\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(762\) 0 0
\(763\) −9.79021e45 + 1.11004e46i −0.741992 + 0.841289i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −7.32402e45 1.26856e46i −0.500000 0.866025i
\(769\) −2.97413e46 −1.98856 −0.994281 0.106798i \(-0.965940\pi\)
−0.994281 + 0.106798i \(0.965940\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 4.89503e45 + 8.47845e45i 0.307524 + 0.532647i
\(773\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)