Properties

Label 216.2.i.a.73.1
Level $216$
Weight $2$
Character 216.73
Analytic conductor $1.725$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 216.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.72476868366\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 72)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 73.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 216.73
Dual form 216.2.i.a.145.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{5} +(1.50000 - 2.59808i) q^{7} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{5} +(1.50000 - 2.59808i) q^{7} +(2.50000 - 4.33013i) q^{11} +(2.50000 + 4.33013i) q^{13} +2.00000 q^{17} -4.00000 q^{19} +(-0.500000 - 0.866025i) q^{23} +(2.00000 - 3.46410i) q^{25} +(-4.50000 + 7.79423i) q^{29} +(0.500000 + 0.866025i) q^{31} -3.00000 q^{35} -6.00000 q^{37} +(1.50000 + 2.59808i) q^{41} +(-0.500000 + 0.866025i) q^{43} +(-1.50000 + 2.59808i) q^{47} +(-1.00000 - 1.73205i) q^{49} -2.00000 q^{53} -5.00000 q^{55} +(5.50000 + 9.52628i) q^{59} +(-3.50000 + 6.06218i) q^{61} +(2.50000 - 4.33013i) q^{65} +(0.500000 + 0.866025i) q^{67} -4.00000 q^{71} -2.00000 q^{73} +(-7.50000 - 12.9904i) q^{77} +(-0.500000 + 0.866025i) q^{79} +(0.500000 - 0.866025i) q^{83} +(-1.00000 - 1.73205i) q^{85} +18.0000 q^{89} +15.0000 q^{91} +(2.00000 + 3.46410i) q^{95} +(6.50000 - 11.2583i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{5} + 3q^{7} + O(q^{10}) \) \( 2q - q^{5} + 3q^{7} + 5q^{11} + 5q^{13} + 4q^{17} - 8q^{19} - q^{23} + 4q^{25} - 9q^{29} + q^{31} - 6q^{35} - 12q^{37} + 3q^{41} - q^{43} - 3q^{47} - 2q^{49} - 4q^{53} - 10q^{55} + 11q^{59} - 7q^{61} + 5q^{65} + q^{67} - 8q^{71} - 4q^{73} - 15q^{77} - q^{79} + q^{83} - 2q^{85} + 36q^{89} + 30q^{91} + 4q^{95} + 13q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).

\(n\) \(55\) \(109\) \(137\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) −0.500000 0.866025i −0.223607 0.387298i 0.732294 0.680989i \(-0.238450\pi\)
−0.955901 + 0.293691i \(0.905116\pi\)
\(6\) 0 0
\(7\) 1.50000 2.59808i 0.566947 0.981981i −0.429919 0.902867i \(-0.641458\pi\)
0.996866 0.0791130i \(-0.0252088\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.50000 4.33013i 0.753778 1.30558i −0.192201 0.981356i \(-0.561563\pi\)
0.945979 0.324227i \(-0.105104\pi\)
\(12\) 0 0
\(13\) 2.50000 + 4.33013i 0.693375 + 1.20096i 0.970725 + 0.240192i \(0.0772105\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 0 0
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.500000 0.866025i −0.104257 0.180579i 0.809177 0.587565i \(-0.199913\pi\)
−0.913434 + 0.406986i \(0.866580\pi\)
\(24\) 0 0
\(25\) 2.00000 3.46410i 0.400000 0.692820i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −4.50000 + 7.79423i −0.835629 + 1.44735i 0.0578882 + 0.998323i \(0.481563\pi\)
−0.893517 + 0.449029i \(0.851770\pi\)
\(30\) 0 0
\(31\) 0.500000 + 0.866025i 0.0898027 + 0.155543i 0.907428 0.420208i \(-0.138043\pi\)
−0.817625 + 0.575751i \(0.804710\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −3.00000 −0.507093
\(36\) 0 0
\(37\) −6.00000 −0.986394 −0.493197 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1.50000 + 2.59808i 0.234261 + 0.405751i 0.959058 0.283211i \(-0.0913998\pi\)
−0.724797 + 0.688963i \(0.758066\pi\)
\(42\) 0 0
\(43\) −0.500000 + 0.866025i −0.0762493 + 0.132068i −0.901629 0.432511i \(-0.857628\pi\)
0.825380 + 0.564578i \(0.190961\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.50000 + 2.59808i −0.218797 + 0.378968i −0.954441 0.298401i \(-0.903547\pi\)
0.735643 + 0.677369i \(0.236880\pi\)
\(48\) 0 0
\(49\) −1.00000 1.73205i −0.142857 0.247436i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −2.00000 −0.274721 −0.137361 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) 0 0
\(55\) −5.00000 −0.674200
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 5.50000 + 9.52628i 0.716039 + 1.24022i 0.962557 + 0.271078i \(0.0873801\pi\)
−0.246518 + 0.969138i \(0.579287\pi\)
\(60\) 0 0
\(61\) −3.50000 + 6.06218i −0.448129 + 0.776182i −0.998264 0.0588933i \(-0.981243\pi\)
0.550135 + 0.835076i \(0.314576\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.50000 4.33013i 0.310087 0.537086i
\(66\) 0 0
\(67\) 0.500000 + 0.866025i 0.0610847 + 0.105802i 0.894951 0.446165i \(-0.147211\pi\)
−0.833866 + 0.551967i \(0.813877\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −4.00000 −0.474713 −0.237356 0.971423i \(-0.576281\pi\)
−0.237356 + 0.971423i \(0.576281\pi\)
\(72\) 0 0
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −7.50000 12.9904i −0.854704 1.48039i
\(78\) 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
\(83\) 0.500000 0.866025i 0.0548821 0.0950586i −0.837279 0.546776i \(-0.815855\pi\)
0.892161 + 0.451717i \(0.149188\pi\)
\(84\) 0 0
\(85\) −1.00000 1.73205i −0.108465 0.187867i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 18.0000 1.90800 0.953998 0.299813i \(-0.0969242\pi\)
0.953998 + 0.299813i \(0.0969242\pi\)
\(90\) 0 0
\(91\) 15.0000 1.57243
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 2.00000 + 3.46410i 0.205196 + 0.355409i
\(96\) 0 0
\(97\) 6.50000 11.2583i 0.659975 1.14311i −0.320647 0.947199i \(-0.603900\pi\)
0.980622 0.195911i \(-0.0627665\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1.50000 2.59808i 0.149256 0.258518i −0.781697 0.623658i \(-0.785646\pi\)
0.930953 + 0.365140i \(0.118979\pi\)
\(102\) 0 0
\(103\) 2.50000 + 4.33013i 0.246332 + 0.426660i 0.962505 0.271263i \(-0.0874412\pi\)
−0.716173 + 0.697923i \(0.754108\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 0 0
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −4.50000 7.79423i −0.423324 0.733219i 0.572938 0.819599i \(-0.305804\pi\)
−0.996262 + 0.0863794i \(0.972470\pi\)
\(114\) 0 0
\(115\) −0.500000 + 0.866025i −0.0466252 + 0.0807573i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 3.00000 5.19615i 0.275010 0.476331i
\(120\) 0 0
\(121\) −7.00000 12.1244i −0.636364 1.10221i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −9.00000 −0.804984
\(126\) 0 0
\(127\) 16.0000 1.41977 0.709885 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −2.50000 4.33013i −0.218426 0.378325i 0.735901 0.677089i \(-0.236759\pi\)
−0.954327 + 0.298764i \(0.903426\pi\)
\(132\) 0 0
\(133\) −6.00000 + 10.3923i −0.520266 + 0.901127i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1.50000 2.59808i 0.128154 0.221969i −0.794808 0.606861i \(-0.792428\pi\)
0.922961 + 0.384893i \(0.125762\pi\)
\(138\) 0 0
\(139\) −1.50000 2.59808i −0.127228 0.220366i 0.795373 0.606120i \(-0.207275\pi\)
−0.922602 + 0.385754i \(0.873941\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 25.0000 2.09061
\(144\) 0 0
\(145\) 9.00000 0.747409
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 9.50000 + 16.4545i 0.778270 + 1.34800i 0.932938 + 0.360037i \(0.117236\pi\)
−0.154668 + 0.987967i \(0.549431\pi\)
\(150\) 0 0
\(151\) −8.50000 + 14.7224i −0.691720 + 1.19809i 0.279554 + 0.960130i \(0.409814\pi\)
−0.971274 + 0.237964i \(0.923520\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0.500000 0.866025i 0.0401610 0.0695608i
\(156\) 0 0
\(157\) −3.50000 6.06218i −0.279330 0.483814i 0.691888 0.722005i \(-0.256779\pi\)
−0.971219 + 0.238190i \(0.923446\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −3.00000 −0.236433
\(162\) 0 0
\(163\) −12.0000 −0.939913 −0.469956 0.882690i \(-0.655730\pi\)
−0.469956 + 0.882690i \(0.655730\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −10.5000 18.1865i −0.812514 1.40732i −0.911099 0.412188i \(-0.864765\pi\)
0.0985846 0.995129i \(-0.468568\pi\)
\(168\) 0 0
\(169\) −6.00000 + 10.3923i −0.461538 + 0.799408i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.50000 2.59808i 0.114043 0.197528i −0.803354 0.595502i \(-0.796953\pi\)
0.917397 + 0.397974i \(0.130287\pi\)
\(174\) 0 0
\(175\) −6.00000 10.3923i −0.453557 0.785584i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) −6.00000 −0.445976 −0.222988 0.974821i \(-0.571581\pi\)
−0.222988 + 0.974821i \(0.571581\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 3.00000 + 5.19615i 0.220564 + 0.382029i
\(186\) 0 0
\(187\) 5.00000 8.66025i 0.365636 0.633300i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −13.5000 + 23.3827i −0.976826 + 1.69191i −0.303052 + 0.952974i \(0.598006\pi\)
−0.673774 + 0.738938i \(0.735328\pi\)
\(192\) 0 0
\(193\) 6.50000 + 11.2583i 0.467880 + 0.810392i 0.999326 0.0366998i \(-0.0116845\pi\)
−0.531446 + 0.847092i \(0.678351\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 0 0
\(199\) −20.0000 −1.41776 −0.708881 0.705328i \(-0.750800\pi\)
−0.708881 + 0.705328i \(0.750800\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 13.5000 + 23.3827i 0.947514 + 1.64114i
\(204\) 0 0
\(205\) 1.50000 2.59808i 0.104765 0.181458i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −10.0000 + 17.3205i −0.691714 + 1.19808i
\(210\) 0 0
\(211\) −3.50000 6.06218i −0.240950 0.417338i 0.720035 0.693938i \(-0.244126\pi\)
−0.960985 + 0.276600i \(0.910792\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.00000 0.0681994
\(216\) 0 0
\(217\) 3.00000 0.203653
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 5.00000 + 8.66025i 0.336336 + 0.582552i
\(222\) 0 0
\(223\) 5.50000 9.52628i 0.368307 0.637927i −0.620994 0.783815i \(-0.713271\pi\)
0.989301 + 0.145889i \(0.0466041\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 10.5000 18.1865i 0.696909 1.20708i −0.272623 0.962121i \(-0.587891\pi\)
0.969533 0.244962i \(-0.0787754\pi\)
\(228\) 0 0
\(229\) 8.50000 + 14.7224i 0.561696 + 0.972886i 0.997349 + 0.0727709i \(0.0231842\pi\)
−0.435653 + 0.900115i \(0.643482\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −26.0000 −1.70332 −0.851658 0.524097i \(-0.824403\pi\)
−0.851658 + 0.524097i \(0.824403\pi\)
\(234\) 0 0
\(235\) 3.00000 0.195698
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −8.50000 14.7224i −0.549819 0.952315i −0.998286 0.0585157i \(-0.981363\pi\)
0.448467 0.893799i \(-0.351970\pi\)
\(240\) 0 0
\(241\) −7.50000 + 12.9904i −0.483117 + 0.836784i −0.999812 0.0193858i \(-0.993829\pi\)
0.516695 + 0.856170i \(0.327162\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1.00000 + 1.73205i −0.0638877 + 0.110657i
\(246\) 0 0
\(247\) −10.0000 17.3205i −0.636285 1.10208i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 20.0000 1.26239 0.631194 0.775625i \(-0.282565\pi\)
0.631194 + 0.775625i \(0.282565\pi\)
\(252\) 0 0
\(253\) −5.00000 −0.314347
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 3.50000 + 6.06218i 0.218324 + 0.378148i 0.954296 0.298864i \(-0.0966077\pi\)
−0.735972 + 0.677012i \(0.763274\pi\)
\(258\) 0 0
\(259\) −9.00000 + 15.5885i −0.559233 + 0.968620i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −3.50000 + 6.06218i −0.215819 + 0.373810i −0.953526 0.301312i \(-0.902576\pi\)
0.737706 + 0.675122i \(0.235909\pi\)
\(264\) 0 0
\(265\) 1.00000 + 1.73205i 0.0614295 + 0.106399i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 14.0000 0.853595 0.426798 0.904347i \(-0.359642\pi\)
0.426798 + 0.904347i \(0.359642\pi\)
\(270\) 0 0
\(271\) 8.00000 0.485965 0.242983 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −10.0000 17.3205i −0.603023 1.04447i
\(276\) 0 0
\(277\) 14.5000 25.1147i 0.871221 1.50900i 0.0104855 0.999945i \(-0.496662\pi\)
0.860735 0.509053i \(-0.170004\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 9.50000 16.4545i 0.566722 0.981592i −0.430165 0.902750i \(-0.641545\pi\)
0.996887 0.0788417i \(-0.0251222\pi\)
\(282\) 0 0
\(283\) 6.50000 + 11.2583i 0.386385 + 0.669238i 0.991960 0.126550i \(-0.0403903\pi\)
−0.605575 + 0.795788i \(0.707057\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 9.00000 0.531253
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −4.50000 7.79423i −0.262893 0.455344i 0.704117 0.710084i \(-0.251343\pi\)
−0.967009 + 0.254741i \(0.918010\pi\)
\(294\) 0 0
\(295\) 5.50000 9.52628i 0.320222 0.554641i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.50000 4.33013i 0.144579 0.250418i
\(300\) 0 0
\(301\) 1.50000 + 2.59808i 0.0864586 + 0.149751i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 7.00000 0.400819
\(306\) 0 0
\(307\) −12.0000 −0.684876 −0.342438 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −4.50000 7.79423i −0.255172 0.441970i 0.709771 0.704433i \(-0.248799\pi\)
−0.964942 + 0.262463i \(0.915465\pi\)
\(312\) 0 0
\(313\) 4.50000 7.79423i 0.254355 0.440556i −0.710365 0.703833i \(-0.751470\pi\)
0.964720 + 0.263278i \(0.0848035\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 7.50000 12.9904i 0.421242 0.729612i −0.574819 0.818280i \(-0.694928\pi\)
0.996061 + 0.0886679i \(0.0282610\pi\)
\(318\) 0 0
\(319\) 22.5000 + 38.9711i 1.25976 + 2.18197i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −8.00000 −0.445132
\(324\) 0 0
\(325\) 20.0000 1.10940
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 4.50000 + 7.79423i 0.248093 + 0.429710i
\(330\) 0 0
\(331\) 9.50000 16.4545i 0.522167 0.904420i −0.477500 0.878632i \(-0.658457\pi\)
0.999667 0.0257885i \(-0.00820965\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0.500000 0.866025i 0.0273179 0.0473160i
\(336\) 0 0
\(337\) 4.50000 + 7.79423i 0.245131 + 0.424579i 0.962168 0.272456i \(-0.0878358\pi\)
−0.717038 + 0.697034i \(0.754502\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 5.00000 0.270765
\(342\) 0 0
\(343\) 15.0000 0.809924
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −4.50000 7.79423i −0.241573 0.418416i 0.719590 0.694399i \(-0.244330\pi\)
−0.961162 + 0.275983i \(0.910997\pi\)
\(348\) 0 0
\(349\) 10.5000 18.1865i 0.562052 0.973503i −0.435265 0.900302i \(-0.643345\pi\)
0.997317 0.0732005i \(-0.0233213\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −2.50000 + 4.33013i −0.133062 + 0.230469i −0.924855 0.380319i \(-0.875814\pi\)
0.791794 + 0.610789i \(0.209147\pi\)
\(354\) 0 0
\(355\) 2.00000 + 3.46410i 0.106149 + 0.183855i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.00000 + 1.73205i 0.0523424 + 0.0906597i
\(366\) 0 0
\(367\) 11.5000 19.9186i 0.600295 1.03974i −0.392481 0.919760i \(-0.628383\pi\)
0.992776 0.119982i \(-0.0382835\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −3.00000 + 5.19615i −0.155752 + 0.269771i
\(372\) 0 0
\(373\) −17.5000 30.3109i −0.906116 1.56944i −0.819413 0.573204i \(-0.805700\pi\)
−0.0867031 0.996234i \(-0.527633\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −45.0000 −2.31762
\(378\) 0 0
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 13.5000 + 23.3827i 0.689818 + 1.19480i 0.971897 + 0.235408i \(0.0756427\pi\)
−0.282079 + 0.959391i \(0.591024\pi\)
\(384\) 0 0
\(385\) −7.50000 + 12.9904i −0.382235 + 0.662051i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 17.5000 30.3109i 0.887285 1.53682i 0.0442134 0.999022i \(-0.485922\pi\)
0.843072 0.537801i \(-0.180745\pi\)
\(390\) 0 0
\(391\) −1.00000 1.73205i −0.0505722 0.0875936i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1.00000 0.0503155
\(396\) 0 0
\(397\) −22.0000 −1.10415 −0.552074 0.833795i \(-0.686163\pi\)
−0.552074 + 0.833795i \(0.686163\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −10.5000 18.1865i −0.524345 0.908192i −0.999598 0.0283431i \(-0.990977\pi\)
0.475253 0.879849i \(-0.342356\pi\)
\(402\) 0 0
\(403\) −2.50000 + 4.33013i −0.124534 + 0.215699i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −15.0000 + 25.9808i −0.743522 + 1.28782i
\(408\) 0 0
\(409\) 16.5000 + 28.5788i 0.815872 + 1.41313i 0.908700 + 0.417450i \(0.137076\pi\)
−0.0928272 + 0.995682i \(0.529590\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 33.0000 1.62382
\(414\) 0 0
\(415\) −1.00000 −0.0490881
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 7.50000 + 12.9904i 0.366399 + 0.634622i 0.989000 0.147918i \(-0.0472572\pi\)
−0.622601 + 0.782540i \(0.713924\pi\)
\(420\) 0 0
\(421\) 0.500000 0.866025i 0.0243685 0.0422075i −0.853584 0.520955i \(-0.825576\pi\)
0.877952 + 0.478748i \(0.158909\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 4.00000 6.92820i 0.194029 0.336067i
\(426\) 0 0
\(427\) 10.5000 + 18.1865i 0.508131 + 0.880108i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 8.00000 0.385346 0.192673 0.981263i \(-0.438284\pi\)
0.192673 + 0.981263i \(0.438284\pi\)
\(432\) 0 0
\(433\) −26.0000 −1.24948 −0.624740 0.780833i \(-0.714795\pi\)
−0.624740 + 0.780833i \(0.714795\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.00000 + 3.46410i 0.0956730 + 0.165710i
\(438\) 0 0
\(439\) −16.5000 + 28.5788i −0.787502 + 1.36399i 0.139991 + 0.990153i \(0.455293\pi\)
−0.927493 + 0.373841i \(0.878041\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −11.5000 + 19.9186i −0.546381 + 0.946360i 0.452137 + 0.891948i \(0.350662\pi\)
−0.998519 + 0.0544120i \(0.982672\pi\)
\(444\) 0 0
\(445\) −9.00000 15.5885i −0.426641 0.738964i
\(446\) 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
\(451\) 15.0000 0.706322
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −7.50000 12.9904i −0.351605 0.608998i
\(456\) 0 0
\(457\) −5.50000 + 9.52628i −0.257279 + 0.445621i −0.965512 0.260358i \(-0.916159\pi\)
0.708233 + 0.705979i \(0.249493\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −12.5000 + 21.6506i −0.582183 + 1.00837i 0.413037 + 0.910714i \(0.364468\pi\)
−0.995220 + 0.0976564i \(0.968865\pi\)
\(462\) 0 0
\(463\) −11.5000 19.9186i −0.534450 0.925695i −0.999190 0.0402476i \(-0.987185\pi\)
0.464739 0.885448i \(-0.346148\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 0 0
\(469\) 3.00000 0.138527
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 2.50000 + 4.33013i 0.114950 + 0.199099i
\(474\) 0 0
\(475\) −8.00000 + 13.8564i −0.367065 + 0.635776i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0.500000 0.866025i 0.0228456 0.0395697i −0.854377 0.519654i \(-0.826061\pi\)
0.877222 + 0.480085i \(0.159394\pi\)
\(480\) 0 0
\(481\) −15.0000 25.9808i −0.683941 1.18462i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −13.0000 −0.590300
\(486\) 0 0
\(487\) −32.0000 −1.45006 −0.725029 0.688718i \(-0.758174\pi\)
−0.725029 + 0.688718i \(0.758174\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 13.5000 + 23.3827i 0.609246 + 1.05525i 0.991365 + 0.131132i \(0.0418613\pi\)
−0.382118 + 0.924113i \(0.624805\pi\)
\(492\) 0 0
\(493\) −9.00000 + 15.5885i −0.405340 + 0.702069i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −6.00000 + 10.3923i −0.269137 + 0.466159i
\(498\) 0 0
\(499\) −13.5000 23.3827i −0.604343 1.04675i −0.992155 0.125014i \(-0.960102\pi\)
0.387812 0.921739i \(-0.373231\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −12.0000 −0.535054 −0.267527 0.963550i \(-0.586206\pi\)
−0.267527 + 0.963550i \(0.586206\pi\)
\(504\) 0 0
\(505\) −3.00000 −0.133498
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 1.50000 + 2.59808i 0.0664863 + 0.115158i 0.897352 0.441315i \(-0.145488\pi\)
−0.830866 + 0.556473i \(0.812154\pi\)
\(510\) 0 0
\(511\) −3.00000 + 5.19615i −0.132712 + 0.229864i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 2.50000 4.33013i 0.110163 0.190808i
\(516\) 0 0
\(517\) 7.50000 + 12.9904i 0.329850 + 0.571316i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −10.0000 −0.438108 −0.219054 0.975713i \(-0.570297\pi\)
−0.219054 + 0.975713i \(0.570297\pi\)
\(522\) 0 0
\(523\) 40.0000 1.74908 0.874539 0.484955i \(-0.161164\pi\)
0.874539 + 0.484955i \(0.161164\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.00000 + 1.73205i 0.0435607 + 0.0754493i
\(528\) 0 0
\(529\) 11.0000 19.0526i 0.478261 0.828372i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −7.50000 + 12.9904i −0.324861 + 0.562676i
\(534\) 0 0
\(535\) 6.00000 + 10.3923i 0.259403 + 0.449299i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −10.0000 −0.430730
\(540\) 0 0
\(541\) 30.0000 1.28980 0.644900 0.764267i \(-0.276899\pi\)
0.644900 + 0.764267i \(0.276899\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −5.00000 8.66025i −0.214176 0.370965i
\(546\) 0 0
\(547\) 9.50000 16.4545i 0.406191 0.703543i −0.588269 0.808666i \(-0.700190\pi\)
0.994459 + 0.105123i \(0.0335235\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 18.0000 31.1769i 0.766826 1.32818i
\(552\) 0 0
\(553\) 1.50000 + 2.59808i 0.0637865 + 0.110481i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 22.0000 0.932170 0.466085 0.884740i \(-0.345664\pi\)
0.466085 + 0.884740i \(0.345664\pi\)
\(558\) 0 0
\(559\) −5.00000 −0.211477
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −0.500000 0.866025i −0.0210725 0.0364986i 0.855297 0.518138i \(-0.173375\pi\)
−0.876369 + 0.481640i \(0.840041\pi\)
\(564\) 0 0
\(565\) −4.50000 + 7.79423i −0.189316 + 0.327906i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −12.5000 + 21.6506i −0.524027 + 0.907642i 0.475581 + 0.879672i \(0.342238\pi\)
−0.999609 + 0.0279702i \(0.991096\pi\)
\(570\) 0 0
\(571\) −7.50000 12.9904i −0.313865 0.543631i 0.665330 0.746549i \(-0.268291\pi\)
−0.979196 + 0.202919i \(0.934957\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −4.00000 −0.166812
\(576\) 0 0
\(577\) 14.0000 0.582828 0.291414 0.956597i \(-0.405874\pi\)
0.291414 + 0.956597i \(0.405874\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.50000 2.59808i −0.0622305 0.107786i
\(582\) 0 0
\(583\) −5.00000 + 8.66025i −0.207079 + 0.358671i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 8.50000 14.7224i 0.350833 0.607660i −0.635563 0.772049i \(-0.719232\pi\)
0.986396 + 0.164389i \(0.0525653\pi\)
\(588\) 0 0
\(589\) −2.00000 3.46410i −0.0824086 0.142736i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 34.0000 1.39621 0.698106 0.715994i \(-0.254026\pi\)
0.698106 + 0.715994i \(0.254026\pi\)
\(594\) 0 0
\(595\) −6.00000 −0.245976
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −10.5000 18.1865i −0.429018 0.743082i 0.567768 0.823189i \(-0.307807\pi\)
−0.996786 + 0.0801071i \(0.974474\pi\)
\(600\) 0 0
\(601\) −9.50000 + 16.4545i −0.387513 + 0.671192i −0.992114 0.125336i \(-0.959999\pi\)
0.604601 + 0.796528i \(0.293332\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −7.00000 + 12.1244i −0.284590 + 0.492925i
\(606\) 0 0
\(607\) 6.50000 + 11.2583i 0.263827 + 0.456962i 0.967256 0.253804i \(-0.0816819\pi\)
−0.703429 + 0.710766i \(0.748349\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −15.0000 −0.606835
\(612\) 0 0
\(613\) 2.00000 0.0807792 0.0403896 0.999184i \(-0.487140\pi\)
0.0403896 + 0.999184i \(0.487140\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.50000 + 2.59808i 0.0603877 + 0.104595i 0.894639 0.446790i \(-0.147433\pi\)
−0.834251 + 0.551385i \(0.814100\pi\)
\(618\) 0 0
\(619\) 5.50000 9.52628i 0.221064 0.382893i −0.734068 0.679076i \(-0.762380\pi\)
0.955131 + 0.296183i \(0.0957138\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 27.0000 46.7654i 1.08173 1.87362i
\(624\) 0 0
\(625\) −5.50000 9.52628i −0.220000 0.381051i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −12.0000 −0.478471
\(630\) 0 0
\(631\) 16.0000 0.636950 0.318475 0.947931i \(-0.396829\pi\)
0.318475 + 0.947931i \(0.396829\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −8.00000 13.8564i −0.317470 0.549875i
\(636\) 0 0
\(637\) 5.00000 8.66025i 0.198107 0.343132i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −0.500000 + 0.866025i −0.0197488 + 0.0342059i −0.875731 0.482800i \(-0.839620\pi\)
0.855982 + 0.517005i \(0.172953\pi\)
\(642\) 0 0
\(643\) −7.50000 12.9904i −0.295771 0.512291i 0.679393 0.733775i \(-0.262243\pi\)
−0.975164 + 0.221484i \(0.928910\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 32.0000 1.25805 0.629025 0.777385i \(-0.283454\pi\)
0.629025 + 0.777385i \(0.283454\pi\)
\(648\) 0 0
\(649\) 55.0000 2.15894
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −16.5000 28.5788i −0.645695 1.11838i −0.984141 0.177390i \(-0.943234\pi\)
0.338446 0.940986i \(-0.390099\pi\)
\(654\) 0 0
\(655\) −2.50000 + 4.33013i −0.0976831 + 0.169192i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 10.5000 18.1865i 0.409022 0.708447i −0.585758 0.810486i \(-0.699203\pi\)
0.994780 + 0.102039i \(0.0325366\pi\)
\(660\) 0 0
\(661\) 12.5000 + 21.6506i 0.486194 + 0.842112i 0.999874 0.0158695i \(-0.00505163\pi\)
−0.513680 + 0.857982i \(0.671718\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 12.0000 0.465340
\(666\) 0 0
\(667\) 9.00000 0.348481
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 17.5000 + 30.3109i 0.675580 + 1.17014i
\(672\) 0 0
\(673\) −9.50000 + 16.4545i −0.366198 + 0.634274i −0.988968 0.148132i \(-0.952674\pi\)
0.622770 + 0.782405i \(0.286007\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 17.5000 30.3109i 0.672580 1.16494i −0.304590 0.952483i \(-0.598520\pi\)
0.977170 0.212459i \(-0.0681471\pi\)
\(678\) 0 0
\(679\) −19.5000 33.7750i −0.748341 1.29617i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 4.00000 0.153056 0.0765279 0.997067i \(-0.475617\pi\)
0.0765279 + 0.997067i \(0.475617\pi\)
\(684\) 0 0
\(685\) −3.00000 −0.114624
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −5.00000 8.66025i −0.190485 0.329929i
\(690\) 0 0
\(691\) −20.5000 + 35.5070i −0.779857 + 1.35075i 0.152167 + 0.988355i \(0.451375\pi\)
−0.932024 + 0.362397i \(0.881959\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.50000 + 2.59808i −0.0568982 + 0.0985506i
\(696\) 0 0
\(697\) 3.00000 + 5.19615i 0.113633 + 0.196818i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 0 0
\(703\) 24.0000 0.905177
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −4.50000 7.79423i −0.169240 0.293132i
\(708\) 0 0
\(709\) −5.50000 + 9.52628i −0.206557 + 0.357767i −0.950628 0.310334i \(-0.899559\pi\)
0.744071 + 0.668101i \(0.232892\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0.500000 0.866025i 0.0187251 0.0324329i
\(714\) 0 0
\(715\) −12.5000 21.6506i −0.467473 0.809688i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −32.0000 −1.19340 −0.596699 0.802465i \(-0.703521\pi\)
−0.596699 + 0.802465i \(0.703521\pi\)
\(720\) 0 0
\(721\) 15.0000 0.558629
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 18.0000 + 31.1769i 0.668503 + 1.15788i
\(726\) 0 0
\(727\) 19.5000 33.7750i 0.723215 1.25265i −0.236490 0.971634i \(-0.575997\pi\)
0.959705 0.281011i \(-0.0906698\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.00000 + 1.73205i −0.0369863 + 0.0640622i
\(732\) 0 0
\(733\) 6.50000 + 11.2583i 0.240083 + 0.415836i 0.960738 0.277458i \(-0.0894920\pi\)
−0.720655 + 0.693294i \(0.756159\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 5.00000 0.184177
\(738\) 0 0
\(739\) −16.0000 −0.588570 −0.294285 0.955718i \(-0.595081\pi\)
−0.294285 + 0.955718i \(0.595081\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 5.50000 + 9.52628i 0.201775 + 0.349485i 0.949101 0.314973i \(-0.101996\pi\)
−0.747325 + 0.664459i \(0.768662\pi\)
\(744\) 0 0
\(745\) 9.50000 16.4545i 0.348053 0.602846i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −18.0000 + 31.1769i −0.657706 + 1.13918i
\(750\) 0 0
\(751\) −13.5000 23.3827i −0.492622 0.853246i 0.507342 0.861745i \(-0.330628\pi\)
−0.999964 + 0.00849853i \(0.997295\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 17.0000 0.618693
\(756\) 0 0
\(757\) −10.0000 −0.363456 −0.181728 0.983349i \(-0.558169\pi\)
−0.181728 + 0.983349i \(0.558169\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −2.50000 4.33013i −0.0906249 0.156967i 0.817149 0.576426i \(-0.195553\pi\)
−0.907774 + 0.419459i \(0.862220\pi\)
\(762\) 0 0
\(763\) 15.0000 25.9808i 0.543036 0.940567i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −27.5000 + 47.6314i −0.992967 + 1.71987i
\(768\) 0 0
\(769\) 0.500000 + 0.866025i 0.0180305 + 0.0312297i 0.874900 0.484304i \(-0.160927\pi\)
−0.856869 + 0.515534i \(0.827594\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −42.0000 −1.51064 −0.755318 0.655359i \(-0.772517\pi\)
−0.755318 + 0.655359i \(0.772517\pi\)
\(774\) 0 0
\(775\) 4.00000 0.143684
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −6.00000 10.3923i −0.214972 0.372343i
\(780\) 0 0
\(781\) −10.0000 + 17.3205i −0.357828 + 0.619777i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −3.50000 + 6.06218i −0.124920 + 0.216368i
\(786\) 0 0
\(787\) 26.5000 + 45.8993i 0.944623 + 1.63614i 0.756504 + 0.653989i \(0.226906\pi\)
0.188119 + 0.982146i \(0.439761\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −27.0000 −0.960009
\(792\) 0 0
\(793\) −35.0000 −1.24289
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −6.50000 11.2583i −0.230242 0.398791i 0.727637 0.685962i \(-0.240618\pi\)
−0.957879 + 0.287171i \(0.907285\pi\)
\(798\) 0 0
\(799\) −3.00000 + 5.19615i −0.106132 + 0.183827i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −5.00000 + 8.66025i −0.176446