Properties

Label 336.4.h.b.239.4
Level $336$
Weight $4$
Character 336.239
Analytic conductor $19.825$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 336.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.8246417619\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 239.4
Character \(\chi\) \(=\) 336.239
Dual form 336.4.h.b.239.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.13038 + 3.15276i) q^{3} -1.18345i q^{5} +7.00000i q^{7} +(7.12016 - 26.0443i) q^{9} +O(q^{10})\) \(q+(-4.13038 + 3.15276i) q^{3} -1.18345i q^{5} +7.00000i q^{7} +(7.12016 - 26.0443i) q^{9} +64.7667 q^{11} -65.6031 q^{13} +(3.73115 + 4.88812i) q^{15} -19.9831i q^{17} -67.2592i q^{19} +(-22.0693 - 28.9127i) q^{21} +79.6645 q^{23} +123.599 q^{25} +(52.7024 + 130.021i) q^{27} +100.562i q^{29} +278.573i q^{31} +(-267.511 + 204.194i) q^{33} +8.28417 q^{35} -45.5075 q^{37} +(270.966 - 206.831i) q^{39} +12.4833i q^{41} +368.590i q^{43} +(-30.8222 - 8.42637i) q^{45} +303.707 q^{47} -49.0000 q^{49} +(63.0019 + 82.5377i) q^{51} +639.462i q^{53} -76.6484i q^{55} +(212.052 + 277.806i) q^{57} -537.860 q^{59} +232.141 q^{61} +(182.310 + 49.8411i) q^{63} +77.6382i q^{65} +533.654i q^{67} +(-329.045 + 251.163i) q^{69} +1015.57 q^{71} -348.158 q^{73} +(-510.513 + 389.680i) q^{75} +453.367i q^{77} +517.278i q^{79} +(-627.607 - 370.878i) q^{81} +1086.03 q^{83} -23.6490 q^{85} +(-317.048 - 415.359i) q^{87} -1432.28i q^{89} -459.222i q^{91} +(-878.276 - 1150.62i) q^{93} -79.5981 q^{95} +1765.36 q^{97} +(461.149 - 1686.80i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 136 q^{9} + O(q^{10}) \) \( 24 q - 136 q^{9} + 96 q^{13} - 112 q^{21} + 168 q^{25} - 320 q^{33} - 864 q^{37} + 592 q^{45} - 1176 q^{49} - 1120 q^{57} - 2304 q^{61} + 1168 q^{69} + 3312 q^{73} - 968 q^{81} - 5808 q^{85} + 1776 q^{93} + 6480 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(1\)

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
\(3\) −4.13038 + 3.15276i −0.794893 + 0.606750i
\(4\) 0 0
\(5\) 1.18345i 0.105851i −0.998598 0.0529256i \(-0.983145\pi\)
0.998598 0.0529256i \(-0.0168546\pi\)
\(6\) 0 0
\(7\) 7.00000i 0.377964i
\(8\) 0 0
\(9\) 7.12016 26.0443i 0.263709 0.964602i
\(10\) 0 0
\(11\) 64.7667 1.77526 0.887632 0.460554i \(-0.152349\pi\)
0.887632 + 0.460554i \(0.152349\pi\)
\(12\) 0 0
\(13\) −65.6031 −1.39962 −0.699809 0.714330i \(-0.746731\pi\)
−0.699809 + 0.714330i \(0.746731\pi\)
\(14\) 0 0
\(15\) 3.73115 + 4.88812i 0.0642252 + 0.0841404i
\(16\) 0 0
\(17\) 19.9831i 0.285094i −0.989788 0.142547i \(-0.954471\pi\)
0.989788 0.142547i \(-0.0455292\pi\)
\(18\) 0 0
\(19\) 67.2592i 0.812122i −0.913846 0.406061i \(-0.866902\pi\)
0.913846 0.406061i \(-0.133098\pi\)
\(20\) 0 0
\(21\) −22.0693 28.9127i −0.229330 0.300441i
\(22\) 0 0
\(23\) 79.6645 0.722226 0.361113 0.932522i \(-0.382397\pi\)
0.361113 + 0.932522i \(0.382397\pi\)
\(24\) 0 0
\(25\) 123.599 0.988796
\(26\) 0 0
\(27\) 52.7024 + 130.021i 0.375651 + 0.926761i
\(28\) 0 0
\(29\) 100.562i 0.643927i 0.946752 + 0.321963i \(0.104343\pi\)
−0.946752 + 0.321963i \(0.895657\pi\)
\(30\) 0 0
\(31\) 278.573i 1.61398i 0.590568 + 0.806988i \(0.298904\pi\)
−0.590568 + 0.806988i \(0.701096\pi\)
\(32\) 0 0
\(33\) −267.511 + 204.194i −1.41114 + 1.07714i
\(34\) 0 0
\(35\) 8.28417 0.0400080
\(36\) 0 0
\(37\) −45.5075 −0.202200 −0.101100 0.994876i \(-0.532236\pi\)
−0.101100 + 0.994876i \(0.532236\pi\)
\(38\) 0 0
\(39\) 270.966 206.831i 1.11255 0.849217i
\(40\) 0 0
\(41\) 12.4833i 0.0475502i 0.999717 + 0.0237751i \(0.00756856\pi\)
−0.999717 + 0.0237751i \(0.992431\pi\)
\(42\) 0 0
\(43\) 368.590i 1.30720i 0.756842 + 0.653598i \(0.226741\pi\)
−0.756842 + 0.653598i \(0.773259\pi\)
\(44\) 0 0
\(45\) −30.8222 8.42637i −0.102104 0.0279140i
\(46\) 0 0
\(47\) 303.707 0.942559 0.471280 0.881984i \(-0.343792\pi\)
0.471280 + 0.881984i \(0.343792\pi\)
\(48\) 0 0
\(49\) −49.0000 −0.142857
\(50\) 0 0
\(51\) 63.0019 + 82.5377i 0.172981 + 0.226619i
\(52\) 0 0
\(53\) 639.462i 1.65730i 0.559768 + 0.828650i \(0.310890\pi\)
−0.559768 + 0.828650i \(0.689110\pi\)
\(54\) 0 0
\(55\) 76.6484i 0.187914i
\(56\) 0 0
\(57\) 212.052 + 277.806i 0.492755 + 0.645550i
\(58\) 0 0
\(59\) −537.860 −1.18684 −0.593419 0.804894i \(-0.702222\pi\)
−0.593419 + 0.804894i \(0.702222\pi\)
\(60\) 0 0
\(61\) 232.141 0.487257 0.243628 0.969869i \(-0.421662\pi\)
0.243628 + 0.969869i \(0.421662\pi\)
\(62\) 0 0
\(63\) 182.310 + 49.8411i 0.364585 + 0.0996728i
\(64\) 0 0
\(65\) 77.6382i 0.148151i
\(66\) 0 0
\(67\) 533.654i 0.973079i 0.873659 + 0.486539i \(0.161741\pi\)
−0.873659 + 0.486539i \(0.838259\pi\)
\(68\) 0 0
\(69\) −329.045 + 251.163i −0.574092 + 0.438210i
\(70\) 0 0
\(71\) 1015.57 1.69755 0.848777 0.528751i \(-0.177339\pi\)
0.848777 + 0.528751i \(0.177339\pi\)
\(72\) 0 0
\(73\) −348.158 −0.558203 −0.279101 0.960262i \(-0.590037\pi\)
−0.279101 + 0.960262i \(0.590037\pi\)
\(74\) 0 0
\(75\) −510.513 + 389.680i −0.785987 + 0.599951i
\(76\) 0 0
\(77\) 453.367i 0.670987i
\(78\) 0 0
\(79\) 517.278i 0.736688i 0.929690 + 0.368344i \(0.120075\pi\)
−0.929690 + 0.368344i \(0.879925\pi\)
\(80\) 0 0
\(81\) −627.607 370.878i −0.860915 0.508749i
\(82\) 0 0
\(83\) 1086.03 1.43623 0.718113 0.695926i \(-0.245006\pi\)
0.718113 + 0.695926i \(0.245006\pi\)
\(84\) 0 0
\(85\) −23.6490 −0.0301776
\(86\) 0 0
\(87\) −317.048 415.359i −0.390703 0.511853i
\(88\) 0 0
\(89\) 1432.28i 1.70586i −0.522023 0.852931i \(-0.674823\pi\)
0.522023 0.852931i \(-0.325177\pi\)
\(90\) 0 0
\(91\) 459.222i 0.529006i
\(92\) 0 0
\(93\) −878.276 1150.62i −0.979280 1.28294i
\(94\) 0 0
\(95\) −79.5981 −0.0859641
\(96\) 0 0
\(97\) 1765.36 1.84789 0.923945 0.382526i \(-0.124946\pi\)
0.923945 + 0.382526i \(0.124946\pi\)
\(98\) 0 0
\(99\) 461.149 1686.80i 0.468154 1.71242i
\(100\) 0 0
\(101\) 167.647i 0.165163i 0.996584 + 0.0825817i \(0.0263165\pi\)
−0.996584 + 0.0825817i \(0.973683\pi\)
\(102\) 0 0
\(103\) 412.022i 0.394153i 0.980388 + 0.197076i \(0.0631447\pi\)
−0.980388 + 0.197076i \(0.936855\pi\)
\(104\) 0 0
\(105\) −34.2168 + 26.1180i −0.0318021 + 0.0242749i
\(106\) 0 0
\(107\) −1231.17 −1.11235 −0.556176 0.831065i \(-0.687732\pi\)
−0.556176 + 0.831065i \(0.687732\pi\)
\(108\) 0 0
\(109\) −208.736 −0.183424 −0.0917122 0.995786i \(-0.529234\pi\)
−0.0917122 + 0.995786i \(0.529234\pi\)
\(110\) 0 0
\(111\) 187.964 143.475i 0.160727 0.122685i
\(112\) 0 0
\(113\) 1005.81i 0.837333i −0.908140 0.418667i \(-0.862498\pi\)
0.908140 0.418667i \(-0.137502\pi\)
\(114\) 0 0
\(115\) 94.2792i 0.0764485i
\(116\) 0 0
\(117\) −467.104 + 1708.58i −0.369092 + 1.35007i
\(118\) 0 0
\(119\) 139.881 0.107755
\(120\) 0 0
\(121\) 2863.73 2.15156
\(122\) 0 0
\(123\) −39.3568 51.5606i −0.0288510 0.0377973i
\(124\) 0 0
\(125\) 294.206i 0.210517i
\(126\) 0 0
\(127\) 277.716i 0.194042i 0.995282 + 0.0970208i \(0.0309313\pi\)
−0.995282 + 0.0970208i \(0.969069\pi\)
\(128\) 0 0
\(129\) −1162.08 1522.42i −0.793141 1.03908i
\(130\) 0 0
\(131\) −1504.95 −1.00373 −0.501864 0.864946i \(-0.667352\pi\)
−0.501864 + 0.864946i \(0.667352\pi\)
\(132\) 0 0
\(133\) 470.814 0.306953
\(134\) 0 0
\(135\) 153.874 62.3709i 0.0980988 0.0397632i
\(136\) 0 0
\(137\) 1007.55i 0.628328i 0.949369 + 0.314164i \(0.101724\pi\)
−0.949369 + 0.314164i \(0.898276\pi\)
\(138\) 0 0
\(139\) 212.644i 0.129757i −0.997893 0.0648786i \(-0.979334\pi\)
0.997893 0.0648786i \(-0.0206660\pi\)
\(140\) 0 0
\(141\) −1254.43 + 957.518i −0.749234 + 0.571898i
\(142\) 0 0
\(143\) −4248.90 −2.48469
\(144\) 0 0
\(145\) 119.010 0.0681605
\(146\) 0 0
\(147\) 202.389 154.485i 0.113556 0.0866785i
\(148\) 0 0
\(149\) 2756.72i 1.51570i −0.652428 0.757851i \(-0.726250\pi\)
0.652428 0.757851i \(-0.273750\pi\)
\(150\) 0 0
\(151\) 2341.55i 1.26194i −0.775808 0.630969i \(-0.782657\pi\)
0.775808 0.630969i \(-0.217343\pi\)
\(152\) 0 0
\(153\) −520.444 142.282i −0.275003 0.0751820i
\(154\) 0 0
\(155\) 329.679 0.170841
\(156\) 0 0
\(157\) 605.528 0.307811 0.153906 0.988086i \(-0.450815\pi\)
0.153906 + 0.988086i \(0.450815\pi\)
\(158\) 0 0
\(159\) −2016.07 2641.22i −1.00557 1.31738i
\(160\) 0 0
\(161\) 557.651i 0.272976i
\(162\) 0 0
\(163\) 1257.83i 0.604424i 0.953241 + 0.302212i \(0.0977250\pi\)
−0.953241 + 0.302212i \(0.902275\pi\)
\(164\) 0 0
\(165\) 241.654 + 316.587i 0.114017 + 0.149371i
\(166\) 0 0
\(167\) −1243.14 −0.576030 −0.288015 0.957626i \(-0.592995\pi\)
−0.288015 + 0.957626i \(0.592995\pi\)
\(168\) 0 0
\(169\) 2106.76 0.958928
\(170\) 0 0
\(171\) −1751.72 478.896i −0.783374 0.214164i
\(172\) 0 0
\(173\) 3555.74i 1.56265i 0.624126 + 0.781324i \(0.285455\pi\)
−0.624126 + 0.781324i \(0.714545\pi\)
\(174\) 0 0
\(175\) 865.196i 0.373730i
\(176\) 0 0
\(177\) 2221.57 1695.75i 0.943408 0.720113i
\(178\) 0 0
\(179\) 1234.43 0.515452 0.257726 0.966218i \(-0.417027\pi\)
0.257726 + 0.966218i \(0.417027\pi\)
\(180\) 0 0
\(181\) 1217.00 0.499772 0.249886 0.968275i \(-0.419607\pi\)
0.249886 + 0.968275i \(0.419607\pi\)
\(182\) 0 0
\(183\) −958.833 + 731.887i −0.387317 + 0.295643i
\(184\) 0 0
\(185\) 53.8561i 0.0214031i
\(186\) 0 0
\(187\) 1294.24i 0.506117i
\(188\) 0 0
\(189\) −910.147 + 368.917i −0.350283 + 0.141983i
\(190\) 0 0
\(191\) 2105.27 0.797549 0.398774 0.917049i \(-0.369436\pi\)
0.398774 + 0.917049i \(0.369436\pi\)
\(192\) 0 0
\(193\) 3241.94 1.20912 0.604560 0.796559i \(-0.293349\pi\)
0.604560 + 0.796559i \(0.293349\pi\)
\(194\) 0 0
\(195\) −244.775 320.676i −0.0898907 0.117764i
\(196\) 0 0
\(197\) 989.805i 0.357973i 0.983852 + 0.178987i \(0.0572818\pi\)
−0.983852 + 0.178987i \(0.942718\pi\)
\(198\) 0 0
\(199\) 1106.83i 0.394277i 0.980376 + 0.197139i \(0.0631649\pi\)
−0.980376 + 0.197139i \(0.936835\pi\)
\(200\) 0 0
\(201\) −1682.49 2204.20i −0.590415 0.773493i
\(202\) 0 0
\(203\) −703.934 −0.243382
\(204\) 0 0
\(205\) 14.7733 0.00503324
\(206\) 0 0
\(207\) 567.224 2074.80i 0.190458 0.696661i
\(208\) 0 0
\(209\) 4356.16i 1.44173i
\(210\) 0 0
\(211\) 346.152i 0.112939i 0.998404 + 0.0564693i \(0.0179843\pi\)
−0.998404 + 0.0564693i \(0.982016\pi\)
\(212\) 0 0
\(213\) −4194.71 + 3201.86i −1.34937 + 1.02999i
\(214\) 0 0
\(215\) 436.209 0.138368
\(216\) 0 0
\(217\) −1950.01 −0.610026
\(218\) 0 0
\(219\) 1438.03 1097.66i 0.443712 0.338690i
\(220\) 0 0
\(221\) 1310.95i 0.399023i
\(222\) 0 0
\(223\) 3147.46i 0.945155i 0.881289 + 0.472578i \(0.156676\pi\)
−0.881289 + 0.472578i \(0.843324\pi\)
\(224\) 0 0
\(225\) 880.047 3219.06i 0.260755 0.953794i
\(226\) 0 0
\(227\) 1568.11 0.458499 0.229250 0.973368i \(-0.426373\pi\)
0.229250 + 0.973368i \(0.426373\pi\)
\(228\) 0 0
\(229\) −2522.74 −0.727979 −0.363989 0.931403i \(-0.618586\pi\)
−0.363989 + 0.931403i \(0.618586\pi\)
\(230\) 0 0
\(231\) −1429.36 1872.58i −0.407121 0.533362i
\(232\) 0 0
\(233\) 5224.03i 1.46883i −0.678700 0.734416i \(-0.737456\pi\)
0.678700 0.734416i \(-0.262544\pi\)
\(234\) 0 0
\(235\) 359.424i 0.0997711i
\(236\) 0 0
\(237\) −1630.86 2136.56i −0.446985 0.585588i
\(238\) 0 0
\(239\) −779.036 −0.210844 −0.105422 0.994428i \(-0.533619\pi\)
−0.105422 + 0.994428i \(0.533619\pi\)
\(240\) 0 0
\(241\) −36.8016 −0.00983651 −0.00491826 0.999988i \(-0.501566\pi\)
−0.00491826 + 0.999988i \(0.501566\pi\)
\(242\) 0 0
\(243\) 3761.55 446.826i 0.993019 0.117958i
\(244\) 0 0
\(245\) 57.9892i 0.0151216i
\(246\) 0 0
\(247\) 4412.41i 1.13666i
\(248\) 0 0
\(249\) −4485.70 + 3423.98i −1.14165 + 0.871430i
\(250\) 0 0
\(251\) 3211.48 0.807596 0.403798 0.914848i \(-0.367690\pi\)
0.403798 + 0.914848i \(0.367690\pi\)
\(252\) 0 0
\(253\) 5159.61 1.28214
\(254\) 0 0
\(255\) 97.6795 74.5597i 0.0239879 0.0183102i
\(256\) 0 0
\(257\) 2038.32i 0.494736i 0.968922 + 0.247368i \(0.0795657\pi\)
−0.968922 + 0.247368i \(0.920434\pi\)
\(258\) 0 0
\(259\) 318.553i 0.0764244i
\(260\) 0 0
\(261\) 2619.06 + 716.017i 0.621133 + 0.169810i
\(262\) 0 0
\(263\) −2703.80 −0.633929 −0.316965 0.948437i \(-0.602664\pi\)
−0.316965 + 0.948437i \(0.602664\pi\)
\(264\) 0 0
\(265\) 756.773 0.175427
\(266\) 0 0
\(267\) 4515.65 + 5915.88i 1.03503 + 1.35598i
\(268\) 0 0
\(269\) 5494.29i 1.24533i 0.782490 + 0.622663i \(0.213949\pi\)
−0.782490 + 0.622663i \(0.786051\pi\)
\(270\) 0 0
\(271\) 3364.83i 0.754240i 0.926164 + 0.377120i \(0.123086\pi\)
−0.926164 + 0.377120i \(0.876914\pi\)
\(272\) 0 0
\(273\) 1447.82 + 1896.76i 0.320974 + 0.420503i
\(274\) 0 0
\(275\) 8005.13 1.75537
\(276\) 0 0
\(277\) −8383.07 −1.81837 −0.909187 0.416388i \(-0.863296\pi\)
−0.909187 + 0.416388i \(0.863296\pi\)
\(278\) 0 0
\(279\) 7255.24 + 1983.49i 1.55684 + 0.425621i
\(280\) 0 0
\(281\) 1391.23i 0.295352i −0.989036 0.147676i \(-0.952821\pi\)
0.989036 0.147676i \(-0.0471793\pi\)
\(282\) 0 0
\(283\) 7260.39i 1.52504i −0.646967 0.762518i \(-0.723963\pi\)
0.646967 0.762518i \(-0.276037\pi\)
\(284\) 0 0
\(285\) 328.771 250.954i 0.0683323 0.0521587i
\(286\) 0 0
\(287\) −87.3828 −0.0179723
\(288\) 0 0
\(289\) 4513.68 0.918721
\(290\) 0 0
\(291\) −7291.62 + 5565.77i −1.46887 + 1.12121i
\(292\) 0 0
\(293\) 3239.83i 0.645983i 0.946402 + 0.322991i \(0.104688\pi\)
−0.946402 + 0.322991i \(0.895312\pi\)
\(294\) 0 0
\(295\) 636.532i 0.125628i
\(296\) 0 0
\(297\) 3413.36 + 8421.03i 0.666880 + 1.64525i
\(298\) 0 0
\(299\) −5226.24 −1.01084
\(300\) 0 0
\(301\) −2580.13 −0.494074
\(302\) 0 0
\(303\) −528.551 692.446i −0.100213 0.131287i
\(304\) 0 0
\(305\) 274.728i 0.0515767i
\(306\) 0 0
\(307\) 4045.04i 0.751995i −0.926621 0.375998i \(-0.877300\pi\)
0.926621 0.375998i \(-0.122700\pi\)
\(308\) 0 0
\(309\) −1299.01 1701.81i −0.239152 0.313309i
\(310\) 0 0
\(311\) 8078.51 1.47296 0.736479 0.676460i \(-0.236487\pi\)
0.736479 + 0.676460i \(0.236487\pi\)
\(312\) 0 0
\(313\) −4511.14 −0.814648 −0.407324 0.913284i \(-0.633538\pi\)
−0.407324 + 0.913284i \(0.633538\pi\)
\(314\) 0 0
\(315\) 58.9846 215.755i 0.0105505 0.0385918i
\(316\) 0 0
\(317\) 7417.92i 1.31430i −0.753762 0.657148i \(-0.771763\pi\)
0.753762 0.657148i \(-0.228237\pi\)
\(318\) 0 0
\(319\) 6513.07i 1.14314i
\(320\) 0 0
\(321\) 5085.20 3881.59i 0.884200 0.674919i
\(322\) 0 0
\(323\) −1344.04 −0.231531
\(324\) 0 0
\(325\) −8108.50 −1.38394
\(326\) 0 0
\(327\) 862.159 658.095i 0.145803 0.111293i
\(328\) 0 0
\(329\) 2125.95i 0.356254i
\(330\) 0 0
\(331\) 9617.61i 1.59707i 0.601945 + 0.798537i \(0.294392\pi\)
−0.601945 + 0.798537i \(0.705608\pi\)
\(332\) 0 0
\(333\) −324.021 + 1185.21i −0.0533220 + 0.195042i
\(334\) 0 0
\(335\) 631.555 0.103002
\(336\) 0 0
\(337\) −8057.75 −1.30247 −0.651237 0.758875i \(-0.725750\pi\)
−0.651237 + 0.758875i \(0.725750\pi\)
\(338\) 0 0
\(339\) 3171.08 + 4154.38i 0.508052 + 0.665590i
\(340\) 0 0
\(341\) 18042.3i 2.86523i
\(342\) 0 0
\(343\) 343.000i 0.0539949i
\(344\) 0 0
\(345\) 297.240 + 389.409i 0.0463851 + 0.0607684i
\(346\) 0 0
\(347\) −2229.45 −0.344908 −0.172454 0.985018i \(-0.555170\pi\)
−0.172454 + 0.985018i \(0.555170\pi\)
\(348\) 0 0
\(349\) 7212.16 1.10618 0.553092 0.833120i \(-0.313448\pi\)
0.553092 + 0.833120i \(0.313448\pi\)
\(350\) 0 0
\(351\) −3457.44 8529.78i −0.525768 1.29711i
\(352\) 0 0
\(353\) 11385.6i 1.71669i 0.513072 + 0.858345i \(0.328507\pi\)
−0.513072 + 0.858345i \(0.671493\pi\)
\(354\) 0 0
\(355\) 1201.88i 0.179688i
\(356\) 0 0
\(357\) −577.764 + 441.013i −0.0856541 + 0.0653806i
\(358\) 0 0
\(359\) 12546.9 1.84456 0.922281 0.386520i \(-0.126323\pi\)
0.922281 + 0.386520i \(0.126323\pi\)
\(360\) 0 0
\(361\) 2335.20 0.340458
\(362\) 0 0
\(363\) −11828.3 + 9028.66i −1.71026 + 1.30546i
\(364\) 0 0
\(365\) 412.029i 0.0590865i
\(366\) 0 0
\(367\) 7402.20i 1.05284i −0.850225 0.526419i \(-0.823534\pi\)
0.850225 0.526419i \(-0.176466\pi\)
\(368\) 0 0
\(369\) 325.117 + 88.8827i 0.0458670 + 0.0125394i
\(370\) 0 0
\(371\) −4476.23 −0.626400
\(372\) 0 0
\(373\) 11298.8 1.56845 0.784223 0.620479i \(-0.213062\pi\)
0.784223 + 0.620479i \(0.213062\pi\)
\(374\) 0 0
\(375\) 927.561 + 1215.18i 0.127731 + 0.167338i
\(376\) 0 0
\(377\) 6597.17i 0.901251i
\(378\) 0 0
\(379\) 3011.81i 0.408196i 0.978950 + 0.204098i \(0.0654262\pi\)
−0.978950 + 0.204098i \(0.934574\pi\)
\(380\) 0 0
\(381\) −875.572 1147.07i −0.117735 0.154242i
\(382\) 0 0
\(383\) −842.726 −0.112432 −0.0562158 0.998419i \(-0.517903\pi\)
−0.0562158 + 0.998419i \(0.517903\pi\)
\(384\) 0 0
\(385\) 536.539 0.0710248
\(386\) 0 0
\(387\) 9599.65 + 2624.42i 1.26092 + 0.344720i
\(388\) 0 0
\(389\) 8773.64i 1.14355i −0.820410 0.571776i \(-0.806255\pi\)
0.820410 0.571776i \(-0.193745\pi\)
\(390\) 0 0
\(391\) 1591.94i 0.205902i
\(392\) 0 0
\(393\) 6216.04 4744.76i 0.797857 0.609012i
\(394\) 0 0
\(395\) 612.174 0.0779793
\(396\) 0 0
\(397\) −9538.13 −1.20581 −0.602903 0.797814i \(-0.705990\pi\)
−0.602903 + 0.797814i \(0.705990\pi\)
\(398\) 0 0
\(399\) −1944.64 + 1484.37i −0.243995 + 0.186244i
\(400\) 0 0
\(401\) 8679.02i 1.08082i −0.841401 0.540411i \(-0.818269\pi\)
0.841401 0.540411i \(-0.181731\pi\)
\(402\) 0 0
\(403\) 18275.3i 2.25895i
\(404\) 0 0
\(405\) −438.917 + 742.743i −0.0538518 + 0.0911289i
\(406\) 0 0
\(407\) −2947.37 −0.358958
\(408\) 0 0
\(409\) −6173.70 −0.746381 −0.373190 0.927755i \(-0.621736\pi\)
−0.373190 + 0.927755i \(0.621736\pi\)
\(410\) 0 0
\(411\) −3176.57 4161.57i −0.381238 0.499453i
\(412\) 0 0
\(413\) 3765.02i 0.448582i
\(414\) 0 0
\(415\) 1285.26i 0.152026i
\(416\) 0 0
\(417\) 670.418 + 878.303i 0.0787302 + 0.103143i
\(418\) 0 0
\(419\) −2444.79 −0.285050 −0.142525 0.989791i \(-0.545522\pi\)
−0.142525 + 0.989791i \(0.545522\pi\)
\(420\) 0 0
\(421\) −11214.6 −1.29826 −0.649130 0.760677i \(-0.724867\pi\)
−0.649130 + 0.760677i \(0.724867\pi\)
\(422\) 0 0
\(423\) 2162.44 7909.84i 0.248562 0.909195i
\(424\) 0 0
\(425\) 2469.89i 0.281900i
\(426\) 0 0
\(427\) 1624.99i 0.184166i
\(428\) 0 0
\(429\) 17549.6 13395.8i 1.97506 1.50758i
\(430\) 0 0
\(431\) −6301.23 −0.704222 −0.352111 0.935958i \(-0.614536\pi\)
−0.352111 + 0.935958i \(0.614536\pi\)
\(432\) 0 0
\(433\) −3871.02 −0.429629 −0.214815 0.976655i \(-0.568915\pi\)
−0.214815 + 0.976655i \(0.568915\pi\)
\(434\) 0 0
\(435\) −491.558 + 375.212i −0.0541803 + 0.0413564i
\(436\) 0 0
\(437\) 5358.17i 0.586535i
\(438\) 0 0
\(439\) 7287.82i 0.792320i −0.918182 0.396160i \(-0.870343\pi\)
0.918182 0.396160i \(-0.129657\pi\)
\(440\) 0 0
\(441\) −348.888 + 1276.17i −0.0376728 + 0.137800i
\(442\) 0 0
\(443\) −6123.28 −0.656717 −0.328359 0.944553i \(-0.606495\pi\)
−0.328359 + 0.944553i \(0.606495\pi\)
\(444\) 0 0
\(445\) −1695.04 −0.180568
\(446\) 0 0
\(447\) 8691.30 + 11386.3i 0.919651 + 1.20482i
\(448\) 0 0
\(449\) 18140.7i 1.90671i −0.301846 0.953357i \(-0.597603\pi\)
0.301846 0.953357i \(-0.402397\pi\)
\(450\) 0 0
\(451\) 808.499i 0.0844141i
\(452\) 0 0
\(453\) 7382.36 + 9671.51i 0.765681 + 1.00311i
\(454\) 0 0
\(455\) −543.467 −0.0559959
\(456\) 0 0
\(457\) −7050.08 −0.721638 −0.360819 0.932636i \(-0.617503\pi\)
−0.360819 + 0.932636i \(0.617503\pi\)
\(458\) 0 0
\(459\) 2598.22 1053.16i 0.264214 0.107096i
\(460\) 0 0
\(461\) 12573.3i 1.27027i −0.772401 0.635135i \(-0.780944\pi\)
0.772401 0.635135i \(-0.219056\pi\)
\(462\) 0 0
\(463\) 11111.1i 1.11528i 0.830082 + 0.557641i \(0.188293\pi\)
−0.830082 + 0.557641i \(0.811707\pi\)
\(464\) 0 0
\(465\) −1361.70 + 1039.40i −0.135801 + 0.103658i
\(466\) 0 0
\(467\) −2093.93 −0.207485 −0.103742 0.994604i \(-0.533082\pi\)
−0.103742 + 0.994604i \(0.533082\pi\)
\(468\) 0 0
\(469\) −3735.58 −0.367789
\(470\) 0 0
\(471\) −2501.06 + 1909.09i −0.244677 + 0.186764i
\(472\) 0 0
\(473\) 23872.4i 2.32062i
\(474\) 0 0
\(475\) 8313.20i 0.803022i
\(476\) 0 0
\(477\) 16654.3 + 4553.07i 1.59863 + 0.437046i
\(478\) 0 0
\(479\) −18334.9 −1.74894 −0.874470 0.485080i \(-0.838790\pi\)
−0.874470 + 0.485080i \(0.838790\pi\)
\(480\) 0 0
\(481\) 2985.44 0.283002
\(482\) 0 0
\(483\) −1758.14 2303.31i −0.165628 0.216986i
\(484\) 0 0
\(485\) 2089.22i 0.195601i
\(486\) 0 0
\(487\) 8221.50i 0.764994i −0.923957 0.382497i \(-0.875064\pi\)
0.923957 0.382497i \(-0.124936\pi\)
\(488\) 0 0
\(489\) −3965.65 5195.33i −0.366734 0.480452i
\(490\) 0 0
\(491\) −2498.42 −0.229637 −0.114819 0.993386i \(-0.536629\pi\)
−0.114819 + 0.993386i \(0.536629\pi\)
\(492\) 0 0
\(493\) 2009.53 0.183580
\(494\) 0 0
\(495\) −1996.25 545.748i −0.181262 0.0495547i
\(496\) 0 0
\(497\) 7109.01i 0.641615i
\(498\) 0 0
\(499\) 19078.0i 1.71152i −0.517377 0.855758i \(-0.673091\pi\)
0.517377 0.855758i \(-0.326909\pi\)
\(500\) 0 0
\(501\) 5134.65 3919.33i 0.457882 0.349506i
\(502\) 0 0
\(503\) −6062.87 −0.537436 −0.268718 0.963219i \(-0.586600\pi\)
−0.268718 + 0.963219i \(0.586600\pi\)
\(504\) 0 0
\(505\) 198.402 0.0174827
\(506\) 0 0
\(507\) −8701.75 + 6642.13i −0.762245 + 0.581829i
\(508\) 0 0
\(509\) 14287.9i 1.24420i −0.782936 0.622102i \(-0.786279\pi\)
0.782936 0.622102i \(-0.213721\pi\)
\(510\) 0 0
\(511\) 2437.11i 0.210981i
\(512\) 0 0
\(513\) 8745.10 3544.72i 0.752643 0.305075i
\(514\) 0 0
\(515\) 487.609 0.0417216
\(516\) 0 0
\(517\) 19670.1 1.67329
\(518\) 0 0
\(519\) −11210.4 14686.6i −0.948136 1.24214i
\(520\) 0 0
\(521\) 21919.6i 1.84321i 0.388127 + 0.921606i \(0.373122\pi\)
−0.388127 + 0.921606i \(0.626878\pi\)
\(522\) 0 0
\(523\) 16921.7i 1.41479i −0.706818 0.707395i \(-0.749870\pi\)
0.706818 0.707395i \(-0.250130\pi\)
\(524\) 0 0
\(525\) −2727.76 3573.59i −0.226760 0.297075i
\(526\) 0 0
\(527\) 5566.75 0.460135
\(528\) 0 0
\(529\) −5820.57 −0.478390
\(530\) 0 0
\(531\) −3829.65 + 14008.2i −0.312980 + 1.14483i
\(532\) 0 0
\(533\) 818.940i 0.0665520i
\(534\) 0 0
\(535\) 1457.03i 0.117744i
\(536\) 0 0
\(537\) −5098.69 + 3891.88i −0.409729 + 0.312750i
\(538\) 0 0
\(539\) −3173.57 −0.253609
\(540\) 0 0
\(541\) −13388.4 −1.06398 −0.531988 0.846752i \(-0.678555\pi\)
−0.531988 + 0.846752i \(0.678555\pi\)
\(542\) 0 0
\(543\) −5026.67 + 3836.91i −0.397265 + 0.303237i
\(544\) 0 0
\(545\) 247.029i 0.0194157i
\(546\) 0 0
\(547\) 8932.60i 0.698228i 0.937080 + 0.349114i \(0.113517\pi\)
−0.937080 + 0.349114i \(0.886483\pi\)
\(548\) 0 0
\(549\) 1652.88 6045.95i 0.128494 0.470009i
\(550\) 0 0
\(551\) 6763.71 0.522947
\(552\) 0 0
\(553\) −3620.95 −0.278442
\(554\) 0 0
\(555\) −169.795 222.446i −0.0129863 0.0170132i
\(556\) 0 0
\(557\) 4587.92i 0.349006i −0.984657 0.174503i \(-0.944168\pi\)
0.984657 0.174503i \(-0.0558319\pi\)
\(558\) 0 0
\(559\) 24180.6i 1.82957i
\(560\) 0 0
\(561\) 4080.42 + 5345.70i 0.307087 + 0.402309i
\(562\) 0 0
\(563\) 618.373 0.0462901 0.0231450 0.999732i \(-0.492632\pi\)
0.0231450 + 0.999732i \(0.492632\pi\)
\(564\) 0 0
\(565\) −1190.33 −0.0886328
\(566\) 0 0
\(567\) 2596.15 4393.25i 0.192289 0.325395i
\(568\) 0 0
\(569\) 9659.94i 0.711715i 0.934540 + 0.355857i \(0.115811\pi\)
−0.934540 + 0.355857i \(0.884189\pi\)
\(570\) 0 0
\(571\) 3186.35i 0.233528i 0.993160 + 0.116764i \(0.0372522\pi\)
−0.993160 + 0.116764i \(0.962748\pi\)
\(572\) 0 0
\(573\) −8695.56 + 6637.41i −0.633966 + 0.483912i
\(574\) 0 0
\(575\) 9846.49 0.714134
\(576\) 0 0
\(577\) −2641.29 −0.190569 −0.0952844 0.995450i \(-0.530376\pi\)
−0.0952844 + 0.995450i \(0.530376\pi\)
\(578\) 0 0
\(579\) −13390.5 + 10221.1i −0.961121 + 0.733634i
\(580\) 0 0
\(581\) 7602.18i 0.542842i
\(582\) 0 0
\(583\) 41415.9i 2.94214i
\(584\) 0 0
\(585\) 2022.03 + 552.796i 0.142907 + 0.0390689i
\(586\) 0 0
\(587\) 17658.4 1.24163 0.620816 0.783956i \(-0.286801\pi\)
0.620816 + 0.783956i \(0.286801\pi\)
\(588\) 0 0
\(589\) 18736.6 1.31075
\(590\) 0 0
\(591\) −3120.62 4088.28i −0.217200 0.284550i
\(592\) 0 0
\(593\) 15773.9i 1.09234i −0.837675 0.546169i \(-0.816086\pi\)
0.837675 0.546169i \(-0.183914\pi\)
\(594\) 0 0
\(595\) 165.543i 0.0114061i
\(596\) 0 0
\(597\) −3489.58 4571.64i −0.239228 0.313408i
\(598\) 0 0
\(599\) −17992.2 −1.22728 −0.613639 0.789587i \(-0.710295\pi\)
−0.613639 + 0.789587i \(0.710295\pi\)
\(600\) 0 0
\(601\) −2205.18 −0.149669 −0.0748344 0.997196i \(-0.523843\pi\)
−0.0748344 + 0.997196i \(0.523843\pi\)
\(602\) 0 0
\(603\) 13898.6 + 3799.70i 0.938634 + 0.256610i
\(604\) 0 0
\(605\) 3389.09i 0.227745i
\(606\) 0 0
\(607\) 27712.9i 1.85310i 0.376172 + 0.926550i \(0.377240\pi\)
−0.376172 + 0.926550i \(0.622760\pi\)
\(608\) 0 0
\(609\) 2907.52 2219.34i 0.193462 0.147672i
\(610\) 0 0
\(611\) −19924.1 −1.31922
\(612\) 0 0
\(613\) −5568.02 −0.366868 −0.183434 0.983032i \(-0.558721\pi\)
−0.183434 + 0.983032i \(0.558721\pi\)
\(614\) 0 0
\(615\) −61.0196 + 46.5769i −0.00400089 + 0.00305392i
\(616\) 0 0
\(617\) 23868.9i 1.55741i 0.627387 + 0.778707i \(0.284124\pi\)
−0.627387 + 0.778707i \(0.715876\pi\)
\(618\) 0 0
\(619\) 12735.2i 0.826931i −0.910520 0.413465i \(-0.864318\pi\)
0.910520 0.413465i \(-0.135682\pi\)
\(620\) 0 0
\(621\) 4198.51 + 10358.1i 0.271305 + 0.669331i
\(622\) 0 0
\(623\) 10026.0 0.644755
\(624\) 0 0
\(625\) 15101.8 0.966512
\(626\) 0 0
\(627\) 13733.9 + 17992.6i 0.874769 + 1.14602i
\(628\) 0 0
\(629\) 909.380i 0.0576460i
\(630\) 0 0
\(631\) 6147.82i 0.387862i −0.981015 0.193931i \(-0.937876\pi\)
0.981015 0.193931i \(-0.0621238\pi\)
\(632\) 0 0
\(633\) −1091.33 1429.74i −0.0685255 0.0897741i
\(634\) 0 0
\(635\) 328.663 0.0205395
\(636\) 0 0
\(637\) 3214.55 0.199945
\(638\) 0 0
\(639\) 7231.04 26449.8i 0.447661 1.63746i
\(640\) 0 0
\(641\) 3596.56i 0.221616i 0.993842 + 0.110808i \(0.0353438\pi\)
−0.993842 + 0.110808i \(0.964656\pi\)
\(642\) 0 0
\(643\) 22806.1i 1.39873i −0.714763 0.699366i \(-0.753466\pi\)
0.714763 0.699366i \(-0.246534\pi\)
\(644\) 0 0
\(645\) −1801.71 + 1375.26i −0.109988 + 0.0839550i
\(646\) 0 0
\(647\) −11623.0 −0.706257 −0.353128 0.935575i \(-0.614882\pi\)
−0.353128 + 0.935575i \(0.614882\pi\)
\(648\) 0 0
\(649\) −34835.4 −2.10695
\(650\) 0 0
\(651\) 8054.31 6147.93i 0.484905 0.370133i
\(652\) 0 0
\(653\) 30428.5i 1.82352i −0.410725 0.911759i \(-0.634724\pi\)
0.410725 0.911759i \(-0.365276\pi\)
\(654\) 0 0
\(655\) 1781.04i 0.106246i
\(656\) 0 0
\(657\) −2478.94 + 9067.52i −0.147203 + 0.538444i
\(658\) 0 0
\(659\) 32213.5 1.90419 0.952094 0.305805i \(-0.0989257\pi\)
0.952094 + 0.305805i \(0.0989257\pi\)
\(660\) 0 0
\(661\) 1968.85 0.115854 0.0579269 0.998321i \(-0.481551\pi\)
0.0579269 + 0.998321i \(0.481551\pi\)
\(662\) 0 0
\(663\) −4133.12 5414.73i −0.242107 0.317180i
\(664\) 0 0
\(665\) 557.187i 0.0324914i
\(666\) 0 0
\(667\) 8011.22i 0.465061i
\(668\) 0 0
\(669\) −9923.20 13000.2i −0.573473 0.751297i
\(670\) 0 0
\(671\) 15035.0 0.865009
\(672\) 0 0
\(673\) −18098.8 −1.03664 −0.518320 0.855186i \(-0.673443\pi\)
−0.518320 + 0.855186i \(0.673443\pi\)
\(674\) 0 0
\(675\) 6513.99 + 16070.5i 0.371442 + 0.916377i
\(676\) 0 0
\(677\) 14654.4i 0.831928i 0.909381 + 0.415964i \(0.136556\pi\)
−0.909381 + 0.415964i \(0.863444\pi\)
\(678\) 0 0
\(679\) 12357.5i 0.698437i
\(680\) 0 0
\(681\) −6476.91 + 4943.89i −0.364458 + 0.278194i
\(682\) 0 0
\(683\) 25524.0 1.42994 0.714969 0.699156i \(-0.246441\pi\)
0.714969 + 0.699156i \(0.246441\pi\)
\(684\) 0 0
\(685\) 1192.39 0.0665093
\(686\) 0 0
\(687\) 10419.9 7953.59i 0.578665 0.441701i
\(688\) 0 0
\(689\) 41950.7i 2.31958i
\(690\) 0 0
\(691\) 1294.40i 0.0712607i 0.999365 + 0.0356303i \(0.0113439\pi\)
−0.999365 + 0.0356303i \(0.988656\pi\)
\(692\) 0 0
\(693\) 11807.6 + 3228.04i 0.647235 + 0.176945i
\(694\) 0 0
\(695\) −251.655 −0.0137350
\(696\) 0 0
\(697\) 249.453 0.0135563
\(698\) 0 0
\(699\) 16470.1 + 21577.3i 0.891213 + 1.16756i
\(700\) 0 0
\(701\) 5528.84i 0.297891i −0.988845 0.148945i \(-0.952412\pi\)
0.988845 0.148945i \(-0.0475878\pi\)
\(702\) 0 0
\(703\) 3060.80i 0.164211i
\(704\) 0 0
\(705\) 1133.18 + 1484.56i 0.0605361 + 0.0793073i
\(706\) 0 0
\(707\) −1173.53 −0.0624259
\(708\) 0 0
\(709\) −16540.4 −0.876146 −0.438073 0.898939i \(-0.644339\pi\)
−0.438073 + 0.898939i \(0.644339\pi\)
\(710\) 0 0
\(711\) 13472.1 + 3683.10i 0.710611 + 0.194272i
\(712\) 0 0
\(713\) 22192.4i 1.16566i
\(714\) 0 0
\(715\) 5028.37i 0.263007i
\(716\) 0 0
\(717\) 3217.72 2456.12i 0.167598 0.127929i
\(718\) 0 0
\(719\) 2837.86 0.147196 0.0735982 0.997288i \(-0.476552\pi\)
0.0735982 + 0.997288i \(0.476552\pi\)
\(720\) 0 0
\(721\) −2884.15 −0.148976
\(722\) 0 0
\(723\) 152.005 116.027i 0.00781897 0.00596830i
\(724\) 0 0
\(725\) 12429.4i 0.636712i
\(726\) 0 0
\(727\) 26062.3i 1.32957i 0.747035 + 0.664785i \(0.231477\pi\)
−0.747035 + 0.664785i \(0.768523\pi\)
\(728\) 0 0
\(729\) −14127.9 + 13704.8i −0.717772 + 0.696278i
\(730\) 0 0
\(731\) 7365.55 0.372674
\(732\) 0 0
\(733\) 24086.8 1.21373 0.606866 0.794804i \(-0.292426\pi\)
0.606866 + 0.794804i \(0.292426\pi\)
\(734\) 0 0
\(735\) −182.826 239.518i −0.00917503 0.0120201i
\(736\) 0 0
\(737\) 34563.0i 1.72747i
\(738\) 0 0
\(739\) 4960.92i 0.246942i −0.992348 0.123471i \(-0.960597\pi\)
0.992348 0.123471i \(-0.0394026\pi\)
\(740\) 0 0
\(741\) −13911.3 18224.9i −0.689668 0.903522i
\(742\) 0 0
\(743\) −24905.0 −1.22971 −0.614855 0.788640i \(-0.710786\pi\)
−0.614855 + 0.788640i \(0.710786\pi\)
\(744\) 0 0
\(745\) −3262.45 −0.160439
\(746\) 0 0
\(747\) 7732.67 28284.7i 0.378746 1.38539i
\(748\) 0 0
\(749\) 8618.18i 0.420429i
\(750\) 0 0
\(751\) 20503.7i 0.996258i 0.867103 + 0.498129i \(0.165979\pi\)
−0.867103 + 0.498129i \(0.834021\pi\)
\(752\) 0 0
\(753\) −13264.6 + 10125.0i −0.641953 + 0.490009i
\(754\) 0 0
\(755\) −2771.12 −0.133578
\(756\) 0 0
\(757\) −18685.3 −0.897132 −0.448566 0.893750i \(-0.648065\pi\)
−0.448566 + 0.893750i \(0.648065\pi\)
\(758\) 0 0
\(759\) −21311.2 + 16267.0i −1.01916 + 0.777939i
\(760\) 0 0
\(761\) 2699.37i 0.128583i 0.997931 + 0.0642917i \(0.0204788\pi\)
−0.997931 + 0.0642917i \(0.979521\pi\)
\(762\) 0 0
\(763\) 1461.15i 0.0693279i
\(764\) 0 0
\(765\) −168.385 + 615.921i −0.00795812 + 0.0291094i
\(766\) 0 0
\(767\) 35285.3 1.66112
\(768\) 0 0
\(769\) 32139.9 1.50714 0.753572 0.657366i \(-0.228329\pi\)
0.753572 + 0.657366i \(0.228329\pi\)
\(770\) 0 0
\(771\) −6426.36 8419.06i −0.300181 0.393262i
\(772\) 0 0
\(773\) 3369.87i 0.156799i 0.996922 + 0.0783997i \(0.0249810\pi\)
−0.996922 + 0.0783997i \(0.975019\pi\)
\(774\) 0 0
\(775\) 34431.5i 1.59589i
\(776\) 0 0
\(777\) 1004.32 + 1315.75i 0.0463705 + 0.0607492i
\(778\) 0 0
\(779\) 839.613 0.0386165
\(780\) 0 0
\(781\) 65775.3 3.01361
\(782\) 0 0
\(783\) −13075.2 + 5299.86i −0.596766 + 0.241892i
\(784\) 0 0
\(785\) 716.614i 0.0325822i
\(786\) 0 0
\(787\) 30361.1i 1.37516i 0.726106 + 0.687582i \(0.241328\pi\)
−0.726106 + 0.687582i \(0.758672\pi\)
\(788\) 0 0
\(789\) 11167.7 8524.44i 0.503906 0.384636i
\(790\) 0 0
\(791\) 7040.67 0.316482
\(792\) 0 0
\(793\) −15229.2 −0.681973
\(794\) 0 0
\(795\) −3125.77 + 2385.93i −0.139446 + 0.106440i
\(796\) 0 0
\(797\) 22114.2i 0.982840i 0.870923 + 0.491420i \(0.163522\pi\)
−0.870923 + 0.491420i \(0.836478\pi\)
\(798\) 0 0
\(799\) 6069.00i 0.268718i