Properties

Label 1512.2.s.b.865.1
Level $1512$
Weight $2$
Character 1512.865
Analytic conductor $12.073$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1512.s (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 865.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1512.865
Dual form 1512.2.s.b.1297.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{5} +(-2.00000 - 1.73205i) q^{7} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{5} +(-2.00000 - 1.73205i) q^{7} +3.00000 q^{13} +(-2.00000 + 3.46410i) q^{17} +(-2.00000 - 3.46410i) q^{19} +(-1.00000 - 1.73205i) q^{23} +(0.500000 - 0.866025i) q^{25} -4.00000 q^{29} +(-0.500000 + 0.866025i) q^{31} +(-1.00000 + 5.19615i) q^{35} +(1.50000 + 2.59808i) q^{37} -8.00000 q^{41} -1.00000 q^{43} +(-4.00000 - 6.92820i) q^{47} +(1.00000 + 6.92820i) q^{49} +(-7.00000 + 12.1244i) q^{53} +(-6.00000 + 10.3923i) q^{59} +(-0.500000 - 0.866025i) q^{61} +(-3.00000 - 5.19615i) q^{65} +(-1.50000 + 2.59808i) q^{67} -6.00000 q^{71} +(-5.00000 + 8.66025i) q^{73} +(-0.500000 - 0.866025i) q^{79} -6.00000 q^{83} +8.00000 q^{85} +(1.00000 + 1.73205i) q^{89} +(-6.00000 - 5.19615i) q^{91} +(-4.00000 + 6.92820i) q^{95} +1.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{5} - 4q^{7} + O(q^{10}) \) \( 2q - 2q^{5} - 4q^{7} + 6q^{13} - 4q^{17} - 4q^{19} - 2q^{23} + q^{25} - 8q^{29} - q^{31} - 2q^{35} + 3q^{37} - 16q^{41} - 2q^{43} - 8q^{47} + 2q^{49} - 14q^{53} - 12q^{59} - q^{61} - 6q^{65} - 3q^{67} - 12q^{71} - 10q^{73} - q^{79} - 12q^{83} + 16q^{85} + 2q^{89} - 12q^{91} - 8q^{95} + 2q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −1.00000 1.73205i −0.447214 0.774597i 0.550990 0.834512i \(-0.314250\pi\)
−0.998203 + 0.0599153i \(0.980917\pi\)
\(6\) 0 0
\(7\) −2.00000 1.73205i −0.755929 0.654654i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(12\) 0 0
\(13\) 3.00000 0.832050 0.416025 0.909353i \(-0.363423\pi\)
0.416025 + 0.909353i \(0.363423\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.00000 + 3.46410i −0.485071 + 0.840168i −0.999853 0.0171533i \(-0.994540\pi\)
0.514782 + 0.857321i \(0.327873\pi\)
\(18\) 0 0
\(19\) −2.00000 3.46410i −0.458831 0.794719i 0.540068 0.841621i \(-0.318398\pi\)
−0.998899 + 0.0469020i \(0.985065\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.00000 1.73205i −0.208514 0.361158i 0.742732 0.669588i \(-0.233529\pi\)
−0.951247 + 0.308431i \(0.900196\pi\)
\(24\) 0 0
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −4.00000 −0.742781 −0.371391 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 0 0
\(31\) −0.500000 + 0.866025i −0.0898027 + 0.155543i −0.907428 0.420208i \(-0.861957\pi\)
0.817625 + 0.575751i \(0.195290\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.00000 + 5.19615i −0.169031 + 0.878310i
\(36\) 0 0
\(37\) 1.50000 + 2.59808i 0.246598 + 0.427121i 0.962580 0.270998i \(-0.0873538\pi\)
−0.715981 + 0.698119i \(0.754020\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −8.00000 −1.24939 −0.624695 0.780869i \(-0.714777\pi\)
−0.624695 + 0.780869i \(0.714777\pi\)
\(42\) 0 0
\(43\) −1.00000 −0.152499 −0.0762493 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.00000 6.92820i −0.583460 1.01058i −0.995066 0.0992202i \(-0.968365\pi\)
0.411606 0.911362i \(-0.364968\pi\)
\(48\) 0 0
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −7.00000 + 12.1244i −0.961524 + 1.66541i −0.242846 + 0.970065i \(0.578081\pi\)
−0.718677 + 0.695344i \(0.755252\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −6.00000 + 10.3923i −0.781133 + 1.35296i 0.150148 + 0.988663i \(0.452025\pi\)
−0.931282 + 0.364299i \(0.881308\pi\)
\(60\) 0 0
\(61\) −0.500000 0.866025i −0.0640184 0.110883i 0.832240 0.554416i \(-0.187058\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −3.00000 5.19615i −0.372104 0.644503i
\(66\) 0 0
\(67\) −1.50000 + 2.59808i −0.183254 + 0.317406i −0.942987 0.332830i \(-0.891996\pi\)
0.759733 + 0.650236i \(0.225330\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 0 0
\(73\) −5.00000 + 8.66025i −0.585206 + 1.01361i 0.409644 + 0.912245i \(0.365653\pi\)
−0.994850 + 0.101361i \(0.967680\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −0.500000 0.866025i −0.0562544 0.0974355i 0.836527 0.547926i \(-0.184582\pi\)
−0.892781 + 0.450490i \(0.851249\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 0 0
\(85\) 8.00000 0.867722
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1.00000 + 1.73205i 0.106000 + 0.183597i 0.914146 0.405385i \(-0.132862\pi\)
−0.808146 + 0.588982i \(0.799529\pi\)
\(90\) 0 0
\(91\) −6.00000 5.19615i −0.628971 0.544705i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −4.00000 + 6.92820i −0.410391 + 0.710819i
\(96\) 0 0
\(97\) 1.00000 0.101535 0.0507673 0.998711i \(-0.483833\pi\)
0.0507673 + 0.998711i \(0.483833\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 9.00000 15.5885i 0.895533 1.55111i 0.0623905 0.998052i \(-0.480128\pi\)
0.833143 0.553058i \(-0.186539\pi\)
\(102\) 0 0
\(103\) −7.50000 12.9904i −0.738997 1.27998i −0.952947 0.303136i \(-0.901966\pi\)
0.213950 0.976845i \(-0.431367\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −3.00000 5.19615i −0.290021 0.502331i 0.683793 0.729676i \(-0.260329\pi\)
−0.973814 + 0.227345i \(0.926996\pi\)
\(108\) 0 0
\(109\) 2.50000 4.33013i 0.239457 0.414751i −0.721102 0.692829i \(-0.756364\pi\)
0.960558 + 0.278078i \(0.0896974\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) −2.00000 + 3.46410i −0.186501 + 0.323029i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 10.0000 3.46410i 0.916698 0.317554i
\(120\) 0 0
\(121\) 5.50000 + 9.52628i 0.500000 + 0.866025i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) 17.0000 1.50851 0.754253 0.656584i \(-0.227999\pi\)
0.754253 + 0.656584i \(0.227999\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −4.00000 6.92820i −0.349482 0.605320i 0.636676 0.771132i \(-0.280309\pi\)
−0.986157 + 0.165812i \(0.946976\pi\)
\(132\) 0 0
\(133\) −2.00000 + 10.3923i −0.173422 + 0.901127i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1.00000 + 1.73205i −0.0854358 + 0.147979i −0.905577 0.424182i \(-0.860562\pi\)
0.820141 + 0.572161i \(0.193895\pi\)
\(138\) 0 0
\(139\) −15.0000 −1.27228 −0.636142 0.771572i \(-0.719471\pi\)
−0.636142 + 0.771572i \(0.719471\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 4.00000 + 6.92820i 0.332182 + 0.575356i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 7.00000 + 12.1244i 0.573462 + 0.993266i 0.996207 + 0.0870170i \(0.0277334\pi\)
−0.422744 + 0.906249i \(0.638933\pi\)
\(150\) 0 0
\(151\) 8.50000 14.7224i 0.691720 1.19809i −0.279554 0.960130i \(-0.590186\pi\)
0.971274 0.237964i \(-0.0764802\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 2.00000 0.160644
\(156\) 0 0
\(157\) 9.00000 15.5885i 0.718278 1.24409i −0.243403 0.969925i \(-0.578264\pi\)
0.961681 0.274169i \(-0.0884028\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1.00000 + 5.19615i −0.0788110 + 0.409514i
\(162\) 0 0
\(163\) −9.50000 16.4545i −0.744097 1.28881i −0.950615 0.310372i \(-0.899546\pi\)
0.206518 0.978443i \(-0.433787\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −6.00000 −0.464294 −0.232147 0.972681i \(-0.574575\pi\)
−0.232147 + 0.972681i \(0.574575\pi\)
\(168\) 0 0
\(169\) −4.00000 −0.307692
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −4.00000 6.92820i −0.304114 0.526742i 0.672949 0.739689i \(-0.265027\pi\)
−0.977064 + 0.212947i \(0.931694\pi\)
\(174\) 0 0
\(175\) −2.50000 + 0.866025i −0.188982 + 0.0654654i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −13.0000 + 22.5167i −0.971666 + 1.68297i −0.281139 + 0.959667i \(0.590712\pi\)
−0.690526 + 0.723307i \(0.742621\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 3.00000 5.19615i 0.220564 0.382029i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −5.00000 8.66025i −0.361787 0.626634i 0.626468 0.779447i \(-0.284500\pi\)
−0.988255 + 0.152813i \(0.951167\pi\)
\(192\) 0 0
\(193\) 4.50000 7.79423i 0.323917 0.561041i −0.657376 0.753563i \(-0.728333\pi\)
0.981293 + 0.192522i \(0.0616668\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 12.0000 0.854965 0.427482 0.904024i \(-0.359401\pi\)
0.427482 + 0.904024i \(0.359401\pi\)
\(198\) 0 0
\(199\) −2.50000 + 4.33013i −0.177220 + 0.306955i −0.940927 0.338608i \(-0.890044\pi\)
0.763707 + 0.645563i \(0.223377\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 8.00000 + 6.92820i 0.561490 + 0.486265i
\(204\) 0 0
\(205\) 8.00000 + 13.8564i 0.558744 + 0.967773i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −25.0000 −1.72107 −0.860535 0.509390i \(-0.829871\pi\)
−0.860535 + 0.509390i \(0.829871\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.00000 + 1.73205i 0.0681994 + 0.118125i
\(216\) 0 0
\(217\) 2.50000 0.866025i 0.169711 0.0587896i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −6.00000 + 10.3923i −0.403604 + 0.699062i
\(222\) 0 0
\(223\) 12.0000 0.803579 0.401790 0.915732i \(-0.368388\pi\)
0.401790 + 0.915732i \(0.368388\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 11.0000 19.0526i 0.730096 1.26456i −0.226746 0.973954i \(-0.572809\pi\)
0.956842 0.290609i \(-0.0938578\pi\)
\(228\) 0 0
\(229\) 0.500000 + 0.866025i 0.0330409 + 0.0572286i 0.882073 0.471113i \(-0.156147\pi\)
−0.849032 + 0.528341i \(0.822814\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 8.00000 + 13.8564i 0.524097 + 0.907763i 0.999606 + 0.0280525i \(0.00893057\pi\)
−0.475509 + 0.879711i \(0.657736\pi\)
\(234\) 0 0
\(235\) −8.00000 + 13.8564i −0.521862 + 0.903892i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 26.0000 1.68180 0.840900 0.541190i \(-0.182026\pi\)
0.840900 + 0.541190i \(0.182026\pi\)
\(240\) 0 0
\(241\) −0.500000 + 0.866025i −0.0322078 + 0.0557856i −0.881680 0.471848i \(-0.843587\pi\)
0.849472 + 0.527633i \(0.176921\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 11.0000 8.66025i 0.702764 0.553283i
\(246\) 0 0
\(247\) −6.00000 10.3923i −0.381771 0.661247i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 10.0000 0.631194 0.315597 0.948893i \(-0.397795\pi\)
0.315597 + 0.948893i \(0.397795\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −15.0000 25.9808i −0.935674 1.62064i −0.773427 0.633885i \(-0.781459\pi\)
−0.162247 0.986750i \(-0.551874\pi\)
\(258\) 0 0
\(259\) 1.50000 7.79423i 0.0932055 0.484310i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 6.00000 10.3923i 0.369976 0.640817i −0.619586 0.784929i \(-0.712699\pi\)
0.989561 + 0.144112i \(0.0460326\pi\)
\(264\) 0 0
\(265\) 28.0000 1.72003
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(270\) 0 0
\(271\) 6.50000 + 11.2583i 0.394847 + 0.683895i 0.993082 0.117426i \(-0.0374643\pi\)
−0.598235 + 0.801321i \(0.704131\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −15.5000 + 26.8468i −0.931305 + 1.61307i −0.150210 + 0.988654i \(0.547995\pi\)
−0.781094 + 0.624413i \(0.785338\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 30.0000 1.78965 0.894825 0.446417i \(-0.147300\pi\)
0.894825 + 0.446417i \(0.147300\pi\)
\(282\) 0 0
\(283\) −11.5000 + 19.9186i −0.683604 + 1.18404i 0.290269 + 0.956945i \(0.406255\pi\)
−0.973873 + 0.227092i \(0.927078\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 16.0000 + 13.8564i 0.944450 + 0.817918i
\(288\) 0 0
\(289\) 0.500000 + 0.866025i 0.0294118 + 0.0509427i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 12.0000 0.701047 0.350524 0.936554i \(-0.386004\pi\)
0.350524 + 0.936554i \(0.386004\pi\)
\(294\) 0 0
\(295\) 24.0000 1.39733
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −3.00000 5.19615i −0.173494 0.300501i
\(300\) 0 0
\(301\) 2.00000 + 1.73205i 0.115278 + 0.0998337i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1.00000 + 1.73205i −0.0572598 + 0.0991769i
\(306\) 0 0
\(307\) −23.0000 −1.31268 −0.656340 0.754466i \(-0.727896\pi\)
−0.656340 + 0.754466i \(0.727896\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 3.00000 5.19615i 0.170114 0.294647i −0.768345 0.640036i \(-0.778920\pi\)
0.938460 + 0.345389i \(0.112253\pi\)
\(312\) 0 0
\(313\) −7.00000 12.1244i −0.395663 0.685309i 0.597522 0.801852i \(-0.296152\pi\)
−0.993186 + 0.116543i \(0.962819\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −12.0000 20.7846i −0.673987 1.16738i −0.976764 0.214318i \(-0.931247\pi\)
0.302777 0.953062i \(-0.402086\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 16.0000 0.890264
\(324\) 0 0
\(325\) 1.50000 2.59808i 0.0832050 0.144115i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −4.00000 + 20.7846i −0.220527 + 1.14589i
\(330\) 0 0
\(331\) −4.00000 6.92820i −0.219860 0.380808i 0.734905 0.678170i \(-0.237227\pi\)
−0.954765 + 0.297361i \(0.903893\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 6.00000 0.327815
\(336\) 0 0
\(337\) −22.0000 −1.19842 −0.599208 0.800593i \(-0.704518\pi\)
−0.599208 + 0.800593i \(0.704518\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 6.00000 10.3923i 0.322097 0.557888i −0.658824 0.752297i \(-0.728946\pi\)
0.980921 + 0.194409i \(0.0622790\pi\)
\(348\) 0 0
\(349\) −19.0000 −1.01705 −0.508523 0.861048i \(-0.669808\pi\)
−0.508523 + 0.861048i \(0.669808\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 12.0000 20.7846i 0.638696 1.10625i −0.347024 0.937856i \(-0.612808\pi\)
0.985719 0.168397i \(-0.0538590\pi\)
\(354\) 0 0
\(355\) 6.00000 + 10.3923i 0.318447 + 0.551566i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3.00000 + 5.19615i 0.158334 + 0.274242i 0.934268 0.356572i \(-0.116054\pi\)
−0.775934 + 0.630814i \(0.782721\pi\)
\(360\) 0 0
\(361\) 1.50000 2.59808i 0.0789474 0.136741i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 20.0000 1.04685
\(366\) 0 0
\(367\) 8.00000 13.8564i 0.417597 0.723299i −0.578101 0.815966i \(-0.696206\pi\)
0.995697 + 0.0926670i \(0.0295392\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 35.0000 12.1244i 1.81711 0.629465i
\(372\) 0 0
\(373\) 11.0000 + 19.0526i 0.569558 + 0.986504i 0.996610 + 0.0822766i \(0.0262191\pi\)
−0.427051 + 0.904227i \(0.640448\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −12.0000 −0.618031
\(378\) 0 0
\(379\) 15.0000 0.770498 0.385249 0.922813i \(-0.374116\pi\)
0.385249 + 0.922813i \(0.374116\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −15.0000 25.9808i −0.766464 1.32755i −0.939469 0.342634i \(-0.888681\pi\)
0.173005 0.984921i \(-0.444652\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −14.0000 + 24.2487i −0.709828 + 1.22946i 0.255092 + 0.966917i \(0.417894\pi\)
−0.964921 + 0.262542i \(0.915439\pi\)
\(390\) 0 0
\(391\) 8.00000 0.404577
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1.00000 + 1.73205i −0.0503155 + 0.0871489i
\(396\) 0 0
\(397\) −6.50000 11.2583i −0.326226 0.565039i 0.655534 0.755166i \(-0.272444\pi\)
−0.981760 + 0.190126i \(0.939110\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(402\) 0 0
\(403\) −1.50000 + 2.59808i −0.0747203 + 0.129419i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 19.5000 33.7750i 0.964213 1.67007i 0.252498 0.967597i \(-0.418748\pi\)
0.711715 0.702468i \(-0.247919\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 30.0000 10.3923i 1.47620 0.511372i
\(414\) 0 0
\(415\) 6.00000 + 10.3923i 0.294528 + 0.510138i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 14.0000 0.683945 0.341972 0.939710i \(-0.388905\pi\)
0.341972 + 0.939710i \(0.388905\pi\)
\(420\) 0 0
\(421\) −38.0000 −1.85201 −0.926003 0.377515i \(-0.876779\pi\)
−0.926003 + 0.377515i \(0.876779\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 2.00000 + 3.46410i 0.0970143 + 0.168034i
\(426\) 0 0
\(427\) −0.500000 + 2.59808i −0.0241967 + 0.125730i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −12.0000 + 20.7846i −0.578020 + 1.00116i 0.417687 + 0.908591i \(0.362841\pi\)
−0.995706 + 0.0925683i \(0.970492\pi\)
\(432\) 0 0
\(433\) 7.00000 0.336399 0.168199 0.985753i \(-0.446205\pi\)
0.168199 + 0.985753i \(0.446205\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4.00000 + 6.92820i −0.191346 + 0.331421i
\(438\) 0 0
\(439\) 12.0000 + 20.7846i 0.572729 + 0.991995i 0.996284 + 0.0861252i \(0.0274485\pi\)
−0.423556 + 0.905870i \(0.639218\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −4.00000 6.92820i −0.190046 0.329169i 0.755219 0.655472i \(-0.227530\pi\)
−0.945265 + 0.326303i \(0.894197\pi\)
\(444\) 0 0
\(445\) 2.00000 3.46410i 0.0948091 0.164214i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 10.0000 0.471929 0.235965 0.971762i \(-0.424175\pi\)
0.235965 + 0.971762i \(0.424175\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −3.00000 + 15.5885i −0.140642 + 0.730798i
\(456\) 0 0
\(457\) −12.5000 21.6506i −0.584725 1.01277i −0.994910 0.100771i \(-0.967869\pi\)
0.410184 0.912003i \(-0.365464\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 8.00000 0.371792 0.185896 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −3.00000 5.19615i −0.138823 0.240449i 0.788228 0.615383i \(-0.210999\pi\)
−0.927052 + 0.374934i \(0.877665\pi\)
\(468\) 0 0
\(469\) 7.50000 2.59808i 0.346318 0.119968i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −4.00000 −0.183533
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −5.00000 + 8.66025i −0.228456 + 0.395697i −0.957351 0.288929i \(-0.906701\pi\)
0.728895 + 0.684626i \(0.240034\pi\)
\(480\) 0 0
\(481\) 4.50000 + 7.79423i 0.205182 + 0.355386i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.00000 1.73205i −0.0454077 0.0786484i
\(486\) 0 0
\(487\) 4.00000 6.92820i 0.181257 0.313947i −0.761052 0.648691i \(-0.775317\pi\)
0.942309 + 0.334744i \(0.108650\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 6.00000 0.270776 0.135388 0.990793i \(-0.456772\pi\)
0.135388 + 0.990793i \(0.456772\pi\)
\(492\) 0 0
\(493\) 8.00000 13.8564i 0.360302 0.624061i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 12.0000 + 10.3923i 0.538274 + 0.466159i
\(498\) 0 0
\(499\) −3.50000 6.06218i −0.156682 0.271380i 0.776989 0.629515i \(-0.216746\pi\)
−0.933670 + 0.358134i \(0.883413\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −14.0000 −0.624229 −0.312115 0.950044i \(-0.601037\pi\)
−0.312115 + 0.950044i \(0.601037\pi\)
\(504\) 0 0
\(505\) −36.0000 −1.60198
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −3.00000 5.19615i −0.132973 0.230315i 0.791849 0.610718i \(-0.209119\pi\)
−0.924821 + 0.380402i \(0.875786\pi\)
\(510\) 0 0
\(511\) 25.0000 8.66025i 1.10593 0.383107i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −15.0000 + 25.9808i −0.660979 + 1.14485i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 3.00000 5.19615i 0.131432 0.227648i −0.792797 0.609486i \(-0.791376\pi\)
0.924229 + 0.381839i \(0.124709\pi\)
\(522\) 0 0
\(523\) 12.5000 + 21.6506i 0.546587 + 0.946716i 0.998505 + 0.0546569i \(0.0174065\pi\)
−0.451918 + 0.892059i \(0.649260\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.00000 3.46410i −0.0871214 0.150899i
\(528\) 0 0
\(529\) 9.50000 16.4545i 0.413043 0.715412i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −24.0000 −1.03956
\(534\) 0 0
\(535\) −6.00000 + 10.3923i −0.259403 + 0.449299i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −17.0000 29.4449i −0.730887 1.26593i −0.956504 0.291718i \(-0.905773\pi\)
0.225617 0.974216i \(-0.427560\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −10.0000 −0.428353
\(546\) 0 0
\(547\) 7.00000 0.299298 0.149649 0.988739i \(-0.452186\pi\)
0.149649 + 0.988739i \(0.452186\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 8.00000 + 13.8564i 0.340811 + 0.590303i
\(552\) 0 0
\(553\) −0.500000 + 2.59808i −0.0212622 + 0.110481i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.00000 1.73205i 0.0423714 0.0733893i −0.844062 0.536246i \(-0.819842\pi\)
0.886433 + 0.462856i \(0.153175\pi\)
\(558\) 0 0
\(559\) −3.00000 −0.126886
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 7.00000 12.1244i 0.295015 0.510981i −0.679974 0.733237i \(-0.738009\pi\)
0.974988 + 0.222256i \(0.0713421\pi\)
\(564\) 0 0
\(565\) −6.00000 10.3923i −0.252422 0.437208i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −3.00000 5.19615i −0.125767 0.217834i 0.796266 0.604947i \(-0.206806\pi\)
−0.922032 + 0.387113i \(0.873472\pi\)
\(570\) 0 0
\(571\) −10.0000 + 17.3205i −0.418487 + 0.724841i −0.995788 0.0916910i \(-0.970773\pi\)
0.577301 + 0.816532i \(0.304106\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −2.00000 −0.0834058
\(576\) 0 0
\(577\) −13.5000 + 23.3827i −0.562012 + 0.973434i 0.435308 + 0.900281i \(0.356639\pi\)
−0.997321 + 0.0731526i \(0.976694\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 12.0000 + 10.3923i 0.497844 + 0.431145i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −38.0000 −1.56843 −0.784214 0.620491i \(-0.786934\pi\)
−0.784214 + 0.620491i \(0.786934\pi\)
\(588\) 0 0
\(589\) 4.00000 0.164817
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −21.0000 36.3731i −0.862367 1.49366i −0.869638 0.493689i \(-0.835648\pi\)
0.00727173 0.999974i \(-0.497685\pi\)
\(594\) 0 0
\(595\) −16.0000 13.8564i −0.655936 0.568057i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −20.0000 + 34.6410i −0.817178 + 1.41539i 0.0905757 + 0.995890i \(0.471129\pi\)
−0.907754 + 0.419504i \(0.862204\pi\)
\(600\) 0 0
\(601\) −5.00000 −0.203954 −0.101977 0.994787i \(-0.532517\pi\)
−0.101977 + 0.994787i \(0.532517\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 11.0000 19.0526i 0.447214 0.774597i
\(606\) 0 0
\(607\) 16.0000 + 27.7128i 0.649420 + 1.12483i 0.983262 + 0.182199i \(0.0583216\pi\)
−0.333842 + 0.942629i \(0.608345\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −12.0000 20.7846i −0.485468 0.840855i
\(612\) 0 0
\(613\) −0.500000 + 0.866025i −0.0201948 + 0.0349784i −0.875946 0.482409i \(-0.839762\pi\)
0.855751 + 0.517387i \(0.173095\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 36.0000 1.44931 0.724653 0.689114i \(-0.242000\pi\)
0.724653 + 0.689114i \(0.242000\pi\)
\(618\) 0 0
\(619\) −13.5000 + 23.3827i −0.542611 + 0.939829i 0.456142 + 0.889907i \(0.349231\pi\)
−0.998753 + 0.0499226i \(0.984103\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1.00000 5.19615i 0.0400642 0.208179i
\(624\) 0 0
\(625\) 9.50000 + 16.4545i 0.380000 + 0.658179i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −12.0000 −0.478471
\(630\) 0 0
\(631\) 47.0000 1.87104 0.935520 0.353273i \(-0.114931\pi\)
0.935520 + 0.353273i \(0.114931\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −17.0000 29.4449i −0.674624 1.16848i
\(636\) 0 0
\(637\) 3.00000 + 20.7846i 0.118864 + 0.823516i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −20.0000 + 34.6410i −0.789953 + 1.36824i 0.136043 + 0.990703i \(0.456562\pi\)
−0.925995 + 0.377535i \(0.876772\pi\)
\(642\) 0 0
\(643\) −29.0000 −1.14365 −0.571824 0.820376i \(-0.693764\pi\)
−0.571824 + 0.820376i \(0.693764\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 12.0000 20.7846i 0.471769 0.817127i −0.527710 0.849425i \(-0.676949\pi\)
0.999478 + 0.0322975i \(0.0102824\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −7.00000 12.1244i −0.273931 0.474463i 0.695934 0.718106i \(-0.254991\pi\)
−0.969865 + 0.243643i \(0.921657\pi\)
\(654\) 0 0
\(655\) −8.00000 + 13.8564i −0.312586 + 0.541415i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −10.0000 −0.389545 −0.194772 0.980848i \(-0.562397\pi\)
−0.194772 + 0.980848i \(0.562397\pi\)
\(660\) 0 0
\(661\) 11.0000 19.0526i 0.427850 0.741059i −0.568831 0.822454i \(-0.692604\pi\)
0.996682 + 0.0813955i \(0.0259377\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 20.0000 6.92820i 0.775567 0.268664i
\(666\) 0 0
\(667\) 4.00000 + 6.92820i 0.154881 + 0.268261i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −26.0000 −1.00223 −0.501113 0.865382i \(-0.667076\pi\)
−0.501113 + 0.865382i \(0.667076\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 18.0000 + 31.1769i 0.691796 + 1.19823i 0.971249 + 0.238067i \(0.0765137\pi\)
−0.279453 + 0.960159i \(0.590153\pi\)
\(678\) 0 0
\(679\) −2.00000 1.73205i −0.0767530 0.0664700i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 9.00000 15.5885i 0.344375 0.596476i −0.640865 0.767654i \(-0.721424\pi\)
0.985240 + 0.171178i \(0.0547574\pi\)
\(684\) 0 0
\(685\) 4.00000 0.152832
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −21.0000 + 36.3731i −0.800036 + 1.38570i
\(690\) 0 0
\(691\) 3.50000 + 6.06218i 0.133146 + 0.230616i 0.924888 0.380240i \(-0.124159\pi\)
−0.791742 + 0.610856i \(0.790825\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 15.0000 + 25.9808i 0.568982 + 0.985506i
\(696\) 0 0
\(697\) 16.0000 27.7128i 0.606043 1.04970i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −44.0000 −1.66186 −0.830929 0.556379i \(-0.812190\pi\)
−0.830929 + 0.556379i \(0.812190\pi\)
\(702\) 0 0
\(703\) 6.00000 10.3923i 0.226294 0.391953i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −45.0000 + 15.5885i −1.69240 + 0.586264i
\(708\) 0 0
\(709\) 8.50000 + 14.7224i 0.319224 + 0.552913i 0.980326 0.197383i \(-0.0632444\pi\)
−0.661102 + 0.750296i \(0.729911\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2.00000 0.0749006
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −9.00000 15.5885i −0.335643 0.581351i 0.647965 0.761670i \(-0.275620\pi\)
−0.983608 + 0.180319i \(0.942287\pi\)
\(720\) 0 0
\(721\) −7.50000 + 38.9711i −0.279315 + 1.45136i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −2.00000 + 3.46410i −0.0742781 + 0.128654i
\(726\) 0 0
\(727\) 23.0000 0.853023 0.426511 0.904482i \(-0.359742\pi\)
0.426511 + 0.904482i \(0.359742\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 2.00000 3.46410i 0.0739727 0.128124i
\(732\) 0 0
\(733\) −15.5000 26.8468i −0.572506 0.991609i −0.996308 0.0858539i \(-0.972638\pi\)
0.423802 0.905755i \(-0.360695\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −9.50000 + 16.4545i −0.349463 + 0.605288i −0.986154 0.165831i \(-0.946969\pi\)
0.636691 + 0.771119i \(0.280303\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 44.0000 1.61420 0.807102 0.590412i \(-0.201035\pi\)
0.807102 + 0.590412i \(0.201035\pi\)
\(744\) 0 0
\(745\) 14.0000 24.2487i 0.512920 0.888404i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3.00000 + 15.5885i −0.109618 + 0.569590i
\(750\) 0 0
\(751\) −10.0000 17.3205i −0.364905 0.632034i 0.623856 0.781540i \(-0.285565\pi\)
−0.988761 + 0.149505i \(0.952232\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −34.0000 −1.23739
\(756\) 0 0
\(757\) −17.0000 −0.617876 −0.308938 0.951082i \(-0.599973\pi\)
−0.308938 + 0.951082i \(0.599973\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −24.0000 41.5692i −0.869999 1.50688i −0.861996 0.506915i \(-0.830786\pi\)
−0.00800331 0.999968i \(-0.502548\pi\)
\(762\) 0 0
\(763\) −12.5000 + 4.33013i −0.452530 + 0.156761i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −18.0000 + 31.1769i −0.649942 + 1.12573i
\(768\) 0 0
\(769\) −26.0000 −0.937584 −0.468792 0.883309i \(-0.655311\pi\)
−0.468792 + 0.883309i \(0.655311\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 10.0000 17.3205i 0.359675 0.622975i −0.628231 0.778027i \(-0.716221\pi\)
0.987906 + 0.155051i \(0.0495542\pi\)
\(774\) 0 0
\(775\) 0.500000 + 0.866025i 0.0179605 + 0.0311086i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 16.0000 + 27.7128i 0.573259 + 0.992915i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −36.0000 −1.28490
\(786\) 0 0
\(787\) −18.5000 + 32.0429i −0.659454 + 1.14221i 0.321303 + 0.946976i \(0.395879\pi\)
−0.980757 + 0.195231i \(0.937454\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −12.0000 10.3923i −0.426671 0.369508i
\(792\) 0 0
\(793\) −1.50000 2.59808i −0.0532666 0.0922604i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −24.0000 −0.850124 −0.425062 0.905164i \(-0.639748\pi\)
−0.425062 + 0.905164i \(0.639748\pi\)
\(798\) 0 0
\(799\) 32.0000 1.13208
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 10.0000 3.46410i 0.352454 0.122094i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −15.0000 + 25.9808i −0.527372 + 0.913435i 0.472119 + 0.881535i \(0.343489\pi\)
−0.999491 + 0.0319002i \(0.989844\pi\)
\(810\) 0 0
\(811\) 12.0000 0.421377 0.210688 0.977553i \(-0.432429\pi\)
0.210688 + 0.977553i \(0.432429\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −19.0000 + 32.9090i −0.665541 + 1.15275i
\(816\) 0 0
\(817\) 2.00000 + 3.46410i 0.0699711 + 0.121194i