Properties

Label 252.4.k.f.109.1
Level $252$
Weight $4$
Character 252.109
Analytic conductor $14.868$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 252.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.8684813214\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{193})\)
Defining polynomial: \(x^{4} - x^{3} + 49 x^{2} + 48 x + 2304\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.1
Root \(3.72311 + 6.44862i\) of defining polynomial
Character \(\chi\) \(=\) 252.109
Dual form 252.4.k.f.37.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.723111 - 1.25246i) q^{5} +(-12.3924 + 13.7633i) q^{7} +O(q^{10})\) \(q+(-0.723111 - 1.25246i) q^{5} +(-12.3924 + 13.7633i) q^{7} +(23.0618 - 39.9442i) q^{11} -32.2311 q^{13} +(38.8924 - 67.3637i) q^{17} +(-6.33067 - 10.9650i) q^{19} +(-50.4622 - 87.4031i) q^{23} +(61.4542 - 106.442i) q^{25} -213.908 q^{29} +(-21.0378 + 36.4385i) q^{31} +(26.1991 + 5.56874i) q^{35} +(-155.040 - 268.537i) q^{37} -44.0320 q^{41} +381.339 q^{43} +(-179.032 - 310.093i) q^{47} +(-35.8547 - 341.121i) q^{49} +(92.4920 - 160.201i) q^{53} -66.7049 q^{55} +(227.325 - 393.738i) q^{59} +(-5.92444 - 10.2614i) q^{61} +(23.3067 + 40.3683i) q^{65} +(-295.180 + 511.266i) q^{67} -494.366 q^{71} +(-487.825 + 844.937i) q^{73} +(263.970 + 812.411i) q^{77} +(-149.667 - 259.231i) q^{79} +1406.07 q^{83} -112.494 q^{85} +(-347.629 - 602.112i) q^{89} +(399.422 - 443.605i) q^{91} +(-9.15555 + 15.8579i) q^{95} +481.940 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 11q^{5} + 6q^{7} + O(q^{10}) \) \( 4q + 11q^{5} + 6q^{7} - 5q^{11} + 10q^{13} + 100q^{17} - 67q^{19} + 76q^{23} + 93q^{25} - 550q^{29} - 362q^{31} + 466q^{35} + 5q^{37} + 324q^{41} + 1442q^{43} - 216q^{47} + 190q^{49} + 495q^{53} - 1406q^{55} + 173q^{59} + 532q^{61} + 510q^{65} - 111q^{67} - 3200q^{71} - 1215q^{73} + 653q^{77} - 1460q^{79} + 2818q^{83} + 328q^{85} - 1974q^{89} + 1945q^{91} + 658q^{95} + 1122q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) −0.723111 1.25246i −0.0646770 0.112024i 0.831874 0.554965i \(-0.187268\pi\)
−0.896551 + 0.442941i \(0.853935\pi\)
\(6\) 0 0
\(7\) −12.3924 + 13.7633i −0.669129 + 0.743146i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 23.0618 39.9442i 0.632126 1.09487i −0.354990 0.934870i \(-0.615516\pi\)
0.987116 0.160005i \(-0.0511509\pi\)
\(12\) 0 0
\(13\) −32.2311 −0.687639 −0.343819 0.939036i \(-0.611721\pi\)
−0.343819 + 0.939036i \(0.611721\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 38.8924 67.3637i 0.554871 0.961064i −0.443043 0.896500i \(-0.646101\pi\)
0.997914 0.0645639i \(-0.0205656\pi\)
\(18\) 0 0
\(19\) −6.33067 10.9650i −0.0764397 0.132397i 0.825272 0.564736i \(-0.191022\pi\)
−0.901711 + 0.432338i \(0.857689\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −50.4622 87.4031i −0.457483 0.792383i 0.541345 0.840801i \(-0.317915\pi\)
−0.998827 + 0.0484177i \(0.984582\pi\)
\(24\) 0 0
\(25\) 61.4542 106.442i 0.491634 0.851535i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −213.908 −1.36972 −0.684859 0.728676i \(-0.740136\pi\)
−0.684859 + 0.728676i \(0.740136\pi\)
\(30\) 0 0
\(31\) −21.0378 + 36.4385i −0.121887 + 0.211114i −0.920512 0.390715i \(-0.872228\pi\)
0.798625 + 0.601829i \(0.205561\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 26.1991 + 5.56874i 0.126527 + 0.0268940i
\(36\) 0 0
\(37\) −155.040 268.537i −0.688876 1.19317i −0.972202 0.234145i \(-0.924771\pi\)
0.283326 0.959024i \(-0.408562\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −44.0320 −0.167723 −0.0838615 0.996477i \(-0.526725\pi\)
−0.0838615 + 0.996477i \(0.526725\pi\)
\(42\) 0 0
\(43\) 381.339 1.35241 0.676205 0.736714i \(-0.263624\pi\)
0.676205 + 0.736714i \(0.263624\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −179.032 310.093i −0.555628 0.962375i −0.997854 0.0654721i \(-0.979145\pi\)
0.442227 0.896903i \(-0.354189\pi\)
\(48\) 0 0
\(49\) −35.8547 341.121i −0.104533 0.994521i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 92.4920 160.201i 0.239712 0.415194i −0.720919 0.693019i \(-0.756280\pi\)
0.960632 + 0.277825i \(0.0896135\pi\)
\(54\) 0 0
\(55\) −66.7049 −0.163536
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 227.325 393.738i 0.501613 0.868820i −0.498385 0.866956i \(-0.666073\pi\)
0.999998 0.00186377i \(-0.000593256\pi\)
\(60\) 0 0
\(61\) −5.92444 10.2614i −0.0124352 0.0215384i 0.859741 0.510731i \(-0.170625\pi\)
−0.872176 + 0.489192i \(0.837292\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 23.3067 + 40.3683i 0.0444744 + 0.0770319i
\(66\) 0 0
\(67\) −295.180 + 511.266i −0.538238 + 0.932255i 0.460761 + 0.887524i \(0.347576\pi\)
−0.998999 + 0.0447309i \(0.985757\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −494.366 −0.826345 −0.413172 0.910653i \(-0.635579\pi\)
−0.413172 + 0.910653i \(0.635579\pi\)
\(72\) 0 0
\(73\) −487.825 + 844.937i −0.782131 + 1.35469i 0.148567 + 0.988902i \(0.452534\pi\)
−0.930698 + 0.365789i \(0.880799\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 263.970 + 812.411i 0.390678 + 1.20237i
\(78\) 0 0
\(79\) −149.667 259.231i −0.213150 0.369187i 0.739549 0.673103i \(-0.235039\pi\)
−0.952699 + 0.303916i \(0.901706\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1406.07 1.85947 0.929735 0.368229i \(-0.120036\pi\)
0.929735 + 0.368229i \(0.120036\pi\)
\(84\) 0 0
\(85\) −112.494 −0.143550
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −347.629 602.112i −0.414030 0.717120i 0.581296 0.813692i \(-0.302546\pi\)
−0.995326 + 0.0965715i \(0.969212\pi\)
\(90\) 0 0
\(91\) 399.422 443.605i 0.460119 0.511016i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −9.15555 + 15.8579i −0.00988779 + 0.0171261i
\(96\) 0 0
\(97\) 481.940 0.504470 0.252235 0.967666i \(-0.418834\pi\)
0.252235 + 0.967666i \(0.418834\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −592.052 + 1025.46i −0.583281 + 1.01027i 0.411806 + 0.911272i \(0.364898\pi\)
−0.995087 + 0.0990014i \(0.968435\pi\)
\(102\) 0 0
\(103\) 641.765 + 1111.57i 0.613932 + 1.06336i 0.990571 + 0.137001i \(0.0437465\pi\)
−0.376639 + 0.926360i \(0.622920\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 806.684 + 1397.22i 0.728833 + 1.26238i 0.957377 + 0.288842i \(0.0932701\pi\)
−0.228544 + 0.973533i \(0.573397\pi\)
\(108\) 0 0
\(109\) 76.9164 133.223i 0.0675895 0.117069i −0.830250 0.557391i \(-0.811803\pi\)
0.897840 + 0.440322i \(0.145136\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1581.08 −1.31625 −0.658123 0.752910i \(-0.728650\pi\)
−0.658123 + 0.752910i \(0.728650\pi\)
\(114\) 0 0
\(115\) −72.9796 + 126.404i −0.0591772 + 0.102498i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 445.172 + 1370.09i 0.342931 + 1.05543i
\(120\) 0 0
\(121\) −398.191 689.687i −0.299167 0.518172i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −358.531 −0.256544
\(126\) 0 0
\(127\) 1916.30 1.33893 0.669465 0.742844i \(-0.266523\pi\)
0.669465 + 0.742844i \(0.266523\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1250.24 + 2165.48i 0.833849 + 1.44427i 0.894964 + 0.446137i \(0.147201\pi\)
−0.0611158 + 0.998131i \(0.519466\pi\)
\(132\) 0 0
\(133\) 229.367 + 48.7530i 0.149539 + 0.0317851i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 145.446 251.920i 0.0907030 0.157102i −0.817104 0.576490i \(-0.804422\pi\)
0.907807 + 0.419388i \(0.137755\pi\)
\(138\) 0 0
\(139\) −1348.77 −0.823028 −0.411514 0.911403i \(-0.635000\pi\)
−0.411514 + 0.911403i \(0.635000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −743.307 + 1287.44i −0.434674 + 0.752878i
\(144\) 0 0
\(145\) 154.680 + 267.913i 0.0885892 + 0.153441i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1424.40 2467.14i −0.783165 1.35648i −0.930089 0.367334i \(-0.880271\pi\)
0.146924 0.989148i \(-0.453063\pi\)
\(150\) 0 0
\(151\) 744.656 1289.78i 0.401320 0.695106i −0.592566 0.805522i \(-0.701885\pi\)
0.993885 + 0.110416i \(0.0352183\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 60.8506 0.0315331
\(156\) 0 0
\(157\) −1821.69 + 3155.26i −0.926030 + 1.60393i −0.136134 + 0.990690i \(0.543468\pi\)
−0.789896 + 0.613241i \(0.789865\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1828.30 + 388.614i 0.894971 + 0.190230i
\(162\) 0 0
\(163\) −384.581 666.114i −0.184802 0.320087i 0.758708 0.651431i \(-0.225831\pi\)
−0.943510 + 0.331345i \(0.892498\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2399.78 1.11198 0.555991 0.831188i \(-0.312339\pi\)
0.555991 + 0.831188i \(0.312339\pi\)
\(168\) 0 0
\(169\) −1158.16 −0.527153
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1668.32 2889.62i −0.733181 1.26991i −0.955517 0.294937i \(-0.904701\pi\)
0.222335 0.974970i \(-0.428632\pi\)
\(174\) 0 0
\(175\) 703.419 + 2164.88i 0.303848 + 0.935142i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1230.89 2131.96i 0.513970 0.890223i −0.485898 0.874015i \(-0.661507\pi\)
0.999869 0.0162074i \(-0.00515919\pi\)
\(180\) 0 0
\(181\) 1316.74 0.540732 0.270366 0.962758i \(-0.412855\pi\)
0.270366 + 0.962758i \(0.412855\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −224.222 + 388.364i −0.0891089 + 0.154341i
\(186\) 0 0
\(187\) −1793.86 3107.05i −0.701497 1.21503i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1633.98 2830.14i −0.619010 1.07216i −0.989667 0.143387i \(-0.954201\pi\)
0.370657 0.928770i \(-0.379133\pi\)
\(192\) 0 0
\(193\) −116.836 + 202.366i −0.0435753 + 0.0754747i −0.886990 0.461788i \(-0.847208\pi\)
0.843415 + 0.537262i \(0.180542\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 31.8632 0.0115236 0.00576182 0.999983i \(-0.498166\pi\)
0.00576182 + 0.999983i \(0.498166\pi\)
\(198\) 0 0
\(199\) 739.451 1280.77i 0.263408 0.456237i −0.703737 0.710461i \(-0.748487\pi\)
0.967145 + 0.254224i \(0.0818200\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 2650.85 2944.08i 0.916518 1.01790i
\(204\) 0 0
\(205\) 31.8400 + 55.1485i 0.0108478 + 0.0187890i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −583.986 −0.193278
\(210\) 0 0
\(211\) −4498.67 −1.46778 −0.733889 0.679269i \(-0.762297\pi\)
−0.733889 + 0.679269i \(0.762297\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −275.750 477.613i −0.0874698 0.151502i
\(216\) 0 0
\(217\) −240.803 741.111i −0.0753308 0.231843i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1253.55 + 2171.21i −0.381551 + 0.660865i
\(222\) 0 0
\(223\) 5382.75 1.61639 0.808196 0.588913i \(-0.200444\pi\)
0.808196 + 0.588913i \(0.200444\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2712.78 + 4698.68i −0.793188 + 1.37384i 0.130795 + 0.991409i \(0.458247\pi\)
−0.923983 + 0.382433i \(0.875086\pi\)
\(228\) 0 0
\(229\) −994.873 1723.17i −0.287088 0.497250i 0.686026 0.727577i \(-0.259354\pi\)
−0.973113 + 0.230327i \(0.926020\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −3148.83 5453.93i −0.885351 1.53347i −0.845311 0.534274i \(-0.820585\pi\)
−0.0400396 0.999198i \(-0.512748\pi\)
\(234\) 0 0
\(235\) −258.920 + 448.463i −0.0718727 + 0.124487i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −3395.77 −0.919054 −0.459527 0.888164i \(-0.651981\pi\)
−0.459527 + 0.888164i \(0.651981\pi\)
\(240\) 0 0
\(241\) 3186.97 5519.99i 0.851829 1.47541i −0.0277273 0.999616i \(-0.508827\pi\)
0.879556 0.475795i \(-0.157840\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −401.315 + 291.575i −0.104649 + 0.0760328i
\(246\) 0 0
\(247\) 204.044 + 353.415i 0.0525629 + 0.0910416i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2650.91 0.666630 0.333315 0.942815i \(-0.391833\pi\)
0.333315 + 0.942815i \(0.391833\pi\)
\(252\) 0 0
\(253\) −4654.99 −1.15675
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −936.035 1621.26i −0.227192 0.393507i 0.729783 0.683679i \(-0.239621\pi\)
−0.956975 + 0.290171i \(0.906288\pi\)
\(258\) 0 0
\(259\) 5617.27 + 1193.98i 1.34765 + 0.286448i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 3063.05 5305.35i 0.718158 1.24389i −0.243570 0.969883i \(-0.578319\pi\)
0.961729 0.274003i \(-0.0883480\pi\)
\(264\) 0 0
\(265\) −267.528 −0.0620155
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −4252.06 + 7364.78i −0.963764 + 1.66929i −0.250866 + 0.968022i \(0.580715\pi\)
−0.712899 + 0.701267i \(0.752618\pi\)
\(270\) 0 0
\(271\) −1060.77 1837.31i −0.237776 0.411840i 0.722300 0.691580i \(-0.243085\pi\)
−0.960076 + 0.279740i \(0.909752\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2834.49 4909.48i −0.621549 1.07655i
\(276\) 0 0
\(277\) 4010.68 6946.71i 0.869959 1.50681i 0.00792096 0.999969i \(-0.497479\pi\)
0.862038 0.506844i \(-0.169188\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 8244.17 1.75020 0.875100 0.483943i \(-0.160796\pi\)
0.875100 + 0.483943i \(0.160796\pi\)
\(282\) 0 0
\(283\) −3050.64 + 5283.86i −0.640784 + 1.10987i 0.344475 + 0.938796i \(0.388057\pi\)
−0.985258 + 0.171074i \(0.945276\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 545.664 606.024i 0.112228 0.124643i
\(288\) 0 0
\(289\) −568.744 985.094i −0.115763 0.200508i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1965.98 0.391993 0.195996 0.980605i \(-0.437206\pi\)
0.195996 + 0.980605i \(0.437206\pi\)
\(294\) 0 0
\(295\) −657.524 −0.129771
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1626.45 + 2817.10i 0.314583 + 0.544873i
\(300\) 0 0
\(301\) −4725.72 + 5248.46i −0.904936 + 1.00504i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −8.56806 + 14.8403i −0.00160854 + 0.00278608i
\(306\) 0 0
\(307\) 997.810 0.185498 0.0927492 0.995690i \(-0.470435\pi\)
0.0927492 + 0.995690i \(0.470435\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −3450.72 + 5976.82i −0.629171 + 1.08976i 0.358547 + 0.933512i \(0.383272\pi\)
−0.987718 + 0.156245i \(0.950061\pi\)
\(312\) 0 0
\(313\) 3170.86 + 5492.08i 0.572612 + 0.991792i 0.996297 + 0.0859827i \(0.0274030\pi\)
−0.423685 + 0.905810i \(0.639264\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 612.487 + 1060.86i 0.108519 + 0.187961i 0.915171 0.403067i \(-0.132056\pi\)
−0.806651 + 0.591028i \(0.798722\pi\)
\(318\) 0 0
\(319\) −4933.11 + 8544.40i −0.865834 + 1.49967i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −984.860 −0.169657
\(324\) 0 0
\(325\) −1980.74 + 3430.74i −0.338066 + 0.585548i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 6486.53 + 1378.74i 1.08697 + 0.231041i
\(330\) 0 0
\(331\) −1868.15 3235.73i −0.310220 0.537317i 0.668190 0.743991i \(-0.267069\pi\)
−0.978410 + 0.206674i \(0.933736\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 853.790 0.139246
\(336\) 0 0
\(337\) −3928.18 −0.634960 −0.317480 0.948265i \(-0.602837\pi\)
−0.317480 + 0.948265i \(0.602837\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 970.337 + 1680.67i 0.154096 + 0.266902i
\(342\) 0 0
\(343\) 5139.26 + 3733.84i 0.809021 + 0.587780i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 271.003 469.390i 0.0419256 0.0726173i −0.844301 0.535869i \(-0.819984\pi\)
0.886227 + 0.463252i \(0.153317\pi\)
\(348\) 0 0
\(349\) 2331.24 0.357561 0.178780 0.983889i \(-0.442785\pi\)
0.178780 + 0.983889i \(0.442785\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1280.15 + 2217.28i −0.193018 + 0.334318i −0.946249 0.323439i \(-0.895161\pi\)
0.753231 + 0.657756i \(0.228494\pi\)
\(354\) 0 0
\(355\) 357.482 + 619.176i 0.0534455 + 0.0925703i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −2284.27 3956.46i −0.335819 0.581655i 0.647823 0.761791i \(-0.275680\pi\)
−0.983642 + 0.180136i \(0.942346\pi\)
\(360\) 0 0
\(361\) 3349.35 5801.24i 0.488314 0.845785i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1411.01 0.202344
\(366\) 0 0
\(367\) 3190.91 5526.82i 0.453854 0.786098i −0.544768 0.838587i \(-0.683382\pi\)
0.998621 + 0.0524893i \(0.0167155\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1058.68 + 3258.27i 0.148151 + 0.455960i
\(372\) 0 0
\(373\) 3186.01 + 5518.33i 0.442266 + 0.766027i 0.997857 0.0654285i \(-0.0208414\pi\)
−0.555591 + 0.831456i \(0.687508\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 6894.51 0.941870
\(378\) 0 0
\(379\) 1494.59 0.202564 0.101282 0.994858i \(-0.467706\pi\)
0.101282 + 0.994858i \(0.467706\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 4410.13 + 7638.57i 0.588374 + 1.01909i 0.994446 + 0.105252i \(0.0335650\pi\)
−0.406072 + 0.913841i \(0.633102\pi\)
\(384\) 0 0
\(385\) 826.637 918.077i 0.109427 0.121531i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −4939.24 + 8555.01i −0.643777 + 1.11505i 0.340806 + 0.940134i \(0.389300\pi\)
−0.984583 + 0.174921i \(0.944033\pi\)
\(390\) 0 0
\(391\) −7850.40 −1.01537
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −216.452 + 374.906i −0.0275718 + 0.0477558i
\(396\) 0 0
\(397\) −970.898 1681.64i −0.122740 0.212593i 0.798107 0.602516i \(-0.205835\pi\)
−0.920847 + 0.389923i \(0.872502\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3792.48 + 6568.77i 0.472288 + 0.818026i 0.999497 0.0317090i \(-0.0100950\pi\)
−0.527209 + 0.849735i \(0.676762\pi\)
\(402\) 0 0
\(403\) 678.071 1174.45i 0.0838142 0.145170i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −14302.0 −1.74183
\(408\) 0 0
\(409\) −4353.90 + 7541.18i −0.526373 + 0.911705i 0.473155 + 0.880979i \(0.343115\pi\)
−0.999528 + 0.0307253i \(0.990218\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 2602.01 + 8008.11i 0.310016 + 0.954124i
\(414\) 0 0
\(415\) −1016.74 1761.05i −0.120265 0.208305i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −6647.96 −0.775117 −0.387558 0.921845i \(-0.626681\pi\)
−0.387558 + 0.921845i \(0.626681\pi\)
\(420\) 0 0
\(421\) 11670.6 1.35105 0.675524 0.737338i \(-0.263917\pi\)
0.675524 + 0.737338i \(0.263917\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −4780.21 8279.57i −0.545586 0.944983i
\(426\) 0 0
\(427\) 214.649 + 45.6246i 0.0243269 + 0.00517079i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −782.821 + 1355.89i −0.0874876 + 0.151533i −0.906449 0.422316i \(-0.861217\pi\)
0.818961 + 0.573849i \(0.194550\pi\)
\(432\) 0 0
\(433\) 15446.4 1.71434 0.857168 0.515037i \(-0.172222\pi\)
0.857168 + 0.515037i \(0.172222\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −638.919 + 1106.64i −0.0699397 + 0.121139i
\(438\) 0 0
\(439\) −5348.70 9264.21i −0.581502 1.00719i −0.995302 0.0968229i \(-0.969132\pi\)
0.413800 0.910368i \(-0.364201\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −526.981 912.758i −0.0565183 0.0978926i 0.836382 0.548147i \(-0.184667\pi\)
−0.892900 + 0.450254i \(0.851333\pi\)
\(444\) 0 0
\(445\) −502.749 + 870.787i −0.0535564 + 0.0927624i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1139.33 −0.119752 −0.0598759 0.998206i \(-0.519070\pi\)
−0.0598759 + 0.998206i \(0.519070\pi\)
\(450\) 0 0
\(451\) −1015.46 + 1758.82i −0.106022 + 0.183636i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −844.427 179.487i −0.0870051 0.0184933i
\(456\) 0 0
\(457\) −2852.08 4939.95i −0.291936 0.505648i 0.682332 0.731043i \(-0.260966\pi\)
−0.974267 + 0.225395i \(0.927633\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 6476.39 0.654307 0.327154 0.944971i \(-0.393911\pi\)
0.327154 + 0.944971i \(0.393911\pi\)
\(462\) 0 0
\(463\) −232.366 −0.0233239 −0.0116619 0.999932i \(-0.503712\pi\)
−0.0116619 + 0.999932i \(0.503712\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −518.583 898.212i −0.0513858 0.0890028i 0.839188 0.543841i \(-0.183030\pi\)
−0.890574 + 0.454838i \(0.849697\pi\)
\(468\) 0 0
\(469\) −3378.69 10398.5i −0.332651 1.02379i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 8794.35 15232.3i 0.854893 1.48072i
\(474\) 0 0
\(475\) −1556.18 −0.150321
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 5142.32 8906.77i 0.490519 0.849605i −0.509421 0.860517i \(-0.670140\pi\)
0.999940 + 0.0109129i \(0.00347374\pi\)
\(480\) 0 0
\(481\) 4997.11 + 8655.25i 0.473698 + 0.820469i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −348.496 603.614i −0.0326276 0.0565127i
\(486\) 0 0
\(487\) −5422.92 + 9392.77i −0.504591 + 0.873977i 0.495395 + 0.868668i \(0.335023\pi\)
−0.999986 + 0.00530928i \(0.998310\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −8442.11 −0.775941 −0.387971 0.921672i \(-0.626824\pi\)
−0.387971 + 0.921672i \(0.626824\pi\)
\(492\) 0 0
\(493\) −8319.42 + 14409.7i −0.760016 + 1.31639i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 6126.41 6804.09i 0.552931 0.614095i
\(498\) 0 0
\(499\) −4905.42 8496.45i −0.440074 0.762231i 0.557620 0.830096i \(-0.311714\pi\)
−0.997694 + 0.0678654i \(0.978381\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 6433.96 0.570330 0.285165 0.958478i \(-0.407952\pi\)
0.285165 + 0.958478i \(0.407952\pi\)
\(504\) 0 0
\(505\) 1712.48 0.150900
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −10280.3 17806.0i −0.895220 1.55057i −0.833532 0.552471i \(-0.813685\pi\)
−0.0616885 0.998095i \(-0.519649\pi\)
\(510\) 0 0
\(511\) −5583.75 17184.9i −0.483387 1.48770i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 928.135 1607.58i 0.0794146 0.137550i
\(516\) 0 0
\(517\) −16515.2 −1.40491
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 9563.06 16563.7i 0.804156 1.39284i −0.112703 0.993629i \(-0.535951\pi\)
0.916859 0.399211i \(-0.130716\pi\)
\(522\) 0 0
\(523\) 1522.33 + 2636.75i 0.127279 + 0.220454i 0.922621 0.385707i \(-0.126042\pi\)
−0.795343 + 0.606160i \(0.792709\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1636.42 + 2834.36i 0.135263 + 0.234282i
\(528\) 0 0
\(529\) 990.629 1715.82i 0.0814193 0.141022i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1419.20 0.115333
\(534\) 0 0
\(535\) 1166.64 2020.69i 0.0942774 0.163293i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −14452.7 6434.67i −1.15495 0.514213i
\(540\) 0 0
\(541\) 2947.55 + 5105.30i 0.234242 + 0.405719i 0.959052 0.283230i \(-0.0914058\pi\)
−0.724810 + 0.688949i \(0.758072\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −222.476 −0.0174860
\(546\) 0 0
\(547\) 11151.1 0.871641 0.435821 0.900034i \(-0.356458\pi\)
0.435821 + 0.900034i \(0.356458\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1354.18 + 2345.51i 0.104701 + 0.181347i
\(552\) 0 0
\(553\) 5422.61 + 1152.60i 0.416985 + 0.0886320i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 872.173 1510.65i 0.0663468 0.114916i −0.830944 0.556356i \(-0.812199\pi\)
0.897291 + 0.441440i \(0.145532\pi\)
\(558\) 0 0
\(559\) −12291.0 −0.929969
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 5762.19 9980.41i 0.431345 0.747112i −0.565644 0.824650i \(-0.691372\pi\)
0.996989 + 0.0775374i \(0.0247057\pi\)
\(564\) 0 0
\(565\) 1143.30 + 1980.25i 0.0851309 + 0.147451i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 1411.38 + 2444.58i 0.103986 + 0.180110i 0.913324 0.407235i \(-0.133507\pi\)
−0.809337 + 0.587344i \(0.800174\pi\)
\(570\) 0 0
\(571\) 2583.82 4475.31i 0.189369 0.327996i −0.755671 0.654951i \(-0.772689\pi\)
0.945040 + 0.326955i \(0.106023\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −12404.5 −0.899656
\(576\) 0 0
\(577\) 7357.61 12743.7i 0.530851 0.919461i −0.468501 0.883463i \(-0.655206\pi\)
0.999352 0.0359981i \(-0.0114610\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −17424.6 + 19352.1i −1.24423 + 1.38186i
\(582\) 0 0
\(583\) −4266.06 7389.03i −0.303057 0.524910i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −9981.64 −0.701851 −0.350925 0.936403i \(-0.614133\pi\)
−0.350925 + 0.936403i \(0.614133\pi\)
\(588\) 0 0
\(589\) 532.733 0.0372680
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −837.605 1450.78i −0.0580039 0.100466i 0.835565 0.549391i \(-0.185140\pi\)
−0.893569 + 0.448925i \(0.851807\pi\)
\(594\) 0 0
\(595\) 1394.08 1548.29i 0.0960532 0.106678i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 519.955 900.588i 0.0354671 0.0614308i −0.847747 0.530401i \(-0.822041\pi\)
0.883214 + 0.468970i \(0.155375\pi\)
\(600\) 0 0
\(601\) 4472.61 0.303563 0.151782 0.988414i \(-0.451499\pi\)
0.151782 + 0.988414i \(0.451499\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −575.873 + 997.441i −0.0386984 + 0.0670277i
\(606\) 0 0
\(607\) 8895.38 + 15407.3i 0.594814 + 1.03025i 0.993573 + 0.113193i \(0.0361078\pi\)
−0.398759 + 0.917056i \(0.630559\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 5770.40 + 9994.63i 0.382071 + 0.661766i
\(612\) 0 0
\(613\) 2163.37 3747.06i 0.142541 0.246888i −0.785912 0.618339i \(-0.787806\pi\)
0.928453 + 0.371450i \(0.121139\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 18866.2 1.23100 0.615498 0.788139i \(-0.288955\pi\)
0.615498 + 0.788139i \(0.288955\pi\)
\(618\) 0 0
\(619\) 5089.69 8815.60i 0.330488 0.572422i −0.652120 0.758116i \(-0.726120\pi\)
0.982608 + 0.185694i \(0.0594534\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 12595.0 + 2677.12i 0.809965 + 0.172162i
\(624\) 0 0
\(625\) −7422.52 12856.2i −0.475041 0.822796i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −24119.5 −1.52895
\(630\) 0 0
\(631\) −1661.72 −0.104837 −0.0524184 0.998625i \(-0.516693\pi\)
−0.0524184 + 0.998625i \(0.516693\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1385.70 2400.10i −0.0865980 0.149992i
\(636\) 0 0
\(637\) 1155.64 + 10994.7i 0.0718806 + 0.683871i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1138.82 + 1972.50i −0.0701728 + 0.121543i −0.898977 0.437996i \(-0.855688\pi\)
0.828804 + 0.559539i \(0.189022\pi\)
\(642\) 0 0
\(643\) 1217.38 0.0746638 0.0373319 0.999303i \(-0.488114\pi\)
0.0373319 + 0.999303i \(0.488114\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 5365.90 9294.01i 0.326052 0.564738i −0.655673 0.755045i \(-0.727615\pi\)
0.981725 + 0.190307i \(0.0609484\pi\)
\(648\) 0 0
\(649\) −10485.0 18160.6i −0.634166 1.09841i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 7614.03 + 13187.9i 0.456294 + 0.790324i 0.998762 0.0497526i \(-0.0158433\pi\)
−0.542468 + 0.840077i \(0.682510\pi\)
\(654\) 0 0
\(655\) 1808.13 3131.77i 0.107862 0.186822i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −10590.8 −0.626038 −0.313019 0.949747i \(-0.601340\pi\)
−0.313019 + 0.949747i \(0.601340\pi\)
\(660\) 0 0
\(661\) 1934.15 3350.04i 0.113812 0.197128i −0.803492 0.595315i \(-0.797027\pi\)
0.917304 + 0.398187i \(0.130361\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −104.796 322.528i −0.00611103 0.0188077i
\(666\) 0 0
\(667\) 10794.3 + 18696.3i 0.626622 + 1.08534i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −546.512 −0.0314424
\(672\) 0 0
\(673\) 11028.7 0.631687 0.315843 0.948811i \(-0.397713\pi\)
0.315843 + 0.948811i \(0.397713\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 9396.24 + 16274.8i 0.533422 + 0.923914i 0.999238 + 0.0390325i \(0.0124276\pi\)
−0.465816 + 0.884882i \(0.654239\pi\)
\(678\) 0 0
\(679\) −5972.42 + 6633.07i −0.337556 + 0.374895i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −10121.9 + 17531.6i −0.567062 + 0.982181i 0.429792 + 0.902928i \(0.358587\pi\)
−0.996855 + 0.0792531i \(0.974746\pi\)
\(684\) 0 0
\(685\) −420.695 −0.0234656
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −2981.12 + 5163.45i −0.164835 + 0.285503i
\(690\) 0 0
\(691\) 9601.45 + 16630.2i 0.528591 + 0.915546i 0.999444 + 0.0333346i \(0.0106127\pi\)
−0.470854 + 0.882211i \(0.656054\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 975.308 + 1689.28i 0.0532310 + 0.0921988i
\(696\) 0 0
\(697\) −1712.51 + 2966.16i −0.0930646 + 0.161193i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 22156.9 1.19380 0.596900 0.802316i \(-0.296399\pi\)
0.596900 + 0.802316i \(0.296399\pi\)
\(702\) 0 0
\(703\) −1963.01 + 3400.04i −0.105315 + 0.182411i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −6776.76 20856.6i −0.360490 1.10947i
\(708\) 0 0
\(709\) 13604.5 + 23563.8i 0.720634 + 1.24817i 0.960746 + 0.277429i \(0.0894823\pi\)
−0.240112 + 0.970745i \(0.577184\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 4246.45 0.223045
\(714\) 0 0
\(715\) 2149.97 0.112454
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 10776.2 + 18664.9i 0.558947 + 0.968125i 0.997585 + 0.0694605i \(0.0221278\pi\)
−0.438638 + 0.898664i \(0.644539\pi\)
\(720\) 0 0
\(721\) −23251.9 4942.29i −1.20103 0.255285i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −13145.6 + 22768.8i −0.673399 + 1.16636i
\(726\) 0 0
\(727\) −20599.1 −1.05086 −0.525431 0.850836i \(-0.676096\pi\)
−0.525431 + 0.850836i \(0.676096\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 14831.2 25688.4i 0.750412 1.29975i
\(732\) 0 0
\(733\) −9880.58 17113.7i −0.497882 0.862357i 0.502115 0.864801i \(-0.332555\pi\)
−0.999997 + 0.00244415i \(0.999222\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 13614.7 + 23581.4i 0.680468 + 1.17861i
\(738\) 0 0
\(739\) −16704.4 + 28933.0i −0.831506 + 1.44021i 0.0653376 + 0.997863i \(0.479188\pi\)
−0.896844 + 0.442348i \(0.854146\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 36225.4 1.78867 0.894335 0.447398i \(-0.147649\pi\)
0.894335 + 0.447398i \(0.147649\pi\)
\(744\) 0 0
\(745\) −2060.00 + 3568.03i −0.101306 + 0.175466i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −29227.1 6212.34i −1.42581 0.303063i
\(750\) 0 0
\(751\) 13660.2 + 23660.2i 0.663740 + 1.14963i 0.979625 + 0.200834i \(0.0643651\pi\)
−0.315885 + 0.948797i \(0.602302\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −2153.88 −0.103825
\(756\) 0 0
\(757\) −9918.43 −0.476211 −0.238105 0.971239i \(-0.576526\pi\)
−0.238105 + 0.971239i \(0.576526\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −2817.52 4880.08i −0.134211 0.232461i 0.791084 0.611707i \(-0.209517\pi\)
−0.925296 + 0.379246i \(0.876183\pi\)
\(762\) 0 0
\(763\) 880.403 + 2709.58i 0.0417729 + 0.128563i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −7326.93 + 12690.6i −0.344929 + 0.597434i
\(768\) 0 0
\(769\) 12089.3 0.566907 0.283453 0.958986i \(-0.408520\pi\)
0.283453 + 0.958986i \(0.408520\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −7085.68 + 12272.8i −0.329695 + 0.571049i −0.982451 0.186519i \(-0.940279\pi\)
0.652756 + 0.757568i \(0.273613\pi\)
\(774\) 0 0
\(775\) 2585.72 + 4478.60i 0.119848 + 0.207582i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 278.752 + 482.812i 0.0128207 + 0.0222061i
\(780\) 0 0
\(781\) −11401.0 + 19747.0i −0.522354 + 0.904744i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 5269.14 0.239571
\(786\) 0 0
\(787\) 12853.8 22263.5i 0.582197 1.00840i −0.413021 0.910721i \(-0.635526\pi\)
0.995218 0.0976740i \(-0.0311403\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 19593.5 21760.9i 0.880739 0.978164i
\(792\) 0 0
\(793\) 190.951 + 330.737i 0.00855092 + 0.0148106i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 6194.68 0.275316 0.137658 0.990480i \(-0.456043\pi\)
0.137658 + 0.990480i \(0.456043\pi\)
\(798\) 0 0
\(799\) −27852.0 −1.23321
\(800\) 0 0