Properties

Label 1512.2.s.e.1297.1
Level $1512$
Weight $2$
Character 1512.1297
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: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1297.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1512.1297
Dual form 1512.2.s.e.865.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{5} +(2.50000 - 0.866025i) q^{7} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{5} +(2.50000 - 0.866025i) q^{7} +(-1.50000 - 2.59808i) q^{11} +6.00000 q^{13} +(-2.00000 - 3.46410i) q^{17} +(-2.00000 + 3.46410i) q^{19} +(2.00000 - 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{25} +5.00000 q^{29} +(-3.50000 - 6.06218i) q^{31} +(-1.00000 + 5.19615i) q^{35} -2.00000 q^{41} +8.00000 q^{43} +(-1.00000 + 1.73205i) q^{47} +(5.50000 - 4.33013i) q^{49} +(5.00000 + 8.66025i) q^{53} +6.00000 q^{55} +(-4.50000 - 7.79423i) q^{59} +(4.00000 - 6.92820i) q^{61} +(-6.00000 + 10.3923i) q^{65} +(3.00000 + 5.19615i) q^{67} +12.0000 q^{71} +(5.50000 + 9.52628i) q^{73} +(-6.00000 - 5.19615i) q^{77} +(-0.500000 + 0.866025i) q^{79} +15.0000 q^{83} +8.00000 q^{85} +(-5.00000 + 8.66025i) q^{89} +(15.0000 - 5.19615i) q^{91} +(-4.00000 - 6.92820i) q^{95} -5.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{5} + 5q^{7} + O(q^{10}) \) \( 2q - 2q^{5} + 5q^{7} - 3q^{11} + 12q^{13} - 4q^{17} - 4q^{19} + 4q^{23} + q^{25} + 10q^{29} - 7q^{31} - 2q^{35} - 4q^{41} + 16q^{43} - 2q^{47} + 11q^{49} + 10q^{53} + 12q^{55} - 9q^{59} + 8q^{61} - 12q^{65} + 6q^{67} + 24q^{71} + 11q^{73} - 12q^{77} - q^{79} + 30q^{83} + 16q^{85} - 10q^{89} + 30q^{91} - 8q^{95} - 10q^{97} + O(q^{100}) \)

Character values

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

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

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 −0.998203 0.0599153i \(-0.980917\pi\)
0.550990 + 0.834512i \(0.314250\pi\)
\(6\) 0 0
\(7\) 2.50000 0.866025i 0.944911 0.327327i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.50000 2.59808i −0.452267 0.783349i 0.546259 0.837616i \(-0.316051\pi\)
−0.998526 + 0.0542666i \(0.982718\pi\)
\(12\) 0 0
\(13\) 6.00000 1.66410 0.832050 0.554700i \(-0.187167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.00000 3.46410i −0.485071 0.840168i 0.514782 0.857321i \(-0.327873\pi\)
−0.999853 + 0.0171533i \(0.994540\pi\)
\(18\) 0 0
\(19\) −2.00000 + 3.46410i −0.458831 + 0.794719i −0.998899 0.0469020i \(-0.985065\pi\)
0.540068 + 0.841621i \(0.318398\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.00000 3.46410i 0.417029 0.722315i −0.578610 0.815604i \(-0.696405\pi\)
0.995639 + 0.0932891i \(0.0297381\pi\)
\(24\) 0 0
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 5.00000 0.928477 0.464238 0.885710i \(-0.346328\pi\)
0.464238 + 0.885710i \(0.346328\pi\)
\(30\) 0 0
\(31\) −3.50000 6.06218i −0.628619 1.08880i −0.987829 0.155543i \(-0.950287\pi\)
0.359211 0.933257i \(-0.383046\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.00000 + 5.19615i −0.169031 + 0.878310i
\(36\) 0 0
\(37\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.00000 + 1.73205i −0.145865 + 0.252646i −0.929695 0.368329i \(-0.879930\pi\)
0.783830 + 0.620975i \(0.213263\pi\)
\(48\) 0 0
\(49\) 5.50000 4.33013i 0.785714 0.618590i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 5.00000 + 8.66025i 0.686803 + 1.18958i 0.972867 + 0.231367i \(0.0743197\pi\)
−0.286064 + 0.958211i \(0.592347\pi\)
\(54\) 0 0
\(55\) 6.00000 0.809040
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.50000 7.79423i −0.585850 1.01472i −0.994769 0.102151i \(-0.967427\pi\)
0.408919 0.912571i \(-0.365906\pi\)
\(60\) 0 0
\(61\) 4.00000 6.92820i 0.512148 0.887066i −0.487753 0.872982i \(-0.662183\pi\)
0.999901 0.0140840i \(-0.00448323\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −6.00000 + 10.3923i −0.744208 + 1.28901i
\(66\) 0 0
\(67\) 3.00000 + 5.19615i 0.366508 + 0.634811i 0.989017 0.147802i \(-0.0472198\pi\)
−0.622509 + 0.782613i \(0.713886\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0 0
\(73\) 5.50000 + 9.52628i 0.643726 + 1.11497i 0.984594 + 0.174855i \(0.0559458\pi\)
−0.340868 + 0.940111i \(0.610721\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −6.00000 5.19615i −0.683763 0.592157i
\(78\) 0 0
\(79\) −0.500000 + 0.866025i −0.0562544 + 0.0974355i −0.892781 0.450490i \(-0.851249\pi\)
0.836527 + 0.547926i \(0.184582\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 15.0000 1.64646 0.823232 0.567705i \(-0.192169\pi\)
0.823232 + 0.567705i \(0.192169\pi\)
\(84\) 0 0
\(85\) 8.00000 0.867722
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −5.00000 + 8.66025i −0.529999 + 0.917985i 0.469389 + 0.882992i \(0.344474\pi\)
−0.999388 + 0.0349934i \(0.988859\pi\)
\(90\) 0 0
\(91\) 15.0000 5.19615i 1.57243 0.544705i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −4.00000 6.92820i −0.410391 0.710819i
\(96\) 0 0
\(97\) −5.00000 −0.507673 −0.253837 0.967247i \(-0.581693\pi\)
−0.253837 + 0.967247i \(0.581693\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 7.50000 + 12.9904i 0.746278 + 1.29259i 0.949595 + 0.313478i \(0.101494\pi\)
−0.203317 + 0.979113i \(0.565172\pi\)
\(102\) 0 0
\(103\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 6.00000 10.3923i 0.580042 1.00466i −0.415432 0.909624i \(-0.636370\pi\)
0.995474 0.0950377i \(-0.0302972\pi\)
\(108\) 0 0
\(109\) −8.00000 13.8564i −0.766261 1.32720i −0.939577 0.342337i \(-0.888782\pi\)
0.173316 0.984866i \(-0.444552\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −12.0000 −1.12887 −0.564433 0.825479i \(-0.690905\pi\)
−0.564433 + 0.825479i \(0.690905\pi\)
\(114\) 0 0
\(115\) 4.00000 + 6.92820i 0.373002 + 0.646058i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −8.00000 6.92820i −0.733359 0.635107i
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 6.50000 11.2583i 0.567908 0.983645i −0.428865 0.903369i \(-0.641086\pi\)
0.996773 0.0802763i \(-0.0255803\pi\)
\(132\) 0 0
\(133\) −2.00000 + 10.3923i −0.173422 + 0.901127i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 8.00000 + 13.8564i 0.683486 + 1.18383i 0.973910 + 0.226935i \(0.0728704\pi\)
−0.290424 + 0.956898i \(0.593796\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −9.00000 15.5885i −0.752618 1.30357i
\(144\) 0 0
\(145\) −5.00000 + 8.66025i −0.415227 + 0.719195i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2.50000 4.33013i 0.204808 0.354738i −0.745264 0.666770i \(-0.767676\pi\)
0.950072 + 0.312032i \(0.101010\pi\)
\(150\) 0 0
\(151\) −9.50000 16.4545i −0.773099 1.33905i −0.935857 0.352381i \(-0.885372\pi\)
0.162758 0.986666i \(-0.447961\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 14.0000 1.12451
\(156\) 0 0
\(157\) 9.00000 + 15.5885i 0.718278 + 1.24409i 0.961681 + 0.274169i \(0.0884028\pi\)
−0.243403 + 0.969925i \(0.578264\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2.00000 10.3923i 0.157622 0.819028i
\(162\) 0 0
\(163\) 7.00000 12.1244i 0.548282 0.949653i −0.450110 0.892973i \(-0.648615\pi\)
0.998392 0.0566798i \(-0.0180514\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −18.0000 −1.39288 −0.696441 0.717614i \(-0.745234\pi\)
−0.696441 + 0.717614i \(0.745234\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −5.50000 + 9.52628i −0.418157 + 0.724270i −0.995754 0.0920525i \(-0.970657\pi\)
0.577597 + 0.816322i \(0.303991\pi\)
\(174\) 0 0
\(175\) 2.00000 + 1.73205i 0.151186 + 0.130931i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0.500000 + 0.866025i 0.0373718 + 0.0647298i 0.884106 0.467286i \(-0.154768\pi\)
−0.846735 + 0.532016i \(0.821435\pi\)
\(180\) 0 0
\(181\) −16.0000 −1.18927 −0.594635 0.803996i \(-0.702704\pi\)
−0.594635 + 0.803996i \(0.702704\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −6.00000 + 10.3923i −0.438763 + 0.759961i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −5.00000 + 8.66025i −0.361787 + 0.626634i −0.988255 0.152813i \(-0.951167\pi\)
0.626468 + 0.779447i \(0.284500\pi\)
\(192\) 0 0
\(193\) −10.5000 18.1865i −0.755807 1.30910i −0.944972 0.327150i \(-0.893912\pi\)
0.189166 0.981945i \(-0.439422\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −3.00000 −0.213741 −0.106871 0.994273i \(-0.534083\pi\)
−0.106871 + 0.994273i \(0.534083\pi\)
\(198\) 0 0
\(199\) 3.50000 + 6.06218i 0.248108 + 0.429736i 0.963001 0.269498i \(-0.0868577\pi\)
−0.714893 + 0.699234i \(0.753524\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 12.5000 4.33013i 0.877328 0.303915i
\(204\) 0 0
\(205\) 2.00000 3.46410i 0.139686 0.241943i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 12.0000 0.830057
\(210\) 0 0
\(211\) −22.0000 −1.51454 −0.757271 0.653101i \(-0.773468\pi\)
−0.757271 + 0.653101i \(0.773468\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −8.00000 + 13.8564i −0.545595 + 0.944999i
\(216\) 0 0
\(217\) −14.0000 12.1244i −0.950382 0.823055i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −12.0000 20.7846i −0.807207 1.39812i
\(222\) 0 0
\(223\) −21.0000 −1.40626 −0.703132 0.711059i \(-0.748216\pi\)
−0.703132 + 0.711059i \(0.748216\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6.50000 + 11.2583i 0.431420 + 0.747242i 0.996996 0.0774548i \(-0.0246793\pi\)
−0.565576 + 0.824696i \(0.691346\pi\)
\(228\) 0 0
\(229\) −10.0000 + 17.3205i −0.660819 + 1.14457i 0.319582 + 0.947559i \(0.396457\pi\)
−0.980401 + 0.197013i \(0.936876\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 5.00000 8.66025i 0.327561 0.567352i −0.654466 0.756091i \(-0.727107\pi\)
0.982027 + 0.188739i \(0.0604400\pi\)
\(234\) 0 0
\(235\) −2.00000 3.46410i −0.130466 0.225973i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −16.0000 −1.03495 −0.517477 0.855697i \(-0.673129\pi\)
−0.517477 + 0.855697i \(0.673129\pi\)
\(240\) 0 0
\(241\) −3.50000 6.06218i −0.225455 0.390499i 0.731001 0.682376i \(-0.239053\pi\)
−0.956456 + 0.291877i \(0.905720\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 2.00000 + 13.8564i 0.127775 + 0.885253i
\(246\) 0 0
\(247\) −12.0000 + 20.7846i −0.763542 + 1.32249i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 13.0000 0.820553 0.410276 0.911961i \(-0.365432\pi\)
0.410276 + 0.911961i \(0.365432\pi\)
\(252\) 0 0
\(253\) −12.0000 −0.754434
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 6.00000 + 10.3923i 0.369976 + 0.640817i 0.989561 0.144112i \(-0.0460326\pi\)
−0.619586 + 0.784929i \(0.712699\pi\)
\(264\) 0 0
\(265\) −20.0000 −1.22859
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 13.5000 + 23.3827i 0.823110 + 1.42567i 0.903356 + 0.428892i \(0.141096\pi\)
−0.0802460 + 0.996775i \(0.525571\pi\)
\(270\) 0 0
\(271\) −4.00000 + 6.92820i −0.242983 + 0.420858i −0.961563 0.274586i \(-0.911459\pi\)
0.718580 + 0.695444i \(0.244792\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.50000 2.59808i 0.0904534 0.156670i
\(276\) 0 0
\(277\) −5.00000 8.66025i −0.300421 0.520344i 0.675810 0.737075i \(-0.263794\pi\)
−0.976231 + 0.216731i \(0.930460\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 0 0
\(283\) −4.00000 6.92820i −0.237775 0.411839i 0.722300 0.691580i \(-0.243085\pi\)
−0.960076 + 0.279741i \(0.909752\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −5.00000 + 1.73205i −0.295141 + 0.102240i
\(288\) 0 0
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 9.00000 0.525786 0.262893 0.964825i \(-0.415323\pi\)
0.262893 + 0.964825i \(0.415323\pi\)
\(294\) 0 0
\(295\) 18.0000 1.04800
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 12.0000 20.7846i 0.693978 1.20201i
\(300\) 0 0
\(301\) 20.0000 6.92820i 1.15278 0.399335i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 8.00000 + 13.8564i 0.458079 + 0.793416i
\(306\) 0 0
\(307\) −2.00000 −0.114146 −0.0570730 0.998370i \(-0.518177\pi\)
−0.0570730 + 0.998370i \(0.518177\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −9.00000 15.5885i −0.510343 0.883940i −0.999928 0.0119847i \(-0.996185\pi\)
0.489585 0.871956i \(-0.337148\pi\)
\(312\) 0 0
\(313\) −13.0000 + 22.5167i −0.734803 + 1.27272i 0.220006 + 0.975499i \(0.429392\pi\)
−0.954810 + 0.297218i \(0.903941\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 13.5000 23.3827i 0.758236 1.31330i −0.185514 0.982642i \(-0.559395\pi\)
0.943750 0.330661i \(-0.107272\pi\)
\(318\) 0 0
\(319\) −7.50000 12.9904i −0.419919 0.727322i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 16.0000 0.890264
\(324\) 0 0
\(325\) 3.00000 + 5.19615i 0.166410 + 0.288231i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1.00000 + 5.19615i −0.0551318 + 0.286473i
\(330\) 0 0
\(331\) −16.0000 + 27.7128i −0.879440 + 1.52323i −0.0274825 + 0.999622i \(0.508749\pi\)
−0.851957 + 0.523612i \(0.824584\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −12.0000 −0.655630
\(336\) 0 0
\(337\) 29.0000 1.57973 0.789865 0.613280i \(-0.210150\pi\)
0.789865 + 0.613280i \(0.210150\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −10.5000 + 18.1865i −0.568607 + 0.984856i
\(342\) 0 0
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.50000 2.59808i −0.0805242 0.139472i 0.822951 0.568112i \(-0.192326\pi\)
−0.903475 + 0.428640i \(0.858993\pi\)
\(348\) 0 0
\(349\) −4.00000 −0.214115 −0.107058 0.994253i \(-0.534143\pi\)
−0.107058 + 0.994253i \(0.534143\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −3.00000 5.19615i −0.159674 0.276563i 0.775077 0.631867i \(-0.217711\pi\)
−0.934751 + 0.355303i \(0.884378\pi\)
\(354\) 0 0
\(355\) −12.0000 + 20.7846i −0.636894 + 1.10313i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −12.0000 + 20.7846i −0.633336 + 1.09697i 0.353529 + 0.935423i \(0.384981\pi\)
−0.986865 + 0.161546i \(0.948352\pi\)
\(360\) 0 0
\(361\) 1.50000 + 2.59808i 0.0789474 + 0.136741i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −22.0000 −1.15153
\(366\) 0 0
\(367\) −10.0000 17.3205i −0.521996 0.904123i −0.999673 0.0255875i \(-0.991854\pi\)
0.477677 0.878536i \(-0.341479\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 20.0000 + 17.3205i 1.03835 + 0.899236i
\(372\) 0 0
\(373\) 2.00000 3.46410i 0.103556 0.179364i −0.809591 0.586994i \(-0.800311\pi\)
0.913147 + 0.407630i \(0.133645\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 30.0000 1.54508
\(378\) 0 0
\(379\) −6.00000 −0.308199 −0.154100 0.988055i \(-0.549248\pi\)
−0.154100 + 0.988055i \(0.549248\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 18.0000 31.1769i 0.919757 1.59307i 0.119974 0.992777i \(-0.461719\pi\)
0.799783 0.600289i \(-0.204948\pi\)
\(384\) 0 0
\(385\) 15.0000 5.19615i 0.764471 0.264820i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −9.50000 16.4545i −0.481669 0.834275i 0.518110 0.855314i \(-0.326636\pi\)
−0.999779 + 0.0210389i \(0.993303\pi\)
\(390\) 0 0
\(391\) −16.0000 −0.809155
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1.00000 1.73205i −0.0503155 0.0871489i
\(396\) 0 0
\(397\) −11.0000 + 19.0526i −0.552074 + 0.956221i 0.446051 + 0.895008i \(0.352830\pi\)
−0.998125 + 0.0612128i \(0.980503\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −9.00000 + 15.5885i −0.449439 + 0.778450i −0.998350 0.0574304i \(-0.981709\pi\)
0.548911 + 0.835881i \(0.315043\pi\)
\(402\) 0 0
\(403\) −21.0000 36.3731i −1.04608 1.81187i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −3.00000 5.19615i −0.148340 0.256933i 0.782274 0.622935i \(-0.214060\pi\)
−0.930614 + 0.366002i \(0.880726\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −18.0000 15.5885i −0.885722 0.767058i
\(414\) 0 0
\(415\) −15.0000 + 25.9808i −0.736321 + 1.27535i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −28.0000 −1.36789 −0.683945 0.729534i \(-0.739737\pi\)
−0.683945 + 0.729534i \(0.739737\pi\)
\(420\) 0 0
\(421\) −26.0000 −1.26716 −0.633581 0.773676i \(-0.718416\pi\)
−0.633581 + 0.773676i \(0.718416\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 2.00000 3.46410i 0.0970143 0.168034i
\(426\) 0 0
\(427\) 4.00000 20.7846i 0.193574 1.00584i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −9.00000 15.5885i −0.433515 0.750870i 0.563658 0.826008i \(-0.309393\pi\)
−0.997173 + 0.0751385i \(0.976060\pi\)
\(432\) 0 0
\(433\) −23.0000 −1.10531 −0.552655 0.833410i \(-0.686385\pi\)
−0.552655 + 0.833410i \(0.686385\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 8.00000 + 13.8564i 0.382692 + 0.662842i
\(438\) 0 0
\(439\) −7.50000 + 12.9904i −0.357955 + 0.619997i −0.987619 0.156871i \(-0.949859\pi\)
0.629664 + 0.776868i \(0.283193\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −14.5000 + 25.1147i −0.688916 + 1.19324i 0.283273 + 0.959039i \(0.408580\pi\)
−0.972189 + 0.234198i \(0.924754\pi\)
\(444\) 0 0
\(445\) −10.0000 17.3205i −0.474045 0.821071i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −2.00000 −0.0943858 −0.0471929 0.998886i \(-0.515028\pi\)
−0.0471929 + 0.998886i \(0.515028\pi\)
\(450\) 0 0
\(451\) 3.00000 + 5.19615i 0.141264 + 0.244677i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −6.00000 + 31.1769i −0.281284 + 1.46160i
\(456\) 0 0
\(457\) −11.0000 + 19.0526i −0.514558 + 0.891241i 0.485299 + 0.874348i \(0.338711\pi\)
−0.999857 + 0.0168929i \(0.994623\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −21.0000 −0.978068 −0.489034 0.872265i \(-0.662651\pi\)
−0.489034 + 0.872265i \(0.662651\pi\)
\(462\) 0 0
\(463\) −1.00000 −0.0464739 −0.0232370 0.999730i \(-0.507397\pi\)
−0.0232370 + 0.999730i \(0.507397\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 7.50000 12.9904i 0.347059 0.601123i −0.638667 0.769483i \(-0.720514\pi\)
0.985726 + 0.168360i \(0.0538472\pi\)
\(468\) 0 0
\(469\) 12.0000 + 10.3923i 0.554109 + 0.479872i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −12.0000 20.7846i −0.551761 0.955677i
\(474\) 0 0
\(475\) −4.00000 −0.183533
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 1.00000 + 1.73205i 0.0456912 + 0.0791394i 0.887967 0.459908i \(-0.152118\pi\)
−0.842275 + 0.539048i \(0.818784\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 5.00000 8.66025i 0.227038 0.393242i
\(486\) 0 0
\(487\) −3.50000 6.06218i −0.158600 0.274703i 0.775764 0.631023i \(-0.217365\pi\)
−0.934364 + 0.356320i \(0.884031\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 36.0000 1.62466 0.812329 0.583200i \(-0.198200\pi\)
0.812329 + 0.583200i \(0.198200\pi\)
\(492\) 0 0
\(493\) −10.0000 17.3205i −0.450377 0.780076i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 30.0000 10.3923i 1.34568 0.466159i
\(498\) 0 0
\(499\) 4.00000 6.92820i 0.179065 0.310149i −0.762496 0.646993i \(-0.776026\pi\)
0.941560 + 0.336844i \(0.109360\pi\)
\(500\) 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
\(505\) −30.0000 −1.33498
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 19.5000 33.7750i 0.864322 1.49705i −0.00339621 0.999994i \(-0.501081\pi\)
0.867719 0.497056i \(-0.165586\pi\)
\(510\) 0 0
\(511\) 22.0000 + 19.0526i 0.973223 + 0.842836i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 6.00000 0.263880
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −12.0000 20.7846i −0.525730 0.910590i −0.999551 0.0299693i \(-0.990459\pi\)
0.473821 0.880621i \(-0.342874\pi\)
\(522\) 0 0
\(523\) −1.00000 + 1.73205i −0.0437269 + 0.0757373i −0.887061 0.461653i \(-0.847256\pi\)
0.843334 + 0.537390i \(0.180590\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −14.0000 + 24.2487i −0.609850 + 1.05629i
\(528\) 0 0
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −12.0000 −0.519778
\(534\) 0 0
\(535\) 12.0000 + 20.7846i 0.518805 + 0.898597i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −19.5000 7.79423i −0.839924 0.335721i
\(540\) 0 0
\(541\) −5.00000 + 8.66025i −0.214967 + 0.372333i −0.953262 0.302144i \(-0.902298\pi\)
0.738296 + 0.674477i \(0.235631\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 32.0000 1.37073
\(546\) 0 0
\(547\) 22.0000 0.940652 0.470326 0.882493i \(-0.344136\pi\)
0.470326 + 0.882493i \(0.344136\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −10.0000 + 17.3205i −0.426014 + 0.737878i
\(552\) 0 0
\(553\) −0.500000 + 2.59808i −0.0212622 + 0.110481i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −3.50000 6.06218i −0.148300 0.256863i 0.782299 0.622903i \(-0.214047\pi\)
−0.930599 + 0.366040i \(0.880713\pi\)
\(558\) 0 0
\(559\) 48.0000 2.03018
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 10.0000 + 17.3205i 0.421450 + 0.729972i 0.996082 0.0884397i \(-0.0281881\pi\)
−0.574632 + 0.818412i \(0.694855\pi\)
\(564\) 0 0
\(565\) 12.0000 20.7846i 0.504844 0.874415i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 18.0000 31.1769i 0.754599 1.30700i −0.190974 0.981595i \(-0.561165\pi\)
0.945573 0.325409i \(-0.105502\pi\)
\(570\) 0 0
\(571\) −16.0000 27.7128i −0.669579 1.15975i −0.978022 0.208502i \(-0.933141\pi\)
0.308443 0.951243i \(-0.400192\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 4.00000 0.166812
\(576\) 0 0
\(577\) −1.50000 2.59808i −0.0624458 0.108159i 0.833112 0.553104i \(-0.186557\pi\)
−0.895558 + 0.444945i \(0.853223\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 37.5000 12.9904i 1.55576 0.538932i
\(582\) 0 0
\(583\) 15.0000 25.9808i 0.621237 1.07601i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −20.0000 −0.825488 −0.412744 0.910847i \(-0.635430\pi\)
−0.412744 + 0.910847i \(0.635430\pi\)
\(588\) 0 0
\(589\) 28.0000 1.15372
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 6.00000 10.3923i 0.246390 0.426761i −0.716131 0.697966i \(-0.754089\pi\)
0.962522 + 0.271205i \(0.0874221\pi\)
\(594\) 0 0
\(595\) 20.0000 6.92820i 0.819920 0.284029i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 7.00000 + 12.1244i 0.286012 + 0.495388i 0.972854 0.231419i \(-0.0743369\pi\)
−0.686842 + 0.726807i \(0.741004\pi\)
\(600\) 0 0
\(601\) 22.0000 0.897399 0.448699 0.893683i \(-0.351887\pi\)
0.448699 + 0.893683i \(0.351887\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 2.00000 + 3.46410i 0.0813116 + 0.140836i
\(606\) 0 0
\(607\) −9.50000 + 16.4545i −0.385593 + 0.667867i −0.991851 0.127401i \(-0.959336\pi\)
0.606258 + 0.795268i \(0.292670\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −6.00000 + 10.3923i −0.242734 + 0.420428i
\(612\) 0 0
\(613\) −17.0000 29.4449i −0.686624 1.18927i −0.972924 0.231127i \(-0.925759\pi\)
0.286300 0.958140i \(-0.407575\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −42.0000 −1.69086 −0.845428 0.534089i \(-0.820655\pi\)
−0.845428 + 0.534089i \(0.820655\pi\)
\(618\) 0 0
\(619\) 18.0000 + 31.1769i 0.723481 + 1.25311i 0.959596 + 0.281381i \(0.0907924\pi\)
−0.236115 + 0.971725i \(0.575874\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −5.00000 + 25.9808i −0.200321 + 1.04090i
\(624\) 0 0
\(625\) 9.50000 16.4545i 0.380000 0.658179i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 41.0000 1.63218 0.816092 0.577922i \(-0.196136\pi\)
0.816092 + 0.577922i \(0.196136\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −8.00000 + 13.8564i −0.317470 + 0.549875i
\(636\) 0 0
\(637\) 33.0000 25.9808i 1.30751 1.02940i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 19.0000 + 32.9090i 0.750455 + 1.29983i 0.947602 + 0.319452i \(0.103499\pi\)
−0.197148 + 0.980374i \(0.563168\pi\)
\(642\) 0 0
\(643\) −26.0000 −1.02534 −0.512670 0.858586i \(-0.671344\pi\)
−0.512670 + 0.858586i \(0.671344\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −9.00000 15.5885i −0.353827 0.612845i 0.633090 0.774078i \(-0.281786\pi\)
−0.986916 + 0.161233i \(0.948453\pi\)
\(648\) 0 0
\(649\) −13.5000 + 23.3827i −0.529921 + 0.917851i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −7.00000 + 12.1244i −0.273931 + 0.474463i −0.969865 0.243643i \(-0.921657\pi\)
0.695934 + 0.718106i \(0.254991\pi\)
\(654\) 0 0
\(655\) 13.0000 + 22.5167i 0.507952 + 0.879799i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 23.0000 0.895953 0.447976 0.894045i \(-0.352145\pi\)
0.447976 + 0.894045i \(0.352145\pi\)
\(660\) 0 0
\(661\) 23.0000 + 39.8372i 0.894596 + 1.54949i 0.834303 + 0.551306i \(0.185870\pi\)
0.0602929 + 0.998181i \(0.480797\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −16.0000 13.8564i −0.620453 0.537328i
\(666\) 0 0
\(667\) 10.0000 17.3205i 0.387202 0.670653i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −24.0000 −0.926510
\(672\) 0 0
\(673\) 34.0000 1.31060 0.655302 0.755367i \(-0.272541\pi\)
0.655302 + 0.755367i \(0.272541\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.50000 + 2.59808i −0.0576497 + 0.0998522i −0.893410 0.449242i \(-0.851694\pi\)
0.835760 + 0.549095i \(0.185027\pi\)
\(678\) 0 0
\(679\) −12.5000 + 4.33013i −0.479706 + 0.166175i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 22.5000 + 38.9711i 0.860939 + 1.49119i 0.871024 + 0.491240i \(0.163456\pi\)
−0.0100856 + 0.999949i \(0.503210\pi\)
\(684\) 0 0
\(685\) −32.0000 −1.22266
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 30.0000 + 51.9615i 1.14291 + 1.97958i
\(690\) 0 0
\(691\) 8.00000 13.8564i 0.304334 0.527123i −0.672779 0.739844i \(-0.734899\pi\)
0.977113 + 0.212721i \(0.0682327\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 4.00000 + 6.92820i 0.151511 + 0.262424i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 46.0000 1.73740 0.868698 0.495342i \(-0.164957\pi\)
0.868698 + 0.495342i \(0.164957\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 30.0000 + 25.9808i 1.12827 + 0.977107i
\(708\) 0 0
\(709\) −20.0000 + 34.6410i −0.751116 + 1.30097i 0.196167 + 0.980571i \(0.437151\pi\)
−0.947282 + 0.320400i \(0.896183\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −28.0000 −1.04861
\(714\) 0 0
\(715\) 36.0000 1.34632
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −21.0000 + 36.3731i −0.783168 + 1.35649i 0.146920 + 0.989148i \(0.453064\pi\)
−0.930087 + 0.367338i \(0.880269\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 2.50000 + 4.33013i 0.0928477 + 0.160817i
\(726\) 0 0
\(727\) −40.0000 −1.48352 −0.741759 0.670667i \(-0.766008\pi\)
−0.741759 + 0.670667i \(0.766008\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −16.0000 27.7128i −0.591781 1.02500i
\(732\) 0 0
\(733\) 10.0000 17.3205i 0.369358 0.639748i −0.620107 0.784517i \(-0.712911\pi\)
0.989465 + 0.144770i \(0.0462441\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 9.00000 15.5885i 0.331519 0.574208i
\(738\) 0 0
\(739\) 7.00000 + 12.1244i 0.257499 + 0.446002i 0.965571 0.260138i \(-0.0837682\pi\)
−0.708072 + 0.706140i \(0.750435\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −34.0000 −1.24734 −0.623670 0.781688i \(-0.714359\pi\)
−0.623670 + 0.781688i \(0.714359\pi\)
\(744\) 0 0
\(745\) 5.00000 + 8.66025i 0.183186 + 0.317287i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 6.00000 31.1769i 0.219235 1.13918i
\(750\) 0 0
\(751\) 14.0000 24.2487i 0.510867 0.884848i −0.489053 0.872254i \(-0.662658\pi\)
0.999921 0.0125942i \(-0.00400897\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 38.0000 1.38296
\(756\) 0 0
\(757\) 46.0000 1.67190 0.835949 0.548807i \(-0.184918\pi\)
0.835949 + 0.548807i \(0.184918\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 24.0000 41.5692i 0.869999 1.50688i 0.00800331 0.999968i \(-0.497452\pi\)
0.861996 0.506915i \(-0.169214\pi\)
\(762\) 0 0
\(763\) −32.0000 27.7128i −1.15848 1.00327i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −27.0000 46.7654i −0.974913 1.68860i
\(768\) 0 0
\(769\) 25.0000 0.901523 0.450762 0.892644i \(-0.351152\pi\)
0.450762 + 0.892644i \(0.351152\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −11.0000 19.0526i −0.395643 0.685273i 0.597540 0.801839i \(-0.296145\pi\)
−0.993183 + 0.116566i \(0.962811\pi\)
\(774\) 0 0
\(775\) 3.50000 6.06218i 0.125724 0.217760i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4.00000 6.92820i 0.143315 0.248229i
\(780\) 0 0
\(781\) −18.0000 31.1769i −0.644091 1.11560i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −36.0000 −1.28490
\(786\) 0 0
\(787\) 7.00000 + 12.1244i 0.249523 + 0.432187i 0.963394 0.268091i \(-0.0863928\pi\)
−0.713871 + 0.700278i \(0.753059\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −30.0000 + 10.3923i −1.06668 + 0.369508i
\(792\) 0 0
\(793\) 24.0000 41.5692i 0.852265 1.47617i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 3.00000 0.106265 0.0531327 0.998587i \(-0.483079\pi\)
0.0531327 + 0.998587i \(0.483079\pi\)
\(798\) 0 0
\(799\) 8.00000 0.283020
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 16.5000 28.5788i 0.582272 1.00853i
\(804\) 0 0
\(805\) 16.0000 + 13.8564i 0.563926 + 0.488374i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −3.00000 5.19615i −0.105474 0.182687i 0.808458 0.588555i \(-0.200303\pi\)
−0.913932 + 0.405868i \(0.866969\pi\)
\(810\) 0 0
\(811\) 6.00000 0.210688 0.105344 0.994436i \(-0.466406\pi\)
0.105344 + 0.994436i \(0.466406\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 14.0000 + 24.2487i 0.490399 + 0.849395i
\(816\) 0 0
\(817\)