Properties

Label 1008.4.bt.a.593.4
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 593.4
Root \(-3.91663 + 2.26127i\) of defining polynomial
Character \(\chi\) \(=\) 1008.593
Dual form 1008.4.bt.a.17.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.632851 + 1.09613i) q^{5} +(-13.4032 - 12.7810i) q^{7} +O(q^{10})\) \(q+(-0.632851 + 1.09613i) q^{5} +(-13.4032 - 12.7810i) q^{7} +(-36.0248 + 20.7989i) q^{11} -85.7355i q^{13} +(38.8929 + 67.3645i) q^{17} +(-42.1638 - 24.3433i) q^{19} +(-78.7639 - 45.4743i) q^{23} +(61.6990 + 106.866i) q^{25} -151.196i q^{29} +(-76.3661 + 44.0900i) q^{31} +(22.4919 - 6.60319i) q^{35} +(-45.2914 + 78.4470i) q^{37} +383.530 q^{41} +227.894 q^{43} +(-69.5529 + 120.469i) q^{47} +(16.2918 + 342.613i) q^{49} +(-289.749 + 167.287i) q^{53} -52.6505i q^{55} +(440.050 + 762.189i) q^{59} +(11.3944 + 6.57854i) q^{61} +(93.9774 + 54.2579i) q^{65} +(-221.212 - 383.151i) q^{67} -341.552i q^{71} +(-798.218 + 460.851i) q^{73} +(748.678 + 181.661i) q^{77} +(-206.564 + 357.780i) q^{79} +954.307 q^{83} -98.4538 q^{85} +(-14.8490 + 25.7193i) q^{89} +(-1095.79 + 1149.13i) q^{91} +(53.3668 - 30.8113i) q^{95} -1199.63i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 56q^{7} + O(q^{10}) \) \( 16q - 56q^{7} + 612q^{19} - 20q^{25} - 1128q^{31} - 1196q^{37} - 328q^{43} + 784q^{49} - 1632q^{61} - 308q^{67} + 4068q^{73} + 2176q^{79} - 4608q^{85} - 924q^{91} + O(q^{100}) \)

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
\(5\) −0.632851 + 1.09613i −0.0566040 + 0.0980409i −0.892939 0.450178i \(-0.851361\pi\)
0.836335 + 0.548219i \(0.184694\pi\)
\(6\) 0 0
\(7\) −13.4032 12.7810i −0.723705 0.690109i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −36.0248 + 20.7989i −0.987443 + 0.570101i −0.904509 0.426454i \(-0.859763\pi\)
−0.0829344 + 0.996555i \(0.526429\pi\)
\(12\) 0 0
\(13\) 85.7355i 1.82914i −0.404433 0.914568i \(-0.632531\pi\)
0.404433 0.914568i \(-0.367469\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 38.8929 + 67.3645i 0.554878 + 0.961076i 0.997913 + 0.0645722i \(0.0205683\pi\)
−0.443035 + 0.896504i \(0.646098\pi\)
\(18\) 0 0
\(19\) −42.1638 24.3433i −0.509107 0.293933i 0.223360 0.974736i \(-0.428298\pi\)
−0.732466 + 0.680803i \(0.761631\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −78.7639 45.4743i −0.714061 0.412263i 0.0985019 0.995137i \(-0.468595\pi\)
−0.812563 + 0.582874i \(0.801928\pi\)
\(24\) 0 0
\(25\) 61.6990 + 106.866i 0.493592 + 0.854926i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 151.196i 0.968151i −0.875026 0.484075i \(-0.839156\pi\)
0.875026 0.484075i \(-0.160844\pi\)
\(30\) 0 0
\(31\) −76.3661 + 44.0900i −0.442444 + 0.255445i −0.704634 0.709571i \(-0.748889\pi\)
0.262190 + 0.965016i \(0.415555\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 22.4919 6.60319i 0.108624 0.0318898i
\(36\) 0 0
\(37\) −45.2914 + 78.4470i −0.201239 + 0.348557i −0.948928 0.315493i \(-0.897830\pi\)
0.747689 + 0.664050i \(0.231164\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 383.530 1.46091 0.730455 0.682961i \(-0.239308\pi\)
0.730455 + 0.682961i \(0.239308\pi\)
\(42\) 0 0
\(43\) 227.894 0.808222 0.404111 0.914710i \(-0.367581\pi\)
0.404111 + 0.914710i \(0.367581\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −69.5529 + 120.469i −0.215858 + 0.373877i −0.953538 0.301274i \(-0.902588\pi\)
0.737680 + 0.675151i \(0.235922\pi\)
\(48\) 0 0
\(49\) 16.2918 + 342.613i 0.0474981 + 0.998871i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −289.749 + 167.287i −0.750945 + 0.433558i −0.826035 0.563619i \(-0.809409\pi\)
0.0750904 + 0.997177i \(0.476075\pi\)
\(54\) 0 0
\(55\) 52.6505i 0.129080i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 440.050 + 762.189i 0.971010 + 1.68184i 0.692518 + 0.721401i \(0.256501\pi\)
0.278493 + 0.960438i \(0.410165\pi\)
\(60\) 0 0
\(61\) 11.3944 + 6.57854i 0.0239164 + 0.0138081i 0.511911 0.859039i \(-0.328938\pi\)
−0.487994 + 0.872847i \(0.662271\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 93.9774 + 54.2579i 0.179330 + 0.103536i
\(66\) 0 0
\(67\) −221.212 383.151i −0.403364 0.698647i 0.590766 0.806843i \(-0.298826\pi\)
−0.994130 + 0.108197i \(0.965492\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 341.552i 0.570912i −0.958392 0.285456i \(-0.907855\pi\)
0.958392 0.285456i \(-0.0921450\pi\)
\(72\) 0 0
\(73\) −798.218 + 460.851i −1.27979 + 0.738885i −0.976809 0.214113i \(-0.931314\pi\)
−0.302977 + 0.952998i \(0.597981\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 748.678 + 181.661i 1.10805 + 0.268859i
\(78\) 0 0
\(79\) −206.564 + 357.780i −0.294181 + 0.509537i −0.974794 0.223107i \(-0.928380\pi\)
0.680613 + 0.732643i \(0.261714\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 954.307 1.26203 0.631017 0.775769i \(-0.282638\pi\)
0.631017 + 0.775769i \(0.282638\pi\)
\(84\) 0 0
\(85\) −98.4538 −0.125633
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −14.8490 + 25.7193i −0.0176853 + 0.0306319i −0.874733 0.484606i \(-0.838963\pi\)
0.857047 + 0.515238i \(0.172296\pi\)
\(90\) 0 0
\(91\) −1095.79 + 1149.13i −1.26230 + 1.32375i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 53.3668 30.8113i 0.0576349 0.0332755i
\(96\) 0 0
\(97\) 1199.63i 1.25572i −0.778328 0.627858i \(-0.783932\pi\)
0.778328 0.627858i \(-0.216068\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 327.422 + 567.111i 0.322571 + 0.558710i 0.981018 0.193918i \(-0.0621195\pi\)
−0.658447 + 0.752628i \(0.728786\pi\)
\(102\) 0 0
\(103\) 1186.01 + 684.744i 1.13457 + 0.655047i 0.945081 0.326836i \(-0.105982\pi\)
0.189493 + 0.981882i \(0.439316\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 371.311 + 214.377i 0.335477 + 0.193688i 0.658270 0.752782i \(-0.271289\pi\)
−0.322793 + 0.946470i \(0.604622\pi\)
\(108\) 0 0
\(109\) 334.261 + 578.957i 0.293728 + 0.508752i 0.974688 0.223568i \(-0.0717706\pi\)
−0.680960 + 0.732321i \(0.738437\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 914.837i 0.761598i 0.924658 + 0.380799i \(0.124351\pi\)
−0.924658 + 0.380799i \(0.875649\pi\)
\(114\) 0 0
\(115\) 99.6917 57.5570i 0.0808374 0.0466715i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 339.696 1399.99i 0.261680 1.07846i
\(120\) 0 0
\(121\) 199.690 345.873i 0.150030 0.259859i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −314.398 −0.224965
\(126\) 0 0
\(127\) −1260.95 −0.881034 −0.440517 0.897744i \(-0.645205\pi\)
−0.440517 + 0.897744i \(0.645205\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −683.600 + 1184.03i −0.455926 + 0.789688i −0.998741 0.0501648i \(-0.984025\pi\)
0.542814 + 0.839853i \(0.317359\pi\)
\(132\) 0 0
\(133\) 253.998 + 865.173i 0.165597 + 0.564060i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −953.631 + 550.579i −0.594702 + 0.343351i −0.766955 0.641701i \(-0.778229\pi\)
0.172252 + 0.985053i \(0.444896\pi\)
\(138\) 0 0
\(139\) 2306.56i 1.40748i 0.710458 + 0.703739i \(0.248488\pi\)
−0.710458 + 0.703739i \(0.751512\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1783.21 + 3088.60i 1.04279 + 1.80617i
\(144\) 0 0
\(145\) 165.730 + 95.6845i 0.0949184 + 0.0548012i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1520.57 + 877.901i 0.836040 + 0.482688i 0.855916 0.517115i \(-0.172994\pi\)
−0.0198764 + 0.999802i \(0.506327\pi\)
\(150\) 0 0
\(151\) −262.491 454.647i −0.141465 0.245024i 0.786584 0.617484i \(-0.211848\pi\)
−0.928048 + 0.372460i \(0.878515\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 111.610i 0.0578368i
\(156\) 0 0
\(157\) −1141.44 + 659.009i −0.580233 + 0.334998i −0.761226 0.648487i \(-0.775402\pi\)
0.180993 + 0.983484i \(0.442069\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 474.481 + 1616.18i 0.232263 + 0.791137i
\(162\) 0 0
\(163\) −223.916 + 387.834i −0.107598 + 0.186365i −0.914797 0.403915i \(-0.867649\pi\)
0.807199 + 0.590280i \(0.200983\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −811.124 −0.375848 −0.187924 0.982184i \(-0.560176\pi\)
−0.187924 + 0.982184i \(0.560176\pi\)
\(168\) 0 0
\(169\) −5153.58 −2.34574
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1121.24 1942.04i 0.492751 0.853470i −0.507214 0.861820i \(-0.669325\pi\)
0.999965 + 0.00834994i \(0.00265790\pi\)
\(174\) 0 0
\(175\) 538.888 2220.92i 0.232778 0.959347i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 2531.77 1461.72i 1.05717 0.610357i 0.132521 0.991180i \(-0.457693\pi\)
0.924648 + 0.380824i \(0.124359\pi\)
\(180\) 0 0
\(181\) 282.859i 0.116159i 0.998312 + 0.0580794i \(0.0184977\pi\)
−0.998312 + 0.0580794i \(0.981502\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −57.3255 99.2906i −0.0227819 0.0394594i
\(186\) 0 0
\(187\) −2802.22 1617.86i −1.09582 0.632672i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3998.63 + 2308.61i 1.51482 + 0.874582i 0.999849 + 0.0173741i \(0.00553064\pi\)
0.514971 + 0.857208i \(0.327803\pi\)
\(192\) 0 0
\(193\) 2077.73 + 3598.73i 0.774912 + 1.34219i 0.934844 + 0.355058i \(0.115539\pi\)
−0.159933 + 0.987128i \(0.551128\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1626.36i 0.588190i 0.955776 + 0.294095i \(0.0950183\pi\)
−0.955776 + 0.294095i \(0.904982\pi\)
\(198\) 0 0
\(199\) −150.861 + 87.0995i −0.0537399 + 0.0310267i −0.526629 0.850095i \(-0.676544\pi\)
0.472889 + 0.881122i \(0.343211\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1932.44 + 2026.51i −0.668130 + 0.700656i
\(204\) 0 0
\(205\) −242.718 + 420.399i −0.0826933 + 0.143229i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2025.25 0.670286
\(210\) 0 0
\(211\) 2942.35 0.959999 0.479999 0.877269i \(-0.340637\pi\)
0.479999 + 0.877269i \(0.340637\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −144.223 + 249.802i −0.0457486 + 0.0792389i
\(216\) 0 0
\(217\) 1587.06 + 385.088i 0.496484 + 0.120468i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 5775.53 3334.51i 1.75794 1.01495i
\(222\) 0 0
\(223\) 3374.75i 1.01341i 0.862120 + 0.506704i \(0.169136\pi\)
−0.862120 + 0.506704i \(0.830864\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1515.43 2624.79i −0.443094 0.767461i 0.554823 0.831968i \(-0.312786\pi\)
−0.997917 + 0.0645069i \(0.979453\pi\)
\(228\) 0 0
\(229\) 960.030 + 554.274i 0.277033 + 0.159945i 0.632080 0.774904i \(-0.282202\pi\)
−0.355046 + 0.934849i \(0.615535\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2684.57 + 1549.94i 0.754815 + 0.435793i 0.827431 0.561567i \(-0.189801\pi\)
−0.0726160 + 0.997360i \(0.523135\pi\)
\(234\) 0 0
\(235\) −88.0333 152.478i −0.0244368 0.0423259i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1735.25i 0.469640i 0.972039 + 0.234820i \(0.0754501\pi\)
−0.972039 + 0.234820i \(0.924550\pi\)
\(240\) 0 0
\(241\) −1039.26 + 600.019i −0.277779 + 0.160376i −0.632418 0.774628i \(-0.717937\pi\)
0.354638 + 0.935004i \(0.384604\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −385.859 198.965i −0.100619 0.0518833i
\(246\) 0 0
\(247\) −2087.08 + 3614.93i −0.537643 + 0.931225i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 3712.56 0.933603 0.466802 0.884362i \(-0.345406\pi\)
0.466802 + 0.884362i \(0.345406\pi\)
\(252\) 0 0
\(253\) 3783.27 0.940126
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −389.574 + 674.762i −0.0945563 + 0.163776i −0.909423 0.415872i \(-0.863477\pi\)
0.814867 + 0.579648i \(0.196810\pi\)
\(258\) 0 0
\(259\) 1609.68 472.572i 0.386180 0.113375i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1702.07 + 982.690i −0.399065 + 0.230400i −0.686080 0.727526i \(-0.740670\pi\)
0.287015 + 0.957926i \(0.407337\pi\)
\(264\) 0 0
\(265\) 423.470i 0.0981644i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1236.41 2141.53i −0.280243 0.485395i 0.691201 0.722662i \(-0.257082\pi\)
−0.971444 + 0.237267i \(0.923748\pi\)
\(270\) 0 0
\(271\) −4095.79 2364.71i −0.918088 0.530058i −0.0350633 0.999385i \(-0.511163\pi\)
−0.883025 + 0.469327i \(0.844497\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −4445.39 2566.54i −0.974788 0.562794i
\(276\) 0 0
\(277\) −586.579 1015.98i −0.127235 0.220378i 0.795369 0.606125i \(-0.207277\pi\)
−0.922604 + 0.385747i \(0.873944\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 8195.18i 1.73980i 0.493229 + 0.869899i \(0.335816\pi\)
−0.493229 + 0.869899i \(0.664184\pi\)
\(282\) 0 0
\(283\) −2242.44 + 1294.67i −0.471021 + 0.271944i −0.716667 0.697415i \(-0.754333\pi\)
0.245646 + 0.969360i \(0.421000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −5140.53 4901.90i −1.05727 1.00819i
\(288\) 0 0
\(289\) −568.820 + 985.225i −0.115779 + 0.200534i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −8871.16 −1.76880 −0.884400 0.466729i \(-0.845432\pi\)
−0.884400 + 0.466729i \(0.845432\pi\)
\(294\) 0 0
\(295\) −1113.94 −0.219852
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −3898.77 + 6752.86i −0.754085 + 1.30611i
\(300\) 0 0
\(301\) −3054.51 2912.72i −0.584915 0.557762i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −14.4219 + 8.32647i −0.00270752 + 0.00156319i
\(306\) 0 0
\(307\) 2707.52i 0.503344i −0.967813 0.251672i \(-0.919020\pi\)
0.967813 0.251672i \(-0.0809804\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1080.55 + 1871.56i 0.197017 + 0.341243i 0.947560 0.319579i \(-0.103541\pi\)
−0.750543 + 0.660822i \(0.770208\pi\)
\(312\) 0 0
\(313\) −7300.25 4214.80i −1.31832 0.761133i −0.334863 0.942267i \(-0.608690\pi\)
−0.983459 + 0.181133i \(0.942023\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −8310.07 4797.82i −1.47237 0.850071i −0.472848 0.881144i \(-0.656774\pi\)
−0.999517 + 0.0310734i \(0.990107\pi\)
\(318\) 0 0
\(319\) 3144.71 + 5446.80i 0.551943 + 0.955994i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 3787.12i 0.652387i
\(324\) 0 0
\(325\) 9162.20 5289.80i 1.56378 0.902847i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 2471.95 725.717i 0.414234 0.121611i
\(330\) 0 0
\(331\) 4271.96 7399.25i 0.709390 1.22870i −0.255694 0.966758i \(-0.582304\pi\)
0.965084 0.261941i \(-0.0843626\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 559.978 0.0913280
\(336\) 0 0
\(337\) 598.875 0.0968036 0.0484018 0.998828i \(-0.484587\pi\)
0.0484018 + 0.998828i \(0.484587\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1834.05 3176.66i 0.291259 0.504475i
\(342\) 0 0
\(343\) 4160.57 4800.34i 0.654956 0.755667i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 6149.62 3550.49i 0.951381 0.549280i 0.0578712 0.998324i \(-0.481569\pi\)
0.893510 + 0.449044i \(0.148235\pi\)
\(348\) 0 0
\(349\) 3620.71i 0.555336i 0.960677 + 0.277668i \(0.0895616\pi\)
−0.960677 + 0.277668i \(0.910438\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1164.89 + 2017.64i 0.175639 + 0.304216i 0.940382 0.340119i \(-0.110467\pi\)
−0.764743 + 0.644335i \(0.777134\pi\)
\(354\) 0 0
\(355\) 374.386 + 216.152i 0.0559727 + 0.0323159i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1522.43 + 878.975i 0.223818 + 0.129222i 0.607717 0.794154i \(-0.292086\pi\)
−0.383899 + 0.923375i \(0.625419\pi\)
\(360\) 0 0
\(361\) −2244.31 3887.26i −0.327207 0.566739i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1166.60i 0.167295i
\(366\) 0 0
\(367\) −1458.89 + 842.290i −0.207503 + 0.119802i −0.600150 0.799887i \(-0.704893\pi\)
0.392648 + 0.919689i \(0.371559\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 6021.65 + 1461.11i 0.842665 + 0.204466i
\(372\) 0 0
\(373\) 148.646 257.462i 0.0206343 0.0357397i −0.855524 0.517763i \(-0.826765\pi\)
0.876158 + 0.482024i \(0.160098\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −12962.9 −1.77088
\(378\) 0 0
\(379\) 7402.78 1.00331 0.501656 0.865067i \(-0.332724\pi\)
0.501656 + 0.865067i \(0.332724\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 6263.77 10849.2i 0.835676 1.44743i −0.0578031 0.998328i \(-0.518410\pi\)
0.893479 0.449105i \(-0.148257\pi\)
\(384\) 0 0
\(385\) −672.926 + 705.685i −0.0890792 + 0.0934157i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 6904.14 3986.11i 0.899881 0.519547i 0.0227196 0.999742i \(-0.492767\pi\)
0.877162 + 0.480195i \(0.159434\pi\)
\(390\) 0 0
\(391\) 7074.52i 0.915023i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −261.449 452.843i −0.0333036 0.0576836i
\(396\) 0 0
\(397\) 10832.5 + 6254.16i 1.36944 + 0.790648i 0.990857 0.134918i \(-0.0430770\pi\)
0.378586 + 0.925566i \(0.376410\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −6943.55 4008.86i −0.864699 0.499234i 0.000883860 1.00000i \(-0.499719\pi\)
−0.865583 + 0.500765i \(0.833052\pi\)
\(402\) 0 0
\(403\) 3780.08 + 6547.29i 0.467243 + 0.809289i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3768.05i 0.458907i
\(408\) 0 0
\(409\) −7566.04 + 4368.26i −0.914711 + 0.528109i −0.881944 0.471354i \(-0.843765\pi\)
−0.0327670 + 0.999463i \(0.510432\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 3843.46 15840.1i 0.457928 1.88726i
\(414\) 0 0
\(415\) −603.935 + 1046.05i −0.0714361 + 0.123731i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −3926.67 −0.457829 −0.228914 0.973447i \(-0.573518\pi\)
−0.228914 + 0.973447i \(0.573518\pi\)
\(420\) 0 0
\(421\) 1443.44 0.167100 0.0835499 0.996504i \(-0.473374\pi\)
0.0835499 + 0.996504i \(0.473374\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −4799.31 + 8312.65i −0.547766 + 0.948759i
\(426\) 0 0
\(427\) −68.6406 233.805i −0.00777928 0.0264979i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −12820.5 + 7401.92i −1.43281 + 0.827234i −0.997334 0.0729655i \(-0.976754\pi\)
−0.435477 + 0.900200i \(0.643420\pi\)
\(432\) 0 0
\(433\) 15872.1i 1.76158i −0.473508 0.880790i \(-0.657012\pi\)
0.473508 0.880790i \(-0.342988\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2213.99 + 3834.74i 0.242356 + 0.419772i
\(438\) 0 0
\(439\) 2626.58 + 1516.45i 0.285557 + 0.164867i 0.635937 0.771741i \(-0.280614\pi\)
−0.350379 + 0.936608i \(0.613947\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −11126.8 6424.08i −1.19334 0.688978i −0.234281 0.972169i \(-0.575274\pi\)
−0.959064 + 0.283191i \(0.908607\pi\)
\(444\) 0 0
\(445\) −18.7945 32.5530i −0.00200212 0.00346777i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 107.668i 0.0113166i 0.999984 + 0.00565831i \(0.00180111\pi\)
−0.999984 + 0.00565831i \(0.998199\pi\)
\(450\) 0 0
\(451\) −13816.6 + 7977.01i −1.44257 + 0.832866i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −566.128 1928.35i −0.0583308 0.198687i
\(456\) 0 0
\(457\) 4888.53 8467.18i 0.500385 0.866691i −0.499615 0.866247i \(-0.666525\pi\)
1.00000 0.000444115i \(-0.000141366\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −638.874 −0.0645452 −0.0322726 0.999479i \(-0.510274\pi\)
−0.0322726 + 0.999479i \(0.510274\pi\)
\(462\) 0 0
\(463\) 5602.26 0.562331 0.281165 0.959659i \(-0.409279\pi\)
0.281165 + 0.959659i \(0.409279\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −2759.44 + 4779.49i −0.273430 + 0.473594i −0.969738 0.244149i \(-0.921491\pi\)
0.696308 + 0.717743i \(0.254825\pi\)
\(468\) 0 0
\(469\) −1932.10 + 7962.76i −0.190226 + 0.783979i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −8209.84 + 4739.95i −0.798074 + 0.460768i
\(474\) 0 0
\(475\) 6007.82i 0.580332i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −2734.40 4736.11i −0.260830 0.451771i 0.705632 0.708578i \(-0.250663\pi\)
−0.966463 + 0.256807i \(0.917330\pi\)
\(480\) 0 0
\(481\) 6725.70 + 3883.08i 0.637558 + 0.368094i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1314.96 + 759.190i 0.123112 + 0.0710785i
\(486\) 0 0
\(487\) −5866.72 10161.5i −0.545886 0.945502i −0.998551 0.0538213i \(-0.982860\pi\)
0.452665 0.891681i \(-0.350473\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 3514.92i 0.323068i −0.986867 0.161534i \(-0.948356\pi\)
0.986867 0.161534i \(-0.0516441\pi\)
\(492\) 0 0
\(493\) 10185.2 5880.45i 0.930467 0.537205i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −4365.38 + 4577.89i −0.393992 + 0.413172i
\(498\) 0 0
\(499\) 4944.49 8564.11i 0.443579 0.768301i −0.554373 0.832268i \(-0.687042\pi\)
0.997952 + 0.0639672i \(0.0203753\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −10172.2 −0.901698 −0.450849 0.892600i \(-0.648879\pi\)
−0.450849 + 0.892600i \(0.648879\pi\)
\(504\) 0 0
\(505\) −828.838 −0.0730353
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 2149.56 3723.15i 0.187186 0.324216i −0.757125 0.653270i \(-0.773397\pi\)
0.944311 + 0.329054i \(0.106730\pi\)
\(510\) 0 0
\(511\) 16588.8 + 4025.14i 1.43610 + 0.348458i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1501.14 + 866.682i −0.128443 + 0.0741565i
\(516\) 0 0
\(517\) 5786.50i 0.492243i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 5496.48 + 9520.18i 0.462198 + 0.800550i 0.999070 0.0431133i \(-0.0137276\pi\)
−0.536872 + 0.843664i \(0.680394\pi\)
\(522\) 0 0
\(523\) −7386.80 4264.77i −0.617595 0.356569i 0.158337 0.987385i \(-0.449387\pi\)
−0.775932 + 0.630817i \(0.782720\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −5940.20 3429.58i −0.491004 0.283481i
\(528\) 0 0
\(529\) −1947.67 3373.46i −0.160078 0.277263i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 32882.2i 2.67220i
\(534\) 0 0
\(535\) −469.970 + 271.337i −0.0379786 + 0.0219270i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −7712.89 12003.7i −0.616359 0.959250i
\(540\) 0 0
\(541\) 4352.93 7539.49i 0.345928 0.599165i −0.639594 0.768713i \(-0.720897\pi\)
0.985522 + 0.169548i \(0.0542308\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −846.150 −0.0665047
\(546\) 0 0
\(547\) −17183.8 −1.34319 −0.671596 0.740917i \(-0.734391\pi\)
−0.671596 + 0.740917i \(0.734391\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −3680.60 + 6374.99i −0.284571 + 0.492892i
\(552\) 0 0
\(553\) 7341.41 2155.30i 0.564536 0.165737i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 8989.79 5190.26i 0.683859 0.394826i −0.117448 0.993079i \(-0.537471\pi\)
0.801307 + 0.598253i \(0.204138\pi\)
\(558\) 0 0
\(559\) 19538.6i 1.47835i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 9248.22 + 16018.4i 0.692302 + 1.19910i 0.971082 + 0.238747i \(0.0767366\pi\)
−0.278780 + 0.960355i \(0.589930\pi\)
\(564\) 0 0
\(565\) −1002.78 578.956i −0.0746678 0.0431095i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 3493.45 + 2016.94i 0.257386 + 0.148602i 0.623142 0.782109i \(-0.285856\pi\)
−0.365755 + 0.930711i \(0.619189\pi\)
\(570\) 0 0
\(571\) 6430.01 + 11137.1i 0.471257 + 0.816241i 0.999459 0.0328777i \(-0.0104672\pi\)
−0.528203 + 0.849118i \(0.677134\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 11222.9i 0.813959i
\(576\) 0 0
\(577\) −17669.2 + 10201.3i −1.27483 + 0.736026i −0.975894 0.218246i \(-0.929967\pi\)
−0.298940 + 0.954272i \(0.596633\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −12790.8 12197.0i −0.913340 0.870941i
\(582\) 0 0
\(583\) 6958.76 12052.9i 0.494344 0.856228i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −16279.7 −1.14470 −0.572348 0.820011i \(-0.693967\pi\)
−0.572348 + 0.820011i \(0.693967\pi\)
\(588\) 0 0
\(589\) 4293.17 0.300335
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1342.16 + 2324.68i −0.0929440 + 0.160984i −0.908749 0.417344i \(-0.862961\pi\)
0.815805 + 0.578328i \(0.196294\pi\)
\(594\) 0 0
\(595\) 1319.60 + 1258.34i 0.0909213 + 0.0867006i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 12224.6 7057.90i 0.833865 0.481432i −0.0213091 0.999773i \(-0.506783\pi\)
0.855174 + 0.518341i \(0.173450\pi\)
\(600\) 0 0
\(601\) 11096.1i 0.753109i 0.926394 + 0.376555i \(0.122891\pi\)
−0.926394 + 0.376555i \(0.877109\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 252.748 + 437.772i 0.0169846 + 0.0294181i
\(606\) 0 0
\(607\) 9592.70 + 5538.35i 0.641442 + 0.370337i 0.785170 0.619280i \(-0.212576\pi\)
−0.143728 + 0.989617i \(0.545909\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 10328.5 + 5963.15i 0.683872 + 0.394834i
\(612\) 0 0
\(613\) 3801.34 + 6584.11i 0.250464 + 0.433817i 0.963654 0.267154i \(-0.0860834\pi\)
−0.713189 + 0.700971i \(0.752750\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 11325.9i 0.738998i 0.929231 + 0.369499i \(0.120471\pi\)
−0.929231 + 0.369499i \(0.879529\pi\)
\(618\) 0 0
\(619\) 16595.2 9581.22i 1.07757 0.622136i 0.147330 0.989087i \(-0.452932\pi\)
0.930240 + 0.366952i \(0.119599\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 527.743 154.935i 0.0339383 0.00996365i
\(624\) 0 0
\(625\) −7513.41 + 13013.6i −0.480858 + 0.832871i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −7046.06 −0.446653
\(630\) 0 0
\(631\) −10140.7 −0.639768 −0.319884 0.947457i \(-0.603644\pi\)
−0.319884 + 0.947457i \(0.603644\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 797.995 1382.17i 0.0498700 0.0863774i
\(636\) 0 0
\(637\) 29374.1 1396.79i 1.82707 0.0868804i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 2950.66 1703.56i 0.181816 0.104972i −0.406330 0.913727i \(-0.633192\pi\)
0.588146 + 0.808755i \(0.299858\pi\)
\(642\) 0 0
\(643\) 659.110i 0.0404242i −0.999796 0.0202121i \(-0.993566\pi\)
0.999796 0.0202121i \(-0.00643415\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 3303.47 + 5721.78i 0.200731 + 0.347676i 0.948764 0.315985i \(-0.102335\pi\)
−0.748033 + 0.663661i \(0.769002\pi\)
\(648\) 0 0
\(649\) −31705.4 18305.1i −1.91764 1.10715i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −22417.1 12942.5i −1.34342 0.775622i −0.356109 0.934444i \(-0.615897\pi\)
−0.987307 + 0.158823i \(0.949230\pi\)
\(654\) 0 0
\(655\) −865.234 1498.63i −0.0516145 0.0893989i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 7468.86i 0.441495i 0.975331 + 0.220748i \(0.0708497\pi\)
−0.975331 + 0.220748i \(0.929150\pi\)
\(660\) 0 0
\(661\) −5501.96 + 3176.56i −0.323754 + 0.186919i −0.653065 0.757302i \(-0.726517\pi\)
0.329311 + 0.944222i \(0.393184\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1109.09 269.111i −0.0646744 0.0156927i
\(666\) 0 0
\(667\) −6875.53 + 11908.8i −0.399133 + 0.691319i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −547.306 −0.0314881
\(672\) 0 0
\(673\) −20238.2 −1.15918 −0.579589 0.814909i \(-0.696787\pi\)
−0.579589 + 0.814909i \(0.696787\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −5658.37 + 9800.59i −0.321224 + 0.556377i −0.980741 0.195313i \(-0.937428\pi\)
0.659516 + 0.751690i \(0.270761\pi\)
\(678\) 0 0
\(679\) −15332.5 + 16078.9i −0.866581 + 0.908768i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 14869.4 8584.87i 0.833035 0.480953i −0.0218557 0.999761i \(-0.506957\pi\)
0.854891 + 0.518808i \(0.173624\pi\)
\(684\) 0 0
\(685\) 1393.74i 0.0777402i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 14342.4 + 24841.8i 0.793037 + 1.37358i
\(690\) 0 0
\(691\) 7238.59 + 4179.20i 0.398508 + 0.230079i 0.685840 0.727752i \(-0.259435\pi\)
−0.287332 + 0.957831i \(0.592768\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2528.29 1459.71i −0.137990 0.0796688i
\(696\) 0 0
\(697\) 14916.6 + 25836.3i 0.810627 + 1.40405i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 19235.8i 1.03641i 0.855256 + 0.518206i \(0.173400\pi\)
−0.855256 + 0.518206i \(0.826600\pi\)
\(702\) 0 0
\(703\) 3819.31 2205.08i 0.204905 0.118302i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 2859.75 11785.9i 0.152124 0.626951i
\(708\) 0 0
\(709\) 5160.17 8937.67i 0.273334 0.473429i −0.696379 0.717674i \(-0.745207\pi\)
0.969714 + 0.244245i \(0.0785401\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 8019.85 0.421242
\(714\) 0 0
\(715\) −4514.02 −0.236105
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −11679.8 + 20229.9i −0.605815 + 1.04930i 0.386107 + 0.922454i \(0.373820\pi\)
−0.991922 + 0.126849i \(0.959514\pi\)
\(720\) 0 0
\(721\) −7144.63 24336.2i −0.369043 1.25704i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 16157.7 9328.63i 0.827698 0.477871i
\(726\) 0 0
\(727\) 22260.4i 1.13561i 0.823162 + 0.567807i \(0.192208\pi\)
−0.823162 + 0.567807i \(0.807792\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 8863.48 + 15352.0i 0.448464 + 0.776763i
\(732\) 0 0
\(733\) 9047.84 + 5223.77i 0.455920 + 0.263226i 0.710327 0.703872i \(-0.248547\pi\)
−0.254407 + 0.967097i \(0.581880\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 15938.2 + 9201.95i 0.796598 + 0.459916i
\(738\) 0 0
\(739\) 6595.44 + 11423.6i 0.328304 + 0.568640i 0.982176 0.187966i \(-0.0601895\pi\)
−0.653871 + 0.756606i \(0.726856\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 35382.2i 1.74703i 0.486795 + 0.873517i \(0.338166\pi\)
−0.486795 + 0.873517i \(0.661834\pi\)
\(744\) 0 0
\(745\) −1924.59 + 1111.16i −0.0946463 + 0.0546441i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −2236.81 7619.07i −0.109121 0.371688i
\(750\) 0 0
\(751\) −14692.3 + 25447.8i −0.713888 + 1.23649i 0.249498 + 0.968375i \(0.419734\pi\)
−0.963387 + 0.268116i \(0.913599\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 664.470 0.0320299
\(756\) 0 0
\(757\) 11329.1 0.543939 0.271969 0.962306i \(-0.412325\pi\)
0.271969 + 0.962306i \(0.412325\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −12696.5 + 21990.9i −0.604792 + 1.04753i 0.387292 + 0.921957i \(0.373411\pi\)
−0.992084 + 0.125574i \(0.959923\pi\)
\(762\) 0 0
\(763\) 2919.48 12032.1i 0.138522 0.570891i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 65346.7 37727.9i 3.07631 1.77611i
\(768\) 0 0
\(769\) 18120.8i 0.849744i −0.905253 0.424872i \(-0.860319\pi\)
0.905253 0.424872i \(-0.139681\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −8673.05 15022.2i −0.403555 0.698978i 0.590597 0.806967i \(-0.298892\pi\)
−0.994152 + 0.107989i \(0.965559\pi\)
\(774\) 0 0
\(775\) −9423.42 5440.61i −0.436773 0.252171i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −16171.1 9336.37i −0.743759 0.429410i
\(780\) 0 0
\(781\) 7103.91 + 12304.3i 0.325477 + 0.563743i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1668.22i 0.0758488i
\(786\) 0 0
\(787\) −1801.52 + 1040.11i −0.0815977 + 0.0471104i −0.540244 0.841509i \(-0.681668\pi\)
0.458646 + 0.888619i \(0.348335\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 11692.5 12261.7i 0.525586 0.551172i
\(792\) 0 0
\(793\) 564.014 976.901i 0.0252569 0.0437463i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 39737.3 1.76608 0.883041 0.469297i \(-0.155493\pi\)
0.883041 + 0.469297i \(0.155493\pi\)
\(798\) 0 0
\(799\) −10820.5 −0.479099
\(800\)