Properties

Label 3024.2.q.f.2305.1
Level $3024$
Weight $2$
Character 3024.2305
Analytic conductor $24.147$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.1467615712\)
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: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2305.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 3024.2305
Dual form 3024.2.q.f.2881.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 + 2.59808i) q^{5} +(2.00000 - 1.73205i) q^{7} +O(q^{10})\) \(q+(1.50000 + 2.59808i) q^{5} +(2.00000 - 1.73205i) q^{7} +(1.50000 - 2.59808i) q^{11} +(0.500000 - 0.866025i) q^{13} +(1.50000 + 2.59808i) q^{17} +(-3.50000 + 6.06218i) q^{19} +(4.50000 + 7.79423i) q^{23} +(-2.00000 + 3.46410i) q^{25} +(1.50000 + 2.59808i) q^{29} -8.00000 q^{31} +(7.50000 + 2.59808i) q^{35} +(0.500000 - 0.866025i) q^{37} +(1.50000 - 2.59808i) q^{41} +(-0.500000 - 0.866025i) q^{43} +(1.00000 - 6.92820i) q^{49} +(1.50000 + 2.59808i) q^{53} +9.00000 q^{55} +2.00000 q^{61} +3.00000 q^{65} +4.00000 q^{67} +12.0000 q^{71} +(-5.50000 - 9.52628i) q^{73} +(-1.50000 - 7.79423i) q^{77} +16.0000 q^{79} +(4.50000 + 7.79423i) q^{83} +(-4.50000 + 7.79423i) q^{85} +(1.50000 - 2.59808i) q^{89} +(-0.500000 - 2.59808i) q^{91} -21.0000 q^{95} +(0.500000 + 0.866025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 3q^{5} + 4q^{7} + O(q^{10}) \) \( 2q + 3q^{5} + 4q^{7} + 3q^{11} + q^{13} + 3q^{17} - 7q^{19} + 9q^{23} - 4q^{25} + 3q^{29} - 16q^{31} + 15q^{35} + q^{37} + 3q^{41} - q^{43} + 2q^{49} + 3q^{53} + 18q^{55} + 4q^{61} + 6q^{65} + 8q^{67} + 24q^{71} - 11q^{73} - 3q^{77} + 32q^{79} + 9q^{83} - 9q^{85} + 3q^{89} - q^{91} - 42q^{95} + q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1135\) \(2593\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) 1.50000 + 2.59808i 0.670820 + 1.16190i 0.977672 + 0.210138i \(0.0673912\pi\)
−0.306851 + 0.951757i \(0.599275\pi\)
\(6\) 0 0
\(7\) 2.00000 1.73205i 0.755929 0.654654i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i \(-0.683949\pi\)
0.998526 + 0.0542666i \(0.0172821\pi\)
\(12\) 0 0
\(13\) 0.500000 0.866025i 0.138675 0.240192i −0.788320 0.615265i \(-0.789049\pi\)
0.926995 + 0.375073i \(0.122382\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.50000 + 2.59808i 0.363803 + 0.630126i 0.988583 0.150675i \(-0.0481447\pi\)
−0.624780 + 0.780801i \(0.714811\pi\)
\(18\) 0 0
\(19\) −3.50000 + 6.06218i −0.802955 + 1.39076i 0.114708 + 0.993399i \(0.463407\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.50000 + 7.79423i 0.938315 + 1.62521i 0.768613 + 0.639713i \(0.220947\pi\)
0.169701 + 0.985496i \(0.445720\pi\)
\(24\) 0 0
\(25\) −2.00000 + 3.46410i −0.400000 + 0.692820i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.50000 + 2.59808i 0.278543 + 0.482451i 0.971023 0.238987i \(-0.0768152\pi\)
−0.692480 + 0.721437i \(0.743482\pi\)
\(30\) 0 0
\(31\) −8.00000 −1.43684 −0.718421 0.695608i \(-0.755135\pi\)
−0.718421 + 0.695608i \(0.755135\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 7.50000 + 2.59808i 1.26773 + 0.439155i
\(36\) 0 0
\(37\) 0.500000 0.866025i 0.0821995 0.142374i −0.821995 0.569495i \(-0.807139\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1.50000 2.59808i 0.234261 0.405751i −0.724797 0.688963i \(-0.758066\pi\)
0.959058 + 0.283211i \(0.0913998\pi\)
\(42\) 0 0
\(43\) −0.500000 0.866025i −0.0762493 0.132068i 0.825380 0.564578i \(-0.190961\pi\)
−0.901629 + 0.432511i \(0.857628\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 1.50000 + 2.59808i 0.206041 + 0.356873i 0.950464 0.310835i \(-0.100609\pi\)
−0.744423 + 0.667708i \(0.767275\pi\)
\(54\) 0 0
\(55\) 9.00000 1.21356
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 3.00000 0.372104
\(66\) 0 0
\(67\) 4.00000 0.488678 0.244339 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) 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 \(-0.944054\pi\)
0.340868 0.940111i \(-0.389279\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1.50000 7.79423i −0.170941 0.888235i
\(78\) 0 0
\(79\) 16.0000 1.80014 0.900070 0.435745i \(-0.143515\pi\)
0.900070 + 0.435745i \(0.143515\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 4.50000 + 7.79423i 0.493939 + 0.855528i 0.999976 0.00698436i \(-0.00222321\pi\)
−0.506036 + 0.862512i \(0.668890\pi\)
\(84\) 0 0
\(85\) −4.50000 + 7.79423i −0.488094 + 0.845403i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1.50000 2.59808i 0.159000 0.275396i −0.775509 0.631337i \(-0.782506\pi\)
0.934508 + 0.355942i \(0.115840\pi\)
\(90\) 0 0
\(91\) −0.500000 2.59808i −0.0524142 0.272352i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −21.0000 −2.15455
\(96\) 0 0
\(97\) 0.500000 + 0.866025i 0.0507673 + 0.0879316i 0.890292 0.455389i \(-0.150500\pi\)
−0.839525 + 0.543321i \(0.817167\pi\)
\(98\) 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
\(103\) −6.50000 11.2583i −0.640464 1.10932i −0.985329 0.170664i \(-0.945409\pi\)
0.344865 0.938652i \(-0.387925\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −4.50000 + 7.79423i −0.435031 + 0.753497i −0.997298 0.0734594i \(-0.976596\pi\)
0.562267 + 0.826956i \(0.309929\pi\)
\(108\) 0 0
\(109\) 6.50000 + 11.2583i 0.622587 + 1.07835i 0.989002 + 0.147901i \(0.0472517\pi\)
−0.366415 + 0.930451i \(0.619415\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −4.50000 + 7.79423i −0.423324 + 0.733219i −0.996262 0.0863794i \(-0.972470\pi\)
0.572938 + 0.819599i \(0.305804\pi\)
\(114\) 0 0
\(115\) −13.5000 + 23.3827i −1.25888 + 2.18045i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 7.50000 + 2.59808i 0.687524 + 0.238165i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 3.00000 0.268328
\(126\) 0 0
\(127\) 4.00000 0.354943 0.177471 0.984126i \(-0.443208\pi\)
0.177471 + 0.984126i \(0.443208\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −7.50000 12.9904i −0.655278 1.13497i −0.981824 0.189794i \(-0.939218\pi\)
0.326546 0.945181i \(-0.394115\pi\)
\(132\) 0 0
\(133\) 3.50000 + 18.1865i 0.303488 + 1.57697i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −4.50000 + 7.79423i −0.384461 + 0.665906i −0.991694 0.128618i \(-0.958946\pi\)
0.607233 + 0.794524i \(0.292279\pi\)
\(138\) 0 0
\(139\) −3.50000 + 6.06218i −0.296866 + 0.514187i −0.975417 0.220366i \(-0.929275\pi\)
0.678551 + 0.734553i \(0.262608\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1.50000 2.59808i −0.125436 0.217262i
\(144\) 0 0
\(145\) −4.50000 + 7.79423i −0.373705 + 0.647275i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −4.50000 7.79423i −0.368654 0.638528i 0.620701 0.784047i \(-0.286848\pi\)
−0.989355 + 0.145519i \(0.953515\pi\)
\(150\) 0 0
\(151\) −3.50000 + 6.06218i −0.284826 + 0.493333i −0.972567 0.232623i \(-0.925269\pi\)
0.687741 + 0.725956i \(0.258602\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −12.0000 20.7846i −0.963863 1.66946i
\(156\) 0 0
\(157\) −22.0000 −1.75579 −0.877896 0.478852i \(-0.841053\pi\)
−0.877896 + 0.478852i \(0.841053\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 22.5000 + 7.79423i 1.77325 + 0.614271i
\(162\) 0 0
\(163\) −9.50000 + 16.4545i −0.744097 + 1.28881i 0.206518 + 0.978443i \(0.433787\pi\)
−0.950615 + 0.310372i \(0.899546\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 7.50000 12.9904i 0.580367 1.00523i −0.415068 0.909790i \(-0.636242\pi\)
0.995436 0.0954356i \(-0.0304244\pi\)
\(168\) 0 0
\(169\) 6.00000 + 10.3923i 0.461538 + 0.799408i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 0 0
\(175\) 2.00000 + 10.3923i 0.151186 + 0.785584i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 10.5000 + 18.1865i 0.784807 + 1.35933i 0.929114 + 0.369792i \(0.120571\pi\)
−0.144308 + 0.989533i \(0.546095\pi\)
\(180\) 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 0.220564
\(186\) 0 0
\(187\) 9.00000 0.658145
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) 14.0000 1.00774 0.503871 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) −12.5000 21.6506i −0.886102 1.53477i −0.844446 0.535641i \(-0.820070\pi\)
−0.0416556 0.999132i \(-0.513263\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 7.50000 + 2.59808i 0.526397 + 0.182349i
\(204\) 0 0
\(205\) 9.00000 0.628587
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 10.5000 + 18.1865i 0.726300 + 1.25799i
\(210\) 0 0
\(211\) 2.50000 4.33013i 0.172107 0.298098i −0.767049 0.641588i \(-0.778276\pi\)
0.939156 + 0.343490i \(0.111609\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.50000 2.59808i 0.102299 0.177187i
\(216\) 0 0
\(217\) −16.0000 + 13.8564i −1.08615 + 0.940634i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 3.00000 0.201802
\(222\) 0 0
\(223\) −0.500000 0.866025i −0.0334825 0.0579934i 0.848799 0.528716i \(-0.177326\pi\)
−0.882281 + 0.470723i \(0.843993\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1.50000 2.59808i 0.0995585 0.172440i −0.811943 0.583736i \(-0.801590\pi\)
0.911502 + 0.411296i \(0.134924\pi\)
\(228\) 0 0
\(229\) 6.50000 + 11.2583i 0.429532 + 0.743971i 0.996832 0.0795401i \(-0.0253452\pi\)
−0.567300 + 0.823511i \(0.692012\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.50000 2.59808i 0.0982683 0.170206i −0.812700 0.582683i \(-0.802003\pi\)
0.910968 + 0.412477i \(0.135336\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.50000 2.59808i 0.0970269 0.168056i −0.813426 0.581669i \(-0.802400\pi\)
0.910453 + 0.413613i \(0.135733\pi\)
\(240\) 0 0
\(241\) 6.50000 11.2583i 0.418702 0.725213i −0.577107 0.816668i \(-0.695819\pi\)
0.995809 + 0.0914555i \(0.0291519\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 19.5000 7.79423i 1.24581 0.497955i
\(246\) 0 0
\(247\) 3.50000 + 6.06218i 0.222700 + 0.385727i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 27.0000 1.69748
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −10.5000 18.1865i −0.654972 1.13444i −0.981901 0.189396i \(-0.939347\pi\)
0.326929 0.945049i \(-0.393986\pi\)
\(258\) 0 0
\(259\) −0.500000 2.59808i −0.0310685 0.161437i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −4.50000 + 7.79423i −0.277482 + 0.480613i −0.970758 0.240059i \(-0.922833\pi\)
0.693276 + 0.720672i \(0.256167\pi\)
\(264\) 0 0
\(265\) −4.50000 + 7.79423i −0.276433 + 0.478796i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 7.50000 + 12.9904i 0.457283 + 0.792038i 0.998816 0.0486418i \(-0.0154893\pi\)
−0.541533 + 0.840679i \(0.682156\pi\)
\(270\) 0 0
\(271\) 2.50000 4.33013i 0.151864 0.263036i −0.780049 0.625719i \(-0.784806\pi\)
0.931913 + 0.362682i \(0.118139\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 6.00000 + 10.3923i 0.361814 + 0.626680i
\(276\) 0 0
\(277\) 0.500000 0.866025i 0.0300421 0.0520344i −0.850613 0.525792i \(-0.823769\pi\)
0.880656 + 0.473757i \(0.157103\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −10.5000 18.1865i −0.626377 1.08492i −0.988273 0.152699i \(-0.951204\pi\)
0.361895 0.932219i \(-0.382130\pi\)
\(282\) 0 0
\(283\) 4.00000 0.237775 0.118888 0.992908i \(-0.462067\pi\)
0.118888 + 0.992908i \(0.462067\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.50000 7.79423i −0.0885422 0.460079i
\(288\) 0 0
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −4.50000 + 7.79423i −0.262893 + 0.455344i −0.967009 0.254741i \(-0.918010\pi\)
0.704117 + 0.710084i \(0.251343\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 9.00000 0.520483
\(300\) 0 0
\(301\) −2.50000 0.866025i −0.144098 0.0499169i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 3.00000 + 5.19615i 0.171780 + 0.297531i
\(306\) 0 0
\(307\) 28.0000 1.59804 0.799022 0.601302i \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −24.0000 −1.36092 −0.680458 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) 0 0
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −18.0000 −1.01098 −0.505490 0.862832i \(-0.668688\pi\)
−0.505490 + 0.862832i \(0.668688\pi\)
\(318\) 0 0
\(319\) 9.00000 0.503903
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −21.0000 −1.16847
\(324\) 0 0
\(325\) 2.00000 + 3.46410i 0.110940 + 0.192154i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −8.00000 −0.439720 −0.219860 0.975531i \(-0.570560\pi\)
−0.219860 + 0.975531i \(0.570560\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 6.00000 + 10.3923i 0.327815 + 0.567792i
\(336\) 0 0
\(337\) 6.50000 11.2583i 0.354078 0.613280i −0.632882 0.774248i \(-0.718128\pi\)
0.986960 + 0.160968i \(0.0514616\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −12.0000 + 20.7846i −0.649836 + 1.12555i
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 12.0000 0.644194 0.322097 0.946707i \(-0.395612\pi\)
0.322097 + 0.946707i \(0.395612\pi\)
\(348\) 0 0
\(349\) −11.5000 19.9186i −0.615581 1.06622i −0.990282 0.139072i \(-0.955588\pi\)
0.374701 0.927146i \(-0.377745\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1.50000 2.59808i 0.0798369 0.138282i −0.823343 0.567545i \(-0.807893\pi\)
0.903179 + 0.429263i \(0.141227\pi\)
\(354\) 0 0
\(355\) 18.0000 + 31.1769i 0.955341 + 1.65470i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −4.50000 + 7.79423i −0.237501 + 0.411364i −0.959997 0.280012i \(-0.909662\pi\)
0.722496 + 0.691375i \(0.242995\pi\)
\(360\) 0 0
\(361\) −15.0000 25.9808i −0.789474 1.36741i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 16.5000 28.5788i 0.863649 1.49588i
\(366\) 0 0
\(367\) 8.50000 14.7224i 0.443696 0.768505i −0.554264 0.832341i \(-0.687000\pi\)
0.997960 + 0.0638362i \(0.0203335\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 7.50000 + 2.59808i 0.389381 + 0.134885i
\(372\) 0 0
\(373\) 6.50000 + 11.2583i 0.336557 + 0.582934i 0.983783 0.179364i \(-0.0574041\pi\)
−0.647225 + 0.762299i \(0.724071\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 3.00000 0.154508
\(378\) 0 0
\(379\) 28.0000 1.43826 0.719132 0.694874i \(-0.244540\pi\)
0.719132 + 0.694874i \(0.244540\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −7.50000 12.9904i −0.383232 0.663777i 0.608290 0.793715i \(-0.291856\pi\)
−0.991522 + 0.129937i \(0.958522\pi\)
\(384\) 0 0
\(385\) 18.0000 15.5885i 0.917365 0.794461i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 13.5000 23.3827i 0.684477 1.18555i −0.289124 0.957292i \(-0.593364\pi\)
0.973601 0.228257i \(-0.0733028\pi\)
\(390\) 0 0
\(391\) −13.5000 + 23.3827i −0.682724 + 1.18251i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 24.0000 + 41.5692i 1.20757 + 2.09157i
\(396\) 0 0
\(397\) 6.50000 11.2583i 0.326226 0.565039i −0.655534 0.755166i \(-0.727556\pi\)
0.981760 + 0.190126i \(0.0608897\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 13.5000 + 23.3827i 0.674158 + 1.16768i 0.976714 + 0.214544i \(0.0688266\pi\)
−0.302556 + 0.953131i \(0.597840\pi\)
\(402\) 0 0
\(403\) −4.00000 + 6.92820i −0.199254 + 0.345118i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.50000 2.59808i −0.0743522 0.128782i
\(408\) 0 0
\(409\) −34.0000 −1.68119 −0.840596 0.541663i \(-0.817795\pi\)
−0.840596 + 0.541663i \(0.817795\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −13.5000 + 23.3827i −0.662689 + 1.14781i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −4.50000 + 7.79423i −0.219839 + 0.380773i −0.954759 0.297382i \(-0.903887\pi\)
0.734919 + 0.678155i \(0.237220\pi\)
\(420\) 0 0
\(421\) −17.5000 30.3109i −0.852898 1.47726i −0.878582 0.477592i \(-0.841510\pi\)
0.0256838 0.999670i \(-0.491824\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −12.0000 −0.582086
\(426\) 0 0
\(427\) 4.00000 3.46410i 0.193574 0.167640i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −13.5000 23.3827i −0.650272 1.12630i −0.983057 0.183301i \(-0.941322\pi\)
0.332785 0.943003i \(-0.392012\pi\)
\(432\) 0 0
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −63.0000 −3.01370
\(438\) 0 0
\(439\) −8.00000 −0.381819 −0.190910 0.981608i \(-0.561144\pi\)
−0.190910 + 0.981608i \(0.561144\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 36.0000 1.71041 0.855206 0.518289i \(-0.173431\pi\)
0.855206 + 0.518289i \(0.173431\pi\)
\(444\) 0 0
\(445\) 9.00000 0.426641
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) 0 0
\(451\) −4.50000 7.79423i −0.211897 0.367016i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 6.00000 5.19615i 0.281284 0.243599i
\(456\) 0 0
\(457\) −10.0000 −0.467780 −0.233890 0.972263i \(-0.575146\pi\)
−0.233890 + 0.972263i \(0.575146\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −4.50000 7.79423i −0.209586 0.363013i 0.741998 0.670402i \(-0.233878\pi\)
−0.951584 + 0.307388i \(0.900545\pi\)
\(462\) 0 0
\(463\) 20.5000 35.5070i 0.952716 1.65015i 0.213205 0.977007i \(-0.431610\pi\)
0.739511 0.673145i \(-0.235057\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.50000 2.59808i 0.0694117 0.120225i −0.829231 0.558906i \(-0.811221\pi\)
0.898642 + 0.438682i \(0.144554\pi\)
\(468\) 0 0
\(469\) 8.00000 6.92820i 0.369406 0.319915i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −3.00000 −0.137940
\(474\) 0 0
\(475\) −14.0000 24.2487i −0.642364 1.11261i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 1.50000 2.59808i 0.0685367 0.118709i −0.829721 0.558179i \(-0.811500\pi\)
0.898257 + 0.439470i \(0.144834\pi\)
\(480\) 0 0
\(481\) −0.500000 0.866025i −0.0227980 0.0394874i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.50000 + 2.59808i −0.0681115 + 0.117973i
\(486\) 0 0
\(487\) −12.5000 21.6506i −0.566429 0.981084i −0.996915 0.0784867i \(-0.974991\pi\)
0.430486 0.902597i \(-0.358342\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −10.5000 + 18.1865i −0.473858 + 0.820747i −0.999552 0.0299272i \(-0.990472\pi\)
0.525694 + 0.850674i \(0.323806\pi\)
\(492\) 0 0
\(493\) −4.50000 + 7.79423i −0.202670 + 0.351034i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 24.0000 20.7846i 1.07655 0.932317i
\(498\) 0 0
\(499\) −12.5000 21.6506i −0.559577 0.969216i −0.997532 0.0702185i \(-0.977630\pi\)
0.437955 0.898997i \(-0.355703\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −24.0000 −1.07011 −0.535054 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) 0 0
\(505\) 9.00000 0.400495
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −4.50000 7.79423i −0.199459 0.345473i 0.748894 0.662690i \(-0.230585\pi\)
−0.948353 + 0.317217i \(0.897252\pi\)
\(510\) 0 0
\(511\) −27.5000 9.52628i −1.21653 0.421418i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 19.5000 33.7750i 0.859273 1.48830i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.50000 + 2.59808i 0.0657162 + 0.113824i 0.897011 0.442007i \(-0.145733\pi\)
−0.831295 + 0.555831i \(0.812400\pi\)
\(522\) 0 0
\(523\) −3.50000 + 6.06218i −0.153044 + 0.265081i −0.932345 0.361569i \(-0.882241\pi\)
0.779301 + 0.626650i \(0.215574\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −12.0000 20.7846i −0.522728 0.905392i
\(528\) 0 0
\(529\) −29.0000 + 50.2295i −1.26087 + 2.18389i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −1.50000 2.59808i −0.0649722 0.112535i
\(534\) 0 0
\(535\) −27.0000 −1.16731
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −16.5000 12.9904i −0.710705 0.559535i
\(540\) 0 0
\(541\) −5.50000 + 9.52628i −0.236463 + 0.409567i −0.959697 0.281037i \(-0.909322\pi\)
0.723234 + 0.690604i \(0.242655\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −19.5000 + 33.7750i −0.835288 + 1.44676i
\(546\) 0 0
\(547\) 5.50000 + 9.52628i 0.235163 + 0.407314i 0.959320 0.282321i \(-0.0911043\pi\)
−0.724157 + 0.689635i \(0.757771\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −21.0000 −0.894630
\(552\) 0 0
\(553\) 32.0000 27.7128i 1.36078 1.17847i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −4.50000 7.79423i −0.190671 0.330252i 0.754802 0.655953i \(-0.227733\pi\)
−0.945473 + 0.325701i \(0.894400\pi\)
\(558\) 0 0
\(559\) −1.00000 −0.0422955
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 12.0000 0.505740 0.252870 0.967500i \(-0.418626\pi\)
0.252870 + 0.967500i \(0.418626\pi\)
\(564\) 0 0
\(565\) −27.0000 −1.13590
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 18.0000 0.754599 0.377300 0.926091i \(-0.376853\pi\)
0.377300 + 0.926091i \(0.376853\pi\)
\(570\) 0 0
\(571\) −32.0000 −1.33916 −0.669579 0.742741i \(-0.733526\pi\)
−0.669579 + 0.742741i \(0.733526\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −36.0000 −1.50130
\(576\) 0 0
\(577\) 12.5000 + 21.6506i 0.520382 + 0.901328i 0.999719 + 0.0236970i \(0.00754370\pi\)
−0.479337 + 0.877631i \(0.659123\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 22.5000 + 7.79423i 0.933457 + 0.323359i
\(582\) 0 0
\(583\) 9.00000 0.372742
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.50000 2.59808i −0.0619116 0.107234i 0.833408 0.552658i \(-0.186386\pi\)
−0.895320 + 0.445424i \(0.853053\pi\)
\(588\) 0 0
\(589\) 28.0000 48.4974i 1.15372 1.99830i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 19.5000 33.7750i 0.800769 1.38697i −0.118342 0.992973i \(-0.537758\pi\)
0.919111 0.394000i \(-0.128909\pi\)
\(594\) 0 0
\(595\) 4.50000 + 23.3827i 0.184482 + 0.958597i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) 0 0
\(601\) 12.5000 + 21.6506i 0.509886 + 0.883148i 0.999934 + 0.0114528i \(0.00364562\pi\)
−0.490049 + 0.871695i \(0.663021\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −3.00000 + 5.19615i −0.121967 + 0.211254i
\(606\) 0 0
\(607\) −6.50000 11.2583i −0.263827 0.456962i 0.703429 0.710766i \(-0.251651\pi\)
−0.967256 + 0.253804i \(0.918318\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −11.5000 19.9186i −0.464481 0.804504i 0.534697 0.845044i \(-0.320426\pi\)
−0.999178 + 0.0405396i \(0.987092\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −22.5000 + 38.9711i −0.905816 + 1.56892i −0.0859976 + 0.996295i \(0.527408\pi\)
−0.819818 + 0.572624i \(0.805926\pi\)
\(618\) 0 0
\(619\) 8.50000 14.7224i 0.341644 0.591744i −0.643094 0.765787i \(-0.722350\pi\)
0.984738 + 0.174042i \(0.0556830\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1.50000 7.79423i −0.0600962 0.312269i
\(624\) 0 0
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 3.00000 0.119618
\(630\) 0 0
\(631\) −8.00000 −0.318475 −0.159237 0.987240i \(-0.550904\pi\)
−0.159237 + 0.987240i \(0.550904\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 6.00000 + 10.3923i 0.238103 + 0.412406i
\(636\) 0 0
\(637\) −5.50000 4.33013i −0.217918 0.171566i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −16.5000 + 28.5788i −0.651711 + 1.12880i 0.330997 + 0.943632i \(0.392615\pi\)
−0.982708 + 0.185164i \(0.940718\pi\)
\(642\) 0 0
\(643\) 14.5000 25.1147i 0.571824 0.990429i −0.424555 0.905402i \(-0.639569\pi\)
0.996379 0.0850262i \(-0.0270974\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 10.5000 + 18.1865i 0.412798 + 0.714986i 0.995194 0.0979182i \(-0.0312184\pi\)
−0.582397 + 0.812905i \(0.697885\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 7.50000 + 12.9904i 0.293498 + 0.508353i 0.974634 0.223803i \(-0.0718474\pi\)
−0.681137 + 0.732156i \(0.738514\pi\)
\(654\) 0 0
\(655\) 22.5000 38.9711i 0.879148 1.52273i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.50000 2.59808i −0.0584317 0.101207i 0.835330 0.549749i \(-0.185277\pi\)
−0.893762 + 0.448542i \(0.851943\pi\)
\(660\) 0 0
\(661\) −22.0000 −0.855701 −0.427850 0.903850i \(-0.640729\pi\)
−0.427850 + 0.903850i \(0.640729\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −42.0000 + 36.3731i −1.62869 + 1.41049i
\(666\) 0 0
\(667\) −13.5000 + 23.3827i −0.522722 + 0.905381i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 3.00000 5.19615i 0.115814 0.200595i
\(672\) 0 0
\(673\) −17.5000 30.3109i −0.674575 1.16840i −0.976593 0.215096i \(-0.930993\pi\)
0.302017 0.953302i \(-0.402340\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 30.0000 1.15299 0.576497 0.817099i \(-0.304419\pi\)
0.576497 + 0.817099i \(0.304419\pi\)
\(678\) 0 0
\(679\) 2.50000 + 0.866025i 0.0959412 + 0.0332350i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 4.50000 + 7.79423i 0.172188 + 0.298238i 0.939184 0.343413i \(-0.111583\pi\)
−0.766997 + 0.641651i \(0.778250\pi\)
\(684\) 0 0
\(685\) −27.0000 −1.03162
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 3.00000 0.114291
\(690\) 0 0
\(691\) −44.0000 −1.67384 −0.836919 0.547326i \(-0.815646\pi\)
−0.836919 + 0.547326i \(0.815646\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −21.0000 −0.796575
\(696\) 0 0
\(697\) 9.00000 0.340899
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 0 0
\(703\) 3.50000 + 6.06218i 0.132005 + 0.228639i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.50000 7.79423i −0.0564133 0.293132i
\(708\) 0 0
\(709\) 26.0000 0.976450 0.488225 0.872718i \(-0.337644\pi\)
0.488225 + 0.872718i \(0.337644\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −36.0000 62.3538i −1.34821 2.33517i
\(714\) 0 0
\(715\) 4.50000 7.79423i 0.168290 0.291488i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 7.50000 12.9904i 0.279703 0.484459i −0.691608 0.722273i \(-0.743097\pi\)
0.971311 + 0.237814i \(0.0764307\pi\)
\(720\) 0 0
\(721\) −32.5000 11.2583i −1.21036 0.419282i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −12.0000 −0.445669
\(726\) 0 0
\(727\) −6.50000 11.2583i −0.241072 0.417548i 0.719948 0.694028i \(-0.244166\pi\)
−0.961020 + 0.276479i \(0.910832\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1.50000 2.59808i 0.0554795 0.0960933i
\(732\) 0 0
\(733\) 0.500000 + 0.866025i 0.0184679 + 0.0319874i 0.875112 0.483921i \(-0.160788\pi\)
−0.856644 + 0.515908i \(0.827454\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 6.00000 10.3923i 0.221013 0.382805i
\(738\) 0 0
\(739\) 11.5000 + 19.9186i 0.423034 + 0.732717i 0.996235 0.0866983i \(-0.0276316\pi\)
−0.573200 + 0.819415i \(0.694298\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −10.5000 + 18.1865i −0.385208 + 0.667199i −0.991798 0.127815i \(-0.959204\pi\)
0.606590 + 0.795015i \(0.292537\pi\)
\(744\) 0 0
\(745\) 13.5000 23.3827i 0.494602 0.856675i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 4.50000 + 23.3827i 0.164426 + 0.854385i
\(750\) 0 0
\(751\) −6.50000 11.2583i −0.237188 0.410822i 0.722718 0.691143i \(-0.242893\pi\)
−0.959906 + 0.280321i \(0.909559\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −21.0000 −0.764268
\(756\) 0 0
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −22.5000 38.9711i −0.815624 1.41270i −0.908879 0.417061i \(-0.863060\pi\)
0.0932544 0.995642i \(-0.470273\pi\)
\(762\) 0 0
\(763\) 32.5000 + 11.2583i 1.17658 + 0.407579i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −11.5000 + 19.9186i −0.414701 + 0.718283i −0.995397 0.0958377i \(-0.969447\pi\)
0.580696 + 0.814120i \(0.302780\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 13.5000 + 23.3827i 0.485561 + 0.841017i 0.999862 0.0165929i \(-0.00528194\pi\)
−0.514301 + 0.857610i \(0.671949\pi\)
\(774\) 0 0
\(775\) 16.0000 27.7128i 0.574737 0.995474i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 10.5000 + 18.1865i 0.376202 + 0.651600i
\(780\) 0 0
\(781\) 18.0000 31.1769i 0.644091 1.11560i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −33.0000 57.1577i −1.17782 2.04004i
\(786\) 0 0
\(787\) 28.0000 0.998092 0.499046 0.866575i \(-0.333684\pi\)
0.499046 + 0.866575i \(0.333684\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 4.50000 + 23.3827i 0.160002 + 0.831393i
\(792\) 0 0
\(793\) 1.00000 1.73205i 0.0355110 0.0615069i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −10.5000 + 18.1865i −0.371929 + 0.644200i −0.989862 0.142031i \(-0.954637\pi\)
0.617933 + 0.786231i \(0.287970\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −33.0000 −1.16454
\(804\) 0 0
\(805\) 13.5000 + 70.1481i 0.475812 + 2.47239i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −16.5000 28.5788i −0.580109 1.00478i −0.995466 0.0951198i \(-0.969677\pi\)
0.415357 0.909659i \(-0.363657\pi\)
\(810\) 0 0
\(811\) −20.0000 −0.702295 −0.351147 0.936320i \(-0.614208\pi\)
−0.351147 + 0.936320i \(0.614208\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −57.0000 −1.99662
\(816\) 0 0