Properties

Label 1008.4.bt.a.17.5
Level $1008$
Weight $4$
Character 1008.17
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 17.5
Root \(3.91663 + 2.26127i\) of defining polynomial
Character \(\chi\) \(=\) 1008.17
Dual form 1008.4.bt.a.593.5

$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

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

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 \(-0.148639\pi\)
−0.836335 + 0.548219i \(0.815306\pi\)
\(6\) 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 \(-0.140237\pi\)
0.0829344 + 0.996555i \(0.473571\pi\)
\(12\) 0 0
\(13\) 85.7355i 1.82914i 0.404433 + 0.914568i \(0.367469\pi\)
−0.404433 + 0.914568i \(0.632531\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −38.8929 + 67.3645i −0.554878 + 0.961076i 0.443035 + 0.896504i \(0.353902\pi\)
−0.997913 + 0.0645722i \(0.979432\pi\)
\(18\) 0 0
\(19\) −42.1638 + 24.3433i −0.509107 + 0.293933i −0.732466 0.680803i \(-0.761631\pi\)
0.223360 + 0.974736i \(0.428298\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 78.7639 45.4743i 0.714061 0.412263i −0.0985019 0.995137i \(-0.531405\pi\)
0.812563 + 0.582874i \(0.198072\pi\)
\(24\) 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 0.262190 0.965016i \(-0.415555\pi\)
−0.704634 + 0.709571i \(0.748889\pi\)
\(32\) 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 0.747689 0.664050i \(-0.231164\pi\)
−0.948928 + 0.315493i \(0.897830\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −383.530 −1.46091 −0.730455 0.682961i \(-0.760692\pi\)
−0.730455 + 0.682961i \(0.760692\pi\)
\(42\) 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 \(-0.0974118\pi\)
−0.737680 + 0.675151i \(0.764078\pi\)
\(48\) 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 \(-0.190591\pi\)
−0.0750904 + 0.997177i \(0.523925\pi\)
\(54\) 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 −0.278493 + 0.960438i \(0.589835\pi\)
−0.692518 + 0.721401i \(0.743499\pi\)
\(60\) 0 0
\(61\) 11.3944 6.57854i 0.0239164 0.0138081i −0.487994 0.872847i \(-0.662271\pi\)
0.511911 + 0.859039i \(0.328938\pi\)
\(62\) 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 −0.994130 0.108197i \(-0.965492\pi\)
0.590766 + 0.806843i \(0.298826\pi\)
\(68\) 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 −0.302977 0.952998i \(-0.597981\pi\)
−0.976809 + 0.214113i \(0.931314\pi\)
\(74\) 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 0.680613 0.732643i \(-0.261714\pi\)
−0.974794 + 0.223107i \(0.928380\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −954.307 −1.26203 −0.631017 0.775769i \(-0.717362\pi\)
−0.631017 + 0.775769i \(0.717362\pi\)
\(84\) 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 \(-0.161037\pi\)
−0.857047 + 0.515238i \(0.827704\pi\)
\(90\) 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 \(0.216068\pi\)
−0.778328 + 0.627858i \(0.783932\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −327.422 + 567.111i −0.322571 + 0.558710i −0.981018 0.193918i \(-0.937881\pi\)
0.658447 + 0.752628i \(0.271214\pi\)
\(102\) 0 0
\(103\) 1186.01 684.744i 1.13457 0.655047i 0.189493 0.981882i \(-0.439316\pi\)
0.945081 + 0.326836i \(0.105982\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −371.311 + 214.377i −0.335477 + 0.193688i −0.658270 0.752782i \(-0.728711\pi\)
0.322793 + 0.946470i \(0.395378\pi\)
\(108\) 0 0
\(109\) 334.261 578.957i 0.293728 0.508752i −0.680960 0.732321i \(-0.738437\pi\)
0.974688 + 0.223568i \(0.0717706\pi\)
\(110\) 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 \(-0.0159747\pi\)
−0.542814 + 0.839853i \(0.682641\pi\)
\(132\) 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 \(-0.221771\pi\)
−0.172252 + 0.985053i \(0.555104\pi\)
\(138\) 0 0
\(139\) 2306.56i 1.40748i −0.710458 0.703739i \(-0.751512\pi\)
0.710458 0.703739i \(-0.248488\pi\)
\(140\) 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 \(-0.827006\pi\)
0.0198764 + 0.999802i \(0.493673\pi\)
\(150\) 0 0
\(151\) −262.491 + 454.647i −0.141465 + 0.245024i −0.928048 0.372460i \(-0.878515\pi\)
0.786584 + 0.617484i \(0.211848\pi\)
\(152\) 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 0.180993 0.983484i \(-0.442069\pi\)
−0.761226 + 0.648487i \(0.775402\pi\)
\(158\) 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 0.807199 0.590280i \(-0.200983\pi\)
−0.914797 + 0.403915i \(0.867649\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 811.124 0.375848 0.187924 0.982184i \(-0.439824\pi\)
0.187924 + 0.982184i \(0.439824\pi\)
\(168\) 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 \(-0.330675\pi\)
−0.999965 + 0.00834994i \(0.997342\pi\)
\(174\) 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 \(-0.542307\pi\)
−0.924648 + 0.380824i \(0.875641\pi\)
\(180\) 0 0
\(181\) 282.859i 0.116159i −0.998312 0.0580794i \(-0.981502\pi\)
0.998312 0.0580794i \(-0.0184977\pi\)
\(182\) 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 −0.514971 + 0.857208i \(0.672197\pi\)
−0.999849 + 0.0173741i \(0.994469\pi\)
\(192\) 0 0
\(193\) 2077.73 3598.73i 0.774912 1.34219i −0.159933 0.987128i \(-0.551128\pi\)
0.934844 0.355058i \(-0.115539\pi\)
\(194\) 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 0.472889 0.881122i \(-0.343211\pi\)
−0.526629 + 0.850095i \(0.676544\pi\)
\(200\) 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 \(-0.830864\pi\)
0.862120 0.506704i \(-0.169136\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1515.43 2624.79i 0.443094 0.767461i −0.554823 0.831968i \(-0.687214\pi\)
0.997917 + 0.0645069i \(0.0205475\pi\)
\(228\) 0 0
\(229\) 960.030 554.274i 0.277033 0.159945i −0.355046 0.934849i \(-0.615535\pi\)
0.632080 + 0.774904i \(0.282202\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −2684.57 + 1549.94i −0.754815 + 0.435793i −0.827431 0.561567i \(-0.810199\pi\)
0.0726160 + 0.997360i \(0.476865\pi\)
\(234\) 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 0.354638 0.935004i \(-0.384604\pi\)
−0.632418 + 0.774628i \(0.717937\pi\)
\(242\) 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 \(-0.654594\pi\)
−0.466802 + 0.884362i \(0.654594\pi\)
\(252\) 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 \(-0.136523\pi\)
−0.814867 + 0.579648i \(0.803190\pi\)
\(258\) 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 \(-0.259330\pi\)
−0.287015 + 0.957926i \(0.592663\pi\)
\(264\) 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 \(-0.742918\pi\)
0.971444 + 0.237267i \(0.0762516\pi\)
\(270\) 0 0
\(271\) −4095.79 + 2364.71i −0.918088 + 0.530058i −0.883025 0.469327i \(-0.844497\pi\)
−0.0350633 + 0.999385i \(0.511163\pi\)
\(272\) 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 −0.922604 0.385747i \(-0.873944\pi\)
0.795369 + 0.606125i \(0.207277\pi\)
\(278\) 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 0.245646 0.969360i \(-0.421000\pi\)
−0.716667 + 0.697415i \(0.754333\pi\)
\(284\) 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 \(-0.154568\pi\)
0.884400 + 0.466729i \(0.154568\pi\)
\(294\) 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 \(0.0809804\pi\)
−0.967813 + 0.251672i \(0.919020\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1080.55 + 1871.56i −0.197017 + 0.341243i −0.947560 0.319579i \(-0.896459\pi\)
0.750543 + 0.660822i \(0.229792\pi\)
\(312\) 0 0
\(313\) −7300.25 + 4214.80i −1.31832 + 0.761133i −0.983459 0.181133i \(-0.942023\pi\)
−0.334863 + 0.942267i \(0.608690\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 8310.07 4797.82i 1.47237 0.850071i 0.472848 0.881144i \(-0.343226\pi\)
0.999517 + 0.0310734i \(0.00989256\pi\)
\(318\) 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 0.965084 + 0.261941i \(0.0843626\pi\)
−0.255694 + 0.966758i \(0.582304\pi\)
\(332\) 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 \(-0.518431\pi\)
−0.893510 + 0.449044i \(0.851765\pi\)
\(348\) 0 0
\(349\) 3620.71i 0.555336i −0.960677 0.277668i \(-0.910438\pi\)
0.960677 0.277668i \(-0.0895616\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1164.89 + 2017.64i −0.175639 + 0.304216i −0.940382 0.340119i \(-0.889533\pi\)
0.764743 + 0.644335i \(0.222866\pi\)
\(354\) 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 \(-0.707914\pi\)
0.383899 + 0.923375i \(0.374581\pi\)
\(360\) 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 0.392648 0.919689i \(-0.371559\pi\)
−0.600150 + 0.799887i \(0.704893\pi\)
\(368\) 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 0.876158 0.482024i \(-0.160098\pi\)
−0.855524 + 0.517763i \(0.826765\pi\)
\(374\) 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 −0.893479 0.449105i \(-0.851743\pi\)
0.0578031 0.998328i \(-0.481590\pi\)
\(384\) 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 \(-0.507233\pi\)
−0.877162 + 0.480195i \(0.840566\pi\)
\(390\) 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 0.378586 0.925566i \(-0.376410\pi\)
0.990857 + 0.134918i \(0.0430770\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 6943.55 4008.86i 0.864699 0.499234i −0.000883860 1.00000i \(-0.500281\pi\)
0.865583 + 0.500765i \(0.166948\pi\)
\(402\) 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 −0.0327670 0.999463i \(-0.510432\pi\)
−0.881944 + 0.471354i \(0.843765\pi\)
\(410\) 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 \(-0.426482\pi\)
0.228914 + 0.973447i \(0.426482\pi\)
\(420\) 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 \(-0.0232463\pi\)
0.435477 + 0.900200i \(0.356580\pi\)
\(432\) 0 0
\(433\) 15872.1i 1.76158i 0.473508 + 0.880790i \(0.342988\pi\)
−0.473508 + 0.880790i \(0.657012\pi\)
\(434\) 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 −0.350379 0.936608i \(-0.613947\pi\)
0.635937 + 0.771741i \(0.280614\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 11126.8 6424.08i 1.19334 0.688978i 0.234281 0.972169i \(-0.424726\pi\)
0.959064 + 0.283191i \(0.0913930\pi\)
\(444\) 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 1.00000 0.000444115i \(0.000141366\pi\)
−0.499615 + 0.866247i \(0.666525\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 638.874 0.0645452 0.0322726 0.999479i \(-0.489726\pi\)
0.0322726 + 0.999479i \(0.489726\pi\)
\(462\) 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 \(-0.0785086\pi\)
−0.696308 + 0.717743i \(0.745175\pi\)
\(468\) 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 \(-0.749337\pi\)
0.966463 + 0.256807i \(0.0826703\pi\)
\(480\) 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 0.452665 + 0.891681i \(0.350473\pi\)
−0.998551 + 0.0538213i \(0.982860\pi\)
\(488\) 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 0.997952 0.0639672i \(-0.0203753\pi\)
−0.554373 + 0.832268i \(0.687042\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 10172.2 0.901698 0.450849 0.892600i \(-0.351121\pi\)
0.450849 + 0.892600i \(0.351121\pi\)
\(504\) 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 \(-0.226603\pi\)
−0.944311 + 0.329054i \(0.893270\pi\)
\(510\) 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 \(-0.986272\pi\)
0.536872 + 0.843664i \(0.319606\pi\)
\(522\) 0 0
\(523\) −7386.80 + 4264.77i −0.617595 + 0.356569i −0.775932 0.630817i \(-0.782720\pi\)
0.158337 + 0.987385i \(0.449387\pi\)
\(524\) 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 0.985522 0.169548i \(-0.0542308\pi\)
−0.639594 + 0.768713i \(0.720897\pi\)
\(542\) 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 \(-0.462529\pi\)
−0.801307 + 0.598253i \(0.795862\pi\)
\(558\) 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 0.278780 + 0.960355i \(0.410070\pi\)
−0.971082 + 0.238747i \(0.923263\pi\)
\(564\) 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 \(-0.714144\pi\)
0.365755 + 0.930711i \(0.380811\pi\)
\(570\) 0 0
\(571\) 6430.01 11137.1i 0.471257 0.816241i −0.528203 0.849118i \(-0.677134\pi\)
0.999459 + 0.0328777i \(0.0104672\pi\)
\(572\) 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 −0.298940 0.954272i \(-0.596633\pi\)
−0.975894 + 0.218246i \(0.929967\pi\)
\(578\) 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 \(-0.306033\pi\)
0.572348 + 0.820011i \(0.306033\pi\)
\(588\) 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 \(-0.137039\pi\)
−0.815805 + 0.578328i \(0.803706\pi\)
\(594\) 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 \(-0.493217\pi\)
−0.855174 + 0.518341i \(0.826550\pi\)
\(600\) 0 0
\(601\) 11096.1i 0.753109i −0.926394 0.376555i \(-0.877109\pi\)
0.926394 0.376555i \(-0.122891\pi\)
\(602\) 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 −0.143728 0.989617i \(-0.545909\pi\)
0.785170 + 0.619280i \(0.212576\pi\)
\(608\) 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 −0.713189 0.700971i \(-0.752750\pi\)
0.963654 + 0.267154i \(0.0860834\pi\)
\(614\) 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 0.930240 0.366952i \(-0.119599\pi\)
0.147330 + 0.989087i \(0.452932\pi\)
\(620\) 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 \(-0.366808\pi\)
−0.588146 + 0.808755i \(0.700142\pi\)
\(642\) 0 0
\(643\) 659.110i 0.0404242i 0.999796 + 0.0202121i \(0.00643415\pi\)
−0.999796 + 0.0202121i \(0.993566\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −3303.47 + 5721.78i −0.200731 + 0.347676i −0.948764 0.315985i \(-0.897665\pi\)
0.748033 + 0.663661i \(0.230998\pi\)
\(648\) 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 \(-0.384103\pi\)
0.987307 + 0.158823i \(0.0507698\pi\)
\(654\) 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 0.329311 0.944222i \(-0.393184\pi\)
−0.653065 + 0.757302i \(0.726517\pi\)
\(662\) 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 \(-0.0625723\pi\)
−0.659516 + 0.751690i \(0.729239\pi\)
\(678\) 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 \(-0.493043\pi\)
−0.854891 + 0.518808i \(0.826376\pi\)
\(684\) 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 −0.287332 0.957831i \(-0.592768\pi\)
0.685840 + 0.727752i \(0.259435\pi\)
\(692\) 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 0.969714 0.244245i \(-0.0785401\pi\)
−0.696379 + 0.717674i \(0.745207\pi\)
\(710\) 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 0.991922 + 0.126849i \(0.0404864\pi\)
−0.386107 + 0.922454i \(0.626180\pi\)
\(720\) 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 \(-0.807792\pi\)
0.823162 0.567807i \(-0.192208\pi\)
\(728\) 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 −0.254407 0.967097i \(-0.581880\pi\)
0.710327 + 0.703872i \(0.248547\pi\)
\(734\) 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 −0.653871 0.756606i \(-0.726856\pi\)
0.982176 + 0.187966i \(0.0601895\pi\)
\(740\) 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 −0.963387 0.268116i \(-0.913599\pi\)
0.249498 0.968375i \(-0.419734\pi\)
\(752\) 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 0.992084 + 0.125574i \(0.0400772\pi\)
−0.387292 + 0.921957i \(0.626589\pi\)
\(762\) 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 \(0.139681\pi\)
−0.905253 + 0.424872i \(0.860319\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 8673.05 15022.2i 0.403555 0.698978i −0.590597 0.806967i \(-0.701108\pi\)
0.994152 + 0.107989i \(0.0344410\pi\)
\(774\) 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 0.458646 0.888619i \(-0.348335\pi\)
−0.540244 + 0.841509i \(0.681668\pi\)
\(788\) 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 \(-0.844507\pi\)
−0.883041 + 0.469297i \(0.844507\pi\)
\(798\) 0 0
\(799\) −10820.5 −0.479099
\(800\) 0