Properties

Label 648.4.i.m.217.1
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 217.1
Root \(1.68614 + 0.396143i\) of defining polynomial
Character \(\chi\) \(=\) 648.217
Dual form 648.4.i.m.433.1

$q$-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 \(-0.768157\pi\)
−0.203330 0.979110i \(-0.565176\pi\)
\(6\) 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 −0.872797 0.488084i \(-0.837696\pi\)
0.859092 + 0.511822i \(0.171029\pi\)
\(12\) 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 \(-0.743039\pi\)
−0.691474 + 0.722401i \(0.743039\pi\)
\(18\) 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 0.913313 0.407257i \(-0.133515\pi\)
−0.809352 + 0.587324i \(0.800181\pi\)
\(24\) 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 −0.569129 0.822249i \(-0.692719\pi\)
0.996652 + 0.0817555i \(0.0260527\pi\)
\(30\) 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 0.850049 0.526704i \(-0.176572\pi\)
−0.881163 + 0.472812i \(0.843239\pi\)
\(42\) 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 −0.601721 0.798707i \(-0.705518\pi\)
0.992561 + 0.121752i \(0.0388513\pi\)
\(48\) 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 \(-0.561444\pi\)
−0.191836 + 0.981427i \(0.561444\pi\)
\(54\) 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 0.903771 0.428017i \(-0.140788\pi\)
−0.822559 + 0.568680i \(0.807454\pi\)
\(60\) 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 \(-0.300689\pi\)
0.586033 + 0.810287i \(0.300689\pi\)
\(72\) 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 −0.914192 0.405281i \(-0.867174\pi\)
0.808079 + 0.589074i \(0.200507\pi\)
\(84\) 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 \(-0.417533\pi\)
0.256190 + 0.966626i \(0.417533\pi\)
\(90\) 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 −0.515567 0.856849i \(-0.672419\pi\)
0.999837 + 0.0180698i \(0.00575212\pi\)
\(102\) 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 \(-0.539224\pi\)
−0.122914 + 0.992417i \(0.539224\pi\)
\(108\) 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 \(0.132156\pi\)
−0.108205 + 0.994129i \(0.534510\pi\)
\(114\) 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 \(0.215414\pi\)
0.152548 + 0.988296i \(0.451252\pi\)
\(132\) 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 −0.599532 0.800351i \(-0.704647\pi\)
0.992890 + 0.119035i \(0.0379801\pi\)
\(138\) 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 0.558392 0.829577i \(-0.311419\pi\)
−0.997631 + 0.0687929i \(0.978085\pi\)
\(150\) 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 0.515242 0.857045i \(-0.327702\pi\)
−0.999844 + 0.0176906i \(0.994369\pi\)
\(168\) 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 \(0.388824\pi\)
−0.984843 + 0.173446i \(0.944510\pi\)
\(174\) 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 \(-0.515418\pi\)
−0.0484191 + 0.998827i \(0.515418\pi\)
\(180\) 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 \(-0.538736\pi\)
0.920316 0.391175i \(-0.127931\pi\)
\(192\) 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 \(-0.691527\pi\)
−0.566044 + 0.824375i \(0.691527\pi\)
\(198\) 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 −0.979405 0.201907i \(-0.935286\pi\)
0.664559 + 0.747236i \(0.268619\pi\)
\(228\) 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 \(-0.689539\pi\)
−0.560886 + 0.827893i \(0.689539\pi\)
\(234\) 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 \(0.114041\pi\)
−0.164575 + 0.986365i \(0.552625\pi\)
\(240\) 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 \(-0.302577\pi\)
0.581217 + 0.813749i \(0.302577\pi\)
\(252\) 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 \(0.0362899\pi\)
−0.398234 + 0.917284i \(0.630377\pi\)
\(258\) 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 \(0.340608\pi\)
−0.999739 + 0.0228519i \(0.992725\pi\)
\(264\) 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 \(-0.331544\pi\)
0.504860 + 0.863201i \(0.331544\pi\)
\(270\) 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 −0.760525 0.649308i \(-0.775059\pi\)
0.942580 + 0.333980i \(0.108392\pi\)
\(282\) 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 0.769707 0.638398i \(-0.220403\pi\)
−0.937722 + 0.347386i \(0.887069\pi\)
\(294\) 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 0.725571 0.688147i \(-0.241576\pi\)
−0.958738 + 0.284290i \(0.908242\pi\)
\(312\) 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 \(-0.594310\pi\)
0.974275 0.225364i \(-0.0723570\pi\)
\(318\) 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 \(-0.957585\pi\)
0.380509 0.924777i \(-0.375749\pi\)
\(348\) 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 \(0.391360\pi\)
−0.983430 + 0.181290i \(0.941973\pi\)
\(354\) 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 \(-0.591955\pi\)
−0.284884 + 0.958562i \(0.591955\pi\)
\(360\) 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 \(-0.874576\pi\)
0.129205 0.991618i \(-0.458757\pi\)
\(384\) 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 \(0.477606\pi\)
−0.899031 + 0.437886i \(0.855728\pi\)
\(390\) 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 0.976293 0.216452i \(-0.0694485\pi\)
−0.675600 + 0.737269i \(0.736115\pi\)
\(402\) 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 0.520985 0.853566i \(-0.325565\pi\)
−0.999702 + 0.0244030i \(0.992232\pi\)
\(420\) 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 \(-0.284606\pi\)
0.626207 + 0.779657i \(0.284606\pi\)
\(432\) 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 −0.935637 0.352964i \(-0.885174\pi\)
0.773494 + 0.633803i \(0.218507\pi\)
\(444\) 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 \(-0.447272\pi\)
0.164895 + 0.986311i \(0.447272\pi\)
\(450\) 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 \(-0.620692\pi\)
0.989588 0.143932i \(-0.0459745\pi\)
\(462\) 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 \(-0.300757\pi\)
0.585860 + 0.810412i \(0.300757\pi\)
\(468\) 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 −0.822526 0.568727i \(-0.807436\pi\)
0.903795 + 0.427965i \(0.140769\pi\)
\(480\) 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 \(-0.786983\pi\)
−0.145099 0.989417i \(-0.546350\pi\)
\(492\) 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 \(-0.292154\pi\)
0.607546 + 0.794285i \(0.292154\pi\)
\(504\) 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 \(-0.986128\pi\)
0.461797 0.886986i \(-0.347205\pi\)
\(510\) 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 \(-0.481029\pi\)
0.0595649 + 0.998224i \(0.481029\pi\)
\(522\) 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 \(-0.313623\pi\)
0.552634 + 0.833424i \(0.313623\pi\)
\(558\) 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 0.991493 0.130158i \(-0.0415484\pi\)
−0.608467 + 0.793579i \(0.708215\pi\)
\(564\) 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 −0.871850 0.489774i \(-0.837079\pi\)
0.860081 + 0.510157i \(0.170413\pi\)
\(570\) 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 \(-0.517434\pi\)
0.892098 0.451843i \(-0.149233\pi\)
\(588\) 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 \(-0.692441\pi\)
−0.568408 + 0.822747i \(0.692441\pi\)
\(594\) 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 0.936216 0.351424i \(-0.114302\pi\)
−0.772450 + 0.635075i \(0.780969\pi\)
\(600\) 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 0.871536 0.490331i \(-0.163124\pi\)
−0.860407 + 0.509607i \(0.829791\pi\)
\(618\) 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 −0.975750 0.218887i \(-0.929757\pi\)
0.677437 + 0.735581i \(0.263091\pi\)
\(642\) 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 \(-0.579300\pi\)
−0.246559 + 0.969128i \(0.579300\pi\)
\(648\) 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 0.912800 0.408407i \(-0.133916\pi\)
−0.810091 + 0.586304i \(0.800582\pi\)
\(654\) 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 −0.586251 0.810129i \(-0.699397\pi\)
0.994718 + 0.102644i \(0.0327302\pi\)
\(660\) 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 −0.967265 0.253769i \(-0.918330\pi\)
0.703403 + 0.710792i \(0.251663\pi\)
\(678\) 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 \(-0.373427\pi\)
0.387243 + 0.921978i \(0.373427\pi\)
\(684\) 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 \(-0.503949\pi\)
−0.0124064 + 0.999923i \(0.503949\pi\)
\(702\) 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 \(-0.368101\pi\)
0.402617 + 0.915368i \(0.368101\pi\)
\(720\) 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 \(-0.875468\pi\)
0.131983 0.991252i \(-0.457865\pi\)
\(744\) 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 0.531898 0.846809i \(-0.321479\pi\)
−0.999307 + 0.0372327i \(0.988146\pi\)
\(762\) 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 \(-0.675722\pi\)
−0.524430 + 0.851454i \(0.675722\pi\)
\(774\) 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 0.887309 0.461175i \(-0.152572\pi\)
−0.843044 + 0.537845i \(0.819239\pi\)
\(798\) 0 0
\(799\) −12207.5 + 21143.9i −0.540511 + 0.936193i
\(800\)