Properties

Label 648.4.i.s.217.2
Level $648$
Weight $4$
Character 648.217
Analytic conductor $38.233$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 648.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(38.2332376837\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
Defining polynomial: \(x^{4} - x^{3} - 2 x^{2} - 3 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{3} \)
Twist minimal: no (minimal twist has level 216)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 217.2
Root \(1.68614 + 0.396143i\) of defining polynomial
Character \(\chi\) \(=\) 648.217
Dual form 648.4.i.s.433.2

$q$-expansion

\(f(q)\) \(=\) \(q+(10.6168 + 18.3889i) q^{5} +(-14.6168 + 25.3171i) q^{7} +O(q^{10})\) \(q+(10.6168 + 18.3889i) q^{5} +(-14.6168 + 25.3171i) q^{7} +(0.500000 - 0.866025i) q^{11} +(26.4674 + 45.8428i) q^{13} +96.9348 q^{17} +126.467 q^{19} +(-11.4674 - 19.8621i) q^{23} +(-162.935 + 282.211i) q^{25} +(-66.7663 + 115.643i) q^{29} +(-50.9158 - 88.1887i) q^{31} -620.739 q^{35} +105.065 q^{37} +(8.16844 + 14.1482i) q^{41} +(100.636 - 174.306i) q^{43} +(-125.935 + 218.125i) q^{47} +(-255.804 - 443.066i) q^{49} +148.038 q^{53} +21.2337 q^{55} +(-36.8043 - 63.7468i) q^{59} +(303.739 - 526.091i) q^{61} +(-562.000 + 973.413i) q^{65} +(-380.973 - 659.864i) q^{67} -701.196 q^{71} -287.000 q^{73} +(14.6168 + 25.3171i) q^{77} +(64.2610 - 111.303i) q^{79} +(80.2390 - 138.978i) q^{83} +(1029.14 + 1782.52i) q^{85} -430.206 q^{89} -1547.48 q^{91} +(1342.68 + 2325.60i) q^{95} +(15.5652 - 26.9598i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 8q^{5} - 24q^{7} + O(q^{10}) \) \( 4q + 8q^{5} - 24q^{7} + 2q^{11} - 32q^{13} + 112q^{17} + 368q^{19} + 92q^{23} - 376q^{25} - 336q^{29} - 376q^{31} - 1380q^{35} + 696q^{37} - 312q^{41} - 80q^{43} - 228q^{47} - 196q^{49} - 304q^{53} + 16q^{55} + 680q^{59} + 112q^{61} - 2248q^{65} - 352q^{67} - 3632q^{71} - 1148q^{73} + 24q^{77} + 1360q^{79} - 782q^{83} + 2600q^{85} - 480q^{89} - 3984q^{91} + 1924q^{95} + 338q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(487\) \(569\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(5\) 10.6168 + 18.3889i 0.949599 + 1.64475i 0.746269 + 0.665644i \(0.231843\pi\)
0.203330 + 0.979110i \(0.434824\pi\)
\(6\) 0 0
\(7\) −14.6168 + 25.3171i −0.789235 + 1.36700i 0.137201 + 0.990543i \(0.456190\pi\)
−0.926436 + 0.376453i \(0.877144\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.500000 0.866025i 0.0137051 0.0237379i −0.859092 0.511822i \(-0.828971\pi\)
0.872797 + 0.488084i \(0.162304\pi\)
\(12\) 0 0
\(13\) 26.4674 + 45.8428i 0.564671 + 0.978040i 0.997080 + 0.0763620i \(0.0243305\pi\)
−0.432409 + 0.901678i \(0.642336\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 96.9348 1.38295 0.691474 0.722401i \(-0.256961\pi\)
0.691474 + 0.722401i \(0.256961\pi\)
\(18\) 0 0
\(19\) 126.467 1.52703 0.763516 0.645789i \(-0.223471\pi\)
0.763516 + 0.645789i \(0.223471\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −11.4674 19.8621i −0.103961 0.180066i 0.809352 0.587324i \(-0.199819\pi\)
−0.913313 + 0.407257i \(0.866485\pi\)
\(24\) 0 0
\(25\) −162.935 + 282.211i −1.30348 + 2.25769i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −66.7663 + 115.643i −0.427524 + 0.740493i −0.996652 0.0817555i \(-0.973947\pi\)
0.569129 + 0.822249i \(0.307281\pi\)
\(30\) 0 0
\(31\) −50.9158 88.1887i −0.294992 0.510941i 0.679991 0.733220i \(-0.261984\pi\)
−0.974983 + 0.222280i \(0.928650\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −620.739 −2.99783
\(36\) 0 0
\(37\) 105.065 0.466828 0.233414 0.972378i \(-0.425010\pi\)
0.233414 + 0.972378i \(0.425010\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 8.16844 + 14.1482i 0.0311145 + 0.0538920i 0.881163 0.472812i \(-0.156761\pi\)
−0.850049 + 0.526704i \(0.823428\pi\)
\(42\) 0 0
\(43\) 100.636 174.306i 0.356903 0.618174i −0.630539 0.776158i \(-0.717166\pi\)
0.987442 + 0.157984i \(0.0504994\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −125.935 + 218.125i −0.390840 + 0.676954i −0.992561 0.121752i \(-0.961149\pi\)
0.601721 + 0.798707i \(0.294482\pi\)
\(48\) 0 0
\(49\) −255.804 443.066i −0.745785 1.29174i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 148.038 0.383671 0.191836 0.981427i \(-0.438556\pi\)
0.191836 + 0.981427i \(0.438556\pi\)
\(54\) 0 0
\(55\) 21.2337 0.0520573
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −36.8043 63.7468i −0.0812120 0.140663i 0.822559 0.568680i \(-0.192546\pi\)
−0.903771 + 0.428017i \(0.859212\pi\)
\(60\) 0 0
\(61\) 303.739 526.091i 0.637538 1.10425i −0.348434 0.937333i \(-0.613286\pi\)
0.985971 0.166914i \(-0.0533803\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −562.000 + 973.413i −1.07242 + 1.85749i
\(66\) 0 0
\(67\) −380.973 659.864i −0.694675 1.20321i −0.970290 0.241944i \(-0.922215\pi\)
0.275615 0.961268i \(-0.411118\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −701.196 −1.17207 −0.586033 0.810287i \(-0.699311\pi\)
−0.586033 + 0.810287i \(0.699311\pi\)
\(72\) 0 0
\(73\) −287.000 −0.460148 −0.230074 0.973173i \(-0.573897\pi\)
−0.230074 + 0.973173i \(0.573897\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 14.6168 + 25.3171i 0.0216330 + 0.0374695i
\(78\) 0 0
\(79\) 64.2610 111.303i 0.0915181 0.158514i −0.816632 0.577159i \(-0.804161\pi\)
0.908150 + 0.418645i \(0.137495\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 80.2390 138.978i 0.106113 0.183793i −0.808079 0.589074i \(-0.799493\pi\)
0.914192 + 0.405281i \(0.132826\pi\)
\(84\) 0 0
\(85\) 1029.14 + 1782.52i 1.31325 + 2.27461i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −430.206 −0.512380 −0.256190 0.966626i \(-0.582467\pi\)
−0.256190 + 0.966626i \(0.582467\pi\)
\(90\) 0 0
\(91\) −1547.48 −1.78263
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1342.68 + 2325.60i 1.45007 + 2.51159i
\(96\) 0 0
\(97\) 15.5652 26.9598i 0.0162929 0.0282201i −0.857764 0.514044i \(-0.828147\pi\)
0.874057 + 0.485824i \(0.161480\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −491.552 + 851.392i −0.484269 + 0.838779i −0.999837 0.0180698i \(-0.994248\pi\)
0.515567 + 0.856849i \(0.327581\pi\)
\(102\) 0 0
\(103\) 476.076 + 824.588i 0.455429 + 0.788826i 0.998713 0.0507234i \(-0.0161527\pi\)
−0.543284 + 0.839549i \(0.682819\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 272.087 0.245828 0.122914 0.992417i \(-0.460776\pi\)
0.122914 + 0.992417i \(0.460776\pi\)
\(108\) 0 0
\(109\) 1355.76 1.19136 0.595680 0.803222i \(-0.296883\pi\)
0.595680 + 0.803222i \(0.296883\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −969.179 1678.67i −0.806838 1.39748i −0.915043 0.403356i \(-0.867844\pi\)
0.108205 0.994129i \(-0.465490\pi\)
\(114\) 0 0
\(115\) 243.495 421.745i 0.197443 0.341982i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1416.88 + 2454.11i −1.09147 + 1.89049i
\(120\) 0 0
\(121\) 665.000 + 1151.81i 0.499624 + 0.865375i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −4265.20 −3.05193
\(126\) 0 0
\(127\) 232.375 0.162362 0.0811808 0.996699i \(-0.474131\pi\)
0.0811808 + 0.996699i \(0.474131\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1397.65 2420.80i −0.932163 1.61455i −0.779616 0.626258i \(-0.784586\pi\)
−0.152548 0.988296i \(-0.548748\pi\)
\(132\) 0 0
\(133\) −1848.55 + 3201.79i −1.20519 + 2.08745i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −630.766 + 1092.52i −0.393358 + 0.681315i −0.992890 0.119035i \(-0.962020\pi\)
0.599532 + 0.800351i \(0.295353\pi\)
\(138\) 0 0
\(139\) 153.684 + 266.189i 0.0937794 + 0.162431i 0.909099 0.416581i \(-0.136772\pi\)
−0.815319 + 0.579012i \(0.803438\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 52.9348 0.0309554
\(144\) 0 0
\(145\) −2835.39 −1.62391
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 798.878 + 1383.70i 0.439239 + 0.760784i 0.997631 0.0687929i \(-0.0219148\pi\)
−0.558392 + 0.829577i \(0.688581\pi\)
\(150\) 0 0
\(151\) 1707.70 2957.83i 0.920337 1.59407i 0.121444 0.992598i \(-0.461248\pi\)
0.798893 0.601473i \(-0.205419\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1081.13 1872.57i 0.560248 0.970378i
\(156\) 0 0
\(157\) −238.413 412.943i −0.121194 0.209914i 0.799045 0.601271i \(-0.205339\pi\)
−0.920239 + 0.391358i \(0.872006\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 670.467 0.328200
\(162\) 0 0
\(163\) 3304.04 1.58768 0.793842 0.608124i \(-0.208078\pi\)
0.793842 + 0.608124i \(0.208078\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1045.83 + 1811.42i 0.484601 + 0.839354i 0.999844 0.0176906i \(-0.00563138\pi\)
−0.515242 + 0.857045i \(0.672298\pi\)
\(168\) 0 0
\(169\) −302.544 + 524.022i −0.137708 + 0.238517i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1462.28 2532.74i 0.642631 1.11307i −0.342213 0.939622i \(-0.611176\pi\)
0.984843 0.173446i \(-0.0554903\pi\)
\(174\) 0 0
\(175\) −4763.18 8250.08i −2.05750 3.56370i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 231.913 0.0968381 0.0484191 0.998827i \(-0.484582\pi\)
0.0484191 + 0.998827i \(0.484582\pi\)
\(180\) 0 0
\(181\) 2291.74 0.941125 0.470562 0.882367i \(-0.344051\pi\)
0.470562 + 0.882367i \(0.344051\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1115.46 + 1932.04i 0.443299 + 0.767817i
\(186\) 0 0
\(187\) 48.4674 83.9480i 0.0189534 0.0328282i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2108.90 + 3652.72i −0.798925 + 1.38378i 0.121391 + 0.992605i \(0.461264\pi\)
−0.920316 + 0.391175i \(0.872069\pi\)
\(192\) 0 0
\(193\) 594.174 + 1029.14i 0.221604 + 0.383829i 0.955295 0.295654i \(-0.0955375\pi\)
−0.733691 + 0.679483i \(0.762204\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3130.25 1.13209 0.566044 0.824375i \(-0.308473\pi\)
0.566044 + 0.824375i \(0.308473\pi\)
\(198\) 0 0
\(199\) −659.146 −0.234802 −0.117401 0.993085i \(-0.537456\pi\)
−0.117401 + 0.993085i \(0.537456\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1951.83 3380.66i −0.674834 1.16885i
\(204\) 0 0
\(205\) −173.446 + 300.417i −0.0590927 + 0.102352i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 63.2337 109.524i 0.0209281 0.0362485i
\(210\) 0 0
\(211\) −1806.97 3129.77i −0.589560 1.02115i −0.994290 0.106711i \(-0.965968\pi\)
0.404730 0.914436i \(-0.367365\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 4273.74 1.35566
\(216\) 0 0
\(217\) 2976.91 0.931272
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 2565.61 + 4443.76i 0.780912 + 1.35258i
\(222\) 0 0
\(223\) 1027.07 1778.93i 0.308419 0.534197i −0.669598 0.742724i \(-0.733534\pi\)
0.978017 + 0.208527i \(0.0668669\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1076.80 1865.08i 0.314846 0.545329i −0.664559 0.747236i \(-0.731381\pi\)
0.979405 + 0.201907i \(0.0647138\pi\)
\(228\) 0 0
\(229\) 909.935 + 1576.05i 0.262577 + 0.454797i 0.966926 0.255057i \(-0.0820942\pi\)
−0.704349 + 0.709854i \(0.748761\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3989.68 1.12177 0.560886 0.827893i \(-0.310461\pi\)
0.560886 + 0.827893i \(0.310461\pi\)
\(234\) 0 0
\(235\) −5348.12 −1.48457
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −2852.16 4940.09i −0.771929 1.33702i −0.936504 0.350656i \(-0.885959\pi\)
0.164575 0.986365i \(-0.447375\pi\)
\(240\) 0 0
\(241\) −3111.98 + 5390.10i −0.831785 + 1.44069i 0.0648372 + 0.997896i \(0.479347\pi\)
−0.896622 + 0.442797i \(0.853986\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 5431.67 9407.92i 1.41639 2.45327i
\(246\) 0 0
\(247\) 3347.26 + 5797.62i 0.862271 + 1.49350i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −4622.52 −1.16243 −0.581217 0.813749i \(-0.697423\pi\)
−0.581217 + 0.813749i \(0.697423\pi\)
\(252\) 0 0
\(253\) −22.9348 −0.00569919
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2452.54 4247.93i −0.595274 1.03104i −0.993508 0.113761i \(-0.963710\pi\)
0.398234 0.917284i \(-0.369623\pi\)
\(258\) 0 0
\(259\) −1535.72 + 2659.95i −0.368437 + 0.638151i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 2216.42 3838.96i 0.519660 0.900077i −0.480079 0.877225i \(-0.659392\pi\)
0.999739 0.0228519i \(-0.00727463\pi\)
\(264\) 0 0
\(265\) 1571.70 + 2722.26i 0.364334 + 0.631045i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −4454.81 −1.00972 −0.504860 0.863201i \(-0.668456\pi\)
−0.504860 + 0.863201i \(0.668456\pi\)
\(270\) 0 0
\(271\) 3256.23 0.729897 0.364948 0.931028i \(-0.381087\pi\)
0.364948 + 0.931028i \(0.381087\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 162.935 + 282.211i 0.0357285 + 0.0618836i
\(276\) 0 0
\(277\) 1710.80 2963.20i 0.371091 0.642749i −0.618642 0.785673i \(-0.712317\pi\)
0.989734 + 0.142924i \(0.0456504\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −857.554 + 1485.33i −0.182055 + 0.315328i −0.942580 0.333980i \(-0.891608\pi\)
0.760525 + 0.649308i \(0.224941\pi\)
\(282\) 0 0
\(283\) 2243.80 + 3886.37i 0.471307 + 0.816328i 0.999461 0.0328205i \(-0.0104490\pi\)
−0.528154 + 0.849149i \(0.677116\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −477.587 −0.0982268
\(288\) 0 0
\(289\) 4483.35 0.912548
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 842.657 + 1459.52i 0.168016 + 0.291011i 0.937722 0.347386i \(-0.112931\pi\)
−0.769707 + 0.638398i \(0.779597\pi\)
\(294\) 0 0
\(295\) 781.490 1353.58i 0.154238 0.267147i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 607.023 1051.39i 0.117408 0.203357i
\(300\) 0 0
\(301\) 2941.96 + 5095.62i 0.563361 + 0.975769i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 12899.0 2.42162
\(306\) 0 0
\(307\) −8079.07 −1.50194 −0.750972 0.660334i \(-0.770415\pi\)
−0.750972 + 0.660334i \(0.770415\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1278.81 + 2214.97i 0.233167 + 0.403857i 0.958738 0.284290i \(-0.0917578\pi\)
−0.725571 + 0.688147i \(0.758424\pi\)
\(312\) 0 0
\(313\) 2040.72 3534.63i 0.368524 0.638303i −0.620811 0.783961i \(-0.713196\pi\)
0.989335 + 0.145658i \(0.0465298\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3850.96 + 6670.06i −0.682308 + 1.18179i 0.291967 + 0.956428i \(0.405690\pi\)
−0.974275 + 0.225364i \(0.927643\pi\)
\(318\) 0 0
\(319\) 66.7663 + 115.643i 0.0117185 + 0.0202970i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 12259.1 2.11181
\(324\) 0 0
\(325\) −17249.8 −2.94415
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −3681.54 6376.61i −0.616929 1.06855i
\(330\) 0 0
\(331\) 178.657 309.443i 0.0296673 0.0513853i −0.850811 0.525473i \(-0.823889\pi\)
0.880478 + 0.474087i \(0.157222\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 8089.46 14011.3i 1.31933 2.28514i
\(336\) 0 0
\(337\) 3329.54 + 5766.94i 0.538195 + 0.932181i 0.999001 + 0.0446806i \(0.0142270\pi\)
−0.460806 + 0.887501i \(0.652440\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −101.832 −0.0161715
\(342\) 0 0
\(343\) 4929.05 0.775929
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 3947.02 + 6836.44i 0.610626 + 1.05763i 0.991135 + 0.132858i \(0.0424154\pi\)
−0.380509 + 0.924777i \(0.624251\pi\)
\(348\) 0 0
\(349\) 627.228 1086.39i 0.0962027 0.166628i −0.813907 0.580995i \(-0.802664\pi\)
0.910110 + 0.414367i \(0.135997\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 4302.46 7452.08i 0.648716 1.12361i −0.334714 0.942320i \(-0.608640\pi\)
0.983430 0.181290i \(-0.0580271\pi\)
\(354\) 0 0
\(355\) −7444.49 12894.2i −1.11299 1.92776i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3875.61 0.569768 0.284884 0.958562i \(-0.408045\pi\)
0.284884 + 0.958562i \(0.408045\pi\)
\(360\) 0 0
\(361\) 9135.00 1.33183
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −3047.03 5277.62i −0.436956 0.756831i
\(366\) 0 0
\(367\) 5945.05 10297.1i 0.845583 1.46459i −0.0395301 0.999218i \(-0.512586\pi\)
0.885114 0.465375i \(-0.154081\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −2163.85 + 3747.89i −0.302807 + 0.524477i
\(372\) 0 0
\(373\) −6192.25 10725.3i −0.859578 1.48883i −0.872332 0.488914i \(-0.837393\pi\)
0.0127544 0.999919i \(-0.495940\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −7068.52 −0.965642
\(378\) 0 0
\(379\) 2062.80 0.279576 0.139788 0.990181i \(-0.455358\pi\)
0.139788 + 0.990181i \(0.455358\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 5952.62 + 10310.2i 0.794164 + 1.37553i 0.923369 + 0.383914i \(0.125424\pi\)
−0.129205 + 0.991618i \(0.541243\pi\)
\(384\) 0 0
\(385\) −310.370 + 537.576i −0.0410854 + 0.0711621i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 6358.29 11012.9i 0.828735 1.43541i −0.0702954 0.997526i \(-0.522394\pi\)
0.899031 0.437886i \(-0.144272\pi\)
\(390\) 0 0
\(391\) −1111.59 1925.33i −0.143773 0.249023i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2729.00 0.347622
\(396\) 0 0
\(397\) −4531.59 −0.572881 −0.286441 0.958098i \(-0.592472\pi\)
−0.286441 + 0.958098i \(0.592472\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2414.58 4182.17i −0.300694 0.520817i 0.675600 0.737269i \(-0.263885\pi\)
−0.976293 + 0.216452i \(0.930552\pi\)
\(402\) 0 0
\(403\) 2695.21 4668.25i 0.333147 0.577027i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 52.5326 90.9892i 0.00639790 0.0110815i
\(408\) 0 0
\(409\) −5742.46 9946.23i −0.694245 1.20247i −0.970435 0.241364i \(-0.922405\pi\)
0.276190 0.961103i \(-0.410928\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 2151.85 0.256381
\(414\) 0 0
\(415\) 3407.54 0.403059
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 4105.82 + 7111.50i 0.478718 + 0.829163i 0.999702 0.0244030i \(-0.00776848\pi\)
−0.520985 + 0.853566i \(0.674435\pi\)
\(420\) 0 0
\(421\) −4894.06 + 8476.77i −0.566561 + 0.981312i 0.430342 + 0.902666i \(0.358393\pi\)
−0.996903 + 0.0786460i \(0.974940\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −15794.0 + 27356.1i −1.80264 + 3.12227i
\(426\) 0 0
\(427\) 8879.41 + 15379.6i 1.00633 + 1.74302i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −11206.3 −1.25241 −0.626207 0.779657i \(-0.715394\pi\)
−0.626207 + 0.779657i \(0.715394\pi\)
\(432\) 0 0
\(433\) 719.306 0.0798329 0.0399165 0.999203i \(-0.487291\pi\)
0.0399165 + 0.999203i \(0.487291\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1450.25 2511.90i −0.158752 0.274967i
\(438\) 0 0
\(439\) −4397.50 + 7616.70i −0.478090 + 0.828075i −0.999684 0.0251179i \(-0.992004\pi\)
0.521595 + 0.853193i \(0.325337\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 1511.83 2618.56i 0.162142 0.280839i −0.773494 0.633803i \(-0.781493\pi\)
0.935637 + 0.352964i \(0.114826\pi\)
\(444\) 0 0
\(445\) −4567.43 7911.03i −0.486555 0.842739i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −3137.67 −0.329790 −0.164895 0.986311i \(-0.552728\pi\)
−0.164895 + 0.986311i \(0.552728\pi\)
\(450\) 0 0
\(451\) 16.3369 0.00170571
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −16429.3 28456.4i −1.69279 2.93200i
\(456\) 0 0
\(457\) 4507.87 7807.86i 0.461421 0.799204i −0.537611 0.843193i \(-0.680673\pi\)
0.999032 + 0.0439888i \(0.0140066\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −6131.30 + 10619.7i −0.619442 + 1.07291i 0.370145 + 0.928974i \(0.379308\pi\)
−0.989588 + 0.143932i \(0.954025\pi\)
\(462\) 0 0
\(463\) −1736.15 3007.10i −0.174267 0.301840i 0.765640 0.643269i \(-0.222422\pi\)
−0.939907 + 0.341429i \(0.889089\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −11825.0 −1.17172 −0.585860 0.810412i \(-0.699243\pi\)
−0.585860 + 0.810412i \(0.699243\pi\)
\(468\) 0 0
\(469\) 22274.5 2.19305
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −100.636 174.306i −0.00978275 0.0169442i
\(474\) 0 0
\(475\) −20605.9 + 35690.5i −1.99045 + 3.44756i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −851.980 + 1475.67i −0.0812692 + 0.140762i −0.903795 0.427965i \(-0.859231\pi\)
0.822526 + 0.568727i \(0.192564\pi\)
\(480\) 0 0
\(481\) 2780.80 + 4816.49i 0.263604 + 0.456576i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 661.015 0.0618869
\(486\) 0 0
\(487\) 7721.95 0.718512 0.359256 0.933239i \(-0.383031\pi\)
0.359256 + 0.933239i \(0.383031\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 10111.8 + 17514.2i 0.929410 + 1.60979i 0.784311 + 0.620368i \(0.213017\pi\)
0.145099 + 0.989417i \(0.453650\pi\)
\(492\) 0 0
\(493\) −6471.98 + 11209.8i −0.591244 + 1.02406i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 10249.3 17752.3i 0.925035 1.60221i
\(498\) 0 0
\(499\) 6851.20 + 11866.6i 0.614633 + 1.06458i 0.990449 + 0.137881i \(0.0440291\pi\)
−0.375816 + 0.926694i \(0.622638\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −13707.6 −1.21509 −0.607546 0.794285i \(-0.707846\pi\)
−0.607546 + 0.794285i \(0.707846\pi\)
\(504\) 0 0
\(505\) −20874.9 −1.83945
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 6169.59 + 10686.0i 0.537254 + 0.930551i 0.999051 + 0.0435650i \(0.0138716\pi\)
−0.461797 + 0.886986i \(0.652795\pi\)
\(510\) 0 0
\(511\) 4195.03 7266.01i 0.363165 0.629020i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −10108.8 + 17509.0i −0.864950 + 1.49814i
\(516\) 0 0
\(517\) 125.935 + 218.125i 0.0107130 + 0.0185554i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1416.70 −0.119130 −0.0595649 0.998224i \(-0.518971\pi\)
−0.0595649 + 0.998224i \(0.518971\pi\)
\(522\) 0 0
\(523\) 6696.15 0.559851 0.279925 0.960022i \(-0.409690\pi\)
0.279925 + 0.960022i \(0.409690\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −4935.51 8548.55i −0.407958 0.706605i
\(528\) 0 0
\(529\) 5820.50 10081.4i 0.478384 0.828585i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −432.394 + 748.929i −0.0351390 + 0.0608625i
\(534\) 0 0
\(535\) 2888.70 + 5003.38i 0.233438 + 0.404327i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −511.609 −0.0408841
\(540\) 0 0
\(541\) 7105.69 0.564691 0.282345 0.959313i \(-0.408888\pi\)
0.282345 + 0.959313i \(0.408888\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 14393.9 + 24931.0i 1.13132 + 1.95950i
\(546\) 0 0
\(547\) −6014.01 + 10416.6i −0.470092 + 0.814224i −0.999415 0.0341968i \(-0.989113\pi\)
0.529323 + 0.848420i \(0.322446\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −8443.76 + 14625.0i −0.652843 + 1.13076i
\(552\) 0 0
\(553\) 1878.59 + 3253.81i 0.144459 + 0.250210i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −14529.5 −1.10527 −0.552634 0.833424i \(-0.686377\pi\)
−0.552634 + 0.833424i \(0.686377\pi\)
\(558\) 0 0
\(559\) 10654.3 0.806131
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −5116.72 8862.42i −0.383027 0.663422i 0.608467 0.793579i \(-0.291785\pi\)
−0.991493 + 0.130158i \(0.958452\pi\)
\(564\) 0 0
\(565\) 20579.2 35644.3i 1.53235 2.65410i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 159.730 276.660i 0.0117684 0.0203835i −0.860081 0.510157i \(-0.829587\pi\)
0.871850 + 0.489774i \(0.162921\pi\)
\(570\) 0 0
\(571\) 3396.98 + 5883.74i 0.248965 + 0.431221i 0.963239 0.268646i \(-0.0865761\pi\)
−0.714274 + 0.699866i \(0.753243\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 7473.74 0.542046
\(576\) 0 0
\(577\) −11145.6 −0.804156 −0.402078 0.915605i \(-0.631712\pi\)
−0.402078 + 0.915605i \(0.631712\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 2345.68 + 4062.84i 0.167496 + 0.290112i
\(582\) 0 0
\(583\) 74.0190 128.205i 0.00525824 0.00910753i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −11908.8 + 20626.6i −0.837356 + 1.45034i 0.0547416 + 0.998501i \(0.482566\pi\)
−0.892098 + 0.451843i \(0.850767\pi\)
\(588\) 0 0
\(589\) −6439.19 11153.0i −0.450462 0.780223i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 16416.2 1.13682 0.568408 0.822747i \(-0.307559\pi\)
0.568408 + 0.822747i \(0.307559\pi\)
\(594\) 0 0
\(595\) −60171.2 −4.14585
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −2400.85 4158.39i −0.163766 0.283652i 0.772450 0.635075i \(-0.219031\pi\)
−0.936216 + 0.351424i \(0.885698\pi\)
\(600\) 0 0
\(601\) −2262.11 + 3918.08i −0.153533 + 0.265927i −0.932524 0.361108i \(-0.882398\pi\)
0.778991 + 0.627035i \(0.215732\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −14120.4 + 24457.3i −0.948886 + 1.64352i
\(606\) 0 0
\(607\) 7489.15 + 12971.6i 0.500783 + 0.867382i 1.00000 0.000904500i \(0.000287911\pi\)
−0.499216 + 0.866477i \(0.666379\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −13332.6 −0.882784
\(612\) 0 0
\(613\) 11651.6 0.767709 0.383854 0.923394i \(-0.374596\pi\)
0.383854 + 0.923394i \(0.374596\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −170.560 295.418i −0.0111288 0.0192757i 0.860407 0.509607i \(-0.170209\pi\)
−0.871536 + 0.490331i \(0.836876\pi\)
\(618\) 0 0
\(619\) −9207.57 + 15948.0i −0.597873 + 1.03555i 0.395262 + 0.918569i \(0.370654\pi\)
−0.993135 + 0.116978i \(0.962679\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 6288.26 10891.6i 0.404388 0.700421i
\(624\) 0 0
\(625\) −24916.1 43156.0i −1.59463 2.76198i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 10184.5 0.645599
\(630\) 0 0
\(631\) 13557.6 0.855341 0.427671 0.903935i \(-0.359334\pi\)
0.427671 + 0.903935i \(0.359334\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 2467.09 + 4273.12i 0.154179 + 0.267045i
\(636\) 0 0
\(637\) 13540.9 23453.6i 0.842247 1.45881i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 4841.27 8385.33i 0.298313 0.516694i −0.677437 0.735581i \(-0.736909\pi\)
0.975750 + 0.218887i \(0.0702427\pi\)
\(642\) 0 0
\(643\) 1629.75 + 2822.81i 0.0999551 + 0.173127i 0.911666 0.410932i \(-0.134797\pi\)
−0.811711 + 0.584060i \(0.801463\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 8115.35 0.493118 0.246559 0.969128i \(-0.420700\pi\)
0.246559 + 0.969128i \(0.420700\pi\)
\(648\) 0 0
\(649\) −73.6085 −0.00445206
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1713.87 2968.51i −0.102709 0.177897i 0.810091 0.586304i \(-0.199418\pi\)
−0.912800 + 0.408407i \(0.866084\pi\)
\(654\) 0 0
\(655\) 29677.3 51402.6i 1.77036 3.06636i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −6910.11 + 11968.7i −0.408467 + 0.707485i −0.994718 0.102644i \(-0.967270\pi\)
0.586251 + 0.810129i \(0.300603\pi\)
\(660\) 0 0
\(661\) 11359.8 + 19675.8i 0.668451 + 1.15779i 0.978337 + 0.207018i \(0.0663759\pi\)
−0.309886 + 0.950774i \(0.600291\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −78503.2 −4.57778
\(666\) 0 0
\(667\) 3062.54 0.177784
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −303.739 526.091i −0.0174750 0.0302676i
\(672\) 0 0
\(673\) 2566.59 4445.46i 0.147005 0.254621i −0.783114 0.621878i \(-0.786370\pi\)
0.930119 + 0.367257i \(0.119703\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 4647.94 8050.46i 0.263862 0.457023i −0.703403 0.710792i \(-0.748337\pi\)
0.967265 + 0.253769i \(0.0816702\pi\)
\(678\) 0 0
\(679\) 455.030 + 788.134i 0.0257179 + 0.0445447i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −13824.3 −0.774486 −0.387243 0.921978i \(-0.626573\pi\)
−0.387243 + 0.921978i \(0.626573\pi\)
\(684\) 0 0
\(685\) −26787.0 −1.49413
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 3918.18 + 6786.48i 0.216648 + 0.375246i
\(690\) 0 0
\(691\) 5507.61 9539.47i 0.303212 0.525179i −0.673650 0.739051i \(-0.735274\pi\)
0.976862 + 0.213872i \(0.0686076\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −3263.29 + 5652.18i −0.178106 + 0.308488i
\(696\) 0 0
\(697\) 791.806 + 1371.45i 0.0430298 + 0.0745298i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 460.523 0.0248127 0.0124064 0.999923i \(-0.496051\pi\)
0.0124064 + 0.999923i \(0.496051\pi\)
\(702\) 0 0
\(703\) 13287.3 0.712861
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −14369.9 24889.3i −0.764405 1.32399i
\(708\) 0 0
\(709\) −13222.5 + 22902.1i −0.700398 + 1.21313i 0.267929 + 0.963439i \(0.413661\pi\)
−0.968327 + 0.249686i \(0.919672\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1167.74 + 2022.59i −0.0613355 + 0.106236i
\(714\) 0 0
\(715\) 562.000 + 973.413i 0.0293953 + 0.0509141i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −15524.4 −0.805235 −0.402617 0.915368i \(-0.631899\pi\)
−0.402617 + 0.915368i \(0.631899\pi\)
\(720\) 0 0
\(721\) −27834.9 −1.43776
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −21757.1 37684.4i −1.11454 1.93043i
\(726\) 0 0
\(727\) −9467.02 + 16397.4i −0.482961 + 0.836513i −0.999809 0.0195647i \(-0.993772\pi\)
0.516848 + 0.856077i \(0.327105\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 9755.11 16896.3i 0.493578 0.854903i
\(732\) 0 0
\(733\) 8389.96 + 14531.8i 0.422770 + 0.732259i 0.996209 0.0869891i \(-0.0277245\pi\)
−0.573439 + 0.819248i \(0.694391\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −761.945 −0.0380823
\(738\) 0 0
\(739\) 30309.0 1.50871 0.754353 0.656469i \(-0.227951\pi\)
0.754353 + 0.656469i \(0.227951\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 16049.4 + 27798.4i 0.792458 + 1.37258i 0.924441 + 0.381325i \(0.124532\pi\)
−0.131983 + 0.991252i \(0.542135\pi\)
\(744\) 0 0
\(745\) −16963.1 + 29381.0i −0.834202 + 1.44488i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3977.05 + 6888.45i −0.194016 + 0.336046i
\(750\) 0 0
\(751\) −4717.04 8170.15i −0.229197 0.396981i 0.728373 0.685181i \(-0.240277\pi\)
−0.957570 + 0.288199i \(0.906943\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 72521.7 3.49581
\(756\) 0 0
\(757\) 1280.65 0.0614876 0.0307438 0.999527i \(-0.490212\pi\)
0.0307438 + 0.999527i \(0.490212\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 9812.37 + 16995.5i 0.467409 + 0.809576i 0.999307 0.0372327i \(-0.0118543\pi\)
−0.531898 + 0.846809i \(0.678521\pi\)
\(762\) 0 0
\(763\) −19816.9 + 34323.9i −0.940264 + 1.62858i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1948.22 3374.42i 0.0917162 0.158857i
\(768\) 0 0
\(769\) −8822.44 15280.9i −0.413713 0.716572i 0.581580 0.813490i \(-0.302435\pi\)
−0.995292 + 0.0969179i \(0.969102\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 22541.7 1.04886 0.524430 0.851454i \(-0.324278\pi\)
0.524430 + 0.851454i \(0.324278\pi\)
\(774\) 0 0
\(775\) 33183.8 1.53806
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1033.04 + 1789.28i 0.0475129 + 0.0822947i
\(780\) 0 0
\(781\) −350.598 + 607.253i −0.0160632 + 0.0278223i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 5062.38 8768.30i 0.230171 0.398668i
\(786\) 0 0
\(787\) 19843.9 + 34370.7i 0.898804 + 1.55677i 0.829025 + 0.559212i \(0.188896\pi\)
0.0697798 + 0.997562i \(0.477770\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 56665.4 2.54714
\(792\) 0 0
\(793\) 32156.7 1.44000
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −995.984 1725.09i −0.0442654 0.0766700i 0.843044 0.537845i \(-0.180761\pi\)
−0.887309 + 0.461175i \(0.847428\pi\)
\(798\) 0 0
\(799\) −12207.5 + 21143.9i −0.540511 + 0.936193i
\(800\) 0