Properties

Label 1008.4.bt.a.593.8
Level $1008$
Weight $4$
Character 1008.593
Analytic conductor $59.474$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1008.bt (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(59.4739252858\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 48 x^{14} + 1647 x^{12} - 27620 x^{10} + 336765 x^{8} - 1200006 x^{6} + 3242464 x^{4} - 1762200 x^{2} + 810000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{10}\cdot 3^{8} \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 593.8
Root \(1.57646 - 0.910170i\) of defining polynomial
Character \(\chi\) \(=\) 1008.593
Dual form 1008.4.bt.a.17.8

$q$-expansion

\(f(q)\) \(=\) \(q+(7.54372 - 13.0661i) q^{5} +(-16.2919 - 8.80760i) q^{7} +O(q^{10})\) \(q+(7.54372 - 13.0661i) q^{5} +(-16.2919 - 8.80760i) q^{7} +(-8.56529 + 4.94517i) q^{11} +67.8891i q^{13} +(-35.0687 - 60.7407i) q^{17} +(53.2242 + 30.7290i) q^{19} +(-113.895 - 65.7575i) q^{23} +(-51.3154 - 88.8809i) q^{25} +158.738i q^{29} +(66.2349 - 38.2407i) q^{31} +(-237.983 + 146.430i) q^{35} +(-174.341 + 301.967i) q^{37} -138.909 q^{41} -539.651 q^{43} +(111.821 - 193.680i) q^{47} +(187.852 + 286.985i) q^{49} +(459.003 - 265.005i) q^{53} +149.220i q^{55} +(271.438 + 470.145i) q^{59} +(-116.218 - 67.0983i) q^{61} +(887.046 + 512.136i) q^{65} +(160.290 + 277.630i) q^{67} +416.958i q^{71} +(472.510 - 272.804i) q^{73} +(183.100 - 5.12660i) q^{77} +(-161.369 + 279.499i) q^{79} +885.170 q^{83} -1058.19 q^{85} +(-812.312 + 1406.97i) q^{89} +(597.940 - 1106.04i) q^{91} +(803.017 - 463.622i) q^{95} -739.155i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 56q^{7} + O(q^{10}) \) \( 16q - 56q^{7} + 612q^{19} - 20q^{25} - 1128q^{31} - 1196q^{37} - 328q^{43} + 784q^{49} - 1632q^{61} - 308q^{67} + 4068q^{73} + 2176q^{79} - 4608q^{85} - 924q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) 7.54372 13.0661i 0.674731 1.16867i −0.301817 0.953366i \(-0.597593\pi\)
0.976547 0.215302i \(-0.0690736\pi\)
\(6\) 0 0
\(7\) −16.2919 8.80760i −0.879680 0.475566i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −8.56529 + 4.94517i −0.234776 + 0.135548i −0.612773 0.790259i \(-0.709946\pi\)
0.377998 + 0.925807i \(0.376613\pi\)
\(12\) 0 0
\(13\) 67.8891i 1.44839i 0.689596 + 0.724194i \(0.257788\pi\)
−0.689596 + 0.724194i \(0.742212\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −35.0687 60.7407i −0.500318 0.866575i −1.00000 0.000366661i \(-0.999883\pi\)
0.499682 0.866209i \(-0.333450\pi\)
\(18\) 0 0
\(19\) 53.2242 + 30.7290i 0.642656 + 0.371038i 0.785637 0.618688i \(-0.212335\pi\)
−0.142981 + 0.989725i \(0.545669\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −113.895 65.7575i −1.03256 0.596147i −0.114841 0.993384i \(-0.536636\pi\)
−0.917716 + 0.397236i \(0.869969\pi\)
\(24\) 0 0
\(25\) −51.3154 88.8809i −0.410523 0.711047i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 158.738i 1.01645i 0.861225 + 0.508223i \(0.169698\pi\)
−0.861225 + 0.508223i \(0.830302\pi\)
\(30\) 0 0
\(31\) 66.2349 38.2407i 0.383746 0.221556i −0.295701 0.955281i \(-0.595553\pi\)
0.679447 + 0.733725i \(0.262220\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −237.983 + 146.430i −1.14933 + 0.707175i
\(36\) 0 0
\(37\) −174.341 + 301.967i −0.774634 + 1.34171i 0.160366 + 0.987058i \(0.448733\pi\)
−0.935000 + 0.354648i \(0.884601\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −138.909 −0.529120 −0.264560 0.964369i \(-0.585227\pi\)
−0.264560 + 0.964369i \(0.585227\pi\)
\(42\) 0 0
\(43\) −539.651 −1.91386 −0.956931 0.290316i \(-0.906240\pi\)
−0.956931 + 0.290316i \(0.906240\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 111.821 193.680i 0.347039 0.601089i −0.638683 0.769470i \(-0.720520\pi\)
0.985722 + 0.168381i \(0.0538538\pi\)
\(48\) 0 0
\(49\) 187.852 + 286.985i 0.547674 + 0.836692i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 459.003 265.005i 1.18960 0.686817i 0.231386 0.972862i \(-0.425674\pi\)
0.958216 + 0.286045i \(0.0923407\pi\)
\(54\) 0 0
\(55\) 149.220i 0.365833i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 271.438 + 470.145i 0.598953 + 1.03742i 0.992976 + 0.118317i \(0.0377498\pi\)
−0.394023 + 0.919101i \(0.628917\pi\)
\(60\) 0 0
\(61\) −116.218 67.0983i −0.243937 0.140837i 0.373048 0.927812i \(-0.378313\pi\)
−0.616985 + 0.786975i \(0.711646\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 887.046 + 512.136i 1.69269 + 0.977272i
\(66\) 0 0
\(67\) 160.290 + 277.630i 0.292276 + 0.506238i 0.974348 0.225048i \(-0.0722539\pi\)
−0.682071 + 0.731286i \(0.738921\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 416.958i 0.696955i 0.937317 + 0.348478i \(0.113301\pi\)
−0.937317 + 0.348478i \(0.886699\pi\)
\(72\) 0 0
\(73\) 472.510 272.804i 0.757577 0.437387i −0.0708484 0.997487i \(-0.522571\pi\)
0.828425 + 0.560100i \(0.189237\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 183.100 5.12660i 0.270989 0.00758740i
\(78\) 0 0
\(79\) −161.369 + 279.499i −0.229815 + 0.398052i −0.957753 0.287591i \(-0.907146\pi\)
0.727938 + 0.685643i \(0.240479\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 885.170 1.17060 0.585301 0.810816i \(-0.300976\pi\)
0.585301 + 0.810816i \(0.300976\pi\)
\(84\) 0 0
\(85\) −1058.19 −1.35032
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −812.312 + 1406.97i −0.967471 + 1.67571i −0.264645 + 0.964346i \(0.585255\pi\)
−0.702826 + 0.711362i \(0.748079\pi\)
\(90\) 0 0
\(91\) 597.940 1106.04i 0.688804 1.27412i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 803.017 463.622i 0.867240 0.500701i
\(96\) 0 0
\(97\) 739.155i 0.773710i −0.922141 0.386855i \(-0.873561\pi\)
0.922141 0.386855i \(-0.126439\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −119.758 207.427i −0.117984 0.204354i 0.800985 0.598685i \(-0.204310\pi\)
−0.918969 + 0.394331i \(0.870976\pi\)
\(102\) 0 0
\(103\) 44.2852 + 25.5681i 0.0423645 + 0.0244592i 0.521033 0.853537i \(-0.325547\pi\)
−0.478668 + 0.877996i \(0.658880\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1031.43 + 595.495i 0.931886 + 0.538025i 0.887408 0.460986i \(-0.152504\pi\)
0.0444785 + 0.999010i \(0.485837\pi\)
\(108\) 0 0
\(109\) −194.585 337.031i −0.170989 0.296162i 0.767777 0.640718i \(-0.221363\pi\)
−0.938766 + 0.344555i \(0.888030\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 718.545i 0.598186i 0.954224 + 0.299093i \(0.0966841\pi\)
−0.954224 + 0.299093i \(0.903316\pi\)
\(114\) 0 0
\(115\) −1718.39 + 992.113i −1.39340 + 0.804478i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 36.3552 + 1298.45i 0.0280057 + 1.00024i
\(120\) 0 0
\(121\) −616.591 + 1067.97i −0.463254 + 0.802379i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 337.493 0.241490
\(126\) 0 0
\(127\) 179.456 0.125387 0.0626934 0.998033i \(-0.480031\pi\)
0.0626934 + 0.998033i \(0.480031\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1223.43 + 2119.05i −0.815968 + 1.41330i 0.0926619 + 0.995698i \(0.470462\pi\)
−0.908630 + 0.417601i \(0.862871\pi\)
\(132\) 0 0
\(133\) −596.474 969.411i −0.388879 0.632020i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 443.021 255.778i 0.276276 0.159508i −0.355460 0.934691i \(-0.615676\pi\)
0.631736 + 0.775183i \(0.282342\pi\)
\(138\) 0 0
\(139\) 599.427i 0.365775i 0.983134 + 0.182888i \(0.0585444\pi\)
−0.983134 + 0.182888i \(0.941456\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −335.723 581.490i −0.196326 0.340046i
\(144\) 0 0
\(145\) 2074.09 + 1197.48i 1.18789 + 0.685828i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1899.63 1096.75i −1.04445 0.603016i −0.123362 0.992362i \(-0.539368\pi\)
−0.921092 + 0.389346i \(0.872701\pi\)
\(150\) 0 0
\(151\) −358.683 621.257i −0.193306 0.334816i 0.753038 0.657977i \(-0.228588\pi\)
−0.946344 + 0.323161i \(0.895254\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1153.91i 0.597963i
\(156\) 0 0
\(157\) −1561.39 + 901.471i −0.793712 + 0.458250i −0.841268 0.540619i \(-0.818190\pi\)
0.0475556 + 0.998869i \(0.484857\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1276.41 + 2074.46i 0.624813 + 1.01547i
\(162\) 0 0
\(163\) −1453.90 + 2518.24i −0.698642 + 1.21008i 0.270296 + 0.962777i \(0.412878\pi\)
−0.968938 + 0.247305i \(0.920455\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3491.37 1.61779 0.808893 0.587956i \(-0.200067\pi\)
0.808893 + 0.587956i \(0.200067\pi\)
\(168\) 0 0
\(169\) −2411.93 −1.09783
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 877.377 1519.66i 0.385583 0.667848i −0.606267 0.795261i \(-0.707334\pi\)
0.991850 + 0.127412i \(0.0406672\pi\)
\(174\) 0 0
\(175\) 53.1981 + 1900.01i 0.0229794 + 0.820725i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −685.639 + 395.854i −0.286296 + 0.165293i −0.636270 0.771466i \(-0.719524\pi\)
0.349974 + 0.936759i \(0.386190\pi\)
\(180\) 0 0
\(181\) 2522.19i 1.03576i 0.855452 + 0.517882i \(0.173279\pi\)
−0.855452 + 0.517882i \(0.826721\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2630.36 + 4555.91i 1.04534 + 1.81058i
\(186\) 0 0
\(187\) 600.746 + 346.841i 0.234925 + 0.135634i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −782.266 451.642i −0.296350 0.171098i 0.344452 0.938804i \(-0.388065\pi\)
−0.640802 + 0.767706i \(0.721398\pi\)
\(192\) 0 0
\(193\) 99.4374 + 172.231i 0.0370863 + 0.0642354i 0.883973 0.467538i \(-0.154859\pi\)
−0.846886 + 0.531774i \(0.821526\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3220.69i 1.16480i 0.812904 + 0.582398i \(0.197886\pi\)
−0.812904 + 0.582398i \(0.802114\pi\)
\(198\) 0 0
\(199\) −2468.10 + 1424.96i −0.879191 + 0.507601i −0.870392 0.492360i \(-0.836134\pi\)
−0.00879944 + 0.999961i \(0.502801\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1398.10 2586.15i 0.483387 0.894148i
\(204\) 0 0
\(205\) −1047.89 + 1815.00i −0.357014 + 0.618366i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −607.841 −0.201173
\(210\) 0 0
\(211\) −1204.50 −0.392993 −0.196496 0.980505i \(-0.562956\pi\)
−0.196496 + 0.980505i \(0.562956\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −4070.98 + 7051.14i −1.29134 + 2.23667i
\(216\) 0 0
\(217\) −1415.90 + 39.6437i −0.442938 + 0.0124018i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 4123.63 2380.78i 1.25514 0.724654i
\(222\) 0 0
\(223\) 3377.73i 1.01430i −0.861857 0.507151i \(-0.830699\pi\)
0.861857 0.507151i \(-0.169301\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2261.98 + 3917.86i 0.661378 + 1.14554i 0.980254 + 0.197744i \(0.0633615\pi\)
−0.318875 + 0.947797i \(0.603305\pi\)
\(228\) 0 0
\(229\) 3389.61 + 1956.99i 0.978131 + 0.564724i 0.901705 0.432351i \(-0.142316\pi\)
0.0764258 + 0.997075i \(0.475649\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −3783.80 2184.58i −1.06388 0.614234i −0.137381 0.990518i \(-0.543868\pi\)
−0.926504 + 0.376284i \(0.877202\pi\)
\(234\) 0 0
\(235\) −1687.10 2922.14i −0.468316 0.811147i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1945.23i 0.526471i −0.964732 0.263235i \(-0.915210\pi\)
0.964732 0.263235i \(-0.0847896\pi\)
\(240\) 0 0
\(241\) −3499.81 + 2020.61i −0.935446 + 0.540080i −0.888530 0.458819i \(-0.848273\pi\)
−0.0469158 + 0.998899i \(0.514939\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 5166.88 289.561i 1.34735 0.0755077i
\(246\) 0 0
\(247\) −2086.16 + 3613.34i −0.537407 + 0.930816i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −4415.70 −1.11042 −0.555212 0.831709i \(-0.687363\pi\)
−0.555212 + 0.831709i \(0.687363\pi\)
\(252\) 0 0
\(253\) 1300.73 0.323226
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 348.800 604.139i 0.0846597 0.146635i −0.820586 0.571522i \(-0.806353\pi\)
0.905246 + 0.424888i \(0.139686\pi\)
\(258\) 0 0
\(259\) 5499.95 3384.10i 1.31950 0.811882i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 690.664 398.755i 0.161932 0.0934915i −0.416844 0.908978i \(-0.636864\pi\)
0.578776 + 0.815487i \(0.303531\pi\)
\(264\) 0 0
\(265\) 7996.51i 1.85367i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −205.351 355.679i −0.0465446 0.0806176i 0.841815 0.539767i \(-0.181488\pi\)
−0.888359 + 0.459149i \(0.848154\pi\)
\(270\) 0 0
\(271\) −3283.42 1895.69i −0.735992 0.424925i 0.0846182 0.996413i \(-0.473033\pi\)
−0.820610 + 0.571488i \(0.806366\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 879.063 + 507.527i 0.192762 + 0.111291i
\(276\) 0 0
\(277\) −1623.31 2811.66i −0.352113 0.609877i 0.634507 0.772917i \(-0.281203\pi\)
−0.986619 + 0.163040i \(0.947870\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1599.58i 0.339583i 0.985480 + 0.169791i \(0.0543094\pi\)
−0.985480 + 0.169791i \(0.945691\pi\)
\(282\) 0 0
\(283\) 3694.70 2133.13i 0.776067 0.448062i −0.0589678 0.998260i \(-0.518781\pi\)
0.835034 + 0.550198i \(0.185448\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2263.09 + 1223.45i 0.465456 + 0.251631i
\(288\) 0 0
\(289\) −3.12079 + 5.40536i −0.000635210 + 0.00110022i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −2926.77 −0.583562 −0.291781 0.956485i \(-0.594248\pi\)
−0.291781 + 0.956485i \(0.594248\pi\)
\(294\) 0 0
\(295\) 8190.62 1.61653
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 4464.22 7732.25i 0.863453 1.49554i
\(300\) 0 0
\(301\) 8791.95 + 4753.03i 1.68359 + 0.910167i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1753.43 + 1012.34i −0.329183 + 0.190054i
\(306\) 0 0
\(307\) 3571.36i 0.663935i 0.943291 + 0.331968i \(0.107712\pi\)
−0.943291 + 0.331968i \(0.892288\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1286.71 + 2228.64i 0.234606 + 0.406349i 0.959158 0.282871i \(-0.0912867\pi\)
−0.724552 + 0.689220i \(0.757953\pi\)
\(312\) 0 0
\(313\) −1278.56 738.176i −0.230889 0.133304i 0.380093 0.924948i \(-0.375892\pi\)
−0.610982 + 0.791644i \(0.709225\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2188.36 + 1263.45i 0.387730 + 0.223856i 0.681176 0.732120i \(-0.261469\pi\)
−0.293446 + 0.955976i \(0.594802\pi\)
\(318\) 0 0
\(319\) −784.988 1359.64i −0.137777 0.238637i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 4310.50i 0.742546i
\(324\) 0 0
\(325\) 6034.05 3483.76i 1.02987 0.594597i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −3527.64 + 2170.54i −0.591141 + 0.363726i
\(330\) 0 0
\(331\) 737.778 1277.87i 0.122513 0.212200i −0.798245 0.602333i \(-0.794238\pi\)
0.920758 + 0.390134i \(0.127571\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 4836.73 0.788832
\(336\) 0 0
\(337\) −6727.28 −1.08741 −0.543706 0.839275i \(-0.682979\pi\)
−0.543706 + 0.839275i \(0.682979\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −378.214 + 655.086i −0.0600629 + 0.104032i
\(342\) 0 0
\(343\) −532.819 6330.06i −0.0838761 0.996476i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 466.060 269.080i 0.0721021 0.0416281i −0.463516 0.886089i \(-0.653412\pi\)
0.535618 + 0.844461i \(0.320079\pi\)
\(348\) 0 0
\(349\) 6975.93i 1.06995i −0.844867 0.534976i \(-0.820321\pi\)
0.844867 0.534976i \(-0.179679\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −4438.40 7687.53i −0.669213 1.15911i −0.978125 0.208020i \(-0.933298\pi\)
0.308912 0.951091i \(-0.400035\pi\)
\(354\) 0 0
\(355\) 5448.02 + 3145.42i 0.814509 + 0.470257i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −9565.96 5522.91i −1.40633 0.811944i −0.411297 0.911502i \(-0.634924\pi\)
−0.995032 + 0.0995575i \(0.968257\pi\)
\(360\) 0 0
\(361\) −1540.96 2669.02i −0.224662 0.389126i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 8231.82i 1.18047i
\(366\) 0 0
\(367\) −7210.59 + 4163.04i −1.02559 + 0.592122i −0.915717 0.401824i \(-0.868376\pi\)
−0.109868 + 0.993946i \(0.535043\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −9812.09 + 274.728i −1.37310 + 0.0384452i
\(372\) 0 0
\(373\) 2272.66 3936.36i 0.315479 0.546426i −0.664060 0.747679i \(-0.731168\pi\)
0.979539 + 0.201253i \(0.0645014\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −10776.6 −1.47221
\(378\) 0 0
\(379\) −11527.2 −1.56230 −0.781151 0.624343i \(-0.785367\pi\)
−0.781151 + 0.624343i \(0.785367\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1960.23 + 3395.22i −0.261522 + 0.452970i −0.966647 0.256114i \(-0.917558\pi\)
0.705124 + 0.709084i \(0.250891\pi\)
\(384\) 0 0
\(385\) 1314.27 2431.08i 0.173978 0.321816i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 689.734 398.218i 0.0898995 0.0519035i −0.454376 0.890810i \(-0.650138\pi\)
0.544276 + 0.838906i \(0.316805\pi\)
\(390\) 0 0
\(391\) 9224.11i 1.19305i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2434.64 + 4216.92i 0.310127 + 0.537155i
\(396\) 0 0
\(397\) 3338.59 + 1927.54i 0.422063 + 0.243678i 0.695960 0.718081i \(-0.254979\pi\)
−0.273896 + 0.961759i \(0.588313\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 4031.65 + 2327.68i 0.502073 + 0.289872i 0.729569 0.683907i \(-0.239721\pi\)
−0.227496 + 0.973779i \(0.573054\pi\)
\(402\) 0 0
\(403\) 2596.13 + 4496.63i 0.320899 + 0.555814i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3448.58i 0.420000i
\(408\) 0 0
\(409\) −8478.82 + 4895.25i −1.02506 + 0.591821i −0.915566 0.402167i \(-0.868257\pi\)
−0.109497 + 0.993987i \(0.534924\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −281.397 10050.3i −0.0335269 1.19744i
\(414\) 0 0
\(415\) 6677.47 11565.7i 0.789842 1.36805i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −3007.46 −0.350654 −0.175327 0.984510i \(-0.556098\pi\)
−0.175327 + 0.984510i \(0.556098\pi\)
\(420\) 0 0
\(421\) 7646.06 0.885145 0.442573 0.896733i \(-0.354066\pi\)
0.442573 + 0.896733i \(0.354066\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −3599.13 + 6233.87i −0.410784 + 0.711499i
\(426\) 0 0
\(427\) 1302.43 + 2116.76i 0.147609 + 0.239899i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 12983.1 7495.81i 1.45099 0.837727i 0.452448 0.891791i \(-0.350551\pi\)
0.998537 + 0.0540641i \(0.0172175\pi\)
\(432\) 0 0
\(433\) 5666.63i 0.628916i 0.949271 + 0.314458i \(0.101823\pi\)
−0.949271 + 0.314458i \(0.898177\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4041.32 6999.78i −0.442386 0.766235i
\(438\) 0 0
\(439\) 4790.07 + 2765.55i 0.520769 + 0.300666i 0.737249 0.675621i \(-0.236124\pi\)
−0.216480 + 0.976287i \(0.569458\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 349.200 + 201.611i 0.0374515 + 0.0216226i 0.518609 0.855012i \(-0.326450\pi\)
−0.481157 + 0.876634i \(0.659783\pi\)
\(444\) 0 0
\(445\) 12255.7 + 21227.5i 1.30556 + 2.26130i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 8429.03i 0.885948i 0.896534 + 0.442974i \(0.146077\pi\)
−0.896534 + 0.442974i \(0.853923\pi\)
\(450\) 0 0
\(451\) 1189.79 686.928i 0.124224 0.0717210i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −9940.98 16156.4i −1.02426 1.66467i
\(456\) 0 0
\(457\) −342.830 + 593.799i −0.0350917 + 0.0607807i −0.883038 0.469302i \(-0.844506\pi\)
0.847946 + 0.530082i \(0.177839\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −4864.48 −0.491456 −0.245728 0.969339i \(-0.579027\pi\)
−0.245728 + 0.969339i \(0.579027\pi\)
\(462\) 0 0
\(463\) 8354.23 0.838562 0.419281 0.907857i \(-0.362282\pi\)
0.419281 + 0.907857i \(0.362282\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 501.469 868.570i 0.0496900 0.0860656i −0.840111 0.542415i \(-0.817510\pi\)
0.889801 + 0.456350i \(0.150843\pi\)
\(468\) 0 0
\(469\) −166.170 5934.89i −0.0163604 0.584324i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 4622.27 2668.67i 0.449328 0.259420i
\(474\) 0 0
\(475\) 6307.49i 0.609279i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −3026.38 5241.84i −0.288682 0.500012i 0.684813 0.728719i \(-0.259884\pi\)
−0.973495 + 0.228706i \(0.926550\pi\)
\(480\) 0 0
\(481\) −20500.3 11835.8i −1.94331 1.12197i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −9657.88 5575.98i −0.904210 0.522046i
\(486\) 0 0
\(487\) 7654.72 + 13258.4i 0.712255 + 1.23366i 0.964009 + 0.265871i \(0.0856596\pi\)
−0.251753 + 0.967791i \(0.581007\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 4291.01i 0.394400i 0.980363 + 0.197200i \(0.0631848\pi\)
−0.980363 + 0.197200i \(0.936815\pi\)
\(492\) 0 0
\(493\) 9641.87 5566.74i 0.880828 0.508546i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 3672.40 6793.04i 0.331448 0.613098i
\(498\) 0 0
\(499\) 3445.77 5968.24i 0.309126 0.535421i −0.669046 0.743221i \(-0.733297\pi\)
0.978171 + 0.207800i \(0.0666303\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −13534.6 −1.19975 −0.599877 0.800092i \(-0.704784\pi\)
−0.599877 + 0.800092i \(0.704784\pi\)
\(504\) 0 0
\(505\) −3613.68 −0.318429
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 6043.91 10468.4i 0.526310 0.911595i −0.473221 0.880944i \(-0.656909\pi\)
0.999530 0.0306510i \(-0.00975805\pi\)
\(510\) 0 0
\(511\) −10100.8 + 282.812i −0.874431 + 0.0244831i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 668.150 385.757i 0.0571693 0.0330067i
\(516\) 0 0
\(517\) 2211.91i 0.188161i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 3812.94 + 6604.20i 0.320629 + 0.555346i 0.980618 0.195930i \(-0.0627724\pi\)
−0.659989 + 0.751275i \(0.729439\pi\)
\(522\) 0 0
\(523\) −13328.7 7695.34i −1.11439 0.643392i −0.174425 0.984670i \(-0.555807\pi\)
−0.939962 + 0.341279i \(0.889140\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −4645.54 2682.10i −0.383990 0.221697i
\(528\) 0 0
\(529\) 2564.60 + 4442.02i 0.210783 + 0.365088i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 9430.40i 0.766371i
\(534\) 0 0
\(535\) 15561.6 8984.49i 1.25754 0.726044i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −3028.20 1529.15i −0.241992 0.122199i
\(540\) 0 0
\(541\) 6850.44 11865.3i 0.544406 0.942939i −0.454238 0.890880i \(-0.650088\pi\)
0.998644 0.0520584i \(-0.0165782\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −5871.58 −0.461487
\(546\) 0 0
\(547\) 6139.00 0.479863 0.239931 0.970790i \(-0.422875\pi\)
0.239931 + 0.970790i \(0.422875\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −4877.87 + 8448.71i −0.377140 + 0.653226i
\(552\) 0 0
\(553\) 5090.72 3132.30i 0.391464 0.240866i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 19687.1 11366.4i 1.49761 0.864646i 0.497615 0.867398i \(-0.334209\pi\)
0.999996 + 0.00275234i \(0.000876098\pi\)
\(558\) 0 0
\(559\) 36636.4i 2.77202i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −4958.81 8588.90i −0.371206 0.642947i 0.618546 0.785749i \(-0.287722\pi\)
−0.989751 + 0.142802i \(0.954389\pi\)
\(564\) 0 0
\(565\) 9388.59 + 5420.51i 0.699081 + 0.403615i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −4448.79 2568.51i −0.327773 0.189240i 0.327079 0.944997i \(-0.393936\pi\)
−0.654852 + 0.755757i \(0.727269\pi\)
\(570\) 0 0
\(571\) −9093.02 15749.6i −0.666429 1.15429i −0.978896 0.204360i \(-0.934489\pi\)
0.312467 0.949929i \(-0.398845\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 13497.5i 0.978930i
\(576\) 0 0
\(577\) 10737.5 6199.32i 0.774713 0.447281i −0.0598401 0.998208i \(-0.519059\pi\)
0.834553 + 0.550927i \(0.185726\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −14421.1 7796.23i −1.02976 0.556699i
\(582\) 0 0
\(583\) −2621.00 + 4539.70i −0.186193 + 0.322496i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −18977.6 −1.33439 −0.667195 0.744883i \(-0.732505\pi\)
−0.667195 + 0.744883i \(0.732505\pi\)
\(588\) 0 0
\(589\) 4700.40 0.328822
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −5364.44 + 9291.48i −0.371486 + 0.643432i −0.989794 0.142503i \(-0.954485\pi\)
0.618308 + 0.785936i \(0.287818\pi\)
\(594\) 0 0
\(595\) 17240.0 + 9320.14i 1.18785 + 0.642165i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −1577.36 + 910.687i −0.107594 + 0.0621196i −0.552832 0.833293i \(-0.686453\pi\)
0.445237 + 0.895413i \(0.353119\pi\)
\(600\) 0 0
\(601\) 18933.3i 1.28503i −0.766273 0.642516i \(-0.777891\pi\)
0.766273 0.642516i \(-0.222109\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 9302.77 + 16112.9i 0.625143 + 1.08278i
\(606\) 0 0
\(607\) −13323.3 7692.20i −0.890898 0.514360i −0.0166621 0.999861i \(-0.505304\pi\)
−0.874236 + 0.485501i \(0.838637\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 13148.8 + 7591.46i 0.870611 + 0.502647i
\(612\) 0 0
\(613\) 2753.60 + 4769.38i 0.181431 + 0.314247i 0.942368 0.334578i \(-0.108594\pi\)
−0.760937 + 0.648825i \(0.775261\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 18134.0i 1.18322i 0.806224 + 0.591610i \(0.201507\pi\)
−0.806224 + 0.591610i \(0.798493\pi\)
\(618\) 0 0
\(619\) −3148.73 + 1817.92i −0.204456 + 0.118043i −0.598732 0.800949i \(-0.704329\pi\)
0.394276 + 0.918992i \(0.370995\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 25626.1 15767.6i 1.64797 1.01399i
\(624\) 0 0
\(625\) 8960.38 15519.8i 0.573464 0.993270i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 24455.6 1.55025
\(630\) 0 0
\(631\) 5912.59 0.373021 0.186511 0.982453i \(-0.440282\pi\)
0.186511 + 0.982453i \(0.440282\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1353.76 2344.79i 0.0846024 0.146536i
\(636\) 0 0
\(637\) −19483.2 + 12753.1i −1.21185 + 0.793245i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −23786.7 + 13733.3i −1.46571 + 0.846227i −0.999265 0.0383236i \(-0.987798\pi\)
−0.466443 + 0.884551i \(0.654465\pi\)
\(642\) 0 0
\(643\) 28474.0i 1.74635i 0.487403 + 0.873177i \(0.337944\pi\)
−0.487403 + 0.873177i \(0.662056\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 661.681 + 1146.06i 0.0402061 + 0.0696390i 0.885428 0.464776i \(-0.153865\pi\)
−0.845222 + 0.534415i \(0.820532\pi\)
\(648\) 0 0
\(649\) −4649.89 2684.62i −0.281239 0.162374i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 3331.38 + 1923.37i 0.199643 + 0.115264i 0.596489 0.802621i \(-0.296562\pi\)
−0.396846 + 0.917885i \(0.629895\pi\)
\(654\) 0 0
\(655\) 18458.5 + 31971.0i 1.10112 + 1.90719i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 6796.84i 0.401771i −0.979615 0.200886i \(-0.935618\pi\)
0.979615 0.200886i \(-0.0643819\pi\)
\(660\) 0 0
\(661\) −26902.5 + 15532.2i −1.58304 + 0.913966i −0.588623 + 0.808408i \(0.700330\pi\)
−0.994413 + 0.105559i \(0.966337\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −17166.1 + 480.631i −1.00101 + 0.0280272i
\(666\) 0 0
\(667\) 10438.2 18079.5i 0.605952 1.04954i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1327.25 0.0763605
\(672\) 0 0
\(673\) 15508.2 0.888259 0.444129 0.895963i \(-0.353513\pi\)
0.444129 + 0.895963i \(0.353513\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 15337.4 26565.2i 0.870701 1.50810i 0.00942744 0.999956i \(-0.496999\pi\)
0.861273 0.508142i \(-0.169668\pi\)
\(678\) 0 0
\(679\) −6510.19 + 12042.2i −0.367950 + 0.680617i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 15292.8 8829.33i 0.856756 0.494648i −0.00616869 0.999981i \(-0.501964\pi\)
0.862925 + 0.505333i \(0.168630\pi\)
\(684\) 0 0
\(685\) 7718.08i 0.430500i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 17991.0 + 31161.3i 0.994778 + 1.72301i
\(690\) 0 0
\(691\) −11402.3 6583.11i −0.627733 0.362422i 0.152141 0.988359i \(-0.451383\pi\)
−0.779874 + 0.625937i \(0.784717\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 7832.18 + 4521.91i 0.427470 + 0.246800i
\(696\) 0 0
\(697\) 4871.35 + 8437.42i 0.264728 + 0.458522i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 25910.0i 1.39602i −0.716090 0.698008i \(-0.754070\pi\)
0.716090 0.698008i \(-0.245930\pi\)
\(702\) 0 0
\(703\) −18558.3 + 10714.6i −0.995646 + 0.574837i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 124.152 + 4434.16i 0.00660424 + 0.235875i
\(708\) 0 0
\(709\) −3104.25 + 5376.71i −0.164432 + 0.284805i −0.936454 0.350792i \(-0.885913\pi\)
0.772021 + 0.635597i \(0.219246\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −10058.5 −0.528320
\(714\) 0 0
\(715\) −10130.4 −0.529868
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 14379.4 24905.9i 0.745843 1.29184i −0.203957 0.978980i \(-0.565380\pi\)
0.949800 0.312858i \(-0.101287\pi\)
\(720\) 0 0
\(721\) −496.296 806.599i −0.0256353 0.0416634i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 14108.8 8145.72i 0.722742 0.417275i
\(726\) 0 0
\(727\) 35275.7i 1.79959i −0.436312 0.899795i \(-0.643716\pi\)
0.436312 0.899795i \(-0.356284\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 18924.8 + 32778.8i 0.957539 + 1.65851i
\(732\) 0 0
\(733\) −6885.15 3975.14i −0.346942 0.200307i 0.316395 0.948627i \(-0.397527\pi\)
−0.663338 + 0.748320i \(0.730861\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −2745.86 1585.32i −0.137239 0.0792348i
\(738\) 0 0
\(739\) 16676.8 + 28885.1i 0.830130 + 1.43783i 0.897935 + 0.440129i \(0.145067\pi\)
−0.0678046 + 0.997699i \(0.521599\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 32933.6i 1.62613i 0.582171 + 0.813066i \(0.302203\pi\)
−0.582171 + 0.813066i \(0.697797\pi\)
\(744\) 0 0
\(745\) −28660.5 + 16547.2i −1.40945 + 0.813747i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −11559.0 18786.1i −0.563895 0.916463i
\(750\) 0 0
\(751\) −19818.3 + 34326.3i −0.962956 + 1.66789i −0.247945 + 0.968774i \(0.579755\pi\)
−0.715010 + 0.699114i \(0.753578\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −10823.2 −0.521718
\(756\) 0 0
\(757\) −3996.51 −0.191883 −0.0959417 0.995387i \(-0.530586\pi\)
−0.0959417 + 0.995387i \(0.530586\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −13117.8 + 22720.8i −0.624863 + 1.08230i 0.363704 + 0.931515i \(0.381512\pi\)
−0.988567 + 0.150781i \(0.951821\pi\)
\(762\) 0 0
\(763\) 201.724 + 7204.70i 0.00957128 + 0.341845i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −31917.7 + 18427.7i −1.50258 + 0.867517i
\(768\) 0 0
\(769\) 36456.9i 1.70958i 0.518971 + 0.854792i \(0.326315\pi\)
−0.518971 + 0.854792i \(0.673685\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 4732.74 + 8197.34i 0.220213 + 0.381420i 0.954873 0.297016i \(-0.0959914\pi\)
−0.734660 + 0.678436i \(0.762658\pi\)
\(774\) 0 0
\(775\) −6797.74 3924.68i −0.315074 0.181908i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −7393.31 4268.53i −0.340042 0.196323i
\(780\) 0 0
\(781\) −2061.93 3571.37i −0.0944707 0.163628i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 27201.8i 1.23678i
\(786\) 0 0
\(787\) −21665.9 + 12508.8i −0.981330 + 0.566571i −0.902671 0.430331i \(-0.858397\pi\)
−0.0786582 + 0.996902i \(0.525064\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 6328.66 11706.5i 0.284477 0.526213i
\(792\) 0 0
\(793\) 4555.24 7889.91i 0.203987 0.353315i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −38893.5 −1.72858 −0.864290 0.502994i \(-0.832232\pi\)
−0.864290 + 0.502994i \(0.832232\pi\)
\(798\) 0 0
\(799\) −15685.7 −0.694519
\(800\) 0